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source: palm/trunk/SOURCE/flow_statistics.f90 @ 936

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

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