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source: palm/trunk/SOURCE/flow_statistics.f90 @ 1112

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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 1112 2013-03-09 00:34:37Z raasch $
27	!
28	! 1111 2013-03-08 23:54:10Z raasch
29	! openACC directive added
30	!
31	! 1053 2012-11-13 17:11:03Z hoffmann
32	! additions for two-moment cloud physics scheme:
33	! +nr, qr, qc, prr
34	!
35	! 1036 2012-10-22 13:43:42Z raasch
36	! code put under GPL (PALM 3.9)
37	!
38	! 1007 2012-09-19 14:30:36Z franke
39	! Calculation of buoyancy flux for humidity in case of WS-scheme is now using
40	! turbulent fluxes of WS-scheme
41	! Bugfix: Calculation of subgridscale buoyancy flux for humidity and cloud
42	! droplets at nzb and nzt added
43	!
44	! 801 2012-01-10 17:30:36Z suehring
45	! Calculation of turbulent fluxes in advec_ws is now thread-safe.
46	!
47	! 743 2011-08-18 16:10:16Z suehring
48	! Calculation of turbulent fluxes with WS-scheme only for the whole model
49	! domain, not for user-defined subregions.
50	!
51	! 709 2011-03-30 09:31:40Z raasch
52	! formatting adjustments
53	!
54	! 699 2011-03-22 17:52:22Z suehring
55	! Bugfix in calculation of vertical velocity skewness. The added absolute value
56	! avoid negative values in the root. Negative values of w'w' can occur at the
57	! top or bottom of the model domain due to degrading the order of advection
58	! scheme. Furthermore the calculation will be the same for all advection
59	! schemes.
60	!
61	! 696 2011-03-18 07:03:49Z raasch
62	! Bugfix: Summation of Wicker-Skamarock scheme fluxes and variances for all
63	! threads
64	!
65	! 678 2011-02-02 14:31:56Z raasch
66	! Bugfix in calculation of the divergence of vertical flux of resolved scale
67	! energy, pressure fluctuations, and flux of pressure fluctuation itself
68	!
69	! 673 2011-01-18 16:19:48Z suehring
70	! Top bc for the horizontal velocity variances added for ocean runs.
71	! Setting the corresponding bottom bc moved to advec_ws.
72	!
73	! 667 2010-12-23 12:06:00Z suehring/gryschka
74	! When advection is computed with ws-scheme, turbulent fluxes are already
75	! computed in the respective advection routines and buffered in arrays
76	! sums_xx_ws_l(). This is due to a consistent treatment of statistics with the
77	! numerics and to avoid unphysical kinks near the surface.
78	! So some if requests has to be done to dicern between fluxes from ws-scheme
79	! other advection schemes.
80	! Furthermore the computation of z_i is only done if the heat flux exceeds a
81	! minimum value. This affects only simulations of a neutral boundary layer and
82	! is due to reasons of computations in the advection scheme.
83	!
84	! 624 2010-12-10 11:46:30Z heinze
85	! Calculation of q*2 added
86	!
87	! 622 2010-12-10 08:08:13Z raasch
88	! optional barriers included in order to speed up collective operations
89	!
90	! 388 2009-09-23 09:40:33Z raasch
91	! Vertical profiles of potential density and hydrostatic pressure are
92	! calculated.
93	! Added missing timeseries calculation of w"q"(0), moved timeseries q* to the
94	! end.
95	! Temperature gradient criterion for estimating the boundary layer height
96	! replaced by the gradient criterion of Sullivan et al. (1998).
97	! Output of messages replaced by message handling routine.
98	!
99	! 197 2008-09-16 15:29:03Z raasch
100	! Spline timeseries splptx etc. removed, timeseries w'u', w'v', w'q' (k=0)
101	! added,
102	! bugfix: divide sums(k,8) (e) and sums(k,34) (e*) by ngp_2dh_s_inner(k,sr)
103	! (like other scalars)
104	!
105	! 133 2007-11-20 10:10:53Z letzel
106	! Vertical profiles now based on nzb_s_inner; they are divided by
107	! ngp_2dh_s_inner (scalars, procucts of scalars) and ngp_2dh (staggered
108	! velocity components and their products, procucts of scalars and velocity
109	! components), respectively.
110	!
111	! 106 2007-08-16 14:30:26Z raasch
112	! Prescribed momentum fluxes at the top surface are used,
113	! profiles for wp and w"e are calculated
114	!
115	! 97 2007-06-21 08:23:15Z raasch
116	! Statistics for ocean version (salinity, density) added,
117	! calculation of z_i and Deardorff velocity scale adjusted to be used with
118	! the ocean version
119	!
120	! 87 2007-05-22 15:46:47Z raasch
121	! Two more arguments added to user_statistics, which is now also called for
122	! user-defined profiles,
123	! var_hom and var_sum renamed pr_palm
124	!
125	! 82 2007-04-16 15:40:52Z raasch
126	! Cpp-directive lcmuk changed to intel_openmp_bug
127	!
128	! 75 2007-03-22 09:54:05Z raasch
129	! Collection of time series quantities moved from routine flow_statistics to
130	! here, routine user_statistics is called for each statistic region,
131	! moisture renamed humidity
132	!
133	! 19 2007-02-23 04:53:48Z raasch
134	! fluxes at top modified (tswst, qswst)
135	!
136	! RCS Log replace by Id keyword, revision history cleaned up
137	!
138	! Revision 1.41 2006/08/04 14:37:50 raasch
139	! Error removed in non-parallel part (sums_l)
140	!
141	! Revision 1.1 1997/08/11 06:15:17 raasch
142	! Initial revision
143	!
144	!
145	! Description:
146	! ------------
147	! Compute average profiles and further average flow quantities for the different
148	! user-defined (sub-)regions. The region indexed 0 is the total model domain.
149	!
150	! NOTE: For simplicity, nzb_s_inner and nzb_diff_s_inner are being used as a
151	! ---- lower vertical index for k-loops for all variables, although strictly
152	! speaking the k-loops would have to be split up according to the staggered
153	! grid. However, this implies no error since staggered velocity components are
154	! zero at the walls and inside buildings.
155	!------------------------------------------------------------------------------!
156
157	USE arrays_3d
158	USE cloud_parameters
159	USE control_parameters
160	USE cpulog
161	USE grid_variables
162	USE indices
163	USE interfaces
164	USE pegrid
165	USE statistics
166
167	IMPLICIT NONE
168
169	INTEGER :: i, j, k, omp_get_thread_num, sr, tn
170	LOGICAL :: first
171	REAL :: dptdz_threshold, height, pts, sums_l_eper, sums_l_etot, ust, &
172	ust2, u2, vst, vst2, v2, w2, z_i(2)
173	REAL :: dptdz(nzb+1:nzt+1)
174	REAL :: sums_ll(nzb:nzt+1,2)
175
176	CALL cpu_log( log_point(10), 'flow_statistics', 'start' )
177
178	!
179	!-- To be on the safe side, check whether flow_statistics has already been
180	!-- called once after the current time step
181	IF ( flow_statistics_called ) THEN
182
183	message_string = 'flow_statistics is called two times within one ' // &
184	'timestep'
185	CALL message( 'flow_statistics', 'PA0190', 1, 2, 0, 6, 0 )
186
187	ENDIF
188
189	!$acc update host( km, kh, e, pt, qs, qsws, rif, shf, ts, u, v, w )
190
191	!
192	!-- Compute statistics for each (sub-)region
193	DO sr = 0, statistic_regions
194
195	!
196	!-- Initialize (local) summation array
197	sums_l = 0.0
198
199	!
200	!-- Store sums that have been computed in other subroutines in summation
201	!-- array
202	sums_l(:,11,:) = sums_l_l(:,sr,:) ! mixing length from diffusivities
203	!-- WARNING: next line still has to be adjusted for OpenMP
204	sums_l(:,21,0) = sums_wsts_bc_l(:,sr) ! heat flux from advec_s_bc
205	sums_l(nzb+9,pr_palm,0) = sums_divold_l(sr) ! old divergence from pres
206	sums_l(nzb+10,pr_palm,0) = sums_divnew_l(sr) ! new divergence from pres
207
208	!
209	!-- Copy the turbulent quantities, evaluated in the advection routines to
210	!-- the local array sums_l() for further computations
211	IF ( ws_scheme_mom .AND. sr == 0 ) THEN
212
213	!
214	!-- According to the Neumann bc for the horizontal velocity components,
215	!-- the corresponding fluxes has to satisfiy the same bc.
216	IF ( ocean ) THEN
217	sums_us2_ws_l(nzt+1,:) = sums_us2_ws_l(nzt,:)
218	sums_vs2_ws_l(nzt+1,:) = sums_vs2_ws_l(nzt,:)
219	ENDIF
220
221	DO i = 0, threads_per_task-1
222	!
223	!-- Swap the turbulent quantities evaluated in advec_ws.
224	sums_l(:,13,i) = sums_wsus_ws_l(:,i) ! wu
225	sums_l(:,15,i) = sums_wsvs_ws_l(:,i) ! wv
226	sums_l(:,30,i) = sums_us2_ws_l(:,i) ! u*2
227	sums_l(:,31,i) = sums_vs2_ws_l(:,i) ! v*2
228	sums_l(:,32,i) = sums_ws2_ws_l(:,i) ! w*2
229	sums_l(:,34,i) = sums_l(:,34,i) + 0.5 * &
230	( sums_us2_ws_l(:,i) + sums_vs2_ws_l(:,i) + &
231	sums_ws2_ws_l(:,i) ) ! e*
232	DO k = nzb, nzt
233	sums_l(nzb+5,pr_palm,i) = sums_l(nzb+5,pr_palm,i) + 0.5 * ( &
234	sums_us2_ws_l(k,i) + &
235	sums_vs2_ws_l(k,i) + &
236	sums_ws2_ws_l(k,i) )
237	ENDDO
238	ENDDO
239
240	ENDIF
241
242	IF ( ws_scheme_sca .AND. sr == 0 ) THEN
243
244	DO i = 0, threads_per_task-1
245	sums_l(:,17,i) = sums_wspts_ws_l(:,i) ! wpt from advec_s_ws
246	IF ( ocean ) sums_l(:,66,i) = sums_wssas_ws_l(:,i) ! wsa
247	IF ( humidity .OR. passive_scalar ) sums_l(:,49,i) = &
248	sums_wsqs_ws_l(:,i) !wq
249	ENDDO
250
251	ENDIF
252	!
253	!-- Horizontally averaged profiles of horizontal velocities and temperature.
254	!-- They must have been computed before, because they are already required
255	!-- for other horizontal averages.
256	tn = 0
257
258	!$OMP PARALLEL PRIVATE( i, j, k, tn )
259	#if defined( __intel_openmp_bug )
260	tn = omp_get_thread_num()
261	#else
262	!$ tn = omp_get_thread_num()
263	#endif
264
265	!$OMP DO
266	DO i = nxl, nxr
267	DO j = nys, nyn
268	DO k = nzb_s_inner(j,i), nzt+1
269	sums_l(k,1,tn) = sums_l(k,1,tn) + u(k,j,i) * rmask(j,i,sr)
270	sums_l(k,2,tn) = sums_l(k,2,tn) + v(k,j,i) * rmask(j,i,sr)
271	sums_l(k,4,tn) = sums_l(k,4,tn) + pt(k,j,i) * rmask(j,i,sr)
272	ENDDO
273	ENDDO
274	ENDDO
275
276	!
277	!-- Horizontally averaged profile of salinity
278	IF ( ocean ) THEN
279	!$OMP DO
280	DO i = nxl, nxr
281	DO j = nys, nyn
282	DO k = nzb_s_inner(j,i), nzt+1
283	sums_l(k,23,tn) = sums_l(k,23,tn) + &
284	sa(k,j,i) * rmask(j,i,sr)
285	ENDDO
286	ENDDO
287	ENDDO
288	ENDIF
289
290	!
291	!-- Horizontally averaged profiles of virtual potential temperature,
292	!-- total water content, specific humidity and liquid water potential
293	!-- temperature
294	IF ( humidity ) THEN
295	!$OMP DO
296	DO i = nxl, nxr
297	DO j = nys, nyn
298	DO k = nzb_s_inner(j,i), nzt+1
299	sums_l(k,44,tn) = sums_l(k,44,tn) + &
300	vpt(k,j,i) * rmask(j,i,sr)
301	sums_l(k,41,tn) = sums_l(k,41,tn) + &
302	q(k,j,i) * rmask(j,i,sr)
303	ENDDO
304	ENDDO
305	ENDDO
306	IF ( cloud_physics ) THEN
307	!$OMP DO
308	DO i = nxl, nxr
309	DO j = nys, nyn
310	DO k = nzb_s_inner(j,i), nzt+1
311	sums_l(k,42,tn) = sums_l(k,42,tn) + &
312	( q(k,j,i) - ql(k,j,i) ) * rmask(j,i,sr)
313	sums_l(k,43,tn) = sums_l(k,43,tn) + ( &
314	pt(k,j,i) + l_d_cppt_d_t(k) ql(k,j,i) &
315	) * rmask(j,i,sr)
316	ENDDO
317	ENDDO
318	ENDDO
319	ENDIF
320	ENDIF
321
322	!
323	!-- Horizontally averaged profiles of passive scalar
324	IF ( passive_scalar ) THEN
325	!$OMP DO
326	DO i = nxl, nxr
327	DO j = nys, nyn
328	DO k = nzb_s_inner(j,i), nzt+1
329	sums_l(k,41,tn) = sums_l(k,41,tn) + q(k,j,i) * rmask(j,i,sr)
330	ENDDO
331	ENDDO
332	ENDDO
333	ENDIF
334	!$OMP END PARALLEL
335	!
336	!-- Summation of thread sums
337	IF ( threads_per_task > 1 ) THEN
338	DO i = 1, threads_per_task-1
339	sums_l(:,1,0) = sums_l(:,1,0) + sums_l(:,1,i)
340	sums_l(:,2,0) = sums_l(:,2,0) + sums_l(:,2,i)
341	sums_l(:,4,0) = sums_l(:,4,0) + sums_l(:,4,i)
342	IF ( ocean ) THEN
343	sums_l(:,23,0) = sums_l(:,23,0) + sums_l(:,23,i)
344	ENDIF
345	IF ( humidity ) THEN
346	sums_l(:,41,0) = sums_l(:,41,0) + sums_l(:,41,i)
347	sums_l(:,44,0) = sums_l(:,44,0) + sums_l(:,44,i)
348	IF ( cloud_physics ) THEN
349	sums_l(:,42,0) = sums_l(:,42,0) + sums_l(:,42,i)
350	sums_l(:,43,0) = sums_l(:,43,0) + sums_l(:,43,i)
351	ENDIF
352	ENDIF
353	IF ( passive_scalar ) THEN
354	sums_l(:,41,0) = sums_l(:,41,0) + sums_l(:,41,i)
355	ENDIF
356	ENDDO
357	ENDIF
358
359	#if defined( __parallel )
360	!
361	!-- Compute total sum from local sums
362	IF ( collective_wait ) CALL MPI_BARRIER( comm2d, ierr )
363	CALL MPI_ALLREDUCE( sums_l(nzb,1,0), sums(nzb,1), nzt+2-nzb, MPI_REAL, &
364	MPI_SUM, comm2d, ierr )
365	IF ( collective_wait ) CALL MPI_BARRIER( comm2d, ierr )
366	CALL MPI_ALLREDUCE( sums_l(nzb,2,0), sums(nzb,2), nzt+2-nzb, MPI_REAL, &
367	MPI_SUM, comm2d, ierr )
368	IF ( collective_wait ) CALL MPI_BARRIER( comm2d, ierr )
369	CALL MPI_ALLREDUCE( sums_l(nzb,4,0), sums(nzb,4), nzt+2-nzb, MPI_REAL, &
370	MPI_SUM, comm2d, ierr )
371	IF ( ocean ) THEN
372	IF ( collective_wait ) CALL MPI_BARRIER( comm2d, ierr )
373	CALL MPI_ALLREDUCE( sums_l(nzb,23,0), sums(nzb,23), nzt+2-nzb, &
374	MPI_REAL, MPI_SUM, comm2d, ierr )
375	ENDIF
376	IF ( humidity ) THEN
377	IF ( collective_wait ) CALL MPI_BARRIER( comm2d, ierr )
378	CALL MPI_ALLREDUCE( sums_l(nzb,44,0), sums(nzb,44), nzt+2-nzb, &
379	MPI_REAL, MPI_SUM, comm2d, ierr )
380	IF ( collective_wait ) CALL MPI_BARRIER( comm2d, ierr )
381	CALL MPI_ALLREDUCE( sums_l(nzb,41,0), sums(nzb,41), nzt+2-nzb, &
382	MPI_REAL, MPI_SUM, comm2d, ierr )
383	IF ( cloud_physics ) THEN
384	IF ( collective_wait ) CALL MPI_BARRIER( comm2d, ierr )
385	CALL MPI_ALLREDUCE( sums_l(nzb,42,0), sums(nzb,42), nzt+2-nzb, &
386	MPI_REAL, MPI_SUM, comm2d, ierr )
387	IF ( collective_wait ) CALL MPI_BARRIER( comm2d, ierr )
388	CALL MPI_ALLREDUCE( sums_l(nzb,43,0), sums(nzb,43), nzt+2-nzb, &
389	MPI_REAL, MPI_SUM, comm2d, ierr )
390	ENDIF
391	ENDIF
392
393	IF ( passive_scalar ) THEN
394	IF ( collective_wait ) CALL MPI_BARRIER( comm2d, ierr )
395	CALL MPI_ALLREDUCE( sums_l(nzb,41,0), sums(nzb,41), nzt+2-nzb, &
396	MPI_REAL, MPI_SUM, comm2d, ierr )
397	ENDIF
398	#else
399	sums(:,1) = sums_l(:,1,0)
400	sums(:,2) = sums_l(:,2,0)
401	sums(:,4) = sums_l(:,4,0)
402	IF ( ocean ) sums(:,23) = sums_l(:,23,0)
403	IF ( humidity ) THEN
404	sums(:,44) = sums_l(:,44,0)
405	sums(:,41) = sums_l(:,41,0)
406	IF ( cloud_physics ) THEN
407	sums(:,42) = sums_l(:,42,0)
408	sums(:,43) = sums_l(:,43,0)
409	ENDIF
410	ENDIF
411	IF ( passive_scalar ) sums(:,41) = sums_l(:,41,0)
412	#endif
413
414	!
415	!-- Final values are obtained by division by the total number of grid points
416	!-- used for summation. After that store profiles.
417	sums(:,1) = sums(:,1) / ngp_2dh(sr)
418	sums(:,2) = sums(:,2) / ngp_2dh(sr)
419	sums(:,4) = sums(:,4) / ngp_2dh_s_inner(:,sr)
420	hom(:,1,1,sr) = sums(:,1) ! u
421	hom(:,1,2,sr) = sums(:,2) ! v
422	hom(:,1,4,sr) = sums(:,4) ! pt
423
424
425	!
426	!-- Salinity
427	IF ( ocean ) THEN
428	sums(:,23) = sums(:,23) / ngp_2dh_s_inner(:,sr)
429	hom(:,1,23,sr) = sums(:,23) ! sa
430	ENDIF
431
432	!
433	!-- Humidity and cloud parameters
434	IF ( humidity ) THEN
435	sums(:,44) = sums(:,44) / ngp_2dh_s_inner(:,sr)
436	sums(:,41) = sums(:,41) / ngp_2dh_s_inner(:,sr)
437	hom(:,1,44,sr) = sums(:,44) ! vpt
438	hom(:,1,41,sr) = sums(:,41) ! qv (q)
439	IF ( cloud_physics ) THEN
440	sums(:,42) = sums(:,42) / ngp_2dh_s_inner(:,sr)
441	sums(:,43) = sums(:,43) / ngp_2dh_s_inner(:,sr)
442	hom(:,1,42,sr) = sums(:,42) ! qv
443	hom(:,1,43,sr) = sums(:,43) ! pt
444	ENDIF
445	ENDIF
446
447	!
448	!-- Passive scalar
449	IF ( passive_scalar ) hom(:,1,41,sr) = sums(:,41) / &
450	ngp_2dh_s_inner(:,sr) ! s (q)
451
452	!
453	!-- Horizontally averaged profiles of the remaining prognostic variables,
454	!-- variances, the total and the perturbation energy (single values in last
455	!-- column of sums_l) and some diagnostic quantities.
456	!-- NOTE: for simplicity, nzb_s_inner is used below, although strictly
457	!-- ---- speaking the following k-loop would have to be split up and
458	!-- rearranged according to the staggered grid.
459	!-- However, this implies no error since staggered velocity components
460	!-- are zero at the walls and inside buildings.
461	tn = 0
462	#if defined( __intel_openmp_bug )
463	!$OMP PARALLEL PRIVATE( i, j, k, pts, sums_ll, sums_l_eper, sums_l_etot, &
464	!$OMP tn, ust, ust2, u2, vst, vst2, v2, w2 )
465	tn = omp_get_thread_num()
466	#else
467	!$OMP PARALLEL PRIVATE( i, j, k, pts, sums_ll, sums_l_eper, sums_l_etot, tn, ust, ust2, u2, vst, vst2, v2, w2 )
468	!$ tn = omp_get_thread_num()
469	#endif
470	!$OMP DO
471	DO i = nxl, nxr
472	DO j = nys, nyn
473	sums_l_etot = 0.0
474	DO k = nzb_s_inner(j,i), nzt+1
475	!
476	!-- Prognostic and diagnostic variables
477	sums_l(k,3,tn) = sums_l(k,3,tn) + w(k,j,i) * rmask(j,i,sr)
478	sums_l(k,8,tn) = sums_l(k,8,tn) + e(k,j,i) * rmask(j,i,sr)
479	sums_l(k,9,tn) = sums_l(k,9,tn) + km(k,j,i) * rmask(j,i,sr)
480	sums_l(k,10,tn) = sums_l(k,10,tn) + kh(k,j,i) * rmask(j,i,sr)
481	sums_l(k,40,tn) = sums_l(k,40,tn) + p(k,j,i)
482
483	sums_l(k,33,tn) = sums_l(k,33,tn) + &
484	( pt(k,j,i)-hom(k,1,4,sr) )*2 rmask(j,i,sr)
485
486	IF ( humidity ) THEN
487	sums_l(k,70,tn) = sums_l(k,70,tn) + &
488	( q(k,j,i)-hom(k,1,41,sr) )*2 rmask(j,i,sr)
489	ENDIF
490
491	!
492	!-- Higher moments
493	!-- (Computation of the skewness of w further below)
494	sums_l(k,38,tn) = sums_l(k,38,tn) + w(k,j,i)*3 rmask(j,i,sr)
495
496	sums_l_etot = sums_l_etot + &
497	0.5 * ( u(k,j,i)2 + v(k,j,i)2 + &
498	w(k,j,i)*2 ) rmask(j,i,sr)
499	ENDDO
500	!
501	!-- Total and perturbation energy for the total domain (being
502	!-- collected in the last column of sums_l). Summation of these
503	!-- quantities is seperated from the previous loop in order to
504	!-- allow vectorization of that loop.
505	sums_l(nzb+4,pr_palm,tn) = sums_l(nzb+4,pr_palm,tn) + sums_l_etot
506	!
507	!-- 2D-arrays (being collected in the last column of sums_l)
508	sums_l(nzb,pr_palm,tn) = sums_l(nzb,pr_palm,tn) + &
509	us(j,i) * rmask(j,i,sr)
510	sums_l(nzb+1,pr_palm,tn) = sums_l(nzb+1,pr_palm,tn) + &
511	usws(j,i) * rmask(j,i,sr)
512	sums_l(nzb+2,pr_palm,tn) = sums_l(nzb+2,pr_palm,tn) + &
513	vsws(j,i) * rmask(j,i,sr)
514	sums_l(nzb+3,pr_palm,tn) = sums_l(nzb+3,pr_palm,tn) + &
515	ts(j,i) * rmask(j,i,sr)
516	IF ( humidity ) THEN
517	sums_l(nzb+12,pr_palm,tn) = sums_l(nzb+12,pr_palm,tn) + &
518	qs(j,i) * rmask(j,i,sr)
519	ENDIF
520	ENDDO
521	ENDDO
522
523	!
524	!-- Computation of statistics when ws-scheme is not used. Else these
525	!-- quantities are evaluated in the advection routines.
526	IF ( .NOT. ws_scheme_mom .OR. sr /= 0 ) THEN
527	!$OMP DO
528	DO i = nxl, nxr
529	DO j = nys, nyn
530	sums_l_eper = 0.0
531	DO k = nzb_s_inner(j,i), nzt+1
532	u2 = u(k,j,i)**2
533	v2 = v(k,j,i)**2
534	w2 = w(k,j,i)**2
535	ust2 = ( u(k,j,i) - hom(k,1,1,sr) )**2
536	vst2 = ( v(k,j,i) - hom(k,1,2,sr) )**2
537
538	sums_l(k,30,tn) = sums_l(k,30,tn) + ust2 * rmask(j,i,sr)
539	sums_l(k,31,tn) = sums_l(k,31,tn) + vst2 * rmask(j,i,sr)
540	sums_l(k,32,tn) = sums_l(k,32,tn) + w2 * rmask(j,i,sr)
541	!
542	!-- Perturbation energy
543
544	sums_l(k,34,tn) = sums_l(k,34,tn) + 0.5 * &
545	( ust2 + vst2 + w2 ) * rmask(j,i,sr)
546	sums_l_eper = sums_l_eper + &
547	0.5 * ( ust2+vst2+w2 ) * rmask(j,i,sr)
548
549	ENDDO
550	sums_l(nzb+5,pr_palm,tn) = sums_l(nzb+5,pr_palm,tn) &
551	+ sums_l_eper
552	ENDDO
553	ENDDO
554	ENDIF
555	!
556	!-- Horizontally averaged profiles of the vertical fluxes
557
558	!$OMP DO
559	DO i = nxl, nxr
560	DO j = nys, nyn
561	!
562	!-- Subgridscale fluxes (without Prandtl layer from k=nzb,
563	!-- oterwise from k=nzb+1)
564	!-- NOTE: for simplicity, nzb_diff_s_inner is used below, although
565	!-- ---- strictly speaking the following k-loop would have to be
566	!-- split up according to the staggered grid.
567	!-- However, this implies no error since staggered velocity
568	!-- components are zero at the walls and inside buildings.
569
570	DO k = nzb_diff_s_inner(j,i)-1, nzt_diff
571	!
572	!-- Momentum flux w"u"
573	sums_l(k,12,tn) = sums_l(k,12,tn) - 0.25 * ( &
574	km(k,j,i)+km(k+1,j,i)+km(k,j,i-1)+km(k+1,j,i-1) &
575	) * ( &
576	( u(k+1,j,i) - u(k,j,i) ) * ddzu(k+1) &
577	+ ( w(k,j,i) - w(k,j,i-1) ) * ddx &
578	) * rmask(j,i,sr)
579	!
580	!-- Momentum flux w"v"
581	sums_l(k,14,tn) = sums_l(k,14,tn) - 0.25 * ( &
582	km(k,j,i)+km(k+1,j,i)+km(k,j-1,i)+km(k+1,j-1,i) &
583	) * ( &
584	( v(k+1,j,i) - v(k,j,i) ) * ddzu(k+1) &
585	+ ( w(k,j,i) - w(k,j-1,i) ) * ddy &
586	) * rmask(j,i,sr)
587	!
588	!-- Heat flux w"pt"
589	sums_l(k,16,tn) = sums_l(k,16,tn) &
590	- 0.5 * ( kh(k,j,i) + kh(k+1,j,i) ) &
591	* ( pt(k+1,j,i) - pt(k,j,i) ) &
592	* ddzu(k+1) * rmask(j,i,sr)
593
594
595	!
596	!-- Salinity flux w"sa"
597	IF ( ocean ) THEN
598	sums_l(k,65,tn) = sums_l(k,65,tn) &
599	- 0.5 * ( kh(k,j,i) + kh(k+1,j,i) ) &
600	* ( sa(k+1,j,i) - sa(k,j,i) ) &
601	* ddzu(k+1) * rmask(j,i,sr)
602	ENDIF
603
604	!
605	!-- Buoyancy flux, water flux (humidity flux) w"q"
606	IF ( humidity ) THEN
607	sums_l(k,45,tn) = sums_l(k,45,tn) &
608	- 0.5 * ( kh(k,j,i) + kh(k+1,j,i) ) &
609	* ( vpt(k+1,j,i) - vpt(k,j,i) ) &
610	* ddzu(k+1) * rmask(j,i,sr)
611	sums_l(k,48,tn) = sums_l(k,48,tn) &
612	- 0.5 * ( kh(k,j,i) + kh(k+1,j,i) ) &
613	* ( q(k+1,j,i) - q(k,j,i) ) &
614	* ddzu(k+1) * rmask(j,i,sr)
615
616	IF ( cloud_physics ) THEN
617	sums_l(k,51,tn) = sums_l(k,51,tn) &
618	- 0.5 * ( kh(k,j,i) + kh(k+1,j,i) ) &
619	* ( ( q(k+1,j,i) - ql(k+1,j,i) )&
620	- ( q(k,j,i) - ql(k,j,i) ) ) &
621	* ddzu(k+1) * rmask(j,i,sr)
622	ENDIF
623	ENDIF
624
625	!
626	!-- Passive scalar flux
627	IF ( passive_scalar ) THEN
628	sums_l(k,48,tn) = sums_l(k,48,tn) &
629	- 0.5 * ( kh(k,j,i) + kh(k+1,j,i) ) &
630	* ( q(k+1,j,i) - q(k,j,i) ) &
631	* ddzu(k+1) * rmask(j,i,sr)
632	ENDIF
633
634	ENDDO
635
636	!
637	!-- Subgridscale fluxes in the Prandtl layer
638	IF ( use_surface_fluxes ) THEN
639	sums_l(nzb,12,tn) = sums_l(nzb,12,tn) + &
640	usws(j,i) * rmask(j,i,sr) ! w"u"
641	sums_l(nzb,14,tn) = sums_l(nzb,14,tn) + &
642	vsws(j,i) * rmask(j,i,sr) ! w"v"
643	sums_l(nzb,16,tn) = sums_l(nzb,16,tn) + &
644	shf(j,i) * rmask(j,i,sr) ! w"pt"
645	sums_l(nzb,58,tn) = sums_l(nzb,58,tn) + &
646	0.0 * rmask(j,i,sr) ! u"pt"
647	sums_l(nzb,61,tn) = sums_l(nzb,61,tn) + &
648	0.0 * rmask(j,i,sr) ! v"pt"
649	IF ( ocean ) THEN
650	sums_l(nzb,65,tn) = sums_l(nzb,65,tn) + &
651	saswsb(j,i) * rmask(j,i,sr) ! w"sa"
652	ENDIF
653	IF ( humidity ) THEN
654	sums_l(nzb,48,tn) = sums_l(nzb,48,tn) + &
655	qsws(j,i) * rmask(j,i,sr) ! w"q" (w"qv")
656	sums_l(nzb,45,tn) = sums_l(nzb,45,tn) + ( &
657	( 1.0 + 0.61 * q(nzb,j,i) ) * &
658	shf(j,i) + 0.61 * pt(nzb,j,i) * &
659	qsws(j,i) )
660	IF ( cloud_droplets ) THEN
661	sums_l(nzb,45,tn) = sums_l(nzb,45,tn) + ( &
662	( 1.0 + 0.61 * q(nzb,j,i) - &
663	ql(nzb,j,i) ) * shf(j,i) + &
664	0.61 * pt(nzb,j,i) * qsws(j,i) )
665	ENDIF
666	IF ( cloud_physics ) THEN
667	!
668	!-- Formula does not work if ql(nzb) /= 0.0
669	sums_l(nzb,51,tn) = sums_l(nzb,51,tn) + & ! w"q" (w"qv")
670	qsws(j,i) * rmask(j,i,sr)
671	ENDIF
672	ENDIF
673	IF ( passive_scalar ) THEN
674	sums_l(nzb,48,tn) = sums_l(nzb,48,tn) + &
675	qsws(j,i) * rmask(j,i,sr) ! w"q" (w"qv")
676	ENDIF
677	ENDIF
678
679	!
680	!-- Subgridscale fluxes at the top surface
681	IF ( use_top_fluxes ) THEN
682	sums_l(nzt:nzt+1,12,tn) = sums_l(nzt:nzt+1,12,tn) + &
683	uswst(j,i) * rmask(j,i,sr) ! w"u"
684	sums_l(nzt:nzt+1,14,tn) = sums_l(nzt:nzt+1,14,tn) + &
685	vswst(j,i) * rmask(j,i,sr) ! w"v"
686	sums_l(nzt:nzt+1,16,tn) = sums_l(nzt:nzt+1,16,tn) + &
687	tswst(j,i) * rmask(j,i,sr) ! w"pt"
688	sums_l(nzt:nzt+1,58,tn) = sums_l(nzt:nzt+1,58,tn) + &
689	0.0 * rmask(j,i,sr) ! u"pt"
690	sums_l(nzt:nzt+1,61,tn) = sums_l(nzt:nzt+1,61,tn) + &
691	0.0 * rmask(j,i,sr) ! v"pt"
692
693	IF ( ocean ) THEN
694	sums_l(nzt,65,tn) = sums_l(nzt,65,tn) + &
695	saswst(j,i) * rmask(j,i,sr) ! w"sa"
696	ENDIF
697	IF ( humidity ) THEN
698	sums_l(nzt,48,tn) = sums_l(nzt,48,tn) + &
699	qswst(j,i) * rmask(j,i,sr) ! w"q" (w"qv")
700	sums_l(nzt,45,tn) = sums_l(nzt,45,tn) + ( &
701	( 1.0 + 0.61 * q(nzt,j,i) ) * &
702	tswst(j,i) + 0.61 * pt(nzt,j,i) * &
703	qswst(j,i) )
704	IF ( cloud_droplets ) THEN
705	sums_l(nzt,45,tn) = sums_l(nzt,45,tn) + ( &
706	( 1.0 + 0.61 * q(nzt,j,i) - &
707	ql(nzt,j,i) ) * tswst(j,i) + &
708	0.61 * pt(nzt,j,i) * qswst(j,i) )
709	ENDIF
710	IF ( cloud_physics ) THEN
711	!
712	!-- Formula does not work if ql(nzb) /= 0.0
713	sums_l(nzt,51,tn) = sums_l(nzt,51,tn) + & ! w"q" (w"qv")
714	qswst(j,i) * rmask(j,i,sr)
715	ENDIF
716	ENDIF
717	IF ( passive_scalar ) THEN
718	sums_l(nzt,48,tn) = sums_l(nzt,48,tn) + &
719	qswst(j,i) * rmask(j,i,sr) ! w"q" (w"qv")
720	ENDIF
721	ENDIF
722
723	!
724	!-- Resolved fluxes (can be computed for all horizontal points)
725	!-- NOTE: for simplicity, nzb_s_inner is used below, although strictly
726	!-- ---- speaking the following k-loop would have to be split up and
727	!-- rearranged according to the staggered grid.
728	DO k = nzb_s_inner(j,i), nzt
729	ust = 0.5 * ( u(k,j,i) - hom(k,1,1,sr) + &
730	u(k+1,j,i) - hom(k+1,1,1,sr) )
731	vst = 0.5 * ( v(k,j,i) - hom(k,1,2,sr) + &
732	v(k+1,j,i) - hom(k+1,1,2,sr) )
733	pts = 0.5 * ( pt(k,j,i) - hom(k,1,4,sr) + &
734	pt(k+1,j,i) - hom(k+1,1,4,sr) )
735
736	!-- Higher moments
737	sums_l(k,35,tn) = sums_l(k,35,tn) + pts * w(k,j,i)*2 &
738	rmask(j,i,sr)
739	sums_l(k,36,tn) = sums_l(k,36,tn) + pts*2 w(k,j,i) * &
740	rmask(j,i,sr)
741
742	!
743	!-- Salinity flux and density (density does not belong to here,
744	!-- but so far there is no other suitable place to calculate)
745	IF ( ocean ) THEN
746	IF( .NOT. ws_scheme_sca .OR. sr /= 0 ) THEN
747	pts = 0.5 * ( sa(k,j,i) - hom(k,1,23,sr) + &
748	sa(k+1,j,i) - hom(k+1,1,23,sr) )
749	sums_l(k,66,tn) = sums_l(k,66,tn) + pts * w(k,j,i) * &
750	rmask(j,i,sr)
751	ENDIF
752	sums_l(k,64,tn) = sums_l(k,64,tn) + rho(k,j,i) * &
753	rmask(j,i,sr)
754	sums_l(k,71,tn) = sums_l(k,71,tn) + prho(k,j,i) * &
755	rmask(j,i,sr)
756	ENDIF
757
758	!
759	!-- Buoyancy flux, water flux, humidity flux, liquid water
760	!-- content, rain drop concentration and rain water content
761	IF ( humidity ) THEN
762	IF ( cloud_physics .OR. cloud_droplets ) THEN
763	pts = 0.5 * ( vpt(k,j,i) - hom(k,1,44,sr) + &
764	vpt(k+1,j,i) - hom(k+1,1,44,sr) )
765	sums_l(k,46,tn) = sums_l(k,46,tn) + pts * w(k,j,i) * &
766	rmask(j,i,sr)
767	IF ( .NOT. cloud_droplets ) THEN
768	pts = 0.5 * &
769	( ( q(k,j,i) - ql(k,j,i) ) - &
770	hom(k,1,42,sr) + &
771	( q(k+1,j,i) - ql(k+1,j,i) ) - &
772	hom(k+1,1,42,sr) )
773	sums_l(k,52,tn) = sums_l(k,52,tn) + pts * w(k,j,i) * &
774	rmask(j,i,sr)
775	IF ( icloud_scheme == 0 ) THEN
776	sums_l(k,54,tn) = sums_l(k,54,tn) + ( ql(k,j,i) + &
777	qr(k,j,i) ) * &
778	rmask(j,i,sr)
779	sums_l(k,73,tn) = sums_l(k,73,tn) + nr(k,j,i) * &
780	rmask(j,i,sr)
781	sums_l(k,74,tn) = sums_l(k,74,tn) + qr(k,j,i) * &
782	rmask(j,i,sr)
783	sums_l(k,75,tn) = sums_l(k,75,tn) + ql(k,j,i) * &
784	rmask(j,i,sr)
785	sums_l(k,76,tn) = sums_l(k,76,tn) + prr(k,j,i) * &
786	rmask(j,i,sr)
787	ELSE
788	sums_l(k,54,tn) = sums_l(k,54,tn) + ql(k,j,i) * &
789	rmask(j,i,sr)
790	ENDIF
791	ELSE
792	sums_l(k,54,tn) = sums_l(k,54,tn) + ql(k,j,i) * &
793	rmask(j,i,sr)
794	ENDIF
795	ELSE
796	IF( .NOT. ws_scheme_sca .OR. sr /= 0 ) THEN
797	pts = 0.5 * ( vpt(k,j,i) - hom(k,1,44,sr) + &
798	vpt(k+1,j,i) - hom(k+1,1,44,sr) )
799	sums_l(k,46,tn) = sums_l(k,46,tn) + pts * w(k,j,i) * &
800	rmask(j,i,sr)
801	ELSE IF ( ws_scheme_sca .AND. sr == 0 ) THEN
802	sums_l(k,46,tn) = ( 1.0 + 0.61 * hom(k,1,41,sr) ) * &
803	sums_l(k,17,tn) + &
804	0.61 * hom(k,1,4,sr) * sums_l(k,49,tn)
805	END IF
806	END IF
807	ENDIF
808	!
809	!-- Passive scalar flux
810	IF ( passive_scalar .AND. ( .NOT. ws_scheme_sca &
811	.OR. sr /= 0 ) ) THEN
812	pts = 0.5 * ( q(k,j,i) - hom(k,1,41,sr) + &
813	q(k+1,j,i) - hom(k+1,1,41,sr) )
814	sums_l(k,49,tn) = sums_l(k,49,tn) + pts * w(k,j,i) * &
815	rmask(j,i,sr)
816	ENDIF
817
818	!
819	!-- Energy flux we
820	!-- has to be adjusted
821	sums_l(k,37,tn) = sums_l(k,37,tn) + w(k,j,i) * 0.5 * &
822	( ust2 + vst2 + w(k,j,i)**2 )&
823	* rmask(j,i,sr)
824	ENDDO
825	ENDDO
826	ENDDO
827	!
828	!-- For speed optimization fluxes which have been computed in part directly
829	!-- inside the WS advection routines are treated seperatly
830	!-- Momentum fluxes first:
831	IF ( .NOT. ws_scheme_mom .OR. sr /= 0 ) THEN
832	!$OMP DO
833	DO i = nxl, nxr
834	DO j = nys, nyn
835	DO k = nzb_diff_s_inner(j,i)-1, nzt_diff
836	ust = 0.5 * ( u(k,j,i) - hom(k,1,1,sr) + &
837	u(k+1,j,i) - hom(k+1,1,1,sr) )
838	vst = 0.5 * ( v(k,j,i) - hom(k,1,2,sr) + &
839	v(k+1,j,i) - hom(k+1,1,2,sr) )
840	!
841	!-- Momentum flux wu
842	sums_l(k,13,tn) = sums_l(k,13,tn) + 0.5 * &
843	( w(k,j,i-1) + w(k,j,i) ) &
844	* ust * rmask(j,i,sr)
845	!
846	!-- Momentum flux wv
847	sums_l(k,15,tn) = sums_l(k,15,tn) + 0.5 * &
848	( w(k,j-1,i) + w(k,j,i) ) &
849	* vst * rmask(j,i,sr)
850	ENDDO
851	ENDDO
852	ENDDO
853
854	ENDIF
855	IF ( .NOT. ws_scheme_sca .OR. sr /= 0 ) THEN
856	!$OMP DO
857	DO i = nxl, nxr
858	DO j = nys, nyn
859	DO k = nzb_diff_s_inner(j,i)-1, nzt_diff
860	!
861	!-- Vertical heat flux
862	sums_l(k,17,tn) = sums_l(k,17,tn) + 0.5 * &
863	( pt(k,j,i) - hom(k,1,4,sr) + &
864	pt(k+1,j,i) - hom(k+1,1,4,sr) ) &
865	* w(k,j,i) * rmask(j,i,sr)
866	IF ( humidity ) THEN
867	pts = 0.5 * ( q(k,j,i) - hom(k,1,41,sr) + &
868	q(k+1,j,i) - hom(k+1,1,41,sr) )
869	sums_l(k,49,tn) = sums_l(k,49,tn) + pts * w(k,j,i) * &
870	rmask(j,i,sr)
871	ENDIF
872	ENDDO
873	ENDDO
874	ENDDO
875
876	ENDIF
877
878
879	!
880	!-- Density at top follows Neumann condition
881	IF ( ocean ) THEN
882	sums_l(nzt+1,64,tn) = sums_l(nzt,64,tn)
883	sums_l(nzt+1,71,tn) = sums_l(nzt,71,tn)
884	ENDIF
885
886	!
887	!-- Divergence of vertical flux of resolved scale energy and pressure
888	!-- fluctuations as well as flux of pressure fluctuation itself (68).
889	!-- First calculate the products, then the divergence.
890	!-- Calculation is time consuming. Do it only, if profiles shall be plotted.
891	IF ( hom(nzb+1,2,55,0) /= 0.0 .OR. hom(nzb+1,2,68,0) /= 0.0 ) THEN
892
893	sums_ll = 0.0 ! local array
894
895	!$OMP DO
896	DO i = nxl, nxr
897	DO j = nys, nyn
898	DO k = nzb_s_inner(j,i)+1, nzt
899
900	sums_ll(k,1) = sums_ll(k,1) + 0.5 * w(k,j,i) * ( &
901	( 0.25 * ( u(k,j,i)+u(k+1,j,i)+u(k,j,i+1)+u(k+1,j,i+1) &
902	- 0.5 * ( hom(k,1,1,sr) + hom(k+1,1,1,sr) ) &
903	) )**2 &
904	+ ( 0.25 * ( v(k,j,i)+v(k+1,j,i)+v(k,j+1,i)+v(k+1,j+1,i) &
905	- 0.5 * ( hom(k,1,2,sr) + hom(k+1,1,2,sr) ) &
906	) )**2 &
907	+ w(k,j,i)**2 )
908
909	sums_ll(k,2) = sums_ll(k,2) + 0.5 * w(k,j,i) &
910	* ( p(k,j,i) + p(k+1,j,i) )
911
912	ENDDO
913	ENDDO
914	ENDDO
915	sums_ll(0,1) = 0.0 ! because w is zero at the bottom
916	sums_ll(nzt+1,1) = 0.0
917	sums_ll(0,2) = 0.0
918	sums_ll(nzt+1,2) = 0.0
919
920	DO k = nzb+1, nzt
921	sums_l(k,55,tn) = ( sums_ll(k,1) - sums_ll(k-1,1) ) * ddzw(k)
922	sums_l(k,56,tn) = ( sums_ll(k,2) - sums_ll(k-1,2) ) * ddzw(k)
923	sums_l(k,68,tn) = sums_ll(k,2)
924	ENDDO
925	sums_l(nzb,55,tn) = sums_l(nzb+1,55,tn)
926	sums_l(nzb,56,tn) = sums_l(nzb+1,56,tn)
927	sums_l(nzb,68,tn) = 0.0 ! because w* = 0 at nzb
928
929	ENDIF
930
931	!
932	!-- Divergence of vertical flux of SGS TKE and the flux itself (69)
933	IF ( hom(nzb+1,2,57,0) /= 0.0 .OR. hom(nzb+1,2,69,0) /= 0.0 ) THEN
934
935	!$OMP DO
936	DO i = nxl, nxr
937	DO j = nys, nyn
938	DO k = nzb_s_inner(j,i)+1, nzt
939
940	sums_l(k,57,tn) = sums_l(k,57,tn) - 0.5 * ( &
941	(km(k,j,i)+km(k+1,j,i)) * (e(k+1,j,i)-e(k,j,i)) * ddzu(k+1) &
942	- (km(k-1,j,i)+km(k,j,i)) * (e(k,j,i)-e(k-1,j,i)) * ddzu(k) &
943	) * ddzw(k)
944
945	sums_l(k,69,tn) = sums_l(k,69,tn) - 0.5 * ( &
946	(km(k,j,i)+km(k+1,j,i)) * (e(k+1,j,i)-e(k,j,i)) * ddzu(k+1) &
947	)
948
949	ENDDO
950	ENDDO
951	ENDDO
952	sums_l(nzb,57,tn) = sums_l(nzb+1,57,tn)
953	sums_l(nzb,69,tn) = sums_l(nzb+1,69,tn)
954
955	ENDIF
956
957	!
958	!-- Horizontal heat fluxes (subgrid, resolved, total).
959	!-- Do it only, if profiles shall be plotted.
960	IF ( hom(nzb+1,2,58,0) /= 0.0 ) THEN
961
962	!$OMP DO
963	DO i = nxl, nxr
964	DO j = nys, nyn
965	DO k = nzb_s_inner(j,i)+1, nzt
966	!
967	!-- Subgrid horizontal heat fluxes u"pt", v"pt"
968	sums_l(k,58,tn) = sums_l(k,58,tn) - 0.5 * &
969	( kh(k,j,i) + kh(k,j,i-1) ) &
970	* ( pt(k,j,i-1) - pt(k,j,i) ) &
971	* ddx * rmask(j,i,sr)
972	sums_l(k,61,tn) = sums_l(k,61,tn) - 0.5 * &
973	( kh(k,j,i) + kh(k,j-1,i) ) &
974	* ( pt(k,j-1,i) - pt(k,j,i) ) &
975	* ddy * rmask(j,i,sr)
976	!
977	!-- Resolved horizontal heat fluxes upt, vpt
978	sums_l(k,59,tn) = sums_l(k,59,tn) + &
979	( u(k,j,i) - hom(k,1,1,sr) ) &
980	* 0.5 * ( pt(k,j,i-1) - hom(k,1,4,sr) + &
981	pt(k,j,i) - hom(k,1,4,sr) )
982	pts = 0.5 * ( pt(k,j-1,i) - hom(k,1,4,sr) + &
983	pt(k,j,i) - hom(k,1,4,sr) )
984	sums_l(k,62,tn) = sums_l(k,62,tn) + &
985	( v(k,j,i) - hom(k,1,2,sr) ) &
986	* 0.5 * ( pt(k,j-1,i) - hom(k,1,4,sr) + &
987	pt(k,j,i) - hom(k,1,4,sr) )
988	ENDDO
989	ENDDO
990	ENDDO
991	!
992	!-- Fluxes at the surface must be zero (e.g. due to the Prandtl-layer)
993	sums_l(nzb,58,tn) = 0.0
994	sums_l(nzb,59,tn) = 0.0
995	sums_l(nzb,60,tn) = 0.0
996	sums_l(nzb,61,tn) = 0.0
997	sums_l(nzb,62,tn) = 0.0
998	sums_l(nzb,63,tn) = 0.0
999
1000	ENDIF
1001
1002	!
1003	!-- Calculate the user-defined profiles
1004	CALL user_statistics( 'profiles', sr, tn )
1005	!$OMP END PARALLEL
1006
1007	!
1008	!-- Summation of thread sums
1009	IF ( threads_per_task > 1 ) THEN
1010	DO i = 1, threads_per_task-1
1011	sums_l(:,3,0) = sums_l(:,3,0) + sums_l(:,3,i)
1012	sums_l(:,4:40,0) = sums_l(:,4:40,0) + sums_l(:,4:40,i)
1013	sums_l(:,45:pr_palm,0) = sums_l(:,45:pr_palm,0) + &
1014	sums_l(:,45:pr_palm,i)
1015	IF ( max_pr_user > 0 ) THEN
1016	sums_l(:,pr_palm+1:pr_palm+max_pr_user,0) = &
1017	sums_l(:,pr_palm+1:pr_palm+max_pr_user,0) + &
1018	sums_l(:,pr_palm+1:pr_palm+max_pr_user,i)
1019	ENDIF
1020	ENDDO
1021	ENDIF
1022
1023	#if defined( __parallel )
1024
1025	!
1026	!-- Compute total sum from local sums
1027	IF ( collective_wait ) CALL MPI_BARRIER( comm2d, ierr )
1028	CALL MPI_ALLREDUCE( sums_l(nzb,1,0), sums(nzb,1), ngp_sums, MPI_REAL, &
1029	MPI_SUM, comm2d, ierr )
1030	#else
1031	sums = sums_l(:,:,0)
1032	#endif
1033
1034	!
1035	!-- Final values are obtained by division by the total number of grid points
1036	!-- used for summation. After that store profiles.
1037	!-- Profiles:
1038	DO k = nzb, nzt+1
1039	sums(k,3) = sums(k,3) / ngp_2dh(sr)
1040	sums(k,8:11) = sums(k,8:11) / ngp_2dh_s_inner(k,sr)
1041	sums(k,12:22) = sums(k,12:22) / ngp_2dh(sr)
1042	sums(k,23:29) = sums(k,23:29) / ngp_2dh_s_inner(k,sr)
1043	sums(k,30:32) = sums(k,30:32) / ngp_2dh(sr)
1044	sums(k,33:34) = sums(k,33:34) / ngp_2dh_s_inner(k,sr)
1045	sums(k,35:39) = sums(k,35:39) / ngp_2dh(sr)
1046	sums(k,40) = sums(k,40) / ngp_2dh_s_inner(k,sr)
1047	sums(k,45:53) = sums(k,45:53) / ngp_2dh(sr)
1048	sums(k,54) = sums(k,54) / ngp_2dh_s_inner(k,sr)
1049	sums(k,55:63) = sums(k,55:63) / ngp_2dh(sr)
1050	sums(k,64) = sums(k,64) / ngp_2dh_s_inner(k,sr)
1051	sums(k,65:69) = sums(k,65:69) / ngp_2dh(sr)
1052	sums(k,70:pr_palm-2) = sums(k,70:pr_palm-2)/ ngp_2dh_s_inner(k,sr)
1053	ENDDO
1054
1055	!-- Upstream-parts
1056	sums(nzb:nzb+11,pr_palm-1) = sums(nzb:nzb+11,pr_palm-1) / ngp_3d(sr)
1057	!-- u* and so on
1058	!-- As sums(nzb:nzb+3,pr_palm) are full 2D arrays (us, usws, vsws, ts) whose
1059	!-- size is always ( nx + 1 ) * ( ny + 1 ), defined at the first grid layer
1060	!-- above the topography, they are being divided by ngp_2dh(sr)
1061	sums(nzb:nzb+3,pr_palm) = sums(nzb:nzb+3,pr_palm) / &
1062	ngp_2dh(sr)
1063	sums(nzb+12,pr_palm) = sums(nzb+12,pr_palm) / & ! qs
1064	ngp_2dh(sr)
1065	!-- eges, e*
1066	sums(nzb+4:nzb+5,pr_palm) = sums(nzb+4:nzb+5,pr_palm) / &
1067	ngp_3d(sr)
1068	!-- Old and new divergence
1069	sums(nzb+9:nzb+10,pr_palm) = sums(nzb+9:nzb+10,pr_palm) / &
1070	ngp_3d_inner(sr)
1071
1072	!-- User-defined profiles
1073	IF ( max_pr_user > 0 ) THEN
1074	DO k = nzb, nzt+1
1075	sums(k,pr_palm+1:pr_palm+max_pr_user) = &
1076	sums(k,pr_palm+1:pr_palm+max_pr_user) / &
1077	ngp_2dh_s_inner(k,sr)
1078	ENDDO
1079	ENDIF
1080
1081	!
1082	!-- Collect horizontal average in hom.
1083	!-- Compute deduced averages (e.g. total heat flux)
1084	hom(:,1,3,sr) = sums(:,3) ! w
1085	hom(:,1,8,sr) = sums(:,8) ! e profiles 5-7 are initial profiles
1086	hom(:,1,9,sr) = sums(:,9) ! km
1087	hom(:,1,10,sr) = sums(:,10) ! kh
1088	hom(:,1,11,sr) = sums(:,11) ! l
1089	hom(:,1,12,sr) = sums(:,12) ! w"u"
1090	hom(:,1,13,sr) = sums(:,13) ! wu
1091	hom(:,1,14,sr) = sums(:,14) ! w"v"
1092	hom(:,1,15,sr) = sums(:,15) ! wv
1093	hom(:,1,16,sr) = sums(:,16) ! w"pt"
1094	hom(:,1,17,sr) = sums(:,17) ! wpt
1095	hom(:,1,18,sr) = sums(:,16) + sums(:,17) ! wpt
1096	hom(:,1,19,sr) = sums(:,12) + sums(:,13) ! wu
1097	hom(:,1,20,sr) = sums(:,14) + sums(:,15) ! wv
1098	hom(:,1,21,sr) = sums(:,21) ! wptBC
1099	hom(:,1,22,sr) = sums(:,16) + sums(:,21) ! wptBC
1100	! profile 24 is initial profile (sa)
1101	! profiles 25-29 left empty for initial
1102	! profiles
1103	hom(:,1,30,sr) = sums(:,30) ! u*2
1104	hom(:,1,31,sr) = sums(:,31) ! v*2
1105	hom(:,1,32,sr) = sums(:,32) ! w*2
1106	hom(:,1,33,sr) = sums(:,33) ! pt*2
1107	hom(:,1,34,sr) = sums(:,34) ! e*
1108	hom(:,1,35,sr) = sums(:,35) ! w2pt
1109	hom(:,1,36,sr) = sums(:,36) ! wpt2
1110	hom(:,1,37,sr) = sums(:,37) ! we
1111	hom(:,1,38,sr) = sums(:,38) ! w*3
1112	hom(:,1,39,sr) = sums(:,38) / ( abs( sums(:,32) ) + 1E-20 )**1.5 ! Sw
1113	hom(:,1,40,sr) = sums(:,40) ! p
1114	hom(:,1,45,sr) = sums(:,45) ! w"vpt"
1115	hom(:,1,46,sr) = sums(:,46) ! wvpt
1116	hom(:,1,47,sr) = sums(:,45) + sums(:,46) ! wvpt
1117	hom(:,1,48,sr) = sums(:,48) ! w"q" (w"qv")
1118	hom(:,1,49,sr) = sums(:,49) ! wq (wqv)
1119	hom(:,1,50,sr) = sums(:,48) + sums(:,49) ! wq (wqv)
1120	hom(:,1,51,sr) = sums(:,51) ! w"qv"
1121	hom(:,1,52,sr) = sums(:,52) ! wqv
1122	hom(:,1,53,sr) = sums(:,52) + sums(:,51) ! wq (wqv)
1123	hom(:,1,54,sr) = sums(:,54) ! ql
1124	hom(:,1,55,sr) = sums(:,55) ! wuu*/dz
1125	hom(:,1,56,sr) = sums(:,56) ! wp/dz
1126	hom(:,1,57,sr) = sums(:,57) ! ( w"e + w"p"/rho )/dz
1127	hom(:,1,58,sr) = sums(:,58) ! u"pt"
1128	hom(:,1,59,sr) = sums(:,59) ! upt
1129	hom(:,1,60,sr) = sums(:,58) + sums(:,59) ! upt_t
1130	hom(:,1,61,sr) = sums(:,61) ! v"pt"
1131	hom(:,1,62,sr) = sums(:,62) ! vpt
1132	hom(:,1,63,sr) = sums(:,61) + sums(:,62) ! vpt_t
1133	hom(:,1,64,sr) = sums(:,64) ! rho
1134	hom(:,1,65,sr) = sums(:,65) ! w"sa"
1135	hom(:,1,66,sr) = sums(:,66) ! wsa
1136	hom(:,1,67,sr) = sums(:,65) + sums(:,66) ! wsa
1137	hom(:,1,68,sr) = sums(:,68) ! wp
1138	hom(:,1,69,sr) = sums(:,69) ! w"e + w"p"/rho
1139	hom(:,1,70,sr) = sums(:,70) ! q*2
1140	hom(:,1,71,sr) = sums(:,71) ! prho
1141	hom(:,1,72,sr) = hyp * 1E-4 ! hyp in dbar
1142	hom(:,1,73,sr) = sums(:,73) ! nr
1143	hom(:,1,74,sr) = sums(:,74) ! qr
1144	hom(:,1,75,sr) = sums(:,75) ! qc
1145	hom(:,1,76,sr) = sums(:,76) ! prr (precipitation rate)
1146
1147	hom(:,1,pr_palm-1,sr) = sums(:,pr_palm-1)
1148	! upstream-parts u_x, u_y, u_z, v_x,
1149	! v_y, usw. (in last but one profile)
1150	hom(:,1,pr_palm,sr) = sums(:,pr_palm)
1151	! u, w'u', w'v', t (in last profile)
1152
1153	IF ( max_pr_user > 0 ) THEN ! user-defined profiles
1154	hom(:,1,pr_palm+1:pr_palm+max_pr_user,sr) = &
1155	sums(:,pr_palm+1:pr_palm+max_pr_user)
1156	ENDIF
1157
1158	!
1159	!-- Determine the boundary layer height using two different schemes.
1160	!-- First scheme: Starting from the Earth's (Ocean's) surface, look for the
1161	!-- first relative minimum (maximum) of the total heat flux.
1162	!-- The corresponding height is assumed as the boundary layer height, if it
1163	!-- is less than 1.5 times the height where the heat flux becomes negative
1164	!-- (positive) for the first time.
1165	z_i(1) = 0.0
1166	first = .TRUE.
1167
1168	IF ( ocean ) THEN
1169	DO k = nzt, nzb+1, -1
1170	IF ( first .AND. hom(k,1,18,sr) < 0.0 &
1171	.AND. abs(hom(k,1,18,sr)) > 1.0E-8) THEN
1172	first = .FALSE.
1173	height = zw(k)
1174	ENDIF
1175	IF ( hom(k,1,18,sr) < 0.0 .AND. &
1176	abs(hom(k,1,18,sr)) > 1.0E-8 .AND. &
1177	hom(k-1,1,18,sr) > hom(k,1,18,sr) ) THEN
1178	IF ( zw(k) < 1.5 * height ) THEN
1179	z_i(1) = zw(k)
1180	ELSE
1181	z_i(1) = height
1182	ENDIF
1183	EXIT
1184	ENDIF
1185	ENDDO
1186	ELSE
1187	DO k = nzb, nzt-1
1188	IF ( first .AND. hom(k,1,18,sr) < 0.0 &
1189	.AND. abs(hom(k,1,18,sr)) > 1.0E-8 ) THEN
1190	first = .FALSE.
1191	height = zw(k)
1192	ENDIF
1193	IF ( hom(k,1,18,sr) < 0.0 .AND. &
1194	abs(hom(k,1,18,sr)) > 1.0E-8 .AND. &
1195	hom(k+1,1,18,sr) > hom(k,1,18,sr) ) THEN
1196	IF ( zw(k) < 1.5 * height ) THEN
1197	z_i(1) = zw(k)
1198	ELSE
1199	z_i(1) = height
1200	ENDIF
1201	EXIT
1202	ENDIF
1203	ENDDO
1204	ENDIF
1205
1206	!
1207	!-- Second scheme: Gradient scheme from Sullivan et al. (1998), modified
1208	!-- by Uhlenbrock(2006). The boundary layer height is the height with the
1209	!-- maximal local temperature gradient: starting from the second (the last
1210	!-- but one) vertical gridpoint, the local gradient must be at least
1211	!-- 0.2K/100m and greater than the next four gradients.
1212	!-- WARNING: The threshold value of 0.2K/100m must be adjusted for the
1213	!-- ocean case!
1214	z_i(2) = 0.0
1215	DO k = nzb+1, nzt+1
1216	dptdz(k) = ( hom(k,1,4,sr) - hom(k-1,1,4,sr) ) * ddzu(k)
1217	ENDDO
1218	dptdz_threshold = 0.2 / 100.0
1219
1220	IF ( ocean ) THEN
1221	DO k = nzt+1, nzb+5, -1
1222	IF ( dptdz(k) > dptdz_threshold .AND. &
1223	dptdz(k) > dptdz(k-1) .AND. dptdz(k) > dptdz(k-2) .AND. &
1224	dptdz(k) > dptdz(k-3) .AND. dptdz(k) > dptdz(k-4) ) THEN
1225	z_i(2) = zw(k-1)
1226	EXIT
1227	ENDIF
1228	ENDDO
1229	ELSE
1230	DO k = nzb+1, nzt-3
1231	IF ( dptdz(k) > dptdz_threshold .AND. &
1232	dptdz(k) > dptdz(k+1) .AND. dptdz(k) > dptdz(k+2) .AND. &
1233	dptdz(k) > dptdz(k+3) .AND. dptdz(k) > dptdz(k+4) ) THEN
1234	z_i(2) = zw(k-1)
1235	EXIT
1236	ENDIF
1237	ENDDO
1238	ENDIF
1239
1240	hom(nzb+6,1,pr_palm,sr) = z_i(1)
1241	hom(nzb+7,1,pr_palm,sr) = z_i(2)
1242
1243	!
1244	!-- Computation of both the characteristic vertical velocity and
1245	!-- the characteristic convective boundary layer temperature.
1246	!-- The horizontal average at nzb+1 is input for the average temperature.
1247	IF ( hom(nzb,1,18,sr) > 0.0 .AND. abs(hom(nzb,1,18,sr)) > 1.0E-8 &
1248	.AND. z_i(1) /= 0.0 ) THEN
1249	hom(nzb+8,1,pr_palm,sr) = ( g / hom(nzb+1,1,4,sr) * &
1250	hom(nzb,1,18,sr) * &
1251	ABS( z_i(1) ) )**0.333333333
1252	!-- so far this only works if Prandtl layer is used
1253	hom(nzb+11,1,pr_palm,sr) = hom(nzb,1,16,sr) / hom(nzb+8,1,pr_palm,sr)
1254	ELSE
1255	hom(nzb+8,1,pr_palm,sr) = 0.0
1256	hom(nzb+11,1,pr_palm,sr) = 0.0
1257	ENDIF
1258
1259	!
1260	!-- Collect the time series quantities
1261	ts_value(1,sr) = hom(nzb+4,1,pr_palm,sr) ! E
1262	ts_value(2,sr) = hom(nzb+5,1,pr_palm,sr) ! E*
1263	ts_value(3,sr) = dt_3d
1264	ts_value(4,sr) = hom(nzb,1,pr_palm,sr) ! u*
1265	ts_value(5,sr) = hom(nzb+3,1,pr_palm,sr) ! th*
1266	ts_value(6,sr) = u_max
1267	ts_value(7,sr) = v_max
1268	ts_value(8,sr) = w_max
1269	ts_value(9,sr) = hom(nzb+10,1,pr_palm,sr) ! new divergence
1270	ts_value(10,sr) = hom(nzb+9,1,pr_palm,sr) ! old Divergence
1271	ts_value(11,sr) = hom(nzb+6,1,pr_palm,sr) ! z_i(1)
1272	ts_value(12,sr) = hom(nzb+7,1,pr_palm,sr) ! z_i(2)
1273	ts_value(13,sr) = hom(nzb+8,1,pr_palm,sr) ! w*
1274	ts_value(14,sr) = hom(nzb,1,16,sr) ! w'pt' at k=0
1275	ts_value(15,sr) = hom(nzb+1,1,16,sr) ! w'pt' at k=1
1276	ts_value(16,sr) = hom(nzb+1,1,18,sr) ! wpt at k=1
1277	ts_value(17,sr) = hom(nzb,1,4,sr) ! pt(0)
1278	ts_value(18,sr) = hom(nzb+1,1,4,sr) ! pt(zp)
1279	ts_value(19,sr) = hom(nzb+1,1,pr_palm,sr) ! u'w' at k=0
1280	ts_value(20,sr) = hom(nzb+2,1,pr_palm,sr) ! v'w' at k=0
1281	ts_value(21,sr) = hom(nzb,1,48,sr) ! w"q" at k=0
1282
1283	IF ( ts_value(5,sr) /= 0.0 ) THEN
1284	ts_value(22,sr) = ts_value(4,sr)**2 / &
1285	( kappa * g * ts_value(5,sr) / ts_value(18,sr) ) ! L
1286	ELSE
1287	ts_value(22,sr) = 10000.0
1288	ENDIF
1289
1290	ts_value(23,sr) = hom(nzb+12,1,pr_palm,sr) ! q*
1291	!
1292	!-- Calculate additional statistics provided by the user interface
1293	CALL user_statistics( 'time_series', sr, 0 )
1294
1295	ENDDO ! loop of the subregions
1296
1297	!
1298	!-- If required, sum up horizontal averages for subsequent time averaging
1299	IF ( do_sum ) THEN
1300	IF ( average_count_pr == 0 ) hom_sum = 0.0
1301	hom_sum = hom_sum + hom(:,1,:,:)
1302	average_count_pr = average_count_pr + 1
1303	do_sum = .FALSE.
1304	ENDIF
1305
1306	!
1307	!-- Set flag for other UPs (e.g. output routines, but also buoyancy).
1308	!-- This flag is reset after each time step in time_integration.
1309	flow_statistics_called = .TRUE.
1310
1311	CALL cpu_log( log_point(10), 'flow_statistics', 'stop' )
1312
1313
1314	END SUBROUTINE flow_statistics

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