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source: palm/trunk/SOURCE/flow_statistics.f90 @ 626

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

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