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source: palm/trunk/SOURCE/diffusion_u.f90 @ 3590

Last change on this file since 3590 was 3547, checked in by suehring, 6 years ago
variable description added some routines
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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 3547 2018-11-21 13:21:24Z forkel $
27	! variables documented
28	!
29	! 3241 2018-09-12 15:02:00Z raasch
30	! unused variables removed
31	!
32	! 2718 2018-01-02 08:49:38Z maronga
33	! Corrected "Former revisions" section
34	!
35	! 2696 2017-12-14 17:12:51Z kanani
36	! Change in file header (GPL part)
37	!
38	! 2638 2017-11-23 12:44:23Z raasch
39	! bugfix for constant top momentumflux
40	!
41	! 2233 2017-05-30 18:08:54Z suehring
42	!
43	! 2232 2017-05-30 17:47:52Z suehring
44	! Adjustments to new topography and surface concept
45	!
46	! 2118 2017-01-17 16:38:49Z raasch
47	! OpenACC version of subroutine removed
48	!
49	! 2037 2016-10-26 11:15:40Z knoop
50	! Anelastic approximation implemented
51	!
52	! 2000 2016-08-20 18:09:15Z knoop
53	! Forced header and separation lines into 80 columns
54	!
55	! 1873 2016-04-18 14:50:06Z maronga
56	! Module renamed (removed _mod)
57	!
58	! 1850 2016-04-08 13:29:27Z maronga
59	! Module renamed
60	!
61	! 1740 2016-01-13 08:19:40Z raasch
62	! unnecessary calculations of kmzm and kmzp in wall bounded parts removed
63	!
64	! 1691 2015-10-26 16:17:44Z maronga
65	! Formatting corrections.
66	!
67	! 1682 2015-10-07 23:56:08Z knoop
68	! Code annotations made doxygen readable
69	!
70	! 1340 2014-03-25 19:45:13Z kanani
71	! REAL constants defined as wp-kind
72	!
73	! 1320 2014-03-20 08:40:49Z raasch
74	! ONLY-attribute added to USE-statements,
75	! kind-parameters added to all INTEGER and REAL declaration statements,
76	! kinds are defined in new module kinds,
77	! revision history before 2012 removed,
78	! comment fields (!:) to be used for variable explanations added to
79	! all variable declaration statements
80	!
81	! 1257 2013-11-08 15:18:40Z raasch
82	! openacc loop and loop vector clauses removed, declare create moved after
83	! the FORTRAN declaration statement
84	!
85	! 1128 2013-04-12 06:19:32Z raasch
86	! loop index bounds in accelerator version replaced by i_left, i_right, j_south,
87	! j_north
88	!
89	! 1036 2012-10-22 13:43:42Z raasch
90	! code put under GPL (PALM 3.9)
91	!
92	! 1015 2012-09-27 09:23:24Z raasch
93	! accelerator version (*_acc) added
94	!
95	! 1001 2012-09-13 14:08:46Z raasch
96	! arrays comunicated by module instead of parameter list
97	!
98	! 978 2012-08-09 08:28:32Z fricke
99	! outflow damping layer removed
100	! kmym_x/_y and kmyp_x/_y change to kmym and kmyp
101	!
102	! Revision 1.1 1997/09/12 06:23:51 raasch
103	! Initial revision
104	!
105	!
106	! Description:
107	! ------------
108	!> Diffusion term of the u-component
109	!> @todo additional damping (needed for non-cyclic bc) causes bad vectorization
110	!> and slows down the speed on NEC about 5-10%
111	!------------------------------------------------------------------------------!
112	MODULE diffusion_u_mod
113
114
115	PRIVATE
116	PUBLIC diffusion_u
117
118	INTERFACE diffusion_u
119	MODULE PROCEDURE diffusion_u
120	MODULE PROCEDURE diffusion_u_ij
121	END INTERFACE diffusion_u
122
123	CONTAINS
124
125
126	!------------------------------------------------------------------------------!
127	! Description:
128	! ------------
129	!> Call for all grid points
130	!------------------------------------------------------------------------------!
131	SUBROUTINE diffusion_u
132
133	USE arrays_3d, &
134	ONLY: ddzu, ddzw, km, tend, u, v, w, drho_air, rho_air_zw
135
136	USE control_parameters, &
137	ONLY: constant_top_momentumflux, use_surface_fluxes, &
138	use_top_fluxes
139
140	USE grid_variables, &
141	ONLY: ddx, ddx2, ddy
142
143	USE indices, &
144	ONLY: nxlu, nxr, nyn, nys, nzb, nzt, wall_flags_0
145
146	USE kinds
147
148	USE surface_mod, &
149	ONLY : surf_def_h, surf_def_v, surf_lsm_h, surf_lsm_v, surf_usm_h, &
150	surf_usm_v
151
152	IMPLICIT NONE
153
154	INTEGER(iwp) :: i !< running index x direction
155	INTEGER(iwp) :: j !< running index y direction
156	INTEGER(iwp) :: k !< running index z direction
157	INTEGER(iwp) :: l !< running index of surface type, south- or north-facing wall
158	INTEGER(iwp) :: m !< running index surface elements
159	INTEGER(iwp) :: surf_e !< end index of surface elements at (j,i)-gridpoint
160	INTEGER(iwp) :: surf_s !< start index of surface elements at (j,i)-gridpoint
161
162	REAL(wp) :: flag !< flag to mask topography grid points
163	REAL(wp) :: kmym !< diffusion coefficient on southward side of the u-gridbox - interpolated onto xu-yv grid
164	REAL(wp) :: kmyp !< diffusion coefficient on northward side of the u-gridbox - interpolated onto xu-yv grid
165	REAL(wp) :: kmzm !< diffusion coefficient on bottom of the gridbox - interpolated onto xu-zw grid
166	REAL(wp) :: kmzp !< diffusion coefficient on top of the gridbox - interpolated onto xu-zw grid
167	REAL(wp) :: mask_bottom !< flag to mask vertical upward-facing surface
168	REAL(wp) :: mask_north !< flag to mask vertical surface north of the grid point
169	REAL(wp) :: mask_south !< flag to mask vertical surface south of the grid point
170	REAL(wp) :: mask_top !< flag to mask vertical downward-facing surface
171
172
173
174	DO i = nxlu, nxr
175	DO j = nys, nyn
176	!
177	!-- Compute horizontal diffusion
178	DO k = nzb+1, nzt
179	!
180	!-- Predetermine flag to mask topography and wall-bounded grid points.
181	!-- It is sufficient to masked only north- and south-facing surfaces, which
182	!-- need special treatment for the u-component.
183	flag = MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_0(k,j,i), 1 ) )
184	mask_south = MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_0(k,j-1,i), 1 ) )
185	mask_north = MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_0(k,j+1,i), 1 ) )
186	!
187	!-- Interpolate eddy diffusivities on staggered gridpoints
188	kmyp = 0.25_wp * &
189	( km(k,j,i)+km(k,j+1,i)+km(k,j,i-1)+km(k,j+1,i-1) )
190	kmym = 0.25_wp * &
191	( km(k,j,i)+km(k,j-1,i)+km(k,j,i-1)+km(k,j-1,i-1) )
192
193	tend(k,j,i) = tend(k,j,i) &
194	+ 2.0_wp * ( &
195	km(k,j,i) * ( u(k,j,i+1) - u(k,j,i) ) &
196	- km(k,j,i-1) * ( u(k,j,i) - u(k,j,i-1) ) &
197	) * ddx2 * flag &
198	+ ( mask_north * ( &
199	kmyp * ( u(k,j+1,i) - u(k,j,i) ) * ddy &
200	+ kmyp * ( v(k,j+1,i) - v(k,j+1,i-1) ) * ddx &
201	) &
202	- mask_south * ( &
203	kmym * ( u(k,j,i) - u(k,j-1,i) ) * ddy &
204	+ kmym * ( v(k,j,i) - v(k,j,i-1) ) * ddx &
205	) &
206	) * ddy * flag
207	ENDDO
208	!
209	!-- Add horizontal momentum flux u'v' at north- (l=0) and south-facing (l=1)
210	!-- surfaces. Note, in the the flat case, loops won't be entered as
211	!-- start_index > end_index. Furtermore, note, no vertical natural surfaces
212	!-- so far.
213	!-- Default-type surfaces
214	DO l = 0, 1
215	surf_s = surf_def_v(l)%start_index(j,i)
216	surf_e = surf_def_v(l)%end_index(j,i)
217	DO m = surf_s, surf_e
218	k = surf_def_v(l)%k(m)
219	tend(k,j,i) = tend(k,j,i) + &
220	surf_def_v(l)%mom_flux_uv(m) * ddy
221	ENDDO
222	ENDDO
223	!
224	!-- Natural-type surfaces
225	DO l = 0, 1
226	surf_s = surf_lsm_v(l)%start_index(j,i)
227	surf_e = surf_lsm_v(l)%end_index(j,i)
228	DO m = surf_s, surf_e
229	k = surf_lsm_v(l)%k(m)
230	tend(k,j,i) = tend(k,j,i) + &
231	surf_lsm_v(l)%mom_flux_uv(m) * ddy
232	ENDDO
233	ENDDO
234	!
235	!-- Urban-type surfaces
236	DO l = 0, 1
237	surf_s = surf_usm_v(l)%start_index(j,i)
238	surf_e = surf_usm_v(l)%end_index(j,i)
239	DO m = surf_s, surf_e
240	k = surf_usm_v(l)%k(m)
241	tend(k,j,i) = tend(k,j,i) + &
242	surf_usm_v(l)%mom_flux_uv(m) * ddy
243	ENDDO
244	ENDDO
245
246	!
247	!-- Compute vertical diffusion. In case of simulating a surface layer,
248	!-- respective grid diffusive fluxes are masked (flag 8) within this
249	!-- loop, and added further below, else, simple gradient approach is
250	!-- applied. Model top is also mask if top-momentum flux is given.
251	DO k = nzb+1, nzt
252	!
253	!-- Determine flags to mask topography below and above. Flag 1 is
254	!-- used to mask topography in general, and flag 8 implies
255	!-- information about use_surface_fluxes. Flag 9 is used to control
256	!-- momentum flux at model top.
257	mask_bottom = MERGE( 1.0_wp, 0.0_wp, &
258	BTEST( wall_flags_0(k-1,j,i), 8 ) )
259	mask_top = MERGE( 1.0_wp, 0.0_wp, &
260	BTEST( wall_flags_0(k+1,j,i), 8 ) ) * &
261	MERGE( 1.0_wp, 0.0_wp, &
262	BTEST( wall_flags_0(k+1,j,i), 9 ) )
263	flag = MERGE( 1.0_wp, 0.0_wp, &
264	BTEST( wall_flags_0(k,j,i), 1 ) )
265	!
266	!-- Interpolate eddy diffusivities on staggered gridpoints
267	kmzp = 0.25_wp * &
268	( km(k,j,i)+km(k+1,j,i)+km(k,j,i-1)+km(k+1,j,i-1) )
269	kmzm = 0.25_wp * &
270	( km(k,j,i)+km(k-1,j,i)+km(k,j,i-1)+km(k-1,j,i-1) )
271
272	tend(k,j,i) = tend(k,j,i) &
273	+ ( kmzp * ( ( u(k+1,j,i) - u(k,j,i) ) * ddzu(k+1) &
274	+ ( w(k,j,i) - w(k,j,i-1) ) * ddx &
275	) * rho_air_zw(k) * mask_top &
276	- kmzm * ( ( u(k,j,i) - u(k-1,j,i) ) * ddzu(k) &
277	+ ( w(k-1,j,i) - w(k-1,j,i-1) ) * ddx &
278	) * rho_air_zw(k-1) * mask_bottom &
279	) * ddzw(k) * drho_air(k) * flag
280	ENDDO
281
282	!
283	!-- Vertical diffusion at the first grid point above the surface,
284	!-- if the momentum flux at the bottom is given by the Prandtl law or
285	!-- if it is prescribed by the user.
286	!-- Difference quotient of the momentum flux is not formed over half
287	!-- of the grid spacing (2.0*ddzw(k)) any more, since the comparison
288	!-- with other (LES) models showed that the values of the momentum
289	!-- flux becomes too large in this case.
290	!-- The term containing w(k-1,..) (see above equation) is removed here
291	!-- because the vertical velocity is assumed to be zero at the surface.
292	IF ( use_surface_fluxes ) THEN
293	!
294	!-- Default-type surfaces, upward-facing
295	surf_s = surf_def_h(0)%start_index(j,i)
296	surf_e = surf_def_h(0)%end_index(j,i)
297	DO m = surf_s, surf_e
298
299	k = surf_def_h(0)%k(m)
300
301	tend(k,j,i) = tend(k,j,i) &
302	+ ( - ( - surf_def_h(0)%usws(m) ) &
303	) * ddzw(k) * drho_air(k)
304	ENDDO
305	!
306	!-- Default-type surfaces, dowward-facing
307	surf_s = surf_def_h(1)%start_index(j,i)
308	surf_e = surf_def_h(1)%end_index(j,i)
309	DO m = surf_s, surf_e
310
311	k = surf_def_h(1)%k(m)
312
313	tend(k,j,i) = tend(k,j,i) &
314	+ ( - surf_def_h(1)%usws(m) &
315	) * ddzw(k) * drho_air(k)
316	ENDDO
317	!
318	!-- Natural-type surfaces, upward-facing
319	surf_s = surf_lsm_h%start_index(j,i)
320	surf_e = surf_lsm_h%end_index(j,i)
321	DO m = surf_s, surf_e
322
323	k = surf_lsm_h%k(m)
324
325	tend(k,j,i) = tend(k,j,i) &
326	+ ( - ( - surf_lsm_h%usws(m) ) &
327	) * ddzw(k) * drho_air(k)
328	ENDDO
329	!
330	!-- Urban-type surfaces, upward-facing
331	surf_s = surf_usm_h%start_index(j,i)
332	surf_e = surf_usm_h%end_index(j,i)
333	DO m = surf_s, surf_e
334
335	k = surf_usm_h%k(m)
336
337	tend(k,j,i) = tend(k,j,i) &
338	+ ( - ( - surf_usm_h%usws(m) ) &
339	) * ddzw(k) * drho_air(k)
340	ENDDO
341
342	ENDIF
343	!
344	!-- Add momentum flux at model top
345	IF ( use_top_fluxes .AND. constant_top_momentumflux ) THEN
346	surf_s = surf_def_h(2)%start_index(j,i)
347	surf_e = surf_def_h(2)%end_index(j,i)
348	DO m = surf_s, surf_e
349
350	k = surf_def_h(2)%k(m)
351
352	tend(k,j,i) = tend(k,j,i) &
353	+ ( - surf_def_h(2)%usws(m) ) * ddzw(k) * drho_air(k)
354	ENDDO
355	ENDIF
356
357	ENDDO
358	ENDDO
359
360	END SUBROUTINE diffusion_u
361
362
363	!------------------------------------------------------------------------------!
364	! Description:
365	! ------------
366	!> Call for grid point i,j
367	!------------------------------------------------------------------------------!
368	SUBROUTINE diffusion_u_ij( i, j )
369
370	USE arrays_3d, &
371	ONLY: ddzu, ddzw, km, tend, u, v, w, drho_air, rho_air_zw
372
373	USE control_parameters, &
374	ONLY: constant_top_momentumflux, use_surface_fluxes, &
375	use_top_fluxes
376
377	USE grid_variables, &
378	ONLY: ddx, ddx2, ddy
379
380	USE indices, &
381	ONLY: nzb, nzt, wall_flags_0
382
383	USE kinds
384
385	USE surface_mod, &
386	ONLY : surf_def_h, surf_def_v, surf_lsm_h, surf_lsm_v, surf_usm_h, &
387	surf_usm_v
388
389	IMPLICIT NONE
390
391	INTEGER(iwp) :: i !< running index x direction
392	INTEGER(iwp) :: j !< running index y direction
393	INTEGER(iwp) :: k !< running index z direction
394	INTEGER(iwp) :: l !< running index of surface type, south- or north-facing wall
395	INTEGER(iwp) :: m !< running index surface elements
396	INTEGER(iwp) :: surf_e !< End index of surface elements at (j,i)-gridpoint
397	INTEGER(iwp) :: surf_s !< Start index of surface elements at (j,i)-gridpoint
398
399	REAL(wp) :: flag !< flag to mask topography grid points
400	REAL(wp) :: kmym !< diffusion coefficient on southward side of the u-gridbox - interpolated onto xu-yv grid
401	REAL(wp) :: kmyp !<diffusion coefficient on northward side of the u-gridbox - interpolated onto xu-yv grid
402	REAL(wp) :: kmzm !< diffusion coefficient on bottom of the gridbox - interpolated onto xu-zw grid
403	REAL(wp) :: kmzp !< diffusion coefficient on top of the gridbox - interpolated onto xu-zw grid
404	REAL(wp) :: mask_bottom !< flag to mask vertical upward-facing surface
405	REAL(wp) :: mask_north !< flag to mask vertical surface north of the grid point
406	REAL(wp) :: mask_south !< flag to mask vertical surface south of the grid point
407	REAL(wp) :: mask_top !< flag to mask vertical downward-facing surface
408	!
409	!-- Compute horizontal diffusion
410	DO k = nzb+1, nzt
411	!
412	!-- Predetermine flag to mask topography and wall-bounded grid points.
413	!-- It is sufficient to masked only north- and south-facing surfaces, which
414	!-- need special treatment for the u-component.
415	flag = MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_0(k,j,i), 1 ) )
416	mask_south = MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_0(k,j-1,i), 1 ) )
417	mask_north = MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_0(k,j+1,i), 1 ) )
418	!
419	!-- Interpolate eddy diffusivities on staggered gridpoints
420	kmyp = 0.25_wp * ( km(k,j,i)+km(k,j+1,i)+km(k,j,i-1)+km(k,j+1,i-1) )
421	kmym = 0.25_wp * ( km(k,j,i)+km(k,j-1,i)+km(k,j,i-1)+km(k,j-1,i-1) )
422
423	tend(k,j,i) = tend(k,j,i) &
424	+ 2.0_wp * ( &
425	km(k,j,i) * ( u(k,j,i+1) - u(k,j,i) ) &
426	- km(k,j,i-1) * ( u(k,j,i) - u(k,j,i-1) ) &
427	) * ddx2 * flag &
428	+ ( &
429	mask_north * kmyp * ( ( u(k,j+1,i) - u(k,j,i) ) * ddy &
430	+ ( v(k,j+1,i) - v(k,j+1,i-1) ) * ddx &
431	) &
432	- mask_south * kmym * ( ( u(k,j,i) - u(k,j-1,i) ) * ddy &
433	+ ( v(k,j,i) - v(k,j,i-1) ) * ddx &
434	) &
435	) * ddy * flag
436	ENDDO
437
438	!
439	!-- Add horizontal momentum flux u'v' at north- (l=0) and south-facing (l=1)
440	!-- surfaces. Note, in the the flat case, loops won't be entered as
441	!-- start_index > end_index. Furtermore, note, no vertical natural surfaces
442	!-- so far.
443	!-- Default-type surfaces
444	DO l = 0, 1
445	surf_s = surf_def_v(l)%start_index(j,i)
446	surf_e = surf_def_v(l)%end_index(j,i)
447	DO m = surf_s, surf_e
448	k = surf_def_v(l)%k(m)
449	tend(k,j,i) = tend(k,j,i) + surf_def_v(l)%mom_flux_uv(m) * ddy
450	ENDDO
451	ENDDO
452	!
453	!-- Natural-type surfaces
454	DO l = 0, 1
455	surf_s = surf_lsm_v(l)%start_index(j,i)
456	surf_e = surf_lsm_v(l)%end_index(j,i)
457	DO m = surf_s, surf_e
458	k = surf_lsm_v(l)%k(m)
459	tend(k,j,i) = tend(k,j,i) + surf_lsm_v(l)%mom_flux_uv(m) * ddy
460	ENDDO
461	ENDDO
462	!
463	!-- Urban-type surfaces
464	DO l = 0, 1
465	surf_s = surf_usm_v(l)%start_index(j,i)
466	surf_e = surf_usm_v(l)%end_index(j,i)
467	DO m = surf_s, surf_e
468	k = surf_usm_v(l)%k(m)
469	tend(k,j,i) = tend(k,j,i) + surf_usm_v(l)%mom_flux_uv(m) * ddy
470	ENDDO
471	ENDDO
472	!
473	!-- Compute vertical diffusion. In case of simulating a surface layer,
474	!-- respective grid diffusive fluxes are masked (flag 8) within this
475	!-- loop, and added further below, else, simple gradient approach is
476	!-- applied. Model top is also mask if top-momentum flux is given.
477	DO k = nzb+1, nzt
478	!
479	!-- Determine flags to mask topography below and above. Flag 1 is
480	!-- used to mask topography in general, and flag 8 implies
481	!-- information about use_surface_fluxes. Flag 9 is used to control
482	!-- momentum flux at model top.
483	mask_bottom = MERGE( 1.0_wp, 0.0_wp, &
484	BTEST( wall_flags_0(k-1,j,i), 8 ) )
485	mask_top = MERGE( 1.0_wp, 0.0_wp, &
486	BTEST( wall_flags_0(k+1,j,i), 8 ) ) * &
487	MERGE( 1.0_wp, 0.0_wp, &
488	BTEST( wall_flags_0(k+1,j,i), 9 ) )
489	flag = MERGE( 1.0_wp, 0.0_wp, &
490	BTEST( wall_flags_0(k,j,i), 1 ) )
491	!
492	!-- Interpolate eddy diffusivities on staggered gridpoints
493	kmzp = 0.25_wp * ( km(k,j,i)+km(k+1,j,i)+km(k,j,i-1)+km(k+1,j,i-1) )
494	kmzm = 0.25_wp * ( km(k,j,i)+km(k-1,j,i)+km(k,j,i-1)+km(k-1,j,i-1) )
495
496	tend(k,j,i) = tend(k,j,i) &
497	+ ( kmzp * ( ( u(k+1,j,i) - u(k,j,i) ) * ddzu(k+1) &
498	+ ( w(k,j,i) - w(k,j,i-1) ) * ddx &
499	) * rho_air_zw(k) * mask_top &
500	- kmzm * ( ( u(k,j,i) - u(k-1,j,i) ) * ddzu(k) &
501	+ ( w(k-1,j,i) - w(k-1,j,i-1) ) * ddx &
502	) * rho_air_zw(k-1) * mask_bottom &
503	) * ddzw(k) * drho_air(k) * flag
504	ENDDO
505
506	!
507	!-- Vertical diffusion at the first surface grid points, if the
508	!-- momentum flux at the bottom is given by the Prandtl law or if it is
509	!-- prescribed by the user.
510	!-- Difference quotient of the momentum flux is not formed over half of
511	!-- the grid spacing (2.0*ddzw(k)) any more, since the comparison with
512	!-- other (LES) models showed that the values of the momentum flux becomes
513	!-- too large in this case.
514	IF ( use_surface_fluxes ) THEN
515	!
516	!-- Default-type surfaces, upward-facing
517	surf_s = surf_def_h(0)%start_index(j,i)
518	surf_e = surf_def_h(0)%end_index(j,i)
519	DO m = surf_s, surf_e
520
521	k = surf_def_h(0)%k(m)
522
523	tend(k,j,i) = tend(k,j,i) &
524	+ ( - ( - surf_def_h(0)%usws(m) ) &
525	) * ddzw(k) * drho_air(k)
526	ENDDO
527	!
528	!-- Default-type surfaces, dowward-facing (except for model-top fluxes)
529	surf_s = surf_def_h(1)%start_index(j,i)
530	surf_e = surf_def_h(1)%end_index(j,i)
531	DO m = surf_s, surf_e
532
533	k = surf_def_h(1)%k(m)
534
535	tend(k,j,i) = tend(k,j,i) &
536	+ ( - surf_def_h(1)%usws(m) &
537	) * ddzw(k) * drho_air(k)
538	ENDDO
539	!
540	!-- Natural-type surfaces, upward-facing
541	surf_s = surf_lsm_h%start_index(j,i)
542	surf_e = surf_lsm_h%end_index(j,i)
543	DO m = surf_s, surf_e
544
545	k = surf_lsm_h%k(m)
546
547	tend(k,j,i) = tend(k,j,i) &
548	+ ( - ( - surf_lsm_h%usws(m) ) &
549	) * ddzw(k) * drho_air(k)
550	ENDDO
551	!
552	!-- Urban-type surfaces, upward-facing
553	surf_s = surf_usm_h%start_index(j,i)
554	surf_e = surf_usm_h%end_index(j,i)
555	DO m = surf_s, surf_e
556
557	k = surf_usm_h%k(m)
558
559	tend(k,j,i) = tend(k,j,i) &
560	+ ( - ( - surf_usm_h%usws(m) ) &
561	) * ddzw(k) * drho_air(k)
562	ENDDO
563
564	ENDIF
565	!
566	!-- Add momentum flux at model top
567	IF ( use_top_fluxes .AND. constant_top_momentumflux ) THEN
568	surf_s = surf_def_h(2)%start_index(j,i)
569	surf_e = surf_def_h(2)%end_index(j,i)
570	DO m = surf_s, surf_e
571
572	k = surf_def_h(2)%k(m)
573
574	tend(k,j,i) = tend(k,j,i) &
575	+ ( - surf_def_h(2)%usws(m) ) * ddzw(k) * drho_air(k)
576	ENDDO
577	ENDIF
578
579
580	END SUBROUTINE diffusion_u_ij
581
582	END MODULE diffusion_u_mod

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