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source: palm/trunk/SOURCE/diffusion_u.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: 24.5 KB

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[1873]	1	!> @file diffusion_u.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_u.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	!
[1692]	46	! 1691 2015-10-26 16:17:44Z maronga
	47	! Formatting corrections.
	48	!
[1683]	49	! 1682 2015-10-07 23:56:08Z knoop
	50	! Code annotations made doxygen readable
	51	!
[1341]	52	! 1340 2014-03-25 19:45:13Z kanani
	53	! REAL constants defined as wp-kind
	54	!
[1321]	55	! 1320 2014-03-20 08:40:49Z raasch
[1320]	56	! ONLY-attribute added to USE-statements,
	57	! kind-parameters added to all INTEGER and REAL declaration statements,
	58	! kinds are defined in new module kinds,
	59	! revision history before 2012 removed,
	60	! comment fields (!:) to be used for variable explanations added to
	61	! all variable declaration statements
[1321]	62	!
[1258]	63	! 1257 2013-11-08 15:18:40Z raasch
	64	! openacc loop and loop vector clauses removed, declare create moved after
	65	! the FORTRAN declaration statement
	66	!
[1132]	67	! 1128 2013-04-12 06:19:32Z raasch
	68	! loop index bounds in accelerator version replaced by i_left, i_right, j_south,
	69	! j_north
	70	!
[1037]	71	! 1036 2012-10-22 13:43:42Z raasch
	72	! code put under GPL (PALM 3.9)
	73	!
[1017]	74	! 1015 2012-09-27 09:23:24Z raasch
	75	! accelerator version (*_acc) added
	76	!
[1002]	77	! 1001 2012-09-13 14:08:46Z raasch
	78	! arrays comunicated by module instead of parameter list
	79	!
[979]	80	! 978 2012-08-09 08:28:32Z fricke
	81	! outflow damping layer removed
	82	! kmym_x/_y and kmyp_x/_y change to kmym and kmyp
	83	!
[1]	84	! Revision 1.1 1997/09/12 06:23:51 raasch
	85	! Initial revision
	86	!
	87	!
	88	! Description:
	89	! ------------
[1682]	90	!> Diffusion term of the u-component
	91	!> @todo additional damping (needed for non-cyclic bc) causes bad vectorization
	92	!> and slows down the speed on NEC about 5-10%
[1]	93	!------------------------------------------------------------------------------!
[1682]	94	MODULE diffusion_u_mod
	95
[1]	96
	97	PRIVATE
[2118]	98	PUBLIC diffusion_u
[1]	99
	100	INTERFACE diffusion_u
	101	MODULE PROCEDURE diffusion_u
	102	MODULE PROCEDURE diffusion_u_ij
	103	END INTERFACE diffusion_u
	104
	105	CONTAINS
	106
	107
	108	!------------------------------------------------------------------------------!
[1682]	109	! Description:
	110	! ------------
	111	!> Call for all grid points
[1]	112	!------------------------------------------------------------------------------!
[1001]	113	SUBROUTINE diffusion_u
[1]	114
[1320]	115	USE arrays_3d, &
[2232]	116	ONLY: ddzu, ddzw, km, tend, u, v, w, drho_air, rho_air_zw
[1320]	117
	118	USE control_parameters, &
[2232]	119	ONLY: constant_top_momentumflux, use_surface_fluxes, &
[1320]	120	use_top_fluxes
	121
	122	USE grid_variables, &
[2232]	123	ONLY: ddx, ddx2, ddy
[1320]	124
	125	USE indices, &
[2232]	126	ONLY: nxl, nxlu, nxr, nyn, nys, nzb, nzt, wall_flags_0
	127
[1320]	128	USE kinds
[1]	129
[2232]	130	USE surface_mod, &
	131	ONLY : surf_def_h, surf_def_v, surf_lsm_h, surf_lsm_v, surf_usm_h, &
	132	surf_usm_v
	133
[1]	134	IMPLICIT NONE
	135
[2232]	136	INTEGER(iwp) :: i !< running index x direction
	137	INTEGER(iwp) :: j !< running index y direction
	138	INTEGER(iwp) :: k !< running index z direction
	139	INTEGER(iwp) :: l !< running index of surface type, south- or north-facing wall
	140	INTEGER(iwp) :: m !< running index surface elements
	141	INTEGER(iwp) :: surf_e !< End index of surface elements at (j,i)-gridpoint
	142	INTEGER(iwp) :: surf_s !< Start index of surface elements at (j,i)-gridpoint
[1001]	143
[2232]	144	REAL(wp) :: flag !< flag to mask topography grid points
	145	REAL(wp) :: kmym !<
	146	REAL(wp) :: kmyp !<
	147	REAL(wp) :: kmzm !<
	148	REAL(wp) :: kmzp !<
	149	REAL(wp) :: mask_bottom !< flag to mask vertical upward-facing surface
	150	REAL(wp) :: mask_north !< flag to mask vertical surface north of the grid point
	151	REAL(wp) :: mask_south !< flag to mask vertical surface south of the grid point
	152	REAL(wp) :: mask_top !< flag to mask vertical downward-facing surface
[1]	153
[56]	154
[2232]	155
[106]	156	DO i = nxlu, nxr
[1001]	157	DO j = nys, nyn
[1]	158	!
	159	!-- Compute horizontal diffusion
[2232]	160	DO k = nzb+1, nzt
[1]	161	!
[2232]	162	!-- Predetermine flag to mask topography and wall-bounded grid points.
	163	!-- It is sufficient to masked only north- and south-facing surfaces, which
	164	!-- need special treatment for the u-component.
	165	flag = MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_0(k,j,i), 1 ) )
	166	mask_south = MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_0(k,j-1,i), 1 ) )
	167	mask_north = MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_0(k,j+1,i), 1 ) )
	168	!
[1]	169	!-- Interpolate eddy diffusivities on staggered gridpoints
[1340]	170	kmyp = 0.25_wp * &
[978]	171	( km(k,j,i)+km(k,j+1,i)+km(k,j,i-1)+km(k,j+1,i-1) )
[1340]	172	kmym = 0.25_wp * &
[978]	173	( km(k,j,i)+km(k,j-1,i)+km(k,j,i-1)+km(k,j-1,i-1) )
[1]	174
[1320]	175	tend(k,j,i) = tend(k,j,i) &
[2232]	176	+ 2.0_wp * ( &
	177	km(k,j,i) * ( u(k,j,i+1) - u(k,j,i) ) &
	178	- km(k,j,i-1) * ( u(k,j,i) - u(k,j,i-1) ) &
	179	) * ddx2 * flag &
	180	+ ( mask_north * ( &
	181	kmyp * ( u(k,j+1,i) - u(k,j,i) ) * ddy &
	182	+ kmyp * ( v(k,j+1,i) - v(k,j+1,i-1) ) * ddx &
	183	) &
	184	- mask_south * ( &
	185	kmym * ( u(k,j,i) - u(k,j-1,i) ) * ddy &
	186	+ kmym * ( v(k,j,i) - v(k,j,i-1) ) * ddx &
	187	) &
	188	) * ddy * flag
[1]	189	ENDDO
	190	!
[2232]	191	!-- Add horizontal momentum flux u'v' at north- (l=0) and south-facing (l=1)
	192	!-- surfaces. Note, in the the flat case, loops won't be entered as
	193	!-- start_index > end_index. Furtermore, note, no vertical natural surfaces
	194	!-- so far.
	195	!-- Default-type surfaces
	196	DO l = 0, 1
	197	surf_s = surf_def_v(l)%start_index(j,i)
	198	surf_e = surf_def_v(l)%end_index(j,i)
	199	DO m = surf_s, surf_e
	200	k = surf_def_v(l)%k(m)
	201	tend(k,j,i) = tend(k,j,i) + &
	202	surf_def_v(l)%mom_flux_uv(m) * ddy
	203	ENDDO
	204	ENDDO
	205	!
	206	!-- Natural-type surfaces
	207	DO l = 0, 1
	208	surf_s = surf_lsm_v(l)%start_index(j,i)
	209	surf_e = surf_lsm_v(l)%end_index(j,i)
	210	DO m = surf_s, surf_e
	211	k = surf_lsm_v(l)%k(m)
	212	tend(k,j,i) = tend(k,j,i) + &
	213	surf_lsm_v(l)%mom_flux_uv(m) * ddy
	214	ENDDO
	215	ENDDO
	216	!
	217	!-- Urban-type surfaces
	218	DO l = 0, 1
	219	surf_s = surf_usm_v(l)%start_index(j,i)
	220	surf_e = surf_usm_v(l)%end_index(j,i)
	221	DO m = surf_s, surf_e
	222	k = surf_usm_v(l)%k(m)
	223	tend(k,j,i) = tend(k,j,i) + &
	224	surf_usm_v(l)%mom_flux_uv(m) * ddy
	225	ENDDO
	226	ENDDO
[51]	227
[1]	228	!
[2232]	229	!-- Compute vertical diffusion. In case of simulating a surface layer,
	230	!-- respective grid diffusive fluxes are masked (flag 8) within this
	231	!-- loop, and added further below, else, simple gradient approach is
	232	!-- applied. Model top is also mask if top-momentum flux is given.
	233	DO k = nzb+1, nzt
[1]	234	!
[2232]	235	!-- Determine flags to mask topography below and above. Flag 1 is
	236	!-- used to mask topography in general, and flag 8 implies
	237	!-- information about use_surface_fluxes. Flag 9 is used to control
	238	!-- momentum flux at model top.
	239	mask_bottom = MERGE( 1.0_wp, 0.0_wp, &
	240	BTEST( wall_flags_0(k-1,j,i), 8 ) )
	241	mask_top = MERGE( 1.0_wp, 0.0_wp, &
	242	BTEST( wall_flags_0(k+1,j,i), 8 ) ) * &
	243	MERGE( 1.0_wp, 0.0_wp, &
	244	BTEST( wall_flags_0(k+1,j,i), 9 ) )
	245	flag = MERGE( 1.0_wp, 0.0_wp, &
	246	BTEST( wall_flags_0(k,j,i), 1 ) )
	247	!
[1]	248	!-- Interpolate eddy diffusivities on staggered gridpoints
[1340]	249	kmzp = 0.25_wp * &
[1]	250	( km(k,j,i)+km(k+1,j,i)+km(k,j,i-1)+km(k+1,j,i-1) )
[1340]	251	kmzm = 0.25_wp * &
[1]	252	( km(k,j,i)+km(k-1,j,i)+km(k,j,i-1)+km(k-1,j,i-1) )
	253
[1320]	254	tend(k,j,i) = tend(k,j,i) &
[2232]	255	+ ( kmzp * ( ( u(k+1,j,i) - u(k,j,i) ) * ddzu(k+1) &
	256	+ ( w(k,j,i) - w(k,j,i-1) ) * ddx &
	257	) * rho_air_zw(k) * mask_top &
	258	- kmzm * ( ( u(k,j,i) - u(k-1,j,i) ) * ddzu(k) &
	259	+ ( w(k-1,j,i) - w(k-1,j,i-1) ) * ddx &
	260	) * rho_air_zw(k-1) * mask_bottom &
	261	) * ddzw(k) * drho_air(k) * flag
[1]	262	ENDDO
	263
	264	!
	265	!-- Vertical diffusion at the first grid point above the surface,
	266	!-- if the momentum flux at the bottom is given by the Prandtl law or
	267	!-- if it is prescribed by the user.
	268	!-- Difference quotient of the momentum flux is not formed over half
	269	!-- of the grid spacing (2.0*ddzw(k)) any more, since the comparison
[1320]	270	!-- with other (LES) models showed that the values of the momentum
[1]	271	!-- flux becomes too large in this case.
	272	!-- The term containing w(k-1,..) (see above equation) is removed here
	273	!-- because the vertical velocity is assumed to be zero at the surface.
	274	IF ( use_surface_fluxes ) THEN
	275	!
[2232]	276	!-- Default-type surfaces, upward-facing
	277	surf_s = surf_def_h(0)%start_index(j,i)
	278	surf_e = surf_def_h(0)%end_index(j,i)
	279	DO m = surf_s, surf_e
[1]	280
[2232]	281	k = surf_def_h(0)%k(m)
[1]	282
[2232]	283	tend(k,j,i) = tend(k,j,i) &
	284	+ ( - ( - surf_def_h(0)%usws(m) ) &
	285	) * ddzw(k) * drho_air(k)
	286	ENDDO
[102]	287	!
[2232]	288	!-- Default-type surfaces, dowward-facing
	289	surf_s = surf_def_h(1)%start_index(j,i)
	290	surf_e = surf_def_h(1)%end_index(j,i)
	291	DO m = surf_s, surf_e
	292
	293	k = surf_def_h(1)%k(m)
	294
	295	tend(k,j,i) = tend(k,j,i) &
	296	+ ( - surf_def_h(1)%usws(m) &
	297	) * ddzw(k) * drho_air(k)
	298	ENDDO
[102]	299	!
[2232]	300	!-- Natural-type surfaces, upward-facing
	301	surf_s = surf_lsm_h%start_index(j,i)
	302	surf_e = surf_lsm_h%end_index(j,i)
	303	DO m = surf_s, surf_e
[102]	304
[2232]	305	k = surf_lsm_h%k(m)
	306
	307	tend(k,j,i) = tend(k,j,i) &
	308	+ ( - ( - surf_lsm_h%usws(m) ) &
	309	) * ddzw(k) * drho_air(k)
	310	ENDDO
	311	!
	312	!-- Urban-type surfaces, upward-facing
	313	surf_s = surf_usm_h%start_index(j,i)
	314	surf_e = surf_usm_h%end_index(j,i)
	315	DO m = surf_s, surf_e
	316
	317	k = surf_usm_h%k(m)
	318
	319	tend(k,j,i) = tend(k,j,i) &
	320	+ ( - ( - surf_usm_h%usws(m) ) &
	321	) * ddzw(k) * drho_air(k)
	322	ENDDO
	323
[102]	324	ENDIF
[2232]	325	!
	326	!-- Add momentum flux at model top
	327	IF ( use_top_fluxes ) THEN
	328	surf_s = surf_def_h(2)%start_index(j,i)
	329	surf_e = surf_def_h(2)%end_index(j,i)
	330	DO m = surf_s, surf_e
[102]	331
[2232]	332	k = surf_def_h(2)%k(m)
	333
	334	tend(k,j,i) = tend(k,j,i) &
	335	+ ( - surf_def_h(2)%usws(m) ) * ddzw(k) * drho_air(k)
	336	ENDDO
	337	ENDIF
	338
[1]	339	ENDDO
	340	ENDDO
	341
	342	END SUBROUTINE diffusion_u
	343
	344
	345	!------------------------------------------------------------------------------!
[1682]	346	! Description:
	347	! ------------
	348	!> Call for grid point i,j
[1]	349	!------------------------------------------------------------------------------!
[1001]	350	SUBROUTINE diffusion_u_ij( i, j )
[1]	351
[1320]	352	USE arrays_3d, &
[2232]	353	ONLY: ddzu, ddzw, km, tend, u, v, w, drho_air, rho_air_zw
[1320]	354
	355	USE control_parameters, &
[2232]	356	ONLY: constant_top_momentumflux, use_surface_fluxes, &
	357	use_top_fluxes
[1320]	358
	359	USE grid_variables, &
[2232]	360	ONLY: ddx, ddx2, ddy
[1320]	361
	362	USE indices, &
[2232]	363	ONLY: nzb, nzt, wall_flags_0
	364
[1320]	365	USE kinds
[1]	366
[2232]	367	USE surface_mod, &
	368	ONLY : surf_def_h, surf_def_v, surf_lsm_h, surf_lsm_v, surf_usm_h, &
	369	surf_usm_v
	370
[1]	371	IMPLICIT NONE
	372
[2232]	373	INTEGER(iwp) :: i !< running index x direction
	374	INTEGER(iwp) :: j !< running index y direction
	375	INTEGER(iwp) :: k !< running index z direction
	376	INTEGER(iwp) :: l !< running index of surface type, south- or north-facing wall
	377	INTEGER(iwp) :: m !< running index surface elements
	378	INTEGER(iwp) :: surf_e !< End index of surface elements at (j,i)-gridpoint
	379	INTEGER(iwp) :: surf_s !< Start index of surface elements at (j,i)-gridpoint
[1]	380
[2232]	381	REAL(wp) :: flag !< flag to mask topography grid points
	382	REAL(wp) :: kmym !<
	383	REAL(wp) :: kmyp !<
	384	REAL(wp) :: kmzm !<
	385	REAL(wp) :: kmzp !<
	386	REAL(wp) :: mask_bottom !< flag to mask vertical upward-facing surface
	387	REAL(wp) :: mask_north !< flag to mask vertical surface north of the grid point
	388	REAL(wp) :: mask_south !< flag to mask vertical surface south of the grid point
	389	REAL(wp) :: mask_top !< flag to mask vertical downward-facing surface
	390	!
[1]	391	!-- Compute horizontal diffusion
[2232]	392	DO k = nzb+1, nzt
[1]	393	!
[2232]	394	!-- Predetermine flag to mask topography and wall-bounded grid points.
	395	!-- It is sufficient to masked only north- and south-facing surfaces, which
	396	!-- need special treatment for the u-component.
	397	flag = MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_0(k,j,i), 1 ) )
	398	mask_south = MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_0(k,j-1,i), 1 ) )
	399	mask_north = MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_0(k,j+1,i), 1 ) )
	400	!
[1]	401	!-- Interpolate eddy diffusivities on staggered gridpoints
[1340]	402	kmyp = 0.25_wp * ( km(k,j,i)+km(k,j+1,i)+km(k,j,i-1)+km(k,j+1,i-1) )
	403	kmym = 0.25_wp * ( km(k,j,i)+km(k,j-1,i)+km(k,j,i-1)+km(k,j-1,i-1) )
[1]	404
[1320]	405	tend(k,j,i) = tend(k,j,i) &
[2232]	406	+ 2.0_wp * ( &
	407	km(k,j,i) * ( u(k,j,i+1) - u(k,j,i) ) &
	408	- km(k,j,i-1) * ( u(k,j,i) - u(k,j,i-1) ) &
	409	) * ddx2 * flag &
	410	+ ( &
	411	mask_north * kmyp * ( ( u(k,j+1,i) - u(k,j,i) ) * ddy &
	412	+ ( v(k,j+1,i) - v(k,j+1,i-1) ) * ddx &
	413	) &
	414	- mask_south * kmym * ( ( u(k,j,i) - u(k,j-1,i) ) * ddy &
	415	+ ( v(k,j,i) - v(k,j,i-1) ) * ddx &
	416	) &
	417	) * ddy * flag
[1]	418	ENDDO
	419
	420	!
[2232]	421	!-- Add horizontal momentum flux u'v' at north- (l=0) and south-facing (l=1)
	422	!-- surfaces. Note, in the the flat case, loops won't be entered as
	423	!-- start_index > end_index. Furtermore, note, no vertical natural surfaces
	424	!-- so far.
	425	!-- Default-type surfaces
	426	DO l = 0, 1
	427	surf_s = surf_def_v(l)%start_index(j,i)
	428	surf_e = surf_def_v(l)%end_index(j,i)
	429	DO m = surf_s, surf_e
	430	k = surf_def_v(l)%k(m)
	431	tend(k,j,i) = tend(k,j,i) + surf_def_v(l)%mom_flux_uv(m) * ddy
	432	ENDDO
	433	ENDDO
[51]	434	!
[2232]	435	!-- Natural-type surfaces
	436	DO l = 0, 1
	437	surf_s = surf_lsm_v(l)%start_index(j,i)
	438	surf_e = surf_lsm_v(l)%end_index(j,i)
	439	DO m = surf_s, surf_e
	440	k = surf_lsm_v(l)%k(m)
	441	tend(k,j,i) = tend(k,j,i) + surf_lsm_v(l)%mom_flux_uv(m) * ddy
	442	ENDDO
	443	ENDDO
[1]	444	!
[2232]	445	!-- Urban-type surfaces
	446	DO l = 0, 1
	447	surf_s = surf_usm_v(l)%start_index(j,i)
	448	surf_e = surf_usm_v(l)%end_index(j,i)
	449	DO m = surf_s, surf_e
	450	k = surf_usm_v(l)%k(m)
	451	tend(k,j,i) = tend(k,j,i) + surf_usm_v(l)%mom_flux_uv(m) * ddy
	452	ENDDO
	453	ENDDO
[1]	454	!
[2232]	455	!-- Compute vertical diffusion. In case of simulating a surface layer,
	456	!-- respective grid diffusive fluxes are masked (flag 8) within this
	457	!-- loop, and added further below, else, simple gradient approach is
	458	!-- applied. Model top is also mask if top-momentum flux is given.
	459	DO k = nzb+1, nzt
	460	!
	461	!-- Determine flags to mask topography below and above. Flag 1 is
	462	!-- used to mask topography in general, and flag 8 implies
	463	!-- information about use_surface_fluxes. Flag 9 is used to control
	464	!-- momentum flux at model top.
	465	mask_bottom = MERGE( 1.0_wp, 0.0_wp, &
	466	BTEST( wall_flags_0(k-1,j,i), 8 ) )
	467	mask_top = MERGE( 1.0_wp, 0.0_wp, &
	468	BTEST( wall_flags_0(k+1,j,i), 8 ) ) * &
	469	MERGE( 1.0_wp, 0.0_wp, &
	470	BTEST( wall_flags_0(k+1,j,i), 9 ) )
	471	flag = MERGE( 1.0_wp, 0.0_wp, &
	472	BTEST( wall_flags_0(k,j,i), 1 ) )
	473	!
[1]	474	!-- Interpolate eddy diffusivities on staggered gridpoints
[1340]	475	kmzp = 0.25_wp * ( km(k,j,i)+km(k+1,j,i)+km(k,j,i-1)+km(k+1,j,i-1) )
	476	kmzm = 0.25_wp * ( km(k,j,i)+km(k-1,j,i)+km(k,j,i-1)+km(k-1,j,i-1) )
[1]	477
[1320]	478	tend(k,j,i) = tend(k,j,i) &
[2232]	479	+ ( kmzp * ( ( u(k+1,j,i) - u(k,j,i) ) * ddzu(k+1) &
	480	+ ( w(k,j,i) - w(k,j,i-1) ) * ddx &
	481	) * rho_air_zw(k) * mask_top &
	482	- kmzm * ( ( u(k,j,i) - u(k-1,j,i) ) * ddzu(k) &
	483	+ ( w(k-1,j,i) - w(k-1,j,i-1) ) * ddx &
	484	) * rho_air_zw(k-1) * mask_bottom &
	485	) * ddzw(k) * drho_air(k) * flag
[1]	486	ENDDO
	487
	488	!
[2232]	489	!-- Vertical diffusion at the first surface grid points, if the
[1]	490	!-- momentum flux at the bottom is given by the Prandtl law or if it is
	491	!-- prescribed by the user.
	492	!-- Difference quotient of the momentum flux is not formed over half of
	493	!-- the grid spacing (2.0*ddzw(k)) any more, since the comparison with
[1320]	494	!-- other (LES) models showed that the values of the momentum flux becomes
[1]	495	!-- too large in this case.
	496	IF ( use_surface_fluxes ) THEN
	497	!
[2232]	498	!-- Default-type surfaces, upward-facing
	499	surf_s = surf_def_h(0)%start_index(j,i)
	500	surf_e = surf_def_h(0)%end_index(j,i)
	501	DO m = surf_s, surf_e
[1]	502
[2232]	503	k = surf_def_h(0)%k(m)
[1]	504
[2232]	505	tend(k,j,i) = tend(k,j,i) &
	506	+ ( - ( - surf_def_h(0)%usws(m) ) &
	507	) * ddzw(k) * drho_air(k)
	508	ENDDO
[102]	509	!
[2232]	510	!-- Default-type surfaces, dowward-facing (except for model-top fluxes)
	511	surf_s = surf_def_h(1)%start_index(j,i)
	512	surf_e = surf_def_h(1)%end_index(j,i)
	513	DO m = surf_s, surf_e
	514
	515	k = surf_def_h(1)%k(m)
	516
	517	tend(k,j,i) = tend(k,j,i) &
	518	+ ( - surf_def_h(1)%usws(m) &
	519	) * ddzw(k) * drho_air(k)
	520	ENDDO
[102]	521	!
[2232]	522	!-- Natural-type surfaces, upward-facing
	523	surf_s = surf_lsm_h%start_index(j,i)
	524	surf_e = surf_lsm_h%end_index(j,i)
	525	DO m = surf_s, surf_e
[102]	526
[2232]	527	k = surf_lsm_h%k(m)
	528
	529	tend(k,j,i) = tend(k,j,i) &
	530	+ ( - ( - surf_lsm_h%usws(m) ) &
	531	) * ddzw(k) * drho_air(k)
	532	ENDDO
	533	!
	534	!-- Urban-type surfaces, upward-facing
	535	surf_s = surf_usm_h%start_index(j,i)
	536	surf_e = surf_usm_h%end_index(j,i)
	537	DO m = surf_s, surf_e
	538
	539	k = surf_usm_h%k(m)
	540
	541	tend(k,j,i) = tend(k,j,i) &
	542	+ ( - ( - surf_usm_h%usws(m) ) &
	543	) * ddzw(k) * drho_air(k)
	544	ENDDO
	545
[102]	546	ENDIF
[2232]	547	!
	548	!-- Add momentum flux at model top
	549	IF ( use_top_fluxes ) THEN
	550	surf_s = surf_def_h(2)%start_index(j,i)
	551	surf_e = surf_def_h(2)%end_index(j,i)
	552	DO m = surf_s, surf_e
[102]	553
[2232]	554	k = surf_def_h(2)%k(m)
	555
	556	tend(k,j,i) = tend(k,j,i) &
	557	+ ( - surf_def_h(2)%usws(m) ) * ddzw(k) * drho_air(k)
	558	ENDDO
	559	ENDIF
	560
	561
[1]	562	END SUBROUTINE diffusion_u_ij
	563
	564	END MODULE diffusion_u_mod

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