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source: palm/trunk/SOURCE/flow_statistics.f90 @ 676

Last change on this file since 676 was 674, checked in by suehring, 13 years ago
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1	SUBROUTINE flow_statistics
2
3	!------------------------------------------------------------------------------!
4	! Current revisions:
5	! -----------------
6	!
7	! Former revisions:
8	! -----------------
9	! $Id: flow_statistics.f90 674 2011-01-18 16:33:31Z suehring $
10	!
11	! 673 2011-01-18 16:19:48Z suehring
12	! Top bc for the horizontal velocity variances added for ocean runs.
13	! Setting the corresponding bottom bc moved to advec_ws.
14	!
15	! 667 2010-12-23 12:06:00Z suehring/gryschka
16	! When advection is computed with ws-scheme, turbulent fluxes are already
17	! computed in the respective advection routines and buffered in arrays
18	! sums_xx_ws_l(). This is due to a consistent treatment of statistics with the
19	! numerics and to avoid unphysical kinks near the surface.
20	! So some if requests has to be done to dicern between fluxes from ws-scheme
21	! other advection schemes.
22	! Furthermore the computation of z_i is only done if the heat flux exceeds a
23	! minimum value. This affects only simulations of a neutral boundary layer and
24	! is due to reasons of computations in the advection scheme.
25	!
26	! 624 2010-12-10 11:46:30Z heinze
27	! Calculation of q*2 added
28	!
29	! 622 2010-12-10 08:08:13Z raasch
30	! optional barriers included in order to speed up collective operations
31	!
32	! 388 2009-09-23 09:40:33Z raasch
33	! Vertical profiles of potential density and hydrostatic pressure are
34	! calculated.
35	! Added missing timeseries calculation of w"q"(0), moved timeseries q* to the
36	! end.
37	! Temperature gradient criterion for estimating the boundary layer height
38	! replaced by the gradient criterion of Sullivan et al. (1998).
39	! Output of messages replaced by message handling routine.
40	!
41	! 197 2008-09-16 15:29:03Z raasch
42	! Spline timeseries splptx etc. removed, timeseries w'u', w'v', w'q' (k=0)
43	! added,
44	! bugfix: divide sums(k,8) (e) and sums(k,34) (e*) by ngp_2dh_s_inner(k,sr)
45	! (like other scalars)
46	!
47	! 133 2007-11-20 10:10:53Z letzel
48	! Vertical profiles now based on nzb_s_inner; they are divided by
49	! ngp_2dh_s_inner (scalars, procucts of scalars) and ngp_2dh (staggered
50	! velocity components and their products, procucts of scalars and velocity
51	! components), respectively.
52	!
53	! 106 2007-08-16 14:30:26Z raasch
54	! Prescribed momentum fluxes at the top surface are used,
55	! profiles for wp and w"e are calculated
56	!
57	! 97 2007-06-21 08:23:15Z raasch
58	! Statistics for ocean version (salinity, density) added,
59	! calculation of z_i and Deardorff velocity scale adjusted to be used with
60	! the ocean version
61	!
62	! 87 2007-05-22 15:46:47Z raasch
63	! Two more arguments added to user_statistics, which is now also called for
64	! user-defined profiles,
65	! var_hom and var_sum renamed pr_palm
66	!
67	! 82 2007-04-16 15:40:52Z raasch
68	! Cpp-directive lcmuk changed to intel_openmp_bug
69	!
70	! 75 2007-03-22 09:54:05Z raasch
71	! Collection of time series quantities moved from routine flow_statistics to
72	! here, routine user_statistics is called for each statistic region,
73	! moisture renamed humidity
74	!
75	! 19 2007-02-23 04:53:48Z raasch
76	! fluxes at top modified (tswst, qswst)
77	!
78	! RCS Log replace by Id keyword, revision history cleaned up
79	!
80	! Revision 1.41 2006/08/04 14:37:50 raasch
81	! Error removed in non-parallel part (sums_l)
82	!
83	! Revision 1.1 1997/08/11 06:15:17 raasch
84	! Initial revision
85	!
86	!
87	! Description:
88	! ------------
89	! Compute average profiles and further average flow quantities for the different
90	! user-defined (sub-)regions. The region indexed 0 is the total model domain.
91	!
92	! NOTE: For simplicity, nzb_s_inner and nzb_diff_s_inner are being used as a
93	! ---- lower vertical index for k-loops for all variables, although strictly
94	! speaking the k-loops would have to be split up according to the staggered
95	! grid. However, this implies no error since staggered velocity components are
96	! zero at the walls and inside buildings.
97	!------------------------------------------------------------------------------!
98
99	USE arrays_3d
100	USE cloud_parameters
101	USE cpulog
102	USE grid_variables
103	USE indices
104	USE interfaces
105	USE pegrid
106	USE statistics
107	USE control_parameters
108
109	IMPLICIT NONE
110
111	INTEGER :: i, j, k, omp_get_thread_num, sr, tn
112	LOGICAL :: first
113	REAL :: dptdz_threshold, height, pts, sums_l_eper, sums_l_etot, ust, &
114	ust2, u2, vst, vst2, v2, w2, z_i(2)
115	REAL :: dptdz(nzb+1:nzt+1)
116	REAL :: sums_ll(nzb:nzt+1,2)
117
118	CALL cpu_log( log_point(10), 'flow_statistics', 'start' )
119
120	!
121	!-- To be on the safe side, check whether flow_statistics has already been
122	!-- called once after the current time step
123	IF ( flow_statistics_called ) THEN
124
125	message_string = 'flow_statistics is called two times within one ' // &
126	'timestep'
127	CALL message( 'flow_statistics', 'PA0190', 1, 2, 0, 6, 0 )
128
129	ENDIF
130
131	!
132	!-- Compute statistics for each (sub-)region
133	DO sr = 0, statistic_regions
134
135	!
136	!-- Initialize (local) summation array
137	sums_l = 0.0
138
139	!
140	!-- Store sums that have been computed in other subroutines in summation
141	!-- array
142	sums_l(:,11,:) = sums_l_l(:,sr,:) ! mixing length from diffusivities
143	!-- WARNING: next line still has to be adjusted for OpenMP
144	sums_l(:,21,0) = sums_wsts_bc_l(:,sr) ! heat flux from advec_s_bc
145	sums_l(nzb+9,pr_palm,0) = sums_divold_l(sr) ! old divergence from pres
146	sums_l(nzb+10,pr_palm,0) = sums_divnew_l(sr) ! new divergence from pres
147
148	!
149	!-- Copy the turbulent quantities, evaluated in the advection routines to
150	!-- the local array sums_l() for further computations
151	IF ( ws_scheme_mom ) THEN
152	!
153	!-- According to the Neumann bc for the horizontal velocity components,
154	!-- the corresponding fluxes has to satisfiy the same bc.
155	IF ( ocean ) THEN
156	sums_us2_ws_l(nzt+1,sr) = sums_us2_ws_l(nzt,sr)
157	sums_vs2_ws_l(nzt+1,sr) = sums_vs2_ws_l(nzt,sr)
158	ENDIF
159	!
160	!-- Swap the turbulent quantities evaluated in advec_ws.
161	sums_l(:,13,0) = sums_wsus_ws_l(:,sr) ! wu
162	sums_l(:,15,0) = sums_wsvs_ws_l(:,sr) ! wv
163	sums_l(:,30,0) = sums_us2_ws_l(:,sr) ! u*2
164	sums_l(:,31,0) = sums_vs2_ws_l(:,sr) ! v*2
165	sums_l(:,32,0) = sums_ws2_ws_l(:,sr) ! w*2
166	sums_l(:,34,0) = sums_l(:,34,0) + 0.5 * &
167	(sums_us2_ws_l(:,sr) + sums_vs2_ws_l(:,sr) &
168	+ sums_ws2_ws_l(:,sr)) ! e*
169	DO k = nzb, nzt
170	sums_l(nzb+5,pr_palm,0) = sums_l(nzb+5,pr_palm,0) + 0.5 * ( &
171	sums_us2_ws_l(k,sr) + sums_vs2_ws_l(k,sr) + &
172	sums_ws2_ws_l(k,sr))
173	ENDDO
174	ENDIF
175	IF ( ws_scheme_sca ) THEN
176	sums_l(:,17,0) = sums_wspts_ws_l(:,sr) ! wpt from advec_s_ws
177	IF ( ocean ) sums_l(:,66,0) = sums_wssas_ws_l(:,sr) ! wsa
178	IF ( humidity .OR. passive_scalar ) sums_l(:,49,0) = &
179	sums_wsqs_ws_l(:,sr) !wq
180	ENDIF
181	!
182	!-- Horizontally averaged profiles of horizontal velocities and temperature.
183	!-- They must have been computed before, because they are already required
184	!-- for other horizontal averages.
185	tn = 0
186
187	!$OMP PARALLEL PRIVATE( i, j, k, tn )
188	#if defined( __intel_openmp_bug )
189	tn = omp_get_thread_num()
190	#else
191	!$ tn = omp_get_thread_num()
192	#endif
193
194	!$OMP DO
195	DO i = nxl, nxr
196	DO j = nys, nyn
197	DO k = nzb_s_inner(j,i), nzt+1
198	sums_l(k,1,tn) = sums_l(k,1,tn) + u(k,j,i) * rmask(j,i,sr)
199	sums_l(k,2,tn) = sums_l(k,2,tn) + v(k,j,i) * rmask(j,i,sr)
200	sums_l(k,4,tn) = sums_l(k,4,tn) + pt(k,j,i) * rmask(j,i,sr)
201	ENDDO
202	ENDDO
203	ENDDO
204
205	!
206	!-- Horizontally averaged profile of salinity
207	IF ( ocean ) THEN
208	!$OMP DO
209	DO i = nxl, nxr
210	DO j = nys, nyn
211	DO k = nzb_s_inner(j,i), nzt+1
212	sums_l(k,23,tn) = sums_l(k,23,tn) + &
213	sa(k,j,i) * rmask(j,i,sr)
214	ENDDO
215	ENDDO
216	ENDDO
217	ENDIF
218
219	!
220	!-- Horizontally averaged profiles of virtual potential temperature,
221	!-- total water content, specific humidity and liquid water potential
222	!-- temperature
223	IF ( humidity ) THEN
224	!$OMP DO
225	DO i = nxl, nxr
226	DO j = nys, nyn
227	DO k = nzb_s_inner(j,i), nzt+1
228	sums_l(k,44,tn) = sums_l(k,44,tn) + &
229	vpt(k,j,i) * rmask(j,i,sr)
230	sums_l(k,41,tn) = sums_l(k,41,tn) + &
231	q(k,j,i) * rmask(j,i,sr)
232	ENDDO
233	ENDDO
234	ENDDO
235	IF ( cloud_physics ) THEN
236	!$OMP DO
237	DO i = nxl, nxr
238	DO j = nys, nyn
239	DO k = nzb_s_inner(j,i), nzt+1
240	sums_l(k,42,tn) = sums_l(k,42,tn) + &
241	( q(k,j,i) - ql(k,j,i) ) * rmask(j,i,sr)
242	sums_l(k,43,tn) = sums_l(k,43,tn) + ( &
243	pt(k,j,i) + l_d_cppt_d_t(k) ql(k,j,i) &
244	) * rmask(j,i,sr)
245	ENDDO
246	ENDDO
247	ENDDO
248	ENDIF
249	ENDIF
250
251	!
252	!-- Horizontally averaged profiles of passive scalar
253	IF ( passive_scalar ) THEN
254	!$OMP DO
255	DO i = nxl, nxr
256	DO j = nys, nyn
257	DO k = nzb_s_inner(j,i), nzt+1
258	sums_l(k,41,tn) = sums_l(k,41,tn) + q(k,j,i) * rmask(j,i,sr)
259	ENDDO
260	ENDDO
261	ENDDO
262	ENDIF
263	!$OMP END PARALLEL
264	!
265	!-- Summation of thread sums
266	IF ( threads_per_task > 1 ) THEN
267	DO i = 1, threads_per_task-1
268	sums_l(:,1,0) = sums_l(:,1,0) + sums_l(:,1,i)
269	sums_l(:,2,0) = sums_l(:,2,0) + sums_l(:,2,i)
270	sums_l(:,4,0) = sums_l(:,4,0) + sums_l(:,4,i)
271	IF ( ocean ) THEN
272	sums_l(:,23,0) = sums_l(:,23,0) + sums_l(:,23,i)
273	ENDIF
274	IF ( humidity ) THEN
275	sums_l(:,41,0) = sums_l(:,41,0) + sums_l(:,41,i)
276	sums_l(:,44,0) = sums_l(:,44,0) + sums_l(:,44,i)
277	IF ( cloud_physics ) THEN
278	sums_l(:,42,0) = sums_l(:,42,0) + sums_l(:,42,i)
279	sums_l(:,43,0) = sums_l(:,43,0) + sums_l(:,43,i)
280	ENDIF
281	ENDIF
282	IF ( passive_scalar ) THEN
283	sums_l(:,41,0) = sums_l(:,41,0) + sums_l(:,41,i)
284	ENDIF
285	ENDDO
286	ENDIF
287
288	#if defined( __parallel )
289	!
290	!-- Compute total sum from local sums
291	IF ( collective_wait ) CALL MPI_BARRIER( comm2d, ierr )
292	CALL MPI_ALLREDUCE( sums_l(nzb,1,0), sums(nzb,1), nzt+2-nzb, MPI_REAL, &
293	MPI_SUM, comm2d, ierr )
294	IF ( collective_wait ) CALL MPI_BARRIER( comm2d, ierr )
295	CALL MPI_ALLREDUCE( sums_l(nzb,2,0), sums(nzb,2), nzt+2-nzb, MPI_REAL, &
296	MPI_SUM, comm2d, ierr )
297	IF ( collective_wait ) CALL MPI_BARRIER( comm2d, ierr )
298	CALL MPI_ALLREDUCE( sums_l(nzb,4,0), sums(nzb,4), nzt+2-nzb, MPI_REAL, &
299	MPI_SUM, comm2d, ierr )
300	IF ( ocean ) THEN
301	IF ( collective_wait ) CALL MPI_BARRIER( comm2d, ierr )
302	CALL MPI_ALLREDUCE( sums_l(nzb,23,0), sums(nzb,23), nzt+2-nzb, &
303	MPI_REAL, MPI_SUM, comm2d, ierr )
304	ENDIF
305	IF ( humidity ) THEN
306	IF ( collective_wait ) CALL MPI_BARRIER( comm2d, ierr )
307	CALL MPI_ALLREDUCE( sums_l(nzb,44,0), sums(nzb,44), nzt+2-nzb, &
308	MPI_REAL, MPI_SUM, comm2d, ierr )
309	IF ( collective_wait ) CALL MPI_BARRIER( comm2d, ierr )
310	CALL MPI_ALLREDUCE( sums_l(nzb,41,0), sums(nzb,41), nzt+2-nzb, &
311	MPI_REAL, MPI_SUM, comm2d, ierr )
312	IF ( cloud_physics ) THEN
313	IF ( collective_wait ) CALL MPI_BARRIER( comm2d, ierr )
314	CALL MPI_ALLREDUCE( sums_l(nzb,42,0), sums(nzb,42), nzt+2-nzb, &
315	MPI_REAL, MPI_SUM, comm2d, ierr )
316	IF ( collective_wait ) CALL MPI_BARRIER( comm2d, ierr )
317	CALL MPI_ALLREDUCE( sums_l(nzb,43,0), sums(nzb,43), nzt+2-nzb, &
318	MPI_REAL, MPI_SUM, comm2d, ierr )
319	ENDIF
320	ENDIF
321
322	IF ( passive_scalar ) THEN
323	IF ( collective_wait ) CALL MPI_BARRIER( comm2d, ierr )
324	CALL MPI_ALLREDUCE( sums_l(nzb,41,0), sums(nzb,41), nzt+2-nzb, &
325	MPI_REAL, MPI_SUM, comm2d, ierr )
326	ENDIF
327	#else
328	sums(:,1) = sums_l(:,1,0)
329	sums(:,2) = sums_l(:,2,0)
330	sums(:,4) = sums_l(:,4,0)
331	IF ( ocean ) sums(:,23) = sums_l(:,23,0)
332	IF ( humidity ) THEN
333	sums(:,44) = sums_l(:,44,0)
334	sums(:,41) = sums_l(:,41,0)
335	IF ( cloud_physics ) THEN
336	sums(:,42) = sums_l(:,42,0)
337	sums(:,43) = sums_l(:,43,0)
338	ENDIF
339	ENDIF
340	IF ( passive_scalar ) sums(:,41) = sums_l(:,41,0)
341	#endif
342
343	!
344	!-- Final values are obtained by division by the total number of grid points
345	!-- used for summation. After that store profiles.
346	sums(:,1) = sums(:,1) / ngp_2dh(sr)
347	sums(:,2) = sums(:,2) / ngp_2dh(sr)
348	sums(:,4) = sums(:,4) / ngp_2dh_s_inner(:,sr)
349	hom(:,1,1,sr) = sums(:,1) ! u
350	hom(:,1,2,sr) = sums(:,2) ! v
351	hom(:,1,4,sr) = sums(:,4) ! pt
352
353
354	!
355	!-- Salinity
356	IF ( ocean ) THEN
357	sums(:,23) = sums(:,23) / ngp_2dh_s_inner(:,sr)
358	hom(:,1,23,sr) = sums(:,23) ! sa
359	ENDIF
360
361	!
362	!-- Humidity and cloud parameters
363	IF ( humidity ) THEN
364	sums(:,44) = sums(:,44) / ngp_2dh_s_inner(:,sr)
365	sums(:,41) = sums(:,41) / ngp_2dh_s_inner(:,sr)
366	hom(:,1,44,sr) = sums(:,44) ! vpt
367	hom(:,1,41,sr) = sums(:,41) ! qv (q)
368	IF ( cloud_physics ) THEN
369	sums(:,42) = sums(:,42) / ngp_2dh_s_inner(:,sr)
370	sums(:,43) = sums(:,43) / ngp_2dh_s_inner(:,sr)
371	hom(:,1,42,sr) = sums(:,42) ! qv
372	hom(:,1,43,sr) = sums(:,43) ! pt
373	ENDIF
374	ENDIF
375
376	!
377	!-- Passive scalar
378	IF ( passive_scalar ) hom(:,1,41,sr) = sums(:,41) / &
379	ngp_2dh_s_inner(:,sr) ! s (q)
380
381	!
382	!-- Horizontally averaged profiles of the remaining prognostic variables,
383	!-- variances, the total and the perturbation energy (single values in last
384	!-- column of sums_l) and some diagnostic quantities.
385	!-- NOTE: for simplicity, nzb_s_inner is used below, although strictly
386	!-- ---- speaking the following k-loop would have to be split up and
387	!-- rearranged according to the staggered grid.
388	!-- However, this implies no error since staggered velocity components
389	!-- are zero at the walls and inside buildings.
390	tn = 0
391	#if defined( __intel_openmp_bug )
392	!$OMP PARALLEL PRIVATE( i, j, k, pts, sums_ll, sums_l_eper, sums_l_etot, &
393	!$OMP tn, ust, ust2, u2, vst, vst2, v2, w2 )
394	tn = omp_get_thread_num()
395	#else
396	!$OMP PARALLEL PRIVATE( i, j, k, pts, sums_ll, sums_l_eper, sums_l_etot, tn, ust, ust2, u2, vst, vst2, v2, w2 )
397	!$ tn = omp_get_thread_num()
398	#endif
399	!$OMP DO
400	DO i = nxl, nxr
401	DO j = nys, nyn
402	sums_l_etot = 0.0
403	DO k = nzb_s_inner(j,i), nzt+1
404	!
405	!-- Prognostic and diagnostic variables
406	sums_l(k,3,tn) = sums_l(k,3,tn) + w(k,j,i) * rmask(j,i,sr)
407	sums_l(k,8,tn) = sums_l(k,8,tn) + e(k,j,i) * rmask(j,i,sr)
408	sums_l(k,9,tn) = sums_l(k,9,tn) + km(k,j,i) * rmask(j,i,sr)
409	sums_l(k,10,tn) = sums_l(k,10,tn) + kh(k,j,i) * rmask(j,i,sr)
410	sums_l(k,40,tn) = sums_l(k,40,tn) + p(k,j,i)
411
412	sums_l(k,33,tn) = sums_l(k,33,tn) + &
413	( pt(k,j,i)-hom(k,1,4,sr) )*2 rmask(j,i,sr)
414
415	IF ( humidity ) THEN
416	sums_l(k,70,tn) = sums_l(k,70,tn) + &
417	( q(k,j,i)-hom(k,1,41,sr) )*2 rmask(j,i,sr)
418	ENDIF
419
420	sums_l_etot = sums_l_etot + &
421	0.5 * ( u(k,j,i)2 + v(k,j,i)2 + &
422	w(k,j,i)*2 ) rmask(j,i,sr)
423	ENDDO
424	!
425	!-- Total and perturbation energy for the total domain (being
426	!-- collected in the last column of sums_l). Summation of these
427	!-- quantities is seperated from the previous loop in order to
428	!-- allow vectorization of that loop.
429	sums_l(nzb+4,pr_palm,tn) = sums_l(nzb+4,pr_palm,tn) + sums_l_etot
430	!
431	!-- 2D-arrays (being collected in the last column of sums_l)
432	sums_l(nzb,pr_palm,tn) = sums_l(nzb,pr_palm,tn) + &
433	us(j,i) * rmask(j,i,sr)
434	sums_l(nzb+1,pr_palm,tn) = sums_l(nzb+1,pr_palm,tn) + &
435	usws(j,i) * rmask(j,i,sr)
436	sums_l(nzb+2,pr_palm,tn) = sums_l(nzb+2,pr_palm,tn) + &
437	vsws(j,i) * rmask(j,i,sr)
438	sums_l(nzb+3,pr_palm,tn) = sums_l(nzb+3,pr_palm,tn) + &
439	ts(j,i) * rmask(j,i,sr)
440	IF ( humidity ) THEN
441	sums_l(nzb+12,pr_palm,tn) = sums_l(nzb+12,pr_palm,tn) + &
442	qs(j,i) * rmask(j,i,sr)
443	ENDIF
444	ENDDO
445	ENDDO
446
447	!
448	!-- Computation of statistics when ws-scheme is not used. Else these
449	!-- quantities are evaluated in the advection routines.
450	IF ( .NOT. ws_scheme_mom ) THEN
451	!$OMP DO
452	DO i = nxl, nxr
453	DO j = nys, nyn
454	sums_l_eper = 0.0
455	DO k = nzb_s_inner(j,i), nzt+1
456	u2 = u(k,j,i)**2
457	v2 = v(k,j,i)**2
458	w2 = w(k,j,i)**2
459	ust2 = ( u(k,j,i) - hom(k,1,1,sr) )**2
460	vst2 = ( v(k,j,i) - hom(k,1,2,sr) )**2
461
462	sums_l(k,30,tn) = sums_l(k,30,tn) + ust2 * rmask(j,i,sr)
463	sums_l(k,31,tn) = sums_l(k,31,tn) + vst2 * rmask(j,i,sr)
464	sums_l(k,32,tn) = sums_l(k,32,tn) + w2 * rmask(j,i,sr)
465	!
466	!-- Higher moments
467	!-- (Computation of the skewness of w further below)
468	sums_l(k,38,tn) = sums_l(k,38,tn) + w(k,j,i) * w2 * &
469	rmask(j,i,sr)
470	!
471	!-- Perturbation energy
472
473	sums_l(k,34,tn) = sums_l(k,34,tn) + 0.5 * &
474	( ust2 + vst2 + w2 ) * rmask(j,i,sr)
475	sums_l_eper = sums_l_eper + &
476	0.5 * ( ust2+vst2+w2 ) * rmask(j,i,sr)
477
478	ENDDO
479	sums_l(nzb+5,pr_palm,tn) = sums_l(nzb+5,pr_palm,tn) &
480	+ sums_l_eper
481	ENDDO
482	ENDDO
483	ELSE
484	!$OMP DO
485	DO i = nxl, nxr
486	DO j = nys, nyn
487	DO k = nzb_s_inner(j,i), nzt + 1
488	w2 = w(k,j,i)**2
489	!
490	!-- Higher moments
491	!-- (Computation of the skewness of w further below)
492	sums_l(k,38,tn) = sums_l(k,38,tn) + w(k,j,i) * w2 * &
493	rmask(j,i,sr)
494	ENDDO
495	ENDDO
496	ENDDO
497	ENDIF
498
499	!
500	!-- Horizontally averaged profiles of the vertical fluxes
501
502	!$OMP DO
503	DO i = nxl, nxr
504	DO j = nys, nyn
505	!
506	!-- Subgridscale fluxes (without Prandtl layer from k=nzb,
507	!-- oterwise from k=nzb+1)
508	!-- NOTE: for simplicity, nzb_diff_s_inner is used below, although
509	!-- ---- strictly speaking the following k-loop would have to be
510	!-- split up according to the staggered grid.
511	!-- However, this implies no error since staggered velocity
512	!-- components are zero at the walls and inside buildings.
513
514	DO k = nzb_diff_s_inner(j,i)-1, nzt_diff
515	!
516	!-- Momentum flux w"u"
517	sums_l(k,12,tn) = sums_l(k,12,tn) - 0.25 * ( &
518	km(k,j,i)+km(k+1,j,i)+km(k,j,i-1)+km(k+1,j,i-1) &
519	) * ( &
520	( u(k+1,j,i) - u(k,j,i) ) * ddzu(k+1) &
521	+ ( w(k,j,i) - w(k,j,i-1) ) * ddx &
522	) * rmask(j,i,sr)
523	!
524	!-- Momentum flux w"v"
525	sums_l(k,14,tn) = sums_l(k,14,tn) - 0.25 * ( &
526	km(k,j,i)+km(k+1,j,i)+km(k,j-1,i)+km(k+1,j-1,i) &
527	) * ( &
528	( v(k+1,j,i) - v(k,j,i) ) * ddzu(k+1) &
529	+ ( w(k,j,i) - w(k,j-1,i) ) * ddy &
530	) * rmask(j,i,sr)
531	!
532	!-- Heat flux w"pt"
533	sums_l(k,16,tn) = sums_l(k,16,tn) &
534	- 0.5 * ( kh(k,j,i) + kh(k+1,j,i) ) &
535	* ( pt(k+1,j,i) - pt(k,j,i) ) &
536	* ddzu(k+1) * rmask(j,i,sr)
537
538
539	!
540	!-- Salinity flux w"sa"
541	IF ( ocean ) THEN
542	sums_l(k,65,tn) = sums_l(k,65,tn) &
543	- 0.5 * ( kh(k,j,i) + kh(k+1,j,i) ) &
544	* ( sa(k+1,j,i) - sa(k,j,i) ) &
545	* ddzu(k+1) * rmask(j,i,sr)
546	ENDIF
547
548	!
549	!-- Buoyancy flux, water flux (humidity flux) w"q"
550	IF ( humidity ) THEN
551	sums_l(k,45,tn) = sums_l(k,45,tn) &
552	- 0.5 * ( kh(k,j,i) + kh(k+1,j,i) ) &
553	* ( vpt(k+1,j,i) - vpt(k,j,i) ) &
554	* ddzu(k+1) * rmask(j,i,sr)
555	sums_l(k,48,tn) = sums_l(k,48,tn) &
556	- 0.5 * ( kh(k,j,i) + kh(k+1,j,i) ) &
557	* ( q(k+1,j,i) - q(k,j,i) ) &
558	* ddzu(k+1) * rmask(j,i,sr)
559	IF ( cloud_physics ) THEN
560	sums_l(k,51,tn) = sums_l(k,51,tn) &
561	- 0.5 * ( kh(k,j,i) + kh(k+1,j,i) ) &
562	* ( ( q(k+1,j,i) - ql(k+1,j,i) )&
563	- ( q(k,j,i) - ql(k,j,i) ) ) &
564	* ddzu(k+1) * rmask(j,i,sr)
565	ENDIF
566	ENDIF
567
568	!
569	!-- Passive scalar flux
570	IF ( passive_scalar ) THEN
571	sums_l(k,48,tn) = sums_l(k,48,tn) &
572	- 0.5 * ( kh(k,j,i) + kh(k+1,j,i) ) &
573	* ( q(k+1,j,i) - q(k,j,i) ) &
574	* ddzu(k+1) * rmask(j,i,sr)
575	ENDIF
576
577	ENDDO
578
579	!
580	!-- Subgridscale fluxes in the Prandtl layer
581	IF ( use_surface_fluxes ) THEN
582	sums_l(nzb,12,tn) = sums_l(nzb,12,tn) + &
583	usws(j,i) * rmask(j,i,sr) ! w"u"
584	sums_l(nzb,14,tn) = sums_l(nzb,14,tn) + &
585	vsws(j,i) * rmask(j,i,sr) ! w"v"
586	sums_l(nzb,16,tn) = sums_l(nzb,16,tn) + &
587	shf(j,i) * rmask(j,i,sr) ! w"pt"
588	sums_l(nzb,58,tn) = sums_l(nzb,58,tn) + &
589	0.0 * rmask(j,i,sr) ! u"pt"
590	sums_l(nzb,61,tn) = sums_l(nzb,61,tn) + &
591	0.0 * rmask(j,i,sr) ! v"pt"
592	IF ( ocean ) THEN
593	sums_l(nzb,65,tn) = sums_l(nzb,65,tn) + &
594	saswsb(j,i) * rmask(j,i,sr) ! w"sa"
595	ENDIF
596	IF ( humidity ) THEN
597	sums_l(nzb,48,tn) = sums_l(nzb,48,tn) + &
598	qsws(j,i) * rmask(j,i,sr) ! w"q" (w"qv")
599	IF ( cloud_physics ) THEN
600	sums_l(nzb,45,tn) = sums_l(nzb,45,tn) + ( &
601	( 1.0 + 0.61 * q(nzb,j,i) ) * &
602	shf(j,i) + 0.61 * pt(nzb,j,i) * &
603	qsws(j,i) &
604	)
605	!
606	!-- Formula does not work if ql(nzb) /= 0.0
607	sums_l(nzb,51,tn) = sums_l(nzb,51,tn) + & ! w"q" (w"qv")
608	qsws(j,i) * rmask(j,i,sr)
609	ENDIF
610	ENDIF
611	IF ( passive_scalar ) THEN
612	sums_l(nzb,48,tn) = sums_l(nzb,48,tn) + &
613	qsws(j,i) * rmask(j,i,sr) ! w"q" (w"qv")
614	ENDIF
615	ENDIF
616
617	!
618	!-- Subgridscale fluxes at the top surface
619	IF ( use_top_fluxes ) THEN
620	sums_l(nzt:nzt+1,12,tn) = sums_l(nzt:nzt+1,12,tn) + &
621	uswst(j,i) * rmask(j,i,sr) ! w"u"
622	sums_l(nzt:nzt+1,14,tn) = sums_l(nzt:nzt+1,14,tn) + &
623	vswst(j,i) * rmask(j,i,sr) ! w"v"
624	sums_l(nzt:nzt+1,16,tn) = sums_l(nzt:nzt+1,16,tn) + &
625	tswst(j,i) * rmask(j,i,sr) ! w"pt"
626	sums_l(nzt:nzt+1,58,tn) = sums_l(nzt:nzt+1,58,tn) + &
627	0.0 * rmask(j,i,sr) ! u"pt"
628	sums_l(nzt:nzt+1,61,tn) = sums_l(nzt:nzt+1,61,tn) + &
629	0.0 * rmask(j,i,sr) ! v"pt"
630
631	IF ( ocean ) THEN
632	sums_l(nzt,65,tn) = sums_l(nzt,65,tn) + &
633	saswst(j,i) * rmask(j,i,sr) ! w"sa"
634	ENDIF
635	IF ( humidity ) THEN
636	sums_l(nzt,48,tn) = sums_l(nzt,48,tn) + &
637	qswst(j,i) * rmask(j,i,sr) ! w"q" (w"qv")
638	IF ( cloud_physics ) THEN
639	sums_l(nzt,45,tn) = sums_l(nzt,45,tn) + ( &
640	( 1.0 + 0.61 * q(nzt,j,i) ) * &
641	tswst(j,i) + 0.61 * pt(nzt,j,i) * &
642	qsws(j,i) &
643	)
644	!
645	!-- Formula does not work if ql(nzb) /= 0.0
646	sums_l(nzt,51,tn) = sums_l(nzt,51,tn) + & ! w"q" (w"qv")
647	qswst(j,i) * rmask(j,i,sr)
648	ENDIF
649	ENDIF
650	IF ( passive_scalar ) THEN
651	sums_l(nzt,48,tn) = sums_l(nzt,48,tn) + &
652	qswst(j,i) * rmask(j,i,sr) ! w"q" (w"qv")
653	ENDIF
654	ENDIF
655
656	!
657	!-- Resolved fluxes (can be computed for all horizontal points)
658	!-- NOTE: for simplicity, nzb_s_inner is used below, although strictly
659	!-- ---- speaking the following k-loop would have to be split up and
660	!-- rearranged according to the staggered grid.
661	DO k = nzb_s_inner(j,i), nzt
662	ust = 0.5 * ( u(k,j,i) - hom(k,1,1,sr) + &
663	u(k+1,j,i) - hom(k+1,1,1,sr) )
664	vst = 0.5 * ( v(k,j,i) - hom(k,1,2,sr) + &
665	v(k+1,j,i) - hom(k+1,1,2,sr) )
666	pts = 0.5 * ( pt(k,j,i) - hom(k,1,4,sr) + &
667	pt(k+1,j,i) - hom(k+1,1,4,sr) )
668
669	!-- Higher moments
670	sums_l(k,35,tn) = sums_l(k,35,tn) + pts * w(k,j,i)*2 &
671	rmask(j,i,sr)
672	sums_l(k,36,tn) = sums_l(k,36,tn) + pts*2 w(k,j,i) * &
673	rmask(j,i,sr)
674
675	!
676	!-- Salinity flux and density (density does not belong to here,
677	!-- but so far there is no other suitable place to calculate)
678	IF ( ocean ) THEN
679	IF( .NOT. ws_scheme_sca ) THEN
680	pts = 0.5 * ( sa(k,j,i) - hom(k,1,23,sr) + &
681	sa(k+1,j,i) - hom(k+1,1,23,sr) )
682	sums_l(k,66,tn) = sums_l(k,66,tn) + pts * w(k,j,i) * &
683	rmask(j,i,sr)
684	ENDIF
685	sums_l(k,64,tn) = sums_l(k,64,tn) + rho(k,j,i) * &
686	rmask(j,i,sr)
687	sums_l(k,71,tn) = sums_l(k,71,tn) + prho(k,j,i) * &
688	rmask(j,i,sr)
689	ENDIF
690
691	!
692	!-- Buoyancy flux, water flux, humidity flux and liquid water
693	!-- content
694	IF ( humidity ) THEN
695	pts = 0.5 * ( vpt(k,j,i) - hom(k,1,44,sr) + &
696	vpt(k+1,j,i) - hom(k+1,1,44,sr) )
697	sums_l(k,46,tn) = sums_l(k,46,tn) + pts * w(k,j,i) * &
698	rmask(j,i,sr)
699
700	IF ( cloud_physics .OR. cloud_droplets ) THEN
701	pts = 0.5 * &
702	( ( q(k,j,i) - ql(k,j,i) ) - hom(k,1,42,sr) &
703	+ ( q(k+1,j,i) - ql(k+1,j,i) ) - hom(k+1,1,42,sr) )
704	sums_l(k,52,tn) = sums_l(k,52,tn) + pts * w(k,j,i) * &
705	rmask(j,i,sr)
706	sums_l(k,54,tn) = sums_l(k,54,tn) + ql(k,j,i) * &
707	rmask(j,i,sr)
708	ENDIF
709	ENDIF
710
711	!
712	!-- Passive scalar flux
713	IF ( passive_scalar .AND. ( .NOT. ws_scheme_sca )) THEN
714	pts = 0.5 * ( q(k,j,i) - hom(k,1,41,sr) + &
715	q(k+1,j,i) - hom(k+1,1,41,sr) )
716	sums_l(k,49,tn) = sums_l(k,49,tn) + pts * w(k,j,i) * &
717	rmask(j,i,sr)
718	ENDIF
719
720	!
721	!-- Energy flux we
722	!-- has to be adjusted
723	sums_l(k,37,tn) = sums_l(k,37,tn) + w(k,j,i) * 0.5 * &
724	( ust2 + vst2 + w(k,j,i)**2 )&
725	* rmask(j,i,sr)
726	ENDDO
727	ENDDO
728	ENDDO
729	!- for reasons of speed optimization the loop is splitted, to avoid if-else
730	!- statements inside the loop
731	!- Fluxes which have been computed in part directly inside the advection routines
732	!- treated seperatly.
733	!- First treat the momentum fluxes
734	IF ( .NOT. ws_scheme_mom ) THEN
735	!$OMP DO
736	DO i = nxl, nxr
737	DO j = nys, nyn
738	DO k = nzb_diff_s_inner(j,i)-1, nzt_diff
739	ust = 0.5 * ( u(k,j,i) - hom(k,1,1,sr) + &
740	u(k+1,j,i) - hom(k+1,1,1,sr) )
741	vst = 0.5 * ( v(k,j,i) - hom(k,1,2,sr) + &
742	v(k+1,j,i) - hom(k+1,1,2,sr) )
743	!
744	!-- Momentum flux wu
745	sums_l(k,13,tn) = sums_l(k,13,tn) + 0.5 * &
746	( w(k,j,i-1) + w(k,j,i) ) &
747	* ust * rmask(j,i,sr)
748	!
749	!-- Momentum flux wv
750	sums_l(k,15,tn) = sums_l(k,15,tn) + 0.5 * &
751	( w(k,j-1,i) + w(k,j,i) ) &
752	* vst * rmask(j,i,sr)
753	ENDDO
754	ENDDO
755	ENDDO
756
757	ENDIF
758	IF ( .NOT. ws_scheme_sca ) THEN
759	!$OMP DO
760	DO i = nxl, nxr
761	DO j = nys, nyn
762	DO k = nzb_diff_s_inner(j,i) - 1, nzt_diff
763	!- vertical heat flux
764	sums_l(k,17,tn) = sums_l(k,17,tn) + 0.5 * &
765	( pt(k,j,i) - hom(k,1,4,sr) + &
766	pt(k+1,j,i) - hom(k+1,1,4,sr) ) &
767	* w(k,j,i) * rmask(j,i,sr)
768	IF ( humidity ) THEN
769	pts = 0.5 * ( q(k,j,i) - hom(k,1,41,sr) + &
770	q(k+1,j,i) - hom(k+1,1,41,sr) )
771	sums_l(k,49,tn) = sums_l(k,49,tn) + pts * w(k,j,i) * &
772	rmask(j,i,sr)
773	ENDIF
774	ENDDO
775	ENDDO
776	ENDDO
777
778	ENDIF
779
780
781	!
782	!-- Density at top follows Neumann condition
783	IF ( ocean ) THEN
784	sums_l(nzt+1,64,tn) = sums_l(nzt,64,tn)
785	sums_l(nzt+1,71,tn) = sums_l(nzt,71,tn)
786	ENDIF
787
788	!
789	!-- Divergence of vertical flux of resolved scale energy and pressure
790	!-- fluctuations as well as flux of pressure fluctuation itself (68).
791	!-- First calculate the products, then the divergence.
792	!-- Calculation is time consuming. Do it only, if profiles shall be plotted.
793	IF ( hom(nzb+1,2,55,0) /= 0.0 .OR. hom(nzb+1,2,68,0) /= 0.0 ) THEN
794
795	sums_ll = 0.0 ! local array
796
797	!$OMP DO
798	DO i = nxl, nxr
799	DO j = nys, nyn
800	DO k = nzb_s_inner(j,i)+1, nzt
801
802	sums_ll(k,1) = sums_ll(k,1) + 0.5 * w(k,j,i) * ( &
803	( 0.25 * ( u(k,j,i)+u(k+1,j,i)+u(k,j,i+1)+u(k+1,j,i+1) &
804	- 2.0 * ( hom(k,1,1,sr) + hom(k+1,1,1,sr) ) &
805	) )**2 &
806	+ ( 0.25 * ( v(k,j,i)+v(k+1,j,i)+v(k,j+1,i)+v(k+1,j+1,i) &
807	- 2.0 * ( hom(k,1,2,sr) + hom(k+1,1,2,sr) ) &
808	) )**2 &
809	+ w(k,j,i)**2 )
810
811	sums_ll(k,2) = sums_ll(k,2) + 0.5 * w(k,j,i) &
812	* ( p(k,j,i) + p(k+1,j,i) )
813
814	ENDDO
815	ENDDO
816	ENDDO
817	sums_ll(0,1) = 0.0 ! because w is zero at the bottom
818	sums_ll(nzt+1,1) = 0.0
819	sums_ll(0,2) = 0.0
820	sums_ll(nzt+1,2) = 0.0
821
822	DO k = nzb_s_inner(j,i)+1, nzt
823	sums_l(k,55,tn) = ( sums_ll(k,1) - sums_ll(k-1,1) ) * ddzw(k)
824	sums_l(k,56,tn) = ( sums_ll(k,2) - sums_ll(k-1,2) ) * ddzw(k)
825	sums_l(k,68,tn) = sums_ll(k,2)
826	ENDDO
827	sums_l(nzb,55,tn) = sums_l(nzb+1,55,tn)
828	sums_l(nzb,56,tn) = sums_l(nzb+1,56,tn)
829	sums_l(nzb,68,tn) = 0.0 ! because w* = 0 at nzb
830
831	ENDIF
832
833	!
834	!-- Divergence of vertical flux of SGS TKE and the flux itself (69)
835	IF ( hom(nzb+1,2,57,0) /= 0.0 .OR. hom(nzb+1,2,69,0) /= 0.0 ) THEN
836
837	!$OMP DO
838	DO i = nxl, nxr
839	DO j = nys, nyn
840	DO k = nzb_s_inner(j,i)+1, nzt
841
842	sums_l(k,57,tn) = sums_l(k,57,tn) - 0.5 * ( &
843	(km(k,j,i)+km(k+1,j,i)) * (e(k+1,j,i)-e(k,j,i)) * ddzu(k+1) &
844	- (km(k-1,j,i)+km(k,j,i)) * (e(k,j,i)-e(k-1,j,i)) * ddzu(k) &
845	) * ddzw(k)
846
847	sums_l(k,69,tn) = sums_l(k,69,tn) - 0.5 * ( &
848	(km(k,j,i)+km(k+1,j,i)) * (e(k+1,j,i)-e(k,j,i)) * ddzu(k+1) &
849	)
850
851	ENDDO
852	ENDDO
853	ENDDO
854	sums_l(nzb,57,tn) = sums_l(nzb+1,57,tn)
855	sums_l(nzb,69,tn) = sums_l(nzb+1,69,tn)
856
857	ENDIF
858
859	!
860	!-- Horizontal heat fluxes (subgrid, resolved, total).
861	!-- Do it only, if profiles shall be plotted.
862	IF ( hom(nzb+1,2,58,0) /= 0.0 ) THEN
863
864	!$OMP DO
865	DO i = nxl, nxr
866	DO j = nys, nyn
867	DO k = nzb_s_inner(j,i)+1, nzt
868	!
869	!-- Subgrid horizontal heat fluxes u"pt", v"pt"
870	sums_l(k,58,tn) = sums_l(k,58,tn) - 0.5 * &
871	( kh(k,j,i) + kh(k,j,i-1) ) &
872	* ( pt(k,j,i-1) - pt(k,j,i) ) &
873	* ddx * rmask(j,i,sr)
874	sums_l(k,61,tn) = sums_l(k,61,tn) - 0.5 * &
875	( kh(k,j,i) + kh(k,j-1,i) ) &
876	* ( pt(k,j-1,i) - pt(k,j,i) ) &
877	* ddy * rmask(j,i,sr)
878	!
879	!-- Resolved horizontal heat fluxes upt, vpt
880	sums_l(k,59,tn) = sums_l(k,59,tn) + &
881	( u(k,j,i) - hom(k,1,1,sr) ) &
882	* 0.5 * ( pt(k,j,i-1) - hom(k,1,4,sr) + &
883	pt(k,j,i) - hom(k,1,4,sr) )
884	pts = 0.5 * ( pt(k,j-1,i) - hom(k,1,4,sr) + &
885	pt(k,j,i) - hom(k,1,4,sr) )
886	sums_l(k,62,tn) = sums_l(k,62,tn) + &
887	( v(k,j,i) - hom(k,1,2,sr) ) &
888	* 0.5 * ( pt(k,j-1,i) - hom(k,1,4,sr) + &
889	pt(k,j,i) - hom(k,1,4,sr) )
890	ENDDO
891	ENDDO
892	ENDDO
893	!
894	!-- Fluxes at the surface must be zero (e.g. due to the Prandtl-layer)
895	sums_l(nzb,58,tn) = 0.0
896	sums_l(nzb,59,tn) = 0.0
897	sums_l(nzb,60,tn) = 0.0
898	sums_l(nzb,61,tn) = 0.0
899	sums_l(nzb,62,tn) = 0.0
900	sums_l(nzb,63,tn) = 0.0
901
902	ENDIF
903
904	!
905	!-- Calculate the user-defined profiles
906	CALL user_statistics( 'profiles', sr, tn )
907	!$OMP END PARALLEL
908
909	!
910	!-- Summation of thread sums
911	IF ( threads_per_task > 1 ) THEN
912	DO i = 1, threads_per_task-1
913	sums_l(:,3,0) = sums_l(:,3,0) + sums_l(:,3,i)
914	sums_l(:,4:40,0) = sums_l(:,4:40,0) + sums_l(:,4:40,i)
915	sums_l(:,45:pr_palm,0) = sums_l(:,45:pr_palm,0) + &
916	sums_l(:,45:pr_palm,i)
917	IF ( max_pr_user > 0 ) THEN
918	sums_l(:,pr_palm+1:pr_palm+max_pr_user,0) = &
919	sums_l(:,pr_palm+1:pr_palm+max_pr_user,0) + &
920	sums_l(:,pr_palm+1:pr_palm+max_pr_user,i)
921	ENDIF
922	ENDDO
923	ENDIF
924
925	#if defined( __parallel )
926
927	!
928	!-- Compute total sum from local sums
929	IF ( collective_wait ) CALL MPI_BARRIER( comm2d, ierr )
930	CALL MPI_ALLREDUCE( sums_l(nzb,1,0), sums(nzb,1), ngp_sums, MPI_REAL, &
931	MPI_SUM, comm2d, ierr )
932	#else
933	sums = sums_l(:,:,0)
934	#endif
935
936	!
937	!-- Final values are obtained by division by the total number of grid points
938	!-- used for summation. After that store profiles.
939	!-- Profiles:
940	DO k = nzb, nzt+1
941	sums(k,3) = sums(k,3) / ngp_2dh(sr)
942	sums(k,8:11) = sums(k,8:11) / ngp_2dh_s_inner(k,sr)
943	sums(k,12:22) = sums(k,12:22) / ngp_2dh(sr)
944	sums(k,23:29) = sums(k,23:29) / ngp_2dh_s_inner(k,sr)
945	sums(k,30:32) = sums(k,30:32) / ngp_2dh(sr)
946	sums(k,33:34) = sums(k,33:34) / ngp_2dh_s_inner(k,sr)
947	sums(k,35:39) = sums(k,35:39) / ngp_2dh(sr)
948	sums(k,40) = sums(k,40) / ngp_2dh_s_inner(k,sr)
949	sums(k,45:53) = sums(k,45:53) / ngp_2dh(sr)
950	sums(k,54) = sums(k,54) / ngp_2dh_s_inner(k,sr)
951	sums(k,55:63) = sums(k,55:63) / ngp_2dh(sr)
952	sums(k,64) = sums(k,64) / ngp_2dh_s_inner(k,sr)
953	sums(k,65:69) = sums(k,65:69) / ngp_2dh(sr)
954	sums(k,70:pr_palm-2) = sums(k,70:pr_palm-2)/ ngp_2dh_s_inner(k,sr)
955	ENDDO
956
957	!-- Upstream-parts
958	sums(nzb:nzb+11,pr_palm-1) = sums(nzb:nzb+11,pr_palm-1) / ngp_3d(sr)
959	!-- u* and so on
960	!-- As sums(nzb:nzb+3,pr_palm) are full 2D arrays (us, usws, vsws, ts) whose
961	!-- size is always ( nx + 1 ) * ( ny + 1 ), defined at the first grid layer
962	!-- above the topography, they are being divided by ngp_2dh(sr)
963	sums(nzb:nzb+3,pr_palm) = sums(nzb:nzb+3,pr_palm) / &
964	ngp_2dh(sr)
965	sums(nzb+12,pr_palm) = sums(nzb+12,pr_palm) / & ! qs
966	ngp_2dh(sr)
967	!-- eges, e*
968	sums(nzb+4:nzb+5,pr_palm) = sums(nzb+4:nzb+5,pr_palm) / &
969	ngp_3d(sr)
970	!-- Old and new divergence
971	sums(nzb+9:nzb+10,pr_palm) = sums(nzb+9:nzb+10,pr_palm) / &
972	ngp_3d_inner(sr)
973
974	!-- User-defined profiles
975	IF ( max_pr_user > 0 ) THEN
976	DO k = nzb, nzt+1
977	sums(k,pr_palm+1:pr_palm+max_pr_user) = &
978	sums(k,pr_palm+1:pr_palm+max_pr_user) / &
979	ngp_2dh_s_inner(k,sr)
980	ENDDO
981	ENDIF
982	!
983	!-- Collect horizontal average in hom.
984	!-- Compute deduced averages (e.g. total heat flux)
985	hom(:,1,3,sr) = sums(:,3) ! w
986	hom(:,1,8,sr) = sums(:,8) ! e profiles 5-7 are initial profiles
987	hom(:,1,9,sr) = sums(:,9) ! km
988	hom(:,1,10,sr) = sums(:,10) ! kh
989	hom(:,1,11,sr) = sums(:,11) ! l
990	hom(:,1,12,sr) = sums(:,12) ! w"u"
991	hom(:,1,13,sr) = sums(:,13) ! wu
992	hom(:,1,14,sr) = sums(:,14) ! w"v"
993	hom(:,1,15,sr) = sums(:,15) ! wv
994	hom(:,1,16,sr) = sums(:,16) ! w"pt"
995	hom(:,1,17,sr) = sums(:,17) ! wpt
996	hom(:,1,18,sr) = sums(:,16) + sums(:,17) ! wpt
997	hom(:,1,19,sr) = sums(:,12) + sums(:,13) ! wu
998	hom(:,1,20,sr) = sums(:,14) + sums(:,15) ! wv
999	hom(:,1,21,sr) = sums(:,21) ! wptBC
1000	hom(:,1,22,sr) = sums(:,16) + sums(:,21) ! wptBC
1001	! profile 24 is initial profile (sa)
1002	! profiles 25-29 left empty for initial
1003	! profiles
1004	hom(:,1,30,sr) = sums(:,30) ! u*2
1005	hom(:,1,31,sr) = sums(:,31) ! v*2
1006	hom(:,1,32,sr) = sums(:,32) ! w*2
1007	hom(:,1,33,sr) = sums(:,33) ! pt*2
1008	hom(:,1,34,sr) = sums(:,34) ! e*
1009	hom(:,1,35,sr) = sums(:,35) ! w2pt
1010	hom(:,1,36,sr) = sums(:,36) ! wpt2
1011	hom(:,1,37,sr) = sums(:,37) ! we
1012	hom(:,1,38,sr) = sums(:,38) ! w*3
1013	hom(:,1,39,sr) = sums(:,38) / ( sums(:,32) + 1E-20 )**1.5 ! Sw
1014	hom(:,1,40,sr) = sums(:,40) ! p
1015	hom(:,1,45,sr) = sums(:,45) ! w"vpt"
1016	hom(:,1,46,sr) = sums(:,46) ! wvpt
1017	hom(:,1,47,sr) = sums(:,45) + sums(:,46) ! wvpt
1018	hom(:,1,48,sr) = sums(:,48) ! w"q" (w"qv")
1019	hom(:,1,49,sr) = sums(:,49) ! wq (wqv)
1020	hom(:,1,50,sr) = sums(:,48) + sums(:,49) ! wq (wqv)
1021	hom(:,1,51,sr) = sums(:,51) ! w"qv"
1022	hom(:,1,52,sr) = sums(:,52) ! wqv
1023	hom(:,1,53,sr) = sums(:,52) + sums(:,51) ! wq (wqv)
1024	hom(:,1,54,sr) = sums(:,54) ! ql
1025	hom(:,1,55,sr) = sums(:,55) ! wuu*/dz
1026	hom(:,1,56,sr) = sums(:,56) ! wp/dz
1027	hom(:,1,57,sr) = sums(:,57) ! ( w"e + w"p"/rho )/dz
1028	hom(:,1,58,sr) = sums(:,58) ! u"pt"
1029	hom(:,1,59,sr) = sums(:,59) ! upt
1030	hom(:,1,60,sr) = sums(:,58) + sums(:,59) ! upt_t
1031	hom(:,1,61,sr) = sums(:,61) ! v"pt"
1032	hom(:,1,62,sr) = sums(:,62) ! vpt
1033	hom(:,1,63,sr) = sums(:,61) + sums(:,62) ! vpt_t
1034	hom(:,1,64,sr) = sums(:,64) ! rho
1035	hom(:,1,65,sr) = sums(:,65) ! w"sa"
1036	hom(:,1,66,sr) = sums(:,66) ! wsa
1037	hom(:,1,67,sr) = sums(:,65) + sums(:,66) ! wsa
1038	hom(:,1,68,sr) = sums(:,68) ! wp
1039	hom(:,1,69,sr) = sums(:,69) ! w"e + w"p"/rho
1040	hom(:,1,70,sr) = sums(:,70) ! q*2
1041	hom(:,1,71,sr) = sums(:,71) ! prho
1042	hom(:,1,72,sr) = hyp * 1E-4 ! hyp in dbar
1043
1044	hom(:,1,pr_palm-1,sr) = sums(:,pr_palm-1)
1045	! upstream-parts u_x, u_y, u_z, v_x,
1046	! v_y, usw. (in last but one profile)
1047	hom(:,1,pr_palm,sr) = sums(:,pr_palm)
1048	! u, w'u', w'v', t (in last profile)
1049
1050	IF ( max_pr_user > 0 ) THEN ! user-defined profiles
1051	hom(:,1,pr_palm+1:pr_palm+max_pr_user,sr) = &
1052	sums(:,pr_palm+1:pr_palm+max_pr_user)
1053	ENDIF
1054
1055	!
1056	!-- Determine the boundary layer height using two different schemes.
1057	!-- First scheme: Starting from the Earth's (Ocean's) surface, look for the
1058	!-- first relative minimum (maximum) of the total heat flux.
1059	!-- The corresponding height is assumed as the boundary layer height, if it
1060	!-- is less than 1.5 times the height where the heat flux becomes negative
1061	!-- (positive) for the first time.
1062	z_i(1) = 0.0
1063	first = .TRUE.
1064
1065	IF ( ocean ) THEN
1066	DO k = nzt, nzb+1, -1
1067	IF ( first .AND. hom(k,1,18,sr) < 0.0 &
1068	.AND. abs(hom(k,1,18,sr)) > 1.0E-8) THEN
1069	first = .FALSE.
1070	height = zw(k)
1071	ENDIF
1072	IF ( hom(k,1,18,sr) < 0.0 .AND. &
1073	abs(hom(k,1,18,sr)) > 1.0E-8 .AND. &
1074	hom(k-1,1,18,sr) > hom(k,1,18,sr) ) THEN
1075	IF ( zw(k) < 1.5 * height ) THEN
1076	z_i(1) = zw(k)
1077	ELSE
1078	z_i(1) = height
1079	ENDIF
1080	EXIT
1081	ENDIF
1082	ENDDO
1083	ELSE
1084	DO k = nzb, nzt-1
1085	IF ( first .AND. hom(k,1,18,sr) < 0.0 &
1086	.AND. abs(hom(k,1,18,sr)) > 1.0E-8 ) THEN
1087	first = .FALSE.
1088	height = zw(k)
1089	ENDIF
1090	IF ( hom(k,1,18,sr) < 0.0 .AND. &
1091	abs(hom(k,1,18,sr)) > 1.0E-8 .AND. &
1092	hom(k+1,1,18,sr) > hom(k,1,18,sr) ) THEN
1093	IF ( zw(k) < 1.5 * height ) THEN
1094	z_i(1) = zw(k)
1095	ELSE
1096	z_i(1) = height
1097	ENDIF
1098	EXIT
1099	ENDIF
1100	ENDDO
1101	ENDIF
1102
1103	!
1104	!-- Second scheme: Gradient scheme from Sullivan et al. (1998), modified
1105	!-- by Uhlenbrock(2006). The boundary layer height is the height with the
1106	!-- maximal local temperature gradient: starting from the second (the last
1107	!-- but one) vertical gridpoint, the local gradient must be at least
1108	!-- 0.2K/100m and greater than the next four gradients.
1109	!-- WARNING: The threshold value of 0.2K/100m must be adjusted for the
1110	!-- ocean case!
1111	z_i(2) = 0.0
1112	DO k = nzb+1, nzt+1
1113	dptdz(k) = ( hom(k,1,4,sr) - hom(k-1,1,4,sr) ) * ddzu(k)
1114	ENDDO
1115	dptdz_threshold = 0.2 / 100.0
1116
1117	IF ( ocean ) THEN
1118	DO k = nzt+1, nzb+5, -1
1119	IF ( dptdz(k) > dptdz_threshold .AND. &
1120	dptdz(k) > dptdz(k-1) .AND. dptdz(k) > dptdz(k-2) .AND. &
1121	dptdz(k) > dptdz(k-3) .AND. dptdz(k) > dptdz(k-4) ) THEN
1122	z_i(2) = zw(k-1)
1123	EXIT
1124	ENDIF
1125	ENDDO
1126	ELSE
1127	DO k = nzb+1, nzt-3
1128	IF ( dptdz(k) > dptdz_threshold .AND. &
1129	dptdz(k) > dptdz(k+1) .AND. dptdz(k) > dptdz(k+2) .AND. &
1130	dptdz(k) > dptdz(k+3) .AND. dptdz(k) > dptdz(k+4) ) THEN
1131	z_i(2) = zw(k-1)
1132	EXIT
1133	ENDIF
1134	ENDDO
1135	ENDIF
1136
1137	hom(nzb+6,1,pr_palm,sr) = z_i(1)
1138	hom(nzb+7,1,pr_palm,sr) = z_i(2)
1139
1140	!
1141	!-- Computation of both the characteristic vertical velocity and
1142	!-- the characteristic convective boundary layer temperature.
1143	!-- The horizontal average at nzb+1 is input for the average temperature.
1144	IF ( hom(nzb,1,18,sr) > 0.0 .AND. abs(hom(nzb,1,18,sr)) > 1.0E-8 &
1145	.AND. z_i(1) /= 0.0 ) THEN
1146	hom(nzb+8,1,pr_palm,sr) = ( g / hom(nzb+1,1,4,sr) * &
1147	hom(nzb,1,18,sr) * &
1148	ABS( z_i(1) ) )**0.333333333
1149	!-- so far this only works if Prandtl layer is used
1150	hom(nzb+11,1,pr_palm,sr) = hom(nzb,1,16,sr) / hom(nzb+8,1,pr_palm,sr)
1151	ELSE
1152	hom(nzb+8,1,pr_palm,sr) = 0.0
1153	hom(nzb+11,1,pr_palm,sr) = 0.0
1154	ENDIF
1155
1156	!
1157	!-- Collect the time series quantities
1158	ts_value(1,sr) = hom(nzb+4,1,pr_palm,sr) ! E
1159	ts_value(2,sr) = hom(nzb+5,1,pr_palm,sr) ! E*
1160	ts_value(3,sr) = dt_3d
1161	ts_value(4,sr) = hom(nzb,1,pr_palm,sr) ! u*
1162	ts_value(5,sr) = hom(nzb+3,1,pr_palm,sr) ! th*
1163	ts_value(6,sr) = u_max
1164	ts_value(7,sr) = v_max
1165	ts_value(8,sr) = w_max
1166	ts_value(9,sr) = hom(nzb+10,1,pr_palm,sr) ! new divergence
1167	ts_value(10,sr) = hom(nzb+9,1,pr_palm,sr) ! old Divergence
1168	ts_value(11,sr) = hom(nzb+6,1,pr_palm,sr) ! z_i(1)
1169	ts_value(12,sr) = hom(nzb+7,1,pr_palm,sr) ! z_i(2)
1170	ts_value(13,sr) = hom(nzb+8,1,pr_palm,sr) ! w*
1171	ts_value(14,sr) = hom(nzb,1,16,sr) ! w'pt' at k=0
1172	ts_value(15,sr) = hom(nzb+1,1,16,sr) ! w'pt' at k=1
1173	ts_value(16,sr) = hom(nzb+1,1,18,sr) ! wpt at k=1
1174	ts_value(17,sr) = hom(nzb,1,4,sr) ! pt(0)
1175	ts_value(18,sr) = hom(nzb+1,1,4,sr) ! pt(zp)
1176	ts_value(19,sr) = hom(nzb+1,1,pr_palm,sr) ! u'w' at k=0
1177	ts_value(20,sr) = hom(nzb+2,1,pr_palm,sr) ! v'w' at k=0
1178	ts_value(21,sr) = hom(nzb,1,48,sr) ! w"q" at k=0
1179
1180	IF ( ts_value(5,sr) /= 0.0 ) THEN
1181	ts_value(22,sr) = ts_value(4,sr)**2 / &
1182	( kappa * g * ts_value(5,sr) / ts_value(18,sr) ) ! L
1183	ELSE
1184	ts_value(22,sr) = 10000.0
1185	ENDIF
1186
1187	ts_value(23,sr) = hom(nzb+12,1,pr_palm,sr) ! q*
1188	!
1189	!-- Calculate additional statistics provided by the user interface
1190	CALL user_statistics( 'time_series', sr, 0 )
1191
1192	ENDDO ! loop of the subregions
1193
1194	!
1195	!-- If required, sum up horizontal averages for subsequent time averaging
1196	IF ( do_sum ) THEN
1197	IF ( average_count_pr == 0 ) hom_sum = 0.0
1198	hom_sum = hom_sum + hom(:,1,:,:)
1199	average_count_pr = average_count_pr + 1
1200	do_sum = .FALSE.
1201	ENDIF
1202
1203	!
1204	!-- Set flag for other UPs (e.g. output routines, but also buoyancy).
1205	!-- This flag is reset after each time step in time_integration.
1206	flow_statistics_called = .TRUE.
1207
1208	CALL cpu_log( log_point(10), 'flow_statistics', 'stop' )
1209
1210
1211	END SUBROUTINE flow_statistics
1212
1213
1214

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