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source: palm/trunk/SOURCE/diffusion_v.f90 @ 3452

Last change on this file since 3452 was 3241, checked in by raasch, 6 years ago
various changes to avoid compiler warnings (mainly removal of unused variables)
Property svn:keywords set to `Id`
File size: 24.2 KB

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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 1997-2018 Leibniz Universitaet Hannover
18	!------------------------------------------------------------------------------!
19	!
20	! Current revisions:
21	! -----------------
22	!
23	!
24	! Former revisions:
25	! -----------------
26	! $Id: diffusion_v.f90 3241 2018-09-12 15:02:00Z schwenkel $
27	! unused variables removed
28	!
29	! 2718 2018-01-02 08:49:38Z maronga
30	! Corrected "Former revisions" section
31	!
32	! 2696 2017-12-14 17:12:51Z kanani
33	! Change in file header (GPL part)
34	!
35	! 2638 2017-11-23 12:44:23Z raasch
36	! bugfix for constant top momentumflux
37	!
38	! 2233 2017-05-30 18:08:54Z suehring
39	!
40	! 2232 2017-05-30 17:47:52Z suehring
41	! Adjustments to new topography and surface concept
42	!
43	! 2118 2017-01-17 16:38:49Z raasch
44	! OpenACC version of subroutine removed
45	!
46	! 2037 2016-10-26 11:15:40Z knoop
47	! Anelastic approximation implemented
48	!
49	! 2000 2016-08-20 18:09:15Z knoop
50	! Forced header and separation lines into 80 columns
51	!
52	! 1873 2016-04-18 14:50:06Z maronga
53	! Module renamed (removed _mod)
54	!
55	! 1850 2016-04-08 13:29:27Z maronga
56	! Module renamed
57	!
58	! 1740 2016-01-13 08:19:40Z raasch
59	! unnecessary calculations of kmzm and kmzp in wall bounded parts removed
60	!
61	! 1682 2015-10-07 23:56:08Z knoop
62	! Code annotations made doxygen readable
63	!
64	! 1340 2014-03-25 19:45:13Z kanani
65	! REAL constants defined as wp-kind
66	!
67	! 1320 2014-03-20 08:40:49Z raasch
68	! ONLY-attribute added to USE-statements,
69	! kind-parameters added to all INTEGER and REAL declaration statements,
70	! kinds are defined in new module kinds,
71	! revision history before 2012 removed,
72	! comment fields (!:) to be used for variable explanations added to
73	! all variable declaration statements
74	!
75	! 1257 2013-11-08 15:18:40Z raasch
76	! openacc loop and loop vector clauses removed, declare create moved after
77	! the FORTRAN declaration statement
78	!
79	! 1128 2013-04-12 06:19:32Z raasch
80	! loop index bounds in accelerator version replaced by i_left, i_right, j_south,
81	! j_north
82	!
83	! 1036 2012-10-22 13:43:42Z raasch
84	! code put under GPL (PALM 3.9)
85	!
86	! 1015 2012-09-27 09:23:24Z raasch
87	! accelerator version (*_acc) added
88	!
89	! 1001 2012-09-13 14:08:46Z raasch
90	! arrays comunicated by module instead of parameter list
91	!
92	! 978 2012-08-09 08:28:32Z fricke
93	! outflow damping layer removed
94	! kmxm_x/_y and kmxp_x/_y change to kmxm and kmxp
95	!
96	! Revision 1.1 1997/09/12 06:24:01 raasch
97	! Initial revision
98	!
99	!
100	! Description:
101	! ------------
102	!> Diffusion term of the v-component
103	!------------------------------------------------------------------------------!
104	MODULE diffusion_v_mod
105
106
107	PRIVATE
108	PUBLIC diffusion_v
109
110	INTERFACE diffusion_v
111	MODULE PROCEDURE diffusion_v
112	MODULE PROCEDURE diffusion_v_ij
113	END INTERFACE diffusion_v
114
115	CONTAINS
116
117
118	!------------------------------------------------------------------------------!
119	! Description:
120	! ------------
121	!> Call for all grid points
122	!------------------------------------------------------------------------------!
123	SUBROUTINE diffusion_v
124
125	USE arrays_3d, &
126	ONLY: ddzu, ddzw, km, tend, u, v, w, drho_air, rho_air_zw
127
128	USE control_parameters, &
129	ONLY: constant_top_momentumflux, use_surface_fluxes, &
130	use_top_fluxes
131
132	USE grid_variables, &
133	ONLY: ddx, ddy, ddy2
134
135	USE indices, &
136	ONLY: nxl, nxr, nyn, nysv, nzb, nzt, wall_flags_0
137
138	USE kinds
139
140	USE surface_mod, &
141	ONLY : surf_def_h, surf_def_v, surf_lsm_h, surf_lsm_v, surf_usm_h, &
142	surf_usm_v
143
144	IMPLICIT NONE
145
146	INTEGER(iwp) :: i !< running index x direction
147	INTEGER(iwp) :: j !< running index y direction
148	INTEGER(iwp) :: k !< running index z direction
149	INTEGER(iwp) :: l !< running index of surface type, south- or north-facing wall
150	INTEGER(iwp) :: m !< running index surface elements
151	INTEGER(iwp) :: surf_e !< End index of surface elements at (j,i)-gridpoint
152	INTEGER(iwp) :: surf_s !< Start index of surface elements at (j,i)-gridpoint
153
154	REAL(wp) :: flag !< flag to mask topography grid points
155	REAL(wp) :: kmxm !<
156	REAL(wp) :: kmxp !<
157	REAL(wp) :: kmzm !<
158	REAL(wp) :: kmzp !<
159	REAL(wp) :: mask_bottom !< flag to mask vertical upward-facing surface
160	REAL(wp) :: mask_east !< flag to mask vertical surface south of the grid point
161	REAL(wp) :: mask_west !< flag to mask vertical surface north of the grid point
162	REAL(wp) :: mask_top !< flag to mask vertical downward-facing surface
163
164	DO i = nxl, nxr
165	DO j = nysv, nyn
166	!
167	!-- Compute horizontal diffusion
168	DO k = nzb+1, nzt
169
170	!
171	!-- Predetermine flag to mask topography and wall-bounded grid points.
172	!-- It is sufficient to masked only east- and west-facing surfaces, which
173	!-- need special treatment for the v-component.
174	flag = MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_0(k,j,i), 2 ) )
175	mask_east = MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_0(k,j,i+1), 2 ) )
176	mask_west = MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_0(k,j,i-1), 2 ) )
177	!
178	!-- Interpolate eddy diffusivities on staggered gridpoints
179	kmxp = 0.25_wp * ( km(k,j,i)+km(k,j,i+1)+km(k,j-1,i)+km(k,j-1,i+1) )
180	kmxm = 0.25_wp * ( km(k,j,i)+km(k,j,i-1)+km(k,j-1,i)+km(k,j-1,i-1) )
181
182	tend(k,j,i) = tend(k,j,i) + ( &
183	mask_east * kmxp * ( &
184	( v(k,j,i+1) - v(k,j,i) ) * ddx &
185	+ ( u(k,j,i+1) - u(k,j-1,i+1) ) * ddy &
186	) &
187	- mask_west * kmxm * ( &
188	( v(k,j,i) - v(k,j,i-1) ) * ddx &
189	+ ( u(k,j,i) - u(k,j-1,i) ) * ddy &
190	) &
191	) * ddx * flag &
192	+ 2.0_wp * ( &
193	km(k,j,i) * ( v(k,j+1,i) - v(k,j,i) ) &
194	- km(k,j-1,i) * ( v(k,j,i) - v(k,j-1,i) ) &
195	) * ddy2 * flag
196
197	ENDDO
198
199	!
200	!-- Add horizontal momentum flux v'u' at east- (l=2) and west-facing (l=3)
201	!-- surfaces. Note, in the the flat case, loops won't be entered as
202	!-- start_index > end_index. Furtermore, note, no vertical natural surfaces
203	!-- so far.
204	!-- Default-type surfaces
205	DO l = 2, 3
206	surf_s = surf_def_v(l)%start_index(j,i)
207	surf_e = surf_def_v(l)%end_index(j,i)
208	DO m = surf_s, surf_e
209	k = surf_def_v(l)%k(m)
210	tend(k,j,i) = tend(k,j,i) + &
211	surf_def_v(l)%mom_flux_uv(m) * ddx
212	ENDDO
213	ENDDO
214	!
215	!-- Natural-type surfaces
216	DO l = 2, 3
217	surf_s = surf_lsm_v(l)%start_index(j,i)
218	surf_e = surf_lsm_v(l)%end_index(j,i)
219	DO m = surf_s, surf_e
220	k = surf_lsm_v(l)%k(m)
221	tend(k,j,i) = tend(k,j,i) + &
222	surf_lsm_v(l)%mom_flux_uv(m) * ddx
223	ENDDO
224	ENDDO
225	!
226	!-- Urban-type surfaces
227	DO l = 2, 3
228	surf_s = surf_usm_v(l)%start_index(j,i)
229	surf_e = surf_usm_v(l)%end_index(j,i)
230	DO m = surf_s, surf_e
231	k = surf_usm_v(l)%k(m)
232	tend(k,j,i) = tend(k,j,i) + &
233	surf_usm_v(l)%mom_flux_uv(m) * ddx
234	ENDDO
235	ENDDO
236	!
237	!-- Compute vertical diffusion. In case of simulating a surface layer,
238	!-- respective grid diffusive fluxes are masked (flag 10) within this
239	!-- loop, and added further below, else, simple gradient approach is
240	!-- applied. Model top is also mask if top-momentum flux is given.
241	DO k = nzb+1, nzt
242	!
243	!-- Determine flags to mask topography below and above. Flag 2 is
244	!-- used to mask topography in general, while flag 8 implies also
245	!-- information about use_surface_fluxes. Flag 9 is used to control
246	!-- momentum flux at model top.
247	mask_bottom = MERGE( 1.0_wp, 0.0_wp, &
248	BTEST( wall_flags_0(k-1,j,i), 8 ) )
249	mask_top = MERGE( 1.0_wp, 0.0_wp, &
250	BTEST( wall_flags_0(k+1,j,i), 8 ) ) * &
251	MERGE( 1.0_wp, 0.0_wp, &
252	BTEST( wall_flags_0(k+1,j,i), 9 ) )
253	flag = MERGE( 1.0_wp, 0.0_wp, &
254	BTEST( wall_flags_0(k,j,i), 2 ) )
255	!
256	!-- Interpolate eddy diffusivities on staggered gridpoints
257	kmzp = 0.25_wp * &
258	( km(k,j,i)+km(k+1,j,i)+km(k,j-1,i)+km(k+1,j-1,i) )
259	kmzm = 0.25_wp * &
260	( km(k,j,i)+km(k-1,j,i)+km(k,j-1,i)+km(k-1,j-1,i) )
261
262	tend(k,j,i) = tend(k,j,i) &
263	& + ( kmzp * ( ( v(k+1,j,i) - v(k,j,i) ) * ddzu(k+1) &
264	& + ( w(k,j,i) - w(k,j-1,i) ) * ddy &
265	& ) * rho_air_zw(k) * mask_top &
266	& - kmzm * ( ( v(k,j,i) - v(k-1,j,i) ) * ddzu(k) &
267	& + ( w(k-1,j,i) - w(k-1,j-1,i) ) * ddy &
268	& ) * rho_air_zw(k-1) * mask_bottom &
269	& ) * ddzw(k) * drho_air(k) * flag
270	ENDDO
271
272	!
273	!-- Vertical diffusion at the first grid point above the surface,
274	!-- if the momentum flux at the bottom is given by the Prandtl law
275	!-- or if it is prescribed by the user.
276	!-- Difference quotient of the momentum flux is not formed over
277	!-- half of the grid spacing (2.0*ddzw(k)) any more, since the
278	!-- comparison with other (LES) models showed that the values of
279	!-- the momentum flux becomes too large in this case.
280	IF ( use_surface_fluxes ) THEN
281	!
282	!-- Default-type surfaces, upward-facing
283	surf_s = surf_def_h(0)%start_index(j,i)
284	surf_e = surf_def_h(0)%end_index(j,i)
285	DO m = surf_s, surf_e
286	k = surf_def_h(0)%k(m)
287
288	tend(k,j,i) = tend(k,j,i) &
289	+ ( - ( - surf_def_h(0)%vsws(m) ) &
290	) * ddzw(k) * drho_air(k)
291	ENDDO
292	!
293	!-- Default-type surfaces, dowward-facing
294	surf_s = surf_def_h(1)%start_index(j,i)
295	surf_e = surf_def_h(1)%end_index(j,i)
296	DO m = surf_s, surf_e
297	k = surf_def_h(1)%k(m)
298
299	tend(k,j,i) = tend(k,j,i) &
300	+ ( - surf_def_h(1)%vsws(m) &
301	) * ddzw(k) * drho_air(k)
302	ENDDO
303	!
304	!-- Natural-type surfaces, upward-facing
305	surf_s = surf_lsm_h%start_index(j,i)
306	surf_e = surf_lsm_h%end_index(j,i)
307	DO m = surf_s, surf_e
308	k = surf_lsm_h%k(m)
309
310	tend(k,j,i) = tend(k,j,i) &
311	+ ( - ( - surf_lsm_h%vsws(m) ) &
312	) * ddzw(k) * drho_air(k)
313
314	ENDDO
315	!
316	!-- Urban-type surfaces, upward-facing
317	surf_s = surf_usm_h%start_index(j,i)
318	surf_e = surf_usm_h%end_index(j,i)
319	DO m = surf_s, surf_e
320	k = surf_usm_h%k(m)
321
322	tend(k,j,i) = tend(k,j,i) &
323	+ ( - ( - surf_usm_h%vsws(m) ) &
324	) * ddzw(k) * drho_air(k)
325
326	ENDDO
327	ENDIF
328	!
329	!-- Add momentum flux at model top
330	IF ( use_top_fluxes .AND. constant_top_momentumflux ) THEN
331	surf_s = surf_def_h(2)%start_index(j,i)
332	surf_e = surf_def_h(2)%end_index(j,i)
333	DO m = surf_s, surf_e
334
335	k = surf_def_h(2)%k(m)
336
337	tend(k,j,i) = tend(k,j,i) &
338	+ ( - surf_def_h(2)%vsws(m) ) * ddzw(k) * drho_air(k)
339	ENDDO
340	ENDIF
341
342	ENDDO
343	ENDDO
344
345	END SUBROUTINE diffusion_v
346
347
348	!------------------------------------------------------------------------------!
349	! Description:
350	! ------------
351	!> Call for grid point i,j
352	!------------------------------------------------------------------------------!
353	SUBROUTINE diffusion_v_ij( i, j )
354
355	USE arrays_3d, &
356	ONLY: ddzu, ddzw, km, tend, u, v, w, drho_air, rho_air_zw
357
358	USE control_parameters, &
359	ONLY: constant_top_momentumflux, use_surface_fluxes, &
360	use_top_fluxes
361
362	USE grid_variables, &
363	ONLY: ddx, ddy, ddy2
364
365	USE indices, &
366	ONLY: nzb, nzt, wall_flags_0
367
368	USE kinds
369
370	USE surface_mod, &
371	ONLY : surf_def_h, surf_def_v, surf_lsm_h, surf_lsm_v, surf_usm_h, &
372	surf_usm_v
373
374	IMPLICIT NONE
375
376
377	INTEGER(iwp) :: i !< running index x direction
378	INTEGER(iwp) :: j !< running index y direction
379	INTEGER(iwp) :: k !< running index z direction
380	INTEGER(iwp) :: l !< running index of surface type, south- or north-facing wall
381	INTEGER(iwp) :: m !< running index surface elements
382	INTEGER(iwp) :: surf_e !< End index of surface elements at (j,i)-gridpoint
383	INTEGER(iwp) :: surf_s !< Start index of surface elements at (j,i)-gridpoint
384
385	REAL(wp) :: flag !< flag to mask topography grid points
386	REAL(wp) :: kmxm !<
387	REAL(wp) :: kmxp !<
388	REAL(wp) :: kmzm !<
389	REAL(wp) :: kmzp !<
390	REAL(wp) :: mask_bottom !< flag to mask vertical upward-facing surface
391	REAL(wp) :: mask_east !< flag to mask vertical surface south of the grid point
392	REAL(wp) :: mask_west !< flag to mask vertical surface north of the grid point
393	REAL(wp) :: mask_top !< flag to mask vertical downward-facing surface
394
395	!
396	!-- Compute horizontal diffusion
397	DO k = nzb+1, nzt
398	!
399	!-- Predetermine flag to mask topography and wall-bounded grid points.
400	!-- It is sufficient to masked only east- and west-facing surfaces, which
401	!-- need special treatment for the v-component.
402	flag = MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_0(k,j,i), 2 ) )
403	mask_east = MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_0(k,j,i+1), 2 ) )
404	mask_west = MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_0(k,j,i-1), 2 ) )
405	!
406	!-- Interpolate eddy diffusivities on staggered gridpoints
407	kmxp = 0.25_wp * ( km(k,j,i)+km(k,j,i+1)+km(k,j-1,i)+km(k,j-1,i+1) )
408	kmxm = 0.25_wp * ( km(k,j,i)+km(k,j,i-1)+km(k,j-1,i)+km(k,j-1,i-1) )
409
410	tend(k,j,i) = tend(k,j,i) + ( &
411	mask_east * kmxp * ( &
412	( v(k,j,i+1) - v(k,j,i) ) * ddx &
413	+ ( u(k,j,i+1) - u(k,j-1,i+1) ) * ddy &
414	) &
415	- mask_west * kmxm * ( &
416	( v(k,j,i) - v(k,j,i-1) ) * ddx &
417	+ ( u(k,j,i) - u(k,j-1,i) ) * ddy &
418	) &
419	) * ddx * flag &
420	+ 2.0_wp * ( &
421	km(k,j,i) * ( v(k,j+1,i) - v(k,j,i) ) &
422	- km(k,j-1,i) * ( v(k,j,i) - v(k,j-1,i) ) &
423	) * ddy2 * flag
424	ENDDO
425
426	!
427	!-- Add horizontal momentum flux v'u' at east- (l=2) and west-facing (l=3)
428	!-- surfaces. Note, in the the flat case, loops won't be entered as
429	!-- start_index > end_index. Furtermore, note, no vertical natural surfaces
430	!-- so far.
431	!-- Default-type surfaces
432	DO l = 2, 3
433	surf_s = surf_def_v(l)%start_index(j,i)
434	surf_e = surf_def_v(l)%end_index(j,i)
435	DO m = surf_s, surf_e
436	k = surf_def_v(l)%k(m)
437	tend(k,j,i) = tend(k,j,i) + surf_def_v(l)%mom_flux_uv(m) * ddx
438	ENDDO
439	ENDDO
440	!
441	!-- Natural-type surfaces
442	DO l = 2, 3
443	surf_s = surf_lsm_v(l)%start_index(j,i)
444	surf_e = surf_lsm_v(l)%end_index(j,i)
445	DO m = surf_s, surf_e
446	k = surf_lsm_v(l)%k(m)
447	tend(k,j,i) = tend(k,j,i) + surf_lsm_v(l)%mom_flux_uv(m) * ddx
448	ENDDO
449	ENDDO
450	!
451	!-- Urban-type surfaces
452	DO l = 2, 3
453	surf_s = surf_usm_v(l)%start_index(j,i)
454	surf_e = surf_usm_v(l)%end_index(j,i)
455	DO m = surf_s, surf_e
456	k = surf_usm_v(l)%k(m)
457	tend(k,j,i) = tend(k,j,i) + surf_usm_v(l)%mom_flux_uv(m) * ddx
458	ENDDO
459	ENDDO
460	!
461	!-- Compute vertical diffusion. In case of simulating a surface layer,
462	!-- respective grid diffusive fluxes are masked (flag 8) within this
463	!-- loop, and added further below, else, simple gradient approach is
464	!-- applied. Model top is also mask if top-momentum flux is given.
465	DO k = nzb+1, nzt
466	!
467	!-- Determine flags to mask topography below and above. Flag 2 is
468	!-- used to mask topography in general, while flag 10 implies also
469	!-- information about use_surface_fluxes. Flag 9 is used to control
470	!-- momentum flux at model top.
471	mask_bottom = MERGE( 1.0_wp, 0.0_wp, &
472	BTEST( wall_flags_0(k-1,j,i), 8 ) )
473	mask_top = MERGE( 1.0_wp, 0.0_wp, &
474	BTEST( wall_flags_0(k+1,j,i), 8 ) ) * &
475	MERGE( 1.0_wp, 0.0_wp, &
476	BTEST( wall_flags_0(k+1,j,i), 9 ) )
477	flag = MERGE( 1.0_wp, 0.0_wp, &
478	BTEST( wall_flags_0(k,j,i), 2 ) )
479	!
480	!-- Interpolate eddy diffusivities on staggered gridpoints
481	kmzp = 0.25_wp * ( km(k,j,i)+km(k+1,j,i)+km(k,j-1,i)+km(k+1,j-1,i) )
482	kmzm = 0.25_wp * ( km(k,j,i)+km(k-1,j,i)+km(k,j-1,i)+km(k-1,j-1,i) )
483
484	tend(k,j,i) = tend(k,j,i) &
485	& + ( kmzp * ( ( v(k+1,j,i) - v(k,j,i) ) * ddzu(k+1) &
486	& + ( w(k,j,i) - w(k,j-1,i) ) * ddy &
487	& ) * rho_air_zw(k) * mask_top &
488	& - kmzm * ( ( v(k,j,i) - v(k-1,j,i) ) * ddzu(k) &
489	& + ( w(k-1,j,i) - w(k-1,j-1,i) ) * ddy &
490	& ) * rho_air_zw(k-1) * mask_bottom &
491	& ) * ddzw(k) * drho_air(k) * flag
492	ENDDO
493
494	!
495	!-- Vertical diffusion at the first grid point above the surface, if the
496	!-- momentum flux at the bottom is given by the Prandtl law or if it is
497	!-- prescribed by the user.
498	!-- Difference quotient of the momentum flux is not formed over half of
499	!-- the grid spacing (2.0*ddzw(k)) any more, since the comparison with
500	!-- other (LES) models showed that the values of the momentum flux becomes
501	!-- too large in this case.
502	IF ( use_surface_fluxes ) THEN
503	!
504	!-- Default-type surfaces, upward-facing
505	surf_s = surf_def_h(0)%start_index(j,i)
506	surf_e = surf_def_h(0)%end_index(j,i)
507	DO m = surf_s, surf_e
508	k = surf_def_h(0)%k(m)
509
510	tend(k,j,i) = tend(k,j,i) &
511	+ ( - ( - surf_def_h(0)%vsws(m) ) &
512	) * ddzw(k) * drho_air(k)
513	ENDDO
514	!
515	!-- Default-type surfaces, dowward-facing
516	surf_s = surf_def_h(1)%start_index(j,i)
517	surf_e = surf_def_h(1)%end_index(j,i)
518	DO m = surf_s, surf_e
519	k = surf_def_h(1)%k(m)
520
521	tend(k,j,i) = tend(k,j,i) &
522	+ ( - surf_def_h(1)%vsws(m) &
523	) * ddzw(k) * drho_air(k)
524	ENDDO
525	!
526	!-- Natural-type surfaces, upward-facing
527	surf_s = surf_lsm_h%start_index(j,i)
528	surf_e = surf_lsm_h%end_index(j,i)
529	DO m = surf_s, surf_e
530	k = surf_lsm_h%k(m)
531
532	tend(k,j,i) = tend(k,j,i) &
533	+ ( - ( - surf_lsm_h%vsws(m) ) &
534	) * ddzw(k) * drho_air(k)
535
536	ENDDO
537	!
538	!-- Urban-type surfaces, upward-facing
539	surf_s = surf_usm_h%start_index(j,i)
540	surf_e = surf_usm_h%end_index(j,i)
541	DO m = surf_s, surf_e
542	k = surf_usm_h%k(m)
543
544	tend(k,j,i) = tend(k,j,i) &
545	+ ( - ( - surf_usm_h%vsws(m) ) &
546	) * ddzw(k) * drho_air(k)
547
548	ENDDO
549	ENDIF
550	!
551	!-- Add momentum flux at model top
552	IF ( use_top_fluxes .AND. constant_top_momentumflux ) THEN
553	surf_s = surf_def_h(2)%start_index(j,i)
554	surf_e = surf_def_h(2)%end_index(j,i)
555	DO m = surf_s, surf_e
556
557	k = surf_def_h(2)%k(m)
558
559	tend(k,j,i) = tend(k,j,i) &
560	+ ( - surf_def_h(2)%vsws(m) ) * ddzw(k) * drho_air(k)
561	ENDDO
562	ENDIF
563
564	END SUBROUTINE diffusion_v_ij
565
566	END MODULE diffusion_v_mod

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