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source: palm/trunk/SOURCE/flow_statistics.f90 @ 692

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

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