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source: palm/trunk/SOURCE/diffusion_v.f90 @ 4622

Last change on this file since 4622 was 4583, checked in by raasch, 4 years ago
files re-formatted to follow the PALM coding standard
Property svn:keywords set to `Id`
File size: 23.5 KB

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[1873]	1	!> @file diffusion_v.f90
[4583]	2	!--------------------------------------------------------------------------------------------------!
[2696]	3	! This file is part of the PALM model system.
[1036]	4	!
[4583]	5	! PALM is free software: you can redistribute it and/or modify it under the terms of the GNU General
	6	! Public License as published by the Free Software Foundation, either version 3 of the License, or
	7	! (at your option) any later version.
[1036]	8	!
[4583]	9	! PALM is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the
	10	! implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General
	11	! Public License for more details.
[1036]	12	!
[4583]	13	! You should have received a copy of the GNU General Public License along with PALM. If not, see
	14	! <http://www.gnu.org/licenses/>.
[1036]	15	!
[4360]	16	! Copyright 1997-2020 Leibniz Universitaet Hannover
[4583]	17	!--------------------------------------------------------------------------------------------------!
[1036]	18	!
[484]	19	! Current revisions:
[1]	20	! -----------------
[1341]	21	!
[2233]	22	!
[1321]	23	! Former revisions:
	24	! -----------------
	25	! $Id: diffusion_v.f90 4583 2020-06-29 12:36:47Z raasch $
[4583]	26	! file re-formatted to follow the PALM coding standard
	27	!
	28	! 4360 2020-01-07 11:25:50Z suehring
	29	! Introduction of wall_flags_total_0, which currently sets bits based on static topography
	30	! information used in wall_flags_static_0
	31	!
[4346]	32	! 4329 2019-12-10 15:46:36Z motisi
[4329]	33	! Renamed wall_flags_0 to wall_flags_static_0
[4583]	34	!
[4329]	35	! 4182 2019-08-22 15:20:23Z scharf
[4182]	36	! Corrected "Former revisions" section
[4583]	37	!
[4182]	38	! 3655 2019-01-07 16:51:22Z knoop
[3634]	39	! OpenACC port for SPEC
[2716]	40	!
[4182]	41	! Revision 1.1 1997/09/12 06:24:01 raasch
	42	! Initial revision
	43	!
	44	!
[1]	45	! Description:
	46	! ------------
[1682]	47	!> Diffusion term of the v-component
[4583]	48	!--------------------------------------------------------------------------------------------------!
[1682]	49	MODULE diffusion_v_mod
[1]	50
[4583]	51
[1]	52	PRIVATE
[2118]	53	PUBLIC diffusion_v
[1]	54
	55	INTERFACE diffusion_v
	56	MODULE PROCEDURE diffusion_v
	57	MODULE PROCEDURE diffusion_v_ij
	58	END INTERFACE diffusion_v
	59
	60	CONTAINS
	61
	62
[4583]	63	!--------------------------------------------------------------------------------------------------!
[1682]	64	! Description:
	65	! ------------
	66	!> Call for all grid points
[4583]	67	!--------------------------------------------------------------------------------------------------!
[1001]	68	SUBROUTINE diffusion_v
[1]	69
[4583]	70	USE arrays_3d, &
	71	ONLY: ddzu, ddzw, drho_air, km, rho_air_zw, tend, u, v, w
	72
	73	USE control_parameters, &
	74	ONLY: constant_top_momentumflux, use_surface_fluxes, use_top_fluxes
	75
	76	USE grid_variables, &
[2232]	77	ONLY: ddx, ddy, ddy2
[4583]	78
	79	USE indices, &
[4346]	80	ONLY: nxl, nxr, nyn, nysv, nzb, nzt, wall_flags_total_0
[4583]	81
[1320]	82	USE kinds
[1]	83
[4583]	84	USE surface_mod, &
	85	ONLY : surf_def_h, surf_def_v, surf_lsm_h, surf_lsm_v, surf_usm_h, surf_usm_v
[2232]	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
[4583]	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	!
[4583]	124	!-- Predetermine flag to mask topography and wall-bounded grid points.
	125	!-- It is sufficient to masked only east- and west-facing surfaces, which need special
	126	!-- treatment for the v-component.
	127	flag = MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,j,i), 2 ) )
[4346]	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
[4583]	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
[2232]	149
[1]	150	ENDDO
	151
	152	!
[4583]	153	!-- Add horizontal momentum flux v'u' at east- (l=2) and west-facing (l=3) surfaces. Note,
	154	!-- in the the flat case, loops won't be entered as start_index > end_index. Furtermore,
	155	!-- note, no vertical natural surfaces so far.
[2232]	156	!-- Default-type surfaces
	157	DO l = 2, 3
	158	surf_s = surf_def_v(l)%start_index(j,i)
	159	surf_e = surf_def_v(l)%end_index(j,i)
	160	DO m = surf_s, surf_e
	161	k = surf_def_v(l)%k(m)
[4583]	162	tend(k,j,i) = tend(k,j,i) + surf_def_v(l)%mom_flux_uv(m) * ddx
	163	ENDDO
[2232]	164	ENDDO
[1]	165	!
[2232]	166	!-- Natural-type surfaces
	167	DO l = 2, 3
	168	surf_s = surf_lsm_v(l)%start_index(j,i)
	169	surf_e = surf_lsm_v(l)%end_index(j,i)
	170	DO m = surf_s, surf_e
	171	k = surf_lsm_v(l)%k(m)
[4583]	172	tend(k,j,i) = tend(k,j,i) + surf_lsm_v(l)%mom_flux_uv(m) * ddx
	173	ENDDO
[2232]	174	ENDDO
[1]	175	!
[2232]	176	!-- Urban-type surfaces
	177	DO l = 2, 3
	178	surf_s = surf_usm_v(l)%start_index(j,i)
	179	surf_e = surf_usm_v(l)%end_index(j,i)
	180	DO m = surf_s, surf_e
	181	k = surf_usm_v(l)%k(m)
[4583]	182	tend(k,j,i) = tend(k,j,i) + surf_usm_v(l)%mom_flux_uv(m) * ddx
	183	ENDDO
[2232]	184	ENDDO
	185	!
[4583]	186	!-- Compute vertical diffusion. In case of simulating a surface layer, respective grid
	187	!-- diffusive fluxes are masked (flag 10) within this loop, and added further below, else,
	188	!-- simple gradient approach is applied. Model top is also mask if top-momentum flux is
	189	!-- given.
[2232]	190	DO k = nzb+1, nzt
	191	!
[4583]	192	!-- Determine flags to mask topography below and above. Flag 2 is used to mask
	193	!-- topography in general, while flag 8 implies also information about
	194	!-- use_surface_fluxes. Flag 9 is used to control momentum flux at model top.
	195	mask_bottom = MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k-1,j,i), 8 ) )
	196	mask_top = MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k+1,j,i), 8 ) ) * &
	197	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k+1,j,i), 9 ) )
	198	flag = MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,j,i), 2 ) )
[2232]	199	!
[1]	200	!-- Interpolate eddy diffusivities on staggered gridpoints
[4583]	201	kmzp = 0.25_wp * ( km(k,j,i)+km(k+1,j,i)+km(k,j-1,i)+km(k+1,j-1,i) )
	202	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]	203
[4583]	204	tend(k,j,i) = tend(k,j,i) &
	205	& + ( kmzp * ( ( v(k+1,j,i) - v(k,j,i) ) * ddzu(k+1) &
	206	& + ( w(k,j,i) - w(k,j-1,i) ) * ddy &
	207	& ) * rho_air_zw(k) * mask_top &
	208	& - kmzm * ( ( v(k,j,i) - v(k-1,j,i) ) * ddzu(k) &
	209	& + ( w(k-1,j,i) - w(k-1,j-1,i) ) * ddy &
	210	& ) * rho_air_zw(k-1) * mask_bottom &
	211	& ) * ddzw(k) * drho_air(k) * flag
[1]	212	ENDDO
	213
	214	!
[4583]	215	!-- Vertical diffusion at the first grid point above the surface, if the momentum flux at
	216	!-- the bottom is given by the Prandtl law or if it is prescribed by the user.
	217	!-- Difference quotient of the momentum flux is not formed over half of the grid spacing
	218	!-- (2.0*ddzw(k)) any more, since the comparison with other (LES) models showed that the
	219	!-- values of the momentum flux becomes too large in this case.
[1]	220	IF ( use_surface_fluxes ) THEN
	221	!
[2232]	222	!-- Default-type surfaces, upward-facing
	223	surf_s = surf_def_h(0)%start_index(j,i)
	224	surf_e = surf_def_h(0)%end_index(j,i)
	225	DO m = surf_s, surf_e
	226	k = surf_def_h(0)%k(m)
[1]	227
[4583]	228	tend(k,j,i) = tend(k,j,i) &
	229	+ ( - ( - surf_def_h(0)%vsws(m) ) ) * ddzw(k) * drho_air(k)
[2232]	230	ENDDO
	231	!
	232	!-- Default-type surfaces, dowward-facing
	233	surf_s = surf_def_h(1)%start_index(j,i)
	234	surf_e = surf_def_h(1)%end_index(j,i)
	235	DO m = surf_s, surf_e
	236	k = surf_def_h(1)%k(m)
[1]	237
[4583]	238	tend(k,j,i) = tend(k,j,i) &
	239	+ ( - surf_def_h(1)%vsws(m) ) * ddzw(k) * drho_air(k)
[2232]	240	ENDDO
[102]	241	!
[2232]	242	!-- Natural-type surfaces, upward-facing
	243	surf_s = surf_lsm_h%start_index(j,i)
	244	surf_e = surf_lsm_h%end_index(j,i)
	245	DO m = surf_s, surf_e
	246	k = surf_lsm_h%k(m)
	247
[4583]	248	tend(k,j,i) = tend(k,j,i) &
	249	+ ( - ( - surf_lsm_h%vsws(m) ) ) * ddzw(k) * drho_air(k)
[2232]	250
	251	ENDDO
[102]	252	!
[2232]	253	!-- Urban-type surfaces, upward-facing
	254	surf_s = surf_usm_h%start_index(j,i)
	255	surf_e = surf_usm_h%end_index(j,i)
	256	DO m = surf_s, surf_e
	257	k = surf_usm_h%k(m)
[102]	258
[4583]	259	tend(k,j,i) = tend(k,j,i) &
	260	+ ( - ( - surf_usm_h%vsws(m) ) ) * ddzw(k) * drho_air(k)
[2232]	261
	262	ENDDO
[102]	263	ENDIF
[2232]	264	!
	265	!-- Add momentum flux at model top
[2638]	266	IF ( use_top_fluxes .AND. constant_top_momentumflux ) THEN
[2232]	267	surf_s = surf_def_h(2)%start_index(j,i)
	268	surf_e = surf_def_h(2)%end_index(j,i)
	269	DO m = surf_s, surf_e
[102]	270
[2232]	271	k = surf_def_h(2)%k(m)
	272
[4583]	273	tend(k,j,i) = tend(k,j,i) &
	274	+ ( - surf_def_h(2)%vsws(m) ) * ddzw(k) * drho_air(k)
[2232]	275	ENDDO
	276	ENDIF
	277
[1]	278	ENDDO
	279	ENDDO
	280
	281	END SUBROUTINE diffusion_v
	282
	283
[4583]	284	!--------------------------------------------------------------------------------------------------!
[1682]	285	! Description:
	286	! ------------
	287	!> Call for grid point i,j
[4583]	288	!--------------------------------------------------------------------------------------------------!
[1001]	289	SUBROUTINE diffusion_v_ij( i, j )
[1]	290
[4583]	291	USE arrays_3d, &
	292	ONLY: ddzu, ddzw, drho_air, km, tend, u, v, w, rho_air_zw
	293
	294	USE control_parameters, &
	295	ONLY: constant_top_momentumflux, use_surface_fluxes, use_top_fluxes
	296
	297	USE grid_variables, &
[2232]	298	ONLY: ddx, ddy, ddy2
[4583]	299
	300	USE indices, &
[4346]	301	ONLY: nzb, nzt, wall_flags_total_0
[4583]	302
[1320]	303	USE kinds
[1]	304
[4583]	305	USE surface_mod, &
	306	ONLY : surf_def_h, surf_def_v, surf_lsm_h, surf_lsm_v, surf_usm_h, surf_usm_v
[2232]	307
[1]	308	IMPLICIT NONE
	309
	310
[2232]	311	INTEGER(iwp) :: i !< running index x direction
	312	INTEGER(iwp) :: j !< running index y direction
	313	INTEGER(iwp) :: k !< running index z direction
	314	INTEGER(iwp) :: l !< running index of surface type, south- or north-facing wall
	315	INTEGER(iwp) :: m !< running index surface elements
	316	INTEGER(iwp) :: surf_e !< End index of surface elements at (j,i)-gridpoint
	317	INTEGER(iwp) :: surf_s !< Start index of surface elements at (j,i)-gridpoint
[1001]	318
[2232]	319	REAL(wp) :: flag !< flag to mask topography grid points
[3547]	320	REAL(wp) :: kmxm !< diffusion coefficient on leftward side of the v-gridbox - interpolated onto xu-yv grid
	321	REAL(wp) :: kmxp !< diffusion coefficient on rightward side of the v-gridbox - interpolated onto xu-yv grid
	322	REAL(wp) :: kmzm !< diffusion coefficient on bottom of the gridbox - interpolated onto xu-zw grid
	323	REAL(wp) :: kmzp !< diffusion coefficient on top of the gridbox - interpolated onto xu-zw grid
[4583]	324	REAL(wp) :: mask_bottom !< flag to mask vertical upward-facing surface
	325	REAL(wp) :: mask_east !< flag to mask vertical surface south of the grid point
	326	REAL(wp) :: mask_west !< flag to mask vertical surface north of the grid point
[2232]	327	REAL(wp) :: mask_top !< flag to mask vertical downward-facing surface
	328
[1]	329	!
	330	!-- Compute horizontal diffusion
[2232]	331	DO k = nzb+1, nzt
[1]	332	!
[4583]	333	!-- Predetermine flag to mask topography and wall-bounded grid points.
	334	!-- It is sufficient to masked only east- and west-facing surfaces, which need special
	335	!-- treatment for the v-component.
	336	flag = MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,j,i), 2 ) )
[4346]	337	mask_east = MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,j,i+1), 2 ) )
	338	mask_west = MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,j,i-1), 2 ) )
[2232]	339	!
[1]	340	!-- Interpolate eddy diffusivities on staggered gridpoints
[1340]	341	kmxp = 0.25_wp * ( km(k,j,i)+km(k,j,i+1)+km(k,j-1,i)+km(k,j-1,i+1) )
	342	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]	343
[4583]	344	tend(k,j,i) = tend(k,j,i) + ( &
	345	mask_east * kmxp * ( &
	346	( v(k,j,i+1) - v(k,j,i) ) * ddx &
	347	+ ( u(k,j,i+1) - u(k,j-1,i+1) ) * ddy &
	348	) &
	349	- mask_west * kmxm * ( &
	350	( v(k,j,i) - v(k,j,i-1) ) * ddx &
	351	+ ( u(k,j,i) - u(k,j-1,i) ) * ddy &
	352	) &
	353	) * ddx * flag &
	354	+ 2.0_wp * ( &
	355	km(k,j,i) * ( v(k,j+1,i) - v(k,j,i) ) &
	356	- km(k,j-1,i) * ( v(k,j,i) - v(k,j-1,i) ) &
[2232]	357	) * ddy2 * flag
[1]	358	ENDDO
	359
	360	!
[4583]	361	!-- Add horizontal momentum flux v'u' at east- (l=2) and west-facing (l=3) surfaces. Note, in the
	362	!-- the flat case, loops won't be entered as start_index > end_index. Furtermore, note, no
	363	!-- vertical natural surfaces so far.
[2232]	364	!-- Default-type surfaces
	365	DO l = 2, 3
	366	surf_s = surf_def_v(l)%start_index(j,i)
	367	surf_e = surf_def_v(l)%end_index(j,i)
	368	DO m = surf_s, surf_e
	369	k = surf_def_v(l)%k(m)
	370	tend(k,j,i) = tend(k,j,i) + surf_def_v(l)%mom_flux_uv(m) * ddx
[4583]	371	ENDDO
[2232]	372	ENDDO
[51]	373	!
[2232]	374	!-- Natural-type surfaces
	375	DO l = 2, 3
	376	surf_s = surf_lsm_v(l)%start_index(j,i)
	377	surf_e = surf_lsm_v(l)%end_index(j,i)
	378	DO m = surf_s, surf_e
	379	k = surf_lsm_v(l)%k(m)
	380	tend(k,j,i) = tend(k,j,i) + surf_lsm_v(l)%mom_flux_uv(m) * ddx
[4583]	381	ENDDO
[2232]	382	ENDDO
[1]	383	!
[2232]	384	!-- Urban-type surfaces
	385	DO l = 2, 3
	386	surf_s = surf_usm_v(l)%start_index(j,i)
	387	surf_e = surf_usm_v(l)%end_index(j,i)
	388	DO m = surf_s, surf_e
	389	k = surf_usm_v(l)%k(m)
	390	tend(k,j,i) = tend(k,j,i) + surf_usm_v(l)%mom_flux_uv(m) * ddx
[4583]	391	ENDDO
[2232]	392	ENDDO
[1]	393	!
[4583]	394	!-- Compute vertical diffusion. In case of simulating a surface layer, respective grid diffusive
	395	!-- fluxes are masked (flag 8) within this loop, and added further below, else, simple gradient
	396	!-- approach is applied. Model top is also mask if top-momentum flux is given.
[2232]	397	DO k = nzb+1, nzt
	398	!
[4583]	399	!-- Determine flags to mask topography below and above. Flag 2 is used to mask topography in
	400	!-- general, while flag 10 implies also information about use_surface_fluxes. Flag 9 is used
	401	!-- to control momentum flux at model top.
	402	mask_bottom = MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k-1,j,i), 8 ) )
	403	mask_top = MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k+1,j,i), 8 ) ) * &
	404	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k+1,j,i), 9 ) )
	405	flag = MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,j,i), 2 ) )
[2232]	406	!
[1]	407	!-- Interpolate eddy diffusivities on staggered gridpoints
[1340]	408	kmzp = 0.25_wp * ( km(k,j,i)+km(k+1,j,i)+km(k,j-1,i)+km(k+1,j-1,i) )
	409	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]	410
[4583]	411	tend(k,j,i) = tend(k,j,i) &
	412	& + ( kmzp * ( ( v(k+1,j,i) - v(k,j,i) ) * ddzu(k+1) &
	413	& + ( w(k,j,i) - w(k,j-1,i) ) * ddy &
	414	& ) * rho_air_zw(k) * mask_top &
	415	& - kmzm * ( ( v(k,j,i) - v(k-1,j,i) ) * ddzu(k) &
	416	& + ( w(k-1,j,i) - w(k-1,j-1,i) ) * ddy &
	417	& ) * rho_air_zw(k-1) * mask_bottom &
	418	& ) * ddzw(k) * drho_air(k) * flag
[1]	419	ENDDO
	420
	421	!
[4583]	422	!-- Vertical diffusion at the first grid point above the surface, if the momentum flux at the
	423	!-- bottom is given by the Prandtl law or if it is prescribed by the user.
	424	!-- Difference quotient of the momentum flux is not formed over half of the grid spacing
	425	!-- (2.0*ddzw(k)) any more, since the comparison with other (LES) models showed that the values
	426	!-- of the momentum flux becomes too large in this case.
[1]	427	IF ( use_surface_fluxes ) THEN
	428	!
[2232]	429	!-- Default-type surfaces, upward-facing
	430	surf_s = surf_def_h(0)%start_index(j,i)
	431	surf_e = surf_def_h(0)%end_index(j,i)
	432	DO m = surf_s, surf_e
	433	k = surf_def_h(0)%k(m)
[1]	434
[4583]	435	tend(k,j,i) = tend(k,j,i) + ( - ( - surf_def_h(0)%vsws(m) ) ) * ddzw(k) * drho_air(k)
[2232]	436	ENDDO
	437	!
	438	!-- Default-type surfaces, dowward-facing
	439	surf_s = surf_def_h(1)%start_index(j,i)
	440	surf_e = surf_def_h(1)%end_index(j,i)
	441	DO m = surf_s, surf_e
	442	k = surf_def_h(1)%k(m)
[1]	443
[4583]	444	tend(k,j,i) = tend(k,j,i) + ( - surf_def_h(1)%vsws(m) ) * ddzw(k) * drho_air(k)
[2232]	445	ENDDO
[102]	446	!
[2232]	447	!-- Natural-type surfaces, upward-facing
	448	surf_s = surf_lsm_h%start_index(j,i)
	449	surf_e = surf_lsm_h%end_index(j,i)
	450	DO m = surf_s, surf_e
	451	k = surf_lsm_h%k(m)
	452
[4583]	453	tend(k,j,i) = tend(k,j,i) + ( - ( - surf_lsm_h%vsws(m) ) ) * ddzw(k) * drho_air(k)
[2232]	454
	455	ENDDO
[102]	456	!
[2232]	457	!-- Urban-type surfaces, upward-facing
	458	surf_s = surf_usm_h%start_index(j,i)
	459	surf_e = surf_usm_h%end_index(j,i)
	460	DO m = surf_s, surf_e
	461	k = surf_usm_h%k(m)
[102]	462
[4583]	463	tend(k,j,i) = tend(k,j,i) + ( - ( - surf_usm_h%vsws(m) ) ) * ddzw(k) * drho_air(k)
[2232]	464
	465	ENDDO
[102]	466	ENDIF
[2232]	467	!
	468	!-- Add momentum flux at model top
[2638]	469	IF ( use_top_fluxes .AND. constant_top_momentumflux ) THEN
[2232]	470	surf_s = surf_def_h(2)%start_index(j,i)
	471	surf_e = surf_def_h(2)%end_index(j,i)
	472	DO m = surf_s, surf_e
[102]	473
[2232]	474	k = surf_def_h(2)%k(m)
	475
[4583]	476	tend(k,j,i) = tend(k,j,i) + ( - surf_def_h(2)%vsws(m) ) * ddzw(k) * drho_air(k)
[2232]	477	ENDDO
	478	ENDIF
	479
[1]	480	END SUBROUTINE diffusion_v_ij
	481
[1321]	482	END MODULE diffusion_v_mod

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