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source: palm/trunk/SOURCE/flow_statistics.f90 @ 1165

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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 1116 2013-03-26 18:49:55Z raasch $
27	!
28	! 1115 2013-03-26 18:16:16Z hoffmann
29	! ql is calculated by calc_liquid_water_content
30	!
31	! 1111 2013-03-08 23:54:10Z raasch
32	! openACC directive added
33	!
34	! 1053 2012-11-13 17:11:03Z hoffmann
35	! additions for two-moment cloud physics scheme:
36	! +nr, qr, qc, prr
37	!
38	! 1036 2012-10-22 13:43:42Z raasch
39	! code put under GPL (PALM 3.9)
40	!
41	! 1007 2012-09-19 14:30:36Z franke
42	! Calculation of buoyancy flux for humidity in case of WS-scheme is now using
43	! turbulent fluxes of WS-scheme
44	! Bugfix: Calculation of subgridscale buoyancy flux for humidity and cloud
45	! droplets at nzb and nzt added
46	!
47	! 801 2012-01-10 17:30:36Z suehring
48	! Calculation of turbulent fluxes in advec_ws is now thread-safe.
49	!
50	! 743 2011-08-18 16:10:16Z suehring
51	! Calculation of turbulent fluxes with WS-scheme only for the whole model
52	! domain, not for user-defined subregions.
53	!
54	! 709 2011-03-30 09:31:40Z raasch
55	! formatting adjustments
56	!
57	! 699 2011-03-22 17:52:22Z suehring
58	! Bugfix in calculation of vertical velocity skewness. The added absolute value
59	! avoid negative values in the root. Negative values of w'w' can occur at the
60	! top or bottom of the model domain due to degrading the order of advection
61	! scheme. Furthermore the calculation will be the same for all advection
62	! schemes.
63	!
64	! 696 2011-03-18 07:03:49Z raasch
65	! Bugfix: Summation of Wicker-Skamarock scheme fluxes and variances for all
66	! threads
67	!
68	! 678 2011-02-02 14:31:56Z raasch
69	! Bugfix in calculation of the divergence of vertical flux of resolved scale
70	! energy, pressure fluctuations, and flux of pressure fluctuation itself
71	!
72	! 673 2011-01-18 16:19:48Z suehring
73	! Top bc for the horizontal velocity variances added for ocean runs.
74	! Setting the corresponding bottom bc moved to advec_ws.
75	!
76	! 667 2010-12-23 12:06:00Z suehring/gryschka
77	! When advection is computed with ws-scheme, turbulent fluxes are already
78	! computed in the respective advection routines and buffered in arrays
79	! sums_xx_ws_l(). This is due to a consistent treatment of statistics with the
80	! numerics and to avoid unphysical kinks near the surface.
81	! So some if requests has to be done to dicern between fluxes from ws-scheme
82	! other advection schemes.
83	! Furthermore the computation of z_i is only done if the heat flux exceeds a
84	! minimum value. This affects only simulations of a neutral boundary layer and
85	! is due to reasons of computations in the advection scheme.
86	!
87	! 624 2010-12-10 11:46:30Z heinze
88	! Calculation of q*2 added
89	!
90	! 622 2010-12-10 08:08:13Z raasch
91	! optional barriers included in order to speed up collective operations
92	!
93	! 388 2009-09-23 09:40:33Z raasch
94	! Vertical profiles of potential density and hydrostatic pressure are
95	! calculated.
96	! Added missing timeseries calculation of w"q"(0), moved timeseries q* to the
97	! end.
98	! Temperature gradient criterion for estimating the boundary layer height
99	! replaced by the gradient criterion of Sullivan et al. (1998).
100	! Output of messages replaced by message handling routine.
101	!
102	! 197 2008-09-16 15:29:03Z raasch
103	! Spline timeseries splptx etc. removed, timeseries w'u', w'v', w'q' (k=0)
104	! added,
105	! bugfix: divide sums(k,8) (e) and sums(k,34) (e*) by ngp_2dh_s_inner(k,sr)
106	! (like other scalars)
107	!
108	! 133 2007-11-20 10:10:53Z letzel
109	! Vertical profiles now based on nzb_s_inner; they are divided by
110	! ngp_2dh_s_inner (scalars, procucts of scalars) and ngp_2dh (staggered
111	! velocity components and their products, procucts of scalars and velocity
112	! components), respectively.
113	!
114	! 106 2007-08-16 14:30:26Z raasch
115	! Prescribed momentum fluxes at the top surface are used,
116	! profiles for wp and w"e are calculated
117	!
118	! 97 2007-06-21 08:23:15Z raasch
119	! Statistics for ocean version (salinity, density) added,
120	! calculation of z_i and Deardorff velocity scale adjusted to be used with
121	! the ocean version
122	!
123	! 87 2007-05-22 15:46:47Z raasch
124	! Two more arguments added to user_statistics, which is now also called for
125	! user-defined profiles,
126	! var_hom and var_sum renamed pr_palm
127	!
128	! 82 2007-04-16 15:40:52Z raasch
129	! Cpp-directive lcmuk changed to intel_openmp_bug
130	!
131	! 75 2007-03-22 09:54:05Z raasch
132	! Collection of time series quantities moved from routine flow_statistics to
133	! here, routine user_statistics is called for each statistic region,
134	! moisture renamed humidity
135	!
136	! 19 2007-02-23 04:53:48Z raasch
137	! fluxes at top modified (tswst, qswst)
138	!
139	! RCS Log replace by Id keyword, revision history cleaned up
140	!
141	! Revision 1.41 2006/08/04 14:37:50 raasch
142	! Error removed in non-parallel part (sums_l)
143	!
144	! Revision 1.1 1997/08/11 06:15:17 raasch
145	! Initial revision
146	!
147	!
148	! Description:
149	! ------------
150	! Compute average profiles and further average flow quantities for the different
151	! user-defined (sub-)regions. The region indexed 0 is the total model domain.
152	!
153	! NOTE: For simplicity, nzb_s_inner and nzb_diff_s_inner are being used as a
154	! ---- lower vertical index for k-loops for all variables, although strictly
155	! speaking the k-loops would have to be split up according to the staggered
156	! grid. However, this implies no error since staggered velocity components are
157	! zero at the walls and inside buildings.
158	!------------------------------------------------------------------------------!
159
160	USE arrays_3d
161	USE cloud_parameters
162	USE control_parameters
163	USE cpulog
164	USE grid_variables
165	USE indices
166	USE interfaces
167	USE pegrid
168	USE statistics
169
170	IMPLICIT NONE
171
172	INTEGER :: i, j, k, omp_get_thread_num, sr, tn
173	LOGICAL :: first
174	REAL :: dptdz_threshold, height, pts, sums_l_eper, sums_l_etot, ust, &
175	ust2, u2, vst, vst2, v2, w2, z_i(2)
176	REAL :: dptdz(nzb+1:nzt+1)
177	REAL :: sums_ll(nzb:nzt+1,2)
178
179	CALL cpu_log( log_point(10), 'flow_statistics', 'start' )
180
181	!
182	!-- To be on the safe side, check whether flow_statistics has already been
183	!-- called once after the current time step
184	IF ( flow_statistics_called ) THEN
185
186	message_string = 'flow_statistics is called two times within one ' // &
187	'timestep'
188	CALL message( 'flow_statistics', 'PA0190', 1, 2, 0, 6, 0 )
189
190	ENDIF
191
192	!$acc update host( km, kh, e, pt, qs, qsws, rif, shf, ts, u, v, w )
193
194	!
195	!-- Compute statistics for each (sub-)region
196	DO sr = 0, statistic_regions
197
198	!
199	!-- Initialize (local) summation array
200	sums_l = 0.0
201
202	!
203	!-- Store sums that have been computed in other subroutines in summation
204	!-- array
205	sums_l(:,11,:) = sums_l_l(:,sr,:) ! mixing length from diffusivities
206	!-- WARNING: next line still has to be adjusted for OpenMP
207	sums_l(:,21,0) = sums_wsts_bc_l(:,sr) ! heat flux from advec_s_bc
208	sums_l(nzb+9,pr_palm,0) = sums_divold_l(sr) ! old divergence from pres
209	sums_l(nzb+10,pr_palm,0) = sums_divnew_l(sr) ! new divergence from pres
210
211	!
212	!-- Copy the turbulent quantities, evaluated in the advection routines to
213	!-- the local array sums_l() for further computations
214	IF ( ws_scheme_mom .AND. sr == 0 ) THEN
215
216	!
217	!-- According to the Neumann bc for the horizontal velocity components,
218	!-- the corresponding fluxes has to satisfiy the same bc.
219	IF ( ocean ) THEN
220	sums_us2_ws_l(nzt+1,:) = sums_us2_ws_l(nzt,:)
221	sums_vs2_ws_l(nzt+1,:) = sums_vs2_ws_l(nzt,:)
222	ENDIF
223
224	DO i = 0, threads_per_task-1
225	!
226	!-- Swap the turbulent quantities evaluated in advec_ws.
227	sums_l(:,13,i) = sums_wsus_ws_l(:,i) ! wu
228	sums_l(:,15,i) = sums_wsvs_ws_l(:,i) ! wv
229	sums_l(:,30,i) = sums_us2_ws_l(:,i) ! u*2
230	sums_l(:,31,i) = sums_vs2_ws_l(:,i) ! v*2
231	sums_l(:,32,i) = sums_ws2_ws_l(:,i) ! w*2
232	sums_l(:,34,i) = sums_l(:,34,i) + 0.5 * &
233	( sums_us2_ws_l(:,i) + sums_vs2_ws_l(:,i) + &
234	sums_ws2_ws_l(:,i) ) ! e*
235	DO k = nzb, nzt
236	sums_l(nzb+5,pr_palm,i) = sums_l(nzb+5,pr_palm,i) + 0.5 * ( &
237	sums_us2_ws_l(k,i) + &
238	sums_vs2_ws_l(k,i) + &
239	sums_ws2_ws_l(k,i) )
240	ENDDO
241	ENDDO
242
243	ENDIF
244
245	IF ( ws_scheme_sca .AND. sr == 0 ) THEN
246
247	DO i = 0, threads_per_task-1
248	sums_l(:,17,i) = sums_wspts_ws_l(:,i) ! wpt from advec_s_ws
249	IF ( ocean ) sums_l(:,66,i) = sums_wssas_ws_l(:,i) ! wsa
250	IF ( humidity .OR. passive_scalar ) sums_l(:,49,i) = &
251	sums_wsqs_ws_l(:,i) !wq
252	ENDDO
253
254	ENDIF
255	!
256	!-- Horizontally averaged profiles of horizontal velocities and temperature.
257	!-- They must have been computed before, because they are already required
258	!-- for other horizontal averages.
259	tn = 0
260
261	!$OMP PARALLEL PRIVATE( i, j, k, tn )
262	#if defined( __intel_openmp_bug )
263	tn = omp_get_thread_num()
264	#else
265	!$ tn = omp_get_thread_num()
266	#endif
267
268	!$OMP DO
269	DO i = nxl, nxr
270	DO j = nys, nyn
271	DO k = nzb_s_inner(j,i), nzt+1
272	sums_l(k,1,tn) = sums_l(k,1,tn) + u(k,j,i) * rmask(j,i,sr)
273	sums_l(k,2,tn) = sums_l(k,2,tn) + v(k,j,i) * rmask(j,i,sr)
274	sums_l(k,4,tn) = sums_l(k,4,tn) + pt(k,j,i) * rmask(j,i,sr)
275	ENDDO
276	ENDDO
277	ENDDO
278
279	!
280	!-- Horizontally averaged profile of salinity
281	IF ( ocean ) THEN
282	!$OMP DO
283	DO i = nxl, nxr
284	DO j = nys, nyn
285	DO k = nzb_s_inner(j,i), nzt+1
286	sums_l(k,23,tn) = sums_l(k,23,tn) + &
287	sa(k,j,i) * rmask(j,i,sr)
288	ENDDO
289	ENDDO
290	ENDDO
291	ENDIF
292
293	!
294	!-- Horizontally averaged profiles of virtual potential temperature,
295	!-- total water content, specific humidity and liquid water potential
296	!-- temperature
297	IF ( humidity ) THEN
298	!$OMP DO
299	DO i = nxl, nxr
300	DO j = nys, nyn
301	DO k = nzb_s_inner(j,i), nzt+1
302	sums_l(k,44,tn) = sums_l(k,44,tn) + &
303	vpt(k,j,i) * rmask(j,i,sr)
304	sums_l(k,41,tn) = sums_l(k,41,tn) + &
305	q(k,j,i) * rmask(j,i,sr)
306	ENDDO
307	ENDDO
308	ENDDO
309	IF ( cloud_physics ) THEN
310	!$OMP DO
311	DO i = nxl, nxr
312	DO j = nys, nyn
313	DO k = nzb_s_inner(j,i), nzt+1
314	sums_l(k,42,tn) = sums_l(k,42,tn) + &
315	( q(k,j,i) - ql(k,j,i) ) * rmask(j,i,sr)
316	sums_l(k,43,tn) = sums_l(k,43,tn) + ( &
317	pt(k,j,i) + l_d_cppt_d_t(k) ql(k,j,i) &
318	) * rmask(j,i,sr)
319	ENDDO
320	ENDDO
321	ENDDO
322	ENDIF
323	ENDIF
324
325	!
326	!-- Horizontally averaged profiles of passive scalar
327	IF ( passive_scalar ) THEN
328	!$OMP DO
329	DO i = nxl, nxr
330	DO j = nys, nyn
331	DO k = nzb_s_inner(j,i), nzt+1
332	sums_l(k,41,tn) = sums_l(k,41,tn) + q(k,j,i) * rmask(j,i,sr)
333	ENDDO
334	ENDDO
335	ENDDO
336	ENDIF
337	!$OMP END PARALLEL
338	!
339	!-- Summation of thread sums
340	IF ( threads_per_task > 1 ) THEN
341	DO i = 1, threads_per_task-1
342	sums_l(:,1,0) = sums_l(:,1,0) + sums_l(:,1,i)
343	sums_l(:,2,0) = sums_l(:,2,0) + sums_l(:,2,i)
344	sums_l(:,4,0) = sums_l(:,4,0) + sums_l(:,4,i)
345	IF ( ocean ) THEN
346	sums_l(:,23,0) = sums_l(:,23,0) + sums_l(:,23,i)
347	ENDIF
348	IF ( humidity ) THEN
349	sums_l(:,41,0) = sums_l(:,41,0) + sums_l(:,41,i)
350	sums_l(:,44,0) = sums_l(:,44,0) + sums_l(:,44,i)
351	IF ( cloud_physics ) THEN
352	sums_l(:,42,0) = sums_l(:,42,0) + sums_l(:,42,i)
353	sums_l(:,43,0) = sums_l(:,43,0) + sums_l(:,43,i)
354	ENDIF
355	ENDIF
356	IF ( passive_scalar ) THEN
357	sums_l(:,41,0) = sums_l(:,41,0) + sums_l(:,41,i)
358	ENDIF
359	ENDDO
360	ENDIF
361
362	#if defined( __parallel )
363	!
364	!-- Compute total sum from local sums
365	IF ( collective_wait ) CALL MPI_BARRIER( comm2d, ierr )
366	CALL MPI_ALLREDUCE( sums_l(nzb,1,0), sums(nzb,1), 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,2,0), sums(nzb,2), nzt+2-nzb, MPI_REAL, &
370	MPI_SUM, comm2d, ierr )
371	IF ( collective_wait ) CALL MPI_BARRIER( comm2d, ierr )
372	CALL MPI_ALLREDUCE( sums_l(nzb,4,0), sums(nzb,4), nzt+2-nzb, MPI_REAL, &
373	MPI_SUM, comm2d, ierr )
374	IF ( ocean ) THEN
375	IF ( collective_wait ) CALL MPI_BARRIER( comm2d, ierr )
376	CALL MPI_ALLREDUCE( sums_l(nzb,23,0), sums(nzb,23), nzt+2-nzb, &
377	MPI_REAL, MPI_SUM, comm2d, ierr )
378	ENDIF
379	IF ( humidity ) THEN
380	IF ( collective_wait ) CALL MPI_BARRIER( comm2d, ierr )
381	CALL MPI_ALLREDUCE( sums_l(nzb,44,0), sums(nzb,44), nzt+2-nzb, &
382	MPI_REAL, MPI_SUM, comm2d, ierr )
383	IF ( collective_wait ) CALL MPI_BARRIER( comm2d, ierr )
384	CALL MPI_ALLREDUCE( sums_l(nzb,41,0), sums(nzb,41), nzt+2-nzb, &
385	MPI_REAL, MPI_SUM, comm2d, ierr )
386	IF ( cloud_physics ) THEN
387	IF ( collective_wait ) CALL MPI_BARRIER( comm2d, ierr )
388	CALL MPI_ALLREDUCE( sums_l(nzb,42,0), sums(nzb,42), nzt+2-nzb, &
389	MPI_REAL, MPI_SUM, comm2d, ierr )
390	IF ( collective_wait ) CALL MPI_BARRIER( comm2d, ierr )
391	CALL MPI_ALLREDUCE( sums_l(nzb,43,0), sums(nzb,43), nzt+2-nzb, &
392	MPI_REAL, MPI_SUM, comm2d, ierr )
393	ENDIF
394	ENDIF
395
396	IF ( passive_scalar ) THEN
397	IF ( collective_wait ) CALL MPI_BARRIER( comm2d, ierr )
398	CALL MPI_ALLREDUCE( sums_l(nzb,41,0), sums(nzb,41), nzt+2-nzb, &
399	MPI_REAL, MPI_SUM, comm2d, ierr )
400	ENDIF
401	#else
402	sums(:,1) = sums_l(:,1,0)
403	sums(:,2) = sums_l(:,2,0)
404	sums(:,4) = sums_l(:,4,0)
405	IF ( ocean ) sums(:,23) = sums_l(:,23,0)
406	IF ( humidity ) THEN
407	sums(:,44) = sums_l(:,44,0)
408	sums(:,41) = sums_l(:,41,0)
409	IF ( cloud_physics ) THEN
410	sums(:,42) = sums_l(:,42,0)
411	sums(:,43) = sums_l(:,43,0)
412	ENDIF
413	ENDIF
414	IF ( passive_scalar ) sums(:,41) = sums_l(:,41,0)
415	#endif
416
417	!
418	!-- Final values are obtained by division by the total number of grid points
419	!-- used for summation. After that store profiles.
420	sums(:,1) = sums(:,1) / ngp_2dh(sr)
421	sums(:,2) = sums(:,2) / ngp_2dh(sr)
422	sums(:,4) = sums(:,4) / ngp_2dh_s_inner(:,sr)
423	hom(:,1,1,sr) = sums(:,1) ! u
424	hom(:,1,2,sr) = sums(:,2) ! v
425	hom(:,1,4,sr) = sums(:,4) ! pt
426
427
428	!
429	!-- Salinity
430	IF ( ocean ) THEN
431	sums(:,23) = sums(:,23) / ngp_2dh_s_inner(:,sr)
432	hom(:,1,23,sr) = sums(:,23) ! sa
433	ENDIF
434
435	!
436	!-- Humidity and cloud parameters
437	IF ( humidity ) THEN
438	sums(:,44) = sums(:,44) / ngp_2dh_s_inner(:,sr)
439	sums(:,41) = sums(:,41) / ngp_2dh_s_inner(:,sr)
440	hom(:,1,44,sr) = sums(:,44) ! vpt
441	hom(:,1,41,sr) = sums(:,41) ! qv (q)
442	IF ( cloud_physics ) THEN
443	sums(:,42) = sums(:,42) / ngp_2dh_s_inner(:,sr)
444	sums(:,43) = sums(:,43) / ngp_2dh_s_inner(:,sr)
445	hom(:,1,42,sr) = sums(:,42) ! qv
446	hom(:,1,43,sr) = sums(:,43) ! pt
447	ENDIF
448	ENDIF
449
450	!
451	!-- Passive scalar
452	IF ( passive_scalar ) hom(:,1,41,sr) = sums(:,41) / &
453	ngp_2dh_s_inner(:,sr) ! s (q)
454
455	!
456	!-- Horizontally averaged profiles of the remaining prognostic variables,
457	!-- variances, the total and the perturbation energy (single values in last
458	!-- column of sums_l) and some diagnostic quantities.
459	!-- NOTE: for simplicity, nzb_s_inner is used below, although strictly
460	!-- ---- speaking the following k-loop would have to be split up and
461	!-- rearranged according to the staggered grid.
462	!-- However, this implies no error since staggered velocity components
463	!-- are zero at the walls and inside buildings.
464	tn = 0
465	#if defined( __intel_openmp_bug )
466	!$OMP PARALLEL PRIVATE( i, j, k, pts, sums_ll, sums_l_eper, sums_l_etot, &
467	!$OMP tn, ust, ust2, u2, vst, vst2, v2, w2 )
468	tn = omp_get_thread_num()
469	#else
470	!$OMP PARALLEL PRIVATE( i, j, k, pts, sums_ll, sums_l_eper, sums_l_etot, tn, ust, ust2, u2, vst, vst2, v2, w2 )
471	!$ tn = omp_get_thread_num()
472	#endif
473	!$OMP DO
474	DO i = nxl, nxr
475	DO j = nys, nyn
476	sums_l_etot = 0.0
477	DO k = nzb_s_inner(j,i), nzt+1
478	!
479	!-- Prognostic and diagnostic variables
480	sums_l(k,3,tn) = sums_l(k,3,tn) + w(k,j,i) * rmask(j,i,sr)
481	sums_l(k,8,tn) = sums_l(k,8,tn) + e(k,j,i) * rmask(j,i,sr)
482	sums_l(k,9,tn) = sums_l(k,9,tn) + km(k,j,i) * rmask(j,i,sr)
483	sums_l(k,10,tn) = sums_l(k,10,tn) + kh(k,j,i) * rmask(j,i,sr)
484	sums_l(k,40,tn) = sums_l(k,40,tn) + p(k,j,i)
485
486	sums_l(k,33,tn) = sums_l(k,33,tn) + &
487	( pt(k,j,i)-hom(k,1,4,sr) )*2 rmask(j,i,sr)
488
489	IF ( humidity ) THEN
490	sums_l(k,70,tn) = sums_l(k,70,tn) + &
491	( q(k,j,i)-hom(k,1,41,sr) )*2 rmask(j,i,sr)
492	ENDIF
493
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)*3 rmask(j,i,sr)
498
499	sums_l_etot = sums_l_etot + &
500	0.5 * ( u(k,j,i)2 + v(k,j,i)2 + &
501	w(k,j,i)*2 ) rmask(j,i,sr)
502	ENDDO
503	!
504	!-- Total and perturbation energy for the total domain (being
505	!-- collected in the last column of sums_l). Summation of these
506	!-- quantities is seperated from the previous loop in order to
507	!-- allow vectorization of that loop.
508	sums_l(nzb+4,pr_palm,tn) = sums_l(nzb+4,pr_palm,tn) + sums_l_etot
509	!
510	!-- 2D-arrays (being collected in the last column of sums_l)
511	sums_l(nzb,pr_palm,tn) = sums_l(nzb,pr_palm,tn) + &
512	us(j,i) * rmask(j,i,sr)
513	sums_l(nzb+1,pr_palm,tn) = sums_l(nzb+1,pr_palm,tn) + &
514	usws(j,i) * rmask(j,i,sr)
515	sums_l(nzb+2,pr_palm,tn) = sums_l(nzb+2,pr_palm,tn) + &
516	vsws(j,i) * rmask(j,i,sr)
517	sums_l(nzb+3,pr_palm,tn) = sums_l(nzb+3,pr_palm,tn) + &
518	ts(j,i) * rmask(j,i,sr)
519	IF ( humidity ) THEN
520	sums_l(nzb+12,pr_palm,tn) = sums_l(nzb+12,pr_palm,tn) + &
521	qs(j,i) * rmask(j,i,sr)
522	ENDIF
523	ENDDO
524	ENDDO
525
526	!
527	!-- Computation of statistics when ws-scheme is not used. Else these
528	!-- quantities are evaluated in the advection routines.
529	IF ( .NOT. ws_scheme_mom .OR. sr /= 0 ) THEN
530	!$OMP DO
531	DO i = nxl, nxr
532	DO j = nys, nyn
533	sums_l_eper = 0.0
534	DO k = nzb_s_inner(j,i), nzt+1
535	u2 = u(k,j,i)**2
536	v2 = v(k,j,i)**2
537	w2 = w(k,j,i)**2
538	ust2 = ( u(k,j,i) - hom(k,1,1,sr) )**2
539	vst2 = ( v(k,j,i) - hom(k,1,2,sr) )**2
540
541	sums_l(k,30,tn) = sums_l(k,30,tn) + ust2 * rmask(j,i,sr)
542	sums_l(k,31,tn) = sums_l(k,31,tn) + vst2 * rmask(j,i,sr)
543	sums_l(k,32,tn) = sums_l(k,32,tn) + w2 * rmask(j,i,sr)
544	!
545	!-- Perturbation energy
546
547	sums_l(k,34,tn) = sums_l(k,34,tn) + 0.5 * &
548	( ust2 + vst2 + w2 ) * rmask(j,i,sr)
549	sums_l_eper = sums_l_eper + &
550	0.5 * ( ust2+vst2+w2 ) * rmask(j,i,sr)
551
552	ENDDO
553	sums_l(nzb+5,pr_palm,tn) = sums_l(nzb+5,pr_palm,tn) &
554	+ sums_l_eper
555	ENDDO
556	ENDDO
557	ENDIF
558	!
559	!-- Horizontally averaged profiles of the vertical fluxes
560
561	!$OMP DO
562	DO i = nxl, nxr
563	DO j = nys, nyn
564	!
565	!-- Subgridscale fluxes (without Prandtl layer from k=nzb,
566	!-- oterwise from k=nzb+1)
567	!-- NOTE: for simplicity, nzb_diff_s_inner is used below, although
568	!-- ---- strictly speaking the following k-loop would have to be
569	!-- split up according to the staggered grid.
570	!-- However, this implies no error since staggered velocity
571	!-- components are zero at the walls and inside buildings.
572
573	DO k = nzb_diff_s_inner(j,i)-1, nzt_diff
574	!
575	!-- Momentum flux w"u"
576	sums_l(k,12,tn) = sums_l(k,12,tn) - 0.25 * ( &
577	km(k,j,i)+km(k+1,j,i)+km(k,j,i-1)+km(k+1,j,i-1) &
578	) * ( &
579	( u(k+1,j,i) - u(k,j,i) ) * ddzu(k+1) &
580	+ ( w(k,j,i) - w(k,j,i-1) ) * ddx &
581	) * rmask(j,i,sr)
582	!
583	!-- Momentum flux w"v"
584	sums_l(k,14,tn) = sums_l(k,14,tn) - 0.25 * ( &
585	km(k,j,i)+km(k+1,j,i)+km(k,j-1,i)+km(k+1,j-1,i) &
586	) * ( &
587	( v(k+1,j,i) - v(k,j,i) ) * ddzu(k+1) &
588	+ ( w(k,j,i) - w(k,j-1,i) ) * ddy &
589	) * rmask(j,i,sr)
590	!
591	!-- Heat flux w"pt"
592	sums_l(k,16,tn) = sums_l(k,16,tn) &
593	- 0.5 * ( kh(k,j,i) + kh(k+1,j,i) ) &
594	* ( pt(k+1,j,i) - pt(k,j,i) ) &
595	* ddzu(k+1) * rmask(j,i,sr)
596
597
598	!
599	!-- Salinity flux w"sa"
600	IF ( ocean ) THEN
601	sums_l(k,65,tn) = sums_l(k,65,tn) &
602	- 0.5 * ( kh(k,j,i) + kh(k+1,j,i) ) &
603	* ( sa(k+1,j,i) - sa(k,j,i) ) &
604	* ddzu(k+1) * rmask(j,i,sr)
605	ENDIF
606
607	!
608	!-- Buoyancy flux, water flux (humidity flux) w"q"
609	IF ( humidity ) THEN
610	sums_l(k,45,tn) = sums_l(k,45,tn) &
611	- 0.5 * ( kh(k,j,i) + kh(k+1,j,i) ) &
612	* ( vpt(k+1,j,i) - vpt(k,j,i) ) &
613	* ddzu(k+1) * rmask(j,i,sr)
614	sums_l(k,48,tn) = sums_l(k,48,tn) &
615	- 0.5 * ( kh(k,j,i) + kh(k+1,j,i) ) &
616	* ( q(k+1,j,i) - q(k,j,i) ) &
617	* ddzu(k+1) * rmask(j,i,sr)
618
619	IF ( cloud_physics ) THEN
620	sums_l(k,51,tn) = sums_l(k,51,tn) &
621	- 0.5 * ( kh(k,j,i) + kh(k+1,j,i) ) &
622	* ( ( q(k+1,j,i) - ql(k+1,j,i) )&
623	- ( q(k,j,i) - ql(k,j,i) ) ) &
624	* ddzu(k+1) * rmask(j,i,sr)
625	ENDIF
626	ENDIF
627
628	!
629	!-- Passive scalar flux
630	IF ( passive_scalar ) THEN
631	sums_l(k,48,tn) = sums_l(k,48,tn) &
632	- 0.5 * ( kh(k,j,i) + kh(k+1,j,i) ) &
633	* ( q(k+1,j,i) - q(k,j,i) ) &
634	* ddzu(k+1) * rmask(j,i,sr)
635	ENDIF
636
637	ENDDO
638
639	!
640	!-- Subgridscale fluxes in the Prandtl layer
641	IF ( use_surface_fluxes ) THEN
642	sums_l(nzb,12,tn) = sums_l(nzb,12,tn) + &
643	usws(j,i) * rmask(j,i,sr) ! w"u"
644	sums_l(nzb,14,tn) = sums_l(nzb,14,tn) + &
645	vsws(j,i) * rmask(j,i,sr) ! w"v"
646	sums_l(nzb,16,tn) = sums_l(nzb,16,tn) + &
647	shf(j,i) * rmask(j,i,sr) ! w"pt"
648	sums_l(nzb,58,tn) = sums_l(nzb,58,tn) + &
649	0.0 * rmask(j,i,sr) ! u"pt"
650	sums_l(nzb,61,tn) = sums_l(nzb,61,tn) + &
651	0.0 * rmask(j,i,sr) ! v"pt"
652	IF ( ocean ) THEN
653	sums_l(nzb,65,tn) = sums_l(nzb,65,tn) + &
654	saswsb(j,i) * rmask(j,i,sr) ! w"sa"
655	ENDIF
656	IF ( humidity ) THEN
657	sums_l(nzb,48,tn) = sums_l(nzb,48,tn) + &
658	qsws(j,i) * rmask(j,i,sr) ! w"q" (w"qv")
659	sums_l(nzb,45,tn) = sums_l(nzb,45,tn) + ( &
660	( 1.0 + 0.61 * q(nzb,j,i) ) * &
661	shf(j,i) + 0.61 * pt(nzb,j,i) * &
662	qsws(j,i) )
663	IF ( cloud_droplets ) THEN
664	sums_l(nzb,45,tn) = sums_l(nzb,45,tn) + ( &
665	( 1.0 + 0.61 * q(nzb,j,i) - &
666	ql(nzb,j,i) ) * shf(j,i) + &
667	0.61 * pt(nzb,j,i) * qsws(j,i) )
668	ENDIF
669	IF ( cloud_physics ) THEN
670	!
671	!-- Formula does not work if ql(nzb) /= 0.0
672	sums_l(nzb,51,tn) = sums_l(nzb,51,tn) + & ! w"q" (w"qv")
673	qsws(j,i) * rmask(j,i,sr)
674	ENDIF
675	ENDIF
676	IF ( passive_scalar ) THEN
677	sums_l(nzb,48,tn) = sums_l(nzb,48,tn) + &
678	qsws(j,i) * rmask(j,i,sr) ! w"q" (w"qv")
679	ENDIF
680	ENDIF
681
682	!
683	!-- Subgridscale fluxes at the top surface
684	IF ( use_top_fluxes ) THEN
685	sums_l(nzt:nzt+1,12,tn) = sums_l(nzt:nzt+1,12,tn) + &
686	uswst(j,i) * rmask(j,i,sr) ! w"u"
687	sums_l(nzt:nzt+1,14,tn) = sums_l(nzt:nzt+1,14,tn) + &
688	vswst(j,i) * rmask(j,i,sr) ! w"v"
689	sums_l(nzt:nzt+1,16,tn) = sums_l(nzt:nzt+1,16,tn) + &
690	tswst(j,i) * rmask(j,i,sr) ! w"pt"
691	sums_l(nzt:nzt+1,58,tn) = sums_l(nzt:nzt+1,58,tn) + &
692	0.0 * rmask(j,i,sr) ! u"pt"
693	sums_l(nzt:nzt+1,61,tn) = sums_l(nzt:nzt+1,61,tn) + &
694	0.0 * rmask(j,i,sr) ! v"pt"
695
696	IF ( ocean ) THEN
697	sums_l(nzt,65,tn) = sums_l(nzt,65,tn) + &
698	saswst(j,i) * rmask(j,i,sr) ! w"sa"
699	ENDIF
700	IF ( humidity ) THEN
701	sums_l(nzt,48,tn) = sums_l(nzt,48,tn) + &
702	qswst(j,i) * rmask(j,i,sr) ! w"q" (w"qv")
703	sums_l(nzt,45,tn) = sums_l(nzt,45,tn) + ( &
704	( 1.0 + 0.61 * q(nzt,j,i) ) * &
705	tswst(j,i) + 0.61 * pt(nzt,j,i) * &
706	qswst(j,i) )
707	IF ( cloud_droplets ) THEN
708	sums_l(nzt,45,tn) = sums_l(nzt,45,tn) + ( &
709	( 1.0 + 0.61 * q(nzt,j,i) - &
710	ql(nzt,j,i) ) * tswst(j,i) + &
711	0.61 * pt(nzt,j,i) * qswst(j,i) )
712	ENDIF
713	IF ( cloud_physics ) THEN
714	!
715	!-- Formula does not work if ql(nzb) /= 0.0
716	sums_l(nzt,51,tn) = sums_l(nzt,51,tn) + & ! w"q" (w"qv")
717	qswst(j,i) * rmask(j,i,sr)
718	ENDIF
719	ENDIF
720	IF ( passive_scalar ) THEN
721	sums_l(nzt,48,tn) = sums_l(nzt,48,tn) + &
722	qswst(j,i) * rmask(j,i,sr) ! w"q" (w"qv")
723	ENDIF
724	ENDIF
725
726	!
727	!-- Resolved fluxes (can be computed for all horizontal points)
728	!-- NOTE: for simplicity, nzb_s_inner is used below, although strictly
729	!-- ---- speaking the following k-loop would have to be split up and
730	!-- rearranged according to the staggered grid.
731	DO k = nzb_s_inner(j,i), nzt
732	ust = 0.5 * ( u(k,j,i) - hom(k,1,1,sr) + &
733	u(k+1,j,i) - hom(k+1,1,1,sr) )
734	vst = 0.5 * ( v(k,j,i) - hom(k,1,2,sr) + &
735	v(k+1,j,i) - hom(k+1,1,2,sr) )
736	pts = 0.5 * ( pt(k,j,i) - hom(k,1,4,sr) + &
737	pt(k+1,j,i) - hom(k+1,1,4,sr) )
738
739	!-- Higher moments
740	sums_l(k,35,tn) = sums_l(k,35,tn) + pts * w(k,j,i)*2 &
741	rmask(j,i,sr)
742	sums_l(k,36,tn) = sums_l(k,36,tn) + pts*2 w(k,j,i) * &
743	rmask(j,i,sr)
744
745	!
746	!-- Salinity flux and density (density does not belong to here,
747	!-- but so far there is no other suitable place to calculate)
748	IF ( ocean ) THEN
749	IF( .NOT. ws_scheme_sca .OR. sr /= 0 ) THEN
750	pts = 0.5 * ( sa(k,j,i) - hom(k,1,23,sr) + &
751	sa(k+1,j,i) - hom(k+1,1,23,sr) )
752	sums_l(k,66,tn) = sums_l(k,66,tn) + pts * w(k,j,i) * &
753	rmask(j,i,sr)
754	ENDIF
755	sums_l(k,64,tn) = sums_l(k,64,tn) + rho(k,j,i) * &
756	rmask(j,i,sr)
757	sums_l(k,71,tn) = sums_l(k,71,tn) + prho(k,j,i) * &
758	rmask(j,i,sr)
759	ENDIF
760
761	!
762	!-- Buoyancy flux, water flux, humidity flux, liquid water
763	!-- content, rain drop concentration and rain water content
764	IF ( humidity ) THEN
765	IF ( cloud_physics .OR. cloud_droplets ) THEN
766	pts = 0.5 * ( vpt(k,j,i) - hom(k,1,44,sr) + &
767	vpt(k+1,j,i) - hom(k+1,1,44,sr) )
768	sums_l(k,46,tn) = sums_l(k,46,tn) + pts * w(k,j,i) * &
769	rmask(j,i,sr)
770	IF ( .NOT. cloud_droplets ) THEN
771	pts = 0.5 * &
772	( ( q(k,j,i) - ql(k,j,i) ) - &
773	hom(k,1,42,sr) + &
774	( q(k+1,j,i) - ql(k+1,j,i) ) - &
775	hom(k+1,1,42,sr) )
776	sums_l(k,52,tn) = sums_l(k,52,tn) + pts * w(k,j,i) * &
777	rmask(j,i,sr)
778	IF ( icloud_scheme == 0 ) THEN
779	sums_l(k,54,tn) = sums_l(k,54,tn) + ql(k,j,i) * &
780	rmask(j,i,sr)
781	sums_l(k,75,tn) = sums_l(k,75,tn) + qc(k,j,i) * &
782	rmask(j,i,sr)
783	IF ( precipitation ) THEN
784	sums_l(k,73,tn) = sums_l(k,73,tn) + nr(k,j,i) * &
785	rmask(j,i,sr)
786	sums_l(k,74,tn) = sums_l(k,74,tn) + qr(k,j,i) * &
787	rmask(j,i,sr)
788	sums_l(k,76,tn) = sums_l(k,76,tn) + prr(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	sums_l(k,54,tn) = sums_l(k,54,tn) + ql(k,j,i) * &
797	rmask(j,i,sr)
798	ENDIF
799	ELSE
800	IF( .NOT. ws_scheme_sca .OR. sr /= 0 ) THEN
801	pts = 0.5 * ( vpt(k,j,i) - hom(k,1,44,sr) + &
802	vpt(k+1,j,i) - hom(k+1,1,44,sr) )
803	sums_l(k,46,tn) = sums_l(k,46,tn) + pts * w(k,j,i) * &
804	rmask(j,i,sr)
805	ELSE IF ( ws_scheme_sca .AND. sr == 0 ) THEN
806	sums_l(k,46,tn) = ( 1.0 + 0.61 * hom(k,1,41,sr) ) * &
807	sums_l(k,17,tn) + &
808	0.61 * hom(k,1,4,sr) * sums_l(k,49,tn)
809	END IF
810	END IF
811	ENDIF
812	!
813	!-- Passive scalar flux
814	IF ( passive_scalar .AND. ( .NOT. ws_scheme_sca &
815	.OR. sr /= 0 ) ) THEN
816	pts = 0.5 * ( q(k,j,i) - hom(k,1,41,sr) + &
817	q(k+1,j,i) - hom(k+1,1,41,sr) )
818	sums_l(k,49,tn) = sums_l(k,49,tn) + pts * w(k,j,i) * &
819	rmask(j,i,sr)
820	ENDIF
821
822	!
823	!-- Energy flux we
824	!-- has to be adjusted
825	sums_l(k,37,tn) = sums_l(k,37,tn) + w(k,j,i) * 0.5 * &
826	( ust2 + vst2 + w(k,j,i)**2 )&
827	* rmask(j,i,sr)
828	ENDDO
829	ENDDO
830	ENDDO
831	!
832	!-- For speed optimization fluxes which have been computed in part directly
833	!-- inside the WS advection routines are treated seperatly
834	!-- Momentum fluxes first:
835	IF ( .NOT. ws_scheme_mom .OR. sr /= 0 ) THEN
836	!$OMP DO
837	DO i = nxl, nxr
838	DO j = nys, nyn
839	DO k = nzb_diff_s_inner(j,i)-1, nzt_diff
840	ust = 0.5 * ( u(k,j,i) - hom(k,1,1,sr) + &
841	u(k+1,j,i) - hom(k+1,1,1,sr) )
842	vst = 0.5 * ( v(k,j,i) - hom(k,1,2,sr) + &
843	v(k+1,j,i) - hom(k+1,1,2,sr) )
844	!
845	!-- Momentum flux wu
846	sums_l(k,13,tn) = sums_l(k,13,tn) + 0.5 * &
847	( w(k,j,i-1) + w(k,j,i) ) &
848	* ust * rmask(j,i,sr)
849	!
850	!-- Momentum flux wv
851	sums_l(k,15,tn) = sums_l(k,15,tn) + 0.5 * &
852	( w(k,j-1,i) + w(k,j,i) ) &
853	* vst * rmask(j,i,sr)
854	ENDDO
855	ENDDO
856	ENDDO
857
858	ENDIF
859	IF ( .NOT. ws_scheme_sca .OR. sr /= 0 ) THEN
860	!$OMP DO
861	DO i = nxl, nxr
862	DO j = nys, nyn
863	DO k = nzb_diff_s_inner(j,i)-1, nzt_diff
864	!
865	!-- Vertical heat flux
866	sums_l(k,17,tn) = sums_l(k,17,tn) + 0.5 * &
867	( pt(k,j,i) - hom(k,1,4,sr) + &
868	pt(k+1,j,i) - hom(k+1,1,4,sr) ) &
869	* w(k,j,i) * rmask(j,i,sr)
870	IF ( humidity ) THEN
871	pts = 0.5 * ( q(k,j,i) - hom(k,1,41,sr) + &
872	q(k+1,j,i) - hom(k+1,1,41,sr) )
873	sums_l(k,49,tn) = sums_l(k,49,tn) + pts * w(k,j,i) * &
874	rmask(j,i,sr)
875	ENDIF
876	ENDDO
877	ENDDO
878	ENDDO
879
880	ENDIF
881
882
883	!
884	!-- Density at top follows Neumann condition
885	IF ( ocean ) THEN
886	sums_l(nzt+1,64,tn) = sums_l(nzt,64,tn)
887	sums_l(nzt+1,71,tn) = sums_l(nzt,71,tn)
888	ENDIF
889
890	!
891	!-- Divergence of vertical flux of resolved scale energy and pressure
892	!-- fluctuations as well as flux of pressure fluctuation itself (68).
893	!-- First calculate the products, then the divergence.
894	!-- Calculation is time consuming. Do it only, if profiles shall be plotted.
895	IF ( hom(nzb+1,2,55,0) /= 0.0 .OR. hom(nzb+1,2,68,0) /= 0.0 ) THEN
896
897	sums_ll = 0.0 ! local array
898
899	!$OMP DO
900	DO i = nxl, nxr
901	DO j = nys, nyn
902	DO k = nzb_s_inner(j,i)+1, nzt
903
904	sums_ll(k,1) = sums_ll(k,1) + 0.5 * w(k,j,i) * ( &
905	( 0.25 * ( u(k,j,i)+u(k+1,j,i)+u(k,j,i+1)+u(k+1,j,i+1) &
906	- 0.5 * ( hom(k,1,1,sr) + hom(k+1,1,1,sr) ) &
907	) )**2 &
908	+ ( 0.25 * ( v(k,j,i)+v(k+1,j,i)+v(k,j+1,i)+v(k+1,j+1,i) &
909	- 0.5 * ( hom(k,1,2,sr) + hom(k+1,1,2,sr) ) &
910	) )**2 &
911	+ w(k,j,i)**2 )
912
913	sums_ll(k,2) = sums_ll(k,2) + 0.5 * w(k,j,i) &
914	* ( p(k,j,i) + p(k+1,j,i) )
915
916	ENDDO
917	ENDDO
918	ENDDO
919	sums_ll(0,1) = 0.0 ! because w is zero at the bottom
920	sums_ll(nzt+1,1) = 0.0
921	sums_ll(0,2) = 0.0
922	sums_ll(nzt+1,2) = 0.0
923
924	DO k = nzb+1, nzt
925	sums_l(k,55,tn) = ( sums_ll(k,1) - sums_ll(k-1,1) ) * ddzw(k)
926	sums_l(k,56,tn) = ( sums_ll(k,2) - sums_ll(k-1,2) ) * ddzw(k)
927	sums_l(k,68,tn) = sums_ll(k,2)
928	ENDDO
929	sums_l(nzb,55,tn) = sums_l(nzb+1,55,tn)
930	sums_l(nzb,56,tn) = sums_l(nzb+1,56,tn)
931	sums_l(nzb,68,tn) = 0.0 ! because w* = 0 at nzb
932
933	ENDIF
934
935	!
936	!-- Divergence of vertical flux of SGS TKE and the flux itself (69)
937	IF ( hom(nzb+1,2,57,0) /= 0.0 .OR. hom(nzb+1,2,69,0) /= 0.0 ) THEN
938
939	!$OMP DO
940	DO i = nxl, nxr
941	DO j = nys, nyn
942	DO k = nzb_s_inner(j,i)+1, nzt
943
944	sums_l(k,57,tn) = sums_l(k,57,tn) - 0.5 * ( &
945	(km(k,j,i)+km(k+1,j,i)) * (e(k+1,j,i)-e(k,j,i)) * ddzu(k+1) &
946	- (km(k-1,j,i)+km(k,j,i)) * (e(k,j,i)-e(k-1,j,i)) * ddzu(k) &
947	) * ddzw(k)
948
949	sums_l(k,69,tn) = sums_l(k,69,tn) - 0.5 * ( &
950	(km(k,j,i)+km(k+1,j,i)) * (e(k+1,j,i)-e(k,j,i)) * ddzu(k+1) &
951	)
952
953	ENDDO
954	ENDDO
955	ENDDO
956	sums_l(nzb,57,tn) = sums_l(nzb+1,57,tn)
957	sums_l(nzb,69,tn) = sums_l(nzb+1,69,tn)
958
959	ENDIF
960
961	!
962	!-- Horizontal heat fluxes (subgrid, resolved, total).
963	!-- Do it only, if profiles shall be plotted.
964	IF ( hom(nzb+1,2,58,0) /= 0.0 ) THEN
965
966	!$OMP DO
967	DO i = nxl, nxr
968	DO j = nys, nyn
969	DO k = nzb_s_inner(j,i)+1, nzt
970	!
971	!-- Subgrid horizontal heat fluxes u"pt", v"pt"
972	sums_l(k,58,tn) = sums_l(k,58,tn) - 0.5 * &
973	( kh(k,j,i) + kh(k,j,i-1) ) &
974	* ( pt(k,j,i-1) - pt(k,j,i) ) &
975	* ddx * rmask(j,i,sr)
976	sums_l(k,61,tn) = sums_l(k,61,tn) - 0.5 * &
977	( kh(k,j,i) + kh(k,j-1,i) ) &
978	* ( pt(k,j-1,i) - pt(k,j,i) ) &
979	* ddy * rmask(j,i,sr)
980	!
981	!-- Resolved horizontal heat fluxes upt, vpt
982	sums_l(k,59,tn) = sums_l(k,59,tn) + &
983	( u(k,j,i) - hom(k,1,1,sr) ) &
984	* 0.5 * ( pt(k,j,i-1) - hom(k,1,4,sr) + &
985	pt(k,j,i) - hom(k,1,4,sr) )
986	pts = 0.5 * ( pt(k,j-1,i) - hom(k,1,4,sr) + &
987	pt(k,j,i) - hom(k,1,4,sr) )
988	sums_l(k,62,tn) = sums_l(k,62,tn) + &
989	( v(k,j,i) - hom(k,1,2,sr) ) &
990	* 0.5 * ( pt(k,j-1,i) - hom(k,1,4,sr) + &
991	pt(k,j,i) - hom(k,1,4,sr) )
992	ENDDO
993	ENDDO
994	ENDDO
995	!
996	!-- Fluxes at the surface must be zero (e.g. due to the Prandtl-layer)
997	sums_l(nzb,58,tn) = 0.0
998	sums_l(nzb,59,tn) = 0.0
999	sums_l(nzb,60,tn) = 0.0
1000	sums_l(nzb,61,tn) = 0.0
1001	sums_l(nzb,62,tn) = 0.0
1002	sums_l(nzb,63,tn) = 0.0
1003
1004	ENDIF
1005
1006	!
1007	!-- Calculate the user-defined profiles
1008	CALL user_statistics( 'profiles', sr, tn )
1009	!$OMP END PARALLEL
1010
1011	!
1012	!-- Summation of thread sums
1013	IF ( threads_per_task > 1 ) THEN
1014	DO i = 1, threads_per_task-1
1015	sums_l(:,3,0) = sums_l(:,3,0) + sums_l(:,3,i)
1016	sums_l(:,4:40,0) = sums_l(:,4:40,0) + sums_l(:,4:40,i)
1017	sums_l(:,45:pr_palm,0) = sums_l(:,45:pr_palm,0) + &
1018	sums_l(:,45:pr_palm,i)
1019	IF ( max_pr_user > 0 ) THEN
1020	sums_l(:,pr_palm+1:pr_palm+max_pr_user,0) = &
1021	sums_l(:,pr_palm+1:pr_palm+max_pr_user,0) + &
1022	sums_l(:,pr_palm+1:pr_palm+max_pr_user,i)
1023	ENDIF
1024	ENDDO
1025	ENDIF
1026
1027	#if defined( __parallel )
1028
1029	!
1030	!-- Compute total sum from local sums
1031	IF ( collective_wait ) CALL MPI_BARRIER( comm2d, ierr )
1032	CALL MPI_ALLREDUCE( sums_l(nzb,1,0), sums(nzb,1), ngp_sums, MPI_REAL, &
1033	MPI_SUM, comm2d, ierr )
1034	#else
1035	sums = sums_l(:,:,0)
1036	#endif
1037
1038	!
1039	!-- Final values are obtained by division by the total number of grid points
1040	!-- used for summation. After that store profiles.
1041	!-- Profiles:
1042	DO k = nzb, nzt+1
1043	sums(k,3) = sums(k,3) / ngp_2dh(sr)
1044	sums(k,8:11) = sums(k,8:11) / ngp_2dh_s_inner(k,sr)
1045	sums(k,12:22) = sums(k,12:22) / ngp_2dh(sr)
1046	sums(k,23:29) = sums(k,23:29) / ngp_2dh_s_inner(k,sr)
1047	sums(k,30:32) = sums(k,30:32) / ngp_2dh(sr)
1048	sums(k,33:34) = sums(k,33:34) / ngp_2dh_s_inner(k,sr)
1049	sums(k,35:39) = sums(k,35:39) / ngp_2dh(sr)
1050	sums(k,40) = sums(k,40) / ngp_2dh_s_inner(k,sr)
1051	sums(k,45:53) = sums(k,45:53) / ngp_2dh(sr)
1052	sums(k,54) = sums(k,54) / ngp_2dh_s_inner(k,sr)
1053	sums(k,55:63) = sums(k,55:63) / ngp_2dh(sr)
1054	sums(k,64) = sums(k,64) / ngp_2dh_s_inner(k,sr)
1055	sums(k,65:69) = sums(k,65:69) / ngp_2dh(sr)
1056	sums(k,70:pr_palm-2) = sums(k,70:pr_palm-2)/ ngp_2dh_s_inner(k,sr)
1057	ENDDO
1058
1059	!-- Upstream-parts
1060	sums(nzb:nzb+11,pr_palm-1) = sums(nzb:nzb+11,pr_palm-1) / ngp_3d(sr)
1061	!-- u* and so on
1062	!-- As sums(nzb:nzb+3,pr_palm) are full 2D arrays (us, usws, vsws, ts) whose
1063	!-- size is always ( nx + 1 ) * ( ny + 1 ), defined at the first grid layer
1064	!-- above the topography, they are being divided by ngp_2dh(sr)
1065	sums(nzb:nzb+3,pr_palm) = sums(nzb:nzb+3,pr_palm) / &
1066	ngp_2dh(sr)
1067	sums(nzb+12,pr_palm) = sums(nzb+12,pr_palm) / & ! qs
1068	ngp_2dh(sr)
1069	!-- eges, e*
1070	sums(nzb+4:nzb+5,pr_palm) = sums(nzb+4:nzb+5,pr_palm) / &
1071	ngp_3d(sr)
1072	!-- Old and new divergence
1073	sums(nzb+9:nzb+10,pr_palm) = sums(nzb+9:nzb+10,pr_palm) / &
1074	ngp_3d_inner(sr)
1075
1076	!-- User-defined profiles
1077	IF ( max_pr_user > 0 ) THEN
1078	DO k = nzb, nzt+1
1079	sums(k,pr_palm+1:pr_palm+max_pr_user) = &
1080	sums(k,pr_palm+1:pr_palm+max_pr_user) / &
1081	ngp_2dh_s_inner(k,sr)
1082	ENDDO
1083	ENDIF
1084
1085	!
1086	!-- Collect horizontal average in hom.
1087	!-- Compute deduced averages (e.g. total heat flux)
1088	hom(:,1,3,sr) = sums(:,3) ! w
1089	hom(:,1,8,sr) = sums(:,8) ! e profiles 5-7 are initial profiles
1090	hom(:,1,9,sr) = sums(:,9) ! km
1091	hom(:,1,10,sr) = sums(:,10) ! kh
1092	hom(:,1,11,sr) = sums(:,11) ! l
1093	hom(:,1,12,sr) = sums(:,12) ! w"u"
1094	hom(:,1,13,sr) = sums(:,13) ! wu
1095	hom(:,1,14,sr) = sums(:,14) ! w"v"
1096	hom(:,1,15,sr) = sums(:,15) ! wv
1097	hom(:,1,16,sr) = sums(:,16) ! w"pt"
1098	hom(:,1,17,sr) = sums(:,17) ! wpt
1099	hom(:,1,18,sr) = sums(:,16) + sums(:,17) ! wpt
1100	hom(:,1,19,sr) = sums(:,12) + sums(:,13) ! wu
1101	hom(:,1,20,sr) = sums(:,14) + sums(:,15) ! wv
1102	hom(:,1,21,sr) = sums(:,21) ! wptBC
1103	hom(:,1,22,sr) = sums(:,16) + sums(:,21) ! wptBC
1104	! profile 24 is initial profile (sa)
1105	! profiles 25-29 left empty for initial
1106	! profiles
1107	hom(:,1,30,sr) = sums(:,30) ! u*2
1108	hom(:,1,31,sr) = sums(:,31) ! v*2
1109	hom(:,1,32,sr) = sums(:,32) ! w*2
1110	hom(:,1,33,sr) = sums(:,33) ! pt*2
1111	hom(:,1,34,sr) = sums(:,34) ! e*
1112	hom(:,1,35,sr) = sums(:,35) ! w2pt
1113	hom(:,1,36,sr) = sums(:,36) ! wpt2
1114	hom(:,1,37,sr) = sums(:,37) ! we
1115	hom(:,1,38,sr) = sums(:,38) ! w*3
1116	hom(:,1,39,sr) = sums(:,38) / ( abs( sums(:,32) ) + 1E-20 )**1.5 ! Sw
1117	hom(:,1,40,sr) = sums(:,40) ! p
1118	hom(:,1,45,sr) = sums(:,45) ! w"vpt"
1119	hom(:,1,46,sr) = sums(:,46) ! wvpt
1120	hom(:,1,47,sr) = sums(:,45) + sums(:,46) ! wvpt
1121	hom(:,1,48,sr) = sums(:,48) ! w"q" (w"qv")
1122	hom(:,1,49,sr) = sums(:,49) ! wq (wqv)
1123	hom(:,1,50,sr) = sums(:,48) + sums(:,49) ! wq (wqv)
1124	hom(:,1,51,sr) = sums(:,51) ! w"qv"
1125	hom(:,1,52,sr) = sums(:,52) ! wqv
1126	hom(:,1,53,sr) = sums(:,52) + sums(:,51) ! wq (wqv)
1127	hom(:,1,54,sr) = sums(:,54) ! ql
1128	hom(:,1,55,sr) = sums(:,55) ! wuu*/dz
1129	hom(:,1,56,sr) = sums(:,56) ! wp/dz
1130	hom(:,1,57,sr) = sums(:,57) ! ( w"e + w"p"/rho )/dz
1131	hom(:,1,58,sr) = sums(:,58) ! u"pt"
1132	hom(:,1,59,sr) = sums(:,59) ! upt
1133	hom(:,1,60,sr) = sums(:,58) + sums(:,59) ! upt_t
1134	hom(:,1,61,sr) = sums(:,61) ! v"pt"
1135	hom(:,1,62,sr) = sums(:,62) ! vpt
1136	hom(:,1,63,sr) = sums(:,61) + sums(:,62) ! vpt_t
1137	hom(:,1,64,sr) = sums(:,64) ! rho
1138	hom(:,1,65,sr) = sums(:,65) ! w"sa"
1139	hom(:,1,66,sr) = sums(:,66) ! wsa
1140	hom(:,1,67,sr) = sums(:,65) + sums(:,66) ! wsa
1141	hom(:,1,68,sr) = sums(:,68) ! wp
1142	hom(:,1,69,sr) = sums(:,69) ! w"e + w"p"/rho
1143	hom(:,1,70,sr) = sums(:,70) ! q*2
1144	hom(:,1,71,sr) = sums(:,71) ! prho
1145	hom(:,1,72,sr) = hyp * 1E-4 ! hyp in dbar
1146	hom(:,1,73,sr) = sums(:,73) ! nr
1147	hom(:,1,74,sr) = sums(:,74) ! qr
1148	hom(:,1,75,sr) = sums(:,75) ! qc
1149	hom(:,1,76,sr) = sums(:,76) ! prr (precipitation rate)
1150
1151	hom(:,1,pr_palm-1,sr) = sums(:,pr_palm-1)
1152	! upstream-parts u_x, u_y, u_z, v_x,
1153	! v_y, usw. (in last but one profile)
1154	hom(:,1,pr_palm,sr) = sums(:,pr_palm)
1155	! u, w'u', w'v', t (in last profile)
1156
1157	IF ( max_pr_user > 0 ) THEN ! user-defined profiles
1158	hom(:,1,pr_palm+1:pr_palm+max_pr_user,sr) = &
1159	sums(:,pr_palm+1:pr_palm+max_pr_user)
1160	ENDIF
1161
1162	!
1163	!-- Determine the boundary layer height using two different schemes.
1164	!-- First scheme: Starting from the Earth's (Ocean's) surface, look for the
1165	!-- first relative minimum (maximum) of the total heat flux.
1166	!-- The corresponding height is assumed as the boundary layer height, if it
1167	!-- is less than 1.5 times the height where the heat flux becomes negative
1168	!-- (positive) for the first time.
1169	z_i(1) = 0.0
1170	first = .TRUE.
1171
1172	IF ( ocean ) THEN
1173	DO k = nzt, nzb+1, -1
1174	IF ( first .AND. hom(k,1,18,sr) < 0.0 &
1175	.AND. abs(hom(k,1,18,sr)) > 1.0E-8) THEN
1176	first = .FALSE.
1177	height = zw(k)
1178	ENDIF
1179	IF ( hom(k,1,18,sr) < 0.0 .AND. &
1180	abs(hom(k,1,18,sr)) > 1.0E-8 .AND. &
1181	hom(k-1,1,18,sr) > hom(k,1,18,sr) ) THEN
1182	IF ( zw(k) < 1.5 * height ) THEN
1183	z_i(1) = zw(k)
1184	ELSE
1185	z_i(1) = height
1186	ENDIF
1187	EXIT
1188	ENDIF
1189	ENDDO
1190	ELSE
1191	DO k = nzb, nzt-1
1192	IF ( first .AND. hom(k,1,18,sr) < 0.0 &
1193	.AND. abs(hom(k,1,18,sr)) > 1.0E-8 ) THEN
1194	first = .FALSE.
1195	height = zw(k)
1196	ENDIF
1197	IF ( hom(k,1,18,sr) < 0.0 .AND. &
1198	abs(hom(k,1,18,sr)) > 1.0E-8 .AND. &
1199	hom(k+1,1,18,sr) > hom(k,1,18,sr) ) THEN
1200	IF ( zw(k) < 1.5 * height ) THEN
1201	z_i(1) = zw(k)
1202	ELSE
1203	z_i(1) = height
1204	ENDIF
1205	EXIT
1206	ENDIF
1207	ENDDO
1208	ENDIF
1209
1210	!
1211	!-- Second scheme: Gradient scheme from Sullivan et al. (1998), modified
1212	!-- by Uhlenbrock(2006). The boundary layer height is the height with the
1213	!-- maximal local temperature gradient: starting from the second (the last
1214	!-- but one) vertical gridpoint, the local gradient must be at least
1215	!-- 0.2K/100m and greater than the next four gradients.
1216	!-- WARNING: The threshold value of 0.2K/100m must be adjusted for the
1217	!-- ocean case!
1218	z_i(2) = 0.0
1219	DO k = nzb+1, nzt+1
1220	dptdz(k) = ( hom(k,1,4,sr) - hom(k-1,1,4,sr) ) * ddzu(k)
1221	ENDDO
1222	dptdz_threshold = 0.2 / 100.0
1223
1224	IF ( ocean ) THEN
1225	DO k = nzt+1, nzb+5, -1
1226	IF ( dptdz(k) > dptdz_threshold .AND. &
1227	dptdz(k) > dptdz(k-1) .AND. dptdz(k) > dptdz(k-2) .AND. &
1228	dptdz(k) > dptdz(k-3) .AND. dptdz(k) > dptdz(k-4) ) THEN
1229	z_i(2) = zw(k-1)
1230	EXIT
1231	ENDIF
1232	ENDDO
1233	ELSE
1234	DO k = nzb+1, nzt-3
1235	IF ( dptdz(k) > dptdz_threshold .AND. &
1236	dptdz(k) > dptdz(k+1) .AND. dptdz(k) > dptdz(k+2) .AND. &
1237	dptdz(k) > dptdz(k+3) .AND. dptdz(k) > dptdz(k+4) ) THEN
1238	z_i(2) = zw(k-1)
1239	EXIT
1240	ENDIF
1241	ENDDO
1242	ENDIF
1243
1244	hom(nzb+6,1,pr_palm,sr) = z_i(1)
1245	hom(nzb+7,1,pr_palm,sr) = z_i(2)
1246
1247	!
1248	!-- Computation of both the characteristic vertical velocity and
1249	!-- the characteristic convective boundary layer temperature.
1250	!-- The horizontal average at nzb+1 is input for the average temperature.
1251	IF ( hom(nzb,1,18,sr) > 0.0 .AND. abs(hom(nzb,1,18,sr)) > 1.0E-8 &
1252	.AND. z_i(1) /= 0.0 ) THEN
1253	hom(nzb+8,1,pr_palm,sr) = ( g / hom(nzb+1,1,4,sr) * &
1254	hom(nzb,1,18,sr) * &
1255	ABS( z_i(1) ) )**0.333333333
1256	!-- so far this only works if Prandtl layer is used
1257	hom(nzb+11,1,pr_palm,sr) = hom(nzb,1,16,sr) / hom(nzb+8,1,pr_palm,sr)
1258	ELSE
1259	hom(nzb+8,1,pr_palm,sr) = 0.0
1260	hom(nzb+11,1,pr_palm,sr) = 0.0
1261	ENDIF
1262
1263	!
1264	!-- Collect the time series quantities
1265	ts_value(1,sr) = hom(nzb+4,1,pr_palm,sr) ! E
1266	ts_value(2,sr) = hom(nzb+5,1,pr_palm,sr) ! E*
1267	ts_value(3,sr) = dt_3d
1268	ts_value(4,sr) = hom(nzb,1,pr_palm,sr) ! u*
1269	ts_value(5,sr) = hom(nzb+3,1,pr_palm,sr) ! th*
1270	ts_value(6,sr) = u_max
1271	ts_value(7,sr) = v_max
1272	ts_value(8,sr) = w_max
1273	ts_value(9,sr) = hom(nzb+10,1,pr_palm,sr) ! new divergence
1274	ts_value(10,sr) = hom(nzb+9,1,pr_palm,sr) ! old Divergence
1275	ts_value(11,sr) = hom(nzb+6,1,pr_palm,sr) ! z_i(1)
1276	ts_value(12,sr) = hom(nzb+7,1,pr_palm,sr) ! z_i(2)
1277	ts_value(13,sr) = hom(nzb+8,1,pr_palm,sr) ! w*
1278	ts_value(14,sr) = hom(nzb,1,16,sr) ! w'pt' at k=0
1279	ts_value(15,sr) = hom(nzb+1,1,16,sr) ! w'pt' at k=1
1280	ts_value(16,sr) = hom(nzb+1,1,18,sr) ! wpt at k=1
1281	ts_value(17,sr) = hom(nzb,1,4,sr) ! pt(0)
1282	ts_value(18,sr) = hom(nzb+1,1,4,sr) ! pt(zp)
1283	ts_value(19,sr) = hom(nzb+1,1,pr_palm,sr) ! u'w' at k=0
1284	ts_value(20,sr) = hom(nzb+2,1,pr_palm,sr) ! v'w' at k=0
1285	ts_value(21,sr) = hom(nzb,1,48,sr) ! w"q" at k=0
1286
1287	IF ( ts_value(5,sr) /= 0.0 ) THEN
1288	ts_value(22,sr) = ts_value(4,sr)**2 / &
1289	( kappa * g * ts_value(5,sr) / ts_value(18,sr) ) ! L
1290	ELSE
1291	ts_value(22,sr) = 10000.0
1292	ENDIF
1293
1294	ts_value(23,sr) = hom(nzb+12,1,pr_palm,sr) ! q*
1295	!
1296	!-- Calculate additional statistics provided by the user interface
1297	CALL user_statistics( 'time_series', sr, 0 )
1298
1299	ENDDO ! loop of the subregions
1300
1301	!
1302	!-- If required, sum up horizontal averages for subsequent time averaging
1303	IF ( do_sum ) THEN
1304	IF ( average_count_pr == 0 ) hom_sum = 0.0
1305	hom_sum = hom_sum + hom(:,1,:,:)
1306	average_count_pr = average_count_pr + 1
1307	do_sum = .FALSE.
1308	ENDIF
1309
1310	!
1311	!-- Set flag for other UPs (e.g. output routines, but also buoyancy).
1312	!-- This flag is reset after each time step in time_integration.
1313	flow_statistics_called = .TRUE.
1314
1315	CALL cpu_log( log_point(10), 'flow_statistics', 'stop' )
1316
1317
1318	END SUBROUTINE flow_statistics

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