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source: palm/trunk/SOURCE/diffusion_v.f90 @ 2834

Last change on this file since 2834 was 2718, checked in by maronga, 7 years ago
deleting of deprecated files; headers updated where needed
Property svn:keywords set to `Id`
File size: 24.2 KB

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[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 2718 2018-01-02 08:49:38Z raasch $
[2716]	27	! Corrected "Former revisions" section
	28	!
	29	! 2696 2017-12-14 17:12:51Z kanani
	30	! Change in file header (GPL part)
	31	!
	32	! 2638 2017-11-23 12:44:23Z raasch
[2638]	33	! bugfix for constant top momentumflux
	34	!
	35	! 2233 2017-05-30 18:08:54Z suehring
[1321]	36	!
[2233]	37	! 2232 2017-05-30 17:47:52Z suehring
	38	! Adjustments to new topography and surface concept
	39	!
[2119]	40	! 2118 2017-01-17 16:38:49Z raasch
	41	! OpenACC version of subroutine removed
	42	!
[2038]	43	! 2037 2016-10-26 11:15:40Z knoop
	44	! Anelastic approximation implemented
	45	!
[2001]	46	! 2000 2016-08-20 18:09:15Z knoop
	47	! Forced header and separation lines into 80 columns
	48	!
[1874]	49	! 1873 2016-04-18 14:50:06Z maronga
	50	! Module renamed (removed _mod)
	51	!
[1851]	52	! 1850 2016-04-08 13:29:27Z maronga
	53	! Module renamed
	54	!
[1741]	55	! 1740 2016-01-13 08:19:40Z raasch
	56	! unnecessary calculations of kmzm and kmzp in wall bounded parts removed
	57	!
[1683]	58	! 1682 2015-10-07 23:56:08Z knoop
	59	! Code annotations made doxygen readable
	60	!
[1341]	61	! 1340 2014-03-25 19:45:13Z kanani
	62	! REAL constants defined as wp-kind
	63	!
[1321]	64	! 1320 2014-03-20 08:40:49Z raasch
[1320]	65	! ONLY-attribute added to USE-statements,
	66	! kind-parameters added to all INTEGER and REAL declaration statements,
	67	! kinds are defined in new module kinds,
	68	! revision history before 2012 removed,
	69	! comment fields (!:) to be used for variable explanations added to
	70	! all variable declaration statements
[1321]	71	!
[1258]	72	! 1257 2013-11-08 15:18:40Z raasch
	73	! openacc loop and loop vector clauses removed, declare create moved after
	74	! the FORTRAN declaration statement
	75	!
[1132]	76	! 1128 2013-04-12 06:19:32Z raasch
	77	! loop index bounds in accelerator version replaced by i_left, i_right, j_south,
	78	! j_north
	79	!
[1037]	80	! 1036 2012-10-22 13:43:42Z raasch
	81	! code put under GPL (PALM 3.9)
	82	!
[1017]	83	! 1015 2012-09-27 09:23:24Z raasch
	84	! accelerator version (*_acc) added
	85	!
[1002]	86	! 1001 2012-09-13 14:08:46Z raasch
	87	! arrays comunicated by module instead of parameter list
	88	!
[979]	89	! 978 2012-08-09 08:28:32Z fricke
	90	! outflow damping layer removed
	91	! kmxm_x/_y and kmxp_x/_y change to kmxm and kmxp
	92	!
[1]	93	! Revision 1.1 1997/09/12 06:24:01 raasch
	94	! Initial revision
	95	!
	96	!
	97	! Description:
	98	! ------------
[1682]	99	!> Diffusion term of the v-component
[1]	100	!------------------------------------------------------------------------------!
[1682]	101	MODULE diffusion_v_mod
	102
[1]	103
	104	PRIVATE
[2118]	105	PUBLIC diffusion_v
[1]	106
	107	INTERFACE diffusion_v
	108	MODULE PROCEDURE diffusion_v
	109	MODULE PROCEDURE diffusion_v_ij
	110	END INTERFACE diffusion_v
	111
	112	CONTAINS
	113
	114
	115	!------------------------------------------------------------------------------!
[1682]	116	! Description:
	117	! ------------
	118	!> Call for all grid points
[1]	119	!------------------------------------------------------------------------------!
[1001]	120	SUBROUTINE diffusion_v
[1]	121
[1320]	122	USE arrays_3d, &
[2232]	123	ONLY: ddzu, ddzw, km, tend, u, v, w, drho_air, rho_air_zw
[1320]	124
	125	USE control_parameters, &
[2232]	126	ONLY: constant_top_momentumflux, use_surface_fluxes, &
[1320]	127	use_top_fluxes
	128
	129	USE grid_variables, &
[2232]	130	ONLY: ddx, ddy, ddy2
[1320]	131
	132	USE indices, &
[2232]	133	ONLY: nxl, nxr, nyn, nys, nysv, nzb, nzt, wall_flags_0
[1320]	134
	135	USE kinds
[1]	136
[2232]	137	USE surface_mod, &
	138	ONLY : surf_def_h, surf_def_v, surf_lsm_h, surf_lsm_v, surf_usm_h, &
	139	surf_usm_v
	140
[1]	141	IMPLICIT NONE
	142
[2232]	143	INTEGER(iwp) :: i !< running index x direction
	144	INTEGER(iwp) :: j !< running index y direction
	145	INTEGER(iwp) :: k !< running index z direction
	146	INTEGER(iwp) :: l !< running index of surface type, south- or north-facing wall
	147	INTEGER(iwp) :: m !< running index surface elements
	148	INTEGER(iwp) :: surf_e !< End index of surface elements at (j,i)-gridpoint
	149	INTEGER(iwp) :: surf_s !< Start index of surface elements at (j,i)-gridpoint
[1001]	150
[2232]	151	REAL(wp) :: flag !< flag to mask topography grid points
	152	REAL(wp) :: kmxm !<
	153	REAL(wp) :: kmxp !<
	154	REAL(wp) :: kmzm !<
	155	REAL(wp) :: kmzp !<
	156	REAL(wp) :: mask_bottom !< flag to mask vertical upward-facing surface
	157	REAL(wp) :: mask_east !< flag to mask vertical surface south of the grid point
	158	REAL(wp) :: mask_west !< flag to mask vertical surface north of the grid point
	159	REAL(wp) :: mask_top !< flag to mask vertical downward-facing surface
[1]	160
	161	DO i = nxl, nxr
[106]	162	DO j = nysv, nyn
[1]	163	!
	164	!-- Compute horizontal diffusion
[2232]	165	DO k = nzb+1, nzt
	166
[1]	167	!
[2232]	168	!-- Predetermine flag to mask topography and wall-bounded grid points.
	169	!-- It is sufficient to masked only east- and west-facing surfaces, which
	170	!-- need special treatment for the v-component.
	171	flag = MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_0(k,j,i), 2 ) )
	172	mask_east = MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_0(k,j,i+1), 2 ) )
	173	mask_west = MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_0(k,j,i-1), 2 ) )
	174	!
[1]	175	!-- Interpolate eddy diffusivities on staggered gridpoints
[2232]	176	kmxp = 0.25_wp * ( km(k,j,i)+km(k,j,i+1)+km(k,j-1,i)+km(k,j-1,i+1) )
	177	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]	178
[2232]	179	tend(k,j,i) = tend(k,j,i) + ( &
	180	mask_east * kmxp * ( &
	181	( v(k,j,i+1) - v(k,j,i) ) * ddx &
	182	+ ( u(k,j,i+1) - u(k,j-1,i+1) ) * ddy &
	183	) &
	184	- mask_west * kmxm * ( &
	185	( v(k,j,i) - v(k,j,i-1) ) * ddx &
	186	+ ( u(k,j,i) - u(k,j-1,i) ) * ddy &
	187	) &
	188	) * ddx * flag &
	189	+ 2.0_wp * ( &
	190	km(k,j,i) * ( v(k,j+1,i) - v(k,j,i) ) &
	191	- km(k,j-1,i) * ( v(k,j,i) - v(k,j-1,i) ) &
	192	) * ddy2 * flag
	193
[1]	194	ENDDO
	195
	196	!
[2232]	197	!-- Add horizontal momentum flux v'u' at east- (l=2) and west-facing (l=3)
	198	!-- surfaces. Note, in the the flat case, loops won't be entered as
	199	!-- start_index > end_index. Furtermore, note, no vertical natural surfaces
	200	!-- so far.
	201	!-- Default-type surfaces
	202	DO l = 2, 3
	203	surf_s = surf_def_v(l)%start_index(j,i)
	204	surf_e = surf_def_v(l)%end_index(j,i)
	205	DO m = surf_s, surf_e
	206	k = surf_def_v(l)%k(m)
	207	tend(k,j,i) = tend(k,j,i) + &
	208	surf_def_v(l)%mom_flux_uv(m) * ddx
	209	ENDDO
	210	ENDDO
[1]	211	!
[2232]	212	!-- Natural-type surfaces
	213	DO l = 2, 3
	214	surf_s = surf_lsm_v(l)%start_index(j,i)
	215	surf_e = surf_lsm_v(l)%end_index(j,i)
	216	DO m = surf_s, surf_e
	217	k = surf_lsm_v(l)%k(m)
	218	tend(k,j,i) = tend(k,j,i) + &
	219	surf_lsm_v(l)%mom_flux_uv(m) * ddx
	220	ENDDO
	221	ENDDO
[1]	222	!
[2232]	223	!-- Urban-type surfaces
	224	DO l = 2, 3
	225	surf_s = surf_usm_v(l)%start_index(j,i)
	226	surf_e = surf_usm_v(l)%end_index(j,i)
	227	DO m = surf_s, surf_e
	228	k = surf_usm_v(l)%k(m)
	229	tend(k,j,i) = tend(k,j,i) + &
	230	surf_usm_v(l)%mom_flux_uv(m) * ddx
	231	ENDDO
	232	ENDDO
	233	!
	234	!-- Compute vertical diffusion. In case of simulating a surface layer,
	235	!-- respective grid diffusive fluxes are masked (flag 10) within this
	236	!-- loop, and added further below, else, simple gradient approach is
	237	!-- applied. Model top is also mask if top-momentum flux is given.
	238	DO k = nzb+1, nzt
	239	!
	240	!-- Determine flags to mask topography below and above. Flag 2 is
	241	!-- used to mask topography in general, while flag 8 implies also
	242	!-- information about use_surface_fluxes. Flag 9 is used to control
	243	!-- momentum flux at model top.
	244	mask_bottom = MERGE( 1.0_wp, 0.0_wp, &
	245	BTEST( wall_flags_0(k-1,j,i), 8 ) )
	246	mask_top = MERGE( 1.0_wp, 0.0_wp, &
	247	BTEST( wall_flags_0(k+1,j,i), 8 ) ) * &
	248	MERGE( 1.0_wp, 0.0_wp, &
	249	BTEST( wall_flags_0(k+1,j,i), 9 ) )
	250	flag = MERGE( 1.0_wp, 0.0_wp, &
	251	BTEST( wall_flags_0(k,j,i), 2 ) )
	252	!
[1]	253	!-- Interpolate eddy diffusivities on staggered gridpoints
[1340]	254	kmzp = 0.25_wp * &
[1]	255	( km(k,j,i)+km(k+1,j,i)+km(k,j-1,i)+km(k+1,j-1,i) )
[1340]	256	kmzm = 0.25_wp * &
[1]	257	( km(k,j,i)+km(k-1,j,i)+km(k,j-1,i)+km(k-1,j-1,i) )
	258
[1320]	259	tend(k,j,i) = tend(k,j,i) &
	260	& + ( kmzp * ( ( v(k+1,j,i) - v(k,j,i) ) * ddzu(k+1) &
	261	& + ( w(k,j,i) - w(k,j-1,i) ) * ddy &
[2232]	262	& ) * rho_air_zw(k) * mask_top &
[1320]	263	& - kmzm * ( ( v(k,j,i) - v(k-1,j,i) ) * ddzu(k) &
	264	& + ( w(k-1,j,i) - w(k-1,j-1,i) ) * ddy &
[2232]	265	& ) * rho_air_zw(k-1) * mask_bottom &
	266	& ) * ddzw(k) * drho_air(k) * flag
[1]	267	ENDDO
	268
	269	!
	270	!-- Vertical diffusion at the first grid point above the surface,
	271	!-- if the momentum flux at the bottom is given by the Prandtl law
	272	!-- or if it is prescribed by the user.
	273	!-- Difference quotient of the momentum flux is not formed over
	274	!-- half of the grid spacing (2.0*ddzw(k)) any more, since the
[1320]	275	!-- comparison with other (LES) models showed that the values of
[1]	276	!-- the momentum flux becomes too large in this case.
	277	IF ( use_surface_fluxes ) THEN
	278	!
[2232]	279	!-- Default-type surfaces, upward-facing
	280	surf_s = surf_def_h(0)%start_index(j,i)
	281	surf_e = surf_def_h(0)%end_index(j,i)
	282	DO m = surf_s, surf_e
	283	k = surf_def_h(0)%k(m)
[1]	284
[2232]	285	tend(k,j,i) = tend(k,j,i) &
	286	+ ( - ( - surf_def_h(0)%vsws(m) ) &
	287	) * ddzw(k) * drho_air(k)
	288	ENDDO
	289	!
	290	!-- Default-type surfaces, dowward-facing
	291	surf_s = surf_def_h(1)%start_index(j,i)
	292	surf_e = surf_def_h(1)%end_index(j,i)
	293	DO m = surf_s, surf_e
	294	k = surf_def_h(1)%k(m)
[1]	295
[2232]	296	tend(k,j,i) = tend(k,j,i) &
	297	+ ( - surf_def_h(1)%vsws(m) &
	298	) * ddzw(k) * drho_air(k)
	299	ENDDO
[102]	300	!
[2232]	301	!-- Natural-type surfaces, upward-facing
	302	surf_s = surf_lsm_h%start_index(j,i)
	303	surf_e = surf_lsm_h%end_index(j,i)
	304	DO m = surf_s, surf_e
	305	k = surf_lsm_h%k(m)
	306
	307	tend(k,j,i) = tend(k,j,i) &
	308	+ ( - ( - surf_lsm_h%vsws(m) ) &
	309	) * ddzw(k) * drho_air(k)
	310
	311	ENDDO
[102]	312	!
[2232]	313	!-- Urban-type surfaces, upward-facing
	314	surf_s = surf_usm_h%start_index(j,i)
	315	surf_e = surf_usm_h%end_index(j,i)
	316	DO m = surf_s, surf_e
	317	k = surf_usm_h%k(m)
[102]	318
[2232]	319	tend(k,j,i) = tend(k,j,i) &
	320	+ ( - ( - surf_usm_h%vsws(m) ) &
	321	) * ddzw(k) * drho_air(k)
	322
	323	ENDDO
[102]	324	ENDIF
[2232]	325	!
	326	!-- Add momentum flux at model top
[2638]	327	IF ( use_top_fluxes .AND. constant_top_momentumflux ) THEN
[2232]	328	surf_s = surf_def_h(2)%start_index(j,i)
	329	surf_e = surf_def_h(2)%end_index(j,i)
	330	DO m = surf_s, surf_e
[102]	331
[2232]	332	k = surf_def_h(2)%k(m)
	333
	334	tend(k,j,i) = tend(k,j,i) &
	335	+ ( - surf_def_h(2)%vsws(m) ) * ddzw(k) * drho_air(k)
	336	ENDDO
	337	ENDIF
	338
[1]	339	ENDDO
	340	ENDDO
	341
	342	END SUBROUTINE diffusion_v
	343
	344
	345	!------------------------------------------------------------------------------!
[1682]	346	! Description:
	347	! ------------
	348	!> Call for grid point i,j
[1]	349	!------------------------------------------------------------------------------!
[1001]	350	SUBROUTINE diffusion_v_ij( i, j )
[1]	351
[1320]	352	USE arrays_3d, &
[2232]	353	ONLY: ddzu, ddzw, km, tend, u, v, w, drho_air, rho_air_zw
[1320]	354
	355	USE control_parameters, &
[2232]	356	ONLY: constant_top_momentumflux, use_surface_fluxes, &
	357	use_top_fluxes
[1320]	358
	359	USE grid_variables, &
[2232]	360	ONLY: ddx, ddy, ddy2
[1320]	361
	362	USE indices, &
[2232]	363	ONLY: nzb, nzt, wall_flags_0
[1320]	364
	365	USE kinds
[1]	366
[2232]	367	USE surface_mod, &
	368	ONLY : surf_def_h, surf_def_v, surf_lsm_h, surf_lsm_v, surf_usm_h, &
	369	surf_usm_v
	370
[1]	371	IMPLICIT NONE
	372
	373
[2232]	374	INTEGER(iwp) :: i !< running index x direction
	375	INTEGER(iwp) :: j !< running index y direction
	376	INTEGER(iwp) :: k !< running index z direction
	377	INTEGER(iwp) :: l !< running index of surface type, south- or north-facing wall
	378	INTEGER(iwp) :: m !< running index surface elements
	379	INTEGER(iwp) :: surf_e !< End index of surface elements at (j,i)-gridpoint
	380	INTEGER(iwp) :: surf_s !< Start index of surface elements at (j,i)-gridpoint
[1001]	381
[2232]	382	REAL(wp) :: flag !< flag to mask topography grid points
	383	REAL(wp) :: kmxm !<
	384	REAL(wp) :: kmxp !<
	385	REAL(wp) :: kmzm !<
	386	REAL(wp) :: kmzp !<
	387	REAL(wp) :: mask_bottom !< flag to mask vertical upward-facing surface
	388	REAL(wp) :: mask_east !< flag to mask vertical surface south of the grid point
	389	REAL(wp) :: mask_west !< flag to mask vertical surface north of the grid point
	390	REAL(wp) :: mask_top !< flag to mask vertical downward-facing surface
	391
[1]	392	!
	393	!-- Compute horizontal diffusion
[2232]	394	DO k = nzb+1, nzt
[1]	395	!
[2232]	396	!-- Predetermine flag to mask topography and wall-bounded grid points.
	397	!-- It is sufficient to masked only east- and west-facing surfaces, which
	398	!-- need special treatment for the v-component.
	399	flag = MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_0(k,j,i), 2 ) )
	400	mask_east = MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_0(k,j,i+1), 2 ) )
	401	mask_west = MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_0(k,j,i-1), 2 ) )
	402	!
[1]	403	!-- Interpolate eddy diffusivities on staggered gridpoints
[1340]	404	kmxp = 0.25_wp * ( km(k,j,i)+km(k,j,i+1)+km(k,j-1,i)+km(k,j-1,i+1) )
	405	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]	406
[2232]	407	tend(k,j,i) = tend(k,j,i) + ( &
	408	mask_east * kmxp * ( &
	409	( v(k,j,i+1) - v(k,j,i) ) * ddx &
	410	+ ( u(k,j,i+1) - u(k,j-1,i+1) ) * ddy &
	411	) &
	412	- mask_west * kmxm * ( &
	413	( v(k,j,i) - v(k,j,i-1) ) * ddx &
	414	+ ( u(k,j,i) - u(k,j-1,i) ) * ddy &
	415	) &
	416	) * ddx * flag &
	417	+ 2.0_wp * ( &
	418	km(k,j,i) * ( v(k,j+1,i) - v(k,j,i) ) &
	419	- km(k,j-1,i) * ( v(k,j,i) - v(k,j-1,i) ) &
	420	) * ddy2 * flag
[1]	421	ENDDO
	422
	423	!
[2232]	424	!-- Add horizontal momentum flux v'u' at east- (l=2) and west-facing (l=3)
	425	!-- surfaces. Note, in the the flat case, loops won't be entered as
	426	!-- start_index > end_index. Furtermore, note, no vertical natural surfaces
	427	!-- so far.
	428	!-- Default-type surfaces
	429	DO l = 2, 3
	430	surf_s = surf_def_v(l)%start_index(j,i)
	431	surf_e = surf_def_v(l)%end_index(j,i)
	432	DO m = surf_s, surf_e
	433	k = surf_def_v(l)%k(m)
	434	tend(k,j,i) = tend(k,j,i) + surf_def_v(l)%mom_flux_uv(m) * ddx
	435	ENDDO
	436	ENDDO
[51]	437	!
[2232]	438	!-- Natural-type surfaces
	439	DO l = 2, 3
	440	surf_s = surf_lsm_v(l)%start_index(j,i)
	441	surf_e = surf_lsm_v(l)%end_index(j,i)
	442	DO m = surf_s, surf_e
	443	k = surf_lsm_v(l)%k(m)
	444	tend(k,j,i) = tend(k,j,i) + surf_lsm_v(l)%mom_flux_uv(m) * ddx
	445	ENDDO
	446	ENDDO
[1]	447	!
[2232]	448	!-- Urban-type surfaces
	449	DO l = 2, 3
	450	surf_s = surf_usm_v(l)%start_index(j,i)
	451	surf_e = surf_usm_v(l)%end_index(j,i)
	452	DO m = surf_s, surf_e
	453	k = surf_usm_v(l)%k(m)
	454	tend(k,j,i) = tend(k,j,i) + surf_usm_v(l)%mom_flux_uv(m) * ddx
	455	ENDDO
	456	ENDDO
[1]	457	!
[2232]	458	!-- Compute vertical diffusion. In case of simulating a surface layer,
	459	!-- respective grid diffusive fluxes are masked (flag 8) within this
	460	!-- loop, and added further below, else, simple gradient approach is
	461	!-- applied. Model top is also mask if top-momentum flux is given.
	462	DO k = nzb+1, nzt
	463	!
	464	!-- Determine flags to mask topography below and above. Flag 2 is
	465	!-- used to mask topography in general, while flag 10 implies also
	466	!-- information about use_surface_fluxes. Flag 9 is used to control
	467	!-- momentum flux at model top.
	468	mask_bottom = MERGE( 1.0_wp, 0.0_wp, &
	469	BTEST( wall_flags_0(k-1,j,i), 8 ) )
	470	mask_top = MERGE( 1.0_wp, 0.0_wp, &
	471	BTEST( wall_flags_0(k+1,j,i), 8 ) ) * &
	472	MERGE( 1.0_wp, 0.0_wp, &
	473	BTEST( wall_flags_0(k+1,j,i), 9 ) )
	474	flag = MERGE( 1.0_wp, 0.0_wp, &
	475	BTEST( wall_flags_0(k,j,i), 2 ) )
	476	!
[1]	477	!-- Interpolate eddy diffusivities on staggered gridpoints
[1340]	478	kmzp = 0.25_wp * ( km(k,j,i)+km(k+1,j,i)+km(k,j-1,i)+km(k+1,j-1,i) )
	479	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]	480
[1320]	481	tend(k,j,i) = tend(k,j,i) &
	482	& + ( kmzp * ( ( v(k+1,j,i) - v(k,j,i) ) * ddzu(k+1) &
	483	& + ( w(k,j,i) - w(k,j-1,i) ) * ddy &
[2232]	484	& ) * rho_air_zw(k) * mask_top &
[1320]	485	& - kmzm * ( ( v(k,j,i) - v(k-1,j,i) ) * ddzu(k) &
	486	& + ( w(k-1,j,i) - w(k-1,j-1,i) ) * ddy &
[2232]	487	& ) * rho_air_zw(k-1) * mask_bottom &
	488	& ) * ddzw(k) * drho_air(k) * flag
[1]	489	ENDDO
	490
	491	!
	492	!-- Vertical diffusion at the first grid point above the surface, if the
	493	!-- momentum flux at the bottom is given by the Prandtl law or if it is
	494	!-- prescribed by the user.
	495	!-- Difference quotient of the momentum flux is not formed over half of
	496	!-- the grid spacing (2.0*ddzw(k)) any more, since the comparison with
[1320]	497	!-- other (LES) models showed that the values of the momentum flux becomes
[1]	498	!-- too large in this case.
	499	IF ( use_surface_fluxes ) THEN
	500	!
[2232]	501	!-- Default-type surfaces, upward-facing
	502	surf_s = surf_def_h(0)%start_index(j,i)
	503	surf_e = surf_def_h(0)%end_index(j,i)
	504	DO m = surf_s, surf_e
	505	k = surf_def_h(0)%k(m)
[1]	506
[2232]	507	tend(k,j,i) = tend(k,j,i) &
	508	+ ( - ( - surf_def_h(0)%vsws(m) ) &
	509	) * ddzw(k) * drho_air(k)
	510	ENDDO
	511	!
	512	!-- Default-type surfaces, dowward-facing
	513	surf_s = surf_def_h(1)%start_index(j,i)
	514	surf_e = surf_def_h(1)%end_index(j,i)
	515	DO m = surf_s, surf_e
	516	k = surf_def_h(1)%k(m)
[1]	517
[2232]	518	tend(k,j,i) = tend(k,j,i) &
	519	+ ( - surf_def_h(1)%vsws(m) &
	520	) * ddzw(k) * drho_air(k)
	521	ENDDO
[102]	522	!
[2232]	523	!-- Natural-type surfaces, upward-facing
	524	surf_s = surf_lsm_h%start_index(j,i)
	525	surf_e = surf_lsm_h%end_index(j,i)
	526	DO m = surf_s, surf_e
	527	k = surf_lsm_h%k(m)
	528
	529	tend(k,j,i) = tend(k,j,i) &
	530	+ ( - ( - surf_lsm_h%vsws(m) ) &
	531	) * ddzw(k) * drho_air(k)
	532
	533	ENDDO
[102]	534	!
[2232]	535	!-- Urban-type surfaces, upward-facing
	536	surf_s = surf_usm_h%start_index(j,i)
	537	surf_e = surf_usm_h%end_index(j,i)
	538	DO m = surf_s, surf_e
	539	k = surf_usm_h%k(m)
[102]	540
[2232]	541	tend(k,j,i) = tend(k,j,i) &
	542	+ ( - ( - surf_usm_h%vsws(m) ) &
	543	) * ddzw(k) * drho_air(k)
	544
	545	ENDDO
[102]	546	ENDIF
[2232]	547	!
	548	!-- Add momentum flux at model top
[2638]	549	IF ( use_top_fluxes .AND. constant_top_momentumflux ) THEN
[2232]	550	surf_s = surf_def_h(2)%start_index(j,i)
	551	surf_e = surf_def_h(2)%end_index(j,i)
	552	DO m = surf_s, surf_e
[102]	553
[2232]	554	k = surf_def_h(2)%k(m)
	555
	556	tend(k,j,i) = tend(k,j,i) &
	557	+ ( - surf_def_h(2)%vsws(m) ) * ddzw(k) * drho_air(k)
	558	ENDDO
	559	ENDIF
	560
[1]	561	END SUBROUTINE diffusion_v_ij
	562
[1321]	563	END MODULE diffusion_v_mod

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