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source: palm/trunk/SOURCE/flow_statistics.f90 @ 23

Last change on this file since 23 was 19, checked in by raasch, 18 years ago
preliminary version of modified boundary conditions at top
Property svn:keywords set to `Id`
File size: 35.1 KB

Rev	Line
[1]	1	SUBROUTINE flow_statistics
	2
	3	!------------------------------------------------------------------------------!
	4	! Actual revisions:
	5	! -----------------
[19]	6	! fluxes at top modified (tswst, qswst)
[1]	7	!
	8	! Former revisions:
	9	! -----------------
[3]	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	!
[1]	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)
[19]	349	ENDDO
	350
	351	DO k = nzb_diff_s_outer(j,i)-1, nzt_diff
[1]	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	!
[19]	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	!
[1]	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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