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flow_statistics.f90 @ 90

Last change on this file since 90 was 90, checked in by raasch, 17 years ago

New:
---
Calculation and output of user-defined profiles. New &userpar parameters data_output_pr_user and max_pr_user.

check_parameters, flow_statistics, modules, parin, read_var_list, user_interface, write_var_list

Changed:

Division through dt_3d replaced by multiplication of the inverse. For performance optimisation, this is done in the loop calculating the divergence instead of using a seperate loop. (pres.f90) var_hom and var_sum renamed pr_palm.

data_output_profiles, flow_statistics, init_3d_model, modules, parin, pres, read_var_list, run_control, time_integration

Errors:

Bugfix: work_fft*_vec removed from some PRIVATE-declarations (poisfft).

Bugfix: field_chr renamed field_char (user_interface).

Bugfix: output of use_upstream_for_tke (header).

header, poisfft, user_interface

Property svn:keywords set to Id

File size: 38.0 KB

Line
1	SUBROUTINE flow_statistics
2
3	!------------------------------------------------------------------------------!
4	! Actual revisions:
5	! -----------------
6	!
7	!
8	! Former revisions:
9	! -----------------
10	! $Id: flow_statistics.f90 90 2007-05-30 09:18:47Z raasch $
11	!
12	! 87 2007-05-22 15:46:47Z raasch
13	! Two more arguments added to user_statistics, which is now also called for
14	! user-defined profiles,
15	! var_hom and var_sum renamed pr_palm
16	!
17	! 82 2007-04-16 15:40:52Z raasch
18	! Cpp-directive lcmuk changed to intel_openmp_bug
19	!
20	! 75 2007-03-22 09:54:05Z raasch
21	! Collection of time series quantities moved from routine flow_statistics to
22	! here, routine user_statistics is called for each statistic region,
23	! moisture renamed humidity
24	!
25	! 19 2007-02-23 04:53:48Z raasch
26	! fluxes at top modified (tswst, qswst)
27	!
28	! RCS Log replace by Id keyword, revision history cleaned up
29	!
30	! Revision 1.41 2006/08/04 14:37:50 raasch
31	! Error removed in non-parallel part (sums_l)
32	!
33	! Revision 1.1 1997/08/11 06:15:17 raasch
34	! Initial revision
35	!
36	!
37	! Description:
38	! ------------
39	! Compute average profiles and further average flow quantities for the different
40	! user-defined (sub-)regions. The region indexed 0 is the total model domain.
41	!
42	! NOTE: For simplicity, nzb_s_outer and nzb_diff_s_outer are being used as a
43	! ---- lower vertical index for k-loops for all variables so that regardless
44	! of the variable and its respective staggered grid always the same number of
45	! grid points is used for 2D averages. The disadvantage: depending on the
46	! variable, up to one grid layer adjacent to the (vertical walls of the)
47	! topography is missed out by this simplification.
48	!------------------------------------------------------------------------------!
49
50	USE arrays_3d
51	USE cloud_parameters
52	USE cpulog
53	USE grid_variables
54	USE indices
55	USE interfaces
56	USE pegrid
57	USE statistics
58	USE control_parameters
59
60	IMPLICIT NONE
61
62	INTEGER :: i, j, k, omp_get_thread_num, sr, tn
63	LOGICAL :: first
64	REAL :: height, pts, sums_l_eper, sums_l_etot, ust, ust2, u2, vst, &
65	vst2, v2, w2, z_i(2)
66	REAL :: sums_ll(nzb:nzt+1,2)
67
68
69	CALL cpu_log( log_point(10), 'flow_statistics', 'start' )
70
71	!
72	!-- To be on the safe side, check whether flow_statistics has already been
73	!-- called once after the current time step
74	IF ( flow_statistics_called ) THEN
75	IF ( myid == 0 ) PRINT*, '+++ WARNING: flow_statistics is called two', &
76	' times within one timestep'
77	CALL local_stop
78	ENDIF
79
80	!
81	!-- Compute statistics for each (sub-)region
82	DO sr = 0, statistic_regions
83
84	!
85	!-- Initialize (local) summation array
86	sums_l = 0.0
87
88	!
89	!-- Store sums that have been computed in other subroutines in summation
90	!-- array
91	sums_l(:,11,:) = sums_l_l(:,sr,:) ! mixing length from diffusivities
92	!-- WARNING: next line still has to be adjusted for OpenMP
93	sums_l(:,21,0) = sums_wsts_bc_l(:,sr) ! heat flux from advec_s_bc
94	sums_l(nzb+9,pr_palm,0) = sums_divold_l(sr) ! old divergence from pres
95	sums_l(nzb+10,pr_palm,0) = sums_divnew_l(sr) ! new divergence from pres
96	!-- WARNING: next four lines still may have to be adjusted for OpenMP
97	sums_l(nzb:nzb+2,pr_palm-1,0) = sums_up_fraction_l(1,1:3,sr)! upstream
98	sums_l(nzb+3:nzb+5,pr_palm-1,0) = sums_up_fraction_l(2,1:3,sr)! parts
99	sums_l(nzb+6:nzb+8,pr_palm-1,0) = sums_up_fraction_l(3,1:3,sr)! from
100	sums_l(nzb+9:nzb+11,pr_palm-1,0) = sums_up_fraction_l(4,1:3,sr)! spline
101
102	!
103	!-- Horizontally averaged profiles of horizontal velocities and temperature.
104	!-- They must have been computed before, because they are already required
105	!-- for other horizontal averages.
106	tn = 0
107	!$OMP PARALLEL PRIVATE( i, j, k, tn )
108	#if defined( __intel_openmp_bug )
109	tn = omp_get_thread_num()
110	#else
111	!$ tn = omp_get_thread_num()
112	#endif
113
114	!$OMP DO
115	DO i = nxl, nxr
116	DO j = nys, nyn
117	DO k = nzb_s_outer(j,i), nzt+1
118	sums_l(k,1,tn) = sums_l(k,1,tn) + u(k,j,i) * rmask(j,i,sr)
119	sums_l(k,2,tn) = sums_l(k,2,tn) + v(k,j,i) * rmask(j,i,sr)
120	sums_l(k,4,tn) = sums_l(k,4,tn) + pt(k,j,i) * rmask(j,i,sr)
121	ENDDO
122	ENDDO
123	ENDDO
124
125	!
126	!-- Horizontally averaged profiles of virtual potential temperature,
127	!-- total water content, specific humidity and liquid water potential
128	!-- temperature
129	IF ( humidity ) THEN
130	!$OMP DO
131	DO i = nxl, nxr
132	DO j = nys, nyn
133	DO k = nzb_s_outer(j,i), nzt+1
134	sums_l(k,44,tn) = sums_l(k,44,tn) + &
135	vpt(k,j,i) * rmask(j,i,sr)
136	sums_l(k,41,tn) = sums_l(k,41,tn) + &
137	q(k,j,i) * rmask(j,i,sr)
138	ENDDO
139	ENDDO
140	ENDDO
141	IF ( cloud_physics ) THEN
142	!$OMP DO
143	DO i = nxl, nxr
144	DO j = nys, nyn
145	DO k = nzb_s_outer(j,i), nzt+1
146	sums_l(k,42,tn) = sums_l(k,42,tn) + &
147	( q(k,j,i) - ql(k,j,i) ) * rmask(j,i,sr)
148	sums_l(k,43,tn) = sums_l(k,43,tn) + ( &
149	pt(k,j,i) + l_d_cppt_d_t(k) ql(k,j,i) &
150	) * rmask(j,i,sr)
151	ENDDO
152	ENDDO
153	ENDDO
154	ENDIF
155	ENDIF
156
157	!
158	!-- Horizontally averaged profiles of passive scalar
159	IF ( passive_scalar ) THEN
160	!$OMP DO
161	DO i = nxl, nxr
162	DO j = nys, nyn
163	DO k = nzb_s_outer(j,i), nzt+1
164	sums_l(k,41,tn) = sums_l(k,41,tn) + q(k,j,i) * rmask(j,i,sr)
165	ENDDO
166	ENDDO
167	ENDDO
168	ENDIF
169	!$OMP END PARALLEL
170
171	!
172	!-- Summation of thread sums
173	IF ( threads_per_task > 1 ) THEN
174	DO i = 1, threads_per_task-1
175	sums_l(:,1,0) = sums_l(:,1,0) + sums_l(:,1,i)
176	sums_l(:,2,0) = sums_l(:,2,0) + sums_l(:,2,i)
177	sums_l(:,4,0) = sums_l(:,4,0) + sums_l(:,4,i)
178	IF ( humidity ) THEN
179	sums_l(:,41,0) = sums_l(:,41,0) + sums_l(:,41,i)
180	sums_l(:,44,0) = sums_l(:,44,0) + sums_l(:,44,i)
181	IF ( cloud_physics ) THEN
182	sums_l(:,42,0) = sums_l(:,42,0) + sums_l(:,42,i)
183	sums_l(:,43,0) = sums_l(:,43,0) + sums_l(:,43,i)
184	ENDIF
185	ENDIF
186	IF ( passive_scalar ) THEN
187	sums_l(:,41,0) = sums_l(:,41,0) + sums_l(:,41,i)
188	ENDIF
189	ENDDO
190	ENDIF
191
192	#if defined( __parallel )
193	!
194	!-- Compute total sum from local sums
195	CALL MPI_ALLREDUCE( sums_l(nzb,1,0), sums(nzb,1), nzt+2-nzb, MPI_REAL, &
196	MPI_SUM, comm2d, ierr )
197	CALL MPI_ALLREDUCE( sums_l(nzb,2,0), sums(nzb,2), nzt+2-nzb, MPI_REAL, &
198	MPI_SUM, comm2d, ierr )
199	CALL MPI_ALLREDUCE( sums_l(nzb,4,0), sums(nzb,4), nzt+2-nzb, MPI_REAL, &
200	MPI_SUM, comm2d, ierr )
201	IF ( humidity ) THEN
202	CALL MPI_ALLREDUCE( sums_l(nzb,44,0), sums(nzb,44), nzt+2-nzb, &
203	MPI_REAL, MPI_SUM, comm2d, ierr )
204	CALL MPI_ALLREDUCE( sums_l(nzb,41,0), sums(nzb,41), nzt+2-nzb, &
205	MPI_REAL, MPI_SUM, comm2d, ierr )
206	IF ( cloud_physics ) THEN
207	CALL MPI_ALLREDUCE( sums_l(nzb,42,0), sums(nzb,42), nzt+2-nzb, &
208	MPI_REAL, MPI_SUM, comm2d, ierr )
209	CALL MPI_ALLREDUCE( sums_l(nzb,43,0), sums(nzb,43), nzt+2-nzb, &
210	MPI_REAL, MPI_SUM, comm2d, ierr )
211	ENDIF
212	ENDIF
213
214	IF ( passive_scalar ) THEN
215	CALL MPI_ALLREDUCE( sums_l(nzb,41,0), sums(nzb,41), nzt+2-nzb, &
216	MPI_REAL, MPI_SUM, comm2d, ierr )
217	ENDIF
218	#else
219	sums(:,1) = sums_l(:,1,0)
220	sums(:,2) = sums_l(:,2,0)
221	sums(:,4) = sums_l(:,4,0)
222	IF ( humidity ) THEN
223	sums(:,44) = sums_l(:,44,0)
224	sums(:,41) = sums_l(:,41,0)
225	IF ( cloud_physics ) THEN
226	sums(:,42) = sums_l(:,42,0)
227	sums(:,43) = sums_l(:,43,0)
228	ENDIF
229	ENDIF
230	IF ( passive_scalar ) sums(:,41) = sums_l(:,41,0)
231	#endif
232
233	!
234	!-- Final values are obtained by division by the total number of grid points
235	!-- used for summation. After that store profiles.
236	sums(:,1) = sums(:,1) / ngp_2dh_outer(:,sr)
237	sums(:,2) = sums(:,2) / ngp_2dh_outer(:,sr)
238	sums(:,4) = sums(:,4) / ngp_2dh_outer(:,sr)
239	hom(:,1,1,sr) = sums(:,1) ! u
240	hom(:,1,2,sr) = sums(:,2) ! v
241	hom(:,1,4,sr) = sums(:,4) ! pt
242
243	!
244	!-- Humidity and cloud parameters
245	IF ( humidity ) THEN
246	sums(:,44) = sums(:,44) / ngp_2dh_outer(:,sr)
247	sums(:,41) = sums(:,41) / ngp_2dh_outer(:,sr)
248	hom(:,1,44,sr) = sums(:,44) ! vpt
249	hom(:,1,41,sr) = sums(:,41) ! qv (q)
250	IF ( cloud_physics ) THEN
251	sums(:,42) = sums(:,42) / ngp_2dh_outer(:,sr)
252	sums(:,43) = sums(:,43) / ngp_2dh_outer(:,sr)
253	hom(:,1,42,sr) = sums(:,42) ! qv
254	hom(:,1,43,sr) = sums(:,43) ! pt
255	ENDIF
256	ENDIF
257
258	!
259	!-- Passive scalar
260	IF ( passive_scalar ) hom(:,1,41,sr) = sums(:,41) / ngp_2dh_outer(:,sr)
261
262	!
263	!-- Horizontally averaged profiles of the remaining prognostic variables,
264	!-- variances, the total and the perturbation energy (single values in last
265	!-- column of sums_l) and some diagnostic quantities.
266	!-- NOTE: for simplicity, nzb_s_outer is used below, although strictly
267	!-- ---- speaking the following k-loop would have to be split up and
268	!-- rearranged according to the staggered grid.
269	tn = 0
270	#if defined( __intel_openmp_bug )
271	!$OMP PARALLEL PRIVATE( i, j, k, pts, sums_ll, sums_l_eper, sums_l_etot, &
272	!$OMP tn, ust, ust2, u2, vst, vst2, v2, w2 )
273	tn = omp_get_thread_num()
274	#else
275	!$OMP PARALLEL PRIVATE( i, j, k, pts, sums_ll, sums_l_eper, sums_l_etot, tn, ust, ust2, u2, vst, vst2, v2, w2 )
276	!$ tn = omp_get_thread_num()
277	#endif
278	!$OMP DO
279	DO i = nxl, nxr
280	DO j = nys, nyn
281	sums_l_etot = 0.0
282	sums_l_eper = 0.0
283	DO k = nzb_s_outer(j,i), nzt+1
284	u2 = u(k,j,i)**2
285	v2 = v(k,j,i)**2
286	w2 = w(k,j,i)**2
287	ust2 = ( u(k,j,i) - hom(k,1,1,sr) )**2
288	vst2 = ( v(k,j,i) - hom(k,1,2,sr) )**2
289	!
290	!-- Prognostic and diagnostic variables
291	sums_l(k,3,tn) = sums_l(k,3,tn) + w(k,j,i) * rmask(j,i,sr)
292	sums_l(k,8,tn) = sums_l(k,8,tn) + e(k,j,i) * rmask(j,i,sr)
293	sums_l(k,9,tn) = sums_l(k,9,tn) + km(k,j,i) * rmask(j,i,sr)
294	sums_l(k,10,tn) = sums_l(k,10,tn) + kh(k,j,i) * rmask(j,i,sr)
295	sums_l(k,40,tn) = sums_l(k,40,tn) + p(k,j,i)
296
297	!
298	!-- Variances
299	sums_l(k,30,tn) = sums_l(k,30,tn) + ust2 * rmask(j,i,sr)
300	sums_l(k,31,tn) = sums_l(k,31,tn) + vst2 * rmask(j,i,sr)
301	sums_l(k,32,tn) = sums_l(k,32,tn) + w2 * rmask(j,i,sr)
302	sums_l(k,33,tn) = sums_l(k,33,tn) + &
303	( pt(k,j,i)-hom(k,1,4,sr) )*2 rmask(j,i,sr)
304	!
305	!-- Higher moments
306	!-- (Computation of the skewness of w further below)
307	sums_l(k,38,tn) = sums_l(k,38,tn) + w(k,j,i) * w2 * &
308	rmask(j,i,sr)
309	!
310	!-- Perturbation energy
311	sums_l(k,34,tn) = sums_l(k,34,tn) + 0.5 * ( ust2 + vst2 + w2 ) &
312	* rmask(j,i,sr)
313	sums_l_etot = sums_l_etot + &
314	0.5 * ( u2 + v2 + w2 ) * rmask(j,i,sr)
315	sums_l_eper = sums_l_eper + &
316	0.5 * ( ust2+vst2+w2 ) * rmask(j,i,sr)
317	ENDDO
318	!
319	!-- Total and perturbation energy for the total domain (being
320	!-- collected in the last column of sums_l). Summation of these
321	!-- quantities is seperated from the previous loop in order to
322	!-- allow vectorization of that loop.
323	sums_l(nzb+4,pr_palm,tn) = sums_l(nzb+4,pr_palm,tn) + sums_l_etot
324	sums_l(nzb+5,pr_palm,tn) = sums_l(nzb+5,pr_palm,tn) + sums_l_eper
325	!
326	!-- 2D-arrays (being collected in the last column of sums_l)
327	sums_l(nzb,pr_palm,tn) = sums_l(nzb,pr_palm,tn) + &
328	us(j,i) * rmask(j,i,sr)
329	sums_l(nzb+1,pr_palm,tn) = sums_l(nzb+1,pr_palm,tn) + &
330	usws(j,i) * rmask(j,i,sr)
331	sums_l(nzb+2,pr_palm,tn) = sums_l(nzb+2,pr_palm,tn) + &
332	vsws(j,i) * rmask(j,i,sr)
333	sums_l(nzb+3,pr_palm,tn) = sums_l(nzb+3,pr_palm,tn) + &
334	ts(j,i) * rmask(j,i,sr)
335	ENDDO
336	ENDDO
337
338	!
339	!-- Horizontally averaged profiles of the vertical fluxes
340	!$OMP DO
341	DO i = nxl, nxr
342	DO j = nys, nyn
343	!
344	!-- Subgridscale fluxes (without Prandtl layer from k=nzb,
345	!-- oterwise from k=nzb+1)
346	!-- NOTE: for simplicity, nzb_diff_s_outer is used below, although
347	!-- ---- strictly speaking the following k-loop would have to be
348	!-- split up according to the staggered grid.
349	DO k = nzb_diff_s_outer(j,i)-1, nzt
350	!
351	!-- Momentum flux w"u"
352	sums_l(k,12,tn) = sums_l(k,12,tn) - 0.25 * ( &
353	km(k,j,i)+km(k+1,j,i)+km(k,j,i-1)+km(k+1,j,i-1) &
354	) * ( &
355	( u(k+1,j,i) - u(k,j,i) ) * ddzu(k+1) &
356	+ ( w(k,j,i) - w(k,j,i-1) ) * ddx &
357	) * rmask(j,i,sr)
358	!
359	!-- Momentum flux w"v"
360	sums_l(k,14,tn) = sums_l(k,14,tn) - 0.25 * ( &
361	km(k,j,i)+km(k+1,j,i)+km(k,j-1,i)+km(k+1,j-1,i) &
362	) * ( &
363	( v(k+1,j,i) - v(k,j,i) ) * ddzu(k+1) &
364	+ ( w(k,j,i) - w(k,j-1,i) ) * ddy &
365	) * rmask(j,i,sr)
366	ENDDO
367
368	DO k = nzb_diff_s_outer(j,i)-1, nzt_diff
369	!
370	!-- Heat flux w"pt"
371	sums_l(k,16,tn) = sums_l(k,16,tn) &
372	- 0.5 * ( kh(k,j,i) + kh(k+1,j,i) ) &
373	* ( pt(k+1,j,i) - pt(k,j,i) ) &
374	* ddzu(k+1) * rmask(j,i,sr)
375
376
377	!
378	!-- Buoyancy flux, water flux (humidity flux) w"q"
379	IF ( humidity ) THEN
380	sums_l(k,45,tn) = sums_l(k,45,tn) &
381	- 0.5 * ( kh(k,j,i) + kh(k+1,j,i) ) &
382	* ( vpt(k+1,j,i) - vpt(k,j,i) ) &
383	* ddzu(k+1) * rmask(j,i,sr)
384	sums_l(k,48,tn) = sums_l(k,48,tn) &
385	- 0.5 * ( kh(k,j,i) + kh(k+1,j,i) ) &
386	* ( q(k+1,j,i) - q(k,j,i) ) &
387	* ddzu(k+1) * rmask(j,i,sr)
388	IF ( cloud_physics ) THEN
389	sums_l(k,51,tn) = sums_l(k,51,tn) &
390	- 0.5 * ( kh(k,j,i) + kh(k+1,j,i) ) &
391	* ( ( q(k+1,j,i) - ql(k+1,j,i) )&
392	- ( q(k,j,i) - ql(k,j,i) ) ) &
393	* ddzu(k+1) * rmask(j,i,sr)
394	ENDIF
395	ENDIF
396
397	!
398	!-- Passive scalar flux
399	IF ( passive_scalar ) THEN
400	sums_l(k,48,tn) = sums_l(k,48,tn) &
401	- 0.5 * ( kh(k,j,i) + kh(k+1,j,i) ) &
402	* ( q(k+1,j,i) - q(k,j,i) ) &
403	* ddzu(k+1) * rmask(j,i,sr)
404	ENDIF
405
406	ENDDO
407
408	!
409	!-- Subgridscale fluxes in the Prandtl layer
410	IF ( use_surface_fluxes ) THEN
411	sums_l(nzb,12,tn) = sums_l(nzb,12,tn) + &
412	usws(j,i) * rmask(j,i,sr) ! w"u"
413	sums_l(nzb,14,tn) = sums_l(nzb,14,tn) + &
414	vsws(j,i) * rmask(j,i,sr) ! w"v"
415	sums_l(nzb,16,tn) = sums_l(nzb,16,tn) + &
416	shf(j,i) * rmask(j,i,sr) ! w"pt"
417	sums_l(nzb,58,tn) = sums_l(nzb,58,tn) + &
418	0.0 * rmask(j,i,sr) ! u"pt"
419	sums_l(nzb,61,tn) = sums_l(nzb,61,tn) + &
420	0.0 * rmask(j,i,sr) ! v"pt"
421	IF ( humidity ) THEN
422	sums_l(nzb,48,tn) = sums_l(nzb,48,tn) + &
423	qsws(j,i) * rmask(j,i,sr) ! w"q" (w"qv")
424	IF ( cloud_physics ) THEN
425	sums_l(nzb,45,tn) = sums_l(nzb,45,tn) + ( &
426	( 1.0 + 0.61 * q(nzb,j,i) ) * &
427	shf(j,i) + 0.61 * pt(nzb,j,i) * &
428	qsws(j,i) &
429	)
430	!
431	!-- Formula does not work if ql(nzb) /= 0.0
432	sums_l(nzb,51,tn) = sums_l(nzb,51,tn) + & ! w"q" (w"qv")
433	qsws(j,i) * rmask(j,i,sr)
434	ENDIF
435	ENDIF
436	IF ( passive_scalar ) THEN
437	sums_l(nzb,48,tn) = sums_l(nzb,48,tn) + &
438	qsws(j,i) * rmask(j,i,sr) ! w"q" (w"qv")
439	ENDIF
440	ENDIF
441
442	!
443	!-- Subgridscale fluxes at the top surface
444	IF ( use_top_fluxes ) THEN
445	sums_l(nzt,16,tn) = sums_l(nzt,16,tn) + &
446	tswst(j,i) * rmask(j,i,sr) ! w"pt"
447	sums_l(nzt,58,tn) = sums_l(nzt,58,tn) + &
448	0.0 * rmask(j,i,sr) ! u"pt"
449	sums_l(nzt,61,tn) = sums_l(nzt,61,tn) + &
450	0.0 * rmask(j,i,sr) ! v"pt"
451	IF ( humidity ) THEN
452	sums_l(nzt,48,tn) = sums_l(nzt,48,tn) + &
453	qswst(j,i) * rmask(j,i,sr) ! w"q" (w"qv")
454	IF ( cloud_physics ) THEN
455	sums_l(nzt,45,tn) = sums_l(nzt,45,tn) + ( &
456	( 1.0 + 0.61 * q(nzt,j,i) ) * &
457	tswst(j,i) + 0.61 * pt(nzt,j,i) * &
458	qsws(j,i) &
459	)
460	!
461	!-- Formula does not work if ql(nzb) /= 0.0
462	sums_l(nzt,51,tn) = sums_l(nzt,51,tn) + & ! w"q" (w"qv")
463	qswst(j,i) * rmask(j,i,sr)
464	ENDIF
465	ENDIF
466	IF ( passive_scalar ) THEN
467	sums_l(nzt,48,tn) = sums_l(nzt,48,tn) + &
468	qswst(j,i) * rmask(j,i,sr) ! w"q" (w"qv")
469	ENDIF
470	ENDIF
471
472	!
473	!-- Resolved fluxes (can be computed for all horizontal points)
474	!-- NOTE: for simplicity, nzb_s_outer is used below, although strictly
475	!-- ---- speaking the following k-loop would have to be split up and
476	!-- rearranged according to the staggered grid.
477	DO k = nzb_s_outer(j,i), nzt
478	ust = 0.5 * ( u(k,j,i) - hom(k,1,1,sr) + &
479	u(k+1,j,i) - hom(k+1,1,1,sr) )
480	vst = 0.5 * ( v(k,j,i) - hom(k,1,2,sr) + &
481	v(k+1,j,i) - hom(k+1,1,2,sr) )
482	pts = 0.5 * ( pt(k,j,i) - hom(k,1,4,sr) + &
483	pt(k+1,j,i) - hom(k+1,1,4,sr) )
484	!
485	!-- Momentum flux wu
486	sums_l(k,13,tn) = sums_l(k,13,tn) + 0.5 * &
487	( w(k,j,i-1) + w(k,j,i) ) &
488	* ust * rmask(j,i,sr)
489	!
490	!-- Momentum flux wv
491	sums_l(k,15,tn) = sums_l(k,15,tn) + 0.5 * &
492	( w(k,j-1,i) + w(k,j,i) ) &
493	* vst * rmask(j,i,sr)
494	!
495	!-- Heat flux wpt
496	!-- The following formula (comment line, not executed) does not
497	!-- work if applied to subregions
498	! sums_l(k,17,tn) = sums_l(k,17,tn) + 0.5 * &
499	! ( pt(k,j,i)+pt(k+1,j,i) ) &
500	! * w(k,j,i) * rmask(j,i,sr)
501	sums_l(k,17,tn) = sums_l(k,17,tn) + pts * w(k,j,i) * &
502	rmask(j,i,sr)
503	!
504	!-- Higher moments
505	sums_l(k,35,tn) = sums_l(k,35,tn) + pts * w(k,j,i)*2 &
506	rmask(j,i,sr)
507	sums_l(k,36,tn) = sums_l(k,36,tn) + pts*2 w(k,j,i) * &
508	rmask(j,i,sr)
509
510	!
511	!-- Buoyancy flux, water flux, humidity flux and liquid water
512	!-- content
513	IF ( humidity ) THEN
514	pts = 0.5 * ( vpt(k,j,i) - hom(k,1,44,sr) + &
515	vpt(k+1,j,i) - hom(k+1,1,44,sr) )
516	sums_l(k,46,tn) = sums_l(k,46,tn) + pts * w(k,j,i) * &
517	rmask(j,i,sr)
518	pts = 0.5 * ( q(k,j,i) - hom(k,1,41,sr) + &
519	q(k+1,j,i) - hom(k+1,1,41,sr) )
520	sums_l(k,49,tn) = sums_l(k,49,tn) + pts * w(k,j,i) * &
521	rmask(j,i,sr)
522	IF ( cloud_physics .OR. cloud_droplets ) THEN
523	pts = 0.5 * &
524	( ( q(k,j,i) - ql(k,j,i) ) - hom(k,1,42,sr) &
525	+ ( q(k+1,j,i) - ql(k+1,j,i) ) - hom(k+1,1,42,sr) )
526	sums_l(k,52,tn) = sums_l(k,52,tn) + pts * w(k,j,i) * &
527	rmask(j,i,sr)
528	sums_l(k,54,tn) = sums_l(k,54,tn) + ql(k,j,i) * &
529	rmask(j,i,sr)
530	ENDIF
531	ENDIF
532
533	!
534	!-- Passive scalar flux
535	IF ( passive_scalar ) THEN
536	pts = 0.5 * ( q(k,j,i) - hom(k,1,41,sr) + &
537	q(k+1,j,i) - hom(k+1,1,41,sr) )
538	sums_l(k,49,tn) = sums_l(k,49,tn) + pts * w(k,j,i) * &
539	rmask(j,i,sr)
540	ENDIF
541
542	!
543	!-- Energy flux we
544	sums_l(k,37,tn) = sums_l(k,37,tn) + w(k,j,i) * 0.5 * &
545	( ust2 + vst2 + w(k,j,i)**2 )&
546	* rmask(j,i,sr)
547
548	ENDDO
549	ENDDO
550	ENDDO
551
552	!
553	!-- Divergence of vertical flux of resolved scale energy and pressure
554	!-- fluctuations. First calculate the products, then the divergence.
555	!-- Calculation is time consuming. Do it only, if profiles shall be plotted.
556	IF ( hom(nzb+1,2,55,0) /= 0.0 ) THEN
557
558	sums_ll = 0.0 ! local array
559
560	!$OMP DO
561	DO i = nxl, nxr
562	DO j = nys, nyn
563	DO k = nzb_s_outer(j,i)+1, nzt
564
565	sums_ll(k,1) = sums_ll(k,1) + 0.5 * w(k,j,i) * ( &
566	( 0.25 * ( u(k,j,i)+u(k+1,j,i)+u(k,j,i+1)+u(k+1,j,i+1) &
567	- 2.0 * ( hom(k,1,1,sr) + hom(k+1,1,1,sr) ) &
568	) )**2 &
569	+ ( 0.25 * ( v(k,j,i)+v(k+1,j,i)+v(k,j+1,i)+v(k+1,j+1,i) &
570	- 2.0 * ( hom(k,1,2,sr) + hom(k+1,1,2,sr) ) &
571	) )**2 &
572	+ w(k,j,i)**2 )
573
574	sums_ll(k,2) = sums_ll(k,2) + 0.5 * w(k,j,i) &
575	* ( p(k,j,i) + p(k+1,j,i) )
576
577	ENDDO
578	ENDDO
579	ENDDO
580	sums_ll(0,1) = 0.0 ! because w is zero at the bottom
581	sums_ll(nzt+1,1) = 0.0
582	sums_ll(0,2) = 0.0
583	sums_ll(nzt+1,2) = 0.0
584
585	DO k = nzb_s_outer(j,i)+1, nzt
586	sums_l(k,55,tn) = ( sums_ll(k,1) - sums_ll(k-1,1) ) * ddzw(k)
587	sums_l(k,56,tn) = ( sums_ll(k,2) - sums_ll(k-1,2) ) * ddzw(k)
588	ENDDO
589	sums_l(nzb,55,tn) = sums_l(nzb+1,55,tn)
590	sums_l(nzb,56,tn) = sums_l(nzb+1,56,tn)
591
592	ENDIF
593
594	!
595	!-- Divergence of vertical flux of SGS TKE
596	IF ( hom(nzb+1,2,57,0) /= 0.0 ) THEN
597
598	!$OMP DO
599	DO i = nxl, nxr
600	DO j = nys, nyn
601	DO k = nzb_s_outer(j,i)+1, nzt
602
603	sums_l(k,57,tn) = sums_l(k,57,tn) + ( &
604	(km(k,j,i)+km(k+1,j,i)) * (e(k+1,j,i)-e(k,j,i)) * ddzu(k+1) &
605	- (km(k-1,j,i)+km(k,j,i)) * (e(k,j,i)-e(k-1,j,i)) * ddzu(k) &
606	) * ddzw(k)
607
608	ENDDO
609	ENDDO
610	ENDDO
611	sums_l(nzb,57,tn) = sums_l(nzb+1,57,tn)
612
613	ENDIF
614
615	!
616	!-- Horizontal heat fluxes (subgrid, resolved, total).
617	!-- Do it only, if profiles shall be plotted.
618	IF ( hom(nzb+1,2,58,0) /= 0.0 ) THEN
619
620	!$OMP DO
621	DO i = nxl, nxr
622	DO j = nys, nyn
623	DO k = nzb_s_outer(j,i)+1, nzt
624	!
625	!-- Subgrid horizontal heat fluxes u"pt", v"pt"
626	sums_l(k,58,tn) = sums_l(k,58,tn) - 0.5 * &
627	( kh(k,j,i) + kh(k,j,i-1) ) &
628	* ( pt(k,j,i-1) - pt(k,j,i) ) &
629	* ddx * rmask(j,i,sr)
630	sums_l(k,61,tn) = sums_l(k,61,tn) - 0.5 * &
631	( kh(k,j,i) + kh(k,j-1,i) ) &
632	* ( pt(k,j-1,i) - pt(k,j,i) ) &
633	* ddy * rmask(j,i,sr)
634	!
635	!-- Resolved horizontal heat fluxes upt, vpt
636	sums_l(k,59,tn) = sums_l(k,59,tn) + &
637	( u(k,j,i) - hom(k,1,1,sr) ) &
638	* 0.5 * ( pt(k,j,i-1) - hom(k,1,4,sr) + &
639	pt(k,j,i) - hom(k,1,4,sr) )
640	pts = 0.5 * ( pt(k,j-1,i) - hom(k,1,4,sr) + &
641	pt(k,j,i) - hom(k,1,4,sr) )
642	sums_l(k,62,tn) = sums_l(k,62,tn) + &
643	( v(k,j,i) - hom(k,1,2,sr) ) &
644	* 0.5 * ( pt(k,j-1,i) - hom(k,1,4,sr) + &
645	pt(k,j,i) - hom(k,1,4,sr) )
646	ENDDO
647	ENDDO
648	ENDDO
649	!
650	!-- Fluxes at the surface must be zero (e.g. due to the Prandtl-layer)
651	sums(nzb,58) = 0.0
652	sums(nzb,59) = 0.0
653	sums(nzb,60) = 0.0
654	sums(nzb,61) = 0.0
655	sums(nzb,62) = 0.0
656	sums(nzb,63) = 0.0
657
658	ENDIF
659
660	!
661	!-- Calculate the user-defined profiles
662	CALL user_statistics( 'profiles', sr, tn )
663	!$OMP END PARALLEL
664
665	!
666	!-- Summation of thread sums
667	IF ( threads_per_task > 1 ) THEN
668	DO i = 1, threads_per_task-1
669	sums_l(:,3,0) = sums_l(:,3,0) + sums_l(:,3,i)
670	sums_l(:,4:40,0) = sums_l(:,4:40,0) + sums_l(:,4:40,i)
671	sums_l(:,45:pr_palm,0) = sums_l(:,45:pr_palm,0) + &
672	sums_l(:,45:pr_palm,i)
673	IF ( max_pr_user > 0 ) THEN
674	sums_l(:,pr_palm+1:pr_palm+max_pr_user,0) = &
675	sums_l(:,pr_palm+1:pr_palm+max_pr_user,0) + &
676	sums_l(:,pr_palm+1:pr_palm+max_pr_user,i)
677	ENDIF
678	ENDDO
679	ENDIF
680
681	#if defined( __parallel )
682	!
683	!-- Compute total sum from local sums
684	CALL MPI_ALLREDUCE( sums_l(nzb,1,0), sums(nzb,1), ngp_sums, MPI_REAL, &
685	MPI_SUM, comm2d, ierr )
686	#else
687	sums = sums_l(:,:,0)
688	#endif
689
690	!
691	!-- Final values are obtained by division by the total number of grid points
692	!-- used for summation. After that store profiles.
693	!-- Profiles:
694	DO k = nzb, nzt+1
695	sums(k,:pr_palm-2) = sums(k,:pr_palm-2) / ngp_2dh_outer(k,sr)
696	ENDDO
697	!-- Upstream-parts
698	sums(nzb:nzb+11,pr_palm-1) = sums(nzb:nzb+11,pr_palm-1) / ngp_3d(sr)
699	!-- u* and so on
700	!-- As sums(nzb:nzb+3,pr_palm) are full 2D arrays (us, usws, vsws, ts) whose
701	!-- size is always ( nx + 1 ) * ( ny + 1 ), defined at the first grid layer
702	!-- above the topography, they are being divided by ngp_2dh(sr)
703	sums(nzb:nzb+3,pr_palm) = sums(nzb:nzb+3,pr_palm) / &
704	ngp_2dh(sr)
705	!-- eges, e*
706	sums(nzb+4:nzb+5,pr_palm) = sums(nzb+4:nzb+5,pr_palm) / &
707	ngp_3d_inner(sr)
708	!-- Old and new divergence
709	sums(nzb+9:nzb+10,pr_palm) = sums(nzb+9:nzb+10,pr_palm) / &
710	ngp_3d_inner(sr)
711
712	!-- User-defined profiles
713	IF ( max_pr_user > 0 ) THEN
714	DO k = nzb, nzt+1
715	sums(k,pr_palm+1:pr_palm+max_pr_user) = &
716	sums(k,pr_palm+1:pr_palm+max_pr_user) / &
717	ngp_2dh_outer(k,sr)
718	ENDDO
719	ENDIF
720
721	!
722	!-- Collect horizontal average in hom.
723	!-- Compute deduced averages (e.g. total heat flux)
724	hom(:,1,3,sr) = sums(:,3) ! w
725	hom(:,1,8,sr) = sums(:,8) ! e profiles 5-7 are initial profiles
726	hom(:,1,9,sr) = sums(:,9) ! km
727	hom(:,1,10,sr) = sums(:,10) ! kh
728	hom(:,1,11,sr) = sums(:,11) ! l
729	hom(:,1,12,sr) = sums(:,12) ! w"u"
730	hom(:,1,13,sr) = sums(:,13) ! wu
731	hom(:,1,14,sr) = sums(:,14) ! w"v"
732	hom(:,1,15,sr) = sums(:,15) ! wv
733	hom(:,1,16,sr) = sums(:,16) ! w"pt"
734	hom(:,1,17,sr) = sums(:,17) ! wpt
735	hom(:,1,18,sr) = sums(:,16) + sums(:,17) ! wpt
736	hom(:,1,19,sr) = sums(:,12) + sums(:,13) ! wu
737	hom(:,1,20,sr) = sums(:,14) + sums(:,15) ! wv
738	hom(:,1,21,sr) = sums(:,21) ! wptBC
739	hom(:,1,22,sr) = sums(:,16) + sums(:,21) ! wptBC
740	! profiles 23-29 left empty for initial
741	! profiles
742	hom(:,1,30,sr) = sums(:,30) ! u*2
743	hom(:,1,31,sr) = sums(:,31) ! v*2
744	hom(:,1,32,sr) = sums(:,32) ! w*2
745	hom(:,1,33,sr) = sums(:,33) ! pt*2
746	hom(:,1,34,sr) = sums(:,34) ! e*
747	hom(:,1,35,sr) = sums(:,35) ! w2pt
748	hom(:,1,36,sr) = sums(:,36) ! wpt2
749	hom(:,1,37,sr) = sums(:,37) ! we
750	hom(:,1,38,sr) = sums(:,38) ! w*3
751	hom(:,1,39,sr) = sums(:,38) / ( sums(:,32) + 1E-20 )**1.5 ! Sw
752	hom(:,1,40,sr) = sums(:,40) ! p
753	hom(:,1,45,sr) = sums(:,45) ! w"q"
754	hom(:,1,46,sr) = sums(:,46) ! wvpt
755	hom(:,1,47,sr) = sums(:,45) + sums(:,46) ! wvpt
756	hom(:,1,48,sr) = sums(:,48) ! w"q" (w"qv")
757	hom(:,1,49,sr) = sums(:,49) ! wq (wqv)
758	hom(:,1,50,sr) = sums(:,48) + sums(:,49) ! wq (wqv)
759	hom(:,1,51,sr) = sums(:,51) ! w"qv"
760	hom(:,1,52,sr) = sums(:,52) ! wqv
761	hom(:,1,53,sr) = sums(:,52) + sums(:,51) ! wq (wqv)
762	hom(:,1,54,sr) = sums(:,54) ! ql
763	hom(:,1,55,sr) = sums(:,55) ! wuu*/dz
764	hom(:,1,56,sr) = sums(:,56) ! wp/dz
765	hom(:,1,57,sr) = sums(:,57) ! w"e/dz
766	hom(:,1,58,sr) = sums(:,58) ! u"pt"
767	hom(:,1,59,sr) = sums(:,59) ! upt
768	hom(:,1,60,sr) = sums(:,58) + sums(:,59) ! upt_t
769	hom(:,1,61,sr) = sums(:,61) ! v"pt"
770	hom(:,1,62,sr) = sums(:,62) ! vpt
771	hom(:,1,63,sr) = sums(:,61) + sums(:,62) ! vpt_t
772
773	hom(:,1,pr_palm-1,sr) = sums(:,pr_palm-1)
774	! upstream-parts u_x, u_y, u_z, v_x,
775	! v_y, usw. (in last but one profile)
776	hom(:,1,pr_palm,sr) = sums(:,pr_palm)
777	! u, w'u', w'v', t (in last profile)
778
779	IF ( max_pr_user > 0 ) THEN ! user-defined profiles
780	hom(:,1,pr_palm+1:pr_palm+max_pr_user,sr) = &
781	sums(:,pr_palm+1:pr_palm+max_pr_user)
782	ENDIF
783
784	!
785	!-- Determine the boundary layer height using two different schemes.
786	!-- First scheme: Starting from the Earth's surface, look for the first
787	!-- relative minimum of the total heat flux. The corresponding height is
788	!-- accepted as the boundary layer height, if it is less than 1.5 times the
789	!-- height where the heat flux becomes negative for the first time.
790	!-- NOTE: This criterion is still capable of improving!
791	z_i(1) = 0.0
792	first = .TRUE.
793	DO k = nzb, nzt-1
794	IF ( first .AND. hom(k,1,18,sr) < 0.0 ) THEN
795	first = .FALSE.
796	height = zw(k)
797	ENDIF
798	IF ( hom(k,1,18,sr) < 0.0 .AND. &
799	hom(k+1,1,18,sr) > hom(k,1,18,sr) ) THEN
800	IF ( zw(k) < 1.5 * height ) THEN
801	z_i(1) = zw(k)
802	ELSE
803	z_i(1) = height
804	ENDIF
805	EXIT
806	ENDIF
807	ENDDO
808
809	!
810	!-- Second scheme: Starting from the top model boundary, look for the first
811	!-- characteristic kink in the temperature profile, where the originally
812	!-- stable stratification notably weakens.
813	z_i(2) = 0.0
814	DO k = nzt-1, nzb+1, -1
815	IF ( ( hom(k+1,1,4,sr) - hom(k,1,4,sr) ) > &
816	2.0 * ( hom(k,1,4,sr) - hom(k-1,1,4,sr) ) ) THEN
817	z_i(2) = zu(k)
818	EXIT
819	ENDIF
820	ENDDO
821
822	hom(nzb+6,1,pr_palm,sr) = z_i(1)
823	hom(nzb+7,1,pr_palm,sr) = z_i(2)
824
825	!
826	!-- Computation of both the characteristic vertical velocity and
827	!-- the characteristic convective boundary layer temperature.
828	!-- The horizontal average at nzb+1 is input for the average temperature.
829	IF ( hom(nzb,1,18,sr) > 0.0 .AND. z_i(1) /= 0.0 ) THEN
830	hom(nzb+8,1,pr_palm,sr) = ( g / hom(nzb+1,1,4,sr) * &
831	hom(nzb,1,18,sr) * z_i(1) )**0.333333333
832	!-- so far this only works if Prandtl layer is used
833	hom(nzb+11,1,pr_palm,sr) = hom(nzb,1,16,sr) / hom(nzb+8,1,pr_palm,sr)
834	ELSE
835	hom(nzb+8,1,pr_palm,sr) = 0.0
836	hom(nzb+11,1,pr_palm,sr) = 0.0
837	ENDIF
838
839	!
840	!-- Collect the time series quantities
841	ts_value(1,sr) = hom(nzb+4,1,pr_palm,sr) ! E
842	ts_value(2,sr) = hom(nzb+5,1,pr_palm,sr) ! E*
843	ts_value(3,sr) = dt_3d
844	ts_value(4,sr) = hom(nzb,1,pr_palm,sr) ! u*
845	ts_value(5,sr) = hom(nzb+3,1,pr_palm,sr) ! th*
846	ts_value(6,sr) = u_max
847	ts_value(7,sr) = v_max
848	ts_value(8,sr) = w_max
849	ts_value(9,sr) = hom(nzb+10,1,pr_palm,sr) ! new divergence
850	ts_value(10,sr) = hom(nzb+9,1,pr_palm,sr) ! old Divergence
851	ts_value(11,sr) = hom(nzb+6,1,pr_palm,sr) ! z_i(1)
852	ts_value(12,sr) = hom(nzb+7,1,pr_palm,sr) ! z_i(2)
853	ts_value(13,sr) = hom(nzb+8,1,pr_palm,sr) ! w*
854	ts_value(14,sr) = hom(nzb,1,16,sr) ! w'pt' at k=0
855	ts_value(15,sr) = hom(nzb+1,1,16,sr) ! w'pt' at k=1
856	ts_value(16,sr) = hom(nzb+1,1,18,sr) ! wpt at k=1
857	ts_value(17,sr) = hom(nzb,1,4,sr) ! pt(0)
858	ts_value(18,sr) = hom(nzb+1,1,4,sr) ! pt(zp)
859	ts_value(19,sr) = hom(nzb+9,1,pr_palm-1,sr) ! splptx
860	ts_value(20,sr) = hom(nzb+10,1,pr_palm-1,sr) ! splpty
861	ts_value(21,sr) = hom(nzb+11,1,pr_palm-1,sr) ! splptz
862	IF ( ts_value(5,sr) /= 0.0 ) THEN
863	ts_value(22,sr) = ts_value(4,sr)**2 / &
864	( kappa * g * ts_value(5,sr) / ts_value(18,sr) ) ! L
865	ELSE
866	ts_value(22,sr) = 10000.0
867	ENDIF
868
869	!
870	!-- Calculate additional statistics provided by the user interface
871	CALL user_statistics( 'time_series', sr, 0 )
872
873	ENDDO ! loop of the subregions
874
875	!
876	!-- If required, sum up horizontal averages for subsequent time averaging
877	IF ( do_sum ) THEN
878	IF ( average_count_pr == 0 ) hom_sum = 0.0
879	hom_sum = hom_sum + hom(:,1,:,:)
880	average_count_pr = average_count_pr + 1
881	do_sum = .FALSE.
882	ENDIF
883
884	!
885	!-- Set flag for other UPs (e.g. output routines, but also buoyancy).
886	!-- This flag is reset after each time step in time_integration.
887	flow_statistics_called = .TRUE.
888
889	CALL cpu_log( log_point(10), 'flow_statistics', 'stop' )
890
891
892	END SUBROUTINE flow_statistics
893
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895

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