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source: palm/trunk/SOURCE/diffusion_v.f90 @ 2232

Last change on this file since 2232 was 2232, checked in by suehring, 7 years ago
Adjustments according new topography and surface-modelling concept implemented
Property svn:keywords set to `Id`
File size: 23.8 KB

Rev	Line
[1873]	1	!> @file diffusion_v.f90
[2000]	2	!------------------------------------------------------------------------------!
[1036]	3	! This file is part of PALM.
	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	!
[2101]	17	! Copyright 1997-2017 Leibniz Universitaet Hannover
[2000]	18	!------------------------------------------------------------------------------!
[1036]	19	!
[484]	20	! Current revisions:
[1]	21	! -----------------
[2232]	22	! Adjustments to new topography and surface concept
[1341]	23	!
[1321]	24	! Former revisions:
	25	! -----------------
	26	! $Id: diffusion_v.f90 2232 2017-05-30 17:47:52Z suehring $
	27	!
[2119]	28	! 2118 2017-01-17 16:38:49Z raasch
	29	! OpenACC version of subroutine removed
	30	!
[2038]	31	! 2037 2016-10-26 11:15:40Z knoop
	32	! Anelastic approximation implemented
	33	!
[2001]	34	! 2000 2016-08-20 18:09:15Z knoop
	35	! Forced header and separation lines into 80 columns
	36	!
[1874]	37	! 1873 2016-04-18 14:50:06Z maronga
	38	! Module renamed (removed _mod)
	39	!
[1851]	40	! 1850 2016-04-08 13:29:27Z maronga
	41	! Module renamed
	42	!
[1741]	43	! 1740 2016-01-13 08:19:40Z raasch
	44	! unnecessary calculations of kmzm and kmzp in wall bounded parts removed
	45	!
[1683]	46	! 1682 2015-10-07 23:56:08Z knoop
	47	! Code annotations made doxygen readable
	48	!
[1341]	49	! 1340 2014-03-25 19:45:13Z kanani
	50	! REAL constants defined as wp-kind
	51	!
[1321]	52	! 1320 2014-03-20 08:40:49Z raasch
[1320]	53	! ONLY-attribute added to USE-statements,
	54	! kind-parameters added to all INTEGER and REAL declaration statements,
	55	! kinds are defined in new module kinds,
	56	! revision history before 2012 removed,
	57	! comment fields (!:) to be used for variable explanations added to
	58	! all variable declaration statements
[1321]	59	!
[1258]	60	! 1257 2013-11-08 15:18:40Z raasch
	61	! openacc loop and loop vector clauses removed, declare create moved after
	62	! the FORTRAN declaration statement
	63	!
[1132]	64	! 1128 2013-04-12 06:19:32Z raasch
	65	! loop index bounds in accelerator version replaced by i_left, i_right, j_south,
	66	! j_north
	67	!
[1037]	68	! 1036 2012-10-22 13:43:42Z raasch
	69	! code put under GPL (PALM 3.9)
	70	!
[1017]	71	! 1015 2012-09-27 09:23:24Z raasch
	72	! accelerator version (*_acc) added
	73	!
[1002]	74	! 1001 2012-09-13 14:08:46Z raasch
	75	! arrays comunicated by module instead of parameter list
	76	!
[979]	77	! 978 2012-08-09 08:28:32Z fricke
	78	! outflow damping layer removed
	79	! kmxm_x/_y and kmxp_x/_y change to kmxm and kmxp
	80	!
[1]	81	! Revision 1.1 1997/09/12 06:24:01 raasch
	82	! Initial revision
	83	!
	84	!
	85	! Description:
	86	! ------------
[1682]	87	!> Diffusion term of the v-component
[1]	88	!------------------------------------------------------------------------------!
[1682]	89	MODULE diffusion_v_mod
	90
[1]	91
	92	PRIVATE
[2118]	93	PUBLIC diffusion_v
[1]	94
	95	INTERFACE diffusion_v
	96	MODULE PROCEDURE diffusion_v
	97	MODULE PROCEDURE diffusion_v_ij
	98	END INTERFACE diffusion_v
	99
	100	CONTAINS
	101
	102
	103	!------------------------------------------------------------------------------!
[1682]	104	! Description:
	105	! ------------
	106	!> Call for all grid points
[1]	107	!------------------------------------------------------------------------------!
[1001]	108	SUBROUTINE diffusion_v
[1]	109
[1320]	110	USE arrays_3d, &
[2232]	111	ONLY: ddzu, ddzw, km, tend, u, v, w, drho_air, rho_air_zw
[1320]	112
	113	USE control_parameters, &
[2232]	114	ONLY: constant_top_momentumflux, use_surface_fluxes, &
[1320]	115	use_top_fluxes
	116
	117	USE grid_variables, &
[2232]	118	ONLY: ddx, ddy, ddy2
[1320]	119
	120	USE indices, &
[2232]	121	ONLY: nxl, nxr, nyn, nys, nysv, nzb, nzt, wall_flags_0
[1320]	122
	123	USE kinds
[1]	124
[2232]	125	USE surface_mod, &
	126	ONLY : surf_def_h, surf_def_v, surf_lsm_h, surf_lsm_v, surf_usm_h, &
	127	surf_usm_v
	128
[1]	129	IMPLICIT NONE
	130
[2232]	131	INTEGER(iwp) :: i !< running index x direction
	132	INTEGER(iwp) :: j !< running index y direction
	133	INTEGER(iwp) :: k !< running index z direction
	134	INTEGER(iwp) :: l !< running index of surface type, south- or north-facing wall
	135	INTEGER(iwp) :: m !< running index surface elements
	136	INTEGER(iwp) :: surf_e !< End index of surface elements at (j,i)-gridpoint
	137	INTEGER(iwp) :: surf_s !< Start index of surface elements at (j,i)-gridpoint
[1001]	138
[2232]	139	REAL(wp) :: flag !< flag to mask topography grid points
	140	REAL(wp) :: kmxm !<
	141	REAL(wp) :: kmxp !<
	142	REAL(wp) :: kmzm !<
	143	REAL(wp) :: kmzp !<
	144	REAL(wp) :: mask_bottom !< flag to mask vertical upward-facing surface
	145	REAL(wp) :: mask_east !< flag to mask vertical surface south of the grid point
	146	REAL(wp) :: mask_west !< flag to mask vertical surface north of the grid point
	147	REAL(wp) :: mask_top !< flag to mask vertical downward-facing surface
[1]	148
	149	DO i = nxl, nxr
[106]	150	DO j = nysv, nyn
[1]	151	!
	152	!-- Compute horizontal diffusion
[2232]	153	DO k = nzb+1, nzt
	154
[1]	155	!
[2232]	156	!-- Predetermine flag to mask topography and wall-bounded grid points.
	157	!-- It is sufficient to masked only east- and west-facing surfaces, which
	158	!-- need special treatment for the v-component.
	159	flag = MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_0(k,j,i), 2 ) )
	160	mask_east = MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_0(k,j,i+1), 2 ) )
	161	mask_west = MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_0(k,j,i-1), 2 ) )
	162	!
[1]	163	!-- Interpolate eddy diffusivities on staggered gridpoints
[2232]	164	kmxp = 0.25_wp * ( km(k,j,i)+km(k,j,i+1)+km(k,j-1,i)+km(k,j-1,i+1) )
	165	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]	166
[2232]	167	tend(k,j,i) = tend(k,j,i) + ( &
	168	mask_east * kmxp * ( &
	169	( v(k,j,i+1) - v(k,j,i) ) * ddx &
	170	+ ( u(k,j,i+1) - u(k,j-1,i+1) ) * ddy &
	171	) &
	172	- mask_west * kmxm * ( &
	173	( v(k,j,i) - v(k,j,i-1) ) * ddx &
	174	+ ( u(k,j,i) - u(k,j-1,i) ) * ddy &
	175	) &
	176	) * ddx * flag &
	177	+ 2.0_wp * ( &
	178	km(k,j,i) * ( v(k,j+1,i) - v(k,j,i) ) &
	179	- km(k,j-1,i) * ( v(k,j,i) - v(k,j-1,i) ) &
	180	) * ddy2 * flag
	181
[1]	182	ENDDO
	183
	184	!
[2232]	185	!-- Add horizontal momentum flux v'u' at east- (l=2) and west-facing (l=3)
	186	!-- surfaces. Note, in the the flat case, loops won't be entered as
	187	!-- start_index > end_index. Furtermore, note, no vertical natural surfaces
	188	!-- so far.
	189	!-- Default-type surfaces
	190	DO l = 2, 3
	191	surf_s = surf_def_v(l)%start_index(j,i)
	192	surf_e = surf_def_v(l)%end_index(j,i)
	193	DO m = surf_s, surf_e
	194	k = surf_def_v(l)%k(m)
	195	tend(k,j,i) = tend(k,j,i) + &
	196	surf_def_v(l)%mom_flux_uv(m) * ddx
	197	ENDDO
	198	ENDDO
[1]	199	!
[2232]	200	!-- Natural-type surfaces
	201	DO l = 2, 3
	202	surf_s = surf_lsm_v(l)%start_index(j,i)
	203	surf_e = surf_lsm_v(l)%end_index(j,i)
	204	DO m = surf_s, surf_e
	205	k = surf_lsm_v(l)%k(m)
	206	tend(k,j,i) = tend(k,j,i) + &
	207	surf_lsm_v(l)%mom_flux_uv(m) * ddx
	208	ENDDO
	209	ENDDO
[1]	210	!
[2232]	211	!-- Urban-type surfaces
	212	DO l = 2, 3
	213	surf_s = surf_usm_v(l)%start_index(j,i)
	214	surf_e = surf_usm_v(l)%end_index(j,i)
	215	DO m = surf_s, surf_e
	216	k = surf_usm_v(l)%k(m)
	217	tend(k,j,i) = tend(k,j,i) + &
	218	surf_usm_v(l)%mom_flux_uv(m) * ddx
	219	ENDDO
	220	ENDDO
	221	!
	222	!-- Compute vertical diffusion. In case of simulating a surface layer,
	223	!-- respective grid diffusive fluxes are masked (flag 10) within this
	224	!-- loop, and added further below, else, simple gradient approach is
	225	!-- applied. Model top is also mask if top-momentum flux is given.
	226	DO k = nzb+1, nzt
	227	!
	228	!-- Determine flags to mask topography below and above. Flag 2 is
	229	!-- used to mask topography in general, while flag 8 implies also
	230	!-- information about use_surface_fluxes. Flag 9 is used to control
	231	!-- momentum flux at model top.
	232	mask_bottom = MERGE( 1.0_wp, 0.0_wp, &
	233	BTEST( wall_flags_0(k-1,j,i), 8 ) )
	234	mask_top = MERGE( 1.0_wp, 0.0_wp, &
	235	BTEST( wall_flags_0(k+1,j,i), 8 ) ) * &
	236	MERGE( 1.0_wp, 0.0_wp, &
	237	BTEST( wall_flags_0(k+1,j,i), 9 ) )
	238	flag = MERGE( 1.0_wp, 0.0_wp, &
	239	BTEST( wall_flags_0(k,j,i), 2 ) )
	240	!
[1]	241	!-- Interpolate eddy diffusivities on staggered gridpoints
[1340]	242	kmzp = 0.25_wp * &
[1]	243	( km(k,j,i)+km(k+1,j,i)+km(k,j-1,i)+km(k+1,j-1,i) )
[1340]	244	kmzm = 0.25_wp * &
[1]	245	( km(k,j,i)+km(k-1,j,i)+km(k,j-1,i)+km(k-1,j-1,i) )
	246
[1320]	247	tend(k,j,i) = tend(k,j,i) &
	248	& + ( kmzp * ( ( v(k+1,j,i) - v(k,j,i) ) * ddzu(k+1) &
	249	& + ( w(k,j,i) - w(k,j-1,i) ) * ddy &
[2232]	250	& ) * rho_air_zw(k) * mask_top &
[1320]	251	& - kmzm * ( ( v(k,j,i) - v(k-1,j,i) ) * ddzu(k) &
	252	& + ( w(k-1,j,i) - w(k-1,j-1,i) ) * ddy &
[2232]	253	& ) * rho_air_zw(k-1) * mask_bottom &
	254	& ) * ddzw(k) * drho_air(k) * flag
[1]	255	ENDDO
	256
	257	!
	258	!-- Vertical diffusion at the first grid point above the surface,
	259	!-- if the momentum flux at the bottom is given by the Prandtl law
	260	!-- or if it is prescribed by the user.
	261	!-- Difference quotient of the momentum flux is not formed over
	262	!-- half of the grid spacing (2.0*ddzw(k)) any more, since the
[1320]	263	!-- comparison with other (LES) models showed that the values of
[1]	264	!-- the momentum flux becomes too large in this case.
	265	IF ( use_surface_fluxes ) THEN
	266	!
[2232]	267	!-- Default-type surfaces, upward-facing
	268	surf_s = surf_def_h(0)%start_index(j,i)
	269	surf_e = surf_def_h(0)%end_index(j,i)
	270	DO m = surf_s, surf_e
	271	k = surf_def_h(0)%k(m)
[1]	272
[2232]	273	tend(k,j,i) = tend(k,j,i) &
	274	+ ( - ( - surf_def_h(0)%vsws(m) ) &
	275	) * ddzw(k) * drho_air(k)
	276	ENDDO
	277	!
	278	!-- Default-type surfaces, dowward-facing
	279	surf_s = surf_def_h(1)%start_index(j,i)
	280	surf_e = surf_def_h(1)%end_index(j,i)
	281	DO m = surf_s, surf_e
	282	k = surf_def_h(1)%k(m)
[1]	283
[2232]	284	tend(k,j,i) = tend(k,j,i) &
	285	+ ( - surf_def_h(1)%vsws(m) &
	286	) * ddzw(k) * drho_air(k)
	287	ENDDO
[102]	288	!
[2232]	289	!-- Natural-type surfaces, upward-facing
	290	surf_s = surf_lsm_h%start_index(j,i)
	291	surf_e = surf_lsm_h%end_index(j,i)
	292	DO m = surf_s, surf_e
	293	k = surf_lsm_h%k(m)
	294
	295	tend(k,j,i) = tend(k,j,i) &
	296	+ ( - ( - surf_lsm_h%vsws(m) ) &
	297	) * ddzw(k) * drho_air(k)
	298
	299	ENDDO
[102]	300	!
[2232]	301	!-- Urban-type surfaces, upward-facing
	302	surf_s = surf_usm_h%start_index(j,i)
	303	surf_e = surf_usm_h%end_index(j,i)
	304	DO m = surf_s, surf_e
	305	k = surf_usm_h%k(m)
[102]	306
[2232]	307	tend(k,j,i) = tend(k,j,i) &
	308	+ ( - ( - surf_usm_h%vsws(m) ) &
	309	) * ddzw(k) * drho_air(k)
	310
	311	ENDDO
[102]	312	ENDIF
[2232]	313	!
	314	!-- Add momentum flux at model top
	315	IF ( use_top_fluxes ) THEN
	316	surf_s = surf_def_h(2)%start_index(j,i)
	317	surf_e = surf_def_h(2)%end_index(j,i)
	318	DO m = surf_s, surf_e
[102]	319
[2232]	320	k = surf_def_h(2)%k(m)
	321
	322	tend(k,j,i) = tend(k,j,i) &
	323	+ ( - surf_def_h(2)%vsws(m) ) * ddzw(k) * drho_air(k)
	324	ENDDO
	325	ENDIF
	326
[1]	327	ENDDO
	328	ENDDO
	329
	330	END SUBROUTINE diffusion_v
	331
	332
	333	!------------------------------------------------------------------------------!
[1682]	334	! Description:
	335	! ------------
	336	!> Call for grid point i,j
[1]	337	!------------------------------------------------------------------------------!
[1001]	338	SUBROUTINE diffusion_v_ij( i, j )
[1]	339
[1320]	340	USE arrays_3d, &
[2232]	341	ONLY: ddzu, ddzw, km, tend, u, v, w, drho_air, rho_air_zw
[1320]	342
	343	USE control_parameters, &
[2232]	344	ONLY: constant_top_momentumflux, use_surface_fluxes, &
	345	use_top_fluxes
[1320]	346
	347	USE grid_variables, &
[2232]	348	ONLY: ddx, ddy, ddy2
[1320]	349
	350	USE indices, &
[2232]	351	ONLY: nzb, nzt, wall_flags_0
[1320]	352
	353	USE kinds
[1]	354
[2232]	355	USE surface_mod, &
	356	ONLY : surf_def_h, surf_def_v, surf_lsm_h, surf_lsm_v, surf_usm_h, &
	357	surf_usm_v
	358
[1]	359	IMPLICIT NONE
	360
	361
[2232]	362	INTEGER(iwp) :: i !< running index x direction
	363	INTEGER(iwp) :: j !< running index y direction
	364	INTEGER(iwp) :: k !< running index z direction
	365	INTEGER(iwp) :: l !< running index of surface type, south- or north-facing wall
	366	INTEGER(iwp) :: m !< running index surface elements
	367	INTEGER(iwp) :: surf_e !< End index of surface elements at (j,i)-gridpoint
	368	INTEGER(iwp) :: surf_s !< Start index of surface elements at (j,i)-gridpoint
[1001]	369
[2232]	370	REAL(wp) :: flag !< flag to mask topography grid points
	371	REAL(wp) :: kmxm !<
	372	REAL(wp) :: kmxp !<
	373	REAL(wp) :: kmzm !<
	374	REAL(wp) :: kmzp !<
	375	REAL(wp) :: mask_bottom !< flag to mask vertical upward-facing surface
	376	REAL(wp) :: mask_east !< flag to mask vertical surface south of the grid point
	377	REAL(wp) :: mask_west !< flag to mask vertical surface north of the grid point
	378	REAL(wp) :: mask_top !< flag to mask vertical downward-facing surface
	379
[1]	380	!
	381	!-- Compute horizontal diffusion
[2232]	382	DO k = nzb+1, nzt
[1]	383	!
[2232]	384	!-- Predetermine flag to mask topography and wall-bounded grid points.
	385	!-- It is sufficient to masked only east- and west-facing surfaces, which
	386	!-- need special treatment for the v-component.
	387	flag = MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_0(k,j,i), 2 ) )
	388	mask_east = MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_0(k,j,i+1), 2 ) )
	389	mask_west = MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_0(k,j,i-1), 2 ) )
	390	!
[1]	391	!-- Interpolate eddy diffusivities on staggered gridpoints
[1340]	392	kmxp = 0.25_wp * ( km(k,j,i)+km(k,j,i+1)+km(k,j-1,i)+km(k,j-1,i+1) )
	393	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]	394
[2232]	395	tend(k,j,i) = tend(k,j,i) + ( &
	396	mask_east * kmxp * ( &
	397	( v(k,j,i+1) - v(k,j,i) ) * ddx &
	398	+ ( u(k,j,i+1) - u(k,j-1,i+1) ) * ddy &
	399	) &
	400	- mask_west * kmxm * ( &
	401	( v(k,j,i) - v(k,j,i-1) ) * ddx &
	402	+ ( u(k,j,i) - u(k,j-1,i) ) * ddy &
	403	) &
	404	) * ddx * flag &
	405	+ 2.0_wp * ( &
	406	km(k,j,i) * ( v(k,j+1,i) - v(k,j,i) ) &
	407	- km(k,j-1,i) * ( v(k,j,i) - v(k,j-1,i) ) &
	408	) * ddy2 * flag
[1]	409	ENDDO
	410
	411	!
[2232]	412	!-- Add horizontal momentum flux v'u' at east- (l=2) and west-facing (l=3)
	413	!-- surfaces. Note, in the the flat case, loops won't be entered as
	414	!-- start_index > end_index. Furtermore, note, no vertical natural surfaces
	415	!-- so far.
	416	!-- Default-type surfaces
	417	DO l = 2, 3
	418	surf_s = surf_def_v(l)%start_index(j,i)
	419	surf_e = surf_def_v(l)%end_index(j,i)
	420	DO m = surf_s, surf_e
	421	k = surf_def_v(l)%k(m)
	422	tend(k,j,i) = tend(k,j,i) + surf_def_v(l)%mom_flux_uv(m) * ddx
	423	ENDDO
	424	ENDDO
[51]	425	!
[2232]	426	!-- Natural-type surfaces
	427	DO l = 2, 3
	428	surf_s = surf_lsm_v(l)%start_index(j,i)
	429	surf_e = surf_lsm_v(l)%end_index(j,i)
	430	DO m = surf_s, surf_e
	431	k = surf_lsm_v(l)%k(m)
	432	tend(k,j,i) = tend(k,j,i) + surf_lsm_v(l)%mom_flux_uv(m) * ddx
	433	ENDDO
	434	ENDDO
[1]	435	!
[2232]	436	!-- Urban-type surfaces
	437	DO l = 2, 3
	438	surf_s = surf_usm_v(l)%start_index(j,i)
	439	surf_e = surf_usm_v(l)%end_index(j,i)
	440	DO m = surf_s, surf_e
	441	k = surf_usm_v(l)%k(m)
	442	tend(k,j,i) = tend(k,j,i) + surf_usm_v(l)%mom_flux_uv(m) * ddx
	443	ENDDO
	444	ENDDO
[1]	445	!
[2232]	446	!-- Compute vertical diffusion. In case of simulating a surface layer,
	447	!-- respective grid diffusive fluxes are masked (flag 8) within this
	448	!-- loop, and added further below, else, simple gradient approach is
	449	!-- applied. Model top is also mask if top-momentum flux is given.
	450	DO k = nzb+1, nzt
	451	!
	452	!-- Determine flags to mask topography below and above. Flag 2 is
	453	!-- used to mask topography in general, while flag 10 implies also
	454	!-- information about use_surface_fluxes. Flag 9 is used to control
	455	!-- momentum flux at model top.
	456	mask_bottom = MERGE( 1.0_wp, 0.0_wp, &
	457	BTEST( wall_flags_0(k-1,j,i), 8 ) )
	458	mask_top = MERGE( 1.0_wp, 0.0_wp, &
	459	BTEST( wall_flags_0(k+1,j,i), 8 ) ) * &
	460	MERGE( 1.0_wp, 0.0_wp, &
	461	BTEST( wall_flags_0(k+1,j,i), 9 ) )
	462	flag = MERGE( 1.0_wp, 0.0_wp, &
	463	BTEST( wall_flags_0(k,j,i), 2 ) )
	464	!
[1]	465	!-- Interpolate eddy diffusivities on staggered gridpoints
[1340]	466	kmzp = 0.25_wp * ( km(k,j,i)+km(k+1,j,i)+km(k,j-1,i)+km(k+1,j-1,i) )
	467	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]	468
[1320]	469	tend(k,j,i) = tend(k,j,i) &
	470	& + ( kmzp * ( ( v(k+1,j,i) - v(k,j,i) ) * ddzu(k+1) &
	471	& + ( w(k,j,i) - w(k,j-1,i) ) * ddy &
[2232]	472	& ) * rho_air_zw(k) * mask_top &
[1320]	473	& - kmzm * ( ( v(k,j,i) - v(k-1,j,i) ) * ddzu(k) &
	474	& + ( w(k-1,j,i) - w(k-1,j-1,i) ) * ddy &
[2232]	475	& ) * rho_air_zw(k-1) * mask_bottom &
	476	& ) * ddzw(k) * drho_air(k) * flag
[1]	477	ENDDO
	478
	479	!
	480	!-- Vertical diffusion at the first grid point above the surface, if the
	481	!-- momentum flux at the bottom is given by the Prandtl law or if it is
	482	!-- prescribed by the user.
	483	!-- Difference quotient of the momentum flux is not formed over half of
	484	!-- the grid spacing (2.0*ddzw(k)) any more, since the comparison with
[1320]	485	!-- other (LES) models showed that the values of the momentum flux becomes
[1]	486	!-- too large in this case.
	487	IF ( use_surface_fluxes ) THEN
	488	!
[2232]	489	!-- Default-type surfaces, upward-facing
	490	surf_s = surf_def_h(0)%start_index(j,i)
	491	surf_e = surf_def_h(0)%end_index(j,i)
	492	DO m = surf_s, surf_e
	493	k = surf_def_h(0)%k(m)
[1]	494
[2232]	495	tend(k,j,i) = tend(k,j,i) &
	496	+ ( - ( - surf_def_h(0)%vsws(m) ) &
	497	) * ddzw(k) * drho_air(k)
	498	ENDDO
	499	!
	500	!-- Default-type surfaces, dowward-facing
	501	surf_s = surf_def_h(1)%start_index(j,i)
	502	surf_e = surf_def_h(1)%end_index(j,i)
	503	DO m = surf_s, surf_e
	504	k = surf_def_h(1)%k(m)
[1]	505
[2232]	506	tend(k,j,i) = tend(k,j,i) &
	507	+ ( - surf_def_h(1)%vsws(m) &
	508	) * ddzw(k) * drho_air(k)
	509	ENDDO
[102]	510	!
[2232]	511	!-- Natural-type surfaces, upward-facing
	512	surf_s = surf_lsm_h%start_index(j,i)
	513	surf_e = surf_lsm_h%end_index(j,i)
	514	DO m = surf_s, surf_e
	515	k = surf_lsm_h%k(m)
	516
	517	tend(k,j,i) = tend(k,j,i) &
	518	+ ( - ( - surf_lsm_h%vsws(m) ) &
	519	) * ddzw(k) * drho_air(k)
	520
	521	ENDDO
[102]	522	!
[2232]	523	!-- Urban-type surfaces, upward-facing
	524	surf_s = surf_usm_h%start_index(j,i)
	525	surf_e = surf_usm_h%end_index(j,i)
	526	DO m = surf_s, surf_e
	527	k = surf_usm_h%k(m)
[102]	528
[2232]	529	tend(k,j,i) = tend(k,j,i) &
	530	+ ( - ( - surf_usm_h%vsws(m) ) &
	531	) * ddzw(k) * drho_air(k)
	532
	533	ENDDO
[102]	534	ENDIF
[2232]	535	!
	536	!-- Add momentum flux at model top
	537	IF ( use_top_fluxes ) THEN
	538	surf_s = surf_def_h(2)%start_index(j,i)
	539	surf_e = surf_def_h(2)%end_index(j,i)
	540	DO m = surf_s, surf_e
[102]	541
[2232]	542	k = surf_def_h(2)%k(m)
	543
	544	tend(k,j,i) = tend(k,j,i) &
	545	+ ( - surf_def_h(2)%vsws(m) ) * ddzw(k) * drho_air(k)
	546	ENDDO
	547	ENDIF
	548
[1]	549	END SUBROUTINE diffusion_v_ij
	550
[1321]	551	END MODULE diffusion_v_mod

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