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source: palm/trunk/SOURCE/diffusion_v.f90 @ 3573

Last change on this file since 3573 was 3547, checked in by suehring, 6 years ago
variable description added some routines
Property svn:keywords set to `Id`
File size: 24.9 KB

Rev	Line
[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 3547 2018-11-21 13:21:24Z raasch $
[3547]	27	! variables documented
	28	!
	29	! 3241 2018-09-12 15:02:00Z raasch
[3241]	30	! unused variables removed
	31	!
	32	! 2718 2018-01-02 08:49:38Z maronga
[2716]	33	! Corrected "Former revisions" section
	34	!
	35	! 2696 2017-12-14 17:12:51Z kanani
	36	! Change in file header (GPL part)
	37	!
	38	! 2638 2017-11-23 12:44:23Z raasch
[2638]	39	! bugfix for constant top momentumflux
	40	!
	41	! 2233 2017-05-30 18:08:54Z suehring
[1321]	42	!
[2233]	43	! 2232 2017-05-30 17:47:52Z suehring
	44	! Adjustments to new topography and surface concept
	45	!
[2119]	46	! 2118 2017-01-17 16:38:49Z raasch
	47	! OpenACC version of subroutine removed
	48	!
[2038]	49	! 2037 2016-10-26 11:15:40Z knoop
	50	! Anelastic approximation implemented
	51	!
[2001]	52	! 2000 2016-08-20 18:09:15Z knoop
	53	! Forced header and separation lines into 80 columns
	54	!
[1874]	55	! 1873 2016-04-18 14:50:06Z maronga
	56	! Module renamed (removed _mod)
	57	!
[1851]	58	! 1850 2016-04-08 13:29:27Z maronga
	59	! Module renamed
	60	!
[1741]	61	! 1740 2016-01-13 08:19:40Z raasch
	62	! unnecessary calculations of kmzm and kmzp in wall bounded parts removed
	63	!
[1683]	64	! 1682 2015-10-07 23:56:08Z knoop
	65	! Code annotations made doxygen readable
	66	!
[1341]	67	! 1340 2014-03-25 19:45:13Z kanani
	68	! REAL constants defined as wp-kind
	69	!
[1321]	70	! 1320 2014-03-20 08:40:49Z raasch
[1320]	71	! ONLY-attribute added to USE-statements,
	72	! kind-parameters added to all INTEGER and REAL declaration statements,
	73	! kinds are defined in new module kinds,
	74	! revision history before 2012 removed,
	75	! comment fields (!:) to be used for variable explanations added to
	76	! all variable declaration statements
[1321]	77	!
[1258]	78	! 1257 2013-11-08 15:18:40Z raasch
	79	! openacc loop and loop vector clauses removed, declare create moved after
	80	! the FORTRAN declaration statement
	81	!
[1132]	82	! 1128 2013-04-12 06:19:32Z raasch
	83	! loop index bounds in accelerator version replaced by i_left, i_right, j_south,
	84	! j_north
	85	!
[1037]	86	! 1036 2012-10-22 13:43:42Z raasch
	87	! code put under GPL (PALM 3.9)
	88	!
[1017]	89	! 1015 2012-09-27 09:23:24Z raasch
	90	! accelerator version (*_acc) added
	91	!
[1002]	92	! 1001 2012-09-13 14:08:46Z raasch
	93	! arrays comunicated by module instead of parameter list
	94	!
[979]	95	! 978 2012-08-09 08:28:32Z fricke
	96	! outflow damping layer removed
	97	! kmxm_x/_y and kmxp_x/_y change to kmxm and kmxp
	98	!
[1]	99	! Revision 1.1 1997/09/12 06:24:01 raasch
	100	! Initial revision
	101	!
	102	!
	103	! Description:
	104	! ------------
[1682]	105	!> Diffusion term of the v-component
[1]	106	!------------------------------------------------------------------------------!
[1682]	107	MODULE diffusion_v_mod
	108
[1]	109
	110	PRIVATE
[2118]	111	PUBLIC diffusion_v
[1]	112
	113	INTERFACE diffusion_v
	114	MODULE PROCEDURE diffusion_v
	115	MODULE PROCEDURE diffusion_v_ij
	116	END INTERFACE diffusion_v
	117
	118	CONTAINS
	119
	120
	121	!------------------------------------------------------------------------------!
[1682]	122	! Description:
	123	! ------------
	124	!> Call for all grid points
[1]	125	!------------------------------------------------------------------------------!
[1001]	126	SUBROUTINE diffusion_v
[1]	127
[1320]	128	USE arrays_3d, &
[2232]	129	ONLY: ddzu, ddzw, km, tend, u, v, w, drho_air, rho_air_zw
[1320]	130
	131	USE control_parameters, &
[2232]	132	ONLY: constant_top_momentumflux, use_surface_fluxes, &
[1320]	133	use_top_fluxes
	134
	135	USE grid_variables, &
[2232]	136	ONLY: ddx, ddy, ddy2
[1320]	137
	138	USE indices, &
[3241]	139	ONLY: nxl, nxr, nyn, nysv, nzb, nzt, wall_flags_0
[1320]	140
	141	USE kinds
[1]	142
[2232]	143	USE surface_mod, &
	144	ONLY : surf_def_h, surf_def_v, surf_lsm_h, surf_lsm_v, surf_usm_h, &
	145	surf_usm_v
	146
[1]	147	IMPLICIT NONE
	148
[2232]	149	INTEGER(iwp) :: i !< running index x direction
	150	INTEGER(iwp) :: j !< running index y direction
	151	INTEGER(iwp) :: k !< running index z direction
	152	INTEGER(iwp) :: l !< running index of surface type, south- or north-facing wall
	153	INTEGER(iwp) :: m !< running index surface elements
	154	INTEGER(iwp) :: surf_e !< End index of surface elements at (j,i)-gridpoint
	155	INTEGER(iwp) :: surf_s !< Start index of surface elements at (j,i)-gridpoint
[1001]	156
[2232]	157	REAL(wp) :: flag !< flag to mask topography grid points
[3547]	158	REAL(wp) :: kmxm !< diffusion coefficient on leftward side of the v-gridbox - interpolated onto xu-yv grid
	159	REAL(wp) :: kmxp !< diffusion coefficient on rightward side of the v-gridbox - interpolated onto xu-yv grid
	160	REAL(wp) :: kmzm !< diffusion coefficient on bottom of the gridbox - interpolated onto yv-zw grid
	161	REAL(wp) :: kmzp !< diffusion coefficient on top of the gridbox - interpolated onto yv-zw grid
[2232]	162	REAL(wp) :: mask_bottom !< flag to mask vertical upward-facing surface
	163	REAL(wp) :: mask_east !< flag to mask vertical surface south of the grid point
	164	REAL(wp) :: mask_west !< flag to mask vertical surface north of the grid point
	165	REAL(wp) :: mask_top !< flag to mask vertical downward-facing surface
[1]	166
	167	DO i = nxl, nxr
[106]	168	DO j = nysv, nyn
[1]	169	!
	170	!-- Compute horizontal diffusion
[2232]	171	DO k = nzb+1, nzt
	172
[1]	173	!
[2232]	174	!-- Predetermine flag to mask topography and wall-bounded grid points.
	175	!-- It is sufficient to masked only east- and west-facing surfaces, which
	176	!-- need special treatment for the v-component.
	177	flag = MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_0(k,j,i), 2 ) )
	178	mask_east = MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_0(k,j,i+1), 2 ) )
	179	mask_west = MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_0(k,j,i-1), 2 ) )
	180	!
[1]	181	!-- Interpolate eddy diffusivities on staggered gridpoints
[2232]	182	kmxp = 0.25_wp * ( km(k,j,i)+km(k,j,i+1)+km(k,j-1,i)+km(k,j-1,i+1) )
	183	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]	184
[2232]	185	tend(k,j,i) = tend(k,j,i) + ( &
	186	mask_east * kmxp * ( &
	187	( v(k,j,i+1) - v(k,j,i) ) * ddx &
	188	+ ( u(k,j,i+1) - u(k,j-1,i+1) ) * ddy &
	189	) &
	190	- mask_west * kmxm * ( &
	191	( v(k,j,i) - v(k,j,i-1) ) * ddx &
	192	+ ( u(k,j,i) - u(k,j-1,i) ) * ddy &
	193	) &
	194	) * ddx * flag &
	195	+ 2.0_wp * ( &
	196	km(k,j,i) * ( v(k,j+1,i) - v(k,j,i) ) &
	197	- km(k,j-1,i) * ( v(k,j,i) - v(k,j-1,i) ) &
	198	) * ddy2 * flag
	199
[1]	200	ENDDO
	201
	202	!
[2232]	203	!-- Add horizontal momentum flux v'u' at east- (l=2) and west-facing (l=3)
	204	!-- surfaces. Note, in the the flat case, loops won't be entered as
	205	!-- start_index > end_index. Furtermore, note, no vertical natural surfaces
	206	!-- so far.
	207	!-- Default-type surfaces
	208	DO l = 2, 3
	209	surf_s = surf_def_v(l)%start_index(j,i)
	210	surf_e = surf_def_v(l)%end_index(j,i)
	211	DO m = surf_s, surf_e
	212	k = surf_def_v(l)%k(m)
	213	tend(k,j,i) = tend(k,j,i) + &
	214	surf_def_v(l)%mom_flux_uv(m) * ddx
	215	ENDDO
	216	ENDDO
[1]	217	!
[2232]	218	!-- Natural-type surfaces
	219	DO l = 2, 3
	220	surf_s = surf_lsm_v(l)%start_index(j,i)
	221	surf_e = surf_lsm_v(l)%end_index(j,i)
	222	DO m = surf_s, surf_e
	223	k = surf_lsm_v(l)%k(m)
	224	tend(k,j,i) = tend(k,j,i) + &
	225	surf_lsm_v(l)%mom_flux_uv(m) * ddx
	226	ENDDO
	227	ENDDO
[1]	228	!
[2232]	229	!-- Urban-type surfaces
	230	DO l = 2, 3
	231	surf_s = surf_usm_v(l)%start_index(j,i)
	232	surf_e = surf_usm_v(l)%end_index(j,i)
	233	DO m = surf_s, surf_e
	234	k = surf_usm_v(l)%k(m)
	235	tend(k,j,i) = tend(k,j,i) + &
	236	surf_usm_v(l)%mom_flux_uv(m) * ddx
	237	ENDDO
	238	ENDDO
	239	!
	240	!-- Compute vertical diffusion. In case of simulating a surface layer,
	241	!-- respective grid diffusive fluxes are masked (flag 10) within this
	242	!-- loop, and added further below, else, simple gradient approach is
	243	!-- applied. Model top is also mask if top-momentum flux is given.
	244	DO k = nzb+1, nzt
	245	!
	246	!-- Determine flags to mask topography below and above. Flag 2 is
	247	!-- used to mask topography in general, while flag 8 implies also
	248	!-- information about use_surface_fluxes. Flag 9 is used to control
	249	!-- momentum flux at model top.
	250	mask_bottom = MERGE( 1.0_wp, 0.0_wp, &
	251	BTEST( wall_flags_0(k-1,j,i), 8 ) )
	252	mask_top = MERGE( 1.0_wp, 0.0_wp, &
	253	BTEST( wall_flags_0(k+1,j,i), 8 ) ) * &
	254	MERGE( 1.0_wp, 0.0_wp, &
	255	BTEST( wall_flags_0(k+1,j,i), 9 ) )
	256	flag = MERGE( 1.0_wp, 0.0_wp, &
	257	BTEST( wall_flags_0(k,j,i), 2 ) )
	258	!
[1]	259	!-- Interpolate eddy diffusivities on staggered gridpoints
[1340]	260	kmzp = 0.25_wp * &
[1]	261	( km(k,j,i)+km(k+1,j,i)+km(k,j-1,i)+km(k+1,j-1,i) )
[1340]	262	kmzm = 0.25_wp * &
[1]	263	( km(k,j,i)+km(k-1,j,i)+km(k,j-1,i)+km(k-1,j-1,i) )
	264
[1320]	265	tend(k,j,i) = tend(k,j,i) &
	266	& + ( kmzp * ( ( v(k+1,j,i) - v(k,j,i) ) * ddzu(k+1) &
	267	& + ( w(k,j,i) - w(k,j-1,i) ) * ddy &
[2232]	268	& ) * rho_air_zw(k) * mask_top &
[1320]	269	& - kmzm * ( ( v(k,j,i) - v(k-1,j,i) ) * ddzu(k) &
	270	& + ( w(k-1,j,i) - w(k-1,j-1,i) ) * ddy &
[2232]	271	& ) * rho_air_zw(k-1) * mask_bottom &
	272	& ) * ddzw(k) * drho_air(k) * flag
[1]	273	ENDDO
	274
	275	!
	276	!-- Vertical diffusion at the first grid point above the surface,
	277	!-- if the momentum flux at the bottom is given by the Prandtl law
	278	!-- or if it is prescribed by the user.
	279	!-- Difference quotient of the momentum flux is not formed over
	280	!-- half of the grid spacing (2.0*ddzw(k)) any more, since the
[1320]	281	!-- comparison with other (LES) models showed that the values of
[1]	282	!-- the momentum flux becomes too large in this case.
	283	IF ( use_surface_fluxes ) THEN
	284	!
[2232]	285	!-- Default-type surfaces, upward-facing
	286	surf_s = surf_def_h(0)%start_index(j,i)
	287	surf_e = surf_def_h(0)%end_index(j,i)
	288	DO m = surf_s, surf_e
	289	k = surf_def_h(0)%k(m)
[1]	290
[2232]	291	tend(k,j,i) = tend(k,j,i) &
	292	+ ( - ( - surf_def_h(0)%vsws(m) ) &
	293	) * ddzw(k) * drho_air(k)
	294	ENDDO
	295	!
	296	!-- Default-type surfaces, dowward-facing
	297	surf_s = surf_def_h(1)%start_index(j,i)
	298	surf_e = surf_def_h(1)%end_index(j,i)
	299	DO m = surf_s, surf_e
	300	k = surf_def_h(1)%k(m)
[1]	301
[2232]	302	tend(k,j,i) = tend(k,j,i) &
	303	+ ( - surf_def_h(1)%vsws(m) &
	304	) * ddzw(k) * drho_air(k)
	305	ENDDO
[102]	306	!
[2232]	307	!-- Natural-type surfaces, upward-facing
	308	surf_s = surf_lsm_h%start_index(j,i)
	309	surf_e = surf_lsm_h%end_index(j,i)
	310	DO m = surf_s, surf_e
	311	k = surf_lsm_h%k(m)
	312
	313	tend(k,j,i) = tend(k,j,i) &
	314	+ ( - ( - surf_lsm_h%vsws(m) ) &
	315	) * ddzw(k) * drho_air(k)
	316
	317	ENDDO
[102]	318	!
[2232]	319	!-- Urban-type surfaces, upward-facing
	320	surf_s = surf_usm_h%start_index(j,i)
	321	surf_e = surf_usm_h%end_index(j,i)
	322	DO m = surf_s, surf_e
	323	k = surf_usm_h%k(m)
[102]	324
[2232]	325	tend(k,j,i) = tend(k,j,i) &
	326	+ ( - ( - surf_usm_h%vsws(m) ) &
	327	) * ddzw(k) * drho_air(k)
	328
	329	ENDDO
[102]	330	ENDIF
[2232]	331	!
	332	!-- Add momentum flux at model top
[2638]	333	IF ( use_top_fluxes .AND. constant_top_momentumflux ) THEN
[2232]	334	surf_s = surf_def_h(2)%start_index(j,i)
	335	surf_e = surf_def_h(2)%end_index(j,i)
	336	DO m = surf_s, surf_e
[102]	337
[2232]	338	k = surf_def_h(2)%k(m)
	339
	340	tend(k,j,i) = tend(k,j,i) &
	341	+ ( - surf_def_h(2)%vsws(m) ) * ddzw(k) * drho_air(k)
	342	ENDDO
	343	ENDIF
	344
[1]	345	ENDDO
	346	ENDDO
	347
	348	END SUBROUTINE diffusion_v
	349
	350
	351	!------------------------------------------------------------------------------!
[1682]	352	! Description:
	353	! ------------
	354	!> Call for grid point i,j
[1]	355	!------------------------------------------------------------------------------!
[1001]	356	SUBROUTINE diffusion_v_ij( i, j )
[1]	357
[1320]	358	USE arrays_3d, &
[2232]	359	ONLY: ddzu, ddzw, km, tend, u, v, w, drho_air, rho_air_zw
[1320]	360
	361	USE control_parameters, &
[2232]	362	ONLY: constant_top_momentumflux, use_surface_fluxes, &
	363	use_top_fluxes
[1320]	364
	365	USE grid_variables, &
[2232]	366	ONLY: ddx, ddy, ddy2
[1320]	367
	368	USE indices, &
[2232]	369	ONLY: nzb, nzt, wall_flags_0
[1320]	370
	371	USE kinds
[1]	372
[2232]	373	USE surface_mod, &
	374	ONLY : surf_def_h, surf_def_v, surf_lsm_h, surf_lsm_v, surf_usm_h, &
	375	surf_usm_v
	376
[1]	377	IMPLICIT NONE
	378
	379
[2232]	380	INTEGER(iwp) :: i !< running index x direction
	381	INTEGER(iwp) :: j !< running index y direction
	382	INTEGER(iwp) :: k !< running index z direction
	383	INTEGER(iwp) :: l !< running index of surface type, south- or north-facing wall
	384	INTEGER(iwp) :: m !< running index surface elements
	385	INTEGER(iwp) :: surf_e !< End index of surface elements at (j,i)-gridpoint
	386	INTEGER(iwp) :: surf_s !< Start index of surface elements at (j,i)-gridpoint
[1001]	387
[2232]	388	REAL(wp) :: flag !< flag to mask topography grid points
[3547]	389	REAL(wp) :: kmxm !< diffusion coefficient on leftward side of the v-gridbox - interpolated onto xu-yv grid
	390	REAL(wp) :: kmxp !< diffusion coefficient on rightward side of the v-gridbox - interpolated onto xu-yv grid
	391	REAL(wp) :: kmzm !< diffusion coefficient on bottom of the gridbox - interpolated onto xu-zw grid
	392	REAL(wp) :: kmzp !< diffusion coefficient on top of the gridbox - interpolated onto xu-zw grid
[2232]	393	REAL(wp) :: mask_bottom !< flag to mask vertical upward-facing surface
	394	REAL(wp) :: mask_east !< flag to mask vertical surface south of the grid point
	395	REAL(wp) :: mask_west !< flag to mask vertical surface north of the grid point
	396	REAL(wp) :: mask_top !< flag to mask vertical downward-facing surface
	397
[1]	398	!
	399	!-- Compute horizontal diffusion
[2232]	400	DO k = nzb+1, nzt
[1]	401	!
[2232]	402	!-- Predetermine flag to mask topography and wall-bounded grid points.
	403	!-- It is sufficient to masked only east- and west-facing surfaces, which
	404	!-- need special treatment for the v-component.
	405	flag = MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_0(k,j,i), 2 ) )
	406	mask_east = MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_0(k,j,i+1), 2 ) )
	407	mask_west = MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_0(k,j,i-1), 2 ) )
	408	!
[1]	409	!-- Interpolate eddy diffusivities on staggered gridpoints
[1340]	410	kmxp = 0.25_wp * ( km(k,j,i)+km(k,j,i+1)+km(k,j-1,i)+km(k,j-1,i+1) )
	411	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]	412
[2232]	413	tend(k,j,i) = tend(k,j,i) + ( &
	414	mask_east * kmxp * ( &
	415	( v(k,j,i+1) - v(k,j,i) ) * ddx &
	416	+ ( u(k,j,i+1) - u(k,j-1,i+1) ) * ddy &
	417	) &
	418	- mask_west * kmxm * ( &
	419	( v(k,j,i) - v(k,j,i-1) ) * ddx &
	420	+ ( u(k,j,i) - u(k,j-1,i) ) * ddy &
	421	) &
	422	) * ddx * flag &
	423	+ 2.0_wp * ( &
	424	km(k,j,i) * ( v(k,j+1,i) - v(k,j,i) ) &
	425	- km(k,j-1,i) * ( v(k,j,i) - v(k,j-1,i) ) &
	426	) * ddy2 * flag
[1]	427	ENDDO
	428
	429	!
[2232]	430	!-- Add horizontal momentum flux v'u' at east- (l=2) and west-facing (l=3)
	431	!-- surfaces. Note, in the the flat case, loops won't be entered as
	432	!-- start_index > end_index. Furtermore, note, no vertical natural surfaces
	433	!-- so far.
	434	!-- Default-type surfaces
	435	DO l = 2, 3
	436	surf_s = surf_def_v(l)%start_index(j,i)
	437	surf_e = surf_def_v(l)%end_index(j,i)
	438	DO m = surf_s, surf_e
	439	k = surf_def_v(l)%k(m)
	440	tend(k,j,i) = tend(k,j,i) + surf_def_v(l)%mom_flux_uv(m) * ddx
	441	ENDDO
	442	ENDDO
[51]	443	!
[2232]	444	!-- Natural-type surfaces
	445	DO l = 2, 3
	446	surf_s = surf_lsm_v(l)%start_index(j,i)
	447	surf_e = surf_lsm_v(l)%end_index(j,i)
	448	DO m = surf_s, surf_e
	449	k = surf_lsm_v(l)%k(m)
	450	tend(k,j,i) = tend(k,j,i) + surf_lsm_v(l)%mom_flux_uv(m) * ddx
	451	ENDDO
	452	ENDDO
[1]	453	!
[2232]	454	!-- Urban-type surfaces
	455	DO l = 2, 3
	456	surf_s = surf_usm_v(l)%start_index(j,i)
	457	surf_e = surf_usm_v(l)%end_index(j,i)
	458	DO m = surf_s, surf_e
	459	k = surf_usm_v(l)%k(m)
	460	tend(k,j,i) = tend(k,j,i) + surf_usm_v(l)%mom_flux_uv(m) * ddx
	461	ENDDO
	462	ENDDO
[1]	463	!
[2232]	464	!-- Compute vertical diffusion. In case of simulating a surface layer,
	465	!-- respective grid diffusive fluxes are masked (flag 8) within this
	466	!-- loop, and added further below, else, simple gradient approach is
	467	!-- applied. Model top is also mask if top-momentum flux is given.
	468	DO k = nzb+1, nzt
	469	!
	470	!-- Determine flags to mask topography below and above. Flag 2 is
	471	!-- used to mask topography in general, while flag 10 implies also
	472	!-- information about use_surface_fluxes. Flag 9 is used to control
	473	!-- momentum flux at model top.
	474	mask_bottom = MERGE( 1.0_wp, 0.0_wp, &
	475	BTEST( wall_flags_0(k-1,j,i), 8 ) )
	476	mask_top = MERGE( 1.0_wp, 0.0_wp, &
	477	BTEST( wall_flags_0(k+1,j,i), 8 ) ) * &
	478	MERGE( 1.0_wp, 0.0_wp, &
	479	BTEST( wall_flags_0(k+1,j,i), 9 ) )
	480	flag = MERGE( 1.0_wp, 0.0_wp, &
	481	BTEST( wall_flags_0(k,j,i), 2 ) )
	482	!
[1]	483	!-- Interpolate eddy diffusivities on staggered gridpoints
[1340]	484	kmzp = 0.25_wp * ( km(k,j,i)+km(k+1,j,i)+km(k,j-1,i)+km(k+1,j-1,i) )
	485	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]	486
[1320]	487	tend(k,j,i) = tend(k,j,i) &
	488	& + ( kmzp * ( ( v(k+1,j,i) - v(k,j,i) ) * ddzu(k+1) &
	489	& + ( w(k,j,i) - w(k,j-1,i) ) * ddy &
[2232]	490	& ) * rho_air_zw(k) * mask_top &
[1320]	491	& - kmzm * ( ( v(k,j,i) - v(k-1,j,i) ) * ddzu(k) &
	492	& + ( w(k-1,j,i) - w(k-1,j-1,i) ) * ddy &
[2232]	493	& ) * rho_air_zw(k-1) * mask_bottom &
	494	& ) * ddzw(k) * drho_air(k) * flag
[1]	495	ENDDO
	496
	497	!
	498	!-- Vertical diffusion at the first grid point above the surface, if the
	499	!-- momentum flux at the bottom is given by the Prandtl law or if it is
	500	!-- prescribed by the user.
	501	!-- Difference quotient of the momentum flux is not formed over half of
	502	!-- the grid spacing (2.0*ddzw(k)) any more, since the comparison with
[1320]	503	!-- other (LES) models showed that the values of the momentum flux becomes
[1]	504	!-- too large in this case.
	505	IF ( use_surface_fluxes ) THEN
	506	!
[2232]	507	!-- Default-type surfaces, upward-facing
	508	surf_s = surf_def_h(0)%start_index(j,i)
	509	surf_e = surf_def_h(0)%end_index(j,i)
	510	DO m = surf_s, surf_e
	511	k = surf_def_h(0)%k(m)
[1]	512
[2232]	513	tend(k,j,i) = tend(k,j,i) &
	514	+ ( - ( - surf_def_h(0)%vsws(m) ) &
	515	) * ddzw(k) * drho_air(k)
	516	ENDDO
	517	!
	518	!-- Default-type surfaces, dowward-facing
	519	surf_s = surf_def_h(1)%start_index(j,i)
	520	surf_e = surf_def_h(1)%end_index(j,i)
	521	DO m = surf_s, surf_e
	522	k = surf_def_h(1)%k(m)
[1]	523
[2232]	524	tend(k,j,i) = tend(k,j,i) &
	525	+ ( - surf_def_h(1)%vsws(m) &
	526	) * ddzw(k) * drho_air(k)
	527	ENDDO
[102]	528	!
[2232]	529	!-- Natural-type surfaces, upward-facing
	530	surf_s = surf_lsm_h%start_index(j,i)
	531	surf_e = surf_lsm_h%end_index(j,i)
	532	DO m = surf_s, surf_e
	533	k = surf_lsm_h%k(m)
	534
	535	tend(k,j,i) = tend(k,j,i) &
	536	+ ( - ( - surf_lsm_h%vsws(m) ) &
	537	) * ddzw(k) * drho_air(k)
	538
	539	ENDDO
[102]	540	!
[2232]	541	!-- Urban-type surfaces, upward-facing
	542	surf_s = surf_usm_h%start_index(j,i)
	543	surf_e = surf_usm_h%end_index(j,i)
	544	DO m = surf_s, surf_e
	545	k = surf_usm_h%k(m)
[102]	546
[2232]	547	tend(k,j,i) = tend(k,j,i) &
	548	+ ( - ( - surf_usm_h%vsws(m) ) &
	549	) * ddzw(k) * drho_air(k)
	550
	551	ENDDO
[102]	552	ENDIF
[2232]	553	!
	554	!-- Add momentum flux at model top
[2638]	555	IF ( use_top_fluxes .AND. constant_top_momentumflux ) THEN
[2232]	556	surf_s = surf_def_h(2)%start_index(j,i)
	557	surf_e = surf_def_h(2)%end_index(j,i)
	558	DO m = surf_s, surf_e
[102]	559
[2232]	560	k = surf_def_h(2)%k(m)
	561
	562	tend(k,j,i) = tend(k,j,i) &
	563	+ ( - surf_def_h(2)%vsws(m) ) * ddzw(k) * drho_air(k)
	564	ENDDO
	565	ENDIF
	566
[1]	567	END SUBROUTINE diffusion_v_ij
	568
[1321]	569	END MODULE diffusion_v_mod

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