LCOV - code coverage report
Current view: | top level - physics/clubb/src/CLUBB_core - setup_clubb_pdf_params.F90 (source / functions) |  |  | Hit | Total | Coverage
Test: | coverage.info |  | Lines: | 0 | 1066 | 0.0 %
Date: | 2024-12-17 22:39:59 |  | Functions: | 0 | 18 | 0.0 %

              Line data    Source code
           1             : !-------------------------------------------------------------------------
           2             : ! $Id$
           3             : !===============================================================================
           4             : module setup_clubb_pdf_params
           5             :
           6             :   implicit none
           7             :
           8             :   private
           9             :
          10             :   public :: setup_pdf_parameters,      &
          11             :             compute_mean_stdev,        &
          12             :             calc_comp_mu_sigma_hm,     &
          13             :             norm_transform_mean_stdev, &
          14             :             comp_corr_norm,            &
          15             :             denorm_transform_corr
          16             :
          17             :   private :: component_corr_w_x,          &
          18             :              component_corr_chi_eta,      &
          19             :              component_corr_w_hm_n_ip,    &
          20             :              component_corr_x_hm_n_ip,    &
          21             :              component_corr_hmx_hmy_n_ip, &
          22             :              component_corr_eta_hm_n_ip,  &
          23             :              calc_corr_w_hm_n,            &
          24             :              pdf_param_hm_stats,          &
          25             :              pdf_param_ln_hm_stats,       &
          26             :              pack_hydromet_pdf_params,    &
          27             :              compute_rtp2_from_chi
          28             :
          29             :   ! The component correlations of w and r_t and the component correlations of
          30             :   ! w and theta_l must both be 0 when using the ADG1 PDF.  In other words, w
          31             :   ! and r_t (theta_l) have overall covariance w'r_t' (w'theta_l'), but the
          32             :   ! individual component covariance and correlation are defined to be 0.
          33             :   ! Since the component covariances (or correlations) of w and chi (old s) and
          34             :   ! of w and eta (old t) are based on the covariances (or correlations) of w
          35             :   ! and r_t and of w and theta_l, the individual component correlation and
          36             :   ! covariance of w and chi, as well of as w and eta, are defined to be 0.
          37             :   !
          38             :   ! The PDF component correlation of w and x, calculated as part of the PDF
          39             :   ! parameters, comes out to be 0 (within numerical roundoff) when the ADG1
          40             :   ! PDF is used.  However, when l_fix_w_chi_eta_correlations is enabled, the
          41             :   ! component correlations of PDF variables are specified, and the values
          42             :   ! that were calculated as part of the PDF parameters are ignored in the
          43             :   ! correlation array.  When this happens, and when the ADG1 PDF is selected,
          44             :   ! the l_follow_ADG1_PDF_standards flag can be used to force the component
          45             :   ! correlations of w and x to have a value of 0, following the ADG1 standard,
          46             :   ! rather than whatever value might be specified in the correlation array.
          47             :   !
          48             :   ! Note:  the ADG2 PDF follows the same standards as the ADG1 PDF.
          49             :   logical, parameter :: &
          50             :     l_follow_ADG1_PDF_standards = .true.
          51             :
          52             :   contains
          53             :
          54             :   !=============================================================================
          55           0 :   subroutine setup_pdf_parameters( gr, nz, ngrdcol, pdf_dim, hydromet_dim, dt, &  ! Intent(in)
          56           0 :                                    Nc_in_cloud, cloud_frac, Kh_zm, &              ! Intent(in)
          57           0 :                                    ice_supersat_frac, hydromet, wphydrometp, &    ! Intent(in)
          58           0 :                                    corr_array_n_cloud, corr_array_n_below, &      ! Intent(in)
          59             :                                    hm_metadata, &                              ! Intent(in)
          60             :                                    pdf_params, &                                  ! Intent(in)
          61             :                                    clubb_params, &                                ! Intent(in)
          62             :                                    iiPDF_type, &                                  ! Intent(in)
          63             :                                    l_use_precip_frac, &                           ! Intent(in)
          64             :                                    l_predict_upwp_vpwp, &                         ! Intent(in)
          65             :                                    l_diagnose_correlations, &                     ! Intent(in)
          66             :                                    l_calc_w_corr, &                               ! Intent(in)
          67             :                                    l_const_Nc_in_cloud, &                         ! Intent(in)
          68             :                                    l_fix_w_chi_eta_correlations, &                ! Intent(in)
          69             :                                    stats_metadata, &                              ! Intent(in)
          70           0 :                                    stats_zt, stats_zm, stats_sfc, &               ! intent(inout)
          71           0 :                                    hydrometp2, &                                  ! Intent(out)
          72           0 :                                    mu_x_1_n, mu_x_2_n, &                          ! Intent(out)
          73           0 :                                    sigma_x_1_n, sigma_x_2_n, &                    ! Intent(out)
          74           0 :                                    corr_array_1_n, corr_array_2_n, &              ! Intent(out)
          75           0 :                                    corr_cholesky_mtx_1, corr_cholesky_mtx_2, &    ! Intent(out)
          76             :                                    precip_fracs, &                                ! Intent(out)
          77           0 :                                    hydromet_pdf_params )                          ! Intent(out)
          78             :
          79             :     ! Description:
          80             :
          81             :     ! References:
          82             :     !-----------------------------------------------------------------------
          83             :
          84             :     use grid_class, only: &
          85             :         grid, & ! Type
          86             :         zm2zt, & ! Procedure(s)
          87             :         zt2zm
          88             :
          89             :     use constants_clubb, only: &
          90             :         one,            & ! Constant(s)
          91             :         zero,           &
          92             :         rc_tol,         &
          93             :         Ncn_tol,        &
          94             :         cloud_frac_min, &
          95             :         fstderr,        &
          96             :         zero_threshold
          97             :
          98             :     use pdf_parameter_module, only: &
          99             :         pdf_parameter  ! Variable(s)
         100             :
         101             :     use hydromet_pdf_parameter_module, only: &
         102             :         hydromet_pdf_parameter,   &  ! Type
         103             :         precipitation_fractions,  &
         104             :         init_hydromet_pdf_params     ! Procedure
         105             :
         106             :     use precipitation_fraction, only: &
         107             :         precip_fraction
         108             :
         109             :     use Nc_Ncn_eqns, only: &
         110             :         Nc_in_cloud_to_Ncnm  ! Procedure(s)
         111             :
         112             :     use parameter_indices, only: &
         113             :         nparams,         & ! Variable(s)
         114             :         ic_K_hm,         &
         115             :         iomicron,        &
         116             :         izeta_vrnce_rat
         117             :
         118             :     use pdf_utilities, only: &
         119             :         calc_xp2,                  &  ! Procedure(s)
         120             :         compute_mean_binormal,     &
         121             :         compute_variance_binormal, &
         122             :         stdev_L2N,                 &
         123             :         corr_NN2NL
         124             :
         125             :     use clip_explicit, only: &
         126             :         clip_covar_level, & ! Procedure(s)
         127             :         clip_wphydrometp    ! Variables(s)
         128             :
         129             :     use clubb_precision, only: &
         130             :         core_rknd        ! Variable(s)
         131             :
         132             :     use matrix_operations, only: &
         133             :         Cholesky_factor  ! Procedure(s)
         134             :
         135             :     use stats_type_utilities, only: &
         136             : !        stat_update_var,    & ! Procedure(s)
         137             :         stat_update_var_pt
         138             :
         139             :     use diagnose_correlations_module, only: &
         140             :         diagnose_correlations, & ! Procedure(s)
         141             :         calc_cholesky_corr_mtx_approx
         142             :
         143             :     use corr_varnce_module, only: &
         144             :         hm_metadata_type,    & ! Type
         145             :         assert_corr_symmetric     ! Procedure(s)
         146             :
         147             :     use error_code, only: &
         148             :         clubb_at_least_debug_level, &   ! Procedure
         149             :         err_code, &                     ! Error Indicator
         150             :         clubb_fatal_error               ! Constant
         151             :
         152             :     use stats_type, only: stats ! Type
         153             :
         154             :     use advance_helper_module, only : &
         155             :         calc_xpwp  ! Procedure(s)
         156             :
         157             :     use stats_variables, only: &
         158             :       stats_metadata_type
         159             :
         160             :     implicit none
         161             :
         162             :     !------------------------ Input Variables ------------------------
         163             :     integer, intent(in) :: &
         164             :       nz,           & ! Number of model vertical grid levels
         165             :       pdf_dim,      & ! Number of variables in the correlation array
         166             :       ngrdcol,      & ! Number of grid columns
         167             :       hydromet_dim    ! Number of hydrometeor species
         168             :
         169             :     type (grid), target, intent(in) :: gr
         170             :
         171             :     real( kind = core_rknd ), intent(in) ::  &
         172             :       dt    ! Model timestep                                           [s]
         173             :
         174             :     real( kind = core_rknd ), dimension(ngrdcol,nz), intent(in) :: &
         175             :       Nc_in_cloud,       & ! Mean (in-cloud) cloud droplet conc.       [num/kg]
         176             :       cloud_frac,        & ! Cloud fraction                            [-]
         177             :       Kh_zm,             & ! Eddy diffusivity coef. on momentum levels [m^2/s]
         178             :       ice_supersat_frac    ! Ice supersaturation fraction              [-]
         179             :
         180             :     real( kind = core_rknd ), dimension(ngrdcol,nz,hydromet_dim), intent(in) :: &
         181             :       hydromet,    & ! Mean of hydrometeor, hm (overall) (t-levs.) [units]
         182             :       wphydrometp    ! Covariance < w'h_m' > (momentum levels)     [(m/s)units]
         183             :
         184             :     real( kind = core_rknd ), dimension(pdf_dim,pdf_dim), intent(in) :: &
         185             :       corr_array_n_cloud, & ! Prescribed normal space corr. array in cloud  [-]
         186             :       corr_array_n_below    ! Prescribed normal space corr. array below cl. [-]
         187             :
         188             :     type (hm_metadata_type), intent(in) :: &
         189             :       hm_metadata
         190             :
         191             :     type(pdf_parameter), intent(in) :: &
         192             :       pdf_params    ! PDF parameters                               [units vary]
         193             :
         194             :     real( kind = core_rknd ), dimension(nparams), intent(in) :: &
         195             :       clubb_params    ! Array of CLUBB's tunable parameters    [units vary]
         196             :
         197             :     integer, intent(in) :: &
         198             :       iiPDF_type    ! Selected option for the two-component normal (double
         199             :                     ! Gaussian) PDF type to use for the w, rt, and theta-l (or
         200             :                     ! w, chi, and eta) portion of CLUBB's multivariate,
         201             :                     ! two-component PDF.
         202             :
         203             :     logical, intent(in) :: &
         204             :       l_use_precip_frac,            & ! Flag to use precipitation fraction in KK microphysics. The
         205             :                                       ! precipitation fraction is automatically set to 1 when this
         206             :                                       ! flag is turned off.
         207             :       l_predict_upwp_vpwp,          & ! Flag to predict <u'w'> and <v'w'> along with <u> and <v>
         208             :                                       ! alongside the advancement of <rt>, <w'rt'>, <thl>,
         209             :                                       ! <wpthlp>, <sclr>, and <w'sclr'> in subroutine
         210             :                                       ! advance_xm_wpxp.  Otherwise, <u'w'> and <v'w'> are still
         211             :                                       ! approximated by eddy diffusivity when <u> and <v> are
         212             :                                       ! advanced in subroutine advance_windm_edsclrm.
         213             :       l_diagnose_correlations,      & ! Diagnose correlations instead of using fixed ones
         214             :       l_calc_w_corr,                & ! Calculate the correlations between w and the hydrometeors
         215             :       l_const_Nc_in_cloud,          & ! Use a constant cloud droplet conc. within cloud (K&K)
         216             :       l_fix_w_chi_eta_correlations    ! Use a fixed correlation for s and t Mellor(chi/eta)
         217             :
         218             :     type (stats_metadata_type), intent(in) :: &
         219             :       stats_metadata
         220             :
         221             :     !------------------------ Input/Output Variables ------------------------
         222             :     type (stats), target, dimension(ngrdcol), intent(inout) :: &
         223             :       stats_zt, &
         224             :       stats_zm, &
         225             :       stats_sfc
         226             :
         227             :     !------------------------ Output Variables ------------------------
         228             :     real( kind = core_rknd ), dimension(ngrdcol,nz,hydromet_dim), intent(out) :: &
         229             :       hydrometp2    ! Variance of a hydrometeor (overall) (m-levs.)   [units^2]
         230             :
         231             :     real( kind = core_rknd ), dimension(ngrdcol,nz,pdf_dim), intent(out) :: &
         232             :       mu_x_1_n,    & ! Mean array (normal space): PDF vars. (comp. 1) [un. vary]
         233             :       mu_x_2_n,    & ! Mean array (normal space): PDF vars. (comp. 2) [un. vary]
         234             :       sigma_x_1_n, & ! Std. dev. array (normal space): PDF vars (comp. 1) [u.v.]
         235             :       sigma_x_2_n    ! Std. dev. array (normal space): PDF vars (comp. 2) [u.v.]
         236             :
         237             :     real( kind = core_rknd ), dimension(ngrdcol,nz,pdf_dim,pdf_dim), intent(out) :: &
         238             :       corr_array_1_n, & ! Corr. array (normal space) of PDF vars. (comp. 1)  [-]
         239             :       corr_array_2_n    ! Corr. array (normal space) of PDF vars. (comp. 2)  [-]
         240             :
         241             :     real( kind = core_rknd ), dimension(ngrdcol,nz,pdf_dim,pdf_dim), intent(out) :: &
         242             :       corr_cholesky_mtx_1, & ! Transposed corr. cholesky matrix, 1st comp. [-]
         243             :       corr_cholesky_mtx_2    ! Transposed corr. cholesky matrix, 2nd comp. [-]
         244             :
         245             :     ! This is only an output, but it contains allocated arrays, so we need to treat it as inout
         246             :     type(precipitation_fractions), intent(inout) :: &
         247             :       precip_fracs           ! Precipitation fractions      [-]
         248             :
         249             :     type(hydromet_pdf_parameter), dimension(ngrdcol,nz), optional, intent(out) :: &
         250             :       hydromet_pdf_params    ! Hydrometeor PDF parameters        [units vary]
         251             :
         252             :     !------------------------ Local Variables ------------------------
         253             :
         254             :     real( kind = core_rknd ), dimension(ngrdcol,nz) :: &
         255           0 :       Kh_zm_c_K_hm    ! Eddy diffusivity coef. on momentum levels [m^2/s]
         256             :
         257             :     real( kind = core_rknd ), dimension(ngrdcol,nz) :: &
         258           0 :       sigma_w_1,    & ! Standard deviation of w (1st PDF component)      [m/s]
         259           0 :       sigma_w_2       ! Standard deviation of w (2nd PDF component)      [m/s]
         260             :
         261             :     real( kind = core_rknd ), dimension(ngrdcol,nz) :: &
         262             :       ice_supersat_frac_1, & ! Ice supersaturation fraction (1st PDF comp.)  [-]
         263             :       ice_supersat_frac_2    ! Ice supersaturation fraction (2nd PDF comp.)  [-]
         264             :
         265             :     real( kind = core_rknd ), dimension(ngrdcol,nz) :: &
         266           0 :       Ncnm    ! Mean cloud nuclei concentration, < N_cn >        [num/kg]
         267             :
         268             :     real( kind = core_rknd ), dimension(ngrdcol,nz) :: &
         269           0 :       rcm_pdf      ! Liquid water mixing ratio          [kg/kg]
         270             :
         271             :     real( kind = core_rknd ), dimension(ngrdcol,nz) ::  &
         272           0 :       wpNcnp_zm, & ! Covariance of N_cn and w (momentum levs.)   [(m/s)(num/kg)]
         273           0 :       wpNcnp_zt    ! Covariance of N_cn and w on thermo. levels  [(m/s)(num/kg)]
         274             :
         275             :     real( kind = core_rknd ), dimension(ngrdcol,nz,hydromet_dim) :: &
         276           0 :       hm_1, & ! Mean of a precip. hydrometeor (1st PDF component)   [units vary]
         277           0 :       hm_2    ! Mean of a precip. hydrometeor (2nd PDF component)   [units vary]
         278             :
         279             :     real( kind = core_rknd ), dimension(ngrdcol,nz,hydromet_dim) :: &
         280           0 :       hydrometp2_zt,  & ! Variance of a hydrometeor (overall); t-lev   [units^2]
         281           0 :       wphydrometp_zt    ! Covariance of w and hm interp. to t-levs. [(m/s)units]
         282             :
         283             :     real( kind = core_rknd ), dimension(ngrdcol,nz,pdf_dim,pdf_dim) :: &
         284           0 :       corr_array_1, & ! Correlation array of PDF vars. (comp. 1)             [-]
         285           0 :       corr_array_2    ! Correlation array of PDF vars. (comp. 2)             [-]
         286             :
         287             :     real( kind = core_rknd ), dimension(ngrdcol,nz,pdf_dim) :: &
         288           0 :       mu_x_1,    & ! Mean array of PDF vars. (1st PDF component)    [units vary]
         289           0 :       mu_x_2,    & ! Mean array of PDF vars. (2nd PDF component)    [units vary]
         290           0 :       sigma_x_1, & ! Standard deviation array of PDF vars (comp. 1) [units vary]
         291           0 :       sigma_x_2    ! Standard deviation array of PDF vars (comp. 2) [units vary]
         292             :
         293             :     real( kind = core_rknd ), dimension(pdf_dim) :: &
         294           0 :       corr_array_scaling
         295             :
         296             :     real( kind = core_rknd ), dimension(ngrdcol,nz,pdf_dim) :: &
         297           0 :       sigma2_on_mu2_ip_1, & ! Ratio array sigma_hm_1^2/mu_hm_1^2             [-]
         298           0 :       sigma2_on_mu2_ip_2    ! Ratio array sigma_hm_2^2/mu_hm_2^2             [-]
         299             :
         300             :     real( kind = core_rknd ), dimension(ngrdcol,nz) :: &
         301           0 :       const_Ncnp2_on_Ncnm2,       & ! Prescribed ratio: <Ncn'^2> to <Ncn>^2  [-]
         302           0 :       stdev_const_Ncnp2_on_Ncnm2, & ! Standard deviation of const_Ncnp2_on_Ncnm2
         303           0 :       const_corr_chi_Ncn,         & ! Prescribed corr. of chi (old s) & Ncn  [-]
         304           0 :       const_corr_chi_Ncn_n_cloud    ! Prescribed corr. of chi & Ncn in cloud [-]
         305             :
         306             :     real( kind = core_rknd ), dimension(ngrdcol) :: &
         307           0 :       precip_frac_tol         ! Min. precip. frac. when hydromet. present    [-]
         308             :
         309             :     real( kind = core_rknd ), dimension(ngrdcol,nz,hydromet_dim) :: &
         310           0 :       wphydrometp_chnge    ! Change in wphydrometp_zt: covar. clip. [(m/s)units]
         311             :
         312             :     real( kind = core_rknd ), dimension(ngrdcol,nz) :: &
         313           0 :       wm_zt,  & ! Mean vertical velocity, <w>, on thermo. levels  [m/s]
         314           0 :       wp2_zt    ! Variance of w, <w'^2> (interp. to t-levs.)      [m^2/s^2]
         315             :
         316             :     real( kind = core_rknd ), dimension(ngrdcol,nz) :: &
         317           0 :       rtp2_zt_from_chi, &
         318           0 :       rtp2_zm_from_chi
         319             :
         320             :     real( kind = core_rknd ) :: &
         321             :       omicron,        & ! Relative width parameter, omicron = R / Rmax    [-]
         322             :       zeta_vrnce_rat    ! Width parameter for sigma_hm_1^2 / mu_hm_1^2    [-]
         323             :
         324             :     logical :: l_corr_array_scaling
         325             :
         326             :     ! Flags used for covariance clipping of <w'hm'>.
         327             :     logical, parameter :: &
         328             :       l_first_clip_ts = .true., & ! First instance of clipping in a timestep.
         329             :       l_last_clip_ts  = .true.    ! Last instance of clipping in a timestep.
         330             :
         331             :     character(len=10) :: &
         332             :       hydromet_name    ! Name of a hydrometeor
         333             :
         334             :     integer :: k, i, j  ! Loop indices
         335             :
         336             :     ! ---- Begin Code ----
         337             :
         338             :     ! Assertion check
         339             :     ! Check that all hydrometeors are positive otherwise exit the program
         340           0 :     if ( clubb_at_least_debug_level( 0 ) ) then
         341           0 :       if ( any(hydromet < zero_threshold) ) then
         342           0 :         do j = 1, hydromet_dim
         343           0 :           hydromet_name = hm_metadata%hydromet_list(j)
         344           0 :           do k = 1, nz
         345           0 :             do i = 1, ngrdcol
         346           0 :               if ( hydromet(i,k,j) < zero_threshold ) then
         347             :                 ! Write error message
         348           0 :                 write(fstderr,*) " at beginning of setup_pdf_parameters: ", &
         349           0 :                                   trim( hydromet_name )//" = ", &
         350           0 :                                   hydromet(i,k,j), " < ", zero_threshold, &
         351           0 :                                   " at k = ", k
         352           0 :                 err_code = clubb_fatal_error
         353           0 :                 return
         354             :               end if ! hydromet(k,i) < 0
         355             :             end do ! k = 1, nz
         356             :           end do ! i = 1, hydromet_dim
         357             :         end do
         358             :       end if
         359             :     end if !clubb_at_least_debug_level( 0 )
         360             :
         361             :     ! Setup some of the PDF parameters
         362           0 :     do k = 1, nz
         363           0 :       do i = 1, ngrdcol
         364           0 :         sigma_w_1(i,k)    = sqrt( pdf_params%varnce_w_1(i,k) )
         365           0 :         sigma_w_2(i,k)    = sqrt( pdf_params%varnce_w_2(i,k) )
         366             :       end do
         367             :     end do
         368             :
         369             :     ! Compute rcm_pdf for use within SILHS
         370           0 :     do i = 1, ngrdcol
         371           0 :       rcm_pdf(i,:) = compute_mean_binormal( pdf_params%rc_1(i,:), pdf_params%rc_2(i,:), &
         372           0 :                                             pdf_params%mixt_frac(i,:) )
         373             :     end do
         374             :
         375             :     ! Note on hydrometeor PDF shape:
         376             :     ! To use a single lognormal over the entire grid level, turn off the
         377             :     ! l_use_precip_frac flag and set omicron to 1 and zeta_vrnce_rat to 0 in
         378             :     ! tunable_parameters.in.
         379             :     ! To use a single delta-lognormal (single lognormal in-precip.), enable the
         380             :     ! l_use_precip_frac flag and set omicron to 1 and zeta_vrnce_rat to 0 in
         381             :     ! tunable_parameters.in.
         382             :     ! Otherwise, with l_use_precip_frac enabled and omicron and zeta_vrnce_rat
         383             :     ! values that are not 1 and 0, respectively, the PDF shape is a double
         384             :     ! delta-lognormal (two independent lognormals in-precip.).
         385             :
         386             :     ! Calculate precipitation fraction.
         387           0 :     if ( l_use_precip_frac ) then
         388             :
         389             :       call precip_fraction( nz, ngrdcol, hydromet_dim,                                    & ! In
         390             :                 hydromet(:,:,:), cloud_frac(:,:), pdf_params%cloud_frac_1(:,:),           & ! In
         391             :                 hm_metadata%l_mix_rat_hm, hm_metadata%l_frozen_hm,                  & ! In
         392             :                 hm_metadata%hydromet_tol,                                              & ! In
         393             :                 pdf_params%cloud_frac_2(:,:), ice_supersat_frac(:,:),                     & ! In
         394             :                 pdf_params%ice_supersat_frac_1(:,:), pdf_params%ice_supersat_frac_2(:,:), & ! In
         395             :                 pdf_params%mixt_frac(:,:), clubb_params,                                  & ! In
         396             :                 stats_metadata,                                                           & ! In
         397             :                 stats_sfc(:),                                                             & ! Inout
         398             :                 precip_fracs%precip_frac(:,:),                                            & ! Out
         399             :                 precip_fracs%precip_frac_1(:,:),                                          & ! Out
         400             :                 precip_fracs%precip_frac_2(:,:),                                          & ! Out
         401           0 :                 precip_frac_tol(:) )                                                        ! Out
         402             :
         403           0 :       if ( err_code == clubb_fatal_error ) then
         404           0 :         write(fstderr,*) " in setup_pdf_parameters after calling precip_fraction"
         405           0 :         return
         406             :       end if
         407             :
         408             :     else
         409             :
         410           0 :       precip_fracs%precip_frac(:,:)   = one
         411           0 :       precip_fracs%precip_frac_1(:,:) = one
         412           0 :       precip_fracs%precip_frac_2(:,:) = one
         413           0 :       precip_frac_tol(:) = cloud_frac_min
         414             :
         415             :     end if
         416             :
         417             :     ! Calculate <N_cn> from Nc_in_cloud, whether Nc_in_cloud is predicted or
         418             :     ! based on a prescribed value, and whether the value is constant or varying
         419             :     ! over the grid level.
         420           0 :     if ( .not. l_const_Nc_in_cloud ) then
         421             :       ! Ncn varies at each vertical level.
         422           0 :       do k = 1, nz
         423           0 :         do i = 1, ngrdcol
         424           0 :          const_Ncnp2_on_Ncnm2(i,k) = hm_metadata%Ncnp2_on_Ncnm2
         425             :         end do
         426             :       end do
         427             :
         428           0 :       stdev_const_Ncnp2_on_Ncnm2(:,:) = stdev_L2N( const_Ncnp2_on_Ncnm2(:,:) )
         429             :
         430             :     else  ! l_const_Nc_in_cloud
         431             :       ! Ncn is constant at each vertical level.
         432           0 :       const_Ncnp2_on_Ncnm2(:,:)       = zero
         433           0 :       stdev_const_Ncnp2_on_Ncnm2(:,:) = zero
         434             :     end if
         435             :
         436           0 :     const_corr_chi_Ncn_n_cloud(:,:) = corr_array_n_cloud( hm_metadata%iiPDF_Ncn,&
         437           0 :                                                           hm_metadata%iiPDF_chi )
         438             :
         439             :     call corr_NN2NL( nz, ngrdcol, & ! intent(in)
         440             :                      const_corr_chi_Ncn_n_cloud(:,:), & ! intent(in)
         441             :                      stdev_const_Ncnp2_on_Ncnm2(:,:), const_Ncnp2_on_Ncnm2(:,:), & ! intent(in)
         442           0 :                      const_corr_chi_Ncn(:,:)  ) ! intent(out)
         443             :
         444             :     Ncnm(:,:) = Nc_in_cloud_to_Ncnm( &
         445           0 :                     pdf_params%chi_1(:,:), pdf_params%chi_2(:,:), pdf_params%stdev_chi_1(:,:), &
         446           0 :                     pdf_params%stdev_chi_2(:,:), pdf_params%mixt_frac(:,:), Nc_in_cloud(:,:), &
         447           0 :                     pdf_params%cloud_frac_1(:,:), pdf_params%cloud_frac_2(:,:), &
         448           0 :                     const_Ncnp2_on_Ncnm2(:,:), const_corr_chi_Ncn(:,:) )
         449             :
         450             :     ! Boundary Condition.
         451             :     ! At thermodynamic level k = 1, which is below the model lower boundary, the
         452             :     ! value of Ncnm does not matter.
         453           0 :     Ncnm(:,1) = Nc_in_cloud(:,1)
         454             :
         455             :
         456             :     ! Calculate the overall variance of a precipitating hydrometeor (hm),
         457             :     !<hm'^2>.
         458           0 :     do j = 1, hydromet_dim
         459           0 :        do k = 1, nz, 1
         460           0 :          do i = 1, ngrdcol
         461             :
         462           0 :             if ( hydromet(i,k,j) >= hm_metadata%hydromet_tol(j) ) then
         463             :               ! There is some of the hydrometeor species found at level k.
         464             :               ! Calculate the variance (overall) of the hydrometeor.
         465             :               hydrometp2_zt(i,k,j) &
         466           0 :               = ( ( hm_metadata%hmp2_ip_on_hmm2_ip(j) + one ) / precip_fracs%precip_frac(i,k) - one ) &
         467           0 :                 * hydromet(i,k,j)**2
         468             :             else
         469           0 :               hydrometp2_zt(i,k,j) = zero
         470             :             end if
         471             :
         472             :          end do ! k = 1, nz, 1
         473             :       end do
         474             :     end do
         475             :
         476             :     ! Interpolate the overall variance of a hydrometeor, <hm'^2>, to its home on
         477             :     ! momentum grid levels.
         478           0 :     do i = 1, hydromet_dim, 1
         479           0 :       hydrometp2(:,:,i)  = zt2zm( nz, ngrdcol, gr, hydrometp2_zt(:,:,i), zero_threshold )
         480           0 :       hydrometp2(:,nz,i) = zero
         481             :     end do
         482             :
         483             :
         484             :     ! Calculate correlations involving w and Ncn by first calculating the
         485             :     ! overall covariance of w and Ncn using the down-gradient approximation.
         486           0 :     if ( l_calc_w_corr ) then
         487             :
         488             :       ! Recalculate wm_zt and wp2_zt.  Mean vertical velocity may not be easy to
         489             :       ! pass into this subroutine from a host model, and wp2_zt needs to have a
         490             :       ! value consistent with the value it had when the PDF parameters involving w
         491             :       ! were originally set in subroutine pdf_closure.  The variable wp2 has since
         492             :       ! been advanced, resulting a new wp2_zt.  However, the value of wp2 here
         493             :       ! needs to be consistent with wp2 at the time the PDF parameters were
         494             :       ! calculated.
         495             :
         496             :       ! Calculate the overall mean of vertical velocity, w, on thermodynamic
         497             :       ! levels.
         498           0 :       wm_zt(:,:) = compute_mean_binormal( pdf_params%w_1(:,:), pdf_params%w_2(:,:), &
         499           0 :                                           pdf_params%mixt_frac(:,:) )
         500             :
         501             :       ! Calculate the overall variance of vertical velocity on thermodynamic
         502             :       ! levels.
         503             :       wp2_zt(:,:) = compute_variance_binormal( wm_zt(:,:), &
         504           0 :                                                pdf_params%w_1(:,:), pdf_params%w_2(:,:), &
         505             :                                                sigma_w_1(:,:), sigma_w_2(:,:), &
         506           0 :                                                pdf_params%mixt_frac(:,:) )
         507             :
         508             :       ! Interpolate the covariances (overall) of w and precipitating
         509             :       ! hydrometeors to thermodynamic grid levels.
         510           0 :       do i = 1, hydromet_dim
         511           0 :         wphydrometp_zt(:,:,i) = zm2zt( nz, ngrdcol, gr, wphydrometp(:,:,i) )
         512             :       end do
         513             :
         514           0 :       do j = 1, hydromet_dim
         515           0 :         do k = 1, nz
         516           0 :           do i = 1, ngrdcol
         517           0 :             if ( hydromet(i,k,j) < hm_metadata%hydromet_tol(j) ) then
         518           0 :               wphydrometp_zt(i,k,j) = zero
         519             :             end if
         520             :           end do
         521             :         end do
         522             :       end do
         523             :
         524             :       ! When the mean value of a precipitating hydrometeor is below tolerance
         525             :       ! value, it is considered to have a value of 0, and the precipitating
         526             :       ! hydrometeor does not vary over the grid level.  Any covariances
         527             :       ! involving that precipitating hydrometeor also have values of 0 at that
         528             :       ! grid level.
         529           0 :       do j = 1, hydromet_dim
         530           0 :         do k = 1, nz, 1
         531           0 :           do i = 1, ngrdcol
         532             :
         533             :             ! Clip the value of covariance <w'hm'> on thermodynamic levels.
         534             :             call clip_covar_level( clip_wphydrometp, k, l_first_clip_ts,  & ! In
         535           0 :                                    l_last_clip_ts, dt, wp2_zt(i,k),       & ! In
         536           0 :                                    hydrometp2_zt(i,k,j),                  & ! In
         537             :                                    l_predict_upwp_vpwp,                   & ! In
         538             :                                    stats_metadata,                        & ! In
         539             :                                    stats_zm(i),                           & ! Inout
         540             :                                    wphydrometp_zt(i,k,j),                 & ! Inout
         541           0 :                                    wphydrometp_chnge(i,k,j) )               ! Out
         542             :
         543             :            end do ! k = 1, nz, 1
         544             :         end do ! i = 1, hydromet_dim, 1
         545             :       end do
         546             :
         547           0 :       Kh_zm_c_K_hm(:,:) = -clubb_params(ic_K_hm) * Kh_zm(:,:)
         548             :
         549             :       call calc_xpwp( nz, ngrdcol, gr, &
         550             :                       Kh_zm_c_K_hm, Ncnm, &
         551           0 :                       wpNcnp_zm )
         552             :
         553             :       ! Boundary conditions; We are assuming zero flux at the top.
         554           0 :       wpNcnp_zm(:,nz) = zero
         555             :
         556             :       ! Interpolate the covariances to thermodynamic grid levels.
         557           0 :       wpNcnp_zt(:,:) = zm2zt( nz, ngrdcol, gr, wpNcnp_zm(:,:) )
         558             :
         559             :       ! When the mean value of Ncn is below tolerance value, it is considered
         560             :       ! to have a value of 0, and Ncn does not vary over the grid level.  Any
         561             :       ! covariance involving Ncn also has a value of 0 at that grid level.
         562           0 :       do k = 1, nz, 1
         563           0 :         do i = 1, ngrdcol
         564           0 :           if ( Ncnm(i,k) <= Ncn_tol ) then
         565           0 :             wpNcnp_zt(i,k) = zero
         566             :           end if
         567             :         end do ! k = 1, nz, 1
         568             :       end do
         569             :
         570             :     end if ! l_calc_w_corr
         571             :
         572             :     ! Unpack CLUBB parameters
         573           0 :     omicron = clubb_params(iomicron)
         574           0 :     zeta_vrnce_rat = clubb_params(izeta_vrnce_rat)
         575             :
         576             :     !!! Calculate the means and standard deviations involving PDF variables
         577             :     !!! -- w, chi, eta, N_cn, and any precipitating hydrometeors (hm in-precip)
         578             :     !!! -- for each PDF component.
         579             :     call compute_mean_stdev( nz, ngrdcol, hydromet_dim, &
         580             :                              hydromet(:,:,:), hydrometp2_zt(:,:,:),         & ! Intent(in)
         581             :                              hm_metadata,                                & ! Intent(in)
         582             :                              Ncnm(:,:), pdf_params%mixt_frac(:,:),          & ! Intent(in)
         583             :                              precip_fracs%precip_frac(:,:),                 & ! Intent(in)
         584             :                              precip_fracs%precip_frac_1(:,:),               & ! Intent(in)
         585             :                              precip_fracs%precip_frac_2(:,:),               & ! Intent(in)
         586             :                              precip_frac_tol(:),                            & ! Intent(in)
         587             :                              pdf_params%w_1(:,:),                           & ! Intent(in)
         588             :                              pdf_params%w_2(:,:),                           & ! Intent(in)
         589             :                              sigma_w_1(:,:),                                & ! Intent(in)
         590             :                              sigma_w_1(:,:),                                & ! Intent(in)
         591             :                              pdf_params%chi_1(:,:),                         & ! Intent(in)
         592             :                              pdf_params%chi_2(:,:),                         & ! Intent(in)
         593             :                              pdf_params%stdev_chi_1(:,:),                   & ! Intent(in)
         594             :                              pdf_params%stdev_chi_2(:,:),                   & ! Intent(in)
         595             :                              pdf_params%stdev_eta_1(:,:),                   & ! Intent(in)
         596             :                              pdf_params%stdev_eta_2(:,:),                   & ! Intent(in)
         597             :                              pdf_params%thl_1(:,:),                         & ! Intent(in)
         598             :                              pdf_params%thl_2(:,:),                         & ! Intent(in)
         599             :                              pdf_dim,                                       & ! Intent(in)
         600             :                              omicron, zeta_vrnce_rat,                       & ! Intent(in)
         601             :                              l_const_Nc_in_cloud,                           & ! Intent(in)
         602             :                              mu_x_1(:,:,:), mu_x_2(:,:,:),                  & ! Intent(out)
         603             :                              sigma_x_1(:,:,:), sigma_x_2(:,:,:),            & ! Intent(out)
         604             :                              hm_1(:,:,:), hm_2(:,:,:),                      & ! Intent(out)
         605             :                              sigma2_on_mu2_ip_1(:,:,:),                     & ! Intent(out)
         606           0 :                              sigma2_on_mu2_ip_2(:,:,:) )                      ! Intent(out)
         607             :
         608             :     !!! Transform the component means and standard deviations involving
         609             :     !!! precipitating hydrometeors (hm in-precip) and N_cn -- ln hm and
         610             :     !!! ln N_cn -- to normal space for each PDF component.
         611             :     call norm_transform_mean_stdev( nz, ngrdcol,                            & ! Intent(in)
         612             :                                     hydromet_dim, hm_metadata,           & ! Intent(in)
         613             :                                     hm_1(:,:,:), hm_2(:,:,:),               & ! Intent(in)
         614             :                                     Ncnm(:,:), pdf_dim,                     & ! Intent(in)
         615             :                                     mu_x_1(:,:,:), mu_x_2(:,:,:),           & ! Intent(in)
         616             :                                     sigma_x_1(:,:,:), sigma_x_2(:,:,:),     & ! Intent(in)
         617             :                                     sigma2_on_mu2_ip_1(:,:,:),              & ! Intent(in)
         618             :                                     sigma2_on_mu2_ip_2(:,:,:),              & ! Intent(in)
         619             :                                     l_const_Nc_in_cloud,                    & ! Intent(in)
         620             :                                     mu_x_1_n(:,:,:), mu_x_2_n(:,:,:),       & ! Intent(out)
         621           0 :                                     sigma_x_1_n(:,:,:), sigma_x_2_n(:,:,:) )  ! Intent(out)
         622             :
         623             :
         624             :     !!! Calculate the normal space correlations.
         625             :     !!! The normal space correlations are the same as the true correlations
         626             :     !!! except when at least one of the variables involved is a precipitating
         627             :     !!! hydrometeor or Ncn.  In these cases, the normal space correlation
         628             :     !!! involves the natural logarithm of the precipitating hydrometeors, ln hm
         629             :     !!! (for example, ln r_r and ln N_r), and ln N_cn for each PDF component.
         630           0 :     if ( l_diagnose_correlations ) then
         631             :
         632           0 :       do k = 2, nz, 1
         633           0 :         do i = 1, ngrdcol
         634             :
         635           0 :           if ( rcm_pdf(i,k) > rc_tol ) then
         636             :
         637             :             call diagnose_correlations( pdf_dim, hm_metadata%iiPDF_w, &  ! In
         638             :                                         corr_array_n_cloud, &               ! In
         639             :                                         l_calc_w_corr, &                    ! In
         640           0 :                                         corr_array_1_n(i,k,:,:) )           ! Out
         641             :
         642             :             call diagnose_correlations( pdf_dim, hm_metadata%iiPDF_w, &  ! In
         643             :                                         corr_array_n_cloud, &               ! In
         644             :                                         l_calc_w_corr, &                    ! In
         645           0 :                                         corr_array_2_n(i,k,:,:) )           ! Out
         646             :
         647             :          else
         648             :
         649             :             call diagnose_correlations( pdf_dim, hm_metadata%iiPDF_w, &  ! In
         650             :                                         corr_array_n_below, &               ! In
         651             :                                         l_calc_w_corr, &                    ! In
         652           0 :                                         corr_array_1_n(i,k,:,:) )           ! Out
         653             :
         654             :             call diagnose_correlations( pdf_dim, hm_metadata%iiPDF_w, &  ! In
         655             :                                         corr_array_n_below, &               ! In
         656             :                                         l_calc_w_corr, &                    ! In
         657           0 :                                         corr_array_2_n(i,k,:,:) )           ! Out
         658             :
         659             :           end if
         660             :
         661             :         end do
         662             :       end do
         663             :
         664           0 :       do k = 2, nz, 1
         665           0 :         do i = 1, ngrdcol
         666             :           call calc_cholesky_corr_mtx_approx ( &
         667             :                   pdf_dim, hm_metadata%iiPDF_w, &                      ! intent(in)
         668           0 :                   corr_array_1_n(i,k,:,:), &                              ! intent(in)
         669           0 :                   corr_cholesky_mtx_1(i,k,:,:), corr_array_1_n(i,k,:,:) ) ! intent(out)
         670             :         end do
         671             :       end do
         672             :
         673           0 :       do k = 2, nz, 1
         674           0 :         do i = 1, ngrdcol
         675             :           call calc_cholesky_corr_mtx_approx( &
         676             :                   pdf_dim, hm_metadata%iiPDF_w, &                      ! intent(in)
         677           0 :                   corr_array_2_n(i,k,:,:), &                              ! intent(in)
         678           0 :                   corr_cholesky_mtx_2(i,k,:,:), corr_array_2_n(i,k,:,:) ) ! intent(out)
         679             :         end do
         680             :       end do
         681             :
         682             :     else ! if .not. l_diagnose_correlations
         683             :
         684             :       if ( l_fix_w_chi_eta_correlations &
         685           0 :            .and. .not. l_calc_w_corr ) then
         686             :
         687             :         ! When the flags are set this way, the correlation matrices do not vary with any vertical
         688             :         ! values, and instead are determined entirely by prescribed values. This results in there
         689             :         ! being only two unique correlation matrices, one for when the grid box is in cloud
         690             :         ! and one for when it is not. So instead of setting up correlation matrices for all
         691             :         ! grid boxes then calculating their Cholesky decomps, we can simply set up two correlation
         692             :         ! matrices, one for in cloud and one for out cloud, calculate the corresponding
         693             :         ! Cholesky decompositions, then use the value of rc at each grid box to determine whether
         694             :         ! we assign the in cloud or out of cloud matrices to that grid box.
         695             :         call calc_corr_norm_and_cholesky_factor( nz, ngrdcol, iiPDF_type,                   & ! intent(in)
         696             :                                                  pdf_dim, hm_metadata,                   & ! intent(in)
         697             :                                                  pdf_params%rc_1, pdf_params%rc_2,          & ! intent(in)
         698             :                                                  corr_array_n_cloud, corr_array_n_below,    & ! intent(out)
         699             :                                                  corr_array_1_n, corr_array_2_n,            & ! intent(out)
         700           0 :                                                  corr_cholesky_mtx_1, corr_cholesky_mtx_2 )   ! out
         701             :
         702             :       else
         703             :
         704             :         ! The correlation matrices can vary with vertical values. So we need to set the
         705             :         ! correlation matrices up for each grid box, then find the Cholesky decomp for each
         706             :         ! grid box individually. This is very computationally expensive.
         707             :
         708             :         call comp_corr_norm( nz, pdf_dim, ngrdcol, hydromet_dim, hm_metadata,      & ! In
         709             :                              wm_zt(:,:), pdf_params%rc_1(:,:), pdf_params%rc_2(:,:),  & ! In
         710             :                              pdf_params%mixt_frac(:,:),                               & ! In
         711             :                              precip_fracs%precip_frac_1(:,:),                         & ! In
         712             :                              precip_fracs%precip_frac_2(:,:),                         & ! In
         713             :                              wpNcnp_zt(:,:), wphydrometp_zt(:,:,:),                   & ! In
         714             :                              mu_x_1(:,:,:), mu_x_2(:,:,:),                            & ! In
         715             :                              sigma_x_1(:,:,:), sigma_x_2(:,:,:),                      & ! In
         716             :                              sigma_x_1_n(:,:,:), sigma_x_2_n(:,:,:),                  & ! In
         717             :                              corr_array_n_cloud, corr_array_n_below,                  & ! In
         718             :                              pdf_params,                                              & ! In
         719             :                              iiPDF_type,                                              & ! In
         720             :                              l_calc_w_corr,                                           & ! In
         721             :                              l_fix_w_chi_eta_correlations,                            & ! In
         722           0 :                              corr_array_1_n(:,:,:,:), corr_array_2_n(:,:,:,:) )         ! Out
         723             :
         724             :         ! Compute choleksy factorization for the correlation matrix of 1st PDF component
         725           0 :         do k = 2, nz, 1
         726           0 :           do i = 1, ngrdcol
         727           0 :             call Cholesky_factor( pdf_dim, corr_array_1_n(i,k,:,:),                 & ! In
         728           0 :                                   corr_array_scaling, corr_cholesky_mtx_1(i,k,:,:), & ! Out
         729           0 :                                   l_corr_array_scaling )                              ! Out
         730             :           end do
         731             :         end do
         732             :
         733             :         ! Compute choleksy factorization for the correlation matrix of 2nd PDF component
         734           0 :         do k = 2, nz, 1
         735           0 :           do i = 1, ngrdcol
         736           0 :             call Cholesky_factor( pdf_dim, corr_array_2_n(i,k,:,:),                 & ! In
         737           0 :                                   corr_array_scaling, corr_cholesky_mtx_2(i,k,:,:), & ! Out
         738           0 :                                   l_corr_array_scaling )                              ! Out
         739             :           end do
         740             :         end do
         741             :
         742             :       end if
         743             :
         744             :     end if ! l_diagnose_correlations
         745             :
         746             :     ! hydromet_pdf_params is optional, so if it is not present we simply skip the steps
         747             :     ! to compute it.
         748           0 :     if ( present(hydromet_pdf_params) ) then
         749             :
         750             :       !!! Calculate the true correlations for each PDF component.
         751             :       call denorm_transform_corr( nz, ngrdcol, pdf_dim, hm_metadata,                   & ! In
         752             :                                   sigma_x_1_n(:,:,:), sigma_x_2_n(:,:,:),                 & ! In
         753             :                                   sigma2_on_mu2_ip_1(:,:,:), sigma2_on_mu2_ip_2(:,:,:),   & ! In
         754             :                                   corr_array_1_n(:,:,:,:),                                & ! In
         755             :                                   corr_array_2_n(:,:,:,:),                                & ! In
         756           0 :                                   corr_array_1(:,:,:,:), corr_array_2(:,:,:,:) )            ! Out
         757             :
         758             :       !!! Pack the PDF parameters
         759             :       call pack_hydromet_pdf_params( nz, ngrdcol,                                     & ! In
         760             :                                      hydromet_dim, hm_metadata,                    & ! In
         761             :                                      hm_1(:,:,:), hm_2(:,:,:), pdf_dim,               & ! In
         762             :                                      mu_x_1(:,:,:), mu_x_2(:,:,:),                    & ! In
         763             :                                      sigma_x_1(:,:,:), sigma_x_2(:,:,:),              & ! In
         764             :                                      corr_array_1(:,:,:,:), corr_array_2(:,:,:,:),    & ! In
         765           0 :                                      hydromet_pdf_params(:,:) )                         ! Out
         766             :
         767           0 :       do i = 1, ngrdcol
         768           0 :         call init_hydromet_pdf_params( hydromet_pdf_params(i,1) ) ! intent(out)
         769             :       end do
         770             :
         771             :     end if
         772             :
         773           0 :     if ( stats_metadata%l_stats_samp ) then
         774             :
         775           0 :       do j = 1, hydromet_dim
         776           0 :         if ( stats_metadata%ihmp2_zt(j) > 0 ) then
         777             :           ! Variance (overall) of the hydrometeor, <hm'^2>.
         778             :           ! call stat_update_var( stats_metadata%ihmp2_zt(i), hydrometp2_zt(:,i), stats_zt )
         779             :           ! Switch back to using stat_update_var once the code is generalized
         780             :           ! to pass in the number of vertical levels.
         781           0 :             do k = 1, nz, 1
         782           0 :               do i = 1, ngrdcol
         783           0 :                 call stat_update_var_pt( stats_metadata%ihmp2_zt(j), k, hydrometp2_zt(i,k,j), & ! intent(in)
         784           0 :                                          stats_zt(i) ) ! intent(inout)
         785             :              end do ! k = 1, nz, 1
         786             :            end do
         787             :         end if
         788             :       end do
         789             :
         790           0 :       do i = 1, ngrdcol
         791             :         call pdf_param_hm_stats( nz, pdf_dim, hydromet_dim, hm_metadata, & ! intent(in)
         792           0 :                                  hm_1(i,:,:), hm_2(i,:,:), & ! intent(in)
         793           0 :                                  mu_x_1(i,:,:), mu_x_2(i,:,:), & ! intent(in)
         794           0 :                                  sigma_x_1(i,:,:), sigma_x_2(i,:,:), & ! intent(in)
         795           0 :                                  corr_array_1(i,:,:,:), corr_array_2(i,:,:,:), & ! intent(in)
         796             :                                  stats_metadata, & ! intent(in)
         797           0 :                                  stats_zt(i) ) ! intent(inout)
         798             :       end do
         799             :
         800             :       !!! Statistics for normal space PDF parameters involving hydrometeors.
         801           0 :       do i = 1, ngrdcol
         802             :         call pdf_param_ln_hm_stats( nz, pdf_dim, hm_metadata,            & ! intent(in)
         803           0 :                                     mu_x_1_n(i,:,:), mu_x_2_n(i,:,:),       & ! intent(in)
         804           0 :                                     sigma_x_1_n(i,:,:), sigma_x_2_n(i,:,:), & ! intent(in)
         805           0 :                                     corr_array_1_n(i,:,:,:),                & ! intent(in)
         806           0 :                                     corr_array_2_n(i,:,:,:),                & ! intent(in)
         807             :                                     stats_metadata,                         & ! intent(in)
         808           0 :                                     stats_zt(i) )                             ! intent(inout)
         809             :       end do
         810             :
         811           0 :       if ( stats_metadata%irtp2_from_chi > 0 ) then
         812             :
         813           0 :         do i = 1, ngrdcol
         814             :           rtp2_zt_from_chi(i,:) &
         815           0 :             = compute_rtp2_from_chi( pdf_params%stdev_chi_1(i,:), pdf_params%stdev_chi_2(i,:), &
         816           0 :                                      pdf_params%stdev_eta_1(i,:), pdf_params%stdev_eta_2(i,:), &
         817           0 :                                      pdf_params%rt_1(i,:), pdf_params%rt_2(j,:),               &
         818           0 :                                      pdf_params%crt_1(i,:), pdf_params%crt_2(i,:),             &
         819           0 :                                      pdf_params%mixt_frac(i,:),                                &
         820           0 :                                      corr_array_1_n(i,:,hm_metadata%iiPDF_chi,hm_metadata%iiPDF_eta),                  &
         821           0 :                                      corr_array_2_n(i,:,hm_metadata%iiPDF_chi,hm_metadata%iiPDF_eta) )
         822             :         end do
         823             :
         824           0 :         rtp2_zm_from_chi = zt2zm( nz, ngrdcol, gr, rtp2_zt_from_chi, zero_threshold )
         825             :
         826             :         ! Switch back to using stat_update_var once the code is generalized
         827             :         ! to pass in the number of vertical levels.
         828             :         ! call stat_update_var( irtp2_from_chi, zt2zm( rtp2_zt_from_chi ), &
         829             :         ! stats_zm )
         830           0 :         do k = 1, nz, 1
         831           0 :           do i = 1, ngrdcol
         832           0 :             call stat_update_var_pt( stats_metadata%irtp2_from_chi, k, rtp2_zm_from_chi(i,k), & !in
         833           0 :                                      stats_zm(i) ) ! intent(inout)
         834             :           end do
         835             :         end do ! k = 1, nz, 1
         836             :
         837             :       end if
         838             :
         839           0 :       do i = 1, ngrdcol
         840             :         ! Switch back to using stat_update_var once the code is generalized
         841             :         ! to pass in the number of vertical levels.
         842           0 :         if ( stats_metadata%iprecip_frac > 0 ) then
         843             :           ! Overall precipitation fraction.
         844             :           ! call stat_update_var( stats_metadata%iprecip_frac, precip_frac, stats_zt )
         845           0 :           do k = 1, nz, 1
         846           0 :             call stat_update_var_pt( stats_metadata%iprecip_frac, k, precip_fracs%precip_frac(i,k), & ! intent(in)
         847           0 :                                      stats_zt(i) ) ! intent(inout)
         848             :           end do ! k = 1, nz, 1
         849             :        end if
         850             :
         851           0 :         if ( stats_metadata%iprecip_frac_1 > 0 ) then
         852             :           ! Precipitation fraction in PDF component 1.
         853             :           ! call stat_update_var( stats_metadata%iprecip_frac_1, precip_frac_1, stats_zt )
         854           0 :           do k = 1, nz, 1
         855           0 :             call stat_update_var_pt( stats_metadata%iprecip_frac_1, k, precip_fracs%precip_frac_1(i,k), & ! In
         856           0 :                                      stats_zt(i) ) ! intent(inout)
         857             :           end do ! k = 1, nz, 1
         858             :         end if
         859             :
         860           0 :         if ( stats_metadata%iprecip_frac_2 > 0 ) then
         861             :           ! Precipitation fraction in PDF component 2.
         862             :           ! call stat_update_var( stats_metadata%iprecip_frac_2, precip_frac_2, stats_zt )
         863           0 :           do k = 1, nz, 1
         864           0 :             call stat_update_var_pt( stats_metadata%iprecip_frac_2, k, precip_fracs%precip_frac_2(i,k), & ! In
         865           0 :                                      stats_zt(i) ) ! intent(inout)
         866             :           end do ! k = 1, nz, 1
         867             :         end if
         868             :
         869           0 :         if ( stats_metadata%iNcnm > 0 ) then
         870             :           ! Mean simplified cloud nuclei concentration (overall).
         871             :           ! call stat_update_var( stats_metadata%iNcnm, Ncnm, stats_zt )
         872           0 :           do k = 1, nz, 1
         873           0 :             call stat_update_var_pt( stats_metadata%iNcnm, k, Ncnm(i,k), & ! intent(in)
         874           0 :                                      stats_zt(i) ) ! intent(inout)
         875             :           end do ! k = 1, nz, 1
         876             :         end if
         877             :       end do
         878             :
         879             :     end if
         880             :
         881             :     ! Boundary conditions for the output variables at k=1.
         882           0 :     mu_x_1_n(:,1,:) = zero
         883           0 :     mu_x_2_n(:,1,:) = zero
         884           0 :     sigma_x_1_n(:,1,:) = zero
         885           0 :     sigma_x_2_n(:,1,:) = zero
         886           0 :     corr_array_1_n(:,1,:,:) = zero
         887           0 :     corr_array_2_n(:,1,:,:) = zero
         888           0 :     corr_cholesky_mtx_1(:,1,:,:) = zero
         889           0 :     corr_cholesky_mtx_2(:,1,:,:) = zero
         890             :
         891           0 :     precip_fracs%precip_frac(:,1)   = zero
         892           0 :     precip_fracs%precip_frac_1(:,1) = zero
         893           0 :     precip_fracs%precip_frac_2(:,1) = zero
         894             :
         895           0 :     if ( clubb_at_least_debug_level( 2 ) ) then
         896           0 :       do k = 2, nz
         897           0 :         do i = 1, ngrdcol
         898           0 :           call assert_corr_symmetric( corr_array_1_n(i,k,:,:), pdf_dim) ! intent(in)
         899           0 :           call assert_corr_symmetric( corr_array_2_n(i,k,:,:), pdf_dim) ! intent(in)
         900             :         end do
         901             :       end do
         902             :     end if
         903             :
         904             :     return
         905             :
         906           0 :   end subroutine setup_pdf_parameters
         907             :
         908             :   !=============================================================================
         909           0 :   subroutine compute_mean_stdev( nz, ngrdcol, hydromet_dim,     & ! Intent(in)
         910           0 :                                  hydromet, hydrometp2_zt,       & ! Intent(in)
         911             :                                  hm_metadata,                & ! Intent(in)
         912           0 :                                  Ncnm, mixt_frac,               & ! Intent(in)
         913           0 :                                  precip_frac,                   & ! Intent(in)
         914           0 :                                  precip_frac_1,                 & ! Intent(in)
         915           0 :                                  precip_frac_2,                 & ! Intent(in)
         916           0 :                                  precip_frac_tol,               & ! Intent(in)
         917           0 :                                  w_1, w_2,                      & ! Intent(in)
         918           0 :                                  stdev_w_1, stdev_w_2,          & ! Intent(in)
         919           0 :                                  chi_1, chi_2,                  & ! Intent(in)
         920           0 :                                  stdev_chi_1, stdev_chi_2,      & ! Intent(in)
         921           0 :                                  stdev_eta_1, stdev_eta_2,      & ! Intent(in)
         922           0 :                                  thl_1, thl_2,                  & ! Intent(in)
         923             :                                  pdf_dim,                       & ! Intent(in)
         924             :                                  omicron, zeta_vrnce_rat,       & ! Intent(in)
         925             :                                  l_const_Nc_in_cloud,           & ! Intent(in)
         926           0 :                                  mu_x_1, mu_x_2,                & ! Intent(out)
         927           0 :                                  sigma_x_1, sigma_x_2,          & ! Intent(out)
         928           0 :                                  hm_1, hm_2,                    & ! Intent(out)
         929           0 :                                  sigma_hm_1_sqd_on_mu_hm_1_sqd, & ! Intent(out)
         930           0 :                                  sigma_hm_2_sqd_on_mu_hm_2_sqd  ) ! Intent(out)
         931             :
         932             :     ! Description:
         933             :     ! Calculates the means and standard deviations (for each PDF component) of
         934             :     ! chi, eta, w, Ncn, and the precipitating hydrometeors.  For the
         935             :     ! precipitating hydrometeors, the component means and standard deviations
         936             :     ! are in-precip.
         937             :
         938             :     ! References:
         939             :     !-----------------------------------------------------------------------
         940             :
         941             :     use constants_clubb, only:  &
         942             :         zero     ! Constant(s)
         943             :
         944             :     use corr_varnce_module, only: &
         945             :       hm_metadata_type
         946             :
         947             :     use index_mapping, only: &
         948             :         pdf2hydromet_idx  ! Procedure(s)
         949             :
         950             :     use clubb_precision, only: &
         951             :         core_rknd  ! Variable(s)
         952             :
         953             :     implicit none
         954             :
         955             :     !----------------------- Input Variables -----------------------
         956             :     integer, intent(in) :: &
         957             :       nz,           & ! Number of model vertical grid levels
         958             :       pdf_dim,      & ! Number of PDF variables
         959             :       ngrdcol,      & ! Number of grid columns
         960             :       hydromet_dim    ! Number of hydrometeor species
         961             :
         962             :     real( kind = core_rknd ), dimension(ngrdcol,nz,hydromet_dim), intent(in) :: &
         963             :       hydromet,       & ! Mean of a hydrometeor (overall)         [hm units]
         964             :       hydrometp2_zt     ! Variance of a hydrometeor (overall)     [(hm units)^2]
         965             :
         966             :     type (hm_metadata_type), intent(in) :: &
         967             :       hm_metadata
         968             :
         969             :     real( kind = core_rknd ), dimension(ngrdcol,nz), intent(in) :: &
         970             :       Ncnm,          & ! Mean simplified cloud nuclei concentration   [num/kg]
         971             :       mixt_frac,     & ! Mixture fraction                             [-]
         972             :       precip_frac,   & ! Precipitation fraction (overall)             [-]
         973             :       precip_frac_1, & ! Precipitation fraction (1st PDF component)   [-]
         974             :       precip_frac_2    ! Precipitation fraction (2nd PDF component)   [-]
         975             :
         976             :     real( kind = core_rknd ), dimension(ngrdcol,nz), intent(in) :: &
         977             :       w_1,         & ! Mean of w (1st PDF component)                  [m/s]
         978             :       w_2,         & ! Mean of w (2nd PDF component)                  [m/s]
         979             :       stdev_w_1,  & ! Variance of w (1st PDF component)              [m^2/s^2]
         980             :       stdev_w_2,  & ! Variance of w (2nd PDF component)              [m^2/s^2]
         981             :       chi_1,       & ! Mean of chi (1st PDF component)                [kg/kg]
         982             :       chi_2,       & ! Mean of chi (2nd PDF component)                [kg/kg]
         983             :       stdev_chi_1, & ! Standard deviation of chi (1st PDF component)  [kg/kg]
         984             :       stdev_chi_2, & ! Standard deviation of chi (2nd PDF component)  [kg/kg]
         985             :       stdev_eta_1, & ! Standard deviation of eta (1st PDF component)  [kg/kg]
         986             :       stdev_eta_2, & ! Standard deviation of eta (2nd PDF component)  [kg/kg]
         987             :       thl_1,       & ! Mean of thl (1st PDF component)                [K]
         988             :       thl_2          ! Mean of thl (2nd PDF component)                [K]
         989             :
         990             :     real( kind = core_rknd ), dimension(ngrdcol), intent(in) :: &
         991             :       precip_frac_tol    ! Minimum precip. frac. when hydromet. are present  [-]
         992             :
         993             :     real( kind = core_rknd ), intent(in) :: &
         994             :       omicron,        & ! Relative width parameter, omicron = R / Rmax    [-]
         995             :       zeta_vrnce_rat    ! Width parameter for sigma_hm_1^2 / mu_hm_1^2    [-]
         996             :
         997             :     logical, intent(in) :: &
         998             :       l_const_Nc_in_cloud ! Use a constant cloud droplet conc. within cloud (K&K)
         999             :
        1000             :     !----------------------- Output Variables -----------------------
        1001             :     ! Note:  This code assumes to be these arrays in the same order as the
        1002             :     ! correlation arrays, etc., which is determined by the iiPDF indices.
        1003             :     ! The order should be as follows:  chi, eta, w, Ncn, <precip. hydrometeors>
        1004             :     ! (indices increasing from left to right).
        1005             :     real( kind = core_rknd ), dimension(ngrdcol,nz,pdf_dim), intent(out) :: &
        1006             :       mu_x_1,    & ! Mean array of PDF vars. (1st PDF component)    [units vary]
        1007             :       mu_x_2,    & ! Mean array of PDF vars. (2nd PDF component)    [units vary]
        1008             :       sigma_x_1, & ! Standard deviation array of PDF vars (comp. 1) [units vary]
        1009             :       sigma_x_2    ! Standard deviation array of PDF vars (comp. 2) [units vary]
        1010             :
        1011             :     real( kind = core_rknd ), dimension(ngrdcol,nz,hydromet_dim), intent(out) :: &
        1012             :       hm_1, & ! Mean of a precip. hydrometeor (1st PDF component)   [units vary]
        1013             :       hm_2    ! Mean of a precip. hydrometeor (2nd PDF component)   [units vary]
        1014             :
        1015             :     real( kind = core_rknd ), dimension(ngrdcol,nz,pdf_dim), intent(out) :: &
        1016             :       sigma_hm_1_sqd_on_mu_hm_1_sqd, & ! Ratio sigma_hm_1^2 / mu_hm_1^2      [-]
        1017             :       sigma_hm_2_sqd_on_mu_hm_2_sqd    ! Ratio sigma_hm_2^2 / mu_hm_2^2      [-]
        1018             :
        1019             :     !----------------------- Local Variables -----------------------
        1020             :     integer :: ivar ! Loop iterator
        1021             :
        1022             :     integer :: hm_idx  ! Hydrometeor array index.
        1023             :
        1024             :     !----------------------- Begin Code -----------------------
        1025             :
        1026             :     !!! Initialize output variables.
        1027           0 :     hm_1(:,:,:)       = zero
        1028           0 :     hm_2(:,:,:)       = zero
        1029           0 :     sigma_hm_1_sqd_on_mu_hm_1_sqd(:,:,:) = zero
        1030           0 :     sigma_hm_2_sqd_on_mu_hm_2_sqd(:,:,:) = zero
        1031             :
        1032             :
        1033             :     !!! Enter the PDF parameters.
        1034             :
        1035             :     !!! Vertical velocity, w.
        1036             :
        1037             :     ! Mean of vertical velocity, w, in PDF component 1.
        1038           0 :     mu_x_1(:,:,hm_metadata%iiPDF_w) = w_1(:,:)
        1039             :
        1040             :     ! Mean of vertical velocity, w, in PDF component 2.
        1041           0 :     mu_x_2(:,:,hm_metadata%iiPDF_w) = w_2(:,:)
        1042             :
        1043             :     ! Standard deviation of vertical velocity, w, in PDF component 1.
        1044           0 :     sigma_x_1(:,:,hm_metadata%iiPDF_w) = stdev_w_1(:,:)
        1045             :
        1046             :     ! Standard deviation of vertical velocity, w, in PDF component 2.
        1047           0 :     sigma_x_2(:,:,hm_metadata%iiPDF_w) = stdev_w_2(:,:)
        1048             :
        1049             :
        1050             :     !!! Extended liquid water mixing ratio, chi.
        1051             :
        1052             :     ! Mean of extended liquid water mixing ratio, chi (old s),
        1053             :     ! in PDF component 1.
        1054           0 :     mu_x_1(:,:,hm_metadata%iiPDF_chi) = chi_1(:,:)
        1055             :
        1056             :     ! Mean of extended liquid water mixing ratio, chi (old s),
        1057             :     ! in PDF component 2.
        1058           0 :     mu_x_2(:,:,hm_metadata%iiPDF_chi) = chi_2(:,:)
        1059             :
        1060             :     ! Standard deviation of extended liquid water mixing ratio, chi (old s),
        1061             :     ! in PDF component 1.
        1062           0 :     sigma_x_1(:,:,hm_metadata%iiPDF_chi) = stdev_chi_1(:,:)
        1063             :
        1064             :     ! Standard deviation of extended liquid water mixing ratio, chi (old s),
        1065             :     ! in PDF component 2.
        1066           0 :     sigma_x_2(:,:,hm_metadata%iiPDF_chi) = stdev_chi_2(:,:)
        1067             :
        1068             :
        1069             :     !!! Coordinate orthogonal to chi, eta.
        1070             :
        1071             :     ! Mean of eta (old t) in PDF component 1.
        1072             :     ! Set the component mean values of eta to 0.
        1073             :     ! The component mean values of eta are not important.  They can be set to
        1074             :     ! anything.  They cancel out in the model code.  However, the best thing to
        1075             :     ! do is to set them to 0 and avoid any kind of numerical error.
        1076           0 :     mu_x_1(:,:,hm_metadata%iiPDF_eta) = zero
        1077             :
        1078             :     ! Mean of eta (old t) in PDF component 2.
        1079             :     ! Set the component mean values of eta to 0.
        1080             :     ! The component mean values of eta are not important.  They can be set to
        1081             :     ! anything.  They cancel out in the model code.  However, the best thing to
        1082             :     ! do is to set them to 0 and avoid any kind of numerical error.
        1083           0 :     mu_x_2(:,:,hm_metadata%iiPDF_eta) = zero
        1084             :
        1085             :     ! Standard deviation of eta (old t) in PDF component 1.
        1086           0 :     sigma_x_1(:,:,hm_metadata%iiPDF_eta) = stdev_eta_1(:,:)
        1087             :
        1088             :     ! Standard deviation of eta (old t) in PDF component 2.
        1089           0 :     sigma_x_2(:,:,hm_metadata%iiPDF_eta) = stdev_eta_2(:,:)
        1090             :
        1091             :
        1092             :     !!! Simplified cloud nuclei concentration, Ncn.
        1093             :
        1094             :     ! Mean of simplified cloud nuclei concentration, Ncn, in PDF component 1.
        1095           0 :     mu_x_1(:,:,hm_metadata%iiPDF_Ncn) = Ncnm(:,:)
        1096             :
        1097             :     ! Mean of simplified cloud nuclei concentration, Ncn, in PDF component 2.
        1098           0 :     mu_x_2(:,:,hm_metadata%iiPDF_Ncn) = Ncnm(:,:)
        1099             :
        1100             :     ! Standard deviation of simplified cloud nuclei concentration, Ncn,
        1101             :     ! in PDF component 1.
        1102           0 :     if ( .not. l_const_Nc_in_cloud ) then
        1103             :
        1104             :       ! Ncn varies in both PDF components.
        1105           0 :       sigma_x_1(:,:,hm_metadata%iiPDF_Ncn) = sqrt( hm_metadata%Ncnp2_on_Ncnm2 ) * Ncnm(:,:)
        1106             :
        1107           0 :       sigma_x_2(:,:,hm_metadata%iiPDF_Ncn) = sqrt( hm_metadata%Ncnp2_on_Ncnm2 ) * Ncnm(:,:)
        1108             :
        1109             :       ! Ncn is not an official hydrometeor.  However, both the
        1110             :       ! sigma_hm_1_sqd_on_mu_hm_1_sqd and sigma_hm_2_sqd_on_mu_hm_2_sqd arrays
        1111             :       ! have size pdf_dim, and both sigma_Ncn_1^2/mu_Ncn_1^2 and
        1112             :       ! sigma_Ncn_2^2/mu_Ncn_2^2 need to be output as part of these arrays.
        1113           0 :       sigma_hm_1_sqd_on_mu_hm_1_sqd(:,:,hm_metadata%iiPDF_Ncn) = hm_metadata%Ncnp2_on_Ncnm2
        1114           0 :       sigma_hm_2_sqd_on_mu_hm_2_sqd(:,:,hm_metadata%iiPDF_Ncn) = hm_metadata%Ncnp2_on_Ncnm2
        1115             :
        1116             :     else ! l_const_Nc_in_cloud
        1117             :
        1118             :       ! Ncn is constant in both PDF components.
        1119           0 :       sigma_x_1(:,:,hm_metadata%iiPDF_Ncn) = zero
        1120             :
        1121           0 :       sigma_x_2(:,:,hm_metadata%iiPDF_Ncn) = zero
        1122             :
        1123             :       ! Ncn is not an official hydrometeor.  However, both the
        1124             :       ! sigma_hm_1_sqd_on_mu_hm_1_sqd and sigma_hm_2_sqd_on_mu_hm_2_sqd arrays
        1125             :       ! have size pdf_dim, and both sigma_Ncn_1^2/mu_Ncn_1^2 and
        1126             :       ! sigma_Ncn_2^2/mu_Ncn_2^2 need to be output as part of these arrays.
        1127           0 :       sigma_hm_1_sqd_on_mu_hm_1_sqd(:,:,hm_metadata%iiPDF_Ncn) = zero
        1128           0 :       sigma_hm_2_sqd_on_mu_hm_2_sqd(:,:,hm_metadata%iiPDF_Ncn) = zero
        1129             :
        1130             :     end if ! .not. l_const_Nc_in_cloud
        1131             :
        1132             :
        1133             :     !!! Precipitating hydrometeor species.
        1134           0 :     do ivar = hm_metadata%iiPDF_Ncn+1, pdf_dim, 1
        1135             :
        1136           0 :       hm_idx = pdf2hydromet_idx(ivar,hm_metadata)
        1137             :
        1138             :       call calc_comp_mu_sigma_hm( nz, ngrdcol,                                       & ! In
        1139             :                                   hydromet(:,:,hm_idx), hydrometp2_zt(:,:,hm_idx),   & ! In
        1140           0 :                                   hm_metadata%hmp2_ip_on_hmm2_ip(hm_idx),         & ! In
        1141             :                                   mixt_frac(:,:), precip_frac(:,:),                  & ! In
        1142             :                                   precip_frac_1(:,:), precip_frac_2(:,:),            & ! In
        1143           0 :                                   hm_metadata%hydromet_tol(hm_idx),               & ! In
        1144             :                                   precip_frac_tol(:),                                & ! In
        1145             :                                   thl_1(:,:), thl_2(:,:),                            & ! In
        1146             :                                   omicron, zeta_vrnce_rat,                           & ! In
        1147             :                                   mu_x_1(:,:,ivar), mu_x_2(:,:,ivar),                & ! Out
        1148             :                                   sigma_x_1(:,:,ivar), sigma_x_2(:,:,ivar),          & ! Out
        1149             :                                   hm_1(:,:,hm_idx), hm_2(:,:,hm_idx),                & ! Out
        1150             :                                   sigma_hm_1_sqd_on_mu_hm_1_sqd(:,:,ivar),           & ! Out
        1151           0 :                                   sigma_hm_2_sqd_on_mu_hm_2_sqd(:,:,ivar) )            ! Out
        1152             :
        1153             :     end do ! ivar = iiPDF_Ncn+1, pdf_dim, 1
        1154             :
        1155             :
        1156           0 :     return
        1157             :
        1158             :   end subroutine compute_mean_stdev
        1159             :
        1160             :   !=============================================================================
        1161           0 :   subroutine calc_corr_norm_and_cholesky_factor( nz, ngrdcol, iiPDF_type, &
        1162             :                                                  pdf_dim, hm_metadata, &
        1163           0 :                                                  rc_1, rc_2, &
        1164           0 :                                                  corr_array_n_cloud, corr_array_n_below, &
        1165           0 :                                                  corr_array_1_n, corr_array_2_n, &
        1166           0 :                                                  corr_cholesky_mtx_1, corr_cholesky_mtx_2 )
        1167             :
        1168             :     ! Description: This subroutine computes the correlation arrays and correlation
        1169             :     !   Cholesky matrices of PDF vars for both components. Here, we assume that
        1170             :     !   there are only two unique correlation arrays, which allows us to compute
        1171             :     !   these two unique arrays and their corresponding Cholesky decompositions,
        1172             :     !   then use rc to determine which one to assign to each grid column and
        1173             :     !   vertical level. If the correlation arrays vary based on vertically varying
        1174             :     !   values, then this subroutine is not appropriate.
        1175             :     !
        1176             :     ! References:
        1177             :     !   https://github.com/larson-group/cam/issues/129#issuecomment-816205563
        1178             :     !-----------------------------------------------------------------------
        1179             :
        1180             :     use constants_clubb, only:  &
        1181             :         rc_tol,      &
        1182             :         zero
        1183             :
        1184             :     use clubb_precision, only: &
        1185             :         core_rknd  ! Variable(s)
        1186             :
        1187             :     use corr_varnce_module, only: &
        1188             :         hm_metadata_type
        1189             :
        1190             :     use model_flags, only: &
        1191             :         iiPDF_ADG1,       & ! Variable(s)
        1192             :         iiPDF_ADG2,       &
        1193             :         iiPDF_new_hybrid
        1194             :
        1195             :     use pdf_parameter_module, only: &
        1196             :         pdf_parameter  ! Variable(s)
        1197             :
        1198             :     use matrix_operations, only: &
        1199             :         Cholesky_factor ! Procedure(s)
        1200             :
        1201             :     implicit none
        1202             :
        1203             :     ! Input Variables
        1204             :     integer, intent(in) :: &
        1205             :       nz,      & ! Number of vertical levels
        1206             :       pdf_dim, & ! Number of variables in the corr/mean/stdev arrays
        1207             :       ngrdcol    ! Number of grid columns
        1208             :
        1209             :     real( kind = core_rknd ), dimension(ngrdcol,nz), intent(in) :: &
        1210             :       rc_1,   & ! Mean of r_c (1st PDF component)                 [kg/kg]
        1211             :       rc_2      ! Mean of r_c (2nd PDF component)                 [kg/kg]
        1212             :
        1213             :     real( kind = core_rknd ), dimension(pdf_dim,pdf_dim), intent(in) :: &
        1214             :       corr_array_n_cloud, & ! Prescribed correlation array in cloud        [-]
        1215             :       corr_array_n_below    ! Prescribed correlation array below cloud     [-]
        1216             :
        1217             :     type (hm_metadata_type), intent(in) :: &
        1218             :       hm_metadata
        1219             :
        1220             :     integer, intent(in) :: &
        1221             :       iiPDF_type    ! Selected option for the two-component normal (double
        1222             :                     ! Gaussian) PDF type to use for the w, rt, and theta-l (or
        1223             :                     ! w, chi, and eta) portion of CLUBB's multivariate,
        1224             :                     ! two-component PDF.
        1225             :
        1226             :     ! Output Variables
        1227             :     real( kind = core_rknd ), dimension(ngrdcol,nz,pdf_dim,pdf_dim), intent(out) :: &
        1228             :       corr_array_1_n,       & ! Corr. array (normal space) of PDF vars. (comp. 1)  [-]
        1229             :       corr_array_2_n,       & ! Corr. array (normal space) of PDF vars. (comp. 2)  [-]
        1230             :       corr_cholesky_mtx_1,  & ! Transposed corr. cholesky matrix, 1st comp.        [-]
        1231             :       corr_cholesky_mtx_2     ! Transposed corr. cholesky matrix, 2nd comp.        [-]
        1232             :
        1233             :     ! Local Variables
        1234             :     real( kind = core_rknd ), dimension(pdf_dim,pdf_dim) :: &
        1235           0 :       corr_array_cloud,         & ! General in cloud corr. matrix
        1236           0 :       corr_array_below,         & ! General out of cloud corr. matrix
        1237           0 :       corr_cholesky_mtx_cloud,  & ! General in cloud Cholesky matrix
        1238           0 :       corr_cholesky_mtx_below     ! General out of cloud Cholesky matrix
        1239             :
        1240             :     logical :: &
        1241             :       l_corr_array_scaling  ! Dummy variable that we need for calling Cholesky_factor
        1242             :
        1243             :     real( kind = core_rknd ), dimension(pdf_dim) :: &
        1244           0 :       corr_array_scaling    ! Dummy variable that we need for calling Cholesky_factor
        1245             :
        1246             :     integer :: ivar, jvar, i, k ! Indices
        1247             :
        1248             :     !-------------------- Begin Code --------------------
        1249             :
        1250             :     ! Initialize correlation arrays with prescribed values
        1251           0 :     corr_array_cloud(:,:) = corr_array_n_cloud(:,:)
        1252           0 :     corr_array_below(:,:) = corr_array_n_below(:,:)
        1253             :
        1254             :     ! The ADG1 PDF fixes the correlation of w and rt and the correlation of
        1255             :     ! w and theta_l to be 0, which means the correlation of w and chi and the
        1256             :     ! correlation of w and eta must also be 0.
        1257             :     if ( ( iiPDF_type == iiPDF_ADG1 .or. iiPDF_type == iiPDF_ADG2 &
        1258             :             .or. iiPDF_type == iiPDF_new_hybrid ) &
        1259           0 :           .and. l_follow_ADG1_PDF_standards ) then
        1260             :
        1261           0 :       corr_array_cloud(hm_metadata%iiPDF_w,hm_metadata%iiPDF_chi) = zero
        1262           0 :       corr_array_below(hm_metadata%iiPDF_w,hm_metadata%iiPDF_chi) = zero
        1263             :
        1264           0 :       corr_array_cloud(hm_metadata%iiPDF_w,hm_metadata%iiPDF_eta) = zero
        1265           0 :       corr_array_below(hm_metadata%iiPDF_w,hm_metadata%iiPDF_eta) = zero
        1266             :
        1267             :     end if
        1268             :
        1269             :     ! Ncn is an inherently in-cloud property, so replace out of cloud correlation values
        1270             :     ! with in cloud ones.
        1271           0 :     corr_array_below(hm_metadata%iiPDF_Ncn,hm_metadata%iiPDF_chi) &
        1272           0 :         = corr_array_cloud(hm_metadata%iiPDF_Ncn,hm_metadata%iiPDF_chi)
        1273             :
        1274           0 :     corr_array_below(hm_metadata%iiPDF_Ncn,hm_metadata%iiPDF_eta) &
        1275           0 :       = corr_array_cloud(hm_metadata%iiPDF_Ncn,hm_metadata%iiPDF_eta)
        1276             :
        1277             :
        1278             :     ! Estimates the correlation of the natural logarithm of a
        1279             :     ! hydrometeor species and eta using the correlation of chi and eta and the
        1280             :     ! correlation of chi and the natural logarithm of the hydrometeor.  This
        1281             :     ! facilitates the Cholesky decomposability of the correlation array that will
        1282             :     ! inevitably be decomposed for SILHS purposes. Without this estimation, we
        1283             :     ! have found that the resulting correlation matrix cannot be decomposed.
        1284           0 :     do jvar = hm_metadata%iiPDF_Ncn+1, pdf_dim
        1285             :
        1286           0 :       corr_array_cloud(jvar,hm_metadata%iiPDF_eta) &
        1287             :                 = corr_array_cloud(hm_metadata%iiPDF_eta,hm_metadata%iiPDF_chi) &
        1288           0 :                   * corr_array_cloud(jvar,hm_metadata%iiPDF_chi)
        1289             :
        1290             :       corr_array_below(jvar,hm_metadata%iiPDF_eta) &
        1291             :                 = corr_array_below(hm_metadata%iiPDF_eta,hm_metadata%iiPDF_chi) &
        1292           0 :                   * corr_array_below(jvar,hm_metadata%iiPDF_chi)
        1293             :
        1294             :     end do
        1295             :
        1296             :     ! Calc in cloud Cholesky
        1297             :     call Cholesky_factor( pdf_dim, corr_array_cloud(:,:), & ! In
        1298             :                           corr_array_scaling, corr_cholesky_mtx_cloud(:,:), &  ! Out
        1299           0 :                           l_corr_array_scaling ) ! Out
        1300             :
        1301             :     ! Calc out of cloud Cholesky
        1302             :     call Cholesky_factor( pdf_dim, corr_array_below(:,:), & ! In
        1303             :                           corr_array_scaling, corr_cholesky_mtx_below(:,:), &  ! Out
        1304           0 :                           l_corr_array_scaling ) ! Out
        1305             :
        1306             :     ! Use rc_1 to determine which correlation and Cholesky matrices to assign to 1st PDF
        1307             :     ! Correlation matrices are symmetric, so we copy ij values to ji indices as well
        1308             :     ! Cholesky matrices are lower triangular, so we only copy those values
        1309           0 :     do ivar = 1, pdf_dim
        1310           0 :       do jvar = ivar, pdf_dim
        1311           0 :         do k = 1, nz
        1312           0 :           do i = 1, ngrdcol
        1313             :
        1314           0 :             if ( rc_1(i,k) > rc_tol ) then
        1315             :               ! Assign in cloud matrices to 1st PDF component
        1316           0 :               corr_array_1_n(i,k,jvar,ivar)      = corr_array_cloud(jvar,ivar)
        1317           0 :               corr_array_1_n(i,k,ivar,jvar)      = corr_array_cloud(jvar,ivar)
        1318           0 :               corr_cholesky_mtx_1(i,k,jvar,ivar) = corr_cholesky_mtx_cloud(jvar,ivar)
        1319             :             else
        1320             :               ! Assign out of cloud matrices to 1st PDF component
        1321           0 :               corr_array_1_n(i,k,jvar,ivar)      = corr_array_below(jvar,ivar)
        1322           0 :               corr_array_1_n(i,k,ivar,jvar)      = corr_array_below(jvar,ivar)
        1323           0 :               corr_cholesky_mtx_1(i,k,jvar,ivar) = corr_cholesky_mtx_below(jvar,ivar)
        1324             :             end if
        1325             :
        1326             :           end do
        1327             :         end do
        1328             :       end do
        1329             :     end do
        1330             :
        1331             :     ! Use rc_1 to determine which correlation and Cholesky matrices to assign to 2nd PDF
        1332             :     ! Correlation matrices are symmetric, so we copy ij values to ji indices as well
        1333             :     ! Cholesky matrices are lower triangular, so we only copy those values
        1334           0 :     do ivar = 1, pdf_dim
        1335           0 :       do jvar = ivar, pdf_dim
        1336           0 :         do k = 1, nz
        1337           0 :           do i = 1, ngrdcol
        1338             :
        1339           0 :             if ( rc_2(i,k) > rc_tol ) then
        1340             :               ! Assign in cloud matrices to 2nd PDF component
        1341           0 :               corr_array_2_n(i,k,jvar,ivar)      = corr_array_cloud(jvar,ivar)
        1342           0 :               corr_array_2_n(i,k,ivar,jvar)      = corr_array_cloud(jvar,ivar)
        1343           0 :               corr_cholesky_mtx_2(i,k,jvar,ivar) = corr_cholesky_mtx_cloud(jvar,ivar)
        1344             :             else
        1345             :               ! Assign out of cloud matrices to 2nd PDF component
        1346           0 :               corr_array_2_n(i,k,jvar,ivar)      = corr_array_below(jvar,ivar)
        1347           0 :               corr_array_2_n(i,k,ivar,jvar)      = corr_array_below(jvar,ivar)
        1348           0 :               corr_cholesky_mtx_2(i,k,jvar,ivar) = corr_cholesky_mtx_below(jvar,ivar)
        1349             :             end if
        1350             :
        1351             :           end do
        1352             :         end do
        1353             :       end do
        1354             :     end do
        1355             :
        1356             :     ! Set upper triangular parts of Cholesky matrices to zero
        1357           0 :     do ivar = 1, pdf_dim
        1358           0 :       do jvar = 1, ivar-1
        1359           0 :         corr_cholesky_mtx_1(:,:,jvar,ivar) = zero
        1360           0 :         corr_cholesky_mtx_2(:,:,jvar,ivar) = zero
        1361             :       end do
        1362             :     end do
        1363             :
        1364           0 :   end subroutine calc_corr_norm_and_cholesky_factor
        1365             :
        1366             :   !=============================================================================
        1367           0 :   subroutine comp_corr_norm( nz, pdf_dim, ngrdcol, hydromet_dim, hm_metadata, &
        1368           0 :                              wm_zt, rc_1, rc_2, &
        1369           0 :                              mixt_frac, &
        1370           0 :                              precip_frac_1, &
        1371           0 :                              precip_frac_2, &
        1372           0 :                              wpNcnp_zt, wphydrometp_zt, &
        1373           0 :                              mu_x_1, mu_x_2, sigma_x_1, sigma_x_2, &
        1374           0 :                              sigma_x_1_n, sigma_x_2_n, &
        1375           0 :                              corr_array_n_cloud, corr_array_n_below, &
        1376             :                              pdf_params, &
        1377             :                              iiPDF_type, &
        1378             :                              l_calc_w_corr, &
        1379             :                              l_fix_w_chi_eta_correlations, &
        1380           0 :                              corr_array_1_n, corr_array_2_n )
        1381             :
        1382             :     ! Description:
        1383             :
        1384             :     ! References:
        1385             :     !-----------------------------------------------------------------------
        1386             :
        1387             :     use constants_clubb, only:  &
        1388             :         Ncn_tol,      &
        1389             :         one,          &
        1390             :         zero
        1391             :
        1392             :     use diagnose_correlations_module, only: &
        1393             :         calc_mean,        & ! Procedure(s)
        1394             :         calc_w_corr
        1395             :
        1396             :     use index_mapping, only: &
        1397             :         pdf2hydromet_idx  ! Procedure(s)
        1398             :
        1399             :     use clubb_precision, only: &
        1400             :         core_rknd  ! Variable(s)
        1401             :
        1402             :     use corr_varnce_module, only: &
        1403             :         hm_metadata_type
        1404             :
        1405             :     use pdf_parameter_module, only: &
        1406             :         pdf_parameter  ! Variable(s)
        1407             :
        1408             :     use matrix_operations, only: &
        1409             :         mirror_lower_triangular_matrix
        1410             :
        1411             :     implicit none
        1412             :
        1413             :     !------------------------ Input Variables ------------------------
        1414             :     integer, intent(in) :: &
        1415             :       nz,           & ! Number of vertical levels
        1416             :       pdf_dim,      & ! Number of variables in the corr/mean/stdev arrays
        1417             :       ngrdcol,      & ! Number of grid columns
        1418             :       hydromet_dim    ! Number of hydrometeor species
        1419             :
        1420             :     type (hm_metadata_type), intent(in) :: &
        1421             :       hm_metadata
        1422             :
        1423             :     real( kind = core_rknd ), dimension(ngrdcol,nz), intent(in) :: &
        1424             :       wm_zt,         & ! Mean vertical velocity, <w>, on thermo. levels    [m/s]
        1425             :       rc_1,          & ! Mean of r_c (1st PDF component)                 [kg/kg]
        1426             :       rc_2,          & ! Mean of r_c (2nd PDF component)                 [kg/kg]
        1427             :       mixt_frac,     & ! Mixture fraction                                    [-]
        1428             :       precip_frac_1, & ! Precipitation fraction (1st PDF component)          [-]
        1429             :       precip_frac_2, & ! Precipitation fraction (2nd PDF component)          [-]
        1430             :       wpNcnp_zt        ! Covariance of w and N_cn on t-levs.      [(m/s) num/kg]
        1431             :
        1432             :     real( kind = core_rknd ), dimension(ngrdcol,nz,hydromet_dim), intent(in) :: &
        1433             :       wphydrometp_zt    ! Covariance of w and hm interp. to t-levs.  [(m/s)u.v.]
        1434             :
        1435             :     real( kind = core_rknd ), dimension(ngrdcol,nz,pdf_dim), intent(in) :: &
        1436             :       mu_x_1,      & ! Mean of x array (1st PDF component)          [units vary]
        1437             :       mu_x_2,      & ! Mean of x array (2nd PDF component)          [units vary]
        1438             :       sigma_x_1,   & ! Standard deviation of x array (1st PDF comp.)  [un. vary]
        1439             :       sigma_x_2,   & ! Standard deviation of x array (2nd PDF comp.)  [un. vary]
        1440             :       sigma_x_1_n, & ! Std. dev. array (normal space): PDF vars (comp. 1) [u.v.]
        1441             :       sigma_x_2_n    ! Std. dev. array (normal space): PDF vars (comp. 2) [u.v.]
        1442             :
        1443             :     real( kind = core_rknd ), dimension(pdf_dim,pdf_dim), &
        1444             :     intent(in) :: &
        1445             :       corr_array_n_cloud, & ! Prescribed correlation array in cloud        [-]
        1446             :       corr_array_n_below    ! Prescribed correlation array below cloud     [-]
        1447             :
        1448             :     type(pdf_parameter), intent(in) :: &
        1449             :       pdf_params    ! PDF parameters                               [units vary]
        1450             :
        1451             :     integer, intent(in) :: &
        1452             :       iiPDF_type    ! Selected option for the two-component normal (double
        1453             :                     ! Gaussian) PDF type to use for the w, rt, and theta-l (or
        1454             :                     ! w, chi, and eta) portion of CLUBB's multivariate,
        1455             :                     ! two-component PDF.
        1456             :
        1457             :     logical, intent(in) :: &
        1458             :       l_calc_w_corr, &                ! Calculate the correlations between w and the hydrometeors
        1459             :       l_fix_w_chi_eta_correlations    ! Use a fixed correlation for s and t Mellor(chi/eta)
        1460             :
        1461             :     !------------------------ Output Variables ------------------------
        1462             :     real( kind = core_rknd ), dimension(ngrdcol,nz,pdf_dim,pdf_dim), intent(out) :: &
        1463             :       corr_array_1_n, & ! Corr. array (normal space) of PDF vars. (comp. 1)  [-]
        1464             :       corr_array_2_n    ! Corr. array (normal space) of PDF vars. (comp. 2)  [-]
        1465             :
        1466             :     !------------------------ Local Variables ------------------------
        1467             :     real( kind = core_rknd ), dimension(ngrdcol,nz,pdf_dim)  :: &
        1468           0 :       corr_w_hm_1_n, & ! Correlation of w and ln hm (1st PDF component) ip   [-]
        1469           0 :       corr_w_hm_2_n    ! Correlation of w and ln hm (2nd PDF component) ip   [-]
        1470             :
        1471             :     real( kind = core_rknd ), dimension(ngrdcol,nz) :: &
        1472           0 :       corr_w_Ncn_1_n, & ! Correlation of w and ln Ncn (1st PDF component)    [-]
        1473           0 :       corr_w_Ncn_2_n    ! Correlation of w and ln Ncn (2nd PDF component)    [-]
        1474             :
        1475             :     real( kind = core_rknd ), dimension(ngrdcol,nz) :: &
        1476           0 :        ones_vector,     & ! Vector of 1s
        1477           0 :        Ncn_tol_in,      & ! Tolerance value for Ncn
        1478           0 :        hydromet_tol_in    ! Tolerance value for hydromet
        1479             :
        1480             :     logical :: &
        1481             :       l_limit_corr_chi_eta    ! Flag to limit the correlation of chi and eta [-]
        1482             :
        1483             :     integer :: ivar, jvar, hm_idx, i, k ! Indices
        1484             :
        1485             :     ! Just to avoid typing hm_metadata%iiPDF_x everywhere
        1486             :     integer :: &
        1487             :       iiPDF_chi, &
        1488             :       iiPDF_eta, &
        1489             :       iiPDF_w,   &
        1490             :       iiPDF_Ncn
        1491             :
        1492             :     !------------------------ Begin Code ------------------------
        1493             :
        1494           0 :     iiPDF_chi = hm_metadata%iiPDF_chi
        1495           0 :     iiPDF_eta = hm_metadata%iiPDF_eta
        1496           0 :     iiPDF_w   = hm_metadata%iiPDF_w
        1497           0 :     iiPDF_Ncn = hm_metadata%iiPDF_Ncn
        1498             :
        1499             :
        1500             :     !!! Normal space correlations
        1501             :
        1502             :     ! Initialize corr_w_hm_1_n and corr_w_hm_2_n arrays to 0.
        1503           0 :     corr_w_hm_1_n(:,:,:) = zero
        1504           0 :     corr_w_hm_2_n(:,:,:) = zero
        1505             :
        1506             :
        1507             :     ! Set ones_vector to a vector of 1s.
        1508           0 :     ones_vector = one
        1509             :
        1510             :     ! Calculate normal space correlations involving w by first calculating total
        1511             :     ! covariances involving w (<w'Ncn'>, etc.) using the down-gradient
        1512             :     ! approximation.
        1513           0 :     if ( l_calc_w_corr ) then
        1514             :
        1515           0 :       Ncn_tol_in = Ncn_tol
        1516             :
        1517             :       ! Calculate the correlation of w and ln Ncn in each PDF component.
        1518             :       ! The subroutine calc_corr_w_hm_n can be used to do this as long as a
        1519             :       ! value of 1 is sent in for precip_frac_1 and precip_frac_2.
        1520           0 :       jvar = iiPDF_Ncn
        1521           0 :       do i = 1, ngrdcol
        1522           0 :         call calc_corr_w_hm_n( wm_zt(i,:), wpNcnp_zt(i,:), &
        1523           0 :                                mu_x_1(i,:,iiPDF_w), mu_x_2(i,:,iiPDF_w), &
        1524           0 :                                mu_x_1(i,:,jvar), mu_x_2(i,:,jvar), &
        1525             :                                sigma_x_1(i,:,iiPDF_w), sigma_x_2(i,:,iiPDF_w), &
        1526             :                                sigma_x_1(i,:,jvar), sigma_x_2(i,:,jvar), &
        1527             :                                sigma_x_1_n(i,:,jvar), sigma_x_2_n(i,:,jvar), &
        1528             :                                mixt_frac(i,:), ones_vector(i,:), &
        1529             :                                ones_vector(i,:), Ncn_tol_in(i,:), &
        1530           0 :                                corr_w_Ncn_1_n(i,:), corr_w_Ncn_2_n(i,:) )
        1531             :       end do
        1532             :
        1533             :       ! Calculate the correlation of w and the natural logarithm of the
        1534             :       ! hydrometeor for each PDF component and each hydrometeor type.
        1535           0 :       do jvar = iiPDF_Ncn+1, pdf_dim
        1536             :
        1537           0 :         hm_idx = pdf2hydromet_idx(jvar,hm_metadata)
        1538             :
        1539           0 :         hydromet_tol_in(:,:) = hm_metadata%hydromet_tol(hm_idx)
        1540             :
        1541           0 :         do i = 1, ngrdcol
        1542           0 :           call calc_corr_w_hm_n( wm_zt(i,:), wphydrometp_zt(i,:,hm_idx), & ! intent(in)
        1543           0 :                                  mu_x_1(i,:,iiPDF_w), mu_x_2(i,:,iiPDF_w), & ! intent(in)
        1544           0 :                                  mu_x_1(i,:,jvar), mu_x_2(i,:,jvar), & ! intent(in)
        1545             :                                  sigma_x_1(i,:,iiPDF_w), sigma_x_2(i,:,iiPDF_w), & ! intent(in)
        1546             :                                  sigma_x_1(i,:,jvar), sigma_x_2(i,:,jvar), & ! intent(in)
        1547             :                                  sigma_x_1_n(i,:,jvar), sigma_x_2_n(i,:,jvar), & ! intent(in)
        1548             :                                  mixt_frac(i,:), precip_frac_1(i,:), & ! intent(in)
        1549             :                                  precip_frac_2(i,:), hydromet_tol_in(i,:), & ! intent(in)
        1550           0 :                                  corr_w_hm_1_n(i,:,jvar), corr_w_hm_2_n(i,:,jvar) ) ! intent(out)
        1551             :         end do
        1552             :
        1553             :       end do ! jvar = iiPDF_Ncn+1, pdf_dim
        1554             :
        1555             :     end if ! l_calc_w_corr
        1556             :
        1557             :     ! In order to decompose the normal space correlation matrix,
        1558             :     ! we must not have a perfect correlation of chi and
        1559             :     ! eta. Thus, we impose a limitation.
        1560           0 :     l_limit_corr_chi_eta = .true.
        1561             :
        1562             :
        1563             :     ! Initialize the normal space correlation arrays
        1564           0 :     corr_array_1_n(:,:,:,:) = zero
        1565           0 :     corr_array_2_n(:,:,:,:) = zero
        1566             :
        1567             :     !!! The corr_arrays are assumed to be lower triangular matrices
        1568             :     ! Set diagonal elements to 1
        1569           0 :     do ivar=1, pdf_dim
        1570           0 :       do k = 1, nz
        1571           0 :         do i = 1, ngrdcol
        1572           0 :           corr_array_1_n(i,k,ivar,ivar) = one
        1573           0 :           corr_array_2_n(i,k,ivar,ivar) = one
        1574             :         end do
        1575             :       end do
        1576             :     end do
        1577             :
        1578             :
        1579             :     !!! This code assumes the following order in the prescribed correlation
        1580             :     !!! arrays (iiPDF indices):
        1581             :     !!! chi, eta, w, Ncn, <hydrometeors> (indices increasing from left to right)
        1582           0 :     if ( l_fix_w_chi_eta_correlations ) then
        1583             :       ! Correlation of chi (old s) and eta (old t)
        1584             :       call component_corr_chi_eta( nz, ngrdcol, & ! intent(in)
        1585             :                                   rc_1(:,:), & ! intent(in)
        1586             :                                   rc_2(:,:), & ! intent(in)
        1587           0 :                                   corr_array_n_cloud(iiPDF_eta,iiPDF_chi), & ! intent(in)
        1588             :                                   corr_array_n_below(iiPDF_eta,iiPDF_chi), & ! intent(in)
        1589             :                                   l_limit_corr_chi_eta, & ! intent(in)
        1590             :                                   corr_array_1_n(:,:,iiPDF_eta,iiPDF_chi), & ! intent(out)
        1591           0 :                                   corr_array_2_n(:,:,iiPDF_eta,iiPDF_chi) ) ! intent(out)
        1592             :     else
        1593             :
        1594             :       ! Preferred, more accurate version.
        1595           0 :       do i = 1, ngrdcol
        1596           0 :         corr_array_1_n(i,:,iiPDF_eta,iiPDF_chi) = pdf_params%corr_chi_eta_1(i,:)
        1597           0 :         corr_array_2_n(i,:,iiPDF_eta,iiPDF_chi) = pdf_params%corr_chi_eta_2(i,:)
        1598             :       end do
        1599             :
        1600             :     end if
        1601             :
        1602           0 :     if ( l_fix_w_chi_eta_correlations ) then
        1603             :       ! Correlation of chi (old s) and w
        1604             :       call component_corr_w_x( nz, ngrdcol, & ! intent(in)
        1605             :                                rc_1(:,:), & ! intent(in)
        1606             :                                rc_2(:,:), & ! intent(in)
        1607           0 :                                corr_array_n_cloud(iiPDF_w,iiPDF_chi), & ! intent(in)
        1608             :                                corr_array_n_below(iiPDF_w,iiPDF_chi), & ! intent(in)
        1609             :                                iiPDF_type, & ! intent(in)
        1610             :                                corr_array_1_n(:,:,iiPDF_w,iiPDF_chi), & ! intent(out)
        1611           0 :                                corr_array_2_n(:,:,iiPDF_w,iiPDF_chi) ) ! intent(out)
        1612             :     else
        1613             :
        1614             :       ! Preferred, more accurate version.
        1615           0 :       do i = 1, ngrdcol
        1616           0 :         corr_array_1_n(i,:,iiPDF_w,iiPDF_chi) = pdf_params%corr_w_chi_1(i,:)
        1617           0 :         corr_array_2_n(i,:,iiPDF_w,iiPDF_chi) = pdf_params%corr_w_chi_2(i,:)
        1618             :       end do
        1619             :
        1620             :     end if
        1621             :
        1622             :
        1623             :     ! Correlation of chi (old s) and ln Ncn, corr_array_n_cloud used twice because
        1624             :     ! Ncn is an inherently in-cloud property.
        1625             :     call component_corr_x_hm_n_ip( nz, ngrdcol, & ! intent(in)
        1626             :                                    rc_1(:,:), & ! intent(in)
        1627             :                                    rc_2(:,:), & ! intent(in)
        1628           0 :                                    corr_array_n_cloud(iiPDF_Ncn,iiPDF_chi), & ! intent(in)
        1629             :                                    corr_array_n_cloud(iiPDF_Ncn,iiPDF_chi), & ! intent(in)
        1630             :                                    corr_array_1_n(:,:,iiPDF_Ncn,iiPDF_chi), & ! intent(out)
        1631           0 :                                    corr_array_2_n(:,:,iiPDF_Ncn,iiPDF_chi) ) ! intent(out)
        1632             :
        1633             :     ! Correlation of chi (old s) and the natural logarithm of the hydrometeors
        1634           0 :     do jvar = iiPDF_Ncn+1, pdf_dim
        1635             :       call component_corr_x_hm_n_ip( nz, ngrdcol, & ! intent(in)
        1636             :                                      rc_1(:,:), & ! intent(in)
        1637             :                                      rc_2(:,:), & ! intent(in)
        1638           0 :                                      corr_array_n_cloud(jvar,iiPDF_chi), & ! intent(in)
        1639             :                                      corr_array_n_below(jvar,iiPDF_chi), & ! intent(in)
        1640             :                                      corr_array_1_n(:,:,jvar,iiPDF_chi), & ! intent(out)
        1641           0 :                                      corr_array_2_n(:,:,jvar,iiPDF_chi) ) ! intent(out)
        1642             :     end do
        1643             :
        1644             :     ! Correlation of eta (old t) and w
        1645           0 :     if ( l_fix_w_chi_eta_correlations ) then
        1646             :       ! Correlation of chi (old s) and w
        1647             :       call component_corr_w_x( nz, ngrdcol, & ! intent(in)
        1648             :                                rc_1(:,:), & ! intent(in)
        1649             :                                rc_2(:,:), & ! intent(in)
        1650           0 :                                corr_array_n_cloud(iiPDF_w,iiPDF_eta), & ! intent(in)
        1651             :                                corr_array_n_below(iiPDF_w,iiPDF_eta), & ! intent(in)
        1652             :                                iiPDF_type, & ! intent(in)
        1653             :                                corr_array_1_n(:,:,iiPDF_w,iiPDF_eta), & ! intent(out)
        1654           0 :                                corr_array_2_n(:,:,iiPDF_w,iiPDF_eta) ) ! intent(out)
        1655             :     else
        1656             :
        1657             :       ! Preferred, more accurate version.
        1658           0 :       do i = 1, ngrdcol
        1659           0 :         corr_array_1_n(i,:,iiPDF_w,iiPDF_chi) = pdf_params%corr_w_chi_1(i,:)
        1660           0 :         corr_array_2_n(i,:,iiPDF_w,iiPDF_chi) = pdf_params%corr_w_chi_2(i,:)
        1661             :       end do
        1662             :
        1663             :     end if
        1664             :
        1665             :     ! Correlation of eta (old t) and ln Ncn, corr_array_n_cloud used twice because
        1666             :     ! Ncn is an inherently in-cloud property.
        1667             :     call component_corr_x_hm_n_ip( nz, ngrdcol, & ! intent(in)
        1668             :                                    rc_1(:,:), & ! intent(in)
        1669             :                                    rc_2(:,:), & ! intent(in)
        1670           0 :                                    corr_array_n_cloud(iiPDF_Ncn,iiPDF_eta), & ! intent(in)
        1671             :                                    corr_array_n_cloud(iiPDF_Ncn,iiPDF_eta), & ! intent(in)
        1672             :                                    corr_array_1_n(:,:,iiPDF_Ncn,iiPDF_eta), & ! intent(out)
        1673           0 :                                    corr_array_2_n(:,:,iiPDF_Ncn,iiPDF_eta) ) ! intent(out)
        1674             :
        1675             :
        1676             :     ! Correlation of eta (old t) and the natural logarithm of the hydrometeors
        1677           0 :     do jvar = iiPDF_Ncn+1, pdf_dim
        1678             :       call component_corr_eta_hm_n_ip( nz, ngrdcol, & ! intent(in)
        1679             :                                        corr_array_1_n(:,:,iiPDF_eta,iiPDF_chi), & ! intent(in)
        1680             :                                        corr_array_1_n(:,:,jvar,iiPDF_chi), & ! intent(in)
        1681             :                                        corr_array_2_n(:,:,iiPDF_eta,iiPDF_chi), & ! intent(in)
        1682             :                                        corr_array_2_n(:,:,jvar,iiPDF_chi), & ! intent(in)
        1683             :                                        corr_array_1_n(:,:,jvar,iiPDF_eta), & ! intent(out)
        1684           0 :                                        corr_array_2_n(:,:,jvar,iiPDF_eta) ) ! intent(out)
        1685             :     end do
        1686             :
        1687             :
        1688             :     ! Correlation of w and ln Ncn
        1689             :     call component_corr_w_hm_n_ip( nz, ngrdcol, & ! intent(in)
        1690             :                                    corr_w_Ncn_1_n(:,:), rc_1(:,:), & ! intent(in)
        1691             :                                    corr_w_Ncn_2_n(:,:), rc_2(:,:), & ! intent(in)
        1692           0 :                                    corr_array_n_cloud(iiPDF_Ncn,iiPDF_w), & ! intent(in)
        1693             :                                    corr_array_n_below(iiPDF_Ncn,iiPDF_w), & ! intent(in)
        1694             :                                    l_calc_w_corr, & ! intent(in)
        1695             :                                    corr_array_1_n(:,:,iiPDF_Ncn,iiPDF_w), & ! intent(out)
        1696           0 :                                    corr_array_2_n(:,:,iiPDF_Ncn,iiPDF_w) ) ! intent(out)
        1697             :
        1698             :     ! Correlation of w and the natural logarithm of the hydrometeors
        1699           0 :     do jvar = iiPDF_Ncn+1, pdf_dim
        1700             :       call component_corr_w_hm_n_ip( nz, ngrdcol, & ! intent(in)
        1701             :                                      corr_w_hm_1_n(:,:,jvar), rc_1(:,:), & ! intent(in)
        1702             :                                      corr_w_hm_2_n(:,:,jvar), rc_2(:,:), & ! intent(in)
        1703           0 :                                      corr_array_n_cloud(jvar,iiPDF_w), & ! intent(in)
        1704             :                                      corr_array_n_below(jvar,iiPDF_w), & ! intent(in)
        1705             :                                      l_calc_w_corr, & ! intent(in)
        1706             :                                      corr_array_1_n(:,:,jvar,iiPDF_w), & ! intent(out)
        1707           0 :                                      corr_array_2_n(:,:,jvar,iiPDF_w) ) ! intent(out)
        1708             :     end do
        1709             :
        1710             :     ! Correlation of ln Ncn and the natural logarithm of the hydrometeors
        1711           0 :     do jvar = iiPDF_Ncn+1, pdf_dim
        1712             :
        1713             :       call component_corr_hmx_hmy_n_ip( nz, ngrdcol, & ! intent(in)
        1714             :                                         rc_1(:,:), & ! intent(in)
        1715             :                                         rc_2(:,:), & ! intent(in)
        1716           0 :                                         corr_array_n_cloud(jvar,iiPDF_Ncn), & ! intent(in)
        1717             :                                         corr_array_n_below(jvar,iiPDF_Ncn), & ! intent(in)
        1718             :                                         corr_array_1_n(:,:,jvar,iiPDF_Ncn), & ! intent(out)
        1719           0 :                                         corr_array_2_n(:,:,jvar,iiPDF_Ncn) ) ! intent(out)
        1720             :     end do
        1721             :
        1722             :     ! Correlation of the natural logarithm of two hydrometeors
        1723           0 :     do ivar = iiPDF_Ncn+1, pdf_dim-1
        1724           0 :       do jvar = ivar+1, pdf_dim
        1725             :
        1726             :
        1727             :         call component_corr_hmx_hmy_n_ip( nz, ngrdcol, & ! intent(in)
        1728             :                                           rc_1(:,:), & ! intent(in)
        1729             :                                           rc_2(:,:), & ! intent(in)
        1730           0 :                                           corr_array_n_cloud(jvar,ivar), & ! intent(in)
        1731             :                                           corr_array_n_below(jvar,ivar), & ! intent(in)
        1732             :                                           corr_array_1_n(:,:,jvar,ivar), & ! intent(out)
        1733           0 :                                           corr_array_2_n(:,:,jvar,ivar) ) ! intent(out)
        1734             :
        1735             :        end do ! jvar
        1736             :     end do ! ivar
        1737             :
        1738             :     ! For ease of use later in the code, we make the correlation arrays
        1739             :     ! symmetrical
        1740           0 :     do k = 2, nz, 1
        1741           0 :       do i = 1, ngrdcol
        1742           0 :         call mirror_lower_triangular_matrix( pdf_dim, corr_array_1_n(i,k,:,:) )
        1743           0 :         call mirror_lower_triangular_matrix( pdf_dim, corr_array_2_n(i,k,:,:) )
        1744             :       end do
        1745             :     end do
        1746             :
        1747           0 :     return
        1748             :
        1749             :   end subroutine comp_corr_norm
        1750             :
        1751             :   !=============================================================================
        1752           0 :   subroutine calc_comp_mu_sigma_hm( nz, ngrdcol, &                   ! In
        1753           0 :                                     hmm, hmp2, &                     ! In
        1754             :                                     hmp2_ip_on_hmm2_ip, &            ! In
        1755           0 :                                     mixt_frac, precip_frac, &        ! In
        1756           0 :                                     precip_frac_1, precip_frac_2, &  ! In
        1757           0 :                                     hm_tol, precip_frac_tol, &       ! In
        1758           0 :                                     mu_thl_1, mu_thl_2, &            ! In
        1759             :                                     omicron, zeta_vrnce_rat_in, &    ! In
        1760           0 :                                     mu_hm_1, mu_hm_2, &              ! Out
        1761           0 :                                     sigma_hm_1, sigma_hm_2, &        ! Out
        1762           0 :                                     hm_1, hm_2, &                    ! Out
        1763           0 :                                     sigma_hm_1_sqd_on_mu_hm_1_sqd, & ! Out
        1764           0 :                                     sigma_hm_2_sqd_on_mu_hm_2_sqd )  ! Out
        1765             :
        1766             :
        1767             :     ! Description:
        1768             :     ! Calculates the in-precipitation mean and in-precipitation standard
        1769             :     ! deviation in both PDF components for a precipitating hydrometeor.
        1770             :     !
        1771             :     ! When precipitation is found in both PDF components (precip_frac_1 > 0 and
        1772             :     ! precip_frac_2 > 0), the method that solves for in-precip. mean and
        1773             :     ! in-precip. standard deviation in each PDF component, preserving overall
        1774             :     ! mean and overall variance, is used.  When precipitation fraction is found
        1775             :     ! in one PDF component but not the other one (precip_frac_1 > 0 and
        1776             :     ! precip_frac_2 = 0, or precip_frac_1 = 0 and precip_frac_2 > 0), the
        1777             :     ! calculation of component in-precip. mean and in-precip. standard deviation
        1778             :     ! is simple.  When precipitation is not found in either component
        1779             :     ! (precip_frac_1 = 0 and precip_frac_2 = 0), there isn't any precipitation
        1780             :     ! found overall (at that grid level).
        1781             :     !
        1782             :     !
        1783             :     ! DESCRIPTION OF THE METHOD THAT SOLVES FOR TWO IN-PRECIPITATION COMPONENTS
        1784             :     ! =========================================================================
        1785             :     !
        1786             :     ! OVERVIEW
        1787             :     !
        1788             :     ! The goal is to calculate the in-precip. mean of the hydrometeor field in
        1789             :     ! each PDF component (mu_hm_1 and mu_hm_2) in a scenario when there is
        1790             :     ! precipitation found in both PDF components.  The fields provided are the
        1791             :     ! overall mean of the hydrometeor, <hm>, the overall variance of the
        1792             :     ! hydrometeor, <hm’^2>, the mixture fraction, a, the overall precipitation
        1793             :     ! fraction, f_p, and the precipitation fraction in each PDF component
        1794             :     ! (f_p_1 and f_p_2).
        1795             :     !
        1796             :     ! The PDF equation for <hm> is:
        1797             :     !
        1798             :     ! <hm> = a * f_p_1 * mu_hm_1 + ( 1- a ) * f_p_2 * mu_hm_2.
        1799             :     !
        1800             :     ! Likewise, the PDF equation for <hm’^2> is:
        1801             :     !
        1802             :     ! <hm’^2> = a * f_p_1 * ( mu_hm_1^2 + sigma_hm_1^2 )
        1803             :     !           + ( 1 - a ) * f_p_2 * ( mu_hm_2^2 + sigma_hm_2^2 )
        1804             :     !           - <hm>^2;
        1805             :     !
        1806             :     ! where sigma_hm_1 and sigma_hm_2 are the in-precip. standard deviations of
        1807             :     ! the hydrometeor field in each PDF component.  This can be rewritten as:
        1808             :     !
        1809             :     ! <hm’^2>
        1810             :     ! = a * f_p_1 * ( 1 + sigma_hm_1^2 / mu_hm_1^2 ) * mu_hm_1^2
        1811             :     !   + ( 1 - a ) * f_p_2 * ( 1 + sigma_hm_2^2 / mu_hm_2^2 ) * mu_hm_2^2
        1812             :     !   - <hm>^2.
        1813             :     !
        1814             :     ! The ratio of sigma_hm_2^2 to mu_hm_2^2 is denoted R:
        1815             :     !
        1816             :     ! R = sigma_hm_2^2 / mu_hm_2^2.
        1817             :     !
        1818             :     ! In order to allow sigma_hm_1^2 / mu_hm_1^2 to have a different ratio, the
        1819             :     ! parameter zeta is introduced, such that:
        1820             :     !
        1821             :     ! R * ( 1 + zeta ) = sigma_hm_1^2 / mu_hm_1^2;
        1822             :     !
        1823             :     ! where zeta > -1.  When -1 < zeta < 0, the ratio sigma_hm_2^2 / mu_hm_2^2
        1824             :     ! grows at the expense of sigma_hm_1^2 / mu_hm_1^2, which narrows.  When
        1825             :     ! zeta = 0, the ratio sigma_hm_1^2 / mu_hm_1^2 is the same as
        1826             :     ! sigma_hm_2^2 / mu_hm_2^2.  When zeta > 0, sigma_hm_1^2 / mu_hm_1^2 grows
        1827             :     ! at the expense of sigma_hm_2^2 / mu_hm_2^2, which narrows.  The component
        1828             :     ! variances are written as:
        1829             :     !
        1830             :     ! sigma_hm_1^2 = R * ( 1 + zeta ) * mu_hm_1^2; and
        1831             :     ! sigma_hm_2^2 = R * mu_hm_2^2,
        1832             :     !
        1833             :     ! and the component standard deviations are simply:
        1834             :     !
        1835             :     ! sigma_hm_1 = sqrt( R * ( 1 + zeta ) ) * mu_hm_1; and
        1836             :     ! sigma_hm_2 = sqrt( R ) * mu_hm_2.
        1837             :     !
        1838             :     ! The equation for <hm’^2> can be rewritten as:
        1839             :     !
        1840             :     ! <hm’^2> = a * f_p_1 * ( 1 + R * ( 1 + zeta ) ) * mu_hm_1^2
        1841             :     !           + ( 1 - a ) * f_p_2 * ( 1 + R ) * mu_hm_2^2
        1842             :     !           - <hm>^2.
        1843             :     !
        1844             :     !
        1845             :     ! HYDROMETEOR IN-PRECIP. VARIANCE:
        1846             :     ! THE SPREAD OF THE MEANS VS. THE STANDARD DEVIATIONS
        1847             :     !
        1848             :     ! Part I:  Minimum and Maximum Values for R
        1849             :     !
        1850             :     ! The in-precip. variance of the hydrometeor is accounted for through a
        1851             :     ! combination of the variance of each PDF component and the spread between
        1852             :     ! the means of each PDF component.  At one extreme, the standard deviation
        1853             :     ! of each component could be set to 0 and the in-prccip. variance could be
        1854             :     ! accounted for by spreading the PDF component (in-precip.) means far apart.
        1855             :     ! The value of R in this scenario would be its minimum possible value, which
        1856             :     ! is 0.  At the other extreme, the means of each component could be set
        1857             :     ! equal to each other and the in-precip. variance could be accounted for
        1858             :     ! entirely by the PDF component (in-precip.) standard deviations.  The value
        1859             :     ! of R in this scenario would be its maximum possible value, which is Rmax.
        1860             :     !
        1861             :     ! In order to calculate the value of Rmax, use the equation set but set
        1862             :     ! mu_hm_1 = mu_hm_2 and R = Rmax.  When this happens:
        1863             :     !
        1864             :     ! <hm> = ( a * f_p_1 + ( 1- a ) * f_p_2 ) * mu_hm_i;
        1865             :     !
        1866             :     ! and since f_p = a * f_p_1 + ( 1 - a ) * f_p_2:
        1867             :     !
        1868             :     ! mu_hm_i = <hm> / f_p = <hm|_ip>;
        1869             :     !
        1870             :     ! where <hm|_ip> is the in-precip. mean of the hydrometeor.  The equation
        1871             :     ! for hydrometeor variance in this scenario becomes:
        1872             :     !
        1873             :     ! <hm’^2> = <hm|_ip>^2 * ( a * f_p_1 * ( 1 + Rmax * ( 1 + zeta ) )
        1874             :     !                          + ( 1 - a ) * f_p_2 * ( 1 + Rmax ) )
        1875             :     !           - <hm>^2.
        1876             :     !
        1877             :     ! The general equation for the in-precip. variance of a hydrometeor,
        1878             :     ! <hm|_ip’^2>, is given by:
        1879             :     !
        1880             :     ! <hm|_ip’^2> = ( <hm’^2> + <hm>^2 - f_p * <hm|_ip>^2 ) / f_p;
        1881             :     !
        1882             :     ! which can be rewritten as:
        1883             :     !
        1884             :     ! <hm’^2> + <hm>^2 = f_p * ( <hm|_ip’^2> + <hm|_ip>^2 ).
        1885             :     !
        1886             :     ! When the above equation is substituted into the modified PDF equation for
        1887             :     ! <hm’^2>, Rmax is solved for and the equation is:
        1888             :     !
        1889             :     ! Rmax = ( f_p / ( a * f_p_1 * ( 1 + zeta ) + ( 1 - a ) * f_p_2 ) )
        1890             :     !        * ( <hm|_ip’^2> / <hm|_ip>^2 ).
        1891             :     !
        1892             :     ! Here, in the scenario that zeta = 0, both PDF components have the same
        1893             :     ! mean and same variance, which reduces the in-precip. distribution to an
        1894             :     ! assumed single lognormal, and the above equation reduces to:
        1895             :     !
        1896             :     ! Rmax = <hm|_ip’^2> / <hm|_ip>^2;
        1897             :     !
        1898             :     ! which is what is expected in that case.
        1899             :     !
        1900             :     !
        1901             :     ! Part II:  Enter omicron
        1902             :     !
        1903             :     ! A parameter is used to prescribe the ratio of R to its maximum value,
        1904             :     ! Rmax.  The prescribed parameter is called omicron, where:
        1905             :     !
        1906             :     ! R = omicron * Rmax;
        1907             :     !
        1908             :     ! where 0 <= omicron <= 1.  When omicron = 0, the standard deviation of each
        1909             :     ! PDF component is 0, and mu_hm_1 is spread as far away from mu_hm_2 as it
        1910             :     ! needs to be to account for the in-precip. variance.  When omicron = 1,
        1911             :     ! mu_hm_1 is equal to mu_hm_2, and the standard deviations of the PDF
        1912             :     ! components account for all of the in-precip. variance (and when zeta = 0,
        1913             :     ! the PDF shape is a single lognormal in-precip.).  At intermediate values
        1914             :     ! of omicron, the means of each PDF component are somewhat spread and each
        1915             :     ! PDF component has some width.  The modified parameters are listed below.
        1916             :     !
        1917             :     ! The ratio of sigma_hm_2^2 to mu_hm_2^2 is:
        1918             :     !
        1919             :     ! sigma_hm_2^2 / mu_hm_2^2 = omicron * Rmax;
        1920             :     !
        1921             :     ! and the ratio of sigma_hm_1^2 / mu_hm_1^2 is:
        1922             :     !
        1923             :     ! sigma_hm_1^2 / mu_hm_1^2 = omicron * Rmax * ( 1 + zeta ).
        1924             :     !
        1925             :     ! The component variances are written as:
        1926             :     !
        1927             :     ! sigma_hm_1^2 = omicron * Rmax * ( 1 + zeta ) * mu_hm_1^2; and
        1928             :     ! sigma_hm_2^2 = omicron * Rmax * mu_hm_2^2,
        1929             :     !
        1930             :     ! and the component standard deviations are simply:
        1931             :     !
        1932             :     ! sigma_hm_1 = sqrt( omicron * Rmax * ( 1 + zeta ) ) * mu_hm_1; and
        1933             :     ! sigma_hm_2 = sqrt( omicron * Rmax ) * mu_hm_2.
        1934             :     !
        1935             :     ! The equation set becomes:
        1936             :     !
        1937             :     ! [1] <hm> = a * f_p_1 * mu_hm_1 + ( 1- a ) * f_p_2 * mu_hm_2; and
        1938             :     !
        1939             :     ! [2] <hm’^2>
        1940             :     !     = a * f_p_1 * ( 1 + omicron * Rmax * ( 1 + zeta ) ) * mu_hm_1^2
        1941             :     !       + ( 1 - a ) * f_p_2 * ( 1 + omicron * Rmax ) * mu_hm_2^2
        1942             :     !       - <hm>^2.
        1943             :     !
        1944             :     !
        1945             :     ! SOLVING THE EQUATION SET FOR MU_HM_1 AND MU_HM_2.
        1946             :     !
        1947             :     ! The above system of two equations can be solved for mu_hm_1 and mu_hm_2.
        1948             :     ! All other quantities in the equation set are known quantities.  The
        1949             :     ! equation for <hm> is rewritten to isolate mu_hm_2:
        1950             :     !
        1951             :     ! mu_hm_2 = ( <hm> - a * f_p_1 * mu_hm_1 ) / ( ( 1 - a ) * f_p_2 ).
        1952             :     !
        1953             :     ! The above equation is substituted into the equation for <hm’^2>.  The
        1954             :     ! equation for <hm’^2> is rewritten, resulting in:
        1955             :     !
        1956             :     ! [ a * f_p_1 * ( 1 + omicron * Rmax * ( 1 + zeta ) )
        1957             :     !   + a^2 * f_p_1^2 * ( 1 + omicron * Rmax ) / ( ( 1 - a ) * f_p_2 ) ]
        1958             :     ! * mu_hm_1^2
        1959             :     ! + [ - 2 * <hm> * a * f_p_1 * ( 1 + omicron * Rmax )
        1960             :     !     / ( ( 1 - a ) * f_p_2 ) ] * mu_hm_1
        1961             :     ! + [ - ( <hm’^2>
        1962             :     !         + ( 1 - ( 1 + omicron * Rmax ) / ( ( 1 - a ) * f_p_2 ) )
        1963             :     !           * <hm>^2 ) ]
        1964             :     ! = 0.
        1965             :     !
        1966             :     ! This equation is of the form:
        1967             :     !
        1968             :     ! A * mu_hm_1^2 + B * mu_hm_1 + C = 0;
        1969             :     !
        1970             :     ! so the solution for mu_hm_1 is:
        1971             :     !
        1972             :     ! mu_hm_1 = ( -B +/- sqrt( B^2 - 4*A*C ) ) / (2*A);
        1973             :     !
        1974             :     ! where:
        1975             :     !
        1976             :     ! A = a * f_p_1 * ( 1 + omicron * Rmax * ( 1 + zeta ) )
        1977             :     !     + a^2 * f_p_1^2 * ( 1 + omicron * Rmax ) / ( ( 1 - a ) * f_p_2 );
        1978             :     !
        1979             :     ! B = - 2 * <hm> * a * f_p_1 * ( 1 + omicron * Rmax )
        1980             :     !     / ( ( 1 - a ) * f_p_2 );
        1981             :     !
        1982             :     ! and
        1983             :     !
        1984             :     ! C = - ( <hm’^2>
        1985             :     !         + ( 1 - ( 1 + omicron * Rmax ) / ( ( 1 - a ) * f_p_2 ) )
        1986             :     !           * <hm>^2 ).
        1987             :     !
        1988             :     ! The signs of the coefficients:
        1989             :     !
        1990             :     ! 1) coefficient A is always positive,
        1991             :     ! 2) coefficient B is always negative (this means that -B is always
        1992             :     !    positive), and
        1993             :     ! 3) coefficient C can be positive, negative, or zero.
        1994             :     !
        1995             :     ! Since ( 1 - ( 1 + omicron * Rmax ) / ( ( 1 - a ) * f_p_2 ) ) * <hm>^2 is
        1996             :     ! always negative and <hm’^2> is always positive, the sign of coefficient C
        1997             :     ! depends on which term is greater in magnitude.
        1998             :     !
        1999             :     ! When <hm’^2> is greater, the sign of coefficient C is negative.  This
        2000             :     ! means that -4*A*C is positive, which in turn means that
        2001             :     ! sqrt( B^2 - 4*A*C ) is greater in magnitude than -B.  If the subtraction
        2002             :     ! option of the +/- were to be chosen, the value of mu_hm_1 would be
        2003             :     ! negative in this scenerio.  So the natural thing to do would be to always
        2004             :     ! choose the addition option.  However, this method requires that mu_hm_1
        2005             :     ! equals mu_hm_2 when omicron = 1.  When zeta >= 0, this happens when the
        2006             :     ! addition option is chosen, but not when the subtraction option is chosen.
        2007             :     ! However, when zeta < 0, this happens when the subtraction option is
        2008             :     ! chosen, but not when the addition option is chosen.  So, the equation for
        2009             :     ! mu_hm_1 becomes:
        2010             :     !
        2011             :     ! mu_hm_1 = ( -B + sqrt( B^2 - 4*A*C ) ) / (2*A); when zeta >= 0; and
        2012             :     ! mu_hm_1 = ( -B - sqrt( B^2 - 4*A*C ) ) / (2*A); when zeta < 0.
        2013             :     !
        2014             :     ! Once this is set, of course:
        2015             :     !
        2016             :     ! mu_hm_2 = ( <hm> - a * f_p_1 * mu_hm_1 ) / ( ( 1 - a ) * f_p_2 ).
        2017             :     !
        2018             :     ! The system has been solved and the in-precip. PDF component means have
        2019             :     ! been found!
        2020             :     !
        2021             :     !
        2022             :     ! NOTES
        2023             :     !
        2024             :     ! Note 1:
        2025             :     !
        2026             :     ! The term B^2 - 4*A*C has been analyzed, and mathematically:
        2027             :     !
        2028             :     ! B^2 - 4*A*C >= 0
        2029             :     !
        2030             :     ! always holds true.  Additionally, the minimum value:
        2031             :     !
        2032             :     ! B^2 - 4*A*C = 0,
        2033             :     !
        2034             :     ! can only occur when omicron = 1 and zeta = 0 (or alternatively to
        2035             :     ! zeta = 0, Rmax = 0, but this only occurs when <hm|_ip'^2> / <hm|_ip>^2 has
        2036             :     ! a value of 0).
        2037             :     !
        2038             :     ! Numerically, when omicron = 1 and zeta = 0, B^2 - 4*A*C can produce very
        2039             :     ! small (on the order of epsilon) negative values.  This is due to numerical
        2040             :     ! round off error.  When this happens, the erroneous small, negative value
        2041             :     ! of B^2 - 4*A*C is simply reset to the value it's supposed to have, which
        2042             :     ! is 0.
        2043             :     !
        2044             :     !
        2045             :     ! Note 2:
        2046             :     !
        2047             :     ! As the value of <hm|_ip'^2> / <hm|_ip>^2 increases and as the value of
        2048             :     ! omicron decreases (narrowing the in-precip standard deviations and
        2049             :     ! increasing the spread between the in-precip means), a situtation arises
        2050             :     ! where the value of one of the component means will become negative.  This
        2051             :     ! is because there is a limit to the amount of in-precip variance that can
        2052             :     ! be represented by this kind of distribution.  In order to prevent
        2053             :     ! out-of-bounds values of mu_hm_1 or mu_hm_2, lower limits will be
        2054             :     ! declared, called mu_hm_1_min and mu_hm_2_min.  The value of the
        2055             :     ! hydrometeor in-precip. component mean will be limited from going any
        2056             :     ! smaller (or negative) at this value.  From there, the value of the other
        2057             :     ! hydrometeor in-precip. component mean is easy to calculate.  Then, both
        2058             :     ! values will be entered into the calculation of hydrometeor variance, which
        2059             :     ! will be rewritten to solve for R.  Then, both the hydrometeor mean and
        2060             :     ! hydrometeor variance will be preserved with a valid distribution.
        2061             :     !
        2062             :     ! In this emergency scenario, the value of R is:
        2063             :     !
        2064             :     ! R = ( <hm'^2> + <hm>^2 - a * f_p_1 * mu_hm_1^2
        2065             :     !       - ( 1 - a ) * f_p_2 * mu_hm_2^2 )
        2066             :     !     / ( a * f_p_1 * ( 1 + zeta ) * mu_hm_1^2
        2067             :     !         + ( 1 - a ) * f_p_2 * mu_hm_2^2 ).
        2068             :     !
        2069             :     ! The minimum values of the in-precip. component means are bounded by:
        2070             :     !
        2071             :     ! mu_hm_1_min >= hm_tol / f_p_1; and
        2072             :     ! mu_hm_2_min >= hm_tol / f_p_2.
        2073             :     !
        2074             :     ! These are set this way because hm_1 ( = mu_hm_1 * f_p_1 ) and
        2075             :     ! hm_2 ( = mu_hm_2 * f_p_2 ) need to have values of at least hm_tol when
        2076             :     ! precipitation is found in both PDF components.
        2077             :     !
        2078             :     ! However, an in-precip. component mean value of hm_tol / f_p_1 or
        2079             :     ! hm_tol / f_p_2 often produces a distribution where one component centers
        2080             :     ! around values that are too small to be a good match with data taken from
        2081             :     ! Large Eddy Simulations (LES).  It is desirable to increase the minimum
        2082             :     ! threshold of mu_hm_1 and mu_hm_2.
        2083             :     !
        2084             :     ! As the minimum threshold increases, the value of the in-precip. component
        2085             :     ! mean that is from the component that is not being set to the minimum
        2086             :     ! threshold decreases.  If the minimum threshold were to be boosted as high
        2087             :     ! as <hm> / f_p (in most cases, <hm> / f_p >> hm_tol / f_p_i), both
        2088             :     ! components would have a value of <hm> / f_p.  The minimum threshold should
        2089             :     ! not be set this high.
        2090             :     !
        2091             :     ! Additionally, the minimum threshold for one in-precip. component mean
        2092             :     ! cannot be set so high as to drive the other in-precip. component mean
        2093             :     ! below hm_tol / f_p_i.  (This doesn't come into play unless <hm> is close
        2094             :     ! to hm_tol.)  The upper limit for the in-precip. mean values are:
        2095             :     !
        2096             :     ! mu_hm_1|_(upper. lim.) = ( <hm> - ( 1 - a ) * f_p_2 * ( hm_tol / f_p_2 ) )
        2097             :     !                          / ( a * f_p_1 ); and
        2098             :     !
        2099             :     ! mu_hm_2|_(upper. lim.) = ( <hm> - a * f_p_1 * ( hm_tol / f_p_1 ) )
        2100             :     !                          / ( ( 1 - a ) * f_p_2 );
        2101             :     !
        2102             :     ! which reduces to:
        2103             :     !
        2104             :     ! mu_hm_1|_(upper. lim.) = ( <hm> - ( 1 - a ) * hm_tol ) / ( a * f_p_1 );
        2105             :     ! and
        2106             :     ! mu_hm_2|_(upper. lim.) = ( <hm> - a * hm_tol ) / ( ( 1 - a ) * f_p_2 ).
        2107             :     !
        2108             :     ! An appropriate minimum value for mu_hm_1 can be set by:
        2109             :     !
        2110             :     ! mu_hm_1_min = | min( hm_tol / f_p_1
        2111             :     !               |      + mu_hm_min_coef * ( <hm> / f_p - hm_tol / f_p_1 ),
        2112             :     !               |      ( <hm> - ( 1 - a ) * hm_tol ) / ( a * f_p_1 ) );
        2113             :     !               |    where <hm> / f_p > hm_tol / f_p_1;
        2114             :     !               | hm_tol / f_p_1;
        2115             :     !               |    where <hm> / f_p <= hm_tol / f_p_1;
        2116             :     !
        2117             :     ! and similarly for mu_hm_2:
        2118             :     !
        2119             :     ! mu_hm_2_min = | min( hm_tol / f_p_2
        2120             :     !               |      + mu_hm_min_coef * ( <hm> / f_p - hm_tol / f_p_2 ),
        2121             :     !               |      ( <hm> - a * hm_tol ) / ( ( 1 - a ) * f_p_2 ) );
        2122             :     !               |    where <hm> / f_p > hm_tol / f_p_2;
        2123             :     !               | hm_tol / f_p_2;
        2124             :     !               |    where <hm> / f_p <= hm_tol / f_p_2;
        2125             :     !
        2126             :     ! where mu_hm_min_coef is a coefficient that has a value
        2127             :     ! 0 <= mu_hm_min_coef < 1.  When the value of mu_hm_min_coef is 0,
        2128             :     ! mu_hm_1_min reverts to hm_tol / f_p_1 and mu_hm_2_min reverts to
        2129             :     ! hm_tol / f_p_2.  An appropriate value for mu_hm_min_coef should be small,
        2130             :     ! such as 0.01 - 0.05.
        2131             :     !
        2132             :     !
        2133             :     ! Note 3:
        2134             :     !
        2135             :     ! When the value of zeta >= 0, the value of mu_hm_1 tends to be larger than
        2136             :     ! the value of mu_hm_2.  Likewise when the value of zeta < 0, the value of
        2137             :     ! mu_hm_2 tends to be larger than the value of mu_hm_1.  Since most cloud
        2138             :     ! water and cloud fraction tends to be found in PDF component 1, it is
        2139             :     ! advantageous to have the larger in-precip. component mean of the
        2140             :     ! hydrometeor also found in PDF component 1.  The recommended value of zeta
        2141             :     ! is a value greater than or equal to 0.
        2142             :     !
        2143             :     !
        2144             :     ! Update:
        2145             :     !
        2146             :     ! In order to better represent the increase in <th_l'^2> near the ground
        2147             :     ! from the evaporation of rain, the code is modified to tend towards a
        2148             :     ! negative correlation of th_l and hm.  When mu_thl_1 <= mu_thl_2,
        2149             :     ! mu_hm_1 >= mu_hm_2; otherwise, when mu_thl_1 > mu_thl_2,
        2150             :     ! mu_hm_1 <= mu_hm_2.
        2151             :     !
        2152             :     ! In the original derivation, mu_hm_1 >= mu_hm_2 when zeta >= 0, and
        2153             :     ! mu_hm_1 < mu_hm_2 when zeta < 0, where zeta is a tunable or adjustable
        2154             :     ! parameter.  In order to allow the relationship of mu_hm_1 to mu_hm_2 to
        2155             :     ! depend on the relationship of mu_thl_1 to mu_thl_2, the value of zeta must
        2156             :     ! also depend on the relationship of mu_thl_1 to mu_thl_2.
        2157             :     !
        2158             :     ! When mu_thl_1 <= mu_thl_2:
        2159             :     !
        2160             :     ! The relationship of mu_hm_1 to mu_hm_2 is mu_hm_1 >= mu_hm_2, so
        2161             :     ! zeta >= 0.  The tunable value of zeta is referred to as zeta_in.  When
        2162             :     ! zeta_in is already greater than 0 (meaning sigma_hm_1^2 / mu_hm_1^2 is
        2163             :     ! greater than sigma_hm_2^2 / mu_hm_2^2), zeta is simply set to zeta_in.  In
        2164             :     ! other words, the component with the greater mean value of the hydrometeor
        2165             :     ! also has the greater value of component variance to the square of the
        2166             :     ! component mean.  However, when zeta_in is less than 0, zeta must be
        2167             :     ! adjusted to be greater than 0.  The following equation is used to set the
        2168             :     ! value of zeta:
        2169             :     !
        2170             :     !        | zeta_in; when zeta_in >= 0
        2171             :     ! zeta = |
        2172             :     !        | ( 1 / ( 1 + zeta_in ) ) - 1; when zeta_in < 0.
        2173             :     !
        2174             :     ! Previously, when zeta_in < 0, mu_hm_1 < mu_hm_2, and
        2175             :     ! sigma_hm_1^2 / mu_hm_1^2 < sigma_hm_2^2 / mu_hm_2^2.  Now that zeta has to
        2176             :     ! be greater than 0, sigma_hm_1^2 / mu_hm_1^2 > sigma_hm_2^2 / mu_hm_2^2.
        2177             :     ! The ratio of the greater variance-over-mean-squared to the smaller
        2178             :     ! variance-over-mean-squared remains the same when using the equation for
        2179             :     ! zeta listed above.
        2180             :     !
        2181             :     ! When mu_thl_1 > mu_thl_2:
        2182             :     !
        2183             :     ! The relationship of mu_hm_1 to mu_hm_2 is mu_hm_1 <= mu_hm_2, so
        2184             :     ! zeta <= 0.  When zeta_in is already less than 0 (meaning
        2185             :     ! sigma_hm_1^2 / mu_hm_1^2 is less than sigma_hm_2^2 / mu_hm_2^2), zeta is
        2186             :     ! simply set to zeta_in.  In other words, the component with the greater
        2187             :     ! mean value of the hydrometeor also has the greater value of component
        2188             :     ! variance to the square of the component mean.  However, when zeta_in is
        2189             :     ! greater than 0, zeta must be adjusted to be less than 0.  The following
        2190             :     ! equation is used to set the value of zeta:
        2191             :     !
        2192             :     !        | zeta_in; when zeta_in <= 0
        2193             :     ! zeta = |
        2194             :     !        | ( 1 / ( 1 + zeta_in ) ) - 1; when zeta_in > 0.
        2195             :     !
        2196             :     ! Previously, when zeta_in > 0, mu_hm_1 > mu_hm_2, and
        2197             :     ! sigma_hm_1^2 / mu_hm_1^2 > sigma_hm_2^2 / mu_hm_2^2.  Now that zeta has to
        2198             :     ! be less than 0, sigma_hm_1^2 / mu_hm_1^2 < sigma_hm_2^2 / mu_hm_2^2.
        2199             :     ! The ratio of the greater variance-over-mean-squared to the smaller
        2200             :     ! variance-over-mean-squared remains the same when using the equation for
        2201             :     ! zeta listed above.
        2202             :     !
        2203             :     !
        2204             :     ! Brian Griffin; February 2015.
        2205             :
        2206             :     ! References:
        2207             :     !-----------------------------------------------------------------------
        2208             :
        2209             :     use constants_clubb, only: &
        2210             :         four, & ! Constant(s)
        2211             :         two,  &
        2212             :         one,  &
        2213             :         zero
        2214             :
        2215             :     use clubb_precision, only: &
        2216             :         core_rknd    ! Variable(s)
        2217             :
        2218             :     implicit none
        2219             :
        2220             :     ! Input Variables
        2221             :     integer, intent(in) :: &
        2222             :       nz,      & ! Number of model vertical grid levels
        2223             :       ngrdcol    ! Number of grid columns
        2224             :
        2225             :     real( kind = core_rknd ), dimension(ngrdcol,nz), intent(in) :: &
        2226             :       hmm,           & ! Hydrometeor mean (overall), <hm>           [hm units]
        2227             :       hmp2,          & ! Hydrometeor variance (overall), <hm'^2>    [hm units^2]
        2228             :       mixt_frac,     & ! Mixture fraction                           [-]
        2229             :       precip_frac,   & ! Precipitation fraction (overall)           [-]
        2230             :       precip_frac_1, & ! Precipitation fraction (1st PDF component) [-]
        2231             :       precip_frac_2, & ! Precipitation fraction (2nd PDF component) [-]
        2232             :       mu_thl_1,      & ! Mean of th_l (1st PDF component)           [K]
        2233             :       mu_thl_2         ! Mean of th_l (2nd PDF component)           [K]
        2234             :
        2235             :     real( kind = core_rknd ), intent(in) :: &
        2236             :       hmp2_ip_on_hmm2_ip, & ! Ratio <hm|_ip'^2> / <hm|_ip>^2                 [-]
        2237             :       hm_tol                ! Tolerance value of hydrometeor          [hm units]
        2238             :
        2239             :     real( kind = core_rknd ), dimension(ngrdcol), intent(in) :: &
        2240             :       precip_frac_tol       ! Min. precip. frac. when hydromet. are present  [-]
        2241             :
        2242             :     real( kind = core_rknd ), intent(in) :: &
        2243             :       omicron,           & ! Relative width parameter, omicron = R / Rmax    [-]
        2244             :       zeta_vrnce_rat_in    ! Width parameter for sigma_hm_1^2 / mu_hm_1^2    [-]
        2245             :
        2246             :     ! Output Variables
        2247             :     real( kind = core_rknd ), dimension(ngrdcol,nz), intent(out) :: &
        2248             :       mu_hm_1,    & ! Mean of hm (1st PDF component) in-precip (ip)      [hm un]
        2249             :       mu_hm_2,    & ! Mean of hm (2nd PDF component) ip                  [hm un]
        2250             :       sigma_hm_1, & ! Standard deviation of hm (1st PDF component) ip    [hm un]
        2251             :       sigma_hm_2, & ! Standard deviation of hm (2nd PDF component) ip    [hm un]
        2252             :       hm_1,       & ! Mean of hm (1st PDF component)                     [hm un]
        2253             :       hm_2          ! Mean of hm (2nd PDF component)                     [hm un]
        2254             :
        2255             :     real( kind = core_rknd ), dimension(ngrdcol,nz), intent(out) :: &
        2256             :       sigma_hm_1_sqd_on_mu_hm_1_sqd, & ! Ratio sigma_hm_1**2 / mu_hm_1**2    [-]
        2257             :       sigma_hm_2_sqd_on_mu_hm_2_sqd    ! Ratio sigma_hm_2**2 / mu_hm_2**2    [-]
        2258             :
        2259             :     ! Local Variables
        2260             :     real( kind = core_rknd ) :: &
        2261             :       Rmax,       & ! Maximum possible value of ratio R                [-]
        2262             :       coef_A,     & ! Coefficient A in A*mu_hm_1^2 + B*mu_hm_1 + C = 0 [-]
        2263             :       coef_B,     & ! Coefficient B in A*mu_hm_1^2 + B*mu_hm_1 + C = 0 [hm un]
        2264             :       coef_C,     & ! Coefficient C in A*mu_hm_1^2 + B*mu_hm_1 + C = 0 [hm un^2]
        2265             :       Bsqd_m_4AC    ! Value B^2 - 4*A*C in quadratic eqn. for mu_hm_1  [hm un^2]
        2266             :
        2267             :     real( kind = core_rknd ) :: &
        2268             :       zeta_vrnce_rat    ! Width parameter for sigma_hm_1^2 / mu_hm_1^2       [-]
        2269             :
        2270             :     real( kind = core_rknd ) :: &
        2271             :       mu_hm_1_min, & ! Minimum value of mu_hm_1 (precip. in both comps.) [hm un]
        2272             :       mu_hm_2_min    ! Minimum value of mu_hm_2 (precip. in both comps.) [hm un]
        2273             :
        2274             :     real( kind = core_rknd ), parameter :: &
        2275             :       mu_hm_min_coef = 0.01_core_rknd  ! Coef. for mu_hm_1_min and mu_hm_2_min
        2276             :
        2277             :     integer :: i, k ! Loop iterators
        2278             :
        2279           0 :     do k = 1, nz
        2280           0 :       do i = 1, ngrdcol
        2281             :
        2282           0 :         if ( hmm(i,k) >= hm_tol &
        2283             :              .and. precip_frac_1(i,k) >= precip_frac_tol(i) &
        2284           0 :              .and. precip_frac_2(i,k) >= precip_frac_tol(i) ) then
        2285             :
        2286             :            ! Adjust the value of zeta based on the relationship of mu_thl_1 to
        2287             :            ! mu_thl_2.
        2288           0 :            if ( mu_thl_1(i,k) <= mu_thl_2(i,k) ) then
        2289           0 :               if ( zeta_vrnce_rat_in >= zero ) then
        2290             :                  zeta_vrnce_rat = zeta_vrnce_rat_in
        2291             :               else ! zeta_vrnce_rat_in < 0
        2292           0 :                  zeta_vrnce_rat = ( one / ( one + zeta_vrnce_rat_in ) ) - one
        2293             :               end if ! zeta_vrnce_rat_in >= 0
        2294             :            else ! mu_thl_1 > mu_thl_2
        2295           0 :               if ( zeta_vrnce_rat_in <= zero ) then
        2296             :                  zeta_vrnce_rat = zeta_vrnce_rat_in
        2297             :               else ! zeta_vrnce_rat_in > 0
        2298           0 :                  zeta_vrnce_rat = ( one / ( one + zeta_vrnce_rat_in ) ) - one
        2299             :               end if ! zeta_vrnce_rat_in <= 0
        2300             :            end if ! mu_thl_1 <= mu_thl_2
        2301             :
        2302             :            ! Calculate the value of Rmax.
        2303             :            ! Rmax = ( f_p / ( a * f_p_1 * ( 1 + zeta ) + ( 1 - a ) * f_p_2 ) )
        2304             :            !        * ( <hm|_ip’^2> / <hm|_ip>^2 ).
        2305             :            ! The parameter zeta is written in the code as zeta_vrnce_rat.
        2306             :            Rmax = ( precip_frac(i,k) &
        2307             :                     / ( mixt_frac(i,k) * precip_frac_1(i,k) * ( one + zeta_vrnce_rat ) &
        2308             :                         + ( one - mixt_frac(i,k) ) * precip_frac_2(i,k) ) ) &
        2309           0 :                   * hmp2_ip_on_hmm2_ip
        2310             :
        2311             :            ! Calculate the value of coefficient A.
        2312             :            ! A = a * f_p_1 * ( 1 + omicron * Rmax * ( 1 + zeta ) )
        2313             :            !     + a^2 * f_p_1^2 * ( 1 + omicron * Rmax ) / ( ( 1 - a ) * f_p_2 ).
        2314             :            coef_A = mixt_frac(i,k) * precip_frac_1(i,k) &
        2315             :                     * ( one + omicron * Rmax * ( one + zeta_vrnce_rat ) ) &
        2316             :                     + mixt_frac(i,k)**2 * precip_frac_1(i,k)**2 &
        2317             :                       * ( one + omicron * Rmax ) &
        2318           0 :                       / ( ( one - mixt_frac(i,k) ) * precip_frac_2(i,k) )
        2319             :
        2320             :            ! Calculate the value of coefficient B.
        2321             :            ! B = - 2 * <hm> * a * f_p_1 * ( 1 + omicron * Rmax )
        2322             :            !     / ( ( 1 - a ) * f_p_2 ).
        2323             :            coef_B = -two * hmm(i,k) * mixt_frac(i,k) * precip_frac_1(i,k) &
        2324             :                      * ( one + omicron * Rmax ) &
        2325           0 :                      / ( ( one - mixt_frac(i,k) ) * precip_frac_2(i,k) )
        2326             :
        2327             :            ! Calculate the value of coefficient C.
        2328             :            ! C = - ( <hm’^2>
        2329             :            !         + ( 1 - ( 1 + omicron * Rmax ) / ( ( 1 - a ) * f_p_2 ) )
        2330             :            !           * <hm>^2 ).
        2331             :            coef_C = - ( hmp2(i,k) + ( one &
        2332             :                                  - ( one + omicron * Rmax ) &
        2333             :                                    / ( ( one - mixt_frac(i,k) ) * precip_frac_2(i,k) ) &
        2334           0 :                                ) * hmm(i,k)**2 )
        2335             :
        2336             :            ! Calculate value of B^2 - 4*A*C.
        2337           0 :            Bsqd_m_4AC = coef_B**2 - four * coef_A * coef_C
        2338             :
        2339             :            ! Mathematically, the value of B^2 - 4*A*C cannot be less than 0.
        2340             :            ! Numerically, this can happen when numerical round off error causes an
        2341             :            ! epsilon-sized negative value.  When this happens, reset the value of
        2342             :            ! B^2 - 4*A*C to 0.
        2343           0 :            if ( Bsqd_m_4AC < zero ) then
        2344           0 :               Bsqd_m_4AC = zero
        2345             :            end if
        2346             :
        2347             :            ! Calculate the mean (in-precip.) of the hydrometeor in the 1st PDF
        2348             :            ! component.
        2349           0 :            if ( mu_thl_1(i,k) <= mu_thl_2(i,k) ) then
        2350           0 :               mu_hm_1(i,k) = ( -coef_B + sqrt( Bsqd_m_4AC ) ) / ( two * coef_A )
        2351             :            else ! mu_thl_1 > mu_thl_2
        2352           0 :               mu_hm_1(i,k) = ( -coef_B - sqrt( Bsqd_m_4AC ) ) / ( two * coef_A )
        2353             :            end if ! mu_thl_1 <= mu_thl_2
        2354             :
        2355             :            ! Calculate the mean (in-precip.) of the hydrometeor in the 2nd PDF
        2356             :            ! component.
        2357             :            mu_hm_2(i,k) = ( hmm(i,k) - mixt_frac(i,k) * precip_frac_1(i,k) * mu_hm_1(i,k) ) &
        2358           0 :                      / ( ( one - mixt_frac(i,k) ) * precip_frac_2(i,k) )
        2359             :
        2360             :            ! Calculate the value of the ratio R (which is sigma_hm_2^2 / mu_hm_2^2),
        2361             :            ! where R = omicron * Rmax.  The name of the variable used for R is
        2362             :            ! sigma_hm_2_sqd_on_mu_hm_2_sqd.
        2363           0 :            sigma_hm_2_sqd_on_mu_hm_2_sqd(i,k) = omicron * Rmax
        2364             :
        2365             :            ! Calculate minimum allowable values for mu_hm_1 and mu_hm_2.
        2366           0 :            if ( hmm(i,k) / precip_frac(i,k) > hm_tol / precip_frac_1(i,k) ) then
        2367             :               mu_hm_1_min &
        2368             :               = min( hm_tol / precip_frac_1(i,k) &
        2369             :                      + mu_hm_min_coef * ( hmm(i,k) / precip_frac(i,k) &
        2370             :                                           - hm_tol / precip_frac_1(i,k) ), &
        2371             :                      ( hmm(i,k) - ( one - mixt_frac(i,k) ) * hm_tol ) &
        2372           0 :                      / ( mixt_frac(i,k) * precip_frac_1(i,k) ) )
        2373             :            else ! hmm / precip_frac <= hm_tol / precip_frac_1
        2374             :               mu_hm_1_min = hm_tol / precip_frac_1(i,k)
        2375             :            end if
        2376           0 :            if ( hmm(i,k) / precip_frac(i,k) > hm_tol / precip_frac_2(i,k) ) then
        2377             :               mu_hm_2_min &
        2378             :               = min( hm_tol / precip_frac_2(i,k) &
        2379             :                      + mu_hm_min_coef * ( hmm(i,k) / precip_frac(i,k) &
        2380             :                                           - hm_tol / precip_frac_2(i,k) ), &
        2381             :                      ( hmm(i,k) - mixt_frac(i,k) * hm_tol ) &
        2382           0 :                      / ( ( one - mixt_frac(i,k) ) * precip_frac_2(i,k) ) )
        2383             :            else ! hmm / precip_frac <= hm_tol / precip_frac_2
        2384             :               mu_hm_2_min = hm_tol / precip_frac_2(i,k)
        2385             :            end if
        2386             :
        2387             :            ! Handle the "emergency" situation when the specified value of omicron is
        2388             :            ! too small for the value of <hm|_ip'^2> / <hm|_ip>^2, resulting in a
        2389             :            ! component mean that is too small (below tolerance value) or negative.
        2390           0 :            if ( mu_hm_1(i,k) < mu_hm_1_min ) then
        2391             :
        2392             :               ! Set the value of mu_hm_1 to the threshold positive value.
        2393           0 :               mu_hm_1(i,k) = mu_hm_1_min
        2394             :
        2395             :               ! Recalculate the mean (in-precip.) of the hydrometeor in the 2nd PDF
        2396             :               ! component.
        2397             :               mu_hm_2(i,k) = ( hmm(i,k) - mixt_frac(i,k) * precip_frac_1(i,k) * mu_hm_1(i,k) ) &
        2398           0 :                         / ( ( one - mixt_frac(i,k) ) * precip_frac_2(i,k) )
        2399             :
        2400             :               ! Recalculate the value of R ( sigma_hm_2^2 / mu_hm_2^2 ) in this
        2401             :               ! scenario.
        2402             :               ! R = ( <hm'^2> + <hm>^2 - a * f_p_1 * mu_hm_1^2
        2403             :               !       - ( 1 - a ) * f_p_2 * mu_hm_2^2 )
        2404             :               !     / ( a * f_p_1 * ( 1 + zeta ) * mu_hm_1^2
        2405             :               !         + ( 1 - a ) * f_p_2 * mu_hm_2^2 ).
        2406             :               sigma_hm_2_sqd_on_mu_hm_2_sqd(i,k) &
        2407             :               = ( hmp2(i,k) + hmm(i,k)**2 - mixt_frac(i,k) * precip_frac_1(i,k) * mu_hm_1(i,k)**2 &
        2408             :                   - ( one - mixt_frac(i,k) ) * precip_frac_2(i,k) * mu_hm_2(i,k)**2 ) &
        2409             :                 / ( mixt_frac(i,k) * precip_frac_1(i,k) &
        2410             :                     * ( one + zeta_vrnce_rat ) * mu_hm_1(i,k)**2 &
        2411           0 :                     + ( one - mixt_frac(i,k) ) * precip_frac_2(i,k) * mu_hm_2(i,k)**2 )
        2412             :
        2413             :               ! Mathematically, this ratio can never be less than 0.  In case
        2414             :               ! numerical round off error produces a negative value in extreme
        2415             :               ! cases, reset the value of R to 0.
        2416           0 :               if ( sigma_hm_2_sqd_on_mu_hm_2_sqd(i,k) < zero ) then
        2417           0 :                  sigma_hm_2_sqd_on_mu_hm_2_sqd(i,k) = zero
        2418             :               end if
        2419             :
        2420           0 :            elseif ( mu_hm_2(i,k) < mu_hm_2_min ) then
        2421             :
        2422             :               ! Set the value of mu_hm_2 to the threshold positive value.
        2423           0 :               mu_hm_2(i,k) = mu_hm_2_min
        2424             :
        2425             :               ! Recalculate the mean (in-precip.) of the hydrometeor in the 1st PDF
        2426             :               ! component.
        2427             :               mu_hm_1(i,k) = ( hmm(i,k) - ( one - mixt_frac(i,k) ) &
        2428             :                                           * precip_frac_2(i,k) * mu_hm_2(i,k) ) &
        2429           0 :                              / ( mixt_frac(i,k) * precip_frac_1(i,k) )
        2430             :
        2431             :               ! Recalculate the value of R ( sigma_hm_2^2 / mu_hm_2^2 ) in this
        2432             :               ! scenario.
        2433             :               ! R = ( <hm'^2> + <hm>^2 - a * f_p_1 * mu_hm_1^2
        2434             :               !       - ( 1 - a ) * f_p_2 * mu_hm_2^2 )
        2435             :               !     / ( a * f_p_1 * ( 1 + zeta ) * mu_hm_1^2
        2436             :               !         + ( 1 - a ) * f_p_2 * mu_hm_2^2 ).
        2437             :               sigma_hm_2_sqd_on_mu_hm_2_sqd(i,k) &
        2438             :               = ( hmp2(i,k) + hmm(i,k)**2 - mixt_frac(i,k) * precip_frac_1(i,k) * mu_hm_1(i,k)**2 &
        2439             :                   - ( one - mixt_frac(i,k) ) * precip_frac_2(i,k) * mu_hm_2(i,k)**2 ) &
        2440             :                 / ( mixt_frac(i,k) * precip_frac_1(i,k) &
        2441             :                     * ( one + zeta_vrnce_rat ) * mu_hm_1(i,k)**2 &
        2442           0 :                     + ( one - mixt_frac(i,k) ) * precip_frac_2(i,k) * mu_hm_2(i,k)**2 )
        2443             :
        2444             :               ! Mathematically, this ratio can never be less than 0.  In case
        2445             :               ! numerical round off error produces a negative value in extreme
        2446             :               ! cases, reset the value of R to 0.
        2447           0 :               if ( sigma_hm_2_sqd_on_mu_hm_2_sqd(i,k) < zero ) then
        2448           0 :                  sigma_hm_2_sqd_on_mu_hm_2_sqd(i,k) = zero
        2449             :               end if
        2450             :
        2451             :            end if
        2452             :
        2453             :            ! Calculate the standard deviation (in-precip.) of the hydrometeor in the
        2454             :            ! 1st PDF component.
        2455             :            sigma_hm_1(i,k) = sqrt( sigma_hm_2_sqd_on_mu_hm_2_sqd(i,k) &
        2456             :                               * ( one + zeta_vrnce_rat ) ) &
        2457           0 :                         * mu_hm_1(i,k)
        2458             :
        2459             :            ! Calculate the standard deviation (in-precip.) of the hydrometeor in the
        2460             :            ! 2nd PDF component.
        2461           0 :            sigma_hm_2(i,k) = sqrt( sigma_hm_2_sqd_on_mu_hm_2_sqd(i,k) ) * mu_hm_2(i,k)
        2462             :
        2463             :            ! Calculate the mean of the hydrometeor in the 1st PDF component.
        2464           0 :            hm_1(i,k) = max( mu_hm_1(i,k) * precip_frac_1(i,k), hm_tol )
        2465             :
        2466             :            ! Calculate the mean of the hydrometeor in the 1st PDF component.
        2467           0 :            hm_2(i,k) = max( mu_hm_2(i,k) * precip_frac_2(i,k), hm_tol )
        2468             :
        2469             :            ! Calculate the ratio of sigma_hm_1^2 / mu_hm_1^2.
        2470           0 :            sigma_hm_1_sqd_on_mu_hm_1_sqd(i,k) = sigma_hm_1(i,k)**2 / mu_hm_1(i,k)**2
        2471             :
        2472             :            ! The value of R, sigma_hm_2_sqd_on_mu_hm_2_sqd, has already been
        2473             :            ! calculated.
        2474             :
        2475             :
        2476           0 :         elseif ( hmm(i,k) >= hm_tol .and. precip_frac_1(i,k) >= precip_frac_tol(i) ) then
        2477             :
        2478             :            ! Precipitation is found in the 1st PDF component, but not in the 2nd
        2479             :            ! PDF component (precip_frac_2 = 0).
        2480           0 :            mu_hm_1(i,k) = hmm(i,k) / ( mixt_frac(i,k) * precip_frac_1(i,k) )
        2481           0 :            mu_hm_2(i,k) = zero
        2482             :
        2483             :            sigma_hm_1(i,k) = sqrt( max( ( hmp2(i,k) + hmm(i,k)**2 &
        2484             :                                      - mixt_frac(i,k) * precip_frac_1(i,k) * mu_hm_1(i,k)**2 ) &
        2485             :                                    / ( mixt_frac(i,k) * precip_frac_1(i,k) ), &
        2486           0 :                                    zero ) )
        2487           0 :            sigma_hm_2(i,k) = zero
        2488             :
        2489           0 :            hm_1(i,k) = mu_hm_1(i,k) * precip_frac_1(i,k)
        2490           0 :            hm_2(i,k) = zero
        2491             :
        2492           0 :            sigma_hm_1_sqd_on_mu_hm_1_sqd(i,k) = sigma_hm_1(i,k)**2 / mu_hm_1(i,k)**2
        2493             :            ! The ratio sigma_hm_2^2 / mu_hm_2^2 is undefined.
        2494           0 :            sigma_hm_2_sqd_on_mu_hm_2_sqd(i,k) = zero
        2495             :
        2496             :
        2497           0 :         elseif ( hmm(i,k) >= hm_tol .and. precip_frac_2(i,k) >= precip_frac_tol(i) ) then
        2498             :
        2499             :            ! Precipitation is found in the 2nd PDF component, but not in the 1st
        2500             :            ! PDF component (precip_frac_1 = 0).
        2501           0 :            mu_hm_1(i,k) = zero
        2502           0 :            mu_hm_2(i,k) = hmm(i,k) / ( ( one - mixt_frac(i,k) ) * precip_frac_2(i,k) )
        2503             :
        2504           0 :            sigma_hm_1(i,k) = zero
        2505             :            sigma_hm_2(i,k) &
        2506             :            = sqrt( max( ( hmp2(i,k) + hmm(i,k)**2 &
        2507             :                           - ( one - mixt_frac(i,k) ) * precip_frac_2(i,k) * mu_hm_2(i,k)**2 ) &
        2508             :                         / ( ( one - mixt_frac(i,k) ) * precip_frac_2(i,k) ), &
        2509           0 :                         zero ) )
        2510             :
        2511           0 :            hm_1(i,k) = zero
        2512           0 :            hm_2(i,k) = mu_hm_2(i,k) * precip_frac_2(i,k)
        2513             :
        2514             :            ! The ratio sigma_hm_1^2 / mu_hm_1^2 is undefined.
        2515           0 :            sigma_hm_1_sqd_on_mu_hm_1_sqd(i,k) = zero
        2516           0 :            sigma_hm_2_sqd_on_mu_hm_2_sqd(i,k) = sigma_hm_2(i,k)**2 / mu_hm_2(i,k)**2
        2517             :
        2518             :
        2519             :         else ! hm < hm_tol or ( precip_frac_1 = 0 and precip_frac_2 = 0 ).
        2520             :
        2521             :            ! Precipitation is not found in either PDF component.
        2522           0 :            mu_hm_1(i,k) = zero
        2523           0 :            mu_hm_2(i,k) = zero
        2524             :
        2525           0 :            sigma_hm_1(i,k) = zero
        2526           0 :            sigma_hm_2(i,k) = zero
        2527             :
        2528           0 :            hm_1(i,k) = zero
        2529           0 :            hm_2(i,k) = zero
        2530             :
        2531             :            ! The ratio sigma_hm_1^2 / mu_hm_1^2 is undefined.
        2532           0 :            sigma_hm_1_sqd_on_mu_hm_1_sqd(i,k) = zero
        2533             :            ! The ratio sigma_hm_2^2 / mu_hm_2^2 is undefined.
        2534           0 :            sigma_hm_2_sqd_on_mu_hm_2_sqd(i,k) = zero
        2535             :
        2536             :
        2537             :         end if ! hmm >= hm_tol and precip_frac_1 >= precip_frac_tol
        2538             :               ! and precip_frac_2 >= precip_frac_tol
        2539             :       end do
        2540             :     end do
        2541             :
        2542           0 :     return
        2543             :
        2544             :   end subroutine calc_comp_mu_sigma_hm
        2545             :
        2546             :   !=============================================================================
        2547           0 :   subroutine component_corr_w_x( nz, ngrdcol, &
        2548           0 :                                  rc_1, &
        2549           0 :                                  rc_2, &
        2550             :                                  corr_w_x_NN_cloud, corr_w_x_NN_below, &
        2551             :                                  iiPDF_type, &
        2552           0 :                                  corr_w_x_1, &
        2553           0 :                                  corr_w_x_2 )
        2554             :
        2555             :     ! Description:
        2556             :     ! Calculates the correlation of w and x within the ith PDF component.
        2557             :     ! Here, x is a variable with a normally distributed individual marginal PDF,
        2558             :     ! such as chi or eta.
        2559             :
        2560             :     ! References:
        2561             :     !-----------------------------------------------------------------------
        2562             :
        2563             :     use constants_clubb, only:  &
        2564             :         zero,   &
        2565             :         rc_tol
        2566             :
        2567             :     use model_flags, only: &
        2568             :         iiPDF_ADG1,       & ! Variable(s)
        2569             :         iiPDF_ADG2,       &
        2570             :         iiPDF_new_hybrid
        2571             :
        2572             :     use clubb_precision, only: &
        2573             :         core_rknd  ! Variable(s)
        2574             :
        2575             :     implicit none
        2576             :
        2577             :     ! Input Variables
        2578             :     integer, intent(in) :: &
        2579             :       nz,     & ! Number of model vertical grid levels
        2580             :       ngrdcol   ! Number of grid columns
        2581             :
        2582             :     real( kind = core_rknd ), dimension(ngrdcol,nz), intent(in) :: &
        2583             :       rc_1,           & ! Mean cloud water mixing ratio (1st PDF comp.)  [kg/kg]
        2584             :       rc_2              ! Mean cloud water mixing ratio (2nd PDF comp.)  [kg/kg]
        2585             :
        2586             :     real( kind = core_rknd ), intent(in) :: &
        2587             :       corr_w_x_NN_cloud, & ! Corr. of w and x (ith PDF comp.); cloudy levs [-]
        2588             :       corr_w_x_NN_below    ! Corr. of w and x (ith PDF comp.); clear levs  [-]
        2589             :
        2590             :     integer, intent(in) :: &
        2591             :       iiPDF_type    ! Selected option for the two-component normal (double
        2592             :                     ! Gaussian) PDF type to use for the w, rt, and theta-l (or
        2593             :                     ! w, chi, and eta) portion of CLUBB's multivariate,
        2594             :                     ! two-component PDF.
        2595             :
        2596             :     ! Output Variable
        2597             :     real( kind = core_rknd ), dimension(ngrdcol,nz), intent(out) :: &
        2598             :       corr_w_x_1, & ! Correlation of w and x (1st PDF component)  [-]
        2599             :       corr_w_x_2    ! Correlation of w and x (2nd PDF component)  [-]
        2600             :
        2601             :     ! Local Variables
        2602             :     integer :: i, k
        2603             :
        2604             :     ! Correlation of w and x in the ith PDF component.
        2605             :
        2606             :     ! The PDF variables chi and eta result from a transformation of the PDF
        2607             :     ! involving r_t and theta_l.  The correlation of w and x (whether x is chi
        2608             :     ! or eta) depends on the correlation of w and r_t, the correlation of w and
        2609             :     ! theta_l, as well as the variances of r_t and theta_l, and other factors.
        2610             :     ! The correlation of w and x is subject to change at every vertical level
        2611             :     ! and model time step, and is calculated as part of the CLUBB PDF
        2612             :     ! parameters.
        2613             :
        2614             :     ! The ADG1 PDF fixes the correlation of w and rt and the correlation of
        2615             :     ! w and theta_l to be 0, which means the correlation of w and chi and the
        2616             :     ! correlation of w and eta must also be 0.
        2617             :     if ( ( iiPDF_type == iiPDF_ADG1 .or. iiPDF_type == iiPDF_ADG2 &
        2618             :             .or. iiPDF_type == iiPDF_new_hybrid ) &
        2619           0 :           .and. l_follow_ADG1_PDF_standards ) then
        2620             :
        2621           0 :       corr_w_x_1(:,:) = zero
        2622           0 :       corr_w_x_2(:,:) = zero
        2623             :
        2624             :     else ! use prescribed paramter values
        2625             :
        2626           0 :       do k = 1, nz
        2627           0 :         do i = 1, ngrdcol
        2628             :
        2629           0 :           if ( rc_1(i,k) > rc_tol ) then
        2630           0 :             corr_w_x_1(i,k) = corr_w_x_NN_cloud
        2631             :           else
        2632           0 :             corr_w_x_1(i,k) = corr_w_x_NN_below
        2633             :           end if
        2634             :
        2635           0 :           if ( rc_2(i,k) > rc_tol ) then
        2636           0 :             corr_w_x_2(i,k) = corr_w_x_NN_cloud
        2637             :           else
        2638           0 :             corr_w_x_2(i,k) = corr_w_x_NN_below
        2639             :           end if
        2640             :
        2641             :         end do
        2642             :       end do
        2643             :
        2644             :     end if ! iiPDF_type
        2645             :
        2646           0 :     return
        2647             :
        2648             :   end subroutine component_corr_w_x
        2649             :
        2650             :   !=============================================================================
        2651           0 :   subroutine component_corr_chi_eta( nz, ngrdcol, &
        2652           0 :                                      rc_1, &
        2653           0 :                                      rc_2, &
        2654             :                                      corr_chi_eta_NN_cloud, &
        2655             :                                      corr_chi_eta_NN_below, &
        2656             :                                      l_limit_corr_chi_eta, &
        2657           0 :                                      corr_chi_eta_1,  &
        2658           0 :                                      corr_chi_eta_2 )
        2659             :
        2660             :     ! Description:
        2661             :     ! Calculates the correlation of chi (old s) and eta (old t) within the
        2662             :     ! ith PDF component.
        2663             :
        2664             :     ! References:
        2665             :     !-----------------------------------------------------------------------
        2666             :
        2667             :     use constants_clubb, only:  &
        2668             :         rc_tol, &
        2669             :         max_mag_correlation
        2670             :
        2671             :     use clubb_precision, only: &
        2672             :         core_rknd  ! Constant
        2673             :
        2674             :     implicit none
        2675             :
        2676             :     ! Input Variables
        2677             :     integer, intent(in) :: &
        2678             :       nz,     & ! Number of model vertical grid levels
        2679             :       ngrdcol   ! Number of grid columns
        2680             :
        2681             :     real( kind = core_rknd ), dimension(ngrdcol,nz), intent(in) :: &
        2682             :       rc_1,               & ! Mean cloud water mix. rat. (1st PDF comp.) [kg/kg]&
        2683             :       rc_2                  ! Mean cloud water mix. rat. (2nd PDF comp.) [kg/kg]
        2684             :
        2685             :     real( kind = core_rknd ), intent(in) :: &
        2686             :       corr_chi_eta_NN_cloud, & ! Corr. of chi & eta (ith PDF comp.); cloudy  [-]
        2687             :       corr_chi_eta_NN_below    ! Corr. of chi & eta (ith PDF comp.); clear   [-]
        2688             :
        2689             :     logical, intent(in) :: &
        2690             :       l_limit_corr_chi_eta    ! We must limit the correlation of chi and eta if
        2691             :                               ! we are to take the Cholesky decomposition of the
        2692             :                               ! resulting correlation matrix. This is because a
        2693             :                               ! perfect correlation of chi and eta was found to
        2694             :                               ! be unrealizable.
        2695             :
        2696             :     ! Output Variable
        2697             :     real( kind = core_rknd ), dimension(ngrdcol,nz), intent(out) :: &
        2698             :       corr_chi_eta_1, & ! Correlation of chi and eta (1st PDF component)     [-]
        2699             :       corr_chi_eta_2    ! Correlation of chi and eta (2nd PDF component)     [-]
        2700             :
        2701             :     ! Local Variables
        2702             :     integer :: i, k
        2703             :
        2704             :     ! Correlation of chi (old s) and eta (old t) in the ith PDF component.
        2705             :
        2706             :     ! The PDF variables chi and eta result from a transformation of the PDF
        2707             :     ! involving r_t and theta_l.  The correlation of chi and eta depends on the
        2708             :     ! correlation of r_t and theta_l, as well as the variances of r_t and
        2709             :     ! theta_l, and other factors.  The correlation of chi and eta is subject to
        2710             :     ! change at every vertical level and model time step, and is calculated as
        2711             :     ! part of the CLUBB PDF parameters.
        2712             :
        2713             :     ! WARNING:  this code is inconsistent with the rest of CLUBB's PDF.  This
        2714             :     !           code is necessary because SILHS is lazy and wussy, and only
        2715             :     !           wants to declare correlation arrays at the start of the model
        2716             :     !           run, rather than updating them throughout the model run.
        2717             :
        2718             :
        2719           0 :     do k = 1, nz
        2720           0 :       do i = 1, ngrdcol
        2721             :
        2722           0 :         if ( rc_1(i,k) > rc_tol ) then
        2723           0 :           corr_chi_eta_1(i,k) = corr_chi_eta_NN_cloud
        2724             :         else
        2725           0 :           corr_chi_eta_1(i,k) = corr_chi_eta_NN_below
        2726             :         end if
        2727             :       end do
        2728             :     end do
        2729             :
        2730           0 :     do k = 1, nz
        2731           0 :       do i = 1, ngrdcol
        2732           0 :         if ( rc_2(i,k) > rc_tol ) then
        2733           0 :           corr_chi_eta_2(i,k) = corr_chi_eta_NN_cloud
        2734             :         else
        2735           0 :           corr_chi_eta_2(i,k) = corr_chi_eta_NN_below
        2736             :         end if
        2737             :       end do
        2738             :     end do
        2739             :
        2740             :
        2741             :
        2742             :     ! We cannot have a perfect correlation of chi (old s) and eta (old t) if we
        2743             :     ! plan to decompose this matrix and we don't want the Cholesky_factor code
        2744             :     ! to throw a fit.
        2745           0 :     if ( l_limit_corr_chi_eta ) then
        2746             :
        2747           0 :       do k = 1, nz
        2748           0 :         do i = 1, ngrdcol
        2749           0 :           corr_chi_eta_1(i,k) = max( min( corr_chi_eta_1(i,k), max_mag_correlation ), &
        2750           0 :                                      -max_mag_correlation )
        2751             :         end do
        2752             :       end do
        2753             :
        2754           0 :       do k = 1, nz
        2755           0 :         do i = 1, ngrdcol
        2756           0 :           corr_chi_eta_2(i,k) = max( min( corr_chi_eta_2(i,k), max_mag_correlation ), &
        2757           0 :                                      -max_mag_correlation )
        2758             :         end do
        2759             :       end do
        2760             :
        2761             :     end if
        2762             :
        2763           0 :     return
        2764             :
        2765             :   end subroutine component_corr_chi_eta
        2766             :
        2767             :   !=============================================================================
        2768           0 :   subroutine component_corr_w_hm_n_ip( nz, ngrdcol, &
        2769           0 :                                        corr_w_hm_1_n_in, rc_1, &
        2770           0 :                                        corr_w_hm_2_n_in, rc_2, &
        2771             :                                        corr_w_hm_n_NL_cloud, &
        2772             :                                        corr_w_hm_n_NL_below, &
        2773             :                                        l_calc_w_corr, &
        2774           0 :                                        corr_w_hm_1_n, &
        2775           0 :                                        corr_w_hm_2_n )
        2776             :
        2777             :     ! Description:
        2778             :     ! Calculates the in-precip correlation of w and the natural logarithm of a
        2779             :     ! hydrometeor species within the ith PDF component.
        2780             :
        2781             :     ! References:
        2782             :     !-----------------------------------------------------------------------
        2783             :
        2784             :     use constants_clubb, only:  &
        2785             :         rc_tol
        2786             :
        2787             :     use clubb_precision, only: &
        2788             :         core_rknd  ! Variable(s)
        2789             :
        2790             :     implicit none
        2791             :
        2792             :     ! Input Variables
        2793             :     integer, intent(in) :: &
        2794             :       nz,     & ! Number of model vertical grid levels
        2795             :       ngrdcol   ! Number of grid columns
        2796             :
        2797             :     real( kind = core_rknd ), dimension(ngrdcol,nz), intent(in) :: &
        2798             :       corr_w_hm_1_n_in, & ! Correlation of w and ln hm (1st PDF comp.) ip    [-]
        2799             :       corr_w_hm_2_n_in, & ! Correlation of w and ln hm (2nd PDF comp.) ip    [-]
        2800             :       rc_1,             & ! Mean cloud water mix. ratio (1st PDF comp.)  [kg/kg]
        2801             :       rc_2                ! Mean cloud water mix. ratio (2nd PDF comp.)  [kg/kg]
        2802             :
        2803             :     real( kind = core_rknd ), intent(in) :: &
        2804             :       corr_w_hm_n_NL_cloud, & ! Corr. of w & ln hm (ith PDF comp.) ip; cloud [-]
        2805             :       corr_w_hm_n_NL_below    ! Corr. of w & ln hm (ith PDF comp.) ip; clear [-]
        2806             :
        2807             :     logical, intent(in) :: &
        2808             :       l_calc_w_corr ! Calculate the correlations between w and the hydrometeors
        2809             :
        2810             :     ! Output Variables
        2811             :     real( kind = core_rknd ), dimension(ngrdcol,nz), intent(out) :: &
        2812             :       corr_w_hm_1_n, & ! Correlation of w and ln hm (1st PDF component) ip   [-]
        2813             :       corr_w_hm_2_n    ! Correlation of w and ln hm (2nd PDF component) ip   [-]
        2814             :
        2815             :     ! Local Variables
        2816             :     integer :: i, k
        2817             :
        2818             :
        2819             :     ! Correlation (in-precip) of w and the natural logarithm of the hydrometeor
        2820             :     ! in the ith PDF component.
        2821           0 :     if ( l_calc_w_corr ) then
        2822             :
        2823           0 :       corr_w_hm_1_n(:,:) = corr_w_hm_1_n_in(:,:)
        2824           0 :       corr_w_hm_2_n(:,:) = corr_w_hm_2_n_in(:,:)
        2825             :
        2826             :
        2827             :     else
        2828             :
        2829           0 :         do k = 1, nz
        2830           0 :           do i = 1, ngrdcol
        2831             :
        2832           0 :             if ( rc_1(i,k) > rc_tol ) then
        2833           0 :                corr_w_hm_1_n(i,k) = corr_w_hm_n_NL_cloud
        2834             :             else
        2835           0 :                corr_w_hm_1_n(i,k) = corr_w_hm_n_NL_below
        2836             :             end if
        2837             :
        2838           0 :             if ( rc_2(i,k) > rc_tol ) then
        2839           0 :                corr_w_hm_2_n(i,k) = corr_w_hm_n_NL_cloud
        2840             :             else
        2841           0 :                corr_w_hm_2_n(i,k) = corr_w_hm_n_NL_below
        2842             :             end if
        2843             :           end do
        2844             :         end do
        2845             :
        2846             :     end if ! l_calc_w_corr
        2847             :
        2848           0 :     return
        2849             :
        2850             :   end subroutine component_corr_w_hm_n_ip
        2851             :
        2852             :   !=============================================================================
        2853           0 :   subroutine component_corr_x_hm_n_ip( nz, ngrdcol, &
        2854           0 :                                        rc_1, &
        2855           0 :                                        rc_2, &
        2856             :                                        corr_x_hm_n_NL_cloud, &
        2857             :                                        corr_x_hm_n_NL_below, &
        2858           0 :                                        corr_x_hm_1_n, &
        2859           0 :                                        corr_x_hm_2_n )
        2860             :
        2861             :     ! Description:
        2862             :     ! Calculates the in-precip correlation of x and a hydrometeor species
        2863             :     ! within the ith PDF component.  Here, x is a variable with a normally
        2864             :     ! distributed individual marginal PDF, such as chi or eta.
        2865             :
        2866             :     ! References:
        2867             :     !-----------------------------------------------------------------------
        2868             :
        2869             :     use constants_clubb, only:  &
        2870             :         rc_tol
        2871             :
        2872             :     use clubb_precision, only: &
        2873             :         core_rknd  ! Variable(s)
        2874             :
        2875             :     implicit none
        2876             :
        2877             :     ! Input Variables
        2878             :     integer, intent(in) :: &
        2879             :       nz,     & ! Number of model vertical grid levels
        2880             :       ngrdcol   ! Number of grid columns
        2881             :
        2882             :     real( kind = core_rknd ), dimension(ngrdcol,nz), intent(in) :: &
        2883             :       rc_1,         & ! Mean cloud water mixing ratio (1st PDF comp.)   [kg/kg]
        2884             :       rc_2            ! Mean cloud water mixing ratio (2nd PDF comp.)   [kg/kg]
        2885             :
        2886             :
        2887             :     real( kind = core_rknd ), intent(in) :: &
        2888             :       corr_x_hm_n_NL_cloud, & ! Corr. of x and ln hm (ith PDF comp.) ip     [-]
        2889             :       corr_x_hm_n_NL_below    ! Corr. of x and ln hm (ith PDF comp.) ip     [-]
        2890             :
        2891             :     ! Output Variables
        2892             :     real( kind = core_rknd ), dimension(ngrdcol,nz), intent(out) :: &
        2893             :       corr_x_hm_1_n, & ! Correlation of x and ln hm (1st PDF component) ip  [-]
        2894             :       corr_x_hm_2_n    ! Correlation of x and ln hm (2nd PDF component) ip  [-]
        2895             :
        2896             :     ! Local Variables
        2897             :     integer :: i, k
        2898             :
        2899           0 :     do k = 1, nz
        2900           0 :       do i = 1, ngrdcol
        2901             :
        2902           0 :         if ( rc_1(i,k) > rc_tol ) then
        2903           0 :           corr_x_hm_1_n(i,k) = corr_x_hm_n_NL_cloud
        2904             :         else
        2905           0 :           corr_x_hm_1_n(i,k) = corr_x_hm_n_NL_below
        2906             :         end if
        2907             :
        2908           0 :         if ( rc_2(i,k) > rc_tol ) then
        2909           0 :           corr_x_hm_2_n(i,k) = corr_x_hm_n_NL_cloud
        2910             :         else
        2911           0 :           corr_x_hm_2_n(i,k) = corr_x_hm_n_NL_below
        2912             :         end if
        2913             :
        2914             :       end do
        2915             :     end do
        2916             :
        2917           0 :     return
        2918             :
        2919             :   end subroutine component_corr_x_hm_n_ip
        2920             :
        2921             :   !=============================================================================
        2922           0 :   subroutine component_corr_hmx_hmy_n_ip( nz, ngrdcol, &
        2923           0 :                                           rc_1, &
        2924           0 :                                           rc_2, &
        2925             :                                           corr_hmx_hmy_n_LL_cloud, &
        2926             :                                           corr_hmx_hmy_n_LL_below, &
        2927           0 :                                           corr_hmx_hmy_1_n, &
        2928           0 :                                           corr_hmx_hmy_2_n )
        2929             :
        2930             :     ! Description:
        2931             :     ! Calculates the in-precip correlation of the natural logarithms of
        2932             :     ! hydrometeor x and hydrometeor y within the ith PDF component.
        2933             :
        2934             :     ! References:
        2935             :     !-----------------------------------------------------------------------
        2936             :
        2937             :     use constants_clubb, only:  &
        2938             :         rc_tol
        2939             :
        2940             :     use clubb_precision, only: &
        2941             :         core_rknd  ! Variable(s)
        2942             :
        2943             :     implicit none
        2944             :
        2945             :     ! Input Variables
        2946             :     integer, intent(in) :: &
        2947             :       nz,     & ! Number of model vertical grid levels
        2948             :       ngrdcol   ! Number of grid columns
        2949             :
        2950             :     real( kind = core_rknd ), dimension(ngrdcol,nz), intent(in) :: &
        2951             :       rc_1,         & ! Mean cloud water mixing ratio (ith PDF comp.) [kg/kg]
        2952             :       rc_2            ! Mean cloud water mixing ratio (ith PDF comp.) [kg/kg]
        2953             :
        2954             :     real( kind = core_rknd ), intent(in) :: &
        2955             :       corr_hmx_hmy_n_LL_cloud, & ! Corr.: ln hmx & ln hmy (ith PDF comp.) ip [-]
        2956             :       corr_hmx_hmy_n_LL_below    ! Corr.: ln hmx & ln hmy (ith PDF comp.) ip [-]
        2957             :
        2958             :     ! Output Variable
        2959             :     real( kind = core_rknd ), dimension(ngrdcol,nz) :: &
        2960             :       corr_hmx_hmy_1_n, & ! Corr. of ln hmx & ln hmy (ith PDF comp.) ip      [-]
        2961             :       corr_hmx_hmy_2_n    ! Corr. of ln hmx & ln hmy (ith PDF comp.) ip      [-]
        2962             :
        2963             :     ! Local Variable
        2964             :     integer :: i, k
        2965             :
        2966             :
        2967             :     ! Correlation (in-precip) of the natural logarithms of hydrometeor x and
        2968             :     ! hydrometeor y in the ith PDF component.
        2969           0 :     do k = 1, nz
        2970           0 :       do i = 1, ngrdcol
        2971             :
        2972           0 :         if ( rc_1(i,k) > rc_tol ) then
        2973           0 :           corr_hmx_hmy_1_n(i,k) = corr_hmx_hmy_n_LL_cloud
        2974             :         else
        2975           0 :           corr_hmx_hmy_1_n(i,k) = corr_hmx_hmy_n_LL_below
        2976             :         end if
        2977             :
        2978           0 :         if ( rc_2(i,k) > rc_tol ) then
        2979           0 :           corr_hmx_hmy_2_n(i,k) = corr_hmx_hmy_n_LL_cloud
        2980             :         else
        2981           0 :           corr_hmx_hmy_2_n(i,k) = corr_hmx_hmy_n_LL_below
        2982             :         end if
        2983             :
        2984             :       end do
        2985             :     end do
        2986             :
        2987           0 :     return
        2988             :
        2989             :   end subroutine component_corr_hmx_hmy_n_ip
        2990             :
        2991             :   !=============================================================================
        2992           0 :   subroutine component_corr_eta_hm_n_ip( nz, ngrdcol, &
        2993           0 :                                          corr_chi_eta_1, &
        2994           0 :                                          corr_chi_hm_n_1, &
        2995           0 :                                          corr_chi_eta_2, &
        2996           0 :                                          corr_chi_hm_n_2, &
        2997           0 :                                          corr_eta_hm_n_1, &
        2998           0 :                                          corr_eta_hm_n_2)
        2999             :     ! Description:
        3000             :     ! Estimates the correlation of eta and the natural logarithm of a
        3001             :     ! hydrometeor species using the correlation of chi and eta and the
        3002             :     ! correlation of chi and the natural logarithm of the hydrometeor.  This
        3003             :     ! facilities the Cholesky decomposability of the correlation array that will
        3004             :     ! inevitably be decomposed for SILHS purposes. Without this estimation, we
        3005             :     ! have found that the resulting correlation matrix cannot be decomposed.
        3006             :
        3007             :     ! References:
        3008             :     !-----------------------------------------------------------------------
        3009             :
        3010             :     use clubb_precision, only: &
        3011             :         core_rknd       ! Constant
        3012             :
        3013             :     implicit none
        3014             :
        3015             :     ! Input Variables
        3016             :     integer, intent(in) :: &
        3017             :       nz,     & ! Number of model vertical grid levels
        3018             :       ngrdcol   ! Number of grid columns
        3019             :
        3020             :
        3021             :     real( kind = core_rknd ), dimension(ngrdcol,nz), intent(in) :: &
        3022             :       corr_chi_eta_1,  & ! Component correlation of chi and eta              [-]
        3023             :       corr_chi_eta_2,  & ! Component correlation of chi and eta              [-]
        3024             :       corr_chi_hm_n_1, & ! Component correlation of chi and ln hm            [-]
        3025             :       corr_chi_hm_n_2    ! Component correlation of chi and ln hm            [-]
        3026             :
        3027             :     ! Output Variables
        3028             :     real( kind = core_rknd ), dimension(ngrdcol,nz), intent(out) :: &
        3029             :       corr_eta_hm_n_1, & ! Component correlation of eta and ln hm            [-]
        3030             :       corr_eta_hm_n_2    ! Component correlation of eta and ln hm            [-]
        3031             :
        3032             :
        3033           0 :     corr_eta_hm_n_1 = corr_chi_eta_1 * corr_chi_hm_n_1
        3034           0 :     corr_eta_hm_n_2 = corr_chi_eta_2 * corr_chi_hm_n_2
        3035             :
        3036             :
        3037           0 :     return
        3038             :
        3039             :   end subroutine component_corr_eta_hm_n_ip
        3040             :
        3041             :   !=============================================================================
        3042           0 :   subroutine norm_transform_mean_stdev( nz, ngrdcol, &
        3043             :                                         hydromet_dim, hm_metadata, &
        3044           0 :                                         hm_1, hm_2, &
        3045           0 :                                         Ncnm, pdf_dim, &
        3046           0 :                                         mu_x_1, mu_x_2, &
        3047           0 :                                         sigma_x_1, sigma_x_2, &
        3048           0 :                                         sigma2_on_mu2_ip_1, &
        3049           0 :                                         sigma2_on_mu2_ip_2, &
        3050             :                                         l_const_Nc_in_cloud, &
        3051           0 :                                         mu_x_1_n, mu_x_2_n, &
        3052           0 :                                         sigma_x_1_n, sigma_x_2_n )
        3053             :
        3054             :     ! Description:
        3055             :     ! Transforms the means and the standard deviations of PDF variables that
        3056             :     ! have assumed lognormal distributions -- which are precipitating
        3057             :     ! hydrometeors (in precipitation) and N_cn -- to normal space for each PDF
        3058             :     ! component.
        3059             :
        3060             :     ! References:
        3061             :     !-----------------------------------------------------------------------
        3062             :
        3063             :     use constants_clubb, only:  &
        3064             :         Ncn_tol, &  ! Constant(s)
        3065             :         zero
        3066             :
        3067             :     use pdf_utilities, only: &
        3068             :         mean_L2N,  & ! Procedure(s)
        3069             :         stdev_L2N
        3070             :
        3071             :     use index_mapping, only: &
        3072             :         pdf2hydromet_idx  ! Procedure(s)
        3073             :
        3074             :     use corr_varnce_module, only: &
        3075             :       hm_metadata_type
        3076             :
        3077             :     use clubb_precision, only: &
        3078             :         core_rknd  ! Variable(s)
        3079             :
        3080             :     implicit none
        3081             :
        3082             :     !--------------------------- Input Variables ---------------------------
        3083             :     integer, intent(in) :: &
        3084             :       nz,           & ! Number of model vertical grid levels
        3085             :       pdf_dim,      & ! Number of variables in CLUBB's PDF
        3086             :       ngrdcol,      & ! Number of grid columns
        3087             :       hydromet_dim    ! Number of hydrometeor species
        3088             :
        3089             :     type (hm_metadata_type), intent(in) :: &
        3090             :       hm_metadata
        3091             :
        3092             :     real( kind = core_rknd ), dimension(ngrdcol,nz,hydromet_dim), intent(in) :: &
        3093             :       hm_1, & ! Mean of a precip. hydrometeor (1st PDF component)   [units vary]
        3094             :       hm_2    ! Mean of a precip. hydrometeor (2nd PDF component)   [units vary]
        3095             :
        3096             :     real( kind = core_rknd ), dimension(ngrdcol,nz), intent(in) :: &
        3097             :       Ncnm    ! Mean cloud nuclei concentration, < N_cn >               [num/kg]
        3098             :
        3099             :     real( kind = core_rknd ), dimension(ngrdcol,nz,pdf_dim), intent(in) :: &
        3100             :       mu_x_1,    & ! Mean array of PDF vars. (1st PDF component)    [units vary]
        3101             :       mu_x_2,    & ! Mean array of PDF vars. (2nd PDF component)    [units vary]
        3102             :       sigma_x_1, & ! Standard deviation array of PDF vars (comp. 1) [units vary]
        3103             :       sigma_x_2    ! Standard deviation array of PDF vars (comp. 2) [units vary]
        3104             :
        3105             :     real( kind = core_rknd ), dimension(ngrdcol,nz,pdf_dim), intent(in) :: &
        3106             :       sigma2_on_mu2_ip_1, & ! Prescribed ratio array: sigma_hm_1^2/mu_hm_1^2 [-]
        3107             :       sigma2_on_mu2_ip_2    ! Prescribed ratio array: sigma_hm_2^2/mu_hm_2^2 [-]
        3108             :
        3109             :     logical, intent(in) :: &
        3110             :       l_const_Nc_in_cloud ! Use a constant cloud droplet conc. within cloud (K&K)
        3111             :
        3112             :     !--------------------------- Output Variables ---------------------------
        3113             :     real( kind = core_rknd ), dimension(ngrdcol,nz,pdf_dim), intent(out) :: &
        3114             :       mu_x_1_n,    & ! Mean array (normal space): PDF vars. (comp. 1) [un. vary]
        3115             :       mu_x_2_n,    & ! Mean array (normal space): PDF vars. (comp. 2) [un. vary]
        3116             :       sigma_x_1_n, & ! Std. dev. array (normal space): PDF vars (comp. 1) [u.v.]
        3117             :       sigma_x_2_n    ! Std. dev. array (normal space): PDF vars (comp. 2) [u.v.]
        3118             :
        3119             :     !--------------------------- Local Variable ---------------------------
        3120             :     integer :: ivar, hm_idx, k, i  ! Indices
        3121             :
        3122             :     ! Just to avoid typing hm_metadata%iiPDF_x everywhere
        3123             :     integer ::  &
        3124             :       iiPDF_w,   &
        3125             :       iiPDF_chi, &
        3126             :       iiPDF_eta, &
        3127             :       iiPDF_Ncn
        3128             :
        3129             :     !--------------------------- Begin Code ---------------------------
        3130             :
        3131           0 :     iiPDF_chi = hm_metadata%iiPDF_chi
        3132           0 :     iiPDF_eta = hm_metadata%iiPDF_eta
        3133           0 :     iiPDF_w   = hm_metadata%iiPDF_w
        3134           0 :     iiPDF_Ncn = hm_metadata%iiPDF_Ncn
        3135             :
        3136             :     ! The means and standard deviations in each PDF component of w, chi (old s),
        3137             :     ! and eta (old t) do not need to be transformed to normal space, since w,
        3138             :     ! chi, and eta already follow assumed normal distributions in each PDF
        3139             :     ! component.  The normal space means and standard deviations are the same as
        3140             :     ! the actual means and standard deviations.
        3141           0 :     do k = 1, nz
        3142           0 :       mu_x_1_n(:,k,iiPDF_chi) = mu_x_1(:,k,iiPDF_chi)
        3143           0 :       mu_x_1_n(:,k,iiPDF_eta) = mu_x_1(:,k,iiPDF_eta)
        3144           0 :       mu_x_1_n(:,k,iiPDF_w)   = mu_x_1(:,k,iiPDF_w)
        3145             :     end do
        3146             :
        3147           0 :     do k = 1, nz
        3148           0 :       mu_x_2_n(:,k,iiPDF_chi) = mu_x_2(:,k,iiPDF_chi)
        3149           0 :       mu_x_2_n(:,k,iiPDF_eta) = mu_x_2(:,k,iiPDF_eta)
        3150           0 :       mu_x_2_n(:,k,iiPDF_w)   = mu_x_2(:,k,iiPDF_w)
        3151             :     end do
        3152             :
        3153           0 :     do k = 1, nz
        3154           0 :       sigma_x_1_n(:,k,iiPDF_chi) = sigma_x_1(:,k,iiPDF_chi)
        3155           0 :       sigma_x_1_n(:,k,iiPDF_eta) = sigma_x_1(:,k,iiPDF_eta)
        3156           0 :       sigma_x_1_n(:,k,iiPDF_w)   = sigma_x_1(:,k,iiPDF_w)
        3157             :     end do
        3158             :
        3159           0 :     do k = 1, nz
        3160           0 :       sigma_x_2_n(:,k,iiPDF_chi) = sigma_x_2(:,k,iiPDF_chi)
        3161           0 :       sigma_x_2_n(:,k,iiPDF_eta) = sigma_x_2(:,k,iiPDF_eta)
        3162           0 :       sigma_x_2_n(:,k,iiPDF_w)   = sigma_x_2(:,k,iiPDF_w)
        3163             :     end do
        3164             :
        3165             :     !!! Transform the mean and standard deviation to normal space in each PDF
        3166             :     !!! component for variables that have an assumed lognormal distribution,
        3167             :     !!! given the mean and standard deviation in each PDF component for those
        3168             :     !!! variables.  A precipitating hydrometeor has an assumed lognormal
        3169             :     !!! distribution in precipitation in each PDF component.  Simplified cloud
        3170             :     !!! nuclei concentration, N_cn, has an assumed lognormal distribution in
        3171             :     !!! each PDF component, and furthermore, mu_Ncn_1 = mu_Ncn_2 and
        3172             :     !!! sigma_Ncn_1 = sigma_Ncn_2, so N_cn has an assumed single lognormal
        3173             :     !!! distribution over the entire domain.
        3174             :
        3175             :     ! Normal space mean of simplified cloud nuclei concentration, N_cn,
        3176             :     ! in PDF component 1.
        3177           0 :     do k = 1, nz
        3178           0 :       do i = 1, ngrdcol
        3179             :
        3180           0 :         if ( Ncnm(i,k) >= Ncn_tol ) then
        3181             :
        3182           0 :            mu_x_1_n(i,k,iiPDF_Ncn) = mean_L2N( mu_x_1(i,k,iiPDF_Ncn), &
        3183           0 :                                                sigma2_on_mu2_ip_1(i,k,iiPDF_Ncn) )
        3184             :
        3185             :         else
        3186             :
        3187             :            ! Mean simplified cloud nuclei concentration in PDF component 1 is less
        3188             :            ! than the tolerance amount.  It is considered to have a value of 0.
        3189             :            ! There are not any cloud nuclei or cloud at this grid level.  The value
        3190             :            ! of mu_Ncn_1_n should be -inf.  It will be set to -huge for purposes of
        3191             :            ! assigning it a value.
        3192           0 :            mu_x_1_n(i,k,iiPDF_Ncn) = -huge( mu_x_1(i,k,iiPDF_Ncn) )
        3193             :
        3194             :         end if
        3195             :
        3196             :       end do
        3197             :     end do
        3198             :
        3199             :     ! Normal space mean of simplified cloud nuclei concentration, N_cn,
        3200             :     ! in PDF component 2.
        3201           0 :     do k = 1, nz
        3202           0 :       do i = 1, ngrdcol
        3203             :
        3204           0 :         if ( Ncnm(i,k) >= Ncn_tol ) then
        3205             :
        3206           0 :            mu_x_2_n(i,k,iiPDF_Ncn) = mean_L2N( mu_x_2(i,k,iiPDF_Ncn), &
        3207           0 :                                                sigma2_on_mu2_ip_1(i,k,iiPDF_Ncn) )
        3208             :
        3209             :         else
        3210             :
        3211             :            ! Mean simplified cloud nuclei concentration in PDF component 1 is less
        3212             :            ! than the tolerance amount.  It is considered to have a value of 0.
        3213             :            ! There are not any cloud nuclei or cloud at this grid level.  The value
        3214             :            ! of mu_Ncn_1_n should be -inf.  It will be set to -huge for purposes of
        3215             :            ! assigning it a value.
        3216           0 :            mu_x_2_n(i,k,iiPDF_Ncn) = -huge( mu_x_2(i,k,iiPDF_Ncn) )
        3217             :
        3218             :         end if
        3219             :
        3220             :       end do
        3221             :     end do
        3222             :
        3223             :     ! Normal space standard deviation of simplified cloud nuclei concentration,
        3224             :     ! N_cn, in PDF components 1 and 2.
        3225           0 :     if ( l_const_Nc_in_cloud ) then
        3226             :       ! Ncn does not vary in the grid box.
        3227           0 :       sigma_x_1_n(:,:,iiPDF_Ncn) = zero
        3228           0 :       sigma_x_2_n(:,:,iiPDF_Ncn) = zero
        3229             :     else
        3230             :        ! Ncn (perhaps) varies in the grid box.
        3231           0 :        sigma_x_1_n(:,:,iiPDF_Ncn) = stdev_L2N( sigma2_on_mu2_ip_1(:,:,iiPDF_Ncn) )
        3232           0 :        sigma_x_2_n(:,:,iiPDF_Ncn) = stdev_L2N( sigma2_on_mu2_ip_2(:,:,iiPDF_Ncn) )
        3233             :     end if
        3234             :
        3235             :     ! Normal space precipitating hydrometeor means and standard deviations.
        3236           0 :     do ivar = iiPDF_Ncn+1, pdf_dim, 1
        3237             :
        3238           0 :       hm_idx = pdf2hydromet_idx(ivar,hm_metadata)
        3239             :
        3240             :       ! Normal space mean of a precipitating hydrometeor, hm, in PDF
        3241             :       ! component 1.
        3242           0 :       do k = 1, nz
        3243           0 :         do i = 1, ngrdcol
        3244             :
        3245           0 :           if ( hm_1(i,k,hm_idx) >= hm_metadata%hydromet_tol(hm_idx) ) then
        3246             :
        3247           0 :             mu_x_1_n(i,k,ivar) = mean_L2N( mu_x_1(i,k,ivar), &
        3248           0 :                                            sigma2_on_mu2_ip_1(i,k,ivar) )
        3249             :
        3250             :           else
        3251             :
        3252             :             ! The mean of a precipitating hydrometeor in PDF component 1 is less
        3253             :             ! than its tolerance amount.  It is considered to have a value of 0.
        3254             :             ! There is not any of this precipitating hydrometeor in the 1st PDF
        3255             :             ! component at this grid level.  The in-precip mean of this
        3256             :             ! precipitating hydrometeor (1st PDF component) is also 0.  The value
        3257             :             ! of mu_hm_1_n should be -inf.  It will be set to -huge for purposes
        3258             :             ! of assigning it a value.
        3259           0 :             mu_x_1_n(i,k,ivar) = -huge( mu_x_1(i,k,ivar) )
        3260             :
        3261             :           end if
        3262             :
        3263             :         end do
        3264             :       end do
        3265             :
        3266             :       ! Normal space standard deviation of a precipitating hydrometeor, hm, in
        3267             :       ! PDF component 1.
        3268           0 :       sigma_x_1_n(:,:,ivar) = stdev_L2N( sigma2_on_mu2_ip_1(:,:,ivar) )
        3269             :
        3270             :       ! Normal space mean of a precipitating hydrometeor, hm, in PDF
        3271             :       ! component 2.
        3272           0 :       do k = 1, nz
        3273           0 :         do i = 1, ngrdcol
        3274             :
        3275           0 :           if ( hm_2(i,k,hm_idx) >= hm_metadata%hydromet_tol(hm_idx) ) then
        3276             :
        3277             :             mu_x_2_n(i,k,ivar) = mean_L2N( mu_x_2(i,k,ivar), &
        3278           0 :                                          sigma2_on_mu2_ip_2(i,k,ivar) )
        3279             :
        3280             :           else
        3281             :
        3282             :             ! The mean of a precipitating hydrometeor in PDF component 2 is less
        3283             :             ! than its tolerance amount.  It is considered to have a value of 0.
        3284             :             ! There is not any of this precipitating hydrometeor in the 2nd PDF
        3285             :             ! component at this grid level.  The in-precip mean of this
        3286             :             ! precipitating hydrometeor (2nd PDF component) is also 0.  The value
        3287             :             ! of mu_hm_2_n should be -inf.  It will be set to -huge for purposes
        3288             :             ! of assigning it a value.
        3289           0 :             mu_x_2_n(i,k,ivar) = -huge( mu_x_2(i,k,ivar) )
        3290             :
        3291             :           end if
        3292             :
        3293             :         end do
        3294             :       end do
        3295             :
        3296             :       ! Normal space standard deviation of a precipitating hydrometeor, hm, in
        3297             :       ! PDF component 2.
        3298           0 :       sigma_x_2_n(:,:,ivar) = stdev_L2N( sigma2_on_mu2_ip_2(:,:,ivar) )
        3299             :
        3300             :     end do ! ivar = iiPDF_Ncn+1, pdf_dim, 1
        3301             :
        3302             :
        3303           0 :     return
        3304             :
        3305             :   end subroutine norm_transform_mean_stdev
        3306             :
        3307             :   !=============================================================================
        3308           0 :   subroutine denorm_transform_corr( nz, ngrdcol, pdf_dim, hm_metadata, &
        3309           0 :                                     sigma_x_1_n, sigma_x_2_n, &
        3310           0 :                                     sigma2_on_mu2_ip_1, sigma2_on_mu2_ip_2, &
        3311           0 :                                     corr_array_1_n, &
        3312           0 :                                     corr_array_2_n, &
        3313           0 :                                     corr_array_1, corr_array_2 )
        3314             :
        3315             :     ! Description:
        3316             :     ! Calculates the true or "real-space" correlations between PDF variables,
        3317             :     ! where at least one of the variables that is part of a correlation has an
        3318             :     ! assumed lognormal distribution -- which are the precipitating hydrometeors
        3319             :     ! (in precipitation) and N_cn.
        3320             :
        3321             :     ! References:
        3322             :     !-----------------------------------------------------------------------
        3323             :
        3324             :     use constants_clubb, only : &
        3325             :         one
        3326             :
        3327             :     use pdf_utilities, only: &
        3328             :         corr_NN2NL, & ! Procedure(s)
        3329             :         corr_NN2LL
        3330             :
        3331             :     use corr_varnce_module, only: &
        3332             :         hm_metadata_type
        3333             :
        3334             :     use clubb_precision, only: &
        3335             :         core_rknd  ! Variable(s)
        3336             :
        3337             :     implicit none
        3338             :
        3339             :     !--------------------------- Input Variables ---------------------------
        3340             :     integer, intent(in) :: &
        3341             :       nz,      & ! Number of vertical levels
        3342             :       pdf_dim, & ! Number of variables
        3343             :       ngrdcol    ! Number of grid columns
        3344             :
        3345             :     type (hm_metadata_type), intent(in) :: &
        3346             :       hm_metadata
        3347             :
        3348             :     real( kind = core_rknd ), dimension(ngrdcol,nz,pdf_dim), intent(in) :: &
        3349             :       sigma_x_1_n, & ! Std. dev. array (normal space): PDF vars (comp. 1) [u.v.]
        3350             :       sigma_x_2_n    ! Std. dev. array (normal space): PDF vars (comp. 2) [u.v.]
        3351             :
        3352             :     real( kind = core_rknd ), dimension(ngrdcol,nz,pdf_dim), intent(in) :: &
        3353             :       sigma2_on_mu2_ip_1, & ! Ratio array sigma_hm_1^2/mu_hm_1^2             [-]
        3354             :       sigma2_on_mu2_ip_2    ! Ratio array sigma_hm_2^2/mu_hm_2^2             [-]
        3355             :
        3356             :     real( kind = core_rknd ), dimension(ngrdcol,nz,pdf_dim,pdf_dim), &
        3357             :     intent(in) :: &
        3358             :       corr_array_1_n, & ! Corr. array (normal space) of PDF vars. (comp. 1)  [-]
        3359             :       corr_array_2_n    ! Corr. array (normal space) of PDF vars. (comp. 2)  [-]
        3360             :
        3361             :     !--------------------------- Output Variables ---------------------------
        3362             :     real( kind = core_rknd ), dimension(ngrdcol,nz,pdf_dim,pdf_dim), &
        3363             :     intent(out) :: &
        3364             :       corr_array_1, & ! Correlation array of PDF vars. (comp. 1)             [-]
        3365             :       corr_array_2    ! Correlation array of PDF vars. (comp. 2)             [-]
        3366             :
        3367             :     !--------------------------- Local Variables ---------------------------
        3368             :     integer :: ivar, jvar ! Loop indices
        3369             :
        3370             :     ! Just to avoid typing hm_metadata%iiPDF_x everywhere
        3371             :     integer :: &
        3372             :       iiPDF_chi, &
        3373             :       iiPDF_eta, &
        3374             :       iiPDF_w,   &
        3375             :       iiPDF_Ncn
        3376             :
        3377             :     !------------------------ Begin Code ------------------------
        3378             :
        3379           0 :     iiPDF_chi = hm_metadata%iiPDF_chi
        3380           0 :     iiPDF_eta = hm_metadata%iiPDF_eta
        3381           0 :     iiPDF_w   = hm_metadata%iiPDF_w
        3382           0 :     iiPDF_Ncn = hm_metadata%iiPDF_Ncn
        3383             :
        3384             :     ! Initialize diagonal elements to one
        3385           0 :     do ivar = 1, pdf_dim
        3386           0 :       corr_array_1(:,:,ivar,ivar) = one
        3387           0 :       corr_array_2(:,:,ivar,ivar) = one
        3388             :     end do
        3389             :
        3390             :     ! The correlations in each PDF component between two of w, chi (old s), and
        3391             :     ! eta (old t) do not need to be transformed to standard space, since w, chi,
        3392             :     ! and eta follow assumed normal distributions in each PDF component.  The
        3393             :     ! normal space correlations between any two of these variables are the same
        3394             :     ! as the actual correlations.
        3395           0 :     corr_array_1(:,:,iiPDF_eta,iiPDF_chi) = corr_array_1_n(:,:,iiPDF_eta,iiPDF_chi)
        3396           0 :     corr_array_1(:,:,iiPDF_w,iiPDF_chi)   = corr_array_1_n(:,:,iiPDF_w,iiPDF_chi)
        3397           0 :     corr_array_1(:,:,iiPDF_w,iiPDF_eta)   = corr_array_1_n(:,:,iiPDF_w,iiPDF_eta)
        3398             :
        3399           0 :     corr_array_2(:,:,iiPDF_eta,iiPDF_chi) = corr_array_2_n(:,:,iiPDF_eta,iiPDF_chi)
        3400           0 :     corr_array_2(:,:,iiPDF_w,iiPDF_chi)   = corr_array_2_n(:,:,iiPDF_w,iiPDF_chi)
        3401           0 :     corr_array_2(:,:,iiPDF_w,iiPDF_eta)   = corr_array_2_n(:,:,iiPDF_w,iiPDF_eta)
        3402             :
        3403             :     !!! Calculate the true correlation of variables that have an assumed normal
        3404             :     !!! distribution and variables that have an assumed lognormal distribution
        3405             :     !!! for the ith PDF component, given their normal space correlation and the
        3406             :     !!! normal space standard deviation of the variable with the assumed
        3407             :     !!! lognormal distribution.
        3408             :
        3409             :     ! Transform the correlations between chi/eta/w and N_cn to standard space.
        3410             :
        3411             :     ! Transform the correlation of chi (old s) and N_cn to standard space in PDF component 1.
        3412             :     call corr_NN2NL( nz, ngrdcol, & ! intent(in)
        3413             :                      corr_array_1_n(:,:,iiPDF_Ncn,iiPDF_chi), & ! intent(in)
        3414             :                      sigma_x_1_n(:,:,iiPDF_Ncn), sigma2_on_mu2_ip_1(:,:,iiPDF_Ncn), & ! intent(in)
        3415           0 :                      corr_array_1(:,:,iiPDF_Ncn,iiPDF_chi)  ) ! intent(out)
        3416             :
        3417             :     ! Transform the correlation of eta (old t) and N_cn to standard space in PDF component 1.
        3418             :     call corr_NN2NL( nz, ngrdcol, & ! intent(in)
        3419             :                      corr_array_1_n(:,:,iiPDF_Ncn,iiPDF_eta), & ! intent(in)
        3420             :                      sigma_x_1_n(:,:,iiPDF_Ncn), sigma2_on_mu2_ip_1(:,:,iiPDF_Ncn), & ! intent(in)
        3421           0 :                      corr_array_1(:,:,iiPDF_Ncn,iiPDF_eta) )! intent(out)
        3422             :
        3423             :     ! Transform the correlation of w and N_cn to standard space in PDF component 1.
        3424             :     call corr_NN2NL( nz, ngrdcol, & ! intent(in)
        3425             :                      corr_array_1_n(:,:,iiPDF_Ncn,iiPDF_w), & ! intent(in)
        3426             :                      sigma_x_1_n(:,:,iiPDF_Ncn), sigma2_on_mu2_ip_1(:,:,iiPDF_Ncn), & ! intent(in)
        3427           0 :                      corr_array_1(:,:,iiPDF_Ncn,iiPDF_w)  ) ! intent(out)
        3428             :
        3429             :     ! Transform the correlation of chi (old s) and N_cn to standard space in PDF component 2.
        3430             :     call corr_NN2NL( nz, ngrdcol, & ! intent(in)
        3431             :                      corr_array_2_n(:,:,iiPDF_Ncn,iiPDF_chi), & ! intent(in)
        3432             :                      sigma_x_2_n(:,:,iiPDF_Ncn), sigma2_on_mu2_ip_1(:,:,iiPDF_Ncn), & ! intent(in)
        3433           0 :                      corr_array_2(:,:,iiPDF_Ncn,iiPDF_chi)  ) ! intent(out)
        3434             :
        3435             :     ! Transform the correlation of eta (old t) and N_cn to standard space in PDF component 2.
        3436             :     call corr_NN2NL( nz, ngrdcol, & ! intent(in)
        3437             :                      corr_array_2_n(:,:,iiPDF_Ncn,iiPDF_eta), & ! intent(in)
        3438             :                      sigma_x_2_n(:,:,iiPDF_Ncn), sigma2_on_mu2_ip_1(:,:,iiPDF_Ncn), & ! intent(in)
        3439           0 :                      corr_array_2(:,:,iiPDF_Ncn,iiPDF_eta)  ) ! intent(out)
        3440             :
        3441             :     ! Transform the correlation of w and N_cn to standard space in PDF component 2.
        3442             :     call corr_NN2NL( nz, ngrdcol, & ! intent(in)
        3443             :                      corr_array_2_n(:,:,iiPDF_Ncn,iiPDF_w), & ! intent(in)
        3444             :                      sigma_x_2_n(:,:,iiPDF_Ncn), sigma2_on_mu2_ip_1(:,:,iiPDF_Ncn), & ! intent(in)
        3445           0 :                      corr_array_2(:,:,iiPDF_Ncn,iiPDF_w)  ) ! intent(out)
        3446             :
        3447             :     ! Transform the correlations (in-precip) between chi/eta/w and the
        3448             :     ! precipitating hydrometeors to standard space.
        3449           0 :     do ivar = iiPDF_chi, iiPDF_w
        3450           0 :       do jvar = iiPDF_Ncn+1, pdf_dim
        3451             :
        3452             :         ! Transform the correlation (in-precip) between w, chi, or eta and a
        3453             :         ! precipitating hydrometeor, hm, to standard space in PDF component 1.
        3454             :         call corr_NN2NL( nz, ngrdcol, & ! intent(in)
        3455             :                          corr_array_1_n(:,:,jvar,ivar), & ! intent(in)
        3456             :                          sigma_x_1_n(:,:,jvar), sigma2_on_mu2_ip_1(:,:,jvar), & ! intent(in)
        3457           0 :                          corr_array_1(:,:,jvar,ivar)  ) ! intent(out)
        3458             :
        3459             :         ! Transform the correlation (in-precip) between w, chi, or eta and a
        3460             :         ! precipitating hydrometeor, hm, to standard space in PDF component 2.
        3461             :         call corr_NN2NL( nz, ngrdcol, & ! intent(in)
        3462             :                          corr_array_2_n(:,:,jvar,ivar), & ! intent(in)
        3463             :                          sigma_x_2_n(:,:,jvar), sigma2_on_mu2_ip_2(:,:,jvar), & ! intent(in)
        3464           0 :                          corr_array_2(:,:,jvar,ivar)  ) ! intent(out)
        3465             :
        3466             :       end do ! jvar = iiPDF_Ncn+1, pdf_dim
        3467             :     end do ! ivar = iiPDF_chi, iiPDF_w
        3468             :
        3469             :
        3470             :     !!! Calculate the true correlation of two variables that both have an
        3471             :     !!! assumed lognormal distribution for the ith PDF component, given their
        3472             :     !!! normal space correlation and both of their normal space standard
        3473             :     !!! deviations.
        3474             :
        3475             :     ! Transform the correlations (in-precip) between N_cn and the precipitating
        3476             :     ! hydrometeors to standard space.
        3477           0 :     do jvar = iiPDF_Ncn+1, pdf_dim
        3478             :
        3479             :       ! Transform the correlation (in-precip) between N_cn and a precipitating
        3480             :       ! hydrometeor, hm, to standard space in PDF component 1.
        3481             :       call corr_NN2LL( nz, ngrdcol, & ! intent(in)
        3482             :                        corr_array_1_n(:,:,jvar,iiPDF_Ncn), & ! intent(in)
        3483             :                        sigma_x_1_n(:,:,iiPDF_Ncn), sigma_x_1_n(:,:,jvar), & ! intent(in)
        3484             :                        sigma2_on_mu2_ip_1(:,:,iiPDF_Ncn), sigma2_on_mu2_ip_1(:,:,jvar), & ! in
        3485           0 :                        corr_array_1(:,:,jvar,iiPDF_Ncn)) ! intent(out)
        3486             :
        3487             :       ! Transform the correlation (in-precip) between N_cn and a precipitating
        3488             :       ! hydrometeor, hm, to standard space in PDF component 2.
        3489             :       call corr_NN2LL( nz, ngrdcol, & ! intent(in)
        3490             :                        corr_array_2_n(:,:,jvar,iiPDF_Ncn), & ! intent(in)
        3491             :                        sigma_x_2_n(:,:,iiPDF_Ncn), sigma_x_2_n(:,:,jvar), & ! intent(in)
        3492             :                        sigma2_on_mu2_ip_1(:,:,iiPDF_Ncn), sigma2_on_mu2_ip_2(:,:,jvar), & ! in
        3493           0 :                        corr_array_2(:,:,jvar,iiPDF_Ncn)) ! intent(out)
        3494             :
        3495             :     end do ! jvar = ivar+1, pdf_dim
        3496             :
        3497             :     ! Transform the correlations (in-precip) between two precipitating
        3498             :     ! hydrometeors to standard space.
        3499           0 :     do ivar = iiPDF_Ncn+1, pdf_dim-1
        3500           0 :       do jvar = ivar+1, pdf_dim
        3501             :
        3502             :         ! Transform the correlation (in-precip) between two precipitating
        3503             :         ! hydrometeors (for example, r_r and N_r) to standard space in PDF
        3504             :         ! component 1.
        3505             :         call corr_NN2LL( nz, ngrdcol, & ! intent(in)
        3506             :                          corr_array_1_n(:,:,jvar,ivar), & ! intent(in)
        3507             :                          sigma_x_1_n(:,:,ivar), sigma_x_1_n(:,:,jvar), & ! intent(in)
        3508             :                          sigma2_on_mu2_ip_1(:,:,ivar), sigma2_on_mu2_ip_1(:,:,jvar), & ! in
        3509           0 :                          corr_array_1(:,:,jvar,ivar)) ! intent(out)
        3510             :
        3511             :         ! Transform the correlation (in-precip) between two precipitating
        3512             :         ! hydrometeors (for example, r_r and N_r) to standard space in PDF
        3513             :         ! component 2.
        3514             :         call corr_NN2LL( nz, ngrdcol, & ! intent(in)
        3515             :                          corr_array_2_n(:,:,jvar,ivar), & ! intent(in)
        3516             :                          sigma_x_2_n(:,:,ivar), sigma_x_2_n(:,:,jvar), & ! intent(in)
        3517             :                          sigma2_on_mu2_ip_2(:,:,ivar), sigma2_on_mu2_ip_2(:,:,jvar), & ! in
        3518           0 :                          corr_array_2(:,:,jvar,ivar)) ! intent(out)
        3519             :
        3520             :       end do ! jvar = ivar+1, pdf_dim
        3521             :     end do ! ivar = iiPDF_Ncn+1, pdf_dim-1
        3522             :
        3523           0 :     return
        3524             :
        3525             :   end subroutine denorm_transform_corr
        3526             :
        3527             :   !=============================================================================
        3528           0 :   elemental subroutine calc_corr_w_hm_n( wm, wphydrometp, &
        3529             :                                          mu_w_1, mu_w_2, &
        3530             :                                          mu_hm_1, mu_hm_2, &
        3531             :                                          sigma_w_1, sigma_w_2, &
        3532             :                                          sigma_hm_1, sigma_hm_2, &
        3533             :                                          sigma_hm_1_n, sigma_hm_2_n, &
        3534             :                                          mixt_frac, precip_frac_1, &
        3535             :                                          precip_frac_2, hm_tol, &
        3536             :                                          corr_w_hm_1_n, corr_w_hm_2_n )
        3537             :
        3538             :     ! Description:
        3539             :     ! Calculates the PDF component correlation (in-precip) between vertical
        3540             :     ! velocity, w, and the natural logarithm of a hydrometeor, ln hm.  The
        3541             :     ! overall covariance of w and hm, <w'hm'> can be written in terms of the PDF
        3542             :     ! parameters.  When both w and hm vary in both PDF components, the equation
        3543             :     ! is written as:
        3544             :     !
        3545             :     ! <w'hm'> = mixt_frac * precip_frac_1
        3546             :     !           * ( mu_w_1 - <w>
        3547             :     !               + corr_w_hm_1_n * sigma_w_1 * sigma_hm_1_n ) * mu_hm_1
        3548             :     !           + ( 1 - mixt_frac ) * precip_frac_2
        3549             :     !             * ( mu_w_2 - <w>
        3550             :     !                 + corr_w_hm_2_n * sigma_w_2 * sigma_hm_2_n ) * mu_hm_2.
        3551             :     !
        3552             :     ! The overall covariance is provided, so the component correlation is solved
        3553             :     ! by setting corr_w_hm_1_n = corr_w_hm_2_n ( = corr_w_hm_n ).  The equation
        3554             :     ! is:
        3555             :     !
        3556             :     ! corr_w_hm_n
        3557             :     ! = ( <w'hm'>
        3558             :     !     - mixt_frac * precip_frac_1 * ( mu_w_1 - <w> ) * mu_hm_1
        3559             :     !     - ( 1 - mixt_frac ) * precip_frac_2 * ( mu_w_2 - <w> ) * mu_hm_2 )
        3560             :     !   / ( mixt_frac * precip_frac_1 * sigma_w_1 * sigma_hm_1_n * mu_hm_1
        3561             :     !       + ( 1 - mixt_frac ) * precip_frac_2
        3562             :     !         * sigma_w_2 * sigma_hm_2_n * mu_hm_2 );
        3563             :     !
        3564             :     ! again, where corr_w_hm_1_n = corr_w_hm_2_n = corr_w_hm_n.  When either w
        3565             :     ! or hm is constant in one PDF component, but both w and hm vary in the
        3566             :     ! other PDF component, the equation for <w'hm'> is written as:
        3567             :     !
        3568             :     ! <w'hm'> = mixt_frac * precip_frac_1
        3569             :     !           * ( mu_w_1 - <w>
        3570             :     !               + corr_w_hm_1_n * sigma_w_1 * sigma_hm_1_n ) * mu_hm_1
        3571             :     !           + ( 1 - mixt_frac ) * precip_frac_2
        3572             :     !             * ( mu_w_2 - <w> ) * mu_hm_2.
        3573             :     !
        3574             :     ! In the above equation, either w or hm (or both) is (are) constant in PDF
        3575             :     ! component 2, but both w and hm vary in PDF component 1.  When both w and
        3576             :     ! hm vary in PDF component 2, but at least one of w or hm is constant in PDF
        3577             :     ! component 1, the equation is similar.  The above equation can be rewritten
        3578             :     ! to solve for corr_w_hm_1_n, such that:
        3579             :     !
        3580             :     ! corr_w_hm_1_n
        3581             :     ! = ( <w'hm'>
        3582             :     !     - mixt_frac * precip_frac_1 * ( mu_w_1 - <w> ) * mu_hm_1
        3583             :     !     - ( 1 - mixt_frac ) * precip_frac_2 * ( mu_w_2 - <w> ) * mu_hm_2 )
        3584             :     !   / ( mixt_frac * precip_frac_1 * sigma_w_1 * sigma_hm_1_n * mu_hm_1 ).
        3585             :     !
        3586             :     ! Since either w or hm is constant in PDF component 2, corr_w_hm_2_n is
        3587             :     ! undefined.  When both w and hm vary in PDF component 2, but at least one
        3588             :     ! of w or hm is constant in PDF component 1, the equation is similar, but
        3589             :     ! is in terms of corr_w_hm_2_n, while corr_w_hm_1_n is undefined.  When
        3590             :     ! either w or hm is constant in both PDF components, the equation for
        3591             :     ! <w'hm'> is:
        3592             :     !
        3593             :     ! <w'hm'> = mixt_frac * precip_frac_1
        3594             :     !           * ( mu_w_1 - <w> ) * mu_hm_1
        3595             :     !           + ( 1 - mixt_frac ) * precip_frac_2
        3596             :     !             * ( mu_w_2 - <w> ) * mu_hm_2.
        3597             :     !
        3598             :     ! When this is the case, both corr_w_hm_1_n and corr_w_hm_2_n are undefined.
        3599             :
        3600             :     ! References:
        3601             :     !-----------------------------------------------------------------------
        3602             :
        3603             :     use constants_clubb, only:  &
        3604             :         one,                 & ! Constant(s)
        3605             :         zero,                &
        3606             :         max_mag_correlation, &
        3607             :         w_tol
        3608             :
        3609             :     use clubb_precision, only: &
        3610             :         core_rknd    ! Variable(s)
        3611             :
        3612             :     implicit none
        3613             :
        3614             :     ! Input Variables
        3615             :     real( kind = core_rknd ), intent(in) :: &
        3616             :       wm,            & ! Mean vertical velocity (overall), <w>             [m/s]
        3617             :       wphydrometp,   & ! Covariance of w and hm (overall), <w'hm'>  [m/s(hm un)]
        3618             :       mu_w_1,        & ! Mean of w (1st PDF component)                     [m/s]
        3619             :       mu_w_2,        & ! Mean of w (2nd PDF component)                     [m/s]
        3620             :       mu_hm_1,       & ! Mean of hm (1st PDF component) in-precip (ip)   [hm un]
        3621             :       mu_hm_2,       & ! Mean of hm (2nd PDF component) ip               [hm un]
        3622             :       sigma_w_1,     & ! Standard deviation of w (1st PDF component)       [m/s]
        3623             :       sigma_w_2,     & ! Standard deviation of w (2nd PDF component)       [m/s]
        3624             :       sigma_hm_1,    & ! Standard deviation of hm (1st PDF component) ip [hm un]
        3625             :       sigma_hm_2,    & ! Standard deviation of hm (2nd PDF component) ip [hm un]
        3626             :       sigma_hm_1_n,  & ! Standard deviation of ln hm (1st PDF component) ip  [-]
        3627             :       sigma_hm_2_n,  & ! Standard deviation of ln hm (2nd PDF component) ip  [-]
        3628             :       mixt_frac,     & ! Mixture fraction                                    [-]
        3629             :       precip_frac_1, & ! Precipitation fraction (1st PDF component)          [-]
        3630             :       precip_frac_2    ! Precipitation fraction (2nd PDF component)          [-]
        3631             :
        3632             :     real( kind = core_rknd ), intent(in) :: &
        3633             :       hm_tol           ! Hydrometeor tolerance value                     [hm un]
        3634             :
        3635             :     ! Output Variables
        3636             :     real( kind = core_rknd ), intent(out) :: &
        3637             :       corr_w_hm_1_n, & ! Correlation of w and ln hm (1st PDF component) ip   [-]
        3638             :       corr_w_hm_2_n    ! Correlation of w and ln hm (2nd PDF component) ip   [-]
        3639             :
        3640             :     ! Local Variables
        3641             :     real( kind = core_rknd ) :: &
        3642             :       corr_w_hm_n    ! Correlation of w and ln hm (both PDF components) ip   [-]
        3643             :
        3644             :
        3645             :     ! Calculate the PDF component correlation of vertical velocity, w, and the
        3646             :     ! natural logarithm of a hydrometeor, ln hm, in precipitation.
        3647             :     if ( sigma_w_1 > w_tol .and. sigma_hm_1 > hm_tol .and. &
        3648           0 :          sigma_w_2 > w_tol .and. sigma_hm_2 > hm_tol ) then
        3649             :
        3650             :        ! Both w and hm vary in both PDF components.
        3651             :        ! Calculate corr_w_hm_n (where corr_w_hm_1_n = corr_w_hm_2_n
        3652             :        ! = corr_w_hm_n).
        3653             :        corr_w_hm_n &
        3654             :        = ( wphydrometp &
        3655             :            - mixt_frac * precip_frac_1 * ( mu_w_1 - wm ) * mu_hm_1 &
        3656             :            - ( one - mixt_frac ) * precip_frac_2 * ( mu_w_2 - wm ) * mu_hm_2 ) &
        3657             :          / ( mixt_frac * precip_frac_1 * sigma_w_1 * sigma_hm_1_n * mu_hm_1 &
        3658             :              + ( one - mixt_frac ) * precip_frac_2 &
        3659           0 :                * sigma_w_2 * sigma_hm_2_n * mu_hm_2 )
        3660             :
        3661             :        ! Check that the PDF component correlations have reasonable values.
        3662           0 :        if ( corr_w_hm_n > max_mag_correlation ) then
        3663             :           corr_w_hm_n = max_mag_correlation
        3664           0 :        elseif ( corr_w_hm_n < -max_mag_correlation ) then
        3665           0 :           corr_w_hm_n = -max_mag_correlation
        3666             :        end if
        3667             :
        3668             :        ! The PDF component correlations between w and ln hm (in-precip) are
        3669             :        ! equal.
        3670           0 :        corr_w_hm_1_n = corr_w_hm_n
        3671           0 :        corr_w_hm_2_n = corr_w_hm_n
        3672             :
        3673             :
        3674           0 :     elseif ( sigma_w_1 > w_tol .and. sigma_hm_1 > hm_tol ) then
        3675             :
        3676             :        ! Both w and hm vary in PDF component 1, but at least one of w and hm is
        3677             :        ! constant in PDF component 2.
        3678             :        ! Calculate the PDF component 1 correlation of w and ln hm (in-precip).
        3679             :        corr_w_hm_1_n &
        3680             :        = ( wphydrometp &
        3681             :            - mixt_frac * precip_frac_1 * ( mu_w_1 - wm ) * mu_hm_1 &
        3682             :            - ( one - mixt_frac ) * precip_frac_2 * ( mu_w_2 - wm ) * mu_hm_2 ) &
        3683           0 :          / ( mixt_frac * precip_frac_1 * sigma_w_1 * sigma_hm_1_n * mu_hm_1 )
        3684             :
        3685             :        ! Check that the PDF component 1 correlation has a reasonable value.
        3686           0 :        if ( corr_w_hm_1_n > max_mag_correlation ) then
        3687           0 :           corr_w_hm_1_n = max_mag_correlation
        3688           0 :        elseif ( corr_w_hm_1_n < -max_mag_correlation ) then
        3689           0 :           corr_w_hm_1_n = -max_mag_correlation
        3690             :        end if
        3691             :
        3692             :        ! The PDF component 2 correlation is undefined.
        3693           0 :        corr_w_hm_2_n = zero
        3694             :
        3695             :
        3696           0 :     elseif ( sigma_w_2 > w_tol .and. sigma_hm_2 > hm_tol ) then
        3697             :
        3698             :        ! Both w and hm vary in PDF component 2, but at least one of w and hm is
        3699             :        ! constant in PDF component 1.
        3700             :        ! Calculate the PDF component 2 correlation of w and ln hm (in-precip).
        3701             :        corr_w_hm_2_n &
        3702             :        = ( wphydrometp &
        3703             :            - mixt_frac * precip_frac_1 * ( mu_w_1 - wm ) * mu_hm_1 &
        3704             :            - ( one - mixt_frac ) * precip_frac_2 * ( mu_w_2 - wm ) * mu_hm_2 ) &
        3705             :          / ( ( one - mixt_frac ) * precip_frac_2 &
        3706           0 :              * sigma_w_2 * sigma_hm_2_n * mu_hm_2 )
        3707             :
        3708             :        ! Check that the PDF component 2 correlation has a reasonable value.
        3709           0 :        if ( corr_w_hm_2_n > max_mag_correlation ) then
        3710           0 :           corr_w_hm_2_n = max_mag_correlation
        3711           0 :        elseif ( corr_w_hm_2_n < -max_mag_correlation ) then
        3712           0 :           corr_w_hm_2_n = -max_mag_correlation
        3713             :        end if
        3714             :
        3715             :        ! The PDF component 1 correlation is undefined.
        3716           0 :        corr_w_hm_1_n = zero
        3717             :
        3718             :
        3719             :     else    ! sigma_w_1 * sigma_hm_1 = 0 .and. sigma_w_2 * sigma_hm_2 = 0.
        3720             :
        3721             :        ! At least one of w and hm is constant in both PDF components.
        3722             :
        3723             :        ! The PDF component 1 and component 2 correlations are both undefined.
        3724           0 :        corr_w_hm_1_n = zero
        3725           0 :        corr_w_hm_2_n = zero
        3726             :
        3727             :
        3728             :     end if
        3729             :
        3730             :
        3731           0 :     return
        3732             :
        3733             :   end subroutine calc_corr_w_hm_n
        3734             :
        3735             :   !=============================================================================
        3736           0 :   subroutine pdf_param_hm_stats( nz, pdf_dim, hydromet_dim, hm_metadata, &
        3737           0 :                                  hm_1, hm_2, &
        3738           0 :                                  mu_x_1, mu_x_2, &
        3739           0 :                                  sigma_x_1, sigma_x_2, &
        3740           0 :                                  corr_array_1, corr_array_2, &
        3741             :                                  stats_metadata, &
        3742             :                                  stats_zt )
        3743             :
        3744             :     ! Description:
        3745             :     ! Record statistics for standard PDF parameters involving hydrometeors.
        3746             :
        3747             :     ! References:
        3748             :     !-----------------------------------------------------------------------
        3749             :
        3750             :     use index_mapping, only: &
        3751             :         pdf2hydromet_idx  ! Procedure(s)
        3752             :
        3753             :     use corr_varnce_module, only: &
        3754             :         hm_metadata_type
        3755             :
        3756             :     use clubb_precision, only: &
        3757             :         core_rknd   ! Variable(s)
        3758             :
        3759             :     use stats_type_utilities, only: &
        3760             :         stat_update_var_pt  ! Procedure(s)
        3761             :
        3762             :     use stats_variables, only: &
        3763             :         stats_metadata_type
        3764             :
        3765             :     use stats_type, only: stats ! Type
        3766             :
        3767             :     implicit none
        3768             :
        3769             :     !--------------------------- Input Variables ---------------------------
        3770             :     integer, intent(in) :: &
        3771             :       nz,           & ! Number of vertical levels
        3772             :       pdf_dim,      & ! Number of variables in the correlation array
        3773             :       hydromet_dim    ! Number of hydrometeor species
        3774             :
        3775             :     type (hm_metadata_type), intent(in) :: &
        3776             :       hm_metadata
        3777             :
        3778             :     real( kind = core_rknd ), dimension(nz,hydromet_dim), intent(in) :: &
        3779             :       hm_1, & ! Mean of a precip. hydrometeor (1st PDF component)   [units vary]
        3780             :       hm_2    ! Mean of a precip. hydrometeor (2nd PDF component)   [units vary]
        3781             :
        3782             :     real( kind = core_rknd ), dimension(nz,pdf_dim), intent(in) :: &
        3783             :       mu_x_1,    & ! Mean array of PDF vars. (1st PDF component)    [units vary]
        3784             :       mu_x_2,    & ! Mean array of PDF vars. (2nd PDF component)    [units vary]
        3785             :       sigma_x_1, & ! Standard deviation array of PDF vars (comp. 1) [units vary]
        3786             :       sigma_x_2    ! Standard deviation array of PDF vars (comp. 2) [units vary]
        3787             :
        3788             :     real( kind = core_rknd ), dimension(nz,pdf_dim,pdf_dim), intent(in) :: &
        3789             :       corr_array_1, & ! Correlation array of PDF vars. (comp. 1)             [-]
        3790             :       corr_array_2    ! Correlation array of PDF vars. (comp. 2)             [-]
        3791             :
        3792             :     type (stats_metadata_type), intent(in) :: &
        3793             :       stats_metadata
        3794             :
        3795             :     !--------------------------- InOut Variable ---------------------------
        3796             :     type (stats), target, intent(inout) :: &
        3797             :       stats_zt
        3798             :
        3799             :     !--------------------------- Local Variable ---------------------------
        3800             :     integer :: ivar, jvar, hm_idx, hm_idx_ivar, hm_idx_jvar, k  ! Indices
        3801             :
        3802             :     ! Just to avoid typing hm_metadata%iiPDF_x everywhere
        3803             :     integer :: &
        3804             :       iiPDF_chi, &
        3805             :       iiPDF_eta, &
        3806             :       iiPDF_w,   &
        3807             :       iiPDF_Ncn
        3808             :
        3809             :     !------------------------ Begin Code ------------------------
        3810             :
        3811           0 :     iiPDF_chi = hm_metadata%iiPDF_chi
        3812           0 :     iiPDF_eta = hm_metadata%iiPDF_eta
        3813           0 :     iiPDF_w   = hm_metadata%iiPDF_w
        3814           0 :     iiPDF_Ncn = hm_metadata%iiPDF_Ncn
        3815             :
        3816             :     !!! Output the statistics for hydrometeor PDF parameters.
        3817             :
        3818             :     ! Statistics
        3819           0 :     if ( stats_metadata%l_stats_samp ) then
        3820             :
        3821             :        ! Switch back to using stat_update_var once the code is generalized
        3822             :        ! to pass in the number of vertical levels.
        3823           0 :        do ivar = 1, hydromet_dim, 1
        3824             :
        3825           0 :           if ( stats_metadata%ihm_1(ivar) > 0 ) then
        3826             :              ! Mean of the precipitating hydrometeor in PDF component 1.
        3827             : !             call stat_update_var( stats_metadata%ihm_1(ivar), hm_1(:,ivar), stats_zt )
        3828           0 :              do k = 1, nz, 1
        3829           0 :                 call stat_update_var_pt( stats_metadata%ihm_1(ivar), k, hm_1(k,ivar), & ! intent(in)
        3830           0 :                                          stats_zt ) ! intent(inout)
        3831             :              end do ! k = 1, nz, 1
        3832             :           end if
        3833             :
        3834           0 :           if ( stats_metadata%ihm_2(ivar) > 0 ) then
        3835             :              ! Mean of the precipitating hydrometeor in PDF component 2.
        3836             : !             call stat_update_var( stats_metadata%ihm_2(ivar), hm_2(:,ivar), stats_zt )
        3837           0 :              do k = 1, nz, 1
        3838           0 :                 call stat_update_var_pt( stats_metadata%ihm_2(ivar), k, hm_2(k,ivar), & ! intent(in)
        3839           0 :                                          stats_zt ) ! intent(inout)
        3840             :              end do ! k = 1, nz, 1
        3841             :           end if
        3842             :
        3843             :        end do ! ivar = 1, hydromet_dim, 1
        3844             :
        3845           0 :        do ivar = iiPDF_Ncn+1, pdf_dim, 1
        3846             :
        3847           0 :           hm_idx = pdf2hydromet_idx(ivar,hm_metadata)
        3848             :
        3849             :           ! Mean of the precipitating hydrometeor (in-precip)
        3850             :           ! in PDF component 1.
        3851           0 :           if ( stats_metadata%imu_hm_1(hm_idx) > 0 ) then
        3852             : !             call stat_update_var( stats_metadata%imu_hm_1(hm_idx), mu_x_1(ivar,:), stats_zt )
        3853           0 :              do k = 1, nz, 1
        3854           0 :                 call stat_update_var_pt( stats_metadata%imu_hm_1(hm_idx), k, mu_x_1(k,ivar), & ! intent(in)
        3855           0 :                                          stats_zt ) ! intent(inout)
        3856             :              end do ! k = 1, nz, 1
        3857             :           end if
        3858             :
        3859             :           ! Mean of the precipitating hydrometeor (in-precip)
        3860             :           ! in PDF component 2.
        3861           0 :           if ( stats_metadata%imu_hm_2(hm_idx) > 0 ) then
        3862             : !             call stat_update_var( stats_metadata%imu_hm_2(hm_idx), mu_x_2(ivar,:), stats_zt )
        3863           0 :              do k = 1, nz, 1
        3864           0 :                 call stat_update_var_pt( stats_metadata%imu_hm_2(hm_idx), k, mu_x_2(k,ivar), & ! intent(in)
        3865           0 :                                          stats_zt ) ! intent(inout)
        3866             :              end do ! k = 1, nz, 1
        3867             :           end if
        3868             :
        3869             :        end do ! ivar = iiPDF_Ncn+1, pdf_dim, 1
        3870             :
        3871             :        ! Mean of cloud nuclei concentration in PDF component 1.
        3872           0 :        if ( stats_metadata%imu_Ncn_1 > 0 ) then
        3873             : !          call stat_update_var( stats_metadata%imu_Ncn_1, mu_x_1(iiPDF_Ncn,:), stats_zt )
        3874           0 :           do k = 1, nz, 1
        3875           0 :              call stat_update_var_pt( stats_metadata%imu_Ncn_1, k, mu_x_1(k,iiPDF_Ncn), & ! intent(in)
        3876           0 :                                       stats_zt ) ! intent(inout)
        3877             :           end do ! k = 1, nz, 1
        3878             :        end if
        3879             :
        3880             :        ! Mean of cloud nuclei concentration in PDF component 2.
        3881           0 :        if ( stats_metadata%imu_Ncn_2 > 0 ) then
        3882             : !          call stat_update_var( stats_metadata%imu_Ncn_2, mu_x_2(iiPDF_Ncn,:), stats_zt )
        3883           0 :           do k = 1, nz, 1
        3884           0 :              call stat_update_var_pt( stats_metadata%imu_Ncn_2, k, mu_x_2(k,iiPDF_Ncn), & ! intent(in)
        3885           0 :                                       stats_zt ) ! intent(inout)
        3886             :           end do ! k = 1, nz, 1
        3887             :        end if
        3888             :
        3889           0 :        do ivar = iiPDF_Ncn+1, pdf_dim, 1
        3890             :
        3891           0 :           hm_idx = pdf2hydromet_idx(ivar,hm_metadata)
        3892             :
        3893             :           ! Standard deviation of the precipitating hydrometeor (in-precip)
        3894             :           ! in PDF component 1.
        3895           0 :           if ( stats_metadata%isigma_hm_1(hm_idx) > 0 ) then
        3896             : !             call stat_update_var( stats_metadata%isigma_hm_1(hm_idx), sigma_x_1(ivar,:), &
        3897             : !                                   stats_zt )
        3898           0 :              do k = 1, nz, 1
        3899           0 :                 call stat_update_var_pt( stats_metadata%isigma_hm_1(hm_idx), k, sigma_x_1(k,ivar), & ! intent(in)
        3900           0 :                                          stats_zt ) ! intent(inout)
        3901             :              end do ! k = 1, nz, 1
        3902             :           end if
        3903             :
        3904             :           ! Standard deviation of the precipitating hydrometeor (in-precip)
        3905             :           ! in PDF component 2.
        3906           0 :           if ( stats_metadata%isigma_hm_2(hm_idx) > 0 ) then
        3907             : !             call stat_update_var( stats_metadata%isigma_hm_2(hm_idx), sigma_x_2(ivar,:), &
        3908             : !                                   stats_zt )
        3909           0 :              do k = 1, nz, 1
        3910           0 :                 call stat_update_var_pt( stats_metadata%isigma_hm_2(hm_idx), k, sigma_x_2(k,ivar), & ! intent(in)
        3911           0 :                                          stats_zt ) ! intent(inout)
        3912             :              end do ! k = 1, nz, 1
        3913             :           end if
        3914             :
        3915             :        end do ! ivar = iiPDF_Ncn+1, pdf_dim, 1
        3916             :
        3917             :        ! Standard deviation of cloud nuclei concentration in PDF component 1.
        3918           0 :        if ( stats_metadata%isigma_Ncn_1 > 0 ) then
        3919             : !          call stat_update_var( stats_metadata%isigma_Ncn_1, sigma_x_1(iiPDF_Ncn,:), stats_zt )
        3920           0 :           do k = 1, nz, 1
        3921           0 :              call stat_update_var_pt( stats_metadata%isigma_Ncn_1, k, sigma_x_1(k,iiPDF_Ncn), & ! intent(in)
        3922           0 :                                       stats_zt ) ! intent(inout)
        3923             :           end do ! k = 1, nz, 1
        3924             :        end if
        3925             :
        3926             :        ! Standard deviation of cloud nuclei concentration in PDF component 2.
        3927           0 :        if ( stats_metadata%isigma_Ncn_2 > 0 ) then
        3928             : !          call stat_update_var( stats_metadata%isigma_Ncn_2, sigma_x_2(iiPDF_Ncn,:), stats_zt )
        3929           0 :           do k = 1, nz, 1
        3930           0 :              call stat_update_var_pt( stats_metadata%isigma_Ncn_2, k, sigma_x_2(k,iiPDF_Ncn), & ! intent(in)
        3931           0 :                                       stats_zt ) ! intent(inout)
        3932             :           end do ! k = 1, nz, 1
        3933             :        end if
        3934             :
        3935             :        ! Correlation of w and chi (old s) in PDF component 1 found in the
        3936             :        ! correlation array.
        3937             :        ! The true correlation of w and chi in each PDF component is solved for
        3938             :        ! by an equation and is part of CLUBB's PDF parameters.  However, there
        3939             :        ! is an option in CLUBB, l_fix_w_chi_eta_correlations, that sets the
        3940             :        ! component correlation of w and chi to a constant, prescribed value
        3941             :        ! because of SILHS.  The correlation of w and chi in PDF component 1
        3942             :        ! that is calculated by an equation is stored in stats as "corr_w_chi_1".
        3943             :        ! Here, "corr_w_chi_1_ca" outputs whatever value is found in the
        3944             :        ! correlation array, whether or not it matches "corr_w_chi_1".
        3945           0 :        if ( stats_metadata%icorr_w_chi_1_ca > 0 ) then
        3946             : !          call stat_update_var( stats_metadata%icorr_w_chi_1_ca, &
        3947             : !                                corr_array_1(iiPDF_w,iiPDF_chi,:), stats_zt )
        3948           0 :           do k = 1, nz, 1
        3949             :              call stat_update_var_pt( stats_metadata%icorr_w_chi_1_ca, k, &
        3950           0 :                                       corr_array_1(k,iiPDF_w,iiPDF_chi), & ! intent(in)
        3951           0 :                                       stats_zt ) ! intent(inout)
        3952             :           end do ! k = 1, nz, 1
        3953             :        end if
        3954             :
        3955             :        ! Correlation of w and chi (old s) in PDF component 2 found in the
        3956             :        ! correlation array.
        3957             :        ! The true correlation of w and chi in each PDF component is solved for
        3958             :        ! by an equation and is part of CLUBB's PDF parameters.  However, there
        3959             :        ! is an option in CLUBB, l_fix_w_chi_eta_correlations, that sets the
        3960             :        ! component correlation of w and chi to a constant, prescribed value
        3961             :        ! because of SILHS.  The correlation of w and chi in PDF component 2
        3962             :        ! that is calculated by an equation is stored in stats as "corr_w_chi_2".
        3963             :        ! Here, "corr_w_chi_2_ca" outputs whatever value is found in the
        3964             :        ! correlation array, whether or not it matches "corr_w_chi_2".
        3965           0 :        if ( stats_metadata%icorr_w_chi_2_ca > 0 ) then
        3966             : !          call stat_update_var( stats_metadata%icorr_w_chi_2_ca, &
        3967             : !                                corr_array_2(iiPDF_w,iiPDF_chi,:), stats_zt )
        3968           0 :           do k = 1, nz, 1
        3969             :              call stat_update_var_pt( stats_metadata%icorr_w_chi_2_ca, k, & ! intent(in)
        3970           0 :                                       corr_array_2(k,iiPDF_w,iiPDF_chi), & ! intent(in)
        3971           0 :                                       stats_zt ) ! intent(inout)
        3972             :           end do ! k = 1, nz, 1
        3973             :        end if
        3974             :
        3975             :        ! Correlation of w and eta (old t) in PDF component 1 found in the
        3976             :        ! correlation array.
        3977             :        ! The true correlation of w and eta in each PDF component is solved for
        3978             :        ! by an equation and is part of CLUBB's PDF parameters.  However, there
        3979             :        ! is an option in CLUBB, l_fix_w_chi_eta_correlations, that sets the
        3980             :        ! component correlation of w and eta to a constant, prescribed value
        3981             :        ! because of SILHS.  The correlation of w and eta in PDF component 1
        3982             :        ! that is calculated by an equation is stored in stats as "corr_w_eta_1".
        3983             :        ! Here, "corr_w_eta_1_ca" outputs whatever value is found in the
        3984             :        ! correlation array, whether or not it matches "corr_w_eta_1".
        3985           0 :        if ( stats_metadata%icorr_w_eta_1_ca > 0 ) then
        3986             : !          call stat_update_var( stats_metadata%icorr_w_eta_1_ca, &
        3987             : !                                corr_array_1(iiPDF_w,iiPDF_eta,:), stats_zt )
        3988           0 :           do k = 1, nz, 1
        3989             :              call stat_update_var_pt( stats_metadata%icorr_w_eta_1_ca, k, & ! intent(in)
        3990           0 :                                       corr_array_1(k,iiPDF_w,iiPDF_eta), & ! intent(in)
        3991           0 :                                       stats_zt ) ! intent(inout)
        3992             :           end do ! k = 1, nz, 1
        3993             :        end if
        3994             :
        3995             :        ! Correlation of w and eta (old t) in PDF component 2 found in the
        3996             :        ! correlation array.
        3997             :        ! The true correlation of w and eta in each PDF component is solved for
        3998             :        ! by an equation and is part of CLUBB's PDF parameters.  However, there
        3999             :        ! is an option in CLUBB, l_fix_w_chi_eta_correlations, that sets the
        4000             :        ! component correlation of w and eta to a constant, prescribed value
        4001             :        ! because of SILHS.  The correlation of w and eta in PDF component 2
        4002             :        ! that is calculated by an equation is stored in stats as "corr_w_eta_2".
        4003             :        ! Here, "corr_w_eta_2_ca" outputs whatever value is found in the
        4004             :        ! correlation array, whether or not it matches "corr_w_eta_2".
        4005           0 :        if ( stats_metadata%icorr_w_eta_2_ca > 0 ) then
        4006             : !          call stat_update_var( stats_metadata%icorr_w_eta_2_ca, &
        4007             : !                                corr_array_2(iiPDF_w,iiPDF_eta,:), stats_zt )
        4008           0 :           do k = 1, nz, 1
        4009             :              call stat_update_var_pt( stats_metadata%icorr_w_eta_2_ca, k, & ! intent(in)
        4010           0 :                                       corr_array_2(k,iiPDF_w,iiPDF_eta), & ! intent(in)
        4011           0 :                                       stats_zt ) ! intent(inout)
        4012             :           end do ! k = 1, nz, 1
        4013             :        end if
        4014             :
        4015           0 :        do ivar = iiPDF_Ncn+1, pdf_dim, 1
        4016             :
        4017           0 :           hm_idx = pdf2hydromet_idx(ivar,hm_metadata)
        4018             :
        4019             :           ! Correlation (in-precip) of w and the precipitating hydrometeor
        4020             :           ! in PDF component 1.
        4021           0 :           if ( stats_metadata%icorr_w_hm_1(hm_idx) > 0 ) then
        4022             : !             call stat_update_var( stats_metadata%icorr_w_hm_1(hm_idx), &
        4023             : !                                   corr_array_1(ivar,iiPDF_w,:), stats_zt )
        4024           0 :              do k = 1, nz, 1
        4025             :                 call stat_update_var_pt( stats_metadata%icorr_w_hm_1(hm_idx), k, & ! intent(in)
        4026           0 :                                          corr_array_1(k,ivar,iiPDF_w), & ! intent(in)
        4027           0 :                                          stats_zt ) ! intent(inout)
        4028             :              end do ! k = 1, nz, 1
        4029             :           end if
        4030             :
        4031             :           ! Correlation (in-precip) of w and the precipitating hydrometeor
        4032             :           ! in PDF component 2.
        4033           0 :           if ( stats_metadata%icorr_w_hm_2(hm_idx) > 0 ) then
        4034             : !             call stat_update_var( stats_metadata%icorr_w_hm_2(hm_idx), &
        4035             : !                                   corr_array_2(ivar,iiPDF_w,:), stats_zt )
        4036           0 :              do k = 1, nz, 1
        4037             :                 call stat_update_var_pt( stats_metadata%icorr_w_hm_2(hm_idx), k, & ! intent(in)
        4038           0 :                                          corr_array_2(k,ivar,iiPDF_w), & ! intent(in)
        4039           0 :                                          stats_zt ) ! intent(inout)
        4040             :              end do ! k = 1, nz, 1
        4041             :           end if
        4042             :
        4043             :        end do ! ivar = iiPDF_Ncn+1, pdf_dim, 1
        4044             :
        4045             :        ! Correlation of w and N_cn in PDF component 1.
        4046           0 :        if ( stats_metadata%icorr_w_Ncn_1 > 0 ) then
        4047             : !          call stat_update_var( stats_metadata%icorr_w_Ncn_1, &
        4048             : !                                corr_array_1(iiPDF_Ncn,iiPDF_w,:), stats_zt )
        4049           0 :           do k = 1, nz, 1
        4050             :              call stat_update_var_pt( stats_metadata%icorr_w_Ncn_1, k, & ! intent(in)
        4051           0 :                                       corr_array_1(k,iiPDF_Ncn,iiPDF_w), & ! intent(in)
        4052           0 :                                       stats_zt ) ! intent(inout)
        4053             :           end do ! k = 1, nz, 1
        4054             :        end if
        4055             :
        4056             :        ! Correlation of w and N_cn in PDF component 2.
        4057           0 :        if ( stats_metadata%icorr_w_Ncn_2 > 0 ) then
        4058             : !          call stat_update_var( stats_metadata%icorr_w_Ncn_2, &
        4059             : !                                corr_array_2(iiPDF_Ncn,iiPDF_w,:), stats_zt )
        4060           0 :           do k = 1, nz, 1
        4061             :              call stat_update_var_pt( stats_metadata%icorr_w_Ncn_2, k, & ! intent(in)
        4062           0 :                                       corr_array_2(k,iiPDF_Ncn,iiPDF_w), & ! intent(in)
        4063           0 :                                       stats_zt ) ! intent(inout)
        4064             :           end do ! k = 1, nz, 1
        4065             :        end if
        4066             :
        4067             :        ! Correlation of chi (old s) and eta (old t) in PDF component 1 found in
        4068             :        ! the correlation array.
        4069             :        ! The true correlation of chi and eta in each PDF component is solved for
        4070             :        ! by an equation and is part of CLUBB's PDF parameters.  However, there
        4071             :        ! is an option in CLUBB, l_fix_w_chi_eta_correlations, that sets the
        4072             :        ! component correlation of chi and eta to a constant, prescribed value
        4073             :        ! because of SILHS.  The correlation of chi and eta in PDF component 1
        4074             :        ! that is calculated by an equation is stored in stats as
        4075             :        ! "corr_chi_eta_1".  Here, "corr_chi_eta_1_ca" outputs whatever value is
        4076             :        ! found in the correlation array, whether or not it matches
        4077             :        ! "corr_chi_eta_1".
        4078           0 :        if ( stats_metadata%icorr_chi_eta_1_ca > 0 ) then
        4079             : !          call stat_update_var( stats_metadata%icorr_chi_eta_1_ca, &
        4080             : !                                corr_array_1(iiPDF_eta,iiPDF_chi,:), stats_zt )
        4081           0 :           do k = 1, nz, 1
        4082             :              call stat_update_var_pt( stats_metadata%icorr_chi_eta_1_ca, k, & ! intent(in)
        4083           0 :                                       corr_array_1(k,iiPDF_eta,iiPDF_chi), & ! intent(in)
        4084           0 :                                       stats_zt ) ! intent(inout)
        4085             :           end do ! k = 1, nz, 1
        4086             :        end if
        4087             :
        4088             :        ! Correlation of chi (old s) and eta (old t) in PDF component 2 found in
        4089             :        ! the correlation array.
        4090             :        ! The true correlation of chi and eta in each PDF component is solved for
        4091             :        ! by an equation and is part of CLUBB's PDF parameters.  However, there
        4092             :        ! is an option in CLUBB, l_fix_w_chi_eta_correlations, that sets the
        4093             :        ! component correlation of chi and eta to a constant, prescribed value
        4094             :        ! because of SILHS.  The correlation of chi and eta in PDF component 2
        4095             :        ! that is calculated by an equation is stored in stats as
        4096             :        ! "corr_chi_eta_2".  Here, "corr_chi_eta_2_ca" outputs whatever value is
        4097             :        ! found in the correlation array, whether or not it matches
        4098             :        ! "corr_chi_eta_2".
        4099           0 :        if ( stats_metadata%icorr_chi_eta_2_ca > 0 ) then
        4100             : !          call stat_update_var( stats_metadata%icorr_chi_eta_2_ca, &
        4101             : !                                corr_array_2(iiPDF_eta,iiPDF_chi,:), stats_zt )
        4102           0 :           do k = 1, nz, 1
        4103             :              call stat_update_var_pt( stats_metadata%icorr_chi_eta_2_ca, k, & ! intent(in)
        4104           0 :                                       corr_array_2(k,iiPDF_eta,iiPDF_chi), & ! intent(in)
        4105           0 :                                       stats_zt ) ! intent(inout)
        4106             :           end do ! k = 1, nz, 1
        4107             :        end if
        4108             :
        4109           0 :        do ivar = iiPDF_Ncn+1, pdf_dim, 1
        4110             :
        4111           0 :           hm_idx = pdf2hydromet_idx(ivar,hm_metadata)
        4112             :
        4113             :           ! Correlation (in-precip) of chi (old s) and the precipitating
        4114             :           ! hydrometeor in PDF component 1.
        4115           0 :           if ( stats_metadata%icorr_chi_hm_1(hm_idx) > 0 ) then
        4116             : !             call stat_update_var( stats_metadata%icorr_chi_hm_1(hm_idx), &
        4117             : !                                   corr_array_1(ivar,iiPDF_chi,:), stats_zt )
        4118           0 :              do k = 1, nz, 1
        4119             :                 call stat_update_var_pt( stats_metadata%icorr_chi_hm_1(hm_idx), k, & ! intent(in)
        4120           0 :                                          corr_array_1(k,ivar,iiPDF_chi), & ! intent(in)
        4121           0 :                                          stats_zt ) ! intent(inout)
        4122             :              end do ! k = 1, nz, 1
        4123             :           end if
        4124             :
        4125             :           ! Correlation (in-precip) of chi (old s) and the precipitating
        4126             :           ! hydrometeor in PDF component 2.
        4127           0 :           if ( stats_metadata%icorr_chi_hm_2(hm_idx) > 0 ) then
        4128             : !             call stat_update_var( stats_metadata%icorr_chi_hm_2(hm_idx), &
        4129             : !                                   corr_array_2(ivar,iiPDF_chi,:), stats_zt )
        4130           0 :              do k = 1, nz, 1
        4131             :                 call stat_update_var_pt( stats_metadata%icorr_chi_hm_2(hm_idx), k, & ! intent(in)
        4132           0 :                                          corr_array_2(k,ivar,iiPDF_chi), & ! intent(in)
        4133           0 :                                          stats_zt ) ! intent(inout)
        4134             :              end do ! k = 1, nz, 1
        4135             :           end if
        4136             :
        4137             :        end do ! ivar = iiPDF_Ncn+1, pdf_dim, 1
        4138             :
        4139             :        ! Correlation of chi (old s) and N_cn in PDF component 1.
        4140           0 :        if ( stats_metadata%icorr_chi_Ncn_1 > 0 ) then
        4141             : !          call stat_update_var( stats_metadata%icorr_chi_Ncn_1, &
        4142             : !                                corr_array_1(iiPDF_Ncn,iiPDF_chi,:), stats_zt )
        4143           0 :           do k = 1, nz, 1
        4144             :              call stat_update_var_pt( stats_metadata%icorr_chi_Ncn_1, k, & ! intent(in)
        4145           0 :                                       corr_array_1(k,iiPDF_Ncn,iiPDF_chi), & ! intent(inout)
        4146           0 :                                       stats_zt ) ! intent(in)
        4147             :           end do ! k = 1, nz, 1
        4148             :        end if
        4149             :
        4150             :        ! Correlation of chi (old s) and N_cn in PDF component 2.
        4151           0 :        if ( stats_metadata%icorr_chi_Ncn_2 > 0 ) then
        4152             : !          call stat_update_var( stats_metadata%icorr_chi_Ncn_2, &
        4153             : !                                corr_array_2(iiPDF_Ncn,iiPDF_chi,:), stats_zt )
        4154           0 :           do k = 1, nz, 1
        4155             :              call stat_update_var_pt( stats_metadata%icorr_chi_Ncn_2, k, & ! intent(in)
        4156           0 :                                       corr_array_2(k,iiPDF_Ncn,iiPDF_chi), & ! intent(in)
        4157           0 :                                       stats_zt ) ! intent(inout)
        4158             :           end do ! k = 1, nz, 1
        4159             :        end if
        4160             :
        4161           0 :        do ivar = iiPDF_Ncn+1, pdf_dim, 1
        4162             :
        4163           0 :           hm_idx = pdf2hydromet_idx(ivar,hm_metadata)
        4164             :
        4165             :           ! Correlation (in-precip) of eta (old t) and the precipitating
        4166             :           ! hydrometeor in PDF component 1.
        4167           0 :           if ( stats_metadata%icorr_eta_hm_1(hm_idx) > 0 ) then
        4168             : !             call stat_update_var( stats_metadata%icorr_eta_hm_1(hm_idx), &
        4169             : !                                   corr_array_1(ivar,iiPDF_eta,:), stats_zt )
        4170           0 :              do k = 1, nz, 1
        4171             :                 call stat_update_var_pt( stats_metadata%icorr_eta_hm_1(hm_idx), k, & ! intent(in)
        4172           0 :                                          corr_array_1(k,ivar,iiPDF_eta), & ! intent(in)
        4173           0 :                                          stats_zt ) ! intent(inout)
        4174             :              end do ! k = 1, nz, 1
        4175             :           end if
        4176             :
        4177             :           ! Correlation (in-precip) of eta (old t) and the precipitating
        4178             :           ! hydrometeor in PDF component 2.
        4179           0 :           if ( stats_metadata%icorr_eta_hm_2(hm_idx) > 0 ) then
        4180             : !             call stat_update_var( stats_metadata%icorr_eta_hm_2(hm_idx), &
        4181             : !                                   corr_array_2(ivar,iiPDF_eta,:), stats_zt )
        4182           0 :              do k = 1, nz, 1
        4183             :                 call stat_update_var_pt( stats_metadata%icorr_eta_hm_2(hm_idx), k, & ! intent(in)
        4184           0 :                                          corr_array_2(k,ivar,iiPDF_eta), & ! intent(in)
        4185           0 :                                          stats_zt ) ! intent(inout)
        4186             :              end do ! k = 1, nz, 1
        4187             :           end if
        4188             :
        4189             :        end do ! ivar = iiPDF_Ncn+1, pdf_dim, 1
        4190             :
        4191             :        ! Correlation of eta (old t) and N_cn in PDF component 1.
        4192           0 :        if ( stats_metadata%icorr_eta_Ncn_1 > 0 ) then
        4193             : !          call stat_update_var( stats_metadata%icorr_eta_Ncn_1, &
        4194             : !                                corr_array_1(iiPDF_Ncn,iiPDF_eta,:), stats_zt )
        4195           0 :           do k = 1, nz, 1
        4196             :              call stat_update_var_pt( stats_metadata%icorr_eta_Ncn_1, k, & ! intent(in)
        4197           0 :                                       corr_array_1(k,iiPDF_Ncn,iiPDF_eta), & ! intent(in)
        4198           0 :                                       stats_zt ) ! intent(inout)
        4199             :           end do ! k = 1, nz, 1
        4200             :        end if
        4201             :
        4202             :        ! Correlation of eta (old t) and N_cn in PDF component 2.
        4203           0 :        if ( stats_metadata%icorr_eta_Ncn_2 > 0 ) then
        4204             : !          call stat_update_var( stats_metadata%icorr_eta_Ncn_2, &
        4205             : !                                corr_array_2(iiPDF_Ncn,iiPDF_eta,:), stats_zt )
        4206           0 :           do k = 1, nz, 1
        4207             :              call stat_update_var_pt( stats_metadata%icorr_eta_Ncn_2, k, & ! intent(in)
        4208           0 :                                       corr_array_2(k,iiPDF_Ncn,iiPDF_eta), & ! intent(in)
        4209           0 :                                       stats_zt ) ! intent(inout)
        4210             :           end do ! k = 1, nz, 1
        4211             :        end if
        4212             :
        4213           0 :        do ivar = iiPDF_Ncn+1, pdf_dim, 1
        4214             :
        4215           0 :           hm_idx = pdf2hydromet_idx(ivar,hm_metadata)
        4216             :
        4217             :           ! Correlation (in-precip) of N_cn and the precipitating
        4218             :           ! hydrometeor in PDF component 1.
        4219           0 :           if ( stats_metadata%icorr_Ncn_hm_1(hm_idx) > 0 ) then
        4220             : !             call stat_update_var( stats_metadata%icorr_Ncn_hm_1(hm_idx), &
        4221             : !                                   corr_array_1(ivar,iiPDF_Ncn,:), stats_zt )
        4222           0 :              do k = 1, nz, 1
        4223             :                 call stat_update_var_pt( stats_metadata%icorr_Ncn_hm_1(hm_idx), k, & ! intent(in)
        4224           0 :                                          corr_array_1(k,ivar,iiPDF_Ncn), & ! intent(in)
        4225           0 :                                          stats_zt ) ! intent(inout)
        4226             :              end do ! k = 1, nz, 1
        4227             :           end if
        4228             :
        4229             :           ! Correlation (in-precip) of N_cn and the precipitating
        4230             :           ! hydrometeor in PDF component 2.
        4231           0 :           if ( stats_metadata%icorr_Ncn_hm_2(hm_idx) > 0 ) then
        4232             : !             call stat_update_var( stats_metadata%icorr_Ncn_hm_2(hm_idx), &
        4233             : !                                   corr_array_2(ivar,iiPDF_Ncn,:), stats_zt )
        4234           0 :              do k = 1, nz, 1
        4235             :                 call stat_update_var_pt( stats_metadata%icorr_Ncn_hm_2(hm_idx), k, & ! intent(in)
        4236           0 :                                          corr_array_2(k,ivar,iiPDF_Ncn), & ! intent(in)
        4237           0 :                                          stats_zt ) ! intent(inout)
        4238             :              end do ! k = 1, nz, 1
        4239             :           end if
        4240             :
        4241             :        end do ! ivar = iiPDF_Ncn+1, pdf_dim, 1
        4242             :
        4243           0 :        do ivar = iiPDF_Ncn+1, pdf_dim, 1
        4244             :
        4245           0 :           hm_idx_ivar = pdf2hydromet_idx(ivar,hm_metadata)
        4246             :
        4247           0 :           do jvar = ivar+1, pdf_dim, 1
        4248             :
        4249           0 :              hm_idx_jvar = pdf2hydromet_idx(jvar,hm_metadata)
        4250             :
        4251             :              ! Correlation (in-precip) of two different hydrometeors (hmx and
        4252             :              ! hmy) in PDF component 1.
        4253           0 :              if ( stats_metadata%icorr_hmx_hmy_1(hm_idx_jvar,hm_idx_ivar) > 0 ) then
        4254             : !               call stat_update_var( stats_metadata%icorr_hmx_hmy_1(hm_idx_jvar,hm_idx_ivar), &
        4255             : !                                     corr_array_1(jvar,ivar,:), stats_zt )
        4256           0 :                do k = 1, nz, 1
        4257             :                   call stat_update_var_pt( stats_metadata%icorr_hmx_hmy_1(hm_idx_jvar,hm_idx_ivar), k, & ! in
        4258           0 :                                            corr_array_1(k,jvar,ivar), & ! intent(in)
        4259           0 :                                            stats_zt ) ! intent(inout)
        4260             :                end do ! k = 1, nz, 1
        4261             :              end if
        4262             :
        4263             :              ! Correlation (in-precip) of two different hydrometeors (hmx and
        4264             :              ! hmy) in PDF component 2.
        4265           0 :              if ( stats_metadata%icorr_hmx_hmy_2(hm_idx_jvar,hm_idx_ivar) > 0 ) then
        4266             : !               call stat_update_var( stats_metadata%icorr_hmx_hmy_2(hm_idx_jvar,hm_idx_ivar), &
        4267             : !                                     corr_array_2(jvar,ivar,:), stats_zt )
        4268           0 :                do k = 1, nz, 1
        4269             :                   call stat_update_var_pt( stats_metadata%icorr_hmx_hmy_2(hm_idx_jvar,hm_idx_ivar), k, & ! in
        4270           0 :                                            corr_array_2(k,jvar,ivar), & ! intent(in)
        4271           0 :                                            stats_zt ) ! intent(inout)
        4272             :                end do ! k = 1, nz, 1
        4273             :              end if
        4274             :
        4275             :           end do ! jvar = ivar+1, pdf_dim, 1
        4276             :        end do ! ivar = iiPDF_Ncn+1, pdf_dim, 1
        4277             :
        4278             :     end if ! stats_metadata%l_stats_samp
        4279             :
        4280             :
        4281           0 :     return
        4282             :
        4283             :   end subroutine pdf_param_hm_stats
        4284             :
        4285             :   !=============================================================================
        4286           0 :   subroutine pdf_param_ln_hm_stats( nz, pdf_dim, hm_metadata, &
        4287           0 :                                     mu_x_1_n, mu_x_2_n, &
        4288           0 :                                     sigma_x_1_n, sigma_x_2_n, &
        4289           0 :                                     corr_array_1_n, &
        4290           0 :                                     corr_array_2_n, &
        4291             :                                     stats_metadata, &
        4292             :                                     stats_zt )
        4293             :
        4294             :     ! Description:
        4295             :     ! Record statistics for normal space PDF parameters involving hydrometeors.
        4296             :
        4297             :     ! References:
        4298             :     !-----------------------------------------------------------------------
        4299             :
        4300             :     use index_mapping, only: &
        4301             :         pdf2hydromet_idx  ! Procedure(s)
        4302             :
        4303             :     use corr_varnce_module, only: &
        4304             :         hm_metadata_type
        4305             :
        4306             :     use clubb_precision, only: &
        4307             :         core_rknd   ! Variable(s)
        4308             :
        4309             :     use stats_type_utilities, only: &
        4310             :         stat_update_var_pt  ! Procedure(s)
        4311             :
        4312             :     use stats_type, only: &
        4313             :         stats ! Type
        4314             :
        4315             :     use stats_variables, only: &
        4316             :         stats_metadata_type
        4317             :
        4318             :     implicit none
        4319             :
        4320             :     !------------------------ Input Variables ------------------------
        4321             :     integer, intent(in) :: &
        4322             :       nz,      & ! Number of vertical levels
        4323             :       pdf_dim    ! Number of variables in the correlation array
        4324             :
        4325             :     type (hm_metadata_type), intent(in) :: &
        4326             :       hm_metadata
        4327             :
        4328             :     real( kind = core_rknd ), dimension(nz,pdf_dim), intent(in) :: &
        4329             :       mu_x_1_n,    & ! Mean array (normal space): PDF vars. (comp. 1) [un. vary]
        4330             :       mu_x_2_n,    & ! Mean array (normal space): PDF vars. (comp. 2) [un. vary]
        4331             :       sigma_x_1_n, & ! Std. dev. array (normal space): PDF vars (comp. 1) [u.v.]
        4332             :       sigma_x_2_n    ! Std. dev. array (normal space): PDF vars (comp. 2) [u.v.]
        4333             :
        4334             :     real( kind = core_rknd ), dimension(nz,pdf_dim,pdf_dim), &
        4335             :     intent(in) :: &
        4336             :       corr_array_1_n, & ! Corr. array (normal space) of PDF vars. (comp. 1)  [-]
        4337             :       corr_array_2_n    ! Corr. array (normal space) of PDF vars. (comp. 2)  [-]
        4338             :
        4339             :     type (stats_metadata_type), intent(in) :: &
        4340             :       stats_metadata
        4341             :
        4342             :     !------------------------ InOut Variables ------------------------
        4343             :     type (stats), target, intent(inout) :: &
        4344             :       stats_zt
        4345             :
        4346             :     !------------------------ Local Variables ------------------------
        4347             :     real( kind = core_rknd ), dimension(nz) :: &
        4348           0 :       mu_hm_1_n,  & ! Mean of ln hm (1st PDF component)    [units vary]
        4349           0 :       mu_hm_2_n,  & ! Mean of ln hm (2nd PDF component)    [units vary]
        4350           0 :       mu_Ncn_1_n, & ! Mean of ln Ncn (1st PDF component)   [ln(num/kg)]
        4351           0 :       mu_Ncn_2_n    ! Mean of ln Ncn (2nd PDF component)   [ln(num/kg)]
        4352             :
        4353             :     integer :: ivar, jvar, hm_idx, hm_idx_ivar, hm_idx_jvar, k  ! Indices
        4354             :
        4355             :     ! Just to avoid typing hm_metadata%iiPDF_x everywhere
        4356             :     integer :: &
        4357             :       iiPDF_chi, &
        4358             :       iiPDF_eta, &
        4359             :       iiPDF_w,   &
        4360             :       iiPDF_Ncn
        4361             :
        4362             :     !------------------------ Begin Code ------------------------
        4363             :
        4364           0 :     iiPDF_chi = hm_metadata%iiPDF_chi
        4365           0 :     iiPDF_eta = hm_metadata%iiPDF_eta
        4366           0 :     iiPDF_w   = hm_metadata%iiPDF_w
        4367           0 :     iiPDF_Ncn = hm_metadata%iiPDF_Ncn
        4368             :
        4369             :     !!! Output the statistics for normal space hydrometeor PDF parameters.
        4370             :
        4371             :     ! Statistics
        4372           0 :     if ( stats_metadata%l_stats_samp ) then
        4373             :
        4374             :        ! Switch back to using stat_update_var once the code is generalized
        4375             :        ! to pass in the number of vertical levels.
        4376           0 :        do ivar = iiPDF_Ncn+1, pdf_dim, 1
        4377             :
        4378           0 :           hm_idx = pdf2hydromet_idx(ivar,hm_metadata)
        4379             :
        4380             :           ! Mean (in-precip) of ln hm in PDF component 1.
        4381           0 :           if ( stats_metadata%imu_hm_1_n(hm_idx) > 0 ) then
        4382           0 :              where ( mu_x_1_n(:,ivar) > real( -huge( 0.0 ), kind = core_rknd ) )
        4383           0 :                 mu_hm_1_n = mu_x_1_n(:,ivar)
        4384             :              elsewhere
        4385             :                 ! When hm_1 is 0 (or below tolerance value), mu_hm_1_n is -inf,
        4386             :                 ! and is set to -huge for the default CLUBB kind.  Some
        4387             :                 ! compilers have issues outputting to stats files (in single
        4388             :                 ! precision) when the default CLUBB kind is in double precision.
        4389             :                 ! Set to -huge for single precision.
        4390             :                 mu_hm_1_n = real( -huge( 0.0 ), kind = core_rknd )
        4391             :              endwhere
        4392             : !             call stat_update_var( stats_metadata%imu_hm_1_n(hm_idx), mu_hm_1_n, stats_zt )
        4393           0 :              do k = 1, nz, 1
        4394           0 :                 call stat_update_var_pt( stats_metadata%imu_hm_1_n(hm_idx), k, mu_hm_1_n(k), & ! intent(in)
        4395           0 :                                          stats_zt ) ! intent(inout)
        4396             :              end do ! k = 1, nz, 1
        4397             :           end if
        4398             :
        4399             :           ! Mean (in-precip) of ln hm in PDF component 2.
        4400           0 :           if ( stats_metadata%imu_hm_2_n(hm_idx) > 0 ) then
        4401           0 :              where ( mu_x_2_n(:,ivar) > real( -huge( 0.0 ), kind = core_rknd ) )
        4402           0 :                 mu_hm_2_n = mu_x_2_n(:,ivar)
        4403             :              elsewhere
        4404             :                 ! When hm_2 is 0 (or below tolerance value), mu_hm_2_n is -inf,
        4405             :                 ! and is set to -huge for the default CLUBB kind.  Some
        4406             :                 ! compilers have issues outputting to stats files (in single
        4407             :                 ! precision) when the default CLUBB kind is in double precision.
        4408             :                 ! Set to -huge for single precision.
        4409             :                 mu_hm_2_n = real( -huge( 0.0 ), kind = core_rknd )
        4410             :              endwhere
        4411             : !             call stat_update_var( stats_metadata%imu_hm_2_n(hm_idx), mu_hm_2_n, stats_zt )
        4412           0 :              do k = 1, nz, 1
        4413           0 :                 call stat_update_var_pt( stats_metadata%imu_hm_2_n(hm_idx), k, mu_hm_2_n(k), & ! intent(in)
        4414           0 :                                          stats_zt ) ! intent(inout)
        4415             :              end do ! k = 1, nz, 1
        4416             :           end if
        4417             :
        4418             :        end do ! ivar = iiPDF_Ncn+1, pdf_dim, 1
        4419             :
        4420             :        ! Mean of ln N_cn in PDF component 1.
        4421           0 :        if ( stats_metadata%imu_Ncn_1_n > 0 ) then
        4422             :           where ( mu_x_1_n(:,iiPDF_Ncn) &
        4423           0 :                   > real( -huge( 0.0 ), kind = core_rknd ) )
        4424           0 :              mu_Ncn_1_n = mu_x_1_n(:,iiPDF_Ncn)
        4425             :           elsewhere
        4426             :              ! When Ncnm is 0 (or below tolerance value), mu_Ncn_1_n is -inf,
        4427             :              ! and is set to -huge for the default CLUBB kind.  Some compilers
        4428             :              ! have issues outputting to stats files (in single precision) when
        4429             :              ! the default CLUBB kind is in double precision.
        4430             :              ! Set to -huge for single precision.
        4431             :              mu_Ncn_1_n = real( -huge( 0.0 ), kind = core_rknd )
        4432             :           endwhere
        4433             : !          call stat_update_var( stats_metadata%imu_Ncn_1_n, mu_Ncn_1_n, stats_zt )
        4434           0 :           do k = 1, nz, 1
        4435           0 :              call stat_update_var_pt( stats_metadata%imu_Ncn_1_n, k, mu_Ncn_1_n(k), & ! intent(in)
        4436           0 :                                       stats_zt ) ! intent(inout)
        4437             :           end do ! k = 1, nz, 1
        4438             :        end if
        4439             :
        4440             :        ! Mean of ln N_cn in PDF component 2.
        4441           0 :        if ( stats_metadata%imu_Ncn_2_n > 0 ) then
        4442             :           where ( mu_x_2_n(:,iiPDF_Ncn) &
        4443           0 :                   > real( -huge( 0.0 ), kind = core_rknd ) )
        4444           0 :              mu_Ncn_2_n = mu_x_2_n(:,iiPDF_Ncn)
        4445             :           elsewhere
        4446             :              ! When Ncnm is 0 (or below tolerance value), mu_Ncn_2_n is -inf,
        4447             :              ! and is set to -huge for the default CLUBB kind.  Some compilers
        4448             :              ! have issues outputting to stats files (in single precision) when
        4449             :              ! the default CLUBB kind is in double precision.
        4450             :              ! Set to -huge for single precision.
        4451             :              mu_Ncn_2_n = real( -huge( 0.0 ), kind = core_rknd )
        4452             :           endwhere
        4453             : !          call stat_update_var( stats_metadata%imu_Ncn_2_n, mu_Ncn_2_n, stats_zt )
        4454           0 :           do k = 1, nz, 1
        4455           0 :              call stat_update_var_pt( stats_metadata%imu_Ncn_2_n, k, mu_Ncn_2_n(k), & ! intent(in)
        4456           0 :                                       stats_zt ) ! intent(inout)
        4457             :           end do ! k = 1, nz, 1
        4458             :        end if
        4459             :
        4460           0 :        do ivar = iiPDF_Ncn+1, pdf_dim, 1
        4461             :
        4462           0 :           hm_idx = pdf2hydromet_idx(ivar,hm_metadata)
        4463             :
        4464             :           ! Standard deviation (in-precip) of ln hm in PDF component 1.
        4465           0 :           if ( stats_metadata%isigma_hm_1_n(hm_idx) > 0 ) then
        4466             : !             call stat_update_var( stats_metadata%isigma_hm_1_n(hm_idx), sigma_x_1_n(ivar,:), &
        4467             : !                                   stats_zt )
        4468           0 :              do k = 1, nz, 1
        4469             :                 call stat_update_var_pt( stats_metadata%isigma_hm_1_n(hm_idx), k, & ! intent(in)
        4470           0 :                                          sigma_x_1_n(k,ivar), & ! intent(in)
        4471           0 :                                          stats_zt ) ! intent(inout)
        4472             :              end do ! k = 1, nz, 1
        4473             :           end if
        4474             :
        4475             :           ! Standard deviation (in-precip) of ln hm in PDF component 2.
        4476           0 :           if ( stats_metadata%isigma_hm_2_n(hm_idx) > 0 ) then
        4477             : !             call stat_update_var( stats_metadata%isigma_hm_2_n(hm_idx), sigma_x_2_n(ivar,:), &
        4478             : !                                   stats_zt )
        4479           0 :              do k = 1, nz, 1
        4480             :                 call stat_update_var_pt( stats_metadata%isigma_hm_2_n(hm_idx), k, & ! intent(in)
        4481           0 :                                          sigma_x_2_n(k,ivar), & ! intent(in)
        4482           0 :                                          stats_zt ) ! intent(inout)
        4483             :              end do ! k = 1, nz, 1
        4484             :           end if
        4485             :
        4486             :        end do ! ivar = iiPDF_Ncn+1, pdf_dim, 1
        4487             :
        4488             :        ! Standard deviation of ln N_cn in PDF component 1.
        4489           0 :        if ( stats_metadata%isigma_Ncn_1_n > 0 ) then
        4490             : !          call stat_update_var( stats_metadata%isigma_Ncn_1_n, sigma_x_1_n(iiPDF_Ncn,:), &
        4491             : !                                stats_zt )
        4492           0 :           do k = 1, nz, 1
        4493             :              call stat_update_var_pt( stats_metadata%isigma_Ncn_1_n, k, & ! intent(in)
        4494           0 :                                       sigma_x_1_n(k,iiPDF_Ncn), & ! intent(in)
        4495           0 :                                       stats_zt ) ! intent(inout)
        4496             :           end do ! k = 1, nz, 1
        4497             :        end if
        4498             :
        4499             :        ! Standard deviation of ln N_cn in PDF component 2.
        4500           0 :        if ( stats_metadata%isigma_Ncn_2_n > 0 ) then
        4501             : !          call stat_update_var( stats_metadata%isigma_Ncn_2_n, sigma_x_2_n(iiPDF_Ncn,:), &
        4502             : !                                stats_zt )
        4503           0 :           do k = 1, nz, 1
        4504             :              call stat_update_var_pt( stats_metadata%isigma_Ncn_2_n, k, & ! intent(in)
        4505           0 :                                       sigma_x_2_n(k,iiPDF_Ncn), & ! intent(in)
        4506           0 :                                       stats_zt ) ! intent(inout)
        4507             :           end do ! k = 1, nz, 1
        4508             :        end if
        4509             :
        4510           0 :        do ivar = iiPDF_Ncn+1, pdf_dim, 1
        4511             :
        4512           0 :           hm_idx = pdf2hydromet_idx(ivar,hm_metadata)
        4513             :
        4514             :           ! Correlation (in-precip) of w and ln hm in PDF component 1.
        4515           0 :           if ( stats_metadata%icorr_w_hm_1_n(hm_idx) > 0 ) then
        4516             : !             call stat_update_var( stats_metadata%icorr_w_hm_1_n(hm_idx), &
        4517             : !                                   corr_array_1_n(ivar,iiPDF_w,:), stats_zt )
        4518           0 :              do k = 1, nz, 1
        4519             :                 call stat_update_var_pt( stats_metadata%icorr_w_hm_1_n(hm_idx), k, & ! intent(in)
        4520           0 :                                          corr_array_1_n(k,ivar,iiPDF_w), & ! intent(in)
        4521           0 :                                          stats_zt ) ! intent(inout)
        4522             :              end do ! k = 1, nz, 1
        4523             :           end if
        4524             :
        4525             :           ! Correlation (in-precip) of w and ln hm in PDF component 2.
        4526           0 :           if ( stats_metadata%icorr_w_hm_2_n(hm_idx) > 0 ) then
        4527             : !             call stat_update_var( stats_metadata%icorr_w_hm_2_n(hm_idx), &
        4528             : !                                   corr_array_2_n(ivar,iiPDF_w,:), stats_zt )
        4529           0 :              do k = 1, nz, 1
        4530             :                 call stat_update_var_pt( stats_metadata%icorr_w_hm_2_n(hm_idx), k, & ! intent(in)
        4531           0 :                                          corr_array_2_n(k,ivar,iiPDF_w), & ! intent(in)
        4532           0 :                                          stats_zt ) ! intent(inout)
        4533             :              end do ! k = 1, nz, 1
        4534             :           end if
        4535             :
        4536             :        end do ! ivar = iiPDF_Ncn+1, pdf_dim, 1
        4537             :
        4538             :        ! Correlation of w and ln N_cn in PDF component 1.
        4539           0 :        if ( stats_metadata%icorr_w_Ncn_1_n > 0 ) then
        4540             : !          call stat_update_var( stats_metadata%icorr_w_Ncn_1_n, &
        4541             : !                                corr_array_1_n(iiPDF_Ncn,iiPDF_w,:), stats_zt )
        4542           0 :           do k = 1, nz, 1
        4543             :              call stat_update_var_pt( stats_metadata%icorr_w_Ncn_1_n, k, & ! intent(in)
        4544           0 :                                       corr_array_1_n(k,iiPDF_Ncn,iiPDF_w), & ! intent(in)
        4545           0 :                                       stats_zt ) ! intent(inout)
        4546             :           end do ! k = 1, nz, 1
        4547             :        end if
        4548             :
        4549             :        ! Correlation of w and ln N_cn in PDF component 2.
        4550           0 :        if ( stats_metadata%icorr_w_Ncn_2_n > 0 ) then
        4551             : !          call stat_update_var( stats_metadata%icorr_w_Ncn_2_n, &
        4552             : !                                corr_array_2_n(iiPDF_Ncn,iiPDF_w,:), stats_zt )
        4553           0 :           do k = 1, nz, 1
        4554             :              call stat_update_var_pt( stats_metadata%icorr_w_Ncn_2_n, k, & ! intent(in)
        4555           0 :                                       corr_array_2_n(k,iiPDF_Ncn,iiPDF_w), & ! intent(in)
        4556           0 :                                       stats_zt ) ! intent(inout)
        4557             :           end do ! k = 1, nz, 1
        4558             :        end if
        4559             :
        4560           0 :        do ivar = iiPDF_Ncn+1, pdf_dim, 1
        4561             :
        4562           0 :           hm_idx = pdf2hydromet_idx(ivar,hm_metadata)
        4563             :
        4564             :           ! Correlation (in-precip) of chi (old s) and ln hm in PDF component 1.
        4565           0 :           if ( stats_metadata%icorr_chi_hm_1_n(hm_idx) > 0 ) then
        4566             : !             call stat_update_var( stats_metadata%icorr_chi_hm_1_n(hm_idx), &
        4567             : !                                   corr_array_1_n(ivar,iiPDF_chi,:), stats_zt )
        4568           0 :              do k = 1, nz, 1
        4569             :                 call stat_update_var_pt( stats_metadata%icorr_chi_hm_1_n(hm_idx), k, & ! intent(in)
        4570           0 :                                          corr_array_1_n(k,ivar,iiPDF_chi), & ! intent(in)
        4571           0 :                                          stats_zt ) ! intent(inout)
        4572             :              end do ! k = 1, nz, 1
        4573             :           end if
        4574             :
        4575             :           ! Correlation (in-precip) of chi( old s) and ln hm in PDF component 2.
        4576           0 :           if ( stats_metadata%icorr_chi_hm_2_n(hm_idx) > 0 ) then
        4577             : !             call stat_update_var( stats_metadata%icorr_chi_hm_2_n(hm_idx), &
        4578             : !                                   corr_array_2_n(ivar,iiPDF_chi,:), stats_zt )
        4579           0 :              do k = 1, nz, 1
        4580             :                 call stat_update_var_pt( stats_metadata%icorr_chi_hm_2_n(hm_idx), k, & ! intent(in)
        4581           0 :                                          corr_array_2_n(k,ivar,iiPDF_chi), & ! intent(in)
        4582           0 :                                          stats_zt ) ! intent(inout)
        4583             :              end do ! k = 1, nz, 1
        4584             :           end if
        4585             :
        4586             :        end do ! ivar = iiPDF_Ncn+1, pdf_dim, 1
        4587             :
        4588             :        ! Correlation of chi (old s) and ln N_cn in PDF component 1.
        4589           0 :        if ( stats_metadata%icorr_chi_Ncn_1_n > 0 ) then
        4590             : !          call stat_update_var( stats_metadata%icorr_chi_Ncn_1_n, &
        4591             : !                                corr_array_1_n(iiPDF_Ncn,iiPDF_chi,:), &
        4592             : !                                stats_zt )
        4593           0 :           do k = 1, nz, 1
        4594             :              call stat_update_var_pt( stats_metadata%icorr_chi_Ncn_1_n, k, & ! intent(in)
        4595           0 :                                       corr_array_1_n(k,iiPDF_Ncn,iiPDF_chi), & ! intent(in)
        4596           0 :                                       stats_zt ) ! intent(inout)
        4597             :           end do ! k = 1, nz, 1
        4598             :        end if
        4599             :
        4600             :        ! Correlation of chi(old s) and ln N_cn in PDF component 2.
        4601           0 :        if ( stats_metadata%icorr_chi_Ncn_2_n > 0 ) then
        4602             : !          call stat_update_var( stats_metadata%icorr_chi_Ncn_2_n, &
        4603             : !                                corr_array_2_n(iiPDF_Ncn,iiPDF_chi,:), &
        4604             : !                                stats_zt )
        4605           0 :           do k = 1, nz, 1
        4606             :              call stat_update_var_pt( stats_metadata%icorr_chi_Ncn_2_n, k, & ! intent(in)
        4607           0 :                                       corr_array_2_n(k,iiPDF_Ncn,iiPDF_chi), & ! intent(in)
        4608           0 :                                       stats_zt ) ! intent(inout)
        4609             :           end do ! k = 1, nz, 1
        4610             :        end if
        4611             :
        4612           0 :        do ivar = iiPDF_Ncn+1, pdf_dim, 1
        4613             :
        4614           0 :           hm_idx = pdf2hydromet_idx(ivar,hm_metadata)
        4615             :
        4616             :           ! Correlation (in-precip) of eta (old t) and ln hm in PDF component 1.
        4617           0 :           if ( stats_metadata%icorr_eta_hm_1_n(hm_idx) > 0 ) then
        4618             : !             call stat_update_var( stats_metadata%icorr_eta_hm_1_n(hm_idx), &
        4619             : !                                   corr_array_1_n(ivar,iiPDF_eta,:), stats_zt )
        4620           0 :              do k = 1, nz, 1
        4621             :                 call stat_update_var_pt( stats_metadata%icorr_eta_hm_1_n(hm_idx), k, & ! intent(in)
        4622           0 :                                          corr_array_1_n(k,ivar,iiPDF_eta), & ! intent(in)
        4623           0 :                                          stats_zt ) ! intent(inout)
        4624             :              end do ! k = 1, nz, 1
        4625             :           end if
        4626             :
        4627             :           ! Correlation (in-precip) of eta (old t) and ln hm in PDF component 2.
        4628           0 :           if ( stats_metadata%icorr_eta_hm_2_n(hm_idx) > 0 ) then
        4629             : !             call stat_update_var( stats_metadata%icorr_eta_hm_2_n(hm_idx), &
        4630             : !                                   corr_array_2_n(ivar,iiPDF_eta,:), stats_zt )
        4631           0 :              do k = 1, nz, 1
        4632             :                 call stat_update_var_pt( stats_metadata%icorr_eta_hm_2_n(hm_idx), k, & ! intent(in)
        4633           0 :                                          corr_array_2_n(k,ivar,iiPDF_eta), & ! intent(in)
        4634           0 :                                          stats_zt ) ! intent(inout)
        4635             :              end do ! k = 1, nz, 1
        4636             :           end if
        4637             :
        4638             :        end do ! ivar = iiPDF_Ncn+1, pdf_dim, 1
        4639             :
        4640             :        ! Correlation of eta (old t) and ln N_cn in PDF component 1.
        4641           0 :        if ( stats_metadata%icorr_eta_Ncn_1_n > 0 ) then
        4642             : !          call stat_update_var( stats_metadata%icorr_eta_Ncn_1_n, &
        4643             : !                                corr_array_1_n(iiPDF_Ncn,iiPDF_eta,:), &
        4644             : !                                stats_zt )
        4645           0 :           do k = 1, nz, 1
        4646             :              call stat_update_var_pt( stats_metadata%icorr_eta_Ncn_1_n, k, & ! intent(in)
        4647           0 :                                       corr_array_1_n(k,iiPDF_Ncn,iiPDF_eta), & ! intent(in)
        4648           0 :                                       stats_zt ) ! intent(inout)
        4649             :           end do ! k = 1, nz, 1
        4650             :        end if
        4651             :
        4652             :        ! Correlation of eta (old t) and ln N_cn in PDF component 2.
        4653           0 :        if ( stats_metadata%icorr_eta_Ncn_2_n > 0 ) then
        4654             : !          call stat_update_var( stats_metadata%icorr_eta_Ncn_2_n, &
        4655             : !                                corr_array_2_n(iiPDF_Ncn,iiPDF_eta,:), &
        4656             : !                                stats_zt )
        4657           0 :           do k = 1, nz, 1
        4658             :              call stat_update_var_pt( stats_metadata%icorr_eta_Ncn_2_n, k, & ! intent(in)
        4659           0 :                                       corr_array_2_n(k,iiPDF_Ncn,iiPDF_eta), & ! intent(in)
        4660           0 :                                       stats_zt ) ! intent(inout)
        4661             :           end do ! k = 1, nz, 1
        4662             :        end if
        4663             :
        4664           0 :        do ivar = iiPDF_Ncn+1, pdf_dim, 1
        4665             :
        4666           0 :           hm_idx = pdf2hydromet_idx(ivar,hm_metadata)
        4667             :
        4668             :           ! Correlation (in-precip) of ln N_cn and ln hm in PDF
        4669             :           ! component 1.
        4670           0 :           if ( stats_metadata%icorr_Ncn_hm_1_n(hm_idx) > 0 ) then
        4671             : !             call stat_update_var( stats_metadata%icorr_Ncn_hm_1_n(hm_idx), &
        4672             : !                                   corr_array_1_n(ivar,iiPDF_Ncn,:), stats_zt )
        4673           0 :              do k = 1, nz, 1
        4674             :                 call stat_update_var_pt( stats_metadata%icorr_Ncn_hm_1_n(hm_idx), k, & ! intent(in)
        4675           0 :                                          corr_array_1_n(k,ivar,iiPDF_Ncn), & ! intent(in)
        4676           0 :                                          stats_zt ) ! intent(inout)
        4677             :              end do ! k = 1, nz, 1
        4678             :           end if
        4679             :
        4680             :           ! Correlation (in-precip) of ln N_cn and ln hm in PDF
        4681             :           ! component 2.
        4682           0 :           if ( stats_metadata%icorr_Ncn_hm_2_n(hm_idx) > 0 ) then
        4683             : !             call stat_update_var( stats_metadata%icorr_Ncn_hm_2_n(hm_idx), &
        4684             : !                                   corr_array_2_n(ivar,iiPDF_Ncn,:), stats_zt )
        4685           0 :              do k = 1, nz, 1
        4686             :                 call stat_update_var_pt( stats_metadata%icorr_Ncn_hm_2_n(hm_idx), k, & ! intent(in)
        4687           0 :                                          corr_array_2_n(k,ivar,iiPDF_Ncn), & ! intent(in)
        4688           0 :                                          stats_zt )! intent(inout)
        4689             :              end do ! k = 1, nz, 1
        4690             :           end if
        4691             :
        4692             :        end do ! ivar = iiPDF_Ncn+1, pdf_dim, 1
        4693             :
        4694           0 :        do ivar = iiPDF_Ncn+1, pdf_dim, 1
        4695             :
        4696           0 :           hm_idx_ivar = pdf2hydromet_idx(ivar,hm_metadata)
        4697             :
        4698           0 :           do jvar = ivar+1, pdf_dim, 1
        4699             :
        4700           0 :              hm_idx_jvar= pdf2hydromet_idx(jvar,hm_metadata)
        4701             :
        4702             :              ! Correlation (in-precip) of ln hmx and ln hmy (two different
        4703             :              ! hydrometeors) in PDF component 1.
        4704           0 :              if ( stats_metadata%icorr_hmx_hmy_1_n(hm_idx_jvar,hm_idx_ivar) > 0 ) then
        4705             : !                call stat_update_var( &
        4706             : !                        stats_metadata%icorr_hmx_hmy_1_n(hm_idx_jvar,hm_idx_ivar), &
        4707             : !                        corr_array_1_n(jvar,ivar,:), stats_zt )
        4708           0 :                 do k = 1, nz, 1
        4709             :                    call stat_update_var_pt( &
        4710             :                         stats_metadata%icorr_hmx_hmy_1_n(hm_idx_jvar,hm_idx_ivar), k, & ! intent(in)
        4711           0 :                         corr_array_1_n(k,jvar,ivar), & ! intent(in)
        4712           0 :                         stats_zt ) ! intent(inout)
        4713             :                 end do ! k = 1, nz, 1
        4714             :              end if
        4715             :
        4716             :              ! Correlation (in-precip) of ln hmx and ln hmy (two different
        4717             :              ! hydrometeors) in PDF component 2.
        4718           0 :              if ( stats_metadata%icorr_hmx_hmy_2_n(hm_idx_jvar,hm_idx_ivar) > 0 ) then
        4719             : !                call stat_update_var( &
        4720             : !                        stats_metadata%icorr_hmx_hmy_2_n(hm_idx_jvar,hm_idx_ivar), &
        4721             : !                        corr_array_2_n(jvar,ivar,:), stats_zt )
        4722           0 :                 do k = 1, nz, 1
        4723             :                    call stat_update_var_pt( &
        4724             :                         stats_metadata%icorr_hmx_hmy_2_n(hm_idx_jvar,hm_idx_ivar), k, & ! intent(in)
        4725           0 :                         corr_array_2_n(k,jvar,ivar), & ! intent(in)
        4726           0 :                         stats_zt ) ! intent(inout)
        4727             :                 end do ! k = 1, nz, 1
        4728             :              end if
        4729             :
        4730             :           end do ! jvar = ivar+1, pdf_dim, 1
        4731             :        end do ! ivar = iiPDF_Ncn+1, pdf_dim, 1
        4732             :
        4733             :     end if ! stats_metadata%l_stats_samp
        4734             :
        4735             :
        4736           0 :     return
        4737             :
        4738             :   end subroutine pdf_param_ln_hm_stats
        4739             :
        4740             :   !=============================================================================
        4741           0 :   subroutine pack_hydromet_pdf_params( nz, ngrdcol,                   & ! In
        4742             :                                        hydromet_dim, hm_metadata,  & ! In
        4743           0 :                                        hm_1, hm_2, pdf_dim, mu_x_1,   & ! In
        4744           0 :                                        mu_x_2, sigma_x_1, sigma_x_2,  & ! In
        4745           0 :                                        corr_array_1, corr_array_2,    & ! In
        4746           0 :                                        hydromet_pdf_params )            ! Out
        4747             :
        4748             :     ! Description:
        4749             :     ! Pack the standard means and variances involving hydrometeors, as well as a
        4750             :     ! few other variables, into the structure hydromet_pdf_params.
        4751             :
        4752             :     ! References:
        4753             :     !-----------------------------------------------------------------------
        4754             :
        4755             :     use constants_clubb, only: &
        4756             :         one  ! Constant(s)
        4757             :
        4758             :     use hydromet_pdf_parameter_module, only: &
        4759             :         hydromet_pdf_parameter  ! Variable(s)
        4760             :
        4761             :     use index_mapping, only: &
        4762             :         hydromet2pdf_idx  ! Procedure(s)
        4763             :
        4764             :     use corr_varnce_module, only: &
        4765             :         hm_metadata_type
        4766             :
        4767             :     use clubb_precision, only: &
        4768             :         core_rknd  ! Variable(s)
        4769             :
        4770             :     implicit none
        4771             :
        4772             :     !-------------------------- Input Variables --------------------------
        4773             :     integer, intent(in) :: &
        4774             :       nz,           & ! Number of vertical grid levels
        4775             :       ngrdcol,      & ! Number of grid columns
        4776             :       hydromet_dim    ! Number of hydrometeor species
        4777             :
        4778             :     real( kind = core_rknd ), dimension(ngrdcol,nz,hydromet_dim), intent(in) :: &
        4779             :       hm_1, & ! Mean of a precip. hydrometeor (1st PDF component)  [units vary]
        4780             :       hm_2    ! Mean of a precip. hydrometeor (2nd PDF component)  [units vary]
        4781             :
        4782             :     integer, intent(in) :: &
        4783             :       pdf_dim   ! Number of variables in the mean/stdev arrays
        4784             :
        4785             :     type (hm_metadata_type), intent(in) :: &
        4786             :       hm_metadata
        4787             :
        4788             :     real( kind = core_rknd ), dimension(ngrdcol,nz,pdf_dim), intent(in) :: &
        4789             :       mu_x_1,    & ! Mean array of PDF vars. (1st PDF component)    [units vary]
        4790             :       mu_x_2,    & ! Mean array of PDF vars. (2nd PDF component)    [units vary]
        4791             :       sigma_x_1, & ! Standard deviation array of PDF vars (comp. 1) [units vary]
        4792             :       sigma_x_2    ! Standard deviation array of PDF vars (comp. 2) [units vary]
        4793             :
        4794             :     real( kind = core_rknd ), dimension(ngrdcol,nz,pdf_dim,pdf_dim), intent(in) :: &
        4795             :       corr_array_1, & ! Correlation array of PDF vars. (comp. 1)    [-]
        4796             :       corr_array_2    ! Correlation array of PDF vars. (comp. 2)    [-]
        4797             :
        4798             :     !-------------------------- Output Variable --------------------------
        4799             :     type(hydromet_pdf_parameter), dimension(ngrdcol,nz), intent(out) :: &
        4800             :       hydromet_pdf_params    ! Hydrometeor PDF parameters        [units vary]
        4801             :
        4802             :     !-------------------------- Local Variables --------------------------
        4803             :     integer :: ivar, jvar, pdf_idx  ! Indices
        4804             :
        4805             :     ! Just to avoid typing hm_metadata%iiPDF_x everywhere
        4806             :     integer :: &
        4807             :       iiPDF_chi, &
        4808             :       iiPDF_eta, &
        4809             :       iiPDF_w,   &
        4810             :       iiPDF_Ncn
        4811             :
        4812             :     !------------------------ Begin Code ------------------------
        4813             :
        4814           0 :     iiPDF_chi = hm_metadata%iiPDF_chi
        4815           0 :     iiPDF_eta = hm_metadata%iiPDF_eta
        4816           0 :     iiPDF_w   = hm_metadata%iiPDF_w
        4817           0 :     iiPDF_Ncn = hm_metadata%iiPDF_Ncn
        4818             :
        4819             :
        4820             :     ! Pack remaining means and standard deviations into hydromet_pdf_params.
        4821           0 :     do ivar = 1, hydromet_dim, 1
        4822             :
        4823           0 :       pdf_idx = hydromet2pdf_idx(ivar,hm_metadata)
        4824             :
        4825             :       ! Mean of a hydrometeor (overall) in the 1st PDF component.
        4826           0 :       hydromet_pdf_params(:,:)%hm_1(ivar) = hm_1(:,:,ivar)
        4827             :       ! Mean of a hydrometeor (overall) in the 2nd PDF component.
        4828           0 :       hydromet_pdf_params(:,:)%hm_2(ivar) = hm_2(:,:,ivar)
        4829             :
        4830             :       ! Mean of a hydrometeor (in-precip) in the 1st PDF component.
        4831           0 :       hydromet_pdf_params(:,:)%mu_hm_1(ivar) = mu_x_1(:,:,pdf_idx)
        4832             :       ! Mean of a hydrometeor (in-precip) in the 2nd PDF component.
        4833           0 :       hydromet_pdf_params(:,:)%mu_hm_2(ivar) = mu_x_2(:,:,pdf_idx)
        4834             :
        4835             :       ! Standard deviation of a hydrometeor (in-precip) in the
        4836             :       ! 1st PDF component.
        4837           0 :       hydromet_pdf_params(:,:)%sigma_hm_1(ivar) = sigma_x_1(:,:,pdf_idx)
        4838             :       ! Standard deviation of a hydrometeor (in-precip) in the
        4839             :       ! 2nd PDF component.
        4840           0 :       hydromet_pdf_params(:,:)%sigma_hm_2(ivar) = sigma_x_2(:,:,pdf_idx)
        4841             :
        4842             :       ! Correlation (in-precip) of w and a hydrometeor in the 1st PDF
        4843             :       ! component.
        4844           0 :       hydromet_pdf_params(:,:)%corr_w_hm_1(ivar) = corr_array_1(:,:,pdf_idx,iiPDF_w)
        4845             :
        4846             :       ! Correlation (in-precip) of w and a hydrometeor in the 2nd PDF
        4847             :       ! component.
        4848           0 :       hydromet_pdf_params(:,:)%corr_w_hm_2(ivar) = corr_array_2(:,:,pdf_idx,iiPDF_w)
        4849             :
        4850             :       ! Correlation (in-precip) of chi and a hydrometeor in the 1st PDF
        4851             :       ! component.
        4852           0 :       hydromet_pdf_params(:,:)%corr_chi_hm_1(ivar) &
        4853           0 :       = corr_array_1(:,:,pdf_idx,iiPDF_chi)
        4854             :
        4855             :       ! Correlation (in-precip) of chi and a hydrometeor in the 2nd PDF
        4856             :       ! component.
        4857           0 :       hydromet_pdf_params(:,:)%corr_chi_hm_2(ivar) &
        4858           0 :       = corr_array_2(:,:,pdf_idx,iiPDF_chi)
        4859             :
        4860             :       ! Correlation (in-precip) of eta and a hydrometeor in the 1st PDF
        4861             :       ! component.
        4862           0 :       hydromet_pdf_params(:,:)%corr_eta_hm_1(ivar) &
        4863           0 :       = corr_array_1(:,:,pdf_idx,iiPDF_eta)
        4864             :
        4865             :       ! Correlation (in-precip) of eta and a hydrometeor in the 2nd PDF
        4866             :       ! component.
        4867           0 :       hydromet_pdf_params(:,:)%corr_eta_hm_2(ivar) &
        4868           0 :       = corr_array_2(:,:,pdf_idx,iiPDF_eta)
        4869             :
        4870             :       ! Correlation (in-precip) of two hydrometeors, hmx and hmy, in the 1st
        4871             :       ! PDF component.
        4872           0 :       hydromet_pdf_params(:,:)%corr_hmx_hmy_1(ivar,ivar) = one
        4873             :
        4874           0 :       do jvar = ivar+1, hydromet_dim, 1
        4875             :
        4876           0 :         hydromet_pdf_params(:,:)%corr_hmx_hmy_1(jvar,ivar) &
        4877           0 :         = corr_array_1(:,:,hydromet2pdf_idx(jvar,hm_metadata),pdf_idx)
        4878             :
        4879           0 :         hydromet_pdf_params(:,:)%corr_hmx_hmy_1(ivar,jvar) &
        4880           0 :         = hydromet_pdf_params(:,:)%corr_hmx_hmy_1(jvar,ivar)
        4881             :
        4882             :       end do ! jvar = ivar+1, hydromet_dim, 1
        4883             :
        4884             :       ! Correlation (in-precip) of two hydrometeors, hmx and hmy, in the 2nd
        4885             :       ! PDF component.
        4886           0 :       hydromet_pdf_params(:,:)%corr_hmx_hmy_2(ivar,ivar) = one
        4887             :
        4888           0 :       do jvar = ivar+1, hydromet_dim, 1
        4889             :
        4890           0 :         hydromet_pdf_params(:,:)%corr_hmx_hmy_2(jvar,ivar) &
        4891           0 :         = corr_array_2(:,:,hydromet2pdf_idx(jvar,hm_metadata),pdf_idx)
        4892             :
        4893           0 :         hydromet_pdf_params(:,:)%corr_hmx_hmy_2(ivar,jvar) &
        4894           0 :         = hydromet_pdf_params(:,:)%corr_hmx_hmy_2(jvar,ivar)
        4895             :
        4896             :       end do ! jvar = ivar+1, hydromet_dim, 1
        4897             :
        4898             :     end do ! ivar = 1, hydromet_dim, 1
        4899             :
        4900             :     ! Mean of Ncn (overall) in the 1st PDF component.
        4901           0 :     hydromet_pdf_params(:,:)%mu_Ncn_1 = mu_x_1(:,:,iiPDF_Ncn)
        4902             :     ! Mean of Ncn (overall) in the 2nd PDF component.
        4903           0 :     hydromet_pdf_params(:,:)%mu_Ncn_2 = mu_x_2(:,:,iiPDF_Ncn)
        4904             :
        4905             :     ! Standard deviation of Ncn (overall) in the 1st PDF component.
        4906           0 :     hydromet_pdf_params(:,:)%sigma_Ncn_1 = sigma_x_1(:,:,iiPDF_Ncn)
        4907             :     ! Standard deviation of Ncn (overall) in the 2nd PDF component.
        4908           0 :     hydromet_pdf_params(:,:)%sigma_Ncn_2 = sigma_x_2(:,:,iiPDF_Ncn)
        4909             :
        4910             :
        4911           0 :     return
        4912             :
        4913             :   end subroutine pack_hydromet_pdf_params
        4914             :
        4915             :   !=============================================================================
        4916           0 :   elemental function compute_rtp2_from_chi( sigma_chi_1, sigma_chi_2,        &
        4917             :                                             sigma_eta_1, sigma_eta_2,        &
        4918             :                                             rt_1, rt_2,                      &
        4919             :                                             crt_1, crt_2,                    &
        4920             :                                             mixt_frac,                       &
        4921             :                                             corr_chi_eta_1, corr_chi_eta_2 ) &
        4922             :   result( rtp2_zt_from_chi )
        4923             :
        4924             :     ! Description:
        4925             :     ! Compute the variance of rt from the distribution of chi and eta. The
        4926             :     ! resulting variance will be consistent with CLUBB's extended PDF
        4927             :     ! involving chi and eta, including if l_fix_w_chi_eta_correlations = .true..
        4928             :
        4929             :     ! References:
        4930             :     !   None
        4931             :     !-----------------------------------------------------------------------
        4932             :
        4933             :     use clubb_precision, only: &
        4934             :         core_rknd    ! Constant
        4935             :
        4936             :     use pdf_utilities, only: &
        4937             :         compute_variance_binormal   ! Procedure
        4938             :
        4939             :     use constants_clubb, only: &
        4940             :         one_half, & ! Constant(s)
        4941             :         one,      &
        4942             :         two
        4943             :
        4944             :     implicit none
        4945             :
        4946             :     ! Input Variables
        4947             :     real( kind = core_rknd ), intent(in) :: &
        4948             :       sigma_chi_1,         & ! Standard deviation of chi (1st PDF comp.) [kg/kg]
        4949             :       sigma_chi_2,         & ! Standard deviation of chi (2nd PDF comp.) [kg/kg]
        4950             :       sigma_eta_1,         & ! Standard deviation of eta (1st PDF comp.) [kg/kg]
        4951             :       sigma_eta_2,         & ! Standard deviation of eta (2nd PDF comp.) [kg/kg]
        4952             :       crt_1,               & ! Coef. of r_t in chi/eta eqns. (1st comp.) [-]
        4953             :       crt_2,               & ! Coef. of r_t in chi/eta eqns. (2nd comp.) [-]
        4954             :       rt_1,                & ! Mean of rt (1st PDF component)            [kg/kg]
        4955             :       rt_2,                & ! Mean of rt (2nd PDF component)            [kg/kg]
        4956             :       mixt_frac              ! Weight of 1st gaussian PDF component      [-]
        4957             :
        4958             :     real( kind = core_rknd ), intent(in) :: &
        4959             :       corr_chi_eta_1, & ! Correlation of chi and eta in 1st PDF component [-]
        4960             :       corr_chi_eta_2    ! Correlation of chi and eta in 2nd PDF component [-]
        4961             :
        4962             :     ! Output Variable
        4963             :     real( kind = core_rknd ) :: &
        4964             :       rtp2_zt_from_chi    ! Grid-box variance of rtp2 on thermo. levels  [kg/kg]
        4965             :
        4966             :     ! Local Variables
        4967             :     real( kind = core_rknd ) :: &
        4968             :       varnce_rt_1_zt_from_chi, varnce_rt_2_zt_from_chi
        4969             :
        4970             :     real( kind = core_rknd ) :: &
        4971             :       rtm, &                 ! Mean of rt (overall) [kg/kg]
        4972             :       sigma_rt_1_from_chi, & ! Standard deviation of rt (1st PDF comp.)  [kg/kg]
        4973             :       sigma_rt_2_from_chi    ! Standard deviation of rt (2nd PDF comp.)  [kg/kg]
        4974             :
        4975             :
        4976             :   !-----------------------------------------------------------------------
        4977             :
        4978             :     !----- Begin Code -----
        4979             :
        4980             :     varnce_rt_1_zt_from_chi &
        4981             :     = ( corr_chi_eta_1 * sigma_chi_1 * sigma_eta_1 &
        4982             :         + one_half * sigma_chi_1**2 + one_half * sigma_eta_1**2 ) &
        4983           0 :         / ( two * crt_1**2 )
        4984             :
        4985             :     varnce_rt_2_zt_from_chi &
        4986             :     = ( corr_chi_eta_2 * sigma_chi_2 * sigma_eta_2 &
        4987             :         + one_half * sigma_chi_2**2 + one_half * sigma_eta_2**2 ) &
        4988           0 :         / ( two * crt_2**2 )
        4989             :
        4990           0 :     rtm = mixt_frac*rt_1 + (one-mixt_frac)*rt_2
        4991             :
        4992           0 :     sigma_rt_1_from_chi = sqrt( varnce_rt_1_zt_from_chi )
        4993           0 :     sigma_rt_2_from_chi = sqrt( varnce_rt_2_zt_from_chi )
        4994             :
        4995             :     rtp2_zt_from_chi &
        4996             :     = compute_variance_binormal( rtm, rt_1, rt_2, sigma_rt_1_from_chi, &
        4997           0 :                                  sigma_rt_2_from_chi, mixt_frac )
        4998             :
        4999             :
        5000             :     return
        5001             :
        5002             :   end function compute_rtp2_from_chi
        5003             :
        5004             : !===============================================================================
        5005             :
        5006             : end module setup_clubb_pdf_params

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