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source: palm/trunk/SOURCE/flow_statistics.f90 @ 291

Last change on this file since 291 was 291, checked in by raasch, 15 years ago
changes for coupling with independent precursor runs; z_i calculation with Sullivan criterion
Property svn:keywords set to `Id`
File size: 45.3 KB

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1	SUBROUTINE flow_statistics
2
3	!------------------------------------------------------------------------------!
4	! Current revisions:
5	! -----------------
6	! Temperature gradient criterion for estimating the boundary layer height
7	! replaced by the gradient criterion of Sullivan et al. (1998).
8	! Output of messages replaced by message handling routine.
9	!
10	!
11	! Former revisions:
12	! -----------------
13	! $Id: flow_statistics.f90 291 2009-04-16 12:07:26Z raasch $
14	!
15	! 197 2008-09-16 15:29:03Z raasch
16	! Spline timeseries splptx etc. removed, timeseries w'u', w'v', w'q' (k=0)
17	! added,
18	! bugfix: divide sums(k,8) (e) and sums(k,34) (e*) by ngp_2dh_s_inner(k,sr)
19	! (like other scalars)
20	!
21	! 133 2007-11-20 10:10:53Z letzel
22	! Vertical profiles now based on nzb_s_inner; they are divided by
23	! ngp_2dh_s_inner (scalars, procucts of scalars) and ngp_2dh (staggered
24	! velocity components and their products, procucts of scalars and velocity
25	! components), respectively.
26	!
27	! 106 2007-08-16 14:30:26Z raasch
28	! Prescribed momentum fluxes at the top surface are used,
29	! profiles for wp and w"e are calculated
30	!
31	! 97 2007-06-21 08:23:15Z raasch
32	! Statistics for ocean version (salinity, density) added,
33	! calculation of z_i and Deardorff velocity scale adjusted to be used with
34	! the ocean version
35	!
36	! 87 2007-05-22 15:46:47Z raasch
37	! Two more arguments added to user_statistics, which is now also called for
38	! user-defined profiles,
39	! var_hom and var_sum renamed pr_palm
40	!
41	! 82 2007-04-16 15:40:52Z raasch
42	! Cpp-directive lcmuk changed to intel_openmp_bug
43	!
44	! 75 2007-03-22 09:54:05Z raasch
45	! Collection of time series quantities moved from routine flow_statistics to
46	! here, routine user_statistics is called for each statistic region,
47	! moisture renamed humidity
48	!
49	! 19 2007-02-23 04:53:48Z raasch
50	! fluxes at top modified (tswst, qswst)
51	!
52	! RCS Log replace by Id keyword, revision history cleaned up
53	!
54	! Revision 1.41 2006/08/04 14:37:50 raasch
55	! Error removed in non-parallel part (sums_l)
56	!
57	! Revision 1.1 1997/08/11 06:15:17 raasch
58	! Initial revision
59	!
60	!
61	! Description:
62	! ------------
63	! Compute average profiles and further average flow quantities for the different
64	! user-defined (sub-)regions. The region indexed 0 is the total model domain.
65	!
66	! NOTE: For simplicity, nzb_s_inner and nzb_diff_s_inner are being used as a
67	! ---- lower vertical index for k-loops for all variables, although strictly
68	! speaking the k-loops would have to be split up according to the staggered
69	! grid. However, this implies no error since staggered velocity components are
70	! zero at the walls and inside buildings.
71	!------------------------------------------------------------------------------!
72
73	USE arrays_3d
74	USE cloud_parameters
75	USE cpulog
76	USE grid_variables
77	USE indices
78	USE interfaces
79	USE pegrid
80	USE statistics
81	USE control_parameters
82
83	IMPLICIT NONE
84
85	INTEGER :: i, j, k, omp_get_thread_num, sr, tn
86	LOGICAL :: first
87	REAL :: dptdz_threshold, height, pts, sums_l_eper, sums_l_etot, ust, &
88	ust2, u2, vst, vst2, v2, w2, z_i(2)
89	REAL :: dptdz(nzb+1:nzt+1)
90	REAL :: sums_ll(nzb:nzt+1,2)
91
92
93	CALL cpu_log( log_point(10), 'flow_statistics', 'start' )
94
95	!
96	!-- To be on the safe side, check whether flow_statistics has already been
97	!-- called once after the current time step
98	IF ( flow_statistics_called ) THEN
99
100	message_string = 'flow_statistics is called two times within one ' // &
101	'timestep'
102	CALL message( 'flow_statistics', 'PA0190', 1, 2, 0, 6, 0 )
103
104	ENDIF
105
106	!
107	!-- Compute statistics for each (sub-)region
108	DO sr = 0, statistic_regions
109
110	!
111	!-- Initialize (local) summation array
112	sums_l = 0.0
113
114	!
115	!-- Store sums that have been computed in other subroutines in summation
116	!-- array
117	sums_l(:,11,:) = sums_l_l(:,sr,:) ! mixing length from diffusivities
118	!-- WARNING: next line still has to be adjusted for OpenMP
119	sums_l(:,21,0) = sums_wsts_bc_l(:,sr) ! heat flux from advec_s_bc
120	sums_l(nzb+9,pr_palm,0) = sums_divold_l(sr) ! old divergence from pres
121	sums_l(nzb+10,pr_palm,0) = sums_divnew_l(sr) ! new divergence from pres
122
123	!
124	!-- Horizontally averaged profiles of horizontal velocities and temperature.
125	!-- They must have been computed before, because they are already required
126	!-- for other horizontal averages.
127	tn = 0
128	!$OMP PARALLEL PRIVATE( i, j, k, tn )
129	#if defined( __intel_openmp_bug )
130	tn = omp_get_thread_num()
131	#else
132	!$ tn = omp_get_thread_num()
133	#endif
134
135	!$OMP DO
136	DO i = nxl, nxr
137	DO j = nys, nyn
138	DO k = nzb_s_inner(j,i), nzt+1
139	sums_l(k,1,tn) = sums_l(k,1,tn) + u(k,j,i) * rmask(j,i,sr)
140	sums_l(k,2,tn) = sums_l(k,2,tn) + v(k,j,i) * rmask(j,i,sr)
141	sums_l(k,4,tn) = sums_l(k,4,tn) + pt(k,j,i) * rmask(j,i,sr)
142	ENDDO
143	ENDDO
144	ENDDO
145
146	!
147	!-- Horizontally averaged profile of salinity
148	IF ( ocean ) THEN
149	!$OMP DO
150	DO i = nxl, nxr
151	DO j = nys, nyn
152	DO k = nzb_s_inner(j,i), nzt+1
153	sums_l(k,23,tn) = sums_l(k,23,tn) + &
154	sa(k,j,i) * rmask(j,i,sr)
155	ENDDO
156	ENDDO
157	ENDDO
158	ENDIF
159
160	!
161	!-- Horizontally averaged profiles of virtual potential temperature,
162	!-- total water content, specific humidity and liquid water potential
163	!-- temperature
164	IF ( humidity ) THEN
165	!$OMP DO
166	DO i = nxl, nxr
167	DO j = nys, nyn
168	DO k = nzb_s_inner(j,i), nzt+1
169	sums_l(k,44,tn) = sums_l(k,44,tn) + &
170	vpt(k,j,i) * rmask(j,i,sr)
171	sums_l(k,41,tn) = sums_l(k,41,tn) + &
172	q(k,j,i) * rmask(j,i,sr)
173	ENDDO
174	ENDDO
175	ENDDO
176	IF ( cloud_physics ) THEN
177	!$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,42,tn) = sums_l(k,42,tn) + &
182	( q(k,j,i) - ql(k,j,i) ) * rmask(j,i,sr)
183	sums_l(k,43,tn) = sums_l(k,43,tn) + ( &
184	pt(k,j,i) + l_d_cppt_d_t(k) ql(k,j,i) &
185	) * rmask(j,i,sr)
186	ENDDO
187	ENDDO
188	ENDDO
189	ENDIF
190	ENDIF
191
192	!
193	!-- Horizontally averaged profiles of passive scalar
194	IF ( passive_scalar ) THEN
195	!$OMP DO
196	DO i = nxl, nxr
197	DO j = nys, nyn
198	DO k = nzb_s_inner(j,i), nzt+1
199	sums_l(k,41,tn) = sums_l(k,41,tn) + q(k,j,i) * rmask(j,i,sr)
200	ENDDO
201	ENDDO
202	ENDDO
203	ENDIF
204	!$OMP END PARALLEL
205
206	!
207	!-- Summation of thread sums
208	IF ( threads_per_task > 1 ) THEN
209	DO i = 1, threads_per_task-1
210	sums_l(:,1,0) = sums_l(:,1,0) + sums_l(:,1,i)
211	sums_l(:,2,0) = sums_l(:,2,0) + sums_l(:,2,i)
212	sums_l(:,4,0) = sums_l(:,4,0) + sums_l(:,4,i)
213	IF ( ocean ) THEN
214	sums_l(:,23,0) = sums_l(:,23,0) + sums_l(:,23,i)
215	ENDIF
216	IF ( humidity ) THEN
217	sums_l(:,41,0) = sums_l(:,41,0) + sums_l(:,41,i)
218	sums_l(:,44,0) = sums_l(:,44,0) + sums_l(:,44,i)
219	IF ( cloud_physics ) THEN
220	sums_l(:,42,0) = sums_l(:,42,0) + sums_l(:,42,i)
221	sums_l(:,43,0) = sums_l(:,43,0) + sums_l(:,43,i)
222	ENDIF
223	ENDIF
224	IF ( passive_scalar ) THEN
225	sums_l(:,41,0) = sums_l(:,41,0) + sums_l(:,41,i)
226	ENDIF
227	ENDDO
228	ENDIF
229
230	#if defined( __parallel )
231	!
232	!-- Compute total sum from local sums
233	CALL MPI_ALLREDUCE( sums_l(nzb,1,0), sums(nzb,1), nzt+2-nzb, MPI_REAL, &
234	MPI_SUM, comm2d, ierr )
235	CALL MPI_ALLREDUCE( sums_l(nzb,2,0), sums(nzb,2), nzt+2-nzb, MPI_REAL, &
236	MPI_SUM, comm2d, ierr )
237	CALL MPI_ALLREDUCE( sums_l(nzb,4,0), sums(nzb,4), nzt+2-nzb, MPI_REAL, &
238	MPI_SUM, comm2d, ierr )
239	IF ( ocean ) THEN
240	CALL MPI_ALLREDUCE( sums_l(nzb,23,0), sums(nzb,23), nzt+2-nzb, &
241	MPI_REAL, MPI_SUM, comm2d, ierr )
242	ENDIF
243	IF ( humidity ) THEN
244	CALL MPI_ALLREDUCE( sums_l(nzb,44,0), sums(nzb,44), nzt+2-nzb, &
245	MPI_REAL, MPI_SUM, comm2d, ierr )
246	CALL MPI_ALLREDUCE( sums_l(nzb,41,0), sums(nzb,41), nzt+2-nzb, &
247	MPI_REAL, MPI_SUM, comm2d, ierr )
248	IF ( cloud_physics ) THEN
249	CALL MPI_ALLREDUCE( sums_l(nzb,42,0), sums(nzb,42), nzt+2-nzb, &
250	MPI_REAL, MPI_SUM, comm2d, ierr )
251	CALL MPI_ALLREDUCE( sums_l(nzb,43,0), sums(nzb,43), nzt+2-nzb, &
252	MPI_REAL, MPI_SUM, comm2d, ierr )
253	ENDIF
254	ENDIF
255
256	IF ( passive_scalar ) THEN
257	CALL MPI_ALLREDUCE( sums_l(nzb,41,0), sums(nzb,41), nzt+2-nzb, &
258	MPI_REAL, MPI_SUM, comm2d, ierr )
259	ENDIF
260	#else
261	sums(:,1) = sums_l(:,1,0)
262	sums(:,2) = sums_l(:,2,0)
263	sums(:,4) = sums_l(:,4,0)
264	IF ( ocean ) sums(:,23) = sums_l(:,23,0)
265	IF ( humidity ) THEN
266	sums(:,44) = sums_l(:,44,0)
267	sums(:,41) = sums_l(:,41,0)
268	IF ( cloud_physics ) THEN
269	sums(:,42) = sums_l(:,42,0)
270	sums(:,43) = sums_l(:,43,0)
271	ENDIF
272	ENDIF
273	IF ( passive_scalar ) sums(:,41) = sums_l(:,41,0)
274	#endif
275
276	!
277	!-- Final values are obtained by division by the total number of grid points
278	!-- used for summation. After that store profiles.
279	sums(:,1) = sums(:,1) / ngp_2dh(sr)
280	sums(:,2) = sums(:,2) / ngp_2dh(sr)
281	sums(:,4) = sums(:,4) / ngp_2dh_s_inner(:,sr)
282	hom(:,1,1,sr) = sums(:,1) ! u
283	hom(:,1,2,sr) = sums(:,2) ! v
284	hom(:,1,4,sr) = sums(:,4) ! pt
285
286	!
287	!-- Salinity
288	IF ( ocean ) THEN
289	sums(:,23) = sums(:,23) / ngp_2dh_s_inner(:,sr)
290	hom(:,1,23,sr) = sums(:,23) ! sa
291	ENDIF
292
293	!
294	!-- Humidity and cloud parameters
295	IF ( humidity ) THEN
296	sums(:,44) = sums(:,44) / ngp_2dh_s_inner(:,sr)
297	sums(:,41) = sums(:,41) / ngp_2dh_s_inner(:,sr)
298	hom(:,1,44,sr) = sums(:,44) ! vpt
299	hom(:,1,41,sr) = sums(:,41) ! qv (q)
300	IF ( cloud_physics ) THEN
301	sums(:,42) = sums(:,42) / ngp_2dh_s_inner(:,sr)
302	sums(:,43) = sums(:,43) / ngp_2dh_s_inner(:,sr)
303	hom(:,1,42,sr) = sums(:,42) ! qv
304	hom(:,1,43,sr) = sums(:,43) ! pt
305	ENDIF
306	ENDIF
307
308	!
309	!-- Passive scalar
310	IF ( passive_scalar ) hom(:,1,41,sr) = sums(:,41) / &
311	ngp_2dh_s_inner(:,sr) ! s (q)
312
313	!
314	!-- Horizontally averaged profiles of the remaining prognostic variables,
315	!-- variances, the total and the perturbation energy (single values in last
316	!-- column of sums_l) and some diagnostic quantities.
317	!-- NOTE: for simplicity, nzb_s_inner is used below, although strictly
318	!-- ---- speaking the following k-loop would have to be split up and
319	!-- rearranged according to the staggered grid.
320	!-- However, this implies no error since staggered velocity components
321	!-- are zero at the walls and inside buildings.
322	tn = 0
323	#if defined( __intel_openmp_bug )
324	!$OMP PARALLEL PRIVATE( i, j, k, pts, sums_ll, sums_l_eper, sums_l_etot, &
325	!$OMP tn, ust, ust2, u2, vst, vst2, v2, w2 )
326	tn = omp_get_thread_num()
327	#else
328	!$OMP PARALLEL PRIVATE( i, j, k, pts, sums_ll, sums_l_eper, sums_l_etot, tn, ust, ust2, u2, vst, vst2, v2, w2 )
329	!$ tn = omp_get_thread_num()
330	#endif
331	!$OMP DO
332	DO i = nxl, nxr
333	DO j = nys, nyn
334	sums_l_etot = 0.0
335	sums_l_eper = 0.0
336	DO k = nzb_s_inner(j,i), nzt+1
337	u2 = u(k,j,i)**2
338	v2 = v(k,j,i)**2
339	w2 = w(k,j,i)**2
340	ust2 = ( u(k,j,i) - hom(k,1,1,sr) )**2
341	vst2 = ( v(k,j,i) - hom(k,1,2,sr) )**2
342	!
343	!-- Prognostic and diagnostic variables
344	sums_l(k,3,tn) = sums_l(k,3,tn) + w(k,j,i) * rmask(j,i,sr)
345	sums_l(k,8,tn) = sums_l(k,8,tn) + e(k,j,i) * rmask(j,i,sr)
346	sums_l(k,9,tn) = sums_l(k,9,tn) + km(k,j,i) * rmask(j,i,sr)
347	sums_l(k,10,tn) = sums_l(k,10,tn) + kh(k,j,i) * rmask(j,i,sr)
348	sums_l(k,40,tn) = sums_l(k,40,tn) + p(k,j,i)
349
350	!
351	!-- Variances
352	sums_l(k,30,tn) = sums_l(k,30,tn) + ust2 * rmask(j,i,sr)
353	sums_l(k,31,tn) = sums_l(k,31,tn) + vst2 * rmask(j,i,sr)
354	sums_l(k,32,tn) = sums_l(k,32,tn) + w2 * rmask(j,i,sr)
355	sums_l(k,33,tn) = sums_l(k,33,tn) + &
356	( pt(k,j,i)-hom(k,1,4,sr) )*2 rmask(j,i,sr)
357	!
358	!-- Higher moments
359	!-- (Computation of the skewness of w further below)
360	sums_l(k,38,tn) = sums_l(k,38,tn) + w(k,j,i) * w2 * &
361	rmask(j,i,sr)
362	!
363	!-- Perturbation energy
364	sums_l(k,34,tn) = sums_l(k,34,tn) + 0.5 * ( ust2 + vst2 + w2 ) &
365	* rmask(j,i,sr)
366	sums_l_etot = sums_l_etot + &
367	0.5 * ( u2 + v2 + w2 ) * rmask(j,i,sr)
368	sums_l_eper = sums_l_eper + &
369	0.5 * ( ust2+vst2+w2 ) * rmask(j,i,sr)
370	ENDDO
371	!
372	!-- Total and perturbation energy for the total domain (being
373	!-- collected in the last column of sums_l). Summation of these
374	!-- quantities is seperated from the previous loop in order to
375	!-- allow vectorization of that loop.
376	sums_l(nzb+4,pr_palm,tn) = sums_l(nzb+4,pr_palm,tn) + sums_l_etot
377	sums_l(nzb+5,pr_palm,tn) = sums_l(nzb+5,pr_palm,tn) + sums_l_eper
378	!
379	!-- 2D-arrays (being collected in the last column of sums_l)
380	sums_l(nzb,pr_palm,tn) = sums_l(nzb,pr_palm,tn) + &
381	us(j,i) * rmask(j,i,sr)
382	sums_l(nzb+1,pr_palm,tn) = sums_l(nzb+1,pr_palm,tn) + &
383	usws(j,i) * rmask(j,i,sr)
384	sums_l(nzb+2,pr_palm,tn) = sums_l(nzb+2,pr_palm,tn) + &
385	vsws(j,i) * rmask(j,i,sr)
386	sums_l(nzb+3,pr_palm,tn) = sums_l(nzb+3,pr_palm,tn) + &
387	ts(j,i) * rmask(j,i,sr)
388	IF ( humidity ) THEN
389	sums_l(nzb+12,pr_palm,tn) = sums_l(nzb+12,pr_palm,tn) + &
390	qs(j,i) * rmask(j,i,sr)
391	ENDIF
392	ENDDO
393	ENDDO
394
395	!
396	!-- Horizontally averaged profiles of the vertical fluxes
397	!$OMP DO
398	DO i = nxl, nxr
399	DO j = nys, nyn
400	!
401	!-- Subgridscale fluxes (without Prandtl layer from k=nzb,
402	!-- oterwise from k=nzb+1)
403	!-- NOTE: for simplicity, nzb_diff_s_inner is used below, although
404	!-- ---- strictly speaking the following k-loop would have to be
405	!-- split up according to the staggered grid.
406	!-- However, this implies no error since staggered velocity
407	!-- components are zero at the walls and inside buildings.
408
409	DO k = nzb_diff_s_inner(j,i)-1, nzt_diff
410	!
411	!-- Momentum flux w"u"
412	sums_l(k,12,tn) = sums_l(k,12,tn) - 0.25 * ( &
413	km(k,j,i)+km(k+1,j,i)+km(k,j,i-1)+km(k+1,j,i-1) &
414	) * ( &
415	( u(k+1,j,i) - u(k,j,i) ) * ddzu(k+1) &
416	+ ( w(k,j,i) - w(k,j,i-1) ) * ddx &
417	) * rmask(j,i,sr)
418	!
419	!-- Momentum flux w"v"
420	sums_l(k,14,tn) = sums_l(k,14,tn) - 0.25 * ( &
421	km(k,j,i)+km(k+1,j,i)+km(k,j-1,i)+km(k+1,j-1,i) &
422	) * ( &
423	( v(k+1,j,i) - v(k,j,i) ) * ddzu(k+1) &
424	+ ( w(k,j,i) - w(k,j-1,i) ) * ddy &
425	) * rmask(j,i,sr)
426	!
427	!-- Heat flux w"pt"
428	sums_l(k,16,tn) = sums_l(k,16,tn) &
429	- 0.5 * ( kh(k,j,i) + kh(k+1,j,i) ) &
430	* ( pt(k+1,j,i) - pt(k,j,i) ) &
431	* ddzu(k+1) * rmask(j,i,sr)
432
433
434	!
435	!-- Salinity flux w"sa"
436	IF ( ocean ) THEN
437	sums_l(k,65,tn) = sums_l(k,65,tn) &
438	- 0.5 * ( kh(k,j,i) + kh(k+1,j,i) ) &
439	* ( sa(k+1,j,i) - sa(k,j,i) ) &
440	* ddzu(k+1) * rmask(j,i,sr)
441	ENDIF
442
443	!
444	!-- Buoyancy flux, water flux (humidity flux) w"q"
445	IF ( humidity ) THEN
446	sums_l(k,45,tn) = sums_l(k,45,tn) &
447	- 0.5 * ( kh(k,j,i) + kh(k+1,j,i) ) &
448	* ( vpt(k+1,j,i) - vpt(k,j,i) ) &
449	* ddzu(k+1) * rmask(j,i,sr)
450	sums_l(k,48,tn) = sums_l(k,48,tn) &
451	- 0.5 * ( kh(k,j,i) + kh(k+1,j,i) ) &
452	* ( q(k+1,j,i) - q(k,j,i) ) &
453	* ddzu(k+1) * rmask(j,i,sr)
454	IF ( cloud_physics ) THEN
455	sums_l(k,51,tn) = sums_l(k,51,tn) &
456	- 0.5 * ( kh(k,j,i) + kh(k+1,j,i) ) &
457	* ( ( q(k+1,j,i) - ql(k+1,j,i) )&
458	- ( q(k,j,i) - ql(k,j,i) ) ) &
459	* ddzu(k+1) * rmask(j,i,sr)
460	ENDIF
461	ENDIF
462
463	!
464	!-- Passive scalar flux
465	IF ( passive_scalar ) THEN
466	sums_l(k,48,tn) = sums_l(k,48,tn) &
467	- 0.5 * ( kh(k,j,i) + kh(k+1,j,i) ) &
468	* ( q(k+1,j,i) - q(k,j,i) ) &
469	* ddzu(k+1) * rmask(j,i,sr)
470	ENDIF
471
472	ENDDO
473
474	!
475	!-- Subgridscale fluxes in the Prandtl layer
476	IF ( use_surface_fluxes ) THEN
477	sums_l(nzb,12,tn) = sums_l(nzb,12,tn) + &
478	usws(j,i) * rmask(j,i,sr) ! w"u"
479	sums_l(nzb,14,tn) = sums_l(nzb,14,tn) + &
480	vsws(j,i) * rmask(j,i,sr) ! w"v"
481	sums_l(nzb,16,tn) = sums_l(nzb,16,tn) + &
482	shf(j,i) * rmask(j,i,sr) ! w"pt"
483	sums_l(nzb,58,tn) = sums_l(nzb,58,tn) + &
484	0.0 * rmask(j,i,sr) ! u"pt"
485	sums_l(nzb,61,tn) = sums_l(nzb,61,tn) + &
486	0.0 * rmask(j,i,sr) ! v"pt"
487	IF ( ocean ) THEN
488	sums_l(nzb,65,tn) = sums_l(nzb,65,tn) + &
489	saswsb(j,i) * rmask(j,i,sr) ! w"sa"
490	ENDIF
491	IF ( humidity ) THEN
492	sums_l(nzb,48,tn) = sums_l(nzb,48,tn) + &
493	qsws(j,i) * rmask(j,i,sr) ! w"q" (w"qv")
494	IF ( cloud_physics ) THEN
495	sums_l(nzb,45,tn) = sums_l(nzb,45,tn) + ( &
496	( 1.0 + 0.61 * q(nzb,j,i) ) * &
497	shf(j,i) + 0.61 * pt(nzb,j,i) * &
498	qsws(j,i) &
499	)
500	!
501	!-- Formula does not work if ql(nzb) /= 0.0
502	sums_l(nzb,51,tn) = sums_l(nzb,51,tn) + & ! w"q" (w"qv")
503	qsws(j,i) * rmask(j,i,sr)
504	ENDIF
505	ENDIF
506	IF ( passive_scalar ) THEN
507	sums_l(nzb,48,tn) = sums_l(nzb,48,tn) + &
508	qsws(j,i) * rmask(j,i,sr) ! w"q" (w"qv")
509	ENDIF
510	ENDIF
511
512	!
513	!-- Subgridscale fluxes at the top surface
514	IF ( use_top_fluxes ) THEN
515	sums_l(nzt,12,tn) = sums_l(nzt,12,tn) + &
516	uswst(j,i) * rmask(j,i,sr) ! w"u"
517	sums_l(nzt,14,tn) = sums_l(nzt,14,tn) + &
518	vswst(j,i) * rmask(j,i,sr) ! w"v"
519	sums_l(nzt,16,tn) = sums_l(nzt,16,tn) + &
520	tswst(j,i) * rmask(j,i,sr) ! w"pt"
521	sums_l(nzt,58,tn) = sums_l(nzt,58,tn) + &
522	0.0 * rmask(j,i,sr) ! u"pt"
523	sums_l(nzt,61,tn) = sums_l(nzt,61,tn) + &
524	0.0 * rmask(j,i,sr) ! v"pt"
525	IF ( ocean ) THEN
526	sums_l(nzt,65,tn) = sums_l(nzt,65,tn) + &
527	saswst(j,i) * rmask(j,i,sr) ! w"sa"
528	ENDIF
529	IF ( humidity ) THEN
530	sums_l(nzt,48,tn) = sums_l(nzt,48,tn) + &
531	qswst(j,i) * rmask(j,i,sr) ! w"q" (w"qv")
532	IF ( cloud_physics ) THEN
533	sums_l(nzt,45,tn) = sums_l(nzt,45,tn) + ( &
534	( 1.0 + 0.61 * q(nzt,j,i) ) * &
535	tswst(j,i) + 0.61 * pt(nzt,j,i) * &
536	qsws(j,i) &
537	)
538	!
539	!-- Formula does not work if ql(nzb) /= 0.0
540	sums_l(nzt,51,tn) = sums_l(nzt,51,tn) + & ! w"q" (w"qv")
541	qswst(j,i) * rmask(j,i,sr)
542	ENDIF
543	ENDIF
544	IF ( passive_scalar ) THEN
545	sums_l(nzt,48,tn) = sums_l(nzt,48,tn) + &
546	qswst(j,i) * rmask(j,i,sr) ! w"q" (w"qv")
547	ENDIF
548	ENDIF
549
550	!
551	!-- Resolved fluxes (can be computed for all horizontal points)
552	!-- NOTE: for simplicity, nzb_s_inner is used below, although strictly
553	!-- ---- speaking the following k-loop would have to be split up and
554	!-- rearranged according to the staggered grid.
555	DO k = nzb_s_inner(j,i), nzt
556	ust = 0.5 * ( u(k,j,i) - hom(k,1,1,sr) + &
557	u(k+1,j,i) - hom(k+1,1,1,sr) )
558	vst = 0.5 * ( v(k,j,i) - hom(k,1,2,sr) + &
559	v(k+1,j,i) - hom(k+1,1,2,sr) )
560	pts = 0.5 * ( pt(k,j,i) - hom(k,1,4,sr) + &
561	pt(k+1,j,i) - hom(k+1,1,4,sr) )
562	!
563	!-- Momentum flux wu
564	sums_l(k,13,tn) = sums_l(k,13,tn) + 0.5 * &
565	( w(k,j,i-1) + w(k,j,i) ) &
566	* ust * rmask(j,i,sr)
567	!
568	!-- Momentum flux wv
569	sums_l(k,15,tn) = sums_l(k,15,tn) + 0.5 * &
570	( w(k,j-1,i) + w(k,j,i) ) &
571	* vst * rmask(j,i,sr)
572	!
573	!-- Heat flux wpt
574	!-- The following formula (comment line, not executed) does not
575	!-- work if applied to subregions
576	! sums_l(k,17,tn) = sums_l(k,17,tn) + 0.5 * &
577	! ( pt(k,j,i)+pt(k+1,j,i) ) &
578	! * w(k,j,i) * rmask(j,i,sr)
579	sums_l(k,17,tn) = sums_l(k,17,tn) + pts * w(k,j,i) * &
580	rmask(j,i,sr)
581	!
582	!-- Higher moments
583	sums_l(k,35,tn) = sums_l(k,35,tn) + pts * w(k,j,i)*2 &
584	rmask(j,i,sr)
585	sums_l(k,36,tn) = sums_l(k,36,tn) + pts*2 w(k,j,i) * &
586	rmask(j,i,sr)
587
588	!
589	!-- Salinity flux and density (density does not belong to here,
590	!-- but so far there is no other suitable place to calculate)
591	IF ( ocean ) THEN
592	pts = 0.5 * ( sa(k,j,i) - hom(k,1,23,sr) + &
593	sa(k+1,j,i) - hom(k+1,1,23,sr) )
594	sums_l(k,66,tn) = sums_l(k,66,tn) + pts * w(k,j,i) * &
595	rmask(j,i,sr)
596	sums_l(k,64,tn) = sums_l(k,64,tn) + rho(k,j,i) * &
597	rmask(j,i,sr)
598	ENDIF
599
600	!
601	!-- Buoyancy flux, water flux, humidity flux and liquid water
602	!-- content
603	IF ( humidity ) THEN
604	pts = 0.5 * ( vpt(k,j,i) - hom(k,1,44,sr) + &
605	vpt(k+1,j,i) - hom(k+1,1,44,sr) )
606	sums_l(k,46,tn) = sums_l(k,46,tn) + pts * w(k,j,i) * &
607	rmask(j,i,sr)
608	pts = 0.5 * ( q(k,j,i) - hom(k,1,41,sr) + &
609	q(k+1,j,i) - hom(k+1,1,41,sr) )
610	sums_l(k,49,tn) = sums_l(k,49,tn) + pts * w(k,j,i) * &
611	rmask(j,i,sr)
612	IF ( cloud_physics .OR. cloud_droplets ) THEN
613	pts = 0.5 * &
614	( ( q(k,j,i) - ql(k,j,i) ) - hom(k,1,42,sr) &
615	+ ( q(k+1,j,i) - ql(k+1,j,i) ) - hom(k+1,1,42,sr) )
616	sums_l(k,52,tn) = sums_l(k,52,tn) + pts * w(k,j,i) * &
617	rmask(j,i,sr)
618	sums_l(k,54,tn) = sums_l(k,54,tn) + ql(k,j,i) * &
619	rmask(j,i,sr)
620	ENDIF
621	ENDIF
622
623	!
624	!-- Passive scalar flux
625	IF ( passive_scalar ) THEN
626	pts = 0.5 * ( q(k,j,i) - hom(k,1,41,sr) + &
627	q(k+1,j,i) - hom(k+1,1,41,sr) )
628	sums_l(k,49,tn) = sums_l(k,49,tn) + pts * w(k,j,i) * &
629	rmask(j,i,sr)
630	ENDIF
631
632	!
633	!-- Energy flux we
634	sums_l(k,37,tn) = sums_l(k,37,tn) + w(k,j,i) * 0.5 * &
635	( ust2 + vst2 + w(k,j,i)**2 )&
636	* rmask(j,i,sr)
637
638	ENDDO
639	ENDDO
640	ENDDO
641
642	!
643	!-- Density at top follows Neumann condition
644	IF ( ocean ) sums_l(nzt+1,64,tn) = sums_l(nzt,64,tn)
645
646	!
647	!-- Divergence of vertical flux of resolved scale energy and pressure
648	!-- fluctuations as well as flux of pressure fluctuation itself (68).
649	!-- First calculate the products, then the divergence.
650	!-- Calculation is time consuming. Do it only, if profiles shall be plotted.
651	IF ( hom(nzb+1,2,55,0) /= 0.0 .OR. hom(nzb+1,2,68,0) /= 0.0 ) THEN
652
653	sums_ll = 0.0 ! local array
654
655	!$OMP DO
656	DO i = nxl, nxr
657	DO j = nys, nyn
658	DO k = nzb_s_inner(j,i)+1, nzt
659
660	sums_ll(k,1) = sums_ll(k,1) + 0.5 * w(k,j,i) * ( &
661	( 0.25 * ( u(k,j,i)+u(k+1,j,i)+u(k,j,i+1)+u(k+1,j,i+1) &
662	- 2.0 * ( hom(k,1,1,sr) + hom(k+1,1,1,sr) ) &
663	) )**2 &
664	+ ( 0.25 * ( v(k,j,i)+v(k+1,j,i)+v(k,j+1,i)+v(k+1,j+1,i) &
665	- 2.0 * ( hom(k,1,2,sr) + hom(k+1,1,2,sr) ) &
666	) )**2 &
667	+ w(k,j,i)**2 )
668
669	sums_ll(k,2) = sums_ll(k,2) + 0.5 * w(k,j,i) &
670	* ( p(k,j,i) + p(k+1,j,i) )
671
672	ENDDO
673	ENDDO
674	ENDDO
675	sums_ll(0,1) = 0.0 ! because w is zero at the bottom
676	sums_ll(nzt+1,1) = 0.0
677	sums_ll(0,2) = 0.0
678	sums_ll(nzt+1,2) = 0.0
679
680	DO k = nzb_s_inner(j,i)+1, nzt
681	sums_l(k,55,tn) = ( sums_ll(k,1) - sums_ll(k-1,1) ) * ddzw(k)
682	sums_l(k,56,tn) = ( sums_ll(k,2) - sums_ll(k-1,2) ) * ddzw(k)
683	sums_l(k,68,tn) = sums_ll(k,2)
684	ENDDO
685	sums_l(nzb,55,tn) = sums_l(nzb+1,55,tn)
686	sums_l(nzb,56,tn) = sums_l(nzb+1,56,tn)
687	sums_l(nzb,68,tn) = 0.0 ! because w* = 0 at nzb
688
689	ENDIF
690
691	!
692	!-- Divergence of vertical flux of SGS TKE and the flux itself (69)
693	IF ( hom(nzb+1,2,57,0) /= 0.0 .OR. hom(nzb+1,2,69,0) /= 0.0 ) THEN
694
695	!$OMP DO
696	DO i = nxl, nxr
697	DO j = nys, nyn
698	DO k = nzb_s_inner(j,i)+1, nzt
699
700	sums_l(k,57,tn) = sums_l(k,57,tn) - 0.5 * ( &
701	(km(k,j,i)+km(k+1,j,i)) * (e(k+1,j,i)-e(k,j,i)) * ddzu(k+1) &
702	- (km(k-1,j,i)+km(k,j,i)) * (e(k,j,i)-e(k-1,j,i)) * ddzu(k) &
703	) * ddzw(k)
704
705	sums_l(k,69,tn) = sums_l(k,69,tn) - 0.5 * ( &
706	(km(k,j,i)+km(k+1,j,i)) * (e(k+1,j,i)-e(k,j,i)) * ddzu(k+1) &
707	)
708
709	ENDDO
710	ENDDO
711	ENDDO
712	sums_l(nzb,57,tn) = sums_l(nzb+1,57,tn)
713	sums_l(nzb,69,tn) = sums_l(nzb+1,69,tn)
714
715	ENDIF
716
717	!
718	!-- Horizontal heat fluxes (subgrid, resolved, total).
719	!-- Do it only, if profiles shall be plotted.
720	IF ( hom(nzb+1,2,58,0) /= 0.0 ) THEN
721
722	!$OMP DO
723	DO i = nxl, nxr
724	DO j = nys, nyn
725	DO k = nzb_s_inner(j,i)+1, nzt
726	!
727	!-- Subgrid horizontal heat fluxes u"pt", v"pt"
728	sums_l(k,58,tn) = sums_l(k,58,tn) - 0.5 * &
729	( kh(k,j,i) + kh(k,j,i-1) ) &
730	* ( pt(k,j,i-1) - pt(k,j,i) ) &
731	* ddx * rmask(j,i,sr)
732	sums_l(k,61,tn) = sums_l(k,61,tn) - 0.5 * &
733	( kh(k,j,i) + kh(k,j-1,i) ) &
734	* ( pt(k,j-1,i) - pt(k,j,i) ) &
735	* ddy * rmask(j,i,sr)
736	!
737	!-- Resolved horizontal heat fluxes upt, vpt
738	sums_l(k,59,tn) = sums_l(k,59,tn) + &
739	( u(k,j,i) - hom(k,1,1,sr) ) &
740	* 0.5 * ( pt(k,j,i-1) - hom(k,1,4,sr) + &
741	pt(k,j,i) - hom(k,1,4,sr) )
742	pts = 0.5 * ( pt(k,j-1,i) - hom(k,1,4,sr) + &
743	pt(k,j,i) - hom(k,1,4,sr) )
744	sums_l(k,62,tn) = sums_l(k,62,tn) + &
745	( v(k,j,i) - hom(k,1,2,sr) ) &
746	* 0.5 * ( pt(k,j-1,i) - hom(k,1,4,sr) + &
747	pt(k,j,i) - hom(k,1,4,sr) )
748	ENDDO
749	ENDDO
750	ENDDO
751	!
752	!-- Fluxes at the surface must be zero (e.g. due to the Prandtl-layer)
753	sums_l(nzb,58,tn) = 0.0
754	sums_l(nzb,59,tn) = 0.0
755	sums_l(nzb,60,tn) = 0.0
756	sums_l(nzb,61,tn) = 0.0
757	sums_l(nzb,62,tn) = 0.0
758	sums_l(nzb,63,tn) = 0.0
759
760	ENDIF
761
762	!
763	!-- Calculate the user-defined profiles
764	CALL user_statistics( 'profiles', sr, tn )
765	!$OMP END PARALLEL
766
767	!
768	!-- Summation of thread sums
769	IF ( threads_per_task > 1 ) THEN
770	DO i = 1, threads_per_task-1
771	sums_l(:,3,0) = sums_l(:,3,0) + sums_l(:,3,i)
772	sums_l(:,4:40,0) = sums_l(:,4:40,0) + sums_l(:,4:40,i)
773	sums_l(:,45:pr_palm,0) = sums_l(:,45:pr_palm,0) + &
774	sums_l(:,45:pr_palm,i)
775	IF ( max_pr_user > 0 ) THEN
776	sums_l(:,pr_palm+1:pr_palm+max_pr_user,0) = &
777	sums_l(:,pr_palm+1:pr_palm+max_pr_user,0) + &
778	sums_l(:,pr_palm+1:pr_palm+max_pr_user,i)
779	ENDIF
780	ENDDO
781	ENDIF
782
783	#if defined( __parallel )
784	!
785	!-- Compute total sum from local sums
786	CALL MPI_ALLREDUCE( sums_l(nzb,1,0), sums(nzb,1), ngp_sums, MPI_REAL, &
787	MPI_SUM, comm2d, ierr )
788	#else
789	sums = sums_l(:,:,0)
790	#endif
791
792	!
793	!-- Final values are obtained by division by the total number of grid points
794	!-- used for summation. After that store profiles.
795	!-- Profiles:
796	DO k = nzb, nzt+1
797	sums(k,3) = sums(k,3) / ngp_2dh(sr)
798	sums(k,8:11) = sums(k,8:11) / ngp_2dh_s_inner(k,sr)
799	sums(k,12:22) = sums(k,12:22) / ngp_2dh(sr)
800	sums(k,23:29) = sums(k,23:29) / ngp_2dh_s_inner(k,sr)
801	sums(k,30:32) = sums(k,30:32) / ngp_2dh(sr)
802	sums(k,33:34) = sums(k,33:34) / ngp_2dh_s_inner(k,sr)
803	sums(k,35:39) = sums(k,35:39) / ngp_2dh(sr)
804	sums(k,40) = sums(k,40) / ngp_2dh_s_inner(k,sr)
805	sums(k,45:53) = sums(k,45:53) / ngp_2dh(sr)
806	sums(k,54) = sums(k,54) / ngp_2dh_s_inner(k,sr)
807	sums(k,55:63) = sums(k,55:63) / ngp_2dh(sr)
808	sums(k,64) = sums(k,64) / ngp_2dh_s_inner(k,sr)
809	sums(k,65:69) = sums(k,65:69) / ngp_2dh(sr)
810	sums(k,70:pr_palm-2) = sums(k,70:pr_palm-2)/ ngp_2dh_s_inner(k,sr)
811	ENDDO
812	!-- Upstream-parts
813	sums(nzb:nzb+11,pr_palm-1) = sums(nzb:nzb+11,pr_palm-1) / ngp_3d(sr)
814	!-- u* and so on
815	!-- As sums(nzb:nzb+3,pr_palm) are full 2D arrays (us, usws, vsws, ts) whose
816	!-- size is always ( nx + 1 ) * ( ny + 1 ), defined at the first grid layer
817	!-- above the topography, they are being divided by ngp_2dh(sr)
818	sums(nzb:nzb+3,pr_palm) = sums(nzb:nzb+3,pr_palm) / &
819	ngp_2dh(sr)
820	sums(nzb+12,pr_palm) = sums(nzb+12,pr_palm) / & ! qs
821	ngp_2dh(sr)
822	!-- eges, e*
823	sums(nzb+4:nzb+5,pr_palm) = sums(nzb+4:nzb+5,pr_palm) / &
824	ngp_3d(sr)
825	!-- Old and new divergence
826	sums(nzb+9:nzb+10,pr_palm) = sums(nzb+9:nzb+10,pr_palm) / &
827	ngp_3d_inner(sr)
828
829	!-- User-defined profiles
830	IF ( max_pr_user > 0 ) THEN
831	DO k = nzb, nzt+1
832	sums(k,pr_palm+1:pr_palm+max_pr_user) = &
833	sums(k,pr_palm+1:pr_palm+max_pr_user) / &
834	ngp_2dh_s_inner(k,sr)
835	ENDDO
836	ENDIF
837
838	!
839	!-- Collect horizontal average in hom.
840	!-- Compute deduced averages (e.g. total heat flux)
841	hom(:,1,3,sr) = sums(:,3) ! w
842	hom(:,1,8,sr) = sums(:,8) ! e profiles 5-7 are initial profiles
843	hom(:,1,9,sr) = sums(:,9) ! km
844	hom(:,1,10,sr) = sums(:,10) ! kh
845	hom(:,1,11,sr) = sums(:,11) ! l
846	hom(:,1,12,sr) = sums(:,12) ! w"u"
847	hom(:,1,13,sr) = sums(:,13) ! wu
848	hom(:,1,14,sr) = sums(:,14) ! w"v"
849	hom(:,1,15,sr) = sums(:,15) ! wv
850	hom(:,1,16,sr) = sums(:,16) ! w"pt"
851	hom(:,1,17,sr) = sums(:,17) ! wpt
852	hom(:,1,18,sr) = sums(:,16) + sums(:,17) ! wpt
853	hom(:,1,19,sr) = sums(:,12) + sums(:,13) ! wu
854	hom(:,1,20,sr) = sums(:,14) + sums(:,15) ! wv
855	hom(:,1,21,sr) = sums(:,21) ! wptBC
856	hom(:,1,22,sr) = sums(:,16) + sums(:,21) ! wptBC
857	! profile 24 is initial profile (sa)
858	! profiles 25-29 left empty for initial
859	! profiles
860	hom(:,1,30,sr) = sums(:,30) ! u*2
861	hom(:,1,31,sr) = sums(:,31) ! v*2
862	hom(:,1,32,sr) = sums(:,32) ! w*2
863	hom(:,1,33,sr) = sums(:,33) ! pt*2
864	hom(:,1,34,sr) = sums(:,34) ! e*
865	hom(:,1,35,sr) = sums(:,35) ! w2pt
866	hom(:,1,36,sr) = sums(:,36) ! wpt2
867	hom(:,1,37,sr) = sums(:,37) ! we
868	hom(:,1,38,sr) = sums(:,38) ! w*3
869	hom(:,1,39,sr) = sums(:,38) / ( sums(:,32) + 1E-20 )**1.5 ! Sw
870	hom(:,1,40,sr) = sums(:,40) ! p
871	hom(:,1,45,sr) = sums(:,45) ! w"q"
872	hom(:,1,46,sr) = sums(:,46) ! wvpt
873	hom(:,1,47,sr) = sums(:,45) + sums(:,46) ! wvpt
874	hom(:,1,48,sr) = sums(:,48) ! w"q" (w"qv")
875	hom(:,1,49,sr) = sums(:,49) ! wq (wqv)
876	hom(:,1,50,sr) = sums(:,48) + sums(:,49) ! wq (wqv)
877	hom(:,1,51,sr) = sums(:,51) ! w"qv"
878	hom(:,1,52,sr) = sums(:,52) ! wqv
879	hom(:,1,53,sr) = sums(:,52) + sums(:,51) ! wq (wqv)
880	hom(:,1,54,sr) = sums(:,54) ! ql
881	hom(:,1,55,sr) = sums(:,55) ! wuu*/dz
882	hom(:,1,56,sr) = sums(:,56) ! wp/dz
883	hom(:,1,57,sr) = sums(:,57) ! ( w"e + w"p"/rho )/dz
884	hom(:,1,58,sr) = sums(:,58) ! u"pt"
885	hom(:,1,59,sr) = sums(:,59) ! upt
886	hom(:,1,60,sr) = sums(:,58) + sums(:,59) ! upt_t
887	hom(:,1,61,sr) = sums(:,61) ! v"pt"
888	hom(:,1,62,sr) = sums(:,62) ! vpt
889	hom(:,1,63,sr) = sums(:,61) + sums(:,62) ! vpt_t
890	hom(:,1,64,sr) = sums(:,64) ! rho
891	hom(:,1,65,sr) = sums(:,65) ! w"sa"
892	hom(:,1,66,sr) = sums(:,66) ! wsa
893	hom(:,1,67,sr) = sums(:,65) + sums(:,66) ! wsa
894	hom(:,1,68,sr) = sums(:,68) ! wp
895	hom(:,1,69,sr) = sums(:,69) ! w"e + w"p"/rho
896	hom(:,1,70,sr) = sums(:,70) ! q*2
897
898	hom(:,1,pr_palm-1,sr) = sums(:,pr_palm-1)
899	! upstream-parts u_x, u_y, u_z, v_x,
900	! v_y, usw. (in last but one profile)
901	hom(:,1,pr_palm,sr) = sums(:,pr_palm)
902	! u, w'u', w'v', t (in last profile)
903
904	IF ( max_pr_user > 0 ) THEN ! user-defined profiles
905	hom(:,1,pr_palm+1:pr_palm+max_pr_user,sr) = &
906	sums(:,pr_palm+1:pr_palm+max_pr_user)
907	ENDIF
908
909	!
910	!-- Determine the boundary layer height using two different schemes.
911	!-- First scheme: Starting from the Earth's (Ocean's) surface, look for the
912	!-- first relative minimum (maximum) of the total heat flux.
913	!-- The corresponding height is assumed as the boundary layer height, if it
914	!-- is less than 1.5 times the height where the heat flux becomes negative
915	!-- (positive) for the first time.
916	!-- NOTE: This criterion is still capable of improving!
917	z_i(1) = 0.0
918	first = .TRUE.
919	IF ( ocean ) THEN
920	DO k = nzt, nzb+1, -1
921	IF ( first .AND. hom(k,1,18,sr) < 0.0 ) THEN
922	first = .FALSE.
923	height = zw(k)
924	ENDIF
925	IF ( hom(k,1,18,sr) < 0.0 .AND. &
926	hom(k-1,1,18,sr) > hom(k,1,18,sr) ) THEN
927	IF ( zw(k) < 1.5 * height ) THEN
928	z_i(1) = zw(k)
929	ELSE
930	z_i(1) = height
931	ENDIF
932	EXIT
933	ENDIF
934	ENDDO
935	ELSE
936	DO k = nzb, nzt-1
937	IF ( first .AND. hom(k,1,18,sr) < 0.0 ) THEN
938	first = .FALSE.
939	height = zw(k)
940	ENDIF
941	IF ( hom(k,1,18,sr) < 0.0 .AND. &
942	hom(k+1,1,18,sr) > hom(k,1,18,sr) ) THEN
943	IF ( zw(k) < 1.5 * height ) THEN
944	z_i(1) = zw(k)
945	ELSE
946	z_i(1) = height
947	ENDIF
948	EXIT
949	ENDIF
950	ENDDO
951	ENDIF
952
953	!
954	!-- Second scheme: Gradient scheme from Sullivan et al. (1998), modified
955	!-- by Uhlenbrock(2006). The boundary layer height is the height with the
956	!-- maximal local temperature gradient: starting from the second (the last
957	!-- but one) vertical gridpoint, the local gradient must be at least
958	!-- 0.2K/100m and greater than the next four gradients.
959	!-- WARNING: The threshold value of 0.2K/100m must be adjusted for the
960	!-- ocean case!
961	z_i(2) = 0.0
962	DO k = nzb+1, nzt+1
963	dptdz(k) = ( hom(k,1,4,sr) - hom(k-1,1,4,sr) ) * ddzu(k)
964	ENDDO
965	dptdz_threshold = 0.2 / 100.0
966
967	IF ( ocean ) THEN
968	DO k = nzt+1, nzb+5, -1
969	IF ( dptdz(k) > dptdz_threshold .AND. &
970	dptdz(k) > dptdz(k-1) .AND. dptdz(k) > dptdz(k-2) .AND. &
971	dptdz(k) > dptdz(k-3) .AND. dptdz(k) > dptdz(k-4) ) THEN
972	z_i(2) = zw(k-1)
973	EXIT
974	ENDIF
975	ENDDO
976	ELSE
977	DO k = nzb+1, nzt-3
978	IF ( dptdz(k) > dptdz_threshold .AND. &
979	dptdz(k) > dptdz(k+1) .AND. dptdz(k) > dptdz(k+2) .AND. &
980	dptdz(k) > dptdz(k+3) .AND. dptdz(k) > dptdz(k+4) ) THEN
981	z_i(2) = zw(k-1)
982	EXIT
983	ENDIF
984	ENDDO
985	ENDIF
986
987	hom(nzb+6,1,pr_palm,sr) = z_i(1)
988	hom(nzb+7,1,pr_palm,sr) = z_i(2)
989
990	!
991	!-- Computation of both the characteristic vertical velocity and
992	!-- the characteristic convective boundary layer temperature.
993	!-- The horizontal average at nzb+1 is input for the average temperature.
994	IF ( hom(nzb,1,18,sr) > 0.0 .AND. z_i(1) /= 0.0 ) THEN
995	hom(nzb+8,1,pr_palm,sr) = ( g / hom(nzb+1,1,4,sr) * &
996	hom(nzb,1,18,sr) * &
997	ABS( z_i(1) ) )**0.333333333
998	!-- so far this only works if Prandtl layer is used
999	hom(nzb+11,1,pr_palm,sr) = hom(nzb,1,16,sr) / hom(nzb+8,1,pr_palm,sr)
1000	ELSE
1001	hom(nzb+8,1,pr_palm,sr) = 0.0
1002	hom(nzb+11,1,pr_palm,sr) = 0.0
1003	ENDIF
1004
1005	!
1006	!-- Collect the time series quantities
1007	ts_value(1,sr) = hom(nzb+4,1,pr_palm,sr) ! E
1008	ts_value(2,sr) = hom(nzb+5,1,pr_palm,sr) ! E*
1009	ts_value(3,sr) = dt_3d
1010	ts_value(4,sr) = hom(nzb,1,pr_palm,sr) ! u*
1011	ts_value(5,sr) = hom(nzb+3,1,pr_palm,sr) ! th*
1012	ts_value(6,sr) = u_max
1013	ts_value(7,sr) = v_max
1014	ts_value(8,sr) = w_max
1015	ts_value(9,sr) = hom(nzb+10,1,pr_palm,sr) ! new divergence
1016	ts_value(10,sr) = hom(nzb+9,1,pr_palm,sr) ! old Divergence
1017	ts_value(11,sr) = hom(nzb+6,1,pr_palm,sr) ! z_i(1)
1018	ts_value(12,sr) = hom(nzb+7,1,pr_palm,sr) ! z_i(2)
1019	ts_value(13,sr) = hom(nzb+8,1,pr_palm,sr) ! w*
1020	ts_value(14,sr) = hom(nzb,1,16,sr) ! w'pt' at k=0
1021	ts_value(15,sr) = hom(nzb+1,1,16,sr) ! w'pt' at k=1
1022	ts_value(16,sr) = hom(nzb+1,1,18,sr) ! wpt at k=1
1023	ts_value(17,sr) = hom(nzb,1,4,sr) ! pt(0)
1024	ts_value(18,sr) = hom(nzb+1,1,4,sr) ! pt(zp)
1025	ts_value(19,sr) = hom(nzb+1,1,pr_palm,sr) ! u'w' at k=0
1026	ts_value(20,sr) = hom(nzb+2,1,pr_palm,sr) ! v'w' at k=0
1027	ts_value(21,sr) = hom(nzb+12,1,pr_palm,sr) ! q*
1028
1029	IF ( ts_value(5,sr) /= 0.0 ) THEN
1030	ts_value(22,sr) = ts_value(4,sr)**2 / &
1031	( kappa * g * ts_value(5,sr) / ts_value(18,sr) ) ! L
1032	ELSE
1033	ts_value(22,sr) = 10000.0
1034	ENDIF
1035
1036	!
1037	!-- Calculate additional statistics provided by the user interface
1038	CALL user_statistics( 'time_series', sr, 0 )
1039
1040	ENDDO ! loop of the subregions
1041
1042	!
1043	!-- If required, sum up horizontal averages for subsequent time averaging
1044	IF ( do_sum ) THEN
1045	IF ( average_count_pr == 0 ) hom_sum = 0.0
1046	hom_sum = hom_sum + hom(:,1,:,:)
1047	average_count_pr = average_count_pr + 1
1048	do_sum = .FALSE.
1049	ENDIF
1050
1051	!
1052	!-- Set flag for other UPs (e.g. output routines, but also buoyancy).
1053	!-- This flag is reset after each time step in time_integration.
1054	flow_statistics_called = .TRUE.
1055
1056	CALL cpu_log( log_point(10), 'flow_statistics', 'stop' )
1057
1058
1059	END SUBROUTINE flow_statistics
1060
1061
1062

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