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source: palm/trunk/SOURCE/flow_statistics.f90 @ 1019

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

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