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source: palm/trunk/SOURCE/diffusion_v.f90 @ 3619

Last change on this file since 3619 was 3547, checked in by suehring, 6 years ago
variable description added some routines
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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 3547 2018-11-21 13:21:24Z suehring $
27	! variables documented
28	!
29	! 3241 2018-09-12 15:02:00Z raasch
30	! unused variables removed
31	!
32	! 2718 2018-01-02 08:49:38Z maronga
33	! Corrected "Former revisions" section
34	!
35	! 2696 2017-12-14 17:12:51Z kanani
36	! Change in file header (GPL part)
37	!
38	! 2638 2017-11-23 12:44:23Z raasch
39	! bugfix for constant top momentumflux
40	!
41	! 2233 2017-05-30 18:08:54Z suehring
42	!
43	! 2232 2017-05-30 17:47:52Z suehring
44	! Adjustments to new topography and surface concept
45	!
46	! 2118 2017-01-17 16:38:49Z raasch
47	! OpenACC version of subroutine removed
48	!
49	! 2037 2016-10-26 11:15:40Z knoop
50	! Anelastic approximation implemented
51	!
52	! 2000 2016-08-20 18:09:15Z knoop
53	! Forced header and separation lines into 80 columns
54	!
55	! 1873 2016-04-18 14:50:06Z maronga
56	! Module renamed (removed _mod)
57	!
58	! 1850 2016-04-08 13:29:27Z maronga
59	! Module renamed
60	!
61	! 1740 2016-01-13 08:19:40Z raasch
62	! unnecessary calculations of kmzm and kmzp in wall bounded parts removed
63	!
64	! 1682 2015-10-07 23:56:08Z knoop
65	! Code annotations made doxygen readable
66	!
67	! 1340 2014-03-25 19:45:13Z kanani
68	! REAL constants defined as wp-kind
69	!
70	! 1320 2014-03-20 08:40:49Z raasch
71	! ONLY-attribute added to USE-statements,
72	! kind-parameters added to all INTEGER and REAL declaration statements,
73	! kinds are defined in new module kinds,
74	! revision history before 2012 removed,
75	! comment fields (!:) to be used for variable explanations added to
76	! all variable declaration statements
77	!
78	! 1257 2013-11-08 15:18:40Z raasch
79	! openacc loop and loop vector clauses removed, declare create moved after
80	! the FORTRAN declaration statement
81	!
82	! 1128 2013-04-12 06:19:32Z raasch
83	! loop index bounds in accelerator version replaced by i_left, i_right, j_south,
84	! j_north
85	!
86	! 1036 2012-10-22 13:43:42Z raasch
87	! code put under GPL (PALM 3.9)
88	!
89	! 1015 2012-09-27 09:23:24Z raasch
90	! accelerator version (*_acc) added
91	!
92	! 1001 2012-09-13 14:08:46Z raasch
93	! arrays comunicated by module instead of parameter list
94	!
95	! 978 2012-08-09 08:28:32Z fricke
96	! outflow damping layer removed
97	! kmxm_x/_y and kmxp_x/_y change to kmxm and kmxp
98	!
99	! Revision 1.1 1997/09/12 06:24:01 raasch
100	! Initial revision
101	!
102	!
103	! Description:
104	! ------------
105	!> Diffusion term of the v-component
106	!------------------------------------------------------------------------------!
107	MODULE diffusion_v_mod
108
109
110	PRIVATE
111	PUBLIC diffusion_v
112
113	INTERFACE diffusion_v
114	MODULE PROCEDURE diffusion_v
115	MODULE PROCEDURE diffusion_v_ij
116	END INTERFACE diffusion_v
117
118	CONTAINS
119
120
121	!------------------------------------------------------------------------------!
122	! Description:
123	! ------------
124	!> Call for all grid points
125	!------------------------------------------------------------------------------!
126	SUBROUTINE diffusion_v
127
128	USE arrays_3d, &
129	ONLY: ddzu, ddzw, km, tend, u, v, w, drho_air, rho_air_zw
130
131	USE control_parameters, &
132	ONLY: constant_top_momentumflux, use_surface_fluxes, &
133	use_top_fluxes
134
135	USE grid_variables, &
136	ONLY: ddx, ddy, ddy2
137
138	USE indices, &
139	ONLY: nxl, nxr, nyn, nysv, nzb, nzt, wall_flags_0
140
141	USE kinds
142
143	USE surface_mod, &
144	ONLY : surf_def_h, surf_def_v, surf_lsm_h, surf_lsm_v, surf_usm_h, &
145	surf_usm_v
146
147	IMPLICIT NONE
148
149	INTEGER(iwp) :: i !< running index x direction
150	INTEGER(iwp) :: j !< running index y direction
151	INTEGER(iwp) :: k !< running index z direction
152	INTEGER(iwp) :: l !< running index of surface type, south- or north-facing wall
153	INTEGER(iwp) :: m !< running index surface elements
154	INTEGER(iwp) :: surf_e !< End index of surface elements at (j,i)-gridpoint
155	INTEGER(iwp) :: surf_s !< Start index of surface elements at (j,i)-gridpoint
156
157	REAL(wp) :: flag !< flag to mask topography grid points
158	REAL(wp) :: kmxm !< diffusion coefficient on leftward side of the v-gridbox - interpolated onto xu-yv grid
159	REAL(wp) :: kmxp !< diffusion coefficient on rightward side of the v-gridbox - interpolated onto xu-yv grid
160	REAL(wp) :: kmzm !< diffusion coefficient on bottom of the gridbox - interpolated onto yv-zw grid
161	REAL(wp) :: kmzp !< diffusion coefficient on top of the gridbox - interpolated onto yv-zw grid
162	REAL(wp) :: mask_bottom !< flag to mask vertical upward-facing surface
163	REAL(wp) :: mask_east !< flag to mask vertical surface south of the grid point
164	REAL(wp) :: mask_west !< flag to mask vertical surface north of the grid point
165	REAL(wp) :: mask_top !< flag to mask vertical downward-facing surface
166
167	DO i = nxl, nxr
168	DO j = nysv, nyn
169	!
170	!-- Compute horizontal diffusion
171	DO k = nzb+1, nzt
172
173	!
174	!-- Predetermine flag to mask topography and wall-bounded grid points.
175	!-- It is sufficient to masked only east- and west-facing surfaces, which
176	!-- need special treatment for the v-component.
177	flag = MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_0(k,j,i), 2 ) )
178	mask_east = MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_0(k,j,i+1), 2 ) )
179	mask_west = MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_0(k,j,i-1), 2 ) )
180	!
181	!-- Interpolate eddy diffusivities on staggered gridpoints
182	kmxp = 0.25_wp * ( km(k,j,i)+km(k,j,i+1)+km(k,j-1,i)+km(k,j-1,i+1) )
183	kmxm = 0.25_wp * ( km(k,j,i)+km(k,j,i-1)+km(k,j-1,i)+km(k,j-1,i-1) )
184
185	tend(k,j,i) = tend(k,j,i) + ( &
186	mask_east * kmxp * ( &
187	( v(k,j,i+1) - v(k,j,i) ) * ddx &
188	+ ( u(k,j,i+1) - u(k,j-1,i+1) ) * ddy &
189	) &
190	- mask_west * kmxm * ( &
191	( v(k,j,i) - v(k,j,i-1) ) * ddx &
192	+ ( u(k,j,i) - u(k,j-1,i) ) * ddy &
193	) &
194	) * ddx * flag &
195	+ 2.0_wp * ( &
196	km(k,j,i) * ( v(k,j+1,i) - v(k,j,i) ) &
197	- km(k,j-1,i) * ( v(k,j,i) - v(k,j-1,i) ) &
198	) * ddy2 * flag
199
200	ENDDO
201
202	!
203	!-- Add horizontal momentum flux v'u' at east- (l=2) and west-facing (l=3)
204	!-- surfaces. Note, in the the flat case, loops won't be entered as
205	!-- start_index > end_index. Furtermore, note, no vertical natural surfaces
206	!-- so far.
207	!-- Default-type surfaces
208	DO l = 2, 3
209	surf_s = surf_def_v(l)%start_index(j,i)
210	surf_e = surf_def_v(l)%end_index(j,i)
211	DO m = surf_s, surf_e
212	k = surf_def_v(l)%k(m)
213	tend(k,j,i) = tend(k,j,i) + &
214	surf_def_v(l)%mom_flux_uv(m) * ddx
215	ENDDO
216	ENDDO
217	!
218	!-- Natural-type surfaces
219	DO l = 2, 3
220	surf_s = surf_lsm_v(l)%start_index(j,i)
221	surf_e = surf_lsm_v(l)%end_index(j,i)
222	DO m = surf_s, surf_e
223	k = surf_lsm_v(l)%k(m)
224	tend(k,j,i) = tend(k,j,i) + &
225	surf_lsm_v(l)%mom_flux_uv(m) * ddx
226	ENDDO
227	ENDDO
228	!
229	!-- Urban-type surfaces
230	DO l = 2, 3
231	surf_s = surf_usm_v(l)%start_index(j,i)
232	surf_e = surf_usm_v(l)%end_index(j,i)
233	DO m = surf_s, surf_e
234	k = surf_usm_v(l)%k(m)
235	tend(k,j,i) = tend(k,j,i) + &
236	surf_usm_v(l)%mom_flux_uv(m) * ddx
237	ENDDO
238	ENDDO
239	!
240	!-- Compute vertical diffusion. In case of simulating a surface layer,
241	!-- respective grid diffusive fluxes are masked (flag 10) within this
242	!-- loop, and added further below, else, simple gradient approach is
243	!-- applied. Model top is also mask if top-momentum flux is given.
244	DO k = nzb+1, nzt
245	!
246	!-- Determine flags to mask topography below and above. Flag 2 is
247	!-- used to mask topography in general, while flag 8 implies also
248	!-- information about use_surface_fluxes. Flag 9 is used to control
249	!-- momentum flux at model top.
250	mask_bottom = MERGE( 1.0_wp, 0.0_wp, &
251	BTEST( wall_flags_0(k-1,j,i), 8 ) )
252	mask_top = MERGE( 1.0_wp, 0.0_wp, &
253	BTEST( wall_flags_0(k+1,j,i), 8 ) ) * &
254	MERGE( 1.0_wp, 0.0_wp, &
255	BTEST( wall_flags_0(k+1,j,i), 9 ) )
256	flag = MERGE( 1.0_wp, 0.0_wp, &
257	BTEST( wall_flags_0(k,j,i), 2 ) )
258	!
259	!-- Interpolate eddy diffusivities on staggered gridpoints
260	kmzp = 0.25_wp * &
261	( km(k,j,i)+km(k+1,j,i)+km(k,j-1,i)+km(k+1,j-1,i) )
262	kmzm = 0.25_wp * &
263	( km(k,j,i)+km(k-1,j,i)+km(k,j-1,i)+km(k-1,j-1,i) )
264
265	tend(k,j,i) = tend(k,j,i) &
266	& + ( kmzp * ( ( v(k+1,j,i) - v(k,j,i) ) * ddzu(k+1) &
267	& + ( w(k,j,i) - w(k,j-1,i) ) * ddy &
268	& ) * rho_air_zw(k) * mask_top &
269	& - kmzm * ( ( v(k,j,i) - v(k-1,j,i) ) * ddzu(k) &
270	& + ( w(k-1,j,i) - w(k-1,j-1,i) ) * ddy &
271	& ) * rho_air_zw(k-1) * mask_bottom &
272	& ) * ddzw(k) * drho_air(k) * flag
273	ENDDO
274
275	!
276	!-- Vertical diffusion at the first grid point above the surface,
277	!-- if the momentum flux at the bottom is given by the Prandtl law
278	!-- or if it is prescribed by the user.
279	!-- Difference quotient of the momentum flux is not formed over
280	!-- half of the grid spacing (2.0*ddzw(k)) any more, since the
281	!-- comparison with other (LES) models showed that the values of
282	!-- the momentum flux becomes too large in this case.
283	IF ( use_surface_fluxes ) THEN
284	!
285	!-- Default-type surfaces, upward-facing
286	surf_s = surf_def_h(0)%start_index(j,i)
287	surf_e = surf_def_h(0)%end_index(j,i)
288	DO m = surf_s, surf_e
289	k = surf_def_h(0)%k(m)
290
291	tend(k,j,i) = tend(k,j,i) &
292	+ ( - ( - surf_def_h(0)%vsws(m) ) &
293	) * ddzw(k) * drho_air(k)
294	ENDDO
295	!
296	!-- Default-type surfaces, dowward-facing
297	surf_s = surf_def_h(1)%start_index(j,i)
298	surf_e = surf_def_h(1)%end_index(j,i)
299	DO m = surf_s, surf_e
300	k = surf_def_h(1)%k(m)
301
302	tend(k,j,i) = tend(k,j,i) &
303	+ ( - surf_def_h(1)%vsws(m) &
304	) * ddzw(k) * drho_air(k)
305	ENDDO
306	!
307	!-- Natural-type surfaces, upward-facing
308	surf_s = surf_lsm_h%start_index(j,i)
309	surf_e = surf_lsm_h%end_index(j,i)
310	DO m = surf_s, surf_e
311	k = surf_lsm_h%k(m)
312
313	tend(k,j,i) = tend(k,j,i) &
314	+ ( - ( - surf_lsm_h%vsws(m) ) &
315	) * ddzw(k) * drho_air(k)
316
317	ENDDO
318	!
319	!-- Urban-type surfaces, upward-facing
320	surf_s = surf_usm_h%start_index(j,i)
321	surf_e = surf_usm_h%end_index(j,i)
322	DO m = surf_s, surf_e
323	k = surf_usm_h%k(m)
324
325	tend(k,j,i) = tend(k,j,i) &
326	+ ( - ( - surf_usm_h%vsws(m) ) &
327	) * ddzw(k) * drho_air(k)
328
329	ENDDO
330	ENDIF
331	!
332	!-- Add momentum flux at model top
333	IF ( use_top_fluxes .AND. constant_top_momentumflux ) THEN
334	surf_s = surf_def_h(2)%start_index(j,i)
335	surf_e = surf_def_h(2)%end_index(j,i)
336	DO m = surf_s, surf_e
337
338	k = surf_def_h(2)%k(m)
339
340	tend(k,j,i) = tend(k,j,i) &
341	+ ( - surf_def_h(2)%vsws(m) ) * ddzw(k) * drho_air(k)
342	ENDDO
343	ENDIF
344
345	ENDDO
346	ENDDO
347
348	END SUBROUTINE diffusion_v
349
350
351	!------------------------------------------------------------------------------!
352	! Description:
353	! ------------
354	!> Call for grid point i,j
355	!------------------------------------------------------------------------------!
356	SUBROUTINE diffusion_v_ij( i, j )
357
358	USE arrays_3d, &
359	ONLY: ddzu, ddzw, km, tend, u, v, w, drho_air, rho_air_zw
360
361	USE control_parameters, &
362	ONLY: constant_top_momentumflux, use_surface_fluxes, &
363	use_top_fluxes
364
365	USE grid_variables, &
366	ONLY: ddx, ddy, ddy2
367
368	USE indices, &
369	ONLY: nzb, nzt, wall_flags_0
370
371	USE kinds
372
373	USE surface_mod, &
374	ONLY : surf_def_h, surf_def_v, surf_lsm_h, surf_lsm_v, surf_usm_h, &
375	surf_usm_v
376
377	IMPLICIT NONE
378
379
380	INTEGER(iwp) :: i !< running index x direction
381	INTEGER(iwp) :: j !< running index y direction
382	INTEGER(iwp) :: k !< running index z direction
383	INTEGER(iwp) :: l !< running index of surface type, south- or north-facing wall
384	INTEGER(iwp) :: m !< running index surface elements
385	INTEGER(iwp) :: surf_e !< End index of surface elements at (j,i)-gridpoint
386	INTEGER(iwp) :: surf_s !< Start index of surface elements at (j,i)-gridpoint
387
388	REAL(wp) :: flag !< flag to mask topography grid points
389	REAL(wp) :: kmxm !< diffusion coefficient on leftward side of the v-gridbox - interpolated onto xu-yv grid
390	REAL(wp) :: kmxp !< diffusion coefficient on rightward side of the v-gridbox - interpolated onto xu-yv grid
391	REAL(wp) :: kmzm !< diffusion coefficient on bottom of the gridbox - interpolated onto xu-zw grid
392	REAL(wp) :: kmzp !< diffusion coefficient on top of the gridbox - interpolated onto xu-zw grid
393	REAL(wp) :: mask_bottom !< flag to mask vertical upward-facing surface
394	REAL(wp) :: mask_east !< flag to mask vertical surface south of the grid point
395	REAL(wp) :: mask_west !< flag to mask vertical surface north of the grid point
396	REAL(wp) :: mask_top !< flag to mask vertical downward-facing surface
397
398	!
399	!-- Compute horizontal diffusion
400	DO k = nzb+1, nzt
401	!
402	!-- Predetermine flag to mask topography and wall-bounded grid points.
403	!-- It is sufficient to masked only east- and west-facing surfaces, which
404	!-- need special treatment for the v-component.
405	flag = MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_0(k,j,i), 2 ) )
406	mask_east = MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_0(k,j,i+1), 2 ) )
407	mask_west = MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_0(k,j,i-1), 2 ) )
408	!
409	!-- Interpolate eddy diffusivities on staggered gridpoints
410	kmxp = 0.25_wp * ( km(k,j,i)+km(k,j,i+1)+km(k,j-1,i)+km(k,j-1,i+1) )
411	kmxm = 0.25_wp * ( km(k,j,i)+km(k,j,i-1)+km(k,j-1,i)+km(k,j-1,i-1) )
412
413	tend(k,j,i) = tend(k,j,i) + ( &
414	mask_east * kmxp * ( &
415	( v(k,j,i+1) - v(k,j,i) ) * ddx &
416	+ ( u(k,j,i+1) - u(k,j-1,i+1) ) * ddy &
417	) &
418	- mask_west * kmxm * ( &
419	( v(k,j,i) - v(k,j,i-1) ) * ddx &
420	+ ( u(k,j,i) - u(k,j-1,i) ) * ddy &
421	) &
422	) * ddx * flag &
423	+ 2.0_wp * ( &
424	km(k,j,i) * ( v(k,j+1,i) - v(k,j,i) ) &
425	- km(k,j-1,i) * ( v(k,j,i) - v(k,j-1,i) ) &
426	) * ddy2 * flag
427	ENDDO
428
429	!
430	!-- Add horizontal momentum flux v'u' at east- (l=2) and west-facing (l=3)
431	!-- surfaces. Note, in the the flat case, loops won't be entered as
432	!-- start_index > end_index. Furtermore, note, no vertical natural surfaces
433	!-- so far.
434	!-- Default-type surfaces
435	DO l = 2, 3
436	surf_s = surf_def_v(l)%start_index(j,i)
437	surf_e = surf_def_v(l)%end_index(j,i)
438	DO m = surf_s, surf_e
439	k = surf_def_v(l)%k(m)
440	tend(k,j,i) = tend(k,j,i) + surf_def_v(l)%mom_flux_uv(m) * ddx
441	ENDDO
442	ENDDO
443	!
444	!-- Natural-type surfaces
445	DO l = 2, 3
446	surf_s = surf_lsm_v(l)%start_index(j,i)
447	surf_e = surf_lsm_v(l)%end_index(j,i)
448	DO m = surf_s, surf_e
449	k = surf_lsm_v(l)%k(m)
450	tend(k,j,i) = tend(k,j,i) + surf_lsm_v(l)%mom_flux_uv(m) * ddx
451	ENDDO
452	ENDDO
453	!
454	!-- Urban-type surfaces
455	DO l = 2, 3
456	surf_s = surf_usm_v(l)%start_index(j,i)
457	surf_e = surf_usm_v(l)%end_index(j,i)
458	DO m = surf_s, surf_e
459	k = surf_usm_v(l)%k(m)
460	tend(k,j,i) = tend(k,j,i) + surf_usm_v(l)%mom_flux_uv(m) * ddx
461	ENDDO
462	ENDDO
463	!
464	!-- Compute vertical diffusion. In case of simulating a surface layer,
465	!-- respective grid diffusive fluxes are masked (flag 8) within this
466	!-- loop, and added further below, else, simple gradient approach is
467	!-- applied. Model top is also mask if top-momentum flux is given.
468	DO k = nzb+1, nzt
469	!
470	!-- Determine flags to mask topography below and above. Flag 2 is
471	!-- used to mask topography in general, while flag 10 implies also
472	!-- information about use_surface_fluxes. Flag 9 is used to control
473	!-- momentum flux at model top.
474	mask_bottom = MERGE( 1.0_wp, 0.0_wp, &
475	BTEST( wall_flags_0(k-1,j,i), 8 ) )
476	mask_top = MERGE( 1.0_wp, 0.0_wp, &
477	BTEST( wall_flags_0(k+1,j,i), 8 ) ) * &
478	MERGE( 1.0_wp, 0.0_wp, &
479	BTEST( wall_flags_0(k+1,j,i), 9 ) )
480	flag = MERGE( 1.0_wp, 0.0_wp, &
481	BTEST( wall_flags_0(k,j,i), 2 ) )
482	!
483	!-- Interpolate eddy diffusivities on staggered gridpoints
484	kmzp = 0.25_wp * ( km(k,j,i)+km(k+1,j,i)+km(k,j-1,i)+km(k+1,j-1,i) )
485	kmzm = 0.25_wp * ( km(k,j,i)+km(k-1,j,i)+km(k,j-1,i)+km(k-1,j-1,i) )
486
487	tend(k,j,i) = tend(k,j,i) &
488	& + ( kmzp * ( ( v(k+1,j,i) - v(k,j,i) ) * ddzu(k+1) &
489	& + ( w(k,j,i) - w(k,j-1,i) ) * ddy &
490	& ) * rho_air_zw(k) * mask_top &
491	& - kmzm * ( ( v(k,j,i) - v(k-1,j,i) ) * ddzu(k) &
492	& + ( w(k-1,j,i) - w(k-1,j-1,i) ) * ddy &
493	& ) * rho_air_zw(k-1) * mask_bottom &
494	& ) * ddzw(k) * drho_air(k) * flag
495	ENDDO
496
497	!
498	!-- Vertical diffusion at the first grid point above the surface, if the
499	!-- momentum flux at the bottom is given by the Prandtl law or if it is
500	!-- prescribed by the user.
501	!-- Difference quotient of the momentum flux is not formed over half of
502	!-- the grid spacing (2.0*ddzw(k)) any more, since the comparison with
503	!-- other (LES) models showed that the values of the momentum flux becomes
504	!-- too large in this case.
505	IF ( use_surface_fluxes ) THEN
506	!
507	!-- Default-type surfaces, upward-facing
508	surf_s = surf_def_h(0)%start_index(j,i)
509	surf_e = surf_def_h(0)%end_index(j,i)
510	DO m = surf_s, surf_e
511	k = surf_def_h(0)%k(m)
512
513	tend(k,j,i) = tend(k,j,i) &
514	+ ( - ( - surf_def_h(0)%vsws(m) ) &
515	) * ddzw(k) * drho_air(k)
516	ENDDO
517	!
518	!-- Default-type surfaces, dowward-facing
519	surf_s = surf_def_h(1)%start_index(j,i)
520	surf_e = surf_def_h(1)%end_index(j,i)
521	DO m = surf_s, surf_e
522	k = surf_def_h(1)%k(m)
523
524	tend(k,j,i) = tend(k,j,i) &
525	+ ( - surf_def_h(1)%vsws(m) &
526	) * ddzw(k) * drho_air(k)
527	ENDDO
528	!
529	!-- Natural-type surfaces, upward-facing
530	surf_s = surf_lsm_h%start_index(j,i)
531	surf_e = surf_lsm_h%end_index(j,i)
532	DO m = surf_s, surf_e
533	k = surf_lsm_h%k(m)
534
535	tend(k,j,i) = tend(k,j,i) &
536	+ ( - ( - surf_lsm_h%vsws(m) ) &
537	) * ddzw(k) * drho_air(k)
538
539	ENDDO
540	!
541	!-- Urban-type surfaces, upward-facing
542	surf_s = surf_usm_h%start_index(j,i)
543	surf_e = surf_usm_h%end_index(j,i)
544	DO m = surf_s, surf_e
545	k = surf_usm_h%k(m)
546
547	tend(k,j,i) = tend(k,j,i) &
548	+ ( - ( - surf_usm_h%vsws(m) ) &
549	) * ddzw(k) * drho_air(k)
550
551	ENDDO
552	ENDIF
553	!
554	!-- Add momentum flux at model top
555	IF ( use_top_fluxes .AND. constant_top_momentumflux ) THEN
556	surf_s = surf_def_h(2)%start_index(j,i)
557	surf_e = surf_def_h(2)%end_index(j,i)
558	DO m = surf_s, surf_e
559
560	k = surf_def_h(2)%k(m)
561
562	tend(k,j,i) = tend(k,j,i) &
563	+ ( - surf_def_h(2)%vsws(m) ) * ddzw(k) * drho_air(k)
564	ENDDO
565	ENDIF
566
567	END SUBROUTINE diffusion_v_ij
568
569	END MODULE diffusion_v_mod

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