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source: palm/trunk/SOURCE/flow_statistics.f90 @ 22

Last change on this file since 22 was 19, checked in by raasch, 17 years ago
preliminary version of modified boundary conditions at top
Property svn:keywords set to `Id`
File size: 35.1 KB

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

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