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source: palm/trunk/SOURCE/flow_statistics.f90 @ 673

Last change on this file since 673 was 673, checked in by suehring, 14 years ago
Right computation of the pressure using Runge-Kutta weighting coefficients. Consideration of the pressure gradient during the time integration removed. Removed bugfix concerning velocity variances.
Property svn:keywords set to `Id`
File size: 51.5 KB

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

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