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source: palm/trunk/SOURCE/flow_statistics.f90 @ 699

Last change on this file since 699 was 699, checked in by suehring, 13 years ago
Bugfix in calculation of vertical velocity skewness.
Property svn:keywords set to `Id`
File size: 51.9 KB

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

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