Line data Source code
1 : module gw_rdg
2 :
3 : !
4 : ! This module handles gravity waves from orographic sources, and was
5 : ! extracted from gw_drag in May 2013.
6 : !
7 : use shr_const_mod, only: pii => shr_const_pi
8 : use gw_utils, only: r8
9 : use gw_common, only: pver
10 : use coords_1d, only: Coords1D
11 : use spmd_utils,only: masterproc
12 : use cam_abortutils, only: endrun
13 :
14 :
15 : implicit none
16 : private
17 : save
18 :
19 : ! Public interface
20 : public :: gw_rdg_readnl
21 : public :: gw_rdg_src
22 : public :: gw_rdg_belowpeak
23 : public :: gw_rdg_break_trap
24 : public :: gw_rdg_do_vdiff
25 :
26 : ! Tunable Parameters
27 : !--------------------
28 : logical :: do_divstream
29 :
30 : !===========================================
31 : ! Parameters for DS2017 (do_divstream=.T.)
32 : !===========================================
33 : ! Amplification factor - 1.0 for
34 : ! high-drag/windstorm regime
35 : real(r8), protected :: C_BetaMax_DS
36 :
37 : ! Max Ratio Fr2:Fr1 - 1.0
38 : real(r8), protected :: C_GammaMax
39 :
40 : ! Normalized limits for Fr2(Frx) function
41 : real(r8), protected :: Frx0
42 : real(r8), protected :: Frx1
43 :
44 :
45 : !===========================================
46 : ! Parameters for SM2000
47 : !===========================================
48 : ! Amplification factor - 1.0 for
49 : ! high-drag/windstorm regime
50 : real(r8), protected :: C_BetaMax_SM
51 :
52 :
53 :
54 : ! NOTE: Critical inverse Froude number Fr_c is
55 : ! 1./(SQRT(2.)~0.707 in SM2000
56 : ! (should be <= 1)
57 : real(r8), protected :: Fr_c
58 :
59 : logical, protected :: gw_rdg_do_vdiff=.true.
60 :
61 : logical :: do_smooth_regimes
62 : logical :: do_adjust_tauoro
63 : logical :: do_backward_compat
64 :
65 :
66 : ! Limiters (min/max values)
67 : ! min surface displacement height for orographic waves (m)
68 : real(r8), protected :: orohmin
69 : ! min wind speed for orographic waves
70 : real(r8), protected :: orovmin
71 : ! min stratification allowing wave behavior
72 : real(r8), protected :: orostratmin
73 : ! min stratification allowing wave behavior
74 : real(r8), protected :: orom2min
75 :
76 : !==========================================================================
77 : contains
78 : !==========================================================================
79 :
80 0 : subroutine gw_rdg_readnl(nlfile)
81 : use namelist_utils, only: find_group_name
82 : use units, only: getunit, freeunit
83 : use spmd_utils, only: mpicom, mstrid=>masterprocid, mpi_real8, mpi_logical
84 :
85 : ! File containing namelist input.
86 : character(len=*), intent(in) :: nlfile
87 :
88 : ! Local variables
89 : integer :: unitn, ierr
90 : character(len=*), parameter :: sub = 'gw_rdg_readnl'
91 :
92 : logical :: gw_rdg_do_divstream, gw_rdg_do_smooth_regimes, gw_rdg_do_adjust_tauoro, &
93 : gw_rdg_do_backward_compat
94 :
95 :
96 : real(r8) :: gw_rdg_C_BetaMax_DS, gw_rdg_C_GammaMax, &
97 : gw_rdg_Frx0, gw_rdg_Frx1, gw_rdg_C_BetaMax_SM, gw_rdg_Fr_c, &
98 : gw_rdg_orohmin, gw_rdg_orovmin, gw_rdg_orostratmin, gw_rdg_orom2min
99 :
100 : namelist /gw_rdg_nl/ gw_rdg_do_divstream, gw_rdg_C_BetaMax_DS, gw_rdg_C_GammaMax, &
101 : gw_rdg_Frx0, gw_rdg_Frx1, gw_rdg_C_BetaMax_SM, gw_rdg_Fr_c, &
102 : gw_rdg_do_smooth_regimes, gw_rdg_do_adjust_tauoro, &
103 : gw_rdg_do_backward_compat, gw_rdg_orohmin, gw_rdg_orovmin, &
104 : gw_rdg_orostratmin, gw_rdg_orom2min, gw_rdg_do_vdiff
105 :
106 : !----------------------------------------------------------------------
107 :
108 0 : if (masterproc) then
109 0 : unitn = getunit()
110 0 : open( unitn, file=trim(nlfile), status='old' )
111 0 : call find_group_name(unitn, 'gw_rdg_nl', status=ierr)
112 0 : if (ierr == 0) then
113 0 : read(unitn, gw_rdg_nl, iostat=ierr)
114 0 : if (ierr /= 0) then
115 0 : call endrun(sub // ':: ERROR reading namelist')
116 : end if
117 : end if
118 0 : close(unitn)
119 0 : call freeunit(unitn)
120 :
121 : ! Set the local variables
122 0 : do_divstream = gw_rdg_do_divstream
123 0 : C_BetaMax_DS = gw_rdg_C_BetaMax_DS
124 0 : C_GammaMax = gw_rdg_C_GammaMax
125 0 : Frx0 = gw_rdg_Frx0
126 0 : Frx1 = gw_rdg_Frx1
127 0 : C_BetaMax_SM = gw_rdg_C_BetaMax_SM
128 0 : Fr_c = gw_rdg_Fr_c
129 0 : do_smooth_regimes = gw_rdg_do_smooth_regimes
130 0 : do_adjust_tauoro = gw_rdg_do_adjust_tauoro
131 0 : do_backward_compat = gw_rdg_do_backward_compat
132 0 : orohmin = gw_rdg_orohmin
133 0 : orovmin = gw_rdg_orovmin
134 0 : orostratmin = gw_rdg_orostratmin
135 0 : orom2min = gw_rdg_orom2min
136 : end if
137 :
138 : ! Broadcast the local variables
139 :
140 0 : call mpi_bcast(do_divstream, 1, mpi_logical, mstrid, mpicom, ierr)
141 0 : if (ierr /= 0) call endrun(sub//": FATAL: mpi_bcast: do_divstream")
142 0 : call mpi_bcast(do_smooth_regimes, 1, mpi_logical, mstrid, mpicom, ierr)
143 0 : if (ierr /= 0) call endrun(sub//": FATAL: mpi_bcast: do_smooth_regimes")
144 0 : call mpi_bcast(do_adjust_tauoro, 1, mpi_logical, mstrid, mpicom, ierr)
145 0 : if (ierr /= 0) call endrun(sub//": FATAL: mpi_bcast: do_adjust_tauoro")
146 0 : call mpi_bcast(do_backward_compat, 1, mpi_logical, mstrid, mpicom, ierr)
147 0 : if (ierr /= 0) call endrun(sub//": FATAL: mpi_bcast: do_backward_compat")
148 :
149 0 : call mpi_bcast(C_BetaMax_DS, 1, mpi_real8, mstrid, mpicom, ierr)
150 0 : if (ierr /= 0) call endrun(sub//": FATAL: mpi_bcast: C_BetaMax_DS")
151 0 : call mpi_bcast(C_GammaMax, 1, mpi_real8, mstrid, mpicom, ierr)
152 0 : if (ierr /= 0) call endrun(sub//": FATAL: mpi_bcast: C_GammaMax")
153 0 : call mpi_bcast(Frx0, 1, mpi_real8, mstrid, mpicom, ierr)
154 0 : if (ierr /= 0) call endrun(sub//": FATAL: mpi_bcast: Frx0")
155 0 : call mpi_bcast(Frx1, 1, mpi_real8, mstrid, mpicom, ierr)
156 0 : if (ierr /= 0) call endrun(sub//": FATAL: mpi_bcast: Frx1")
157 0 : call mpi_bcast(C_BetaMax_SM, 1, mpi_real8, mstrid, mpicom, ierr)
158 0 : if (ierr /= 0) call endrun(sub//": FATAL: mpi_bcast: C_BetaMax_SM")
159 0 : call mpi_bcast(Fr_c, 1, mpi_real8, mstrid, mpicom, ierr)
160 0 : if (ierr /= 0) call endrun(sub//": FATAL: mpi_bcast: Fr_c")
161 0 : call mpi_bcast(orohmin, 1, mpi_real8, mstrid, mpicom, ierr)
162 0 : if (ierr /= 0) call endrun(sub//": FATAL: mpi_bcast: orohmin")
163 0 : call mpi_bcast(orovmin, 1, mpi_real8, mstrid, mpicom, ierr)
164 0 : if (ierr /= 0) call endrun(sub//": FATAL: mpi_bcast: orovmin")
165 0 : call mpi_bcast(orostratmin, 1, mpi_real8, mstrid, mpicom, ierr)
166 0 : if (ierr /= 0) call endrun(sub//": FATAL: mpi_bcast: orostratmin")
167 0 : call mpi_bcast(orom2min, 1, mpi_real8, mstrid, mpicom, ierr)
168 0 : if (ierr /= 0) call endrun(sub//": FATAL: mpi_bcast: orom2min")
169 :
170 0 : call mpi_bcast(gw_rdg_do_vdiff, 1, mpi_logical, mstrid, mpicom, ierr)
171 0 : if (ierr /= 0) call endrun(sub//": FATAL: mpi_bcast: gw_rdg_do_vdiff")
172 :
173 0 : if (Fr_c > 1.0_r8) call endrun(sub//": FATAL: Fr_c must be <= 1")
174 :
175 0 : end subroutine gw_rdg_readnl
176 :
177 :
178 0 : subroutine gw_rdg_src(ncol, band, p, &
179 0 : u, v, t, mxdis, angxy, anixy, kwvrdg, iso, zi, nm, &
180 0 : src_level, tend_level, bwv_level ,tlb_level , tau, ubm, ubi, xv, yv, &
181 0 : ubmsrc, usrc, vsrc, nsrc, rsrc, m2src, tlb, bwv, Fr1, Fr2, Frx, c)
182 : use gw_common, only: rair, GWBand
183 : use gw_utils, only: dot_2d, midpoint_interp
184 : !-----------------------------------------------------------------------
185 : ! Orographic source for multiple gravity wave drag parameterization.
186 : !
187 : ! The stress is returned for a single wave with c=0, over orography.
188 : ! For points where the orographic variance is small (including ocean),
189 : ! the returned stress is zero.
190 : !------------------------------Arguments--------------------------------
191 : ! Column dimension.
192 : integer, intent(in) :: ncol
193 :
194 : ! Band to emit orographic waves in.
195 : ! Regardless, we will only ever emit into l = 0.
196 : type(GWBand), intent(in) :: band
197 : ! Pressure coordinates.
198 : type(Coords1D), intent(in) :: p
199 :
200 :
201 : ! Midpoint zonal/meridional winds. ( m s-1)
202 : real(r8), intent(in) :: u(ncol,pver), v(ncol,pver)
203 : ! Midpoint temperatures. (K)
204 : real(r8), intent(in) :: t(ncol,pver)
205 : ! Height estimate for ridge (m) [anisotropic orography].
206 : real(r8), intent(in) :: mxdis(ncol)
207 : ! Angle of ridge axis w/resp to north (degrees) [anisotropic orography].
208 : real(r8), intent(in) :: angxy(ncol)
209 : ! Anisotropy parameter [anisotropic orography].
210 : real(r8), intent(in) :: anixy(ncol)
211 : ! horiz wavenumber [anisotropic orography].
212 : real(r8), intent(in) :: kwvrdg(ncol)
213 : ! Isotropic source flag [anisotropic orography].
214 : integer, intent(in) :: iso(ncol)
215 : ! Interface altitudes above ground (m).
216 : real(r8), intent(in) :: zi(ncol,pver+1)
217 : ! Midpoint Brunt-Vaisalla frequencies (s-1).
218 : real(r8), intent(in) :: nm(ncol,pver)
219 :
220 : ! Indices of top gravity wave source level and lowest level where wind
221 : ! tendencies are allowed.
222 : integer, intent(out) :: src_level(ncol)
223 : integer, intent(out) :: tend_level(ncol)
224 : integer, intent(out) :: bwv_level(ncol),tlb_level(ncol)
225 :
226 : ! Averages over source region.
227 : real(r8), intent(out) :: nsrc(ncol) ! B-V frequency.
228 : real(r8), intent(out) :: rsrc(ncol) ! Density.
229 : real(r8), intent(out) :: usrc(ncol) ! Zonal wind.
230 : real(r8), intent(out) :: vsrc(ncol) ! Meridional wind.
231 : real(r8), intent(out) :: ubmsrc(ncol) ! On-ridge wind.
232 : ! Top of low-level flow layer.
233 : real(r8), intent(out) :: tlb(ncol)
234 : ! Bottom of linear wave region.
235 : real(r8), intent(out) :: bwv(ncol)
236 : ! normalized wavenumber
237 : real(r8), intent(out) :: m2src(ncol)
238 :
239 :
240 : ! Wave Reynolds stress.
241 : real(r8), intent(out) :: tau(ncol,-band%ngwv:band%ngwv,pver+1)
242 : ! Projection of wind at midpoints and interfaces.
243 : real(r8), intent(out) :: ubm(ncol,pver), ubi(ncol,pver+1)
244 : ! Unit vectors of source wind (zonal and meridional components).
245 : real(r8), intent(out) :: xv(ncol), yv(ncol)
246 : ! Phase speeds.
247 : real(r8), intent(out) :: c(ncol,-band%ngwv:band%ngwv)
248 : ! Froude numbers for flow/drag regimes
249 : real(r8), intent(out) :: Fr1(ncol), Fr2(ncol), Frx(ncol)
250 :
251 : !---------------------------Local Storage-------------------------------
252 : ! Column and level indices.
253 : integer :: i, k
254 :
255 : ! Surface streamline displacement height (2*sgh).
256 0 : real(r8) :: hdsp(ncol)
257 :
258 : ! Difference in interface pressure across source region.
259 0 : real(r8) :: dpsrc(ncol)
260 : ! Thickness of downslope wind region.
261 0 : real(r8) :: ddw(ncol)
262 : ! Thickness of linear wave region.
263 0 : real(r8) :: dwv(ncol)
264 : ! Wind speed in source region.
265 0 : real(r8) :: wmsrc(ncol)
266 :
267 0 : real(r8) :: ragl(ncol)
268 :
269 : !--------------------------------------------------------------------------
270 : ! Check that ngwav is equal to zero, otherwise end the job
271 : !--------------------------------------------------------------------------
272 0 : if (band%ngwv /= 0) call endrun(' gw_rdg_src :: ERROR - band%ngwv must be zero and it is not')
273 :
274 : !--------------------------------------------------------------------------
275 : ! Average the basic state variables for the wave source over the depth of
276 : ! the orographic standard deviation. Here we assume that the appropiate
277 : ! values of wind, stability, etc. for determining the wave source are
278 : ! averages over the depth of the atmosphere penterated by the typical
279 : ! mountain.
280 : ! Reduces to the bottom midpoint values when mxdis=0, such as over ocean.
281 : !--------------------------------------------------------------------------
282 :
283 0 : hdsp = mxdis ! no longer multipied by 2
284 0 : src_level = pver+1
285 0 : bwv_level = -1
286 0 : tlb_level = -1
287 :
288 0 : tau(:,0,:) = 0.0_r8
289 :
290 : ! Find depth of "source layer" for mountain waves
291 : ! i.e., between ground and mountain top
292 0 : do k = pver, 1, -1
293 0 : do i = 1, ncol
294 : ! Need to have h >= z(k+1) here or code will bomb when h=0.
295 0 : if ( (hdsp(i) >= zi(i,k+1)) .and. (hdsp(i) < zi(i,k)) ) then
296 0 : src_level(i) = k
297 : end if
298 : end do
299 : end do
300 :
301 0 : rsrc = 0._r8
302 0 : usrc = 0._r8
303 0 : vsrc = 0._r8
304 0 : nsrc = 0._r8
305 0 : do i = 1, ncol
306 0 : do k = pver, src_level(i), -1
307 0 : rsrc(i) = rsrc(i) + p%mid(i,k) / (rair*t(i,k))* p%del(i,k)
308 0 : usrc(i) = usrc(i) + u(i,k) * p%del(i,k)
309 0 : vsrc(i) = vsrc(i) + v(i,k) * p%del(i,k)
310 0 : nsrc(i) = nsrc(i) + nm(i,k)* p%del(i,k)
311 : end do
312 : end do
313 :
314 :
315 0 : do i = 1, ncol
316 0 : dpsrc(i) = p%ifc(i,pver+1) - p%ifc(i,src_level(i))
317 : end do
318 :
319 0 : rsrc = rsrc / dpsrc
320 0 : usrc = usrc / dpsrc
321 0 : vsrc = vsrc / dpsrc
322 0 : nsrc = nsrc / dpsrc
323 :
324 0 : wmsrc = sqrt( usrc**2 + vsrc**2 )
325 :
326 :
327 : ! Get the unit vector components
328 : ! Want agl=0 with U>0 to give xv=1
329 :
330 0 : ragl = angxy * pii/180._r8
331 :
332 : ! protect from wierd "bad" angles
333 : ! that may occur if hdsp is zero
334 0 : where( hdsp <= orohmin )
335 : ragl = 0._r8
336 : end where
337 :
338 0 : yv =-sin( ragl )
339 0 : xv = cos( ragl )
340 :
341 :
342 : ! Kluge in possible "isotropic" obstacle.
343 0 : where( ( iso == 1 ) .and. (wmsrc > orovmin) )
344 : xv = usrc/wmsrc
345 : yv = vsrc/wmsrc
346 : end where
347 :
348 :
349 : ! Project the local wind at midpoints into the on-ridge direction
350 0 : do k = 1, pver
351 0 : ubm(:,k) = dot_2d(u(:,k), v(:,k), xv, yv)
352 : end do
353 0 : ubmsrc = dot_2d(usrc , vsrc , xv, yv)
354 :
355 : ! Ensure on-ridge wind is positive at source level
356 0 : do k = 1, pver
357 0 : ubm(:,k) = sign( ubmsrc*0._r8+1._r8 , ubmsrc ) * ubm(:,k)
358 : end do
359 :
360 : ! Sean says just use 1._r8 as
361 : ! first argument
362 0 : xv = sign( ubmsrc*0._r8+1._r8 , ubmsrc ) * xv
363 0 : yv = sign( ubmsrc*0._r8+1._r8 , ubmsrc ) * yv
364 :
365 : ! Now make ubmsrc positive and protect
366 : ! against zero
367 0 : ubmsrc = abs(ubmsrc)
368 0 : ubmsrc = max( 0.01_r8 , ubmsrc )
369 :
370 :
371 : ! The minimum stratification allowing GW behavior
372 : ! should really depend on horizontal scale since
373 : !
374 : ! m^2 ~ (N/U)^2 - k^2
375 : !
376 : ! Should also think about parameterizing
377 : ! trapped lee-waves.
378 :
379 :
380 : ! This needs to be made constistent with later
381 : ! treatment of nonhydrostatic effects.
382 0 : m2src = ( (nsrc/(ubmsrc+0.01_r8))**2 - kwvrdg**2 ) /((nsrc/(ubmsrc+0.01_r8))**2)
383 :
384 :
385 : !-------------------------------------------------------------
386 : ! Calculate provisional limits (in Z [m]) for 3 regimes. This
387 : ! will modified later if wave breaking or trapping are
388 : ! diagnosed
389 : !
390 : ! ^
391 : ! | *** linear propagation ***
392 : ! (H) -------- mountain top ------------- | *** or wave breaking ****
393 : ! | *** regimes *************
394 : ! (BWV)------ bottom of linear waves ---- |
395 : ! : |
396 : ! ******* |
397 : ! : |
398 : ! (TLB)--- top of flow diversion layer--- '
399 : ! :
400 : ! **** flow diversion *****
401 : ! :
402 : !============================================
403 :
404 : !============================================
405 : ! For Dividing streamline para (DS2017)
406 : !--------------------------------------------
407 : ! High-drag downslope wind regime exists
408 : ! between bottom of linear waves and top of
409 : ! flow diversion. Linear waves can only
410 : ! attain vertical displacment of f1*U/N. So,
411 : ! bottom of linear waves is given by
412 : !
413 : ! BWV = H - Fr1*U/N
414 : !
415 : ! Downslope wind layer begins at BWV and
416 : ! extends below it until some maximum high
417 : ! drag obstacle height Fr2*U/N is attained
418 : ! (where Fr2 >= f1). Below downslope wind
419 : ! there is flow diversion, so top of
420 : ! diversion layer (TLB) is equivalent to
421 : ! bottom of downslope wind layer and is;
422 : !
423 : ! TLB = H - Fr2*U/N
424 : !
425 : !-----------------------------------------
426 :
427 : ! Critical inverse Froude number
428 : !-----------------------------------------------
429 0 : Fr1(:) = Fr_c * 1.00_r8
430 0 : Frx(:) = hdsp(:)*nsrc(:)/abs( ubmsrc(:) ) / Fr_c
431 :
432 0 : if ( do_divstream ) then
433 : !------------------------------------------------
434 : ! Calculate Fr2(Frx) for DS2017
435 : !------------------------------------------------
436 0 : where(Frx <= Frx0)
437 : Fr2(:) = Fr1(:) + Fr1(:)* C_GammaMax * anixy(:)
438 : elsewhere((Frx > Frx0).and.(Frx <= Frx1) )
439 : Fr2(:) = Fr1(:) + Fr1(:)* C_GammaMax * anixy(:) &
440 : * (Frx1 - Frx(:))/(Frx1-Frx0)
441 : elsewhere(Frx > Frx1)
442 : Fr2(:)=Fr1(:)
443 : endwhere
444 : else
445 : !------------------------------------------
446 : ! Regime distinctions entirely carried by
447 : ! amplification of taudsw (next subr)
448 : !------------------------------------------
449 0 : Fr2(:)=Fr1(:)
450 : end if
451 :
452 :
453 :
454 0 : where( m2src > orom2min )
455 : ddw = Fr2 * ( abs(ubmsrc) )/nsrc
456 : elsewhere
457 : ddw = 0._r8
458 : endwhere
459 :
460 :
461 : ! If TLB is less than zero then obstacle is not
462 : ! high enough to produce an low-level diversion layer
463 0 : tlb = mxdis - ddw
464 0 : where( tlb < 0._r8)
465 : tlb = 0._r8
466 : endwhere
467 0 : do k = pver, pver/2, -1
468 0 : do i = 1, ncol
469 0 : if ( (tlb(i) > zi(i,k+1)) .and. (tlb(i) <= zi(i,k)) ) then
470 0 : tlb_level(i) = k
471 : end if
472 : end do
473 : end do
474 :
475 :
476 : ! Find *BOTTOM* of linear wave layer (BWV)
477 : !where ( nsrc > orostratmin )
478 0 : where( m2src > orom2min )
479 : dwv = Fr1 * ( abs(ubmsrc) )/nsrc
480 : elsewhere
481 : dwv = -9.999e9_r8 ! if weak strat - no waves
482 : endwhere
483 :
484 0 : bwv = mxdis - dwv
485 0 : where(( bwv < 0._r8) .or. (dwv < 0._r8) )
486 : bwv = 0._r8
487 : endwhere
488 0 : do k = pver,1, -1
489 0 : do i = 1, ncol
490 0 : if ( (bwv(i) > zi(i,k+1)) .and. (bwv(i) <= zi(i,k)) ) then
491 0 : bwv_level(i) = k+1
492 : end if
493 : end do
494 : end do
495 :
496 :
497 :
498 : ! Compute the interface wind projection by averaging the midpoint winds.
499 : ! Use the top level wind at the top interface.
500 0 : ubi(:,1) = ubm(:,1)
501 0 : ubi(:,2:pver) = midpoint_interp(ubm)
502 0 : ubi(:,pver+1) = ubm(:,pver)
503 :
504 : ! Allow wind tendencies all the way to the model bottom.
505 0 : tend_level = pver
506 :
507 : ! No spectrum; phase speed is just 0.
508 0 : c = 0._r8
509 :
510 0 : where( m2src < orom2min )
511 : tlb = mxdis
512 : tlb_level = src_level
513 : endwhere
514 :
515 :
516 0 : end subroutine gw_rdg_src
517 :
518 :
519 : !==========================================================================
520 :
521 0 : subroutine gw_rdg_belowpeak(ncol, band, rdg_cd_llb, &
522 0 : t, mxdis, anixy, kwvrdg, zi, nm, ni, rhoi, &
523 0 : src_level , tau, &
524 0 : ubmsrc, nsrc, rsrc, m2src,tlb,bwv,Fr1,Fr2,Frx, &
525 0 : tauoro,taudsw, hdspwv,hdspdw )
526 :
527 : use gw_common, only: GWBand
528 : !-----------------------------------------------------------------------
529 : ! Orographic source for multiple gravity wave drag parameterization.
530 : !
531 : ! The stress is returned for a single wave with c=0, over orography.
532 : ! For points where the orographic variance is small (including ocean),
533 : ! the returned stress is zero.
534 : !------------------------------Arguments--------------------------------
535 : ! Column dimension.
536 : integer, intent(in) :: ncol
537 : ! Band to emit orographic waves in.
538 : ! Regardless, we will only ever emit into l = 0.
539 : type(GWBand), intent(in) :: band
540 : ! Drag coefficient for low-level flow
541 : real(r8), intent(in) :: rdg_cd_llb
542 :
543 :
544 : ! Midpoint temperatures. (K)
545 : real(r8), intent(in) :: t(ncol,pver)
546 : ! Height estimate for ridge (m) [anisotropic orography].
547 : real(r8), intent(in) :: mxdis(ncol)
548 : ! Anisotropy parameter [0-1] [anisotropic orography].
549 : real(r8), intent(in) :: anixy(ncol)
550 : ! Inverse cross-ridge lengthscale (m-1) [anisotropic orography].
551 : real(r8), intent(inout) :: kwvrdg(ncol)
552 : ! Interface altitudes above ground (m).
553 : real(r8), intent(in) :: zi(ncol,pver+1)
554 : ! Midpoint Brunt-Vaisalla frequencies (s-1).
555 : real(r8), intent(in) :: nm(ncol,pver)
556 : ! Interface Brunt-Vaisalla frequencies (s-1).
557 : real(r8), intent(in) :: ni(ncol,pver+1)
558 : ! Interface density (kg m-3).
559 : real(r8), intent(in) :: rhoi(ncol,pver+1)
560 :
561 : ! Indices of top gravity wave source level
562 : integer, intent(inout) :: src_level(ncol)
563 :
564 : ! Wave Reynolds stress.
565 : real(r8), intent(inout) :: tau(ncol,-band%ngwv:band%ngwv,pver+1)
566 : ! Top of low-level flow layer.
567 : real(r8), intent(in) :: tlb(ncol)
568 : ! Bottom of linear wave region.
569 : real(r8), intent(in) :: bwv(ncol)
570 : ! surface stress from linear waves.
571 : real(r8), intent(out) :: tauoro(ncol)
572 : ! surface stress for downslope wind regime.
573 : real(r8), intent(out) :: taudsw(ncol)
574 :
575 : ! Surface streamline displacement height for linear waves.
576 : real(r8), intent(out) :: hdspwv(ncol)
577 : ! Surface streamline displacement height for downslope wind regime.
578 : real(r8), intent(out) :: hdspdw(ncol)
579 :
580 :
581 :
582 : ! Froude numbers for flow/drag regimes
583 : real(r8), intent(in) :: Fr1(ncol), Fr2(ncol),Frx(ncol)
584 :
585 : ! Averages over source region.
586 : real(r8), intent(in) :: m2src(ncol) ! normalized non-hydro wavenumber
587 : real(r8), intent(in) :: nsrc(ncol) ! B-V frequency.
588 : real(r8), intent(in) :: rsrc(ncol) ! Density.
589 : real(r8), intent(in) :: ubmsrc(ncol) ! On-ridge wind.
590 :
591 :
592 : !logical, intent(in), optional :: forcetlb
593 :
594 : !---------------------------Local Storage-------------------------------
595 : ! Column and level indices.
596 : integer :: i, k
597 :
598 0 : real(r8) :: Coeff_LB(ncol),tausat,ubsrcx(ncol),dswamp
599 0 : real(r8) :: taulin(ncol),BetaMax
600 :
601 : ! ubsrcx introduced to account for situations with high shear, strong strat.
602 0 : do i = 1, ncol
603 0 : ubsrcx(i) = max( ubmsrc(i) , 0._r8 )
604 : end do
605 :
606 0 : do i = 1, ncol
607 0 : if ( m2src(i) > orom2min ) then
608 0 : hdspwv(i) = min( mxdis(i) , Fr1(i) * ubsrcx(i) / nsrc(i) )
609 : else
610 0 : hdspwv(i) = 0._r8
611 : end if
612 : end do
613 :
614 0 : if (do_divstream) then
615 0 : do i = 1, ncol
616 0 : if ( m2src(i) > orom2min ) then
617 0 : hdspdw(i) = min( mxdis(i) , Fr2(i) * ubsrcx(i) / nsrc(i) )
618 : else
619 0 : hdspdw(i) = 0._r8
620 : end if
621 : end do
622 : else
623 0 : do i = 1, ncol
624 : ! Needed only to mark where a DSW occurs
625 0 : if ( m2src(i) > orom2min ) then
626 0 : hdspdw(i) = mxdis(i)
627 : else
628 0 : hdspdw(i) = 0._r8
629 : end if
630 : end do
631 : end if
632 :
633 : ! Calculate form drag coefficient ("CD")
634 : !--------------------------------------
635 0 : Coeff_LB = rdg_cd_llb*anixy
636 :
637 : ! Determine the orographic c=0 source term following McFarlane (1987).
638 : ! Set the source top interface index to pver, if the orographic term is
639 : ! zero.
640 : !
641 : ! This formula is basically from
642 : !
643 : ! tau(src) = rho * u' * w'
644 : ! where
645 : ! u' ~ N*h' and w' ~ U*h'/b (b="breite")
646 : !
647 : ! and 1/b has been replaced with k (kwvrdg)
648 : !
649 0 : do i = 1, ncol
650 0 : if ( ( src_level(i) > 0 ) .and. ( m2src(i) > orom2min ) ) then
651 : tauoro(i) = kwvrdg(i) * ( hdspwv(i)**2 ) * rsrc(i) * nsrc(i) &
652 0 : * ubsrcx(i)
653 : taudsw(i) = kwvrdg(i) * ( hdspdw(i)**2 ) * rsrc(i) * nsrc(i) &
654 0 : * ubsrcx(i)
655 : else
656 0 : tauoro(i) = 0._r8
657 0 : taudsw(i) = 0._r8
658 : end if
659 : end do
660 :
661 0 : if (do_divstream) then
662 0 : do i = 1, ncol
663 0 : taulin(i) = 0._r8
664 : end do
665 : !---------------------------------------
666 : ! Need linear drag when divstream is not used is used
667 : !---------------------------------------
668 : else
669 0 : do i = 1, ncol
670 0 : if ( ( src_level(i) > 0 ) .and. ( m2src(i) > orom2min ) ) then
671 : taulin(i) = kwvrdg(i) * ( mxdis(i)**2 ) * rsrc(i) * nsrc(i) &
672 0 : * ubsrcx(i)
673 : else
674 0 : taulin(i) = 0._r8
675 : end if
676 : end do
677 : end if
678 :
679 0 : if ( do_divstream ) then
680 : ! Amplify DSW between Frx=1. and Frx=Frx1
681 0 : do i = 1,ncol
682 0 : dswamp=0._r8
683 0 : BetaMax = C_BetaMax_DS * anixy(i)
684 0 : if ( (Frx(i)>1._r8).and.(Frx(i)<=Frx1)) then
685 0 : dswamp = (Frx(i)-1._r8)*(Frx1-Frx(i))/(0.25_r8*(Frx1-1._r8)**2)
686 : end if
687 0 : taudsw(i) = (1._r8 + BetaMax*dswamp)*taudsw(i)
688 : end do
689 : else
690 : !-------------------
691 : ! Scinocca&McFarlane
692 : !--------------------
693 0 : do i = 1, ncol
694 0 : BetaMax = C_BetaMax_SM * anixy(i)
695 0 : if ( (Frx(i) >=1._r8) .and. (Frx(i) < 1.5_r8) ) then
696 0 : dswamp = 2._r8 * BetaMax * (Frx(i) -1._r8)
697 0 : else if ( ( Frx(i) >= 1.5_r8 ) .and. (Frx(i) < 3._r8 ) ) then
698 : dswamp = ( 1._r8 + BetaMax - (0.666_r8**2) ) * ( 0.666_r8*(3._r8 - Frx(i) ))**2 &
699 0 : + ( 1._r8 / Frx(i) )**2 -1._r8
700 : else
701 : dswamp = 0._r8
702 : end if
703 0 : if ( (Frx(i) >=1._r8) .and. (Frx(i) < 3._r8) ) then
704 0 : taudsw(i) = (1._r8 + dswamp )*taulin(i) - tauoro(i)
705 : else
706 0 : taudsw(i) = 0._r8
707 : endif
708 : ! This code defines "taudsw" as SUM of freely-propagating
709 : ! DSW enhancement. Different than in SM2000
710 0 : taudsw(i) = taudsw(i) + tauoro(i)
711 : end do
712 : !----------------------------------------------------
713 : end if
714 :
715 :
716 0 : do i = 1, ncol
717 0 : if ( m2src(i) > orom2min ) then
718 0 : where ( ( zi(i,:) < mxdis(i) ) .and. ( zi(i,:) >= bwv(i) ) )
719 0 : tau(i,0,:) = tauoro(i)
720 : else where ( ( zi(i,:) < bwv(i) ) .and. ( zi(i,:) >= tlb(i) ) )
721 : tau(i,0,:) = tauoro(i) +( taudsw(i)-tauoro(i) )* &
722 : ( bwv(i) - zi(i,:) ) / &
723 : ( bwv(i) - tlb(i) )
724 : endwhere
725 : ! low-level form drag on obstacle. Quantity kwvrdg (~1/b) appears for consistency
726 : ! with tauoro and taudsw forms. Should be weighted by L*b/A_g before applied to flow.
727 0 : where ( ( zi(i,:) < tlb(i) ) .and. ( zi(i,:) >= 0._r8 ) )
728 : tau(i,0,:) = taudsw(i) + &
729 : Coeff_LB(i) * kwvrdg(i) * rsrc(i) * 0.5_r8 * (ubsrcx(i)**2) * ( tlb(i) - zi(i,:) )
730 : endwhere
731 :
732 0 : if (do_smooth_regimes) then
733 : ! This blocks accounts for case where both mxdis and tlb fall
734 : ! between adjacent edges
735 0 : do k=1,pver
736 0 : if ( (zi(i,k) >= tlb(i)).and.(zi(i,k+1) < tlb(i)).and. &
737 0 : (zi(i,k) >= mxdis(i)).and.(zi(i,k+1) < mxdis(i)) ) then
738 0 : src_level(i) = src_level(i)-1
739 0 : tau(i,0,k) = tauoro(i)
740 : end if
741 : end do
742 : end if
743 :
744 : else !----------------------------------------------
745 : ! This block allows low-level dynamics to occur
746 : ! even if m2 is less than orom2min
747 0 : where ( ( zi(i,:) < tlb(i) ) .and. ( zi(i,:) >= 0._r8 ) )
748 0 : tau(i,0,:) = taudsw(i) + &
749 : Coeff_LB(i) * kwvrdg(i) * rsrc(i) * 0.5_r8 * &
750 : (ubsrcx(i)**2) * ( tlb(i) - zi(i,:) )
751 : endwhere
752 : endif
753 : end do
754 :
755 : ! This may be redundant with newest version of gw_drag_prof.
756 : ! That code reaches down to level k=src_level+1. (jtb 1/5/16)
757 0 : do i = 1, ncol
758 0 : k=src_level(i)
759 0 : if ( ni(i,k) > orostratmin ) then
760 : tausat = (Fr_c**2) * kwvrdg(i) * rhoi(i,k) * ubsrcx(i)**3 / &
761 0 : (1._r8*ni(i,k))
762 : else
763 : tausat = 0._r8
764 : endif
765 0 : tau(i,0,src_level(i)) = min( tauoro(i), tausat )
766 : end do
767 :
768 :
769 :
770 : ! Final clean-up. Do nothing if obstacle less than orohmin
771 0 : do i = 1, ncol
772 0 : if ( mxdis(i) < orohmin ) then
773 0 : tau(i,0,:) = 0._r8
774 0 : tauoro(i) = 0._r8
775 0 : taudsw(i) = 0._r8
776 : endif
777 : end do
778 :
779 : ! Disable vertical propagation if Scorer param is
780 : ! too small.
781 0 : do i = 1, ncol
782 0 : if ( m2src(i) <= orom2min ) then
783 0 : src_level(i)=1
784 : endif
785 : end do
786 :
787 :
788 :
789 0 : end subroutine gw_rdg_belowpeak
790 :
791 : !==========================================================================
792 0 : subroutine gw_rdg_break_trap(ncol, band, &
793 0 : zi, nm, ni, ubm, ubi, rhoi, kwvrdg, bwv, tlb, wbr, &
794 0 : src_level, tlb_level, &
795 0 : hdspwv, hdspdw, mxdis, &
796 0 : tauoro, taudsw, tau, &
797 : ldo_trapped_waves, wdth_kwv_scale_in )
798 : use gw_common, only: GWBand
799 : !-----------------------------------------------------------------------
800 : ! Parameterization of high-drag regimes and trapped lee-waves for CAM
801 : !
802 : !------------------------------Arguments--------------------------------
803 : ! Column dimension.
804 : integer, intent(in) :: ncol
805 : ! Band to emit orographic waves in.
806 : ! Regardless, we will only ever emit into l = 0.
807 : type(GWBand), intent(in) :: band
808 :
809 :
810 : ! Height estimate for ridge (m) [anisotropic orography].
811 : !real(r8), intent(in) :: mxdis(ncol)
812 : ! Horz wavenumber for ridge (1/m) [anisotropic orography].
813 : real(r8), intent(in) :: kwvrdg(ncol)
814 : ! Interface altitudes above ground (m).
815 : real(r8), intent(in) :: zi(ncol,pver+1)
816 : ! Midpoint Brunt-Vaisalla frequencies (s-1).
817 : real(r8), intent(in) :: nm(ncol,pver)
818 : ! Interface Brunt-Vaisalla frequencies (s-1).
819 : real(r8), intent(in) :: ni(ncol,pver+1)
820 :
821 : ! Indices of gravity wave sources.
822 : integer, intent(inout) :: src_level(ncol), tlb_level(ncol)
823 :
824 : ! Wave Reynolds stress.
825 : real(r8), intent(inout) :: tau(ncol,-band%ngwv:band%ngwv,pver+1)
826 : ! Wave Reynolds stresses at source.
827 : real(r8), intent(in) :: taudsw(ncol)
828 : real(r8), intent(inout) :: tauoro(ncol)
829 : ! Projection of wind at midpoints and interfaces.
830 : real(r8), intent(in) :: ubm(ncol,pver)
831 : real(r8), intent(in) :: ubi(ncol,pver+1)
832 : ! Interface density (kg m-3).
833 : real(r8), intent(in) :: rhoi(ncol,pver+1)
834 :
835 : ! Top of low-level flow layer.
836 : real(r8), intent(in) :: tlb(ncol)
837 : ! Bottom of linear wave region.
838 : real(r8), intent(in) :: bwv(ncol)
839 :
840 : ! Surface streamline displacement height for linear waves.
841 : real(r8), intent(in) :: hdspwv(ncol)
842 : ! Surface streamline displacement height for downslope wind regime.
843 : real(r8), intent(in) :: hdspdw(ncol)
844 : ! Ridge height.
845 : real(r8), intent(in) :: mxdis(ncol)
846 :
847 :
848 : ! Wave breaking level
849 : real(r8), intent(out) :: wbr(ncol)
850 :
851 : logical, intent(in), optional :: ldo_trapped_waves
852 : real(r8), intent(in), optional :: wdth_kwv_scale_in
853 :
854 : !---------------------------Local Storage-------------------------------
855 : ! Column and level indices.
856 : integer :: i, k, kp1, non_hydro
857 0 : real(r8):: m2(ncol,pver),delz(ncol),tausat(ncol),trn(ncol)
858 0 : real(r8):: wbrx(ncol)
859 0 : real(r8):: phswkb(ncol,pver+1)
860 : logical :: lldo_trapped_waves
861 : real(r8):: wdth_kwv_scale
862 : ! Indices of important levels.
863 0 : integer :: trn_level(ncol)
864 :
865 0 : if (present(ldo_trapped_waves)) then
866 0 : lldo_trapped_waves = ldo_trapped_waves
867 0 : if(lldo_trapped_waves) then
868 : non_hydro = 1
869 : else
870 0 : non_hydro = 0
871 : endif
872 : else
873 : lldo_trapped_waves = .false.
874 : non_hydro = 0
875 : endif
876 :
877 0 : if (present(wdth_kwv_scale_in)) then
878 0 : wdth_kwv_scale = wdth_kwv_scale_in
879 : else
880 : wdth_kwv_scale = 1._r8
881 : endif
882 :
883 : ! Calculate vertical wavenumber**2
884 : !---------------------------------
885 0 : m2 = (nm / (abs(ubm)+.01_r8))**2
886 0 : do k=pver,1,-1
887 0 : m2(:,k) = m2(:,k) - non_hydro*(wdth_kwv_scale*kwvrdg)**2
888 : ! sweeping up, zero out m2 above first occurence
889 : ! of m2(:,k)<=0
890 0 : kp1=min( k+1, pver )
891 0 : where( (m2(:,k) <= 0.0_r8 ).or.(m2(:,kp1) <= 0.0_r8 ) )
892 : m2(:,k) = 0._r8
893 : endwhere
894 : end do
895 :
896 : ! Take square root of m**2 and
897 : ! do vertical integral to find
898 : ! WKB phase.
899 : !-----------------------------
900 0 : m2 = SQRT( m2 )
901 0 : phswkb(:,:)=0
902 0 : do k=pver,1,-1
903 0 : where( zi(:,k) > tlb(:) )
904 0 : delz(:) = min( zi(:,k)-zi(:,k+1) , zi(:,k)-tlb(:) )
905 0 : phswkb(:,k) = phswkb(:,k+1) + m2(:,k)*delz(:)
906 : endwhere
907 : end do
908 :
909 : ! Identify top edge of layer in which phswkb reaches 3*pi/2
910 : ! - approximately the "breaking level"
911 : !----------------------------------------------------------
912 0 : wbr(:)=0._r8
913 0 : wbrx(:)=0._r8
914 0 : if (do_smooth_regimes) then
915 0 : do k=pver,1,-1
916 0 : where( (phswkb(:,k+1)<1.5_r8*pii).and.(phswkb(:,k)>=1.5_r8*pii) &
917 0 : .and.(hdspdw(:)>hdspwv(:)) )
918 : wbr(:) = zi(:,k)
919 : ! Extrapolation to make regime
920 : ! transitions smoother
921 : wbrx(:) = zi(:,k) - ( phswkb(:,k) - 1.5_r8*pii ) &
922 0 : / ( m2(:,k) + 1.e-6_r8 )
923 : src_level(:) = k-1
924 : endwhere
925 : end do
926 : else
927 0 : do k=pver,1,-1
928 0 : where( (phswkb(:,k+1)<1.5_r8*pii).and.(phswkb(:,k)>=1.5_r8*pii) &
929 0 : .and.(hdspdw(:)>hdspwv(:)) )
930 : wbr(:) = zi(:,k)
931 : src_level(:) = k
932 : endwhere
933 : end do
934 : end if
935 :
936 : ! Adjust tauoro at new source levels if needed.
937 : ! This is problematic if Fr_c<1.0. Not sure why.
938 : !----------------------------------------------------------
939 0 : if (do_adjust_tauoro) then
940 0 : do i = 1,ncol
941 0 : if (wbr(i) > 0._r8 ) then
942 0 : tausat(i) = (Fr_c**2) * kwvrdg(i) * rhoi( i, src_level(i) ) &
943 : * abs(ubi(i , src_level(i) ))**3 &
944 0 : / ni( i , src_level(i) )
945 0 : tauoro(i) = min( tauoro(i), tausat(i) )
946 : end if
947 : end do
948 : end if
949 :
950 0 : if (do_smooth_regimes) then
951 0 : do i = 1, ncol
952 0 : do k=1,pver+1
953 0 : if ( ( zi(i,k) <= wbr(i) ) .and. ( zi(i,k) > tlb(i) ) ) then
954 0 : tau(i,0,k) = tauoro(i) + (taudsw(i)-tauoro(i)) * &
955 : ( wbrx(i) - zi(i,k) ) / &
956 0 : ( wbrx(i) - tlb(i) )
957 0 : tau(i,0,k) = max( tau(i,0,k), tauoro(i) )
958 : endif
959 : end do
960 : end do
961 : else
962 : ! Following is for backwards B4B compatibility with earlier versions
963 : ! ("N1" and "N5" -- Note: "N5" used do_backward_compat=.true.)
964 0 : if (.not.do_backward_compat) then
965 0 : do i = 1, ncol
966 0 : do k=1,pver+1
967 0 : if ( ( zi(i,k) < wbr(i) ) .and. ( zi(i,k) >= tlb(i) ) ) then
968 0 : tau(i,0,k) = tauoro(i) + (taudsw(i)-tauoro(i)) * &
969 : ( wbr(i) - zi(i,k) ) / &
970 0 : ( wbr(i) - tlb(i) )
971 : endif
972 : end do
973 : end do
974 : else
975 0 : do i = 1, ncol
976 0 : do k=1,pver+1
977 0 : if ( ( zi(i,k) <= wbr(i) ) .and. ( zi(i,k) > tlb(i) ) ) then
978 0 : tau(i,0,k) = tauoro(i) + (taudsw(i)-tauoro(i)) * &
979 : ( wbr(i) - zi(i,k) ) / &
980 0 : ( wbr(i) - tlb(i) )
981 : endif
982 : end do
983 : end do
984 : end if
985 : end if
986 :
987 0 : if (lldo_trapped_waves) then
988 :
989 : ! Identify top edge of layer in which Scorer param drops below 0
990 : ! - approximately the "turning level"
991 : !----------------------------------------------------------
992 0 : trn(:)=1.e8_r8
993 0 : trn_level(:) = 0 ! pver+1
994 0 : where( m2(:,pver)<= 0._r8 )
995 0 : trn(:) = zi(:,pver)
996 : trn_level(:) = pver
997 : endwhere
998 0 : do k=pver-1,1,-1
999 0 : where( (m2(:,k+1)> 0._r8).and.(m2(:,k)<= 0._r8) )
1000 0 : trn(:) = zi(:,k)
1001 : trn_level(:) = k
1002 : endwhere
1003 : end do
1004 :
1005 0 : do i = 1,ncol
1006 : ! Case: Turning below mountain top
1007 0 : if ( (trn(i) < mxdis(i)).and.(trn_level(i)>=1) ) then
1008 0 : tau(i,0,:) = tau(i,0,:) - max( tauoro(i),taudsw(i) )
1009 0 : tau(i,0,:) = max( tau(i,0,:) , 0._r8 )
1010 0 : tau(i,0,1:tlb_level(i))=0._r8
1011 0 : src_level(i) = 1 ! disable any more tau calculation
1012 : end if
1013 : ! Case: Turning but no breaking
1014 0 : if ( (wbr(i) == 0._r8 ).and.(trn(i)>mxdis(i)).and.(trn_level(i)>=1) ) then
1015 0 : where ( ( zi(i,:) <= trn(i) ) .and. ( zi(i,:) >= bwv(i) ) )
1016 0 : tau(i,0,:) = tauoro(i) * &
1017 : ( trn(i) - zi(i,:) ) / &
1018 : ( trn(i) - bwv(i) )
1019 : end where
1020 0 : src_level(i) = 1 ! disable any more tau calculation
1021 : end if
1022 : ! Case: Turning AND breaking. Turning ABOVE breaking
1023 0 : if ( (wbr(i) > 0._r8 ).and.(trn(i) >= wbr(i)).and.(trn_level(i)>=1) ) then
1024 0 : where ( ( zi(i,:) <= trn(i) ) .and. ( zi(i,:) >= wbr(i) ) )
1025 0 : tau(i,0,:) = tauoro(i) * &
1026 : ( trn(i) - zi(i,:) ) / &
1027 : ( trn(i) - wbr(i) )
1028 : endwhere
1029 0 : src_level(i) = 1 ! disable any more tau calculation
1030 : end if
1031 : ! Case: Turning AND breaking. Turning BELOW breaking
1032 0 : if ( (wbr(i) > 0._r8 ).and.(trn(i) < wbr(i)).and.(trn_level(i)>=1) ) then
1033 0 : tauoro(i) = 0._r8
1034 0 : where ( ( zi(i,:) < wbr(i) ) .and. ( zi(i,:) >= tlb(i) ) )
1035 0 : tau(i,0,:) = tauoro(i) + (taudsw(i)-tauoro(i)) * &
1036 : ( wbr(i) - zi(i,:) ) / &
1037 : ( wbr(i) - tlb(i) )
1038 : endwhere
1039 0 : src_level(i) = 1 ! disable any more tau calculation
1040 : end if
1041 : end do
1042 : end if
1043 :
1044 0 : end subroutine gw_rdg_break_trap
1045 : !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
1046 :
1047 :
1048 :
1049 : end module gw_rdg
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