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source: palm/trunk/SOURCE/diffusion_u.f90 @ 4338

Last change on this file since 4338 was 4329, checked in by motisi, 5 years ago
Renamed wall_flags_0 to wall_flags_static_0
Property svn:keywords set to `Id`
File size: 24.3 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 1997-2019 Leibniz Universitaet Hannover
18	!------------------------------------------------------------------------------!
19	!
20	! Current revisions:
21	! -----------------
22	!
23	!
24	! Former revisions:
25	! -----------------
26	! $Id: diffusion_u.f90 4329 2019-12-10 15:46:36Z suehring $
27	! Renamed wall_flags_0 to wall_flags_static_0
28	!
29	! 4182 2019-08-22 15:20:23Z scharf
30	! Corrected "Former revisions" section
31	!
32	! 3655 2019-01-07 16:51:22Z knoop
33	! OpenACC port for SPEC
34	!
35	! Revision 1.1 1997/09/12 06:23:51 raasch
36	! Initial revision
37	!
38	!
39	! Description:
40	! ------------
41	!> Diffusion term of the u-component
42	!> @todo additional damping (needed for non-cyclic bc) causes bad vectorization
43	!> and slows down the speed on NEC about 5-10%
44	!------------------------------------------------------------------------------!
45	MODULE diffusion_u_mod
46
47
48	PRIVATE
49	PUBLIC diffusion_u
50
51	INTERFACE diffusion_u
52	MODULE PROCEDURE diffusion_u
53	MODULE PROCEDURE diffusion_u_ij
54	END INTERFACE diffusion_u
55
56	CONTAINS
57
58
59	!------------------------------------------------------------------------------!
60	! Description:
61	! ------------
62	!> Call for all grid points
63	!------------------------------------------------------------------------------!
64	SUBROUTINE diffusion_u
65
66	USE arrays_3d, &
67	ONLY: ddzu, ddzw, km, tend, u, v, w, drho_air, rho_air_zw
68
69	USE control_parameters, &
70	ONLY: constant_top_momentumflux, use_surface_fluxes, &
71	use_top_fluxes
72
73	USE grid_variables, &
74	ONLY: ddx, ddx2, ddy
75
76	USE indices, &
77	ONLY: nxlu, nxr, nyn, nys, nzb, nzt, wall_flags_static_0
78
79	USE kinds
80
81	USE surface_mod, &
82	ONLY : surf_def_h, surf_def_v, surf_lsm_h, surf_lsm_v, surf_usm_h, &
83	surf_usm_v
84
85	IMPLICIT NONE
86
87	INTEGER(iwp) :: i !< running index x direction
88	INTEGER(iwp) :: j !< running index y direction
89	INTEGER(iwp) :: k !< running index z direction
90	INTEGER(iwp) :: l !< running index of surface type, south- or north-facing wall
91	INTEGER(iwp) :: m !< running index surface elements
92	INTEGER(iwp) :: surf_e !< end index of surface elements at (j,i)-gridpoint
93	INTEGER(iwp) :: surf_s !< start index of surface elements at (j,i)-gridpoint
94
95	REAL(wp) :: flag !< flag to mask topography grid points
96	REAL(wp) :: kmym !< diffusion coefficient on southward side of the u-gridbox - interpolated onto xu-yv grid
97	REAL(wp) :: kmyp !< diffusion coefficient on northward side of the u-gridbox - interpolated onto xu-yv grid
98	REAL(wp) :: kmzm !< diffusion coefficient on bottom of the gridbox - interpolated onto xu-zw grid
99	REAL(wp) :: kmzp !< diffusion coefficient on top of the gridbox - interpolated onto xu-zw grid
100	REAL(wp) :: mask_bottom !< flag to mask vertical upward-facing surface
101	REAL(wp) :: mask_north !< flag to mask vertical surface north of the grid point
102	REAL(wp) :: mask_south !< flag to mask vertical surface south of the grid point
103	REAL(wp) :: mask_top !< flag to mask vertical downward-facing surface
104
105
106
107	!$ACC PARALLEL LOOP COLLAPSE(2) PRIVATE(i, j, k, l, m) &
108	!$ACC PRIVATE(surf_e, surf_s, flag, kmym, kmyp, kmzm, kmzp) &
109	!$ACC PRIVATE(mask_bottom, mask_north, mask_south, mask_top) &
110	!$ACC PRESENT(wall_flags_static_0, km) &
111	!$ACC PRESENT(u, v, w) &
112	!$ACC PRESENT(ddzu, ddzw, drho_air, rho_air_zw) &
113	!$ACC PRESENT(surf_def_h(0:2), surf_def_v(0:1)) &
114	!$ACC PRESENT(surf_lsm_h, surf_lsm_v(0:1)) &
115	!$ACC PRESENT(surf_usm_h, surf_usm_v(0:1)) &
116	!$ACC PRESENT(tend)
117	DO i = nxlu, nxr
118	DO j = nys, nyn
119	!
120	!-- Compute horizontal diffusion
121	DO k = nzb+1, nzt
122	!
123	!-- Predetermine flag to mask topography and wall-bounded grid points.
124	!-- It is sufficient to masked only north- and south-facing surfaces, which
125	!-- need special treatment for the u-component.
126	flag = MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_static_0(k,j,i), 1 ) )
127	mask_south = MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_static_0(k,j-1,i), 1 ) )
128	mask_north = MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_static_0(k,j+1,i), 1 ) )
129	!
130	!-- Interpolate eddy diffusivities on staggered gridpoints
131	kmyp = 0.25_wp * &
132	( km(k,j,i)+km(k,j+1,i)+km(k,j,i-1)+km(k,j+1,i-1) )
133	kmym = 0.25_wp * &
134	( km(k,j,i)+km(k,j-1,i)+km(k,j,i-1)+km(k,j-1,i-1) )
135
136	tend(k,j,i) = tend(k,j,i) &
137	+ 2.0_wp * ( &
138	km(k,j,i) * ( u(k,j,i+1) - u(k,j,i) ) &
139	- km(k,j,i-1) * ( u(k,j,i) - u(k,j,i-1) ) &
140	) * ddx2 * flag &
141	+ ( mask_north * ( &
142	kmyp * ( u(k,j+1,i) - u(k,j,i) ) * ddy &
143	+ kmyp * ( v(k,j+1,i) - v(k,j+1,i-1) ) * ddx &
144	) &
145	- mask_south * ( &
146	kmym * ( u(k,j,i) - u(k,j-1,i) ) * ddy &
147	+ kmym * ( v(k,j,i) - v(k,j,i-1) ) * ddx &
148	) &
149	) * ddy * flag
150	ENDDO
151	!
152	!-- Add horizontal momentum flux u'v' at north- (l=0) and south-facing (l=1)
153	!-- surfaces. Note, in the the flat case, loops won't be entered as
154	!-- start_index > end_index. Furtermore, note, no vertical natural surfaces
155	!-- so far.
156	!-- Default-type surfaces
157	DO l = 0, 1
158	surf_s = surf_def_v(l)%start_index(j,i)
159	surf_e = surf_def_v(l)%end_index(j,i)
160	DO m = surf_s, surf_e
161	k = surf_def_v(l)%k(m)
162	tend(k,j,i) = tend(k,j,i) + &
163	surf_def_v(l)%mom_flux_uv(m) * ddy
164	ENDDO
165	ENDDO
166	!
167	!-- Natural-type surfaces
168	DO l = 0, 1
169	surf_s = surf_lsm_v(l)%start_index(j,i)
170	surf_e = surf_lsm_v(l)%end_index(j,i)
171	DO m = surf_s, surf_e
172	k = surf_lsm_v(l)%k(m)
173	tend(k,j,i) = tend(k,j,i) + &
174	surf_lsm_v(l)%mom_flux_uv(m) * ddy
175	ENDDO
176	ENDDO
177	!
178	!-- Urban-type surfaces
179	DO l = 0, 1
180	surf_s = surf_usm_v(l)%start_index(j,i)
181	surf_e = surf_usm_v(l)%end_index(j,i)
182	DO m = surf_s, surf_e
183	k = surf_usm_v(l)%k(m)
184	tend(k,j,i) = tend(k,j,i) + &
185	surf_usm_v(l)%mom_flux_uv(m) * ddy
186	ENDDO
187	ENDDO
188
189	!
190	!-- Compute vertical diffusion. In case of simulating a surface layer,
191	!-- respective grid diffusive fluxes are masked (flag 8) within this
192	!-- loop, and added further below, else, simple gradient approach is
193	!-- applied. Model top is also mask if top-momentum flux is given.
194	DO k = nzb+1, nzt
195	!
196	!-- Determine flags to mask topography below and above. Flag 1 is
197	!-- used to mask topography in general, and flag 8 implies
198	!-- information about use_surface_fluxes. Flag 9 is used to control
199	!-- momentum flux at model top.
200	mask_bottom = MERGE( 1.0_wp, 0.0_wp, &
201	BTEST( wall_flags_static_0(k-1,j,i), 8 ) )
202	mask_top = MERGE( 1.0_wp, 0.0_wp, &
203	BTEST( wall_flags_static_0(k+1,j,i), 8 ) ) * &
204	MERGE( 1.0_wp, 0.0_wp, &
205	BTEST( wall_flags_static_0(k+1,j,i), 9 ) )
206	flag = MERGE( 1.0_wp, 0.0_wp, &
207	BTEST( wall_flags_static_0(k,j,i), 1 ) )
208	!
209	!-- Interpolate eddy diffusivities on staggered gridpoints
210	kmzp = 0.25_wp * &
211	( km(k,j,i)+km(k+1,j,i)+km(k,j,i-1)+km(k+1,j,i-1) )
212	kmzm = 0.25_wp * &
213	( km(k,j,i)+km(k-1,j,i)+km(k,j,i-1)+km(k-1,j,i-1) )
214
215	tend(k,j,i) = tend(k,j,i) &
216	+ ( kmzp * ( ( u(k+1,j,i) - u(k,j,i) ) * ddzu(k+1) &
217	+ ( w(k,j,i) - w(k,j,i-1) ) * ddx &
218	) * rho_air_zw(k) * mask_top &
219	- kmzm * ( ( u(k,j,i) - u(k-1,j,i) ) * ddzu(k) &
220	+ ( w(k-1,j,i) - w(k-1,j,i-1) ) * ddx &
221	) * rho_air_zw(k-1) * mask_bottom &
222	) * ddzw(k) * drho_air(k) * flag
223	ENDDO
224
225	!
226	!-- Vertical diffusion at the first grid point above the surface,
227	!-- if the momentum flux at the bottom is given by the Prandtl law or
228	!-- if it is prescribed by the user.
229	!-- Difference quotient of the momentum flux is not formed over half
230	!-- of the grid spacing (2.0*ddzw(k)) any more, since the comparison
231	!-- with other (LES) models showed that the values of the momentum
232	!-- flux becomes too large in this case.
233	!-- The term containing w(k-1,..) (see above equation) is removed here
234	!-- because the vertical velocity is assumed to be zero at the surface.
235	IF ( use_surface_fluxes ) THEN
236	!
237	!-- Default-type surfaces, upward-facing
238	surf_s = surf_def_h(0)%start_index(j,i)
239	surf_e = surf_def_h(0)%end_index(j,i)
240	DO m = surf_s, surf_e
241
242	k = surf_def_h(0)%k(m)
243
244	tend(k,j,i) = tend(k,j,i) &
245	+ ( - ( - surf_def_h(0)%usws(m) ) &
246	) * ddzw(k) * drho_air(k)
247	ENDDO
248	!
249	!-- Default-type surfaces, dowward-facing
250	surf_s = surf_def_h(1)%start_index(j,i)
251	surf_e = surf_def_h(1)%end_index(j,i)
252	DO m = surf_s, surf_e
253
254	k = surf_def_h(1)%k(m)
255
256	tend(k,j,i) = tend(k,j,i) &
257	+ ( - surf_def_h(1)%usws(m) &
258	) * ddzw(k) * drho_air(k)
259	ENDDO
260	!
261	!-- Natural-type surfaces, upward-facing
262	surf_s = surf_lsm_h%start_index(j,i)
263	surf_e = surf_lsm_h%end_index(j,i)
264	DO m = surf_s, surf_e
265
266	k = surf_lsm_h%k(m)
267
268	tend(k,j,i) = tend(k,j,i) &
269	+ ( - ( - surf_lsm_h%usws(m) ) &
270	) * ddzw(k) * drho_air(k)
271	ENDDO
272	!
273	!-- Urban-type surfaces, upward-facing
274	surf_s = surf_usm_h%start_index(j,i)
275	surf_e = surf_usm_h%end_index(j,i)
276	DO m = surf_s, surf_e
277
278	k = surf_usm_h%k(m)
279
280	tend(k,j,i) = tend(k,j,i) &
281	+ ( - ( - surf_usm_h%usws(m) ) &
282	) * ddzw(k) * drho_air(k)
283	ENDDO
284
285	ENDIF
286	!
287	!-- Add momentum flux at model top
288	IF ( use_top_fluxes .AND. constant_top_momentumflux ) THEN
289	surf_s = surf_def_h(2)%start_index(j,i)
290	surf_e = surf_def_h(2)%end_index(j,i)
291	DO m = surf_s, surf_e
292
293	k = surf_def_h(2)%k(m)
294
295	tend(k,j,i) = tend(k,j,i) &
296	+ ( - surf_def_h(2)%usws(m) ) * ddzw(k) * drho_air(k)
297	ENDDO
298	ENDIF
299
300	ENDDO
301	ENDDO
302
303	END SUBROUTINE diffusion_u
304
305
306	!------------------------------------------------------------------------------!
307	! Description:
308	! ------------
309	!> Call for grid point i,j
310	!------------------------------------------------------------------------------!
311	SUBROUTINE diffusion_u_ij( i, j )
312
313	USE arrays_3d, &
314	ONLY: ddzu, ddzw, km, tend, u, v, w, drho_air, rho_air_zw
315
316	USE control_parameters, &
317	ONLY: constant_top_momentumflux, use_surface_fluxes, &
318	use_top_fluxes
319
320	USE grid_variables, &
321	ONLY: ddx, ddx2, ddy
322
323	USE indices, &
324	ONLY: nzb, nzt, wall_flags_static_0
325
326	USE kinds
327
328	USE surface_mod, &
329	ONLY : surf_def_h, surf_def_v, surf_lsm_h, surf_lsm_v, surf_usm_h, &
330	surf_usm_v
331
332	IMPLICIT NONE
333
334	INTEGER(iwp) :: i !< running index x direction
335	INTEGER(iwp) :: j !< running index y direction
336	INTEGER(iwp) :: k !< running index z direction
337	INTEGER(iwp) :: l !< running index of surface type, south- or north-facing wall
338	INTEGER(iwp) :: m !< running index surface elements
339	INTEGER(iwp) :: surf_e !< End index of surface elements at (j,i)-gridpoint
340	INTEGER(iwp) :: surf_s !< Start index of surface elements at (j,i)-gridpoint
341
342	REAL(wp) :: flag !< flag to mask topography grid points
343	REAL(wp) :: kmym !< diffusion coefficient on southward side of the u-gridbox - interpolated onto xu-yv grid
344	REAL(wp) :: kmyp !<diffusion coefficient on northward side of the u-gridbox - interpolated onto xu-yv grid
345	REAL(wp) :: kmzm !< diffusion coefficient on bottom of the gridbox - interpolated onto xu-zw grid
346	REAL(wp) :: kmzp !< diffusion coefficient on top of the gridbox - interpolated onto xu-zw grid
347	REAL(wp) :: mask_bottom !< flag to mask vertical upward-facing surface
348	REAL(wp) :: mask_north !< flag to mask vertical surface north of the grid point
349	REAL(wp) :: mask_south !< flag to mask vertical surface south of the grid point
350	REAL(wp) :: mask_top !< flag to mask vertical downward-facing surface
351	!
352	!-- Compute horizontal diffusion
353	DO k = nzb+1, nzt
354	!
355	!-- Predetermine flag to mask topography and wall-bounded grid points.
356	!-- It is sufficient to masked only north- and south-facing surfaces, which
357	!-- need special treatment for the u-component.
358	flag = MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_static_0(k,j,i), 1 ) )
359	mask_south = MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_static_0(k,j-1,i), 1 ) )
360	mask_north = MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_static_0(k,j+1,i), 1 ) )
361	!
362	!-- Interpolate eddy diffusivities on staggered gridpoints
363	kmyp = 0.25_wp * ( km(k,j,i)+km(k,j+1,i)+km(k,j,i-1)+km(k,j+1,i-1) )
364	kmym = 0.25_wp * ( km(k,j,i)+km(k,j-1,i)+km(k,j,i-1)+km(k,j-1,i-1) )
365
366	tend(k,j,i) = tend(k,j,i) &
367	+ 2.0_wp * ( &
368	km(k,j,i) * ( u(k,j,i+1) - u(k,j,i) ) &
369	- km(k,j,i-1) * ( u(k,j,i) - u(k,j,i-1) ) &
370	) * ddx2 * flag &
371	+ ( &
372	mask_north * kmyp * ( ( u(k,j+1,i) - u(k,j,i) ) * ddy &
373	+ ( v(k,j+1,i) - v(k,j+1,i-1) ) * ddx &
374	) &
375	- mask_south * kmym * ( ( u(k,j,i) - u(k,j-1,i) ) * ddy &
376	+ ( v(k,j,i) - v(k,j,i-1) ) * ddx &
377	) &
378	) * ddy * flag
379	ENDDO
380
381	!
382	!-- Add horizontal momentum flux u'v' at north- (l=0) and south-facing (l=1)
383	!-- surfaces. Note, in the the flat case, loops won't be entered as
384	!-- start_index > end_index. Furtermore, note, no vertical natural surfaces
385	!-- so far.
386	!-- Default-type surfaces
387	DO l = 0, 1
388	surf_s = surf_def_v(l)%start_index(j,i)
389	surf_e = surf_def_v(l)%end_index(j,i)
390	DO m = surf_s, surf_e
391	k = surf_def_v(l)%k(m)
392	tend(k,j,i) = tend(k,j,i) + surf_def_v(l)%mom_flux_uv(m) * ddy
393	ENDDO
394	ENDDO
395	!
396	!-- Natural-type surfaces
397	DO l = 0, 1
398	surf_s = surf_lsm_v(l)%start_index(j,i)
399	surf_e = surf_lsm_v(l)%end_index(j,i)
400	DO m = surf_s, surf_e
401	k = surf_lsm_v(l)%k(m)
402	tend(k,j,i) = tend(k,j,i) + surf_lsm_v(l)%mom_flux_uv(m) * ddy
403	ENDDO
404	ENDDO
405	!
406	!-- Urban-type surfaces
407	DO l = 0, 1
408	surf_s = surf_usm_v(l)%start_index(j,i)
409	surf_e = surf_usm_v(l)%end_index(j,i)
410	DO m = surf_s, surf_e
411	k = surf_usm_v(l)%k(m)
412	tend(k,j,i) = tend(k,j,i) + surf_usm_v(l)%mom_flux_uv(m) * ddy
413	ENDDO
414	ENDDO
415	!
416	!-- Compute vertical diffusion. In case of simulating a surface layer,
417	!-- respective grid diffusive fluxes are masked (flag 8) within this
418	!-- loop, and added further below, else, simple gradient approach is
419	!-- applied. Model top is also mask if top-momentum flux is given.
420	DO k = nzb+1, nzt
421	!
422	!-- Determine flags to mask topography below and above. Flag 1 is
423	!-- used to mask topography in general, and flag 8 implies
424	!-- information about use_surface_fluxes. Flag 9 is used to control
425	!-- momentum flux at model top.
426	mask_bottom = MERGE( 1.0_wp, 0.0_wp, &
427	BTEST( wall_flags_static_0(k-1,j,i), 8 ) )
428	mask_top = MERGE( 1.0_wp, 0.0_wp, &
429	BTEST( wall_flags_static_0(k+1,j,i), 8 ) ) * &
430	MERGE( 1.0_wp, 0.0_wp, &
431	BTEST( wall_flags_static_0(k+1,j,i), 9 ) )
432	flag = MERGE( 1.0_wp, 0.0_wp, &
433	BTEST( wall_flags_static_0(k,j,i), 1 ) )
434	!
435	!-- Interpolate eddy diffusivities on staggered gridpoints
436	kmzp = 0.25_wp * ( km(k,j,i)+km(k+1,j,i)+km(k,j,i-1)+km(k+1,j,i-1) )
437	kmzm = 0.25_wp * ( km(k,j,i)+km(k-1,j,i)+km(k,j,i-1)+km(k-1,j,i-1) )
438
439	tend(k,j,i) = tend(k,j,i) &
440	+ ( kmzp * ( ( u(k+1,j,i) - u(k,j,i) ) * ddzu(k+1) &
441	+ ( w(k,j,i) - w(k,j,i-1) ) * ddx &
442	) * rho_air_zw(k) * mask_top &
443	- kmzm * ( ( u(k,j,i) - u(k-1,j,i) ) * ddzu(k) &
444	+ ( w(k-1,j,i) - w(k-1,j,i-1) ) * ddx &
445	) * rho_air_zw(k-1) * mask_bottom &
446	) * ddzw(k) * drho_air(k) * flag
447	ENDDO
448
449	!
450	!-- Vertical diffusion at the first surface grid points, if the
451	!-- momentum flux at the bottom is given by the Prandtl law or if it is
452	!-- prescribed by the user.
453	!-- Difference quotient of the momentum flux is not formed over half of
454	!-- the grid spacing (2.0*ddzw(k)) any more, since the comparison with
455	!-- other (LES) models showed that the values of the momentum flux becomes
456	!-- too large in this case.
457	IF ( use_surface_fluxes ) THEN
458	!
459	!-- Default-type surfaces, upward-facing
460	surf_s = surf_def_h(0)%start_index(j,i)
461	surf_e = surf_def_h(0)%end_index(j,i)
462	DO m = surf_s, surf_e
463
464	k = surf_def_h(0)%k(m)
465
466	tend(k,j,i) = tend(k,j,i) &
467	+ ( - ( - surf_def_h(0)%usws(m) ) &
468	) * ddzw(k) * drho_air(k)
469	ENDDO
470	!
471	!-- Default-type surfaces, dowward-facing (except for model-top fluxes)
472	surf_s = surf_def_h(1)%start_index(j,i)
473	surf_e = surf_def_h(1)%end_index(j,i)
474	DO m = surf_s, surf_e
475
476	k = surf_def_h(1)%k(m)
477
478	tend(k,j,i) = tend(k,j,i) &
479	+ ( - surf_def_h(1)%usws(m) &
480	) * ddzw(k) * drho_air(k)
481	ENDDO
482	!
483	!-- Natural-type surfaces, upward-facing
484	surf_s = surf_lsm_h%start_index(j,i)
485	surf_e = surf_lsm_h%end_index(j,i)
486	DO m = surf_s, surf_e
487
488	k = surf_lsm_h%k(m)
489
490	tend(k,j,i) = tend(k,j,i) &
491	+ ( - ( - surf_lsm_h%usws(m) ) &
492	) * ddzw(k) * drho_air(k)
493	ENDDO
494	!
495	!-- Urban-type surfaces, upward-facing
496	surf_s = surf_usm_h%start_index(j,i)
497	surf_e = surf_usm_h%end_index(j,i)
498	DO m = surf_s, surf_e
499
500	k = surf_usm_h%k(m)
501
502	tend(k,j,i) = tend(k,j,i) &
503	+ ( - ( - surf_usm_h%usws(m) ) &
504	) * ddzw(k) * drho_air(k)
505	ENDDO
506
507	ENDIF
508	!
509	!-- Add momentum flux at model top
510	IF ( use_top_fluxes .AND. constant_top_momentumflux ) THEN
511	surf_s = surf_def_h(2)%start_index(j,i)
512	surf_e = surf_def_h(2)%end_index(j,i)
513	DO m = surf_s, surf_e
514
515	k = surf_def_h(2)%k(m)
516
517	tend(k,j,i) = tend(k,j,i) &
518	+ ( - surf_def_h(2)%usws(m) ) * ddzw(k) * drho_air(k)
519	ENDDO
520	ENDIF
521
522
523	END SUBROUTINE diffusion_u_ij
524
525	END MODULE diffusion_u_mod

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