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source: palm/trunk/SOURCE/flow_statistics.f90 @ 388

Last change on this file since 388 was 388, checked in by raasch, 15 years ago
in-situ AND potential density are calculated and used in the ocean version
Property svn:keywords set to `Id`
File size: 45.8 KB

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

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