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source: palm/trunk/SOURCE/boundary_conds.f90 @ 2556

Last change on this file since 2556 was 2365, checked in by kanani, 7 years ago
Vertical nesting implemented (SadiqHuq?)
Property svn:keywords set to `Id`
File size: 39.6 KB

Rev	Line
[1682]	1	!> @file boundary_conds.f90
[2000]	2	!------------------------------------------------------------------------------!
[1036]	3	! This file is part of PALM.
	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	! -----------------
[1933]	22	!
[2233]	23	!
[1321]	24	! Former revisions:
	25	! -----------------
	26	! $Id: boundary_conds.f90 2365 2017-08-21 14:59:59Z scharf $
[2365]	27	! Vertical grid nesting implemented: exclude setting vertical velocity to zero
	28	! on fine grid (SadiqHuq)
	29	!
	30	! 2320 2017-07-21 12:47:43Z suehring
[2320]	31	! Remove unused control parameter large_scale_forcing from only-list
	32	!
	33	! 2292 2017-06-20 09:51:42Z schwenkel
[2292]	34	! Implementation of new microphysic scheme: cloud_scheme = 'morrison'
	35	! includes two more prognostic equations for cloud drop concentration (nc)
	36	! and cloud water content (qc).
	37	!
	38	! 2233 2017-05-30 18:08:54Z suehring
[1321]	39	!
[2233]	40	! 2232 2017-05-30 17:47:52Z suehring
	41	! Set boundary conditions on topography top using flag method.
	42	!
[2119]	43	! 2118 2017-01-17 16:38:49Z raasch
	44	! OpenACC directives removed
	45	!
[2001]	46	! 2000 2016-08-20 18:09:15Z knoop
	47	! Forced header and separation lines into 80 columns
	48	!
[1993]	49	! 1992 2016-08-12 15:14:59Z suehring
	50	! Adjustments for top boundary condition for passive scalar
	51	!
[1961]	52	! 1960 2016-07-12 16:34:24Z suehring
	53	! Treat humidity and passive scalar separately
	54	!
[1933]	55	! 1823 2016-04-07 08:57:52Z hoffmann
	56	! Initial version of purely vertical nesting introduced.
	57	!
[1823]	58	! 1822 2016-04-07 07:49:42Z hoffmann
	59	! icloud_scheme removed. microphyisics_seifert added.
	60	!
[1765]	61	! 1764 2016-02-28 12:45:19Z raasch
	62	! index bug for u_p at left outflow removed
	63	!
[1763]	64	! 1762 2016-02-25 12:31:13Z hellstea
	65	! Introduction of nested domain feature
	66	!
[1744]	67	! 1742 2016-01-13 09:50:06Z raasch
	68	! bugfix for outflow Neumann boundary conditions at bottom and top
	69	!
[1718]	70	! 1717 2015-11-11 15:09:47Z raasch
	71	! Bugfix: index error in outflow conditions for left boundary
	72	!
[1683]	73	! 1682 2015-10-07 23:56:08Z knoop
	74	! Code annotations made doxygen readable
	75	!
[1717]	76	! 1410 2014-05-23 12:16:18Z suehring
[1463]	77	! Bugfix: set dirichlet boundary condition for passive_scalar at model domain
	78	! top
	79	!
[1410]	80	! 1399 2014-05-07 11:16:25Z heinze
	81	! Bugfix: set inflow boundary conditions also if no humidity or passive_scalar
	82	! is used.
	83	!
[1399]	84	! 1398 2014-05-07 11:15:00Z heinze
	85	! Dirichlet-condition at the top for u and v changed to u_init and v_init also
	86	! for large_scale_forcing
	87	!
[1381]	88	! 1380 2014-04-28 12:40:45Z heinze
	89	! Adjust Dirichlet-condition at the top for pt in case of nudging
	90	!
[1362]	91	! 1361 2014-04-16 15:17:48Z hoffmann
	92	! Bottom and top boundary conditions of rain water content (qr) and
	93	! rain drop concentration (nr) changed to Dirichlet
	94	!
[1354]	95	! 1353 2014-04-08 15:21:23Z heinze
	96	! REAL constants provided with KIND-attribute
	97	!
[1321]	98	! 1320 2014-03-20 08:40:49Z raasch
[1320]	99	! ONLY-attribute added to USE-statements,
	100	! kind-parameters added to all INTEGER and REAL declaration statements,
	101	! kinds are defined in new module kinds,
	102	! revision history before 2012 removed,
	103	! comment fields (!:) to be used for variable explanations added to
	104	! all variable declaration statements
[1160]	105	!
[1258]	106	! 1257 2013-11-08 15:18:40Z raasch
	107	! loop independent clauses added
	108	!
[1242]	109	! 1241 2013-10-30 11:36:58Z heinze
	110	! Adjust ug and vg at each timestep in case of large_scale_forcing
	111	!
[1160]	112	! 1159 2013-05-21 11:58:22Z fricke
[1159]	113	! Bugfix: Neumann boundary conditions for the velocity components at the
	114	! outflow are in fact radiation boundary conditions using the maximum phase
	115	! velocity that ensures numerical stability (CFL-condition).
	116	! Hence, logical operator use_cmax is now used instead of bc_lr_dirneu/_neudir.
	117	! Bugfix: In case of use_cmax at the outflow, u, v, w are replaced by
	118	! u_p, v_p, w_p
[1116]	119	!
	120	! 1115 2013-03-26 18:16:16Z hoffmann
	121	! boundary conditions of two-moment cloud scheme are restricted to Neumann-
	122	! boundary-conditions
	123	!
[1114]	124	! 1113 2013-03-10 02:48:14Z raasch
	125	! GPU-porting
	126	! dummy argument "range" removed
	127	! Bugfix: wrong index in loops of radiation boundary condition
[1113]	128	!
[1054]	129	! 1053 2012-11-13 17:11:03Z hoffmann
	130	! boundary conditions for the two new prognostic equations (nr, qr) of the
	131	! two-moment cloud scheme
	132	!
[1037]	133	! 1036 2012-10-22 13:43:42Z raasch
	134	! code put under GPL (PALM 3.9)
	135	!
[997]	136	! 996 2012-09-07 10:41:47Z raasch
	137	! little reformatting
	138	!
[979]	139	! 978 2012-08-09 08:28:32Z fricke
	140	! Neumann boudnary conditions are added at the inflow boundary for the SGS-TKE.
	141	! Outflow boundary conditions for the velocity components can be set to Neumann
	142	! conditions or to radiation conditions with a horizontal averaged phase
	143	! velocity.
	144	!
[876]	145	! 875 2012-04-02 15:35:15Z gryschka
	146	! Bugfix in case of dirichlet inflow bc at the right or north boundary
	147	!
[1]	148	! Revision 1.1 1997/09/12 06:21:34 raasch
	149	! Initial revision
	150	!
	151	!
	152	! Description:
	153	! ------------
[1682]	154	!> Boundary conditions for the prognostic quantities.
	155	!> One additional bottom boundary condition is applied for the TKE (=(u)*2)
	156	!> in prandtl_fluxes. The cyclic lateral boundary conditions are implicitly
	157	!> handled in routine exchange_horiz. Pressure boundary conditions are
	158	!> explicitly set in routines pres, poisfft, poismg and sor.
[1]	159	!------------------------------------------------------------------------------!
[1682]	160	SUBROUTINE boundary_conds
	161
[1]	162
[1320]	163	USE arrays_3d, &
	164	ONLY: c_u, c_u_m, c_u_m_l, c_v, c_v_m, c_v_m_l, c_w, c_w_m, c_w_m_l, &
[2292]	165	dzu, e_p, nc_p, nr_p, pt, pt_p, q, q_p, qc_p, qr_p, s, s_p, sa, &
	166	sa_p, u, ug, u_init, u_m_l, u_m_n, u_m_r, u_m_s, u_p, &
[1320]	167	v, vg, v_init, v_m_l, v_m_n, v_m_r, v_m_s, v_p, &
[1960]	168	w, w_p, w_m_l, w_m_n, w_m_r, w_m_s, pt_init
[2292]	169
[1320]	170	USE control_parameters, &
[1960]	171	ONLY: bc_pt_t_val, bc_q_t_val, bc_s_t_val, constant_diffusion, &
[2365]	172	cloud_physics, coupling_mode, dt_3d, humidity, &
[1960]	173	ibc_pt_b, ibc_pt_t, ibc_q_b, ibc_q_t, ibc_s_b, ibc_s_t, &
	174	ibc_sa_t, ibc_uv_b, ibc_uv_t, inflow_l, inflow_n, inflow_r, &
[2320]	175	inflow_s, intermediate_timestep_count, &
[2292]	176	microphysics_morrison, microphysics_seifert, nest_domain, &
	177	nest_bound_l, nest_bound_s, nudging, ocean, outflow_l, &
	178	outflow_n, outflow_r, outflow_s, passive_scalar, tsc, use_cmax
[1320]	179
	180	USE grid_variables, &
	181	ONLY: ddx, ddy, dx, dy
	182
	183	USE indices, &
	184	ONLY: nx, nxl, nxlg, nxr, nxrg, ny, nyn, nyng, nys, nysg, &
[2232]	185	nzb, nzt, wall_flags_0
[1320]	186
	187	USE kinds
	188
[1]	189	USE pegrid
	190
[1933]	191	USE pmc_interface, &
	192	ONLY : nesting_mode
[1320]	193
[2232]	194	USE surface_mod, &
	195	ONLY : bc_h
[1933]	196
[1]	197	IMPLICIT NONE
	198
[2232]	199	INTEGER(iwp) :: i !< grid index x direction
	200	INTEGER(iwp) :: j !< grid index y direction
	201	INTEGER(iwp) :: k !< grid index z direction
	202	INTEGER(iwp) :: kb !< variable to set respective boundary value, depends on facing.
	203	INTEGER(iwp) :: l !< running index boundary type, for up- and downward-facing walls
	204	INTEGER(iwp) :: m !< running index surface elements
[1]	205
[1682]	206	REAL(wp) :: c_max !<
	207	REAL(wp) :: denom !<
[1]	208
[73]	209
[1]	210	!
[1113]	211	!-- Bottom boundary
	212	IF ( ibc_uv_b == 1 ) THEN
	213	u_p(nzb,:,:) = u_p(nzb+1,:,:)
	214	v_p(nzb,:,:) = v_p(nzb+1,:,:)
	215	ENDIF
[2232]	216	!
	217	!-- Set zero vertical velocity at topography top (l=0), or bottom (l=1) in case
	218	!-- of downward-facing surfaces.
	219	DO l = 0, 1
	220	!
	221	!-- Set kb, for upward-facing surfaces value at topography top (k-1) is set,
	222	!-- for downward-facing surfaces at topography bottom (k+1).
	223	kb = MERGE( -1, 1, l == 0 )
	224	!$OMP PARALLEL DO PRIVATE( i, j, k )
	225	DO m = 1, bc_h(l)%ns
	226	i = bc_h(l)%i(m)
	227	j = bc_h(l)%j(m)
	228	k = bc_h(l)%k(m)
	229	w_p(k+kb,j,i) = 0.0_wp
[1113]	230	ENDDO
	231	ENDDO
	232
	233	!
[1762]	234	!-- Top boundary. A nested domain ( ibc_uv_t = 3 ) does not require settings.
[1113]	235	IF ( ibc_uv_t == 0 ) THEN
	236	u_p(nzt+1,:,:) = u_init(nzt+1)
	237	v_p(nzt+1,:,:) = v_init(nzt+1)
[1762]	238	ELSEIF ( ibc_uv_t == 1 ) THEN
[1113]	239	u_p(nzt+1,:,:) = u_p(nzt,:,:)
	240	v_p(nzt+1,:,:) = v_p(nzt,:,:)
	241	ENDIF
	242
[2365]	243	!
	244	!-- Vertical nesting: Vertical velocity not zero at the top of the fine grid
	245	IF ( .NOT. nest_domain .AND. &
	246	TRIM(coupling_mode) /= 'vnested_fine' ) THEN
	247	w_p(nzt:nzt+1,:,:) = 0.0_wp !< nzt is not a prognostic level (but cf. pres)
[1762]	248	ENDIF
	249
[1113]	250	!
[2232]	251	!-- Temperature at bottom and top boundary.
[1113]	252	!-- In case of coupled runs (ibc_pt_b = 2) the temperature is given by
	253	!-- the sea surface temperature of the coupled ocean model.
[2232]	254	!-- Dirichlet
[1113]	255	IF ( ibc_pt_b == 0 ) THEN
[2232]	256	DO l = 0, 1
	257	!
	258	!-- Set kb, for upward-facing surfaces value at topography top (k-1) is set,
	259	!-- for downward-facing surfaces at topography bottom (k+1).
	260	kb = MERGE( -1, 1, l == 0 )
	261	!$OMP PARALLEL DO PRIVATE( i, j, k )
	262	DO m = 1, bc_h(l)%ns
	263	i = bc_h(l)%i(m)
	264	j = bc_h(l)%j(m)
	265	k = bc_h(l)%k(m)
	266	pt_p(k+kb,j,i) = pt(k+kb,j,i)
[1]	267	ENDDO
	268	ENDDO
[2232]	269	!
	270	!-- Neumann, zero-gradient
[1113]	271	ELSEIF ( ibc_pt_b == 1 ) THEN
[2232]	272	DO l = 0, 1
	273	!
	274	!-- Set kb, for upward-facing surfaces value at topography top (k-1) is set,
	275	!-- for downward-facing surfaces at topography bottom (k+1).
	276	kb = MERGE( -1, 1, l == 0 )
	277	!$OMP PARALLEL DO PRIVATE( i, j, k )
	278	DO m = 1, bc_h(l)%ns
	279	i = bc_h(l)%i(m)
	280	j = bc_h(l)%j(m)
	281	k = bc_h(l)%k(m)
	282	pt_p(k+kb,j,i) = pt_p(k,j,i)
[1113]	283	ENDDO
	284	ENDDO
	285	ENDIF
[1]	286
	287	!
[1113]	288	!-- Temperature at top boundary
	289	IF ( ibc_pt_t == 0 ) THEN
	290	pt_p(nzt+1,:,:) = pt(nzt+1,:,:)
[1380]	291	!
	292	!-- In case of nudging adjust top boundary to pt which is
	293	!-- read in from NUDGING-DATA
	294	IF ( nudging ) THEN
	295	pt_p(nzt+1,:,:) = pt_init(nzt+1)
	296	ENDIF
[1113]	297	ELSEIF ( ibc_pt_t == 1 ) THEN
	298	pt_p(nzt+1,:,:) = pt_p(nzt,:,:)
	299	ELSEIF ( ibc_pt_t == 2 ) THEN
[1992]	300	pt_p(nzt+1,:,:) = pt_p(nzt,:,:) + bc_pt_t_val * dzu(nzt+1)
[1113]	301	ENDIF
[1]	302
	303	!
[1113]	304	!-- Boundary conditions for TKE
	305	!-- Generally Neumann conditions with de/dz=0 are assumed
	306	IF ( .NOT. constant_diffusion ) THEN
[2232]	307
	308	DO l = 0, 1
	309	!
	310	!-- Set kb, for upward-facing surfaces value at topography top (k-1) is set,
	311	!-- for downward-facing surfaces at topography bottom (k+1).
	312	kb = MERGE( -1, 1, l == 0 )
	313	!$OMP PARALLEL DO PRIVATE( i, j, k )
	314	DO m = 1, bc_h(l)%ns
	315	i = bc_h(l)%i(m)
	316	j = bc_h(l)%j(m)
	317	k = bc_h(l)%k(m)
	318	e_p(k+kb,j,i) = e_p(k,j,i)
[73]	319	ENDDO
[1113]	320	ENDDO
[2232]	321
[1762]	322	IF ( .NOT. nest_domain ) THEN
	323	e_p(nzt+1,:,:) = e_p(nzt,:,:)
	324	ENDIF
[1113]	325	ENDIF
	326
	327	!
	328	!-- Boundary conditions for salinity
	329	IF ( ocean ) THEN
	330	!
	331	!-- Bottom boundary: Neumann condition because salinity flux is always
[2232]	332	!-- given.
	333	DO l = 0, 1
	334	!
	335	!-- Set kb, for upward-facing surfaces value at topography top (k-1) is set,
	336	!-- for downward-facing surfaces at topography bottom (k+1).
	337	kb = MERGE( -1, 1, l == 0 )
	338	!$OMP PARALLEL DO PRIVATE( i, j, k )
	339	DO m = 1, bc_h(l)%ns
	340	i = bc_h(l)%i(m)
	341	j = bc_h(l)%j(m)
	342	k = bc_h(l)%k(m)
	343	sa_p(k+kb,j,i) = sa_p(k,j,i)
[1]	344	ENDDO
[1113]	345	ENDDO
[1]	346	!
[1113]	347	!-- Top boundary: Dirichlet or Neumann
	348	IF ( ibc_sa_t == 0 ) THEN
	349	sa_p(nzt+1,:,:) = sa(nzt+1,:,:)
	350	ELSEIF ( ibc_sa_t == 1 ) THEN
	351	sa_p(nzt+1,:,:) = sa_p(nzt,:,:)
[1]	352	ENDIF
	353
[1113]	354	ENDIF
	355
[1]	356	!
[1960]	357	!-- Boundary conditions for total water content,
[1113]	358	!-- bottom and top boundary (see also temperature)
[1960]	359	IF ( humidity ) THEN
[1113]	360	!
	361	!-- Surface conditions for constant_humidity_flux
[2232]	362	!-- Run loop over all non-natural and natural walls. Note, in wall-datatype
	363	!-- the k coordinate belongs to the atmospheric grid point, therefore, set
	364	!-- q_p at k-1
[1113]	365	IF ( ibc_q_b == 0 ) THEN
[2232]	366
	367	DO l = 0, 1
	368	!
	369	!-- Set kb, for upward-facing surfaces value at topography top (k-1) is set,
	370	!-- for downward-facing surfaces at topography bottom (k+1).
	371	kb = MERGE( -1, 1, l == 0 )
	372	!$OMP PARALLEL DO PRIVATE( i, j, k )
	373	DO m = 1, bc_h(l)%ns
	374	i = bc_h(l)%i(m)
	375	j = bc_h(l)%j(m)
	376	k = bc_h(l)%k(m)
	377	q_p(k+kb,j,i) = q(k+kb,j,i)
[1]	378	ENDDO
	379	ENDDO
[2232]	380
[1113]	381	ELSE
[2232]	382	!$OMP PARALLEL DO PRIVATE( i, j, k )
	383	DO m = 1, bc_h(0)%ns
	384	i = bc_h(0)%i(m)
	385	j = bc_h(0)%j(m)
	386	k = bc_h(0)%k(m)
	387	q_p(k-1,j,i) = q_p(k,j,i)
	388	ENDDO
	389
	390	DO l = 0, 1
	391	!
	392	!-- Set kb, for upward-facing surfaces value at topography top (k-1) is set,
	393	!-- for downward-facing surfaces at topography bottom (k+1).
	394	kb = MERGE( -1, 1, l == 0 )
	395	!$OMP PARALLEL DO PRIVATE( i, j, k )
	396	DO m = 1, bc_h(l)%ns
	397	i = bc_h(l)%i(m)
	398	j = bc_h(l)%j(m)
	399	k = bc_h(l)%k(m)
	400	q_p(k+kb,j,i) = q_p(k,j,i)
[95]	401	ENDDO
	402	ENDDO
[1113]	403	ENDIF
[95]	404	!
[1113]	405	!-- Top boundary
[1462]	406	IF ( ibc_q_t == 0 ) THEN
	407	q_p(nzt+1,:,:) = q(nzt+1,:,:)
	408	ELSEIF ( ibc_q_t == 1 ) THEN
[1992]	409	q_p(nzt+1,:,:) = q_p(nzt,:,:) + bc_q_t_val * dzu(nzt+1)
[1462]	410	ENDIF
[95]	411
[2292]	412	IF ( cloud_physics .AND. microphysics_morrison ) THEN
	413	!
	414	!-- Surface conditions cloud water (Dirichlet)
	415	!-- Run loop over all non-natural and natural walls. Note, in wall-datatype
	416	!-- the k coordinate belongs to the atmospheric grid point, therefore, set
	417	!-- qr_p and nr_p at k-1
	418	!$OMP PARALLEL DO PRIVATE( i, j, k )
	419	DO m = 1, bc_h(0)%ns
	420	i = bc_h(0)%i(m)
	421	j = bc_h(0)%j(m)
	422	k = bc_h(0)%k(m)
	423	qc_p(k-1,j,i) = 0.0_wp
	424	nc_p(k-1,j,i) = 0.0_wp
	425	ENDDO
	426	!
	427	!-- Top boundary condition for cloud water (Dirichlet)
	428	qc_p(nzt+1,:,:) = 0.0_wp
	429	nc_p(nzt+1,:,:) = 0.0_wp
	430
	431	ENDIF
	432
[1822]	433	IF ( cloud_physics .AND. microphysics_seifert ) THEN
[1113]	434	!
[1361]	435	!-- Surface conditions rain water (Dirichlet)
[2232]	436	!-- Run loop over all non-natural and natural walls. Note, in wall-datatype
	437	!-- the k coordinate belongs to the atmospheric grid point, therefore, set
	438	!-- qr_p and nr_p at k-1
	439	!$OMP PARALLEL DO PRIVATE( i, j, k )
	440	DO m = 1, bc_h(0)%ns
	441	i = bc_h(0)%i(m)
	442	j = bc_h(0)%j(m)
	443	k = bc_h(0)%k(m)
	444	qr_p(k-1,j,i) = 0.0_wp
	445	nr_p(k-1,j,i) = 0.0_wp
[1115]	446	ENDDO
[1]	447	!
[1361]	448	!-- Top boundary condition for rain water (Dirichlet)
	449	qr_p(nzt+1,:,:) = 0.0_wp
	450	nr_p(nzt+1,:,:) = 0.0_wp
[1115]	451
[1]	452	ENDIF
[1409]	453	ENDIF
[1]	454	!
[1960]	455	!-- Boundary conditions for scalar,
	456	!-- bottom and top boundary (see also temperature)
	457	IF ( passive_scalar ) THEN
	458	!
	459	!-- Surface conditions for constant_humidity_flux
[2232]	460	!-- Run loop over all non-natural and natural walls. Note, in wall-datatype
	461	!-- the k coordinate belongs to the atmospheric grid point, therefore, set
	462	!-- s_p at k-1
[1960]	463	IF ( ibc_s_b == 0 ) THEN
[2232]	464
	465	DO l = 0, 1
	466	!
	467	!-- Set kb, for upward-facing surfaces value at topography top (k-1) is set,
	468	!-- for downward-facing surfaces at topography bottom (k+1).
	469	kb = MERGE( -1, 1, l == 0 )
	470	!$OMP PARALLEL DO PRIVATE( i, j, k )
	471	DO m = 1, bc_h(l)%ns
	472	i = bc_h(l)%i(m)
	473	j = bc_h(l)%j(m)
	474	k = bc_h(l)%k(m)
	475	s_p(k+kb,j,i) = s(k+kb,j,i)
[1960]	476	ENDDO
	477	ENDDO
[2232]	478
[1960]	479	ELSE
[2232]	480	!$OMP PARALLEL DO PRIVATE( i, j, k )
	481	DO m = 1, bc_h(0)%ns
	482	i = bc_h(0)%i(m)
	483	j = bc_h(0)%j(m)
	484	k = bc_h(0)%k(m)
	485	s_p(k-1,j,i) = s_p(k,j,i)
	486	ENDDO
	487
	488	DO l = 0, 1
	489	!
	490	!-- Set kb, for upward-facing surfaces value at topography top (k-1) is set,
	491	!-- for downward-facing surfaces at topography bottom (k+1).
	492	kb = MERGE( -1, 1, l == 0 )
	493	!$OMP PARALLEL DO PRIVATE( i, j, k )
	494	DO m = 1, bc_h(l)%ns
	495	i = bc_h(l)%i(m)
	496	j = bc_h(l)%j(m)
	497	k = bc_h(l)%k(m)
	498	s_p(k+kb,j,i) = s_p(k,j,i)
[1960]	499	ENDDO
	500	ENDDO
	501	ENDIF
	502	!
[1992]	503	!-- Top boundary condition
	504	IF ( ibc_s_t == 0 ) THEN
[1960]	505	s_p(nzt+1,:,:) = s(nzt+1,:,:)
[1992]	506	ELSEIF ( ibc_s_t == 1 ) THEN
	507	s_p(nzt+1,:,:) = s_p(nzt,:,:)
	508	ELSEIF ( ibc_s_t == 2 ) THEN
	509	s_p(nzt+1,:,:) = s_p(nzt,:,:) + bc_s_t_val * dzu(nzt+1)
[1960]	510	ENDIF
	511
	512	ENDIF
	513	!
[1762]	514	!-- In case of inflow or nest boundary at the south boundary the boundary for v
	515	!-- is at nys and in case of inflow or nest boundary at the left boundary the
	516	!-- boundary for u is at nxl. Since in prognostic_equations (cache optimized
	517	!-- version) these levels are handled as a prognostic level, boundary values
	518	!-- have to be restored here.
[1409]	519	!-- For the SGS-TKE, Neumann boundary conditions are used at the inflow.
	520	IF ( inflow_s ) THEN
	521	v_p(:,nys,:) = v_p(:,nys-1,:)
	522	IF ( .NOT. constant_diffusion ) e_p(:,nys-1,:) = e_p(:,nys,:)
	523	ELSEIF ( inflow_n ) THEN
	524	IF ( .NOT. constant_diffusion ) e_p(:,nyn+1,:) = e_p(:,nyn,:)
	525	ELSEIF ( inflow_l ) THEN
	526	u_p(:,:,nxl) = u_p(:,:,nxl-1)
	527	IF ( .NOT. constant_diffusion ) e_p(:,:,nxl-1) = e_p(:,:,nxl)
	528	ELSEIF ( inflow_r ) THEN
	529	IF ( .NOT. constant_diffusion ) e_p(:,:,nxr+1) = e_p(:,:,nxr)
	530	ENDIF
[1]	531
	532	!
[1762]	533	!-- The same restoration for u at i=nxl and v at j=nys as above must be made
[1933]	534	!-- in case of nest boundaries. This must not be done in case of vertical nesting
	535	!-- mode as in that case the lateral boundaries are actually cyclic.
	536	IF ( nesting_mode /= 'vertical' ) THEN
	537	IF ( nest_bound_s ) THEN
	538	v_p(:,nys,:) = v_p(:,nys-1,:)
	539	ENDIF
	540	IF ( nest_bound_l ) THEN
	541	u_p(:,:,nxl) = u_p(:,:,nxl-1)
	542	ENDIF
[1762]	543	ENDIF
	544
	545	!
[1409]	546	!-- Lateral boundary conditions for scalar quantities at the outflow
	547	IF ( outflow_s ) THEN
	548	pt_p(:,nys-1,:) = pt_p(:,nys,:)
[2232]	549	IF ( .NOT. constant_diffusion ) e_p(:,nys-1,:) = e_p(:,nys,:)
[1960]	550	IF ( humidity ) THEN
[1409]	551	q_p(:,nys-1,:) = q_p(:,nys,:)
[2292]	552	IF ( cloud_physics .AND. microphysics_morrison ) THEN
	553	qc_p(:,nys-1,:) = qc_p(:,nys,:)
	554	nc_p(:,nys-1,:) = nc_p(:,nys,:)
	555	ENDIF
[1822]	556	IF ( cloud_physics .AND. microphysics_seifert ) THEN
[1409]	557	qr_p(:,nys-1,:) = qr_p(:,nys,:)
	558	nr_p(:,nys-1,:) = nr_p(:,nys,:)
[1053]	559	ENDIF
[1409]	560	ENDIF
[1960]	561	IF ( passive_scalar ) s_p(:,nys-1,:) = s_p(:,nys,:)
[1409]	562	ELSEIF ( outflow_n ) THEN
	563	pt_p(:,nyn+1,:) = pt_p(:,nyn,:)
	564	IF ( .NOT. constant_diffusion ) e_p(:,nyn+1,:) = e_p(:,nyn,:)
[1960]	565	IF ( humidity ) THEN
[1409]	566	q_p(:,nyn+1,:) = q_p(:,nyn,:)
[2292]	567	IF ( cloud_physics .AND. microphysics_morrison ) THEN
	568	qc_p(:,nyn+1,:) = qc_p(:,nyn,:)
	569	nc_p(:,nyn+1,:) = nc_p(:,nyn,:)
	570	ENDIF
[1822]	571	IF ( cloud_physics .AND. microphysics_seifert ) THEN
[1409]	572	qr_p(:,nyn+1,:) = qr_p(:,nyn,:)
	573	nr_p(:,nyn+1,:) = nr_p(:,nyn,:)
[1053]	574	ENDIF
[1409]	575	ENDIF
[1960]	576	IF ( passive_scalar ) s_p(:,nyn+1,:) = s_p(:,nyn,:)
[1409]	577	ELSEIF ( outflow_l ) THEN
	578	pt_p(:,:,nxl-1) = pt_p(:,:,nxl)
	579	IF ( .NOT. constant_diffusion ) e_p(:,:,nxl-1) = e_p(:,:,nxl)
[1960]	580	IF ( humidity ) THEN
[1409]	581	q_p(:,:,nxl-1) = q_p(:,:,nxl)
[2292]	582	IF ( cloud_physics .AND. microphysics_morrison ) THEN
	583	qc_p(:,:,nxl-1) = qc_p(:,:,nxl)
	584	nc_p(:,:,nxl-1) = nc_p(:,:,nxl)
	585	ENDIF
[1822]	586	IF ( cloud_physics .AND. microphysics_seifert ) THEN
[1409]	587	qr_p(:,:,nxl-1) = qr_p(:,:,nxl)
	588	nr_p(:,:,nxl-1) = nr_p(:,:,nxl)
[1053]	589	ENDIF
[1409]	590	ENDIF
[1960]	591	IF ( passive_scalar ) s_p(:,:,nxl-1) = s_p(:,:,nxl)
[1409]	592	ELSEIF ( outflow_r ) THEN
	593	pt_p(:,:,nxr+1) = pt_p(:,:,nxr)
	594	IF ( .NOT. constant_diffusion ) e_p(:,:,nxr+1) = e_p(:,:,nxr)
[1960]	595	IF ( humidity ) THEN
[1409]	596	q_p(:,:,nxr+1) = q_p(:,:,nxr)
[2292]	597	IF ( cloud_physics .AND. microphysics_morrison ) THEN
	598	qc_p(:,:,nxr+1) = qc_p(:,:,nxr)
	599	nc_p(:,:,nxr+1) = nc_p(:,:,nxr)
	600	ENDIF
[1822]	601	IF ( cloud_physics .AND. microphysics_seifert ) THEN
[1409]	602	qr_p(:,:,nxr+1) = qr_p(:,:,nxr)
	603	nr_p(:,:,nxr+1) = nr_p(:,:,nxr)
[1053]	604	ENDIF
[1]	605	ENDIF
[1960]	606	IF ( passive_scalar ) s_p(:,:,nxr+1) = s_p(:,:,nxr)
[1]	607	ENDIF
	608
	609	!
[1159]	610	!-- Radiation boundary conditions for the velocities at the respective outflow.
	611	!-- The phase velocity is either assumed to the maximum phase velocity that
	612	!-- ensures numerical stability (CFL-condition) or calculated after
	613	!-- Orlanski(1976) and averaged along the outflow boundary.
[106]	614	IF ( outflow_s ) THEN
[75]	615
[1159]	616	IF ( use_cmax ) THEN
	617	u_p(:,-1,:) = u(:,0,:)
	618	v_p(:,0,:) = v(:,1,:)
	619	w_p(:,-1,:) = w(:,0,:)
	620	ELSEIF ( .NOT. use_cmax ) THEN
[75]	621
[978]	622	c_max = dy / dt_3d
[75]	623
[1353]	624	c_u_m_l = 0.0_wp
	625	c_v_m_l = 0.0_wp
	626	c_w_m_l = 0.0_wp
[978]	627
[1353]	628	c_u_m = 0.0_wp
	629	c_v_m = 0.0_wp
	630	c_w_m = 0.0_wp
[978]	631
[75]	632	!
[996]	633	!-- Calculate the phase speeds for u, v, and w, first local and then
	634	!-- average along the outflow boundary.
	635	DO k = nzb+1, nzt+1
	636	DO i = nxl, nxr
[75]	637
[106]	638	denom = u_m_s(k,0,i) - u_m_s(k,1,i)
	639
[1353]	640	IF ( denom /= 0.0_wp ) THEN
[996]	641	c_u(k,i) = -c_max * ( u(k,0,i) - u_m_s(k,0,i) ) / ( denom * tsc(2) )
[1353]	642	IF ( c_u(k,i) < 0.0_wp ) THEN
	643	c_u(k,i) = 0.0_wp
[106]	644	ELSEIF ( c_u(k,i) > c_max ) THEN
	645	c_u(k,i) = c_max
	646	ENDIF
	647	ELSE
	648	c_u(k,i) = c_max
[75]	649	ENDIF
	650
[106]	651	denom = v_m_s(k,1,i) - v_m_s(k,2,i)
	652
[1353]	653	IF ( denom /= 0.0_wp ) THEN
[996]	654	c_v(k,i) = -c_max * ( v(k,1,i) - v_m_s(k,1,i) ) / ( denom * tsc(2) )
[1353]	655	IF ( c_v(k,i) < 0.0_wp ) THEN
	656	c_v(k,i) = 0.0_wp
[106]	657	ELSEIF ( c_v(k,i) > c_max ) THEN
	658	c_v(k,i) = c_max
	659	ENDIF
	660	ELSE
	661	c_v(k,i) = c_max
[75]	662	ENDIF
	663
[106]	664	denom = w_m_s(k,0,i) - w_m_s(k,1,i)
[75]	665
[1353]	666	IF ( denom /= 0.0_wp ) THEN
[996]	667	c_w(k,i) = -c_max * ( w(k,0,i) - w_m_s(k,0,i) ) / ( denom * tsc(2) )
[1353]	668	IF ( c_w(k,i) < 0.0_wp ) THEN
	669	c_w(k,i) = 0.0_wp
[106]	670	ELSEIF ( c_w(k,i) > c_max ) THEN
	671	c_w(k,i) = c_max
	672	ENDIF
	673	ELSE
	674	c_w(k,i) = c_max
[75]	675	ENDIF
[106]	676
[978]	677	c_u_m_l(k) = c_u_m_l(k) + c_u(k,i)
	678	c_v_m_l(k) = c_v_m_l(k) + c_v(k,i)
	679	c_w_m_l(k) = c_w_m_l(k) + c_w(k,i)
[106]	680
[978]	681	ENDDO
	682	ENDDO
[75]	683
[978]	684	#if defined( __parallel )
	685	IF ( collective_wait ) CALL MPI_BARRIER( comm1dx, ierr )
	686	CALL MPI_ALLREDUCE( c_u_m_l(nzb+1), c_u_m(nzb+1), nzt-nzb, MPI_REAL, &
	687	MPI_SUM, comm1dx, ierr )
	688	IF ( collective_wait ) CALL MPI_BARRIER( comm1dx, ierr )
	689	CALL MPI_ALLREDUCE( c_v_m_l(nzb+1), c_v_m(nzb+1), nzt-nzb, MPI_REAL, &
	690	MPI_SUM, comm1dx, ierr )
	691	IF ( collective_wait ) CALL MPI_BARRIER( comm1dx, ierr )
	692	CALL MPI_ALLREDUCE( c_w_m_l(nzb+1), c_w_m(nzb+1), nzt-nzb, MPI_REAL, &
	693	MPI_SUM, comm1dx, ierr )
	694	#else
	695	c_u_m = c_u_m_l
	696	c_v_m = c_v_m_l
	697	c_w_m = c_w_m_l
	698	#endif
	699
	700	c_u_m = c_u_m / (nx+1)
	701	c_v_m = c_v_m / (nx+1)
	702	c_w_m = c_w_m / (nx+1)
	703
[75]	704	!
[978]	705	!-- Save old timelevels for the next timestep
	706	IF ( intermediate_timestep_count == 1 ) THEN
	707	u_m_s(:,:,:) = u(:,0:1,:)
	708	v_m_s(:,:,:) = v(:,1:2,:)
	709	w_m_s(:,:,:) = w(:,0:1,:)
	710	ENDIF
	711
	712	!
	713	!-- Calculate the new velocities
[996]	714	DO k = nzb+1, nzt+1
	715	DO i = nxlg, nxrg
[978]	716	u_p(k,-1,i) = u(k,-1,i) - dt_3d * tsc(2) * c_u_m(k) * &
[75]	717	( u(k,-1,i) - u(k,0,i) ) * ddy
	718
[978]	719	v_p(k,0,i) = v(k,0,i) - dt_3d * tsc(2) * c_v_m(k) * &
[106]	720	( v(k,0,i) - v(k,1,i) ) * ddy
[75]	721
[978]	722	w_p(k,-1,i) = w(k,-1,i) - dt_3d * tsc(2) * c_w_m(k) * &
[75]	723	( w(k,-1,i) - w(k,0,i) ) * ddy
[978]	724	ENDDO
[75]	725	ENDDO
	726
	727	!
[978]	728	!-- Bottom boundary at the outflow
	729	IF ( ibc_uv_b == 0 ) THEN
[1353]	730	u_p(nzb,-1,:) = 0.0_wp
	731	v_p(nzb,0,:) = 0.0_wp
[978]	732	ELSE
	733	u_p(nzb,-1,:) = u_p(nzb+1,-1,:)
	734	v_p(nzb,0,:) = v_p(nzb+1,0,:)
	735	ENDIF
[1353]	736	w_p(nzb,-1,:) = 0.0_wp
[73]	737
[75]	738	!
[978]	739	!-- Top boundary at the outflow
	740	IF ( ibc_uv_t == 0 ) THEN
	741	u_p(nzt+1,-1,:) = u_init(nzt+1)
	742	v_p(nzt+1,0,:) = v_init(nzt+1)
	743	ELSE
[1742]	744	u_p(nzt+1,-1,:) = u_p(nzt,-1,:)
	745	v_p(nzt+1,0,:) = v_p(nzt,0,:)
[978]	746	ENDIF
[1353]	747	w_p(nzt:nzt+1,-1,:) = 0.0_wp
[978]	748
[75]	749	ENDIF
[73]	750
[75]	751	ENDIF
[73]	752
[106]	753	IF ( outflow_n ) THEN
[73]	754
[1159]	755	IF ( use_cmax ) THEN
	756	u_p(:,ny+1,:) = u(:,ny,:)
	757	v_p(:,ny+1,:) = v(:,ny,:)
	758	w_p(:,ny+1,:) = w(:,ny,:)
	759	ELSEIF ( .NOT. use_cmax ) THEN
[75]	760
[978]	761	c_max = dy / dt_3d
[75]	762
[1353]	763	c_u_m_l = 0.0_wp
	764	c_v_m_l = 0.0_wp
	765	c_w_m_l = 0.0_wp
[978]	766
[1353]	767	c_u_m = 0.0_wp
	768	c_v_m = 0.0_wp
	769	c_w_m = 0.0_wp
[978]	770
[1]	771	!
[996]	772	!-- Calculate the phase speeds for u, v, and w, first local and then
	773	!-- average along the outflow boundary.
	774	DO k = nzb+1, nzt+1
	775	DO i = nxl, nxr
[73]	776
[106]	777	denom = u_m_n(k,ny,i) - u_m_n(k,ny-1,i)
	778
[1353]	779	IF ( denom /= 0.0_wp ) THEN
[996]	780	c_u(k,i) = -c_max * ( u(k,ny,i) - u_m_n(k,ny,i) ) / ( denom * tsc(2) )
[1353]	781	IF ( c_u(k,i) < 0.0_wp ) THEN
	782	c_u(k,i) = 0.0_wp
[106]	783	ELSEIF ( c_u(k,i) > c_max ) THEN
	784	c_u(k,i) = c_max
	785	ENDIF
	786	ELSE
	787	c_u(k,i) = c_max
[73]	788	ENDIF
	789
[106]	790	denom = v_m_n(k,ny,i) - v_m_n(k,ny-1,i)
[73]	791
[1353]	792	IF ( denom /= 0.0_wp ) THEN
[996]	793	c_v(k,i) = -c_max * ( v(k,ny,i) - v_m_n(k,ny,i) ) / ( denom * tsc(2) )
[1353]	794	IF ( c_v(k,i) < 0.0_wp ) THEN
	795	c_v(k,i) = 0.0_wp
[106]	796	ELSEIF ( c_v(k,i) > c_max ) THEN
	797	c_v(k,i) = c_max
	798	ENDIF
	799	ELSE
	800	c_v(k,i) = c_max
[73]	801	ENDIF
	802
[106]	803	denom = w_m_n(k,ny,i) - w_m_n(k,ny-1,i)
[73]	804
[1353]	805	IF ( denom /= 0.0_wp ) THEN
[996]	806	c_w(k,i) = -c_max * ( w(k,ny,i) - w_m_n(k,ny,i) ) / ( denom * tsc(2) )
[1353]	807	IF ( c_w(k,i) < 0.0_wp ) THEN
	808	c_w(k,i) = 0.0_wp
[106]	809	ELSEIF ( c_w(k,i) > c_max ) THEN
	810	c_w(k,i) = c_max
	811	ENDIF
	812	ELSE
	813	c_w(k,i) = c_max
[73]	814	ENDIF
[106]	815
[978]	816	c_u_m_l(k) = c_u_m_l(k) + c_u(k,i)
	817	c_v_m_l(k) = c_v_m_l(k) + c_v(k,i)
	818	c_w_m_l(k) = c_w_m_l(k) + c_w(k,i)
[106]	819
[978]	820	ENDDO
	821	ENDDO
[73]	822
[978]	823	#if defined( __parallel )
	824	IF ( collective_wait ) CALL MPI_BARRIER( comm1dx, ierr )
	825	CALL MPI_ALLREDUCE( c_u_m_l(nzb+1), c_u_m(nzb+1), nzt-nzb, MPI_REAL, &
	826	MPI_SUM, comm1dx, ierr )
	827	IF ( collective_wait ) CALL MPI_BARRIER( comm1dx, ierr )
	828	CALL MPI_ALLREDUCE( c_v_m_l(nzb+1), c_v_m(nzb+1), nzt-nzb, MPI_REAL, &
	829	MPI_SUM, comm1dx, ierr )
	830	IF ( collective_wait ) CALL MPI_BARRIER( comm1dx, ierr )
	831	CALL MPI_ALLREDUCE( c_w_m_l(nzb+1), c_w_m(nzb+1), nzt-nzb, MPI_REAL, &
	832	MPI_SUM, comm1dx, ierr )
	833	#else
	834	c_u_m = c_u_m_l
	835	c_v_m = c_v_m_l
	836	c_w_m = c_w_m_l
	837	#endif
	838
	839	c_u_m = c_u_m / (nx+1)
	840	c_v_m = c_v_m / (nx+1)
	841	c_w_m = c_w_m / (nx+1)
	842
[73]	843	!
[978]	844	!-- Save old timelevels for the next timestep
	845	IF ( intermediate_timestep_count == 1 ) THEN
	846	u_m_n(:,:,:) = u(:,ny-1:ny,:)
	847	v_m_n(:,:,:) = v(:,ny-1:ny,:)
	848	w_m_n(:,:,:) = w(:,ny-1:ny,:)
	849	ENDIF
[73]	850
[978]	851	!
	852	!-- Calculate the new velocities
[996]	853	DO k = nzb+1, nzt+1
	854	DO i = nxlg, nxrg
[978]	855	u_p(k,ny+1,i) = u(k,ny+1,i) - dt_3d * tsc(2) * c_u_m(k) * &
	856	( u(k,ny+1,i) - u(k,ny,i) ) * ddy
[73]	857
[978]	858	v_p(k,ny+1,i) = v(k,ny+1,i) - dt_3d * tsc(2) * c_v_m(k) * &
	859	( v(k,ny+1,i) - v(k,ny,i) ) * ddy
[73]	860
[978]	861	w_p(k,ny+1,i) = w(k,ny+1,i) - dt_3d * tsc(2) * c_w_m(k) * &
	862	( w(k,ny+1,i) - w(k,ny,i) ) * ddy
	863	ENDDO
[1]	864	ENDDO
	865
	866	!
[978]	867	!-- Bottom boundary at the outflow
	868	IF ( ibc_uv_b == 0 ) THEN
[1353]	869	u_p(nzb,ny+1,:) = 0.0_wp
	870	v_p(nzb,ny+1,:) = 0.0_wp
[978]	871	ELSE
	872	u_p(nzb,ny+1,:) = u_p(nzb+1,ny+1,:)
	873	v_p(nzb,ny+1,:) = v_p(nzb+1,ny+1,:)
	874	ENDIF
[1353]	875	w_p(nzb,ny+1,:) = 0.0_wp
[73]	876
	877	!
[978]	878	!-- Top boundary at the outflow
	879	IF ( ibc_uv_t == 0 ) THEN
	880	u_p(nzt+1,ny+1,:) = u_init(nzt+1)
	881	v_p(nzt+1,ny+1,:) = v_init(nzt+1)
	882	ELSE
	883	u_p(nzt+1,ny+1,:) = u_p(nzt,nyn+1,:)
	884	v_p(nzt+1,ny+1,:) = v_p(nzt,nyn+1,:)
	885	ENDIF
[1353]	886	w_p(nzt:nzt+1,ny+1,:) = 0.0_wp
[978]	887
[1]	888	ENDIF
	889
[75]	890	ENDIF
	891
[106]	892	IF ( outflow_l ) THEN
[75]	893
[1159]	894	IF ( use_cmax ) THEN
[1717]	895	u_p(:,:,0) = u(:,:,1)
	896	v_p(:,:,-1) = v(:,:,0)
[1159]	897	w_p(:,:,-1) = w(:,:,0)
	898	ELSEIF ( .NOT. use_cmax ) THEN
[75]	899
[978]	900	c_max = dx / dt_3d
[75]	901
[1353]	902	c_u_m_l = 0.0_wp
	903	c_v_m_l = 0.0_wp
	904	c_w_m_l = 0.0_wp
[978]	905
[1353]	906	c_u_m = 0.0_wp
	907	c_v_m = 0.0_wp
	908	c_w_m = 0.0_wp
[978]	909
[1]	910	!
[996]	911	!-- Calculate the phase speeds for u, v, and w, first local and then
	912	!-- average along the outflow boundary.
	913	DO k = nzb+1, nzt+1
	914	DO j = nys, nyn
[75]	915
[106]	916	denom = u_m_l(k,j,1) - u_m_l(k,j,2)
	917
[1353]	918	IF ( denom /= 0.0_wp ) THEN
[996]	919	c_u(k,j) = -c_max * ( u(k,j,1) - u_m_l(k,j,1) ) / ( denom * tsc(2) )
[1353]	920	IF ( c_u(k,j) < 0.0_wp ) THEN
	921	c_u(k,j) = 0.0_wp
[107]	922	ELSEIF ( c_u(k,j) > c_max ) THEN
	923	c_u(k,j) = c_max
[106]	924	ENDIF
	925	ELSE
[107]	926	c_u(k,j) = c_max
[75]	927	ENDIF
	928
[106]	929	denom = v_m_l(k,j,0) - v_m_l(k,j,1)
[75]	930
[1353]	931	IF ( denom /= 0.0_wp ) THEN
[996]	932	c_v(k,j) = -c_max * ( v(k,j,0) - v_m_l(k,j,0) ) / ( denom * tsc(2) )
[1353]	933	IF ( c_v(k,j) < 0.0_wp ) THEN
	934	c_v(k,j) = 0.0_wp
[106]	935	ELSEIF ( c_v(k,j) > c_max ) THEN
	936	c_v(k,j) = c_max
	937	ENDIF
	938	ELSE
	939	c_v(k,j) = c_max
[75]	940	ENDIF
	941
[106]	942	denom = w_m_l(k,j,0) - w_m_l(k,j,1)
[75]	943
[1353]	944	IF ( denom /= 0.0_wp ) THEN
[996]	945	c_w(k,j) = -c_max * ( w(k,j,0) - w_m_l(k,j,0) ) / ( denom * tsc(2) )
[1353]	946	IF ( c_w(k,j) < 0.0_wp ) THEN
	947	c_w(k,j) = 0.0_wp
[106]	948	ELSEIF ( c_w(k,j) > c_max ) THEN
	949	c_w(k,j) = c_max
	950	ENDIF
	951	ELSE
	952	c_w(k,j) = c_max
[75]	953	ENDIF
[106]	954
[978]	955	c_u_m_l(k) = c_u_m_l(k) + c_u(k,j)
	956	c_v_m_l(k) = c_v_m_l(k) + c_v(k,j)
	957	c_w_m_l(k) = c_w_m_l(k) + c_w(k,j)
[106]	958
[978]	959	ENDDO
	960	ENDDO
[75]	961
[978]	962	#if defined( __parallel )
	963	IF ( collective_wait ) CALL MPI_BARRIER( comm1dy, ierr )
	964	CALL MPI_ALLREDUCE( c_u_m_l(nzb+1), c_u_m(nzb+1), nzt-nzb, MPI_REAL, &
	965	MPI_SUM, comm1dy, ierr )
	966	IF ( collective_wait ) CALL MPI_BARRIER( comm1dy, ierr )
	967	CALL MPI_ALLREDUCE( c_v_m_l(nzb+1), c_v_m(nzb+1), nzt-nzb, MPI_REAL, &
	968	MPI_SUM, comm1dy, ierr )
	969	IF ( collective_wait ) CALL MPI_BARRIER( comm1dy, ierr )
	970	CALL MPI_ALLREDUCE( c_w_m_l(nzb+1), c_w_m(nzb+1), nzt-nzb, MPI_REAL, &
	971	MPI_SUM, comm1dy, ierr )
	972	#else
	973	c_u_m = c_u_m_l
	974	c_v_m = c_v_m_l
	975	c_w_m = c_w_m_l
	976	#endif
	977
	978	c_u_m = c_u_m / (ny+1)
	979	c_v_m = c_v_m / (ny+1)
	980	c_w_m = c_w_m / (ny+1)
	981
[73]	982	!
[978]	983	!-- Save old timelevels for the next timestep
	984	IF ( intermediate_timestep_count == 1 ) THEN
	985	u_m_l(:,:,:) = u(:,:,1:2)
	986	v_m_l(:,:,:) = v(:,:,0:1)
	987	w_m_l(:,:,:) = w(:,:,0:1)
	988	ENDIF
	989
	990	!
	991	!-- Calculate the new velocities
[996]	992	DO k = nzb+1, nzt+1
[1113]	993	DO j = nysg, nyng
[978]	994	u_p(k,j,0) = u(k,j,0) - dt_3d * tsc(2) * c_u_m(k) * &
[106]	995	( u(k,j,0) - u(k,j,1) ) * ddx
[75]	996
[978]	997	v_p(k,j,-1) = v(k,j,-1) - dt_3d * tsc(2) * c_v_m(k) * &
[75]	998	( v(k,j,-1) - v(k,j,0) ) * ddx
	999
[978]	1000	w_p(k,j,-1) = w(k,j,-1) - dt_3d * tsc(2) * c_w_m(k) * &
[75]	1001	( w(k,j,-1) - w(k,j,0) ) * ddx
[978]	1002	ENDDO
[75]	1003	ENDDO
	1004
	1005	!
[978]	1006	!-- Bottom boundary at the outflow
	1007	IF ( ibc_uv_b == 0 ) THEN
[1353]	1008	u_p(nzb,:,0) = 0.0_wp
	1009	v_p(nzb,:,-1) = 0.0_wp
[978]	1010	ELSE
	1011	u_p(nzb,:,0) = u_p(nzb+1,:,0)
	1012	v_p(nzb,:,-1) = v_p(nzb+1,:,-1)
	1013	ENDIF
[1353]	1014	w_p(nzb,:,-1) = 0.0_wp
[1]	1015
[75]	1016	!
[978]	1017	!-- Top boundary at the outflow
	1018	IF ( ibc_uv_t == 0 ) THEN
[1764]	1019	u_p(nzt+1,:,0) = u_init(nzt+1)
[978]	1020	v_p(nzt+1,:,-1) = v_init(nzt+1)
	1021	ELSE
[1764]	1022	u_p(nzt+1,:,0) = u_p(nzt,:,0)
[978]	1023	v_p(nzt+1,:,-1) = v_p(nzt,:,-1)
	1024	ENDIF
[1353]	1025	w_p(nzt:nzt+1,:,-1) = 0.0_wp
[978]	1026
[75]	1027	ENDIF
[73]	1028
[75]	1029	ENDIF
[73]	1030
[106]	1031	IF ( outflow_r ) THEN
[73]	1032
[1159]	1033	IF ( use_cmax ) THEN
	1034	u_p(:,:,nx+1) = u(:,:,nx)
	1035	v_p(:,:,nx+1) = v(:,:,nx)
	1036	w_p(:,:,nx+1) = w(:,:,nx)
	1037	ELSEIF ( .NOT. use_cmax ) THEN
[75]	1038
[978]	1039	c_max = dx / dt_3d
[75]	1040
[1353]	1041	c_u_m_l = 0.0_wp
	1042	c_v_m_l = 0.0_wp
	1043	c_w_m_l = 0.0_wp
[978]	1044
[1353]	1045	c_u_m = 0.0_wp
	1046	c_v_m = 0.0_wp
	1047	c_w_m = 0.0_wp
[978]	1048
[1]	1049	!
[996]	1050	!-- Calculate the phase speeds for u, v, and w, first local and then
	1051	!-- average along the outflow boundary.
	1052	DO k = nzb+1, nzt+1
	1053	DO j = nys, nyn
[73]	1054
[106]	1055	denom = u_m_r(k,j,nx) - u_m_r(k,j,nx-1)
	1056
[1353]	1057	IF ( denom /= 0.0_wp ) THEN
[996]	1058	c_u(k,j) = -c_max * ( u(k,j,nx) - u_m_r(k,j,nx) ) / ( denom * tsc(2) )
[1353]	1059	IF ( c_u(k,j) < 0.0_wp ) THEN
	1060	c_u(k,j) = 0.0_wp
[106]	1061	ELSEIF ( c_u(k,j) > c_max ) THEN
	1062	c_u(k,j) = c_max
	1063	ENDIF
	1064	ELSE
	1065	c_u(k,j) = c_max
[73]	1066	ENDIF
	1067
[106]	1068	denom = v_m_r(k,j,nx) - v_m_r(k,j,nx-1)
[73]	1069
[1353]	1070	IF ( denom /= 0.0_wp ) THEN
[996]	1071	c_v(k,j) = -c_max * ( v(k,j,nx) - v_m_r(k,j,nx) ) / ( denom * tsc(2) )
[1353]	1072	IF ( c_v(k,j) < 0.0_wp ) THEN
	1073	c_v(k,j) = 0.0_wp
[106]	1074	ELSEIF ( c_v(k,j) > c_max ) THEN
	1075	c_v(k,j) = c_max
	1076	ENDIF
	1077	ELSE
	1078	c_v(k,j) = c_max
[73]	1079	ENDIF
	1080
[106]	1081	denom = w_m_r(k,j,nx) - w_m_r(k,j,nx-1)
[73]	1082
[1353]	1083	IF ( denom /= 0.0_wp ) THEN
[996]	1084	c_w(k,j) = -c_max * ( w(k,j,nx) - w_m_r(k,j,nx) ) / ( denom * tsc(2) )
[1353]	1085	IF ( c_w(k,j) < 0.0_wp ) THEN
	1086	c_w(k,j) = 0.0_wp
[106]	1087	ELSEIF ( c_w(k,j) > c_max ) THEN
	1088	c_w(k,j) = c_max
	1089	ENDIF
	1090	ELSE
	1091	c_w(k,j) = c_max
[73]	1092	ENDIF
[106]	1093
[978]	1094	c_u_m_l(k) = c_u_m_l(k) + c_u(k,j)
	1095	c_v_m_l(k) = c_v_m_l(k) + c_v(k,j)
	1096	c_w_m_l(k) = c_w_m_l(k) + c_w(k,j)
[106]	1097
[978]	1098	ENDDO
	1099	ENDDO
[73]	1100
[978]	1101	#if defined( __parallel )
	1102	IF ( collective_wait ) CALL MPI_BARRIER( comm1dy, ierr )
	1103	CALL MPI_ALLREDUCE( c_u_m_l(nzb+1), c_u_m(nzb+1), nzt-nzb, MPI_REAL, &
	1104	MPI_SUM, comm1dy, ierr )
	1105	IF ( collective_wait ) CALL MPI_BARRIER( comm1dy, ierr )
	1106	CALL MPI_ALLREDUCE( c_v_m_l(nzb+1), c_v_m(nzb+1), nzt-nzb, MPI_REAL, &
	1107	MPI_SUM, comm1dy, ierr )
	1108	IF ( collective_wait ) CALL MPI_BARRIER( comm1dy, ierr )
	1109	CALL MPI_ALLREDUCE( c_w_m_l(nzb+1), c_w_m(nzb+1), nzt-nzb, MPI_REAL, &
	1110	MPI_SUM, comm1dy, ierr )
	1111	#else
	1112	c_u_m = c_u_m_l
	1113	c_v_m = c_v_m_l
	1114	c_w_m = c_w_m_l
	1115	#endif
	1116
	1117	c_u_m = c_u_m / (ny+1)
	1118	c_v_m = c_v_m / (ny+1)
	1119	c_w_m = c_w_m / (ny+1)
	1120
[73]	1121	!
[978]	1122	!-- Save old timelevels for the next timestep
	1123	IF ( intermediate_timestep_count == 1 ) THEN
	1124	u_m_r(:,:,:) = u(:,:,nx-1:nx)
	1125	v_m_r(:,:,:) = v(:,:,nx-1:nx)
	1126	w_m_r(:,:,:) = w(:,:,nx-1:nx)
	1127	ENDIF
[73]	1128
[978]	1129	!
	1130	!-- Calculate the new velocities
[996]	1131	DO k = nzb+1, nzt+1
[1113]	1132	DO j = nysg, nyng
[978]	1133	u_p(k,j,nx+1) = u(k,j,nx+1) - dt_3d * tsc(2) * c_u_m(k) * &
	1134	( u(k,j,nx+1) - u(k,j,nx) ) * ddx
[73]	1135
[978]	1136	v_p(k,j,nx+1) = v(k,j,nx+1) - dt_3d * tsc(2) * c_v_m(k) * &
	1137	( v(k,j,nx+1) - v(k,j,nx) ) * ddx
[73]	1138
[978]	1139	w_p(k,j,nx+1) = w(k,j,nx+1) - dt_3d * tsc(2) * c_w_m(k) * &
	1140	( w(k,j,nx+1) - w(k,j,nx) ) * ddx
	1141	ENDDO
[73]	1142	ENDDO
	1143
	1144	!
[978]	1145	!-- Bottom boundary at the outflow
	1146	IF ( ibc_uv_b == 0 ) THEN
[1353]	1147	u_p(nzb,:,nx+1) = 0.0_wp
	1148	v_p(nzb,:,nx+1) = 0.0_wp
[978]	1149	ELSE
	1150	u_p(nzb,:,nx+1) = u_p(nzb+1,:,nx+1)
	1151	v_p(nzb,:,nx+1) = v_p(nzb+1,:,nx+1)
	1152	ENDIF
[1353]	1153	w_p(nzb,:,nx+1) = 0.0_wp
[73]	1154
	1155	!
[978]	1156	!-- Top boundary at the outflow
	1157	IF ( ibc_uv_t == 0 ) THEN
	1158	u_p(nzt+1,:,nx+1) = u_init(nzt+1)
	1159	v_p(nzt+1,:,nx+1) = v_init(nzt+1)
	1160	ELSE
	1161	u_p(nzt+1,:,nx+1) = u_p(nzt,:,nx+1)
	1162	v_p(nzt+1,:,nx+1) = v_p(nzt,:,nx+1)
	1163	ENDIF
[1742]	1164	w_p(nzt:nzt+1,:,nx+1) = 0.0_wp
[978]	1165
[1]	1166	ENDIF
	1167
	1168	ENDIF
	1169
	1170	END SUBROUTINE boundary_conds

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