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source: palm/trunk/SOURCE/diffusion_v.f90 @ 4232

Last change on this file since 4232 was 4182, checked in by scharf, 5 years ago
corrected "Former revisions" section minor formatting in "Former revisions" section added "Author" section
Property svn:keywords set to `Id`
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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 4182 2019-08-22 15:20:23Z knoop $
[4182]	27	! Corrected "Former revisions" section
	28	!
	29	! 3655 2019-01-07 16:51:22Z knoop
[3634]	30	! OpenACC port for SPEC
[2716]	31	!
[4182]	32	! Revision 1.1 1997/09/12 06:24:01 raasch
	33	! Initial revision
	34	!
	35	!
[1]	36	! Description:
	37	! ------------
[1682]	38	!> Diffusion term of the v-component
[1]	39	!------------------------------------------------------------------------------!
[1682]	40	MODULE diffusion_v_mod
	41
[1]	42
	43	PRIVATE
[2118]	44	PUBLIC diffusion_v
[1]	45
	46	INTERFACE diffusion_v
	47	MODULE PROCEDURE diffusion_v
	48	MODULE PROCEDURE diffusion_v_ij
	49	END INTERFACE diffusion_v
	50
	51	CONTAINS
	52
	53
	54	!------------------------------------------------------------------------------!
[1682]	55	! Description:
	56	! ------------
	57	!> Call for all grid points
[1]	58	!------------------------------------------------------------------------------!
[1001]	59	SUBROUTINE diffusion_v
[1]	60
[1320]	61	USE arrays_3d, &
[2232]	62	ONLY: ddzu, ddzw, km, tend, u, v, w, drho_air, rho_air_zw
[1320]	63
	64	USE control_parameters, &
[2232]	65	ONLY: constant_top_momentumflux, use_surface_fluxes, &
[1320]	66	use_top_fluxes
	67
	68	USE grid_variables, &
[2232]	69	ONLY: ddx, ddy, ddy2
[1320]	70
	71	USE indices, &
[3241]	72	ONLY: nxl, nxr, nyn, nysv, nzb, nzt, wall_flags_0
[1320]	73
	74	USE kinds
[1]	75
[2232]	76	USE surface_mod, &
	77	ONLY : surf_def_h, surf_def_v, surf_lsm_h, surf_lsm_v, surf_usm_h, &
	78	surf_usm_v
	79
[1]	80	IMPLICIT NONE
	81
[2232]	82	INTEGER(iwp) :: i !< running index x direction
	83	INTEGER(iwp) :: j !< running index y direction
	84	INTEGER(iwp) :: k !< running index z direction
	85	INTEGER(iwp) :: l !< running index of surface type, south- or north-facing wall
	86	INTEGER(iwp) :: m !< running index surface elements
	87	INTEGER(iwp) :: surf_e !< End index of surface elements at (j,i)-gridpoint
	88	INTEGER(iwp) :: surf_s !< Start index of surface elements at (j,i)-gridpoint
[1001]	89
[2232]	90	REAL(wp) :: flag !< flag to mask topography grid points
[3547]	91	REAL(wp) :: kmxm !< diffusion coefficient on leftward side of the v-gridbox - interpolated onto xu-yv grid
	92	REAL(wp) :: kmxp !< diffusion coefficient on rightward side of the v-gridbox - interpolated onto xu-yv grid
	93	REAL(wp) :: kmzm !< diffusion coefficient on bottom of the gridbox - interpolated onto yv-zw grid
	94	REAL(wp) :: kmzp !< diffusion coefficient on top of the gridbox - interpolated onto yv-zw grid
[2232]	95	REAL(wp) :: mask_bottom !< flag to mask vertical upward-facing surface
	96	REAL(wp) :: mask_east !< flag to mask vertical surface south of the grid point
	97	REAL(wp) :: mask_west !< flag to mask vertical surface north of the grid point
	98	REAL(wp) :: mask_top !< flag to mask vertical downward-facing surface
[1]	99
[3634]	100	!$ACC PARALLEL LOOP COLLAPSE(2) PRIVATE(i, j, k, l, m) &
	101	!$ACC PRIVATE(surf_e, surf_s, flag, kmxm, kmxp, kmzm, kmzp) &
	102	!$ACC PRIVATE(mask_bottom, mask_east, mask_west, mask_top) &
	103	!$ACC PRESENT(wall_flags_0, km) &
	104	!$ACC PRESENT(u, v, w) &
	105	!$ACC PRESENT(ddzu, ddzw, drho_air, rho_air_zw) &
	106	!$ACC PRESENT(surf_def_h(0:2), surf_def_v(2:3)) &
	107	!$ACC PRESENT(surf_lsm_h, surf_lsm_v(2:3)) &
	108	!$ACC PRESENT(surf_usm_h, surf_usm_v(0:3)) &
	109	!$ACC PRESENT(tend)
[1]	110	DO i = nxl, nxr
[106]	111	DO j = nysv, nyn
[1]	112	!
	113	!-- Compute horizontal diffusion
[2232]	114	DO k = nzb+1, nzt
	115
[1]	116	!
[2232]	117	!-- Predetermine flag to mask topography and wall-bounded grid points.
	118	!-- It is sufficient to masked only east- and west-facing surfaces, which
	119	!-- need special treatment for the v-component.
	120	flag = MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_0(k,j,i), 2 ) )
	121	mask_east = MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_0(k,j,i+1), 2 ) )
	122	mask_west = MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_0(k,j,i-1), 2 ) )
	123	!
[1]	124	!-- Interpolate eddy diffusivities on staggered gridpoints
[2232]	125	kmxp = 0.25_wp * ( km(k,j,i)+km(k,j,i+1)+km(k,j-1,i)+km(k,j-1,i+1) )
	126	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]	127
[2232]	128	tend(k,j,i) = tend(k,j,i) + ( &
	129	mask_east * kmxp * ( &
	130	( v(k,j,i+1) - v(k,j,i) ) * ddx &
	131	+ ( u(k,j,i+1) - u(k,j-1,i+1) ) * ddy &
	132	) &
	133	- mask_west * kmxm * ( &
	134	( v(k,j,i) - v(k,j,i-1) ) * ddx &
	135	+ ( u(k,j,i) - u(k,j-1,i) ) * ddy &
	136	) &
	137	) * ddx * flag &
	138	+ 2.0_wp * ( &
	139	km(k,j,i) * ( v(k,j+1,i) - v(k,j,i) ) &
	140	- km(k,j-1,i) * ( v(k,j,i) - v(k,j-1,i) ) &
	141	) * ddy2 * flag
	142
[1]	143	ENDDO
	144
	145	!
[2232]	146	!-- Add horizontal momentum flux v'u' at east- (l=2) and west-facing (l=3)
	147	!-- surfaces. Note, in the the flat case, loops won't be entered as
	148	!-- start_index > end_index. Furtermore, note, no vertical natural surfaces
	149	!-- so far.
	150	!-- Default-type surfaces
	151	DO l = 2, 3
	152	surf_s = surf_def_v(l)%start_index(j,i)
	153	surf_e = surf_def_v(l)%end_index(j,i)
	154	DO m = surf_s, surf_e
	155	k = surf_def_v(l)%k(m)
	156	tend(k,j,i) = tend(k,j,i) + &
	157	surf_def_v(l)%mom_flux_uv(m) * ddx
	158	ENDDO
	159	ENDDO
[1]	160	!
[2232]	161	!-- Natural-type surfaces
	162	DO l = 2, 3
	163	surf_s = surf_lsm_v(l)%start_index(j,i)
	164	surf_e = surf_lsm_v(l)%end_index(j,i)
	165	DO m = surf_s, surf_e
	166	k = surf_lsm_v(l)%k(m)
	167	tend(k,j,i) = tend(k,j,i) + &
	168	surf_lsm_v(l)%mom_flux_uv(m) * ddx
	169	ENDDO
	170	ENDDO
[1]	171	!
[2232]	172	!-- Urban-type surfaces
	173	DO l = 2, 3
	174	surf_s = surf_usm_v(l)%start_index(j,i)
	175	surf_e = surf_usm_v(l)%end_index(j,i)
	176	DO m = surf_s, surf_e
	177	k = surf_usm_v(l)%k(m)
	178	tend(k,j,i) = tend(k,j,i) + &
	179	surf_usm_v(l)%mom_flux_uv(m) * ddx
	180	ENDDO
	181	ENDDO
	182	!
	183	!-- Compute vertical diffusion. In case of simulating a surface layer,
	184	!-- respective grid diffusive fluxes are masked (flag 10) within this
	185	!-- loop, and added further below, else, simple gradient approach is
	186	!-- applied. Model top is also mask if top-momentum flux is given.
	187	DO k = nzb+1, nzt
	188	!
	189	!-- Determine flags to mask topography below and above. Flag 2 is
	190	!-- used to mask topography in general, while flag 8 implies also
	191	!-- information about use_surface_fluxes. Flag 9 is used to control
	192	!-- momentum flux at model top.
	193	mask_bottom = MERGE( 1.0_wp, 0.0_wp, &
	194	BTEST( wall_flags_0(k-1,j,i), 8 ) )
	195	mask_top = MERGE( 1.0_wp, 0.0_wp, &
	196	BTEST( wall_flags_0(k+1,j,i), 8 ) ) * &
	197	MERGE( 1.0_wp, 0.0_wp, &
	198	BTEST( wall_flags_0(k+1,j,i), 9 ) )
	199	flag = MERGE( 1.0_wp, 0.0_wp, &
	200	BTEST( wall_flags_0(k,j,i), 2 ) )
	201	!
[1]	202	!-- Interpolate eddy diffusivities on staggered gridpoints
[1340]	203	kmzp = 0.25_wp * &
[1]	204	( km(k,j,i)+km(k+1,j,i)+km(k,j-1,i)+km(k+1,j-1,i) )
[1340]	205	kmzm = 0.25_wp * &
[1]	206	( km(k,j,i)+km(k-1,j,i)+km(k,j-1,i)+km(k-1,j-1,i) )
	207
[1320]	208	tend(k,j,i) = tend(k,j,i) &
	209	& + ( kmzp * ( ( v(k+1,j,i) - v(k,j,i) ) * ddzu(k+1) &
	210	& + ( w(k,j,i) - w(k,j-1,i) ) * ddy &
[2232]	211	& ) * rho_air_zw(k) * mask_top &
[1320]	212	& - kmzm * ( ( v(k,j,i) - v(k-1,j,i) ) * ddzu(k) &
	213	& + ( w(k-1,j,i) - w(k-1,j-1,i) ) * ddy &
[2232]	214	& ) * rho_air_zw(k-1) * mask_bottom &
	215	& ) * ddzw(k) * drho_air(k) * flag
[1]	216	ENDDO
	217
	218	!
	219	!-- Vertical diffusion at the first grid point above the surface,
	220	!-- if the momentum flux at the bottom is given by the Prandtl law
	221	!-- or if it is prescribed by the user.
	222	!-- Difference quotient of the momentum flux is not formed over
	223	!-- half of the grid spacing (2.0*ddzw(k)) any more, since the
[1320]	224	!-- comparison with other (LES) models showed that the values of
[1]	225	!-- the momentum flux becomes too large in this case.
	226	IF ( use_surface_fluxes ) THEN
	227	!
[2232]	228	!-- Default-type surfaces, upward-facing
	229	surf_s = surf_def_h(0)%start_index(j,i)
	230	surf_e = surf_def_h(0)%end_index(j,i)
	231	DO m = surf_s, surf_e
	232	k = surf_def_h(0)%k(m)
[1]	233
[2232]	234	tend(k,j,i) = tend(k,j,i) &
	235	+ ( - ( - surf_def_h(0)%vsws(m) ) &
	236	) * ddzw(k) * drho_air(k)
	237	ENDDO
	238	!
	239	!-- Default-type surfaces, dowward-facing
	240	surf_s = surf_def_h(1)%start_index(j,i)
	241	surf_e = surf_def_h(1)%end_index(j,i)
	242	DO m = surf_s, surf_e
	243	k = surf_def_h(1)%k(m)
[1]	244
[2232]	245	tend(k,j,i) = tend(k,j,i) &
	246	+ ( - surf_def_h(1)%vsws(m) &
	247	) * ddzw(k) * drho_air(k)
	248	ENDDO
[102]	249	!
[2232]	250	!-- Natural-type surfaces, upward-facing
	251	surf_s = surf_lsm_h%start_index(j,i)
	252	surf_e = surf_lsm_h%end_index(j,i)
	253	DO m = surf_s, surf_e
	254	k = surf_lsm_h%k(m)
	255
	256	tend(k,j,i) = tend(k,j,i) &
	257	+ ( - ( - surf_lsm_h%vsws(m) ) &
	258	) * ddzw(k) * drho_air(k)
	259
	260	ENDDO
[102]	261	!
[2232]	262	!-- Urban-type surfaces, upward-facing
	263	surf_s = surf_usm_h%start_index(j,i)
	264	surf_e = surf_usm_h%end_index(j,i)
	265	DO m = surf_s, surf_e
	266	k = surf_usm_h%k(m)
[102]	267
[2232]	268	tend(k,j,i) = tend(k,j,i) &
	269	+ ( - ( - surf_usm_h%vsws(m) ) &
	270	) * ddzw(k) * drho_air(k)
	271
	272	ENDDO
[102]	273	ENDIF
[2232]	274	!
	275	!-- Add momentum flux at model top
[2638]	276	IF ( use_top_fluxes .AND. constant_top_momentumflux ) THEN
[2232]	277	surf_s = surf_def_h(2)%start_index(j,i)
	278	surf_e = surf_def_h(2)%end_index(j,i)
	279	DO m = surf_s, surf_e
[102]	280
[2232]	281	k = surf_def_h(2)%k(m)
	282
	283	tend(k,j,i) = tend(k,j,i) &
	284	+ ( - surf_def_h(2)%vsws(m) ) * ddzw(k) * drho_air(k)
	285	ENDDO
	286	ENDIF
	287
[1]	288	ENDDO
	289	ENDDO
	290
	291	END SUBROUTINE diffusion_v
	292
	293
	294	!------------------------------------------------------------------------------!
[1682]	295	! Description:
	296	! ------------
	297	!> Call for grid point i,j
[1]	298	!------------------------------------------------------------------------------!
[1001]	299	SUBROUTINE diffusion_v_ij( i, j )
[1]	300
[1320]	301	USE arrays_3d, &
[2232]	302	ONLY: ddzu, ddzw, km, tend, u, v, w, drho_air, rho_air_zw
[1320]	303
	304	USE control_parameters, &
[2232]	305	ONLY: constant_top_momentumflux, use_surface_fluxes, &
	306	use_top_fluxes
[1320]	307
	308	USE grid_variables, &
[2232]	309	ONLY: ddx, ddy, ddy2
[1320]	310
	311	USE indices, &
[2232]	312	ONLY: nzb, nzt, wall_flags_0
[1320]	313
	314	USE kinds
[1]	315
[2232]	316	USE surface_mod, &
	317	ONLY : surf_def_h, surf_def_v, surf_lsm_h, surf_lsm_v, surf_usm_h, &
	318	surf_usm_v
	319
[1]	320	IMPLICIT NONE
	321
	322
[2232]	323	INTEGER(iwp) :: i !< running index x direction
	324	INTEGER(iwp) :: j !< running index y direction
	325	INTEGER(iwp) :: k !< running index z direction
	326	INTEGER(iwp) :: l !< running index of surface type, south- or north-facing wall
	327	INTEGER(iwp) :: m !< running index surface elements
	328	INTEGER(iwp) :: surf_e !< End index of surface elements at (j,i)-gridpoint
	329	INTEGER(iwp) :: surf_s !< Start index of surface elements at (j,i)-gridpoint
[1001]	330
[2232]	331	REAL(wp) :: flag !< flag to mask topography grid points
[3547]	332	REAL(wp) :: kmxm !< diffusion coefficient on leftward side of the v-gridbox - interpolated onto xu-yv grid
	333	REAL(wp) :: kmxp !< diffusion coefficient on rightward side of the v-gridbox - interpolated onto xu-yv grid
	334	REAL(wp) :: kmzm !< diffusion coefficient on bottom of the gridbox - interpolated onto xu-zw grid
	335	REAL(wp) :: kmzp !< diffusion coefficient on top of the gridbox - interpolated onto xu-zw grid
[2232]	336	REAL(wp) :: mask_bottom !< flag to mask vertical upward-facing surface
	337	REAL(wp) :: mask_east !< flag to mask vertical surface south of the grid point
	338	REAL(wp) :: mask_west !< flag to mask vertical surface north of the grid point
	339	REAL(wp) :: mask_top !< flag to mask vertical downward-facing surface
	340
[1]	341	!
	342	!-- Compute horizontal diffusion
[2232]	343	DO k = nzb+1, nzt
[1]	344	!
[2232]	345	!-- Predetermine flag to mask topography and wall-bounded grid points.
	346	!-- It is sufficient to masked only east- and west-facing surfaces, which
	347	!-- need special treatment for the v-component.
	348	flag = MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_0(k,j,i), 2 ) )
	349	mask_east = MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_0(k,j,i+1), 2 ) )
	350	mask_west = MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_0(k,j,i-1), 2 ) )
	351	!
[1]	352	!-- Interpolate eddy diffusivities on staggered gridpoints
[1340]	353	kmxp = 0.25_wp * ( km(k,j,i)+km(k,j,i+1)+km(k,j-1,i)+km(k,j-1,i+1) )
	354	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]	355
[2232]	356	tend(k,j,i) = tend(k,j,i) + ( &
	357	mask_east * kmxp * ( &
	358	( v(k,j,i+1) - v(k,j,i) ) * ddx &
	359	+ ( u(k,j,i+1) - u(k,j-1,i+1) ) * ddy &
	360	) &
	361	- mask_west * kmxm * ( &
	362	( v(k,j,i) - v(k,j,i-1) ) * ddx &
	363	+ ( u(k,j,i) - u(k,j-1,i) ) * ddy &
	364	) &
	365	) * ddx * flag &
	366	+ 2.0_wp * ( &
	367	km(k,j,i) * ( v(k,j+1,i) - v(k,j,i) ) &
	368	- km(k,j-1,i) * ( v(k,j,i) - v(k,j-1,i) ) &
	369	) * ddy2 * flag
[1]	370	ENDDO
	371
	372	!
[2232]	373	!-- Add horizontal momentum flux v'u' at east- (l=2) and west-facing (l=3)
	374	!-- surfaces. Note, in the the flat case, loops won't be entered as
	375	!-- start_index > end_index. Furtermore, note, no vertical natural surfaces
	376	!-- so far.
	377	!-- Default-type surfaces
	378	DO l = 2, 3
	379	surf_s = surf_def_v(l)%start_index(j,i)
	380	surf_e = surf_def_v(l)%end_index(j,i)
	381	DO m = surf_s, surf_e
	382	k = surf_def_v(l)%k(m)
	383	tend(k,j,i) = tend(k,j,i) + surf_def_v(l)%mom_flux_uv(m) * ddx
	384	ENDDO
	385	ENDDO
[51]	386	!
[2232]	387	!-- Natural-type surfaces
	388	DO l = 2, 3
	389	surf_s = surf_lsm_v(l)%start_index(j,i)
	390	surf_e = surf_lsm_v(l)%end_index(j,i)
	391	DO m = surf_s, surf_e
	392	k = surf_lsm_v(l)%k(m)
	393	tend(k,j,i) = tend(k,j,i) + surf_lsm_v(l)%mom_flux_uv(m) * ddx
	394	ENDDO
	395	ENDDO
[1]	396	!
[2232]	397	!-- Urban-type surfaces
	398	DO l = 2, 3
	399	surf_s = surf_usm_v(l)%start_index(j,i)
	400	surf_e = surf_usm_v(l)%end_index(j,i)
	401	DO m = surf_s, surf_e
	402	k = surf_usm_v(l)%k(m)
	403	tend(k,j,i) = tend(k,j,i) + surf_usm_v(l)%mom_flux_uv(m) * ddx
	404	ENDDO
	405	ENDDO
[1]	406	!
[2232]	407	!-- Compute vertical diffusion. In case of simulating a surface layer,
	408	!-- respective grid diffusive fluxes are masked (flag 8) within this
	409	!-- loop, and added further below, else, simple gradient approach is
	410	!-- applied. Model top is also mask if top-momentum flux is given.
	411	DO k = nzb+1, nzt
	412	!
	413	!-- Determine flags to mask topography below and above. Flag 2 is
	414	!-- used to mask topography in general, while flag 10 implies also
	415	!-- information about use_surface_fluxes. Flag 9 is used to control
	416	!-- momentum flux at model top.
	417	mask_bottom = MERGE( 1.0_wp, 0.0_wp, &
	418	BTEST( wall_flags_0(k-1,j,i), 8 ) )
	419	mask_top = MERGE( 1.0_wp, 0.0_wp, &
	420	BTEST( wall_flags_0(k+1,j,i), 8 ) ) * &
	421	MERGE( 1.0_wp, 0.0_wp, &
	422	BTEST( wall_flags_0(k+1,j,i), 9 ) )
	423	flag = MERGE( 1.0_wp, 0.0_wp, &
	424	BTEST( wall_flags_0(k,j,i), 2 ) )
	425	!
[1]	426	!-- Interpolate eddy diffusivities on staggered gridpoints
[1340]	427	kmzp = 0.25_wp * ( km(k,j,i)+km(k+1,j,i)+km(k,j-1,i)+km(k+1,j-1,i) )
	428	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]	429
[1320]	430	tend(k,j,i) = tend(k,j,i) &
	431	& + ( kmzp * ( ( v(k+1,j,i) - v(k,j,i) ) * ddzu(k+1) &
	432	& + ( w(k,j,i) - w(k,j-1,i) ) * ddy &
[2232]	433	& ) * rho_air_zw(k) * mask_top &
[1320]	434	& - kmzm * ( ( v(k,j,i) - v(k-1,j,i) ) * ddzu(k) &
	435	& + ( w(k-1,j,i) - w(k-1,j-1,i) ) * ddy &
[2232]	436	& ) * rho_air_zw(k-1) * mask_bottom &
	437	& ) * ddzw(k) * drho_air(k) * flag
[1]	438	ENDDO
	439
	440	!
	441	!-- Vertical diffusion at the first grid point above the surface, if the
	442	!-- momentum flux at the bottom is given by the Prandtl law or if it is
	443	!-- prescribed by the user.
	444	!-- Difference quotient of the momentum flux is not formed over half of
	445	!-- the grid spacing (2.0*ddzw(k)) any more, since the comparison with
[1320]	446	!-- other (LES) models showed that the values of the momentum flux becomes
[1]	447	!-- too large in this case.
	448	IF ( use_surface_fluxes ) THEN
	449	!
[2232]	450	!-- Default-type surfaces, upward-facing
	451	surf_s = surf_def_h(0)%start_index(j,i)
	452	surf_e = surf_def_h(0)%end_index(j,i)
	453	DO m = surf_s, surf_e
	454	k = surf_def_h(0)%k(m)
[1]	455
[2232]	456	tend(k,j,i) = tend(k,j,i) &
	457	+ ( - ( - surf_def_h(0)%vsws(m) ) &
	458	) * ddzw(k) * drho_air(k)
	459	ENDDO
	460	!
	461	!-- Default-type surfaces, dowward-facing
	462	surf_s = surf_def_h(1)%start_index(j,i)
	463	surf_e = surf_def_h(1)%end_index(j,i)
	464	DO m = surf_s, surf_e
	465	k = surf_def_h(1)%k(m)
[1]	466
[2232]	467	tend(k,j,i) = tend(k,j,i) &
	468	+ ( - surf_def_h(1)%vsws(m) &
	469	) * ddzw(k) * drho_air(k)
	470	ENDDO
[102]	471	!
[2232]	472	!-- Natural-type surfaces, upward-facing
	473	surf_s = surf_lsm_h%start_index(j,i)
	474	surf_e = surf_lsm_h%end_index(j,i)
	475	DO m = surf_s, surf_e
	476	k = surf_lsm_h%k(m)
	477
	478	tend(k,j,i) = tend(k,j,i) &
	479	+ ( - ( - surf_lsm_h%vsws(m) ) &
	480	) * ddzw(k) * drho_air(k)
	481
	482	ENDDO
[102]	483	!
[2232]	484	!-- Urban-type surfaces, upward-facing
	485	surf_s = surf_usm_h%start_index(j,i)
	486	surf_e = surf_usm_h%end_index(j,i)
	487	DO m = surf_s, surf_e
	488	k = surf_usm_h%k(m)
[102]	489
[2232]	490	tend(k,j,i) = tend(k,j,i) &
	491	+ ( - ( - surf_usm_h%vsws(m) ) &
	492	) * ddzw(k) * drho_air(k)
	493
	494	ENDDO
[102]	495	ENDIF
[2232]	496	!
	497	!-- Add momentum flux at model top
[2638]	498	IF ( use_top_fluxes .AND. constant_top_momentumflux ) THEN
[2232]	499	surf_s = surf_def_h(2)%start_index(j,i)
	500	surf_e = surf_def_h(2)%end_index(j,i)
	501	DO m = surf_s, surf_e
[102]	502
[2232]	503	k = surf_def_h(2)%k(m)
	504
	505	tend(k,j,i) = tend(k,j,i) &
	506	+ ( - surf_def_h(2)%vsws(m) ) * ddzw(k) * drho_air(k)
	507	ENDDO
	508	ENDIF
	509
[1]	510	END SUBROUTINE diffusion_v_ij
	511
[1321]	512	END MODULE diffusion_v_mod

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