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source: palm/trunk/SOURCE/diffusion_u.f90 @ 4533

Last change on this file since 4533 was 4360, checked in by suehring, 5 years ago
Bugfix in output of time-averaged plant-canopy quanities; Output of plant-canopy data only where tall canopy is defined; land-surface model: fix wrong location strings; tests: update urban test case; all source code files: copyright update
Property svn:keywords set to `Id`
File size: 24.4 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 1997-2020 Leibniz Universitaet Hannover
18	!------------------------------------------------------------------------------!
19	!
20	! Current revisions:
21	! -----------------
22	!
23	!
24	! Former revisions:
25	! -----------------
26	! $Id: diffusion_u.f90 4360 2020-01-07 11:25:50Z schwenkel $
27	! Introduction of wall_flags_total_0, which currently sets bits based on static
28	! topography information used in wall_flags_static_0
29	!
30	! 4329 2019-12-10 15:46:36Z motisi
31	! Renamed wall_flags_0 to wall_flags_static_0
32	!
33	! 4182 2019-08-22 15:20:23Z scharf
34	! Corrected "Former revisions" section
35	!
36	! 3655 2019-01-07 16:51:22Z knoop
37	! OpenACC port for SPEC
38	!
39	! Revision 1.1 1997/09/12 06:23:51 raasch
40	! Initial revision
41	!
42	!
43	! Description:
44	! ------------
45	!> Diffusion term of the u-component
46	!> @todo additional damping (needed for non-cyclic bc) causes bad vectorization
47	!> and slows down the speed on NEC about 5-10%
48	!------------------------------------------------------------------------------!
49	MODULE diffusion_u_mod
50
51
52	PRIVATE
53	PUBLIC diffusion_u
54
55	INTERFACE diffusion_u
56	MODULE PROCEDURE diffusion_u
57	MODULE PROCEDURE diffusion_u_ij
58	END INTERFACE diffusion_u
59
60	CONTAINS
61
62
63	!------------------------------------------------------------------------------!
64	! Description:
65	! ------------
66	!> Call for all grid points
67	!------------------------------------------------------------------------------!
68	SUBROUTINE diffusion_u
69
70	USE arrays_3d, &
71	ONLY: ddzu, ddzw, km, tend, u, v, w, drho_air, rho_air_zw
72
73	USE control_parameters, &
74	ONLY: constant_top_momentumflux, use_surface_fluxes, &
75	use_top_fluxes
76
77	USE grid_variables, &
78	ONLY: ddx, ddx2, ddy
79
80	USE indices, &
81	ONLY: nxlu, nxr, nyn, nys, nzb, nzt, wall_flags_total_0
82
83	USE kinds
84
85	USE surface_mod, &
86	ONLY : surf_def_h, surf_def_v, surf_lsm_h, surf_lsm_v, surf_usm_h, &
87	surf_usm_v
88
89	IMPLICIT NONE
90
91	INTEGER(iwp) :: i !< running index x direction
92	INTEGER(iwp) :: j !< running index y direction
93	INTEGER(iwp) :: k !< running index z direction
94	INTEGER(iwp) :: l !< running index of surface type, south- or north-facing wall
95	INTEGER(iwp) :: m !< running index surface elements
96	INTEGER(iwp) :: surf_e !< end index of surface elements at (j,i)-gridpoint
97	INTEGER(iwp) :: surf_s !< start index of surface elements at (j,i)-gridpoint
98
99	REAL(wp) :: flag !< flag to mask topography grid points
100	REAL(wp) :: kmym !< diffusion coefficient on southward side of the u-gridbox - interpolated onto xu-yv grid
101	REAL(wp) :: kmyp !< diffusion coefficient on northward side of the u-gridbox - interpolated onto xu-yv grid
102	REAL(wp) :: kmzm !< diffusion coefficient on bottom of the gridbox - interpolated onto xu-zw grid
103	REAL(wp) :: kmzp !< diffusion coefficient on top of the gridbox - interpolated onto xu-zw grid
104	REAL(wp) :: mask_bottom !< flag to mask vertical upward-facing surface
105	REAL(wp) :: mask_north !< flag to mask vertical surface north of the grid point
106	REAL(wp) :: mask_south !< flag to mask vertical surface south of the grid point
107	REAL(wp) :: mask_top !< flag to mask vertical downward-facing surface
108
109
110
111	!$ACC PARALLEL LOOP COLLAPSE(2) PRIVATE(i, j, k, l, m) &
112	!$ACC PRIVATE(surf_e, surf_s, flag, kmym, kmyp, kmzm, kmzp) &
113	!$ACC PRIVATE(mask_bottom, mask_north, mask_south, mask_top) &
114	!$ACC PRESENT(wall_flags_total_0, km) &
115	!$ACC PRESENT(u, v, w) &
116	!$ACC PRESENT(ddzu, ddzw, drho_air, rho_air_zw) &
117	!$ACC PRESENT(surf_def_h(0:2), surf_def_v(0:1)) &
118	!$ACC PRESENT(surf_lsm_h, surf_lsm_v(0:1)) &
119	!$ACC PRESENT(surf_usm_h, surf_usm_v(0:1)) &
120	!$ACC PRESENT(tend)
121	DO i = nxlu, nxr
122	DO j = nys, nyn
123	!
124	!-- Compute horizontal diffusion
125	DO k = nzb+1, nzt
126	!
127	!-- Predetermine flag to mask topography and wall-bounded grid points.
128	!-- It is sufficient to masked only north- and south-facing surfaces, which
129	!-- need special treatment for the u-component.
130	flag = MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,j,i), 1 ) )
131	mask_south = MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,j-1,i), 1 ) )
132	mask_north = MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,j+1,i), 1 ) )
133	!
134	!-- Interpolate eddy diffusivities on staggered gridpoints
135	kmyp = 0.25_wp * &
136	( km(k,j,i)+km(k,j+1,i)+km(k,j,i-1)+km(k,j+1,i-1) )
137	kmym = 0.25_wp * &
138	( km(k,j,i)+km(k,j-1,i)+km(k,j,i-1)+km(k,j-1,i-1) )
139
140	tend(k,j,i) = tend(k,j,i) &
141	+ 2.0_wp * ( &
142	km(k,j,i) * ( u(k,j,i+1) - u(k,j,i) ) &
143	- km(k,j,i-1) * ( u(k,j,i) - u(k,j,i-1) ) &
144	) * ddx2 * flag &
145	+ ( mask_north * ( &
146	kmyp * ( u(k,j+1,i) - u(k,j,i) ) * ddy &
147	+ kmyp * ( v(k,j+1,i) - v(k,j+1,i-1) ) * ddx &
148	) &
149	- mask_south * ( &
150	kmym * ( u(k,j,i) - u(k,j-1,i) ) * ddy &
151	+ kmym * ( v(k,j,i) - v(k,j,i-1) ) * ddx &
152	) &
153	) * ddy * flag
154	ENDDO
155	!
156	!-- Add horizontal momentum flux u'v' at north- (l=0) and south-facing (l=1)
157	!-- surfaces. Note, in the the flat case, loops won't be entered as
158	!-- start_index > end_index. Furtermore, note, no vertical natural surfaces
159	!-- so far.
160	!-- Default-type surfaces
161	DO l = 0, 1
162	surf_s = surf_def_v(l)%start_index(j,i)
163	surf_e = surf_def_v(l)%end_index(j,i)
164	DO m = surf_s, surf_e
165	k = surf_def_v(l)%k(m)
166	tend(k,j,i) = tend(k,j,i) + &
167	surf_def_v(l)%mom_flux_uv(m) * ddy
168	ENDDO
169	ENDDO
170	!
171	!-- Natural-type surfaces
172	DO l = 0, 1
173	surf_s = surf_lsm_v(l)%start_index(j,i)
174	surf_e = surf_lsm_v(l)%end_index(j,i)
175	DO m = surf_s, surf_e
176	k = surf_lsm_v(l)%k(m)
177	tend(k,j,i) = tend(k,j,i) + &
178	surf_lsm_v(l)%mom_flux_uv(m) * ddy
179	ENDDO
180	ENDDO
181	!
182	!-- Urban-type surfaces
183	DO l = 0, 1
184	surf_s = surf_usm_v(l)%start_index(j,i)
185	surf_e = surf_usm_v(l)%end_index(j,i)
186	DO m = surf_s, surf_e
187	k = surf_usm_v(l)%k(m)
188	tend(k,j,i) = tend(k,j,i) + &
189	surf_usm_v(l)%mom_flux_uv(m) * ddy
190	ENDDO
191	ENDDO
192
193	!
194	!-- Compute vertical diffusion. In case of simulating a surface layer,
195	!-- respective grid diffusive fluxes are masked (flag 8) within this
196	!-- loop, and added further below, else, simple gradient approach is
197	!-- applied. Model top is also mask if top-momentum flux is given.
198	DO k = nzb+1, nzt
199	!
200	!-- Determine flags to mask topography below and above. Flag 1 is
201	!-- used to mask topography in general, and flag 8 implies
202	!-- information about use_surface_fluxes. Flag 9 is used to control
203	!-- momentum flux at model top.
204	mask_bottom = MERGE( 1.0_wp, 0.0_wp, &
205	BTEST( wall_flags_total_0(k-1,j,i), 8 ) )
206	mask_top = MERGE( 1.0_wp, 0.0_wp, &
207	BTEST( wall_flags_total_0(k+1,j,i), 8 ) ) * &
208	MERGE( 1.0_wp, 0.0_wp, &
209	BTEST( wall_flags_total_0(k+1,j,i), 9 ) )
210	flag = MERGE( 1.0_wp, 0.0_wp, &
211	BTEST( wall_flags_total_0(k,j,i), 1 ) )
212	!
213	!-- Interpolate eddy diffusivities on staggered gridpoints
214	kmzp = 0.25_wp * &
215	( km(k,j,i)+km(k+1,j,i)+km(k,j,i-1)+km(k+1,j,i-1) )
216	kmzm = 0.25_wp * &
217	( km(k,j,i)+km(k-1,j,i)+km(k,j,i-1)+km(k-1,j,i-1) )
218
219	tend(k,j,i) = tend(k,j,i) &
220	+ ( kmzp * ( ( u(k+1,j,i) - u(k,j,i) ) * ddzu(k+1) &
221	+ ( w(k,j,i) - w(k,j,i-1) ) * ddx &
222	) * rho_air_zw(k) * mask_top &
223	- kmzm * ( ( u(k,j,i) - u(k-1,j,i) ) * ddzu(k) &
224	+ ( w(k-1,j,i) - w(k-1,j,i-1) ) * ddx &
225	) * rho_air_zw(k-1) * mask_bottom &
226	) * ddzw(k) * drho_air(k) * flag
227	ENDDO
228
229	!
230	!-- Vertical diffusion at the first grid point above the surface,
231	!-- if the momentum flux at the bottom is given by the Prandtl law or
232	!-- if it is prescribed by the user.
233	!-- Difference quotient of the momentum flux is not formed over half
234	!-- of the grid spacing (2.0*ddzw(k)) any more, since the comparison
235	!-- with other (LES) models showed that the values of the momentum
236	!-- flux becomes too large in this case.
237	!-- The term containing w(k-1,..) (see above equation) is removed here
238	!-- because the vertical velocity is assumed to be zero at the surface.
239	IF ( use_surface_fluxes ) THEN
240	!
241	!-- Default-type surfaces, upward-facing
242	surf_s = surf_def_h(0)%start_index(j,i)
243	surf_e = surf_def_h(0)%end_index(j,i)
244	DO m = surf_s, surf_e
245
246	k = surf_def_h(0)%k(m)
247
248	tend(k,j,i) = tend(k,j,i) &
249	+ ( - ( - surf_def_h(0)%usws(m) ) &
250	) * ddzw(k) * drho_air(k)
251	ENDDO
252	!
253	!-- Default-type surfaces, dowward-facing
254	surf_s = surf_def_h(1)%start_index(j,i)
255	surf_e = surf_def_h(1)%end_index(j,i)
256	DO m = surf_s, surf_e
257
258	k = surf_def_h(1)%k(m)
259
260	tend(k,j,i) = tend(k,j,i) &
261	+ ( - surf_def_h(1)%usws(m) &
262	) * ddzw(k) * drho_air(k)
263	ENDDO
264	!
265	!-- Natural-type surfaces, upward-facing
266	surf_s = surf_lsm_h%start_index(j,i)
267	surf_e = surf_lsm_h%end_index(j,i)
268	DO m = surf_s, surf_e
269
270	k = surf_lsm_h%k(m)
271
272	tend(k,j,i) = tend(k,j,i) &
273	+ ( - ( - surf_lsm_h%usws(m) ) &
274	) * ddzw(k) * drho_air(k)
275	ENDDO
276	!
277	!-- Urban-type surfaces, upward-facing
278	surf_s = surf_usm_h%start_index(j,i)
279	surf_e = surf_usm_h%end_index(j,i)
280	DO m = surf_s, surf_e
281
282	k = surf_usm_h%k(m)
283
284	tend(k,j,i) = tend(k,j,i) &
285	+ ( - ( - surf_usm_h%usws(m) ) &
286	) * ddzw(k) * drho_air(k)
287	ENDDO
288
289	ENDIF
290	!
291	!-- Add momentum flux at model top
292	IF ( use_top_fluxes .AND. constant_top_momentumflux ) THEN
293	surf_s = surf_def_h(2)%start_index(j,i)
294	surf_e = surf_def_h(2)%end_index(j,i)
295	DO m = surf_s, surf_e
296
297	k = surf_def_h(2)%k(m)
298
299	tend(k,j,i) = tend(k,j,i) &
300	+ ( - surf_def_h(2)%usws(m) ) * ddzw(k) * drho_air(k)
301	ENDDO
302	ENDIF
303
304	ENDDO
305	ENDDO
306
307	END SUBROUTINE diffusion_u
308
309
310	!------------------------------------------------------------------------------!
311	! Description:
312	! ------------
313	!> Call for grid point i,j
314	!------------------------------------------------------------------------------!
315	SUBROUTINE diffusion_u_ij( i, j )
316
317	USE arrays_3d, &
318	ONLY: ddzu, ddzw, km, tend, u, v, w, drho_air, rho_air_zw
319
320	USE control_parameters, &
321	ONLY: constant_top_momentumflux, use_surface_fluxes, &
322	use_top_fluxes
323
324	USE grid_variables, &
325	ONLY: ddx, ddx2, ddy
326
327	USE indices, &
328	ONLY: nzb, nzt, wall_flags_total_0
329
330	USE kinds
331
332	USE surface_mod, &
333	ONLY : surf_def_h, surf_def_v, surf_lsm_h, surf_lsm_v, surf_usm_h, &
334	surf_usm_v
335
336	IMPLICIT NONE
337
338	INTEGER(iwp) :: i !< running index x direction
339	INTEGER(iwp) :: j !< running index y direction
340	INTEGER(iwp) :: k !< running index z direction
341	INTEGER(iwp) :: l !< running index of surface type, south- or north-facing wall
342	INTEGER(iwp) :: m !< running index surface elements
343	INTEGER(iwp) :: surf_e !< End index of surface elements at (j,i)-gridpoint
344	INTEGER(iwp) :: surf_s !< Start index of surface elements at (j,i)-gridpoint
345
346	REAL(wp) :: flag !< flag to mask topography grid points
347	REAL(wp) :: kmym !< diffusion coefficient on southward side of the u-gridbox - interpolated onto xu-yv grid
348	REAL(wp) :: kmyp !<diffusion coefficient on northward side of the u-gridbox - interpolated onto xu-yv grid
349	REAL(wp) :: kmzm !< diffusion coefficient on bottom of the gridbox - interpolated onto xu-zw grid
350	REAL(wp) :: kmzp !< diffusion coefficient on top of the gridbox - interpolated onto xu-zw grid
351	REAL(wp) :: mask_bottom !< flag to mask vertical upward-facing surface
352	REAL(wp) :: mask_north !< flag to mask vertical surface north of the grid point
353	REAL(wp) :: mask_south !< flag to mask vertical surface south of the grid point
354	REAL(wp) :: mask_top !< flag to mask vertical downward-facing surface
355	!
356	!-- Compute horizontal diffusion
357	DO k = nzb+1, nzt
358	!
359	!-- Predetermine flag to mask topography and wall-bounded grid points.
360	!-- It is sufficient to masked only north- and south-facing surfaces, which
361	!-- need special treatment for the u-component.
362	flag = MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,j,i), 1 ) )
363	mask_south = MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,j-1,i), 1 ) )
364	mask_north = MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,j+1,i), 1 ) )
365	!
366	!-- Interpolate eddy diffusivities on staggered gridpoints
367	kmyp = 0.25_wp * ( km(k,j,i)+km(k,j+1,i)+km(k,j,i-1)+km(k,j+1,i-1) )
368	kmym = 0.25_wp * ( km(k,j,i)+km(k,j-1,i)+km(k,j,i-1)+km(k,j-1,i-1) )
369
370	tend(k,j,i) = tend(k,j,i) &
371	+ 2.0_wp * ( &
372	km(k,j,i) * ( u(k,j,i+1) - u(k,j,i) ) &
373	- km(k,j,i-1) * ( u(k,j,i) - u(k,j,i-1) ) &
374	) * ddx2 * flag &
375	+ ( &
376	mask_north * kmyp * ( ( u(k,j+1,i) - u(k,j,i) ) * ddy &
377	+ ( v(k,j+1,i) - v(k,j+1,i-1) ) * ddx &
378	) &
379	- mask_south * kmym * ( ( u(k,j,i) - u(k,j-1,i) ) * ddy &
380	+ ( v(k,j,i) - v(k,j,i-1) ) * ddx &
381	) &
382	) * ddy * flag
383	ENDDO
384
385	!
386	!-- Add horizontal momentum flux u'v' at north- (l=0) and south-facing (l=1)
387	!-- surfaces. Note, in the the flat case, loops won't be entered as
388	!-- start_index > end_index. Furtermore, note, no vertical natural surfaces
389	!-- so far.
390	!-- Default-type surfaces
391	DO l = 0, 1
392	surf_s = surf_def_v(l)%start_index(j,i)
393	surf_e = surf_def_v(l)%end_index(j,i)
394	DO m = surf_s, surf_e
395	k = surf_def_v(l)%k(m)
396	tend(k,j,i) = tend(k,j,i) + surf_def_v(l)%mom_flux_uv(m) * ddy
397	ENDDO
398	ENDDO
399	!
400	!-- Natural-type surfaces
401	DO l = 0, 1
402	surf_s = surf_lsm_v(l)%start_index(j,i)
403	surf_e = surf_lsm_v(l)%end_index(j,i)
404	DO m = surf_s, surf_e
405	k = surf_lsm_v(l)%k(m)
406	tend(k,j,i) = tend(k,j,i) + surf_lsm_v(l)%mom_flux_uv(m) * ddy
407	ENDDO
408	ENDDO
409	!
410	!-- Urban-type surfaces
411	DO l = 0, 1
412	surf_s = surf_usm_v(l)%start_index(j,i)
413	surf_e = surf_usm_v(l)%end_index(j,i)
414	DO m = surf_s, surf_e
415	k = surf_usm_v(l)%k(m)
416	tend(k,j,i) = tend(k,j,i) + surf_usm_v(l)%mom_flux_uv(m) * ddy
417	ENDDO
418	ENDDO
419	!
420	!-- Compute vertical diffusion. In case of simulating a surface layer,
421	!-- respective grid diffusive fluxes are masked (flag 8) within this
422	!-- loop, and added further below, else, simple gradient approach is
423	!-- applied. Model top is also mask if top-momentum flux is given.
424	DO k = nzb+1, nzt
425	!
426	!-- Determine flags to mask topography below and above. Flag 1 is
427	!-- used to mask topography in general, and flag 8 implies
428	!-- information about use_surface_fluxes. Flag 9 is used to control
429	!-- momentum flux at model top.
430	mask_bottom = MERGE( 1.0_wp, 0.0_wp, &
431	BTEST( wall_flags_total_0(k-1,j,i), 8 ) )
432	mask_top = MERGE( 1.0_wp, 0.0_wp, &
433	BTEST( wall_flags_total_0(k+1,j,i), 8 ) ) * &
434	MERGE( 1.0_wp, 0.0_wp, &
435	BTEST( wall_flags_total_0(k+1,j,i), 9 ) )
436	flag = MERGE( 1.0_wp, 0.0_wp, &
437	BTEST( wall_flags_total_0(k,j,i), 1 ) )
438	!
439	!-- Interpolate eddy diffusivities on staggered gridpoints
440	kmzp = 0.25_wp * ( km(k,j,i)+km(k+1,j,i)+km(k,j,i-1)+km(k+1,j,i-1) )
441	kmzm = 0.25_wp * ( km(k,j,i)+km(k-1,j,i)+km(k,j,i-1)+km(k-1,j,i-1) )
442
443	tend(k,j,i) = tend(k,j,i) &
444	+ ( kmzp * ( ( u(k+1,j,i) - u(k,j,i) ) * ddzu(k+1) &
445	+ ( w(k,j,i) - w(k,j,i-1) ) * ddx &
446	) * rho_air_zw(k) * mask_top &
447	- kmzm * ( ( u(k,j,i) - u(k-1,j,i) ) * ddzu(k) &
448	+ ( w(k-1,j,i) - w(k-1,j,i-1) ) * ddx &
449	) * rho_air_zw(k-1) * mask_bottom &
450	) * ddzw(k) * drho_air(k) * flag
451	ENDDO
452
453	!
454	!-- Vertical diffusion at the first surface grid points, if the
455	!-- momentum flux at the bottom is given by the Prandtl law or if it is
456	!-- prescribed by the user.
457	!-- Difference quotient of the momentum flux is not formed over half of
458	!-- the grid spacing (2.0*ddzw(k)) any more, since the comparison with
459	!-- other (LES) models showed that the values of the momentum flux becomes
460	!-- too large in this case.
461	IF ( use_surface_fluxes ) THEN
462	!
463	!-- Default-type surfaces, upward-facing
464	surf_s = surf_def_h(0)%start_index(j,i)
465	surf_e = surf_def_h(0)%end_index(j,i)
466	DO m = surf_s, surf_e
467
468	k = surf_def_h(0)%k(m)
469
470	tend(k,j,i) = tend(k,j,i) &
471	+ ( - ( - surf_def_h(0)%usws(m) ) &
472	) * ddzw(k) * drho_air(k)
473	ENDDO
474	!
475	!-- Default-type surfaces, dowward-facing (except for model-top fluxes)
476	surf_s = surf_def_h(1)%start_index(j,i)
477	surf_e = surf_def_h(1)%end_index(j,i)
478	DO m = surf_s, surf_e
479
480	k = surf_def_h(1)%k(m)
481
482	tend(k,j,i) = tend(k,j,i) &
483	+ ( - surf_def_h(1)%usws(m) &
484	) * ddzw(k) * drho_air(k)
485	ENDDO
486	!
487	!-- Natural-type surfaces, upward-facing
488	surf_s = surf_lsm_h%start_index(j,i)
489	surf_e = surf_lsm_h%end_index(j,i)
490	DO m = surf_s, surf_e
491
492	k = surf_lsm_h%k(m)
493
494	tend(k,j,i) = tend(k,j,i) &
495	+ ( - ( - surf_lsm_h%usws(m) ) &
496	) * ddzw(k) * drho_air(k)
497	ENDDO
498	!
499	!-- Urban-type surfaces, upward-facing
500	surf_s = surf_usm_h%start_index(j,i)
501	surf_e = surf_usm_h%end_index(j,i)
502	DO m = surf_s, surf_e
503
504	k = surf_usm_h%k(m)
505
506	tend(k,j,i) = tend(k,j,i) &
507	+ ( - ( - surf_usm_h%usws(m) ) &
508	) * ddzw(k) * drho_air(k)
509	ENDDO
510
511	ENDIF
512	!
513	!-- Add momentum flux at model top
514	IF ( use_top_fluxes .AND. constant_top_momentumflux ) THEN
515	surf_s = surf_def_h(2)%start_index(j,i)
516	surf_e = surf_def_h(2)%end_index(j,i)
517	DO m = surf_s, surf_e
518
519	k = surf_def_h(2)%k(m)
520
521	tend(k,j,i) = tend(k,j,i) &
522	+ ( - surf_def_h(2)%usws(m) ) * ddzw(k) * drho_air(k)
523	ENDDO
524	ENDIF
525
526
527	END SUBROUTINE diffusion_u_ij
528
529	END MODULE diffusion_u_mod

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