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source: palm/trunk/SOURCE/diffusion_v.f90 @ 4351

Last change on this file since 4351 was 4346, checked in by motisi, 5 years ago
Introduction of wall_flags_total_0, which currently sets bits based on static topography information used in wall_flags_static_0
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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	!
[3655]	17	! Copyright 1997-2019 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 4346 2019-12-18 11:55:56Z oliver.maas $
[4346]	27	! Introduction of wall_flags_total_0, which currently sets bits based on static
	28	! topography information used in wall_flags_static_0
	29	!
	30	! 4329 2019-12-10 15:46:36Z motisi
[4329]	31	! Renamed wall_flags_0 to wall_flags_static_0
	32	!
	33	! 4182 2019-08-22 15:20:23Z scharf
[4182]	34	! Corrected "Former revisions" section
	35	!
	36	! 3655 2019-01-07 16:51:22Z knoop
[3634]	37	! OpenACC port for SPEC
[2716]	38	!
[4182]	39	! Revision 1.1 1997/09/12 06:24:01 raasch
	40	! Initial revision
	41	!
	42	!
[1]	43	! Description:
	44	! ------------
[1682]	45	!> Diffusion term of the v-component
[1]	46	!------------------------------------------------------------------------------!
[1682]	47	MODULE diffusion_v_mod
	48
[1]	49
	50	PRIVATE
[2118]	51	PUBLIC diffusion_v
[1]	52
	53	INTERFACE diffusion_v
	54	MODULE PROCEDURE diffusion_v
	55	MODULE PROCEDURE diffusion_v_ij
	56	END INTERFACE diffusion_v
	57
	58	CONTAINS
	59
	60
	61	!------------------------------------------------------------------------------!
[1682]	62	! Description:
	63	! ------------
	64	!> Call for all grid points
[1]	65	!------------------------------------------------------------------------------!
[1001]	66	SUBROUTINE diffusion_v
[1]	67
[1320]	68	USE arrays_3d, &
[2232]	69	ONLY: ddzu, ddzw, km, tend, u, v, w, drho_air, rho_air_zw
[1320]	70
	71	USE control_parameters, &
[2232]	72	ONLY: constant_top_momentumflux, use_surface_fluxes, &
[1320]	73	use_top_fluxes
	74
	75	USE grid_variables, &
[2232]	76	ONLY: ddx, ddy, ddy2
[1320]	77
	78	USE indices, &
[4346]	79	ONLY: nxl, nxr, nyn, nysv, nzb, nzt, wall_flags_total_0
[1320]	80
	81	USE kinds
[1]	82
[2232]	83	USE surface_mod, &
	84	ONLY : surf_def_h, surf_def_v, surf_lsm_h, surf_lsm_v, surf_usm_h, &
	85	surf_usm_v
	86
[1]	87	IMPLICIT NONE
	88
[2232]	89	INTEGER(iwp) :: i !< running index x direction
	90	INTEGER(iwp) :: j !< running index y direction
	91	INTEGER(iwp) :: k !< running index z direction
	92	INTEGER(iwp) :: l !< running index of surface type, south- or north-facing wall
	93	INTEGER(iwp) :: m !< running index surface elements
	94	INTEGER(iwp) :: surf_e !< End index of surface elements at (j,i)-gridpoint
	95	INTEGER(iwp) :: surf_s !< Start index of surface elements at (j,i)-gridpoint
[1001]	96
[2232]	97	REAL(wp) :: flag !< flag to mask topography grid points
[3547]	98	REAL(wp) :: kmxm !< diffusion coefficient on leftward side of the v-gridbox - interpolated onto xu-yv grid
	99	REAL(wp) :: kmxp !< diffusion coefficient on rightward side of the v-gridbox - interpolated onto xu-yv grid
	100	REAL(wp) :: kmzm !< diffusion coefficient on bottom of the gridbox - interpolated onto yv-zw grid
	101	REAL(wp) :: kmzp !< diffusion coefficient on top of the gridbox - interpolated onto yv-zw grid
[2232]	102	REAL(wp) :: mask_bottom !< flag to mask vertical upward-facing surface
	103	REAL(wp) :: mask_east !< flag to mask vertical surface south of the grid point
	104	REAL(wp) :: mask_west !< flag to mask vertical surface north of the grid point
	105	REAL(wp) :: mask_top !< flag to mask vertical downward-facing surface
[1]	106
[3634]	107	!$ACC PARALLEL LOOP COLLAPSE(2) PRIVATE(i, j, k, l, m) &
	108	!$ACC PRIVATE(surf_e, surf_s, flag, kmxm, kmxp, kmzm, kmzp) &
	109	!$ACC PRIVATE(mask_bottom, mask_east, mask_west, mask_top) &
[4346]	110	!$ACC PRESENT(wall_flags_total_0, km) &
[3634]	111	!$ACC PRESENT(u, v, w) &
	112	!$ACC PRESENT(ddzu, ddzw, drho_air, rho_air_zw) &
	113	!$ACC PRESENT(surf_def_h(0:2), surf_def_v(2:3)) &
	114	!$ACC PRESENT(surf_lsm_h, surf_lsm_v(2:3)) &
	115	!$ACC PRESENT(surf_usm_h, surf_usm_v(0:3)) &
	116	!$ACC PRESENT(tend)
[1]	117	DO i = nxl, nxr
[106]	118	DO j = nysv, nyn
[1]	119	!
	120	!-- Compute horizontal diffusion
[2232]	121	DO k = nzb+1, nzt
	122
[1]	123	!
[2232]	124	!-- Predetermine flag to mask topography and wall-bounded grid points.
	125	!-- It is sufficient to masked only east- and west-facing surfaces, which
	126	!-- need special treatment for the v-component.
[4346]	127	flag = MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,j,i), 2 ) )
	128	mask_east = MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,j,i+1), 2 ) )
	129	mask_west = MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,j,i-1), 2 ) )
[2232]	130	!
[1]	131	!-- Interpolate eddy diffusivities on staggered gridpoints
[2232]	132	kmxp = 0.25_wp * ( km(k,j,i)+km(k,j,i+1)+km(k,j-1,i)+km(k,j-1,i+1) )
	133	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]	134
[2232]	135	tend(k,j,i) = tend(k,j,i) + ( &
	136	mask_east * kmxp * ( &
	137	( v(k,j,i+1) - v(k,j,i) ) * ddx &
	138	+ ( u(k,j,i+1) - u(k,j-1,i+1) ) * ddy &
	139	) &
	140	- mask_west * kmxm * ( &
	141	( v(k,j,i) - v(k,j,i-1) ) * ddx &
	142	+ ( u(k,j,i) - u(k,j-1,i) ) * ddy &
	143	) &
	144	) * ddx * flag &
	145	+ 2.0_wp * ( &
	146	km(k,j,i) * ( v(k,j+1,i) - v(k,j,i) ) &
	147	- km(k,j-1,i) * ( v(k,j,i) - v(k,j-1,i) ) &
	148	) * ddy2 * flag
	149
[1]	150	ENDDO
	151
	152	!
[2232]	153	!-- Add horizontal momentum flux v'u' at east- (l=2) and west-facing (l=3)
	154	!-- surfaces. Note, in the the flat case, loops won't be entered as
	155	!-- start_index > end_index. Furtermore, note, no vertical natural surfaces
	156	!-- so far.
	157	!-- Default-type surfaces
	158	DO l = 2, 3
	159	surf_s = surf_def_v(l)%start_index(j,i)
	160	surf_e = surf_def_v(l)%end_index(j,i)
	161	DO m = surf_s, surf_e
	162	k = surf_def_v(l)%k(m)
	163	tend(k,j,i) = tend(k,j,i) + &
	164	surf_def_v(l)%mom_flux_uv(m) * ddx
	165	ENDDO
	166	ENDDO
[1]	167	!
[2232]	168	!-- Natural-type surfaces
	169	DO l = 2, 3
	170	surf_s = surf_lsm_v(l)%start_index(j,i)
	171	surf_e = surf_lsm_v(l)%end_index(j,i)
	172	DO m = surf_s, surf_e
	173	k = surf_lsm_v(l)%k(m)
	174	tend(k,j,i) = tend(k,j,i) + &
	175	surf_lsm_v(l)%mom_flux_uv(m) * ddx
	176	ENDDO
	177	ENDDO
[1]	178	!
[2232]	179	!-- Urban-type surfaces
	180	DO l = 2, 3
	181	surf_s = surf_usm_v(l)%start_index(j,i)
	182	surf_e = surf_usm_v(l)%end_index(j,i)
	183	DO m = surf_s, surf_e
	184	k = surf_usm_v(l)%k(m)
	185	tend(k,j,i) = tend(k,j,i) + &
	186	surf_usm_v(l)%mom_flux_uv(m) * ddx
	187	ENDDO
	188	ENDDO
	189	!
	190	!-- Compute vertical diffusion. In case of simulating a surface layer,
	191	!-- respective grid diffusive fluxes are masked (flag 10) within this
	192	!-- loop, and added further below, else, simple gradient approach is
	193	!-- applied. Model top is also mask if top-momentum flux is given.
	194	DO k = nzb+1, nzt
	195	!
	196	!-- Determine flags to mask topography below and above. Flag 2 is
	197	!-- used to mask topography in general, while flag 8 implies also
	198	!-- information about use_surface_fluxes. Flag 9 is used to control
	199	!-- momentum flux at model top.
	200	mask_bottom = MERGE( 1.0_wp, 0.0_wp, &
[4346]	201	BTEST( wall_flags_total_0(k-1,j,i), 8 ) )
[2232]	202	mask_top = MERGE( 1.0_wp, 0.0_wp, &
[4346]	203	BTEST( wall_flags_total_0(k+1,j,i), 8 ) ) * &
[2232]	204	MERGE( 1.0_wp, 0.0_wp, &
[4346]	205	BTEST( wall_flags_total_0(k+1,j,i), 9 ) )
[2232]	206	flag = MERGE( 1.0_wp, 0.0_wp, &
[4346]	207	BTEST( wall_flags_total_0(k,j,i), 2 ) )
[2232]	208	!
[1]	209	!-- Interpolate eddy diffusivities on staggered gridpoints
[1340]	210	kmzp = 0.25_wp * &
[1]	211	( km(k,j,i)+km(k+1,j,i)+km(k,j-1,i)+km(k+1,j-1,i) )
[1340]	212	kmzm = 0.25_wp * &
[1]	213	( km(k,j,i)+km(k-1,j,i)+km(k,j-1,i)+km(k-1,j-1,i) )
	214
[1320]	215	tend(k,j,i) = tend(k,j,i) &
	216	& + ( kmzp * ( ( v(k+1,j,i) - v(k,j,i) ) * ddzu(k+1) &
	217	& + ( w(k,j,i) - w(k,j-1,i) ) * ddy &
[2232]	218	& ) * rho_air_zw(k) * mask_top &
[1320]	219	& - kmzm * ( ( v(k,j,i) - v(k-1,j,i) ) * ddzu(k) &
	220	& + ( w(k-1,j,i) - w(k-1,j-1,i) ) * ddy &
[2232]	221	& ) * rho_air_zw(k-1) * mask_bottom &
	222	& ) * ddzw(k) * drho_air(k) * flag
[1]	223	ENDDO
	224
	225	!
	226	!-- Vertical diffusion at the first grid point above the surface,
	227	!-- if the momentum flux at the bottom is given by the Prandtl law
	228	!-- or if it is prescribed by the user.
	229	!-- Difference quotient of the momentum flux is not formed over
	230	!-- half of the grid spacing (2.0*ddzw(k)) any more, since the
[1320]	231	!-- comparison with other (LES) models showed that the values of
[1]	232	!-- the momentum flux becomes too large in this case.
	233	IF ( use_surface_fluxes ) THEN
	234	!
[2232]	235	!-- Default-type surfaces, upward-facing
	236	surf_s = surf_def_h(0)%start_index(j,i)
	237	surf_e = surf_def_h(0)%end_index(j,i)
	238	DO m = surf_s, surf_e
	239	k = surf_def_h(0)%k(m)
[1]	240
[2232]	241	tend(k,j,i) = tend(k,j,i) &
	242	+ ( - ( - surf_def_h(0)%vsws(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	k = surf_def_h(1)%k(m)
[1]	251
[2232]	252	tend(k,j,i) = tend(k,j,i) &
	253	+ ( - surf_def_h(1)%vsws(m) &
	254	) * ddzw(k) * drho_air(k)
	255	ENDDO
[102]	256	!
[2232]	257	!-- Natural-type surfaces, upward-facing
	258	surf_s = surf_lsm_h%start_index(j,i)
	259	surf_e = surf_lsm_h%end_index(j,i)
	260	DO m = surf_s, surf_e
	261	k = surf_lsm_h%k(m)
	262
	263	tend(k,j,i) = tend(k,j,i) &
	264	+ ( - ( - surf_lsm_h%vsws(m) ) &
	265	) * ddzw(k) * drho_air(k)
	266
	267	ENDDO
[102]	268	!
[2232]	269	!-- Urban-type surfaces, upward-facing
	270	surf_s = surf_usm_h%start_index(j,i)
	271	surf_e = surf_usm_h%end_index(j,i)
	272	DO m = surf_s, surf_e
	273	k = surf_usm_h%k(m)
[102]	274
[2232]	275	tend(k,j,i) = tend(k,j,i) &
	276	+ ( - ( - surf_usm_h%vsws(m) ) &
	277	) * ddzw(k) * drho_air(k)
	278
	279	ENDDO
[102]	280	ENDIF
[2232]	281	!
	282	!-- Add momentum flux at model top
[2638]	283	IF ( use_top_fluxes .AND. constant_top_momentumflux ) THEN
[2232]	284	surf_s = surf_def_h(2)%start_index(j,i)
	285	surf_e = surf_def_h(2)%end_index(j,i)
	286	DO m = surf_s, surf_e
[102]	287
[2232]	288	k = surf_def_h(2)%k(m)
	289
	290	tend(k,j,i) = tend(k,j,i) &
	291	+ ( - surf_def_h(2)%vsws(m) ) * ddzw(k) * drho_air(k)
	292	ENDDO
	293	ENDIF
	294
[1]	295	ENDDO
	296	ENDDO
	297
	298	END SUBROUTINE diffusion_v
	299
	300
	301	!------------------------------------------------------------------------------!
[1682]	302	! Description:
	303	! ------------
	304	!> Call for grid point i,j
[1]	305	!------------------------------------------------------------------------------!
[1001]	306	SUBROUTINE diffusion_v_ij( i, j )
[1]	307
[1320]	308	USE arrays_3d, &
[2232]	309	ONLY: ddzu, ddzw, km, tend, u, v, w, drho_air, rho_air_zw
[1320]	310
	311	USE control_parameters, &
[2232]	312	ONLY: constant_top_momentumflux, use_surface_fluxes, &
	313	use_top_fluxes
[1320]	314
	315	USE grid_variables, &
[2232]	316	ONLY: ddx, ddy, ddy2
[1320]	317
	318	USE indices, &
[4346]	319	ONLY: nzb, nzt, wall_flags_total_0
[1320]	320
	321	USE kinds
[1]	322
[2232]	323	USE surface_mod, &
	324	ONLY : surf_def_h, surf_def_v, surf_lsm_h, surf_lsm_v, surf_usm_h, &
	325	surf_usm_v
	326
[1]	327	IMPLICIT NONE
	328
	329
[2232]	330	INTEGER(iwp) :: i !< running index x direction
	331	INTEGER(iwp) :: j !< running index y direction
	332	INTEGER(iwp) :: k !< running index z direction
	333	INTEGER(iwp) :: l !< running index of surface type, south- or north-facing wall
	334	INTEGER(iwp) :: m !< running index surface elements
	335	INTEGER(iwp) :: surf_e !< End index of surface elements at (j,i)-gridpoint
	336	INTEGER(iwp) :: surf_s !< Start index of surface elements at (j,i)-gridpoint
[1001]	337
[2232]	338	REAL(wp) :: flag !< flag to mask topography grid points
[3547]	339	REAL(wp) :: kmxm !< diffusion coefficient on leftward side of the v-gridbox - interpolated onto xu-yv grid
	340	REAL(wp) :: kmxp !< diffusion coefficient on rightward side of the v-gridbox - interpolated onto xu-yv grid
	341	REAL(wp) :: kmzm !< diffusion coefficient on bottom of the gridbox - interpolated onto xu-zw grid
	342	REAL(wp) :: kmzp !< diffusion coefficient on top of the gridbox - interpolated onto xu-zw grid
[2232]	343	REAL(wp) :: mask_bottom !< flag to mask vertical upward-facing surface
	344	REAL(wp) :: mask_east !< flag to mask vertical surface south of the grid point
	345	REAL(wp) :: mask_west !< flag to mask vertical surface north of the grid point
	346	REAL(wp) :: mask_top !< flag to mask vertical downward-facing surface
	347
[1]	348	!
	349	!-- Compute horizontal diffusion
[2232]	350	DO k = nzb+1, nzt
[1]	351	!
[2232]	352	!-- Predetermine flag to mask topography and wall-bounded grid points.
	353	!-- It is sufficient to masked only east- and west-facing surfaces, which
	354	!-- need special treatment for the v-component.
[4346]	355	flag = MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,j,i), 2 ) )
	356	mask_east = MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,j,i+1), 2 ) )
	357	mask_west = MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,j,i-1), 2 ) )
[2232]	358	!
[1]	359	!-- Interpolate eddy diffusivities on staggered gridpoints
[1340]	360	kmxp = 0.25_wp * ( km(k,j,i)+km(k,j,i+1)+km(k,j-1,i)+km(k,j-1,i+1) )
	361	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]	362
[2232]	363	tend(k,j,i) = tend(k,j,i) + ( &
	364	mask_east * kmxp * ( &
	365	( v(k,j,i+1) - v(k,j,i) ) * ddx &
	366	+ ( u(k,j,i+1) - u(k,j-1,i+1) ) * ddy &
	367	) &
	368	- mask_west * kmxm * ( &
	369	( v(k,j,i) - v(k,j,i-1) ) * ddx &
	370	+ ( u(k,j,i) - u(k,j-1,i) ) * ddy &
	371	) &
	372	) * ddx * flag &
	373	+ 2.0_wp * ( &
	374	km(k,j,i) * ( v(k,j+1,i) - v(k,j,i) ) &
	375	- km(k,j-1,i) * ( v(k,j,i) - v(k,j-1,i) ) &
	376	) * ddy2 * flag
[1]	377	ENDDO
	378
	379	!
[2232]	380	!-- Add horizontal momentum flux v'u' at east- (l=2) and west-facing (l=3)
	381	!-- surfaces. Note, in the the flat case, loops won't be entered as
	382	!-- start_index > end_index. Furtermore, note, no vertical natural surfaces
	383	!-- so far.
	384	!-- Default-type surfaces
	385	DO l = 2, 3
	386	surf_s = surf_def_v(l)%start_index(j,i)
	387	surf_e = surf_def_v(l)%end_index(j,i)
	388	DO m = surf_s, surf_e
	389	k = surf_def_v(l)%k(m)
	390	tend(k,j,i) = tend(k,j,i) + surf_def_v(l)%mom_flux_uv(m) * ddx
	391	ENDDO
	392	ENDDO
[51]	393	!
[2232]	394	!-- Natural-type surfaces
	395	DO l = 2, 3
	396	surf_s = surf_lsm_v(l)%start_index(j,i)
	397	surf_e = surf_lsm_v(l)%end_index(j,i)
	398	DO m = surf_s, surf_e
	399	k = surf_lsm_v(l)%k(m)
	400	tend(k,j,i) = tend(k,j,i) + surf_lsm_v(l)%mom_flux_uv(m) * ddx
	401	ENDDO
	402	ENDDO
[1]	403	!
[2232]	404	!-- Urban-type surfaces
	405	DO l = 2, 3
	406	surf_s = surf_usm_v(l)%start_index(j,i)
	407	surf_e = surf_usm_v(l)%end_index(j,i)
	408	DO m = surf_s, surf_e
	409	k = surf_usm_v(l)%k(m)
	410	tend(k,j,i) = tend(k,j,i) + surf_usm_v(l)%mom_flux_uv(m) * ddx
	411	ENDDO
	412	ENDDO
[1]	413	!
[2232]	414	!-- Compute vertical diffusion. In case of simulating a surface layer,
	415	!-- respective grid diffusive fluxes are masked (flag 8) within this
	416	!-- loop, and added further below, else, simple gradient approach is
	417	!-- applied. Model top is also mask if top-momentum flux is given.
	418	DO k = nzb+1, nzt
	419	!
	420	!-- Determine flags to mask topography below and above. Flag 2 is
	421	!-- used to mask topography in general, while flag 10 implies also
	422	!-- information about use_surface_fluxes. Flag 9 is used to control
	423	!-- momentum flux at model top.
	424	mask_bottom = MERGE( 1.0_wp, 0.0_wp, &
[4346]	425	BTEST( wall_flags_total_0(k-1,j,i), 8 ) )
[2232]	426	mask_top = MERGE( 1.0_wp, 0.0_wp, &
[4346]	427	BTEST( wall_flags_total_0(k+1,j,i), 8 ) ) * &
[2232]	428	MERGE( 1.0_wp, 0.0_wp, &
[4346]	429	BTEST( wall_flags_total_0(k+1,j,i), 9 ) )
[2232]	430	flag = MERGE( 1.0_wp, 0.0_wp, &
[4346]	431	BTEST( wall_flags_total_0(k,j,i), 2 ) )
[2232]	432	!
[1]	433	!-- Interpolate eddy diffusivities on staggered gridpoints
[1340]	434	kmzp = 0.25_wp * ( km(k,j,i)+km(k+1,j,i)+km(k,j-1,i)+km(k+1,j-1,i) )
	435	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]	436
[1320]	437	tend(k,j,i) = tend(k,j,i) &
	438	& + ( kmzp * ( ( v(k+1,j,i) - v(k,j,i) ) * ddzu(k+1) &
	439	& + ( w(k,j,i) - w(k,j-1,i) ) * ddy &
[2232]	440	& ) * rho_air_zw(k) * mask_top &
[1320]	441	& - kmzm * ( ( v(k,j,i) - v(k-1,j,i) ) * ddzu(k) &
	442	& + ( w(k-1,j,i) - w(k-1,j-1,i) ) * ddy &
[2232]	443	& ) * rho_air_zw(k-1) * mask_bottom &
	444	& ) * ddzw(k) * drho_air(k) * flag
[1]	445	ENDDO
	446
	447	!
	448	!-- Vertical diffusion at the first grid point above the surface, if the
	449	!-- momentum flux at the bottom is given by the Prandtl law or if it is
	450	!-- prescribed by the user.
	451	!-- Difference quotient of the momentum flux is not formed over half of
	452	!-- the grid spacing (2.0*ddzw(k)) any more, since the comparison with
[1320]	453	!-- other (LES) models showed that the values of the momentum flux becomes
[1]	454	!-- too large in this case.
	455	IF ( use_surface_fluxes ) THEN
	456	!
[2232]	457	!-- Default-type surfaces, upward-facing
	458	surf_s = surf_def_h(0)%start_index(j,i)
	459	surf_e = surf_def_h(0)%end_index(j,i)
	460	DO m = surf_s, surf_e
	461	k = surf_def_h(0)%k(m)
[1]	462
[2232]	463	tend(k,j,i) = tend(k,j,i) &
	464	+ ( - ( - surf_def_h(0)%vsws(m) ) &
	465	) * ddzw(k) * drho_air(k)
	466	ENDDO
	467	!
	468	!-- Default-type surfaces, dowward-facing
	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	k = surf_def_h(1)%k(m)
[1]	473
[2232]	474	tend(k,j,i) = tend(k,j,i) &
	475	+ ( - surf_def_h(1)%vsws(m) &
	476	) * ddzw(k) * drho_air(k)
	477	ENDDO
[102]	478	!
[2232]	479	!-- Natural-type surfaces, upward-facing
	480	surf_s = surf_lsm_h%start_index(j,i)
	481	surf_e = surf_lsm_h%end_index(j,i)
	482	DO m = surf_s, surf_e
	483	k = surf_lsm_h%k(m)
	484
	485	tend(k,j,i) = tend(k,j,i) &
	486	+ ( - ( - surf_lsm_h%vsws(m) ) &
	487	) * ddzw(k) * drho_air(k)
	488
	489	ENDDO
[102]	490	!
[2232]	491	!-- Urban-type surfaces, upward-facing
	492	surf_s = surf_usm_h%start_index(j,i)
	493	surf_e = surf_usm_h%end_index(j,i)
	494	DO m = surf_s, surf_e
	495	k = surf_usm_h%k(m)
[102]	496
[2232]	497	tend(k,j,i) = tend(k,j,i) &
	498	+ ( - ( - surf_usm_h%vsws(m) ) &
	499	) * ddzw(k) * drho_air(k)
	500
	501	ENDDO
[102]	502	ENDIF
[2232]	503	!
	504	!-- Add momentum flux at model top
[2638]	505	IF ( use_top_fluxes .AND. constant_top_momentumflux ) THEN
[2232]	506	surf_s = surf_def_h(2)%start_index(j,i)
	507	surf_e = surf_def_h(2)%end_index(j,i)
	508	DO m = surf_s, surf_e
[102]	509
[2232]	510	k = surf_def_h(2)%k(m)
	511
	512	tend(k,j,i) = tend(k,j,i) &
	513	+ ( - surf_def_h(2)%vsws(m) ) * ddzw(k) * drho_air(k)
	514	ENDDO
	515	ENDIF
	516
[1]	517	END SUBROUTINE diffusion_v_ij
	518
[1321]	519	END MODULE diffusion_v_mod

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