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source: palm/trunk/SOURCE/flow_statistics.f90 @ 586

Last change on this file since 586 was 550, checked in by maronga, 14 years ago
bugfix: calculation of subgrid-scale flux at nzt for use_top_fluxes=.T.
Property svn:keywords set to `Id`
File size: 45.9 KB

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

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