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source: palm/trunk/SOURCE/diffusion_u.f90 @ 3208

Last change on this file since 3208 was 2718, checked in by maronga, 7 years ago
deleting of deprecated files; headers updated where needed
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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 2718 2018-01-02 08:49:38Z sward $
27	! Corrected "Former revisions" section
28	!
29	! 2696 2017-12-14 17:12:51Z kanani
30	! Change in file header (GPL part)
31	!
32	! 2638 2017-11-23 12:44:23Z raasch
33	! bugfix for constant top momentumflux
34	!
35	! 2233 2017-05-30 18:08:54Z suehring
36	!
37	! 2232 2017-05-30 17:47:52Z suehring
38	! Adjustments to new topography and surface concept
39	!
40	! 2118 2017-01-17 16:38:49Z raasch
41	! OpenACC version of subroutine removed
42	!
43	! 2037 2016-10-26 11:15:40Z knoop
44	! Anelastic approximation implemented
45	!
46	! 2000 2016-08-20 18:09:15Z knoop
47	! Forced header and separation lines into 80 columns
48	!
49	! 1873 2016-04-18 14:50:06Z maronga
50	! Module renamed (removed _mod)
51	!
52	! 1850 2016-04-08 13:29:27Z maronga
53	! Module renamed
54	!
55	! 1740 2016-01-13 08:19:40Z raasch
56	! unnecessary calculations of kmzm and kmzp in wall bounded parts removed
57	!
58	! 1691 2015-10-26 16:17:44Z maronga
59	! Formatting corrections.
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	! kmym_x/_y and kmyp_x/_y change to kmym and kmyp
95	!
96	! Revision 1.1 1997/09/12 06:23:51 raasch
97	! Initial revision
98	!
99	!
100	! Description:
101	! ------------
102	!> Diffusion term of the u-component
103	!> @todo additional damping (needed for non-cyclic bc) causes bad vectorization
104	!> and slows down the speed on NEC about 5-10%
105	!------------------------------------------------------------------------------!
106	MODULE diffusion_u_mod
107
108
109	PRIVATE
110	PUBLIC diffusion_u
111
112	INTERFACE diffusion_u
113	MODULE PROCEDURE diffusion_u
114	MODULE PROCEDURE diffusion_u_ij
115	END INTERFACE diffusion_u
116
117	CONTAINS
118
119
120	!------------------------------------------------------------------------------!
121	! Description:
122	! ------------
123	!> Call for all grid points
124	!------------------------------------------------------------------------------!
125	SUBROUTINE diffusion_u
126
127	USE arrays_3d, &
128	ONLY: ddzu, ddzw, km, tend, u, v, w, drho_air, rho_air_zw
129
130	USE control_parameters, &
131	ONLY: constant_top_momentumflux, use_surface_fluxes, &
132	use_top_fluxes
133
134	USE grid_variables, &
135	ONLY: ddx, ddx2, ddy
136
137	USE indices, &
138	ONLY: nxl, nxlu, nxr, nyn, nys, nzb, nzt, wall_flags_0
139
140	USE kinds
141
142	USE surface_mod, &
143	ONLY : surf_def_h, surf_def_v, surf_lsm_h, surf_lsm_v, surf_usm_h, &
144	surf_usm_v
145
146	IMPLICIT NONE
147
148	INTEGER(iwp) :: i !< running index x direction
149	INTEGER(iwp) :: j !< running index y direction
150	INTEGER(iwp) :: k !< running index z direction
151	INTEGER(iwp) :: l !< running index of surface type, south- or north-facing wall
152	INTEGER(iwp) :: m !< running index surface elements
153	INTEGER(iwp) :: surf_e !< End index of surface elements at (j,i)-gridpoint
154	INTEGER(iwp) :: surf_s !< Start index of surface elements at (j,i)-gridpoint
155
156	REAL(wp) :: flag !< flag to mask topography grid points
157	REAL(wp) :: kmym !<
158	REAL(wp) :: kmyp !<
159	REAL(wp) :: kmzm !<
160	REAL(wp) :: kmzp !<
161	REAL(wp) :: mask_bottom !< flag to mask vertical upward-facing surface
162	REAL(wp) :: mask_north !< flag to mask vertical surface north of the grid point
163	REAL(wp) :: mask_south !< flag to mask vertical surface south of the grid point
164	REAL(wp) :: mask_top !< flag to mask vertical downward-facing surface
165
166
167
168	DO i = nxlu, nxr
169	DO j = nys, nyn
170	!
171	!-- Compute horizontal diffusion
172	DO k = nzb+1, nzt
173	!
174	!-- Predetermine flag to mask topography and wall-bounded grid points.
175	!-- It is sufficient to masked only north- and south-facing surfaces, which
176	!-- need special treatment for the u-component.
177	flag = MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_0(k,j,i), 1 ) )
178	mask_south = MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_0(k,j-1,i), 1 ) )
179	mask_north = MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_0(k,j+1,i), 1 ) )
180	!
181	!-- Interpolate eddy diffusivities on staggered gridpoints
182	kmyp = 0.25_wp * &
183	( km(k,j,i)+km(k,j+1,i)+km(k,j,i-1)+km(k,j+1,i-1) )
184	kmym = 0.25_wp * &
185	( km(k,j,i)+km(k,j-1,i)+km(k,j,i-1)+km(k,j-1,i-1) )
186
187	tend(k,j,i) = tend(k,j,i) &
188	+ 2.0_wp * ( &
189	km(k,j,i) * ( u(k,j,i+1) - u(k,j,i) ) &
190	- km(k,j,i-1) * ( u(k,j,i) - u(k,j,i-1) ) &
191	) * ddx2 * flag &
192	+ ( mask_north * ( &
193	kmyp * ( u(k,j+1,i) - u(k,j,i) ) * ddy &
194	+ kmyp * ( v(k,j+1,i) - v(k,j+1,i-1) ) * ddx &
195	) &
196	- mask_south * ( &
197	kmym * ( u(k,j,i) - u(k,j-1,i) ) * ddy &
198	+ kmym * ( v(k,j,i) - v(k,j,i-1) ) * ddx &
199	) &
200	) * ddy * flag
201	ENDDO
202	!
203	!-- Add horizontal momentum flux u'v' at north- (l=0) and south-facing (l=1)
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 = 0, 1
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) * ddy
215	ENDDO
216	ENDDO
217	!
218	!-- Natural-type surfaces
219	DO l = 0, 1
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) * ddy
226	ENDDO
227	ENDDO
228	!
229	!-- Urban-type surfaces
230	DO l = 0, 1
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) * ddy
237	ENDDO
238	ENDDO
239
240	!
241	!-- Compute vertical diffusion. In case of simulating a surface layer,
242	!-- respective grid diffusive fluxes are masked (flag 8) within this
243	!-- loop, and added further below, else, simple gradient approach is
244	!-- applied. Model top is also mask if top-momentum flux is given.
245	DO k = nzb+1, nzt
246	!
247	!-- Determine flags to mask topography below and above. Flag 1 is
248	!-- used to mask topography in general, and flag 8 implies
249	!-- information about use_surface_fluxes. Flag 9 is used to control
250	!-- momentum flux at model top.
251	mask_bottom = MERGE( 1.0_wp, 0.0_wp, &
252	BTEST( wall_flags_0(k-1,j,i), 8 ) )
253	mask_top = MERGE( 1.0_wp, 0.0_wp, &
254	BTEST( wall_flags_0(k+1,j,i), 8 ) ) * &
255	MERGE( 1.0_wp, 0.0_wp, &
256	BTEST( wall_flags_0(k+1,j,i), 9 ) )
257	flag = MERGE( 1.0_wp, 0.0_wp, &
258	BTEST( wall_flags_0(k,j,i), 1 ) )
259	!
260	!-- Interpolate eddy diffusivities on staggered gridpoints
261	kmzp = 0.25_wp * &
262	( km(k,j,i)+km(k+1,j,i)+km(k,j,i-1)+km(k+1,j,i-1) )
263	kmzm = 0.25_wp * &
264	( km(k,j,i)+km(k-1,j,i)+km(k,j,i-1)+km(k-1,j,i-1) )
265
266	tend(k,j,i) = tend(k,j,i) &
267	+ ( kmzp * ( ( u(k+1,j,i) - u(k,j,i) ) * ddzu(k+1) &
268	+ ( w(k,j,i) - w(k,j,i-1) ) * ddx &
269	) * rho_air_zw(k) * mask_top &
270	- kmzm * ( ( u(k,j,i) - u(k-1,j,i) ) * ddzu(k) &
271	+ ( w(k-1,j,i) - w(k-1,j,i-1) ) * ddx &
272	) * rho_air_zw(k-1) * mask_bottom &
273	) * ddzw(k) * drho_air(k) * flag
274	ENDDO
275
276	!
277	!-- Vertical diffusion at the first grid point above the surface,
278	!-- if the momentum flux at the bottom is given by the Prandtl law or
279	!-- if it is prescribed by the user.
280	!-- Difference quotient of the momentum flux is not formed over half
281	!-- of the grid spacing (2.0*ddzw(k)) any more, since the comparison
282	!-- with other (LES) models showed that the values of the momentum
283	!-- flux becomes too large in this case.
284	!-- The term containing w(k-1,..) (see above equation) is removed here
285	!-- because the vertical velocity is assumed to be zero at the surface.
286	IF ( use_surface_fluxes ) THEN
287	!
288	!-- Default-type surfaces, upward-facing
289	surf_s = surf_def_h(0)%start_index(j,i)
290	surf_e = surf_def_h(0)%end_index(j,i)
291	DO m = surf_s, surf_e
292
293	k = surf_def_h(0)%k(m)
294
295	tend(k,j,i) = tend(k,j,i) &
296	+ ( - ( - surf_def_h(0)%usws(m) ) &
297	) * ddzw(k) * drho_air(k)
298	ENDDO
299	!
300	!-- Default-type surfaces, dowward-facing
301	surf_s = surf_def_h(1)%start_index(j,i)
302	surf_e = surf_def_h(1)%end_index(j,i)
303	DO m = surf_s, surf_e
304
305	k = surf_def_h(1)%k(m)
306
307	tend(k,j,i) = tend(k,j,i) &
308	+ ( - surf_def_h(1)%usws(m) &
309	) * ddzw(k) * drho_air(k)
310	ENDDO
311	!
312	!-- Natural-type surfaces, upward-facing
313	surf_s = surf_lsm_h%start_index(j,i)
314	surf_e = surf_lsm_h%end_index(j,i)
315	DO m = surf_s, surf_e
316
317	k = surf_lsm_h%k(m)
318
319	tend(k,j,i) = tend(k,j,i) &
320	+ ( - ( - surf_lsm_h%usws(m) ) &
321	) * ddzw(k) * drho_air(k)
322	ENDDO
323	!
324	!-- Urban-type surfaces, upward-facing
325	surf_s = surf_usm_h%start_index(j,i)
326	surf_e = surf_usm_h%end_index(j,i)
327	DO m = surf_s, surf_e
328
329	k = surf_usm_h%k(m)
330
331	tend(k,j,i) = tend(k,j,i) &
332	+ ( - ( - surf_usm_h%usws(m) ) &
333	) * ddzw(k) * drho_air(k)
334	ENDDO
335
336	ENDIF
337	!
338	!-- Add momentum flux at model top
339	IF ( use_top_fluxes .AND. constant_top_momentumflux ) THEN
340	surf_s = surf_def_h(2)%start_index(j,i)
341	surf_e = surf_def_h(2)%end_index(j,i)
342	DO m = surf_s, surf_e
343
344	k = surf_def_h(2)%k(m)
345
346	tend(k,j,i) = tend(k,j,i) &
347	+ ( - surf_def_h(2)%usws(m) ) * ddzw(k) * drho_air(k)
348	ENDDO
349	ENDIF
350
351	ENDDO
352	ENDDO
353
354	END SUBROUTINE diffusion_u
355
356
357	!------------------------------------------------------------------------------!
358	! Description:
359	! ------------
360	!> Call for grid point i,j
361	!------------------------------------------------------------------------------!
362	SUBROUTINE diffusion_u_ij( i, j )
363
364	USE arrays_3d, &
365	ONLY: ddzu, ddzw, km, tend, u, v, w, drho_air, rho_air_zw
366
367	USE control_parameters, &
368	ONLY: constant_top_momentumflux, use_surface_fluxes, &
369	use_top_fluxes
370
371	USE grid_variables, &
372	ONLY: ddx, ddx2, ddy
373
374	USE indices, &
375	ONLY: nzb, nzt, wall_flags_0
376
377	USE kinds
378
379	USE surface_mod, &
380	ONLY : surf_def_h, surf_def_v, surf_lsm_h, surf_lsm_v, surf_usm_h, &
381	surf_usm_v
382
383	IMPLICIT NONE
384
385	INTEGER(iwp) :: i !< running index x direction
386	INTEGER(iwp) :: j !< running index y direction
387	INTEGER(iwp) :: k !< running index z direction
388	INTEGER(iwp) :: l !< running index of surface type, south- or north-facing wall
389	INTEGER(iwp) :: m !< running index surface elements
390	INTEGER(iwp) :: surf_e !< End index of surface elements at (j,i)-gridpoint
391	INTEGER(iwp) :: surf_s !< Start index of surface elements at (j,i)-gridpoint
392
393	REAL(wp) :: flag !< flag to mask topography grid points
394	REAL(wp) :: kmym !<
395	REAL(wp) :: kmyp !<
396	REAL(wp) :: kmzm !<
397	REAL(wp) :: kmzp !<
398	REAL(wp) :: mask_bottom !< flag to mask vertical upward-facing surface
399	REAL(wp) :: mask_north !< flag to mask vertical surface north of the grid point
400	REAL(wp) :: mask_south !< flag to mask vertical surface south of the grid point
401	REAL(wp) :: mask_top !< flag to mask vertical downward-facing surface
402	!
403	!-- Compute horizontal diffusion
404	DO k = nzb+1, nzt
405	!
406	!-- Predetermine flag to mask topography and wall-bounded grid points.
407	!-- It is sufficient to masked only north- and south-facing surfaces, which
408	!-- need special treatment for the u-component.
409	flag = MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_0(k,j,i), 1 ) )
410	mask_south = MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_0(k,j-1,i), 1 ) )
411	mask_north = MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_0(k,j+1,i), 1 ) )
412	!
413	!-- Interpolate eddy diffusivities on staggered gridpoints
414	kmyp = 0.25_wp * ( km(k,j,i)+km(k,j+1,i)+km(k,j,i-1)+km(k,j+1,i-1) )
415	kmym = 0.25_wp * ( km(k,j,i)+km(k,j-1,i)+km(k,j,i-1)+km(k,j-1,i-1) )
416
417	tend(k,j,i) = tend(k,j,i) &
418	+ 2.0_wp * ( &
419	km(k,j,i) * ( u(k,j,i+1) - u(k,j,i) ) &
420	- km(k,j,i-1) * ( u(k,j,i) - u(k,j,i-1) ) &
421	) * ddx2 * flag &
422	+ ( &
423	mask_north * kmyp * ( ( u(k,j+1,i) - u(k,j,i) ) * ddy &
424	+ ( v(k,j+1,i) - v(k,j+1,i-1) ) * ddx &
425	) &
426	- mask_south * kmym * ( ( u(k,j,i) - u(k,j-1,i) ) * ddy &
427	+ ( v(k,j,i) - v(k,j,i-1) ) * ddx &
428	) &
429	) * ddy * flag
430	ENDDO
431
432	!
433	!-- Add horizontal momentum flux u'v' at north- (l=0) and south-facing (l=1)
434	!-- surfaces. Note, in the the flat case, loops won't be entered as
435	!-- start_index > end_index. Furtermore, note, no vertical natural surfaces
436	!-- so far.
437	!-- Default-type surfaces
438	DO l = 0, 1
439	surf_s = surf_def_v(l)%start_index(j,i)
440	surf_e = surf_def_v(l)%end_index(j,i)
441	DO m = surf_s, surf_e
442	k = surf_def_v(l)%k(m)
443	tend(k,j,i) = tend(k,j,i) + surf_def_v(l)%mom_flux_uv(m) * ddy
444	ENDDO
445	ENDDO
446	!
447	!-- Natural-type surfaces
448	DO l = 0, 1
449	surf_s = surf_lsm_v(l)%start_index(j,i)
450	surf_e = surf_lsm_v(l)%end_index(j,i)
451	DO m = surf_s, surf_e
452	k = surf_lsm_v(l)%k(m)
453	tend(k,j,i) = tend(k,j,i) + surf_lsm_v(l)%mom_flux_uv(m) * ddy
454	ENDDO
455	ENDDO
456	!
457	!-- Urban-type surfaces
458	DO l = 0, 1
459	surf_s = surf_usm_v(l)%start_index(j,i)
460	surf_e = surf_usm_v(l)%end_index(j,i)
461	DO m = surf_s, surf_e
462	k = surf_usm_v(l)%k(m)
463	tend(k,j,i) = tend(k,j,i) + surf_usm_v(l)%mom_flux_uv(m) * ddy
464	ENDDO
465	ENDDO
466	!
467	!-- Compute vertical diffusion. In case of simulating a surface layer,
468	!-- respective grid diffusive fluxes are masked (flag 8) within this
469	!-- loop, and added further below, else, simple gradient approach is
470	!-- applied. Model top is also mask if top-momentum flux is given.
471	DO k = nzb+1, nzt
472	!
473	!-- Determine flags to mask topography below and above. Flag 1 is
474	!-- used to mask topography in general, and flag 8 implies
475	!-- information about use_surface_fluxes. Flag 9 is used to control
476	!-- momentum flux at model top.
477	mask_bottom = MERGE( 1.0_wp, 0.0_wp, &
478	BTEST( wall_flags_0(k-1,j,i), 8 ) )
479	mask_top = MERGE( 1.0_wp, 0.0_wp, &
480	BTEST( wall_flags_0(k+1,j,i), 8 ) ) * &
481	MERGE( 1.0_wp, 0.0_wp, &
482	BTEST( wall_flags_0(k+1,j,i), 9 ) )
483	flag = MERGE( 1.0_wp, 0.0_wp, &
484	BTEST( wall_flags_0(k,j,i), 1 ) )
485	!
486	!-- Interpolate eddy diffusivities on staggered gridpoints
487	kmzp = 0.25_wp * ( km(k,j,i)+km(k+1,j,i)+km(k,j,i-1)+km(k+1,j,i-1) )
488	kmzm = 0.25_wp * ( km(k,j,i)+km(k-1,j,i)+km(k,j,i-1)+km(k-1,j,i-1) )
489
490	tend(k,j,i) = tend(k,j,i) &
491	+ ( kmzp * ( ( u(k+1,j,i) - u(k,j,i) ) * ddzu(k+1) &
492	+ ( w(k,j,i) - w(k,j,i-1) ) * ddx &
493	) * rho_air_zw(k) * mask_top &
494	- kmzm * ( ( u(k,j,i) - u(k-1,j,i) ) * ddzu(k) &
495	+ ( w(k-1,j,i) - w(k-1,j,i-1) ) * ddx &
496	) * rho_air_zw(k-1) * mask_bottom &
497	) * ddzw(k) * drho_air(k) * flag
498	ENDDO
499
500	!
501	!-- Vertical diffusion at the first surface grid points, if the
502	!-- momentum flux at the bottom is given by the Prandtl law or if it is
503	!-- prescribed by the user.
504	!-- Difference quotient of the momentum flux is not formed over half of
505	!-- the grid spacing (2.0*ddzw(k)) any more, since the comparison with
506	!-- other (LES) models showed that the values of the momentum flux becomes
507	!-- too large in this case.
508	IF ( use_surface_fluxes ) THEN
509	!
510	!-- Default-type surfaces, upward-facing
511	surf_s = surf_def_h(0)%start_index(j,i)
512	surf_e = surf_def_h(0)%end_index(j,i)
513	DO m = surf_s, surf_e
514
515	k = surf_def_h(0)%k(m)
516
517	tend(k,j,i) = tend(k,j,i) &
518	+ ( - ( - surf_def_h(0)%usws(m) ) &
519	) * ddzw(k) * drho_air(k)
520	ENDDO
521	!
522	!-- Default-type surfaces, dowward-facing (except for model-top fluxes)
523	surf_s = surf_def_h(1)%start_index(j,i)
524	surf_e = surf_def_h(1)%end_index(j,i)
525	DO m = surf_s, surf_e
526
527	k = surf_def_h(1)%k(m)
528
529	tend(k,j,i) = tend(k,j,i) &
530	+ ( - surf_def_h(1)%usws(m) &
531	) * ddzw(k) * drho_air(k)
532	ENDDO
533	!
534	!-- Natural-type surfaces, upward-facing
535	surf_s = surf_lsm_h%start_index(j,i)
536	surf_e = surf_lsm_h%end_index(j,i)
537	DO m = surf_s, surf_e
538
539	k = surf_lsm_h%k(m)
540
541	tend(k,j,i) = tend(k,j,i) &
542	+ ( - ( - surf_lsm_h%usws(m) ) &
543	) * ddzw(k) * drho_air(k)
544	ENDDO
545	!
546	!-- Urban-type surfaces, upward-facing
547	surf_s = surf_usm_h%start_index(j,i)
548	surf_e = surf_usm_h%end_index(j,i)
549	DO m = surf_s, surf_e
550
551	k = surf_usm_h%k(m)
552
553	tend(k,j,i) = tend(k,j,i) &
554	+ ( - ( - surf_usm_h%usws(m) ) &
555	) * ddzw(k) * drho_air(k)
556	ENDDO
557
558	ENDIF
559	!
560	!-- Add momentum flux at model top
561	IF ( use_top_fluxes .AND. constant_top_momentumflux ) THEN
562	surf_s = surf_def_h(2)%start_index(j,i)
563	surf_e = surf_def_h(2)%end_index(j,i)
564	DO m = surf_s, surf_e
565
566	k = surf_def_h(2)%k(m)
567
568	tend(k,j,i) = tend(k,j,i) &
569	+ ( - surf_def_h(2)%usws(m) ) * ddzw(k) * drho_air(k)
570	ENDDO
571	ENDIF
572
573
574	END SUBROUTINE diffusion_u_ij
575
576	END MODULE diffusion_u_mod

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