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source: palm/trunk/SOURCE/flow_statistics.f90 @ 1

Last change on this file since 1 was 1, checked in by raasch, 17 years ago
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1	SUBROUTINE flow_statistics
2
3	!------------------------------------------------------------------------------!
4	! Actual revisions:
5	! -----------------
6	!
7	!
8	! Former revisions:
9	! -----------------
10	! $Log: flow_statistics.f90,v $
11	! Revision 1.41 2006/08/04 14:37:50 raasch
12	! Error removed in non-parallel part (sums_l)
13	!
14	! Revision 1.40 2006/04/26 14:06:01 raasch
15	! Call of omp_get_thread_num written as comment line. Since lcmuk does not
16	! understand this comment, a cpp-directive is required.
17	!
18	! Revision 1.39 2006/04/26 12:19:16 raasch
19	! OpenMP optimization, thread number added as third dimension of sums_l,
20	! nzb_s_inner(j,i) replaced by nzb in determination of z_i
21	!
22	! Revision 1.38 2006/02/23 12:23:15 raasch
23	! nzb and nzb_diff replaced by nzb_s_outer and nzb_diff_s_outer resrectively,
24	! nanz_sums, nanz_2dh, nanz_3d renamed ngp_sums, ngp_2dh and ngp_3d,
25	! respectively,
26	! ngp_2dh and ngp_3d partially replaced by ngp_2dh_outer and ngp_3d_inner,
27	! respectively
28	!
29	! Revision 1.37 2005/12/06 16:40:21 raasch
30	! Calculation of ql (54) profile in case of using cloud droplets
31	!
32	! Revision 1.36 2005/04/23 09:10:27 raasch
33	! +local array sums_ll instead of temporarily using sums_l
34	!
35	! Revision 1.35 2004/04/30 11:46:56 raasch
36	! leap_frog changed to time_integration
37	!
38	! Revision 1.34 2003/05/09 14:25:12 raasch
39	! Parameters in MPI_ALLREDUCE call changed
40	!
41	! Revision 1.33 2003/03/31 15:42:53 raasch
42	! Calculation of horizontal temperature fluxes modified and cleaned up
43	!
44	! Revision 1.32 2003/03/16 09:39:07 raasch
45	! Two underscores (_) are placed in front of all define-strings
46	!
47	! Revision 1.31 2003/03/12 16:30:07 raasch
48	! Calculation of perturbation and total energy of the total domain
49	! re-arranged in order to allow vectorization of the respective loop
50	!
51	! Revision 1.30 2003/03/04 11:26:35 raasch
52	! Error in calculation of the vertical flux of resolved scale energy
53	! (profile 57) removed
54	!
55	! Revision 1.29 2002/12/19 14:50:02 raasch
56	! STOP statement replaced by call of subroutine local_stop
57	!
58	! Revision 1.28 2002/04/16 08:04:19 raasch
59	! Error in passive scalar profile (hom(..41..)) removed
60	!
61	! Revision 1.27 2002/04/11 16:31:03 schroeter
62	! No changes.
63	!
64	! Revision 1.26 2001/09/04 12:00:12 12:00:12 raasch (Siegfried Raasch)
65	! Calculation of the vertical flux of resolved scale energy and pressure
66	! fluctuations
67	!
68	! Revision 1.25 2001/08/21 08:32:24 raasch
69	! Special calculation of surface fluxes whenever they are prescribed (not only
70	! in case of a Prandtl layer), call of user_interface
71	!
72	! Revision 1.24 2001/03/30 07:23:34 raasch
73	! Translation of remaining German identifiers (variables, subroutines, etc.)
74	!
75	! Revision 1.23 2001/02/07 06:48:25 raasch
76	! Error in non-parallel passive scalar code removed
77	!
78	! Revision 1.22 2001/01/29 12:25:02 raasch
79	! Passive scalar is considered
80	!
81	! Revision 1.21 2001/01/22 06:49:27 raasch
82	! Module test_variables removed
83	!
84	! Revision 1.20 2000/04/13 13:54:15 schroeter
85	! + computation of new profiles for calculations with
86	! cloud_physics
87	!
88	! Revision 1.19 2000/01/26 09:32:58 09:32:58 letzel (Marcus Letzel)
89	! All comments translated into English
90	!
91	! Revision 1.16 1998/04/21 15:54:54 raasch
92	! Berechnung von w* beruecksichtigt jetzt den Fall z_i=0,
93	! Faktor 0.5 bei Energietransport hinzugefuegt
94	!
95	! Revision 1.6 1998/02/10 15:06:02 raasch
96	! Berechnung des Gesamtwaermestroms, in aufgeloesten Waermestroemen wird das
97	! horizontale Temperaturmittel nicht mehr abgezogen, Berechnung der
98	! Gesamtimpulsfluesse
99	!
100	! Revision 1.1 1997/08/11 06:15:17 raasch
101	! Initial revision
102	!
103	!
104	! Description:
105	! ------------
106	! Compute average profiles and further average flow quantities for the different
107	! user-defined (sub-)regions. The region indexed 0 is the total model domain.
108	!
109	! NOTE: For simplicity, nzb_s_outer and nzb_diff_s_outer are being used as a
110	! ---- lower vertical index for k-loops for all variables so that regardless
111	! of the variable and its respective staggered grid always the same number of
112	! grid points is used for 2D averages. The disadvantage: depending on the
113	! variable, up to one grid layer adjacent to the (vertical walls of the)
114	! topography is missed out by this simplification.
115	!------------------------------------------------------------------------------!
116
117	USE arrays_3d
118	USE cloud_parameters
119	USE cpulog
120	USE grid_variables
121	USE indices
122	USE interfaces
123	USE pegrid
124	USE statistics
125	USE control_parameters
126
127	IMPLICIT NONE
128
129	INTEGER :: i, j, k, omp_get_thread_num, sr, tn
130	LOGICAL :: first
131	REAL :: height, pts, sums_l_eper, sums_l_etot, ust, ust2, u2, vst, &
132	vst2, v2, w2, z_i(2)
133	REAL :: sums_ll(nzb:nzt+1,2)
134
135
136	CALL cpu_log( log_point(10), 'flow_statistics', 'start' )
137
138	!
139	!-- To be on the safe side, check whether flow_statistics has already been
140	!-- called once after the current time step
141	IF ( flow_statistics_called ) THEN
142	IF ( myid == 0 ) PRINT*, '+++ WARNING: flow_statistics is called two', &
143	' times within one timestep'
144	CALL local_stop
145	ENDIF
146
147	!
148	!-- Compute statistics for each (sub-)region
149	DO sr = 0, statistic_regions
150
151	!
152	!-- Initialize (local) summation array
153	sums_l = 0.0
154
155	!
156	!-- Store sums that have been computed in other subroutines in summation
157	!-- array
158	sums_l(:,11,:) = sums_l_l(:,sr,:) ! mixing length from diffusivities
159	!-- WARNING: next line still has to be adjusted for OpenMP
160	sums_l(:,21,0) = sums_wsts_bc_l(:,sr) ! heat flux from advec_s_bc
161	sums_l(nzb+9,var_sum,0) = sums_divold_l(sr) ! old divergence from pres
162	sums_l(nzb+10,var_sum,0) = sums_divnew_l(sr) ! new divergence from pres
163	!-- WARNING: next four lines still may have to be adjusted for OpenMP
164	sums_l(nzb:nzb+2,var_sum-1,0) = sums_up_fraction_l(1,1:3,sr)! upstream
165	sums_l(nzb+3:nzb+5,var_sum-1,0) = sums_up_fraction_l(2,1:3,sr)! parts
166	sums_l(nzb+6:nzb+8,var_sum-1,0) = sums_up_fraction_l(3,1:3,sr)! from
167	sums_l(nzb+9:nzb+11,var_sum-1,0) = sums_up_fraction_l(4,1:3,sr)! spline
168
169	!
170	!-- Horizontally averaged profiles of horizontal velocities and temperature.
171	!-- They must have been computed before, because they are already required
172	!-- for other horizontal averages.
173	tn = 0
174	!$OMP PARALLEL PRIVATE( i, j, k, tn )
175	#if defined( __lcmuk )
176	tn = omp_get_thread_num()
177	#else
178	!$ tn = omp_get_thread_num()
179	#endif
180
181	!$OMP DO
182	DO i = nxl, nxr
183	DO j = nys, nyn
184	DO k = nzb_s_outer(j,i), nzt+1
185	sums_l(k,1,tn) = sums_l(k,1,tn) + u(k,j,i) * rmask(j,i,sr)
186	sums_l(k,2,tn) = sums_l(k,2,tn) + v(k,j,i) * rmask(j,i,sr)
187	sums_l(k,4,tn) = sums_l(k,4,tn) + pt(k,j,i) * rmask(j,i,sr)
188	ENDDO
189	ENDDO
190	ENDDO
191
192	!
193	!-- Horizontally averaged profiles of virtual potential temperature,
194	!-- total water content, specific humidity and liquid water potential
195	!-- temperature
196	IF ( moisture ) THEN
197	!$OMP DO
198	DO i = nxl, nxr
199	DO j = nys, nyn
200	DO k = nzb_s_outer(j,i), nzt+1
201	sums_l(k,44,tn) = sums_l(k,44,tn) + &
202	vpt(k,j,i) * rmask(j,i,sr)
203	sums_l(k,41,tn) = sums_l(k,41,tn) + &
204	q(k,j,i) * rmask(j,i,sr)
205	ENDDO
206	ENDDO
207	ENDDO
208	IF ( cloud_physics ) THEN
209	!$OMP DO
210	DO i = nxl, nxr
211	DO j = nys, nyn
212	DO k = nzb_s_outer(j,i), nzt+1
213	sums_l(k,42,tn) = sums_l(k,42,tn) + &
214	( q(k,j,i) - ql(k,j,i) ) * rmask(j,i,sr)
215	sums_l(k,43,tn) = sums_l(k,43,tn) + ( &
216	pt(k,j,i) + l_d_cppt_d_t(k) ql(k,j,i) &
217	) * rmask(j,i,sr)
218	ENDDO
219	ENDDO
220	ENDDO
221	ENDIF
222	ENDIF
223
224	!
225	!-- Horizontally averaged profiles of passive scalar
226	IF ( passive_scalar ) THEN
227	!$OMP DO
228	DO i = nxl, nxr
229	DO j = nys, nyn
230	DO k = nzb_s_outer(j,i), nzt+1
231	sums_l(k,41,tn) = sums_l(k,41,tn) + q(k,j,i) * rmask(j,i,sr)
232	ENDDO
233	ENDDO
234	ENDDO
235	ENDIF
236	!$OMP END PARALLEL
237
238	!
239	!-- Summation of thread sums
240	IF ( threads_per_task > 1 ) THEN
241	DO i = 1, threads_per_task-1
242	sums_l(:,1,0) = sums_l(:,1,0) + sums_l(:,1,i)
243	sums_l(:,2,0) = sums_l(:,2,0) + sums_l(:,2,i)
244	sums_l(:,4,0) = sums_l(:,4,0) + sums_l(:,4,i)
245	IF ( moisture ) THEN
246	sums_l(:,41,0) = sums_l(:,41,0) + sums_l(:,41,i)
247	sums_l(:,44,0) = sums_l(:,44,0) + sums_l(:,44,i)
248	IF ( cloud_physics ) THEN
249	sums_l(:,42,0) = sums_l(:,42,0) + sums_l(:,42,i)
250	sums_l(:,43,0) = sums_l(:,43,0) + sums_l(:,43,i)
251	ENDIF
252	ENDIF
253	IF ( passive_scalar ) THEN
254	sums_l(:,41,0) = sums_l(:,41,0) + sums_l(:,41,i)
255	ENDIF
256	ENDDO
257	ENDIF
258
259	#if defined( __parallel )
260	!
261	!-- Compute total sum from local sums
262	CALL MPI_ALLREDUCE( sums_l(nzb,1,0), sums(nzb,1), nzt+2-nzb, MPI_REAL, &
263	MPI_SUM, comm2d, ierr )
264	CALL MPI_ALLREDUCE( sums_l(nzb,2,0), sums(nzb,2), nzt+2-nzb, MPI_REAL, &
265	MPI_SUM, comm2d, ierr )
266	CALL MPI_ALLREDUCE( sums_l(nzb,4,0), sums(nzb,4), nzt+2-nzb, MPI_REAL, &
267	MPI_SUM, comm2d, ierr )
268	IF ( moisture ) THEN
269	CALL MPI_ALLREDUCE( sums_l(nzb,44,0), sums(nzb,44), nzt+2-nzb, &
270	MPI_REAL, MPI_SUM, comm2d, ierr )
271	CALL MPI_ALLREDUCE( sums_l(nzb,41,0), sums(nzb,41), nzt+2-nzb, &
272	MPI_REAL, MPI_SUM, comm2d, ierr )
273	IF ( cloud_physics ) THEN
274	CALL MPI_ALLREDUCE( sums_l(nzb,42,0), sums(nzb,42), nzt+2-nzb, &
275	MPI_REAL, MPI_SUM, comm2d, ierr )
276	CALL MPI_ALLREDUCE( sums_l(nzb,43,0), sums(nzb,43), nzt+2-nzb, &
277	MPI_REAL, MPI_SUM, comm2d, ierr )
278	ENDIF
279	ENDIF
280
281	IF ( passive_scalar ) THEN
282	CALL MPI_ALLREDUCE( sums_l(nzb,41,0), sums(nzb,41), nzt+2-nzb, &
283	MPI_REAL, MPI_SUM, comm2d, ierr )
284	ENDIF
285	#else
286	sums(:,1) = sums_l(:,1,0)
287	sums(:,2) = sums_l(:,2,0)
288	sums(:,4) = sums_l(:,4,0)
289	IF ( moisture ) THEN
290	sums(:,44) = sums_l(:,44,0)
291	sums(:,41) = sums_l(:,41,0)
292	IF ( cloud_physics ) THEN
293	sums(:,42) = sums_l(:,42,0)
294	sums(:,43) = sums_l(:,43,0)
295	ENDIF
296	ENDIF
297	IF ( passive_scalar ) sums(:,41) = sums_l(:,41,0)
298	#endif
299
300	!
301	!-- Final values are obtained by division by the total number of grid points
302	!-- used for summation. After that store profiles.
303	sums(:,1) = sums(:,1) / ngp_2dh_outer(:,sr)
304	sums(:,2) = sums(:,2) / ngp_2dh_outer(:,sr)
305	sums(:,4) = sums(:,4) / ngp_2dh_outer(:,sr)
306	hom(:,1,1,sr) = sums(:,1) ! u
307	hom(:,1,2,sr) = sums(:,2) ! v
308	hom(:,1,4,sr) = sums(:,4) ! pt
309
310	!
311	!-- Humidity and cloud parameters
312	IF ( moisture ) THEN
313	sums(:,44) = sums(:,44) / ngp_2dh_outer(:,sr)
314	sums(:,41) = sums(:,41) / ngp_2dh_outer(:,sr)
315	hom(:,1,44,sr) = sums(:,44) ! vpt
316	hom(:,1,41,sr) = sums(:,41) ! qv (q)
317	IF ( cloud_physics ) THEN
318	sums(:,42) = sums(:,42) / ngp_2dh_outer(:,sr)
319	sums(:,43) = sums(:,43) / ngp_2dh_outer(:,sr)
320	hom(:,1,42,sr) = sums(:,42) ! qv
321	hom(:,1,43,sr) = sums(:,43) ! pt
322	ENDIF
323	ENDIF
324
325	!
326	!-- Passive scalar
327	IF ( passive_scalar ) hom(:,1,41,sr) = sums(:,41) / ngp_2dh_outer(:,sr)
328
329	!
330	!-- Horizontally averaged profiles of the remaining prognostic variables,
331	!-- variances, the total and the perturbation energy (single values in last
332	!-- column of sums_l) and some diagnostic quantities.
333	!-- NOTE: for simplicity, nzb_s_outer is used below, although strictly
334	!-- ---- speaking the following k-loop would have to be split up and
335	!-- rearranged according to the staggered grid.
336	tn = 0
337	#if defined( __lcmuk )
338	!$OMP PARALLEL PRIVATE( i, j, k, pts, sums_ll, sums_l_eper, sums_l_etot, &
339	!$OMP tn, ust, ust2, u2, vst, vst2, v2, w2 )
340	tn = omp_get_thread_num()
341	#else
342	!$OMP PARALLEL PRIVATE( i, j, k, pts, sums_ll, sums_l_eper, sums_l_etot, tn, ust, ust2, u2, vst, vst2, v2, w2 )
343	!$ tn = omp_get_thread_num()
344	#endif
345	!$OMP DO
346	DO i = nxl, nxr
347	DO j = nys, nyn
348	sums_l_etot = 0.0
349	sums_l_eper = 0.0
350	DO k = nzb_s_outer(j,i), nzt+1
351	u2 = u(k,j,i)**2
352	v2 = v(k,j,i)**2
353	w2 = w(k,j,i)**2
354	ust2 = ( u(k,j,i) - hom(k,1,1,sr) )**2
355	vst2 = ( v(k,j,i) - hom(k,1,2,sr) )**2
356	!
357	!-- Prognostic and diagnostic variables
358	sums_l(k,3,tn) = sums_l(k,3,tn) + w(k,j,i) * rmask(j,i,sr)
359	sums_l(k,8,tn) = sums_l(k,8,tn) + e(k,j,i) * rmask(j,i,sr)
360	sums_l(k,9,tn) = sums_l(k,9,tn) + km(k,j,i) * rmask(j,i,sr)
361	sums_l(k,10,tn) = sums_l(k,10,tn) + kh(k,j,i) * rmask(j,i,sr)
362	sums_l(k,40,tn) = sums_l(k,40,tn) + p(k,j,i)
363
364	!
365	!-- Variances
366	sums_l(k,30,tn) = sums_l(k,30,tn) + ust2 * rmask(j,i,sr)
367	sums_l(k,31,tn) = sums_l(k,31,tn) + vst2 * rmask(j,i,sr)
368	sums_l(k,32,tn) = sums_l(k,32,tn) + w2 * rmask(j,i,sr)
369	sums_l(k,33,tn) = sums_l(k,33,tn) + &
370	( pt(k,j,i)-hom(k,1,4,sr) )*2 rmask(j,i,sr)
371	!
372	!-- Higher moments
373	!-- (Computation of the skewness of w further below)
374	sums_l(k,38,tn) = sums_l(k,38,tn) + w(k,j,i) * w2 * &
375	rmask(j,i,sr)
376	!
377	!-- Perturbation energy
378	sums_l(k,34,tn) = sums_l(k,34,tn) + 0.5 * ( ust2 + vst2 + w2 ) &
379	* rmask(j,i,sr)
380	sums_l_etot = sums_l_etot + &
381	0.5 * ( u2 + v2 + w2 ) * rmask(j,i,sr)
382	sums_l_eper = sums_l_eper + &
383	0.5 * ( ust2+vst2+w2 ) * rmask(j,i,sr)
384	ENDDO
385	!
386	!-- Total and perturbation energy for the total domain (being
387	!-- collected in the last column of sums_l). Summation of these
388	!-- quantities is seperated from the previous loop in order to
389	!-- allow vectorization of that loop.
390	sums_l(nzb+4,var_sum,tn) = sums_l(nzb+4,var_sum,tn) + sums_l_etot
391	sums_l(nzb+5,var_sum,tn) = sums_l(nzb+5,var_sum,tn) + sums_l_eper
392	!
393	!-- 2D-arrays (being collected in the last column of sums_l)
394	sums_l(nzb,var_sum,tn) = sums_l(nzb,var_sum,tn) + &
395	us(j,i) * rmask(j,i,sr)
396	sums_l(nzb+1,var_sum,tn) = sums_l(nzb+1,var_sum,tn) + &
397	usws(j,i) * rmask(j,i,sr)
398	sums_l(nzb+2,var_sum,tn) = sums_l(nzb+2,var_sum,tn) + &
399	vsws(j,i) * rmask(j,i,sr)
400	sums_l(nzb+3,var_sum,tn) = sums_l(nzb+3,var_sum,tn) + &
401	ts(j,i) * rmask(j,i,sr)
402	ENDDO
403	ENDDO
404
405	!
406	!-- Horizontally averaged profiles of the vertical fluxes
407	!$OMP DO
408	DO i = nxl, nxr
409	DO j = nys, nyn
410	!
411	!-- Subgridscale fluxes (without Prandtl layer from k=nzb,
412	!-- oterwise from k=nzb+1)
413	!-- NOTE: for simplicity, nzb_diff_s_outer is used below, although
414	!-- ---- strictly speaking the following k-loop would have to be
415	!-- split up according to the staggered grid.
416	DO k = nzb_diff_s_outer(j,i)-1, nzt
417	!
418	!-- Momentum flux w"u"
419	sums_l(k,12,tn) = sums_l(k,12,tn) - 0.25 * ( &
420	km(k,j,i)+km(k+1,j,i)+km(k,j,i-1)+km(k+1,j,i-1) &
421	) * ( &
422	( u(k+1,j,i) - u(k,j,i) ) * ddzu(k+1) &
423	+ ( w(k,j,i) - w(k,j,i-1) ) * ddx &
424	) * rmask(j,i,sr)
425	!
426	!-- Momentum flux w"v"
427	sums_l(k,14,tn) = sums_l(k,14,tn) - 0.25 * ( &
428	km(k,j,i)+km(k+1,j,i)+km(k,j-1,i)+km(k+1,j-1,i) &
429	) * ( &
430	( v(k+1,j,i) - v(k,j,i) ) * ddzu(k+1) &
431	+ ( w(k,j,i) - w(k,j-1,i) ) * ddy &
432	) * rmask(j,i,sr)
433	!
434	!-- Heat flux w"pt"
435	sums_l(k,16,tn) = sums_l(k,16,tn) &
436	- 0.5 * ( kh(k,j,i) + kh(k+1,j,i) ) &
437	* ( pt(k+1,j,i) - pt(k,j,i) ) &
438	* ddzu(k+1) * rmask(j,i,sr)
439
440
441	!
442	!-- Buoyancy flux, water flux (humidity flux) w"q"
443	IF ( moisture ) THEN
444	sums_l(k,45,tn) = sums_l(k,45,tn) &
445	- 0.5 * ( kh(k,j,i) + kh(k+1,j,i) ) &
446	* ( vpt(k+1,j,i) - vpt(k,j,i) ) &
447	* ddzu(k+1) * rmask(j,i,sr)
448	sums_l(k,48,tn) = sums_l(k,48,tn) &
449	- 0.5 * ( kh(k,j,i) + kh(k+1,j,i) ) &
450	* ( q(k+1,j,i) - q(k,j,i) ) &
451	* ddzu(k+1) * rmask(j,i,sr)
452	IF ( cloud_physics ) THEN
453	sums_l(k,51,tn) = sums_l(k,51,tn) &
454	- 0.5 * ( kh(k,j,i) + kh(k+1,j,i) ) &
455	* ( ( q(k+1,j,i) - ql(k+1,j,i) )&
456	- ( q(k,j,i) - ql(k,j,i) ) ) &
457	* ddzu(k+1) * rmask(j,i,sr)
458	ENDIF
459	ENDIF
460
461	!
462	!-- Passive scalar flux
463	IF ( passive_scalar ) THEN
464	sums_l(k,48,tn) = sums_l(k,48,tn) &
465	- 0.5 * ( kh(k,j,i) + kh(k+1,j,i) ) &
466	* ( q(k+1,j,i) - q(k,j,i) ) &
467	* ddzu(k+1) * rmask(j,i,sr)
468	ENDIF
469
470	ENDDO
471
472	!
473	!-- Subgridscale fluxes in the Prandtl layer
474	IF ( use_surface_fluxes ) THEN
475	sums_l(nzb,12,tn) = sums_l(nzb,12,tn) + &
476	usws(j,i) * rmask(j,i,sr) ! w"u"
477	sums_l(nzb,14,tn) = sums_l(nzb,14,tn) + &
478	vsws(j,i) * rmask(j,i,sr) ! w"v"
479	sums_l(nzb,16,tn) = sums_l(nzb,16,tn) + &
480	shf(j,i) * rmask(j,i,sr) ! w"pt"
481	sums_l(nzb,58,tn) = sums_l(nzb,58,tn) + &
482	0.0 * rmask(j,i,sr) ! u"pt"
483	sums_l(nzb,61,tn) = sums_l(nzb,61,tn) + &
484	0.0 * rmask(j,i,sr) ! v"pt"
485	IF ( moisture ) THEN
486	sums_l(nzb,48,tn) = sums_l(nzb,48,tn) + &
487	qsws(j,i) * rmask(j,i,sr) ! w"q" (w"qv")
488	IF ( cloud_physics ) THEN
489	sums_l(nzb,45,tn) = sums_l(nzb,45,tn) + ( &
490	( 1.0 + 0.61 * q(nzb,j,i) ) * &
491	shf(j,i) + 0.61 * pt(nzb,j,i) * &
492	qsws(j,i) &
493	)
494	!
495	!-- Formula does not work if ql(nzb) /= 0.0
496	sums_l(nzb,51,tn) = sums_l(nzb,51,tn) + & ! w"q" (w"qv")
497	qsws(j,i) * rmask(j,i,sr)
498	ENDIF
499	ENDIF
500	IF ( passive_scalar ) THEN
501	sums_l(nzb,48,tn) = sums_l(nzb,48,tn) + &
502	qsws(j,i) * rmask(j,i,sr) ! w"q" (w"qv")
503	ENDIF
504	ENDIF
505
506	!
507	!-- Resolved fluxes (can be computed for all horizontal points)
508	!-- NOTE: for simplicity, nzb_s_outer is used below, although strictly
509	!-- ---- speaking the following k-loop would have to be split up and
510	!-- rearranged according to the staggered grid.
511	DO k = nzb_s_outer(j,i), nzt
512	ust = 0.5 * ( u(k,j,i) - hom(k,1,1,sr) + &
513	u(k+1,j,i) - hom(k+1,1,1,sr) )
514	vst = 0.5 * ( v(k,j,i) - hom(k,1,2,sr) + &
515	v(k+1,j,i) - hom(k+1,1,2,sr) )
516	pts = 0.5 * ( pt(k,j,i) - hom(k,1,4,sr) + &
517	pt(k+1,j,i) - hom(k+1,1,4,sr) )
518	!
519	!-- Momentum flux wu
520	sums_l(k,13,tn) = sums_l(k,13,tn) + 0.5 * &
521	( w(k,j,i-1) + w(k,j,i) ) &
522	* ust * rmask(j,i,sr)
523	!
524	!-- Momentum flux wv
525	sums_l(k,15,tn) = sums_l(k,15,tn) + 0.5 * &
526	( w(k,j-1,i) + w(k,j,i) ) &
527	* vst * rmask(j,i,sr)
528	!
529	!-- Heat flux wpt
530	!-- The following formula (comment line, not executed) does not
531	!-- work if applied to subregions
532	! sums_l(k,17,tn) = sums_l(k,17,tn) + 0.5 * &
533	! ( pt(k,j,i)+pt(k+1,j,i) ) &
534	! * w(k,j,i) * rmask(j,i,sr)
535	sums_l(k,17,tn) = sums_l(k,17,tn) + pts * w(k,j,i) * &
536	rmask(j,i,sr)
537	!
538	!-- Higher moments
539	sums_l(k,35,tn) = sums_l(k,35,tn) + pts * w(k,j,i)*2 &
540	rmask(j,i,sr)
541	sums_l(k,36,tn) = sums_l(k,36,tn) + pts*2 w(k,j,i) * &
542	rmask(j,i,sr)
543
544	!
545	!-- Buoyancy flux, water flux, humidity flux and liquid water
546	!-- content
547	IF ( moisture ) THEN
548	pts = 0.5 * ( vpt(k,j,i) - hom(k,1,44,sr) + &
549	vpt(k+1,j,i) - hom(k+1,1,44,sr) )
550	sums_l(k,46,tn) = sums_l(k,46,tn) + pts * w(k,j,i) * &
551	rmask(j,i,sr)
552	pts = 0.5 * ( q(k,j,i) - hom(k,1,41,sr) + &
553	q(k+1,j,i) - hom(k+1,1,41,sr) )
554	sums_l(k,49,tn) = sums_l(k,49,tn) + pts * w(k,j,i) * &
555	rmask(j,i,sr)
556	IF ( cloud_physics .OR. cloud_droplets ) THEN
557	pts = 0.5 * &
558	( ( q(k,j,i) - ql(k,j,i) ) - hom(k,1,42,sr) &
559	+ ( q(k+1,j,i) - ql(k+1,j,i) ) - hom(k+1,1,42,sr) )
560	sums_l(k,52,tn) = sums_l(k,52,tn) + pts * w(k,j,i) * &
561	rmask(j,i,sr)
562	sums_l(k,54,tn) = sums_l(k,54,tn) + ql(k,j,i) * &
563	rmask(j,i,sr)
564	ENDIF
565	ENDIF
566
567	!
568	!-- Passive scalar flux
569	IF ( passive_scalar ) THEN
570	pts = 0.5 * ( q(k,j,i) - hom(k,1,41,sr) + &
571	q(k+1,j,i) - hom(k+1,1,41,sr) )
572	sums_l(k,49,tn) = sums_l(k,49,tn) + pts * w(k,j,i) * &
573	rmask(j,i,sr)
574	ENDIF
575
576	!
577	!-- Energy flux we
578	sums_l(k,37,tn) = sums_l(k,37,tn) + w(k,j,i) * 0.5 * &
579	( ust2 + vst2 + w(k,j,i)**2 )&
580	* rmask(j,i,sr)
581
582	ENDDO
583	ENDDO
584	ENDDO
585
586	!
587	!-- Divergence of vertical flux of resolved scale energy and pressure
588	!-- fluctuations. First calculate the products, then the divergence.
589	!-- Calculation is time consuming. Do it only, if profiles shall be plotted.
590	IF ( hom(nzb+1,2,55,0) /= 0.0 ) THEN
591
592	sums_ll = 0.0 ! local array
593
594	!$OMP DO
595	DO i = nxl, nxr
596	DO j = nys, nyn
597	DO k = nzb_s_outer(j,i)+1, nzt
598
599	sums_ll(k,1) = sums_ll(k,1) + 0.5 * w(k,j,i) * ( &
600	( 0.25 * ( u(k,j,i)+u(k+1,j,i)+u(k,j,i+1)+u(k+1,j,i+1) &
601	- 2.0 * ( hom(k,1,1,sr) + hom(k+1,1,1,sr) ) &
602	) )**2 &
603	+ ( 0.25 * ( v(k,j,i)+v(k+1,j,i)+v(k,j+1,i)+v(k+1,j+1,i) &
604	- 2.0 * ( hom(k,1,2,sr) + hom(k+1,1,2,sr) ) &
605	) )**2 &
606	+ w(k,j,i)**2 )
607
608	sums_ll(k,2) = sums_ll(k,2) + 0.5 * w(k,j,i) &
609	* ( p(k,j,i) + p(k+1,j,i) )
610
611	ENDDO
612	ENDDO
613	ENDDO
614	sums_ll(0,1) = 0.0 ! because w is zero at the bottom
615	sums_ll(nzt+1,1) = 0.0
616	sums_ll(0,2) = 0.0
617	sums_ll(nzt+1,2) = 0.0
618
619	DO k = nzb_s_outer(j,i)+1, nzt
620	sums_l(k,55,tn) = ( sums_ll(k,1) - sums_ll(k-1,1) ) * ddzw(k)
621	sums_l(k,56,tn) = ( sums_ll(k,2) - sums_ll(k-1,2) ) * ddzw(k)
622	ENDDO
623	sums_l(nzb,55,tn) = sums_l(nzb+1,55,tn)
624	sums_l(nzb,56,tn) = sums_l(nzb+1,56,tn)
625
626	ENDIF
627
628	!
629	!-- Divergence of vertical flux of SGS TKE
630	IF ( hom(nzb+1,2,57,0) /= 0.0 ) THEN
631
632	!$OMP DO
633	DO i = nxl, nxr
634	DO j = nys, nyn
635	DO k = nzb_s_outer(j,i)+1, nzt
636
637	sums_l(k,57,tn) = sums_l(k,57,tn) + ( &
638	(km(k,j,i)+km(k+1,j,i)) * (e(k+1,j,i)-e(k,j,i)) * ddzu(k+1) &
639	- (km(k-1,j,i)+km(k,j,i)) * (e(k,j,i)-e(k-1,j,i)) * ddzu(k) &
640	) * ddzw(k)
641
642	ENDDO
643	ENDDO
644	ENDDO
645	sums_l(nzb,57,tn) = sums_l(nzb+1,57,tn)
646
647	ENDIF
648
649	!
650	!-- Horizontal heat fluxes (subgrid, resolved, total).
651	!-- Do it only, if profiles shall be plotted.
652	IF ( hom(nzb+1,2,58,0) /= 0.0 ) THEN
653
654	!$OMP DO
655	DO i = nxl, nxr
656	DO j = nys, nyn
657	DO k = nzb_s_outer(j,i)+1, nzt
658	!
659	!-- Subgrid horizontal heat fluxes u"pt", v"pt"
660	sums_l(k,58,tn) = sums_l(k,58,tn) - 0.5 * &
661	( kh(k,j,i) + kh(k,j,i-1) ) &
662	* ( pt(k,j,i-1) - pt(k,j,i) ) &
663	* ddx * rmask(j,i,sr)
664	sums_l(k,61,tn) = sums_l(k,61,tn) - 0.5 * &
665	( kh(k,j,i) + kh(k,j-1,i) ) &
666	* ( pt(k,j-1,i) - pt(k,j,i) ) &
667	* ddy * rmask(j,i,sr)
668	!
669	!-- Resolved horizontal heat fluxes upt, vpt
670	sums_l(k,59,tn) = sums_l(k,59,tn) + &
671	( u(k,j,i) - hom(k,1,1,sr) ) &
672	* 0.5 * ( pt(k,j,i-1) - hom(k,1,4,sr) + &
673	pt(k,j,i) - hom(k,1,4,sr) )
674	pts = 0.5 * ( pt(k,j-1,i) - hom(k,1,4,sr) + &
675	pt(k,j,i) - hom(k,1,4,sr) )
676	sums_l(k,62,tn) = sums_l(k,62,tn) + &
677	( v(k,j,i) - hom(k,1,2,sr) ) &
678	* 0.5 * ( pt(k,j-1,i) - hom(k,1,4,sr) + &
679	pt(k,j,i) - hom(k,1,4,sr) )
680	ENDDO
681	ENDDO
682	ENDDO
683	!
684	!-- Fluxes at the surface must be zero (e.g. due to the Prandtl-layer)
685	sums(nzb,58) = 0.0
686	sums(nzb,59) = 0.0
687	sums(nzb,60) = 0.0
688	sums(nzb,61) = 0.0
689	sums(nzb,62) = 0.0
690	sums(nzb,63) = 0.0
691
692	ENDIF
693	!$OMP END PARALLEL
694
695	!
696	!-- Summation of thread sums
697	IF ( threads_per_task > 1 ) THEN
698	DO i = 1, threads_per_task-1
699	sums_l(:,3,0) = sums_l(:,3,0) + sums_l(:,3,i)
700	sums_l(:,4:40,0) = sums_l(:,4:40,0) + sums_l(:,4:40,i)
701	sums_l(:,45:var_sum,0) = sums_l(:,45:var_sum,0) + &
702	sums_l(:,45:var_sum,i)
703	ENDDO
704	ENDIF
705
706	#if defined( __parallel )
707	!
708	!-- Compute total sum from local sums
709	CALL MPI_ALLREDUCE( sums_l(nzb,1,0), sums(nzb,1), ngp_sums, MPI_REAL, &
710	MPI_SUM, comm2d, ierr )
711	#else
712	sums = sums_l(:,:,0)
713	#endif
714
715	!
716	!-- Final values are obtained by division by the total number of grid points
717	!-- used for summation. After that store profiles.
718	!-- Profiles:
719	DO k = nzb, nzt+1
720	sums(k,:var_sum-2) = sums(k,:var_sum-2) / ngp_2dh_outer(k,sr)
721	ENDDO
722	!-- Upstream-parts
723	sums(nzb:nzb+11,var_sum-1) = sums(nzb:nzb+11,var_sum-1) / ngp_3d(sr)
724	!-- u* and so on
725	!-- As sums(nzb:nzb+3,var_sum) are full 2D arrays (us, usws, vsws, ts) whose
726	!-- size is always ( nx + 1 ) * ( ny + 1 ), defined at the first grid layer
727	!-- above the topography, they are being divided by ngp_2dh(sr)
728	sums(nzb:nzb+3,var_sum) = sums(nzb:nzb+3,var_sum) / &
729	ngp_2dh(sr)
730	!-- eges, e*
731	sums(nzb+4:nzb+5,var_sum) = sums(nzb+4:nzb+5,var_sum) / &
732	ngp_3d_inner(sr)
733	!-- Old and new divergence
734	sums(nzb+9:nzb+10,var_sum) = sums(nzb+9:nzb+10,var_sum) / &
735	ngp_3d_inner(sr)
736
737	!
738	!-- Collect horizontal average in hom.
739	!-- Compute deduced averages (e.g. total heat flux)
740	hom(:,1,3,sr) = sums(:,3) ! w
741	hom(:,1,8,sr) = sums(:,8) ! e profiles 5-7 are initial profiles
742	hom(:,1,9,sr) = sums(:,9) ! km
743	hom(:,1,10,sr) = sums(:,10) ! kh
744	hom(:,1,11,sr) = sums(:,11) ! l
745	hom(:,1,12,sr) = sums(:,12) ! w"u"
746	hom(:,1,13,sr) = sums(:,13) ! wu
747	hom(:,1,14,sr) = sums(:,14) ! w"v"
748	hom(:,1,15,sr) = sums(:,15) ! wv
749	hom(:,1,16,sr) = sums(:,16) ! w"pt"
750	hom(:,1,17,sr) = sums(:,17) ! wpt
751	hom(:,1,18,sr) = sums(:,16) + sums(:,17) ! wpt
752	hom(:,1,19,sr) = sums(:,12) + sums(:,13) ! wu
753	hom(:,1,20,sr) = sums(:,14) + sums(:,15) ! wv
754	hom(:,1,21,sr) = sums(:,21) ! wptBC
755	hom(:,1,22,sr) = sums(:,16) + sums(:,21) ! wptBC
756	! profiles 23-29 left empty for initial
757	! profiles
758	hom(:,1,30,sr) = sums(:,30) ! u*2
759	hom(:,1,31,sr) = sums(:,31) ! v*2
760	hom(:,1,32,sr) = sums(:,32) ! w*2
761	hom(:,1,33,sr) = sums(:,33) ! pt*2
762	hom(:,1,34,sr) = sums(:,34) ! e*
763	hom(:,1,35,sr) = sums(:,35) ! w2pt
764	hom(:,1,36,sr) = sums(:,36) ! wpt2
765	hom(:,1,37,sr) = sums(:,37) ! we
766	hom(:,1,38,sr) = sums(:,38) ! w*3
767	hom(:,1,39,sr) = sums(:,38) / ( sums(:,32) + 1E-20 )**1.5 ! Sw
768	hom(:,1,40,sr) = sums(:,40) ! p
769	hom(:,1,45,sr) = sums(:,45) ! w"q"
770	hom(:,1,46,sr) = sums(:,46) ! wvpt
771	hom(:,1,47,sr) = sums(:,45) + sums(:,46) ! wvpt
772	hom(:,1,48,sr) = sums(:,48) ! w"q" (w"qv")
773	hom(:,1,49,sr) = sums(:,49) ! wq (wqv)
774	hom(:,1,50,sr) = sums(:,48) + sums(:,49) ! wq (wqv)
775	hom(:,1,51,sr) = sums(:,51) ! w"qv"
776	hom(:,1,52,sr) = sums(:,52) ! wqv
777	hom(:,1,53,sr) = sums(:,52) + sums(:,51) ! wq (wqv)
778	hom(:,1,54,sr) = sums(:,54) ! ql
779	hom(:,1,55,sr) = sums(:,55) ! wuu*/dz
780	hom(:,1,56,sr) = sums(:,56) ! wp/dz
781	hom(:,1,57,sr) = sums(:,57) ! w"e/dz
782	hom(:,1,58,sr) = sums(:,58) ! u"pt"
783	hom(:,1,59,sr) = sums(:,59) ! upt
784	hom(:,1,60,sr) = sums(:,58) + sums(:,59) ! upt_t
785	hom(:,1,61,sr) = sums(:,61) ! v"pt"
786	hom(:,1,62,sr) = sums(:,62) ! vpt
787	hom(:,1,63,sr) = sums(:,61) + sums(:,62) ! vpt_t
788
789	hom(:,1,var_hom-1,sr) = sums(:,var_sum-1)
790	! upstream-parts u_x, u_y, u_z, v_x,
791	! v_y, usw. (in last but one profile)
792	hom(:,1,var_hom,sr) = sums(:,var_sum)
793	! u, w'u', w'v', t (in last profile)
794
795	!
796	!-- Determine the boundary layer height using two different schemes.
797	!-- First scheme: Starting from the Earth's surface, look for the first
798	!-- relative minimum of the total heat flux. The corresponding height is
799	!-- accepted as the boundary layer height, if it is less than 1.5 times the
800	!-- height where the heat flux becomes negative for the first time.
801	!-- NOTE: This criterion is still capable of improving!
802	z_i(1) = 0.0
803	first = .TRUE.
804	DO k = nzb, nzt-1
805	IF ( first .AND. hom(k,1,18,sr) < 0.0 ) THEN
806	first = .FALSE.
807	height = zw(k)
808	ENDIF
809	IF ( hom(k,1,18,sr) < 0.0 .AND. &
810	hom(k+1,1,18,sr) > hom(k,1,18,sr) ) THEN
811	IF ( zw(k) < 1.5 * height ) THEN
812	z_i(1) = zw(k)
813	ELSE
814	z_i(1) = height
815	ENDIF
816	EXIT
817	ENDIF
818	ENDDO
819
820	!
821	!-- Second scheme: Starting from the top model boundary, look for the first
822	!-- characteristic kink in the temperature profile, where the originally
823	!-- stable stratification notably weakens.
824	z_i(2) = 0.0
825	DO k = nzt-1, nzb+1, -1
826	IF ( ( hom(k+1,1,4,sr) - hom(k,1,4,sr) ) > &
827	2.0 * ( hom(k,1,4,sr) - hom(k-1,1,4,sr) ) ) THEN
828	z_i(2) = zu(k)
829	EXIT
830	ENDIF
831	ENDDO
832
833	hom(nzb+6,1,var_hom,sr) = z_i(1)
834	hom(nzb+7,1,var_hom,sr) = z_i(2)
835
836	!
837	!-- Computation of both the characteristic vertical velocity and
838	!-- the characteristic convective boundary layer temperature.
839	!-- The horizontal average at nzb+1 is input for the average temperature.
840	IF ( hom(nzb,1,18,sr) > 0.0 .AND. z_i(1) /= 0.0 ) THEN
841	hom(nzb+8,1,var_hom,sr) = ( g / hom(nzb+1,1,4,sr) * &
842	hom(nzb,1,18,sr) * z_i(1) )**0.333333333
843	!-- so far this only works if Prandtl layer is used
844	hom(nzb+11,1,var_hom,sr) = hom(nzb,1,16,sr) / hom(nzb+8,1,var_hom,sr)
845	ELSE
846	hom(nzb+8,1,var_hom,sr) = 0.0
847	hom(nzb+11,1,var_hom,sr) = 0.0
848	ENDIF
849
850	ENDDO ! loop of the subregions
851
852	!
853	!-- Calculate additional statistics provided by the user interface
854	CALL user_statistics
855
856	!
857	!-- If required, sum up horizontal averages for subsequent time averaging
858	IF ( do_sum ) THEN
859	IF ( average_count_pr == 0 ) hom_sum = 0.0
860	hom_sum = hom_sum + hom(:,1,:,:)
861	average_count_pr = average_count_pr + 1
862	do_sum = .FALSE.
863	ENDIF
864
865	!
866	!-- Set flag for other UPs (e.g. output routines, but also buoyancy).
867	!-- This flag is reset after each time step in time_integration.
868	flow_statistics_called = .TRUE.
869
870	CALL cpu_log( log_point(10), 'flow_statistics', 'stop' )
871
872
873	END SUBROUTINE flow_statistics
874
875
876

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