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source: palm/trunk/SOURCE/diffusion_u.f90 @ 2699

Last change on this file since 2699 was 2696, checked in by kanani, 7 years ago
Merge of branch palm4u into trunk
Property svn:keywords set to `Id`
File size: 24.7 KB

Rev	Line
[1873]	1	!> @file diffusion_u.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	!
[2101]	17	! Copyright 1997-2017 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_u.f90 2696 2017-12-14 17:12:51Z kanani $
[2638]	27	! bugfix for constant top momentumflux
	28	!
	29	! 2233 2017-05-30 18:08:54Z suehring
[1321]	30	!
[2233]	31	! 2232 2017-05-30 17:47:52Z suehring
	32	! Adjustments to new topography and surface concept
	33	!
[2119]	34	! 2118 2017-01-17 16:38:49Z raasch
	35	! OpenACC version of subroutine removed
	36	!
[2038]	37	! 2037 2016-10-26 11:15:40Z knoop
	38	! Anelastic approximation implemented
	39	!
[2001]	40	! 2000 2016-08-20 18:09:15Z knoop
	41	! Forced header and separation lines into 80 columns
	42	!
[1874]	43	! 1873 2016-04-18 14:50:06Z maronga
	44	! Module renamed (removed _mod)
	45	!
[1851]	46	! 1850 2016-04-08 13:29:27Z maronga
	47	! Module renamed
	48	!
[1741]	49	! 1740 2016-01-13 08:19:40Z raasch
	50	! unnecessary calculations of kmzm and kmzp in wall bounded parts removed
	51	!
[1692]	52	! 1691 2015-10-26 16:17:44Z maronga
	53	! Formatting corrections.
	54	!
[1683]	55	! 1682 2015-10-07 23:56:08Z knoop
	56	! Code annotations made doxygen readable
	57	!
[1341]	58	! 1340 2014-03-25 19:45:13Z kanani
	59	! REAL constants defined as wp-kind
	60	!
[1321]	61	! 1320 2014-03-20 08:40:49Z raasch
[1320]	62	! ONLY-attribute added to USE-statements,
	63	! kind-parameters added to all INTEGER and REAL declaration statements,
	64	! kinds are defined in new module kinds,
	65	! revision history before 2012 removed,
	66	! comment fields (!:) to be used for variable explanations added to
	67	! all variable declaration statements
[1321]	68	!
[1258]	69	! 1257 2013-11-08 15:18:40Z raasch
	70	! openacc loop and loop vector clauses removed, declare create moved after
	71	! the FORTRAN declaration statement
	72	!
[1132]	73	! 1128 2013-04-12 06:19:32Z raasch
	74	! loop index bounds in accelerator version replaced by i_left, i_right, j_south,
	75	! j_north
	76	!
[1037]	77	! 1036 2012-10-22 13:43:42Z raasch
	78	! code put under GPL (PALM 3.9)
	79	!
[1017]	80	! 1015 2012-09-27 09:23:24Z raasch
	81	! accelerator version (*_acc) added
	82	!
[1002]	83	! 1001 2012-09-13 14:08:46Z raasch
	84	! arrays comunicated by module instead of parameter list
	85	!
[979]	86	! 978 2012-08-09 08:28:32Z fricke
	87	! outflow damping layer removed
	88	! kmym_x/_y and kmyp_x/_y change to kmym and kmyp
	89	!
[1]	90	! Revision 1.1 1997/09/12 06:23:51 raasch
	91	! Initial revision
	92	!
	93	!
	94	! Description:
	95	! ------------
[1682]	96	!> Diffusion term of the u-component
	97	!> @todo additional damping (needed for non-cyclic bc) causes bad vectorization
	98	!> and slows down the speed on NEC about 5-10%
[1]	99	!------------------------------------------------------------------------------!
[1682]	100	MODULE diffusion_u_mod
	101
[1]	102
	103	PRIVATE
[2118]	104	PUBLIC diffusion_u
[1]	105
	106	INTERFACE diffusion_u
	107	MODULE PROCEDURE diffusion_u
	108	MODULE PROCEDURE diffusion_u_ij
	109	END INTERFACE diffusion_u
	110
	111	CONTAINS
	112
	113
	114	!------------------------------------------------------------------------------!
[1682]	115	! Description:
	116	! ------------
	117	!> Call for all grid points
[1]	118	!------------------------------------------------------------------------------!
[1001]	119	SUBROUTINE diffusion_u
[1]	120
[1320]	121	USE arrays_3d, &
[2232]	122	ONLY: ddzu, ddzw, km, tend, u, v, w, drho_air, rho_air_zw
[1320]	123
	124	USE control_parameters, &
[2232]	125	ONLY: constant_top_momentumflux, use_surface_fluxes, &
[1320]	126	use_top_fluxes
	127
	128	USE grid_variables, &
[2232]	129	ONLY: ddx, ddx2, ddy
[1320]	130
	131	USE indices, &
[2232]	132	ONLY: nxl, nxlu, nxr, nyn, nys, nzb, nzt, wall_flags_0
	133
[1320]	134	USE kinds
[1]	135
[2232]	136	USE surface_mod, &
	137	ONLY : surf_def_h, surf_def_v, surf_lsm_h, surf_lsm_v, surf_usm_h, &
	138	surf_usm_v
	139
[1]	140	IMPLICIT NONE
	141
[2232]	142	INTEGER(iwp) :: i !< running index x direction
	143	INTEGER(iwp) :: j !< running index y direction
	144	INTEGER(iwp) :: k !< running index z direction
	145	INTEGER(iwp) :: l !< running index of surface type, south- or north-facing wall
	146	INTEGER(iwp) :: m !< running index surface elements
	147	INTEGER(iwp) :: surf_e !< End index of surface elements at (j,i)-gridpoint
	148	INTEGER(iwp) :: surf_s !< Start index of surface elements at (j,i)-gridpoint
[1001]	149
[2232]	150	REAL(wp) :: flag !< flag to mask topography grid points
	151	REAL(wp) :: kmym !<
	152	REAL(wp) :: kmyp !<
	153	REAL(wp) :: kmzm !<
	154	REAL(wp) :: kmzp !<
	155	REAL(wp) :: mask_bottom !< flag to mask vertical upward-facing surface
	156	REAL(wp) :: mask_north !< flag to mask vertical surface north of the grid point
	157	REAL(wp) :: mask_south !< flag to mask vertical surface south of the grid point
	158	REAL(wp) :: mask_top !< flag to mask vertical downward-facing surface
[1]	159
[56]	160
[2232]	161
[106]	162	DO i = nxlu, nxr
[1001]	163	DO j = nys, nyn
[1]	164	!
	165	!-- Compute horizontal diffusion
[2232]	166	DO k = nzb+1, nzt
[1]	167	!
[2232]	168	!-- Predetermine flag to mask topography and wall-bounded grid points.
	169	!-- It is sufficient to masked only north- and south-facing surfaces, which
	170	!-- need special treatment for the u-component.
	171	flag = MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_0(k,j,i), 1 ) )
	172	mask_south = MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_0(k,j-1,i), 1 ) )
	173	mask_north = MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_0(k,j+1,i), 1 ) )
	174	!
[1]	175	!-- Interpolate eddy diffusivities on staggered gridpoints
[1340]	176	kmyp = 0.25_wp * &
[978]	177	( km(k,j,i)+km(k,j+1,i)+km(k,j,i-1)+km(k,j+1,i-1) )
[1340]	178	kmym = 0.25_wp * &
[978]	179	( km(k,j,i)+km(k,j-1,i)+km(k,j,i-1)+km(k,j-1,i-1) )
[1]	180
[1320]	181	tend(k,j,i) = tend(k,j,i) &
[2232]	182	+ 2.0_wp * ( &
	183	km(k,j,i) * ( u(k,j,i+1) - u(k,j,i) ) &
	184	- km(k,j,i-1) * ( u(k,j,i) - u(k,j,i-1) ) &
	185	) * ddx2 * flag &
	186	+ ( mask_north * ( &
	187	kmyp * ( u(k,j+1,i) - u(k,j,i) ) * ddy &
	188	+ kmyp * ( v(k,j+1,i) - v(k,j+1,i-1) ) * ddx &
	189	) &
	190	- mask_south * ( &
	191	kmym * ( u(k,j,i) - u(k,j-1,i) ) * ddy &
	192	+ kmym * ( v(k,j,i) - v(k,j,i-1) ) * ddx &
	193	) &
	194	) * ddy * flag
[1]	195	ENDDO
	196	!
[2232]	197	!-- Add horizontal momentum flux u'v' at north- (l=0) and south-facing (l=1)
	198	!-- surfaces. Note, in the the flat case, loops won't be entered as
	199	!-- start_index > end_index. Furtermore, note, no vertical natural surfaces
	200	!-- so far.
	201	!-- Default-type surfaces
	202	DO l = 0, 1
	203	surf_s = surf_def_v(l)%start_index(j,i)
	204	surf_e = surf_def_v(l)%end_index(j,i)
	205	DO m = surf_s, surf_e
	206	k = surf_def_v(l)%k(m)
	207	tend(k,j,i) = tend(k,j,i) + &
	208	surf_def_v(l)%mom_flux_uv(m) * ddy
	209	ENDDO
	210	ENDDO
	211	!
	212	!-- Natural-type surfaces
	213	DO l = 0, 1
	214	surf_s = surf_lsm_v(l)%start_index(j,i)
	215	surf_e = surf_lsm_v(l)%end_index(j,i)
	216	DO m = surf_s, surf_e
	217	k = surf_lsm_v(l)%k(m)
	218	tend(k,j,i) = tend(k,j,i) + &
	219	surf_lsm_v(l)%mom_flux_uv(m) * ddy
	220	ENDDO
	221	ENDDO
	222	!
	223	!-- Urban-type surfaces
	224	DO l = 0, 1
	225	surf_s = surf_usm_v(l)%start_index(j,i)
	226	surf_e = surf_usm_v(l)%end_index(j,i)
	227	DO m = surf_s, surf_e
	228	k = surf_usm_v(l)%k(m)
	229	tend(k,j,i) = tend(k,j,i) + &
	230	surf_usm_v(l)%mom_flux_uv(m) * ddy
	231	ENDDO
	232	ENDDO
[51]	233
[1]	234	!
[2232]	235	!-- Compute vertical diffusion. In case of simulating a surface layer,
	236	!-- respective grid diffusive fluxes are masked (flag 8) within this
	237	!-- loop, and added further below, else, simple gradient approach is
	238	!-- applied. Model top is also mask if top-momentum flux is given.
	239	DO k = nzb+1, nzt
[1]	240	!
[2232]	241	!-- Determine flags to mask topography below and above. Flag 1 is
	242	!-- used to mask topography in general, and flag 8 implies
	243	!-- information about use_surface_fluxes. Flag 9 is used to control
	244	!-- momentum flux at model top.
	245	mask_bottom = MERGE( 1.0_wp, 0.0_wp, &
	246	BTEST( wall_flags_0(k-1,j,i), 8 ) )
	247	mask_top = MERGE( 1.0_wp, 0.0_wp, &
	248	BTEST( wall_flags_0(k+1,j,i), 8 ) ) * &
	249	MERGE( 1.0_wp, 0.0_wp, &
	250	BTEST( wall_flags_0(k+1,j,i), 9 ) )
	251	flag = MERGE( 1.0_wp, 0.0_wp, &
	252	BTEST( wall_flags_0(k,j,i), 1 ) )
	253	!
[1]	254	!-- Interpolate eddy diffusivities on staggered gridpoints
[1340]	255	kmzp = 0.25_wp * &
[1]	256	( km(k,j,i)+km(k+1,j,i)+km(k,j,i-1)+km(k+1,j,i-1) )
[1340]	257	kmzm = 0.25_wp * &
[1]	258	( km(k,j,i)+km(k-1,j,i)+km(k,j,i-1)+km(k-1,j,i-1) )
	259
[1320]	260	tend(k,j,i) = tend(k,j,i) &
[2232]	261	+ ( kmzp * ( ( u(k+1,j,i) - u(k,j,i) ) * ddzu(k+1) &
	262	+ ( w(k,j,i) - w(k,j,i-1) ) * ddx &
	263	) * rho_air_zw(k) * mask_top &
	264	- kmzm * ( ( u(k,j,i) - u(k-1,j,i) ) * ddzu(k) &
	265	+ ( w(k-1,j,i) - w(k-1,j,i-1) ) * ddx &
	266	) * rho_air_zw(k-1) * mask_bottom &
	267	) * ddzw(k) * drho_air(k) * flag
[1]	268	ENDDO
	269
	270	!
	271	!-- Vertical diffusion at the first grid point above the surface,
	272	!-- if the momentum flux at the bottom is given by the Prandtl law or
	273	!-- if it is prescribed by the user.
	274	!-- Difference quotient of the momentum flux is not formed over half
	275	!-- of the grid spacing (2.0*ddzw(k)) any more, since the comparison
[1320]	276	!-- with other (LES) models showed that the values of the momentum
[1]	277	!-- flux becomes too large in this case.
	278	!-- The term containing w(k-1,..) (see above equation) is removed here
	279	!-- because the vertical velocity is assumed to be zero at the surface.
	280	IF ( use_surface_fluxes ) THEN
	281	!
[2232]	282	!-- Default-type surfaces, upward-facing
	283	surf_s = surf_def_h(0)%start_index(j,i)
	284	surf_e = surf_def_h(0)%end_index(j,i)
	285	DO m = surf_s, surf_e
[1]	286
[2232]	287	k = surf_def_h(0)%k(m)
[1]	288
[2232]	289	tend(k,j,i) = tend(k,j,i) &
	290	+ ( - ( - surf_def_h(0)%usws(m) ) &
	291	) * ddzw(k) * drho_air(k)
	292	ENDDO
[102]	293	!
[2232]	294	!-- Default-type surfaces, dowward-facing
	295	surf_s = surf_def_h(1)%start_index(j,i)
	296	surf_e = surf_def_h(1)%end_index(j,i)
	297	DO m = surf_s, surf_e
	298
	299	k = surf_def_h(1)%k(m)
	300
	301	tend(k,j,i) = tend(k,j,i) &
	302	+ ( - surf_def_h(1)%usws(m) &
	303	) * ddzw(k) * drho_air(k)
	304	ENDDO
[102]	305	!
[2232]	306	!-- Natural-type surfaces, upward-facing
	307	surf_s = surf_lsm_h%start_index(j,i)
	308	surf_e = surf_lsm_h%end_index(j,i)
	309	DO m = surf_s, surf_e
[102]	310
[2232]	311	k = surf_lsm_h%k(m)
	312
	313	tend(k,j,i) = tend(k,j,i) &
	314	+ ( - ( - surf_lsm_h%usws(m) ) &
	315	) * ddzw(k) * drho_air(k)
	316	ENDDO
	317	!
	318	!-- Urban-type surfaces, upward-facing
	319	surf_s = surf_usm_h%start_index(j,i)
	320	surf_e = surf_usm_h%end_index(j,i)
	321	DO m = surf_s, surf_e
	322
	323	k = surf_usm_h%k(m)
	324
	325	tend(k,j,i) = tend(k,j,i) &
	326	+ ( - ( - surf_usm_h%usws(m) ) &
	327	) * ddzw(k) * drho_air(k)
	328	ENDDO
	329
[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)%usws(m) ) * ddzw(k) * drho_air(k)
	342	ENDDO
	343	ENDIF
	344
[1]	345	ENDDO
	346	ENDDO
	347
	348	END SUBROUTINE diffusion_u
	349
	350
	351	!------------------------------------------------------------------------------!
[1682]	352	! Description:
	353	! ------------
	354	!> Call for grid point i,j
[1]	355	!------------------------------------------------------------------------------!
[1001]	356	SUBROUTINE diffusion_u_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, ddx2, ddy
[1320]	367
	368	USE indices, &
[2232]	369	ONLY: nzb, nzt, wall_flags_0
	370
[1320]	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
[2232]	379	INTEGER(iwp) :: i !< running index x direction
	380	INTEGER(iwp) :: j !< running index y direction
	381	INTEGER(iwp) :: k !< running index z direction
	382	INTEGER(iwp) :: l !< running index of surface type, south- or north-facing wall
	383	INTEGER(iwp) :: m !< running index surface elements
	384	INTEGER(iwp) :: surf_e !< End index of surface elements at (j,i)-gridpoint
	385	INTEGER(iwp) :: surf_s !< Start index of surface elements at (j,i)-gridpoint
[1]	386
[2232]	387	REAL(wp) :: flag !< flag to mask topography grid points
	388	REAL(wp) :: kmym !<
	389	REAL(wp) :: kmyp !<
	390	REAL(wp) :: kmzm !<
	391	REAL(wp) :: kmzp !<
	392	REAL(wp) :: mask_bottom !< flag to mask vertical upward-facing surface
	393	REAL(wp) :: mask_north !< flag to mask vertical surface north of the grid point
	394	REAL(wp) :: mask_south !< flag to mask vertical surface south of the grid point
	395	REAL(wp) :: mask_top !< flag to mask vertical downward-facing surface
	396	!
[1]	397	!-- Compute horizontal diffusion
[2232]	398	DO k = nzb+1, nzt
[1]	399	!
[2232]	400	!-- Predetermine flag to mask topography and wall-bounded grid points.
	401	!-- It is sufficient to masked only north- and south-facing surfaces, which
	402	!-- need special treatment for the u-component.
	403	flag = MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_0(k,j,i), 1 ) )
	404	mask_south = MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_0(k,j-1,i), 1 ) )
	405	mask_north = MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_0(k,j+1,i), 1 ) )
	406	!
[1]	407	!-- Interpolate eddy diffusivities on staggered gridpoints
[1340]	408	kmyp = 0.25_wp * ( km(k,j,i)+km(k,j+1,i)+km(k,j,i-1)+km(k,j+1,i-1) )
	409	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]	410
[1320]	411	tend(k,j,i) = tend(k,j,i) &
[2232]	412	+ 2.0_wp * ( &
	413	km(k,j,i) * ( u(k,j,i+1) - u(k,j,i) ) &
	414	- km(k,j,i-1) * ( u(k,j,i) - u(k,j,i-1) ) &
	415	) * ddx2 * flag &
	416	+ ( &
	417	mask_north * kmyp * ( ( u(k,j+1,i) - u(k,j,i) ) * ddy &
	418	+ ( v(k,j+1,i) - v(k,j+1,i-1) ) * ddx &
	419	) &
	420	- mask_south * kmym * ( ( u(k,j,i) - u(k,j-1,i) ) * ddy &
	421	+ ( v(k,j,i) - v(k,j,i-1) ) * ddx &
	422	) &
	423	) * ddy * flag
[1]	424	ENDDO
	425
	426	!
[2232]	427	!-- Add horizontal momentum flux u'v' at north- (l=0) and south-facing (l=1)
	428	!-- surfaces. Note, in the the flat case, loops won't be entered as
	429	!-- start_index > end_index. Furtermore, note, no vertical natural surfaces
	430	!-- so far.
	431	!-- Default-type surfaces
	432	DO l = 0, 1
	433	surf_s = surf_def_v(l)%start_index(j,i)
	434	surf_e = surf_def_v(l)%end_index(j,i)
	435	DO m = surf_s, surf_e
	436	k = surf_def_v(l)%k(m)
	437	tend(k,j,i) = tend(k,j,i) + surf_def_v(l)%mom_flux_uv(m) * ddy
	438	ENDDO
	439	ENDDO
[51]	440	!
[2232]	441	!-- Natural-type surfaces
	442	DO l = 0, 1
	443	surf_s = surf_lsm_v(l)%start_index(j,i)
	444	surf_e = surf_lsm_v(l)%end_index(j,i)
	445	DO m = surf_s, surf_e
	446	k = surf_lsm_v(l)%k(m)
	447	tend(k,j,i) = tend(k,j,i) + surf_lsm_v(l)%mom_flux_uv(m) * ddy
	448	ENDDO
	449	ENDDO
[1]	450	!
[2232]	451	!-- Urban-type surfaces
	452	DO l = 0, 1
	453	surf_s = surf_usm_v(l)%start_index(j,i)
	454	surf_e = surf_usm_v(l)%end_index(j,i)
	455	DO m = surf_s, surf_e
	456	k = surf_usm_v(l)%k(m)
	457	tend(k,j,i) = tend(k,j,i) + surf_usm_v(l)%mom_flux_uv(m) * ddy
	458	ENDDO
	459	ENDDO
[1]	460	!
[2232]	461	!-- Compute vertical diffusion. In case of simulating a surface layer,
	462	!-- respective grid diffusive fluxes are masked (flag 8) within this
	463	!-- loop, and added further below, else, simple gradient approach is
	464	!-- applied. Model top is also mask if top-momentum flux is given.
	465	DO k = nzb+1, nzt
	466	!
	467	!-- Determine flags to mask topography below and above. Flag 1 is
	468	!-- used to mask topography in general, and flag 8 implies
	469	!-- information about use_surface_fluxes. Flag 9 is used to control
	470	!-- momentum flux at model top.
	471	mask_bottom = MERGE( 1.0_wp, 0.0_wp, &
	472	BTEST( wall_flags_0(k-1,j,i), 8 ) )
	473	mask_top = MERGE( 1.0_wp, 0.0_wp, &
	474	BTEST( wall_flags_0(k+1,j,i), 8 ) ) * &
	475	MERGE( 1.0_wp, 0.0_wp, &
	476	BTEST( wall_flags_0(k+1,j,i), 9 ) )
	477	flag = MERGE( 1.0_wp, 0.0_wp, &
	478	BTEST( wall_flags_0(k,j,i), 1 ) )
	479	!
[1]	480	!-- Interpolate eddy diffusivities on staggered gridpoints
[1340]	481	kmzp = 0.25_wp * ( km(k,j,i)+km(k+1,j,i)+km(k,j,i-1)+km(k+1,j,i-1) )
	482	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]	483
[1320]	484	tend(k,j,i) = tend(k,j,i) &
[2232]	485	+ ( kmzp * ( ( u(k+1,j,i) - u(k,j,i) ) * ddzu(k+1) &
	486	+ ( w(k,j,i) - w(k,j,i-1) ) * ddx &
	487	) * rho_air_zw(k) * mask_top &
	488	- kmzm * ( ( u(k,j,i) - u(k-1,j,i) ) * ddzu(k) &
	489	+ ( w(k-1,j,i) - w(k-1,j,i-1) ) * ddx &
	490	) * rho_air_zw(k-1) * mask_bottom &
	491	) * ddzw(k) * drho_air(k) * flag
[1]	492	ENDDO
	493
	494	!
[2232]	495	!-- Vertical diffusion at the first surface grid points, if the
[1]	496	!-- momentum flux at the bottom is given by the Prandtl law or if it is
	497	!-- prescribed by the user.
	498	!-- Difference quotient of the momentum flux is not formed over half of
	499	!-- the grid spacing (2.0*ddzw(k)) any more, since the comparison with
[1320]	500	!-- other (LES) models showed that the values of the momentum flux becomes
[1]	501	!-- too large in this case.
	502	IF ( use_surface_fluxes ) THEN
	503	!
[2232]	504	!-- Default-type surfaces, upward-facing
	505	surf_s = surf_def_h(0)%start_index(j,i)
	506	surf_e = surf_def_h(0)%end_index(j,i)
	507	DO m = surf_s, surf_e
[1]	508
[2232]	509	k = surf_def_h(0)%k(m)
[1]	510
[2232]	511	tend(k,j,i) = tend(k,j,i) &
	512	+ ( - ( - surf_def_h(0)%usws(m) ) &
	513	) * ddzw(k) * drho_air(k)
	514	ENDDO
[102]	515	!
[2232]	516	!-- Default-type surfaces, dowward-facing (except for model-top fluxes)
	517	surf_s = surf_def_h(1)%start_index(j,i)
	518	surf_e = surf_def_h(1)%end_index(j,i)
	519	DO m = surf_s, surf_e
	520
	521	k = surf_def_h(1)%k(m)
	522
	523	tend(k,j,i) = tend(k,j,i) &
	524	+ ( - surf_def_h(1)%usws(m) &
	525	) * ddzw(k) * drho_air(k)
	526	ENDDO
[102]	527	!
[2232]	528	!-- Natural-type surfaces, upward-facing
	529	surf_s = surf_lsm_h%start_index(j,i)
	530	surf_e = surf_lsm_h%end_index(j,i)
	531	DO m = surf_s, surf_e
[102]	532
[2232]	533	k = surf_lsm_h%k(m)
	534
	535	tend(k,j,i) = tend(k,j,i) &
	536	+ ( - ( - surf_lsm_h%usws(m) ) &
	537	) * ddzw(k) * drho_air(k)
	538	ENDDO
	539	!
	540	!-- Urban-type surfaces, upward-facing
	541	surf_s = surf_usm_h%start_index(j,i)
	542	surf_e = surf_usm_h%end_index(j,i)
	543	DO m = surf_s, surf_e
	544
	545	k = surf_usm_h%k(m)
	546
	547	tend(k,j,i) = tend(k,j,i) &
	548	+ ( - ( - surf_usm_h%usws(m) ) &
	549	) * ddzw(k) * drho_air(k)
	550	ENDDO
	551
[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)%usws(m) ) * ddzw(k) * drho_air(k)
	564	ENDDO
	565	ENDIF
	566
	567
[1]	568	END SUBROUTINE diffusion_u_ij
	569
	570	END MODULE diffusion_u_mod

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