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source: palm/trunk/SOURCE/flow_statistics.f90 @ 1039

Last change on this file since 1039 was 1037, checked in by raasch, 12 years ago
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1	SUBROUTINE flow_statistics
2
3	!--------------------------------------------------------------------------------!
4	! This file is part of PALM.
5	!
6	! PALM is free software: you can redistribute it and/or modify it under the terms
7	! of the GNU General Public License as published by the Free Software Foundation,
8	! either version 3 of the License, or (at your option) any later version.
9	!
10	! PALM is distributed in the hope that it will be useful, but WITHOUT ANY
11	! WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
12	! A PARTICULAR PURPOSE. See the GNU General Public License for more details.
13	!
14	! You should have received a copy of the GNU General Public License along with
15	! PALM. If not, see <http://www.gnu.org/licenses/>.
16	!
17	! Copyright 1997-2012 Leibniz University Hannover
18	!--------------------------------------------------------------------------------!
19	!
20	! Current revisions:
21	! -----------------
22	!
23	!
24	! Former revisions:
25	! -----------------
26	! $Id: flow_statistics.f90 1037 2012-10-22 14:10:22Z raasch $
27	!
28	! 1036 2012-10-22 13:43:42Z raasch
29	! code put under GPL (PALM 3.9)
30	!
31	! 1007 2012-09-19 14:30:36Z franke
32	! Calculation of buoyancy flux for humidity in case of WS-scheme is now using
33	! turbulent fluxes of WS-scheme
34	! Bugfix: Calculation of subgridscale buoyancy flux for humidity and cloud
35	! droplets at nzb and nzt added
36	!
37	! 801 2012-01-10 17:30:36Z suehring
38	! Calculation of turbulent fluxes in advec_ws is now thread-safe.
39	!
40	! 743 2011-08-18 16:10:16Z suehring
41	! Calculation of turbulent fluxes with WS-scheme only for the whole model
42	! domain, not for user-defined subregions.
43	!
44	! 709 2011-03-30 09:31:40Z raasch
45	! formatting adjustments
46	!
47	! 699 2011-03-22 17:52:22Z suehring
48	! Bugfix in calculation of vertical velocity skewness. The added absolute value
49	! avoid negative values in the root. Negative values of w'w' can occur at the
50	! top or bottom of the model domain due to degrading the order of advection
51	! scheme. Furthermore the calculation will be the same for all advection
52	! schemes.
53	!
54	! 696 2011-03-18 07:03:49Z raasch
55	! Bugfix: Summation of Wicker-Skamarock scheme fluxes and variances for all
56	! threads
57	!
58	! 678 2011-02-02 14:31:56Z raasch
59	! Bugfix in calculation of the divergence of vertical flux of resolved scale
60	! energy, pressure fluctuations, and flux of pressure fluctuation itself
61	!
62	! 673 2011-01-18 16:19:48Z suehring
63	! Top bc for the horizontal velocity variances added for ocean runs.
64	! Setting the corresponding bottom bc moved to advec_ws.
65	!
66	! 667 2010-12-23 12:06:00Z suehring/gryschka
67	! When advection is computed with ws-scheme, turbulent fluxes are already
68	! computed in the respective advection routines and buffered in arrays
69	! sums_xx_ws_l(). This is due to a consistent treatment of statistics with the
70	! numerics and to avoid unphysical kinks near the surface.
71	! So some if requests has to be done to dicern between fluxes from ws-scheme
72	! other advection schemes.
73	! Furthermore the computation of z_i is only done if the heat flux exceeds a
74	! minimum value. This affects only simulations of a neutral boundary layer and
75	! is due to reasons of computations in the advection scheme.
76	!
77	! 624 2010-12-10 11:46:30Z heinze
78	! Calculation of q*2 added
79	!
80	! 622 2010-12-10 08:08:13Z raasch
81	! optional barriers included in order to speed up collective operations
82	!
83	! 388 2009-09-23 09:40:33Z raasch
84	! Vertical profiles of potential density and hydrostatic pressure are
85	! calculated.
86	! Added missing timeseries calculation of w"q"(0), moved timeseries q* to the
87	! end.
88	! Temperature gradient criterion for estimating the boundary layer height
89	! replaced by the gradient criterion of Sullivan et al. (1998).
90	! Output of messages replaced by message handling routine.
91	!
92	! 197 2008-09-16 15:29:03Z raasch
93	! Spline timeseries splptx etc. removed, timeseries w'u', w'v', w'q' (k=0)
94	! added,
95	! bugfix: divide sums(k,8) (e) and sums(k,34) (e*) by ngp_2dh_s_inner(k,sr)
96	! (like other scalars)
97	!
98	! 133 2007-11-20 10:10:53Z letzel
99	! Vertical profiles now based on nzb_s_inner; they are divided by
100	! ngp_2dh_s_inner (scalars, procucts of scalars) and ngp_2dh (staggered
101	! velocity components and their products, procucts of scalars and velocity
102	! components), respectively.
103	!
104	! 106 2007-08-16 14:30:26Z raasch
105	! Prescribed momentum fluxes at the top surface are used,
106	! profiles for wp and w"e are calculated
107	!
108	! 97 2007-06-21 08:23:15Z raasch
109	! Statistics for ocean version (salinity, density) added,
110	! calculation of z_i and Deardorff velocity scale adjusted to be used with
111	! the ocean version
112	!
113	! 87 2007-05-22 15:46:47Z raasch
114	! Two more arguments added to user_statistics, which is now also called for
115	! user-defined profiles,
116	! var_hom and var_sum renamed pr_palm
117	!
118	! 82 2007-04-16 15:40:52Z raasch
119	! Cpp-directive lcmuk changed to intel_openmp_bug
120	!
121	! 75 2007-03-22 09:54:05Z raasch
122	! Collection of time series quantities moved from routine flow_statistics to
123	! here, routine user_statistics is called for each statistic region,
124	! moisture renamed humidity
125	!
126	! 19 2007-02-23 04:53:48Z raasch
127	! fluxes at top modified (tswst, qswst)
128	!
129	! RCS Log replace by Id keyword, revision history cleaned up
130	!
131	! Revision 1.41 2006/08/04 14:37:50 raasch
132	! Error removed in non-parallel part (sums_l)
133	!
134	! Revision 1.1 1997/08/11 06:15:17 raasch
135	! Initial revision
136	!
137	!
138	! Description:
139	! ------------
140	! Compute average profiles and further average flow quantities for the different
141	! user-defined (sub-)regions. The region indexed 0 is the total model domain.
142	!
143	! NOTE: For simplicity, nzb_s_inner and nzb_diff_s_inner are being used as a
144	! ---- lower vertical index for k-loops for all variables, although strictly
145	! speaking the k-loops would have to be split up according to the staggered
146	! grid. However, this implies no error since staggered velocity components are
147	! zero at the walls and inside buildings.
148	!------------------------------------------------------------------------------!
149
150	USE arrays_3d
151	USE cloud_parameters
152	USE control_parameters
153	USE cpulog
154	USE grid_variables
155	USE indices
156	USE interfaces
157	USE pegrid
158	USE statistics
159
160	IMPLICIT NONE
161
162	INTEGER :: i, j, k, omp_get_thread_num, sr, tn
163	LOGICAL :: first
164	REAL :: dptdz_threshold, height, pts, sums_l_eper, sums_l_etot, ust, &
165	ust2, u2, vst, vst2, v2, w2, z_i(2)
166	REAL :: dptdz(nzb+1:nzt+1)
167	REAL :: sums_ll(nzb:nzt+1,2)
168
169	CALL cpu_log( log_point(10), 'flow_statistics', 'start' )
170
171	!
172	!-- To be on the safe side, check whether flow_statistics has already been
173	!-- called once after the current time step
174	IF ( flow_statistics_called ) THEN
175
176	message_string = 'flow_statistics is called two times within one ' // &
177	'timestep'
178	CALL message( 'flow_statistics', 'PA0190', 1, 2, 0, 6, 0 )
179
180	ENDIF
181
182	!
183	!-- Compute statistics for each (sub-)region
184	DO sr = 0, statistic_regions
185
186	!
187	!-- Initialize (local) summation array
188	sums_l = 0.0
189
190	!
191	!-- Store sums that have been computed in other subroutines in summation
192	!-- array
193	sums_l(:,11,:) = sums_l_l(:,sr,:) ! mixing length from diffusivities
194	!-- WARNING: next line still has to be adjusted for OpenMP
195	sums_l(:,21,0) = sums_wsts_bc_l(:,sr) ! heat flux from advec_s_bc
196	sums_l(nzb+9,pr_palm,0) = sums_divold_l(sr) ! old divergence from pres
197	sums_l(nzb+10,pr_palm,0) = sums_divnew_l(sr) ! new divergence from pres
198
199	!
200	!-- Copy the turbulent quantities, evaluated in the advection routines to
201	!-- the local array sums_l() for further computations
202	IF ( ws_scheme_mom .AND. sr == 0 ) THEN
203
204	!
205	!-- According to the Neumann bc for the horizontal velocity components,
206	!-- the corresponding fluxes has to satisfiy the same bc.
207	IF ( ocean ) THEN
208	sums_us2_ws_l(nzt+1,:) = sums_us2_ws_l(nzt,:)
209	sums_vs2_ws_l(nzt+1,:) = sums_vs2_ws_l(nzt,:)
210	ENDIF
211
212	DO i = 0, threads_per_task-1
213	!
214	!-- Swap the turbulent quantities evaluated in advec_ws.
215	sums_l(:,13,i) = sums_wsus_ws_l(:,i) ! wu
216	sums_l(:,15,i) = sums_wsvs_ws_l(:,i) ! wv
217	sums_l(:,30,i) = sums_us2_ws_l(:,i) ! u*2
218	sums_l(:,31,i) = sums_vs2_ws_l(:,i) ! v*2
219	sums_l(:,32,i) = sums_ws2_ws_l(:,i) ! w*2
220	sums_l(:,34,i) = sums_l(:,34,i) + 0.5 * &
221	( sums_us2_ws_l(:,i) + sums_vs2_ws_l(:,i) + &
222	sums_ws2_ws_l(:,i) ) ! e*
223	DO k = nzb, nzt
224	sums_l(nzb+5,pr_palm,i) = sums_l(nzb+5,pr_palm,i) + 0.5 * ( &
225	sums_us2_ws_l(k,i) + &
226	sums_vs2_ws_l(k,i) + &
227	sums_ws2_ws_l(k,i) )
228	ENDDO
229	ENDDO
230
231	ENDIF
232
233	IF ( ws_scheme_sca .AND. sr == 0 ) THEN
234
235	DO i = 0, threads_per_task-1
236	sums_l(:,17,i) = sums_wspts_ws_l(:,i) ! wpt from advec_s_ws
237	IF ( ocean ) sums_l(:,66,i) = sums_wssas_ws_l(:,i) ! wsa
238	IF ( humidity .OR. passive_scalar ) sums_l(:,49,i) = &
239	sums_wsqs_ws_l(:,i) !wq
240	ENDDO
241
242	ENDIF
243	!
244	!-- Horizontally averaged profiles of horizontal velocities and temperature.
245	!-- They must have been computed before, because they are already required
246	!-- for other horizontal averages.
247	tn = 0
248
249	!$OMP PARALLEL PRIVATE( i, j, k, tn )
250	#if defined( __intel_openmp_bug )
251	tn = omp_get_thread_num()
252	#else
253	!$ tn = omp_get_thread_num()
254	#endif
255
256	!$OMP DO
257	DO i = nxl, nxr
258	DO j = nys, nyn
259	DO k = nzb_s_inner(j,i), nzt+1
260	sums_l(k,1,tn) = sums_l(k,1,tn) + u(k,j,i) * rmask(j,i,sr)
261	sums_l(k,2,tn) = sums_l(k,2,tn) + v(k,j,i) * rmask(j,i,sr)
262	sums_l(k,4,tn) = sums_l(k,4,tn) + pt(k,j,i) * rmask(j,i,sr)
263	ENDDO
264	ENDDO
265	ENDDO
266
267	!
268	!-- Horizontally averaged profile of salinity
269	IF ( ocean ) THEN
270	!$OMP DO
271	DO i = nxl, nxr
272	DO j = nys, nyn
273	DO k = nzb_s_inner(j,i), nzt+1
274	sums_l(k,23,tn) = sums_l(k,23,tn) + &
275	sa(k,j,i) * rmask(j,i,sr)
276	ENDDO
277	ENDDO
278	ENDDO
279	ENDIF
280
281	!
282	!-- Horizontally averaged profiles of virtual potential temperature,
283	!-- total water content, specific humidity and liquid water potential
284	!-- temperature
285	IF ( humidity ) THEN
286	!$OMP DO
287	DO i = nxl, nxr
288	DO j = nys, nyn
289	DO k = nzb_s_inner(j,i), nzt+1
290	sums_l(k,44,tn) = sums_l(k,44,tn) + &
291	vpt(k,j,i) * rmask(j,i,sr)
292	sums_l(k,41,tn) = sums_l(k,41,tn) + &
293	q(k,j,i) * rmask(j,i,sr)
294	ENDDO
295	ENDDO
296	ENDDO
297	IF ( cloud_physics ) THEN
298	!$OMP DO
299	DO i = nxl, nxr
300	DO j = nys, nyn
301	DO k = nzb_s_inner(j,i), nzt+1
302	sums_l(k,42,tn) = sums_l(k,42,tn) + &
303	( q(k,j,i) - ql(k,j,i) ) * rmask(j,i,sr)
304	sums_l(k,43,tn) = sums_l(k,43,tn) + ( &
305	pt(k,j,i) + l_d_cppt_d_t(k) ql(k,j,i) &
306	) * rmask(j,i,sr)
307	ENDDO
308	ENDDO
309	ENDDO
310	ENDIF
311	ENDIF
312
313	!
314	!-- Horizontally averaged profiles of passive scalar
315	IF ( passive_scalar ) THEN
316	!$OMP DO
317	DO i = nxl, nxr
318	DO j = nys, nyn
319	DO k = nzb_s_inner(j,i), nzt+1
320	sums_l(k,41,tn) = sums_l(k,41,tn) + q(k,j,i) * rmask(j,i,sr)
321	ENDDO
322	ENDDO
323	ENDDO
324	ENDIF
325	!$OMP END PARALLEL
326	!
327	!-- Summation of thread sums
328	IF ( threads_per_task > 1 ) THEN
329	DO i = 1, threads_per_task-1
330	sums_l(:,1,0) = sums_l(:,1,0) + sums_l(:,1,i)
331	sums_l(:,2,0) = sums_l(:,2,0) + sums_l(:,2,i)
332	sums_l(:,4,0) = sums_l(:,4,0) + sums_l(:,4,i)
333	IF ( ocean ) THEN
334	sums_l(:,23,0) = sums_l(:,23,0) + sums_l(:,23,i)
335	ENDIF
336	IF ( humidity ) THEN
337	sums_l(:,41,0) = sums_l(:,41,0) + sums_l(:,41,i)
338	sums_l(:,44,0) = sums_l(:,44,0) + sums_l(:,44,i)
339	IF ( cloud_physics ) THEN
340	sums_l(:,42,0) = sums_l(:,42,0) + sums_l(:,42,i)
341	sums_l(:,43,0) = sums_l(:,43,0) + sums_l(:,43,i)
342	ENDIF
343	ENDIF
344	IF ( passive_scalar ) THEN
345	sums_l(:,41,0) = sums_l(:,41,0) + sums_l(:,41,i)
346	ENDIF
347	ENDDO
348	ENDIF
349
350	#if defined( __parallel )
351	!
352	!-- Compute total sum from local sums
353	IF ( collective_wait ) CALL MPI_BARRIER( comm2d, ierr )
354	CALL MPI_ALLREDUCE( sums_l(nzb,1,0), sums(nzb,1), nzt+2-nzb, MPI_REAL, &
355	MPI_SUM, comm2d, ierr )
356	IF ( collective_wait ) CALL MPI_BARRIER( comm2d, ierr )
357	CALL MPI_ALLREDUCE( sums_l(nzb,2,0), sums(nzb,2), nzt+2-nzb, MPI_REAL, &
358	MPI_SUM, comm2d, ierr )
359	IF ( collective_wait ) CALL MPI_BARRIER( comm2d, ierr )
360	CALL MPI_ALLREDUCE( sums_l(nzb,4,0), sums(nzb,4), nzt+2-nzb, MPI_REAL, &
361	MPI_SUM, comm2d, ierr )
362	IF ( ocean ) THEN
363	IF ( collective_wait ) CALL MPI_BARRIER( comm2d, ierr )
364	CALL MPI_ALLREDUCE( sums_l(nzb,23,0), sums(nzb,23), nzt+2-nzb, &
365	MPI_REAL, MPI_SUM, comm2d, ierr )
366	ENDIF
367	IF ( humidity ) THEN
368	IF ( collective_wait ) CALL MPI_BARRIER( comm2d, ierr )
369	CALL MPI_ALLREDUCE( sums_l(nzb,44,0), sums(nzb,44), nzt+2-nzb, &
370	MPI_REAL, MPI_SUM, comm2d, ierr )
371	IF ( collective_wait ) CALL MPI_BARRIER( comm2d, ierr )
372	CALL MPI_ALLREDUCE( sums_l(nzb,41,0), sums(nzb,41), nzt+2-nzb, &
373	MPI_REAL, MPI_SUM, comm2d, ierr )
374	IF ( cloud_physics ) THEN
375	IF ( collective_wait ) CALL MPI_BARRIER( comm2d, ierr )
376	CALL MPI_ALLREDUCE( sums_l(nzb,42,0), sums(nzb,42), nzt+2-nzb, &
377	MPI_REAL, MPI_SUM, comm2d, ierr )
378	IF ( collective_wait ) CALL MPI_BARRIER( comm2d, ierr )
379	CALL MPI_ALLREDUCE( sums_l(nzb,43,0), sums(nzb,43), nzt+2-nzb, &
380	MPI_REAL, MPI_SUM, comm2d, ierr )
381	ENDIF
382	ENDIF
383
384	IF ( passive_scalar ) THEN
385	IF ( collective_wait ) CALL MPI_BARRIER( comm2d, ierr )
386	CALL MPI_ALLREDUCE( sums_l(nzb,41,0), sums(nzb,41), nzt+2-nzb, &
387	MPI_REAL, MPI_SUM, comm2d, ierr )
388	ENDIF
389	#else
390	sums(:,1) = sums_l(:,1,0)
391	sums(:,2) = sums_l(:,2,0)
392	sums(:,4) = sums_l(:,4,0)
393	IF ( ocean ) sums(:,23) = sums_l(:,23,0)
394	IF ( humidity ) THEN
395	sums(:,44) = sums_l(:,44,0)
396	sums(:,41) = sums_l(:,41,0)
397	IF ( cloud_physics ) THEN
398	sums(:,42) = sums_l(:,42,0)
399	sums(:,43) = sums_l(:,43,0)
400	ENDIF
401	ENDIF
402	IF ( passive_scalar ) sums(:,41) = sums_l(:,41,0)
403	#endif
404
405	!
406	!-- Final values are obtained by division by the total number of grid points
407	!-- used for summation. After that store profiles.
408	sums(:,1) = sums(:,1) / ngp_2dh(sr)
409	sums(:,2) = sums(:,2) / ngp_2dh(sr)
410	sums(:,4) = sums(:,4) / ngp_2dh_s_inner(:,sr)
411	hom(:,1,1,sr) = sums(:,1) ! u
412	hom(:,1,2,sr) = sums(:,2) ! v
413	hom(:,1,4,sr) = sums(:,4) ! pt
414
415
416	!
417	!-- Salinity
418	IF ( ocean ) THEN
419	sums(:,23) = sums(:,23) / ngp_2dh_s_inner(:,sr)
420	hom(:,1,23,sr) = sums(:,23) ! sa
421	ENDIF
422
423	!
424	!-- Humidity and cloud parameters
425	IF ( humidity ) THEN
426	sums(:,44) = sums(:,44) / ngp_2dh_s_inner(:,sr)
427	sums(:,41) = sums(:,41) / ngp_2dh_s_inner(:,sr)
428	hom(:,1,44,sr) = sums(:,44) ! vpt
429	hom(:,1,41,sr) = sums(:,41) ! qv (q)
430	IF ( cloud_physics ) THEN
431	sums(:,42) = sums(:,42) / ngp_2dh_s_inner(:,sr)
432	sums(:,43) = sums(:,43) / ngp_2dh_s_inner(:,sr)
433	hom(:,1,42,sr) = sums(:,42) ! qv
434	hom(:,1,43,sr) = sums(:,43) ! pt
435	ENDIF
436	ENDIF
437
438	!
439	!-- Passive scalar
440	IF ( passive_scalar ) hom(:,1,41,sr) = sums(:,41) / &
441	ngp_2dh_s_inner(:,sr) ! s (q)
442
443	!
444	!-- Horizontally averaged profiles of the remaining prognostic variables,
445	!-- variances, the total and the perturbation energy (single values in last
446	!-- column of sums_l) and some diagnostic quantities.
447	!-- NOTE: for simplicity, nzb_s_inner is used below, although strictly
448	!-- ---- speaking the following k-loop would have to be split up and
449	!-- rearranged according to the staggered grid.
450	!-- However, this implies no error since staggered velocity components
451	!-- are zero at the walls and inside buildings.
452	tn = 0
453	#if defined( __intel_openmp_bug )
454	!$OMP PARALLEL PRIVATE( i, j, k, pts, sums_ll, sums_l_eper, sums_l_etot, &
455	!$OMP tn, ust, ust2, u2, vst, vst2, v2, w2 )
456	tn = omp_get_thread_num()
457	#else
458	!$OMP PARALLEL PRIVATE( i, j, k, pts, sums_ll, sums_l_eper, sums_l_etot, tn, ust, ust2, u2, vst, vst2, v2, w2 )
459	!$ tn = omp_get_thread_num()
460	#endif
461	!$OMP DO
462	DO i = nxl, nxr
463	DO j = nys, nyn
464	sums_l_etot = 0.0
465	DO k = nzb_s_inner(j,i), nzt+1
466	!
467	!-- Prognostic and diagnostic variables
468	sums_l(k,3,tn) = sums_l(k,3,tn) + w(k,j,i) * rmask(j,i,sr)
469	sums_l(k,8,tn) = sums_l(k,8,tn) + e(k,j,i) * rmask(j,i,sr)
470	sums_l(k,9,tn) = sums_l(k,9,tn) + km(k,j,i) * rmask(j,i,sr)
471	sums_l(k,10,tn) = sums_l(k,10,tn) + kh(k,j,i) * rmask(j,i,sr)
472	sums_l(k,40,tn) = sums_l(k,40,tn) + p(k,j,i)
473
474	sums_l(k,33,tn) = sums_l(k,33,tn) + &
475	( pt(k,j,i)-hom(k,1,4,sr) )*2 rmask(j,i,sr)
476
477	IF ( humidity ) THEN
478	sums_l(k,70,tn) = sums_l(k,70,tn) + &
479	( q(k,j,i)-hom(k,1,41,sr) )*2 rmask(j,i,sr)
480	ENDIF
481
482	!
483	!-- Higher moments
484	!-- (Computation of the skewness of w further below)
485	sums_l(k,38,tn) = sums_l(k,38,tn) + w(k,j,i)*3 rmask(j,i,sr)
486
487	sums_l_etot = sums_l_etot + &
488	0.5 * ( u(k,j,i)2 + v(k,j,i)2 + &
489	w(k,j,i)*2 ) rmask(j,i,sr)
490	ENDDO
491	!
492	!-- Total and perturbation energy for the total domain (being
493	!-- collected in the last column of sums_l). Summation of these
494	!-- quantities is seperated from the previous loop in order to
495	!-- allow vectorization of that loop.
496	sums_l(nzb+4,pr_palm,tn) = sums_l(nzb+4,pr_palm,tn) + sums_l_etot
497	!
498	!-- 2D-arrays (being collected in the last column of sums_l)
499	sums_l(nzb,pr_palm,tn) = sums_l(nzb,pr_palm,tn) + &
500	us(j,i) * rmask(j,i,sr)
501	sums_l(nzb+1,pr_palm,tn) = sums_l(nzb+1,pr_palm,tn) + &
502	usws(j,i) * rmask(j,i,sr)
503	sums_l(nzb+2,pr_palm,tn) = sums_l(nzb+2,pr_palm,tn) + &
504	vsws(j,i) * rmask(j,i,sr)
505	sums_l(nzb+3,pr_palm,tn) = sums_l(nzb+3,pr_palm,tn) + &
506	ts(j,i) * rmask(j,i,sr)
507	IF ( humidity ) THEN
508	sums_l(nzb+12,pr_palm,tn) = sums_l(nzb+12,pr_palm,tn) + &
509	qs(j,i) * rmask(j,i,sr)
510	ENDIF
511	ENDDO
512	ENDDO
513
514	!
515	!-- Computation of statistics when ws-scheme is not used. Else these
516	!-- quantities are evaluated in the advection routines.
517	IF ( .NOT. ws_scheme_mom .OR. sr /= 0 ) THEN
518	!$OMP DO
519	DO i = nxl, nxr
520	DO j = nys, nyn
521	sums_l_eper = 0.0
522	DO k = nzb_s_inner(j,i), nzt+1
523	u2 = u(k,j,i)**2
524	v2 = v(k,j,i)**2
525	w2 = w(k,j,i)**2
526	ust2 = ( u(k,j,i) - hom(k,1,1,sr) )**2
527	vst2 = ( v(k,j,i) - hom(k,1,2,sr) )**2
528
529	sums_l(k,30,tn) = sums_l(k,30,tn) + ust2 * rmask(j,i,sr)
530	sums_l(k,31,tn) = sums_l(k,31,tn) + vst2 * rmask(j,i,sr)
531	sums_l(k,32,tn) = sums_l(k,32,tn) + w2 * rmask(j,i,sr)
532	!
533	!-- Perturbation energy
534
535	sums_l(k,34,tn) = sums_l(k,34,tn) + 0.5 * &
536	( ust2 + vst2 + w2 ) * rmask(j,i,sr)
537	sums_l_eper = sums_l_eper + &
538	0.5 * ( ust2+vst2+w2 ) * rmask(j,i,sr)
539
540	ENDDO
541	sums_l(nzb+5,pr_palm,tn) = sums_l(nzb+5,pr_palm,tn) &
542	+ sums_l_eper
543	ENDDO
544	ENDDO
545	ENDIF
546	!
547	!-- Horizontally averaged profiles of the vertical fluxes
548
549	!$OMP DO
550	DO i = nxl, nxr
551	DO j = nys, nyn
552	!
553	!-- Subgridscale fluxes (without Prandtl layer from k=nzb,
554	!-- oterwise from k=nzb+1)
555	!-- NOTE: for simplicity, nzb_diff_s_inner is used below, although
556	!-- ---- strictly speaking the following k-loop would have to be
557	!-- split up according to the staggered grid.
558	!-- However, this implies no error since staggered velocity
559	!-- components are zero at the walls and inside buildings.
560
561	DO k = nzb_diff_s_inner(j,i)-1, nzt_diff
562	!
563	!-- Momentum flux w"u"
564	sums_l(k,12,tn) = sums_l(k,12,tn) - 0.25 * ( &
565	km(k,j,i)+km(k+1,j,i)+km(k,j,i-1)+km(k+1,j,i-1) &
566	) * ( &
567	( u(k+1,j,i) - u(k,j,i) ) * ddzu(k+1) &
568	+ ( w(k,j,i) - w(k,j,i-1) ) * ddx &
569	) * rmask(j,i,sr)
570	!
571	!-- Momentum flux w"v"
572	sums_l(k,14,tn) = sums_l(k,14,tn) - 0.25 * ( &
573	km(k,j,i)+km(k+1,j,i)+km(k,j-1,i)+km(k+1,j-1,i) &
574	) * ( &
575	( v(k+1,j,i) - v(k,j,i) ) * ddzu(k+1) &
576	+ ( w(k,j,i) - w(k,j-1,i) ) * ddy &
577	) * rmask(j,i,sr)
578	!
579	!-- Heat flux w"pt"
580	sums_l(k,16,tn) = sums_l(k,16,tn) &
581	- 0.5 * ( kh(k,j,i) + kh(k+1,j,i) ) &
582	* ( pt(k+1,j,i) - pt(k,j,i) ) &
583	* ddzu(k+1) * rmask(j,i,sr)
584
585
586	!
587	!-- Salinity flux w"sa"
588	IF ( ocean ) THEN
589	sums_l(k,65,tn) = sums_l(k,65,tn) &
590	- 0.5 * ( kh(k,j,i) + kh(k+1,j,i) ) &
591	* ( sa(k+1,j,i) - sa(k,j,i) ) &
592	* ddzu(k+1) * rmask(j,i,sr)
593	ENDIF
594
595	!
596	!-- Buoyancy flux, water flux (humidity flux) w"q"
597	IF ( humidity ) THEN
598	sums_l(k,45,tn) = sums_l(k,45,tn) &
599	- 0.5 * ( kh(k,j,i) + kh(k+1,j,i) ) &
600	* ( vpt(k+1,j,i) - vpt(k,j,i) ) &
601	* ddzu(k+1) * rmask(j,i,sr)
602	sums_l(k,48,tn) = sums_l(k,48,tn) &
603	- 0.5 * ( kh(k,j,i) + kh(k+1,j,i) ) &
604	* ( q(k+1,j,i) - q(k,j,i) ) &
605	* ddzu(k+1) * rmask(j,i,sr)
606
607	IF ( cloud_physics ) THEN
608	sums_l(k,51,tn) = sums_l(k,51,tn) &
609	- 0.5 * ( kh(k,j,i) + kh(k+1,j,i) ) &
610	* ( ( q(k+1,j,i) - ql(k+1,j,i) )&
611	- ( q(k,j,i) - ql(k,j,i) ) ) &
612	* ddzu(k+1) * rmask(j,i,sr)
613	ENDIF
614	ENDIF
615
616	!
617	!-- Passive scalar flux
618	IF ( passive_scalar ) THEN
619	sums_l(k,48,tn) = sums_l(k,48,tn) &
620	- 0.5 * ( kh(k,j,i) + kh(k+1,j,i) ) &
621	* ( q(k+1,j,i) - q(k,j,i) ) &
622	* ddzu(k+1) * rmask(j,i,sr)
623	ENDIF
624
625	ENDDO
626
627	!
628	!-- Subgridscale fluxes in the Prandtl layer
629	IF ( use_surface_fluxes ) THEN
630	sums_l(nzb,12,tn) = sums_l(nzb,12,tn) + &
631	usws(j,i) * rmask(j,i,sr) ! w"u"
632	sums_l(nzb,14,tn) = sums_l(nzb,14,tn) + &
633	vsws(j,i) * rmask(j,i,sr) ! w"v"
634	sums_l(nzb,16,tn) = sums_l(nzb,16,tn) + &
635	shf(j,i) * rmask(j,i,sr) ! w"pt"
636	sums_l(nzb,58,tn) = sums_l(nzb,58,tn) + &
637	0.0 * rmask(j,i,sr) ! u"pt"
638	sums_l(nzb,61,tn) = sums_l(nzb,61,tn) + &
639	0.0 * rmask(j,i,sr) ! v"pt"
640	IF ( ocean ) THEN
641	sums_l(nzb,65,tn) = sums_l(nzb,65,tn) + &
642	saswsb(j,i) * rmask(j,i,sr) ! w"sa"
643	ENDIF
644	IF ( humidity ) THEN
645	sums_l(nzb,48,tn) = sums_l(nzb,48,tn) + &
646	qsws(j,i) * rmask(j,i,sr) ! w"q" (w"qv")
647	sums_l(nzb,45,tn) = sums_l(nzb,45,tn) + ( &
648	( 1.0 + 0.61 * q(nzb,j,i) ) * &
649	shf(j,i) + 0.61 * pt(nzb,j,i) * &
650	qsws(j,i) )
651	IF ( cloud_droplets ) THEN
652	sums_l(nzb,45,tn) = sums_l(nzb,45,tn) + ( &
653	( 1.0 + 0.61 * q(nzb,j,i) - &
654	ql(nzb,j,i) ) * shf(j,i) + &
655	0.61 * pt(nzb,j,i) * qsws(j,i) )
656	ENDIF
657	IF ( cloud_physics ) THEN
658	!
659	!-- Formula does not work if ql(nzb) /= 0.0
660	sums_l(nzb,51,tn) = sums_l(nzb,51,tn) + & ! w"q" (w"qv")
661	qsws(j,i) * rmask(j,i,sr)
662	ENDIF
663	ENDIF
664	IF ( passive_scalar ) THEN
665	sums_l(nzb,48,tn) = sums_l(nzb,48,tn) + &
666	qsws(j,i) * rmask(j,i,sr) ! w"q" (w"qv")
667	ENDIF
668	ENDIF
669
670	!
671	!-- Subgridscale fluxes at the top surface
672	IF ( use_top_fluxes ) THEN
673	sums_l(nzt:nzt+1,12,tn) = sums_l(nzt:nzt+1,12,tn) + &
674	uswst(j,i) * rmask(j,i,sr) ! w"u"
675	sums_l(nzt:nzt+1,14,tn) = sums_l(nzt:nzt+1,14,tn) + &
676	vswst(j,i) * rmask(j,i,sr) ! w"v"
677	sums_l(nzt:nzt+1,16,tn) = sums_l(nzt:nzt+1,16,tn) + &
678	tswst(j,i) * rmask(j,i,sr) ! w"pt"
679	sums_l(nzt:nzt+1,58,tn) = sums_l(nzt:nzt+1,58,tn) + &
680	0.0 * rmask(j,i,sr) ! u"pt"
681	sums_l(nzt:nzt+1,61,tn) = sums_l(nzt:nzt+1,61,tn) + &
682	0.0 * rmask(j,i,sr) ! v"pt"
683
684	IF ( ocean ) THEN
685	sums_l(nzt,65,tn) = sums_l(nzt,65,tn) + &
686	saswst(j,i) * rmask(j,i,sr) ! w"sa"
687	ENDIF
688	IF ( humidity ) THEN
689	sums_l(nzt,48,tn) = sums_l(nzt,48,tn) + &
690	qswst(j,i) * rmask(j,i,sr) ! w"q" (w"qv")
691	sums_l(nzt,45,tn) = sums_l(nzt,45,tn) + ( &
692	( 1.0 + 0.61 * q(nzt,j,i) ) * &
693	tswst(j,i) + 0.61 * pt(nzt,j,i) * &
694	qswst(j,i) )
695	IF ( cloud_droplets ) THEN
696	sums_l(nzt,45,tn) = sums_l(nzt,45,tn) + ( &
697	( 1.0 + 0.61 * q(nzt,j,i) - &
698	ql(nzt,j,i) ) * tswst(j,i) + &
699	0.61 * pt(nzt,j,i) * qswst(j,i) )
700	ENDIF
701	IF ( cloud_physics ) THEN
702	!
703	!-- Formula does not work if ql(nzb) /= 0.0
704	sums_l(nzt,51,tn) = sums_l(nzt,51,tn) + & ! w"q" (w"qv")
705	qswst(j,i) * rmask(j,i,sr)
706	ENDIF
707	ENDIF
708	IF ( passive_scalar ) THEN
709	sums_l(nzt,48,tn) = sums_l(nzt,48,tn) + &
710	qswst(j,i) * rmask(j,i,sr) ! w"q" (w"qv")
711	ENDIF
712	ENDIF
713
714	!
715	!-- Resolved fluxes (can be computed for all horizontal points)
716	!-- NOTE: for simplicity, nzb_s_inner is used below, although strictly
717	!-- ---- speaking the following k-loop would have to be split up and
718	!-- rearranged according to the staggered grid.
719	DO k = nzb_s_inner(j,i), nzt
720	ust = 0.5 * ( u(k,j,i) - hom(k,1,1,sr) + &
721	u(k+1,j,i) - hom(k+1,1,1,sr) )
722	vst = 0.5 * ( v(k,j,i) - hom(k,1,2,sr) + &
723	v(k+1,j,i) - hom(k+1,1,2,sr) )
724	pts = 0.5 * ( pt(k,j,i) - hom(k,1,4,sr) + &
725	pt(k+1,j,i) - hom(k+1,1,4,sr) )
726
727	!-- Higher moments
728	sums_l(k,35,tn) = sums_l(k,35,tn) + pts * w(k,j,i)*2 &
729	rmask(j,i,sr)
730	sums_l(k,36,tn) = sums_l(k,36,tn) + pts*2 w(k,j,i) * &
731	rmask(j,i,sr)
732
733	!
734	!-- Salinity flux and density (density does not belong to here,
735	!-- but so far there is no other suitable place to calculate)
736	IF ( ocean ) THEN
737	IF( .NOT. ws_scheme_sca .OR. sr /= 0 ) THEN
738	pts = 0.5 * ( sa(k,j,i) - hom(k,1,23,sr) + &
739	sa(k+1,j,i) - hom(k+1,1,23,sr) )
740	sums_l(k,66,tn) = sums_l(k,66,tn) + pts * w(k,j,i) * &
741	rmask(j,i,sr)
742	ENDIF
743	sums_l(k,64,tn) = sums_l(k,64,tn) + rho(k,j,i) * &
744	rmask(j,i,sr)
745	sums_l(k,71,tn) = sums_l(k,71,tn) + prho(k,j,i) * &
746	rmask(j,i,sr)
747	ENDIF
748
749	!
750	!-- Buoyancy flux, water flux, humidity flux and liquid water
751	!-- content
752	IF ( humidity ) THEN
753	IF ( cloud_physics .OR. cloud_droplets ) THEN
754	pts = 0.5 * ( vpt(k,j,i) - hom(k,1,44,sr) + &
755	vpt(k+1,j,i) - hom(k+1,1,44,sr) )
756	sums_l(k,46,tn) = sums_l(k,46,tn) + pts * w(k,j,i) * &
757	rmask(j,i,sr)
758	sums_l(k,54,tn) = sums_l(k,54,tn) + ql(k,j,i) * &
759	rmask(j,i,sr)
760	ELSE
761	IF( .NOT. ws_scheme_sca .OR. sr /= 0 ) THEN
762	pts = 0.5 * ( vpt(k,j,i) - hom(k,1,44,sr) + &
763	vpt(k+1,j,i) - hom(k+1,1,44,sr) )
764	sums_l(k,46,tn) = sums_l(k,46,tn) + pts * w(k,j,i) * &
765	rmask(j,i,sr)
766	ELSE IF ( ws_scheme_sca .AND. sr == 0 ) THEN
767	sums_l(k,46,tn) = ( 1.0 + 0.61 * hom(k,1,41,sr) ) * &
768	sums_l(k,17,tn) + &
769	0.61 * hom(k,1,4,sr) * sums_l(k,49,tn)
770	END IF
771	END IF
772	ENDIF
773	!
774	!-- Passive scalar flux
775	IF ( passive_scalar .AND. ( .NOT. ws_scheme_sca &
776	.OR. sr /= 0 ) ) THEN
777	pts = 0.5 * ( q(k,j,i) - hom(k,1,41,sr) + &
778	q(k+1,j,i) - hom(k+1,1,41,sr) )
779	sums_l(k,49,tn) = sums_l(k,49,tn) + pts * w(k,j,i) * &
780	rmask(j,i,sr)
781	ENDIF
782
783	!
784	!-- Energy flux we
785	!-- has to be adjusted
786	sums_l(k,37,tn) = sums_l(k,37,tn) + w(k,j,i) * 0.5 * &
787	( ust2 + vst2 + w(k,j,i)**2 )&
788	* rmask(j,i,sr)
789	ENDDO
790	ENDDO
791	ENDDO
792	!
793	!-- For speed optimization fluxes which have been computed in part directly
794	!-- inside the WS advection routines are treated seperatly
795	!-- Momentum fluxes first:
796	IF ( .NOT. ws_scheme_mom .OR. sr /= 0 ) THEN
797	!$OMP DO
798	DO i = nxl, nxr
799	DO j = nys, nyn
800	DO k = nzb_diff_s_inner(j,i)-1, nzt_diff
801	ust = 0.5 * ( u(k,j,i) - hom(k,1,1,sr) + &
802	u(k+1,j,i) - hom(k+1,1,1,sr) )
803	vst = 0.5 * ( v(k,j,i) - hom(k,1,2,sr) + &
804	v(k+1,j,i) - hom(k+1,1,2,sr) )
805	!
806	!-- Momentum flux wu
807	sums_l(k,13,tn) = sums_l(k,13,tn) + 0.5 * &
808	( w(k,j,i-1) + w(k,j,i) ) &
809	* ust * rmask(j,i,sr)
810	!
811	!-- Momentum flux wv
812	sums_l(k,15,tn) = sums_l(k,15,tn) + 0.5 * &
813	( w(k,j-1,i) + w(k,j,i) ) &
814	* vst * rmask(j,i,sr)
815	ENDDO
816	ENDDO
817	ENDDO
818
819	ENDIF
820	IF ( .NOT. ws_scheme_sca .OR. sr /= 0 ) THEN
821	!$OMP DO
822	DO i = nxl, nxr
823	DO j = nys, nyn
824	DO k = nzb_diff_s_inner(j,i)-1, nzt_diff
825	!
826	!-- Vertical heat flux
827	sums_l(k,17,tn) = sums_l(k,17,tn) + 0.5 * &
828	( pt(k,j,i) - hom(k,1,4,sr) + &
829	pt(k+1,j,i) - hom(k+1,1,4,sr) ) &
830	* w(k,j,i) * rmask(j,i,sr)
831	IF ( humidity ) THEN
832	pts = 0.5 * ( q(k,j,i) - hom(k,1,41,sr) + &
833	q(k+1,j,i) - hom(k+1,1,41,sr) )
834	sums_l(k,49,tn) = sums_l(k,49,tn) + pts * w(k,j,i) * &
835	rmask(j,i,sr)
836	ENDIF
837	ENDDO
838	ENDDO
839	ENDDO
840
841	ENDIF
842
843
844	!
845	!-- Density at top follows Neumann condition
846	IF ( ocean ) THEN
847	sums_l(nzt+1,64,tn) = sums_l(nzt,64,tn)
848	sums_l(nzt+1,71,tn) = sums_l(nzt,71,tn)
849	ENDIF
850
851	!
852	!-- Divergence of vertical flux of resolved scale energy and pressure
853	!-- fluctuations as well as flux of pressure fluctuation itself (68).
854	!-- First calculate the products, then the divergence.
855	!-- Calculation is time consuming. Do it only, if profiles shall be plotted.
856	IF ( hom(nzb+1,2,55,0) /= 0.0 .OR. hom(nzb+1,2,68,0) /= 0.0 ) THEN
857
858	sums_ll = 0.0 ! local array
859
860	!$OMP DO
861	DO i = nxl, nxr
862	DO j = nys, nyn
863	DO k = nzb_s_inner(j,i)+1, nzt
864
865	sums_ll(k,1) = sums_ll(k,1) + 0.5 * w(k,j,i) * ( &
866	( 0.25 * ( u(k,j,i)+u(k+1,j,i)+u(k,j,i+1)+u(k+1,j,i+1) &
867	- 0.5 * ( hom(k,1,1,sr) + hom(k+1,1,1,sr) ) &
868	) )**2 &
869	+ ( 0.25 * ( v(k,j,i)+v(k+1,j,i)+v(k,j+1,i)+v(k+1,j+1,i) &
870	- 0.5 * ( hom(k,1,2,sr) + hom(k+1,1,2,sr) ) &
871	) )**2 &
872	+ w(k,j,i)**2 )
873
874	sums_ll(k,2) = sums_ll(k,2) + 0.5 * w(k,j,i) &
875	* ( p(k,j,i) + p(k+1,j,i) )
876
877	ENDDO
878	ENDDO
879	ENDDO
880	sums_ll(0,1) = 0.0 ! because w is zero at the bottom
881	sums_ll(nzt+1,1) = 0.0
882	sums_ll(0,2) = 0.0
883	sums_ll(nzt+1,2) = 0.0
884
885	DO k = nzb+1, nzt
886	sums_l(k,55,tn) = ( sums_ll(k,1) - sums_ll(k-1,1) ) * ddzw(k)
887	sums_l(k,56,tn) = ( sums_ll(k,2) - sums_ll(k-1,2) ) * ddzw(k)
888	sums_l(k,68,tn) = sums_ll(k,2)
889	ENDDO
890	sums_l(nzb,55,tn) = sums_l(nzb+1,55,tn)
891	sums_l(nzb,56,tn) = sums_l(nzb+1,56,tn)
892	sums_l(nzb,68,tn) = 0.0 ! because w* = 0 at nzb
893
894	ENDIF
895
896	!
897	!-- Divergence of vertical flux of SGS TKE and the flux itself (69)
898	IF ( hom(nzb+1,2,57,0) /= 0.0 .OR. hom(nzb+1,2,69,0) /= 0.0 ) THEN
899
900	!$OMP DO
901	DO i = nxl, nxr
902	DO j = nys, nyn
903	DO k = nzb_s_inner(j,i)+1, nzt
904
905	sums_l(k,57,tn) = sums_l(k,57,tn) - 0.5 * ( &
906	(km(k,j,i)+km(k+1,j,i)) * (e(k+1,j,i)-e(k,j,i)) * ddzu(k+1) &
907	- (km(k-1,j,i)+km(k,j,i)) * (e(k,j,i)-e(k-1,j,i)) * ddzu(k) &
908	) * ddzw(k)
909
910	sums_l(k,69,tn) = sums_l(k,69,tn) - 0.5 * ( &
911	(km(k,j,i)+km(k+1,j,i)) * (e(k+1,j,i)-e(k,j,i)) * ddzu(k+1) &
912	)
913
914	ENDDO
915	ENDDO
916	ENDDO
917	sums_l(nzb,57,tn) = sums_l(nzb+1,57,tn)
918	sums_l(nzb,69,tn) = sums_l(nzb+1,69,tn)
919
920	ENDIF
921
922	!
923	!-- Horizontal heat fluxes (subgrid, resolved, total).
924	!-- Do it only, if profiles shall be plotted.
925	IF ( hom(nzb+1,2,58,0) /= 0.0 ) THEN
926
927	!$OMP DO
928	DO i = nxl, nxr
929	DO j = nys, nyn
930	DO k = nzb_s_inner(j,i)+1, nzt
931	!
932	!-- Subgrid horizontal heat fluxes u"pt", v"pt"
933	sums_l(k,58,tn) = sums_l(k,58,tn) - 0.5 * &
934	( kh(k,j,i) + kh(k,j,i-1) ) &
935	* ( pt(k,j,i-1) - pt(k,j,i) ) &
936	* ddx * rmask(j,i,sr)
937	sums_l(k,61,tn) = sums_l(k,61,tn) - 0.5 * &
938	( kh(k,j,i) + kh(k,j-1,i) ) &
939	* ( pt(k,j-1,i) - pt(k,j,i) ) &
940	* ddy * rmask(j,i,sr)
941	!
942	!-- Resolved horizontal heat fluxes upt, vpt
943	sums_l(k,59,tn) = sums_l(k,59,tn) + &
944	( u(k,j,i) - hom(k,1,1,sr) ) &
945	* 0.5 * ( pt(k,j,i-1) - hom(k,1,4,sr) + &
946	pt(k,j,i) - hom(k,1,4,sr) )
947	pts = 0.5 * ( pt(k,j-1,i) - hom(k,1,4,sr) + &
948	pt(k,j,i) - hom(k,1,4,sr) )
949	sums_l(k,62,tn) = sums_l(k,62,tn) + &
950	( v(k,j,i) - hom(k,1,2,sr) ) &
951	* 0.5 * ( pt(k,j-1,i) - hom(k,1,4,sr) + &
952	pt(k,j,i) - hom(k,1,4,sr) )
953	ENDDO
954	ENDDO
955	ENDDO
956	!
957	!-- Fluxes at the surface must be zero (e.g. due to the Prandtl-layer)
958	sums_l(nzb,58,tn) = 0.0
959	sums_l(nzb,59,tn) = 0.0
960	sums_l(nzb,60,tn) = 0.0
961	sums_l(nzb,61,tn) = 0.0
962	sums_l(nzb,62,tn) = 0.0
963	sums_l(nzb,63,tn) = 0.0
964
965	ENDIF
966
967	!
968	!-- Calculate the user-defined profiles
969	CALL user_statistics( 'profiles', sr, tn )
970	!$OMP END PARALLEL
971
972	!
973	!-- Summation of thread sums
974	IF ( threads_per_task > 1 ) THEN
975	DO i = 1, threads_per_task-1
976	sums_l(:,3,0) = sums_l(:,3,0) + sums_l(:,3,i)
977	sums_l(:,4:40,0) = sums_l(:,4:40,0) + sums_l(:,4:40,i)
978	sums_l(:,45:pr_palm,0) = sums_l(:,45:pr_palm,0) + &
979	sums_l(:,45:pr_palm,i)
980	IF ( max_pr_user > 0 ) THEN
981	sums_l(:,pr_palm+1:pr_palm+max_pr_user,0) = &
982	sums_l(:,pr_palm+1:pr_palm+max_pr_user,0) + &
983	sums_l(:,pr_palm+1:pr_palm+max_pr_user,i)
984	ENDIF
985	ENDDO
986	ENDIF
987
988	#if defined( __parallel )
989
990	!
991	!-- Compute total sum from local sums
992	IF ( collective_wait ) CALL MPI_BARRIER( comm2d, ierr )
993	CALL MPI_ALLREDUCE( sums_l(nzb,1,0), sums(nzb,1), ngp_sums, MPI_REAL, &
994	MPI_SUM, comm2d, ierr )
995	#else
996	sums = sums_l(:,:,0)
997	#endif
998
999	!
1000	!-- Final values are obtained by division by the total number of grid points
1001	!-- used for summation. After that store profiles.
1002	!-- Profiles:
1003	DO k = nzb, nzt+1
1004	sums(k,3) = sums(k,3) / ngp_2dh(sr)
1005	sums(k,8:11) = sums(k,8:11) / ngp_2dh_s_inner(k,sr)
1006	sums(k,12:22) = sums(k,12:22) / ngp_2dh(sr)
1007	sums(k,23:29) = sums(k,23:29) / ngp_2dh_s_inner(k,sr)
1008	sums(k,30:32) = sums(k,30:32) / ngp_2dh(sr)
1009	sums(k,33:34) = sums(k,33:34) / ngp_2dh_s_inner(k,sr)
1010	sums(k,35:39) = sums(k,35:39) / ngp_2dh(sr)
1011	sums(k,40) = sums(k,40) / ngp_2dh_s_inner(k,sr)
1012	sums(k,45:53) = sums(k,45:53) / ngp_2dh(sr)
1013	sums(k,54) = sums(k,54) / ngp_2dh_s_inner(k,sr)
1014	sums(k,55:63) = sums(k,55:63) / ngp_2dh(sr)
1015	sums(k,64) = sums(k,64) / ngp_2dh_s_inner(k,sr)
1016	sums(k,65:69) = sums(k,65:69) / ngp_2dh(sr)
1017	sums(k,70:pr_palm-2) = sums(k,70:pr_palm-2)/ ngp_2dh_s_inner(k,sr)
1018	ENDDO
1019
1020	!-- Upstream-parts
1021	sums(nzb:nzb+11,pr_palm-1) = sums(nzb:nzb+11,pr_palm-1) / ngp_3d(sr)
1022	!-- u* and so on
1023	!-- As sums(nzb:nzb+3,pr_palm) are full 2D arrays (us, usws, vsws, ts) whose
1024	!-- size is always ( nx + 1 ) * ( ny + 1 ), defined at the first grid layer
1025	!-- above the topography, they are being divided by ngp_2dh(sr)
1026	sums(nzb:nzb+3,pr_palm) = sums(nzb:nzb+3,pr_palm) / &
1027	ngp_2dh(sr)
1028	sums(nzb+12,pr_palm) = sums(nzb+12,pr_palm) / & ! qs
1029	ngp_2dh(sr)
1030	!-- eges, e*
1031	sums(nzb+4:nzb+5,pr_palm) = sums(nzb+4:nzb+5,pr_palm) / &
1032	ngp_3d(sr)
1033	!-- Old and new divergence
1034	sums(nzb+9:nzb+10,pr_palm) = sums(nzb+9:nzb+10,pr_palm) / &
1035	ngp_3d_inner(sr)
1036
1037	!-- User-defined profiles
1038	IF ( max_pr_user > 0 ) THEN
1039	DO k = nzb, nzt+1
1040	sums(k,pr_palm+1:pr_palm+max_pr_user) = &
1041	sums(k,pr_palm+1:pr_palm+max_pr_user) / &
1042	ngp_2dh_s_inner(k,sr)
1043	ENDDO
1044	ENDIF
1045
1046	!
1047	!-- Collect horizontal average in hom.
1048	!-- Compute deduced averages (e.g. total heat flux)
1049	hom(:,1,3,sr) = sums(:,3) ! w
1050	hom(:,1,8,sr) = sums(:,8) ! e profiles 5-7 are initial profiles
1051	hom(:,1,9,sr) = sums(:,9) ! km
1052	hom(:,1,10,sr) = sums(:,10) ! kh
1053	hom(:,1,11,sr) = sums(:,11) ! l
1054	hom(:,1,12,sr) = sums(:,12) ! w"u"
1055	hom(:,1,13,sr) = sums(:,13) ! wu
1056	hom(:,1,14,sr) = sums(:,14) ! w"v"
1057	hom(:,1,15,sr) = sums(:,15) ! wv
1058	hom(:,1,16,sr) = sums(:,16) ! w"pt"
1059	hom(:,1,17,sr) = sums(:,17) ! wpt
1060	hom(:,1,18,sr) = sums(:,16) + sums(:,17) ! wpt
1061	hom(:,1,19,sr) = sums(:,12) + sums(:,13) ! wu
1062	hom(:,1,20,sr) = sums(:,14) + sums(:,15) ! wv
1063	hom(:,1,21,sr) = sums(:,21) ! wptBC
1064	hom(:,1,22,sr) = sums(:,16) + sums(:,21) ! wptBC
1065	! profile 24 is initial profile (sa)
1066	! profiles 25-29 left empty for initial
1067	! profiles
1068	hom(:,1,30,sr) = sums(:,30) ! u*2
1069	hom(:,1,31,sr) = sums(:,31) ! v*2
1070	hom(:,1,32,sr) = sums(:,32) ! w*2
1071	hom(:,1,33,sr) = sums(:,33) ! pt*2
1072	hom(:,1,34,sr) = sums(:,34) ! e*
1073	hom(:,1,35,sr) = sums(:,35) ! w2pt
1074	hom(:,1,36,sr) = sums(:,36) ! wpt2
1075	hom(:,1,37,sr) = sums(:,37) ! we
1076	hom(:,1,38,sr) = sums(:,38) ! w*3
1077	hom(:,1,39,sr) = sums(:,38) / ( abs( sums(:,32) ) + 1E-20 )**1.5 ! Sw
1078	hom(:,1,40,sr) = sums(:,40) ! p
1079	hom(:,1,45,sr) = sums(:,45) ! w"vpt"
1080	hom(:,1,46,sr) = sums(:,46) ! wvpt
1081	hom(:,1,47,sr) = sums(:,45) + sums(:,46) ! wvpt
1082	hom(:,1,48,sr) = sums(:,48) ! w"q" (w"qv")
1083	hom(:,1,49,sr) = sums(:,49) ! wq (wqv)
1084	hom(:,1,50,sr) = sums(:,48) + sums(:,49) ! wq (wqv)
1085	hom(:,1,51,sr) = sums(:,51) ! w"qv"
1086	hom(:,1,52,sr) = sums(:,52) ! wqv
1087	hom(:,1,53,sr) = sums(:,52) + sums(:,51) ! wq (wqv)
1088	hom(:,1,54,sr) = sums(:,54) ! ql
1089	hom(:,1,55,sr) = sums(:,55) ! wuu*/dz
1090	hom(:,1,56,sr) = sums(:,56) ! wp/dz
1091	hom(:,1,57,sr) = sums(:,57) ! ( w"e + w"p"/rho )/dz
1092	hom(:,1,58,sr) = sums(:,58) ! u"pt"
1093	hom(:,1,59,sr) = sums(:,59) ! upt
1094	hom(:,1,60,sr) = sums(:,58) + sums(:,59) ! upt_t
1095	hom(:,1,61,sr) = sums(:,61) ! v"pt"
1096	hom(:,1,62,sr) = sums(:,62) ! vpt
1097	hom(:,1,63,sr) = sums(:,61) + sums(:,62) ! vpt_t
1098	hom(:,1,64,sr) = sums(:,64) ! rho
1099	hom(:,1,65,sr) = sums(:,65) ! w"sa"
1100	hom(:,1,66,sr) = sums(:,66) ! wsa
1101	hom(:,1,67,sr) = sums(:,65) + sums(:,66) ! wsa
1102	hom(:,1,68,sr) = sums(:,68) ! wp
1103	hom(:,1,69,sr) = sums(:,69) ! w"e + w"p"/rho
1104	hom(:,1,70,sr) = sums(:,70) ! q*2
1105	hom(:,1,71,sr) = sums(:,71) ! prho
1106	hom(:,1,72,sr) = hyp * 1E-4 ! hyp in dbar
1107
1108	hom(:,1,pr_palm-1,sr) = sums(:,pr_palm-1)
1109	! upstream-parts u_x, u_y, u_z, v_x,
1110	! v_y, usw. (in last but one profile)
1111	hom(:,1,pr_palm,sr) = sums(:,pr_palm)
1112	! u, w'u', w'v', t (in last profile)
1113
1114	IF ( max_pr_user > 0 ) THEN ! user-defined profiles
1115	hom(:,1,pr_palm+1:pr_palm+max_pr_user,sr) = &
1116	sums(:,pr_palm+1:pr_palm+max_pr_user)
1117	ENDIF
1118
1119	!
1120	!-- Determine the boundary layer height using two different schemes.
1121	!-- First scheme: Starting from the Earth's (Ocean's) surface, look for the
1122	!-- first relative minimum (maximum) of the total heat flux.
1123	!-- The corresponding height is assumed as the boundary layer height, if it
1124	!-- is less than 1.5 times the height where the heat flux becomes negative
1125	!-- (positive) for the first time.
1126	z_i(1) = 0.0
1127	first = .TRUE.
1128
1129	IF ( ocean ) THEN
1130	DO k = nzt, nzb+1, -1
1131	IF ( first .AND. hom(k,1,18,sr) < 0.0 &
1132	.AND. abs(hom(k,1,18,sr)) > 1.0E-8) THEN
1133	first = .FALSE.
1134	height = zw(k)
1135	ENDIF
1136	IF ( hom(k,1,18,sr) < 0.0 .AND. &
1137	abs(hom(k,1,18,sr)) > 1.0E-8 .AND. &
1138	hom(k-1,1,18,sr) > hom(k,1,18,sr) ) THEN
1139	IF ( zw(k) < 1.5 * height ) THEN
1140	z_i(1) = zw(k)
1141	ELSE
1142	z_i(1) = height
1143	ENDIF
1144	EXIT
1145	ENDIF
1146	ENDDO
1147	ELSE
1148	DO k = nzb, nzt-1
1149	IF ( first .AND. hom(k,1,18,sr) < 0.0 &
1150	.AND. abs(hom(k,1,18,sr)) > 1.0E-8 ) THEN
1151	first = .FALSE.
1152	height = zw(k)
1153	ENDIF
1154	IF ( hom(k,1,18,sr) < 0.0 .AND. &
1155	abs(hom(k,1,18,sr)) > 1.0E-8 .AND. &
1156	hom(k+1,1,18,sr) > hom(k,1,18,sr) ) THEN
1157	IF ( zw(k) < 1.5 * height ) THEN
1158	z_i(1) = zw(k)
1159	ELSE
1160	z_i(1) = height
1161	ENDIF
1162	EXIT
1163	ENDIF
1164	ENDDO
1165	ENDIF
1166
1167	!
1168	!-- Second scheme: Gradient scheme from Sullivan et al. (1998), modified
1169	!-- by Uhlenbrock(2006). The boundary layer height is the height with the
1170	!-- maximal local temperature gradient: starting from the second (the last
1171	!-- but one) vertical gridpoint, the local gradient must be at least
1172	!-- 0.2K/100m and greater than the next four gradients.
1173	!-- WARNING: The threshold value of 0.2K/100m must be adjusted for the
1174	!-- ocean case!
1175	z_i(2) = 0.0
1176	DO k = nzb+1, nzt+1
1177	dptdz(k) = ( hom(k,1,4,sr) - hom(k-1,1,4,sr) ) * ddzu(k)
1178	ENDDO
1179	dptdz_threshold = 0.2 / 100.0
1180
1181	IF ( ocean ) THEN
1182	DO k = nzt+1, nzb+5, -1
1183	IF ( dptdz(k) > dptdz_threshold .AND. &
1184	dptdz(k) > dptdz(k-1) .AND. dptdz(k) > dptdz(k-2) .AND. &
1185	dptdz(k) > dptdz(k-3) .AND. dptdz(k) > dptdz(k-4) ) THEN
1186	z_i(2) = zw(k-1)
1187	EXIT
1188	ENDIF
1189	ENDDO
1190	ELSE
1191	DO k = nzb+1, nzt-3
1192	IF ( dptdz(k) > dptdz_threshold .AND. &
1193	dptdz(k) > dptdz(k+1) .AND. dptdz(k) > dptdz(k+2) .AND. &
1194	dptdz(k) > dptdz(k+3) .AND. dptdz(k) > dptdz(k+4) ) THEN
1195	z_i(2) = zw(k-1)
1196	EXIT
1197	ENDIF
1198	ENDDO
1199	ENDIF
1200
1201	hom(nzb+6,1,pr_palm,sr) = z_i(1)
1202	hom(nzb+7,1,pr_palm,sr) = z_i(2)
1203
1204	!
1205	!-- Computation of both the characteristic vertical velocity and
1206	!-- the characteristic convective boundary layer temperature.
1207	!-- The horizontal average at nzb+1 is input for the average temperature.
1208	IF ( hom(nzb,1,18,sr) > 0.0 .AND. abs(hom(nzb,1,18,sr)) > 1.0E-8 &
1209	.AND. z_i(1) /= 0.0 ) THEN
1210	hom(nzb+8,1,pr_palm,sr) = ( g / hom(nzb+1,1,4,sr) * &
1211	hom(nzb,1,18,sr) * &
1212	ABS( z_i(1) ) )**0.333333333
1213	!-- so far this only works if Prandtl layer is used
1214	hom(nzb+11,1,pr_palm,sr) = hom(nzb,1,16,sr) / hom(nzb+8,1,pr_palm,sr)
1215	ELSE
1216	hom(nzb+8,1,pr_palm,sr) = 0.0
1217	hom(nzb+11,1,pr_palm,sr) = 0.0
1218	ENDIF
1219
1220	!
1221	!-- Collect the time series quantities
1222	ts_value(1,sr) = hom(nzb+4,1,pr_palm,sr) ! E
1223	ts_value(2,sr) = hom(nzb+5,1,pr_palm,sr) ! E*
1224	ts_value(3,sr) = dt_3d
1225	ts_value(4,sr) = hom(nzb,1,pr_palm,sr) ! u*
1226	ts_value(5,sr) = hom(nzb+3,1,pr_palm,sr) ! th*
1227	ts_value(6,sr) = u_max
1228	ts_value(7,sr) = v_max
1229	ts_value(8,sr) = w_max
1230	ts_value(9,sr) = hom(nzb+10,1,pr_palm,sr) ! new divergence
1231	ts_value(10,sr) = hom(nzb+9,1,pr_palm,sr) ! old Divergence
1232	ts_value(11,sr) = hom(nzb+6,1,pr_palm,sr) ! z_i(1)
1233	ts_value(12,sr) = hom(nzb+7,1,pr_palm,sr) ! z_i(2)
1234	ts_value(13,sr) = hom(nzb+8,1,pr_palm,sr) ! w*
1235	ts_value(14,sr) = hom(nzb,1,16,sr) ! w'pt' at k=0
1236	ts_value(15,sr) = hom(nzb+1,1,16,sr) ! w'pt' at k=1
1237	ts_value(16,sr) = hom(nzb+1,1,18,sr) ! wpt at k=1
1238	ts_value(17,sr) = hom(nzb,1,4,sr) ! pt(0)
1239	ts_value(18,sr) = hom(nzb+1,1,4,sr) ! pt(zp)
1240	ts_value(19,sr) = hom(nzb+1,1,pr_palm,sr) ! u'w' at k=0
1241	ts_value(20,sr) = hom(nzb+2,1,pr_palm,sr) ! v'w' at k=0
1242	ts_value(21,sr) = hom(nzb,1,48,sr) ! w"q" at k=0
1243
1244	IF ( ts_value(5,sr) /= 0.0 ) THEN
1245	ts_value(22,sr) = ts_value(4,sr)**2 / &
1246	( kappa * g * ts_value(5,sr) / ts_value(18,sr) ) ! L
1247	ELSE
1248	ts_value(22,sr) = 10000.0
1249	ENDIF
1250
1251	ts_value(23,sr) = hom(nzb+12,1,pr_palm,sr) ! q*
1252	!
1253	!-- Calculate additional statistics provided by the user interface
1254	CALL user_statistics( 'time_series', sr, 0 )
1255
1256	ENDDO ! loop of the subregions
1257
1258	!
1259	!-- If required, sum up horizontal averages for subsequent time averaging
1260	IF ( do_sum ) THEN
1261	IF ( average_count_pr == 0 ) hom_sum = 0.0
1262	hom_sum = hom_sum + hom(:,1,:,:)
1263	average_count_pr = average_count_pr + 1
1264	do_sum = .FALSE.
1265	ENDIF
1266
1267	!
1268	!-- Set flag for other UPs (e.g. output routines, but also buoyancy).
1269	!-- This flag is reset after each time step in time_integration.
1270	flow_statistics_called = .TRUE.
1271
1272	CALL cpu_log( log_point(10), 'flow_statistics', 'stop' )
1273
1274
1275	END SUBROUTINE flow_statistics

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