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source: palm/trunk/SOURCE/diffusion_v.f90 @ 3545

Last change on this file since 3545 was 3241, checked in by raasch, 6 years ago
various changes to avoid compiler warnings (mainly removal of unused variables)
Property svn:keywords set to `Id`
File size: 24.2 KB

Rev	Line
[1873]	1	!> @file diffusion_v.f90
[2000]	2	!------------------------------------------------------------------------------!
[2696]	3	! This file is part of the PALM model system.
[1036]	4	!
[2000]	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.
[1036]	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	!
[2718]	17	! Copyright 1997-2018 Leibniz Universitaet Hannover
[2000]	18	!------------------------------------------------------------------------------!
[1036]	19	!
[484]	20	! Current revisions:
[1]	21	! -----------------
[1341]	22	!
[2233]	23	!
[1321]	24	! Former revisions:
	25	! -----------------
	26	! $Id: diffusion_v.f90 3241 2018-09-12 15:02:00Z gronemeier $
[3241]	27	! unused variables removed
	28	!
	29	! 2718 2018-01-02 08:49:38Z maronga
[2716]	30	! Corrected "Former revisions" section
	31	!
	32	! 2696 2017-12-14 17:12:51Z kanani
	33	! Change in file header (GPL part)
	34	!
	35	! 2638 2017-11-23 12:44:23Z raasch
[2638]	36	! bugfix for constant top momentumflux
	37	!
	38	! 2233 2017-05-30 18:08:54Z suehring
[1321]	39	!
[2233]	40	! 2232 2017-05-30 17:47:52Z suehring
	41	! Adjustments to new topography and surface concept
	42	!
[2119]	43	! 2118 2017-01-17 16:38:49Z raasch
	44	! OpenACC version of subroutine removed
	45	!
[2038]	46	! 2037 2016-10-26 11:15:40Z knoop
	47	! Anelastic approximation implemented
	48	!
[2001]	49	! 2000 2016-08-20 18:09:15Z knoop
	50	! Forced header and separation lines into 80 columns
	51	!
[1874]	52	! 1873 2016-04-18 14:50:06Z maronga
	53	! Module renamed (removed _mod)
	54	!
[1851]	55	! 1850 2016-04-08 13:29:27Z maronga
	56	! Module renamed
	57	!
[1741]	58	! 1740 2016-01-13 08:19:40Z raasch
	59	! unnecessary calculations of kmzm and kmzp in wall bounded parts removed
	60	!
[1683]	61	! 1682 2015-10-07 23:56:08Z knoop
	62	! Code annotations made doxygen readable
	63	!
[1341]	64	! 1340 2014-03-25 19:45:13Z kanani
	65	! REAL constants defined as wp-kind
	66	!
[1321]	67	! 1320 2014-03-20 08:40:49Z raasch
[1320]	68	! ONLY-attribute added to USE-statements,
	69	! kind-parameters added to all INTEGER and REAL declaration statements,
	70	! kinds are defined in new module kinds,
	71	! revision history before 2012 removed,
	72	! comment fields (!:) to be used for variable explanations added to
	73	! all variable declaration statements
[1321]	74	!
[1258]	75	! 1257 2013-11-08 15:18:40Z raasch
	76	! openacc loop and loop vector clauses removed, declare create moved after
	77	! the FORTRAN declaration statement
	78	!
[1132]	79	! 1128 2013-04-12 06:19:32Z raasch
	80	! loop index bounds in accelerator version replaced by i_left, i_right, j_south,
	81	! j_north
	82	!
[1037]	83	! 1036 2012-10-22 13:43:42Z raasch
	84	! code put under GPL (PALM 3.9)
	85	!
[1017]	86	! 1015 2012-09-27 09:23:24Z raasch
	87	! accelerator version (*_acc) added
	88	!
[1002]	89	! 1001 2012-09-13 14:08:46Z raasch
	90	! arrays comunicated by module instead of parameter list
	91	!
[979]	92	! 978 2012-08-09 08:28:32Z fricke
	93	! outflow damping layer removed
	94	! kmxm_x/_y and kmxp_x/_y change to kmxm and kmxp
	95	!
[1]	96	! Revision 1.1 1997/09/12 06:24:01 raasch
	97	! Initial revision
	98	!
	99	!
	100	! Description:
	101	! ------------
[1682]	102	!> Diffusion term of the v-component
[1]	103	!------------------------------------------------------------------------------!
[1682]	104	MODULE diffusion_v_mod
	105
[1]	106
	107	PRIVATE
[2118]	108	PUBLIC diffusion_v
[1]	109
	110	INTERFACE diffusion_v
	111	MODULE PROCEDURE diffusion_v
	112	MODULE PROCEDURE diffusion_v_ij
	113	END INTERFACE diffusion_v
	114
	115	CONTAINS
	116
	117
	118	!------------------------------------------------------------------------------!
[1682]	119	! Description:
	120	! ------------
	121	!> Call for all grid points
[1]	122	!------------------------------------------------------------------------------!
[1001]	123	SUBROUTINE diffusion_v
[1]	124
[1320]	125	USE arrays_3d, &
[2232]	126	ONLY: ddzu, ddzw, km, tend, u, v, w, drho_air, rho_air_zw
[1320]	127
	128	USE control_parameters, &
[2232]	129	ONLY: constant_top_momentumflux, use_surface_fluxes, &
[1320]	130	use_top_fluxes
	131
	132	USE grid_variables, &
[2232]	133	ONLY: ddx, ddy, ddy2
[1320]	134
	135	USE indices, &
[3241]	136	ONLY: nxl, nxr, nyn, nysv, nzb, nzt, wall_flags_0
[1320]	137
	138	USE kinds
[1]	139
[2232]	140	USE surface_mod, &
	141	ONLY : surf_def_h, surf_def_v, surf_lsm_h, surf_lsm_v, surf_usm_h, &
	142	surf_usm_v
	143
[1]	144	IMPLICIT NONE
	145
[2232]	146	INTEGER(iwp) :: i !< running index x direction
	147	INTEGER(iwp) :: j !< running index y direction
	148	INTEGER(iwp) :: k !< running index z direction
	149	INTEGER(iwp) :: l !< running index of surface type, south- or north-facing wall
	150	INTEGER(iwp) :: m !< running index surface elements
	151	INTEGER(iwp) :: surf_e !< End index of surface elements at (j,i)-gridpoint
	152	INTEGER(iwp) :: surf_s !< Start index of surface elements at (j,i)-gridpoint
[1001]	153
[2232]	154	REAL(wp) :: flag !< flag to mask topography grid points
	155	REAL(wp) :: kmxm !<
	156	REAL(wp) :: kmxp !<
	157	REAL(wp) :: kmzm !<
	158	REAL(wp) :: kmzp !<
	159	REAL(wp) :: mask_bottom !< flag to mask vertical upward-facing surface
	160	REAL(wp) :: mask_east !< flag to mask vertical surface south of the grid point
	161	REAL(wp) :: mask_west !< flag to mask vertical surface north of the grid point
	162	REAL(wp) :: mask_top !< flag to mask vertical downward-facing surface
[1]	163
	164	DO i = nxl, nxr
[106]	165	DO j = nysv, nyn
[1]	166	!
	167	!-- Compute horizontal diffusion
[2232]	168	DO k = nzb+1, nzt
	169
[1]	170	!
[2232]	171	!-- Predetermine flag to mask topography and wall-bounded grid points.
	172	!-- It is sufficient to masked only east- and west-facing surfaces, which
	173	!-- need special treatment for the v-component.
	174	flag = MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_0(k,j,i), 2 ) )
	175	mask_east = MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_0(k,j,i+1), 2 ) )
	176	mask_west = MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_0(k,j,i-1), 2 ) )
	177	!
[1]	178	!-- Interpolate eddy diffusivities on staggered gridpoints
[2232]	179	kmxp = 0.25_wp * ( km(k,j,i)+km(k,j,i+1)+km(k,j-1,i)+km(k,j-1,i+1) )
	180	kmxm = 0.25_wp * ( km(k,j,i)+km(k,j,i-1)+km(k,j-1,i)+km(k,j-1,i-1) )
[1]	181
[2232]	182	tend(k,j,i) = tend(k,j,i) + ( &
	183	mask_east * kmxp * ( &
	184	( v(k,j,i+1) - v(k,j,i) ) * ddx &
	185	+ ( u(k,j,i+1) - u(k,j-1,i+1) ) * ddy &
	186	) &
	187	- mask_west * kmxm * ( &
	188	( v(k,j,i) - v(k,j,i-1) ) * ddx &
	189	+ ( u(k,j,i) - u(k,j-1,i) ) * ddy &
	190	) &
	191	) * ddx * flag &
	192	+ 2.0_wp * ( &
	193	km(k,j,i) * ( v(k,j+1,i) - v(k,j,i) ) &
	194	- km(k,j-1,i) * ( v(k,j,i) - v(k,j-1,i) ) &
	195	) * ddy2 * flag
	196
[1]	197	ENDDO
	198
	199	!
[2232]	200	!-- Add horizontal momentum flux v'u' at east- (l=2) and west-facing (l=3)
	201	!-- surfaces. Note, in the the flat case, loops won't be entered as
	202	!-- start_index > end_index. Furtermore, note, no vertical natural surfaces
	203	!-- so far.
	204	!-- Default-type surfaces
	205	DO l = 2, 3
	206	surf_s = surf_def_v(l)%start_index(j,i)
	207	surf_e = surf_def_v(l)%end_index(j,i)
	208	DO m = surf_s, surf_e
	209	k = surf_def_v(l)%k(m)
	210	tend(k,j,i) = tend(k,j,i) + &
	211	surf_def_v(l)%mom_flux_uv(m) * ddx
	212	ENDDO
	213	ENDDO
[1]	214	!
[2232]	215	!-- Natural-type surfaces
	216	DO l = 2, 3
	217	surf_s = surf_lsm_v(l)%start_index(j,i)
	218	surf_e = surf_lsm_v(l)%end_index(j,i)
	219	DO m = surf_s, surf_e
	220	k = surf_lsm_v(l)%k(m)
	221	tend(k,j,i) = tend(k,j,i) + &
	222	surf_lsm_v(l)%mom_flux_uv(m) * ddx
	223	ENDDO
	224	ENDDO
[1]	225	!
[2232]	226	!-- Urban-type surfaces
	227	DO l = 2, 3
	228	surf_s = surf_usm_v(l)%start_index(j,i)
	229	surf_e = surf_usm_v(l)%end_index(j,i)
	230	DO m = surf_s, surf_e
	231	k = surf_usm_v(l)%k(m)
	232	tend(k,j,i) = tend(k,j,i) + &
	233	surf_usm_v(l)%mom_flux_uv(m) * ddx
	234	ENDDO
	235	ENDDO
	236	!
	237	!-- Compute vertical diffusion. In case of simulating a surface layer,
	238	!-- respective grid diffusive fluxes are masked (flag 10) within this
	239	!-- loop, and added further below, else, simple gradient approach is
	240	!-- applied. Model top is also mask if top-momentum flux is given.
	241	DO k = nzb+1, nzt
	242	!
	243	!-- Determine flags to mask topography below and above. Flag 2 is
	244	!-- used to mask topography in general, while flag 8 implies also
	245	!-- information about use_surface_fluxes. Flag 9 is used to control
	246	!-- momentum flux at model top.
	247	mask_bottom = MERGE( 1.0_wp, 0.0_wp, &
	248	BTEST( wall_flags_0(k-1,j,i), 8 ) )
	249	mask_top = MERGE( 1.0_wp, 0.0_wp, &
	250	BTEST( wall_flags_0(k+1,j,i), 8 ) ) * &
	251	MERGE( 1.0_wp, 0.0_wp, &
	252	BTEST( wall_flags_0(k+1,j,i), 9 ) )
	253	flag = MERGE( 1.0_wp, 0.0_wp, &
	254	BTEST( wall_flags_0(k,j,i), 2 ) )
	255	!
[1]	256	!-- Interpolate eddy diffusivities on staggered gridpoints
[1340]	257	kmzp = 0.25_wp * &
[1]	258	( km(k,j,i)+km(k+1,j,i)+km(k,j-1,i)+km(k+1,j-1,i) )
[1340]	259	kmzm = 0.25_wp * &
[1]	260	( km(k,j,i)+km(k-1,j,i)+km(k,j-1,i)+km(k-1,j-1,i) )
	261
[1320]	262	tend(k,j,i) = tend(k,j,i) &
	263	& + ( kmzp * ( ( v(k+1,j,i) - v(k,j,i) ) * ddzu(k+1) &
	264	& + ( w(k,j,i) - w(k,j-1,i) ) * ddy &
[2232]	265	& ) * rho_air_zw(k) * mask_top &
[1320]	266	& - kmzm * ( ( v(k,j,i) - v(k-1,j,i) ) * ddzu(k) &
	267	& + ( w(k-1,j,i) - w(k-1,j-1,i) ) * ddy &
[2232]	268	& ) * rho_air_zw(k-1) * mask_bottom &
	269	& ) * ddzw(k) * drho_air(k) * flag
[1]	270	ENDDO
	271
	272	!
	273	!-- Vertical diffusion at the first grid point above the surface,
	274	!-- if the momentum flux at the bottom is given by the Prandtl law
	275	!-- or if it is prescribed by the user.
	276	!-- Difference quotient of the momentum flux is not formed over
	277	!-- half of the grid spacing (2.0*ddzw(k)) any more, since the
[1320]	278	!-- comparison with other (LES) models showed that the values of
[1]	279	!-- the momentum flux becomes too large in this case.
	280	IF ( use_surface_fluxes ) THEN
	281	!
[2232]	282	!-- Default-type surfaces, upward-facing
	283	surf_s = surf_def_h(0)%start_index(j,i)
	284	surf_e = surf_def_h(0)%end_index(j,i)
	285	DO m = surf_s, surf_e
	286	k = surf_def_h(0)%k(m)
[1]	287
[2232]	288	tend(k,j,i) = tend(k,j,i) &
	289	+ ( - ( - surf_def_h(0)%vsws(m) ) &
	290	) * ddzw(k) * drho_air(k)
	291	ENDDO
	292	!
	293	!-- Default-type surfaces, dowward-facing
	294	surf_s = surf_def_h(1)%start_index(j,i)
	295	surf_e = surf_def_h(1)%end_index(j,i)
	296	DO m = surf_s, surf_e
	297	k = surf_def_h(1)%k(m)
[1]	298
[2232]	299	tend(k,j,i) = tend(k,j,i) &
	300	+ ( - surf_def_h(1)%vsws(m) &
	301	) * ddzw(k) * drho_air(k)
	302	ENDDO
[102]	303	!
[2232]	304	!-- Natural-type surfaces, upward-facing
	305	surf_s = surf_lsm_h%start_index(j,i)
	306	surf_e = surf_lsm_h%end_index(j,i)
	307	DO m = surf_s, surf_e
	308	k = surf_lsm_h%k(m)
	309
	310	tend(k,j,i) = tend(k,j,i) &
	311	+ ( - ( - surf_lsm_h%vsws(m) ) &
	312	) * ddzw(k) * drho_air(k)
	313
	314	ENDDO
[102]	315	!
[2232]	316	!-- Urban-type surfaces, upward-facing
	317	surf_s = surf_usm_h%start_index(j,i)
	318	surf_e = surf_usm_h%end_index(j,i)
	319	DO m = surf_s, surf_e
	320	k = surf_usm_h%k(m)
[102]	321
[2232]	322	tend(k,j,i) = tend(k,j,i) &
	323	+ ( - ( - surf_usm_h%vsws(m) ) &
	324	) * ddzw(k) * drho_air(k)
	325
	326	ENDDO
[102]	327	ENDIF
[2232]	328	!
	329	!-- Add momentum flux at model top
[2638]	330	IF ( use_top_fluxes .AND. constant_top_momentumflux ) THEN
[2232]	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
[102]	334
[2232]	335	k = surf_def_h(2)%k(m)
	336
	337	tend(k,j,i) = tend(k,j,i) &
	338	+ ( - surf_def_h(2)%vsws(m) ) * ddzw(k) * drho_air(k)
	339	ENDDO
	340	ENDIF
	341
[1]	342	ENDDO
	343	ENDDO
	344
	345	END SUBROUTINE diffusion_v
	346
	347
	348	!------------------------------------------------------------------------------!
[1682]	349	! Description:
	350	! ------------
	351	!> Call for grid point i,j
[1]	352	!------------------------------------------------------------------------------!
[1001]	353	SUBROUTINE diffusion_v_ij( i, j )
[1]	354
[1320]	355	USE arrays_3d, &
[2232]	356	ONLY: ddzu, ddzw, km, tend, u, v, w, drho_air, rho_air_zw
[1320]	357
	358	USE control_parameters, &
[2232]	359	ONLY: constant_top_momentumflux, use_surface_fluxes, &
	360	use_top_fluxes
[1320]	361
	362	USE grid_variables, &
[2232]	363	ONLY: ddx, ddy, ddy2
[1320]	364
	365	USE indices, &
[2232]	366	ONLY: nzb, nzt, wall_flags_0
[1320]	367
	368	USE kinds
[1]	369
[2232]	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
[1]	374	IMPLICIT NONE
	375
	376
[2232]	377	INTEGER(iwp) :: i !< running index x direction
	378	INTEGER(iwp) :: j !< running index y direction
	379	INTEGER(iwp) :: k !< running index z direction
	380	INTEGER(iwp) :: l !< running index of surface type, south- or north-facing wall
	381	INTEGER(iwp) :: m !< running index surface elements
	382	INTEGER(iwp) :: surf_e !< End index of surface elements at (j,i)-gridpoint
	383	INTEGER(iwp) :: surf_s !< Start index of surface elements at (j,i)-gridpoint
[1001]	384
[2232]	385	REAL(wp) :: flag !< flag to mask topography grid points
	386	REAL(wp) :: kmxm !<
	387	REAL(wp) :: kmxp !<
	388	REAL(wp) :: kmzm !<
	389	REAL(wp) :: kmzp !<
	390	REAL(wp) :: mask_bottom !< flag to mask vertical upward-facing surface
	391	REAL(wp) :: mask_east !< flag to mask vertical surface south of the grid point
	392	REAL(wp) :: mask_west !< flag to mask vertical surface north of the grid point
	393	REAL(wp) :: mask_top !< flag to mask vertical downward-facing surface
	394
[1]	395	!
	396	!-- Compute horizontal diffusion
[2232]	397	DO k = nzb+1, nzt
[1]	398	!
[2232]	399	!-- Predetermine flag to mask topography and wall-bounded grid points.
	400	!-- It is sufficient to masked only east- and west-facing surfaces, which
	401	!-- need special treatment for the v-component.
	402	flag = MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_0(k,j,i), 2 ) )
	403	mask_east = MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_0(k,j,i+1), 2 ) )
	404	mask_west = MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_0(k,j,i-1), 2 ) )
	405	!
[1]	406	!-- Interpolate eddy diffusivities on staggered gridpoints
[1340]	407	kmxp = 0.25_wp * ( km(k,j,i)+km(k,j,i+1)+km(k,j-1,i)+km(k,j-1,i+1) )
	408	kmxm = 0.25_wp * ( km(k,j,i)+km(k,j,i-1)+km(k,j-1,i)+km(k,j-1,i-1) )
[1]	409
[2232]	410	tend(k,j,i) = tend(k,j,i) + ( &
	411	mask_east * kmxp * ( &
	412	( v(k,j,i+1) - v(k,j,i) ) * ddx &
	413	+ ( u(k,j,i+1) - u(k,j-1,i+1) ) * ddy &
	414	) &
	415	- mask_west * kmxm * ( &
	416	( v(k,j,i) - v(k,j,i-1) ) * ddx &
	417	+ ( u(k,j,i) - u(k,j-1,i) ) * ddy &
	418	) &
	419	) * ddx * flag &
	420	+ 2.0_wp * ( &
	421	km(k,j,i) * ( v(k,j+1,i) - v(k,j,i) ) &
	422	- km(k,j-1,i) * ( v(k,j,i) - v(k,j-1,i) ) &
	423	) * ddy2 * flag
[1]	424	ENDDO
	425
	426	!
[2232]	427	!-- Add horizontal momentum flux v'u' at east- (l=2) and west-facing (l=3)
	428	!-- surfaces. Note, in the the flat case, loops won't be entered as
	429	!-- start_index > end_index. Furtermore, note, no vertical natural surfaces
	430	!-- so far.
	431	!-- Default-type surfaces
	432	DO l = 2, 3
	433	surf_s = surf_def_v(l)%start_index(j,i)
	434	surf_e = surf_def_v(l)%end_index(j,i)
	435	DO m = surf_s, surf_e
	436	k = surf_def_v(l)%k(m)
	437	tend(k,j,i) = tend(k,j,i) + surf_def_v(l)%mom_flux_uv(m) * ddx
	438	ENDDO
	439	ENDDO
[51]	440	!
[2232]	441	!-- Natural-type surfaces
	442	DO l = 2, 3
	443	surf_s = surf_lsm_v(l)%start_index(j,i)
	444	surf_e = surf_lsm_v(l)%end_index(j,i)
	445	DO m = surf_s, surf_e
	446	k = surf_lsm_v(l)%k(m)
	447	tend(k,j,i) = tend(k,j,i) + surf_lsm_v(l)%mom_flux_uv(m) * ddx
	448	ENDDO
	449	ENDDO
[1]	450	!
[2232]	451	!-- Urban-type surfaces
	452	DO l = 2, 3
	453	surf_s = surf_usm_v(l)%start_index(j,i)
	454	surf_e = surf_usm_v(l)%end_index(j,i)
	455	DO m = surf_s, surf_e
	456	k = surf_usm_v(l)%k(m)
	457	tend(k,j,i) = tend(k,j,i) + surf_usm_v(l)%mom_flux_uv(m) * ddx
	458	ENDDO
	459	ENDDO
[1]	460	!
[2232]	461	!-- Compute vertical diffusion. In case of simulating a surface layer,
	462	!-- respective grid diffusive fluxes are masked (flag 8) within this
	463	!-- loop, and added further below, else, simple gradient approach is
	464	!-- applied. Model top is also mask if top-momentum flux is given.
	465	DO k = nzb+1, nzt
	466	!
	467	!-- Determine flags to mask topography below and above. Flag 2 is
	468	!-- used to mask topography in general, while flag 10 implies also
	469	!-- information about use_surface_fluxes. Flag 9 is used to control
	470	!-- momentum flux at model top.
	471	mask_bottom = MERGE( 1.0_wp, 0.0_wp, &
	472	BTEST( wall_flags_0(k-1,j,i), 8 ) )
	473	mask_top = MERGE( 1.0_wp, 0.0_wp, &
	474	BTEST( wall_flags_0(k+1,j,i), 8 ) ) * &
	475	MERGE( 1.0_wp, 0.0_wp, &
	476	BTEST( wall_flags_0(k+1,j,i), 9 ) )
	477	flag = MERGE( 1.0_wp, 0.0_wp, &
	478	BTEST( wall_flags_0(k,j,i), 2 ) )
	479	!
[1]	480	!-- Interpolate eddy diffusivities on staggered gridpoints
[1340]	481	kmzp = 0.25_wp * ( km(k,j,i)+km(k+1,j,i)+km(k,j-1,i)+km(k+1,j-1,i) )
	482	kmzm = 0.25_wp * ( km(k,j,i)+km(k-1,j,i)+km(k,j-1,i)+km(k-1,j-1,i) )
[1]	483
[1320]	484	tend(k,j,i) = tend(k,j,i) &
	485	& + ( kmzp * ( ( v(k+1,j,i) - v(k,j,i) ) * ddzu(k+1) &
	486	& + ( w(k,j,i) - w(k,j-1,i) ) * ddy &
[2232]	487	& ) * rho_air_zw(k) * mask_top &
[1320]	488	& - kmzm * ( ( v(k,j,i) - v(k-1,j,i) ) * ddzu(k) &
	489	& + ( w(k-1,j,i) - w(k-1,j-1,i) ) * ddy &
[2232]	490	& ) * rho_air_zw(k-1) * mask_bottom &
	491	& ) * ddzw(k) * drho_air(k) * flag
[1]	492	ENDDO
	493
	494	!
	495	!-- Vertical diffusion at the first grid point above the surface, if the
	496	!-- momentum flux at the bottom is given by the Prandtl law or if it is
	497	!-- prescribed by the user.
	498	!-- Difference quotient of the momentum flux is not formed over half of
	499	!-- the grid spacing (2.0*ddzw(k)) any more, since the comparison with
[1320]	500	!-- other (LES) models showed that the values of the momentum flux becomes
[1]	501	!-- too large in this case.
	502	IF ( use_surface_fluxes ) THEN
	503	!
[2232]	504	!-- Default-type surfaces, upward-facing
	505	surf_s = surf_def_h(0)%start_index(j,i)
	506	surf_e = surf_def_h(0)%end_index(j,i)
	507	DO m = surf_s, surf_e
	508	k = surf_def_h(0)%k(m)
[1]	509
[2232]	510	tend(k,j,i) = tend(k,j,i) &
	511	+ ( - ( - surf_def_h(0)%vsws(m) ) &
	512	) * ddzw(k) * drho_air(k)
	513	ENDDO
	514	!
	515	!-- Default-type surfaces, dowward-facing
	516	surf_s = surf_def_h(1)%start_index(j,i)
	517	surf_e = surf_def_h(1)%end_index(j,i)
	518	DO m = surf_s, surf_e
	519	k = surf_def_h(1)%k(m)
[1]	520
[2232]	521	tend(k,j,i) = tend(k,j,i) &
	522	+ ( - surf_def_h(1)%vsws(m) &
	523	) * ddzw(k) * drho_air(k)
	524	ENDDO
[102]	525	!
[2232]	526	!-- Natural-type surfaces, upward-facing
	527	surf_s = surf_lsm_h%start_index(j,i)
	528	surf_e = surf_lsm_h%end_index(j,i)
	529	DO m = surf_s, surf_e
	530	k = surf_lsm_h%k(m)
	531
	532	tend(k,j,i) = tend(k,j,i) &
	533	+ ( - ( - surf_lsm_h%vsws(m) ) &
	534	) * ddzw(k) * drho_air(k)
	535
	536	ENDDO
[102]	537	!
[2232]	538	!-- Urban-type surfaces, upward-facing
	539	surf_s = surf_usm_h%start_index(j,i)
	540	surf_e = surf_usm_h%end_index(j,i)
	541	DO m = surf_s, surf_e
	542	k = surf_usm_h%k(m)
[102]	543
[2232]	544	tend(k,j,i) = tend(k,j,i) &
	545	+ ( - ( - surf_usm_h%vsws(m) ) &
	546	) * ddzw(k) * drho_air(k)
	547
	548	ENDDO
[102]	549	ENDIF
[2232]	550	!
	551	!-- Add momentum flux at model top
[2638]	552	IF ( use_top_fluxes .AND. constant_top_momentumflux ) THEN
[2232]	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
[102]	556
[2232]	557	k = surf_def_h(2)%k(m)
	558
	559	tend(k,j,i) = tend(k,j,i) &
	560	+ ( - surf_def_h(2)%vsws(m) ) * ddzw(k) * drho_air(k)
	561	ENDDO
	562	ENDIF
	563
[1]	564	END SUBROUTINE diffusion_v_ij
	565
[1321]	566	END MODULE diffusion_v_mod

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