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source: palm/trunk/SOURCE/flow_statistics.f90 @ 743

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

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