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source: palm/trunk/SOURCE/flow_statistics.f90 @ 1069

Last change on this file since 1069 was 1054, checked in by hoffmann, 12 years ago
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[1]	1	SUBROUTINE flow_statistics
	2
[1036]	3	!--------------------------------------------------------------------------------!
	4	! This file is part of PALM.
	5	!
	6	! PALM is free software: you can redistribute it and/or modify it under the terms
	7	! of the GNU General Public License as published by the Free Software Foundation,
	8	! either version 3 of the License, or (at your option) any later version.
	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	!
	17	! Copyright 1997-2012 Leibniz University Hannover
	18	!--------------------------------------------------------------------------------!
	19	!
[254]	20	! Current revisions:
[1]	21	! -----------------
[1008]	22	!
	23	! Former revisions:
	24	! -----------------
	25	! $Id: flow_statistics.f90 1054 2012-11-13 17:30:09Z maronga $
	26	!
[1054]	27	! 1053 2012-11-13 17:11:03Z hoffmann
	28	! necessary additions for two-moment cloud physics scheme:
	29	! +nr, qr, qc, prr
	30	!
[1037]	31	! 1036 2012-10-22 13:43:42Z raasch
	32	! code put under GPL (PALM 3.9)
	33	!
[1008]	34	! 1007 2012-09-19 14:30:36Z franke
[1007]	35	! Calculation of buoyancy flux for humidity in case of WS-scheme is now using
	36	! turbulent fluxes of WS-scheme
	37	! Bugfix: Calculation of subgridscale buoyancy flux for humidity and cloud
	38	! droplets at nzb and nzt added
[700]	39	!
[802]	40	! 801 2012-01-10 17:30:36Z suehring
	41	! Calculation of turbulent fluxes in advec_ws is now thread-safe.
	42	!
[744]	43	! 743 2011-08-18 16:10:16Z suehring
	44	! Calculation of turbulent fluxes with WS-scheme only for the whole model
	45	! domain, not for user-defined subregions.
	46	!
[710]	47	! 709 2011-03-30 09:31:40Z raasch
	48	! formatting adjustments
	49	!
[700]	50	! 699 2011-03-22 17:52:22Z suehring
[699]	51	! Bugfix in calculation of vertical velocity skewness. The added absolute value
	52	! avoid negative values in the root. Negative values of w'w' can occur at the
	53	! top or bottom of the model domain due to degrading the order of advection
	54	! scheme. Furthermore the calculation will be the same for all advection
	55	! schemes.
[392]	56	!
[697]	57	! 696 2011-03-18 07:03:49Z raasch
	58	! Bugfix: Summation of Wicker-Skamarock scheme fluxes and variances for all
	59	! threads
	60	!
[679]	61	! 678 2011-02-02 14:31:56Z raasch
	62	! Bugfix in calculation of the divergence of vertical flux of resolved scale
	63	! energy, pressure fluctuations, and flux of pressure fluctuation itself
	64	!
[674]	65	! 673 2011-01-18 16:19:48Z suehring
	66	! Top bc for the horizontal velocity variances added for ocean runs.
	67	! Setting the corresponding bottom bc moved to advec_ws.
	68	!
[668]	69	! 667 2010-12-23 12:06:00Z suehring/gryschka
	70	! When advection is computed with ws-scheme, turbulent fluxes are already
	71	! computed in the respective advection routines and buffered in arrays
	72	! sums_xx_ws_l(). This is due to a consistent treatment of statistics with the
	73	! numerics and to avoid unphysical kinks near the surface.
	74	! So some if requests has to be done to dicern between fluxes from ws-scheme
	75	! other advection schemes.
	76	! Furthermore the computation of z_i is only done if the heat flux exceeds a
	77	! minimum value. This affects only simulations of a neutral boundary layer and
	78	! is due to reasons of computations in the advection scheme.
	79	!
[625]	80	! 624 2010-12-10 11:46:30Z heinze
	81	! Calculation of q*2 added
	82	!
[623]	83	! 622 2010-12-10 08:08:13Z raasch
	84	! optional barriers included in order to speed up collective operations
	85	!
[392]	86	! 388 2009-09-23 09:40:33Z raasch
[388]	87	! Vertical profiles of potential density and hydrostatic pressure are
	88	! calculated.
[343]	89	! Added missing timeseries calculation of w"q"(0), moved timeseries q* to the
	90	! end.
[291]	91	! Temperature gradient criterion for estimating the boundary layer height
	92	! replaced by the gradient criterion of Sullivan et al. (1998).
[254]	93	! Output of messages replaced by message handling routine.
[1]	94	!
[198]	95	! 197 2008-09-16 15:29:03Z raasch
	96	! Spline timeseries splptx etc. removed, timeseries w'u', w'v', w'q' (k=0)
	97	! added,
	98	! bugfix: divide sums(k,8) (e) and sums(k,34) (e*) by ngp_2dh_s_inner(k,sr)
	99	! (like other scalars)
	100	!
[139]	101	! 133 2007-11-20 10:10:53Z letzel
	102	! Vertical profiles now based on nzb_s_inner; they are divided by
	103	! ngp_2dh_s_inner (scalars, procucts of scalars) and ngp_2dh (staggered
	104	! velocity components and their products, procucts of scalars and velocity
	105	! components), respectively.
	106	!
[110]	107	! 106 2007-08-16 14:30:26Z raasch
	108	! Prescribed momentum fluxes at the top surface are used,
	109	! profiles for wp and w"e are calculated
	110	!
[98]	111	! 97 2007-06-21 08:23:15Z raasch
	112	! Statistics for ocean version (salinity, density) added,
	113	! calculation of z_i and Deardorff velocity scale adjusted to be used with
	114	! the ocean version
	115	!
[90]	116	! 87 2007-05-22 15:46:47Z raasch
	117	! Two more arguments added to user_statistics, which is now also called for
	118	! user-defined profiles,
	119	! var_hom and var_sum renamed pr_palm
	120	!
[83]	121	! 82 2007-04-16 15:40:52Z raasch
	122	! Cpp-directive lcmuk changed to intel_openmp_bug
	123	!
[77]	124	! 75 2007-03-22 09:54:05Z raasch
	125	! Collection of time series quantities moved from routine flow_statistics to
	126	! here, routine user_statistics is called for each statistic region,
	127	! moisture renamed humidity
	128	!
[39]	129	! 19 2007-02-23 04:53:48Z raasch
[77]	130	! fluxes at top modified (tswst, qswst)
[39]	131	!
[3]	132	! RCS Log replace by Id keyword, revision history cleaned up
	133	!
[1]	134	! Revision 1.41 2006/08/04 14:37:50 raasch
	135	! Error removed in non-parallel part (sums_l)
	136	!
	137	! Revision 1.1 1997/08/11 06:15:17 raasch
	138	! Initial revision
	139	!
	140	!
	141	! Description:
	142	! ------------
	143	! Compute average profiles and further average flow quantities for the different
	144	! user-defined (sub-)regions. The region indexed 0 is the total model domain.
	145	!
[132]	146	! NOTE: For simplicity, nzb_s_inner and nzb_diff_s_inner are being used as a
	147	! ---- lower vertical index for k-loops for all variables, although strictly
	148	! speaking the k-loops would have to be split up according to the staggered
	149	! grid. However, this implies no error since staggered velocity components are
	150	! zero at the walls and inside buildings.
[1]	151	!------------------------------------------------------------------------------!
	152
	153	USE arrays_3d
	154	USE cloud_parameters
[709]	155	USE control_parameters
[1]	156	USE cpulog
	157	USE grid_variables
	158	USE indices
	159	USE interfaces
	160	USE pegrid
	161	USE statistics
	162
	163	IMPLICIT NONE
	164
	165	INTEGER :: i, j, k, omp_get_thread_num, sr, tn
	166	LOGICAL :: first
[291]	167	REAL :: dptdz_threshold, height, pts, sums_l_eper, sums_l_etot, ust, &
	168	ust2, u2, vst, vst2, v2, w2, z_i(2)
	169	REAL :: dptdz(nzb+1:nzt+1)
[1]	170	REAL :: sums_ll(nzb:nzt+1,2)
	171
	172	CALL cpu_log( log_point(10), 'flow_statistics', 'start' )
	173
	174	!
	175	!-- To be on the safe side, check whether flow_statistics has already been
	176	!-- called once after the current time step
	177	IF ( flow_statistics_called ) THEN
[254]	178
[274]	179	message_string = 'flow_statistics is called two times within one ' // &
	180	'timestep'
[254]	181	CALL message( 'flow_statistics', 'PA0190', 1, 2, 0, 6, 0 )
[1007]	182
[1]	183	ENDIF
	184
	185	!
	186	!-- Compute statistics for each (sub-)region
	187	DO sr = 0, statistic_regions
	188
	189	!
	190	!-- Initialize (local) summation array
	191	sums_l = 0.0
	192
	193	!
	194	!-- Store sums that have been computed in other subroutines in summation
	195	!-- array
	196	sums_l(:,11,:) = sums_l_l(:,sr,:) ! mixing length from diffusivities
	197	!-- WARNING: next line still has to be adjusted for OpenMP
	198	sums_l(:,21,0) = sums_wsts_bc_l(:,sr) ! heat flux from advec_s_bc
[87]	199	sums_l(nzb+9,pr_palm,0) = sums_divold_l(sr) ! old divergence from pres
	200	sums_l(nzb+10,pr_palm,0) = sums_divnew_l(sr) ! new divergence from pres
[1]	201
[667]	202	!
	203	!-- Copy the turbulent quantities, evaluated in the advection routines to
	204	!-- the local array sums_l() for further computations
[743]	205	IF ( ws_scheme_mom .AND. sr == 0 ) THEN
[696]	206
[1007]	207	!
[673]	208	!-- According to the Neumann bc for the horizontal velocity components,
	209	!-- the corresponding fluxes has to satisfiy the same bc.
	210	IF ( ocean ) THEN
[801]	211	sums_us2_ws_l(nzt+1,:) = sums_us2_ws_l(nzt,:)
[1007]	212	sums_vs2_ws_l(nzt+1,:) = sums_vs2_ws_l(nzt,:)
[673]	213	ENDIF
[696]	214
	215	DO i = 0, threads_per_task-1
[1007]	216	!
[696]	217	!-- Swap the turbulent quantities evaluated in advec_ws.
[801]	218	sums_l(:,13,i) = sums_wsus_ws_l(:,i) ! wu
	219	sums_l(:,15,i) = sums_wsvs_ws_l(:,i) ! wv
	220	sums_l(:,30,i) = sums_us2_ws_l(:,i) ! u*2
	221	sums_l(:,31,i) = sums_vs2_ws_l(:,i) ! v*2
	222	sums_l(:,32,i) = sums_ws2_ws_l(:,i) ! w*2
[696]	223	sums_l(:,34,i) = sums_l(:,34,i) + 0.5 * &
[801]	224	( sums_us2_ws_l(:,i) + sums_vs2_ws_l(:,i) + &
	225	sums_ws2_ws_l(:,i) ) ! e*
[696]	226	DO k = nzb, nzt
[801]	227	sums_l(nzb+5,pr_palm,i) = sums_l(nzb+5,pr_palm,i) + 0.5 * ( &
	228	sums_us2_ws_l(k,i) + &
	229	sums_vs2_ws_l(k,i) + &
	230	sums_ws2_ws_l(k,i) )
[696]	231	ENDDO
[667]	232	ENDDO
[696]	233
[667]	234	ENDIF
[696]	235
[743]	236	IF ( ws_scheme_sca .AND. sr == 0 ) THEN
[696]	237
	238	DO i = 0, threads_per_task-1
[801]	239	sums_l(:,17,i) = sums_wspts_ws_l(:,i) ! wpt from advec_s_ws
	240	IF ( ocean ) sums_l(:,66,i) = sums_wssas_ws_l(:,i) ! wsa
[696]	241	IF ( humidity .OR. passive_scalar ) sums_l(:,49,i) = &
[801]	242	sums_wsqs_ws_l(:,i) !wq
[696]	243	ENDDO
	244
[667]	245	ENDIF
[305]	246	!
[1]	247	!-- Horizontally averaged profiles of horizontal velocities and temperature.
	248	!-- They must have been computed before, because they are already required
	249	!-- for other horizontal averages.
	250	tn = 0
[667]	251
[1]	252	!$OMP PARALLEL PRIVATE( i, j, k, tn )
[82]	253	#if defined( __intel_openmp_bug )
[1]	254	tn = omp_get_thread_num()
	255	#else
	256	!$ tn = omp_get_thread_num()
	257	#endif
	258
	259	!$OMP DO
	260	DO i = nxl, nxr
	261	DO j = nys, nyn
[132]	262	DO k = nzb_s_inner(j,i), nzt+1
[1]	263	sums_l(k,1,tn) = sums_l(k,1,tn) + u(k,j,i) * rmask(j,i,sr)
	264	sums_l(k,2,tn) = sums_l(k,2,tn) + v(k,j,i) * rmask(j,i,sr)
	265	sums_l(k,4,tn) = sums_l(k,4,tn) + pt(k,j,i) * rmask(j,i,sr)
	266	ENDDO
	267	ENDDO
	268	ENDDO
	269
	270	!
[96]	271	!-- Horizontally averaged profile of salinity
	272	IF ( ocean ) THEN
	273	!$OMP DO
	274	DO i = nxl, nxr
	275	DO j = nys, nyn
[132]	276	DO k = nzb_s_inner(j,i), nzt+1
[96]	277	sums_l(k,23,tn) = sums_l(k,23,tn) + &
	278	sa(k,j,i) * rmask(j,i,sr)
	279	ENDDO
	280	ENDDO
	281	ENDDO
	282	ENDIF
	283
	284	!
[1]	285	!-- Horizontally averaged profiles of virtual potential temperature,
	286	!-- total water content, specific humidity and liquid water potential
	287	!-- temperature
[75]	288	IF ( humidity ) THEN
[1]	289	!$OMP DO
	290	DO i = nxl, nxr
	291	DO j = nys, nyn
[132]	292	DO k = nzb_s_inner(j,i), nzt+1
[1]	293	sums_l(k,44,tn) = sums_l(k,44,tn) + &
	294	vpt(k,j,i) * rmask(j,i,sr)
	295	sums_l(k,41,tn) = sums_l(k,41,tn) + &
	296	q(k,j,i) * rmask(j,i,sr)
	297	ENDDO
	298	ENDDO
	299	ENDDO
	300	IF ( cloud_physics ) THEN
	301	!$OMP DO
	302	DO i = nxl, nxr
	303	DO j = nys, nyn
[132]	304	DO k = nzb_s_inner(j,i), nzt+1
[1]	305	sums_l(k,42,tn) = sums_l(k,42,tn) + &
	306	( q(k,j,i) - ql(k,j,i) ) * rmask(j,i,sr)
	307	sums_l(k,43,tn) = sums_l(k,43,tn) + ( &
	308	pt(k,j,i) + l_d_cppt_d_t(k) ql(k,j,i) &
	309	) * rmask(j,i,sr)
	310	ENDDO
	311	ENDDO
	312	ENDDO
	313	ENDIF
	314	ENDIF
	315
	316	!
	317	!-- Horizontally averaged profiles of passive scalar
	318	IF ( passive_scalar ) THEN
	319	!$OMP DO
	320	DO i = nxl, nxr
	321	DO j = nys, nyn
[132]	322	DO k = nzb_s_inner(j,i), nzt+1
[1]	323	sums_l(k,41,tn) = sums_l(k,41,tn) + q(k,j,i) * rmask(j,i,sr)
	324	ENDDO
	325	ENDDO
	326	ENDDO
	327	ENDIF
	328	!$OMP END PARALLEL
	329	!
	330	!-- Summation of thread sums
	331	IF ( threads_per_task > 1 ) THEN
	332	DO i = 1, threads_per_task-1
	333	sums_l(:,1,0) = sums_l(:,1,0) + sums_l(:,1,i)
	334	sums_l(:,2,0) = sums_l(:,2,0) + sums_l(:,2,i)
	335	sums_l(:,4,0) = sums_l(:,4,0) + sums_l(:,4,i)
[96]	336	IF ( ocean ) THEN
	337	sums_l(:,23,0) = sums_l(:,23,0) + sums_l(:,23,i)
	338	ENDIF
[75]	339	IF ( humidity ) THEN
[1]	340	sums_l(:,41,0) = sums_l(:,41,0) + sums_l(:,41,i)
	341	sums_l(:,44,0) = sums_l(:,44,0) + sums_l(:,44,i)
	342	IF ( cloud_physics ) THEN
	343	sums_l(:,42,0) = sums_l(:,42,0) + sums_l(:,42,i)
	344	sums_l(:,43,0) = sums_l(:,43,0) + sums_l(:,43,i)
	345	ENDIF
	346	ENDIF
	347	IF ( passive_scalar ) THEN
	348	sums_l(:,41,0) = sums_l(:,41,0) + sums_l(:,41,i)
	349	ENDIF
	350	ENDDO
	351	ENDIF
	352
	353	#if defined( __parallel )
	354	!
	355	!-- Compute total sum from local sums
[622]	356	IF ( collective_wait ) CALL MPI_BARRIER( comm2d, ierr )
[1]	357	CALL MPI_ALLREDUCE( sums_l(nzb,1,0), sums(nzb,1), nzt+2-nzb, MPI_REAL, &
	358	MPI_SUM, comm2d, ierr )
[622]	359	IF ( collective_wait ) CALL MPI_BARRIER( comm2d, ierr )
[1]	360	CALL MPI_ALLREDUCE( sums_l(nzb,2,0), sums(nzb,2), nzt+2-nzb, MPI_REAL, &
	361	MPI_SUM, comm2d, ierr )
[622]	362	IF ( collective_wait ) CALL MPI_BARRIER( comm2d, ierr )
[1]	363	CALL MPI_ALLREDUCE( sums_l(nzb,4,0), sums(nzb,4), nzt+2-nzb, MPI_REAL, &
	364	MPI_SUM, comm2d, ierr )
[96]	365	IF ( ocean ) THEN
[622]	366	IF ( collective_wait ) CALL MPI_BARRIER( comm2d, ierr )
[96]	367	CALL MPI_ALLREDUCE( sums_l(nzb,23,0), sums(nzb,23), nzt+2-nzb, &
	368	MPI_REAL, MPI_SUM, comm2d, ierr )
	369	ENDIF
[75]	370	IF ( humidity ) THEN
[622]	371	IF ( collective_wait ) CALL MPI_BARRIER( comm2d, ierr )
[1]	372	CALL MPI_ALLREDUCE( sums_l(nzb,44,0), sums(nzb,44), nzt+2-nzb, &
	373	MPI_REAL, MPI_SUM, comm2d, ierr )
[622]	374	IF ( collective_wait ) CALL MPI_BARRIER( comm2d, ierr )
[1]	375	CALL MPI_ALLREDUCE( sums_l(nzb,41,0), sums(nzb,41), nzt+2-nzb, &
	376	MPI_REAL, MPI_SUM, comm2d, ierr )
	377	IF ( cloud_physics ) THEN
[622]	378	IF ( collective_wait ) CALL MPI_BARRIER( comm2d, ierr )
[1]	379	CALL MPI_ALLREDUCE( sums_l(nzb,42,0), sums(nzb,42), nzt+2-nzb, &
	380	MPI_REAL, MPI_SUM, comm2d, ierr )
[622]	381	IF ( collective_wait ) CALL MPI_BARRIER( comm2d, ierr )
[1]	382	CALL MPI_ALLREDUCE( sums_l(nzb,43,0), sums(nzb,43), nzt+2-nzb, &
	383	MPI_REAL, MPI_SUM, comm2d, ierr )
	384	ENDIF
	385	ENDIF
	386
	387	IF ( passive_scalar ) THEN
[622]	388	IF ( collective_wait ) CALL MPI_BARRIER( comm2d, ierr )
[1]	389	CALL MPI_ALLREDUCE( sums_l(nzb,41,0), sums(nzb,41), nzt+2-nzb, &
	390	MPI_REAL, MPI_SUM, comm2d, ierr )
	391	ENDIF
	392	#else
	393	sums(:,1) = sums_l(:,1,0)
	394	sums(:,2) = sums_l(:,2,0)
	395	sums(:,4) = sums_l(:,4,0)
[96]	396	IF ( ocean ) sums(:,23) = sums_l(:,23,0)
[75]	397	IF ( humidity ) THEN
[1]	398	sums(:,44) = sums_l(:,44,0)
	399	sums(:,41) = sums_l(:,41,0)
	400	IF ( cloud_physics ) THEN
	401	sums(:,42) = sums_l(:,42,0)
	402	sums(:,43) = sums_l(:,43,0)
	403	ENDIF
	404	ENDIF
	405	IF ( passive_scalar ) sums(:,41) = sums_l(:,41,0)
	406	#endif
	407
	408	!
	409	!-- Final values are obtained by division by the total number of grid points
	410	!-- used for summation. After that store profiles.
[132]	411	sums(:,1) = sums(:,1) / ngp_2dh(sr)
	412	sums(:,2) = sums(:,2) / ngp_2dh(sr)
	413	sums(:,4) = sums(:,4) / ngp_2dh_s_inner(:,sr)
[1]	414	hom(:,1,1,sr) = sums(:,1) ! u
	415	hom(:,1,2,sr) = sums(:,2) ! v
	416	hom(:,1,4,sr) = sums(:,4) ! pt
	417
[667]	418
[1]	419	!
[96]	420	!-- Salinity
	421	IF ( ocean ) THEN
[132]	422	sums(:,23) = sums(:,23) / ngp_2dh_s_inner(:,sr)
[96]	423	hom(:,1,23,sr) = sums(:,23) ! sa
	424	ENDIF
	425
	426	!
[1]	427	!-- Humidity and cloud parameters
[75]	428	IF ( humidity ) THEN
[132]	429	sums(:,44) = sums(:,44) / ngp_2dh_s_inner(:,sr)
	430	sums(:,41) = sums(:,41) / ngp_2dh_s_inner(:,sr)
[1]	431	hom(:,1,44,sr) = sums(:,44) ! vpt
	432	hom(:,1,41,sr) = sums(:,41) ! qv (q)
	433	IF ( cloud_physics ) THEN
[132]	434	sums(:,42) = sums(:,42) / ngp_2dh_s_inner(:,sr)
	435	sums(:,43) = sums(:,43) / ngp_2dh_s_inner(:,sr)
[1]	436	hom(:,1,42,sr) = sums(:,42) ! qv
	437	hom(:,1,43,sr) = sums(:,43) ! pt
	438	ENDIF
	439	ENDIF
	440
	441	!
	442	!-- Passive scalar
[132]	443	IF ( passive_scalar ) hom(:,1,41,sr) = sums(:,41) / &
	444	ngp_2dh_s_inner(:,sr) ! s (q)
[1]	445
	446	!
	447	!-- Horizontally averaged profiles of the remaining prognostic variables,
	448	!-- variances, the total and the perturbation energy (single values in last
	449	!-- column of sums_l) and some diagnostic quantities.
[132]	450	!-- NOTE: for simplicity, nzb_s_inner is used below, although strictly
[1]	451	!-- ---- speaking the following k-loop would have to be split up and
	452	!-- rearranged according to the staggered grid.
[132]	453	!-- However, this implies no error since staggered velocity components
	454	!-- are zero at the walls and inside buildings.
[1]	455	tn = 0
[82]	456	#if defined( __intel_openmp_bug )
[1]	457	!$OMP PARALLEL PRIVATE( i, j, k, pts, sums_ll, sums_l_eper, sums_l_etot, &
	458	!$OMP tn, ust, ust2, u2, vst, vst2, v2, w2 )
	459	tn = omp_get_thread_num()
	460	#else
	461	!$OMP PARALLEL PRIVATE( i, j, k, pts, sums_ll, sums_l_eper, sums_l_etot, tn, ust, ust2, u2, vst, vst2, v2, w2 )
	462	!$ tn = omp_get_thread_num()
	463	#endif
	464	!$OMP DO
	465	DO i = nxl, nxr
	466	DO j = nys, nyn
	467	sums_l_etot = 0.0
[132]	468	DO k = nzb_s_inner(j,i), nzt+1
[1]	469	!
	470	!-- Prognostic and diagnostic variables
	471	sums_l(k,3,tn) = sums_l(k,3,tn) + w(k,j,i) * rmask(j,i,sr)
	472	sums_l(k,8,tn) = sums_l(k,8,tn) + e(k,j,i) * rmask(j,i,sr)
	473	sums_l(k,9,tn) = sums_l(k,9,tn) + km(k,j,i) * rmask(j,i,sr)
	474	sums_l(k,10,tn) = sums_l(k,10,tn) + kh(k,j,i) * rmask(j,i,sr)
	475	sums_l(k,40,tn) = sums_l(k,40,tn) + p(k,j,i)
	476
	477	sums_l(k,33,tn) = sums_l(k,33,tn) + &
	478	( pt(k,j,i)-hom(k,1,4,sr) )*2 rmask(j,i,sr)
[624]	479
	480	IF ( humidity ) THEN
	481	sums_l(k,70,tn) = sums_l(k,70,tn) + &
	482	( q(k,j,i)-hom(k,1,41,sr) )*2 rmask(j,i,sr)
	483	ENDIF
[1007]	484
[699]	485	!
	486	!-- Higher moments
	487	!-- (Computation of the skewness of w further below)
	488	sums_l(k,38,tn) = sums_l(k,38,tn) + w(k,j,i)*3 rmask(j,i,sr)
[667]	489
[1]	490	sums_l_etot = sums_l_etot + &
[667]	491	0.5 * ( u(k,j,i)2 + v(k,j,i)2 + &
	492	w(k,j,i)*2 ) rmask(j,i,sr)
[1]	493	ENDDO
	494	!
	495	!-- Total and perturbation energy for the total domain (being
	496	!-- collected in the last column of sums_l). Summation of these
	497	!-- quantities is seperated from the previous loop in order to
	498	!-- allow vectorization of that loop.
[87]	499	sums_l(nzb+4,pr_palm,tn) = sums_l(nzb+4,pr_palm,tn) + sums_l_etot
[1]	500	!
	501	!-- 2D-arrays (being collected in the last column of sums_l)
[87]	502	sums_l(nzb,pr_palm,tn) = sums_l(nzb,pr_palm,tn) + &
[1]	503	us(j,i) * rmask(j,i,sr)
[87]	504	sums_l(nzb+1,pr_palm,tn) = sums_l(nzb+1,pr_palm,tn) + &
[1]	505	usws(j,i) * rmask(j,i,sr)
[87]	506	sums_l(nzb+2,pr_palm,tn) = sums_l(nzb+2,pr_palm,tn) + &
[1]	507	vsws(j,i) * rmask(j,i,sr)
[87]	508	sums_l(nzb+3,pr_palm,tn) = sums_l(nzb+3,pr_palm,tn) + &
[1]	509	ts(j,i) * rmask(j,i,sr)
[197]	510	IF ( humidity ) THEN
	511	sums_l(nzb+12,pr_palm,tn) = sums_l(nzb+12,pr_palm,tn) + &
	512	qs(j,i) * rmask(j,i,sr)
	513	ENDIF
[1]	514	ENDDO
	515	ENDDO
	516
	517	!
[667]	518	!-- Computation of statistics when ws-scheme is not used. Else these
	519	!-- quantities are evaluated in the advection routines.
[743]	520	IF ( .NOT. ws_scheme_mom .OR. sr /= 0 ) THEN
[667]	521	!$OMP DO
	522	DO i = nxl, nxr
	523	DO j = nys, nyn
	524	sums_l_eper = 0.0
	525	DO k = nzb_s_inner(j,i), nzt+1
	526	u2 = u(k,j,i)**2
	527	v2 = v(k,j,i)**2
	528	w2 = w(k,j,i)**2
	529	ust2 = ( u(k,j,i) - hom(k,1,1,sr) )**2
	530	vst2 = ( v(k,j,i) - hom(k,1,2,sr) )**2
	531
	532	sums_l(k,30,tn) = sums_l(k,30,tn) + ust2 * rmask(j,i,sr)
	533	sums_l(k,31,tn) = sums_l(k,31,tn) + vst2 * rmask(j,i,sr)
	534	sums_l(k,32,tn) = sums_l(k,32,tn) + w2 * rmask(j,i,sr)
	535	!
	536	!-- Perturbation energy
	537
	538	sums_l(k,34,tn) = sums_l(k,34,tn) + 0.5 * &
	539	( ust2 + vst2 + w2 ) * rmask(j,i,sr)
	540	sums_l_eper = sums_l_eper + &
	541	0.5 * ( ust2+vst2+w2 ) * rmask(j,i,sr)
	542
	543	ENDDO
	544	sums_l(nzb+5,pr_palm,tn) = sums_l(nzb+5,pr_palm,tn) &
	545	+ sums_l_eper
	546	ENDDO
	547	ENDDO
	548	ENDIF
	549	!
[1]	550	!-- Horizontally averaged profiles of the vertical fluxes
[667]	551
[1]	552	!$OMP DO
	553	DO i = nxl, nxr
	554	DO j = nys, nyn
	555	!
	556	!-- Subgridscale fluxes (without Prandtl layer from k=nzb,
	557	!-- oterwise from k=nzb+1)
[132]	558	!-- NOTE: for simplicity, nzb_diff_s_inner is used below, although
[1]	559	!-- ---- strictly speaking the following k-loop would have to be
	560	!-- split up according to the staggered grid.
[132]	561	!-- However, this implies no error since staggered velocity
	562	!-- components are zero at the walls and inside buildings.
	563
	564	DO k = nzb_diff_s_inner(j,i)-1, nzt_diff
[1]	565	!
	566	!-- Momentum flux w"u"
	567	sums_l(k,12,tn) = sums_l(k,12,tn) - 0.25 * ( &
	568	km(k,j,i)+km(k+1,j,i)+km(k,j,i-1)+km(k+1,j,i-1) &
	569	) * ( &
	570	( u(k+1,j,i) - u(k,j,i) ) * ddzu(k+1) &
	571	+ ( w(k,j,i) - w(k,j,i-1) ) * ddx &
	572	) * rmask(j,i,sr)
	573	!
	574	!-- Momentum flux w"v"
	575	sums_l(k,14,tn) = sums_l(k,14,tn) - 0.25 * ( &
	576	km(k,j,i)+km(k+1,j,i)+km(k,j-1,i)+km(k+1,j-1,i) &
	577	) * ( &
	578	( v(k+1,j,i) - v(k,j,i) ) * ddzu(k+1) &
	579	+ ( w(k,j,i) - w(k,j-1,i) ) * ddy &
	580	) * rmask(j,i,sr)
	581	!
	582	!-- Heat flux w"pt"
	583	sums_l(k,16,tn) = sums_l(k,16,tn) &
	584	- 0.5 * ( kh(k,j,i) + kh(k+1,j,i) ) &
	585	* ( pt(k+1,j,i) - pt(k,j,i) ) &
	586	* ddzu(k+1) * rmask(j,i,sr)
	587
	588
	589	!
[96]	590	!-- Salinity flux w"sa"
	591	IF ( ocean ) THEN
	592	sums_l(k,65,tn) = sums_l(k,65,tn) &
	593	- 0.5 * ( kh(k,j,i) + kh(k+1,j,i) ) &
	594	* ( sa(k+1,j,i) - sa(k,j,i) ) &
	595	* ddzu(k+1) * rmask(j,i,sr)
	596	ENDIF
	597
	598	!
[1]	599	!-- Buoyancy flux, water flux (humidity flux) w"q"
[75]	600	IF ( humidity ) THEN
[1]	601	sums_l(k,45,tn) = sums_l(k,45,tn) &
	602	- 0.5 * ( kh(k,j,i) + kh(k+1,j,i) ) &
	603	* ( vpt(k+1,j,i) - vpt(k,j,i) ) &
	604	* ddzu(k+1) * rmask(j,i,sr)
	605	sums_l(k,48,tn) = sums_l(k,48,tn) &
	606	- 0.5 * ( kh(k,j,i) + kh(k+1,j,i) ) &
	607	* ( q(k+1,j,i) - q(k,j,i) ) &
	608	* ddzu(k+1) * rmask(j,i,sr)
[1007]	609
[1]	610	IF ( cloud_physics ) THEN
	611	sums_l(k,51,tn) = sums_l(k,51,tn) &
	612	- 0.5 * ( kh(k,j,i) + kh(k+1,j,i) ) &
	613	* ( ( q(k+1,j,i) - ql(k+1,j,i) )&
	614	- ( q(k,j,i) - ql(k,j,i) ) ) &
	615	* ddzu(k+1) * rmask(j,i,sr)
	616	ENDIF
	617	ENDIF
	618
	619	!
	620	!-- Passive scalar flux
	621	IF ( passive_scalar ) THEN
	622	sums_l(k,48,tn) = sums_l(k,48,tn) &
	623	- 0.5 * ( kh(k,j,i) + kh(k+1,j,i) ) &
	624	* ( q(k+1,j,i) - q(k,j,i) ) &
	625	* ddzu(k+1) * rmask(j,i,sr)
	626	ENDIF
	627
	628	ENDDO
	629
	630	!
	631	!-- Subgridscale fluxes in the Prandtl layer
	632	IF ( use_surface_fluxes ) THEN
	633	sums_l(nzb,12,tn) = sums_l(nzb,12,tn) + &
	634	usws(j,i) * rmask(j,i,sr) ! w"u"
	635	sums_l(nzb,14,tn) = sums_l(nzb,14,tn) + &
	636	vsws(j,i) * rmask(j,i,sr) ! w"v"
	637	sums_l(nzb,16,tn) = sums_l(nzb,16,tn) + &
	638	shf(j,i) * rmask(j,i,sr) ! w"pt"
	639	sums_l(nzb,58,tn) = sums_l(nzb,58,tn) + &
	640	0.0 * rmask(j,i,sr) ! u"pt"
	641	sums_l(nzb,61,tn) = sums_l(nzb,61,tn) + &
	642	0.0 * rmask(j,i,sr) ! v"pt"
[96]	643	IF ( ocean ) THEN
	644	sums_l(nzb,65,tn) = sums_l(nzb,65,tn) + &
	645	saswsb(j,i) * rmask(j,i,sr) ! w"sa"
	646	ENDIF
[75]	647	IF ( humidity ) THEN
[1]	648	sums_l(nzb,48,tn) = sums_l(nzb,48,tn) + &
	649	qsws(j,i) * rmask(j,i,sr) ! w"q" (w"qv")
[1007]	650	sums_l(nzb,45,tn) = sums_l(nzb,45,tn) + ( &
	651	( 1.0 + 0.61 * q(nzb,j,i) ) * &
	652	shf(j,i) + 0.61 * pt(nzb,j,i) * &
	653	qsws(j,i) )
	654	IF ( cloud_droplets ) THEN
	655	sums_l(nzb,45,tn) = sums_l(nzb,45,tn) + ( &
	656	( 1.0 + 0.61 * q(nzb,j,i) - &
	657	ql(nzb,j,i) ) * shf(j,i) + &
	658	0.61 * pt(nzb,j,i) * qsws(j,i) )
	659	ENDIF
[1]	660	IF ( cloud_physics ) THEN
	661	!
	662	!-- Formula does not work if ql(nzb) /= 0.0
	663	sums_l(nzb,51,tn) = sums_l(nzb,51,tn) + & ! w"q" (w"qv")
	664	qsws(j,i) * rmask(j,i,sr)
	665	ENDIF
	666	ENDIF
	667	IF ( passive_scalar ) THEN
	668	sums_l(nzb,48,tn) = sums_l(nzb,48,tn) + &
	669	qsws(j,i) * rmask(j,i,sr) ! w"q" (w"qv")
	670	ENDIF
	671	ENDIF
	672
	673	!
[19]	674	!-- Subgridscale fluxes at the top surface
	675	IF ( use_top_fluxes ) THEN
[550]	676	sums_l(nzt:nzt+1,12,tn) = sums_l(nzt:nzt+1,12,tn) + &
[102]	677	uswst(j,i) * rmask(j,i,sr) ! w"u"
[550]	678	sums_l(nzt:nzt+1,14,tn) = sums_l(nzt:nzt+1,14,tn) + &
[102]	679	vswst(j,i) * rmask(j,i,sr) ! w"v"
[550]	680	sums_l(nzt:nzt+1,16,tn) = sums_l(nzt:nzt+1,16,tn) + &
[19]	681	tswst(j,i) * rmask(j,i,sr) ! w"pt"
[550]	682	sums_l(nzt:nzt+1,58,tn) = sums_l(nzt:nzt+1,58,tn) + &
[19]	683	0.0 * rmask(j,i,sr) ! u"pt"
[550]	684	sums_l(nzt:nzt+1,61,tn) = sums_l(nzt:nzt+1,61,tn) + &
	685	0.0 * rmask(j,i,sr) ! v"pt"
	686
[96]	687	IF ( ocean ) THEN
	688	sums_l(nzt,65,tn) = sums_l(nzt,65,tn) + &
	689	saswst(j,i) * rmask(j,i,sr) ! w"sa"
	690	ENDIF
[75]	691	IF ( humidity ) THEN
[19]	692	sums_l(nzt,48,tn) = sums_l(nzt,48,tn) + &
[388]	693	qswst(j,i) * rmask(j,i,sr) ! w"q" (w"qv")
[1007]	694	sums_l(nzt,45,tn) = sums_l(nzt,45,tn) + ( &
	695	( 1.0 + 0.61 * q(nzt,j,i) ) * &
	696	tswst(j,i) + 0.61 * pt(nzt,j,i) * &
	697	qswst(j,i) )
	698	IF ( cloud_droplets ) THEN
	699	sums_l(nzt,45,tn) = sums_l(nzt,45,tn) + ( &
	700	( 1.0 + 0.61 * q(nzt,j,i) - &
	701	ql(nzt,j,i) ) * tswst(j,i) + &
	702	0.61 * pt(nzt,j,i) * qswst(j,i) )
	703	ENDIF
[19]	704	IF ( cloud_physics ) THEN
	705	!
	706	!-- Formula does not work if ql(nzb) /= 0.0
	707	sums_l(nzt,51,tn) = sums_l(nzt,51,tn) + & ! w"q" (w"qv")
	708	qswst(j,i) * rmask(j,i,sr)
	709	ENDIF
	710	ENDIF
	711	IF ( passive_scalar ) THEN
	712	sums_l(nzt,48,tn) = sums_l(nzt,48,tn) + &
[388]	713	qswst(j,i) * rmask(j,i,sr) ! w"q" (w"qv")
[19]	714	ENDIF
	715	ENDIF
	716
	717	!
[1]	718	!-- Resolved fluxes (can be computed for all horizontal points)
[132]	719	!-- NOTE: for simplicity, nzb_s_inner is used below, although strictly
[1]	720	!-- ---- speaking the following k-loop would have to be split up and
	721	!-- rearranged according to the staggered grid.
[132]	722	DO k = nzb_s_inner(j,i), nzt
[1]	723	ust = 0.5 * ( u(k,j,i) - hom(k,1,1,sr) + &
	724	u(k+1,j,i) - hom(k+1,1,1,sr) )
	725	vst = 0.5 * ( v(k,j,i) - hom(k,1,2,sr) + &
	726	v(k+1,j,i) - hom(k+1,1,2,sr) )
	727	pts = 0.5 * ( pt(k,j,i) - hom(k,1,4,sr) + &
	728	pt(k+1,j,i) - hom(k+1,1,4,sr) )
[667]	729
[1]	730	!-- Higher moments
	731	sums_l(k,35,tn) = sums_l(k,35,tn) + pts * w(k,j,i)*2 &
	732	rmask(j,i,sr)
	733	sums_l(k,36,tn) = sums_l(k,36,tn) + pts*2 w(k,j,i) * &
	734	rmask(j,i,sr)
	735
	736	!
[96]	737	!-- Salinity flux and density (density does not belong to here,
[97]	738	!-- but so far there is no other suitable place to calculate)
[96]	739	IF ( ocean ) THEN
[743]	740	IF( .NOT. ws_scheme_sca .OR. sr /= 0 ) THEN
[667]	741	pts = 0.5 * ( sa(k,j,i) - hom(k,1,23,sr) + &
[96]	742	sa(k+1,j,i) - hom(k+1,1,23,sr) )
[667]	743	sums_l(k,66,tn) = sums_l(k,66,tn) + pts * w(k,j,i) * &
[96]	744	rmask(j,i,sr)
[667]	745	ENDIF
[96]	746	sums_l(k,64,tn) = sums_l(k,64,tn) + rho(k,j,i) * &
	747	rmask(j,i,sr)
[388]	748	sums_l(k,71,tn) = sums_l(k,71,tn) + prho(k,j,i) * &
	749	rmask(j,i,sr)
[96]	750	ENDIF
	751
	752	!
[1053]	753	!-- Buoyancy flux, water flux, humidity flux, liquid water
	754	!-- content, rain drop concentration and rain water content
[75]	755	IF ( humidity ) THEN
[1007]	756	IF ( cloud_physics .OR. cloud_droplets ) THEN
[1053]	757	pts = 0.5 * ( vpt(k,j,i) - hom(k,1,44,sr) + &
[1007]	758	vpt(k+1,j,i) - hom(k+1,1,44,sr) )
	759	sums_l(k,46,tn) = sums_l(k,46,tn) + pts * w(k,j,i) * &
[1]	760	rmask(j,i,sr)
[1053]	761	IF ( .NOT. cloud_droplets ) THEN
	762	pts = 0.5 * &
	763	( ( q(k,j,i) - ql(k,j,i) ) - &
	764	hom(k,1,42,sr) + &
	765	( q(k+1,j,i) - ql(k+1,j,i) ) - &
	766	hom(k+1,1,42,sr) )
	767	sums_l(k,52,tn) = sums_l(k,52,tn) + pts * w(k,j,i) * &
	768	rmask(j,i,sr)
	769	IF ( icloud_scheme == 0 ) THEN
	770	sums_l(k,54,tn) = sums_l(k,54,tn) + ( ql(k,j,i) + &
	771	qr(k,j,i) ) * &
	772	rmask(j,i,sr)
	773	sums_l(k,73,tn) = sums_l(k,73,tn) + nr(k,j,i) * &
	774	rmask(j,i,sr)
	775	sums_l(k,74,tn) = sums_l(k,74,tn) + qr(k,j,i) * &
	776	rmask(j,i,sr)
	777	sums_l(k,75,tn) = sums_l(k,75,tn) + ql(k,j,i) * &
	778	rmask(j,i,sr)
	779	sums_l(k,76,tn) = sums_l(k,76,tn) + prr(k,j,i) * &
	780	rmask(j,i,sr)
	781	ELSE
	782	sums_l(k,54,tn) = sums_l(k,54,tn) + ql(k,j,i) * &
	783	rmask(j,i,sr)
	784	ENDIF
	785	ELSE
	786	sums_l(k,54,tn) = sums_l(k,54,tn) + ql(k,j,i) * &
	787	rmask(j,i,sr)
	788	ENDIF
[1007]	789	ELSE
	790	IF( .NOT. ws_scheme_sca .OR. sr /= 0 ) THEN
	791	pts = 0.5 * ( vpt(k,j,i) - hom(k,1,44,sr) + &
	792	vpt(k+1,j,i) - hom(k+1,1,44,sr) )
	793	sums_l(k,46,tn) = sums_l(k,46,tn) + pts * w(k,j,i) * &
	794	rmask(j,i,sr)
	795	ELSE IF ( ws_scheme_sca .AND. sr == 0 ) THEN
[1053]	796	sums_l(k,46,tn) = ( 1.0 + 0.61 * hom(k,1,41,sr) ) * &
[1007]	797	sums_l(k,17,tn) + &
	798	0.61 * hom(k,1,4,sr) * sums_l(k,49,tn)
	799	END IF
	800	END IF
[1]	801	ENDIF
	802	!
	803	!-- Passive scalar flux
[743]	804	IF ( passive_scalar .AND. ( .NOT. ws_scheme_sca &
	805	.OR. sr /= 0 ) ) THEN
[1]	806	pts = 0.5 * ( q(k,j,i) - hom(k,1,41,sr) + &
	807	q(k+1,j,i) - hom(k+1,1,41,sr) )
	808	sums_l(k,49,tn) = sums_l(k,49,tn) + pts * w(k,j,i) * &
	809	rmask(j,i,sr)
	810	ENDIF
	811
	812	!
	813	!-- Energy flux we
[667]	814	!-- has to be adjusted
	815	sums_l(k,37,tn) = sums_l(k,37,tn) + w(k,j,i) * 0.5 * &
	816	( ust2 + vst2 + w(k,j,i)**2 )&
	817	* rmask(j,i,sr)
[1]	818	ENDDO
	819	ENDDO
	820	ENDDO
[709]	821	!
	822	!-- For speed optimization fluxes which have been computed in part directly
	823	!-- inside the WS advection routines are treated seperatly
	824	!-- Momentum fluxes first:
[743]	825	IF ( .NOT. ws_scheme_mom .OR. sr /= 0 ) THEN
[667]	826	!$OMP DO
	827	DO i = nxl, nxr
	828	DO j = nys, nyn
	829	DO k = nzb_diff_s_inner(j,i)-1, nzt_diff
	830	ust = 0.5 * ( u(k,j,i) - hom(k,1,1,sr) + &
	831	u(k+1,j,i) - hom(k+1,1,1,sr) )
	832	vst = 0.5 * ( v(k,j,i) - hom(k,1,2,sr) + &
	833	v(k+1,j,i) - hom(k+1,1,2,sr) )
[1007]	834	!
[667]	835	!-- Momentum flux wu
	836	sums_l(k,13,tn) = sums_l(k,13,tn) + 0.5 * &
	837	( w(k,j,i-1) + w(k,j,i) ) &
	838	* ust * rmask(j,i,sr)
	839	!
	840	!-- Momentum flux wv
	841	sums_l(k,15,tn) = sums_l(k,15,tn) + 0.5 * &
	842	( w(k,j-1,i) + w(k,j,i) ) &
	843	* vst * rmask(j,i,sr)
	844	ENDDO
	845	ENDDO
	846	ENDDO
[1]	847
[667]	848	ENDIF
[743]	849	IF ( .NOT. ws_scheme_sca .OR. sr /= 0 ) THEN
[667]	850	!$OMP DO
	851	DO i = nxl, nxr
	852	DO j = nys, nyn
[709]	853	DO k = nzb_diff_s_inner(j,i)-1, nzt_diff
	854	!
	855	!-- Vertical heat flux
[667]	856	sums_l(k,17,tn) = sums_l(k,17,tn) + 0.5 * &
	857	( pt(k,j,i) - hom(k,1,4,sr) + &
	858	pt(k+1,j,i) - hom(k+1,1,4,sr) ) &
	859	* w(k,j,i) * rmask(j,i,sr)
	860	IF ( humidity ) THEN
	861	pts = 0.5 * ( q(k,j,i) - hom(k,1,41,sr) + &
	862	q(k+1,j,i) - hom(k+1,1,41,sr) )
	863	sums_l(k,49,tn) = sums_l(k,49,tn) + pts * w(k,j,i) * &
	864	rmask(j,i,sr)
	865	ENDIF
	866	ENDDO
	867	ENDDO
	868	ENDDO
	869
	870	ENDIF
	871
	872
[1]	873	!
[97]	874	!-- Density at top follows Neumann condition
[388]	875	IF ( ocean ) THEN
	876	sums_l(nzt+1,64,tn) = sums_l(nzt,64,tn)
	877	sums_l(nzt+1,71,tn) = sums_l(nzt,71,tn)
	878	ENDIF
[97]	879
	880	!
[1]	881	!-- Divergence of vertical flux of resolved scale energy and pressure
[106]	882	!-- fluctuations as well as flux of pressure fluctuation itself (68).
	883	!-- First calculate the products, then the divergence.
[1]	884	!-- Calculation is time consuming. Do it only, if profiles shall be plotted.
[106]	885	IF ( hom(nzb+1,2,55,0) /= 0.0 .OR. hom(nzb+1,2,68,0) /= 0.0 ) THEN
[1]	886
	887	sums_ll = 0.0 ! local array
	888
	889	!$OMP DO
	890	DO i = nxl, nxr
	891	DO j = nys, nyn
[132]	892	DO k = nzb_s_inner(j,i)+1, nzt
[1]	893
	894	sums_ll(k,1) = sums_ll(k,1) + 0.5 * w(k,j,i) * ( &
	895	( 0.25 * ( u(k,j,i)+u(k+1,j,i)+u(k,j,i+1)+u(k+1,j,i+1) &
[678]	896	- 0.5 * ( hom(k,1,1,sr) + hom(k+1,1,1,sr) ) &
[1]	897	) )**2 &
	898	+ ( 0.25 * ( v(k,j,i)+v(k+1,j,i)+v(k,j+1,i)+v(k+1,j+1,i) &
[678]	899	- 0.5 * ( hom(k,1,2,sr) + hom(k+1,1,2,sr) ) &
[1]	900	) )**2 &
	901	+ w(k,j,i)**2 )
	902
	903	sums_ll(k,2) = sums_ll(k,2) + 0.5 * w(k,j,i) &
	904	* ( p(k,j,i) + p(k+1,j,i) )
	905
	906	ENDDO
	907	ENDDO
	908	ENDDO
	909	sums_ll(0,1) = 0.0 ! because w is zero at the bottom
	910	sums_ll(nzt+1,1) = 0.0
	911	sums_ll(0,2) = 0.0
	912	sums_ll(nzt+1,2) = 0.0
	913
[678]	914	DO k = nzb+1, nzt
[1]	915	sums_l(k,55,tn) = ( sums_ll(k,1) - sums_ll(k-1,1) ) * ddzw(k)
	916	sums_l(k,56,tn) = ( sums_ll(k,2) - sums_ll(k-1,2) ) * ddzw(k)
[106]	917	sums_l(k,68,tn) = sums_ll(k,2)
[1]	918	ENDDO
	919	sums_l(nzb,55,tn) = sums_l(nzb+1,55,tn)
	920	sums_l(nzb,56,tn) = sums_l(nzb+1,56,tn)
[106]	921	sums_l(nzb,68,tn) = 0.0 ! because w* = 0 at nzb
[1]	922
	923	ENDIF
	924
	925	!
[106]	926	!-- Divergence of vertical flux of SGS TKE and the flux itself (69)
	927	IF ( hom(nzb+1,2,57,0) /= 0.0 .OR. hom(nzb+1,2,69,0) /= 0.0 ) THEN
[1]	928
	929	!$OMP DO
	930	DO i = nxl, nxr
	931	DO j = nys, nyn
[132]	932	DO k = nzb_s_inner(j,i)+1, nzt
[1]	933
[106]	934	sums_l(k,57,tn) = sums_l(k,57,tn) - 0.5 * ( &
[1]	935	(km(k,j,i)+km(k+1,j,i)) * (e(k+1,j,i)-e(k,j,i)) * ddzu(k+1) &
	936	- (km(k-1,j,i)+km(k,j,i)) * (e(k,j,i)-e(k-1,j,i)) * ddzu(k) &
[106]	937	) * ddzw(k)
[1]	938
[106]	939	sums_l(k,69,tn) = sums_l(k,69,tn) - 0.5 * ( &
	940	(km(k,j,i)+km(k+1,j,i)) * (e(k+1,j,i)-e(k,j,i)) * ddzu(k+1) &
	941	)
	942
[1]	943	ENDDO
	944	ENDDO
	945	ENDDO
	946	sums_l(nzb,57,tn) = sums_l(nzb+1,57,tn)
[106]	947	sums_l(nzb,69,tn) = sums_l(nzb+1,69,tn)
[1]	948
	949	ENDIF
	950
	951	!
	952	!-- Horizontal heat fluxes (subgrid, resolved, total).
	953	!-- Do it only, if profiles shall be plotted.
	954	IF ( hom(nzb+1,2,58,0) /= 0.0 ) THEN
	955
	956	!$OMP DO
	957	DO i = nxl, nxr
	958	DO j = nys, nyn
[132]	959	DO k = nzb_s_inner(j,i)+1, nzt
[1]	960	!
	961	!-- Subgrid horizontal heat fluxes u"pt", v"pt"
	962	sums_l(k,58,tn) = sums_l(k,58,tn) - 0.5 * &
	963	( kh(k,j,i) + kh(k,j,i-1) ) &
	964	* ( pt(k,j,i-1) - pt(k,j,i) ) &
	965	* ddx * rmask(j,i,sr)
	966	sums_l(k,61,tn) = sums_l(k,61,tn) - 0.5 * &
	967	( kh(k,j,i) + kh(k,j-1,i) ) &
	968	* ( pt(k,j-1,i) - pt(k,j,i) ) &
	969	* ddy * rmask(j,i,sr)
	970	!
	971	!-- Resolved horizontal heat fluxes upt, vpt
	972	sums_l(k,59,tn) = sums_l(k,59,tn) + &
	973	( u(k,j,i) - hom(k,1,1,sr) ) &
	974	* 0.5 * ( pt(k,j,i-1) - hom(k,1,4,sr) + &
	975	pt(k,j,i) - hom(k,1,4,sr) )
	976	pts = 0.5 * ( pt(k,j-1,i) - hom(k,1,4,sr) + &
	977	pt(k,j,i) - hom(k,1,4,sr) )
	978	sums_l(k,62,tn) = sums_l(k,62,tn) + &
	979	( v(k,j,i) - hom(k,1,2,sr) ) &
	980	* 0.5 * ( pt(k,j-1,i) - hom(k,1,4,sr) + &
	981	pt(k,j,i) - hom(k,1,4,sr) )
	982	ENDDO
	983	ENDDO
	984	ENDDO
	985	!
	986	!-- Fluxes at the surface must be zero (e.g. due to the Prandtl-layer)
[97]	987	sums_l(nzb,58,tn) = 0.0
	988	sums_l(nzb,59,tn) = 0.0
	989	sums_l(nzb,60,tn) = 0.0
	990	sums_l(nzb,61,tn) = 0.0
	991	sums_l(nzb,62,tn) = 0.0
	992	sums_l(nzb,63,tn) = 0.0
[1]	993
	994	ENDIF
[87]	995
	996	!
	997	!-- Calculate the user-defined profiles
	998	CALL user_statistics( 'profiles', sr, tn )
[1]	999	!$OMP END PARALLEL
	1000
	1001	!
	1002	!-- Summation of thread sums
	1003	IF ( threads_per_task > 1 ) THEN
	1004	DO i = 1, threads_per_task-1
	1005	sums_l(:,3,0) = sums_l(:,3,0) + sums_l(:,3,i)
	1006	sums_l(:,4:40,0) = sums_l(:,4:40,0) + sums_l(:,4:40,i)
[87]	1007	sums_l(:,45:pr_palm,0) = sums_l(:,45:pr_palm,0) + &
	1008	sums_l(:,45:pr_palm,i)
	1009	IF ( max_pr_user > 0 ) THEN
	1010	sums_l(:,pr_palm+1:pr_palm+max_pr_user,0) = &
	1011	sums_l(:,pr_palm+1:pr_palm+max_pr_user,0) + &
	1012	sums_l(:,pr_palm+1:pr_palm+max_pr_user,i)
	1013	ENDIF
[1]	1014	ENDDO
	1015	ENDIF
	1016
	1017	#if defined( __parallel )
[667]	1018
[1]	1019	!
	1020	!-- Compute total sum from local sums
[622]	1021	IF ( collective_wait ) CALL MPI_BARRIER( comm2d, ierr )
[1]	1022	CALL MPI_ALLREDUCE( sums_l(nzb,1,0), sums(nzb,1), ngp_sums, MPI_REAL, &
	1023	MPI_SUM, comm2d, ierr )
	1024	#else
	1025	sums = sums_l(:,:,0)
	1026	#endif
	1027
	1028	!
	1029	!-- Final values are obtained by division by the total number of grid points
	1030	!-- used for summation. After that store profiles.
	1031	!-- Profiles:
	1032	DO k = nzb, nzt+1
[132]	1033	sums(k,3) = sums(k,3) / ngp_2dh(sr)
[142]	1034	sums(k,8:11) = sums(k,8:11) / ngp_2dh_s_inner(k,sr)
[132]	1035	sums(k,12:22) = sums(k,12:22) / ngp_2dh(sr)
	1036	sums(k,23:29) = sums(k,23:29) / ngp_2dh_s_inner(k,sr)
	1037	sums(k,30:32) = sums(k,30:32) / ngp_2dh(sr)
[142]	1038	sums(k,33:34) = sums(k,33:34) / ngp_2dh_s_inner(k,sr)
	1039	sums(k,35:39) = sums(k,35:39) / ngp_2dh(sr)
[132]	1040	sums(k,40) = sums(k,40) / ngp_2dh_s_inner(k,sr)
	1041	sums(k,45:53) = sums(k,45:53) / ngp_2dh(sr)
	1042	sums(k,54) = sums(k,54) / ngp_2dh_s_inner(k,sr)
	1043	sums(k,55:63) = sums(k,55:63) / ngp_2dh(sr)
	1044	sums(k,64) = sums(k,64) / ngp_2dh_s_inner(k,sr)
	1045	sums(k,65:69) = sums(k,65:69) / ngp_2dh(sr)
	1046	sums(k,70:pr_palm-2) = sums(k,70:pr_palm-2)/ ngp_2dh_s_inner(k,sr)
[1]	1047	ENDDO
[667]	1048
[1]	1049	!-- Upstream-parts
[87]	1050	sums(nzb:nzb+11,pr_palm-1) = sums(nzb:nzb+11,pr_palm-1) / ngp_3d(sr)
[1]	1051	!-- u* and so on
[87]	1052	!-- As sums(nzb:nzb+3,pr_palm) are full 2D arrays (us, usws, vsws, ts) whose
[1]	1053	!-- size is always ( nx + 1 ) * ( ny + 1 ), defined at the first grid layer
	1054	!-- above the topography, they are being divided by ngp_2dh(sr)
[87]	1055	sums(nzb:nzb+3,pr_palm) = sums(nzb:nzb+3,pr_palm) / &
[1]	1056	ngp_2dh(sr)
[197]	1057	sums(nzb+12,pr_palm) = sums(nzb+12,pr_palm) / & ! qs
	1058	ngp_2dh(sr)
[1]	1059	!-- eges, e*
[87]	1060	sums(nzb+4:nzb+5,pr_palm) = sums(nzb+4:nzb+5,pr_palm) / &
[132]	1061	ngp_3d(sr)
[1]	1062	!-- Old and new divergence
[87]	1063	sums(nzb+9:nzb+10,pr_palm) = sums(nzb+9:nzb+10,pr_palm) / &
[1]	1064	ngp_3d_inner(sr)
	1065
[87]	1066	!-- User-defined profiles
	1067	IF ( max_pr_user > 0 ) THEN
	1068	DO k = nzb, nzt+1
	1069	sums(k,pr_palm+1:pr_palm+max_pr_user) = &
	1070	sums(k,pr_palm+1:pr_palm+max_pr_user) / &
[132]	1071	ngp_2dh_s_inner(k,sr)
[87]	1072	ENDDO
	1073	ENDIF
[1007]	1074
[1]	1075	!
	1076	!-- Collect horizontal average in hom.
	1077	!-- Compute deduced averages (e.g. total heat flux)
	1078	hom(:,1,3,sr) = sums(:,3) ! w
	1079	hom(:,1,8,sr) = sums(:,8) ! e profiles 5-7 are initial profiles
	1080	hom(:,1,9,sr) = sums(:,9) ! km
	1081	hom(:,1,10,sr) = sums(:,10) ! kh
	1082	hom(:,1,11,sr) = sums(:,11) ! l
	1083	hom(:,1,12,sr) = sums(:,12) ! w"u"
	1084	hom(:,1,13,sr) = sums(:,13) ! wu
	1085	hom(:,1,14,sr) = sums(:,14) ! w"v"
	1086	hom(:,1,15,sr) = sums(:,15) ! wv
	1087	hom(:,1,16,sr) = sums(:,16) ! w"pt"
	1088	hom(:,1,17,sr) = sums(:,17) ! wpt
	1089	hom(:,1,18,sr) = sums(:,16) + sums(:,17) ! wpt
	1090	hom(:,1,19,sr) = sums(:,12) + sums(:,13) ! wu
	1091	hom(:,1,20,sr) = sums(:,14) + sums(:,15) ! wv
	1092	hom(:,1,21,sr) = sums(:,21) ! wptBC
	1093	hom(:,1,22,sr) = sums(:,16) + sums(:,21) ! wptBC
[96]	1094	! profile 24 is initial profile (sa)
	1095	! profiles 25-29 left empty for initial
[1]	1096	! profiles
	1097	hom(:,1,30,sr) = sums(:,30) ! u*2
	1098	hom(:,1,31,sr) = sums(:,31) ! v*2
	1099	hom(:,1,32,sr) = sums(:,32) ! w*2
	1100	hom(:,1,33,sr) = sums(:,33) ! pt*2
	1101	hom(:,1,34,sr) = sums(:,34) ! e*
	1102	hom(:,1,35,sr) = sums(:,35) ! w2pt
	1103	hom(:,1,36,sr) = sums(:,36) ! wpt2
	1104	hom(:,1,37,sr) = sums(:,37) ! we
	1105	hom(:,1,38,sr) = sums(:,38) ! w*3
[699]	1106	hom(:,1,39,sr) = sums(:,38) / ( abs( sums(:,32) ) + 1E-20 )**1.5 ! Sw
[1]	1107	hom(:,1,40,sr) = sums(:,40) ! p
[531]	1108	hom(:,1,45,sr) = sums(:,45) ! w"vpt"
[1]	1109	hom(:,1,46,sr) = sums(:,46) ! wvpt
	1110	hom(:,1,47,sr) = sums(:,45) + sums(:,46) ! wvpt
	1111	hom(:,1,48,sr) = sums(:,48) ! w"q" (w"qv")
	1112	hom(:,1,49,sr) = sums(:,49) ! wq (wqv)
	1113	hom(:,1,50,sr) = sums(:,48) + sums(:,49) ! wq (wqv)
	1114	hom(:,1,51,sr) = sums(:,51) ! w"qv"
	1115	hom(:,1,52,sr) = sums(:,52) ! wqv
	1116	hom(:,1,53,sr) = sums(:,52) + sums(:,51) ! wq (wqv)
	1117	hom(:,1,54,sr) = sums(:,54) ! ql
	1118	hom(:,1,55,sr) = sums(:,55) ! wuu*/dz
	1119	hom(:,1,56,sr) = sums(:,56) ! wp/dz
[106]	1120	hom(:,1,57,sr) = sums(:,57) ! ( w"e + w"p"/rho )/dz
[1]	1121	hom(:,1,58,sr) = sums(:,58) ! u"pt"
	1122	hom(:,1,59,sr) = sums(:,59) ! upt
	1123	hom(:,1,60,sr) = sums(:,58) + sums(:,59) ! upt_t
	1124	hom(:,1,61,sr) = sums(:,61) ! v"pt"
	1125	hom(:,1,62,sr) = sums(:,62) ! vpt
	1126	hom(:,1,63,sr) = sums(:,61) + sums(:,62) ! vpt_t
[96]	1127	hom(:,1,64,sr) = sums(:,64) ! rho
	1128	hom(:,1,65,sr) = sums(:,65) ! w"sa"
	1129	hom(:,1,66,sr) = sums(:,66) ! wsa
	1130	hom(:,1,67,sr) = sums(:,65) + sums(:,66) ! wsa
[106]	1131	hom(:,1,68,sr) = sums(:,68) ! wp
	1132	hom(:,1,69,sr) = sums(:,69) ! w"e + w"p"/rho
[197]	1133	hom(:,1,70,sr) = sums(:,70) ! q*2
[388]	1134	hom(:,1,71,sr) = sums(:,71) ! prho
[531]	1135	hom(:,1,72,sr) = hyp * 1E-4 ! hyp in dbar
[1053]	1136	hom(:,1,73,sr) = sums(:,73) ! nr
	1137	hom(:,1,74,sr) = sums(:,74) ! qr
	1138	hom(:,1,75,sr) = sums(:,75) ! qc
	1139	hom(:,1,76,sr) = sums(:,76) ! prr (precipitation rate)
[1]	1140
[87]	1141	hom(:,1,pr_palm-1,sr) = sums(:,pr_palm-1)
[1]	1142	! upstream-parts u_x, u_y, u_z, v_x,
	1143	! v_y, usw. (in last but one profile)
[667]	1144	hom(:,1,pr_palm,sr) = sums(:,pr_palm)
[1]	1145	! u, w'u', w'v', t (in last profile)
	1146
[87]	1147	IF ( max_pr_user > 0 ) THEN ! user-defined profiles
	1148	hom(:,1,pr_palm+1:pr_palm+max_pr_user,sr) = &
	1149	sums(:,pr_palm+1:pr_palm+max_pr_user)
	1150	ENDIF
	1151
[1]	1152	!
	1153	!-- Determine the boundary layer height using two different schemes.
[94]	1154	!-- First scheme: Starting from the Earth's (Ocean's) surface, look for the
	1155	!-- first relative minimum (maximum) of the total heat flux.
	1156	!-- The corresponding height is assumed as the boundary layer height, if it
	1157	!-- is less than 1.5 times the height where the heat flux becomes negative
	1158	!-- (positive) for the first time.
[1]	1159	z_i(1) = 0.0
	1160	first = .TRUE.
[667]	1161
[97]	1162	IF ( ocean ) THEN
	1163	DO k = nzt, nzb+1, -1
[667]	1164	IF ( first .AND. hom(k,1,18,sr) < 0.0 &
	1165	.AND. abs(hom(k,1,18,sr)) > 1.0E-8) THEN
[97]	1166	first = .FALSE.
	1167	height = zw(k)
	1168	ENDIF
	1169	IF ( hom(k,1,18,sr) < 0.0 .AND. &
[667]	1170	abs(hom(k,1,18,sr)) > 1.0E-8 .AND. &
[97]	1171	hom(k-1,1,18,sr) > hom(k,1,18,sr) ) THEN
	1172	IF ( zw(k) < 1.5 * height ) THEN
	1173	z_i(1) = zw(k)
	1174	ELSE
	1175	z_i(1) = height
	1176	ENDIF
	1177	EXIT
	1178	ENDIF
	1179	ENDDO
	1180	ELSE
[94]	1181	DO k = nzb, nzt-1
[667]	1182	IF ( first .AND. hom(k,1,18,sr) < 0.0 &
	1183	.AND. abs(hom(k,1,18,sr)) > 1.0E-8 ) THEN
[94]	1184	first = .FALSE.
	1185	height = zw(k)
[1]	1186	ENDIF
[667]	1187	IF ( hom(k,1,18,sr) < 0.0 .AND. &
	1188	abs(hom(k,1,18,sr)) > 1.0E-8 .AND. &
[94]	1189	hom(k+1,1,18,sr) > hom(k,1,18,sr) ) THEN
	1190	IF ( zw(k) < 1.5 * height ) THEN
	1191	z_i(1) = zw(k)
	1192	ELSE
	1193	z_i(1) = height
	1194	ENDIF
	1195	EXIT
	1196	ENDIF
	1197	ENDDO
[97]	1198	ENDIF
[1]	1199
	1200	!
[291]	1201	!-- Second scheme: Gradient scheme from Sullivan et al. (1998), modified
	1202	!-- by Uhlenbrock(2006). The boundary layer height is the height with the
	1203	!-- maximal local temperature gradient: starting from the second (the last
	1204	!-- but one) vertical gridpoint, the local gradient must be at least
	1205	!-- 0.2K/100m and greater than the next four gradients.
	1206	!-- WARNING: The threshold value of 0.2K/100m must be adjusted for the
	1207	!-- ocean case!
[1]	1208	z_i(2) = 0.0
[291]	1209	DO k = nzb+1, nzt+1
	1210	dptdz(k) = ( hom(k,1,4,sr) - hom(k-1,1,4,sr) ) * ddzu(k)
	1211	ENDDO
	1212	dptdz_threshold = 0.2 / 100.0
	1213
[97]	1214	IF ( ocean ) THEN
[291]	1215	DO k = nzt+1, nzb+5, -1
	1216	IF ( dptdz(k) > dptdz_threshold .AND. &
	1217	dptdz(k) > dptdz(k-1) .AND. dptdz(k) > dptdz(k-2) .AND. &
	1218	dptdz(k) > dptdz(k-3) .AND. dptdz(k) > dptdz(k-4) ) THEN
	1219	z_i(2) = zw(k-1)
[97]	1220	EXIT
	1221	ENDIF
	1222	ENDDO
	1223	ELSE
[291]	1224	DO k = nzb+1, nzt-3
	1225	IF ( dptdz(k) > dptdz_threshold .AND. &
	1226	dptdz(k) > dptdz(k+1) .AND. dptdz(k) > dptdz(k+2) .AND. &
	1227	dptdz(k) > dptdz(k+3) .AND. dptdz(k) > dptdz(k+4) ) THEN
	1228	z_i(2) = zw(k-1)
[97]	1229	EXIT
	1230	ENDIF
	1231	ENDDO
	1232	ENDIF
[1]	1233
[87]	1234	hom(nzb+6,1,pr_palm,sr) = z_i(1)
	1235	hom(nzb+7,1,pr_palm,sr) = z_i(2)
[1]	1236
	1237	!
	1238	!-- Computation of both the characteristic vertical velocity and
	1239	!-- the characteristic convective boundary layer temperature.
	1240	!-- The horizontal average at nzb+1 is input for the average temperature.
[667]	1241	IF ( hom(nzb,1,18,sr) > 0.0 .AND. abs(hom(nzb,1,18,sr)) > 1.0E-8 &
	1242	.AND. z_i(1) /= 0.0 ) THEN
[87]	1243	hom(nzb+8,1,pr_palm,sr) = ( g / hom(nzb+1,1,4,sr) * &
[94]	1244	hom(nzb,1,18,sr) * &
	1245	ABS( z_i(1) ) )**0.333333333
[1]	1246	!-- so far this only works if Prandtl layer is used
[87]	1247	hom(nzb+11,1,pr_palm,sr) = hom(nzb,1,16,sr) / hom(nzb+8,1,pr_palm,sr)
[1]	1248	ELSE
[87]	1249	hom(nzb+8,1,pr_palm,sr) = 0.0
	1250	hom(nzb+11,1,pr_palm,sr) = 0.0
[1]	1251	ENDIF
	1252
[48]	1253	!
	1254	!-- Collect the time series quantities
[87]	1255	ts_value(1,sr) = hom(nzb+4,1,pr_palm,sr) ! E
	1256	ts_value(2,sr) = hom(nzb+5,1,pr_palm,sr) ! E*
[48]	1257	ts_value(3,sr) = dt_3d
[87]	1258	ts_value(4,sr) = hom(nzb,1,pr_palm,sr) ! u*
	1259	ts_value(5,sr) = hom(nzb+3,1,pr_palm,sr) ! th*
[48]	1260	ts_value(6,sr) = u_max
	1261	ts_value(7,sr) = v_max
	1262	ts_value(8,sr) = w_max
[87]	1263	ts_value(9,sr) = hom(nzb+10,1,pr_palm,sr) ! new divergence
	1264	ts_value(10,sr) = hom(nzb+9,1,pr_palm,sr) ! old Divergence
	1265	ts_value(11,sr) = hom(nzb+6,1,pr_palm,sr) ! z_i(1)
	1266	ts_value(12,sr) = hom(nzb+7,1,pr_palm,sr) ! z_i(2)
	1267	ts_value(13,sr) = hom(nzb+8,1,pr_palm,sr) ! w*
[48]	1268	ts_value(14,sr) = hom(nzb,1,16,sr) ! w'pt' at k=0
	1269	ts_value(15,sr) = hom(nzb+1,1,16,sr) ! w'pt' at k=1
	1270	ts_value(16,sr) = hom(nzb+1,1,18,sr) ! wpt at k=1
	1271	ts_value(17,sr) = hom(nzb,1,4,sr) ! pt(0)
	1272	ts_value(18,sr) = hom(nzb+1,1,4,sr) ! pt(zp)
[197]	1273	ts_value(19,sr) = hom(nzb+1,1,pr_palm,sr) ! u'w' at k=0
	1274	ts_value(20,sr) = hom(nzb+2,1,pr_palm,sr) ! v'w' at k=0
[343]	1275	ts_value(21,sr) = hom(nzb,1,48,sr) ! w"q" at k=0
[197]	1276
[48]	1277	IF ( ts_value(5,sr) /= 0.0 ) THEN
	1278	ts_value(22,sr) = ts_value(4,sr)**2 / &
	1279	( kappa * g * ts_value(5,sr) / ts_value(18,sr) ) ! L
	1280	ELSE
	1281	ts_value(22,sr) = 10000.0
	1282	ENDIF
[1]	1283
[343]	1284	ts_value(23,sr) = hom(nzb+12,1,pr_palm,sr) ! q*
[1]	1285	!
[48]	1286	!-- Calculate additional statistics provided by the user interface
[87]	1287	CALL user_statistics( 'time_series', sr, 0 )
[1]	1288
[48]	1289	ENDDO ! loop of the subregions
	1290
[1]	1291	!
	1292	!-- If required, sum up horizontal averages for subsequent time averaging
	1293	IF ( do_sum ) THEN
	1294	IF ( average_count_pr == 0 ) hom_sum = 0.0
	1295	hom_sum = hom_sum + hom(:,1,:,:)
	1296	average_count_pr = average_count_pr + 1
	1297	do_sum = .FALSE.
	1298	ENDIF
	1299
	1300	!
	1301	!-- Set flag for other UPs (e.g. output routines, but also buoyancy).
	1302	!-- This flag is reset after each time step in time_integration.
	1303	flow_statistics_called = .TRUE.
	1304
	1305	CALL cpu_log( log_point(10), 'flow_statistics', 'stop' )
	1306
	1307
	1308	END SUBROUTINE flow_statistics

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