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source: palm/trunk/SOURCE/diffusion_u.f90 @ 3038

Last change on this file since 3038 was 2718, checked in by maronga, 7 years ago
deleting of deprecated files; headers updated where needed
Property svn:keywords set to `Id`
File size: 24.8 KB

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[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	!
[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_u.f90 2718 2018-01-02 08:49:38Z gronemeier $
[2716]	27	! Corrected "Former revisions" section
	28	!
	29	! 2696 2017-12-14 17:12:51Z kanani
	30	! Change in file header (GPL part)
	31	!
	32	! 2638 2017-11-23 12:44:23Z raasch
[2638]	33	! bugfix for constant top momentumflux
	34	!
	35	! 2233 2017-05-30 18:08:54Z suehring
[1321]	36	!
[2233]	37	! 2232 2017-05-30 17:47:52Z suehring
	38	! Adjustments to new topography and surface concept
	39	!
[2119]	40	! 2118 2017-01-17 16:38:49Z raasch
	41	! OpenACC version of subroutine removed
	42	!
[2038]	43	! 2037 2016-10-26 11:15:40Z knoop
	44	! Anelastic approximation implemented
	45	!
[2001]	46	! 2000 2016-08-20 18:09:15Z knoop
	47	! Forced header and separation lines into 80 columns
	48	!
[1874]	49	! 1873 2016-04-18 14:50:06Z maronga
	50	! Module renamed (removed _mod)
	51	!
[1851]	52	! 1850 2016-04-08 13:29:27Z maronga
	53	! Module renamed
	54	!
[1741]	55	! 1740 2016-01-13 08:19:40Z raasch
	56	! unnecessary calculations of kmzm and kmzp in wall bounded parts removed
	57	!
[1692]	58	! 1691 2015-10-26 16:17:44Z maronga
	59	! Formatting corrections.
	60	!
[1683]	61	! 1682 2015-10-07 23:56:08Z knoop
	62	! Code annotations made doxygen readable
	63	!
[1341]	64	! 1340 2014-03-25 19:45:13Z kanani
	65	! REAL constants defined as wp-kind
	66	!
[1321]	67	! 1320 2014-03-20 08:40:49Z raasch
[1320]	68	! ONLY-attribute added to USE-statements,
	69	! kind-parameters added to all INTEGER and REAL declaration statements,
	70	! kinds are defined in new module kinds,
	71	! revision history before 2012 removed,
	72	! comment fields (!:) to be used for variable explanations added to
	73	! all variable declaration statements
[1321]	74	!
[1258]	75	! 1257 2013-11-08 15:18:40Z raasch
	76	! openacc loop and loop vector clauses removed, declare create moved after
	77	! the FORTRAN declaration statement
	78	!
[1132]	79	! 1128 2013-04-12 06:19:32Z raasch
	80	! loop index bounds in accelerator version replaced by i_left, i_right, j_south,
	81	! j_north
	82	!
[1037]	83	! 1036 2012-10-22 13:43:42Z raasch
	84	! code put under GPL (PALM 3.9)
	85	!
[1017]	86	! 1015 2012-09-27 09:23:24Z raasch
	87	! accelerator version (*_acc) added
	88	!
[1002]	89	! 1001 2012-09-13 14:08:46Z raasch
	90	! arrays comunicated by module instead of parameter list
	91	!
[979]	92	! 978 2012-08-09 08:28:32Z fricke
	93	! outflow damping layer removed
	94	! kmym_x/_y and kmyp_x/_y change to kmym and kmyp
	95	!
[1]	96	! Revision 1.1 1997/09/12 06:23:51 raasch
	97	! Initial revision
	98	!
	99	!
	100	! Description:
	101	! ------------
[1682]	102	!> Diffusion term of the u-component
	103	!> @todo additional damping (needed for non-cyclic bc) causes bad vectorization
	104	!> and slows down the speed on NEC about 5-10%
[1]	105	!------------------------------------------------------------------------------!
[1682]	106	MODULE diffusion_u_mod
	107
[1]	108
	109	PRIVATE
[2118]	110	PUBLIC diffusion_u
[1]	111
	112	INTERFACE diffusion_u
	113	MODULE PROCEDURE diffusion_u
	114	MODULE PROCEDURE diffusion_u_ij
	115	END INTERFACE diffusion_u
	116
	117	CONTAINS
	118
	119
	120	!------------------------------------------------------------------------------!
[1682]	121	! Description:
	122	! ------------
	123	!> Call for all grid points
[1]	124	!------------------------------------------------------------------------------!
[1001]	125	SUBROUTINE diffusion_u
[1]	126
[1320]	127	USE arrays_3d, &
[2232]	128	ONLY: ddzu, ddzw, km, tend, u, v, w, drho_air, rho_air_zw
[1320]	129
	130	USE control_parameters, &
[2232]	131	ONLY: constant_top_momentumflux, use_surface_fluxes, &
[1320]	132	use_top_fluxes
	133
	134	USE grid_variables, &
[2232]	135	ONLY: ddx, ddx2, ddy
[1320]	136
	137	USE indices, &
[2232]	138	ONLY: nxl, nxlu, nxr, nyn, nys, nzb, nzt, wall_flags_0
	139
[1320]	140	USE kinds
[1]	141
[2232]	142	USE surface_mod, &
	143	ONLY : surf_def_h, surf_def_v, surf_lsm_h, surf_lsm_v, surf_usm_h, &
	144	surf_usm_v
	145
[1]	146	IMPLICIT NONE
	147
[2232]	148	INTEGER(iwp) :: i !< running index x direction
	149	INTEGER(iwp) :: j !< running index y direction
	150	INTEGER(iwp) :: k !< running index z direction
	151	INTEGER(iwp) :: l !< running index of surface type, south- or north-facing wall
	152	INTEGER(iwp) :: m !< running index surface elements
	153	INTEGER(iwp) :: surf_e !< End index of surface elements at (j,i)-gridpoint
	154	INTEGER(iwp) :: surf_s !< Start index of surface elements at (j,i)-gridpoint
[1001]	155
[2232]	156	REAL(wp) :: flag !< flag to mask topography grid points
	157	REAL(wp) :: kmym !<
	158	REAL(wp) :: kmyp !<
	159	REAL(wp) :: kmzm !<
	160	REAL(wp) :: kmzp !<
	161	REAL(wp) :: mask_bottom !< flag to mask vertical upward-facing surface
	162	REAL(wp) :: mask_north !< flag to mask vertical surface north of the grid point
	163	REAL(wp) :: mask_south !< flag to mask vertical surface south of the grid point
	164	REAL(wp) :: mask_top !< flag to mask vertical downward-facing surface
[1]	165
[56]	166
[2232]	167
[106]	168	DO i = nxlu, nxr
[1001]	169	DO j = nys, nyn
[1]	170	!
	171	!-- Compute horizontal diffusion
[2232]	172	DO k = nzb+1, nzt
[1]	173	!
[2232]	174	!-- Predetermine flag to mask topography and wall-bounded grid points.
	175	!-- It is sufficient to masked only north- and south-facing surfaces, which
	176	!-- need special treatment for the u-component.
	177	flag = MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_0(k,j,i), 1 ) )
	178	mask_south = MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_0(k,j-1,i), 1 ) )
	179	mask_north = MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_0(k,j+1,i), 1 ) )
	180	!
[1]	181	!-- Interpolate eddy diffusivities on staggered gridpoints
[1340]	182	kmyp = 0.25_wp * &
[978]	183	( km(k,j,i)+km(k,j+1,i)+km(k,j,i-1)+km(k,j+1,i-1) )
[1340]	184	kmym = 0.25_wp * &
[978]	185	( km(k,j,i)+km(k,j-1,i)+km(k,j,i-1)+km(k,j-1,i-1) )
[1]	186
[1320]	187	tend(k,j,i) = tend(k,j,i) &
[2232]	188	+ 2.0_wp * ( &
	189	km(k,j,i) * ( u(k,j,i+1) - u(k,j,i) ) &
	190	- km(k,j,i-1) * ( u(k,j,i) - u(k,j,i-1) ) &
	191	) * ddx2 * flag &
	192	+ ( mask_north * ( &
	193	kmyp * ( u(k,j+1,i) - u(k,j,i) ) * ddy &
	194	+ kmyp * ( v(k,j+1,i) - v(k,j+1,i-1) ) * ddx &
	195	) &
	196	- mask_south * ( &
	197	kmym * ( u(k,j,i) - u(k,j-1,i) ) * ddy &
	198	+ kmym * ( v(k,j,i) - v(k,j,i-1) ) * ddx &
	199	) &
	200	) * ddy * flag
[1]	201	ENDDO
	202	!
[2232]	203	!-- Add horizontal momentum flux u'v' at north- (l=0) and south-facing (l=1)
	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 = 0, 1
	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) * ddy
	215	ENDDO
	216	ENDDO
	217	!
	218	!-- Natural-type surfaces
	219	DO l = 0, 1
	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) * ddy
	226	ENDDO
	227	ENDDO
	228	!
	229	!-- Urban-type surfaces
	230	DO l = 0, 1
	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) * ddy
	237	ENDDO
	238	ENDDO
[51]	239
[1]	240	!
[2232]	241	!-- Compute vertical diffusion. In case of simulating a surface layer,
	242	!-- respective grid diffusive fluxes are masked (flag 8) within this
	243	!-- loop, and added further below, else, simple gradient approach is
	244	!-- applied. Model top is also mask if top-momentum flux is given.
	245	DO k = nzb+1, nzt
[1]	246	!
[2232]	247	!-- Determine flags to mask topography below and above. Flag 1 is
	248	!-- used to mask topography in general, and flag 8 implies
	249	!-- information about use_surface_fluxes. Flag 9 is used to control
	250	!-- momentum flux at model top.
	251	mask_bottom = MERGE( 1.0_wp, 0.0_wp, &
	252	BTEST( wall_flags_0(k-1,j,i), 8 ) )
	253	mask_top = MERGE( 1.0_wp, 0.0_wp, &
	254	BTEST( wall_flags_0(k+1,j,i), 8 ) ) * &
	255	MERGE( 1.0_wp, 0.0_wp, &
	256	BTEST( wall_flags_0(k+1,j,i), 9 ) )
	257	flag = MERGE( 1.0_wp, 0.0_wp, &
	258	BTEST( wall_flags_0(k,j,i), 1 ) )
	259	!
[1]	260	!-- Interpolate eddy diffusivities on staggered gridpoints
[1340]	261	kmzp = 0.25_wp * &
[1]	262	( km(k,j,i)+km(k+1,j,i)+km(k,j,i-1)+km(k+1,j,i-1) )
[1340]	263	kmzm = 0.25_wp * &
[1]	264	( km(k,j,i)+km(k-1,j,i)+km(k,j,i-1)+km(k-1,j,i-1) )
	265
[1320]	266	tend(k,j,i) = tend(k,j,i) &
[2232]	267	+ ( kmzp * ( ( u(k+1,j,i) - u(k,j,i) ) * ddzu(k+1) &
	268	+ ( w(k,j,i) - w(k,j,i-1) ) * ddx &
	269	) * rho_air_zw(k) * mask_top &
	270	- kmzm * ( ( u(k,j,i) - u(k-1,j,i) ) * ddzu(k) &
	271	+ ( w(k-1,j,i) - w(k-1,j,i-1) ) * ddx &
	272	) * rho_air_zw(k-1) * mask_bottom &
	273	) * ddzw(k) * drho_air(k) * flag
[1]	274	ENDDO
	275
	276	!
	277	!-- Vertical diffusion at the first grid point above the surface,
	278	!-- if the momentum flux at the bottom is given by the Prandtl law or
	279	!-- if it is prescribed by the user.
	280	!-- Difference quotient of the momentum flux is not formed over half
	281	!-- of the grid spacing (2.0*ddzw(k)) any more, since the comparison
[1320]	282	!-- with other (LES) models showed that the values of the momentum
[1]	283	!-- flux becomes too large in this case.
	284	!-- The term containing w(k-1,..) (see above equation) is removed here
	285	!-- because the vertical velocity is assumed to be zero at the surface.
	286	IF ( use_surface_fluxes ) THEN
	287	!
[2232]	288	!-- Default-type surfaces, upward-facing
	289	surf_s = surf_def_h(0)%start_index(j,i)
	290	surf_e = surf_def_h(0)%end_index(j,i)
	291	DO m = surf_s, surf_e
[1]	292
[2232]	293	k = surf_def_h(0)%k(m)
[1]	294
[2232]	295	tend(k,j,i) = tend(k,j,i) &
	296	+ ( - ( - surf_def_h(0)%usws(m) ) &
	297	) * ddzw(k) * drho_air(k)
	298	ENDDO
[102]	299	!
[2232]	300	!-- Default-type surfaces, dowward-facing
	301	surf_s = surf_def_h(1)%start_index(j,i)
	302	surf_e = surf_def_h(1)%end_index(j,i)
	303	DO m = surf_s, surf_e
	304
	305	k = surf_def_h(1)%k(m)
	306
	307	tend(k,j,i) = tend(k,j,i) &
	308	+ ( - surf_def_h(1)%usws(m) &
	309	) * ddzw(k) * drho_air(k)
	310	ENDDO
[102]	311	!
[2232]	312	!-- Natural-type surfaces, upward-facing
	313	surf_s = surf_lsm_h%start_index(j,i)
	314	surf_e = surf_lsm_h%end_index(j,i)
	315	DO m = surf_s, surf_e
[102]	316
[2232]	317	k = surf_lsm_h%k(m)
	318
	319	tend(k,j,i) = tend(k,j,i) &
	320	+ ( - ( - surf_lsm_h%usws(m) ) &
	321	) * ddzw(k) * drho_air(k)
	322	ENDDO
	323	!
	324	!-- Urban-type surfaces, upward-facing
	325	surf_s = surf_usm_h%start_index(j,i)
	326	surf_e = surf_usm_h%end_index(j,i)
	327	DO m = surf_s, surf_e
	328
	329	k = surf_usm_h%k(m)
	330
	331	tend(k,j,i) = tend(k,j,i) &
	332	+ ( - ( - surf_usm_h%usws(m) ) &
	333	) * ddzw(k) * drho_air(k)
	334	ENDDO
	335
[102]	336	ENDIF
[2232]	337	!
	338	!-- Add momentum flux at model top
[2638]	339	IF ( use_top_fluxes .AND. constant_top_momentumflux ) THEN
[2232]	340	surf_s = surf_def_h(2)%start_index(j,i)
	341	surf_e = surf_def_h(2)%end_index(j,i)
	342	DO m = surf_s, surf_e
[102]	343
[2232]	344	k = surf_def_h(2)%k(m)
	345
	346	tend(k,j,i) = tend(k,j,i) &
	347	+ ( - surf_def_h(2)%usws(m) ) * ddzw(k) * drho_air(k)
	348	ENDDO
	349	ENDIF
	350
[1]	351	ENDDO
	352	ENDDO
	353
	354	END SUBROUTINE diffusion_u
	355
	356
	357	!------------------------------------------------------------------------------!
[1682]	358	! Description:
	359	! ------------
	360	!> Call for grid point i,j
[1]	361	!------------------------------------------------------------------------------!
[1001]	362	SUBROUTINE diffusion_u_ij( i, j )
[1]	363
[1320]	364	USE arrays_3d, &
[2232]	365	ONLY: ddzu, ddzw, km, tend, u, v, w, drho_air, rho_air_zw
[1320]	366
	367	USE control_parameters, &
[2232]	368	ONLY: constant_top_momentumflux, use_surface_fluxes, &
	369	use_top_fluxes
[1320]	370
	371	USE grid_variables, &
[2232]	372	ONLY: ddx, ddx2, ddy
[1320]	373
	374	USE indices, &
[2232]	375	ONLY: nzb, nzt, wall_flags_0
	376
[1320]	377	USE kinds
[1]	378
[2232]	379	USE surface_mod, &
	380	ONLY : surf_def_h, surf_def_v, surf_lsm_h, surf_lsm_v, surf_usm_h, &
	381	surf_usm_v
	382
[1]	383	IMPLICIT NONE
	384
[2232]	385	INTEGER(iwp) :: i !< running index x direction
	386	INTEGER(iwp) :: j !< running index y direction
	387	INTEGER(iwp) :: k !< running index z direction
	388	INTEGER(iwp) :: l !< running index of surface type, south- or north-facing wall
	389	INTEGER(iwp) :: m !< running index surface elements
	390	INTEGER(iwp) :: surf_e !< End index of surface elements at (j,i)-gridpoint
	391	INTEGER(iwp) :: surf_s !< Start index of surface elements at (j,i)-gridpoint
[1]	392
[2232]	393	REAL(wp) :: flag !< flag to mask topography grid points
	394	REAL(wp) :: kmym !<
	395	REAL(wp) :: kmyp !<
	396	REAL(wp) :: kmzm !<
	397	REAL(wp) :: kmzp !<
	398	REAL(wp) :: mask_bottom !< flag to mask vertical upward-facing surface
	399	REAL(wp) :: mask_north !< flag to mask vertical surface north of the grid point
	400	REAL(wp) :: mask_south !< flag to mask vertical surface south of the grid point
	401	REAL(wp) :: mask_top !< flag to mask vertical downward-facing surface
	402	!
[1]	403	!-- Compute horizontal diffusion
[2232]	404	DO k = nzb+1, nzt
[1]	405	!
[2232]	406	!-- Predetermine flag to mask topography and wall-bounded grid points.
	407	!-- It is sufficient to masked only north- and south-facing surfaces, which
	408	!-- need special treatment for the u-component.
	409	flag = MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_0(k,j,i), 1 ) )
	410	mask_south = MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_0(k,j-1,i), 1 ) )
	411	mask_north = MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_0(k,j+1,i), 1 ) )
	412	!
[1]	413	!-- Interpolate eddy diffusivities on staggered gridpoints
[1340]	414	kmyp = 0.25_wp * ( km(k,j,i)+km(k,j+1,i)+km(k,j,i-1)+km(k,j+1,i-1) )
	415	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]	416
[1320]	417	tend(k,j,i) = tend(k,j,i) &
[2232]	418	+ 2.0_wp * ( &
	419	km(k,j,i) * ( u(k,j,i+1) - u(k,j,i) ) &
	420	- km(k,j,i-1) * ( u(k,j,i) - u(k,j,i-1) ) &
	421	) * ddx2 * flag &
	422	+ ( &
	423	mask_north * kmyp * ( ( u(k,j+1,i) - u(k,j,i) ) * ddy &
	424	+ ( v(k,j+1,i) - v(k,j+1,i-1) ) * ddx &
	425	) &
	426	- mask_south * kmym * ( ( u(k,j,i) - u(k,j-1,i) ) * ddy &
	427	+ ( v(k,j,i) - v(k,j,i-1) ) * ddx &
	428	) &
	429	) * ddy * flag
[1]	430	ENDDO
	431
	432	!
[2232]	433	!-- Add horizontal momentum flux u'v' at north- (l=0) and south-facing (l=1)
	434	!-- surfaces. Note, in the the flat case, loops won't be entered as
	435	!-- start_index > end_index. Furtermore, note, no vertical natural surfaces
	436	!-- so far.
	437	!-- Default-type surfaces
	438	DO l = 0, 1
	439	surf_s = surf_def_v(l)%start_index(j,i)
	440	surf_e = surf_def_v(l)%end_index(j,i)
	441	DO m = surf_s, surf_e
	442	k = surf_def_v(l)%k(m)
	443	tend(k,j,i) = tend(k,j,i) + surf_def_v(l)%mom_flux_uv(m) * ddy
	444	ENDDO
	445	ENDDO
[51]	446	!
[2232]	447	!-- Natural-type surfaces
	448	DO l = 0, 1
	449	surf_s = surf_lsm_v(l)%start_index(j,i)
	450	surf_e = surf_lsm_v(l)%end_index(j,i)
	451	DO m = surf_s, surf_e
	452	k = surf_lsm_v(l)%k(m)
	453	tend(k,j,i) = tend(k,j,i) + surf_lsm_v(l)%mom_flux_uv(m) * ddy
	454	ENDDO
	455	ENDDO
[1]	456	!
[2232]	457	!-- Urban-type surfaces
	458	DO l = 0, 1
	459	surf_s = surf_usm_v(l)%start_index(j,i)
	460	surf_e = surf_usm_v(l)%end_index(j,i)
	461	DO m = surf_s, surf_e
	462	k = surf_usm_v(l)%k(m)
	463	tend(k,j,i) = tend(k,j,i) + surf_usm_v(l)%mom_flux_uv(m) * ddy
	464	ENDDO
	465	ENDDO
[1]	466	!
[2232]	467	!-- Compute vertical diffusion. In case of simulating a surface layer,
	468	!-- respective grid diffusive fluxes are masked (flag 8) within this
	469	!-- loop, and added further below, else, simple gradient approach is
	470	!-- applied. Model top is also mask if top-momentum flux is given.
	471	DO k = nzb+1, nzt
	472	!
	473	!-- Determine flags to mask topography below and above. Flag 1 is
	474	!-- used to mask topography in general, and flag 8 implies
	475	!-- information about use_surface_fluxes. Flag 9 is used to control
	476	!-- momentum flux at model top.
	477	mask_bottom = MERGE( 1.0_wp, 0.0_wp, &
	478	BTEST( wall_flags_0(k-1,j,i), 8 ) )
	479	mask_top = MERGE( 1.0_wp, 0.0_wp, &
	480	BTEST( wall_flags_0(k+1,j,i), 8 ) ) * &
	481	MERGE( 1.0_wp, 0.0_wp, &
	482	BTEST( wall_flags_0(k+1,j,i), 9 ) )
	483	flag = MERGE( 1.0_wp, 0.0_wp, &
	484	BTEST( wall_flags_0(k,j,i), 1 ) )
	485	!
[1]	486	!-- Interpolate eddy diffusivities on staggered gridpoints
[1340]	487	kmzp = 0.25_wp * ( km(k,j,i)+km(k+1,j,i)+km(k,j,i-1)+km(k+1,j,i-1) )
	488	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]	489
[1320]	490	tend(k,j,i) = tend(k,j,i) &
[2232]	491	+ ( kmzp * ( ( u(k+1,j,i) - u(k,j,i) ) * ddzu(k+1) &
	492	+ ( w(k,j,i) - w(k,j,i-1) ) * ddx &
	493	) * rho_air_zw(k) * mask_top &
	494	- kmzm * ( ( u(k,j,i) - u(k-1,j,i) ) * ddzu(k) &
	495	+ ( w(k-1,j,i) - w(k-1,j,i-1) ) * ddx &
	496	) * rho_air_zw(k-1) * mask_bottom &
	497	) * ddzw(k) * drho_air(k) * flag
[1]	498	ENDDO
	499
	500	!
[2232]	501	!-- Vertical diffusion at the first surface grid points, if the
[1]	502	!-- momentum flux at the bottom is given by the Prandtl law or if it is
	503	!-- prescribed by the user.
	504	!-- Difference quotient of the momentum flux is not formed over half of
	505	!-- the grid spacing (2.0*ddzw(k)) any more, since the comparison with
[1320]	506	!-- other (LES) models showed that the values of the momentum flux becomes
[1]	507	!-- too large in this case.
	508	IF ( use_surface_fluxes ) THEN
	509	!
[2232]	510	!-- Default-type surfaces, upward-facing
	511	surf_s = surf_def_h(0)%start_index(j,i)
	512	surf_e = surf_def_h(0)%end_index(j,i)
	513	DO m = surf_s, surf_e
[1]	514
[2232]	515	k = surf_def_h(0)%k(m)
[1]	516
[2232]	517	tend(k,j,i) = tend(k,j,i) &
	518	+ ( - ( - surf_def_h(0)%usws(m) ) &
	519	) * ddzw(k) * drho_air(k)
	520	ENDDO
[102]	521	!
[2232]	522	!-- Default-type surfaces, dowward-facing (except for model-top fluxes)
	523	surf_s = surf_def_h(1)%start_index(j,i)
	524	surf_e = surf_def_h(1)%end_index(j,i)
	525	DO m = surf_s, surf_e
	526
	527	k = surf_def_h(1)%k(m)
	528
	529	tend(k,j,i) = tend(k,j,i) &
	530	+ ( - surf_def_h(1)%usws(m) &
	531	) * ddzw(k) * drho_air(k)
	532	ENDDO
[102]	533	!
[2232]	534	!-- Natural-type surfaces, upward-facing
	535	surf_s = surf_lsm_h%start_index(j,i)
	536	surf_e = surf_lsm_h%end_index(j,i)
	537	DO m = surf_s, surf_e
[102]	538
[2232]	539	k = surf_lsm_h%k(m)
	540
	541	tend(k,j,i) = tend(k,j,i) &
	542	+ ( - ( - surf_lsm_h%usws(m) ) &
	543	) * ddzw(k) * drho_air(k)
	544	ENDDO
	545	!
	546	!-- Urban-type surfaces, upward-facing
	547	surf_s = surf_usm_h%start_index(j,i)
	548	surf_e = surf_usm_h%end_index(j,i)
	549	DO m = surf_s, surf_e
	550
	551	k = surf_usm_h%k(m)
	552
	553	tend(k,j,i) = tend(k,j,i) &
	554	+ ( - ( - surf_usm_h%usws(m) ) &
	555	) * ddzw(k) * drho_air(k)
	556	ENDDO
	557
[102]	558	ENDIF
[2232]	559	!
	560	!-- Add momentum flux at model top
[2638]	561	IF ( use_top_fluxes .AND. constant_top_momentumflux ) THEN
[2232]	562	surf_s = surf_def_h(2)%start_index(j,i)
	563	surf_e = surf_def_h(2)%end_index(j,i)
	564	DO m = surf_s, surf_e
[102]	565
[2232]	566	k = surf_def_h(2)%k(m)
	567
	568	tend(k,j,i) = tend(k,j,i) &
	569	+ ( - surf_def_h(2)%usws(m) ) * ddzw(k) * drho_air(k)
	570	ENDDO
	571	ENDIF
	572
	573
[1]	574	END SUBROUTINE diffusion_u_ij
	575
	576	END MODULE diffusion_u_mod

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