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source: palm/trunk/SOURCE/diffusion_u.f90 @ 4541

Last change on this file since 4541 was 4360, checked in by suehring, 5 years ago
Bugfix in output of time-averaged plant-canopy quanities; Output of plant-canopy data only where tall canopy is defined; land-surface model: fix wrong location strings; tests: update urban test case; all source code files: copyright update
Property svn:keywords set to `Id`
File size: 24.4 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	!
[4360]	17	! Copyright 1997-2020 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 4360 2020-01-07 11:25:50Z suehring $
[4346]	27	! Introduction of wall_flags_total_0, which currently sets bits based on static
	28	! topography information used in wall_flags_static_0
	29	!
	30	! 4329 2019-12-10 15:46:36Z motisi
[4329]	31	! Renamed wall_flags_0 to wall_flags_static_0
	32	!
	33	! 4182 2019-08-22 15:20:23Z scharf
[4182]	34	! Corrected "Former revisions" section
	35	!
	36	! 3655 2019-01-07 16:51:22Z knoop
[3634]	37	! OpenACC port for SPEC
[2716]	38	!
[4182]	39	! Revision 1.1 1997/09/12 06:23:51 raasch
	40	! Initial revision
	41	!
	42	!
[1]	43	! Description:
	44	! ------------
[1682]	45	!> Diffusion term of the u-component
	46	!> @todo additional damping (needed for non-cyclic bc) causes bad vectorization
	47	!> and slows down the speed on NEC about 5-10%
[1]	48	!------------------------------------------------------------------------------!
[1682]	49	MODULE diffusion_u_mod
	50
[1]	51
	52	PRIVATE
[2118]	53	PUBLIC diffusion_u
[1]	54
	55	INTERFACE diffusion_u
	56	MODULE PROCEDURE diffusion_u
	57	MODULE PROCEDURE diffusion_u_ij
	58	END INTERFACE diffusion_u
	59
	60	CONTAINS
	61
	62
	63	!------------------------------------------------------------------------------!
[1682]	64	! Description:
	65	! ------------
	66	!> Call for all grid points
[1]	67	!------------------------------------------------------------------------------!
[1001]	68	SUBROUTINE diffusion_u
[1]	69
[1320]	70	USE arrays_3d, &
[2232]	71	ONLY: ddzu, ddzw, km, tend, u, v, w, drho_air, rho_air_zw
[1320]	72
	73	USE control_parameters, &
[2232]	74	ONLY: constant_top_momentumflux, use_surface_fluxes, &
[1320]	75	use_top_fluxes
	76
	77	USE grid_variables, &
[2232]	78	ONLY: ddx, ddx2, ddy
[1320]	79
	80	USE indices, &
[4346]	81	ONLY: nxlu, nxr, nyn, nys, nzb, nzt, wall_flags_total_0
[2232]	82
[1320]	83	USE kinds
[1]	84
[2232]	85	USE surface_mod, &
	86	ONLY : surf_def_h, surf_def_v, surf_lsm_h, surf_lsm_v, surf_usm_h, &
	87	surf_usm_v
	88
[1]	89	IMPLICIT NONE
	90
[2232]	91	INTEGER(iwp) :: i !< running index x direction
	92	INTEGER(iwp) :: j !< running index y direction
	93	INTEGER(iwp) :: k !< running index z direction
	94	INTEGER(iwp) :: l !< running index of surface type, south- or north-facing wall
	95	INTEGER(iwp) :: m !< running index surface elements
[3547]	96	INTEGER(iwp) :: surf_e !< end index of surface elements at (j,i)-gridpoint
	97	INTEGER(iwp) :: surf_s !< start index of surface elements at (j,i)-gridpoint
[1001]	98
[2232]	99	REAL(wp) :: flag !< flag to mask topography grid points
[3547]	100	REAL(wp) :: kmym !< diffusion coefficient on southward side of the u-gridbox - interpolated onto xu-yv grid
	101	REAL(wp) :: kmyp !< diffusion coefficient on northward side of the u-gridbox - interpolated onto xu-yv grid
	102	REAL(wp) :: kmzm !< diffusion coefficient on bottom of the gridbox - interpolated onto xu-zw grid
	103	REAL(wp) :: kmzp !< diffusion coefficient on top of the gridbox - interpolated onto xu-zw grid
[2232]	104	REAL(wp) :: mask_bottom !< flag to mask vertical upward-facing surface
	105	REAL(wp) :: mask_north !< flag to mask vertical surface north of the grid point
	106	REAL(wp) :: mask_south !< flag to mask vertical surface south of the grid point
	107	REAL(wp) :: mask_top !< flag to mask vertical downward-facing surface
[1]	108
[56]	109
[2232]	110
[3634]	111	!$ACC PARALLEL LOOP COLLAPSE(2) PRIVATE(i, j, k, l, m) &
	112	!$ACC PRIVATE(surf_e, surf_s, flag, kmym, kmyp, kmzm, kmzp) &
	113	!$ACC PRIVATE(mask_bottom, mask_north, mask_south, mask_top) &
[4346]	114	!$ACC PRESENT(wall_flags_total_0, km) &
[3634]	115	!$ACC PRESENT(u, v, w) &
	116	!$ACC PRESENT(ddzu, ddzw, drho_air, rho_air_zw) &
	117	!$ACC PRESENT(surf_def_h(0:2), surf_def_v(0:1)) &
	118	!$ACC PRESENT(surf_lsm_h, surf_lsm_v(0:1)) &
	119	!$ACC PRESENT(surf_usm_h, surf_usm_v(0:1)) &
	120	!$ACC PRESENT(tend)
[106]	121	DO i = nxlu, nxr
[1001]	122	DO j = nys, nyn
[1]	123	!
	124	!-- Compute horizontal diffusion
[2232]	125	DO k = nzb+1, nzt
[1]	126	!
[2232]	127	!-- Predetermine flag to mask topography and wall-bounded grid points.
	128	!-- It is sufficient to masked only north- and south-facing surfaces, which
	129	!-- need special treatment for the u-component.
[4346]	130	flag = MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,j,i), 1 ) )
	131	mask_south = MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,j-1,i), 1 ) )
	132	mask_north = MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,j+1,i), 1 ) )
[2232]	133	!
[1]	134	!-- Interpolate eddy diffusivities on staggered gridpoints
[1340]	135	kmyp = 0.25_wp * &
[978]	136	( km(k,j,i)+km(k,j+1,i)+km(k,j,i-1)+km(k,j+1,i-1) )
[1340]	137	kmym = 0.25_wp * &
[978]	138	( km(k,j,i)+km(k,j-1,i)+km(k,j,i-1)+km(k,j-1,i-1) )
[1]	139
[1320]	140	tend(k,j,i) = tend(k,j,i) &
[2232]	141	+ 2.0_wp * ( &
	142	km(k,j,i) * ( u(k,j,i+1) - u(k,j,i) ) &
	143	- km(k,j,i-1) * ( u(k,j,i) - u(k,j,i-1) ) &
	144	) * ddx2 * flag &
	145	+ ( mask_north * ( &
	146	kmyp * ( u(k,j+1,i) - u(k,j,i) ) * ddy &
	147	+ kmyp * ( v(k,j+1,i) - v(k,j+1,i-1) ) * ddx &
	148	) &
	149	- mask_south * ( &
	150	kmym * ( u(k,j,i) - u(k,j-1,i) ) * ddy &
	151	+ kmym * ( v(k,j,i) - v(k,j,i-1) ) * ddx &
	152	) &
	153	) * ddy * flag
[1]	154	ENDDO
	155	!
[2232]	156	!-- Add horizontal momentum flux u'v' at north- (l=0) and south-facing (l=1)
	157	!-- surfaces. Note, in the the flat case, loops won't be entered as
	158	!-- start_index > end_index. Furtermore, note, no vertical natural surfaces
	159	!-- so far.
	160	!-- Default-type surfaces
	161	DO l = 0, 1
	162	surf_s = surf_def_v(l)%start_index(j,i)
	163	surf_e = surf_def_v(l)%end_index(j,i)
	164	DO m = surf_s, surf_e
	165	k = surf_def_v(l)%k(m)
	166	tend(k,j,i) = tend(k,j,i) + &
	167	surf_def_v(l)%mom_flux_uv(m) * ddy
	168	ENDDO
	169	ENDDO
	170	!
	171	!-- Natural-type surfaces
	172	DO l = 0, 1
	173	surf_s = surf_lsm_v(l)%start_index(j,i)
	174	surf_e = surf_lsm_v(l)%end_index(j,i)
	175	DO m = surf_s, surf_e
	176	k = surf_lsm_v(l)%k(m)
	177	tend(k,j,i) = tend(k,j,i) + &
	178	surf_lsm_v(l)%mom_flux_uv(m) * ddy
	179	ENDDO
	180	ENDDO
	181	!
	182	!-- Urban-type surfaces
	183	DO l = 0, 1
	184	surf_s = surf_usm_v(l)%start_index(j,i)
	185	surf_e = surf_usm_v(l)%end_index(j,i)
	186	DO m = surf_s, surf_e
	187	k = surf_usm_v(l)%k(m)
	188	tend(k,j,i) = tend(k,j,i) + &
	189	surf_usm_v(l)%mom_flux_uv(m) * ddy
	190	ENDDO
	191	ENDDO
[51]	192
[1]	193	!
[2232]	194	!-- Compute vertical diffusion. In case of simulating a surface layer,
	195	!-- respective grid diffusive fluxes are masked (flag 8) within this
	196	!-- loop, and added further below, else, simple gradient approach is
	197	!-- applied. Model top is also mask if top-momentum flux is given.
	198	DO k = nzb+1, nzt
[1]	199	!
[2232]	200	!-- Determine flags to mask topography below and above. Flag 1 is
	201	!-- used to mask topography in general, and flag 8 implies
	202	!-- information about use_surface_fluxes. Flag 9 is used to control
	203	!-- momentum flux at model top.
	204	mask_bottom = MERGE( 1.0_wp, 0.0_wp, &
[4346]	205	BTEST( wall_flags_total_0(k-1,j,i), 8 ) )
[2232]	206	mask_top = MERGE( 1.0_wp, 0.0_wp, &
[4346]	207	BTEST( wall_flags_total_0(k+1,j,i), 8 ) ) * &
[2232]	208	MERGE( 1.0_wp, 0.0_wp, &
[4346]	209	BTEST( wall_flags_total_0(k+1,j,i), 9 ) )
[2232]	210	flag = MERGE( 1.0_wp, 0.0_wp, &
[4346]	211	BTEST( wall_flags_total_0(k,j,i), 1 ) )
[2232]	212	!
[1]	213	!-- Interpolate eddy diffusivities on staggered gridpoints
[1340]	214	kmzp = 0.25_wp * &
[1]	215	( km(k,j,i)+km(k+1,j,i)+km(k,j,i-1)+km(k+1,j,i-1) )
[1340]	216	kmzm = 0.25_wp * &
[1]	217	( km(k,j,i)+km(k-1,j,i)+km(k,j,i-1)+km(k-1,j,i-1) )
	218
[1320]	219	tend(k,j,i) = tend(k,j,i) &
[2232]	220	+ ( kmzp * ( ( u(k+1,j,i) - u(k,j,i) ) * ddzu(k+1) &
	221	+ ( w(k,j,i) - w(k,j,i-1) ) * ddx &
	222	) * rho_air_zw(k) * mask_top &
	223	- kmzm * ( ( u(k,j,i) - u(k-1,j,i) ) * ddzu(k) &
	224	+ ( w(k-1,j,i) - w(k-1,j,i-1) ) * ddx &
	225	) * rho_air_zw(k-1) * mask_bottom &
	226	) * ddzw(k) * drho_air(k) * flag
[1]	227	ENDDO
	228
	229	!
	230	!-- Vertical diffusion at the first grid point above the surface,
	231	!-- if the momentum flux at the bottom is given by the Prandtl law or
	232	!-- if it is prescribed by the user.
	233	!-- Difference quotient of the momentum flux is not formed over half
	234	!-- of the grid spacing (2.0*ddzw(k)) any more, since the comparison
[1320]	235	!-- with other (LES) models showed that the values of the momentum
[1]	236	!-- flux becomes too large in this case.
	237	!-- The term containing w(k-1,..) (see above equation) is removed here
	238	!-- because the vertical velocity is assumed to be zero at the surface.
	239	IF ( use_surface_fluxes ) THEN
	240	!
[2232]	241	!-- Default-type surfaces, upward-facing
	242	surf_s = surf_def_h(0)%start_index(j,i)
	243	surf_e = surf_def_h(0)%end_index(j,i)
	244	DO m = surf_s, surf_e
[1]	245
[2232]	246	k = surf_def_h(0)%k(m)
[1]	247
[2232]	248	tend(k,j,i) = tend(k,j,i) &
	249	+ ( - ( - surf_def_h(0)%usws(m) ) &
	250	) * ddzw(k) * drho_air(k)
	251	ENDDO
[102]	252	!
[2232]	253	!-- Default-type surfaces, dowward-facing
	254	surf_s = surf_def_h(1)%start_index(j,i)
	255	surf_e = surf_def_h(1)%end_index(j,i)
	256	DO m = surf_s, surf_e
	257
	258	k = surf_def_h(1)%k(m)
	259
	260	tend(k,j,i) = tend(k,j,i) &
	261	+ ( - surf_def_h(1)%usws(m) &
	262	) * ddzw(k) * drho_air(k)
	263	ENDDO
[102]	264	!
[2232]	265	!-- Natural-type surfaces, upward-facing
	266	surf_s = surf_lsm_h%start_index(j,i)
	267	surf_e = surf_lsm_h%end_index(j,i)
	268	DO m = surf_s, surf_e
[102]	269
[2232]	270	k = surf_lsm_h%k(m)
	271
	272	tend(k,j,i) = tend(k,j,i) &
	273	+ ( - ( - surf_lsm_h%usws(m) ) &
	274	) * ddzw(k) * drho_air(k)
	275	ENDDO
	276	!
	277	!-- Urban-type surfaces, upward-facing
	278	surf_s = surf_usm_h%start_index(j,i)
	279	surf_e = surf_usm_h%end_index(j,i)
	280	DO m = surf_s, surf_e
	281
	282	k = surf_usm_h%k(m)
	283
	284	tend(k,j,i) = tend(k,j,i) &
	285	+ ( - ( - surf_usm_h%usws(m) ) &
	286	) * ddzw(k) * drho_air(k)
	287	ENDDO
	288
[102]	289	ENDIF
[2232]	290	!
	291	!-- Add momentum flux at model top
[2638]	292	IF ( use_top_fluxes .AND. constant_top_momentumflux ) THEN
[2232]	293	surf_s = surf_def_h(2)%start_index(j,i)
	294	surf_e = surf_def_h(2)%end_index(j,i)
	295	DO m = surf_s, surf_e
[102]	296
[2232]	297	k = surf_def_h(2)%k(m)
	298
	299	tend(k,j,i) = tend(k,j,i) &
	300	+ ( - surf_def_h(2)%usws(m) ) * ddzw(k) * drho_air(k)
	301	ENDDO
	302	ENDIF
	303
[1]	304	ENDDO
	305	ENDDO
	306
	307	END SUBROUTINE diffusion_u
	308
	309
	310	!------------------------------------------------------------------------------!
[1682]	311	! Description:
	312	! ------------
	313	!> Call for grid point i,j
[1]	314	!------------------------------------------------------------------------------!
[1001]	315	SUBROUTINE diffusion_u_ij( i, j )
[1]	316
[1320]	317	USE arrays_3d, &
[2232]	318	ONLY: ddzu, ddzw, km, tend, u, v, w, drho_air, rho_air_zw
[1320]	319
	320	USE control_parameters, &
[2232]	321	ONLY: constant_top_momentumflux, use_surface_fluxes, &
	322	use_top_fluxes
[1320]	323
	324	USE grid_variables, &
[2232]	325	ONLY: ddx, ddx2, ddy
[1320]	326
	327	USE indices, &
[4346]	328	ONLY: nzb, nzt, wall_flags_total_0
[2232]	329
[1320]	330	USE kinds
[1]	331
[2232]	332	USE surface_mod, &
	333	ONLY : surf_def_h, surf_def_v, surf_lsm_h, surf_lsm_v, surf_usm_h, &
	334	surf_usm_v
	335
[1]	336	IMPLICIT NONE
	337
[2232]	338	INTEGER(iwp) :: i !< running index x direction
	339	INTEGER(iwp) :: j !< running index y direction
	340	INTEGER(iwp) :: k !< running index z direction
	341	INTEGER(iwp) :: l !< running index of surface type, south- or north-facing wall
	342	INTEGER(iwp) :: m !< running index surface elements
	343	INTEGER(iwp) :: surf_e !< End index of surface elements at (j,i)-gridpoint
	344	INTEGER(iwp) :: surf_s !< Start index of surface elements at (j,i)-gridpoint
[1]	345
[2232]	346	REAL(wp) :: flag !< flag to mask topography grid points
[3547]	347	REAL(wp) :: kmym !< diffusion coefficient on southward side of the u-gridbox - interpolated onto xu-yv grid
	348	REAL(wp) :: kmyp !<diffusion coefficient on northward side of the u-gridbox - interpolated onto xu-yv grid
	349	REAL(wp) :: kmzm !< diffusion coefficient on bottom of the gridbox - interpolated onto xu-zw grid
	350	REAL(wp) :: kmzp !< diffusion coefficient on top of the gridbox - interpolated onto xu-zw grid
[2232]	351	REAL(wp) :: mask_bottom !< flag to mask vertical upward-facing surface
	352	REAL(wp) :: mask_north !< flag to mask vertical surface north of the grid point
	353	REAL(wp) :: mask_south !< flag to mask vertical surface south of the grid point
	354	REAL(wp) :: mask_top !< flag to mask vertical downward-facing surface
	355	!
[1]	356	!-- Compute horizontal diffusion
[2232]	357	DO k = nzb+1, nzt
[1]	358	!
[2232]	359	!-- Predetermine flag to mask topography and wall-bounded grid points.
	360	!-- It is sufficient to masked only north- and south-facing surfaces, which
	361	!-- need special treatment for the u-component.
[4346]	362	flag = MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,j,i), 1 ) )
	363	mask_south = MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,j-1,i), 1 ) )
	364	mask_north = MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,j+1,i), 1 ) )
[2232]	365	!
[1]	366	!-- Interpolate eddy diffusivities on staggered gridpoints
[1340]	367	kmyp = 0.25_wp * ( km(k,j,i)+km(k,j+1,i)+km(k,j,i-1)+km(k,j+1,i-1) )
	368	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]	369
[1320]	370	tend(k,j,i) = tend(k,j,i) &
[2232]	371	+ 2.0_wp * ( &
	372	km(k,j,i) * ( u(k,j,i+1) - u(k,j,i) ) &
	373	- km(k,j,i-1) * ( u(k,j,i) - u(k,j,i-1) ) &
	374	) * ddx2 * flag &
	375	+ ( &
	376	mask_north * kmyp * ( ( u(k,j+1,i) - u(k,j,i) ) * ddy &
	377	+ ( v(k,j+1,i) - v(k,j+1,i-1) ) * ddx &
	378	) &
	379	- mask_south * kmym * ( ( u(k,j,i) - u(k,j-1,i) ) * ddy &
	380	+ ( v(k,j,i) - v(k,j,i-1) ) * ddx &
	381	) &
	382	) * ddy * flag
[1]	383	ENDDO
	384
	385	!
[2232]	386	!-- Add horizontal momentum flux u'v' at north- (l=0) and south-facing (l=1)
	387	!-- surfaces. Note, in the the flat case, loops won't be entered as
	388	!-- start_index > end_index. Furtermore, note, no vertical natural surfaces
	389	!-- so far.
	390	!-- Default-type surfaces
	391	DO l = 0, 1
	392	surf_s = surf_def_v(l)%start_index(j,i)
	393	surf_e = surf_def_v(l)%end_index(j,i)
	394	DO m = surf_s, surf_e
	395	k = surf_def_v(l)%k(m)
	396	tend(k,j,i) = tend(k,j,i) + surf_def_v(l)%mom_flux_uv(m) * ddy
	397	ENDDO
	398	ENDDO
[51]	399	!
[2232]	400	!-- Natural-type surfaces
	401	DO l = 0, 1
	402	surf_s = surf_lsm_v(l)%start_index(j,i)
	403	surf_e = surf_lsm_v(l)%end_index(j,i)
	404	DO m = surf_s, surf_e
	405	k = surf_lsm_v(l)%k(m)
	406	tend(k,j,i) = tend(k,j,i) + surf_lsm_v(l)%mom_flux_uv(m) * ddy
	407	ENDDO
	408	ENDDO
[1]	409	!
[2232]	410	!-- Urban-type surfaces
	411	DO l = 0, 1
	412	surf_s = surf_usm_v(l)%start_index(j,i)
	413	surf_e = surf_usm_v(l)%end_index(j,i)
	414	DO m = surf_s, surf_e
	415	k = surf_usm_v(l)%k(m)
	416	tend(k,j,i) = tend(k,j,i) + surf_usm_v(l)%mom_flux_uv(m) * ddy
	417	ENDDO
	418	ENDDO
[1]	419	!
[2232]	420	!-- Compute vertical diffusion. In case of simulating a surface layer,
	421	!-- respective grid diffusive fluxes are masked (flag 8) within this
	422	!-- loop, and added further below, else, simple gradient approach is
	423	!-- applied. Model top is also mask if top-momentum flux is given.
	424	DO k = nzb+1, nzt
	425	!
	426	!-- Determine flags to mask topography below and above. Flag 1 is
	427	!-- used to mask topography in general, and flag 8 implies
	428	!-- information about use_surface_fluxes. Flag 9 is used to control
	429	!-- momentum flux at model top.
	430	mask_bottom = MERGE( 1.0_wp, 0.0_wp, &
[4346]	431	BTEST( wall_flags_total_0(k-1,j,i), 8 ) )
[2232]	432	mask_top = MERGE( 1.0_wp, 0.0_wp, &
[4346]	433	BTEST( wall_flags_total_0(k+1,j,i), 8 ) ) * &
[2232]	434	MERGE( 1.0_wp, 0.0_wp, &
[4346]	435	BTEST( wall_flags_total_0(k+1,j,i), 9 ) )
[2232]	436	flag = MERGE( 1.0_wp, 0.0_wp, &
[4346]	437	BTEST( wall_flags_total_0(k,j,i), 1 ) )
[2232]	438	!
[1]	439	!-- Interpolate eddy diffusivities on staggered gridpoints
[1340]	440	kmzp = 0.25_wp * ( km(k,j,i)+km(k+1,j,i)+km(k,j,i-1)+km(k+1,j,i-1) )
	441	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]	442
[1320]	443	tend(k,j,i) = tend(k,j,i) &
[2232]	444	+ ( kmzp * ( ( u(k+1,j,i) - u(k,j,i) ) * ddzu(k+1) &
	445	+ ( w(k,j,i) - w(k,j,i-1) ) * ddx &
	446	) * rho_air_zw(k) * mask_top &
	447	- kmzm * ( ( u(k,j,i) - u(k-1,j,i) ) * ddzu(k) &
	448	+ ( w(k-1,j,i) - w(k-1,j,i-1) ) * ddx &
	449	) * rho_air_zw(k-1) * mask_bottom &
	450	) * ddzw(k) * drho_air(k) * flag
[1]	451	ENDDO
	452
	453	!
[2232]	454	!-- Vertical diffusion at the first surface grid points, if the
[1]	455	!-- momentum flux at the bottom is given by the Prandtl law or if it is
	456	!-- prescribed by the user.
	457	!-- Difference quotient of the momentum flux is not formed over half of
	458	!-- the grid spacing (2.0*ddzw(k)) any more, since the comparison with
[1320]	459	!-- other (LES) models showed that the values of the momentum flux becomes
[1]	460	!-- too large in this case.
	461	IF ( use_surface_fluxes ) THEN
	462	!
[2232]	463	!-- Default-type surfaces, upward-facing
	464	surf_s = surf_def_h(0)%start_index(j,i)
	465	surf_e = surf_def_h(0)%end_index(j,i)
	466	DO m = surf_s, surf_e
[1]	467
[2232]	468	k = surf_def_h(0)%k(m)
[1]	469
[2232]	470	tend(k,j,i) = tend(k,j,i) &
	471	+ ( - ( - surf_def_h(0)%usws(m) ) &
	472	) * ddzw(k) * drho_air(k)
	473	ENDDO
[102]	474	!
[2232]	475	!-- Default-type surfaces, dowward-facing (except for model-top fluxes)
	476	surf_s = surf_def_h(1)%start_index(j,i)
	477	surf_e = surf_def_h(1)%end_index(j,i)
	478	DO m = surf_s, surf_e
	479
	480	k = surf_def_h(1)%k(m)
	481
	482	tend(k,j,i) = tend(k,j,i) &
	483	+ ( - surf_def_h(1)%usws(m) &
	484	) * ddzw(k) * drho_air(k)
	485	ENDDO
[102]	486	!
[2232]	487	!-- Natural-type surfaces, upward-facing
	488	surf_s = surf_lsm_h%start_index(j,i)
	489	surf_e = surf_lsm_h%end_index(j,i)
	490	DO m = surf_s, surf_e
[102]	491
[2232]	492	k = surf_lsm_h%k(m)
	493
	494	tend(k,j,i) = tend(k,j,i) &
	495	+ ( - ( - surf_lsm_h%usws(m) ) &
	496	) * ddzw(k) * drho_air(k)
	497	ENDDO
	498	!
	499	!-- Urban-type surfaces, upward-facing
	500	surf_s = surf_usm_h%start_index(j,i)
	501	surf_e = surf_usm_h%end_index(j,i)
	502	DO m = surf_s, surf_e
	503
	504	k = surf_usm_h%k(m)
	505
	506	tend(k,j,i) = tend(k,j,i) &
	507	+ ( - ( - surf_usm_h%usws(m) ) &
	508	) * ddzw(k) * drho_air(k)
	509	ENDDO
	510
[102]	511	ENDIF
[2232]	512	!
	513	!-- Add momentum flux at model top
[2638]	514	IF ( use_top_fluxes .AND. constant_top_momentumflux ) THEN
[2232]	515	surf_s = surf_def_h(2)%start_index(j,i)
	516	surf_e = surf_def_h(2)%end_index(j,i)
	517	DO m = surf_s, surf_e
[102]	518
[2232]	519	k = surf_def_h(2)%k(m)
	520
	521	tend(k,j,i) = tend(k,j,i) &
	522	+ ( - surf_def_h(2)%usws(m) ) * ddzw(k) * drho_air(k)
	523	ENDDO
	524	ENDIF
	525
	526
[1]	527	END SUBROUTINE diffusion_u_ij
	528
	529	END MODULE diffusion_u_mod

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