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source: palm/trunk/SOURCE/diffusion_v.f90 @ 2703

Last change on this file since 2703 was 2696, checked in by kanani, 7 years ago
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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 1997-2017 Leibniz Universitaet Hannover
18	!------------------------------------------------------------------------------!
19	!
20	! Current revisions:
21	! -----------------
22	!
23	!
24	! Former revisions:
25	! -----------------
26	! $Id: diffusion_v.f90 2696 2017-12-14 17:12:51Z maronga $
27	! bugfix for constant top momentumflux
28	!
29	! 2233 2017-05-30 18:08:54Z suehring
30	!
31	! 2232 2017-05-30 17:47:52Z suehring
32	! Adjustments to new topography and surface concept
33	!
34	! 2118 2017-01-17 16:38:49Z raasch
35	! OpenACC version of subroutine removed
36	!
37	! 2037 2016-10-26 11:15:40Z knoop
38	! Anelastic approximation implemented
39	!
40	! 2000 2016-08-20 18:09:15Z knoop
41	! Forced header and separation lines into 80 columns
42	!
43	! 1873 2016-04-18 14:50:06Z maronga
44	! Module renamed (removed _mod)
45	!
46	! 1850 2016-04-08 13:29:27Z maronga
47	! Module renamed
48	!
49	! 1740 2016-01-13 08:19:40Z raasch
50	! unnecessary calculations of kmzm and kmzp in wall bounded parts removed
51	!
52	! 1682 2015-10-07 23:56:08Z knoop
53	! Code annotations made doxygen readable
54	!
55	! 1340 2014-03-25 19:45:13Z kanani
56	! REAL constants defined as wp-kind
57	!
58	! 1320 2014-03-20 08:40:49Z raasch
59	! ONLY-attribute added to USE-statements,
60	! kind-parameters added to all INTEGER and REAL declaration statements,
61	! kinds are defined in new module kinds,
62	! revision history before 2012 removed,
63	! comment fields (!:) to be used for variable explanations added to
64	! all variable declaration statements
65	!
66	! 1257 2013-11-08 15:18:40Z raasch
67	! openacc loop and loop vector clauses removed, declare create moved after
68	! the FORTRAN declaration statement
69	!
70	! 1128 2013-04-12 06:19:32Z raasch
71	! loop index bounds in accelerator version replaced by i_left, i_right, j_south,
72	! j_north
73	!
74	! 1036 2012-10-22 13:43:42Z raasch
75	! code put under GPL (PALM 3.9)
76	!
77	! 1015 2012-09-27 09:23:24Z raasch
78	! accelerator version (*_acc) added
79	!
80	! 1001 2012-09-13 14:08:46Z raasch
81	! arrays comunicated by module instead of parameter list
82	!
83	! 978 2012-08-09 08:28:32Z fricke
84	! outflow damping layer removed
85	! kmxm_x/_y and kmxp_x/_y change to kmxm and kmxp
86	!
87	! Revision 1.1 1997/09/12 06:24:01 raasch
88	! Initial revision
89	!
90	!
91	! Description:
92	! ------------
93	!> Diffusion term of the v-component
94	!------------------------------------------------------------------------------!
95	MODULE diffusion_v_mod
96
97
98	PRIVATE
99	PUBLIC diffusion_v
100
101	INTERFACE diffusion_v
102	MODULE PROCEDURE diffusion_v
103	MODULE PROCEDURE diffusion_v_ij
104	END INTERFACE diffusion_v
105
106	CONTAINS
107
108
109	!------------------------------------------------------------------------------!
110	! Description:
111	! ------------
112	!> Call for all grid points
113	!------------------------------------------------------------------------------!
114	SUBROUTINE diffusion_v
115
116	USE arrays_3d, &
117	ONLY: ddzu, ddzw, km, tend, u, v, w, drho_air, rho_air_zw
118
119	USE control_parameters, &
120	ONLY: constant_top_momentumflux, use_surface_fluxes, &
121	use_top_fluxes
122
123	USE grid_variables, &
124	ONLY: ddx, ddy, ddy2
125
126	USE indices, &
127	ONLY: nxl, nxr, nyn, nys, nysv, nzb, nzt, wall_flags_0
128
129	USE kinds
130
131	USE surface_mod, &
132	ONLY : surf_def_h, surf_def_v, surf_lsm_h, surf_lsm_v, surf_usm_h, &
133	surf_usm_v
134
135	IMPLICIT NONE
136
137	INTEGER(iwp) :: i !< running index x direction
138	INTEGER(iwp) :: j !< running index y direction
139	INTEGER(iwp) :: k !< running index z direction
140	INTEGER(iwp) :: l !< running index of surface type, south- or north-facing wall
141	INTEGER(iwp) :: m !< running index surface elements
142	INTEGER(iwp) :: surf_e !< End index of surface elements at (j,i)-gridpoint
143	INTEGER(iwp) :: surf_s !< Start index of surface elements at (j,i)-gridpoint
144
145	REAL(wp) :: flag !< flag to mask topography grid points
146	REAL(wp) :: kmxm !<
147	REAL(wp) :: kmxp !<
148	REAL(wp) :: kmzm !<
149	REAL(wp) :: kmzp !<
150	REAL(wp) :: mask_bottom !< flag to mask vertical upward-facing surface
151	REAL(wp) :: mask_east !< flag to mask vertical surface south of the grid point
152	REAL(wp) :: mask_west !< flag to mask vertical surface north of the grid point
153	REAL(wp) :: mask_top !< flag to mask vertical downward-facing surface
154
155	DO i = nxl, nxr
156	DO j = nysv, nyn
157	!
158	!-- Compute horizontal diffusion
159	DO k = nzb+1, nzt
160
161	!
162	!-- Predetermine flag to mask topography and wall-bounded grid points.
163	!-- It is sufficient to masked only east- and west-facing surfaces, which
164	!-- need special treatment for the v-component.
165	flag = MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_0(k,j,i), 2 ) )
166	mask_east = MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_0(k,j,i+1), 2 ) )
167	mask_west = MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_0(k,j,i-1), 2 ) )
168	!
169	!-- Interpolate eddy diffusivities on staggered gridpoints
170	kmxp = 0.25_wp * ( km(k,j,i)+km(k,j,i+1)+km(k,j-1,i)+km(k,j-1,i+1) )
171	kmxm = 0.25_wp * ( km(k,j,i)+km(k,j,i-1)+km(k,j-1,i)+km(k,j-1,i-1) )
172
173	tend(k,j,i) = tend(k,j,i) + ( &
174	mask_east * kmxp * ( &
175	( v(k,j,i+1) - v(k,j,i) ) * ddx &
176	+ ( u(k,j,i+1) - u(k,j-1,i+1) ) * ddy &
177	) &
178	- mask_west * kmxm * ( &
179	( v(k,j,i) - v(k,j,i-1) ) * ddx &
180	+ ( u(k,j,i) - u(k,j-1,i) ) * ddy &
181	) &
182	) * ddx * flag &
183	+ 2.0_wp * ( &
184	km(k,j,i) * ( v(k,j+1,i) - v(k,j,i) ) &
185	- km(k,j-1,i) * ( v(k,j,i) - v(k,j-1,i) ) &
186	) * ddy2 * flag
187
188	ENDDO
189
190	!
191	!-- Add horizontal momentum flux v'u' at east- (l=2) and west-facing (l=3)
192	!-- surfaces. Note, in the the flat case, loops won't be entered as
193	!-- start_index > end_index. Furtermore, note, no vertical natural surfaces
194	!-- so far.
195	!-- Default-type surfaces
196	DO l = 2, 3
197	surf_s = surf_def_v(l)%start_index(j,i)
198	surf_e = surf_def_v(l)%end_index(j,i)
199	DO m = surf_s, surf_e
200	k = surf_def_v(l)%k(m)
201	tend(k,j,i) = tend(k,j,i) + &
202	surf_def_v(l)%mom_flux_uv(m) * ddx
203	ENDDO
204	ENDDO
205	!
206	!-- Natural-type surfaces
207	DO l = 2, 3
208	surf_s = surf_lsm_v(l)%start_index(j,i)
209	surf_e = surf_lsm_v(l)%end_index(j,i)
210	DO m = surf_s, surf_e
211	k = surf_lsm_v(l)%k(m)
212	tend(k,j,i) = tend(k,j,i) + &
213	surf_lsm_v(l)%mom_flux_uv(m) * ddx
214	ENDDO
215	ENDDO
216	!
217	!-- Urban-type surfaces
218	DO l = 2, 3
219	surf_s = surf_usm_v(l)%start_index(j,i)
220	surf_e = surf_usm_v(l)%end_index(j,i)
221	DO m = surf_s, surf_e
222	k = surf_usm_v(l)%k(m)
223	tend(k,j,i) = tend(k,j,i) + &
224	surf_usm_v(l)%mom_flux_uv(m) * ddx
225	ENDDO
226	ENDDO
227	!
228	!-- Compute vertical diffusion. In case of simulating a surface layer,
229	!-- respective grid diffusive fluxes are masked (flag 10) within this
230	!-- loop, and added further below, else, simple gradient approach is
231	!-- applied. Model top is also mask if top-momentum flux is given.
232	DO k = nzb+1, nzt
233	!
234	!-- Determine flags to mask topography below and above. Flag 2 is
235	!-- used to mask topography in general, while flag 8 implies also
236	!-- information about use_surface_fluxes. Flag 9 is used to control
237	!-- momentum flux at model top.
238	mask_bottom = MERGE( 1.0_wp, 0.0_wp, &
239	BTEST( wall_flags_0(k-1,j,i), 8 ) )
240	mask_top = MERGE( 1.0_wp, 0.0_wp, &
241	BTEST( wall_flags_0(k+1,j,i), 8 ) ) * &
242	MERGE( 1.0_wp, 0.0_wp, &
243	BTEST( wall_flags_0(k+1,j,i), 9 ) )
244	flag = MERGE( 1.0_wp, 0.0_wp, &
245	BTEST( wall_flags_0(k,j,i), 2 ) )
246	!
247	!-- Interpolate eddy diffusivities on staggered gridpoints
248	kmzp = 0.25_wp * &
249	( km(k,j,i)+km(k+1,j,i)+km(k,j-1,i)+km(k+1,j-1,i) )
250	kmzm = 0.25_wp * &
251	( km(k,j,i)+km(k-1,j,i)+km(k,j-1,i)+km(k-1,j-1,i) )
252
253	tend(k,j,i) = tend(k,j,i) &
254	& + ( kmzp * ( ( v(k+1,j,i) - v(k,j,i) ) * ddzu(k+1) &
255	& + ( w(k,j,i) - w(k,j-1,i) ) * ddy &
256	& ) * rho_air_zw(k) * mask_top &
257	& - kmzm * ( ( v(k,j,i) - v(k-1,j,i) ) * ddzu(k) &
258	& + ( w(k-1,j,i) - w(k-1,j-1,i) ) * ddy &
259	& ) * rho_air_zw(k-1) * mask_bottom &
260	& ) * ddzw(k) * drho_air(k) * flag
261	ENDDO
262
263	!
264	!-- Vertical diffusion at the first grid point above the surface,
265	!-- if the momentum flux at the bottom is given by the Prandtl law
266	!-- or if it is prescribed by the user.
267	!-- Difference quotient of the momentum flux is not formed over
268	!-- half of the grid spacing (2.0*ddzw(k)) any more, since the
269	!-- comparison with other (LES) models showed that the values of
270	!-- the momentum flux becomes too large in this case.
271	IF ( use_surface_fluxes ) THEN
272	!
273	!-- Default-type surfaces, upward-facing
274	surf_s = surf_def_h(0)%start_index(j,i)
275	surf_e = surf_def_h(0)%end_index(j,i)
276	DO m = surf_s, surf_e
277	k = surf_def_h(0)%k(m)
278
279	tend(k,j,i) = tend(k,j,i) &
280	+ ( - ( - surf_def_h(0)%vsws(m) ) &
281	) * ddzw(k) * drho_air(k)
282	ENDDO
283	!
284	!-- Default-type surfaces, dowward-facing
285	surf_s = surf_def_h(1)%start_index(j,i)
286	surf_e = surf_def_h(1)%end_index(j,i)
287	DO m = surf_s, surf_e
288	k = surf_def_h(1)%k(m)
289
290	tend(k,j,i) = tend(k,j,i) &
291	+ ( - surf_def_h(1)%vsws(m) &
292	) * ddzw(k) * drho_air(k)
293	ENDDO
294	!
295	!-- Natural-type surfaces, upward-facing
296	surf_s = surf_lsm_h%start_index(j,i)
297	surf_e = surf_lsm_h%end_index(j,i)
298	DO m = surf_s, surf_e
299	k = surf_lsm_h%k(m)
300
301	tend(k,j,i) = tend(k,j,i) &
302	+ ( - ( - surf_lsm_h%vsws(m) ) &
303	) * ddzw(k) * drho_air(k)
304
305	ENDDO
306	!
307	!-- Urban-type surfaces, upward-facing
308	surf_s = surf_usm_h%start_index(j,i)
309	surf_e = surf_usm_h%end_index(j,i)
310	DO m = surf_s, surf_e
311	k = surf_usm_h%k(m)
312
313	tend(k,j,i) = tend(k,j,i) &
314	+ ( - ( - surf_usm_h%vsws(m) ) &
315	) * ddzw(k) * drho_air(k)
316
317	ENDDO
318	ENDIF
319	!
320	!-- Add momentum flux at model top
321	IF ( use_top_fluxes .AND. constant_top_momentumflux ) THEN
322	surf_s = surf_def_h(2)%start_index(j,i)
323	surf_e = surf_def_h(2)%end_index(j,i)
324	DO m = surf_s, surf_e
325
326	k = surf_def_h(2)%k(m)
327
328	tend(k,j,i) = tend(k,j,i) &
329	+ ( - surf_def_h(2)%vsws(m) ) * ddzw(k) * drho_air(k)
330	ENDDO
331	ENDIF
332
333	ENDDO
334	ENDDO
335
336	END SUBROUTINE diffusion_v
337
338
339	!------------------------------------------------------------------------------!
340	! Description:
341	! ------------
342	!> Call for grid point i,j
343	!------------------------------------------------------------------------------!
344	SUBROUTINE diffusion_v_ij( i, j )
345
346	USE arrays_3d, &
347	ONLY: ddzu, ddzw, km, tend, u, v, w, drho_air, rho_air_zw
348
349	USE control_parameters, &
350	ONLY: constant_top_momentumflux, use_surface_fluxes, &
351	use_top_fluxes
352
353	USE grid_variables, &
354	ONLY: ddx, ddy, ddy2
355
356	USE indices, &
357	ONLY: nzb, nzt, wall_flags_0
358
359	USE kinds
360
361	USE surface_mod, &
362	ONLY : surf_def_h, surf_def_v, surf_lsm_h, surf_lsm_v, surf_usm_h, &
363	surf_usm_v
364
365	IMPLICIT NONE
366
367
368	INTEGER(iwp) :: i !< running index x direction
369	INTEGER(iwp) :: j !< running index y direction
370	INTEGER(iwp) :: k !< running index z direction
371	INTEGER(iwp) :: l !< running index of surface type, south- or north-facing wall
372	INTEGER(iwp) :: m !< running index surface elements
373	INTEGER(iwp) :: surf_e !< End index of surface elements at (j,i)-gridpoint
374	INTEGER(iwp) :: surf_s !< Start index of surface elements at (j,i)-gridpoint
375
376	REAL(wp) :: flag !< flag to mask topography grid points
377	REAL(wp) :: kmxm !<
378	REAL(wp) :: kmxp !<
379	REAL(wp) :: kmzm !<
380	REAL(wp) :: kmzp !<
381	REAL(wp) :: mask_bottom !< flag to mask vertical upward-facing surface
382	REAL(wp) :: mask_east !< flag to mask vertical surface south of the grid point
383	REAL(wp) :: mask_west !< flag to mask vertical surface north of the grid point
384	REAL(wp) :: mask_top !< flag to mask vertical downward-facing surface
385
386	!
387	!-- Compute horizontal diffusion
388	DO k = nzb+1, nzt
389	!
390	!-- Predetermine flag to mask topography and wall-bounded grid points.
391	!-- It is sufficient to masked only east- and west-facing surfaces, which
392	!-- need special treatment for the v-component.
393	flag = MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_0(k,j,i), 2 ) )
394	mask_east = MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_0(k,j,i+1), 2 ) )
395	mask_west = MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_0(k,j,i-1), 2 ) )
396	!
397	!-- Interpolate eddy diffusivities on staggered gridpoints
398	kmxp = 0.25_wp * ( km(k,j,i)+km(k,j,i+1)+km(k,j-1,i)+km(k,j-1,i+1) )
399	kmxm = 0.25_wp * ( km(k,j,i)+km(k,j,i-1)+km(k,j-1,i)+km(k,j-1,i-1) )
400
401	tend(k,j,i) = tend(k,j,i) + ( &
402	mask_east * kmxp * ( &
403	( v(k,j,i+1) - v(k,j,i) ) * ddx &
404	+ ( u(k,j,i+1) - u(k,j-1,i+1) ) * ddy &
405	) &
406	- mask_west * kmxm * ( &
407	( v(k,j,i) - v(k,j,i-1) ) * ddx &
408	+ ( u(k,j,i) - u(k,j-1,i) ) * ddy &
409	) &
410	) * ddx * flag &
411	+ 2.0_wp * ( &
412	km(k,j,i) * ( v(k,j+1,i) - v(k,j,i) ) &
413	- km(k,j-1,i) * ( v(k,j,i) - v(k,j-1,i) ) &
414	) * ddy2 * flag
415	ENDDO
416
417	!
418	!-- Add horizontal momentum flux v'u' at east- (l=2) and west-facing (l=3)
419	!-- surfaces. Note, in the the flat case, loops won't be entered as
420	!-- start_index > end_index. Furtermore, note, no vertical natural surfaces
421	!-- so far.
422	!-- Default-type surfaces
423	DO l = 2, 3
424	surf_s = surf_def_v(l)%start_index(j,i)
425	surf_e = surf_def_v(l)%end_index(j,i)
426	DO m = surf_s, surf_e
427	k = surf_def_v(l)%k(m)
428	tend(k,j,i) = tend(k,j,i) + surf_def_v(l)%mom_flux_uv(m) * ddx
429	ENDDO
430	ENDDO
431	!
432	!-- Natural-type surfaces
433	DO l = 2, 3
434	surf_s = surf_lsm_v(l)%start_index(j,i)
435	surf_e = surf_lsm_v(l)%end_index(j,i)
436	DO m = surf_s, surf_e
437	k = surf_lsm_v(l)%k(m)
438	tend(k,j,i) = tend(k,j,i) + surf_lsm_v(l)%mom_flux_uv(m) * ddx
439	ENDDO
440	ENDDO
441	!
442	!-- Urban-type surfaces
443	DO l = 2, 3
444	surf_s = surf_usm_v(l)%start_index(j,i)
445	surf_e = surf_usm_v(l)%end_index(j,i)
446	DO m = surf_s, surf_e
447	k = surf_usm_v(l)%k(m)
448	tend(k,j,i) = tend(k,j,i) + surf_usm_v(l)%mom_flux_uv(m) * ddx
449	ENDDO
450	ENDDO
451	!
452	!-- Compute vertical diffusion. In case of simulating a surface layer,
453	!-- respective grid diffusive fluxes are masked (flag 8) within this
454	!-- loop, and added further below, else, simple gradient approach is
455	!-- applied. Model top is also mask if top-momentum flux is given.
456	DO k = nzb+1, nzt
457	!
458	!-- Determine flags to mask topography below and above. Flag 2 is
459	!-- used to mask topography in general, while flag 10 implies also
460	!-- information about use_surface_fluxes. Flag 9 is used to control
461	!-- momentum flux at model top.
462	mask_bottom = MERGE( 1.0_wp, 0.0_wp, &
463	BTEST( wall_flags_0(k-1,j,i), 8 ) )
464	mask_top = MERGE( 1.0_wp, 0.0_wp, &
465	BTEST( wall_flags_0(k+1,j,i), 8 ) ) * &
466	MERGE( 1.0_wp, 0.0_wp, &
467	BTEST( wall_flags_0(k+1,j,i), 9 ) )
468	flag = MERGE( 1.0_wp, 0.0_wp, &
469	BTEST( wall_flags_0(k,j,i), 2 ) )
470	!
471	!-- Interpolate eddy diffusivities on staggered gridpoints
472	kmzp = 0.25_wp * ( km(k,j,i)+km(k+1,j,i)+km(k,j-1,i)+km(k+1,j-1,i) )
473	kmzm = 0.25_wp * ( km(k,j,i)+km(k-1,j,i)+km(k,j-1,i)+km(k-1,j-1,i) )
474
475	tend(k,j,i) = tend(k,j,i) &
476	& + ( kmzp * ( ( v(k+1,j,i) - v(k,j,i) ) * ddzu(k+1) &
477	& + ( w(k,j,i) - w(k,j-1,i) ) * ddy &
478	& ) * rho_air_zw(k) * mask_top &
479	& - kmzm * ( ( v(k,j,i) - v(k-1,j,i) ) * ddzu(k) &
480	& + ( w(k-1,j,i) - w(k-1,j-1,i) ) * ddy &
481	& ) * rho_air_zw(k-1) * mask_bottom &
482	& ) * ddzw(k) * drho_air(k) * flag
483	ENDDO
484
485	!
486	!-- Vertical diffusion at the first grid point above the surface, if the
487	!-- momentum flux at the bottom is given by the Prandtl law or if it is
488	!-- prescribed by the user.
489	!-- Difference quotient of the momentum flux is not formed over half of
490	!-- the grid spacing (2.0*ddzw(k)) any more, since the comparison with
491	!-- other (LES) models showed that the values of the momentum flux becomes
492	!-- too large in this case.
493	IF ( use_surface_fluxes ) THEN
494	!
495	!-- Default-type surfaces, upward-facing
496	surf_s = surf_def_h(0)%start_index(j,i)
497	surf_e = surf_def_h(0)%end_index(j,i)
498	DO m = surf_s, surf_e
499	k = surf_def_h(0)%k(m)
500
501	tend(k,j,i) = tend(k,j,i) &
502	+ ( - ( - surf_def_h(0)%vsws(m) ) &
503	) * ddzw(k) * drho_air(k)
504	ENDDO
505	!
506	!-- Default-type surfaces, dowward-facing
507	surf_s = surf_def_h(1)%start_index(j,i)
508	surf_e = surf_def_h(1)%end_index(j,i)
509	DO m = surf_s, surf_e
510	k = surf_def_h(1)%k(m)
511
512	tend(k,j,i) = tend(k,j,i) &
513	+ ( - surf_def_h(1)%vsws(m) &
514	) * ddzw(k) * drho_air(k)
515	ENDDO
516	!
517	!-- Natural-type surfaces, upward-facing
518	surf_s = surf_lsm_h%start_index(j,i)
519	surf_e = surf_lsm_h%end_index(j,i)
520	DO m = surf_s, surf_e
521	k = surf_lsm_h%k(m)
522
523	tend(k,j,i) = tend(k,j,i) &
524	+ ( - ( - surf_lsm_h%vsws(m) ) &
525	) * ddzw(k) * drho_air(k)
526
527	ENDDO
528	!
529	!-- Urban-type surfaces, upward-facing
530	surf_s = surf_usm_h%start_index(j,i)
531	surf_e = surf_usm_h%end_index(j,i)
532	DO m = surf_s, surf_e
533	k = surf_usm_h%k(m)
534
535	tend(k,j,i) = tend(k,j,i) &
536	+ ( - ( - surf_usm_h%vsws(m) ) &
537	) * ddzw(k) * drho_air(k)
538
539	ENDDO
540	ENDIF
541	!
542	!-- Add momentum flux at model top
543	IF ( use_top_fluxes .AND. constant_top_momentumflux ) THEN
544	surf_s = surf_def_h(2)%start_index(j,i)
545	surf_e = surf_def_h(2)%end_index(j,i)
546	DO m = surf_s, surf_e
547
548	k = surf_def_h(2)%k(m)
549
550	tend(k,j,i) = tend(k,j,i) &
551	+ ( - surf_def_h(2)%vsws(m) ) * ddzw(k) * drho_air(k)
552	ENDDO
553	ENDIF
554
555	END SUBROUTINE diffusion_v_ij
556
557	END MODULE diffusion_v_mod

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