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source: palm/trunk/SOURCE/diffusion_v.f90 @ 4356

Last change on this file since 4356 was 4346, checked in by motisi, 5 years ago
Introduction of wall_flags_total_0, which currently sets bits based on static topography information used in wall_flags_static_0
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1	!> @file diffusion_v.f90
2	!------------------------------------------------------------------------------!
3	! This file is part of the PALM model system.
4	!
5	! PALM is free software: you can redistribute it and/or modify it under the
6	! terms of the GNU General Public License as published by the Free Software
7	! Foundation, either version 3 of the License, or (at your option) any later
8	! version.
9	!
10	! PALM is distributed in the hope that it will be useful, but WITHOUT ANY
11	! WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
12	! A PARTICULAR PURPOSE. See the GNU General Public License for more details.
13	!
14	! You should have received a copy of the GNU General Public License along with
15	! PALM. If not, see <http://www.gnu.org/licenses/>.
16	!
17	! Copyright 1997-2019 Leibniz Universitaet Hannover
18	!------------------------------------------------------------------------------!
19	!
20	! Current revisions:
21	! -----------------
22	!
23	!
24	! Former revisions:
25	! -----------------
26	! $Id: diffusion_v.f90 4346 2019-12-18 11:55:56Z suehring $
27	! Introduction of wall_flags_total_0, which currently sets bits based on static
28	! topography information used in wall_flags_static_0
29	!
30	! 4329 2019-12-10 15:46:36Z motisi
31	! Renamed wall_flags_0 to wall_flags_static_0
32	!
33	! 4182 2019-08-22 15:20:23Z scharf
34	! Corrected "Former revisions" section
35	!
36	! 3655 2019-01-07 16:51:22Z knoop
37	! OpenACC port for SPEC
38	!
39	! Revision 1.1 1997/09/12 06:24:01 raasch
40	! Initial revision
41	!
42	!
43	! Description:
44	! ------------
45	!> Diffusion term of the v-component
46	!------------------------------------------------------------------------------!
47	MODULE diffusion_v_mod
48
49
50	PRIVATE
51	PUBLIC diffusion_v
52
53	INTERFACE diffusion_v
54	MODULE PROCEDURE diffusion_v
55	MODULE PROCEDURE diffusion_v_ij
56	END INTERFACE diffusion_v
57
58	CONTAINS
59
60
61	!------------------------------------------------------------------------------!
62	! Description:
63	! ------------
64	!> Call for all grid points
65	!------------------------------------------------------------------------------!
66	SUBROUTINE diffusion_v
67
68	USE arrays_3d, &
69	ONLY: ddzu, ddzw, km, tend, u, v, w, drho_air, rho_air_zw
70
71	USE control_parameters, &
72	ONLY: constant_top_momentumflux, use_surface_fluxes, &
73	use_top_fluxes
74
75	USE grid_variables, &
76	ONLY: ddx, ddy, ddy2
77
78	USE indices, &
79	ONLY: nxl, nxr, nyn, nysv, nzb, nzt, wall_flags_total_0
80
81	USE kinds
82
83	USE surface_mod, &
84	ONLY : surf_def_h, surf_def_v, surf_lsm_h, surf_lsm_v, surf_usm_h, &
85	surf_usm_v
86
87	IMPLICIT NONE
88
89	INTEGER(iwp) :: i !< running index x direction
90	INTEGER(iwp) :: j !< running index y direction
91	INTEGER(iwp) :: k !< running index z direction
92	INTEGER(iwp) :: l !< running index of surface type, south- or north-facing wall
93	INTEGER(iwp) :: m !< running index surface elements
94	INTEGER(iwp) :: surf_e !< End index of surface elements at (j,i)-gridpoint
95	INTEGER(iwp) :: surf_s !< Start index of surface elements at (j,i)-gridpoint
96
97	REAL(wp) :: flag !< flag to mask topography grid points
98	REAL(wp) :: kmxm !< diffusion coefficient on leftward side of the v-gridbox - interpolated onto xu-yv grid
99	REAL(wp) :: kmxp !< diffusion coefficient on rightward side of the v-gridbox - interpolated onto xu-yv grid
100	REAL(wp) :: kmzm !< diffusion coefficient on bottom of the gridbox - interpolated onto yv-zw grid
101	REAL(wp) :: kmzp !< diffusion coefficient on top of the gridbox - interpolated onto yv-zw grid
102	REAL(wp) :: mask_bottom !< flag to mask vertical upward-facing surface
103	REAL(wp) :: mask_east !< flag to mask vertical surface south of the grid point
104	REAL(wp) :: mask_west !< flag to mask vertical surface north of the grid point
105	REAL(wp) :: mask_top !< flag to mask vertical downward-facing surface
106
107	!$ACC PARALLEL LOOP COLLAPSE(2) PRIVATE(i, j, k, l, m) &
108	!$ACC PRIVATE(surf_e, surf_s, flag, kmxm, kmxp, kmzm, kmzp) &
109	!$ACC PRIVATE(mask_bottom, mask_east, mask_west, mask_top) &
110	!$ACC PRESENT(wall_flags_total_0, km) &
111	!$ACC PRESENT(u, v, w) &
112	!$ACC PRESENT(ddzu, ddzw, drho_air, rho_air_zw) &
113	!$ACC PRESENT(surf_def_h(0:2), surf_def_v(2:3)) &
114	!$ACC PRESENT(surf_lsm_h, surf_lsm_v(2:3)) &
115	!$ACC PRESENT(surf_usm_h, surf_usm_v(0:3)) &
116	!$ACC PRESENT(tend)
117	DO i = nxl, nxr
118	DO j = nysv, nyn
119	!
120	!-- Compute horizontal diffusion
121	DO k = nzb+1, nzt
122
123	!
124	!-- Predetermine flag to mask topography and wall-bounded grid points.
125	!-- It is sufficient to masked only east- and west-facing surfaces, which
126	!-- need special treatment for the v-component.
127	flag = MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,j,i), 2 ) )
128	mask_east = MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,j,i+1), 2 ) )
129	mask_west = MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,j,i-1), 2 ) )
130	!
131	!-- Interpolate eddy diffusivities on staggered gridpoints
132	kmxp = 0.25_wp * ( km(k,j,i)+km(k,j,i+1)+km(k,j-1,i)+km(k,j-1,i+1) )
133	kmxm = 0.25_wp * ( km(k,j,i)+km(k,j,i-1)+km(k,j-1,i)+km(k,j-1,i-1) )
134
135	tend(k,j,i) = tend(k,j,i) + ( &
136	mask_east * kmxp * ( &
137	( v(k,j,i+1) - v(k,j,i) ) * ddx &
138	+ ( u(k,j,i+1) - u(k,j-1,i+1) ) * ddy &
139	) &
140	- mask_west * kmxm * ( &
141	( v(k,j,i) - v(k,j,i-1) ) * ddx &
142	+ ( u(k,j,i) - u(k,j-1,i) ) * ddy &
143	) &
144	) * ddx * flag &
145	+ 2.0_wp * ( &
146	km(k,j,i) * ( v(k,j+1,i) - v(k,j,i) ) &
147	- km(k,j-1,i) * ( v(k,j,i) - v(k,j-1,i) ) &
148	) * ddy2 * flag
149
150	ENDDO
151
152	!
153	!-- Add horizontal momentum flux v'u' at east- (l=2) and west-facing (l=3)
154	!-- surfaces. Note, in the the flat case, loops won't be entered as
155	!-- start_index > end_index. Furtermore, note, no vertical natural surfaces
156	!-- so far.
157	!-- Default-type surfaces
158	DO l = 2, 3
159	surf_s = surf_def_v(l)%start_index(j,i)
160	surf_e = surf_def_v(l)%end_index(j,i)
161	DO m = surf_s, surf_e
162	k = surf_def_v(l)%k(m)
163	tend(k,j,i) = tend(k,j,i) + &
164	surf_def_v(l)%mom_flux_uv(m) * ddx
165	ENDDO
166	ENDDO
167	!
168	!-- Natural-type surfaces
169	DO l = 2, 3
170	surf_s = surf_lsm_v(l)%start_index(j,i)
171	surf_e = surf_lsm_v(l)%end_index(j,i)
172	DO m = surf_s, surf_e
173	k = surf_lsm_v(l)%k(m)
174	tend(k,j,i) = tend(k,j,i) + &
175	surf_lsm_v(l)%mom_flux_uv(m) * ddx
176	ENDDO
177	ENDDO
178	!
179	!-- Urban-type surfaces
180	DO l = 2, 3
181	surf_s = surf_usm_v(l)%start_index(j,i)
182	surf_e = surf_usm_v(l)%end_index(j,i)
183	DO m = surf_s, surf_e
184	k = surf_usm_v(l)%k(m)
185	tend(k,j,i) = tend(k,j,i) + &
186	surf_usm_v(l)%mom_flux_uv(m) * ddx
187	ENDDO
188	ENDDO
189	!
190	!-- Compute vertical diffusion. In case of simulating a surface layer,
191	!-- respective grid diffusive fluxes are masked (flag 10) within this
192	!-- loop, and added further below, else, simple gradient approach is
193	!-- applied. Model top is also mask if top-momentum flux is given.
194	DO k = nzb+1, nzt
195	!
196	!-- Determine flags to mask topography below and above. Flag 2 is
197	!-- used to mask topography in general, while flag 8 implies also
198	!-- information about use_surface_fluxes. Flag 9 is used to control
199	!-- momentum flux at model top.
200	mask_bottom = MERGE( 1.0_wp, 0.0_wp, &
201	BTEST( wall_flags_total_0(k-1,j,i), 8 ) )
202	mask_top = MERGE( 1.0_wp, 0.0_wp, &
203	BTEST( wall_flags_total_0(k+1,j,i), 8 ) ) * &
204	MERGE( 1.0_wp, 0.0_wp, &
205	BTEST( wall_flags_total_0(k+1,j,i), 9 ) )
206	flag = MERGE( 1.0_wp, 0.0_wp, &
207	BTEST( wall_flags_total_0(k,j,i), 2 ) )
208	!
209	!-- Interpolate eddy diffusivities on staggered gridpoints
210	kmzp = 0.25_wp * &
211	( km(k,j,i)+km(k+1,j,i)+km(k,j-1,i)+km(k+1,j-1,i) )
212	kmzm = 0.25_wp * &
213	( km(k,j,i)+km(k-1,j,i)+km(k,j-1,i)+km(k-1,j-1,i) )
214
215	tend(k,j,i) = tend(k,j,i) &
216	& + ( kmzp * ( ( v(k+1,j,i) - v(k,j,i) ) * ddzu(k+1) &
217	& + ( w(k,j,i) - w(k,j-1,i) ) * ddy &
218	& ) * rho_air_zw(k) * mask_top &
219	& - kmzm * ( ( v(k,j,i) - v(k-1,j,i) ) * ddzu(k) &
220	& + ( w(k-1,j,i) - w(k-1,j-1,i) ) * ddy &
221	& ) * rho_air_zw(k-1) * mask_bottom &
222	& ) * ddzw(k) * drho_air(k) * flag
223	ENDDO
224
225	!
226	!-- Vertical diffusion at the first grid point above the surface,
227	!-- if the momentum flux at the bottom is given by the Prandtl law
228	!-- or if it is prescribed by the user.
229	!-- Difference quotient of the momentum flux is not formed over
230	!-- half of the grid spacing (2.0*ddzw(k)) any more, since the
231	!-- comparison with other (LES) models showed that the values of
232	!-- the momentum flux becomes too large in this case.
233	IF ( use_surface_fluxes ) THEN
234	!
235	!-- Default-type surfaces, upward-facing
236	surf_s = surf_def_h(0)%start_index(j,i)
237	surf_e = surf_def_h(0)%end_index(j,i)
238	DO m = surf_s, surf_e
239	k = surf_def_h(0)%k(m)
240
241	tend(k,j,i) = tend(k,j,i) &
242	+ ( - ( - surf_def_h(0)%vsws(m) ) &
243	) * ddzw(k) * drho_air(k)
244	ENDDO
245	!
246	!-- Default-type surfaces, dowward-facing
247	surf_s = surf_def_h(1)%start_index(j,i)
248	surf_e = surf_def_h(1)%end_index(j,i)
249	DO m = surf_s, surf_e
250	k = surf_def_h(1)%k(m)
251
252	tend(k,j,i) = tend(k,j,i) &
253	+ ( - surf_def_h(1)%vsws(m) &
254	) * ddzw(k) * drho_air(k)
255	ENDDO
256	!
257	!-- Natural-type surfaces, upward-facing
258	surf_s = surf_lsm_h%start_index(j,i)
259	surf_e = surf_lsm_h%end_index(j,i)
260	DO m = surf_s, surf_e
261	k = surf_lsm_h%k(m)
262
263	tend(k,j,i) = tend(k,j,i) &
264	+ ( - ( - surf_lsm_h%vsws(m) ) &
265	) * ddzw(k) * drho_air(k)
266
267	ENDDO
268	!
269	!-- Urban-type surfaces, upward-facing
270	surf_s = surf_usm_h%start_index(j,i)
271	surf_e = surf_usm_h%end_index(j,i)
272	DO m = surf_s, surf_e
273	k = surf_usm_h%k(m)
274
275	tend(k,j,i) = tend(k,j,i) &
276	+ ( - ( - surf_usm_h%vsws(m) ) &
277	) * ddzw(k) * drho_air(k)
278
279	ENDDO
280	ENDIF
281	!
282	!-- Add momentum flux at model top
283	IF ( use_top_fluxes .AND. constant_top_momentumflux ) THEN
284	surf_s = surf_def_h(2)%start_index(j,i)
285	surf_e = surf_def_h(2)%end_index(j,i)
286	DO m = surf_s, surf_e
287
288	k = surf_def_h(2)%k(m)
289
290	tend(k,j,i) = tend(k,j,i) &
291	+ ( - surf_def_h(2)%vsws(m) ) * ddzw(k) * drho_air(k)
292	ENDDO
293	ENDIF
294
295	ENDDO
296	ENDDO
297
298	END SUBROUTINE diffusion_v
299
300
301	!------------------------------------------------------------------------------!
302	! Description:
303	! ------------
304	!> Call for grid point i,j
305	!------------------------------------------------------------------------------!
306	SUBROUTINE diffusion_v_ij( i, j )
307
308	USE arrays_3d, &
309	ONLY: ddzu, ddzw, km, tend, u, v, w, drho_air, rho_air_zw
310
311	USE control_parameters, &
312	ONLY: constant_top_momentumflux, use_surface_fluxes, &
313	use_top_fluxes
314
315	USE grid_variables, &
316	ONLY: ddx, ddy, ddy2
317
318	USE indices, &
319	ONLY: nzb, nzt, wall_flags_total_0
320
321	USE kinds
322
323	USE surface_mod, &
324	ONLY : surf_def_h, surf_def_v, surf_lsm_h, surf_lsm_v, surf_usm_h, &
325	surf_usm_v
326
327	IMPLICIT NONE
328
329
330	INTEGER(iwp) :: i !< running index x direction
331	INTEGER(iwp) :: j !< running index y direction
332	INTEGER(iwp) :: k !< running index z direction
333	INTEGER(iwp) :: l !< running index of surface type, south- or north-facing wall
334	INTEGER(iwp) :: m !< running index surface elements
335	INTEGER(iwp) :: surf_e !< End index of surface elements at (j,i)-gridpoint
336	INTEGER(iwp) :: surf_s !< Start index of surface elements at (j,i)-gridpoint
337
338	REAL(wp) :: flag !< flag to mask topography grid points
339	REAL(wp) :: kmxm !< diffusion coefficient on leftward side of the v-gridbox - interpolated onto xu-yv grid
340	REAL(wp) :: kmxp !< diffusion coefficient on rightward side of the v-gridbox - interpolated onto xu-yv grid
341	REAL(wp) :: kmzm !< diffusion coefficient on bottom of the gridbox - interpolated onto xu-zw grid
342	REAL(wp) :: kmzp !< diffusion coefficient on top of the gridbox - interpolated onto xu-zw grid
343	REAL(wp) :: mask_bottom !< flag to mask vertical upward-facing surface
344	REAL(wp) :: mask_east !< flag to mask vertical surface south of the grid point
345	REAL(wp) :: mask_west !< flag to mask vertical surface north of the grid point
346	REAL(wp) :: mask_top !< flag to mask vertical downward-facing surface
347
348	!
349	!-- Compute horizontal diffusion
350	DO k = nzb+1, nzt
351	!
352	!-- Predetermine flag to mask topography and wall-bounded grid points.
353	!-- It is sufficient to masked only east- and west-facing surfaces, which
354	!-- need special treatment for the v-component.
355	flag = MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,j,i), 2 ) )
356	mask_east = MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,j,i+1), 2 ) )
357	mask_west = MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,j,i-1), 2 ) )
358	!
359	!-- Interpolate eddy diffusivities on staggered gridpoints
360	kmxp = 0.25_wp * ( km(k,j,i)+km(k,j,i+1)+km(k,j-1,i)+km(k,j-1,i+1) )
361	kmxm = 0.25_wp * ( km(k,j,i)+km(k,j,i-1)+km(k,j-1,i)+km(k,j-1,i-1) )
362
363	tend(k,j,i) = tend(k,j,i) + ( &
364	mask_east * kmxp * ( &
365	( v(k,j,i+1) - v(k,j,i) ) * ddx &
366	+ ( u(k,j,i+1) - u(k,j-1,i+1) ) * ddy &
367	) &
368	- mask_west * kmxm * ( &
369	( v(k,j,i) - v(k,j,i-1) ) * ddx &
370	+ ( u(k,j,i) - u(k,j-1,i) ) * ddy &
371	) &
372	) * ddx * flag &
373	+ 2.0_wp * ( &
374	km(k,j,i) * ( v(k,j+1,i) - v(k,j,i) ) &
375	- km(k,j-1,i) * ( v(k,j,i) - v(k,j-1,i) ) &
376	) * ddy2 * flag
377	ENDDO
378
379	!
380	!-- Add horizontal momentum flux v'u' at east- (l=2) and west-facing (l=3)
381	!-- surfaces. Note, in the the flat case, loops won't be entered as
382	!-- start_index > end_index. Furtermore, note, no vertical natural surfaces
383	!-- so far.
384	!-- Default-type surfaces
385	DO l = 2, 3
386	surf_s = surf_def_v(l)%start_index(j,i)
387	surf_e = surf_def_v(l)%end_index(j,i)
388	DO m = surf_s, surf_e
389	k = surf_def_v(l)%k(m)
390	tend(k,j,i) = tend(k,j,i) + surf_def_v(l)%mom_flux_uv(m) * ddx
391	ENDDO
392	ENDDO
393	!
394	!-- Natural-type surfaces
395	DO l = 2, 3
396	surf_s = surf_lsm_v(l)%start_index(j,i)
397	surf_e = surf_lsm_v(l)%end_index(j,i)
398	DO m = surf_s, surf_e
399	k = surf_lsm_v(l)%k(m)
400	tend(k,j,i) = tend(k,j,i) + surf_lsm_v(l)%mom_flux_uv(m) * ddx
401	ENDDO
402	ENDDO
403	!
404	!-- Urban-type surfaces
405	DO l = 2, 3
406	surf_s = surf_usm_v(l)%start_index(j,i)
407	surf_e = surf_usm_v(l)%end_index(j,i)
408	DO m = surf_s, surf_e
409	k = surf_usm_v(l)%k(m)
410	tend(k,j,i) = tend(k,j,i) + surf_usm_v(l)%mom_flux_uv(m) * ddx
411	ENDDO
412	ENDDO
413	!
414	!-- Compute vertical diffusion. In case of simulating a surface layer,
415	!-- respective grid diffusive fluxes are masked (flag 8) within this
416	!-- loop, and added further below, else, simple gradient approach is
417	!-- applied. Model top is also mask if top-momentum flux is given.
418	DO k = nzb+1, nzt
419	!
420	!-- Determine flags to mask topography below and above. Flag 2 is
421	!-- used to mask topography in general, while flag 10 implies also
422	!-- information about use_surface_fluxes. Flag 9 is used to control
423	!-- momentum flux at model top.
424	mask_bottom = MERGE( 1.0_wp, 0.0_wp, &
425	BTEST( wall_flags_total_0(k-1,j,i), 8 ) )
426	mask_top = MERGE( 1.0_wp, 0.0_wp, &
427	BTEST( wall_flags_total_0(k+1,j,i), 8 ) ) * &
428	MERGE( 1.0_wp, 0.0_wp, &
429	BTEST( wall_flags_total_0(k+1,j,i), 9 ) )
430	flag = MERGE( 1.0_wp, 0.0_wp, &
431	BTEST( wall_flags_total_0(k,j,i), 2 ) )
432	!
433	!-- Interpolate eddy diffusivities on staggered gridpoints
434	kmzp = 0.25_wp * ( km(k,j,i)+km(k+1,j,i)+km(k,j-1,i)+km(k+1,j-1,i) )
435	kmzm = 0.25_wp * ( km(k,j,i)+km(k-1,j,i)+km(k,j-1,i)+km(k-1,j-1,i) )
436
437	tend(k,j,i) = tend(k,j,i) &
438	& + ( kmzp * ( ( v(k+1,j,i) - v(k,j,i) ) * ddzu(k+1) &
439	& + ( w(k,j,i) - w(k,j-1,i) ) * ddy &
440	& ) * rho_air_zw(k) * mask_top &
441	& - kmzm * ( ( v(k,j,i) - v(k-1,j,i) ) * ddzu(k) &
442	& + ( w(k-1,j,i) - w(k-1,j-1,i) ) * ddy &
443	& ) * rho_air_zw(k-1) * mask_bottom &
444	& ) * ddzw(k) * drho_air(k) * flag
445	ENDDO
446
447	!
448	!-- Vertical diffusion at the first grid point above the surface, if the
449	!-- momentum flux at the bottom is given by the Prandtl law or if it is
450	!-- prescribed by the user.
451	!-- Difference quotient of the momentum flux is not formed over half of
452	!-- the grid spacing (2.0*ddzw(k)) any more, since the comparison with
453	!-- other (LES) models showed that the values of the momentum flux becomes
454	!-- too large in this case.
455	IF ( use_surface_fluxes ) THEN
456	!
457	!-- Default-type surfaces, upward-facing
458	surf_s = surf_def_h(0)%start_index(j,i)
459	surf_e = surf_def_h(0)%end_index(j,i)
460	DO m = surf_s, surf_e
461	k = surf_def_h(0)%k(m)
462
463	tend(k,j,i) = tend(k,j,i) &
464	+ ( - ( - surf_def_h(0)%vsws(m) ) &
465	) * ddzw(k) * drho_air(k)
466	ENDDO
467	!
468	!-- Default-type surfaces, dowward-facing
469	surf_s = surf_def_h(1)%start_index(j,i)
470	surf_e = surf_def_h(1)%end_index(j,i)
471	DO m = surf_s, surf_e
472	k = surf_def_h(1)%k(m)
473
474	tend(k,j,i) = tend(k,j,i) &
475	+ ( - surf_def_h(1)%vsws(m) &
476	) * ddzw(k) * drho_air(k)
477	ENDDO
478	!
479	!-- Natural-type surfaces, upward-facing
480	surf_s = surf_lsm_h%start_index(j,i)
481	surf_e = surf_lsm_h%end_index(j,i)
482	DO m = surf_s, surf_e
483	k = surf_lsm_h%k(m)
484
485	tend(k,j,i) = tend(k,j,i) &
486	+ ( - ( - surf_lsm_h%vsws(m) ) &
487	) * ddzw(k) * drho_air(k)
488
489	ENDDO
490	!
491	!-- Urban-type surfaces, upward-facing
492	surf_s = surf_usm_h%start_index(j,i)
493	surf_e = surf_usm_h%end_index(j,i)
494	DO m = surf_s, surf_e
495	k = surf_usm_h%k(m)
496
497	tend(k,j,i) = tend(k,j,i) &
498	+ ( - ( - surf_usm_h%vsws(m) ) &
499	) * ddzw(k) * drho_air(k)
500
501	ENDDO
502	ENDIF
503	!
504	!-- Add momentum flux at model top
505	IF ( use_top_fluxes .AND. constant_top_momentumflux ) THEN
506	surf_s = surf_def_h(2)%start_index(j,i)
507	surf_e = surf_def_h(2)%end_index(j,i)
508	DO m = surf_s, surf_e
509
510	k = surf_def_h(2)%k(m)
511
512	tend(k,j,i) = tend(k,j,i) &
513	+ ( - surf_def_h(2)%vsws(m) ) * ddzw(k) * drho_air(k)
514	ENDDO
515	ENDIF
516
517	END SUBROUTINE diffusion_v_ij
518
519	END MODULE diffusion_v_mod

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