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flow_statistics.f90 @ 1111

Last change on this file since 1111 was 1111, checked in by raasch, 11 years ago

New:
---

GPU porting of pres, swap_timelevel. Adjustments of openACC directives.
Further porting of poisfft, which now runs completely on GPU without any
host/device data transfer for serial an parallel runs (but parallel runs
require data transfer before and after the MPI transpositions).
GPU-porting of tridiagonal solver:
tridiagonal routines split into extermal subroutines (instead using CONTAINS),
no distinction between parallel/non-parallel in poisfft and tridia any more,
tridia routines moved to end of file because of probable bug in PGI compiler
(otherwise "invalid device function" is indicated during runtime).
(cuda_fft_interfaces, fft_xy, flow_statistics, init_3d_model, palm, poisfft, pres, prognostic_equations, swap_timelevel, time_integration, transpose)
output of accelerator board information. (header)

optimization of tridia routines: constant elements and coefficients of tri are
stored in seperate arrays ddzuw and tric, last dimension of tri reduced from 5 to 2,
(init_grid, init_3d_model, modules, palm, poisfft)

poisfft_init is now called internally from poisfft,
(Makefile, Makefile_check, init_pegrid, poisfft, poisfft_hybrid)

CPU-time per grid point and timestep is output to CPU_MEASURES file
(cpu_statistics, modules, time_integration)

Changed:

resorting from/to array work changed, work now has 4 dimensions instead of 1 (transpose)
array diss allocated only if required (init_3d_model)

pressure boundary condition "Neumann+inhomo" removed from the code
(check_parameters, header, poisfft, poisfft_hybrid, pres)

Errors:

bugfix: dependency added for cuda_fft_interfaces (Makefile)
bugfix: CUDA fft plans adjusted for domain decomposition (before they always
used total domain) (fft_xy)

Property svn:keywords set to Id

File size: 56.3 KB

Line
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	! openACC directive added
23	!
24	! Former revisions:
25	! -----------------
26	! $Id: flow_statistics.f90 1111 2013-03-08 23:54:10Z raasch $
27	!
28	! 1053 2012-11-13 17:11:03Z hoffmann
29	! necessary additions for two-moment cloud physics scheme:
30	! +nr, qr, qc, prr
31	!
32	! 1036 2012-10-22 13:43:42Z raasch
33	! code put under GPL (PALM 3.9)
34	!
35	! 1007 2012-09-19 14:30:36Z franke
36	! Calculation of buoyancy flux for humidity in case of WS-scheme is now using
37	! turbulent fluxes of WS-scheme
38	! Bugfix: Calculation of subgridscale buoyancy flux for humidity and cloud
39	! droplets at nzb and nzt added
40	!
41	! 801 2012-01-10 17:30:36Z suehring
42	! Calculation of turbulent fluxes in advec_ws is now thread-safe.
43	!
44	! 743 2011-08-18 16:10:16Z suehring
45	! Calculation of turbulent fluxes with WS-scheme only for the whole model
46	! domain, not for user-defined subregions.
47	!
48	! 709 2011-03-30 09:31:40Z raasch
49	! formatting adjustments
50	!
51	! 699 2011-03-22 17:52:22Z suehring
52	! Bugfix in calculation of vertical velocity skewness. The added absolute value
53	! avoid negative values in the root. Negative values of w'w' can occur at the
54	! top or bottom of the model domain due to degrading the order of advection
55	! scheme. Furthermore the calculation will be the same for all advection
56	! schemes.
57	!
58	! 696 2011-03-18 07:03:49Z raasch
59	! Bugfix: Summation of Wicker-Skamarock scheme fluxes and variances for all
60	! threads
61	!
62	! 678 2011-02-02 14:31:56Z raasch
63	! Bugfix in calculation of the divergence of vertical flux of resolved scale
64	! energy, pressure fluctuations, and flux of pressure fluctuation itself
65	!
66	! 673 2011-01-18 16:19:48Z suehring
67	! Top bc for the horizontal velocity variances added for ocean runs.
68	! Setting the corresponding bottom bc moved to advec_ws.
69	!
70	! 667 2010-12-23 12:06:00Z suehring/gryschka
71	! When advection is computed with ws-scheme, turbulent fluxes are already
72	! computed in the respective advection routines and buffered in arrays
73	! sums_xx_ws_l(). This is due to a consistent treatment of statistics with the
74	! numerics and to avoid unphysical kinks near the surface.
75	! So some if requests has to be done to dicern between fluxes from ws-scheme
76	! other advection schemes.
77	! Furthermore the computation of z_i is only done if the heat flux exceeds a
78	! minimum value. This affects only simulations of a neutral boundary layer and
79	! is due to reasons of computations in the advection scheme.
80	!
81	! 624 2010-12-10 11:46:30Z heinze
82	! Calculation of q*2 added
83	!
84	! 622 2010-12-10 08:08:13Z raasch
85	! optional barriers included in order to speed up collective operations
86	!
87	! 388 2009-09-23 09:40:33Z raasch
88	! Vertical profiles of potential density and hydrostatic pressure are
89	! calculated.
90	! Added missing timeseries calculation of w"q"(0), moved timeseries q* to the
91	! end.
92	! Temperature gradient criterion for estimating the boundary layer height
93	! replaced by the gradient criterion of Sullivan et al. (1998).
94	! Output of messages replaced by message handling routine.
95	!
96	! 197 2008-09-16 15:29:03Z raasch
97	! Spline timeseries splptx etc. removed, timeseries w'u', w'v', w'q' (k=0)
98	! added,
99	! bugfix: divide sums(k,8) (e) and sums(k,34) (e*) by ngp_2dh_s_inner(k,sr)
100	! (like other scalars)
101	!
102	! 133 2007-11-20 10:10:53Z letzel
103	! Vertical profiles now based on nzb_s_inner; they are divided by
104	! ngp_2dh_s_inner (scalars, procucts of scalars) and ngp_2dh (staggered
105	! velocity components and their products, procucts of scalars and velocity
106	! components), respectively.
107	!
108	! 106 2007-08-16 14:30:26Z raasch
109	! Prescribed momentum fluxes at the top surface are used,
110	! profiles for wp and w"e are calculated
111	!
112	! 97 2007-06-21 08:23:15Z raasch
113	! Statistics for ocean version (salinity, density) added,
114	! calculation of z_i and Deardorff velocity scale adjusted to be used with
115	! the ocean version
116	!
117	! 87 2007-05-22 15:46:47Z raasch
118	! Two more arguments added to user_statistics, which is now also called for
119	! user-defined profiles,
120	! var_hom and var_sum renamed pr_palm
121	!
122	! 82 2007-04-16 15:40:52Z raasch
123	! Cpp-directive lcmuk changed to intel_openmp_bug
124	!
125	! 75 2007-03-22 09:54:05Z raasch
126	! Collection of time series quantities moved from routine flow_statistics to
127	! here, routine user_statistics is called for each statistic region,
128	! moisture renamed humidity
129	!
130	! 19 2007-02-23 04:53:48Z raasch
131	! fluxes at top modified (tswst, qswst)
132	!
133	! RCS Log replace by Id keyword, revision history cleaned up
134	!
135	! Revision 1.41 2006/08/04 14:37:50 raasch
136	! Error removed in non-parallel part (sums_l)
137	!
138	! Revision 1.1 1997/08/11 06:15:17 raasch
139	! Initial revision
140	!
141	!
142	! Description:
143	! ------------
144	! Compute average profiles and further average flow quantities for the different
145	! user-defined (sub-)regions. The region indexed 0 is the total model domain.
146	!
147	! NOTE: For simplicity, nzb_s_inner and nzb_diff_s_inner are being used as a
148	! ---- lower vertical index for k-loops for all variables, although strictly
149	! speaking the k-loops would have to be split up according to the staggered
150	! grid. However, this implies no error since staggered velocity components are
151	! zero at the walls and inside buildings.
152	!------------------------------------------------------------------------------!
153
154	USE arrays_3d
155	USE cloud_parameters
156	USE control_parameters
157	USE cpulog
158	USE grid_variables
159	USE indices
160	USE interfaces
161	USE pegrid
162	USE statistics
163
164	IMPLICIT NONE
165
166	INTEGER :: i, j, k, omp_get_thread_num, sr, tn
167	LOGICAL :: first
168	REAL :: dptdz_threshold, height, pts, sums_l_eper, sums_l_etot, ust, &
169	ust2, u2, vst, vst2, v2, w2, z_i(2)
170	REAL :: dptdz(nzb+1:nzt+1)
171	REAL :: sums_ll(nzb:nzt+1,2)
172
173	CALL cpu_log( log_point(10), 'flow_statistics', 'start' )
174
175	!
176	!-- To be on the safe side, check whether flow_statistics has already been
177	!-- called once after the current time step
178	IF ( flow_statistics_called ) THEN
179
180	message_string = 'flow_statistics is called two times within one ' // &
181	'timestep'
182	CALL message( 'flow_statistics', 'PA0190', 1, 2, 0, 6, 0 )
183
184	ENDIF
185
186	!$acc update host( km, kh, e, pt, qs, qsws, rif, shf, ts, u, v, w )
187
188	!
189	!-- Compute statistics for each (sub-)region
190	DO sr = 0, statistic_regions
191
192	!
193	!-- Initialize (local) summation array
194	sums_l = 0.0
195
196	!
197	!-- Store sums that have been computed in other subroutines in summation
198	!-- array
199	sums_l(:,11,:) = sums_l_l(:,sr,:) ! mixing length from diffusivities
200	!-- WARNING: next line still has to be adjusted for OpenMP
201	sums_l(:,21,0) = sums_wsts_bc_l(:,sr) ! heat flux from advec_s_bc
202	sums_l(nzb+9,pr_palm,0) = sums_divold_l(sr) ! old divergence from pres
203	sums_l(nzb+10,pr_palm,0) = sums_divnew_l(sr) ! new divergence from pres
204
205	!
206	!-- Copy the turbulent quantities, evaluated in the advection routines to
207	!-- the local array sums_l() for further computations
208	IF ( ws_scheme_mom .AND. sr == 0 ) THEN
209
210	!
211	!-- According to the Neumann bc for the horizontal velocity components,
212	!-- the corresponding fluxes has to satisfiy the same bc.
213	IF ( ocean ) THEN
214	sums_us2_ws_l(nzt+1,:) = sums_us2_ws_l(nzt,:)
215	sums_vs2_ws_l(nzt+1,:) = sums_vs2_ws_l(nzt,:)
216	ENDIF
217
218	DO i = 0, threads_per_task-1
219	!
220	!-- Swap the turbulent quantities evaluated in advec_ws.
221	sums_l(:,13,i) = sums_wsus_ws_l(:,i) ! wu
222	sums_l(:,15,i) = sums_wsvs_ws_l(:,i) ! wv
223	sums_l(:,30,i) = sums_us2_ws_l(:,i) ! u*2
224	sums_l(:,31,i) = sums_vs2_ws_l(:,i) ! v*2
225	sums_l(:,32,i) = sums_ws2_ws_l(:,i) ! w*2
226	sums_l(:,34,i) = sums_l(:,34,i) + 0.5 * &
227	( sums_us2_ws_l(:,i) + sums_vs2_ws_l(:,i) + &
228	sums_ws2_ws_l(:,i) ) ! e*
229	DO k = nzb, nzt
230	sums_l(nzb+5,pr_palm,i) = sums_l(nzb+5,pr_palm,i) + 0.5 * ( &
231	sums_us2_ws_l(k,i) + &
232	sums_vs2_ws_l(k,i) + &
233	sums_ws2_ws_l(k,i) )
234	ENDDO
235	ENDDO
236
237	ENDIF
238
239	IF ( ws_scheme_sca .AND. sr == 0 ) THEN
240
241	DO i = 0, threads_per_task-1
242	sums_l(:,17,i) = sums_wspts_ws_l(:,i) ! wpt from advec_s_ws
243	IF ( ocean ) sums_l(:,66,i) = sums_wssas_ws_l(:,i) ! wsa
244	IF ( humidity .OR. passive_scalar ) sums_l(:,49,i) = &
245	sums_wsqs_ws_l(:,i) !wq
246	ENDDO
247
248	ENDIF
249	!
250	!-- Horizontally averaged profiles of horizontal velocities and temperature.
251	!-- They must have been computed before, because they are already required
252	!-- for other horizontal averages.
253	tn = 0
254
255	!$OMP PARALLEL PRIVATE( i, j, k, tn )
256	#if defined( __intel_openmp_bug )
257	tn = omp_get_thread_num()
258	#else
259	!$ tn = omp_get_thread_num()
260	#endif
261
262	!$OMP DO
263	DO i = nxl, nxr
264	DO j = nys, nyn
265	DO k = nzb_s_inner(j,i), nzt+1
266	sums_l(k,1,tn) = sums_l(k,1,tn) + u(k,j,i) * rmask(j,i,sr)
267	sums_l(k,2,tn) = sums_l(k,2,tn) + v(k,j,i) * rmask(j,i,sr)
268	sums_l(k,4,tn) = sums_l(k,4,tn) + pt(k,j,i) * rmask(j,i,sr)
269	ENDDO
270	ENDDO
271	ENDDO
272
273	!
274	!-- Horizontally averaged profile of salinity
275	IF ( ocean ) THEN
276	!$OMP DO
277	DO i = nxl, nxr
278	DO j = nys, nyn
279	DO k = nzb_s_inner(j,i), nzt+1
280	sums_l(k,23,tn) = sums_l(k,23,tn) + &
281	sa(k,j,i) * rmask(j,i,sr)
282	ENDDO
283	ENDDO
284	ENDDO
285	ENDIF
286
287	!
288	!-- Horizontally averaged profiles of virtual potential temperature,
289	!-- total water content, specific humidity and liquid water potential
290	!-- temperature
291	IF ( humidity ) THEN
292	!$OMP DO
293	DO i = nxl, nxr
294	DO j = nys, nyn
295	DO k = nzb_s_inner(j,i), nzt+1
296	sums_l(k,44,tn) = sums_l(k,44,tn) + &
297	vpt(k,j,i) * rmask(j,i,sr)
298	sums_l(k,41,tn) = sums_l(k,41,tn) + &
299	q(k,j,i) * rmask(j,i,sr)
300	ENDDO
301	ENDDO
302	ENDDO
303	IF ( cloud_physics ) THEN
304	!$OMP DO
305	DO i = nxl, nxr
306	DO j = nys, nyn
307	DO k = nzb_s_inner(j,i), nzt+1
308	sums_l(k,42,tn) = sums_l(k,42,tn) + &
309	( q(k,j,i) - ql(k,j,i) ) * rmask(j,i,sr)
310	sums_l(k,43,tn) = sums_l(k,43,tn) + ( &
311	pt(k,j,i) + l_d_cppt_d_t(k) ql(k,j,i) &
312	) * rmask(j,i,sr)
313	ENDDO
314	ENDDO
315	ENDDO
316	ENDIF
317	ENDIF
318
319	!
320	!-- Horizontally averaged profiles of passive scalar
321	IF ( passive_scalar ) THEN
322	!$OMP DO
323	DO i = nxl, nxr
324	DO j = nys, nyn
325	DO k = nzb_s_inner(j,i), nzt+1
326	sums_l(k,41,tn) = sums_l(k,41,tn) + q(k,j,i) * rmask(j,i,sr)
327	ENDDO
328	ENDDO
329	ENDDO
330	ENDIF
331	!$OMP END PARALLEL
332	!
333	!-- Summation of thread sums
334	IF ( threads_per_task > 1 ) THEN
335	DO i = 1, threads_per_task-1
336	sums_l(:,1,0) = sums_l(:,1,0) + sums_l(:,1,i)
337	sums_l(:,2,0) = sums_l(:,2,0) + sums_l(:,2,i)
338	sums_l(:,4,0) = sums_l(:,4,0) + sums_l(:,4,i)
339	IF ( ocean ) THEN
340	sums_l(:,23,0) = sums_l(:,23,0) + sums_l(:,23,i)
341	ENDIF
342	IF ( humidity ) THEN
343	sums_l(:,41,0) = sums_l(:,41,0) + sums_l(:,41,i)
344	sums_l(:,44,0) = sums_l(:,44,0) + sums_l(:,44,i)
345	IF ( cloud_physics ) THEN
346	sums_l(:,42,0) = sums_l(:,42,0) + sums_l(:,42,i)
347	sums_l(:,43,0) = sums_l(:,43,0) + sums_l(:,43,i)
348	ENDIF
349	ENDIF
350	IF ( passive_scalar ) THEN
351	sums_l(:,41,0) = sums_l(:,41,0) + sums_l(:,41,i)
352	ENDIF
353	ENDDO
354	ENDIF
355
356	#if defined( __parallel )
357	!
358	!-- Compute total sum from local sums
359	IF ( collective_wait ) CALL MPI_BARRIER( comm2d, ierr )
360	CALL MPI_ALLREDUCE( sums_l(nzb,1,0), sums(nzb,1), nzt+2-nzb, MPI_REAL, &
361	MPI_SUM, comm2d, ierr )
362	IF ( collective_wait ) CALL MPI_BARRIER( comm2d, ierr )
363	CALL MPI_ALLREDUCE( sums_l(nzb,2,0), sums(nzb,2), 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,4,0), sums(nzb,4), nzt+2-nzb, MPI_REAL, &
367	MPI_SUM, comm2d, ierr )
368	IF ( ocean ) THEN
369	IF ( collective_wait ) CALL MPI_BARRIER( comm2d, ierr )
370	CALL MPI_ALLREDUCE( sums_l(nzb,23,0), sums(nzb,23), nzt+2-nzb, &
371	MPI_REAL, MPI_SUM, comm2d, ierr )
372	ENDIF
373	IF ( humidity ) THEN
374	IF ( collective_wait ) CALL MPI_BARRIER( comm2d, ierr )
375	CALL MPI_ALLREDUCE( sums_l(nzb,44,0), sums(nzb,44), nzt+2-nzb, &
376	MPI_REAL, MPI_SUM, comm2d, ierr )
377	IF ( collective_wait ) CALL MPI_BARRIER( comm2d, ierr )
378	CALL MPI_ALLREDUCE( sums_l(nzb,41,0), sums(nzb,41), nzt+2-nzb, &
379	MPI_REAL, MPI_SUM, comm2d, ierr )
380	IF ( cloud_physics ) THEN
381	IF ( collective_wait ) CALL MPI_BARRIER( comm2d, ierr )
382	CALL MPI_ALLREDUCE( sums_l(nzb,42,0), sums(nzb,42), nzt+2-nzb, &
383	MPI_REAL, MPI_SUM, comm2d, ierr )
384	IF ( collective_wait ) CALL MPI_BARRIER( comm2d, ierr )
385	CALL MPI_ALLREDUCE( sums_l(nzb,43,0), sums(nzb,43), nzt+2-nzb, &
386	MPI_REAL, MPI_SUM, comm2d, ierr )
387	ENDIF
388	ENDIF
389
390	IF ( passive_scalar ) THEN
391	IF ( collective_wait ) CALL MPI_BARRIER( comm2d, ierr )
392	CALL MPI_ALLREDUCE( sums_l(nzb,41,0), sums(nzb,41), nzt+2-nzb, &
393	MPI_REAL, MPI_SUM, comm2d, ierr )
394	ENDIF
395	#else
396	sums(:,1) = sums_l(:,1,0)
397	sums(:,2) = sums_l(:,2,0)
398	sums(:,4) = sums_l(:,4,0)
399	IF ( ocean ) sums(:,23) = sums_l(:,23,0)
400	IF ( humidity ) THEN
401	sums(:,44) = sums_l(:,44,0)
402	sums(:,41) = sums_l(:,41,0)
403	IF ( cloud_physics ) THEN
404	sums(:,42) = sums_l(:,42,0)
405	sums(:,43) = sums_l(:,43,0)
406	ENDIF
407	ENDIF
408	IF ( passive_scalar ) sums(:,41) = sums_l(:,41,0)
409	#endif
410
411	!
412	!-- Final values are obtained by division by the total number of grid points
413	!-- used for summation. After that store profiles.
414	sums(:,1) = sums(:,1) / ngp_2dh(sr)
415	sums(:,2) = sums(:,2) / ngp_2dh(sr)
416	sums(:,4) = sums(:,4) / ngp_2dh_s_inner(:,sr)
417	hom(:,1,1,sr) = sums(:,1) ! u
418	hom(:,1,2,sr) = sums(:,2) ! v
419	hom(:,1,4,sr) = sums(:,4) ! pt
420
421
422	!
423	!-- Salinity
424	IF ( ocean ) THEN
425	sums(:,23) = sums(:,23) / ngp_2dh_s_inner(:,sr)
426	hom(:,1,23,sr) = sums(:,23) ! sa
427	ENDIF
428
429	!
430	!-- Humidity and cloud parameters
431	IF ( humidity ) THEN
432	sums(:,44) = sums(:,44) / ngp_2dh_s_inner(:,sr)
433	sums(:,41) = sums(:,41) / ngp_2dh_s_inner(:,sr)
434	hom(:,1,44,sr) = sums(:,44) ! vpt
435	hom(:,1,41,sr) = sums(:,41) ! qv (q)
436	IF ( cloud_physics ) THEN
437	sums(:,42) = sums(:,42) / ngp_2dh_s_inner(:,sr)
438	sums(:,43) = sums(:,43) / ngp_2dh_s_inner(:,sr)
439	hom(:,1,42,sr) = sums(:,42) ! qv
440	hom(:,1,43,sr) = sums(:,43) ! pt
441	ENDIF
442	ENDIF
443
444	!
445	!-- Passive scalar
446	IF ( passive_scalar ) hom(:,1,41,sr) = sums(:,41) / &
447	ngp_2dh_s_inner(:,sr) ! s (q)
448
449	!
450	!-- Horizontally averaged profiles of the remaining prognostic variables,
451	!-- variances, the total and the perturbation energy (single values in last
452	!-- column of sums_l) and some diagnostic quantities.
453	!-- NOTE: for simplicity, nzb_s_inner is used below, although strictly
454	!-- ---- speaking the following k-loop would have to be split up and
455	!-- rearranged according to the staggered grid.
456	!-- However, this implies no error since staggered velocity components
457	!-- are zero at the walls and inside buildings.
458	tn = 0
459	#if defined( __intel_openmp_bug )
460	!$OMP PARALLEL PRIVATE( i, j, k, pts, sums_ll, sums_l_eper, sums_l_etot, &
461	!$OMP tn, ust, ust2, u2, vst, vst2, v2, w2 )
462	tn = omp_get_thread_num()
463	#else
464	!$OMP PARALLEL PRIVATE( i, j, k, pts, sums_ll, sums_l_eper, sums_l_etot, tn, ust, ust2, u2, vst, vst2, v2, w2 )
465	!$ tn = omp_get_thread_num()
466	#endif
467	!$OMP DO
468	DO i = nxl, nxr
469	DO j = nys, nyn
470	sums_l_etot = 0.0
471	DO k = nzb_s_inner(j,i), nzt+1
472	!
473	!-- Prognostic and diagnostic variables
474	sums_l(k,3,tn) = sums_l(k,3,tn) + w(k,j,i) * rmask(j,i,sr)
475	sums_l(k,8,tn) = sums_l(k,8,tn) + e(k,j,i) * rmask(j,i,sr)
476	sums_l(k,9,tn) = sums_l(k,9,tn) + km(k,j,i) * rmask(j,i,sr)
477	sums_l(k,10,tn) = sums_l(k,10,tn) + kh(k,j,i) * rmask(j,i,sr)
478	sums_l(k,40,tn) = sums_l(k,40,tn) + p(k,j,i)
479
480	sums_l(k,33,tn) = sums_l(k,33,tn) + &
481	( pt(k,j,i)-hom(k,1,4,sr) )*2 rmask(j,i,sr)
482
483	IF ( humidity ) THEN
484	sums_l(k,70,tn) = sums_l(k,70,tn) + &
485	( q(k,j,i)-hom(k,1,41,sr) )*2 rmask(j,i,sr)
486	ENDIF
487
488	!
489	!-- Higher moments
490	!-- (Computation of the skewness of w further below)
491	sums_l(k,38,tn) = sums_l(k,38,tn) + w(k,j,i)*3 rmask(j,i,sr)
492
493	sums_l_etot = sums_l_etot + &
494	0.5 * ( u(k,j,i)2 + v(k,j,i)2 + &
495	w(k,j,i)*2 ) rmask(j,i,sr)
496	ENDDO
497	!
498	!-- Total and perturbation energy for the total domain (being
499	!-- collected in the last column of sums_l). Summation of these
500	!-- quantities is seperated from the previous loop in order to
501	!-- allow vectorization of that loop.
502	sums_l(nzb+4,pr_palm,tn) = sums_l(nzb+4,pr_palm,tn) + sums_l_etot
503	!
504	!-- 2D-arrays (being collected in the last column of sums_l)
505	sums_l(nzb,pr_palm,tn) = sums_l(nzb,pr_palm,tn) + &
506	us(j,i) * rmask(j,i,sr)
507	sums_l(nzb+1,pr_palm,tn) = sums_l(nzb+1,pr_palm,tn) + &
508	usws(j,i) * rmask(j,i,sr)
509	sums_l(nzb+2,pr_palm,tn) = sums_l(nzb+2,pr_palm,tn) + &
510	vsws(j,i) * rmask(j,i,sr)
511	sums_l(nzb+3,pr_palm,tn) = sums_l(nzb+3,pr_palm,tn) + &
512	ts(j,i) * rmask(j,i,sr)
513	IF ( humidity ) THEN
514	sums_l(nzb+12,pr_palm,tn) = sums_l(nzb+12,pr_palm,tn) + &
515	qs(j,i) * rmask(j,i,sr)
516	ENDIF
517	ENDDO
518	ENDDO
519
520	!
521	!-- Computation of statistics when ws-scheme is not used. Else these
522	!-- quantities are evaluated in the advection routines.
523	IF ( .NOT. ws_scheme_mom .OR. sr /= 0 ) THEN
524	!$OMP DO
525	DO i = nxl, nxr
526	DO j = nys, nyn
527	sums_l_eper = 0.0
528	DO k = nzb_s_inner(j,i), nzt+1
529	u2 = u(k,j,i)**2
530	v2 = v(k,j,i)**2
531	w2 = w(k,j,i)**2
532	ust2 = ( u(k,j,i) - hom(k,1,1,sr) )**2
533	vst2 = ( v(k,j,i) - hom(k,1,2,sr) )**2
534
535	sums_l(k,30,tn) = sums_l(k,30,tn) + ust2 * rmask(j,i,sr)
536	sums_l(k,31,tn) = sums_l(k,31,tn) + vst2 * rmask(j,i,sr)
537	sums_l(k,32,tn) = sums_l(k,32,tn) + w2 * rmask(j,i,sr)
538	!
539	!-- Perturbation energy
540
541	sums_l(k,34,tn) = sums_l(k,34,tn) + 0.5 * &
542	( ust2 + vst2 + w2 ) * rmask(j,i,sr)
543	sums_l_eper = sums_l_eper + &
544	0.5 * ( ust2+vst2+w2 ) * rmask(j,i,sr)
545
546	ENDDO
547	sums_l(nzb+5,pr_palm,tn) = sums_l(nzb+5,pr_palm,tn) &
548	+ sums_l_eper
549	ENDDO
550	ENDDO
551	ENDIF
552	!
553	!-- Horizontally averaged profiles of the vertical fluxes
554
555	!$OMP DO
556	DO i = nxl, nxr
557	DO j = nys, nyn
558	!
559	!-- Subgridscale fluxes (without Prandtl layer from k=nzb,
560	!-- oterwise from k=nzb+1)
561	!-- NOTE: for simplicity, nzb_diff_s_inner is used below, although
562	!-- ---- strictly speaking the following k-loop would have to be
563	!-- split up according to the staggered grid.
564	!-- However, this implies no error since staggered velocity
565	!-- components are zero at the walls and inside buildings.
566
567	DO k = nzb_diff_s_inner(j,i)-1, nzt_diff
568	!
569	!-- Momentum flux w"u"
570	sums_l(k,12,tn) = sums_l(k,12,tn) - 0.25 * ( &
571	km(k,j,i)+km(k+1,j,i)+km(k,j,i-1)+km(k+1,j,i-1) &
572	) * ( &
573	( u(k+1,j,i) - u(k,j,i) ) * ddzu(k+1) &
574	+ ( w(k,j,i) - w(k,j,i-1) ) * ddx &
575	) * rmask(j,i,sr)
576	!
577	!-- Momentum flux w"v"
578	sums_l(k,14,tn) = sums_l(k,14,tn) - 0.25 * ( &
579	km(k,j,i)+km(k+1,j,i)+km(k,j-1,i)+km(k+1,j-1,i) &
580	) * ( &
581	( v(k+1,j,i) - v(k,j,i) ) * ddzu(k+1) &
582	+ ( w(k,j,i) - w(k,j-1,i) ) * ddy &
583	) * rmask(j,i,sr)
584	!
585	!-- Heat flux w"pt"
586	sums_l(k,16,tn) = sums_l(k,16,tn) &
587	- 0.5 * ( kh(k,j,i) + kh(k+1,j,i) ) &
588	* ( pt(k+1,j,i) - pt(k,j,i) ) &
589	* ddzu(k+1) * rmask(j,i,sr)
590
591
592	!
593	!-- Salinity flux w"sa"
594	IF ( ocean ) THEN
595	sums_l(k,65,tn) = sums_l(k,65,tn) &
596	- 0.5 * ( kh(k,j,i) + kh(k+1,j,i) ) &
597	* ( sa(k+1,j,i) - sa(k,j,i) ) &
598	* ddzu(k+1) * rmask(j,i,sr)
599	ENDIF
600
601	!
602	!-- Buoyancy flux, water flux (humidity flux) w"q"
603	IF ( humidity ) THEN
604	sums_l(k,45,tn) = sums_l(k,45,tn) &
605	- 0.5 * ( kh(k,j,i) + kh(k+1,j,i) ) &
606	* ( vpt(k+1,j,i) - vpt(k,j,i) ) &
607	* ddzu(k+1) * rmask(j,i,sr)
608	sums_l(k,48,tn) = sums_l(k,48,tn) &
609	- 0.5 * ( kh(k,j,i) + kh(k+1,j,i) ) &
610	* ( q(k+1,j,i) - q(k,j,i) ) &
611	* ddzu(k+1) * rmask(j,i,sr)
612
613	IF ( cloud_physics ) THEN
614	sums_l(k,51,tn) = sums_l(k,51,tn) &
615	- 0.5 * ( kh(k,j,i) + kh(k+1,j,i) ) &
616	* ( ( q(k+1,j,i) - ql(k+1,j,i) )&
617	- ( q(k,j,i) - ql(k,j,i) ) ) &
618	* ddzu(k+1) * rmask(j,i,sr)
619	ENDIF
620	ENDIF
621
622	!
623	!-- Passive scalar flux
624	IF ( passive_scalar ) THEN
625	sums_l(k,48,tn) = sums_l(k,48,tn) &
626	- 0.5 * ( kh(k,j,i) + kh(k+1,j,i) ) &
627	* ( q(k+1,j,i) - q(k,j,i) ) &
628	* ddzu(k+1) * rmask(j,i,sr)
629	ENDIF
630
631	ENDDO
632
633	!
634	!-- Subgridscale fluxes in the Prandtl layer
635	IF ( use_surface_fluxes ) THEN
636	sums_l(nzb,12,tn) = sums_l(nzb,12,tn) + &
637	usws(j,i) * rmask(j,i,sr) ! w"u"
638	sums_l(nzb,14,tn) = sums_l(nzb,14,tn) + &
639	vsws(j,i) * rmask(j,i,sr) ! w"v"
640	sums_l(nzb,16,tn) = sums_l(nzb,16,tn) + &
641	shf(j,i) * rmask(j,i,sr) ! w"pt"
642	sums_l(nzb,58,tn) = sums_l(nzb,58,tn) + &
643	0.0 * rmask(j,i,sr) ! u"pt"
644	sums_l(nzb,61,tn) = sums_l(nzb,61,tn) + &
645	0.0 * rmask(j,i,sr) ! v"pt"
646	IF ( ocean ) THEN
647	sums_l(nzb,65,tn) = sums_l(nzb,65,tn) + &
648	saswsb(j,i) * rmask(j,i,sr) ! w"sa"
649	ENDIF
650	IF ( humidity ) THEN
651	sums_l(nzb,48,tn) = sums_l(nzb,48,tn) + &
652	qsws(j,i) * rmask(j,i,sr) ! w"q" (w"qv")
653	sums_l(nzb,45,tn) = sums_l(nzb,45,tn) + ( &
654	( 1.0 + 0.61 * q(nzb,j,i) ) * &
655	shf(j,i) + 0.61 * pt(nzb,j,i) * &
656	qsws(j,i) )
657	IF ( cloud_droplets ) THEN
658	sums_l(nzb,45,tn) = sums_l(nzb,45,tn) + ( &
659	( 1.0 + 0.61 * q(nzb,j,i) - &
660	ql(nzb,j,i) ) * shf(j,i) + &
661	0.61 * pt(nzb,j,i) * qsws(j,i) )
662	ENDIF
663	IF ( cloud_physics ) THEN
664	!
665	!-- Formula does not work if ql(nzb) /= 0.0
666	sums_l(nzb,51,tn) = sums_l(nzb,51,tn) + & ! w"q" (w"qv")
667	qsws(j,i) * rmask(j,i,sr)
668	ENDIF
669	ENDIF
670	IF ( passive_scalar ) THEN
671	sums_l(nzb,48,tn) = sums_l(nzb,48,tn) + &
672	qsws(j,i) * rmask(j,i,sr) ! w"q" (w"qv")
673	ENDIF
674	ENDIF
675
676	!
677	!-- Subgridscale fluxes at the top surface
678	IF ( use_top_fluxes ) THEN
679	sums_l(nzt:nzt+1,12,tn) = sums_l(nzt:nzt+1,12,tn) + &
680	uswst(j,i) * rmask(j,i,sr) ! w"u"
681	sums_l(nzt:nzt+1,14,tn) = sums_l(nzt:nzt+1,14,tn) + &
682	vswst(j,i) * rmask(j,i,sr) ! w"v"
683	sums_l(nzt:nzt+1,16,tn) = sums_l(nzt:nzt+1,16,tn) + &
684	tswst(j,i) * rmask(j,i,sr) ! w"pt"
685	sums_l(nzt:nzt+1,58,tn) = sums_l(nzt:nzt+1,58,tn) + &
686	0.0 * rmask(j,i,sr) ! u"pt"
687	sums_l(nzt:nzt+1,61,tn) = sums_l(nzt:nzt+1,61,tn) + &
688	0.0 * rmask(j,i,sr) ! v"pt"
689
690	IF ( ocean ) THEN
691	sums_l(nzt,65,tn) = sums_l(nzt,65,tn) + &
692	saswst(j,i) * rmask(j,i,sr) ! w"sa"
693	ENDIF
694	IF ( humidity ) THEN
695	sums_l(nzt,48,tn) = sums_l(nzt,48,tn) + &
696	qswst(j,i) * rmask(j,i,sr) ! w"q" (w"qv")
697	sums_l(nzt,45,tn) = sums_l(nzt,45,tn) + ( &
698	( 1.0 + 0.61 * q(nzt,j,i) ) * &
699	tswst(j,i) + 0.61 * pt(nzt,j,i) * &
700	qswst(j,i) )
701	IF ( cloud_droplets ) THEN
702	sums_l(nzt,45,tn) = sums_l(nzt,45,tn) + ( &
703	( 1.0 + 0.61 * q(nzt,j,i) - &
704	ql(nzt,j,i) ) * tswst(j,i) + &
705	0.61 * pt(nzt,j,i) * qswst(j,i) )
706	ENDIF
707	IF ( cloud_physics ) THEN
708	!
709	!-- Formula does not work if ql(nzb) /= 0.0
710	sums_l(nzt,51,tn) = sums_l(nzt,51,tn) + & ! w"q" (w"qv")
711	qswst(j,i) * rmask(j,i,sr)
712	ENDIF
713	ENDIF
714	IF ( passive_scalar ) THEN
715	sums_l(nzt,48,tn) = sums_l(nzt,48,tn) + &
716	qswst(j,i) * rmask(j,i,sr) ! w"q" (w"qv")
717	ENDIF
718	ENDIF
719
720	!
721	!-- Resolved fluxes (can be computed for all horizontal points)
722	!-- NOTE: for simplicity, nzb_s_inner is used below, although strictly
723	!-- ---- speaking the following k-loop would have to be split up and
724	!-- rearranged according to the staggered grid.
725	DO k = nzb_s_inner(j,i), nzt
726	ust = 0.5 * ( u(k,j,i) - hom(k,1,1,sr) + &
727	u(k+1,j,i) - hom(k+1,1,1,sr) )
728	vst = 0.5 * ( v(k,j,i) - hom(k,1,2,sr) + &
729	v(k+1,j,i) - hom(k+1,1,2,sr) )
730	pts = 0.5 * ( pt(k,j,i) - hom(k,1,4,sr) + &
731	pt(k+1,j,i) - hom(k+1,1,4,sr) )
732
733	!-- Higher moments
734	sums_l(k,35,tn) = sums_l(k,35,tn) + pts * w(k,j,i)*2 &
735	rmask(j,i,sr)
736	sums_l(k,36,tn) = sums_l(k,36,tn) + pts*2 w(k,j,i) * &
737	rmask(j,i,sr)
738
739	!
740	!-- Salinity flux and density (density does not belong to here,
741	!-- but so far there is no other suitable place to calculate)
742	IF ( ocean ) THEN
743	IF( .NOT. ws_scheme_sca .OR. sr /= 0 ) THEN
744	pts = 0.5 * ( sa(k,j,i) - hom(k,1,23,sr) + &
745	sa(k+1,j,i) - hom(k+1,1,23,sr) )
746	sums_l(k,66,tn) = sums_l(k,66,tn) + pts * w(k,j,i) * &
747	rmask(j,i,sr)
748	ENDIF
749	sums_l(k,64,tn) = sums_l(k,64,tn) + rho(k,j,i) * &
750	rmask(j,i,sr)
751	sums_l(k,71,tn) = sums_l(k,71,tn) + prho(k,j,i) * &
752	rmask(j,i,sr)
753	ENDIF
754
755	!
756	!-- Buoyancy flux, water flux, humidity flux, liquid water
757	!-- content, rain drop concentration and rain water content
758	IF ( humidity ) THEN
759	IF ( cloud_physics .OR. cloud_droplets ) THEN
760	pts = 0.5 * ( vpt(k,j,i) - hom(k,1,44,sr) + &
761	vpt(k+1,j,i) - hom(k+1,1,44,sr) )
762	sums_l(k,46,tn) = sums_l(k,46,tn) + pts * w(k,j,i) * &
763	rmask(j,i,sr)
764	IF ( .NOT. cloud_droplets ) THEN
765	pts = 0.5 * &
766	( ( q(k,j,i) - ql(k,j,i) ) - &
767	hom(k,1,42,sr) + &
768	( q(k+1,j,i) - ql(k+1,j,i) ) - &
769	hom(k+1,1,42,sr) )
770	sums_l(k,52,tn) = sums_l(k,52,tn) + pts * w(k,j,i) * &
771	rmask(j,i,sr)
772	IF ( icloud_scheme == 0 ) THEN
773	sums_l(k,54,tn) = sums_l(k,54,tn) + ( ql(k,j,i) + &
774	qr(k,j,i) ) * &
775	rmask(j,i,sr)
776	sums_l(k,73,tn) = sums_l(k,73,tn) + nr(k,j,i) * &
777	rmask(j,i,sr)
778	sums_l(k,74,tn) = sums_l(k,74,tn) + qr(k,j,i) * &
779	rmask(j,i,sr)
780	sums_l(k,75,tn) = sums_l(k,75,tn) + ql(k,j,i) * &
781	rmask(j,i,sr)
782	sums_l(k,76,tn) = sums_l(k,76,tn) + prr(k,j,i) * &
783	rmask(j,i,sr)
784	ELSE
785	sums_l(k,54,tn) = sums_l(k,54,tn) + ql(k,j,i) * &
786	rmask(j,i,sr)
787	ENDIF
788	ELSE
789	sums_l(k,54,tn) = sums_l(k,54,tn) + ql(k,j,i) * &
790	rmask(j,i,sr)
791	ENDIF
792	ELSE
793	IF( .NOT. ws_scheme_sca .OR. sr /= 0 ) THEN
794	pts = 0.5 * ( vpt(k,j,i) - hom(k,1,44,sr) + &
795	vpt(k+1,j,i) - hom(k+1,1,44,sr) )
796	sums_l(k,46,tn) = sums_l(k,46,tn) + pts * w(k,j,i) * &
797	rmask(j,i,sr)
798	ELSE IF ( ws_scheme_sca .AND. sr == 0 ) THEN
799	sums_l(k,46,tn) = ( 1.0 + 0.61 * hom(k,1,41,sr) ) * &
800	sums_l(k,17,tn) + &
801	0.61 * hom(k,1,4,sr) * sums_l(k,49,tn)
802	END IF
803	END IF
804	ENDIF
805	!
806	!-- Passive scalar flux
807	IF ( passive_scalar .AND. ( .NOT. ws_scheme_sca &
808	.OR. sr /= 0 ) ) THEN
809	pts = 0.5 * ( q(k,j,i) - hom(k,1,41,sr) + &
810	q(k+1,j,i) - hom(k+1,1,41,sr) )
811	sums_l(k,49,tn) = sums_l(k,49,tn) + pts * w(k,j,i) * &
812	rmask(j,i,sr)
813	ENDIF
814
815	!
816	!-- Energy flux we
817	!-- has to be adjusted
818	sums_l(k,37,tn) = sums_l(k,37,tn) + w(k,j,i) * 0.5 * &
819	( ust2 + vst2 + w(k,j,i)**2 )&
820	* rmask(j,i,sr)
821	ENDDO
822	ENDDO
823	ENDDO
824	!
825	!-- For speed optimization fluxes which have been computed in part directly
826	!-- inside the WS advection routines are treated seperatly
827	!-- Momentum fluxes first:
828	IF ( .NOT. ws_scheme_mom .OR. sr /= 0 ) THEN
829	!$OMP DO
830	DO i = nxl, nxr
831	DO j = nys, nyn
832	DO k = nzb_diff_s_inner(j,i)-1, nzt_diff
833	ust = 0.5 * ( u(k,j,i) - hom(k,1,1,sr) + &
834	u(k+1,j,i) - hom(k+1,1,1,sr) )
835	vst = 0.5 * ( v(k,j,i) - hom(k,1,2,sr) + &
836	v(k+1,j,i) - hom(k+1,1,2,sr) )
837	!
838	!-- Momentum flux wu
839	sums_l(k,13,tn) = sums_l(k,13,tn) + 0.5 * &
840	( w(k,j,i-1) + w(k,j,i) ) &
841	* ust * rmask(j,i,sr)
842	!
843	!-- Momentum flux wv
844	sums_l(k,15,tn) = sums_l(k,15,tn) + 0.5 * &
845	( w(k,j-1,i) + w(k,j,i) ) &
846	* vst * rmask(j,i,sr)
847	ENDDO
848	ENDDO
849	ENDDO
850
851	ENDIF
852	IF ( .NOT. ws_scheme_sca .OR. sr /= 0 ) THEN
853	!$OMP DO
854	DO i = nxl, nxr
855	DO j = nys, nyn
856	DO k = nzb_diff_s_inner(j,i)-1, nzt_diff
857	!
858	!-- Vertical heat flux
859	sums_l(k,17,tn) = sums_l(k,17,tn) + 0.5 * &
860	( pt(k,j,i) - hom(k,1,4,sr) + &
861	pt(k+1,j,i) - hom(k+1,1,4,sr) ) &
862	* w(k,j,i) * rmask(j,i,sr)
863	IF ( humidity ) THEN
864	pts = 0.5 * ( q(k,j,i) - hom(k,1,41,sr) + &
865	q(k+1,j,i) - hom(k+1,1,41,sr) )
866	sums_l(k,49,tn) = sums_l(k,49,tn) + pts * w(k,j,i) * &
867	rmask(j,i,sr)
868	ENDIF
869	ENDDO
870	ENDDO
871	ENDDO
872
873	ENDIF
874
875
876	!
877	!-- Density at top follows Neumann condition
878	IF ( ocean ) THEN
879	sums_l(nzt+1,64,tn) = sums_l(nzt,64,tn)
880	sums_l(nzt+1,71,tn) = sums_l(nzt,71,tn)
881	ENDIF
882
883	!
884	!-- Divergence of vertical flux of resolved scale energy and pressure
885	!-- fluctuations as well as flux of pressure fluctuation itself (68).
886	!-- First calculate the products, then the divergence.
887	!-- Calculation is time consuming. Do it only, if profiles shall be plotted.
888	IF ( hom(nzb+1,2,55,0) /= 0.0 .OR. hom(nzb+1,2,68,0) /= 0.0 ) THEN
889
890	sums_ll = 0.0 ! local array
891
892	!$OMP DO
893	DO i = nxl, nxr
894	DO j = nys, nyn
895	DO k = nzb_s_inner(j,i)+1, nzt
896
897	sums_ll(k,1) = sums_ll(k,1) + 0.5 * w(k,j,i) * ( &
898	( 0.25 * ( u(k,j,i)+u(k+1,j,i)+u(k,j,i+1)+u(k+1,j,i+1) &
899	- 0.5 * ( hom(k,1,1,sr) + hom(k+1,1,1,sr) ) &
900	) )**2 &
901	+ ( 0.25 * ( v(k,j,i)+v(k+1,j,i)+v(k,j+1,i)+v(k+1,j+1,i) &
902	- 0.5 * ( hom(k,1,2,sr) + hom(k+1,1,2,sr) ) &
903	) )**2 &
904	+ w(k,j,i)**2 )
905
906	sums_ll(k,2) = sums_ll(k,2) + 0.5 * w(k,j,i) &
907	* ( p(k,j,i) + p(k+1,j,i) )
908
909	ENDDO
910	ENDDO
911	ENDDO
912	sums_ll(0,1) = 0.0 ! because w is zero at the bottom
913	sums_ll(nzt+1,1) = 0.0
914	sums_ll(0,2) = 0.0
915	sums_ll(nzt+1,2) = 0.0
916
917	DO k = nzb+1, nzt
918	sums_l(k,55,tn) = ( sums_ll(k,1) - sums_ll(k-1,1) ) * ddzw(k)
919	sums_l(k,56,tn) = ( sums_ll(k,2) - sums_ll(k-1,2) ) * ddzw(k)
920	sums_l(k,68,tn) = sums_ll(k,2)
921	ENDDO
922	sums_l(nzb,55,tn) = sums_l(nzb+1,55,tn)
923	sums_l(nzb,56,tn) = sums_l(nzb+1,56,tn)
924	sums_l(nzb,68,tn) = 0.0 ! because w* = 0 at nzb
925
926	ENDIF
927
928	!
929	!-- Divergence of vertical flux of SGS TKE and the flux itself (69)
930	IF ( hom(nzb+1,2,57,0) /= 0.0 .OR. hom(nzb+1,2,69,0) /= 0.0 ) THEN
931
932	!$OMP DO
933	DO i = nxl, nxr
934	DO j = nys, nyn
935	DO k = nzb_s_inner(j,i)+1, nzt
936
937	sums_l(k,57,tn) = sums_l(k,57,tn) - 0.5 * ( &
938	(km(k,j,i)+km(k+1,j,i)) * (e(k+1,j,i)-e(k,j,i)) * ddzu(k+1) &
939	- (km(k-1,j,i)+km(k,j,i)) * (e(k,j,i)-e(k-1,j,i)) * ddzu(k) &
940	) * ddzw(k)
941
942	sums_l(k,69,tn) = sums_l(k,69,tn) - 0.5 * ( &
943	(km(k,j,i)+km(k+1,j,i)) * (e(k+1,j,i)-e(k,j,i)) * ddzu(k+1) &
944	)
945
946	ENDDO
947	ENDDO
948	ENDDO
949	sums_l(nzb,57,tn) = sums_l(nzb+1,57,tn)
950	sums_l(nzb,69,tn) = sums_l(nzb+1,69,tn)
951
952	ENDIF
953
954	!
955	!-- Horizontal heat fluxes (subgrid, resolved, total).
956	!-- Do it only, if profiles shall be plotted.
957	IF ( hom(nzb+1,2,58,0) /= 0.0 ) THEN
958
959	!$OMP DO
960	DO i = nxl, nxr
961	DO j = nys, nyn
962	DO k = nzb_s_inner(j,i)+1, nzt
963	!
964	!-- Subgrid horizontal heat fluxes u"pt", v"pt"
965	sums_l(k,58,tn) = sums_l(k,58,tn) - 0.5 * &
966	( kh(k,j,i) + kh(k,j,i-1) ) &
967	* ( pt(k,j,i-1) - pt(k,j,i) ) &
968	* ddx * rmask(j,i,sr)
969	sums_l(k,61,tn) = sums_l(k,61,tn) - 0.5 * &
970	( kh(k,j,i) + kh(k,j-1,i) ) &
971	* ( pt(k,j-1,i) - pt(k,j,i) ) &
972	* ddy * rmask(j,i,sr)
973	!
974	!-- Resolved horizontal heat fluxes upt, vpt
975	sums_l(k,59,tn) = sums_l(k,59,tn) + &
976	( u(k,j,i) - hom(k,1,1,sr) ) &
977	* 0.5 * ( pt(k,j,i-1) - hom(k,1,4,sr) + &
978	pt(k,j,i) - hom(k,1,4,sr) )
979	pts = 0.5 * ( pt(k,j-1,i) - hom(k,1,4,sr) + &
980	pt(k,j,i) - hom(k,1,4,sr) )
981	sums_l(k,62,tn) = sums_l(k,62,tn) + &
982	( v(k,j,i) - hom(k,1,2,sr) ) &
983	* 0.5 * ( pt(k,j-1,i) - hom(k,1,4,sr) + &
984	pt(k,j,i) - hom(k,1,4,sr) )
985	ENDDO
986	ENDDO
987	ENDDO
988	!
989	!-- Fluxes at the surface must be zero (e.g. due to the Prandtl-layer)
990	sums_l(nzb,58,tn) = 0.0
991	sums_l(nzb,59,tn) = 0.0
992	sums_l(nzb,60,tn) = 0.0
993	sums_l(nzb,61,tn) = 0.0
994	sums_l(nzb,62,tn) = 0.0
995	sums_l(nzb,63,tn) = 0.0
996
997	ENDIF
998
999	!
1000	!-- Calculate the user-defined profiles
1001	CALL user_statistics( 'profiles', sr, tn )
1002	!$OMP END PARALLEL
1003
1004	!
1005	!-- Summation of thread sums
1006	IF ( threads_per_task > 1 ) THEN
1007	DO i = 1, threads_per_task-1
1008	sums_l(:,3,0) = sums_l(:,3,0) + sums_l(:,3,i)
1009	sums_l(:,4:40,0) = sums_l(:,4:40,0) + sums_l(:,4:40,i)
1010	sums_l(:,45:pr_palm,0) = sums_l(:,45:pr_palm,0) + &
1011	sums_l(:,45:pr_palm,i)
1012	IF ( max_pr_user > 0 ) THEN
1013	sums_l(:,pr_palm+1:pr_palm+max_pr_user,0) = &
1014	sums_l(:,pr_palm+1:pr_palm+max_pr_user,0) + &
1015	sums_l(:,pr_palm+1:pr_palm+max_pr_user,i)
1016	ENDIF
1017	ENDDO
1018	ENDIF
1019
1020	#if defined( __parallel )
1021
1022	!
1023	!-- Compute total sum from local sums
1024	IF ( collective_wait ) CALL MPI_BARRIER( comm2d, ierr )
1025	CALL MPI_ALLREDUCE( sums_l(nzb,1,0), sums(nzb,1), ngp_sums, MPI_REAL, &
1026	MPI_SUM, comm2d, ierr )
1027	#else
1028	sums = sums_l(:,:,0)
1029	#endif
1030
1031	!
1032	!-- Final values are obtained by division by the total number of grid points
1033	!-- used for summation. After that store profiles.
1034	!-- Profiles:
1035	DO k = nzb, nzt+1
1036	sums(k,3) = sums(k,3) / ngp_2dh(sr)
1037	sums(k,8:11) = sums(k,8:11) / ngp_2dh_s_inner(k,sr)
1038	sums(k,12:22) = sums(k,12:22) / ngp_2dh(sr)
1039	sums(k,23:29) = sums(k,23:29) / ngp_2dh_s_inner(k,sr)
1040	sums(k,30:32) = sums(k,30:32) / ngp_2dh(sr)
1041	sums(k,33:34) = sums(k,33:34) / ngp_2dh_s_inner(k,sr)
1042	sums(k,35:39) = sums(k,35:39) / ngp_2dh(sr)
1043	sums(k,40) = sums(k,40) / ngp_2dh_s_inner(k,sr)
1044	sums(k,45:53) = sums(k,45:53) / ngp_2dh(sr)
1045	sums(k,54) = sums(k,54) / ngp_2dh_s_inner(k,sr)
1046	sums(k,55:63) = sums(k,55:63) / ngp_2dh(sr)
1047	sums(k,64) = sums(k,64) / ngp_2dh_s_inner(k,sr)
1048	sums(k,65:69) = sums(k,65:69) / ngp_2dh(sr)
1049	sums(k,70:pr_palm-2) = sums(k,70:pr_palm-2)/ ngp_2dh_s_inner(k,sr)
1050	ENDDO
1051
1052	!-- Upstream-parts
1053	sums(nzb:nzb+11,pr_palm-1) = sums(nzb:nzb+11,pr_palm-1) / ngp_3d(sr)
1054	!-- u* and so on
1055	!-- As sums(nzb:nzb+3,pr_palm) are full 2D arrays (us, usws, vsws, ts) whose
1056	!-- size is always ( nx + 1 ) * ( ny + 1 ), defined at the first grid layer
1057	!-- above the topography, they are being divided by ngp_2dh(sr)
1058	sums(nzb:nzb+3,pr_palm) = sums(nzb:nzb+3,pr_palm) / &
1059	ngp_2dh(sr)
1060	sums(nzb+12,pr_palm) = sums(nzb+12,pr_palm) / & ! qs
1061	ngp_2dh(sr)
1062	!-- eges, e*
1063	sums(nzb+4:nzb+5,pr_palm) = sums(nzb+4:nzb+5,pr_palm) / &
1064	ngp_3d(sr)
1065	!-- Old and new divergence
1066	sums(nzb+9:nzb+10,pr_palm) = sums(nzb+9:nzb+10,pr_palm) / &
1067	ngp_3d_inner(sr)
1068
1069	!-- User-defined profiles
1070	IF ( max_pr_user > 0 ) THEN
1071	DO k = nzb, nzt+1
1072	sums(k,pr_palm+1:pr_palm+max_pr_user) = &
1073	sums(k,pr_palm+1:pr_palm+max_pr_user) / &
1074	ngp_2dh_s_inner(k,sr)
1075	ENDDO
1076	ENDIF
1077
1078	!
1079	!-- Collect horizontal average in hom.
1080	!-- Compute deduced averages (e.g. total heat flux)
1081	hom(:,1,3,sr) = sums(:,3) ! w
1082	hom(:,1,8,sr) = sums(:,8) ! e profiles 5-7 are initial profiles
1083	hom(:,1,9,sr) = sums(:,9) ! km
1084	hom(:,1,10,sr) = sums(:,10) ! kh
1085	hom(:,1,11,sr) = sums(:,11) ! l
1086	hom(:,1,12,sr) = sums(:,12) ! w"u"
1087	hom(:,1,13,sr) = sums(:,13) ! wu
1088	hom(:,1,14,sr) = sums(:,14) ! w"v"
1089	hom(:,1,15,sr) = sums(:,15) ! wv
1090	hom(:,1,16,sr) = sums(:,16) ! w"pt"
1091	hom(:,1,17,sr) = sums(:,17) ! wpt
1092	hom(:,1,18,sr) = sums(:,16) + sums(:,17) ! wpt
1093	hom(:,1,19,sr) = sums(:,12) + sums(:,13) ! wu
1094	hom(:,1,20,sr) = sums(:,14) + sums(:,15) ! wv
1095	hom(:,1,21,sr) = sums(:,21) ! wptBC
1096	hom(:,1,22,sr) = sums(:,16) + sums(:,21) ! wptBC
1097	! profile 24 is initial profile (sa)
1098	! profiles 25-29 left empty for initial
1099	! profiles
1100	hom(:,1,30,sr) = sums(:,30) ! u*2
1101	hom(:,1,31,sr) = sums(:,31) ! v*2
1102	hom(:,1,32,sr) = sums(:,32) ! w*2
1103	hom(:,1,33,sr) = sums(:,33) ! pt*2
1104	hom(:,1,34,sr) = sums(:,34) ! e*
1105	hom(:,1,35,sr) = sums(:,35) ! w2pt
1106	hom(:,1,36,sr) = sums(:,36) ! wpt2
1107	hom(:,1,37,sr) = sums(:,37) ! we
1108	hom(:,1,38,sr) = sums(:,38) ! w*3
1109	hom(:,1,39,sr) = sums(:,38) / ( abs( sums(:,32) ) + 1E-20 )**1.5 ! Sw
1110	hom(:,1,40,sr) = sums(:,40) ! p
1111	hom(:,1,45,sr) = sums(:,45) ! w"vpt"
1112	hom(:,1,46,sr) = sums(:,46) ! wvpt
1113	hom(:,1,47,sr) = sums(:,45) + sums(:,46) ! wvpt
1114	hom(:,1,48,sr) = sums(:,48) ! w"q" (w"qv")
1115	hom(:,1,49,sr) = sums(:,49) ! wq (wqv)
1116	hom(:,1,50,sr) = sums(:,48) + sums(:,49) ! wq (wqv)
1117	hom(:,1,51,sr) = sums(:,51) ! w"qv"
1118	hom(:,1,52,sr) = sums(:,52) ! wqv
1119	hom(:,1,53,sr) = sums(:,52) + sums(:,51) ! wq (wqv)
1120	hom(:,1,54,sr) = sums(:,54) ! ql
1121	hom(:,1,55,sr) = sums(:,55) ! wuu*/dz
1122	hom(:,1,56,sr) = sums(:,56) ! wp/dz
1123	hom(:,1,57,sr) = sums(:,57) ! ( w"e + w"p"/rho )/dz
1124	hom(:,1,58,sr) = sums(:,58) ! u"pt"
1125	hom(:,1,59,sr) = sums(:,59) ! upt
1126	hom(:,1,60,sr) = sums(:,58) + sums(:,59) ! upt_t
1127	hom(:,1,61,sr) = sums(:,61) ! v"pt"
1128	hom(:,1,62,sr) = sums(:,62) ! vpt
1129	hom(:,1,63,sr) = sums(:,61) + sums(:,62) ! vpt_t
1130	hom(:,1,64,sr) = sums(:,64) ! rho
1131	hom(:,1,65,sr) = sums(:,65) ! w"sa"
1132	hom(:,1,66,sr) = sums(:,66) ! wsa
1133	hom(:,1,67,sr) = sums(:,65) + sums(:,66) ! wsa
1134	hom(:,1,68,sr) = sums(:,68) ! wp
1135	hom(:,1,69,sr) = sums(:,69) ! w"e + w"p"/rho
1136	hom(:,1,70,sr) = sums(:,70) ! q*2
1137	hom(:,1,71,sr) = sums(:,71) ! prho
1138	hom(:,1,72,sr) = hyp * 1E-4 ! hyp in dbar
1139	hom(:,1,73,sr) = sums(:,73) ! nr
1140	hom(:,1,74,sr) = sums(:,74) ! qr
1141	hom(:,1,75,sr) = sums(:,75) ! qc
1142	hom(:,1,76,sr) = sums(:,76) ! prr (precipitation rate)
1143
1144	hom(:,1,pr_palm-1,sr) = sums(:,pr_palm-1)
1145	! upstream-parts u_x, u_y, u_z, v_x,
1146	! v_y, usw. (in last but one profile)
1147	hom(:,1,pr_palm,sr) = sums(:,pr_palm)
1148	! u, w'u', w'v', t (in last profile)
1149
1150	IF ( max_pr_user > 0 ) THEN ! user-defined profiles
1151	hom(:,1,pr_palm+1:pr_palm+max_pr_user,sr) = &
1152	sums(:,pr_palm+1:pr_palm+max_pr_user)
1153	ENDIF
1154
1155	!
1156	!-- Determine the boundary layer height using two different schemes.
1157	!-- First scheme: Starting from the Earth's (Ocean's) surface, look for the
1158	!-- first relative minimum (maximum) of the total heat flux.
1159	!-- The corresponding height is assumed as the boundary layer height, if it
1160	!-- is less than 1.5 times the height where the heat flux becomes negative
1161	!-- (positive) for the first time.
1162	z_i(1) = 0.0
1163	first = .TRUE.
1164
1165	IF ( ocean ) THEN
1166	DO k = nzt, nzb+1, -1
1167	IF ( first .AND. hom(k,1,18,sr) < 0.0 &
1168	.AND. abs(hom(k,1,18,sr)) > 1.0E-8) THEN
1169	first = .FALSE.
1170	height = zw(k)
1171	ENDIF
1172	IF ( hom(k,1,18,sr) < 0.0 .AND. &
1173	abs(hom(k,1,18,sr)) > 1.0E-8 .AND. &
1174	hom(k-1,1,18,sr) > hom(k,1,18,sr) ) THEN
1175	IF ( zw(k) < 1.5 * height ) THEN
1176	z_i(1) = zw(k)
1177	ELSE
1178	z_i(1) = height
1179	ENDIF
1180	EXIT
1181	ENDIF
1182	ENDDO
1183	ELSE
1184	DO k = nzb, nzt-1
1185	IF ( first .AND. hom(k,1,18,sr) < 0.0 &
1186	.AND. abs(hom(k,1,18,sr)) > 1.0E-8 ) THEN
1187	first = .FALSE.
1188	height = zw(k)
1189	ENDIF
1190	IF ( hom(k,1,18,sr) < 0.0 .AND. &
1191	abs(hom(k,1,18,sr)) > 1.0E-8 .AND. &
1192	hom(k+1,1,18,sr) > hom(k,1,18,sr) ) THEN
1193	IF ( zw(k) < 1.5 * height ) THEN
1194	z_i(1) = zw(k)
1195	ELSE
1196	z_i(1) = height
1197	ENDIF
1198	EXIT
1199	ENDIF
1200	ENDDO
1201	ENDIF
1202
1203	!
1204	!-- Second scheme: Gradient scheme from Sullivan et al. (1998), modified
1205	!-- by Uhlenbrock(2006). The boundary layer height is the height with the
1206	!-- maximal local temperature gradient: starting from the second (the last
1207	!-- but one) vertical gridpoint, the local gradient must be at least
1208	!-- 0.2K/100m and greater than the next four gradients.
1209	!-- WARNING: The threshold value of 0.2K/100m must be adjusted for the
1210	!-- ocean case!
1211	z_i(2) = 0.0
1212	DO k = nzb+1, nzt+1
1213	dptdz(k) = ( hom(k,1,4,sr) - hom(k-1,1,4,sr) ) * ddzu(k)
1214	ENDDO
1215	dptdz_threshold = 0.2 / 100.0
1216
1217	IF ( ocean ) THEN
1218	DO k = nzt+1, nzb+5, -1
1219	IF ( dptdz(k) > dptdz_threshold .AND. &
1220	dptdz(k) > dptdz(k-1) .AND. dptdz(k) > dptdz(k-2) .AND. &
1221	dptdz(k) > dptdz(k-3) .AND. dptdz(k) > dptdz(k-4) ) THEN
1222	z_i(2) = zw(k-1)
1223	EXIT
1224	ENDIF
1225	ENDDO
1226	ELSE
1227	DO k = nzb+1, nzt-3
1228	IF ( dptdz(k) > dptdz_threshold .AND. &
1229	dptdz(k) > dptdz(k+1) .AND. dptdz(k) > dptdz(k+2) .AND. &
1230	dptdz(k) > dptdz(k+3) .AND. dptdz(k) > dptdz(k+4) ) THEN
1231	z_i(2) = zw(k-1)
1232	EXIT
1233	ENDIF
1234	ENDDO
1235	ENDIF
1236
1237	hom(nzb+6,1,pr_palm,sr) = z_i(1)
1238	hom(nzb+7,1,pr_palm,sr) = z_i(2)
1239
1240	!
1241	!-- Computation of both the characteristic vertical velocity and
1242	!-- the characteristic convective boundary layer temperature.
1243	!-- The horizontal average at nzb+1 is input for the average temperature.
1244	IF ( hom(nzb,1,18,sr) > 0.0 .AND. abs(hom(nzb,1,18,sr)) > 1.0E-8 &
1245	.AND. z_i(1) /= 0.0 ) THEN
1246	hom(nzb+8,1,pr_palm,sr) = ( g / hom(nzb+1,1,4,sr) * &
1247	hom(nzb,1,18,sr) * &
1248	ABS( z_i(1) ) )**0.333333333
1249	!-- so far this only works if Prandtl layer is used
1250	hom(nzb+11,1,pr_palm,sr) = hom(nzb,1,16,sr) / hom(nzb+8,1,pr_palm,sr)
1251	ELSE
1252	hom(nzb+8,1,pr_palm,sr) = 0.0
1253	hom(nzb+11,1,pr_palm,sr) = 0.0
1254	ENDIF
1255
1256	!
1257	!-- Collect the time series quantities
1258	ts_value(1,sr) = hom(nzb+4,1,pr_palm,sr) ! E
1259	ts_value(2,sr) = hom(nzb+5,1,pr_palm,sr) ! E*
1260	ts_value(3,sr) = dt_3d
1261	ts_value(4,sr) = hom(nzb,1,pr_palm,sr) ! u*
1262	ts_value(5,sr) = hom(nzb+3,1,pr_palm,sr) ! th*
1263	ts_value(6,sr) = u_max
1264	ts_value(7,sr) = v_max
1265	ts_value(8,sr) = w_max
1266	ts_value(9,sr) = hom(nzb+10,1,pr_palm,sr) ! new divergence
1267	ts_value(10,sr) = hom(nzb+9,1,pr_palm,sr) ! old Divergence
1268	ts_value(11,sr) = hom(nzb+6,1,pr_palm,sr) ! z_i(1)
1269	ts_value(12,sr) = hom(nzb+7,1,pr_palm,sr) ! z_i(2)
1270	ts_value(13,sr) = hom(nzb+8,1,pr_palm,sr) ! w*
1271	ts_value(14,sr) = hom(nzb,1,16,sr) ! w'pt' at k=0
1272	ts_value(15,sr) = hom(nzb+1,1,16,sr) ! w'pt' at k=1
1273	ts_value(16,sr) = hom(nzb+1,1,18,sr) ! wpt at k=1
1274	ts_value(17,sr) = hom(nzb,1,4,sr) ! pt(0)
1275	ts_value(18,sr) = hom(nzb+1,1,4,sr) ! pt(zp)
1276	ts_value(19,sr) = hom(nzb+1,1,pr_palm,sr) ! u'w' at k=0
1277	ts_value(20,sr) = hom(nzb+2,1,pr_palm,sr) ! v'w' at k=0
1278	ts_value(21,sr) = hom(nzb,1,48,sr) ! w"q" at k=0
1279
1280	IF ( ts_value(5,sr) /= 0.0 ) THEN
1281	ts_value(22,sr) = ts_value(4,sr)**2 / &
1282	( kappa * g * ts_value(5,sr) / ts_value(18,sr) ) ! L
1283	ELSE
1284	ts_value(22,sr) = 10000.0
1285	ENDIF
1286
1287	ts_value(23,sr) = hom(nzb+12,1,pr_palm,sr) ! q*
1288	!
1289	!-- Calculate additional statistics provided by the user interface
1290	CALL user_statistics( 'time_series', sr, 0 )
1291
1292	ENDDO ! loop of the subregions
1293
1294	!
1295	!-- If required, sum up horizontal averages for subsequent time averaging
1296	IF ( do_sum ) THEN
1297	IF ( average_count_pr == 0 ) hom_sum = 0.0
1298	hom_sum = hom_sum + hom(:,1,:,:)
1299	average_count_pr = average_count_pr + 1
1300	do_sum = .FALSE.
1301	ENDIF
1302
1303	!
1304	!-- Set flag for other UPs (e.g. output routines, but also buoyancy).
1305	!-- This flag is reset after each time step in time_integration.
1306	flow_statistics_called = .TRUE.
1307
1308	CALL cpu_log( log_point(10), 'flow_statistics', 'stop' )
1309
1310
1311	END SUBROUTINE flow_statistics

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