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source: palm/trunk/SOURCE/diffusion_u.f90 @ 4311

Last change on this file since 4311 was 4182, checked in by scharf, 5 years ago
corrected "Former revisions" section minor formatting in "Former revisions" section added "Author" section
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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 4182 2019-08-22 15:20:23Z maronga $
27	! Corrected "Former revisions" section
28	!
29	! 3655 2019-01-07 16:51:22Z knoop
30	! OpenACC port for SPEC
31	!
32	! Revision 1.1 1997/09/12 06:23:51 raasch
33	! Initial revision
34	!
35	!
36	! Description:
37	! ------------
38	!> Diffusion term of the u-component
39	!> @todo additional damping (needed for non-cyclic bc) causes bad vectorization
40	!> and slows down the speed on NEC about 5-10%
41	!------------------------------------------------------------------------------!
42	MODULE diffusion_u_mod
43
44
45	PRIVATE
46	PUBLIC diffusion_u
47
48	INTERFACE diffusion_u
49	MODULE PROCEDURE diffusion_u
50	MODULE PROCEDURE diffusion_u_ij
51	END INTERFACE diffusion_u
52
53	CONTAINS
54
55
56	!------------------------------------------------------------------------------!
57	! Description:
58	! ------------
59	!> Call for all grid points
60	!------------------------------------------------------------------------------!
61	SUBROUTINE diffusion_u
62
63	USE arrays_3d, &
64	ONLY: ddzu, ddzw, km, tend, u, v, w, drho_air, rho_air_zw
65
66	USE control_parameters, &
67	ONLY: constant_top_momentumflux, use_surface_fluxes, &
68	use_top_fluxes
69
70	USE grid_variables, &
71	ONLY: ddx, ddx2, ddy
72
73	USE indices, &
74	ONLY: nxlu, nxr, nyn, nys, nzb, nzt, wall_flags_0
75
76	USE kinds
77
78	USE surface_mod, &
79	ONLY : surf_def_h, surf_def_v, surf_lsm_h, surf_lsm_v, surf_usm_h, &
80	surf_usm_v
81
82	IMPLICIT NONE
83
84	INTEGER(iwp) :: i !< running index x direction
85	INTEGER(iwp) :: j !< running index y direction
86	INTEGER(iwp) :: k !< running index z direction
87	INTEGER(iwp) :: l !< running index of surface type, south- or north-facing wall
88	INTEGER(iwp) :: m !< running index surface elements
89	INTEGER(iwp) :: surf_e !< end index of surface elements at (j,i)-gridpoint
90	INTEGER(iwp) :: surf_s !< start index of surface elements at (j,i)-gridpoint
91
92	REAL(wp) :: flag !< flag to mask topography grid points
93	REAL(wp) :: kmym !< diffusion coefficient on southward side of the u-gridbox - interpolated onto xu-yv grid
94	REAL(wp) :: kmyp !< diffusion coefficient on northward side of the u-gridbox - interpolated onto xu-yv grid
95	REAL(wp) :: kmzm !< diffusion coefficient on bottom of the gridbox - interpolated onto xu-zw grid
96	REAL(wp) :: kmzp !< diffusion coefficient on top of the gridbox - interpolated onto xu-zw grid
97	REAL(wp) :: mask_bottom !< flag to mask vertical upward-facing surface
98	REAL(wp) :: mask_north !< flag to mask vertical surface north of the grid point
99	REAL(wp) :: mask_south !< flag to mask vertical surface south of the grid point
100	REAL(wp) :: mask_top !< flag to mask vertical downward-facing surface
101
102
103
104	!$ACC PARALLEL LOOP COLLAPSE(2) PRIVATE(i, j, k, l, m) &
105	!$ACC PRIVATE(surf_e, surf_s, flag, kmym, kmyp, kmzm, kmzp) &
106	!$ACC PRIVATE(mask_bottom, mask_north, mask_south, mask_top) &
107	!$ACC PRESENT(wall_flags_0, km) &
108	!$ACC PRESENT(u, v, w) &
109	!$ACC PRESENT(ddzu, ddzw, drho_air, rho_air_zw) &
110	!$ACC PRESENT(surf_def_h(0:2), surf_def_v(0:1)) &
111	!$ACC PRESENT(surf_lsm_h, surf_lsm_v(0:1)) &
112	!$ACC PRESENT(surf_usm_h, surf_usm_v(0:1)) &
113	!$ACC PRESENT(tend)
114	DO i = nxlu, nxr
115	DO j = nys, nyn
116	!
117	!-- Compute horizontal diffusion
118	DO k = nzb+1, nzt
119	!
120	!-- Predetermine flag to mask topography and wall-bounded grid points.
121	!-- It is sufficient to masked only north- and south-facing surfaces, which
122	!-- need special treatment for the u-component.
123	flag = MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_0(k,j,i), 1 ) )
124	mask_south = MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_0(k,j-1,i), 1 ) )
125	mask_north = MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_0(k,j+1,i), 1 ) )
126	!
127	!-- Interpolate eddy diffusivities on staggered gridpoints
128	kmyp = 0.25_wp * &
129	( km(k,j,i)+km(k,j+1,i)+km(k,j,i-1)+km(k,j+1,i-1) )
130	kmym = 0.25_wp * &
131	( km(k,j,i)+km(k,j-1,i)+km(k,j,i-1)+km(k,j-1,i-1) )
132
133	tend(k,j,i) = tend(k,j,i) &
134	+ 2.0_wp * ( &
135	km(k,j,i) * ( u(k,j,i+1) - u(k,j,i) ) &
136	- km(k,j,i-1) * ( u(k,j,i) - u(k,j,i-1) ) &
137	) * ddx2 * flag &
138	+ ( mask_north * ( &
139	kmyp * ( u(k,j+1,i) - u(k,j,i) ) * ddy &
140	+ kmyp * ( v(k,j+1,i) - v(k,j+1,i-1) ) * ddx &
141	) &
142	- mask_south * ( &
143	kmym * ( u(k,j,i) - u(k,j-1,i) ) * ddy &
144	+ kmym * ( v(k,j,i) - v(k,j,i-1) ) * ddx &
145	) &
146	) * ddy * flag
147	ENDDO
148	!
149	!-- Add horizontal momentum flux u'v' at north- (l=0) and south-facing (l=1)
150	!-- surfaces. Note, in the the flat case, loops won't be entered as
151	!-- start_index > end_index. Furtermore, note, no vertical natural surfaces
152	!-- so far.
153	!-- Default-type surfaces
154	DO l = 0, 1
155	surf_s = surf_def_v(l)%start_index(j,i)
156	surf_e = surf_def_v(l)%end_index(j,i)
157	DO m = surf_s, surf_e
158	k = surf_def_v(l)%k(m)
159	tend(k,j,i) = tend(k,j,i) + &
160	surf_def_v(l)%mom_flux_uv(m) * ddy
161	ENDDO
162	ENDDO
163	!
164	!-- Natural-type surfaces
165	DO l = 0, 1
166	surf_s = surf_lsm_v(l)%start_index(j,i)
167	surf_e = surf_lsm_v(l)%end_index(j,i)
168	DO m = surf_s, surf_e
169	k = surf_lsm_v(l)%k(m)
170	tend(k,j,i) = tend(k,j,i) + &
171	surf_lsm_v(l)%mom_flux_uv(m) * ddy
172	ENDDO
173	ENDDO
174	!
175	!-- Urban-type surfaces
176	DO l = 0, 1
177	surf_s = surf_usm_v(l)%start_index(j,i)
178	surf_e = surf_usm_v(l)%end_index(j,i)
179	DO m = surf_s, surf_e
180	k = surf_usm_v(l)%k(m)
181	tend(k,j,i) = tend(k,j,i) + &
182	surf_usm_v(l)%mom_flux_uv(m) * ddy
183	ENDDO
184	ENDDO
185
186	!
187	!-- Compute vertical diffusion. In case of simulating a surface layer,
188	!-- respective grid diffusive fluxes are masked (flag 8) within this
189	!-- loop, and added further below, else, simple gradient approach is
190	!-- applied. Model top is also mask if top-momentum flux is given.
191	DO k = nzb+1, nzt
192	!
193	!-- Determine flags to mask topography below and above. Flag 1 is
194	!-- used to mask topography in general, and flag 8 implies
195	!-- information about use_surface_fluxes. Flag 9 is used to control
196	!-- momentum flux at model top.
197	mask_bottom = MERGE( 1.0_wp, 0.0_wp, &
198	BTEST( wall_flags_0(k-1,j,i), 8 ) )
199	mask_top = MERGE( 1.0_wp, 0.0_wp, &
200	BTEST( wall_flags_0(k+1,j,i), 8 ) ) * &
201	MERGE( 1.0_wp, 0.0_wp, &
202	BTEST( wall_flags_0(k+1,j,i), 9 ) )
203	flag = MERGE( 1.0_wp, 0.0_wp, &
204	BTEST( wall_flags_0(k,j,i), 1 ) )
205	!
206	!-- Interpolate eddy diffusivities on staggered gridpoints
207	kmzp = 0.25_wp * &
208	( km(k,j,i)+km(k+1,j,i)+km(k,j,i-1)+km(k+1,j,i-1) )
209	kmzm = 0.25_wp * &
210	( km(k,j,i)+km(k-1,j,i)+km(k,j,i-1)+km(k-1,j,i-1) )
211
212	tend(k,j,i) = tend(k,j,i) &
213	+ ( kmzp * ( ( u(k+1,j,i) - u(k,j,i) ) * ddzu(k+1) &
214	+ ( w(k,j,i) - w(k,j,i-1) ) * ddx &
215	) * rho_air_zw(k) * mask_top &
216	- kmzm * ( ( u(k,j,i) - u(k-1,j,i) ) * ddzu(k) &
217	+ ( w(k-1,j,i) - w(k-1,j,i-1) ) * ddx &
218	) * rho_air_zw(k-1) * mask_bottom &
219	) * ddzw(k) * drho_air(k) * flag
220	ENDDO
221
222	!
223	!-- Vertical diffusion at the first grid point above the surface,
224	!-- if the momentum flux at the bottom is given by the Prandtl law or
225	!-- if it is prescribed by the user.
226	!-- Difference quotient of the momentum flux is not formed over half
227	!-- of the grid spacing (2.0*ddzw(k)) any more, since the comparison
228	!-- with other (LES) models showed that the values of the momentum
229	!-- flux becomes too large in this case.
230	!-- The term containing w(k-1,..) (see above equation) is removed here
231	!-- because the vertical velocity is assumed to be zero at the surface.
232	IF ( use_surface_fluxes ) THEN
233	!
234	!-- Default-type surfaces, upward-facing
235	surf_s = surf_def_h(0)%start_index(j,i)
236	surf_e = surf_def_h(0)%end_index(j,i)
237	DO m = surf_s, surf_e
238
239	k = surf_def_h(0)%k(m)
240
241	tend(k,j,i) = tend(k,j,i) &
242	+ ( - ( - surf_def_h(0)%usws(m) ) &
243	) * ddzw(k) * drho_air(k)
244	ENDDO
245	!
246	!-- Default-type surfaces, dowward-facing
247	surf_s = surf_def_h(1)%start_index(j,i)
248	surf_e = surf_def_h(1)%end_index(j,i)
249	DO m = surf_s, surf_e
250
251	k = surf_def_h(1)%k(m)
252
253	tend(k,j,i) = tend(k,j,i) &
254	+ ( - surf_def_h(1)%usws(m) &
255	) * ddzw(k) * drho_air(k)
256	ENDDO
257	!
258	!-- Natural-type surfaces, upward-facing
259	surf_s = surf_lsm_h%start_index(j,i)
260	surf_e = surf_lsm_h%end_index(j,i)
261	DO m = surf_s, surf_e
262
263	k = surf_lsm_h%k(m)
264
265	tend(k,j,i) = tend(k,j,i) &
266	+ ( - ( - surf_lsm_h%usws(m) ) &
267	) * ddzw(k) * drho_air(k)
268	ENDDO
269	!
270	!-- Urban-type surfaces, upward-facing
271	surf_s = surf_usm_h%start_index(j,i)
272	surf_e = surf_usm_h%end_index(j,i)
273	DO m = surf_s, surf_e
274
275	k = surf_usm_h%k(m)
276
277	tend(k,j,i) = tend(k,j,i) &
278	+ ( - ( - surf_usm_h%usws(m) ) &
279	) * ddzw(k) * drho_air(k)
280	ENDDO
281
282	ENDIF
283	!
284	!-- Add momentum flux at model top
285	IF ( use_top_fluxes .AND. constant_top_momentumflux ) THEN
286	surf_s = surf_def_h(2)%start_index(j,i)
287	surf_e = surf_def_h(2)%end_index(j,i)
288	DO m = surf_s, surf_e
289
290	k = surf_def_h(2)%k(m)
291
292	tend(k,j,i) = tend(k,j,i) &
293	+ ( - surf_def_h(2)%usws(m) ) * ddzw(k) * drho_air(k)
294	ENDDO
295	ENDIF
296
297	ENDDO
298	ENDDO
299
300	END SUBROUTINE diffusion_u
301
302
303	!------------------------------------------------------------------------------!
304	! Description:
305	! ------------
306	!> Call for grid point i,j
307	!------------------------------------------------------------------------------!
308	SUBROUTINE diffusion_u_ij( i, j )
309
310	USE arrays_3d, &
311	ONLY: ddzu, ddzw, km, tend, u, v, w, drho_air, rho_air_zw
312
313	USE control_parameters, &
314	ONLY: constant_top_momentumflux, use_surface_fluxes, &
315	use_top_fluxes
316
317	USE grid_variables, &
318	ONLY: ddx, ddx2, ddy
319
320	USE indices, &
321	ONLY: nzb, nzt, wall_flags_0
322
323	USE kinds
324
325	USE surface_mod, &
326	ONLY : surf_def_h, surf_def_v, surf_lsm_h, surf_lsm_v, surf_usm_h, &
327	surf_usm_v
328
329	IMPLICIT NONE
330
331	INTEGER(iwp) :: i !< running index x direction
332	INTEGER(iwp) :: j !< running index y direction
333	INTEGER(iwp) :: k !< running index z direction
334	INTEGER(iwp) :: l !< running index of surface type, south- or north-facing wall
335	INTEGER(iwp) :: m !< running index surface elements
336	INTEGER(iwp) :: surf_e !< End index of surface elements at (j,i)-gridpoint
337	INTEGER(iwp) :: surf_s !< Start index of surface elements at (j,i)-gridpoint
338
339	REAL(wp) :: flag !< flag to mask topography grid points
340	REAL(wp) :: kmym !< diffusion coefficient on southward side of the u-gridbox - interpolated onto xu-yv grid
341	REAL(wp) :: kmyp !<diffusion coefficient on northward side of the u-gridbox - interpolated onto xu-yv grid
342	REAL(wp) :: kmzm !< diffusion coefficient on bottom of the gridbox - interpolated onto xu-zw grid
343	REAL(wp) :: kmzp !< diffusion coefficient on top of the gridbox - interpolated onto xu-zw grid
344	REAL(wp) :: mask_bottom !< flag to mask vertical upward-facing surface
345	REAL(wp) :: mask_north !< flag to mask vertical surface north of the grid point
346	REAL(wp) :: mask_south !< flag to mask vertical surface south of the grid point
347	REAL(wp) :: mask_top !< flag to mask vertical downward-facing surface
348	!
349	!-- Compute horizontal diffusion
350	DO k = nzb+1, nzt
351	!
352	!-- Predetermine flag to mask topography and wall-bounded grid points.
353	!-- It is sufficient to masked only north- and south-facing surfaces, which
354	!-- need special treatment for the u-component.
355	flag = MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_0(k,j,i), 1 ) )
356	mask_south = MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_0(k,j-1,i), 1 ) )
357	mask_north = MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_0(k,j+1,i), 1 ) )
358	!
359	!-- Interpolate eddy diffusivities on staggered gridpoints
360	kmyp = 0.25_wp * ( km(k,j,i)+km(k,j+1,i)+km(k,j,i-1)+km(k,j+1,i-1) )
361	kmym = 0.25_wp * ( km(k,j,i)+km(k,j-1,i)+km(k,j,i-1)+km(k,j-1,i-1) )
362
363	tend(k,j,i) = tend(k,j,i) &
364	+ 2.0_wp * ( &
365	km(k,j,i) * ( u(k,j,i+1) - u(k,j,i) ) &
366	- km(k,j,i-1) * ( u(k,j,i) - u(k,j,i-1) ) &
367	) * ddx2 * flag &
368	+ ( &
369	mask_north * kmyp * ( ( u(k,j+1,i) - u(k,j,i) ) * ddy &
370	+ ( v(k,j+1,i) - v(k,j+1,i-1) ) * ddx &
371	) &
372	- mask_south * kmym * ( ( u(k,j,i) - u(k,j-1,i) ) * ddy &
373	+ ( v(k,j,i) - v(k,j,i-1) ) * ddx &
374	) &
375	) * ddy * flag
376	ENDDO
377
378	!
379	!-- Add horizontal momentum flux u'v' at north- (l=0) and south-facing (l=1)
380	!-- surfaces. Note, in the the flat case, loops won't be entered as
381	!-- start_index > end_index. Furtermore, note, no vertical natural surfaces
382	!-- so far.
383	!-- Default-type surfaces
384	DO l = 0, 1
385	surf_s = surf_def_v(l)%start_index(j,i)
386	surf_e = surf_def_v(l)%end_index(j,i)
387	DO m = surf_s, surf_e
388	k = surf_def_v(l)%k(m)
389	tend(k,j,i) = tend(k,j,i) + surf_def_v(l)%mom_flux_uv(m) * ddy
390	ENDDO
391	ENDDO
392	!
393	!-- Natural-type surfaces
394	DO l = 0, 1
395	surf_s = surf_lsm_v(l)%start_index(j,i)
396	surf_e = surf_lsm_v(l)%end_index(j,i)
397	DO m = surf_s, surf_e
398	k = surf_lsm_v(l)%k(m)
399	tend(k,j,i) = tend(k,j,i) + surf_lsm_v(l)%mom_flux_uv(m) * ddy
400	ENDDO
401	ENDDO
402	!
403	!-- Urban-type surfaces
404	DO l = 0, 1
405	surf_s = surf_usm_v(l)%start_index(j,i)
406	surf_e = surf_usm_v(l)%end_index(j,i)
407	DO m = surf_s, surf_e
408	k = surf_usm_v(l)%k(m)
409	tend(k,j,i) = tend(k,j,i) + surf_usm_v(l)%mom_flux_uv(m) * ddy
410	ENDDO
411	ENDDO
412	!
413	!-- Compute vertical diffusion. In case of simulating a surface layer,
414	!-- respective grid diffusive fluxes are masked (flag 8) within this
415	!-- loop, and added further below, else, simple gradient approach is
416	!-- applied. Model top is also mask if top-momentum flux is given.
417	DO k = nzb+1, nzt
418	!
419	!-- Determine flags to mask topography below and above. Flag 1 is
420	!-- used to mask topography in general, and flag 8 implies
421	!-- information about use_surface_fluxes. Flag 9 is used to control
422	!-- momentum flux at model top.
423	mask_bottom = MERGE( 1.0_wp, 0.0_wp, &
424	BTEST( wall_flags_0(k-1,j,i), 8 ) )
425	mask_top = MERGE( 1.0_wp, 0.0_wp, &
426	BTEST( wall_flags_0(k+1,j,i), 8 ) ) * &
427	MERGE( 1.0_wp, 0.0_wp, &
428	BTEST( wall_flags_0(k+1,j,i), 9 ) )
429	flag = MERGE( 1.0_wp, 0.0_wp, &
430	BTEST( wall_flags_0(k,j,i), 1 ) )
431	!
432	!-- Interpolate eddy diffusivities on staggered gridpoints
433	kmzp = 0.25_wp * ( km(k,j,i)+km(k+1,j,i)+km(k,j,i-1)+km(k+1,j,i-1) )
434	kmzm = 0.25_wp * ( km(k,j,i)+km(k-1,j,i)+km(k,j,i-1)+km(k-1,j,i-1) )
435
436	tend(k,j,i) = tend(k,j,i) &
437	+ ( kmzp * ( ( u(k+1,j,i) - u(k,j,i) ) * ddzu(k+1) &
438	+ ( w(k,j,i) - w(k,j,i-1) ) * ddx &
439	) * rho_air_zw(k) * mask_top &
440	- kmzm * ( ( u(k,j,i) - u(k-1,j,i) ) * ddzu(k) &
441	+ ( w(k-1,j,i) - w(k-1,j,i-1) ) * ddx &
442	) * rho_air_zw(k-1) * mask_bottom &
443	) * ddzw(k) * drho_air(k) * flag
444	ENDDO
445
446	!
447	!-- Vertical diffusion at the first surface grid points, if the
448	!-- momentum flux at the bottom is given by the Prandtl law or if it is
449	!-- prescribed by the user.
450	!-- Difference quotient of the momentum flux is not formed over half of
451	!-- the grid spacing (2.0*ddzw(k)) any more, since the comparison with
452	!-- other (LES) models showed that the values of the momentum flux becomes
453	!-- too large in this case.
454	IF ( use_surface_fluxes ) THEN
455	!
456	!-- Default-type surfaces, upward-facing
457	surf_s = surf_def_h(0)%start_index(j,i)
458	surf_e = surf_def_h(0)%end_index(j,i)
459	DO m = surf_s, surf_e
460
461	k = surf_def_h(0)%k(m)
462
463	tend(k,j,i) = tend(k,j,i) &
464	+ ( - ( - surf_def_h(0)%usws(m) ) &
465	) * ddzw(k) * drho_air(k)
466	ENDDO
467	!
468	!-- Default-type surfaces, dowward-facing (except for model-top fluxes)
469	surf_s = surf_def_h(1)%start_index(j,i)
470	surf_e = surf_def_h(1)%end_index(j,i)
471	DO m = surf_s, surf_e
472
473	k = surf_def_h(1)%k(m)
474
475	tend(k,j,i) = tend(k,j,i) &
476	+ ( - surf_def_h(1)%usws(m) &
477	) * ddzw(k) * drho_air(k)
478	ENDDO
479	!
480	!-- Natural-type surfaces, upward-facing
481	surf_s = surf_lsm_h%start_index(j,i)
482	surf_e = surf_lsm_h%end_index(j,i)
483	DO m = surf_s, surf_e
484
485	k = surf_lsm_h%k(m)
486
487	tend(k,j,i) = tend(k,j,i) &
488	+ ( - ( - surf_lsm_h%usws(m) ) &
489	) * ddzw(k) * drho_air(k)
490	ENDDO
491	!
492	!-- Urban-type surfaces, upward-facing
493	surf_s = surf_usm_h%start_index(j,i)
494	surf_e = surf_usm_h%end_index(j,i)
495	DO m = surf_s, surf_e
496
497	k = surf_usm_h%k(m)
498
499	tend(k,j,i) = tend(k,j,i) &
500	+ ( - ( - surf_usm_h%usws(m) ) &
501	) * ddzw(k) * drho_air(k)
502	ENDDO
503
504	ENDIF
505	!
506	!-- Add momentum flux at model top
507	IF ( use_top_fluxes .AND. constant_top_momentumflux ) THEN
508	surf_s = surf_def_h(2)%start_index(j,i)
509	surf_e = surf_def_h(2)%end_index(j,i)
510	DO m = surf_s, surf_e
511
512	k = surf_def_h(2)%k(m)
513
514	tend(k,j,i) = tend(k,j,i) &
515	+ ( - surf_def_h(2)%usws(m) ) * ddzw(k) * drho_air(k)
516	ENDDO
517	ENDIF
518
519
520	END SUBROUTINE diffusion_u_ij
521
522	END MODULE diffusion_u_mod

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