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

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