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source: palm/trunk/SOURCE/flow_statistics.f90 @ 623

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

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