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source: palm/trunk/SOURCE/flow_statistics.f90 @ 50

Last change on this file since 50 was 48, checked in by raasch, 18 years ago
preliminary version, several changes to be explained later
Property svn:keywords set to `Id`
File size: 36.6 KB

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

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