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source: palm/trunk/SOURCE/diffusion_u.f90 @ 3428

Last change on this file since 3428 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: 24.9 KB

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1	!> @file diffusion_u.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_u.f90 3241 2018-09-12 15:02:00Z gronemeier $
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	! 1691 2015-10-26 16:17:44Z maronga
62	! Formatting corrections.
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	! kmym_x/_y and kmyp_x/_y change to kmym and kmyp
98	!
99	! Revision 1.1 1997/09/12 06:23:51 raasch
100	! Initial revision
101	!
102	!
103	! Description:
104	! ------------
105	!> Diffusion term of the u-component
106	!> @todo additional damping (needed for non-cyclic bc) causes bad vectorization
107	!> and slows down the speed on NEC about 5-10%
108	!------------------------------------------------------------------------------!
109	MODULE diffusion_u_mod
110
111
112	PRIVATE
113	PUBLIC diffusion_u
114
115	INTERFACE diffusion_u
116	MODULE PROCEDURE diffusion_u
117	MODULE PROCEDURE diffusion_u_ij
118	END INTERFACE diffusion_u
119
120	CONTAINS
121
122
123	!------------------------------------------------------------------------------!
124	! Description:
125	! ------------
126	!> Call for all grid points
127	!------------------------------------------------------------------------------!
128	SUBROUTINE diffusion_u
129
130	USE arrays_3d, &
131	ONLY: ddzu, ddzw, km, tend, u, v, w, drho_air, rho_air_zw
132
133	USE control_parameters, &
134	ONLY: constant_top_momentumflux, use_surface_fluxes, &
135	use_top_fluxes
136
137	USE grid_variables, &
138	ONLY: ddx, ddx2, ddy
139
140	USE indices, &
141	ONLY: nxlu, nxr, nyn, nys, nzb, nzt, wall_flags_0
142
143	USE kinds
144
145	USE surface_mod, &
146	ONLY : surf_def_h, surf_def_v, surf_lsm_h, surf_lsm_v, surf_usm_h, &
147	surf_usm_v
148
149	IMPLICIT NONE
150
151	INTEGER(iwp) :: i !< running index x direction
152	INTEGER(iwp) :: j !< running index y direction
153	INTEGER(iwp) :: k !< running index z direction
154	INTEGER(iwp) :: l !< running index of surface type, south- or north-facing wall
155	INTEGER(iwp) :: m !< running index surface elements
156	INTEGER(iwp) :: surf_e !< End index of surface elements at (j,i)-gridpoint
157	INTEGER(iwp) :: surf_s !< Start index of surface elements at (j,i)-gridpoint
158
159	REAL(wp) :: flag !< flag to mask topography grid points
160	REAL(wp) :: kmym !<
161	REAL(wp) :: kmyp !<
162	REAL(wp) :: kmzm !<
163	REAL(wp) :: kmzp !<
164	REAL(wp) :: mask_bottom !< flag to mask vertical upward-facing surface
165	REAL(wp) :: mask_north !< flag to mask vertical surface north of the grid point
166	REAL(wp) :: mask_south !< flag to mask vertical surface south of the grid point
167	REAL(wp) :: mask_top !< flag to mask vertical downward-facing surface
168
169
170
171	DO i = nxlu, nxr
172	DO j = nys, nyn
173	!
174	!-- Compute horizontal diffusion
175	DO k = nzb+1, nzt
176	!
177	!-- Predetermine flag to mask topography and wall-bounded grid points.
178	!-- It is sufficient to masked only north- and south-facing surfaces, which
179	!-- need special treatment for the u-component.
180	flag = MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_0(k,j,i), 1 ) )
181	mask_south = MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_0(k,j-1,i), 1 ) )
182	mask_north = MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_0(k,j+1,i), 1 ) )
183	!
184	!-- Interpolate eddy diffusivities on staggered gridpoints
185	kmyp = 0.25_wp * &
186	( km(k,j,i)+km(k,j+1,i)+km(k,j,i-1)+km(k,j+1,i-1) )
187	kmym = 0.25_wp * &
188	( km(k,j,i)+km(k,j-1,i)+km(k,j,i-1)+km(k,j-1,i-1) )
189
190	tend(k,j,i) = tend(k,j,i) &
191	+ 2.0_wp * ( &
192	km(k,j,i) * ( u(k,j,i+1) - u(k,j,i) ) &
193	- km(k,j,i-1) * ( u(k,j,i) - u(k,j,i-1) ) &
194	) * ddx2 * flag &
195	+ ( mask_north * ( &
196	kmyp * ( u(k,j+1,i) - u(k,j,i) ) * ddy &
197	+ kmyp * ( v(k,j+1,i) - v(k,j+1,i-1) ) * ddx &
198	) &
199	- mask_south * ( &
200	kmym * ( u(k,j,i) - u(k,j-1,i) ) * ddy &
201	+ kmym * ( v(k,j,i) - v(k,j,i-1) ) * ddx &
202	) &
203	) * ddy * flag
204	ENDDO
205	!
206	!-- Add horizontal momentum flux u'v' at north- (l=0) and south-facing (l=1)
207	!-- surfaces. Note, in the the flat case, loops won't be entered as
208	!-- start_index > end_index. Furtermore, note, no vertical natural surfaces
209	!-- so far.
210	!-- Default-type surfaces
211	DO l = 0, 1
212	surf_s = surf_def_v(l)%start_index(j,i)
213	surf_e = surf_def_v(l)%end_index(j,i)
214	DO m = surf_s, surf_e
215	k = surf_def_v(l)%k(m)
216	tend(k,j,i) = tend(k,j,i) + &
217	surf_def_v(l)%mom_flux_uv(m) * ddy
218	ENDDO
219	ENDDO
220	!
221	!-- Natural-type surfaces
222	DO l = 0, 1
223	surf_s = surf_lsm_v(l)%start_index(j,i)
224	surf_e = surf_lsm_v(l)%end_index(j,i)
225	DO m = surf_s, surf_e
226	k = surf_lsm_v(l)%k(m)
227	tend(k,j,i) = tend(k,j,i) + &
228	surf_lsm_v(l)%mom_flux_uv(m) * ddy
229	ENDDO
230	ENDDO
231	!
232	!-- Urban-type surfaces
233	DO l = 0, 1
234	surf_s = surf_usm_v(l)%start_index(j,i)
235	surf_e = surf_usm_v(l)%end_index(j,i)
236	DO m = surf_s, surf_e
237	k = surf_usm_v(l)%k(m)
238	tend(k,j,i) = tend(k,j,i) + &
239	surf_usm_v(l)%mom_flux_uv(m) * ddy
240	ENDDO
241	ENDDO
242
243	!
244	!-- Compute vertical diffusion. In case of simulating a surface layer,
245	!-- respective grid diffusive fluxes are masked (flag 8) within this
246	!-- loop, and added further below, else, simple gradient approach is
247	!-- applied. Model top is also mask if top-momentum flux is given.
248	DO k = nzb+1, nzt
249	!
250	!-- Determine flags to mask topography below and above. Flag 1 is
251	!-- used to mask topography in general, and flag 8 implies
252	!-- information about use_surface_fluxes. Flag 9 is used to control
253	!-- momentum flux at model top.
254	mask_bottom = MERGE( 1.0_wp, 0.0_wp, &
255	BTEST( wall_flags_0(k-1,j,i), 8 ) )
256	mask_top = MERGE( 1.0_wp, 0.0_wp, &
257	BTEST( wall_flags_0(k+1,j,i), 8 ) ) * &
258	MERGE( 1.0_wp, 0.0_wp, &
259	BTEST( wall_flags_0(k+1,j,i), 9 ) )
260	flag = MERGE( 1.0_wp, 0.0_wp, &
261	BTEST( wall_flags_0(k,j,i), 1 ) )
262	!
263	!-- Interpolate eddy diffusivities on staggered gridpoints
264	kmzp = 0.25_wp * &
265	( km(k,j,i)+km(k+1,j,i)+km(k,j,i-1)+km(k+1,j,i-1) )
266	kmzm = 0.25_wp * &
267	( km(k,j,i)+km(k-1,j,i)+km(k,j,i-1)+km(k-1,j,i-1) )
268
269	tend(k,j,i) = tend(k,j,i) &
270	+ ( kmzp * ( ( u(k+1,j,i) - u(k,j,i) ) * ddzu(k+1) &
271	+ ( w(k,j,i) - w(k,j,i-1) ) * ddx &
272	) * rho_air_zw(k) * mask_top &
273	- kmzm * ( ( u(k,j,i) - u(k-1,j,i) ) * ddzu(k) &
274	+ ( w(k-1,j,i) - w(k-1,j,i-1) ) * ddx &
275	) * rho_air_zw(k-1) * mask_bottom &
276	) * ddzw(k) * drho_air(k) * flag
277	ENDDO
278
279	!
280	!-- Vertical diffusion at the first grid point above the surface,
281	!-- if the momentum flux at the bottom is given by the Prandtl law or
282	!-- if it is prescribed by the user.
283	!-- Difference quotient of the momentum flux is not formed over half
284	!-- of the grid spacing (2.0*ddzw(k)) any more, since the comparison
285	!-- with other (LES) models showed that the values of the momentum
286	!-- flux becomes too large in this case.
287	!-- The term containing w(k-1,..) (see above equation) is removed here
288	!-- because the vertical velocity is assumed to be zero at the surface.
289	IF ( use_surface_fluxes ) THEN
290	!
291	!-- Default-type surfaces, upward-facing
292	surf_s = surf_def_h(0)%start_index(j,i)
293	surf_e = surf_def_h(0)%end_index(j,i)
294	DO m = surf_s, surf_e
295
296	k = surf_def_h(0)%k(m)
297
298	tend(k,j,i) = tend(k,j,i) &
299	+ ( - ( - surf_def_h(0)%usws(m) ) &
300	) * ddzw(k) * drho_air(k)
301	ENDDO
302	!
303	!-- Default-type surfaces, dowward-facing
304	surf_s = surf_def_h(1)%start_index(j,i)
305	surf_e = surf_def_h(1)%end_index(j,i)
306	DO m = surf_s, surf_e
307
308	k = surf_def_h(1)%k(m)
309
310	tend(k,j,i) = tend(k,j,i) &
311	+ ( - surf_def_h(1)%usws(m) &
312	) * ddzw(k) * drho_air(k)
313	ENDDO
314	!
315	!-- Natural-type surfaces, upward-facing
316	surf_s = surf_lsm_h%start_index(j,i)
317	surf_e = surf_lsm_h%end_index(j,i)
318	DO m = surf_s, surf_e
319
320	k = surf_lsm_h%k(m)
321
322	tend(k,j,i) = tend(k,j,i) &
323	+ ( - ( - surf_lsm_h%usws(m) ) &
324	) * ddzw(k) * drho_air(k)
325	ENDDO
326	!
327	!-- Urban-type surfaces, upward-facing
328	surf_s = surf_usm_h%start_index(j,i)
329	surf_e = surf_usm_h%end_index(j,i)
330	DO m = surf_s, surf_e
331
332	k = surf_usm_h%k(m)
333
334	tend(k,j,i) = tend(k,j,i) &
335	+ ( - ( - surf_usm_h%usws(m) ) &
336	) * ddzw(k) * drho_air(k)
337	ENDDO
338
339	ENDIF
340	!
341	!-- Add momentum flux at model top
342	IF ( use_top_fluxes .AND. constant_top_momentumflux ) THEN
343	surf_s = surf_def_h(2)%start_index(j,i)
344	surf_e = surf_def_h(2)%end_index(j,i)
345	DO m = surf_s, surf_e
346
347	k = surf_def_h(2)%k(m)
348
349	tend(k,j,i) = tend(k,j,i) &
350	+ ( - surf_def_h(2)%usws(m) ) * ddzw(k) * drho_air(k)
351	ENDDO
352	ENDIF
353
354	ENDDO
355	ENDDO
356
357	END SUBROUTINE diffusion_u
358
359
360	!------------------------------------------------------------------------------!
361	! Description:
362	! ------------
363	!> Call for grid point i,j
364	!------------------------------------------------------------------------------!
365	SUBROUTINE diffusion_u_ij( i, j )
366
367	USE arrays_3d, &
368	ONLY: ddzu, ddzw, km, tend, u, v, w, drho_air, rho_air_zw
369
370	USE control_parameters, &
371	ONLY: constant_top_momentumflux, use_surface_fluxes, &
372	use_top_fluxes
373
374	USE grid_variables, &
375	ONLY: ddx, ddx2, ddy
376
377	USE indices, &
378	ONLY: nzb, nzt, wall_flags_0
379
380	USE kinds
381
382	USE surface_mod, &
383	ONLY : surf_def_h, surf_def_v, surf_lsm_h, surf_lsm_v, surf_usm_h, &
384	surf_usm_v
385
386	IMPLICIT NONE
387
388	INTEGER(iwp) :: i !< running index x direction
389	INTEGER(iwp) :: j !< running index y direction
390	INTEGER(iwp) :: k !< running index z direction
391	INTEGER(iwp) :: l !< running index of surface type, south- or north-facing wall
392	INTEGER(iwp) :: m !< running index surface elements
393	INTEGER(iwp) :: surf_e !< End index of surface elements at (j,i)-gridpoint
394	INTEGER(iwp) :: surf_s !< Start index of surface elements at (j,i)-gridpoint
395
396	REAL(wp) :: flag !< flag to mask topography grid points
397	REAL(wp) :: kmym !<
398	REAL(wp) :: kmyp !<
399	REAL(wp) :: kmzm !<
400	REAL(wp) :: kmzp !<
401	REAL(wp) :: mask_bottom !< flag to mask vertical upward-facing surface
402	REAL(wp) :: mask_north !< flag to mask vertical surface north of the grid point
403	REAL(wp) :: mask_south !< flag to mask vertical surface south of the grid point
404	REAL(wp) :: mask_top !< flag to mask vertical downward-facing surface
405	!
406	!-- Compute horizontal diffusion
407	DO k = nzb+1, nzt
408	!
409	!-- Predetermine flag to mask topography and wall-bounded grid points.
410	!-- It is sufficient to masked only north- and south-facing surfaces, which
411	!-- need special treatment for the u-component.
412	flag = MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_0(k,j,i), 1 ) )
413	mask_south = MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_0(k,j-1,i), 1 ) )
414	mask_north = MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_0(k,j+1,i), 1 ) )
415	!
416	!-- Interpolate eddy diffusivities on staggered gridpoints
417	kmyp = 0.25_wp * ( km(k,j,i)+km(k,j+1,i)+km(k,j,i-1)+km(k,j+1,i-1) )
418	kmym = 0.25_wp * ( km(k,j,i)+km(k,j-1,i)+km(k,j,i-1)+km(k,j-1,i-1) )
419
420	tend(k,j,i) = tend(k,j,i) &
421	+ 2.0_wp * ( &
422	km(k,j,i) * ( u(k,j,i+1) - u(k,j,i) ) &
423	- km(k,j,i-1) * ( u(k,j,i) - u(k,j,i-1) ) &
424	) * ddx2 * flag &
425	+ ( &
426	mask_north * kmyp * ( ( u(k,j+1,i) - u(k,j,i) ) * ddy &
427	+ ( v(k,j+1,i) - v(k,j+1,i-1) ) * ddx &
428	) &
429	- mask_south * kmym * ( ( u(k,j,i) - u(k,j-1,i) ) * ddy &
430	+ ( v(k,j,i) - v(k,j,i-1) ) * ddx &
431	) &
432	) * ddy * flag
433	ENDDO
434
435	!
436	!-- Add horizontal momentum flux u'v' at north- (l=0) and south-facing (l=1)
437	!-- surfaces. Note, in the the flat case, loops won't be entered as
438	!-- start_index > end_index. Furtermore, note, no vertical natural surfaces
439	!-- so far.
440	!-- Default-type surfaces
441	DO l = 0, 1
442	surf_s = surf_def_v(l)%start_index(j,i)
443	surf_e = surf_def_v(l)%end_index(j,i)
444	DO m = surf_s, surf_e
445	k = surf_def_v(l)%k(m)
446	tend(k,j,i) = tend(k,j,i) + surf_def_v(l)%mom_flux_uv(m) * ddy
447	ENDDO
448	ENDDO
449	!
450	!-- Natural-type surfaces
451	DO l = 0, 1
452	surf_s = surf_lsm_v(l)%start_index(j,i)
453	surf_e = surf_lsm_v(l)%end_index(j,i)
454	DO m = surf_s, surf_e
455	k = surf_lsm_v(l)%k(m)
456	tend(k,j,i) = tend(k,j,i) + surf_lsm_v(l)%mom_flux_uv(m) * ddy
457	ENDDO
458	ENDDO
459	!
460	!-- Urban-type surfaces
461	DO l = 0, 1
462	surf_s = surf_usm_v(l)%start_index(j,i)
463	surf_e = surf_usm_v(l)%end_index(j,i)
464	DO m = surf_s, surf_e
465	k = surf_usm_v(l)%k(m)
466	tend(k,j,i) = tend(k,j,i) + surf_usm_v(l)%mom_flux_uv(m) * ddy
467	ENDDO
468	ENDDO
469	!
470	!-- Compute vertical diffusion. In case of simulating a surface layer,
471	!-- respective grid diffusive fluxes are masked (flag 8) within this
472	!-- loop, and added further below, else, simple gradient approach is
473	!-- applied. Model top is also mask if top-momentum flux is given.
474	DO k = nzb+1, nzt
475	!
476	!-- Determine flags to mask topography below and above. Flag 1 is
477	!-- used to mask topography in general, and flag 8 implies
478	!-- information about use_surface_fluxes. Flag 9 is used to control
479	!-- momentum flux at model top.
480	mask_bottom = MERGE( 1.0_wp, 0.0_wp, &
481	BTEST( wall_flags_0(k-1,j,i), 8 ) )
482	mask_top = MERGE( 1.0_wp, 0.0_wp, &
483	BTEST( wall_flags_0(k+1,j,i), 8 ) ) * &
484	MERGE( 1.0_wp, 0.0_wp, &
485	BTEST( wall_flags_0(k+1,j,i), 9 ) )
486	flag = MERGE( 1.0_wp, 0.0_wp, &
487	BTEST( wall_flags_0(k,j,i), 1 ) )
488	!
489	!-- Interpolate eddy diffusivities on staggered gridpoints
490	kmzp = 0.25_wp * ( km(k,j,i)+km(k+1,j,i)+km(k,j,i-1)+km(k+1,j,i-1) )
491	kmzm = 0.25_wp * ( km(k,j,i)+km(k-1,j,i)+km(k,j,i-1)+km(k-1,j,i-1) )
492
493	tend(k,j,i) = tend(k,j,i) &
494	+ ( kmzp * ( ( u(k+1,j,i) - u(k,j,i) ) * ddzu(k+1) &
495	+ ( w(k,j,i) - w(k,j,i-1) ) * ddx &
496	) * rho_air_zw(k) * mask_top &
497	- kmzm * ( ( u(k,j,i) - u(k-1,j,i) ) * ddzu(k) &
498	+ ( w(k-1,j,i) - w(k-1,j,i-1) ) * ddx &
499	) * rho_air_zw(k-1) * mask_bottom &
500	) * ddzw(k) * drho_air(k) * flag
501	ENDDO
502
503	!
504	!-- Vertical diffusion at the first surface grid points, if the
505	!-- momentum flux at the bottom is given by the Prandtl law or if it is
506	!-- prescribed by the user.
507	!-- Difference quotient of the momentum flux is not formed over half of
508	!-- the grid spacing (2.0*ddzw(k)) any more, since the comparison with
509	!-- other (LES) models showed that the values of the momentum flux becomes
510	!-- too large in this case.
511	IF ( use_surface_fluxes ) THEN
512	!
513	!-- Default-type surfaces, upward-facing
514	surf_s = surf_def_h(0)%start_index(j,i)
515	surf_e = surf_def_h(0)%end_index(j,i)
516	DO m = surf_s, surf_e
517
518	k = surf_def_h(0)%k(m)
519
520	tend(k,j,i) = tend(k,j,i) &
521	+ ( - ( - surf_def_h(0)%usws(m) ) &
522	) * ddzw(k) * drho_air(k)
523	ENDDO
524	!
525	!-- Default-type surfaces, dowward-facing (except for model-top fluxes)
526	surf_s = surf_def_h(1)%start_index(j,i)
527	surf_e = surf_def_h(1)%end_index(j,i)
528	DO m = surf_s, surf_e
529
530	k = surf_def_h(1)%k(m)
531
532	tend(k,j,i) = tend(k,j,i) &
533	+ ( - surf_def_h(1)%usws(m) &
534	) * ddzw(k) * drho_air(k)
535	ENDDO
536	!
537	!-- Natural-type surfaces, upward-facing
538	surf_s = surf_lsm_h%start_index(j,i)
539	surf_e = surf_lsm_h%end_index(j,i)
540	DO m = surf_s, surf_e
541
542	k = surf_lsm_h%k(m)
543
544	tend(k,j,i) = tend(k,j,i) &
545	+ ( - ( - surf_lsm_h%usws(m) ) &
546	) * ddzw(k) * drho_air(k)
547	ENDDO
548	!
549	!-- Urban-type surfaces, upward-facing
550	surf_s = surf_usm_h%start_index(j,i)
551	surf_e = surf_usm_h%end_index(j,i)
552	DO m = surf_s, surf_e
553
554	k = surf_usm_h%k(m)
555
556	tend(k,j,i) = tend(k,j,i) &
557	+ ( - ( - surf_usm_h%usws(m) ) &
558	) * ddzw(k) * drho_air(k)
559	ENDDO
560
561	ENDIF
562	!
563	!-- Add momentum flux at model top
564	IF ( use_top_fluxes .AND. constant_top_momentumflux ) THEN
565	surf_s = surf_def_h(2)%start_index(j,i)
566	surf_e = surf_def_h(2)%end_index(j,i)
567	DO m = surf_s, surf_e
568
569	k = surf_def_h(2)%k(m)
570
571	tend(k,j,i) = tend(k,j,i) &
572	+ ( - surf_def_h(2)%usws(m) ) * ddzw(k) * drho_air(k)
573	ENDDO
574	ENDIF
575
576
577	END SUBROUTINE diffusion_u_ij
578
579	END MODULE diffusion_u_mod

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