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source: palm/trunk/SOURCE/flow_statistics.f90 @ 703

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

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