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1	!> @file diffusion_u.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_u.f90 2233 2017-05-30 18:08:54Z suehring $
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	! 1691 2015-10-26 16:17:44Z maronga
50	! Formatting corrections.
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	! kmym_x/_y and kmyp_x/_y change to kmym and kmyp
86	!
87	! Revision 1.1 1997/09/12 06:23:51 raasch
88	! Initial revision
89	!
90	!
91	! Description:
92	! ------------
93	!> Diffusion term of the u-component
94	!> @todo additional damping (needed for non-cyclic bc) causes bad vectorization
95	!> and slows down the speed on NEC about 5-10%
96	!------------------------------------------------------------------------------!
97	MODULE diffusion_u_mod
98
99
100	PRIVATE
101	PUBLIC diffusion_u
102
103	INTERFACE diffusion_u
104	MODULE PROCEDURE diffusion_u
105	MODULE PROCEDURE diffusion_u_ij
106	END INTERFACE diffusion_u
107
108	CONTAINS
109
110
111	!------------------------------------------------------------------------------!
112	! Description:
113	! ------------
114	!> Call for all grid points
115	!------------------------------------------------------------------------------!
116	SUBROUTINE diffusion_u
117
118	USE arrays_3d, &
119	ONLY: ddzu, ddzw, km, tend, u, v, w, drho_air, rho_air_zw
120
121	USE control_parameters, &
122	ONLY: constant_top_momentumflux, use_surface_fluxes, &
123	use_top_fluxes
124
125	USE grid_variables, &
126	ONLY: ddx, ddx2, ddy
127
128	USE indices, &
129	ONLY: nxl, nxlu, nxr, nyn, nys, nzb, nzt, wall_flags_0
130
131	USE kinds
132
133	USE surface_mod, &
134	ONLY : surf_def_h, surf_def_v, surf_lsm_h, surf_lsm_v, surf_usm_h, &
135	surf_usm_v
136
137	IMPLICIT NONE
138
139	INTEGER(iwp) :: i !< running index x direction
140	INTEGER(iwp) :: j !< running index y direction
141	INTEGER(iwp) :: k !< running index z direction
142	INTEGER(iwp) :: l !< running index of surface type, south- or north-facing wall
143	INTEGER(iwp) :: m !< running index surface elements
144	INTEGER(iwp) :: surf_e !< End index of surface elements at (j,i)-gridpoint
145	INTEGER(iwp) :: surf_s !< Start index of surface elements at (j,i)-gridpoint
146
147	REAL(wp) :: flag !< flag to mask topography grid points
148	REAL(wp) :: kmym !<
149	REAL(wp) :: kmyp !<
150	REAL(wp) :: kmzm !<
151	REAL(wp) :: kmzp !<
152	REAL(wp) :: mask_bottom !< flag to mask vertical upward-facing surface
153	REAL(wp) :: mask_north !< flag to mask vertical surface north of the grid point
154	REAL(wp) :: mask_south !< flag to mask vertical surface south of the grid point
155	REAL(wp) :: mask_top !< flag to mask vertical downward-facing surface
156
157
158
159	DO i = nxlu, nxr
160	DO j = nys, nyn
161	!
162	!-- Compute horizontal diffusion
163	DO k = nzb+1, nzt
164	!
165	!-- Predetermine flag to mask topography and wall-bounded grid points.
166	!-- It is sufficient to masked only north- and south-facing surfaces, which
167	!-- need special treatment for the u-component.
168	flag = MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_0(k,j,i), 1 ) )
169	mask_south = MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_0(k,j-1,i), 1 ) )
170	mask_north = MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_0(k,j+1,i), 1 ) )
171	!
172	!-- Interpolate eddy diffusivities on staggered gridpoints
173	kmyp = 0.25_wp * &
174	( km(k,j,i)+km(k,j+1,i)+km(k,j,i-1)+km(k,j+1,i-1) )
175	kmym = 0.25_wp * &
176	( km(k,j,i)+km(k,j-1,i)+km(k,j,i-1)+km(k,j-1,i-1) )
177
178	tend(k,j,i) = tend(k,j,i) &
179	+ 2.0_wp * ( &
180	km(k,j,i) * ( u(k,j,i+1) - u(k,j,i) ) &
181	- km(k,j,i-1) * ( u(k,j,i) - u(k,j,i-1) ) &
182	) * ddx2 * flag &
183	+ ( mask_north * ( &
184	kmyp * ( u(k,j+1,i) - u(k,j,i) ) * ddy &
185	+ kmyp * ( v(k,j+1,i) - v(k,j+1,i-1) ) * ddx &
186	) &
187	- mask_south * ( &
188	kmym * ( u(k,j,i) - u(k,j-1,i) ) * ddy &
189	+ kmym * ( v(k,j,i) - v(k,j,i-1) ) * ddx &
190	) &
191	) * ddy * flag
192	ENDDO
193	!
194	!-- Add horizontal momentum flux u'v' at north- (l=0) and south-facing (l=1)
195	!-- surfaces. Note, in the the flat case, loops won't be entered as
196	!-- start_index > end_index. Furtermore, note, no vertical natural surfaces
197	!-- so far.
198	!-- Default-type surfaces
199	DO l = 0, 1
200	surf_s = surf_def_v(l)%start_index(j,i)
201	surf_e = surf_def_v(l)%end_index(j,i)
202	DO m = surf_s, surf_e
203	k = surf_def_v(l)%k(m)
204	tend(k,j,i) = tend(k,j,i) + &
205	surf_def_v(l)%mom_flux_uv(m) * ddy
206	ENDDO
207	ENDDO
208	!
209	!-- Natural-type surfaces
210	DO l = 0, 1
211	surf_s = surf_lsm_v(l)%start_index(j,i)
212	surf_e = surf_lsm_v(l)%end_index(j,i)
213	DO m = surf_s, surf_e
214	k = surf_lsm_v(l)%k(m)
215	tend(k,j,i) = tend(k,j,i) + &
216	surf_lsm_v(l)%mom_flux_uv(m) * ddy
217	ENDDO
218	ENDDO
219	!
220	!-- Urban-type surfaces
221	DO l = 0, 1
222	surf_s = surf_usm_v(l)%start_index(j,i)
223	surf_e = surf_usm_v(l)%end_index(j,i)
224	DO m = surf_s, surf_e
225	k = surf_usm_v(l)%k(m)
226	tend(k,j,i) = tend(k,j,i) + &
227	surf_usm_v(l)%mom_flux_uv(m) * ddy
228	ENDDO
229	ENDDO
230
231	!
232	!-- Compute vertical diffusion. In case of simulating a surface layer,
233	!-- respective grid diffusive fluxes are masked (flag 8) within this
234	!-- loop, and added further below, else, simple gradient approach is
235	!-- applied. Model top is also mask if top-momentum flux is given.
236	DO k = nzb+1, nzt
237	!
238	!-- Determine flags to mask topography below and above. Flag 1 is
239	!-- used to mask topography in general, and flag 8 implies
240	!-- information about use_surface_fluxes. Flag 9 is used to control
241	!-- momentum flux at model top.
242	mask_bottom = MERGE( 1.0_wp, 0.0_wp, &
243	BTEST( wall_flags_0(k-1,j,i), 8 ) )
244	mask_top = MERGE( 1.0_wp, 0.0_wp, &
245	BTEST( wall_flags_0(k+1,j,i), 8 ) ) * &
246	MERGE( 1.0_wp, 0.0_wp, &
247	BTEST( wall_flags_0(k+1,j,i), 9 ) )
248	flag = MERGE( 1.0_wp, 0.0_wp, &
249	BTEST( wall_flags_0(k,j,i), 1 ) )
250	!
251	!-- Interpolate eddy diffusivities on staggered gridpoints
252	kmzp = 0.25_wp * &
253	( km(k,j,i)+km(k+1,j,i)+km(k,j,i-1)+km(k+1,j,i-1) )
254	kmzm = 0.25_wp * &
255	( km(k,j,i)+km(k-1,j,i)+km(k,j,i-1)+km(k-1,j,i-1) )
256
257	tend(k,j,i) = tend(k,j,i) &
258	+ ( kmzp * ( ( u(k+1,j,i) - u(k,j,i) ) * ddzu(k+1) &
259	+ ( w(k,j,i) - w(k,j,i-1) ) * ddx &
260	) * rho_air_zw(k) * mask_top &
261	- kmzm * ( ( u(k,j,i) - u(k-1,j,i) ) * ddzu(k) &
262	+ ( w(k-1,j,i) - w(k-1,j,i-1) ) * ddx &
263	) * rho_air_zw(k-1) * mask_bottom &
264	) * ddzw(k) * drho_air(k) * flag
265	ENDDO
266
267	!
268	!-- Vertical diffusion at the first grid point above the surface,
269	!-- if the momentum flux at the bottom is given by the Prandtl law or
270	!-- if it is prescribed by the user.
271	!-- Difference quotient of the momentum flux is not formed over half
272	!-- of the grid spacing (2.0*ddzw(k)) any more, since the comparison
273	!-- with other (LES) models showed that the values of the momentum
274	!-- flux becomes too large in this case.
275	!-- The term containing w(k-1,..) (see above equation) is removed here
276	!-- because the vertical velocity is assumed to be zero at the surface.
277	IF ( use_surface_fluxes ) THEN
278	!
279	!-- Default-type surfaces, upward-facing
280	surf_s = surf_def_h(0)%start_index(j,i)
281	surf_e = surf_def_h(0)%end_index(j,i)
282	DO m = surf_s, surf_e
283
284	k = surf_def_h(0)%k(m)
285
286	tend(k,j,i) = tend(k,j,i) &
287	+ ( - ( - surf_def_h(0)%usws(m) ) &
288	) * ddzw(k) * drho_air(k)
289	ENDDO
290	!
291	!-- Default-type surfaces, dowward-facing
292	surf_s = surf_def_h(1)%start_index(j,i)
293	surf_e = surf_def_h(1)%end_index(j,i)
294	DO m = surf_s, surf_e
295
296	k = surf_def_h(1)%k(m)
297
298	tend(k,j,i) = tend(k,j,i) &
299	+ ( - surf_def_h(1)%usws(m) &
300	) * ddzw(k) * drho_air(k)
301	ENDDO
302	!
303	!-- Natural-type surfaces, upward-facing
304	surf_s = surf_lsm_h%start_index(j,i)
305	surf_e = surf_lsm_h%end_index(j,i)
306	DO m = surf_s, surf_e
307
308	k = surf_lsm_h%k(m)
309
310	tend(k,j,i) = tend(k,j,i) &
311	+ ( - ( - surf_lsm_h%usws(m) ) &
312	) * ddzw(k) * drho_air(k)
313	ENDDO
314	!
315	!-- Urban-type surfaces, upward-facing
316	surf_s = surf_usm_h%start_index(j,i)
317	surf_e = surf_usm_h%end_index(j,i)
318	DO m = surf_s, surf_e
319
320	k = surf_usm_h%k(m)
321
322	tend(k,j,i) = tend(k,j,i) &
323	+ ( - ( - surf_usm_h%usws(m) ) &
324	) * ddzw(k) * drho_air(k)
325	ENDDO
326
327	ENDIF
328	!
329	!-- Add momentum flux at model top
330	IF ( use_top_fluxes ) THEN
331	surf_s = surf_def_h(2)%start_index(j,i)
332	surf_e = surf_def_h(2)%end_index(j,i)
333	DO m = surf_s, surf_e
334
335	k = surf_def_h(2)%k(m)
336
337	tend(k,j,i) = tend(k,j,i) &
338	+ ( - surf_def_h(2)%usws(m) ) * ddzw(k) * drho_air(k)
339	ENDDO
340	ENDIF
341
342	ENDDO
343	ENDDO
344
345	END SUBROUTINE diffusion_u
346
347
348	!------------------------------------------------------------------------------!
349	! Description:
350	! ------------
351	!> Call for grid point i,j
352	!------------------------------------------------------------------------------!
353	SUBROUTINE diffusion_u_ij( i, j )
354
355	USE arrays_3d, &
356	ONLY: ddzu, ddzw, km, tend, u, v, w, drho_air, rho_air_zw
357
358	USE control_parameters, &
359	ONLY: constant_top_momentumflux, use_surface_fluxes, &
360	use_top_fluxes
361
362	USE grid_variables, &
363	ONLY: ddx, ddx2, ddy
364
365	USE indices, &
366	ONLY: nzb, nzt, wall_flags_0
367
368	USE kinds
369
370	USE surface_mod, &
371	ONLY : surf_def_h, surf_def_v, surf_lsm_h, surf_lsm_v, surf_usm_h, &
372	surf_usm_v
373
374	IMPLICIT NONE
375
376	INTEGER(iwp) :: i !< running index x direction
377	INTEGER(iwp) :: j !< running index y direction
378	INTEGER(iwp) :: k !< running index z direction
379	INTEGER(iwp) :: l !< running index of surface type, south- or north-facing wall
380	INTEGER(iwp) :: m !< running index surface elements
381	INTEGER(iwp) :: surf_e !< End index of surface elements at (j,i)-gridpoint
382	INTEGER(iwp) :: surf_s !< Start index of surface elements at (j,i)-gridpoint
383
384	REAL(wp) :: flag !< flag to mask topography grid points
385	REAL(wp) :: kmym !<
386	REAL(wp) :: kmyp !<
387	REAL(wp) :: kmzm !<
388	REAL(wp) :: kmzp !<
389	REAL(wp) :: mask_bottom !< flag to mask vertical upward-facing surface
390	REAL(wp) :: mask_north !< flag to mask vertical surface north of the grid point
391	REAL(wp) :: mask_south !< flag to mask vertical surface south of the grid point
392	REAL(wp) :: mask_top !< flag to mask vertical downward-facing surface
393	!
394	!-- Compute horizontal diffusion
395	DO k = nzb+1, nzt
396	!
397	!-- Predetermine flag to mask topography and wall-bounded grid points.
398	!-- It is sufficient to masked only north- and south-facing surfaces, which
399	!-- need special treatment for the u-component.
400	flag = MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_0(k,j,i), 1 ) )
401	mask_south = MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_0(k,j-1,i), 1 ) )
402	mask_north = MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_0(k,j+1,i), 1 ) )
403	!
404	!-- Interpolate eddy diffusivities on staggered gridpoints
405	kmyp = 0.25_wp * ( km(k,j,i)+km(k,j+1,i)+km(k,j,i-1)+km(k,j+1,i-1) )
406	kmym = 0.25_wp * ( km(k,j,i)+km(k,j-1,i)+km(k,j,i-1)+km(k,j-1,i-1) )
407
408	tend(k,j,i) = tend(k,j,i) &
409	+ 2.0_wp * ( &
410	km(k,j,i) * ( u(k,j,i+1) - u(k,j,i) ) &
411	- km(k,j,i-1) * ( u(k,j,i) - u(k,j,i-1) ) &
412	) * ddx2 * flag &
413	+ ( &
414	mask_north * kmyp * ( ( u(k,j+1,i) - u(k,j,i) ) * ddy &
415	+ ( v(k,j+1,i) - v(k,j+1,i-1) ) * ddx &
416	) &
417	- mask_south * kmym * ( ( u(k,j,i) - u(k,j-1,i) ) * ddy &
418	+ ( v(k,j,i) - v(k,j,i-1) ) * ddx &
419	) &
420	) * ddy * flag
421	ENDDO
422
423	!
424	!-- Add horizontal momentum flux u'v' at north- (l=0) and south-facing (l=1)
425	!-- surfaces. Note, in the the flat case, loops won't be entered as
426	!-- start_index > end_index. Furtermore, note, no vertical natural surfaces
427	!-- so far.
428	!-- Default-type surfaces
429	DO l = 0, 1
430	surf_s = surf_def_v(l)%start_index(j,i)
431	surf_e = surf_def_v(l)%end_index(j,i)
432	DO m = surf_s, surf_e
433	k = surf_def_v(l)%k(m)
434	tend(k,j,i) = tend(k,j,i) + surf_def_v(l)%mom_flux_uv(m) * ddy
435	ENDDO
436	ENDDO
437	!
438	!-- Natural-type surfaces
439	DO l = 0, 1
440	surf_s = surf_lsm_v(l)%start_index(j,i)
441	surf_e = surf_lsm_v(l)%end_index(j,i)
442	DO m = surf_s, surf_e
443	k = surf_lsm_v(l)%k(m)
444	tend(k,j,i) = tend(k,j,i) + surf_lsm_v(l)%mom_flux_uv(m) * ddy
445	ENDDO
446	ENDDO
447	!
448	!-- Urban-type surfaces
449	DO l = 0, 1
450	surf_s = surf_usm_v(l)%start_index(j,i)
451	surf_e = surf_usm_v(l)%end_index(j,i)
452	DO m = surf_s, surf_e
453	k = surf_usm_v(l)%k(m)
454	tend(k,j,i) = tend(k,j,i) + surf_usm_v(l)%mom_flux_uv(m) * ddy
455	ENDDO
456	ENDDO
457	!
458	!-- Compute vertical diffusion. In case of simulating a surface layer,
459	!-- respective grid diffusive fluxes are masked (flag 8) within this
460	!-- loop, and added further below, else, simple gradient approach is
461	!-- applied. Model top is also mask if top-momentum flux is given.
462	DO k = nzb+1, nzt
463	!
464	!-- Determine flags to mask topography below and above. Flag 1 is
465	!-- used to mask topography in general, and flag 8 implies
466	!-- information about use_surface_fluxes. Flag 9 is used to control
467	!-- momentum flux at model top.
468	mask_bottom = MERGE( 1.0_wp, 0.0_wp, &
469	BTEST( wall_flags_0(k-1,j,i), 8 ) )
470	mask_top = MERGE( 1.0_wp, 0.0_wp, &
471	BTEST( wall_flags_0(k+1,j,i), 8 ) ) * &
472	MERGE( 1.0_wp, 0.0_wp, &
473	BTEST( wall_flags_0(k+1,j,i), 9 ) )
474	flag = MERGE( 1.0_wp, 0.0_wp, &
475	BTEST( wall_flags_0(k,j,i), 1 ) )
476	!
477	!-- Interpolate eddy diffusivities on staggered gridpoints
478	kmzp = 0.25_wp * ( km(k,j,i)+km(k+1,j,i)+km(k,j,i-1)+km(k+1,j,i-1) )
479	kmzm = 0.25_wp * ( km(k,j,i)+km(k-1,j,i)+km(k,j,i-1)+km(k-1,j,i-1) )
480
481	tend(k,j,i) = tend(k,j,i) &
482	+ ( kmzp * ( ( u(k+1,j,i) - u(k,j,i) ) * ddzu(k+1) &
483	+ ( w(k,j,i) - w(k,j,i-1) ) * ddx &
484	) * rho_air_zw(k) * mask_top &
485	- kmzm * ( ( u(k,j,i) - u(k-1,j,i) ) * ddzu(k) &
486	+ ( w(k-1,j,i) - w(k-1,j,i-1) ) * ddx &
487	) * rho_air_zw(k-1) * mask_bottom &
488	) * ddzw(k) * drho_air(k) * flag
489	ENDDO
490
491	!
492	!-- Vertical diffusion at the first surface grid points, if the
493	!-- momentum flux at the bottom is given by the Prandtl law or if it is
494	!-- prescribed by the user.
495	!-- Difference quotient of the momentum flux is not formed over half of
496	!-- the grid spacing (2.0*ddzw(k)) any more, since the comparison with
497	!-- other (LES) models showed that the values of the momentum flux becomes
498	!-- too large in this case.
499	IF ( use_surface_fluxes ) THEN
500	!
501	!-- Default-type surfaces, upward-facing
502	surf_s = surf_def_h(0)%start_index(j,i)
503	surf_e = surf_def_h(0)%end_index(j,i)
504	DO m = surf_s, surf_e
505
506	k = surf_def_h(0)%k(m)
507
508	tend(k,j,i) = tend(k,j,i) &
509	+ ( - ( - surf_def_h(0)%usws(m) ) &
510	) * ddzw(k) * drho_air(k)
511	ENDDO
512	!
513	!-- Default-type surfaces, dowward-facing (except for model-top fluxes)
514	surf_s = surf_def_h(1)%start_index(j,i)
515	surf_e = surf_def_h(1)%end_index(j,i)
516	DO m = surf_s, surf_e
517
518	k = surf_def_h(1)%k(m)
519
520	tend(k,j,i) = tend(k,j,i) &
521	+ ( - surf_def_h(1)%usws(m) &
522	) * ddzw(k) * drho_air(k)
523	ENDDO
524	!
525	!-- Natural-type surfaces, upward-facing
526	surf_s = surf_lsm_h%start_index(j,i)
527	surf_e = surf_lsm_h%end_index(j,i)
528	DO m = surf_s, surf_e
529
530	k = surf_lsm_h%k(m)
531
532	tend(k,j,i) = tend(k,j,i) &
533	+ ( - ( - surf_lsm_h%usws(m) ) &
534	) * ddzw(k) * drho_air(k)
535	ENDDO
536	!
537	!-- Urban-type surfaces, upward-facing
538	surf_s = surf_usm_h%start_index(j,i)
539	surf_e = surf_usm_h%end_index(j,i)
540	DO m = surf_s, surf_e
541
542	k = surf_usm_h%k(m)
543
544	tend(k,j,i) = tend(k,j,i) &
545	+ ( - ( - surf_usm_h%usws(m) ) &
546	) * ddzw(k) * drho_air(k)
547	ENDDO
548
549	ENDIF
550	!
551	!-- Add momentum flux at model top
552	IF ( use_top_fluxes ) THEN
553	surf_s = surf_def_h(2)%start_index(j,i)
554	surf_e = surf_def_h(2)%end_index(j,i)
555	DO m = surf_s, surf_e
556
557	k = surf_def_h(2)%k(m)
558
559	tend(k,j,i) = tend(k,j,i) &
560	+ ( - surf_def_h(2)%usws(m) ) * ddzw(k) * drho_air(k)
561	ENDDO
562	ENDIF
563
564
565	END SUBROUTINE diffusion_u_ij
566
567	END MODULE diffusion_u_mod

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