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source: palm/trunk/SOURCE/flow_statistics.f90 @ 597

Last change on this file since 597 was 550, checked in by maronga, 14 years ago
bugfix: calculation of subgrid-scale flux at nzt for use_top_fluxes=.T.
Property svn:keywords set to `Id`
File size: 45.9 KB

Rev	Line
[1]	1	SUBROUTINE flow_statistics
	2
	3	!------------------------------------------------------------------------------!
[254]	4	! Current revisions:
[1]	5	! -----------------
[392]	6	!
	7	!
	8	! Former revisions:
	9	! -----------------
	10	! $Id: flow_statistics.f90 550 2010-08-24 09:17:48Z maronga $
	11	!
	12	! 388 2009-09-23 09:40:33Z raasch
[388]	13	! Vertical profiles of potential density and hydrostatic pressure are
	14	! calculated.
[343]	15	! Added missing timeseries calculation of w"q"(0), moved timeseries q* to the
	16	! end.
[291]	17	! Temperature gradient criterion for estimating the boundary layer height
	18	! replaced by the gradient criterion of Sullivan et al. (1998).
[254]	19	! Output of messages replaced by message handling routine.
[1]	20	!
[198]	21	! 197 2008-09-16 15:29:03Z raasch
	22	! Spline timeseries splptx etc. removed, timeseries w'u', w'v', w'q' (k=0)
	23	! added,
	24	! bugfix: divide sums(k,8) (e) and sums(k,34) (e*) by ngp_2dh_s_inner(k,sr)
	25	! (like other scalars)
	26	!
[139]	27	! 133 2007-11-20 10:10:53Z letzel
	28	! Vertical profiles now based on nzb_s_inner; they are divided by
	29	! ngp_2dh_s_inner (scalars, procucts of scalars) and ngp_2dh (staggered
	30	! velocity components and their products, procucts of scalars and velocity
	31	! components), respectively.
	32	!
[110]	33	! 106 2007-08-16 14:30:26Z raasch
	34	! Prescribed momentum fluxes at the top surface are used,
	35	! profiles for wp and w"e are calculated
	36	!
[98]	37	! 97 2007-06-21 08:23:15Z raasch
	38	! Statistics for ocean version (salinity, density) added,
	39	! calculation of z_i and Deardorff velocity scale adjusted to be used with
	40	! the ocean version
	41	!
[90]	42	! 87 2007-05-22 15:46:47Z raasch
	43	! Two more arguments added to user_statistics, which is now also called for
	44	! user-defined profiles,
	45	! var_hom and var_sum renamed pr_palm
	46	!
[83]	47	! 82 2007-04-16 15:40:52Z raasch
	48	! Cpp-directive lcmuk changed to intel_openmp_bug
	49	!
[77]	50	! 75 2007-03-22 09:54:05Z raasch
	51	! Collection of time series quantities moved from routine flow_statistics to
	52	! here, routine user_statistics is called for each statistic region,
	53	! moisture renamed humidity
	54	!
[39]	55	! 19 2007-02-23 04:53:48Z raasch
[77]	56	! fluxes at top modified (tswst, qswst)
[39]	57	!
[3]	58	! RCS Log replace by Id keyword, revision history cleaned up
	59	!
[1]	60	! Revision 1.41 2006/08/04 14:37:50 raasch
	61	! Error removed in non-parallel part (sums_l)
	62	!
	63	! Revision 1.1 1997/08/11 06:15:17 raasch
	64	! Initial revision
	65	!
	66	!
	67	! Description:
	68	! ------------
	69	! Compute average profiles and further average flow quantities for the different
	70	! user-defined (sub-)regions. The region indexed 0 is the total model domain.
	71	!
[132]	72	! NOTE: For simplicity, nzb_s_inner and nzb_diff_s_inner are being used as a
	73	! ---- lower vertical index for k-loops for all variables, although strictly
	74	! speaking the k-loops would have to be split up according to the staggered
	75	! grid. However, this implies no error since staggered velocity components are
	76	! zero at the walls and inside buildings.
[1]	77	!------------------------------------------------------------------------------!
	78
	79	USE arrays_3d
	80	USE cloud_parameters
	81	USE cpulog
	82	USE grid_variables
	83	USE indices
	84	USE interfaces
	85	USE pegrid
	86	USE statistics
	87	USE control_parameters
	88
	89	IMPLICIT NONE
	90
	91	INTEGER :: i, j, k, omp_get_thread_num, sr, tn
	92	LOGICAL :: first
[291]	93	REAL :: dptdz_threshold, height, pts, sums_l_eper, sums_l_etot, ust, &
	94	ust2, u2, vst, vst2, v2, w2, z_i(2)
	95	REAL :: dptdz(nzb+1:nzt+1)
[1]	96	REAL :: sums_ll(nzb:nzt+1,2)
	97
	98
	99	CALL cpu_log( log_point(10), 'flow_statistics', 'start' )
	100
	101	!
	102	!-- To be on the safe side, check whether flow_statistics has already been
	103	!-- called once after the current time step
	104	IF ( flow_statistics_called ) THEN
[254]	105
[274]	106	message_string = 'flow_statistics is called two times within one ' // &
	107	'timestep'
[254]	108	CALL message( 'flow_statistics', 'PA0190', 1, 2, 0, 6, 0 )
	109
[1]	110	ENDIF
	111
	112	!
	113	!-- Compute statistics for each (sub-)region
	114	DO sr = 0, statistic_regions
	115
	116	!
	117	!-- Initialize (local) summation array
	118	sums_l = 0.0
	119
	120	!
	121	!-- Store sums that have been computed in other subroutines in summation
	122	!-- array
	123	sums_l(:,11,:) = sums_l_l(:,sr,:) ! mixing length from diffusivities
	124	!-- WARNING: next line still has to be adjusted for OpenMP
	125	sums_l(:,21,0) = sums_wsts_bc_l(:,sr) ! heat flux from advec_s_bc
[87]	126	sums_l(nzb+9,pr_palm,0) = sums_divold_l(sr) ! old divergence from pres
	127	sums_l(nzb+10,pr_palm,0) = sums_divnew_l(sr) ! new divergence from pres
[1]	128
[305]	129	!
[1]	130	!-- Horizontally averaged profiles of horizontal velocities and temperature.
	131	!-- They must have been computed before, because they are already required
	132	!-- for other horizontal averages.
	133	tn = 0
	134	!$OMP PARALLEL PRIVATE( i, j, k, tn )
[82]	135	#if defined( __intel_openmp_bug )
[1]	136	tn = omp_get_thread_num()
	137	#else
	138	!$ tn = omp_get_thread_num()
	139	#endif
	140
	141	!$OMP DO
	142	DO i = nxl, nxr
	143	DO j = nys, nyn
[132]	144	DO k = nzb_s_inner(j,i), nzt+1
[1]	145	sums_l(k,1,tn) = sums_l(k,1,tn) + u(k,j,i) * rmask(j,i,sr)
	146	sums_l(k,2,tn) = sums_l(k,2,tn) + v(k,j,i) * rmask(j,i,sr)
	147	sums_l(k,4,tn) = sums_l(k,4,tn) + pt(k,j,i) * rmask(j,i,sr)
	148	ENDDO
	149	ENDDO
	150	ENDDO
	151
	152	!
[96]	153	!-- Horizontally averaged profile of salinity
	154	IF ( ocean ) THEN
	155	!$OMP DO
	156	DO i = nxl, nxr
	157	DO j = nys, nyn
[132]	158	DO k = nzb_s_inner(j,i), nzt+1
[96]	159	sums_l(k,23,tn) = sums_l(k,23,tn) + &
	160	sa(k,j,i) * rmask(j,i,sr)
	161	ENDDO
	162	ENDDO
	163	ENDDO
	164	ENDIF
	165
	166	!
[1]	167	!-- Horizontally averaged profiles of virtual potential temperature,
	168	!-- total water content, specific humidity and liquid water potential
	169	!-- temperature
[75]	170	IF ( humidity ) THEN
[1]	171	!$OMP DO
	172	DO i = nxl, nxr
	173	DO j = nys, nyn
[132]	174	DO k = nzb_s_inner(j,i), nzt+1
[1]	175	sums_l(k,44,tn) = sums_l(k,44,tn) + &
	176	vpt(k,j,i) * rmask(j,i,sr)
	177	sums_l(k,41,tn) = sums_l(k,41,tn) + &
	178	q(k,j,i) * rmask(j,i,sr)
	179	ENDDO
	180	ENDDO
	181	ENDDO
	182	IF ( cloud_physics ) THEN
	183	!$OMP DO
	184	DO i = nxl, nxr
	185	DO j = nys, nyn
[132]	186	DO k = nzb_s_inner(j,i), nzt+1
[1]	187	sums_l(k,42,tn) = sums_l(k,42,tn) + &
	188	( q(k,j,i) - ql(k,j,i) ) * rmask(j,i,sr)
	189	sums_l(k,43,tn) = sums_l(k,43,tn) + ( &
	190	pt(k,j,i) + l_d_cppt_d_t(k) ql(k,j,i) &
	191	) * rmask(j,i,sr)
	192	ENDDO
	193	ENDDO
	194	ENDDO
	195	ENDIF
	196	ENDIF
	197
	198	!
	199	!-- Horizontally averaged profiles of passive scalar
	200	IF ( passive_scalar ) THEN
	201	!$OMP DO
	202	DO i = nxl, nxr
	203	DO j = nys, nyn
[132]	204	DO k = nzb_s_inner(j,i), nzt+1
[1]	205	sums_l(k,41,tn) = sums_l(k,41,tn) + q(k,j,i) * rmask(j,i,sr)
	206	ENDDO
	207	ENDDO
	208	ENDDO
	209	ENDIF
	210	!$OMP END PARALLEL
	211
	212	!
	213	!-- Summation of thread sums
	214	IF ( threads_per_task > 1 ) THEN
	215	DO i = 1, threads_per_task-1
	216	sums_l(:,1,0) = sums_l(:,1,0) + sums_l(:,1,i)
	217	sums_l(:,2,0) = sums_l(:,2,0) + sums_l(:,2,i)
	218	sums_l(:,4,0) = sums_l(:,4,0) + sums_l(:,4,i)
[96]	219	IF ( ocean ) THEN
	220	sums_l(:,23,0) = sums_l(:,23,0) + sums_l(:,23,i)
	221	ENDIF
[75]	222	IF ( humidity ) THEN
[1]	223	sums_l(:,41,0) = sums_l(:,41,0) + sums_l(:,41,i)
	224	sums_l(:,44,0) = sums_l(:,44,0) + sums_l(:,44,i)
	225	IF ( cloud_physics ) THEN
	226	sums_l(:,42,0) = sums_l(:,42,0) + sums_l(:,42,i)
	227	sums_l(:,43,0) = sums_l(:,43,0) + sums_l(:,43,i)
	228	ENDIF
	229	ENDIF
	230	IF ( passive_scalar ) THEN
	231	sums_l(:,41,0) = sums_l(:,41,0) + sums_l(:,41,i)
	232	ENDIF
	233	ENDDO
	234	ENDIF
	235
	236	#if defined( __parallel )
	237	!
	238	!-- Compute total sum from local sums
	239	CALL MPI_ALLREDUCE( sums_l(nzb,1,0), sums(nzb,1), nzt+2-nzb, MPI_REAL, &
	240	MPI_SUM, comm2d, ierr )
	241	CALL MPI_ALLREDUCE( sums_l(nzb,2,0), sums(nzb,2), nzt+2-nzb, MPI_REAL, &
	242	MPI_SUM, comm2d, ierr )
	243	CALL MPI_ALLREDUCE( sums_l(nzb,4,0), sums(nzb,4), nzt+2-nzb, MPI_REAL, &
	244	MPI_SUM, comm2d, ierr )
[96]	245	IF ( ocean ) THEN
	246	CALL MPI_ALLREDUCE( sums_l(nzb,23,0), sums(nzb,23), nzt+2-nzb, &
	247	MPI_REAL, MPI_SUM, comm2d, ierr )
	248	ENDIF
[75]	249	IF ( humidity ) THEN
[1]	250	CALL MPI_ALLREDUCE( sums_l(nzb,44,0), sums(nzb,44), nzt+2-nzb, &
	251	MPI_REAL, MPI_SUM, comm2d, ierr )
	252	CALL MPI_ALLREDUCE( sums_l(nzb,41,0), sums(nzb,41), nzt+2-nzb, &
	253	MPI_REAL, MPI_SUM, comm2d, ierr )
	254	IF ( cloud_physics ) THEN
	255	CALL MPI_ALLREDUCE( sums_l(nzb,42,0), sums(nzb,42), nzt+2-nzb, &
	256	MPI_REAL, MPI_SUM, comm2d, ierr )
	257	CALL MPI_ALLREDUCE( sums_l(nzb,43,0), sums(nzb,43), nzt+2-nzb, &
	258	MPI_REAL, MPI_SUM, comm2d, ierr )
	259	ENDIF
	260	ENDIF
	261
	262	IF ( passive_scalar ) THEN
	263	CALL MPI_ALLREDUCE( sums_l(nzb,41,0), sums(nzb,41), nzt+2-nzb, &
	264	MPI_REAL, MPI_SUM, comm2d, ierr )
	265	ENDIF
	266	#else
	267	sums(:,1) = sums_l(:,1,0)
	268	sums(:,2) = sums_l(:,2,0)
	269	sums(:,4) = sums_l(:,4,0)
[96]	270	IF ( ocean ) sums(:,23) = sums_l(:,23,0)
[75]	271	IF ( humidity ) THEN
[1]	272	sums(:,44) = sums_l(:,44,0)
	273	sums(:,41) = sums_l(:,41,0)
	274	IF ( cloud_physics ) THEN
	275	sums(:,42) = sums_l(:,42,0)
	276	sums(:,43) = sums_l(:,43,0)
	277	ENDIF
	278	ENDIF
	279	IF ( passive_scalar ) sums(:,41) = sums_l(:,41,0)
	280	#endif
	281
	282	!
	283	!-- Final values are obtained by division by the total number of grid points
	284	!-- used for summation. After that store profiles.
[132]	285	sums(:,1) = sums(:,1) / ngp_2dh(sr)
	286	sums(:,2) = sums(:,2) / ngp_2dh(sr)
	287	sums(:,4) = sums(:,4) / ngp_2dh_s_inner(:,sr)
[1]	288	hom(:,1,1,sr) = sums(:,1) ! u
	289	hom(:,1,2,sr) = sums(:,2) ! v
	290	hom(:,1,4,sr) = sums(:,4) ! pt
	291
	292	!
[96]	293	!-- Salinity
	294	IF ( ocean ) THEN
[132]	295	sums(:,23) = sums(:,23) / ngp_2dh_s_inner(:,sr)
[96]	296	hom(:,1,23,sr) = sums(:,23) ! sa
	297	ENDIF
	298
	299	!
[1]	300	!-- Humidity and cloud parameters
[75]	301	IF ( humidity ) THEN
[132]	302	sums(:,44) = sums(:,44) / ngp_2dh_s_inner(:,sr)
	303	sums(:,41) = sums(:,41) / ngp_2dh_s_inner(:,sr)
[1]	304	hom(:,1,44,sr) = sums(:,44) ! vpt
	305	hom(:,1,41,sr) = sums(:,41) ! qv (q)
	306	IF ( cloud_physics ) THEN
[132]	307	sums(:,42) = sums(:,42) / ngp_2dh_s_inner(:,sr)
	308	sums(:,43) = sums(:,43) / ngp_2dh_s_inner(:,sr)
[1]	309	hom(:,1,42,sr) = sums(:,42) ! qv
	310	hom(:,1,43,sr) = sums(:,43) ! pt
	311	ENDIF
	312	ENDIF
	313
	314	!
	315	!-- Passive scalar
[132]	316	IF ( passive_scalar ) hom(:,1,41,sr) = sums(:,41) / &
	317	ngp_2dh_s_inner(:,sr) ! s (q)
[1]	318
	319	!
	320	!-- Horizontally averaged profiles of the remaining prognostic variables,
	321	!-- variances, the total and the perturbation energy (single values in last
	322	!-- column of sums_l) and some diagnostic quantities.
[132]	323	!-- NOTE: for simplicity, nzb_s_inner is used below, although strictly
[1]	324	!-- ---- speaking the following k-loop would have to be split up and
	325	!-- rearranged according to the staggered grid.
[132]	326	!-- However, this implies no error since staggered velocity components
	327	!-- are zero at the walls and inside buildings.
[1]	328	tn = 0
[82]	329	#if defined( __intel_openmp_bug )
[1]	330	!$OMP PARALLEL PRIVATE( i, j, k, pts, sums_ll, sums_l_eper, sums_l_etot, &
	331	!$OMP tn, ust, ust2, u2, vst, vst2, v2, w2 )
	332	tn = omp_get_thread_num()
	333	#else
	334	!$OMP PARALLEL PRIVATE( i, j, k, pts, sums_ll, sums_l_eper, sums_l_etot, tn, ust, ust2, u2, vst, vst2, v2, w2 )
	335	!$ tn = omp_get_thread_num()
	336	#endif
	337	!$OMP DO
	338	DO i = nxl, nxr
	339	DO j = nys, nyn
	340	sums_l_etot = 0.0
	341	sums_l_eper = 0.0
[132]	342	DO k = nzb_s_inner(j,i), nzt+1
[1]	343	u2 = u(k,j,i)**2
	344	v2 = v(k,j,i)**2
	345	w2 = w(k,j,i)**2
	346	ust2 = ( u(k,j,i) - hom(k,1,1,sr) )**2
	347	vst2 = ( v(k,j,i) - hom(k,1,2,sr) )**2
	348	!
	349	!-- Prognostic and diagnostic variables
	350	sums_l(k,3,tn) = sums_l(k,3,tn) + w(k,j,i) * rmask(j,i,sr)
	351	sums_l(k,8,tn) = sums_l(k,8,tn) + e(k,j,i) * rmask(j,i,sr)
	352	sums_l(k,9,tn) = sums_l(k,9,tn) + km(k,j,i) * rmask(j,i,sr)
	353	sums_l(k,10,tn) = sums_l(k,10,tn) + kh(k,j,i) * rmask(j,i,sr)
	354	sums_l(k,40,tn) = sums_l(k,40,tn) + p(k,j,i)
	355
	356	!
	357	!-- Variances
	358	sums_l(k,30,tn) = sums_l(k,30,tn) + ust2 * rmask(j,i,sr)
	359	sums_l(k,31,tn) = sums_l(k,31,tn) + vst2 * rmask(j,i,sr)
	360	sums_l(k,32,tn) = sums_l(k,32,tn) + w2 * rmask(j,i,sr)
	361	sums_l(k,33,tn) = sums_l(k,33,tn) + &
	362	( pt(k,j,i)-hom(k,1,4,sr) )*2 rmask(j,i,sr)
	363	!
	364	!-- Higher moments
	365	!-- (Computation of the skewness of w further below)
	366	sums_l(k,38,tn) = sums_l(k,38,tn) + w(k,j,i) * w2 * &
	367	rmask(j,i,sr)
	368	!
	369	!-- Perturbation energy
	370	sums_l(k,34,tn) = sums_l(k,34,tn) + 0.5 * ( ust2 + vst2 + w2 ) &
	371	* rmask(j,i,sr)
	372	sums_l_etot = sums_l_etot + &
	373	0.5 * ( u2 + v2 + w2 ) * rmask(j,i,sr)
	374	sums_l_eper = sums_l_eper + &
	375	0.5 * ( ust2+vst2+w2 ) * rmask(j,i,sr)
	376	ENDDO
	377	!
	378	!-- Total and perturbation energy for the total domain (being
	379	!-- collected in the last column of sums_l). Summation of these
	380	!-- quantities is seperated from the previous loop in order to
	381	!-- allow vectorization of that loop.
[87]	382	sums_l(nzb+4,pr_palm,tn) = sums_l(nzb+4,pr_palm,tn) + sums_l_etot
	383	sums_l(nzb+5,pr_palm,tn) = sums_l(nzb+5,pr_palm,tn) + sums_l_eper
[1]	384	!
	385	!-- 2D-arrays (being collected in the last column of sums_l)
[87]	386	sums_l(nzb,pr_palm,tn) = sums_l(nzb,pr_palm,tn) + &
[1]	387	us(j,i) * rmask(j,i,sr)
[87]	388	sums_l(nzb+1,pr_palm,tn) = sums_l(nzb+1,pr_palm,tn) + &
[1]	389	usws(j,i) * rmask(j,i,sr)
[87]	390	sums_l(nzb+2,pr_palm,tn) = sums_l(nzb+2,pr_palm,tn) + &
[1]	391	vsws(j,i) * rmask(j,i,sr)
[87]	392	sums_l(nzb+3,pr_palm,tn) = sums_l(nzb+3,pr_palm,tn) + &
[1]	393	ts(j,i) * rmask(j,i,sr)
[197]	394	IF ( humidity ) THEN
	395	sums_l(nzb+12,pr_palm,tn) = sums_l(nzb+12,pr_palm,tn) + &
	396	qs(j,i) * rmask(j,i,sr)
	397	ENDIF
[1]	398	ENDDO
	399	ENDDO
	400
	401	!
	402	!-- Horizontally averaged profiles of the vertical fluxes
	403	!$OMP DO
	404	DO i = nxl, nxr
	405	DO j = nys, nyn
	406	!
	407	!-- Subgridscale fluxes (without Prandtl layer from k=nzb,
	408	!-- oterwise from k=nzb+1)
[132]	409	!-- NOTE: for simplicity, nzb_diff_s_inner is used below, although
[1]	410	!-- ---- strictly speaking the following k-loop would have to be
	411	!-- split up according to the staggered grid.
[132]	412	!-- However, this implies no error since staggered velocity
	413	!-- components are zero at the walls and inside buildings.
	414
	415	DO k = nzb_diff_s_inner(j,i)-1, nzt_diff
[1]	416	!
	417	!-- Momentum flux w"u"
	418	sums_l(k,12,tn) = sums_l(k,12,tn) - 0.25 * ( &
	419	km(k,j,i)+km(k+1,j,i)+km(k,j,i-1)+km(k+1,j,i-1) &
	420	) * ( &
	421	( u(k+1,j,i) - u(k,j,i) ) * ddzu(k+1) &
	422	+ ( w(k,j,i) - w(k,j,i-1) ) * ddx &
	423	) * rmask(j,i,sr)
	424	!
	425	!-- Momentum flux w"v"
	426	sums_l(k,14,tn) = sums_l(k,14,tn) - 0.25 * ( &
	427	km(k,j,i)+km(k+1,j,i)+km(k,j-1,i)+km(k+1,j-1,i) &
	428	) * ( &
	429	( v(k+1,j,i) - v(k,j,i) ) * ddzu(k+1) &
	430	+ ( w(k,j,i) - w(k,j-1,i) ) * ddy &
	431	) * rmask(j,i,sr)
	432	!
	433	!-- Heat flux w"pt"
	434	sums_l(k,16,tn) = sums_l(k,16,tn) &
	435	- 0.5 * ( kh(k,j,i) + kh(k+1,j,i) ) &
	436	* ( pt(k+1,j,i) - pt(k,j,i) ) &
	437	* ddzu(k+1) * rmask(j,i,sr)
	438
	439
	440	!
[96]	441	!-- Salinity flux w"sa"
	442	IF ( ocean ) THEN
	443	sums_l(k,65,tn) = sums_l(k,65,tn) &
	444	- 0.5 * ( kh(k,j,i) + kh(k+1,j,i) ) &
	445	* ( sa(k+1,j,i) - sa(k,j,i) ) &
	446	* ddzu(k+1) * rmask(j,i,sr)
	447	ENDIF
	448
	449	!
[1]	450	!-- Buoyancy flux, water flux (humidity flux) w"q"
[75]	451	IF ( humidity ) THEN
[1]	452	sums_l(k,45,tn) = sums_l(k,45,tn) &
	453	- 0.5 * ( kh(k,j,i) + kh(k+1,j,i) ) &
	454	* ( vpt(k+1,j,i) - vpt(k,j,i) ) &
	455	* ddzu(k+1) * rmask(j,i,sr)
	456	sums_l(k,48,tn) = sums_l(k,48,tn) &
	457	- 0.5 * ( kh(k,j,i) + kh(k+1,j,i) ) &
	458	* ( q(k+1,j,i) - q(k,j,i) ) &
	459	* ddzu(k+1) * rmask(j,i,sr)
	460	IF ( cloud_physics ) THEN
	461	sums_l(k,51,tn) = sums_l(k,51,tn) &
	462	- 0.5 * ( kh(k,j,i) + kh(k+1,j,i) ) &
	463	* ( ( q(k+1,j,i) - ql(k+1,j,i) )&
	464	- ( q(k,j,i) - ql(k,j,i) ) ) &
	465	* ddzu(k+1) * rmask(j,i,sr)
	466	ENDIF
	467	ENDIF
	468
	469	!
	470	!-- Passive scalar flux
	471	IF ( passive_scalar ) THEN
	472	sums_l(k,48,tn) = sums_l(k,48,tn) &
	473	- 0.5 * ( kh(k,j,i) + kh(k+1,j,i) ) &
	474	* ( q(k+1,j,i) - q(k,j,i) ) &
	475	* ddzu(k+1) * rmask(j,i,sr)
	476	ENDIF
	477
	478	ENDDO
	479
	480	!
	481	!-- Subgridscale fluxes in the Prandtl layer
	482	IF ( use_surface_fluxes ) THEN
	483	sums_l(nzb,12,tn) = sums_l(nzb,12,tn) + &
	484	usws(j,i) * rmask(j,i,sr) ! w"u"
	485	sums_l(nzb,14,tn) = sums_l(nzb,14,tn) + &
	486	vsws(j,i) * rmask(j,i,sr) ! w"v"
	487	sums_l(nzb,16,tn) = sums_l(nzb,16,tn) + &
	488	shf(j,i) * rmask(j,i,sr) ! w"pt"
	489	sums_l(nzb,58,tn) = sums_l(nzb,58,tn) + &
	490	0.0 * rmask(j,i,sr) ! u"pt"
	491	sums_l(nzb,61,tn) = sums_l(nzb,61,tn) + &
	492	0.0 * rmask(j,i,sr) ! v"pt"
[96]	493	IF ( ocean ) THEN
	494	sums_l(nzb,65,tn) = sums_l(nzb,65,tn) + &
	495	saswsb(j,i) * rmask(j,i,sr) ! w"sa"
	496	ENDIF
[75]	497	IF ( humidity ) THEN
[1]	498	sums_l(nzb,48,tn) = sums_l(nzb,48,tn) + &
	499	qsws(j,i) * rmask(j,i,sr) ! w"q" (w"qv")
	500	IF ( cloud_physics ) THEN
	501	sums_l(nzb,45,tn) = sums_l(nzb,45,tn) + ( &
	502	( 1.0 + 0.61 * q(nzb,j,i) ) * &
	503	shf(j,i) + 0.61 * pt(nzb,j,i) * &
	504	qsws(j,i) &
	505	)
	506	!
	507	!-- Formula does not work if ql(nzb) /= 0.0
	508	sums_l(nzb,51,tn) = sums_l(nzb,51,tn) + & ! w"q" (w"qv")
	509	qsws(j,i) * rmask(j,i,sr)
	510	ENDIF
	511	ENDIF
	512	IF ( passive_scalar ) THEN
	513	sums_l(nzb,48,tn) = sums_l(nzb,48,tn) + &
	514	qsws(j,i) * rmask(j,i,sr) ! w"q" (w"qv")
	515	ENDIF
	516	ENDIF
	517
	518	!
[19]	519	!-- Subgridscale fluxes at the top surface
	520	IF ( use_top_fluxes ) THEN
[550]	521	sums_l(nzt:nzt+1,12,tn) = sums_l(nzt:nzt+1,12,tn) + &
[102]	522	uswst(j,i) * rmask(j,i,sr) ! w"u"
[550]	523	sums_l(nzt:nzt+1,14,tn) = sums_l(nzt:nzt+1,14,tn) + &
[102]	524	vswst(j,i) * rmask(j,i,sr) ! w"v"
[550]	525	sums_l(nzt:nzt+1,16,tn) = sums_l(nzt:nzt+1,16,tn) + &
[19]	526	tswst(j,i) * rmask(j,i,sr) ! w"pt"
[550]	527	sums_l(nzt:nzt+1,58,tn) = sums_l(nzt:nzt+1,58,tn) + &
[19]	528	0.0 * rmask(j,i,sr) ! u"pt"
[550]	529	sums_l(nzt:nzt+1,61,tn) = sums_l(nzt:nzt+1,61,tn) + &
	530	0.0 * rmask(j,i,sr) ! v"pt"
	531
[96]	532	IF ( ocean ) THEN
	533	sums_l(nzt,65,tn) = sums_l(nzt,65,tn) + &
	534	saswst(j,i) * rmask(j,i,sr) ! w"sa"
	535	ENDIF
[75]	536	IF ( humidity ) THEN
[19]	537	sums_l(nzt,48,tn) = sums_l(nzt,48,tn) + &
[388]	538	qswst(j,i) * rmask(j,i,sr) ! w"q" (w"qv")
[19]	539	IF ( cloud_physics ) THEN
	540	sums_l(nzt,45,tn) = sums_l(nzt,45,tn) + ( &
	541	( 1.0 + 0.61 * q(nzt,j,i) ) * &
	542	tswst(j,i) + 0.61 * pt(nzt,j,i) * &
	543	qsws(j,i) &
	544	)
	545	!
	546	!-- Formula does not work if ql(nzb) /= 0.0
	547	sums_l(nzt,51,tn) = sums_l(nzt,51,tn) + & ! w"q" (w"qv")
	548	qswst(j,i) * rmask(j,i,sr)
	549	ENDIF
	550	ENDIF
	551	IF ( passive_scalar ) THEN
	552	sums_l(nzt,48,tn) = sums_l(nzt,48,tn) + &
[388]	553	qswst(j,i) * rmask(j,i,sr) ! w"q" (w"qv")
[19]	554	ENDIF
	555	ENDIF
	556
	557	!
[1]	558	!-- Resolved fluxes (can be computed for all horizontal points)
[132]	559	!-- NOTE: for simplicity, nzb_s_inner is used below, although strictly
[1]	560	!-- ---- speaking the following k-loop would have to be split up and
	561	!-- rearranged according to the staggered grid.
[132]	562	DO k = nzb_s_inner(j,i), nzt
[1]	563	ust = 0.5 * ( u(k,j,i) - hom(k,1,1,sr) + &
	564	u(k+1,j,i) - hom(k+1,1,1,sr) )
	565	vst = 0.5 * ( v(k,j,i) - hom(k,1,2,sr) + &
	566	v(k+1,j,i) - hom(k+1,1,2,sr) )
	567	pts = 0.5 * ( pt(k,j,i) - hom(k,1,4,sr) + &
	568	pt(k+1,j,i) - hom(k+1,1,4,sr) )
	569	!
	570	!-- Momentum flux wu
	571	sums_l(k,13,tn) = sums_l(k,13,tn) + 0.5 * &
	572	( w(k,j,i-1) + w(k,j,i) ) &
	573	* ust * rmask(j,i,sr)
	574	!
	575	!-- Momentum flux wv
	576	sums_l(k,15,tn) = sums_l(k,15,tn) + 0.5 * &
	577	( w(k,j-1,i) + w(k,j,i) ) &
	578	* vst * rmask(j,i,sr)
	579	!
	580	!-- Heat flux wpt
	581	!-- The following formula (comment line, not executed) does not
	582	!-- work if applied to subregions
	583	! sums_l(k,17,tn) = sums_l(k,17,tn) + 0.5 * &
	584	! ( pt(k,j,i)+pt(k+1,j,i) ) &
	585	! * w(k,j,i) * rmask(j,i,sr)
	586	sums_l(k,17,tn) = sums_l(k,17,tn) + pts * w(k,j,i) * &
	587	rmask(j,i,sr)
	588	!
	589	!-- Higher moments
	590	sums_l(k,35,tn) = sums_l(k,35,tn) + pts * w(k,j,i)*2 &
	591	rmask(j,i,sr)
	592	sums_l(k,36,tn) = sums_l(k,36,tn) + pts*2 w(k,j,i) * &
	593	rmask(j,i,sr)
	594
	595	!
[96]	596	!-- Salinity flux and density (density does not belong to here,
[97]	597	!-- but so far there is no other suitable place to calculate)
[96]	598	IF ( ocean ) THEN
	599	pts = 0.5 * ( sa(k,j,i) - hom(k,1,23,sr) + &
	600	sa(k+1,j,i) - hom(k+1,1,23,sr) )
	601	sums_l(k,66,tn) = sums_l(k,66,tn) + pts * w(k,j,i) * &
	602	rmask(j,i,sr)
	603	sums_l(k,64,tn) = sums_l(k,64,tn) + rho(k,j,i) * &
	604	rmask(j,i,sr)
[388]	605	sums_l(k,71,tn) = sums_l(k,71,tn) + prho(k,j,i) * &
	606	rmask(j,i,sr)
[96]	607	ENDIF
	608
	609	!
[1]	610	!-- Buoyancy flux, water flux, humidity flux and liquid water
	611	!-- content
[75]	612	IF ( humidity ) THEN
[1]	613	pts = 0.5 * ( vpt(k,j,i) - hom(k,1,44,sr) + &
	614	vpt(k+1,j,i) - hom(k+1,1,44,sr) )
	615	sums_l(k,46,tn) = sums_l(k,46,tn) + pts * w(k,j,i) * &
	616	rmask(j,i,sr)
	617	pts = 0.5 * ( q(k,j,i) - hom(k,1,41,sr) + &
	618	q(k+1,j,i) - hom(k+1,1,41,sr) )
	619	sums_l(k,49,tn) = sums_l(k,49,tn) + pts * w(k,j,i) * &
	620	rmask(j,i,sr)
	621	IF ( cloud_physics .OR. cloud_droplets ) THEN
	622	pts = 0.5 * &
	623	( ( q(k,j,i) - ql(k,j,i) ) - hom(k,1,42,sr) &
	624	+ ( q(k+1,j,i) - ql(k+1,j,i) ) - hom(k+1,1,42,sr) )
	625	sums_l(k,52,tn) = sums_l(k,52,tn) + pts * w(k,j,i) * &
	626	rmask(j,i,sr)
	627	sums_l(k,54,tn) = sums_l(k,54,tn) + ql(k,j,i) * &
	628	rmask(j,i,sr)
	629	ENDIF
	630	ENDIF
	631
	632	!
	633	!-- Passive scalar flux
	634	IF ( passive_scalar ) THEN
	635	pts = 0.5 * ( q(k,j,i) - hom(k,1,41,sr) + &
	636	q(k+1,j,i) - hom(k+1,1,41,sr) )
	637	sums_l(k,49,tn) = sums_l(k,49,tn) + pts * w(k,j,i) * &
	638	rmask(j,i,sr)
	639	ENDIF
	640
	641	!
	642	!-- Energy flux we
	643	sums_l(k,37,tn) = sums_l(k,37,tn) + w(k,j,i) * 0.5 * &
	644	( ust2 + vst2 + w(k,j,i)**2 )&
	645	* rmask(j,i,sr)
	646
	647	ENDDO
	648	ENDDO
	649	ENDDO
	650
	651	!
[97]	652	!-- Density at top follows Neumann condition
[388]	653	IF ( ocean ) THEN
	654	sums_l(nzt+1,64,tn) = sums_l(nzt,64,tn)
	655	sums_l(nzt+1,71,tn) = sums_l(nzt,71,tn)
	656	ENDIF
[97]	657
	658	!
[1]	659	!-- Divergence of vertical flux of resolved scale energy and pressure
[106]	660	!-- fluctuations as well as flux of pressure fluctuation itself (68).
	661	!-- First calculate the products, then the divergence.
[1]	662	!-- Calculation is time consuming. Do it only, if profiles shall be plotted.
[106]	663	IF ( hom(nzb+1,2,55,0) /= 0.0 .OR. hom(nzb+1,2,68,0) /= 0.0 ) THEN
[1]	664
	665	sums_ll = 0.0 ! local array
	666
	667	!$OMP DO
	668	DO i = nxl, nxr
	669	DO j = nys, nyn
[132]	670	DO k = nzb_s_inner(j,i)+1, nzt
[1]	671
	672	sums_ll(k,1) = sums_ll(k,1) + 0.5 * w(k,j,i) * ( &
	673	( 0.25 * ( u(k,j,i)+u(k+1,j,i)+u(k,j,i+1)+u(k+1,j,i+1) &
	674	- 2.0 * ( hom(k,1,1,sr) + hom(k+1,1,1,sr) ) &
	675	) )**2 &
	676	+ ( 0.25 * ( v(k,j,i)+v(k+1,j,i)+v(k,j+1,i)+v(k+1,j+1,i) &
	677	- 2.0 * ( hom(k,1,2,sr) + hom(k+1,1,2,sr) ) &
	678	) )**2 &
	679	+ w(k,j,i)**2 )
	680
	681	sums_ll(k,2) = sums_ll(k,2) + 0.5 * w(k,j,i) &
	682	* ( p(k,j,i) + p(k+1,j,i) )
	683
	684	ENDDO
	685	ENDDO
	686	ENDDO
	687	sums_ll(0,1) = 0.0 ! because w is zero at the bottom
	688	sums_ll(nzt+1,1) = 0.0
	689	sums_ll(0,2) = 0.0
	690	sums_ll(nzt+1,2) = 0.0
	691
[132]	692	DO k = nzb_s_inner(j,i)+1, nzt
[1]	693	sums_l(k,55,tn) = ( sums_ll(k,1) - sums_ll(k-1,1) ) * ddzw(k)
	694	sums_l(k,56,tn) = ( sums_ll(k,2) - sums_ll(k-1,2) ) * ddzw(k)
[106]	695	sums_l(k,68,tn) = sums_ll(k,2)
[1]	696	ENDDO
	697	sums_l(nzb,55,tn) = sums_l(nzb+1,55,tn)
	698	sums_l(nzb,56,tn) = sums_l(nzb+1,56,tn)
[106]	699	sums_l(nzb,68,tn) = 0.0 ! because w* = 0 at nzb
[1]	700
	701	ENDIF
	702
	703	!
[106]	704	!-- Divergence of vertical flux of SGS TKE and the flux itself (69)
	705	IF ( hom(nzb+1,2,57,0) /= 0.0 .OR. hom(nzb+1,2,69,0) /= 0.0 ) THEN
[1]	706
	707	!$OMP DO
	708	DO i = nxl, nxr
	709	DO j = nys, nyn
[132]	710	DO k = nzb_s_inner(j,i)+1, nzt
[1]	711
[106]	712	sums_l(k,57,tn) = sums_l(k,57,tn) - 0.5 * ( &
[1]	713	(km(k,j,i)+km(k+1,j,i)) * (e(k+1,j,i)-e(k,j,i)) * ddzu(k+1) &
	714	- (km(k-1,j,i)+km(k,j,i)) * (e(k,j,i)-e(k-1,j,i)) * ddzu(k) &
[106]	715	) * ddzw(k)
[1]	716
[106]	717	sums_l(k,69,tn) = sums_l(k,69,tn) - 0.5 * ( &
	718	(km(k,j,i)+km(k+1,j,i)) * (e(k+1,j,i)-e(k,j,i)) * ddzu(k+1) &
	719	)
	720
[1]	721	ENDDO
	722	ENDDO
	723	ENDDO
	724	sums_l(nzb,57,tn) = sums_l(nzb+1,57,tn)
[106]	725	sums_l(nzb,69,tn) = sums_l(nzb+1,69,tn)
[1]	726
	727	ENDIF
	728
	729	!
	730	!-- Horizontal heat fluxes (subgrid, resolved, total).
	731	!-- Do it only, if profiles shall be plotted.
	732	IF ( hom(nzb+1,2,58,0) /= 0.0 ) THEN
	733
	734	!$OMP DO
	735	DO i = nxl, nxr
	736	DO j = nys, nyn
[132]	737	DO k = nzb_s_inner(j,i)+1, nzt
[1]	738	!
	739	!-- Subgrid horizontal heat fluxes u"pt", v"pt"
	740	sums_l(k,58,tn) = sums_l(k,58,tn) - 0.5 * &
	741	( kh(k,j,i) + kh(k,j,i-1) ) &
	742	* ( pt(k,j,i-1) - pt(k,j,i) ) &
	743	* ddx * rmask(j,i,sr)
	744	sums_l(k,61,tn) = sums_l(k,61,tn) - 0.5 * &
	745	( kh(k,j,i) + kh(k,j-1,i) ) &
	746	* ( pt(k,j-1,i) - pt(k,j,i) ) &
	747	* ddy * rmask(j,i,sr)
	748	!
	749	!-- Resolved horizontal heat fluxes upt, vpt
	750	sums_l(k,59,tn) = sums_l(k,59,tn) + &
	751	( u(k,j,i) - hom(k,1,1,sr) ) &
	752	* 0.5 * ( pt(k,j,i-1) - hom(k,1,4,sr) + &
	753	pt(k,j,i) - hom(k,1,4,sr) )
	754	pts = 0.5 * ( pt(k,j-1,i) - hom(k,1,4,sr) + &
	755	pt(k,j,i) - hom(k,1,4,sr) )
	756	sums_l(k,62,tn) = sums_l(k,62,tn) + &
	757	( v(k,j,i) - hom(k,1,2,sr) ) &
	758	* 0.5 * ( pt(k,j-1,i) - hom(k,1,4,sr) + &
	759	pt(k,j,i) - hom(k,1,4,sr) )
	760	ENDDO
	761	ENDDO
	762	ENDDO
	763	!
	764	!-- Fluxes at the surface must be zero (e.g. due to the Prandtl-layer)
[97]	765	sums_l(nzb,58,tn) = 0.0
	766	sums_l(nzb,59,tn) = 0.0
	767	sums_l(nzb,60,tn) = 0.0
	768	sums_l(nzb,61,tn) = 0.0
	769	sums_l(nzb,62,tn) = 0.0
	770	sums_l(nzb,63,tn) = 0.0
[1]	771
	772	ENDIF
[87]	773
	774	!
	775	!-- Calculate the user-defined profiles
	776	CALL user_statistics( 'profiles', sr, tn )
[1]	777	!$OMP END PARALLEL
	778
	779	!
	780	!-- Summation of thread sums
	781	IF ( threads_per_task > 1 ) THEN
	782	DO i = 1, threads_per_task-1
	783	sums_l(:,3,0) = sums_l(:,3,0) + sums_l(:,3,i)
	784	sums_l(:,4:40,0) = sums_l(:,4:40,0) + sums_l(:,4:40,i)
[87]	785	sums_l(:,45:pr_palm,0) = sums_l(:,45:pr_palm,0) + &
	786	sums_l(:,45:pr_palm,i)
	787	IF ( max_pr_user > 0 ) THEN
	788	sums_l(:,pr_palm+1:pr_palm+max_pr_user,0) = &
	789	sums_l(:,pr_palm+1:pr_palm+max_pr_user,0) + &
	790	sums_l(:,pr_palm+1:pr_palm+max_pr_user,i)
	791	ENDIF
[1]	792	ENDDO
	793	ENDIF
	794
	795	#if defined( __parallel )
	796	!
	797	!-- Compute total sum from local sums
	798	CALL MPI_ALLREDUCE( sums_l(nzb,1,0), sums(nzb,1), ngp_sums, MPI_REAL, &
	799	MPI_SUM, comm2d, ierr )
	800	#else
	801	sums = sums_l(:,:,0)
	802	#endif
	803
	804	!
	805	!-- Final values are obtained by division by the total number of grid points
	806	!-- used for summation. After that store profiles.
	807	!-- Profiles:
	808	DO k = nzb, nzt+1
[132]	809	sums(k,3) = sums(k,3) / ngp_2dh(sr)
[142]	810	sums(k,8:11) = sums(k,8:11) / ngp_2dh_s_inner(k,sr)
[132]	811	sums(k,12:22) = sums(k,12:22) / ngp_2dh(sr)
	812	sums(k,23:29) = sums(k,23:29) / ngp_2dh_s_inner(k,sr)
	813	sums(k,30:32) = sums(k,30:32) / ngp_2dh(sr)
[142]	814	sums(k,33:34) = sums(k,33:34) / ngp_2dh_s_inner(k,sr)
	815	sums(k,35:39) = sums(k,35:39) / ngp_2dh(sr)
[132]	816	sums(k,40) = sums(k,40) / ngp_2dh_s_inner(k,sr)
	817	sums(k,45:53) = sums(k,45:53) / ngp_2dh(sr)
	818	sums(k,54) = sums(k,54) / ngp_2dh_s_inner(k,sr)
	819	sums(k,55:63) = sums(k,55:63) / ngp_2dh(sr)
	820	sums(k,64) = sums(k,64) / ngp_2dh_s_inner(k,sr)
	821	sums(k,65:69) = sums(k,65:69) / ngp_2dh(sr)
	822	sums(k,70:pr_palm-2) = sums(k,70:pr_palm-2)/ ngp_2dh_s_inner(k,sr)
[1]	823	ENDDO
	824	!-- Upstream-parts
[87]	825	sums(nzb:nzb+11,pr_palm-1) = sums(nzb:nzb+11,pr_palm-1) / ngp_3d(sr)
[1]	826	!-- u* and so on
[87]	827	!-- As sums(nzb:nzb+3,pr_palm) are full 2D arrays (us, usws, vsws, ts) whose
[1]	828	!-- size is always ( nx + 1 ) * ( ny + 1 ), defined at the first grid layer
	829	!-- above the topography, they are being divided by ngp_2dh(sr)
[87]	830	sums(nzb:nzb+3,pr_palm) = sums(nzb:nzb+3,pr_palm) / &
[1]	831	ngp_2dh(sr)
[197]	832	sums(nzb+12,pr_palm) = sums(nzb+12,pr_palm) / & ! qs
	833	ngp_2dh(sr)
[1]	834	!-- eges, e*
[87]	835	sums(nzb+4:nzb+5,pr_palm) = sums(nzb+4:nzb+5,pr_palm) / &
[132]	836	ngp_3d(sr)
[1]	837	!-- Old and new divergence
[87]	838	sums(nzb+9:nzb+10,pr_palm) = sums(nzb+9:nzb+10,pr_palm) / &
[1]	839	ngp_3d_inner(sr)
	840
[87]	841	!-- User-defined profiles
	842	IF ( max_pr_user > 0 ) THEN
	843	DO k = nzb, nzt+1
	844	sums(k,pr_palm+1:pr_palm+max_pr_user) = &
	845	sums(k,pr_palm+1:pr_palm+max_pr_user) / &
[132]	846	ngp_2dh_s_inner(k,sr)
[87]	847	ENDDO
	848	ENDIF
	849
[1]	850	!
	851	!-- Collect horizontal average in hom.
	852	!-- Compute deduced averages (e.g. total heat flux)
	853	hom(:,1,3,sr) = sums(:,3) ! w
	854	hom(:,1,8,sr) = sums(:,8) ! e profiles 5-7 are initial profiles
	855	hom(:,1,9,sr) = sums(:,9) ! km
	856	hom(:,1,10,sr) = sums(:,10) ! kh
	857	hom(:,1,11,sr) = sums(:,11) ! l
	858	hom(:,1,12,sr) = sums(:,12) ! w"u"
	859	hom(:,1,13,sr) = sums(:,13) ! wu
	860	hom(:,1,14,sr) = sums(:,14) ! w"v"
	861	hom(:,1,15,sr) = sums(:,15) ! wv
	862	hom(:,1,16,sr) = sums(:,16) ! w"pt"
	863	hom(:,1,17,sr) = sums(:,17) ! wpt
	864	hom(:,1,18,sr) = sums(:,16) + sums(:,17) ! wpt
	865	hom(:,1,19,sr) = sums(:,12) + sums(:,13) ! wu
	866	hom(:,1,20,sr) = sums(:,14) + sums(:,15) ! wv
	867	hom(:,1,21,sr) = sums(:,21) ! wptBC
	868	hom(:,1,22,sr) = sums(:,16) + sums(:,21) ! wptBC
[96]	869	! profile 24 is initial profile (sa)
	870	! profiles 25-29 left empty for initial
[1]	871	! profiles
	872	hom(:,1,30,sr) = sums(:,30) ! u*2
	873	hom(:,1,31,sr) = sums(:,31) ! v*2
	874	hom(:,1,32,sr) = sums(:,32) ! w*2
	875	hom(:,1,33,sr) = sums(:,33) ! pt*2
	876	hom(:,1,34,sr) = sums(:,34) ! e*
	877	hom(:,1,35,sr) = sums(:,35) ! w2pt
	878	hom(:,1,36,sr) = sums(:,36) ! wpt2
	879	hom(:,1,37,sr) = sums(:,37) ! we
	880	hom(:,1,38,sr) = sums(:,38) ! w*3
	881	hom(:,1,39,sr) = sums(:,38) / ( sums(:,32) + 1E-20 )**1.5 ! Sw
	882	hom(:,1,40,sr) = sums(:,40) ! p
[531]	883	hom(:,1,45,sr) = sums(:,45) ! w"vpt"
[1]	884	hom(:,1,46,sr) = sums(:,46) ! wvpt
	885	hom(:,1,47,sr) = sums(:,45) + sums(:,46) ! wvpt
	886	hom(:,1,48,sr) = sums(:,48) ! w"q" (w"qv")
	887	hom(:,1,49,sr) = sums(:,49) ! wq (wqv)
	888	hom(:,1,50,sr) = sums(:,48) + sums(:,49) ! wq (wqv)
	889	hom(:,1,51,sr) = sums(:,51) ! w"qv"
	890	hom(:,1,52,sr) = sums(:,52) ! wqv
	891	hom(:,1,53,sr) = sums(:,52) + sums(:,51) ! wq (wqv)
	892	hom(:,1,54,sr) = sums(:,54) ! ql
	893	hom(:,1,55,sr) = sums(:,55) ! wuu*/dz
	894	hom(:,1,56,sr) = sums(:,56) ! wp/dz
[106]	895	hom(:,1,57,sr) = sums(:,57) ! ( w"e + w"p"/rho )/dz
[1]	896	hom(:,1,58,sr) = sums(:,58) ! u"pt"
	897	hom(:,1,59,sr) = sums(:,59) ! upt
	898	hom(:,1,60,sr) = sums(:,58) + sums(:,59) ! upt_t
	899	hom(:,1,61,sr) = sums(:,61) ! v"pt"
	900	hom(:,1,62,sr) = sums(:,62) ! vpt
	901	hom(:,1,63,sr) = sums(:,61) + sums(:,62) ! vpt_t
[96]	902	hom(:,1,64,sr) = sums(:,64) ! rho
	903	hom(:,1,65,sr) = sums(:,65) ! w"sa"
	904	hom(:,1,66,sr) = sums(:,66) ! wsa
	905	hom(:,1,67,sr) = sums(:,65) + sums(:,66) ! wsa
[106]	906	hom(:,1,68,sr) = sums(:,68) ! wp
	907	hom(:,1,69,sr) = sums(:,69) ! w"e + w"p"/rho
[197]	908	hom(:,1,70,sr) = sums(:,70) ! q*2
[388]	909	hom(:,1,71,sr) = sums(:,71) ! prho
[531]	910	hom(:,1,72,sr) = hyp * 1E-4 ! hyp in dbar
[1]	911
[87]	912	hom(:,1,pr_palm-1,sr) = sums(:,pr_palm-1)
[1]	913	! upstream-parts u_x, u_y, u_z, v_x,
	914	! v_y, usw. (in last but one profile)
[87]	915	hom(:,1,pr_palm,sr) = sums(:,pr_palm)
[1]	916	! u, w'u', w'v', t (in last profile)
	917
[87]	918	IF ( max_pr_user > 0 ) THEN ! user-defined profiles
	919	hom(:,1,pr_palm+1:pr_palm+max_pr_user,sr) = &
	920	sums(:,pr_palm+1:pr_palm+max_pr_user)
	921	ENDIF
	922
[1]	923	!
	924	!-- Determine the boundary layer height using two different schemes.
[94]	925	!-- First scheme: Starting from the Earth's (Ocean's) surface, look for the
	926	!-- first relative minimum (maximum) of the total heat flux.
	927	!-- The corresponding height is assumed as the boundary layer height, if it
	928	!-- is less than 1.5 times the height where the heat flux becomes negative
	929	!-- (positive) for the first time.
[1]	930	z_i(1) = 0.0
	931	first = .TRUE.
[97]	932	IF ( ocean ) THEN
	933	DO k = nzt, nzb+1, -1
	934	IF ( first .AND. hom(k,1,18,sr) < 0.0 ) THEN
	935	first = .FALSE.
	936	height = zw(k)
	937	ENDIF
	938	IF ( hom(k,1,18,sr) < 0.0 .AND. &
	939	hom(k-1,1,18,sr) > hom(k,1,18,sr) ) THEN
	940	IF ( zw(k) < 1.5 * height ) THEN
	941	z_i(1) = zw(k)
	942	ELSE
	943	z_i(1) = height
	944	ENDIF
	945	EXIT
	946	ENDIF
	947	ENDDO
	948	ELSE
[94]	949	DO k = nzb, nzt-1
	950	IF ( first .AND. hom(k,1,18,sr) < 0.0 ) THEN
	951	first = .FALSE.
	952	height = zw(k)
[1]	953	ENDIF
[94]	954	IF ( hom(k,1,18,sr) < 0.0 .AND. &
	955	hom(k+1,1,18,sr) > hom(k,1,18,sr) ) THEN
	956	IF ( zw(k) < 1.5 * height ) THEN
	957	z_i(1) = zw(k)
	958	ELSE
	959	z_i(1) = height
	960	ENDIF
	961	EXIT
	962	ENDIF
	963	ENDDO
[97]	964	ENDIF
[1]	965
	966	!
[291]	967	!-- Second scheme: Gradient scheme from Sullivan et al. (1998), modified
	968	!-- by Uhlenbrock(2006). The boundary layer height is the height with the
	969	!-- maximal local temperature gradient: starting from the second (the last
	970	!-- but one) vertical gridpoint, the local gradient must be at least
	971	!-- 0.2K/100m and greater than the next four gradients.
	972	!-- WARNING: The threshold value of 0.2K/100m must be adjusted for the
	973	!-- ocean case!
[1]	974	z_i(2) = 0.0
[291]	975	DO k = nzb+1, nzt+1
	976	dptdz(k) = ( hom(k,1,4,sr) - hom(k-1,1,4,sr) ) * ddzu(k)
	977	ENDDO
	978	dptdz_threshold = 0.2 / 100.0
	979
[97]	980	IF ( ocean ) THEN
[291]	981	DO k = nzt+1, nzb+5, -1
	982	IF ( dptdz(k) > dptdz_threshold .AND. &
	983	dptdz(k) > dptdz(k-1) .AND. dptdz(k) > dptdz(k-2) .AND. &
	984	dptdz(k) > dptdz(k-3) .AND. dptdz(k) > dptdz(k-4) ) THEN
	985	z_i(2) = zw(k-1)
[97]	986	EXIT
	987	ENDIF
	988	ENDDO
	989	ELSE
[291]	990	DO k = nzb+1, nzt-3
	991	IF ( dptdz(k) > dptdz_threshold .AND. &
	992	dptdz(k) > dptdz(k+1) .AND. dptdz(k) > dptdz(k+2) .AND. &
	993	dptdz(k) > dptdz(k+3) .AND. dptdz(k) > dptdz(k+4) ) THEN
	994	z_i(2) = zw(k-1)
[97]	995	EXIT
	996	ENDIF
	997	ENDDO
	998	ENDIF
[1]	999
[87]	1000	hom(nzb+6,1,pr_palm,sr) = z_i(1)
	1001	hom(nzb+7,1,pr_palm,sr) = z_i(2)
[1]	1002
	1003	!
	1004	!-- Computation of both the characteristic vertical velocity and
	1005	!-- the characteristic convective boundary layer temperature.
	1006	!-- The horizontal average at nzb+1 is input for the average temperature.
	1007	IF ( hom(nzb,1,18,sr) > 0.0 .AND. z_i(1) /= 0.0 ) THEN
[87]	1008	hom(nzb+8,1,pr_palm,sr) = ( g / hom(nzb+1,1,4,sr) * &
[94]	1009	hom(nzb,1,18,sr) * &
	1010	ABS( z_i(1) ) )**0.333333333
[1]	1011	!-- so far this only works if Prandtl layer is used
[87]	1012	hom(nzb+11,1,pr_palm,sr) = hom(nzb,1,16,sr) / hom(nzb+8,1,pr_palm,sr)
[1]	1013	ELSE
[87]	1014	hom(nzb+8,1,pr_palm,sr) = 0.0
	1015	hom(nzb+11,1,pr_palm,sr) = 0.0
[1]	1016	ENDIF
	1017
[48]	1018	!
	1019	!-- Collect the time series quantities
[87]	1020	ts_value(1,sr) = hom(nzb+4,1,pr_palm,sr) ! E
	1021	ts_value(2,sr) = hom(nzb+5,1,pr_palm,sr) ! E*
[48]	1022	ts_value(3,sr) = dt_3d
[87]	1023	ts_value(4,sr) = hom(nzb,1,pr_palm,sr) ! u*
	1024	ts_value(5,sr) = hom(nzb+3,1,pr_palm,sr) ! th*
[48]	1025	ts_value(6,sr) = u_max
	1026	ts_value(7,sr) = v_max
	1027	ts_value(8,sr) = w_max
[87]	1028	ts_value(9,sr) = hom(nzb+10,1,pr_palm,sr) ! new divergence
	1029	ts_value(10,sr) = hom(nzb+9,1,pr_palm,sr) ! old Divergence
	1030	ts_value(11,sr) = hom(nzb+6,1,pr_palm,sr) ! z_i(1)
	1031	ts_value(12,sr) = hom(nzb+7,1,pr_palm,sr) ! z_i(2)
	1032	ts_value(13,sr) = hom(nzb+8,1,pr_palm,sr) ! w*
[48]	1033	ts_value(14,sr) = hom(nzb,1,16,sr) ! w'pt' at k=0
	1034	ts_value(15,sr) = hom(nzb+1,1,16,sr) ! w'pt' at k=1
	1035	ts_value(16,sr) = hom(nzb+1,1,18,sr) ! wpt at k=1
	1036	ts_value(17,sr) = hom(nzb,1,4,sr) ! pt(0)
	1037	ts_value(18,sr) = hom(nzb+1,1,4,sr) ! pt(zp)
[197]	1038	ts_value(19,sr) = hom(nzb+1,1,pr_palm,sr) ! u'w' at k=0
	1039	ts_value(20,sr) = hom(nzb+2,1,pr_palm,sr) ! v'w' at k=0
[343]	1040	ts_value(21,sr) = hom(nzb,1,48,sr) ! w"q" at k=0
[197]	1041
[48]	1042	IF ( ts_value(5,sr) /= 0.0 ) THEN
	1043	ts_value(22,sr) = ts_value(4,sr)**2 / &
	1044	( kappa * g * ts_value(5,sr) / ts_value(18,sr) ) ! L
	1045	ELSE
	1046	ts_value(22,sr) = 10000.0
	1047	ENDIF
[1]	1048
[343]	1049	ts_value(23,sr) = hom(nzb+12,1,pr_palm,sr) ! q*
[1]	1050	!
[48]	1051	!-- Calculate additional statistics provided by the user interface
[87]	1052	CALL user_statistics( 'time_series', sr, 0 )
[1]	1053
[48]	1054	ENDDO ! loop of the subregions
	1055
[1]	1056	!
	1057	!-- If required, sum up horizontal averages for subsequent time averaging
	1058	IF ( do_sum ) THEN
	1059	IF ( average_count_pr == 0 ) hom_sum = 0.0
	1060	hom_sum = hom_sum + hom(:,1,:,:)
	1061	average_count_pr = average_count_pr + 1
	1062	do_sum = .FALSE.
	1063	ENDIF
	1064
	1065	!
	1066	!-- Set flag for other UPs (e.g. output routines, but also buoyancy).
	1067	!-- This flag is reset after each time step in time_integration.
	1068	flow_statistics_called = .TRUE.
	1069
	1070	CALL cpu_log( log_point(10), 'flow_statistics', 'stop' )
	1071
	1072
	1073	END SUBROUTINE flow_statistics
	1074
	1075
	1076

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