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source: palm/trunk/SOURCE/diffusion_u.f90 @ 3386

Last change on this file since 3386 was 3241, checked in by raasch, 6 years ago
various changes to avoid compiler warnings (mainly removal of unused variables)
Property svn:keywords set to `Id`
File size: 24.9 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	!
[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 3241 2018-09-12 15:02:00Z gronemeier $
[3241]	27	! unused variables removed
	28	!
	29	! 2718 2018-01-02 08:49:38Z maronga
[2716]	30	! Corrected "Former revisions" section
	31	!
	32	! 2696 2017-12-14 17:12:51Z kanani
	33	! Change in file header (GPL part)
	34	!
	35	! 2638 2017-11-23 12:44:23Z raasch
[2638]	36	! bugfix for constant top momentumflux
	37	!
	38	! 2233 2017-05-30 18:08:54Z suehring
[1321]	39	!
[2233]	40	! 2232 2017-05-30 17:47:52Z suehring
	41	! Adjustments to new topography and surface concept
	42	!
[2119]	43	! 2118 2017-01-17 16:38:49Z raasch
	44	! OpenACC version of subroutine removed
	45	!
[2038]	46	! 2037 2016-10-26 11:15:40Z knoop
	47	! Anelastic approximation implemented
	48	!
[2001]	49	! 2000 2016-08-20 18:09:15Z knoop
	50	! Forced header and separation lines into 80 columns
	51	!
[1874]	52	! 1873 2016-04-18 14:50:06Z maronga
	53	! Module renamed (removed _mod)
	54	!
[1851]	55	! 1850 2016-04-08 13:29:27Z maronga
	56	! Module renamed
	57	!
[1741]	58	! 1740 2016-01-13 08:19:40Z raasch
	59	! unnecessary calculations of kmzm and kmzp in wall bounded parts removed
	60	!
[1692]	61	! 1691 2015-10-26 16:17:44Z maronga
	62	! Formatting corrections.
	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	! kmym_x/_y and kmyp_x/_y change to kmym and kmyp
	98	!
[1]	99	! Revision 1.1 1997/09/12 06:23:51 raasch
	100	! Initial revision
	101	!
	102	!
	103	! Description:
	104	! ------------
[1682]	105	!> Diffusion term of the u-component
	106	!> @todo additional damping (needed for non-cyclic bc) causes bad vectorization
	107	!> and slows down the speed on NEC about 5-10%
[1]	108	!------------------------------------------------------------------------------!
[1682]	109	MODULE diffusion_u_mod
	110
[1]	111
	112	PRIVATE
[2118]	113	PUBLIC diffusion_u
[1]	114
	115	INTERFACE diffusion_u
	116	MODULE PROCEDURE diffusion_u
	117	MODULE PROCEDURE diffusion_u_ij
	118	END INTERFACE diffusion_u
	119
	120	CONTAINS
	121
	122
	123	!------------------------------------------------------------------------------!
[1682]	124	! Description:
	125	! ------------
	126	!> Call for all grid points
[1]	127	!------------------------------------------------------------------------------!
[1001]	128	SUBROUTINE diffusion_u
[1]	129
[1320]	130	USE arrays_3d, &
[2232]	131	ONLY: ddzu, ddzw, km, tend, u, v, w, drho_air, rho_air_zw
[1320]	132
	133	USE control_parameters, &
[2232]	134	ONLY: constant_top_momentumflux, use_surface_fluxes, &
[1320]	135	use_top_fluxes
	136
	137	USE grid_variables, &
[2232]	138	ONLY: ddx, ddx2, ddy
[1320]	139
	140	USE indices, &
[3241]	141	ONLY: nxlu, nxr, nyn, nys, nzb, nzt, wall_flags_0
[2232]	142
[1320]	143	USE kinds
[1]	144
[2232]	145	USE surface_mod, &
	146	ONLY : surf_def_h, surf_def_v, surf_lsm_h, surf_lsm_v, surf_usm_h, &
	147	surf_usm_v
	148
[1]	149	IMPLICIT NONE
	150
[2232]	151	INTEGER(iwp) :: i !< running index x direction
	152	INTEGER(iwp) :: j !< running index y direction
	153	INTEGER(iwp) :: k !< running index z direction
	154	INTEGER(iwp) :: l !< running index of surface type, south- or north-facing wall
	155	INTEGER(iwp) :: m !< running index surface elements
	156	INTEGER(iwp) :: surf_e !< End index of surface elements at (j,i)-gridpoint
	157	INTEGER(iwp) :: surf_s !< Start index of surface elements at (j,i)-gridpoint
[1001]	158
[2232]	159	REAL(wp) :: flag !< flag to mask topography grid points
	160	REAL(wp) :: kmym !<
	161	REAL(wp) :: kmyp !<
	162	REAL(wp) :: kmzm !<
	163	REAL(wp) :: kmzp !<
	164	REAL(wp) :: mask_bottom !< flag to mask vertical upward-facing surface
	165	REAL(wp) :: mask_north !< flag to mask vertical surface north of the grid point
	166	REAL(wp) :: mask_south !< flag to mask vertical surface south of the grid point
	167	REAL(wp) :: mask_top !< flag to mask vertical downward-facing surface
[1]	168
[56]	169
[2232]	170
[106]	171	DO i = nxlu, nxr
[1001]	172	DO j = nys, nyn
[1]	173	!
	174	!-- Compute horizontal diffusion
[2232]	175	DO k = nzb+1, nzt
[1]	176	!
[2232]	177	!-- Predetermine flag to mask topography and wall-bounded grid points.
	178	!-- It is sufficient to masked only north- and south-facing surfaces, which
	179	!-- need special treatment for the u-component.
	180	flag = MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_0(k,j,i), 1 ) )
	181	mask_south = MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_0(k,j-1,i), 1 ) )
	182	mask_north = MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_0(k,j+1,i), 1 ) )
	183	!
[1]	184	!-- Interpolate eddy diffusivities on staggered gridpoints
[1340]	185	kmyp = 0.25_wp * &
[978]	186	( km(k,j,i)+km(k,j+1,i)+km(k,j,i-1)+km(k,j+1,i-1) )
[1340]	187	kmym = 0.25_wp * &
[978]	188	( km(k,j,i)+km(k,j-1,i)+km(k,j,i-1)+km(k,j-1,i-1) )
[1]	189
[1320]	190	tend(k,j,i) = tend(k,j,i) &
[2232]	191	+ 2.0_wp * ( &
	192	km(k,j,i) * ( u(k,j,i+1) - u(k,j,i) ) &
	193	- km(k,j,i-1) * ( u(k,j,i) - u(k,j,i-1) ) &
	194	) * ddx2 * flag &
	195	+ ( mask_north * ( &
	196	kmyp * ( u(k,j+1,i) - u(k,j,i) ) * ddy &
	197	+ kmyp * ( v(k,j+1,i) - v(k,j+1,i-1) ) * ddx &
	198	) &
	199	- mask_south * ( &
	200	kmym * ( u(k,j,i) - u(k,j-1,i) ) * ddy &
	201	+ kmym * ( v(k,j,i) - v(k,j,i-1) ) * ddx &
	202	) &
	203	) * ddy * flag
[1]	204	ENDDO
	205	!
[2232]	206	!-- Add horizontal momentum flux u'v' at north- (l=0) and south-facing (l=1)
	207	!-- surfaces. Note, in the the flat case, loops won't be entered as
	208	!-- start_index > end_index. Furtermore, note, no vertical natural surfaces
	209	!-- so far.
	210	!-- Default-type surfaces
	211	DO l = 0, 1
	212	surf_s = surf_def_v(l)%start_index(j,i)
	213	surf_e = surf_def_v(l)%end_index(j,i)
	214	DO m = surf_s, surf_e
	215	k = surf_def_v(l)%k(m)
	216	tend(k,j,i) = tend(k,j,i) + &
	217	surf_def_v(l)%mom_flux_uv(m) * ddy
	218	ENDDO
	219	ENDDO
	220	!
	221	!-- Natural-type surfaces
	222	DO l = 0, 1
	223	surf_s = surf_lsm_v(l)%start_index(j,i)
	224	surf_e = surf_lsm_v(l)%end_index(j,i)
	225	DO m = surf_s, surf_e
	226	k = surf_lsm_v(l)%k(m)
	227	tend(k,j,i) = tend(k,j,i) + &
	228	surf_lsm_v(l)%mom_flux_uv(m) * ddy
	229	ENDDO
	230	ENDDO
	231	!
	232	!-- Urban-type surfaces
	233	DO l = 0, 1
	234	surf_s = surf_usm_v(l)%start_index(j,i)
	235	surf_e = surf_usm_v(l)%end_index(j,i)
	236	DO m = surf_s, surf_e
	237	k = surf_usm_v(l)%k(m)
	238	tend(k,j,i) = tend(k,j,i) + &
	239	surf_usm_v(l)%mom_flux_uv(m) * ddy
	240	ENDDO
	241	ENDDO
[51]	242
[1]	243	!
[2232]	244	!-- Compute vertical diffusion. In case of simulating a surface layer,
	245	!-- respective grid diffusive fluxes are masked (flag 8) within this
	246	!-- loop, and added further below, else, simple gradient approach is
	247	!-- applied. Model top is also mask if top-momentum flux is given.
	248	DO k = nzb+1, nzt
[1]	249	!
[2232]	250	!-- Determine flags to mask topography below and above. Flag 1 is
	251	!-- used to mask topography in general, and flag 8 implies
	252	!-- information about use_surface_fluxes. Flag 9 is used to control
	253	!-- momentum flux at model top.
	254	mask_bottom = MERGE( 1.0_wp, 0.0_wp, &
	255	BTEST( wall_flags_0(k-1,j,i), 8 ) )
	256	mask_top = MERGE( 1.0_wp, 0.0_wp, &
	257	BTEST( wall_flags_0(k+1,j,i), 8 ) ) * &
	258	MERGE( 1.0_wp, 0.0_wp, &
	259	BTEST( wall_flags_0(k+1,j,i), 9 ) )
	260	flag = MERGE( 1.0_wp, 0.0_wp, &
	261	BTEST( wall_flags_0(k,j,i), 1 ) )
	262	!
[1]	263	!-- Interpolate eddy diffusivities on staggered gridpoints
[1340]	264	kmzp = 0.25_wp * &
[1]	265	( km(k,j,i)+km(k+1,j,i)+km(k,j,i-1)+km(k+1,j,i-1) )
[1340]	266	kmzm = 0.25_wp * &
[1]	267	( km(k,j,i)+km(k-1,j,i)+km(k,j,i-1)+km(k-1,j,i-1) )
	268
[1320]	269	tend(k,j,i) = tend(k,j,i) &
[2232]	270	+ ( kmzp * ( ( u(k+1,j,i) - u(k,j,i) ) * ddzu(k+1) &
	271	+ ( w(k,j,i) - w(k,j,i-1) ) * ddx &
	272	) * rho_air_zw(k) * mask_top &
	273	- kmzm * ( ( u(k,j,i) - u(k-1,j,i) ) * ddzu(k) &
	274	+ ( w(k-1,j,i) - w(k-1,j,i-1) ) * ddx &
	275	) * rho_air_zw(k-1) * mask_bottom &
	276	) * ddzw(k) * drho_air(k) * flag
[1]	277	ENDDO
	278
	279	!
	280	!-- Vertical diffusion at the first grid point above the surface,
	281	!-- if the momentum flux at the bottom is given by the Prandtl law or
	282	!-- if it is prescribed by the user.
	283	!-- Difference quotient of the momentum flux is not formed over half
	284	!-- of the grid spacing (2.0*ddzw(k)) any more, since the comparison
[1320]	285	!-- with other (LES) models showed that the values of the momentum
[1]	286	!-- flux becomes too large in this case.
	287	!-- The term containing w(k-1,..) (see above equation) is removed here
	288	!-- because the vertical velocity is assumed to be zero at the surface.
	289	IF ( use_surface_fluxes ) THEN
	290	!
[2232]	291	!-- Default-type surfaces, upward-facing
	292	surf_s = surf_def_h(0)%start_index(j,i)
	293	surf_e = surf_def_h(0)%end_index(j,i)
	294	DO m = surf_s, surf_e
[1]	295
[2232]	296	k = surf_def_h(0)%k(m)
[1]	297
[2232]	298	tend(k,j,i) = tend(k,j,i) &
	299	+ ( - ( - surf_def_h(0)%usws(m) ) &
	300	) * ddzw(k) * drho_air(k)
	301	ENDDO
[102]	302	!
[2232]	303	!-- Default-type surfaces, dowward-facing
	304	surf_s = surf_def_h(1)%start_index(j,i)
	305	surf_e = surf_def_h(1)%end_index(j,i)
	306	DO m = surf_s, surf_e
	307
	308	k = surf_def_h(1)%k(m)
	309
	310	tend(k,j,i) = tend(k,j,i) &
	311	+ ( - surf_def_h(1)%usws(m) &
	312	) * ddzw(k) * drho_air(k)
	313	ENDDO
[102]	314	!
[2232]	315	!-- Natural-type surfaces, upward-facing
	316	surf_s = surf_lsm_h%start_index(j,i)
	317	surf_e = surf_lsm_h%end_index(j,i)
	318	DO m = surf_s, surf_e
[102]	319
[2232]	320	k = surf_lsm_h%k(m)
	321
	322	tend(k,j,i) = tend(k,j,i) &
	323	+ ( - ( - surf_lsm_h%usws(m) ) &
	324	) * ddzw(k) * drho_air(k)
	325	ENDDO
	326	!
	327	!-- Urban-type surfaces, upward-facing
	328	surf_s = surf_usm_h%start_index(j,i)
	329	surf_e = surf_usm_h%end_index(j,i)
	330	DO m = surf_s, surf_e
	331
	332	k = surf_usm_h%k(m)
	333
	334	tend(k,j,i) = tend(k,j,i) &
	335	+ ( - ( - surf_usm_h%usws(m) ) &
	336	) * ddzw(k) * drho_air(k)
	337	ENDDO
	338
[102]	339	ENDIF
[2232]	340	!
	341	!-- Add momentum flux at model top
[2638]	342	IF ( use_top_fluxes .AND. constant_top_momentumflux ) THEN
[2232]	343	surf_s = surf_def_h(2)%start_index(j,i)
	344	surf_e = surf_def_h(2)%end_index(j,i)
	345	DO m = surf_s, surf_e
[102]	346
[2232]	347	k = surf_def_h(2)%k(m)
	348
	349	tend(k,j,i) = tend(k,j,i) &
	350	+ ( - surf_def_h(2)%usws(m) ) * ddzw(k) * drho_air(k)
	351	ENDDO
	352	ENDIF
	353
[1]	354	ENDDO
	355	ENDDO
	356
	357	END SUBROUTINE diffusion_u
	358
	359
	360	!------------------------------------------------------------------------------!
[1682]	361	! Description:
	362	! ------------
	363	!> Call for grid point i,j
[1]	364	!------------------------------------------------------------------------------!
[1001]	365	SUBROUTINE diffusion_u_ij( i, j )
[1]	366
[1320]	367	USE arrays_3d, &
[2232]	368	ONLY: ddzu, ddzw, km, tend, u, v, w, drho_air, rho_air_zw
[1320]	369
	370	USE control_parameters, &
[2232]	371	ONLY: constant_top_momentumflux, use_surface_fluxes, &
	372	use_top_fluxes
[1320]	373
	374	USE grid_variables, &
[2232]	375	ONLY: ddx, ddx2, ddy
[1320]	376
	377	USE indices, &
[2232]	378	ONLY: nzb, nzt, wall_flags_0
	379
[1320]	380	USE kinds
[1]	381
[2232]	382	USE surface_mod, &
	383	ONLY : surf_def_h, surf_def_v, surf_lsm_h, surf_lsm_v, surf_usm_h, &
	384	surf_usm_v
	385
[1]	386	IMPLICIT NONE
	387
[2232]	388	INTEGER(iwp) :: i !< running index x direction
	389	INTEGER(iwp) :: j !< running index y direction
	390	INTEGER(iwp) :: k !< running index z direction
	391	INTEGER(iwp) :: l !< running index of surface type, south- or north-facing wall
	392	INTEGER(iwp) :: m !< running index surface elements
	393	INTEGER(iwp) :: surf_e !< End index of surface elements at (j,i)-gridpoint
	394	INTEGER(iwp) :: surf_s !< Start index of surface elements at (j,i)-gridpoint
[1]	395
[2232]	396	REAL(wp) :: flag !< flag to mask topography grid points
	397	REAL(wp) :: kmym !<
	398	REAL(wp) :: kmyp !<
	399	REAL(wp) :: kmzm !<
	400	REAL(wp) :: kmzp !<
	401	REAL(wp) :: mask_bottom !< flag to mask vertical upward-facing surface
	402	REAL(wp) :: mask_north !< flag to mask vertical surface north of the grid point
	403	REAL(wp) :: mask_south !< flag to mask vertical surface south of the grid point
	404	REAL(wp) :: mask_top !< flag to mask vertical downward-facing surface
	405	!
[1]	406	!-- Compute horizontal diffusion
[2232]	407	DO k = nzb+1, nzt
[1]	408	!
[2232]	409	!-- Predetermine flag to mask topography and wall-bounded grid points.
	410	!-- It is sufficient to masked only north- and south-facing surfaces, which
	411	!-- need special treatment for the u-component.
	412	flag = MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_0(k,j,i), 1 ) )
	413	mask_south = MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_0(k,j-1,i), 1 ) )
	414	mask_north = MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_0(k,j+1,i), 1 ) )
	415	!
[1]	416	!-- Interpolate eddy diffusivities on staggered gridpoints
[1340]	417	kmyp = 0.25_wp * ( km(k,j,i)+km(k,j+1,i)+km(k,j,i-1)+km(k,j+1,i-1) )
	418	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]	419
[1320]	420	tend(k,j,i) = tend(k,j,i) &
[2232]	421	+ 2.0_wp * ( &
	422	km(k,j,i) * ( u(k,j,i+1) - u(k,j,i) ) &
	423	- km(k,j,i-1) * ( u(k,j,i) - u(k,j,i-1) ) &
	424	) * ddx2 * flag &
	425	+ ( &
	426	mask_north * kmyp * ( ( u(k,j+1,i) - u(k,j,i) ) * ddy &
	427	+ ( v(k,j+1,i) - v(k,j+1,i-1) ) * ddx &
	428	) &
	429	- mask_south * kmym * ( ( u(k,j,i) - u(k,j-1,i) ) * ddy &
	430	+ ( v(k,j,i) - v(k,j,i-1) ) * ddx &
	431	) &
	432	) * ddy * flag
[1]	433	ENDDO
	434
	435	!
[2232]	436	!-- Add horizontal momentum flux u'v' at north- (l=0) and south-facing (l=1)
	437	!-- surfaces. Note, in the the flat case, loops won't be entered as
	438	!-- start_index > end_index. Furtermore, note, no vertical natural surfaces
	439	!-- so far.
	440	!-- Default-type surfaces
	441	DO l = 0, 1
	442	surf_s = surf_def_v(l)%start_index(j,i)
	443	surf_e = surf_def_v(l)%end_index(j,i)
	444	DO m = surf_s, surf_e
	445	k = surf_def_v(l)%k(m)
	446	tend(k,j,i) = tend(k,j,i) + surf_def_v(l)%mom_flux_uv(m) * ddy
	447	ENDDO
	448	ENDDO
[51]	449	!
[2232]	450	!-- Natural-type surfaces
	451	DO l = 0, 1
	452	surf_s = surf_lsm_v(l)%start_index(j,i)
	453	surf_e = surf_lsm_v(l)%end_index(j,i)
	454	DO m = surf_s, surf_e
	455	k = surf_lsm_v(l)%k(m)
	456	tend(k,j,i) = tend(k,j,i) + surf_lsm_v(l)%mom_flux_uv(m) * ddy
	457	ENDDO
	458	ENDDO
[1]	459	!
[2232]	460	!-- Urban-type surfaces
	461	DO l = 0, 1
	462	surf_s = surf_usm_v(l)%start_index(j,i)
	463	surf_e = surf_usm_v(l)%end_index(j,i)
	464	DO m = surf_s, surf_e
	465	k = surf_usm_v(l)%k(m)
	466	tend(k,j,i) = tend(k,j,i) + surf_usm_v(l)%mom_flux_uv(m) * ddy
	467	ENDDO
	468	ENDDO
[1]	469	!
[2232]	470	!-- Compute vertical diffusion. In case of simulating a surface layer,
	471	!-- respective grid diffusive fluxes are masked (flag 8) within this
	472	!-- loop, and added further below, else, simple gradient approach is
	473	!-- applied. Model top is also mask if top-momentum flux is given.
	474	DO k = nzb+1, nzt
	475	!
	476	!-- Determine flags to mask topography below and above. Flag 1 is
	477	!-- used to mask topography in general, and flag 8 implies
	478	!-- information about use_surface_fluxes. Flag 9 is used to control
	479	!-- momentum flux at model top.
	480	mask_bottom = MERGE( 1.0_wp, 0.0_wp, &
	481	BTEST( wall_flags_0(k-1,j,i), 8 ) )
	482	mask_top = MERGE( 1.0_wp, 0.0_wp, &
	483	BTEST( wall_flags_0(k+1,j,i), 8 ) ) * &
	484	MERGE( 1.0_wp, 0.0_wp, &
	485	BTEST( wall_flags_0(k+1,j,i), 9 ) )
	486	flag = MERGE( 1.0_wp, 0.0_wp, &
	487	BTEST( wall_flags_0(k,j,i), 1 ) )
	488	!
[1]	489	!-- Interpolate eddy diffusivities on staggered gridpoints
[1340]	490	kmzp = 0.25_wp * ( km(k,j,i)+km(k+1,j,i)+km(k,j,i-1)+km(k+1,j,i-1) )
	491	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]	492
[1320]	493	tend(k,j,i) = tend(k,j,i) &
[2232]	494	+ ( kmzp * ( ( u(k+1,j,i) - u(k,j,i) ) * ddzu(k+1) &
	495	+ ( w(k,j,i) - w(k,j,i-1) ) * ddx &
	496	) * rho_air_zw(k) * mask_top &
	497	- kmzm * ( ( u(k,j,i) - u(k-1,j,i) ) * ddzu(k) &
	498	+ ( w(k-1,j,i) - w(k-1,j,i-1) ) * ddx &
	499	) * rho_air_zw(k-1) * mask_bottom &
	500	) * ddzw(k) * drho_air(k) * flag
[1]	501	ENDDO
	502
	503	!
[2232]	504	!-- Vertical diffusion at the first surface grid points, if the
[1]	505	!-- momentum flux at the bottom is given by the Prandtl law or if it is
	506	!-- prescribed by the user.
	507	!-- Difference quotient of the momentum flux is not formed over half of
	508	!-- the grid spacing (2.0*ddzw(k)) any more, since the comparison with
[1320]	509	!-- other (LES) models showed that the values of the momentum flux becomes
[1]	510	!-- too large in this case.
	511	IF ( use_surface_fluxes ) THEN
	512	!
[2232]	513	!-- Default-type surfaces, upward-facing
	514	surf_s = surf_def_h(0)%start_index(j,i)
	515	surf_e = surf_def_h(0)%end_index(j,i)
	516	DO m = surf_s, surf_e
[1]	517
[2232]	518	k = surf_def_h(0)%k(m)
[1]	519
[2232]	520	tend(k,j,i) = tend(k,j,i) &
	521	+ ( - ( - surf_def_h(0)%usws(m) ) &
	522	) * ddzw(k) * drho_air(k)
	523	ENDDO
[102]	524	!
[2232]	525	!-- Default-type surfaces, dowward-facing (except for model-top fluxes)
	526	surf_s = surf_def_h(1)%start_index(j,i)
	527	surf_e = surf_def_h(1)%end_index(j,i)
	528	DO m = surf_s, surf_e
	529
	530	k = surf_def_h(1)%k(m)
	531
	532	tend(k,j,i) = tend(k,j,i) &
	533	+ ( - surf_def_h(1)%usws(m) &
	534	) * ddzw(k) * drho_air(k)
	535	ENDDO
[102]	536	!
[2232]	537	!-- Natural-type surfaces, upward-facing
	538	surf_s = surf_lsm_h%start_index(j,i)
	539	surf_e = surf_lsm_h%end_index(j,i)
	540	DO m = surf_s, surf_e
[102]	541
[2232]	542	k = surf_lsm_h%k(m)
	543
	544	tend(k,j,i) = tend(k,j,i) &
	545	+ ( - ( - surf_lsm_h%usws(m) ) &
	546	) * ddzw(k) * drho_air(k)
	547	ENDDO
	548	!
	549	!-- Urban-type surfaces, upward-facing
	550	surf_s = surf_usm_h%start_index(j,i)
	551	surf_e = surf_usm_h%end_index(j,i)
	552	DO m = surf_s, surf_e
	553
	554	k = surf_usm_h%k(m)
	555
	556	tend(k,j,i) = tend(k,j,i) &
	557	+ ( - ( - surf_usm_h%usws(m) ) &
	558	) * ddzw(k) * drho_air(k)
	559	ENDDO
	560
[102]	561	ENDIF
[2232]	562	!
	563	!-- Add momentum flux at model top
[2638]	564	IF ( use_top_fluxes .AND. constant_top_momentumflux ) THEN
[2232]	565	surf_s = surf_def_h(2)%start_index(j,i)
	566	surf_e = surf_def_h(2)%end_index(j,i)
	567	DO m = surf_s, surf_e
[102]	568
[2232]	569	k = surf_def_h(2)%k(m)
	570
	571	tend(k,j,i) = tend(k,j,i) &
	572	+ ( - surf_def_h(2)%usws(m) ) * ddzw(k) * drho_air(k)
	573	ENDDO
	574	ENDIF
	575
	576
[1]	577	END SUBROUTINE diffusion_u_ij
	578
	579	END MODULE diffusion_u_mod

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