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source: palm/trunk/SOURCE/flow_statistics.f90 @ 106

Last change on this file since 106 was 106, checked in by raasch, 17 years ago
preliminary update of bugfixes and extensions for non-cyclic BCs
Property svn:keywords set to `Id`
File size: 42.8 KB

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1	SUBROUTINE flow_statistics
2
3	!------------------------------------------------------------------------------!
4	! Actual revisions:
5	! -----------------
6	! Prescribed momentum fluxes at the top surface are used,
7	! profiles for wp and w"e are calculated
8	!
9	! Former revisions:
10	! -----------------
11	! $Id: flow_statistics.f90 106 2007-08-16 14:30:26Z raasch $
12	!
13	! 97 2007-06-21 08:23:15Z raasch
14	! Statistics for ocean version (salinity, density) added,
15	! calculation of z_i and Deardorff velocity scale adjusted to be used with
16	! the ocean version
17	!
18	! 87 2007-05-22 15:46:47Z raasch
19	! Two more arguments added to user_statistics, which is now also called for
20	! user-defined profiles,
21	! var_hom and var_sum renamed pr_palm
22	!
23	! 82 2007-04-16 15:40:52Z raasch
24	! Cpp-directive lcmuk changed to intel_openmp_bug
25	!
26	! 75 2007-03-22 09:54:05Z raasch
27	! Collection of time series quantities moved from routine flow_statistics to
28	! here, routine user_statistics is called for each statistic region,
29	! moisture renamed humidity
30	!
31	! 19 2007-02-23 04:53:48Z raasch
32	! fluxes at top modified (tswst, qswst)
33	!
34	! RCS Log replace by Id keyword, revision history cleaned up
35	!
36	! Revision 1.41 2006/08/04 14:37:50 raasch
37	! Error removed in non-parallel part (sums_l)
38	!
39	! Revision 1.1 1997/08/11 06:15:17 raasch
40	! Initial revision
41	!
42	!
43	! Description:
44	! ------------
45	! Compute average profiles and further average flow quantities for the different
46	! user-defined (sub-)regions. The region indexed 0 is the total model domain.
47	!
48	! NOTE: For simplicity, nzb_s_outer and nzb_diff_s_outer are being used as a
49	! ---- lower vertical index for k-loops for all variables so that regardless
50	! of the variable and its respective staggered grid always the same number of
51	! grid points is used for 2D averages. The disadvantage: depending on the
52	! variable, up to one grid layer adjacent to the (vertical walls of the)
53	! topography is missed out by this simplification.
54	!------------------------------------------------------------------------------!
55
56	USE arrays_3d
57	USE cloud_parameters
58	USE cpulog
59	USE grid_variables
60	USE indices
61	USE interfaces
62	USE pegrid
63	USE statistics
64	USE control_parameters
65
66	IMPLICIT NONE
67
68	INTEGER :: i, j, k, omp_get_thread_num, sr, tn
69	LOGICAL :: first
70	REAL :: height, pts, sums_l_eper, sums_l_etot, ust, ust2, u2, vst, &
71	vst2, v2, w2, z_i(2)
72	REAL :: sums_ll(nzb:nzt+1,2)
73
74
75	CALL cpu_log( log_point(10), 'flow_statistics', 'start' )
76
77	!
78	!-- To be on the safe side, check whether flow_statistics has already been
79	!-- called once after the current time step
80	IF ( flow_statistics_called ) THEN
81	IF ( myid == 0 ) PRINT*, '+++ WARNING: flow_statistics is called two', &
82	' times within one timestep'
83	CALL local_stop
84	ENDIF
85
86	!
87	!-- Compute statistics for each (sub-)region
88	DO sr = 0, statistic_regions
89
90	!
91	!-- Initialize (local) summation array
92	sums_l = 0.0
93
94	!
95	!-- Store sums that have been computed in other subroutines in summation
96	!-- array
97	sums_l(:,11,:) = sums_l_l(:,sr,:) ! mixing length from diffusivities
98	!-- WARNING: next line still has to be adjusted for OpenMP
99	sums_l(:,21,0) = sums_wsts_bc_l(:,sr) ! heat flux from advec_s_bc
100	sums_l(nzb+9,pr_palm,0) = sums_divold_l(sr) ! old divergence from pres
101	sums_l(nzb+10,pr_palm,0) = sums_divnew_l(sr) ! new divergence from pres
102	!-- WARNING: next four lines still may have to be adjusted for OpenMP
103	sums_l(nzb:nzb+2,pr_palm-1,0) = sums_up_fraction_l(1,1:3,sr)! upstream
104	sums_l(nzb+3:nzb+5,pr_palm-1,0) = sums_up_fraction_l(2,1:3,sr)! parts
105	sums_l(nzb+6:nzb+8,pr_palm-1,0) = sums_up_fraction_l(3,1:3,sr)! from
106	sums_l(nzb+9:nzb+11,pr_palm-1,0) = sums_up_fraction_l(4,1:3,sr)! spline
107
108	!
109	!-- Horizontally averaged profiles of horizontal velocities and temperature.
110	!-- They must have been computed before, because they are already required
111	!-- for other horizontal averages.
112	tn = 0
113	!$OMP PARALLEL PRIVATE( i, j, k, tn )
114	#if defined( __intel_openmp_bug )
115	tn = omp_get_thread_num()
116	#else
117	!$ tn = omp_get_thread_num()
118	#endif
119
120	!$OMP DO
121	DO i = nxl, nxr
122	DO j = nys, nyn
123	DO k = nzb_s_outer(j,i), nzt+1
124	sums_l(k,1,tn) = sums_l(k,1,tn) + u(k,j,i) * rmask(j,i,sr)
125	sums_l(k,2,tn) = sums_l(k,2,tn) + v(k,j,i) * rmask(j,i,sr)
126	sums_l(k,4,tn) = sums_l(k,4,tn) + pt(k,j,i) * rmask(j,i,sr)
127	ENDDO
128	ENDDO
129	ENDDO
130
131	!
132	!-- Horizontally averaged profile of salinity
133	IF ( ocean ) THEN
134	!$OMP DO
135	DO i = nxl, nxr
136	DO j = nys, nyn
137	DO k = nzb_s_outer(j,i), nzt+1
138	sums_l(k,23,tn) = sums_l(k,23,tn) + &
139	sa(k,j,i) * rmask(j,i,sr)
140	ENDDO
141	ENDDO
142	ENDDO
143	ENDIF
144
145	!
146	!-- Horizontally averaged profiles of virtual potential temperature,
147	!-- total water content, specific humidity and liquid water potential
148	!-- temperature
149	IF ( humidity ) THEN
150	!$OMP DO
151	DO i = nxl, nxr
152	DO j = nys, nyn
153	DO k = nzb_s_outer(j,i), nzt+1
154	sums_l(k,44,tn) = sums_l(k,44,tn) + &
155	vpt(k,j,i) * rmask(j,i,sr)
156	sums_l(k,41,tn) = sums_l(k,41,tn) + &
157	q(k,j,i) * rmask(j,i,sr)
158	ENDDO
159	ENDDO
160	ENDDO
161	IF ( cloud_physics ) THEN
162	!$OMP DO
163	DO i = nxl, nxr
164	DO j = nys, nyn
165	DO k = nzb_s_outer(j,i), nzt+1
166	sums_l(k,42,tn) = sums_l(k,42,tn) + &
167	( q(k,j,i) - ql(k,j,i) ) * rmask(j,i,sr)
168	sums_l(k,43,tn) = sums_l(k,43,tn) + ( &
169	pt(k,j,i) + l_d_cppt_d_t(k) ql(k,j,i) &
170	) * rmask(j,i,sr)
171	ENDDO
172	ENDDO
173	ENDDO
174	ENDIF
175	ENDIF
176
177	!
178	!-- Horizontally averaged profiles of passive scalar
179	IF ( passive_scalar ) THEN
180	!$OMP DO
181	DO i = nxl, nxr
182	DO j = nys, nyn
183	DO k = nzb_s_outer(j,i), nzt+1
184	sums_l(k,41,tn) = sums_l(k,41,tn) + q(k,j,i) * rmask(j,i,sr)
185	ENDDO
186	ENDDO
187	ENDDO
188	ENDIF
189	!$OMP END PARALLEL
190
191	!
192	!-- Summation of thread sums
193	IF ( threads_per_task > 1 ) THEN
194	DO i = 1, threads_per_task-1
195	sums_l(:,1,0) = sums_l(:,1,0) + sums_l(:,1,i)
196	sums_l(:,2,0) = sums_l(:,2,0) + sums_l(:,2,i)
197	sums_l(:,4,0) = sums_l(:,4,0) + sums_l(:,4,i)
198	IF ( ocean ) THEN
199	sums_l(:,23,0) = sums_l(:,23,0) + sums_l(:,23,i)
200	ENDIF
201	IF ( humidity ) THEN
202	sums_l(:,41,0) = sums_l(:,41,0) + sums_l(:,41,i)
203	sums_l(:,44,0) = sums_l(:,44,0) + sums_l(:,44,i)
204	IF ( cloud_physics ) THEN
205	sums_l(:,42,0) = sums_l(:,42,0) + sums_l(:,42,i)
206	sums_l(:,43,0) = sums_l(:,43,0) + sums_l(:,43,i)
207	ENDIF
208	ENDIF
209	IF ( passive_scalar ) THEN
210	sums_l(:,41,0) = sums_l(:,41,0) + sums_l(:,41,i)
211	ENDIF
212	ENDDO
213	ENDIF
214
215	#if defined( __parallel )
216	!
217	!-- Compute total sum from local sums
218	CALL MPI_ALLREDUCE( sums_l(nzb,1,0), sums(nzb,1), nzt+2-nzb, MPI_REAL, &
219	MPI_SUM, comm2d, ierr )
220	CALL MPI_ALLREDUCE( sums_l(nzb,2,0), sums(nzb,2), nzt+2-nzb, MPI_REAL, &
221	MPI_SUM, comm2d, ierr )
222	CALL MPI_ALLREDUCE( sums_l(nzb,4,0), sums(nzb,4), nzt+2-nzb, MPI_REAL, &
223	MPI_SUM, comm2d, ierr )
224	IF ( ocean ) THEN
225	CALL MPI_ALLREDUCE( sums_l(nzb,23,0), sums(nzb,23), nzt+2-nzb, &
226	MPI_REAL, MPI_SUM, comm2d, ierr )
227	ENDIF
228	IF ( humidity ) THEN
229	CALL MPI_ALLREDUCE( sums_l(nzb,44,0), sums(nzb,44), nzt+2-nzb, &
230	MPI_REAL, MPI_SUM, comm2d, ierr )
231	CALL MPI_ALLREDUCE( sums_l(nzb,41,0), sums(nzb,41), nzt+2-nzb, &
232	MPI_REAL, MPI_SUM, comm2d, ierr )
233	IF ( cloud_physics ) THEN
234	CALL MPI_ALLREDUCE( sums_l(nzb,42,0), sums(nzb,42), nzt+2-nzb, &
235	MPI_REAL, MPI_SUM, comm2d, ierr )
236	CALL MPI_ALLREDUCE( sums_l(nzb,43,0), sums(nzb,43), nzt+2-nzb, &
237	MPI_REAL, MPI_SUM, comm2d, ierr )
238	ENDIF
239	ENDIF
240
241	IF ( passive_scalar ) THEN
242	CALL MPI_ALLREDUCE( sums_l(nzb,41,0), sums(nzb,41), nzt+2-nzb, &
243	MPI_REAL, MPI_SUM, comm2d, ierr )
244	ENDIF
245	#else
246	sums(:,1) = sums_l(:,1,0)
247	sums(:,2) = sums_l(:,2,0)
248	sums(:,4) = sums_l(:,4,0)
249	IF ( ocean ) sums(:,23) = sums_l(:,23,0)
250	IF ( humidity ) THEN
251	sums(:,44) = sums_l(:,44,0)
252	sums(:,41) = sums_l(:,41,0)
253	IF ( cloud_physics ) THEN
254	sums(:,42) = sums_l(:,42,0)
255	sums(:,43) = sums_l(:,43,0)
256	ENDIF
257	ENDIF
258	IF ( passive_scalar ) sums(:,41) = sums_l(:,41,0)
259	#endif
260
261	!
262	!-- Final values are obtained by division by the total number of grid points
263	!-- used for summation. After that store profiles.
264	sums(:,1) = sums(:,1) / ngp_2dh_outer(:,sr)
265	sums(:,2) = sums(:,2) / ngp_2dh_outer(:,sr)
266	sums(:,4) = sums(:,4) / ngp_2dh_outer(:,sr)
267	hom(:,1,1,sr) = sums(:,1) ! u
268	hom(:,1,2,sr) = sums(:,2) ! v
269	hom(:,1,4,sr) = sums(:,4) ! pt
270
271	!
272	!-- Salinity
273	IF ( ocean ) THEN
274	sums(:,23) = sums(:,23) / ngp_2dh_outer(:,sr)
275	hom(:,1,23,sr) = sums(:,23) ! sa
276	ENDIF
277
278	!
279	!-- Humidity and cloud parameters
280	IF ( humidity ) THEN
281	sums(:,44) = sums(:,44) / ngp_2dh_outer(:,sr)
282	sums(:,41) = sums(:,41) / ngp_2dh_outer(:,sr)
283	hom(:,1,44,sr) = sums(:,44) ! vpt
284	hom(:,1,41,sr) = sums(:,41) ! qv (q)
285	IF ( cloud_physics ) THEN
286	sums(:,42) = sums(:,42) / ngp_2dh_outer(:,sr)
287	sums(:,43) = sums(:,43) / ngp_2dh_outer(:,sr)
288	hom(:,1,42,sr) = sums(:,42) ! qv
289	hom(:,1,43,sr) = sums(:,43) ! pt
290	ENDIF
291	ENDIF
292
293	!
294	!-- Passive scalar
295	IF ( passive_scalar ) hom(:,1,41,sr) = sums(:,41) / ngp_2dh_outer(:,sr)
296
297	!
298	!-- Horizontally averaged profiles of the remaining prognostic variables,
299	!-- variances, the total and the perturbation energy (single values in last
300	!-- column of sums_l) and some diagnostic quantities.
301	!-- NOTE: for simplicity, nzb_s_outer is used below, although strictly
302	!-- ---- speaking the following k-loop would have to be split up and
303	!-- rearranged according to the staggered grid.
304	tn = 0
305	#if defined( __intel_openmp_bug )
306	!$OMP PARALLEL PRIVATE( i, j, k, pts, sums_ll, sums_l_eper, sums_l_etot, &
307	!$OMP tn, ust, ust2, u2, vst, vst2, v2, w2 )
308	tn = omp_get_thread_num()
309	#else
310	!$OMP PARALLEL PRIVATE( i, j, k, pts, sums_ll, sums_l_eper, sums_l_etot, tn, ust, ust2, u2, vst, vst2, v2, w2 )
311	!$ tn = omp_get_thread_num()
312	#endif
313	!$OMP DO
314	DO i = nxl, nxr
315	DO j = nys, nyn
316	sums_l_etot = 0.0
317	sums_l_eper = 0.0
318	DO k = nzb_s_outer(j,i), nzt+1
319	u2 = u(k,j,i)**2
320	v2 = v(k,j,i)**2
321	w2 = w(k,j,i)**2
322	ust2 = ( u(k,j,i) - hom(k,1,1,sr) )**2
323	vst2 = ( v(k,j,i) - hom(k,1,2,sr) )**2
324	!
325	!-- Prognostic and diagnostic variables
326	sums_l(k,3,tn) = sums_l(k,3,tn) + w(k,j,i) * rmask(j,i,sr)
327	sums_l(k,8,tn) = sums_l(k,8,tn) + e(k,j,i) * rmask(j,i,sr)
328	sums_l(k,9,tn) = sums_l(k,9,tn) + km(k,j,i) * rmask(j,i,sr)
329	sums_l(k,10,tn) = sums_l(k,10,tn) + kh(k,j,i) * rmask(j,i,sr)
330	sums_l(k,40,tn) = sums_l(k,40,tn) + p(k,j,i)
331
332	!
333	!-- Variances
334	sums_l(k,30,tn) = sums_l(k,30,tn) + ust2 * rmask(j,i,sr)
335	sums_l(k,31,tn) = sums_l(k,31,tn) + vst2 * rmask(j,i,sr)
336	sums_l(k,32,tn) = sums_l(k,32,tn) + w2 * rmask(j,i,sr)
337	sums_l(k,33,tn) = sums_l(k,33,tn) + &
338	( pt(k,j,i)-hom(k,1,4,sr) )*2 rmask(j,i,sr)
339	!
340	!-- Higher moments
341	!-- (Computation of the skewness of w further below)
342	sums_l(k,38,tn) = sums_l(k,38,tn) + w(k,j,i) * w2 * &
343	rmask(j,i,sr)
344	!
345	!-- Perturbation energy
346	sums_l(k,34,tn) = sums_l(k,34,tn) + 0.5 * ( ust2 + vst2 + w2 ) &
347	* rmask(j,i,sr)
348	sums_l_etot = sums_l_etot + &
349	0.5 * ( u2 + v2 + w2 ) * rmask(j,i,sr)
350	sums_l_eper = sums_l_eper + &
351	0.5 * ( ust2+vst2+w2 ) * rmask(j,i,sr)
352	ENDDO
353	!
354	!-- Total and perturbation energy for the total domain (being
355	!-- collected in the last column of sums_l). Summation of these
356	!-- quantities is seperated from the previous loop in order to
357	!-- allow vectorization of that loop.
358	sums_l(nzb+4,pr_palm,tn) = sums_l(nzb+4,pr_palm,tn) + sums_l_etot
359	sums_l(nzb+5,pr_palm,tn) = sums_l(nzb+5,pr_palm,tn) + sums_l_eper
360	!
361	!-- 2D-arrays (being collected in the last column of sums_l)
362	sums_l(nzb,pr_palm,tn) = sums_l(nzb,pr_palm,tn) + &
363	us(j,i) * rmask(j,i,sr)
364	sums_l(nzb+1,pr_palm,tn) = sums_l(nzb+1,pr_palm,tn) + &
365	usws(j,i) * rmask(j,i,sr)
366	sums_l(nzb+2,pr_palm,tn) = sums_l(nzb+2,pr_palm,tn) + &
367	vsws(j,i) * rmask(j,i,sr)
368	sums_l(nzb+3,pr_palm,tn) = sums_l(nzb+3,pr_palm,tn) + &
369	ts(j,i) * rmask(j,i,sr)
370	ENDDO
371	ENDDO
372
373	!
374	!-- Horizontally averaged profiles of the vertical fluxes
375	!$OMP DO
376	DO i = nxl, nxr
377	DO j = nys, nyn
378	!
379	!-- Subgridscale fluxes (without Prandtl layer from k=nzb,
380	!-- oterwise from k=nzb+1)
381	!-- NOTE: for simplicity, nzb_diff_s_outer is used below, although
382	!-- ---- strictly speaking the following k-loop would have to be
383	!-- split up according to the staggered grid.
384	DO k = nzb_diff_s_outer(j,i)-1, nzt_diff
385	!
386	!-- Momentum flux w"u"
387	sums_l(k,12,tn) = sums_l(k,12,tn) - 0.25 * ( &
388	km(k,j,i)+km(k+1,j,i)+km(k,j,i-1)+km(k+1,j,i-1) &
389	) * ( &
390	( u(k+1,j,i) - u(k,j,i) ) * ddzu(k+1) &
391	+ ( w(k,j,i) - w(k,j,i-1) ) * ddx &
392	) * rmask(j,i,sr)
393	!
394	!-- Momentum flux w"v"
395	sums_l(k,14,tn) = sums_l(k,14,tn) - 0.25 * ( &
396	km(k,j,i)+km(k+1,j,i)+km(k,j-1,i)+km(k+1,j-1,i) &
397	) * ( &
398	( v(k+1,j,i) - v(k,j,i) ) * ddzu(k+1) &
399	+ ( w(k,j,i) - w(k,j-1,i) ) * ddy &
400	) * rmask(j,i,sr)
401	!
402	!-- Heat flux w"pt"
403	sums_l(k,16,tn) = sums_l(k,16,tn) &
404	- 0.5 * ( kh(k,j,i) + kh(k+1,j,i) ) &
405	* ( pt(k+1,j,i) - pt(k,j,i) ) &
406	* ddzu(k+1) * rmask(j,i,sr)
407
408
409	!
410	!-- Salinity flux w"sa"
411	IF ( ocean ) THEN
412	sums_l(k,65,tn) = sums_l(k,65,tn) &
413	- 0.5 * ( kh(k,j,i) + kh(k+1,j,i) ) &
414	* ( sa(k+1,j,i) - sa(k,j,i) ) &
415	* ddzu(k+1) * rmask(j,i,sr)
416	ENDIF
417
418	!
419	!-- Buoyancy flux, water flux (humidity flux) w"q"
420	IF ( humidity ) THEN
421	sums_l(k,45,tn) = sums_l(k,45,tn) &
422	- 0.5 * ( kh(k,j,i) + kh(k+1,j,i) ) &
423	* ( vpt(k+1,j,i) - vpt(k,j,i) ) &
424	* ddzu(k+1) * rmask(j,i,sr)
425	sums_l(k,48,tn) = sums_l(k,48,tn) &
426	- 0.5 * ( kh(k,j,i) + kh(k+1,j,i) ) &
427	* ( q(k+1,j,i) - q(k,j,i) ) &
428	* ddzu(k+1) * rmask(j,i,sr)
429	IF ( cloud_physics ) THEN
430	sums_l(k,51,tn) = sums_l(k,51,tn) &
431	- 0.5 * ( kh(k,j,i) + kh(k+1,j,i) ) &
432	* ( ( q(k+1,j,i) - ql(k+1,j,i) )&
433	- ( q(k,j,i) - ql(k,j,i) ) ) &
434	* ddzu(k+1) * rmask(j,i,sr)
435	ENDIF
436	ENDIF
437
438	!
439	!-- Passive scalar flux
440	IF ( passive_scalar ) THEN
441	sums_l(k,48,tn) = sums_l(k,48,tn) &
442	- 0.5 * ( kh(k,j,i) + kh(k+1,j,i) ) &
443	* ( q(k+1,j,i) - q(k,j,i) ) &
444	* ddzu(k+1) * rmask(j,i,sr)
445	ENDIF
446
447	ENDDO
448
449	!
450	!-- Subgridscale fluxes in the Prandtl layer
451	IF ( use_surface_fluxes ) THEN
452	sums_l(nzb,12,tn) = sums_l(nzb,12,tn) + &
453	usws(j,i) * rmask(j,i,sr) ! w"u"
454	sums_l(nzb,14,tn) = sums_l(nzb,14,tn) + &
455	vsws(j,i) * rmask(j,i,sr) ! w"v"
456	sums_l(nzb,16,tn) = sums_l(nzb,16,tn) + &
457	shf(j,i) * rmask(j,i,sr) ! w"pt"
458	sums_l(nzb,58,tn) = sums_l(nzb,58,tn) + &
459	0.0 * rmask(j,i,sr) ! u"pt"
460	sums_l(nzb,61,tn) = sums_l(nzb,61,tn) + &
461	0.0 * rmask(j,i,sr) ! v"pt"
462	IF ( ocean ) THEN
463	sums_l(nzb,65,tn) = sums_l(nzb,65,tn) + &
464	saswsb(j,i) * rmask(j,i,sr) ! w"sa"
465	ENDIF
466	IF ( humidity ) THEN
467	sums_l(nzb,48,tn) = sums_l(nzb,48,tn) + &
468	qsws(j,i) * rmask(j,i,sr) ! w"q" (w"qv")
469	IF ( cloud_physics ) THEN
470	sums_l(nzb,45,tn) = sums_l(nzb,45,tn) + ( &
471	( 1.0 + 0.61 * q(nzb,j,i) ) * &
472	shf(j,i) + 0.61 * pt(nzb,j,i) * &
473	qsws(j,i) &
474	)
475	!
476	!-- Formula does not work if ql(nzb) /= 0.0
477	sums_l(nzb,51,tn) = sums_l(nzb,51,tn) + & ! w"q" (w"qv")
478	qsws(j,i) * rmask(j,i,sr)
479	ENDIF
480	ENDIF
481	IF ( passive_scalar ) THEN
482	sums_l(nzb,48,tn) = sums_l(nzb,48,tn) + &
483	qsws(j,i) * rmask(j,i,sr) ! w"q" (w"qv")
484	ENDIF
485	ENDIF
486
487	!
488	!-- Subgridscale fluxes at the top surface
489	IF ( use_top_fluxes ) THEN
490	sums_l(nzt,12,tn) = sums_l(nzt,12,tn) + &
491	uswst(j,i) * rmask(j,i,sr) ! w"u"
492	sums_l(nzt,14,tn) = sums_l(nzt,14,tn) + &
493	vswst(j,i) * rmask(j,i,sr) ! w"v"
494	sums_l(nzt,16,tn) = sums_l(nzt,16,tn) + &
495	tswst(j,i) * rmask(j,i,sr) ! w"pt"
496	sums_l(nzt,58,tn) = sums_l(nzt,58,tn) + &
497	0.0 * rmask(j,i,sr) ! u"pt"
498	sums_l(nzt,61,tn) = sums_l(nzt,61,tn) + &
499	0.0 * rmask(j,i,sr) ! v"pt"
500	IF ( ocean ) THEN
501	sums_l(nzt,65,tn) = sums_l(nzt,65,tn) + &
502	saswst(j,i) * rmask(j,i,sr) ! w"sa"
503	ENDIF
504	IF ( humidity ) THEN
505	sums_l(nzt,48,tn) = sums_l(nzt,48,tn) + &
506	qswst(j,i) * rmask(j,i,sr) ! w"q" (w"qv")
507	IF ( cloud_physics ) THEN
508	sums_l(nzt,45,tn) = sums_l(nzt,45,tn) + ( &
509	( 1.0 + 0.61 * q(nzt,j,i) ) * &
510	tswst(j,i) + 0.61 * pt(nzt,j,i) * &
511	qsws(j,i) &
512	)
513	!
514	!-- Formula does not work if ql(nzb) /= 0.0
515	sums_l(nzt,51,tn) = sums_l(nzt,51,tn) + & ! w"q" (w"qv")
516	qswst(j,i) * rmask(j,i,sr)
517	ENDIF
518	ENDIF
519	IF ( passive_scalar ) THEN
520	sums_l(nzt,48,tn) = sums_l(nzt,48,tn) + &
521	qswst(j,i) * rmask(j,i,sr) ! w"q" (w"qv")
522	ENDIF
523	ENDIF
524
525	!
526	!-- Resolved fluxes (can be computed for all horizontal points)
527	!-- NOTE: for simplicity, nzb_s_outer is used below, although strictly
528	!-- ---- speaking the following k-loop would have to be split up and
529	!-- rearranged according to the staggered grid.
530	DO k = nzb_s_outer(j,i), nzt
531	ust = 0.5 * ( u(k,j,i) - hom(k,1,1,sr) + &
532	u(k+1,j,i) - hom(k+1,1,1,sr) )
533	vst = 0.5 * ( v(k,j,i) - hom(k,1,2,sr) + &
534	v(k+1,j,i) - hom(k+1,1,2,sr) )
535	pts = 0.5 * ( pt(k,j,i) - hom(k,1,4,sr) + &
536	pt(k+1,j,i) - hom(k+1,1,4,sr) )
537	!
538	!-- Momentum flux wu
539	sums_l(k,13,tn) = sums_l(k,13,tn) + 0.5 * &
540	( w(k,j,i-1) + w(k,j,i) ) &
541	* ust * rmask(j,i,sr)
542	!
543	!-- Momentum flux wv
544	sums_l(k,15,tn) = sums_l(k,15,tn) + 0.5 * &
545	( w(k,j-1,i) + w(k,j,i) ) &
546	* vst * rmask(j,i,sr)
547	!
548	!-- Heat flux wpt
549	!-- The following formula (comment line, not executed) does not
550	!-- work if applied to subregions
551	! sums_l(k,17,tn) = sums_l(k,17,tn) + 0.5 * &
552	! ( pt(k,j,i)+pt(k+1,j,i) ) &
553	! * w(k,j,i) * rmask(j,i,sr)
554	sums_l(k,17,tn) = sums_l(k,17,tn) + pts * w(k,j,i) * &
555	rmask(j,i,sr)
556	!
557	!-- Higher moments
558	sums_l(k,35,tn) = sums_l(k,35,tn) + pts * w(k,j,i)*2 &
559	rmask(j,i,sr)
560	sums_l(k,36,tn) = sums_l(k,36,tn) + pts*2 w(k,j,i) * &
561	rmask(j,i,sr)
562
563	!
564	!-- Salinity flux and density (density does not belong to here,
565	!-- but so far there is no other suitable place to calculate)
566	IF ( ocean ) THEN
567	pts = 0.5 * ( sa(k,j,i) - hom(k,1,23,sr) + &
568	sa(k+1,j,i) - hom(k+1,1,23,sr) )
569	sums_l(k,66,tn) = sums_l(k,66,tn) + pts * w(k,j,i) * &
570	rmask(j,i,sr)
571	sums_l(k,64,tn) = sums_l(k,64,tn) + rho(k,j,i) * &
572	rmask(j,i,sr)
573	ENDIF
574
575	!
576	!-- Buoyancy flux, water flux, humidity flux and liquid water
577	!-- content
578	IF ( humidity ) THEN
579	pts = 0.5 * ( vpt(k,j,i) - hom(k,1,44,sr) + &
580	vpt(k+1,j,i) - hom(k+1,1,44,sr) )
581	sums_l(k,46,tn) = sums_l(k,46,tn) + pts * w(k,j,i) * &
582	rmask(j,i,sr)
583	pts = 0.5 * ( q(k,j,i) - hom(k,1,41,sr) + &
584	q(k+1,j,i) - hom(k+1,1,41,sr) )
585	sums_l(k,49,tn) = sums_l(k,49,tn) + pts * w(k,j,i) * &
586	rmask(j,i,sr)
587	IF ( cloud_physics .OR. cloud_droplets ) THEN
588	pts = 0.5 * &
589	( ( q(k,j,i) - ql(k,j,i) ) - hom(k,1,42,sr) &
590	+ ( q(k+1,j,i) - ql(k+1,j,i) ) - hom(k+1,1,42,sr) )
591	sums_l(k,52,tn) = sums_l(k,52,tn) + pts * w(k,j,i) * &
592	rmask(j,i,sr)
593	sums_l(k,54,tn) = sums_l(k,54,tn) + ql(k,j,i) * &
594	rmask(j,i,sr)
595	ENDIF
596	ENDIF
597
598	!
599	!-- Passive scalar flux
600	IF ( passive_scalar ) THEN
601	pts = 0.5 * ( q(k,j,i) - hom(k,1,41,sr) + &
602	q(k+1,j,i) - hom(k+1,1,41,sr) )
603	sums_l(k,49,tn) = sums_l(k,49,tn) + pts * w(k,j,i) * &
604	rmask(j,i,sr)
605	ENDIF
606
607	!
608	!-- Energy flux we
609	sums_l(k,37,tn) = sums_l(k,37,tn) + w(k,j,i) * 0.5 * &
610	( ust2 + vst2 + w(k,j,i)**2 )&
611	* rmask(j,i,sr)
612
613	ENDDO
614	ENDDO
615	ENDDO
616
617	!
618	!-- Density at top follows Neumann condition
619	IF ( ocean ) sums_l(nzt+1,64,tn) = sums_l(nzt,64,tn)
620
621	!
622	!-- Divergence of vertical flux of resolved scale energy and pressure
623	!-- fluctuations as well as flux of pressure fluctuation itself (68).
624	!-- First calculate the products, then the divergence.
625	!-- Calculation is time consuming. Do it only, if profiles shall be plotted.
626	IF ( hom(nzb+1,2,55,0) /= 0.0 .OR. hom(nzb+1,2,68,0) /= 0.0 ) THEN
627
628	sums_ll = 0.0 ! local array
629
630	!$OMP DO
631	DO i = nxl, nxr
632	DO j = nys, nyn
633	DO k = nzb_s_outer(j,i)+1, nzt
634
635	sums_ll(k,1) = sums_ll(k,1) + 0.5 * w(k,j,i) * ( &
636	( 0.25 * ( u(k,j,i)+u(k+1,j,i)+u(k,j,i+1)+u(k+1,j,i+1) &
637	- 2.0 * ( hom(k,1,1,sr) + hom(k+1,1,1,sr) ) &
638	) )**2 &
639	+ ( 0.25 * ( v(k,j,i)+v(k+1,j,i)+v(k,j+1,i)+v(k+1,j+1,i) &
640	- 2.0 * ( hom(k,1,2,sr) + hom(k+1,1,2,sr) ) &
641	) )**2 &
642	+ w(k,j,i)**2 )
643
644	sums_ll(k,2) = sums_ll(k,2) + 0.5 * w(k,j,i) &
645	* ( p(k,j,i) + p(k+1,j,i) )
646
647	ENDDO
648	ENDDO
649	ENDDO
650	sums_ll(0,1) = 0.0 ! because w is zero at the bottom
651	sums_ll(nzt+1,1) = 0.0
652	sums_ll(0,2) = 0.0
653	sums_ll(nzt+1,2) = 0.0
654
655	DO k = nzb_s_outer(j,i)+1, nzt
656	sums_l(k,55,tn) = ( sums_ll(k,1) - sums_ll(k-1,1) ) * ddzw(k)
657	sums_l(k,56,tn) = ( sums_ll(k,2) - sums_ll(k-1,2) ) * ddzw(k)
658	sums_l(k,68,tn) = sums_ll(k,2)
659	ENDDO
660	sums_l(nzb,55,tn) = sums_l(nzb+1,55,tn)
661	sums_l(nzb,56,tn) = sums_l(nzb+1,56,tn)
662	sums_l(nzb,68,tn) = 0.0 ! because w* = 0 at nzb
663
664	ENDIF
665
666	!
667	!-- Divergence of vertical flux of SGS TKE and the flux itself (69)
668	IF ( hom(nzb+1,2,57,0) /= 0.0 .OR. hom(nzb+1,2,69,0) /= 0.0 ) THEN
669
670	!$OMP DO
671	DO i = nxl, nxr
672	DO j = nys, nyn
673	DO k = nzb_s_outer(j,i)+1, nzt
674
675	sums_l(k,57,tn) = sums_l(k,57,tn) - 0.5 * ( &
676	(km(k,j,i)+km(k+1,j,i)) * (e(k+1,j,i)-e(k,j,i)) * ddzu(k+1) &
677	- (km(k-1,j,i)+km(k,j,i)) * (e(k,j,i)-e(k-1,j,i)) * ddzu(k) &
678	) * ddzw(k)
679
680	sums_l(k,69,tn) = sums_l(k,69,tn) - 0.5 * ( &
681	(km(k,j,i)+km(k+1,j,i)) * (e(k+1,j,i)-e(k,j,i)) * ddzu(k+1) &
682	)
683
684	ENDDO
685	ENDDO
686	ENDDO
687	sums_l(nzb,57,tn) = sums_l(nzb+1,57,tn)
688	sums_l(nzb,69,tn) = sums_l(nzb+1,69,tn)
689
690	ENDIF
691
692	!
693	!-- Horizontal heat fluxes (subgrid, resolved, total).
694	!-- Do it only, if profiles shall be plotted.
695	IF ( hom(nzb+1,2,58,0) /= 0.0 ) THEN
696
697	!$OMP DO
698	DO i = nxl, nxr
699	DO j = nys, nyn
700	DO k = nzb_s_outer(j,i)+1, nzt
701	!
702	!-- Subgrid horizontal heat fluxes u"pt", v"pt"
703	sums_l(k,58,tn) = sums_l(k,58,tn) - 0.5 * &
704	( kh(k,j,i) + kh(k,j,i-1) ) &
705	* ( pt(k,j,i-1) - pt(k,j,i) ) &
706	* ddx * rmask(j,i,sr)
707	sums_l(k,61,tn) = sums_l(k,61,tn) - 0.5 * &
708	( kh(k,j,i) + kh(k,j-1,i) ) &
709	* ( pt(k,j-1,i) - pt(k,j,i) ) &
710	* ddy * rmask(j,i,sr)
711	!
712	!-- Resolved horizontal heat fluxes upt, vpt
713	sums_l(k,59,tn) = sums_l(k,59,tn) + &
714	( u(k,j,i) - hom(k,1,1,sr) ) &
715	* 0.5 * ( pt(k,j,i-1) - hom(k,1,4,sr) + &
716	pt(k,j,i) - hom(k,1,4,sr) )
717	pts = 0.5 * ( pt(k,j-1,i) - hom(k,1,4,sr) + &
718	pt(k,j,i) - hom(k,1,4,sr) )
719	sums_l(k,62,tn) = sums_l(k,62,tn) + &
720	( v(k,j,i) - hom(k,1,2,sr) ) &
721	* 0.5 * ( pt(k,j-1,i) - hom(k,1,4,sr) + &
722	pt(k,j,i) - hom(k,1,4,sr) )
723	ENDDO
724	ENDDO
725	ENDDO
726	!
727	!-- Fluxes at the surface must be zero (e.g. due to the Prandtl-layer)
728	sums_l(nzb,58,tn) = 0.0
729	sums_l(nzb,59,tn) = 0.0
730	sums_l(nzb,60,tn) = 0.0
731	sums_l(nzb,61,tn) = 0.0
732	sums_l(nzb,62,tn) = 0.0
733	sums_l(nzb,63,tn) = 0.0
734
735	ENDIF
736
737	!
738	!-- Calculate the user-defined profiles
739	CALL user_statistics( 'profiles', sr, tn )
740	!$OMP END PARALLEL
741
742	!
743	!-- Summation of thread sums
744	IF ( threads_per_task > 1 ) THEN
745	DO i = 1, threads_per_task-1
746	sums_l(:,3,0) = sums_l(:,3,0) + sums_l(:,3,i)
747	sums_l(:,4:40,0) = sums_l(:,4:40,0) + sums_l(:,4:40,i)
748	sums_l(:,45:pr_palm,0) = sums_l(:,45:pr_palm,0) + &
749	sums_l(:,45:pr_palm,i)
750	IF ( max_pr_user > 0 ) THEN
751	sums_l(:,pr_palm+1:pr_palm+max_pr_user,0) = &
752	sums_l(:,pr_palm+1:pr_palm+max_pr_user,0) + &
753	sums_l(:,pr_palm+1:pr_palm+max_pr_user,i)
754	ENDIF
755	ENDDO
756	ENDIF
757
758	#if defined( __parallel )
759	!
760	!-- Compute total sum from local sums
761	CALL MPI_ALLREDUCE( sums_l(nzb,1,0), sums(nzb,1), ngp_sums, MPI_REAL, &
762	MPI_SUM, comm2d, ierr )
763	#else
764	sums = sums_l(:,:,0)
765	#endif
766
767	!
768	!-- Final values are obtained by division by the total number of grid points
769	!-- used for summation. After that store profiles.
770	!-- Profiles:
771	DO k = nzb, nzt+1
772	sums(k,:pr_palm-2) = sums(k,:pr_palm-2) / ngp_2dh_outer(k,sr)
773	ENDDO
774	!-- Upstream-parts
775	sums(nzb:nzb+11,pr_palm-1) = sums(nzb:nzb+11,pr_palm-1) / ngp_3d(sr)
776	!-- u* and so on
777	!-- As sums(nzb:nzb+3,pr_palm) are full 2D arrays (us, usws, vsws, ts) whose
778	!-- size is always ( nx + 1 ) * ( ny + 1 ), defined at the first grid layer
779	!-- above the topography, they are being divided by ngp_2dh(sr)
780	sums(nzb:nzb+3,pr_palm) = sums(nzb:nzb+3,pr_palm) / &
781	ngp_2dh(sr)
782	!-- eges, e*
783	sums(nzb+4:nzb+5,pr_palm) = sums(nzb+4:nzb+5,pr_palm) / &
784	ngp_3d_inner(sr)
785	!-- Old and new divergence
786	sums(nzb+9:nzb+10,pr_palm) = sums(nzb+9:nzb+10,pr_palm) / &
787	ngp_3d_inner(sr)
788
789	!-- User-defined profiles
790	IF ( max_pr_user > 0 ) THEN
791	DO k = nzb, nzt+1
792	sums(k,pr_palm+1:pr_palm+max_pr_user) = &
793	sums(k,pr_palm+1:pr_palm+max_pr_user) / &
794	ngp_2dh_outer(k,sr)
795	ENDDO
796	ENDIF
797
798	!
799	!-- Collect horizontal average in hom.
800	!-- Compute deduced averages (e.g. total heat flux)
801	hom(:,1,3,sr) = sums(:,3) ! w
802	hom(:,1,8,sr) = sums(:,8) ! e profiles 5-7 are initial profiles
803	hom(:,1,9,sr) = sums(:,9) ! km
804	hom(:,1,10,sr) = sums(:,10) ! kh
805	hom(:,1,11,sr) = sums(:,11) ! l
806	hom(:,1,12,sr) = sums(:,12) ! w"u"
807	hom(:,1,13,sr) = sums(:,13) ! wu
808	hom(:,1,14,sr) = sums(:,14) ! w"v"
809	hom(:,1,15,sr) = sums(:,15) ! wv
810	hom(:,1,16,sr) = sums(:,16) ! w"pt"
811	hom(:,1,17,sr) = sums(:,17) ! wpt
812	hom(:,1,18,sr) = sums(:,16) + sums(:,17) ! wpt
813	hom(:,1,19,sr) = sums(:,12) + sums(:,13) ! wu
814	hom(:,1,20,sr) = sums(:,14) + sums(:,15) ! wv
815	hom(:,1,21,sr) = sums(:,21) ! wptBC
816	hom(:,1,22,sr) = sums(:,16) + sums(:,21) ! wptBC
817	! profile 24 is initial profile (sa)
818	! profiles 25-29 left empty for initial
819	! profiles
820	hom(:,1,30,sr) = sums(:,30) ! u*2
821	hom(:,1,31,sr) = sums(:,31) ! v*2
822	hom(:,1,32,sr) = sums(:,32) ! w*2
823	hom(:,1,33,sr) = sums(:,33) ! pt*2
824	hom(:,1,34,sr) = sums(:,34) ! e*
825	hom(:,1,35,sr) = sums(:,35) ! w2pt
826	hom(:,1,36,sr) = sums(:,36) ! wpt2
827	hom(:,1,37,sr) = sums(:,37) ! we
828	hom(:,1,38,sr) = sums(:,38) ! w*3
829	hom(:,1,39,sr) = sums(:,38) / ( sums(:,32) + 1E-20 )**1.5 ! Sw
830	hom(:,1,40,sr) = sums(:,40) ! p
831	hom(:,1,45,sr) = sums(:,45) ! w"q"
832	hom(:,1,46,sr) = sums(:,46) ! wvpt
833	hom(:,1,47,sr) = sums(:,45) + sums(:,46) ! wvpt
834	hom(:,1,48,sr) = sums(:,48) ! w"q" (w"qv")
835	hom(:,1,49,sr) = sums(:,49) ! wq (wqv)
836	hom(:,1,50,sr) = sums(:,48) + sums(:,49) ! wq (wqv)
837	hom(:,1,51,sr) = sums(:,51) ! w"qv"
838	hom(:,1,52,sr) = sums(:,52) ! wqv
839	hom(:,1,53,sr) = sums(:,52) + sums(:,51) ! wq (wqv)
840	hom(:,1,54,sr) = sums(:,54) ! ql
841	hom(:,1,55,sr) = sums(:,55) ! wuu*/dz
842	hom(:,1,56,sr) = sums(:,56) ! wp/dz
843	hom(:,1,57,sr) = sums(:,57) ! ( w"e + w"p"/rho )/dz
844	hom(:,1,58,sr) = sums(:,58) ! u"pt"
845	hom(:,1,59,sr) = sums(:,59) ! upt
846	hom(:,1,60,sr) = sums(:,58) + sums(:,59) ! upt_t
847	hom(:,1,61,sr) = sums(:,61) ! v"pt"
848	hom(:,1,62,sr) = sums(:,62) ! vpt
849	hom(:,1,63,sr) = sums(:,61) + sums(:,62) ! vpt_t
850	hom(:,1,64,sr) = sums(:,64) ! rho
851	hom(:,1,65,sr) = sums(:,65) ! w"sa"
852	hom(:,1,66,sr) = sums(:,66) ! wsa
853	hom(:,1,67,sr) = sums(:,65) + sums(:,66) ! wsa
854	hom(:,1,68,sr) = sums(:,68) ! wp
855	hom(:,1,69,sr) = sums(:,69) ! w"e + w"p"/rho
856
857	hom(:,1,pr_palm-1,sr) = sums(:,pr_palm-1)
858	! upstream-parts u_x, u_y, u_z, v_x,
859	! v_y, usw. (in last but one profile)
860	hom(:,1,pr_palm,sr) = sums(:,pr_palm)
861	! u, w'u', w'v', t (in last profile)
862
863	IF ( max_pr_user > 0 ) THEN ! user-defined profiles
864	hom(:,1,pr_palm+1:pr_palm+max_pr_user,sr) = &
865	sums(:,pr_palm+1:pr_palm+max_pr_user)
866	ENDIF
867
868	!
869	!-- Determine the boundary layer height using two different schemes.
870	!-- First scheme: Starting from the Earth's (Ocean's) surface, look for the
871	!-- first relative minimum (maximum) of the total heat flux.
872	!-- The corresponding height is assumed as the boundary layer height, if it
873	!-- is less than 1.5 times the height where the heat flux becomes negative
874	!-- (positive) for the first time.
875	!-- NOTE: This criterion is still capable of improving!
876	z_i(1) = 0.0
877	first = .TRUE.
878	IF ( ocean ) THEN
879	DO k = nzt, nzb+1, -1
880	IF ( first .AND. hom(k,1,18,sr) < 0.0 ) THEN
881	first = .FALSE.
882	height = zw(k)
883	ENDIF
884	IF ( hom(k,1,18,sr) < 0.0 .AND. &
885	hom(k-1,1,18,sr) > hom(k,1,18,sr) ) THEN
886	IF ( zw(k) < 1.5 * height ) THEN
887	z_i(1) = zw(k)
888	ELSE
889	z_i(1) = height
890	ENDIF
891	EXIT
892	ENDIF
893	ENDDO
894	ELSE
895	DO k = nzb, nzt-1
896	IF ( first .AND. hom(k,1,18,sr) < 0.0 ) THEN
897	first = .FALSE.
898	height = zw(k)
899	ENDIF
900	IF ( hom(k,1,18,sr) < 0.0 .AND. &
901	hom(k+1,1,18,sr) > hom(k,1,18,sr) ) THEN
902	IF ( zw(k) < 1.5 * height ) THEN
903	z_i(1) = zw(k)
904	ELSE
905	z_i(1) = height
906	ENDIF
907	EXIT
908	ENDIF
909	ENDDO
910	ENDIF
911
912	!
913	!-- Second scheme: Starting from the top/bottom model boundary, look for
914	!-- the first characteristic kink in the temperature profile, where the
915	!-- originally stable stratification notably weakens.
916	z_i(2) = 0.0
917	IF ( ocean ) THEN
918	DO k = nzb+1, nzt-1
919	IF ( ( hom(k,1,4,sr) - hom(k-1,1,4,sr) ) > &
920	2.0 * ( hom(k+1,1,4,sr) - hom(k,1,4,sr) ) ) THEN
921	z_i(2) = zu(k)
922	EXIT
923	ENDIF
924	ENDDO
925	ELSE
926	DO k = nzt-1, nzb+1, -1
927	IF ( ( hom(k+1,1,4,sr) - hom(k,1,4,sr) ) > &
928	2.0 * ( hom(k,1,4,sr) - hom(k-1,1,4,sr) ) ) THEN
929	z_i(2) = zu(k)
930	EXIT
931	ENDIF
932	ENDDO
933	ENDIF
934
935	hom(nzb+6,1,pr_palm,sr) = z_i(1)
936	hom(nzb+7,1,pr_palm,sr) = z_i(2)
937
938	!
939	!-- Computation of both the characteristic vertical velocity and
940	!-- the characteristic convective boundary layer temperature.
941	!-- The horizontal average at nzb+1 is input for the average temperature.
942	IF ( hom(nzb,1,18,sr) > 0.0 .AND. z_i(1) /= 0.0 ) THEN
943	hom(nzb+8,1,pr_palm,sr) = ( g / hom(nzb+1,1,4,sr) * &
944	hom(nzb,1,18,sr) * &
945	ABS( z_i(1) ) )**0.333333333
946	!-- so far this only works if Prandtl layer is used
947	hom(nzb+11,1,pr_palm,sr) = hom(nzb,1,16,sr) / hom(nzb+8,1,pr_palm,sr)
948	ELSE
949	hom(nzb+8,1,pr_palm,sr) = 0.0
950	hom(nzb+11,1,pr_palm,sr) = 0.0
951	ENDIF
952
953	!
954	!-- Collect the time series quantities
955	ts_value(1,sr) = hom(nzb+4,1,pr_palm,sr) ! E
956	ts_value(2,sr) = hom(nzb+5,1,pr_palm,sr) ! E*
957	ts_value(3,sr) = dt_3d
958	ts_value(4,sr) = hom(nzb,1,pr_palm,sr) ! u*
959	ts_value(5,sr) = hom(nzb+3,1,pr_palm,sr) ! th*
960	ts_value(6,sr) = u_max
961	ts_value(7,sr) = v_max
962	ts_value(8,sr) = w_max
963	ts_value(9,sr) = hom(nzb+10,1,pr_palm,sr) ! new divergence
964	ts_value(10,sr) = hom(nzb+9,1,pr_palm,sr) ! old Divergence
965	ts_value(11,sr) = hom(nzb+6,1,pr_palm,sr) ! z_i(1)
966	ts_value(12,sr) = hom(nzb+7,1,pr_palm,sr) ! z_i(2)
967	ts_value(13,sr) = hom(nzb+8,1,pr_palm,sr) ! w*
968	ts_value(14,sr) = hom(nzb,1,16,sr) ! w'pt' at k=0
969	ts_value(15,sr) = hom(nzb+1,1,16,sr) ! w'pt' at k=1
970	ts_value(16,sr) = hom(nzb+1,1,18,sr) ! wpt at k=1
971	ts_value(17,sr) = hom(nzb,1,4,sr) ! pt(0)
972	ts_value(18,sr) = hom(nzb+1,1,4,sr) ! pt(zp)
973	ts_value(19,sr) = hom(nzb+9,1,pr_palm-1,sr) ! splptx
974	ts_value(20,sr) = hom(nzb+10,1,pr_palm-1,sr) ! splpty
975	ts_value(21,sr) = hom(nzb+11,1,pr_palm-1,sr) ! splptz
976	IF ( ts_value(5,sr) /= 0.0 ) THEN
977	ts_value(22,sr) = ts_value(4,sr)**2 / &
978	( kappa * g * ts_value(5,sr) / ts_value(18,sr) ) ! L
979	ELSE
980	ts_value(22,sr) = 10000.0
981	ENDIF
982
983	!
984	!-- Calculate additional statistics provided by the user interface
985	CALL user_statistics( 'time_series', sr, 0 )
986
987	ENDDO ! loop of the subregions
988
989	!
990	!-- If required, sum up horizontal averages for subsequent time averaging
991	IF ( do_sum ) THEN
992	IF ( average_count_pr == 0 ) hom_sum = 0.0
993	hom_sum = hom_sum + hom(:,1,:,:)
994	average_count_pr = average_count_pr + 1
995	do_sum = .FALSE.
996	ENDIF
997
998	!
999	!-- Set flag for other UPs (e.g. output routines, but also buoyancy).
1000	!-- This flag is reset after each time step in time_integration.
1001	flow_statistics_called = .TRUE.
1002
1003	CALL cpu_log( log_point(10), 'flow_statistics', 'stop' )
1004
1005
1006	END SUBROUTINE flow_statistics
1007
1008
1009

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