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source: palm/trunk/SOURCE/diffusion_v.f90 @ 1035

Last change on this file since 1035 was 1017, checked in by raasch, 12 years ago
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[1]	1	MODULE diffusion_v_mod
	2
	3	!------------------------------------------------------------------------------!
[484]	4	! Current revisions:
[1]	5	! -----------------
	6	!
[1017]	7	!
[1]	8	! Former revisions:
	9	! -----------------
[3]	10	! $Id: diffusion_v.f90 1017 2012-09-27 11:28:50Z raasch $
[39]	11	!
[1017]	12	! 1015 2012-09-27 09:23:24Z raasch
	13	! accelerator version (*_acc) added
	14	!
[1002]	15	! 1001 2012-09-13 14:08:46Z raasch
	16	! arrays comunicated by module instead of parameter list
	17	!
[979]	18	! 978 2012-08-09 08:28:32Z fricke
	19	! outflow damping layer removed
	20	! kmxm_x/_y and kmxp_x/_y change to kmxm and kmxp
	21	!
[668]	22	! 667 2010-12-23 12:06:00Z suehring/gryschka
	23	! nxl-1, nxr+1, nys-1, nyn+1 replaced by nxlg, nxrg, nysg, nyng
	24	!
[392]	25	! 366 2009-08-25 08:06:27Z raasch
	26	! bc_lr replaced by bc_lr_cyc
	27	!
[110]	28	! 106 2007-08-16 14:30:26Z raasch
	29	! Momentumflux at top (vswst) included as boundary condition,
	30	! j loop is starting from nysv (needed for non-cyclic boundary conditions)
	31	!
[77]	32	! 75 2007-03-22 09:54:05Z raasch
	33	! Wall functions now include diabatic conditions, call of routine wall_fluxes,
	34	! z0 removed from argument list, vynp eliminated
	35	!
[39]	36	! 20 2007-02-26 00:12:32Z raasch
	37	! Bugfix: ddzw dimensioned 1:nzt"+1"
	38	!
[3]	39	! RCS Log replace by Id keyword, revision history cleaned up
	40	!
[1]	41	! Revision 1.15 2006/02/23 10:36:00 raasch
	42	! nzb_2d replaced by nzb_v_outer in horizontal diffusion and by nzb_v_inner
	43	! or nzb_diff_v, respectively, in vertical diffusion,
	44	! wall functions added for north and south walls, +z0 in argument list,
	45	! terms containing w(k-1,..) are removed from the Prandtl-layer equation
	46	! because they cause errors at the edges of topography
	47	! WARNING: loops containing the MAX function are still not properly vectorized!
	48	!
	49	! Revision 1.1 1997/09/12 06:24:01 raasch
	50	! Initial revision
	51	!
	52	!
	53	! Description:
	54	! ------------
	55	! Diffusion term of the v-component
	56	!------------------------------------------------------------------------------!
	57
[56]	58	USE wall_fluxes_mod
	59
[1]	60	PRIVATE
[1015]	61	PUBLIC diffusion_v, diffusion_v_acc
[1]	62
	63	INTERFACE diffusion_v
	64	MODULE PROCEDURE diffusion_v
	65	MODULE PROCEDURE diffusion_v_ij
	66	END INTERFACE diffusion_v
	67
[1015]	68	INTERFACE diffusion_v_acc
	69	MODULE PROCEDURE diffusion_v_acc
	70	END INTERFACE diffusion_v_acc
	71
[1]	72	CONTAINS
	73
	74
	75	!------------------------------------------------------------------------------!
	76	! Call for all grid points
	77	!------------------------------------------------------------------------------!
[1001]	78	SUBROUTINE diffusion_v
[1]	79
[1001]	80	USE arrays_3d
[1]	81	USE control_parameters
	82	USE grid_variables
	83	USE indices
	84
	85	IMPLICIT NONE
	86
	87	INTEGER :: i, j, k
[978]	88	REAL :: kmxm, kmxp, kmzm, kmzp
[1001]	89
[75]	90	REAL, DIMENSION(nzb:nzt+1,nys:nyn,nxl:nxr) :: vsus
[1]	91
[56]	92	!
	93	!-- First calculate horizontal momentum flux v'u' at vertical walls,
	94	!-- if neccessary
	95	IF ( topography /= 'flat' ) THEN
[75]	96	CALL wall_fluxes( vsus, 0.0, 1.0, 0.0, 0.0, nzb_v_inner, &
[56]	97	nzb_v_outer, wall_v )
	98	ENDIF
	99
[1]	100	DO i = nxl, nxr
[106]	101	DO j = nysv, nyn
[1]	102	!
	103	!-- Compute horizontal diffusion
	104	DO k = nzb_v_outer(j,i)+1, nzt
	105	!
	106	!-- Interpolate eddy diffusivities on staggered gridpoints
[978]	107	kmxp = 0.25 * &
	108	( km(k,j,i)+km(k,j,i+1)+km(k,j-1,i)+km(k,j-1,i+1) )
	109	kmxm = 0.25 * &
	110	( km(k,j,i)+km(k,j,i-1)+km(k,j-1,i)+km(k,j-1,i-1) )
[1]	111
	112	tend(k,j,i) = tend(k,j,i) &
[978]	113	& + ( kmxp * ( v(k,j,i+1) - v(k,j,i) ) * ddx &
	114	& + kmxp * ( u(k,j,i+1) - u(k,j-1,i+1) ) * ddy &
	115	& - kmxm * ( v(k,j,i) - v(k,j,i-1) ) * ddx &
	116	& - kmxm * ( u(k,j,i) - u(k,j-1,i) ) * ddy &
[1]	117	& ) * ddx &
	118	& + 2.0 * ( &
	119	& km(k,j,i) * ( v(k,j+1,i) - v(k,j,i) ) &
	120	& - km(k,j-1,i) * ( v(k,j,i) - v(k,j-1,i) ) &
	121	& ) * ddy2
	122	ENDDO
	123
	124	!
	125	!-- Wall functions at the left and right walls, respectively
	126	IF ( wall_v(j,i) /= 0.0 ) THEN
[51]	127
[1]	128	DO k = nzb_v_inner(j,i)+1, nzb_v_outer(j,i)
[978]	129	kmxp = 0.25 * &
	130	( km(k,j,i)+km(k,j,i+1)+km(k,j-1,i)+km(k,j-1,i+1) )
	131	kmxm = 0.25 * &
	132	( km(k,j,i)+km(k,j,i-1)+km(k,j-1,i)+km(k,j-1,i-1) )
	133
[1]	134	tend(k,j,i) = tend(k,j,i) &
	135	+ 2.0 * ( &
	136	km(k,j,i) * ( v(k,j+1,i) - v(k,j,i) ) &
	137	- km(k,j-1,i) * ( v(k,j,i) - v(k,j-1,i) ) &
	138	) * ddy2 &
	139	+ ( fxp(j,i) * ( &
[978]	140	kmxp * ( v(k,j,i+1) - v(k,j,i) ) * ddx &
	141	+ kmxp * ( u(k,j,i+1) - u(k,j-1,i+1) ) * ddy &
[1]	142	) &
	143	- fxm(j,i) * ( &
[978]	144	kmxm * ( v(k,j,i) - v(k,j,i-1) ) * ddx &
	145	+ kmxm * ( u(k,j,i) - u(k,j-1,i) ) * ddy &
[1]	146	) &
[56]	147	+ wall_v(j,i) * vsus(k,j,i) &
[1]	148	) * ddx
	149	ENDDO
	150	ENDIF
	151
	152	!
	153	!-- Compute vertical diffusion. In case of simulating a Prandtl
	154	!-- layer, index k starts at nzb_v_inner+2.
[102]	155	DO k = nzb_diff_v(j,i), nzt_diff
[1]	156	!
	157	!-- Interpolate eddy diffusivities on staggered gridpoints
	158	kmzp = 0.25 * &
	159	( km(k,j,i)+km(k+1,j,i)+km(k,j-1,i)+km(k+1,j-1,i) )
	160	kmzm = 0.25 * &
	161	( km(k,j,i)+km(k-1,j,i)+km(k,j-1,i)+km(k-1,j-1,i) )
	162
	163	tend(k,j,i) = tend(k,j,i) &
	164	& + ( kmzp * ( ( v(k+1,j,i) - v(k,j,i) ) * ddzu(k+1) &
	165	& + ( w(k,j,i) - w(k,j-1,i) ) * ddy &
	166	& ) &
	167	& - kmzm * ( ( v(k,j,i) - v(k-1,j,i) ) * ddzu(k) &
	168	& + ( w(k-1,j,i) - w(k-1,j-1,i) ) * ddy &
	169	& ) &
	170	& ) * ddzw(k)
	171	ENDDO
	172
	173	!
	174	!-- Vertical diffusion at the first grid point above the surface,
	175	!-- if the momentum flux at the bottom is given by the Prandtl law
	176	!-- or if it is prescribed by the user.
	177	!-- Difference quotient of the momentum flux is not formed over
	178	!-- half of the grid spacing (2.0*ddzw(k)) any more, since the
	179	!-- comparison with other (LES) modell showed that the values of
	180	!-- the momentum flux becomes too large in this case.
	181	!-- The term containing w(k-1,..) (see above equation) is removed here
	182	!-- because the vertical velocity is assumed to be zero at the surface.
	183	IF ( use_surface_fluxes ) THEN
	184	k = nzb_v_inner(j,i)+1
	185	!
	186	!-- Interpolate eddy diffusivities on staggered gridpoints
	187	kmzp = 0.25 * &
	188	( km(k,j,i)+km(k+1,j,i)+km(k,j-1,i)+km(k+1,j-1,i) )
	189	kmzm = 0.25 * &
	190	( km(k,j,i)+km(k-1,j,i)+km(k,j-1,i)+km(k-1,j-1,i) )
	191
	192	tend(k,j,i) = tend(k,j,i) &
	193	& + ( kmzp * ( w(k,j,i) - w(k,j-1,i) ) * ddy &
	194	& ) * ddzw(k) &
[102]	195	& + ( kmzp * ( v(k+1,j,i) - v(k,j,i) ) * ddzu(k+1) &
[1]	196	& + vsws(j,i) &
	197	& ) * ddzw(k)
	198	ENDIF
	199
[102]	200	!
	201	!-- Vertical diffusion at the first gridpoint below the top boundary,
	202	!-- if the momentum flux at the top is prescribed by the user
[103]	203	IF ( use_top_fluxes .AND. constant_top_momentumflux ) THEN
[102]	204	k = nzt
	205	!
	206	!-- Interpolate eddy diffusivities on staggered gridpoints
	207	kmzp = 0.25 * &
	208	( km(k,j,i)+km(k+1,j,i)+km(k,j-1,i)+km(k+1,j-1,i) )
	209	kmzm = 0.25 * &
	210	( km(k,j,i)+km(k-1,j,i)+km(k,j-1,i)+km(k-1,j-1,i) )
	211
	212	tend(k,j,i) = tend(k,j,i) &
	213	& - ( kmzm * ( w(k-1,j,i) - w(k-1,j-1,i) ) * ddy &
	214	& ) * ddzw(k) &
	215	& + ( -vswst(j,i) &
	216	& - kmzm * ( v(k,j,i) - v(k-1,j,i) ) * ddzu(k) &
	217	& ) * ddzw(k)
	218	ENDIF
	219
[1]	220	ENDDO
	221	ENDDO
	222
	223	END SUBROUTINE diffusion_v
	224
	225
	226	!------------------------------------------------------------------------------!
[1015]	227	! Call for all grid points - accelerator version
	228	!------------------------------------------------------------------------------!
	229	SUBROUTINE diffusion_v_acc
	230
	231	USE arrays_3d
	232	USE control_parameters
	233	USE grid_variables
	234	USE indices
	235
	236	IMPLICIT NONE
	237
	238	INTEGER :: i, j, k
	239	REAL :: kmxm, kmxp, kmzm, kmzp
	240
	241	!$acc declare create ( vsus )
	242	REAL, DIMENSION(nzb:nzt+1,nys:nyn,nxl:nxr) :: vsus
	243
	244	!
	245	!-- First calculate horizontal momentum flux v'u' at vertical walls,
	246	!-- if neccessary
	247	IF ( topography /= 'flat' ) THEN
	248	CALL wall_fluxes_acc( vsus, 0.0, 1.0, 0.0, 0.0, nzb_v_inner, &
	249	nzb_v_outer, wall_v )
	250	ENDIF
	251
	252	!$acc kernels present ( u, v, w, km, tend, vsws, vswst ) &
	253	!$acc present ( ddzu, ddzw, fxm, fxp, wall_v ) &
	254	!$acc present ( nzb_v_inner, nzb_v_outer, nzb_diff_v )
	255	!$acc loop
	256	DO i = nxl, nxr
	257	DO j = nysv, nyn
	258	!
	259	!-- Compute horizontal diffusion
	260	!$acc loop vector(32)
	261	DO k = 1, nzt
	262	IF ( k > nzb_v_outer(j,i) ) THEN
	263	!
	264	!-- Interpolate eddy diffusivities on staggered gridpoints
	265	kmxp = 0.25 * &
	266	( km(k,j,i)+km(k,j,i+1)+km(k,j-1,i)+km(k,j-1,i+1) )
	267	kmxm = 0.25 * &
	268	( km(k,j,i)+km(k,j,i-1)+km(k,j-1,i)+km(k,j-1,i-1) )
	269
	270	tend(k,j,i) = tend(k,j,i) &
	271	& + ( kmxp * ( v(k,j,i+1) - v(k,j,i) ) * ddx &
	272	& + kmxp * ( u(k,j,i+1) - u(k,j-1,i+1) ) * ddy &
	273	& - kmxm * ( v(k,j,i) - v(k,j,i-1) ) * ddx &
	274	& - kmxm * ( u(k,j,i) - u(k,j-1,i) ) * ddy &
	275	& ) * ddx &
	276	& + 2.0 * ( &
	277	& km(k,j,i) * ( v(k,j+1,i) - v(k,j,i) ) &
	278	& - km(k,j-1,i) * ( v(k,j,i) - v(k,j-1,i) ) &
	279	& ) * ddy2
	280	ENDIF
	281	ENDDO
	282
	283	!
	284	!-- Wall functions at the left and right walls, respectively
	285	!$acc loop vector(32)
	286	DO k = 1, nzt
	287	IF( k > nzb_v_inner(j,i) .AND. k <= nzb_v_outer(j,i) .AND. &
	288	wall_v(j,i) /= 0.0 ) THEN
	289
	290	kmxp = 0.25 * &
	291	( km(k,j,i)+km(k,j,i+1)+km(k,j-1,i)+km(k,j-1,i+1) )
	292	kmxm = 0.25 * &
	293	( km(k,j,i)+km(k,j,i-1)+km(k,j-1,i)+km(k,j-1,i-1) )
	294
	295	tend(k,j,i) = tend(k,j,i) &
	296	+ 2.0 * ( &
	297	km(k,j,i) * ( v(k,j+1,i) - v(k,j,i) ) &
	298	- km(k,j-1,i) * ( v(k,j,i) - v(k,j-1,i) ) &
	299	) * ddy2 &
	300	+ ( fxp(j,i) * ( &
	301	kmxp * ( v(k,j,i+1) - v(k,j,i) ) * ddx &
	302	+ kmxp * ( u(k,j,i+1) - u(k,j-1,i+1) ) * ddy &
	303	) &
	304	- fxm(j,i) * ( &
	305	kmxm * ( v(k,j,i) - v(k,j,i-1) ) * ddx &
	306	+ kmxm * ( u(k,j,i) - u(k,j-1,i) ) * ddy &
	307	) &
	308	+ wall_v(j,i) * vsus(k,j,i) &
	309	) * ddx
	310	ENDIF
	311	ENDDO
	312
	313	!
	314	!-- Compute vertical diffusion. In case of simulating a Prandtl
	315	!-- layer, index k starts at nzb_v_inner+2.
	316	!$acc loop vector(32)
	317	DO k = 1, nzt_diff
	318	IF ( k >= nzb_diff_v(j,i) ) THEN
	319	!
	320	!-- Interpolate eddy diffusivities on staggered gridpoints
	321	kmzp = 0.25 * &
	322	( km(k,j,i)+km(k+1,j,i)+km(k,j-1,i)+km(k+1,j-1,i) )
	323	kmzm = 0.25 * &
	324	( km(k,j,i)+km(k-1,j,i)+km(k,j-1,i)+km(k-1,j-1,i) )
	325
	326	tend(k,j,i) = tend(k,j,i) &
	327	& + ( kmzp * ( ( v(k+1,j,i) - v(k,j,i) ) * ddzu(k+1)&
	328	& + ( w(k,j,i) - w(k,j-1,i) ) * ddy &
	329	& ) &
	330	& - kmzm * ( ( v(k,j,i) - v(k-1,j,i) ) * ddzu(k)&
	331	& + ( w(k-1,j,i) - w(k-1,j-1,i) ) * ddy &
	332	& ) &
	333	& ) * ddzw(k)
	334	ENDIF
	335	ENDDO
	336
	337	ENDDO
	338	ENDDO
	339
	340	!
	341	!-- Vertical diffusion at the first grid point above the surface,
	342	!-- if the momentum flux at the bottom is given by the Prandtl law
	343	!-- or if it is prescribed by the user.
	344	!-- Difference quotient of the momentum flux is not formed over
	345	!-- half of the grid spacing (2.0*ddzw(k)) any more, since the
	346	!-- comparison with other (LES) modell showed that the values of
	347	!-- the momentum flux becomes too large in this case.
	348	!-- The term containing w(k-1,..) (see above equation) is removed here
	349	!-- because the vertical velocity is assumed to be zero at the surface.
	350	IF ( use_surface_fluxes ) THEN
	351
	352	!$acc loop
	353	DO i = nxl, nxr
	354	!$acc loop vector(32)
	355	DO j = nysv, nyn
	356
	357	k = nzb_v_inner(j,i)+1
	358	!
	359	!-- Interpolate eddy diffusivities on staggered gridpoints
	360	kmzp = 0.25 * &
	361	( km(k,j,i)+km(k+1,j,i)+km(k,j-1,i)+km(k+1,j-1,i) )
	362	kmzm = 0.25 * &
	363	( km(k,j,i)+km(k-1,j,i)+km(k,j-1,i)+km(k-1,j-1,i) )
	364
	365	tend(k,j,i) = tend(k,j,i) &
	366	& + ( kmzp * ( w(k,j,i) - w(k,j-1,i) ) * ddy &
	367	& ) * ddzw(k) &
	368	& + ( kmzp * ( v(k+1,j,i) - v(k,j,i) ) * ddzu(k+1) &
	369	& + vsws(j,i) &
	370	& ) * ddzw(k)
	371	ENDDO
	372	ENDDO
	373
	374	ENDIF
	375
	376	!
	377	!-- Vertical diffusion at the first gridpoint below the top boundary,
	378	!-- if the momentum flux at the top is prescribed by the user
	379	IF ( use_top_fluxes .AND. constant_top_momentumflux ) THEN
	380
	381	k = nzt
	382
	383	!$acc loop
	384	DO i = nxl, nxr
	385	!$acc loop vector(32)
	386	DO j = nysv, nyn
	387
	388	!
	389	!-- Interpolate eddy diffusivities on staggered gridpoints
	390	kmzp = 0.25 * &
	391	( km(k,j,i)+km(k+1,j,i)+km(k,j-1,i)+km(k+1,j-1,i) )
	392	kmzm = 0.25 * &
	393	( km(k,j,i)+km(k-1,j,i)+km(k,j-1,i)+km(k-1,j-1,i) )
	394
	395	tend(k,j,i) = tend(k,j,i) &
	396	& - ( kmzm * ( w(k-1,j,i) - w(k-1,j-1,i) ) * ddy &
	397	& ) * ddzw(k) &
	398	& + ( -vswst(j,i) &
	399	& - kmzm * ( v(k,j,i) - v(k-1,j,i) ) * ddzu(k) &
	400	& ) * ddzw(k)
	401	ENDDO
	402	ENDDO
	403
	404	ENDIF
	405	!$acc end kernels
	406
	407	END SUBROUTINE diffusion_v_acc
	408
	409
	410	!------------------------------------------------------------------------------!
[1]	411	! Call for grid point i,j
	412	!------------------------------------------------------------------------------!
[1001]	413	SUBROUTINE diffusion_v_ij( i, j )
[1]	414
[1001]	415	USE arrays_3d
[1]	416	USE control_parameters
	417	USE grid_variables
	418	USE indices
	419
	420	IMPLICIT NONE
	421
	422	INTEGER :: i, j, k
[978]	423	REAL :: kmxm, kmxp, kmzm, kmzp
[1]	424
[1001]	425	REAL, DIMENSION(nzb:nzt+1) :: vsus
	426
[1]	427	!
	428	!-- Compute horizontal diffusion
	429	DO k = nzb_v_outer(j,i)+1, nzt
	430	!
	431	!-- Interpolate eddy diffusivities on staggered gridpoints
[978]	432	kmxp = 0.25 * ( km(k,j,i)+km(k,j,i+1)+km(k,j-1,i)+km(k,j-1,i+1) )
	433	kmxm = 0.25 * ( km(k,j,i)+km(k,j,i-1)+km(k,j-1,i)+km(k,j-1,i-1) )
[1]	434
	435	tend(k,j,i) = tend(k,j,i) &
[978]	436	& + ( kmxp * ( v(k,j,i+1) - v(k,j,i) ) * ddx &
	437	& + kmxp * ( u(k,j,i+1) - u(k,j-1,i+1) ) * ddy &
	438	& - kmxm * ( v(k,j,i) - v(k,j,i-1) ) * ddx &
	439	& - kmxm * ( u(k,j,i) - u(k,j-1,i) ) * ddy &
[1]	440	& ) * ddx &
	441	& + 2.0 * ( &
	442	& km(k,j,i) * ( v(k,j+1,i) - v(k,j,i) ) &
	443	& - km(k,j-1,i) * ( v(k,j,i) - v(k,j-1,i) ) &
	444	& ) * ddy2
	445	ENDDO
	446
	447	!
	448	!-- Wall functions at the left and right walls, respectively
	449	IF ( wall_v(j,i) /= 0.0 ) THEN
[51]	450
	451	!
	452	!-- Calculate the horizontal momentum flux v'u'
	453	CALL wall_fluxes( i, j, nzb_v_inner(j,i)+1, nzb_v_outer(j,i), &
	454	vsus, 0.0, 1.0, 0.0, 0.0 )
	455
[1]	456	DO k = nzb_v_inner(j,i)+1, nzb_v_outer(j,i)
[978]	457	kmxp = 0.25 * &
	458	( km(k,j,i)+km(k,j,i+1)+km(k,j-1,i)+km(k,j-1,i+1) )
	459	kmxm = 0.25 * &
	460	( km(k,j,i)+km(k,j,i-1)+km(k,j-1,i)+km(k,j-1,i-1) )
[1]	461
	462	tend(k,j,i) = tend(k,j,i) &
	463	+ 2.0 * ( &
	464	km(k,j,i) * ( v(k,j+1,i) - v(k,j,i) ) &
	465	- km(k,j-1,i) * ( v(k,j,i) - v(k,j-1,i) ) &
	466	) * ddy2 &
	467	+ ( fxp(j,i) * ( &
[978]	468	kmxp * ( v(k,j,i+1) - v(k,j,i) ) * ddx &
	469	+ kmxp * ( u(k,j,i+1) - u(k,j-1,i+1) ) * ddy &
[1]	470	) &
	471	- fxm(j,i) * ( &
[978]	472	kmxm * ( v(k,j,i) - v(k,j,i-1) ) * ddx &
	473	+ kmxm * ( u(k,j,i) - u(k,j-1,i) ) * ddy &
[1]	474	) &
[51]	475	+ wall_v(j,i) * vsus(k) &
[1]	476	) * ddx
	477	ENDDO
	478	ENDIF
	479
	480	!
	481	!-- Compute vertical diffusion. In case of simulating a Prandtl layer,
	482	!-- index k starts at nzb_v_inner+2.
[102]	483	DO k = nzb_diff_v(j,i), nzt_diff
[1]	484	!
	485	!-- Interpolate eddy diffusivities on staggered gridpoints
	486	kmzp = 0.25 * ( km(k,j,i)+km(k+1,j,i)+km(k,j-1,i)+km(k+1,j-1,i) )
	487	kmzm = 0.25 * ( km(k,j,i)+km(k-1,j,i)+km(k,j-1,i)+km(k-1,j-1,i) )
	488
	489	tend(k,j,i) = tend(k,j,i) &
	490	& + ( kmzp * ( ( v(k+1,j,i) - v(k,j,i) ) * ddzu(k+1) &
	491	& + ( w(k,j,i) - w(k,j-1,i) ) * ddy &
	492	& ) &
	493	& - kmzm * ( ( v(k,j,i) - v(k-1,j,i) ) * ddzu(k) &
	494	& + ( w(k-1,j,i) - w(k-1,j-1,i) ) * ddy &
	495	& ) &
	496	& ) * ddzw(k)
	497	ENDDO
	498
	499	!
	500	!-- Vertical diffusion at the first grid point above the surface, if the
	501	!-- momentum flux at the bottom is given by the Prandtl law or if it is
	502	!-- prescribed by the user.
	503	!-- Difference quotient of the momentum flux is not formed over half of
	504	!-- the grid spacing (2.0*ddzw(k)) any more, since the comparison with
	505	!-- other (LES) modell showed that the values of the momentum flux becomes
	506	!-- too large in this case.
	507	!-- The term containing w(k-1,..) (see above equation) is removed here
	508	!-- because the vertical velocity is assumed to be zero at the surface.
	509	IF ( use_surface_fluxes ) THEN
	510	k = nzb_v_inner(j,i)+1
	511	!
	512	!-- Interpolate eddy diffusivities on staggered gridpoints
	513	kmzp = 0.25 * ( km(k,j,i)+km(k+1,j,i)+km(k,j-1,i)+km(k+1,j-1,i) )
	514	kmzm = 0.25 * ( km(k,j,i)+km(k-1,j,i)+km(k,j-1,i)+km(k-1,j-1,i) )
	515
	516	tend(k,j,i) = tend(k,j,i) &
	517	& + ( kmzp * ( w(k,j,i) - w(k,j-1,i) ) * ddy &
	518	& ) * ddzw(k) &
[102]	519	& + ( kmzp * ( v(k+1,j,i) - v(k,j,i) ) * ddzu(k+1) &
[1]	520	& + vsws(j,i) &
	521	& ) * ddzw(k)
	522	ENDIF
	523
[102]	524	!
	525	!-- Vertical diffusion at the first gridpoint below the top boundary,
	526	!-- if the momentum flux at the top is prescribed by the user
[103]	527	IF ( use_top_fluxes .AND. constant_top_momentumflux ) THEN
[102]	528	k = nzt
	529	!
	530	!-- Interpolate eddy diffusivities on staggered gridpoints
	531	kmzp = 0.25 * &
	532	( km(k,j,i)+km(k+1,j,i)+km(k,j-1,i)+km(k+1,j-1,i) )
	533	kmzm = 0.25 * &
	534	( km(k,j,i)+km(k-1,j,i)+km(k,j-1,i)+km(k-1,j-1,i) )
	535
	536	tend(k,j,i) = tend(k,j,i) &
	537	& - ( kmzm * ( w(k-1,j,i) - w(k-1,j-1,i) ) * ddy &
	538	& ) * ddzw(k) &
	539	& + ( -vswst(j,i) &
	540	& - kmzm * ( v(k,j,i) - v(k-1,j,i) ) * ddzu(k) &
	541	& ) * ddzw(k)
	542	ENDIF
	543
[1]	544	END SUBROUTINE diffusion_v_ij
	545
	546	END MODULE diffusion_v_mod

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