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source: palm/trunk/SOURCE/flow_statistics.f90 @ 71

Last change on this file since 71 was 51, checked in by raasch, 18 years ago
preliminary version, several changes to be explained later
Property svn:keywords set to `Id`
File size: 36.7 KB

Rev	Line
[1]	1	SUBROUTINE flow_statistics
	2
	3	!------------------------------------------------------------------------------!
	4	! Actual revisions:
	5	! -----------------
[51]	6	! Collection of time series quantities moved from routine flow_statistics to
	7	! here, routine user_statistics is called for each statistic region
[1]	8	!
	9	! Former revisions:
	10	! -----------------
[3]	11	! $Id: flow_statistics.f90 51 2007-03-07 08:38:00Z raasch $
[39]	12	! fluxes at top modified (tswst, qswst)
	13	!
	14	! 19 2007-02-23 04:53:48Z raasch
	15	!
[3]	16	! RCS Log replace by Id keyword, revision history cleaned up
	17	!
[1]	18	! Revision 1.41 2006/08/04 14:37:50 raasch
	19	! Error removed in non-parallel part (sums_l)
	20	!
	21	! Revision 1.1 1997/08/11 06:15:17 raasch
	22	! Initial revision
	23	!
	24	!
	25	! Description:
	26	! ------------
	27	! Compute average profiles and further average flow quantities for the different
	28	! user-defined (sub-)regions. The region indexed 0 is the total model domain.
	29	!
	30	! NOTE: For simplicity, nzb_s_outer and nzb_diff_s_outer are being used as a
	31	! ---- lower vertical index for k-loops for all variables so that regardless
	32	! of the variable and its respective staggered grid always the same number of
	33	! grid points is used for 2D averages. The disadvantage: depending on the
	34	! variable, up to one grid layer adjacent to the (vertical walls of the)
	35	! topography is missed out by this simplification.
	36	!------------------------------------------------------------------------------!
	37
	38	USE arrays_3d
	39	USE cloud_parameters
	40	USE cpulog
	41	USE grid_variables
	42	USE indices
	43	USE interfaces
	44	USE pegrid
	45	USE statistics
	46	USE control_parameters
	47
	48	IMPLICIT NONE
	49
	50	INTEGER :: i, j, k, omp_get_thread_num, sr, tn
	51	LOGICAL :: first
	52	REAL :: height, pts, sums_l_eper, sums_l_etot, ust, ust2, u2, vst, &
	53	vst2, v2, w2, z_i(2)
	54	REAL :: sums_ll(nzb:nzt+1,2)
	55
	56
	57	CALL cpu_log( log_point(10), 'flow_statistics', 'start' )
	58
	59	!
	60	!-- To be on the safe side, check whether flow_statistics has already been
	61	!-- called once after the current time step
	62	IF ( flow_statistics_called ) THEN
	63	IF ( myid == 0 ) PRINT*, '+++ WARNING: flow_statistics is called two', &
	64	' times within one timestep'
	65	CALL local_stop
	66	ENDIF
	67
	68	!
	69	!-- Compute statistics for each (sub-)region
	70	DO sr = 0, statistic_regions
	71
	72	!
	73	!-- Initialize (local) summation array
	74	sums_l = 0.0
	75
	76	!
	77	!-- Store sums that have been computed in other subroutines in summation
	78	!-- array
	79	sums_l(:,11,:) = sums_l_l(:,sr,:) ! mixing length from diffusivities
	80	!-- WARNING: next line still has to be adjusted for OpenMP
	81	sums_l(:,21,0) = sums_wsts_bc_l(:,sr) ! heat flux from advec_s_bc
	82	sums_l(nzb+9,var_sum,0) = sums_divold_l(sr) ! old divergence from pres
	83	sums_l(nzb+10,var_sum,0) = sums_divnew_l(sr) ! new divergence from pres
	84	!-- WARNING: next four lines still may have to be adjusted for OpenMP
	85	sums_l(nzb:nzb+2,var_sum-1,0) = sums_up_fraction_l(1,1:3,sr)! upstream
	86	sums_l(nzb+3:nzb+5,var_sum-1,0) = sums_up_fraction_l(2,1:3,sr)! parts
	87	sums_l(nzb+6:nzb+8,var_sum-1,0) = sums_up_fraction_l(3,1:3,sr)! from
	88	sums_l(nzb+9:nzb+11,var_sum-1,0) = sums_up_fraction_l(4,1:3,sr)! spline
	89
	90	!
	91	!-- Horizontally averaged profiles of horizontal velocities and temperature.
	92	!-- They must have been computed before, because they are already required
	93	!-- for other horizontal averages.
	94	tn = 0
	95	!$OMP PARALLEL PRIVATE( i, j, k, tn )
	96	#if defined( __lcmuk )
	97	tn = omp_get_thread_num()
	98	#else
	99	!$ tn = omp_get_thread_num()
	100	#endif
	101
	102	!$OMP DO
	103	DO i = nxl, nxr
	104	DO j = nys, nyn
	105	DO k = nzb_s_outer(j,i), nzt+1
	106	sums_l(k,1,tn) = sums_l(k,1,tn) + u(k,j,i) * rmask(j,i,sr)
	107	sums_l(k,2,tn) = sums_l(k,2,tn) + v(k,j,i) * rmask(j,i,sr)
	108	sums_l(k,4,tn) = sums_l(k,4,tn) + pt(k,j,i) * rmask(j,i,sr)
	109	ENDDO
	110	ENDDO
	111	ENDDO
	112
	113	!
	114	!-- Horizontally averaged profiles of virtual potential temperature,
	115	!-- total water content, specific humidity and liquid water potential
	116	!-- temperature
	117	IF ( moisture ) THEN
	118	!$OMP DO
	119	DO i = nxl, nxr
	120	DO j = nys, nyn
	121	DO k = nzb_s_outer(j,i), nzt+1
	122	sums_l(k,44,tn) = sums_l(k,44,tn) + &
	123	vpt(k,j,i) * rmask(j,i,sr)
	124	sums_l(k,41,tn) = sums_l(k,41,tn) + &
	125	q(k,j,i) * rmask(j,i,sr)
	126	ENDDO
	127	ENDDO
	128	ENDDO
	129	IF ( cloud_physics ) THEN
	130	!$OMP DO
	131	DO i = nxl, nxr
	132	DO j = nys, nyn
	133	DO k = nzb_s_outer(j,i), nzt+1
	134	sums_l(k,42,tn) = sums_l(k,42,tn) + &
	135	( q(k,j,i) - ql(k,j,i) ) * rmask(j,i,sr)
	136	sums_l(k,43,tn) = sums_l(k,43,tn) + ( &
	137	pt(k,j,i) + l_d_cppt_d_t(k) ql(k,j,i) &
	138	) * rmask(j,i,sr)
	139	ENDDO
	140	ENDDO
	141	ENDDO
	142	ENDIF
	143	ENDIF
	144
	145	!
	146	!-- Horizontally averaged profiles of passive scalar
	147	IF ( passive_scalar ) THEN
	148	!$OMP DO
	149	DO i = nxl, nxr
	150	DO j = nys, nyn
	151	DO k = nzb_s_outer(j,i), nzt+1
	152	sums_l(k,41,tn) = sums_l(k,41,tn) + q(k,j,i) * rmask(j,i,sr)
	153	ENDDO
	154	ENDDO
	155	ENDDO
	156	ENDIF
	157	!$OMP END PARALLEL
	158
	159	!
	160	!-- Summation of thread sums
	161	IF ( threads_per_task > 1 ) THEN
	162	DO i = 1, threads_per_task-1
	163	sums_l(:,1,0) = sums_l(:,1,0) + sums_l(:,1,i)
	164	sums_l(:,2,0) = sums_l(:,2,0) + sums_l(:,2,i)
	165	sums_l(:,4,0) = sums_l(:,4,0) + sums_l(:,4,i)
	166	IF ( moisture ) THEN
	167	sums_l(:,41,0) = sums_l(:,41,0) + sums_l(:,41,i)
	168	sums_l(:,44,0) = sums_l(:,44,0) + sums_l(:,44,i)
	169	IF ( cloud_physics ) THEN
	170	sums_l(:,42,0) = sums_l(:,42,0) + sums_l(:,42,i)
	171	sums_l(:,43,0) = sums_l(:,43,0) + sums_l(:,43,i)
	172	ENDIF
	173	ENDIF
	174	IF ( passive_scalar ) THEN
	175	sums_l(:,41,0) = sums_l(:,41,0) + sums_l(:,41,i)
	176	ENDIF
	177	ENDDO
	178	ENDIF
	179
	180	#if defined( __parallel )
	181	!
	182	!-- Compute total sum from local sums
	183	CALL MPI_ALLREDUCE( sums_l(nzb,1,0), sums(nzb,1), nzt+2-nzb, MPI_REAL, &
	184	MPI_SUM, comm2d, ierr )
	185	CALL MPI_ALLREDUCE( sums_l(nzb,2,0), sums(nzb,2), nzt+2-nzb, MPI_REAL, &
	186	MPI_SUM, comm2d, ierr )
	187	CALL MPI_ALLREDUCE( sums_l(nzb,4,0), sums(nzb,4), nzt+2-nzb, MPI_REAL, &
	188	MPI_SUM, comm2d, ierr )
	189	IF ( moisture ) THEN
	190	CALL MPI_ALLREDUCE( sums_l(nzb,44,0), sums(nzb,44), nzt+2-nzb, &
	191	MPI_REAL, MPI_SUM, comm2d, ierr )
	192	CALL MPI_ALLREDUCE( sums_l(nzb,41,0), sums(nzb,41), nzt+2-nzb, &
	193	MPI_REAL, MPI_SUM, comm2d, ierr )
	194	IF ( cloud_physics ) THEN
	195	CALL MPI_ALLREDUCE( sums_l(nzb,42,0), sums(nzb,42), nzt+2-nzb, &
	196	MPI_REAL, MPI_SUM, comm2d, ierr )
	197	CALL MPI_ALLREDUCE( sums_l(nzb,43,0), sums(nzb,43), nzt+2-nzb, &
	198	MPI_REAL, MPI_SUM, comm2d, ierr )
	199	ENDIF
	200	ENDIF
	201
	202	IF ( passive_scalar ) THEN
	203	CALL MPI_ALLREDUCE( sums_l(nzb,41,0), sums(nzb,41), nzt+2-nzb, &
	204	MPI_REAL, MPI_SUM, comm2d, ierr )
	205	ENDIF
	206	#else
	207	sums(:,1) = sums_l(:,1,0)
	208	sums(:,2) = sums_l(:,2,0)
	209	sums(:,4) = sums_l(:,4,0)
	210	IF ( moisture ) THEN
	211	sums(:,44) = sums_l(:,44,0)
	212	sums(:,41) = sums_l(:,41,0)
	213	IF ( cloud_physics ) THEN
	214	sums(:,42) = sums_l(:,42,0)
	215	sums(:,43) = sums_l(:,43,0)
	216	ENDIF
	217	ENDIF
	218	IF ( passive_scalar ) sums(:,41) = sums_l(:,41,0)
	219	#endif
	220
	221	!
	222	!-- Final values are obtained by division by the total number of grid points
	223	!-- used for summation. After that store profiles.
	224	sums(:,1) = sums(:,1) / ngp_2dh_outer(:,sr)
	225	sums(:,2) = sums(:,2) / ngp_2dh_outer(:,sr)
	226	sums(:,4) = sums(:,4) / ngp_2dh_outer(:,sr)
	227	hom(:,1,1,sr) = sums(:,1) ! u
	228	hom(:,1,2,sr) = sums(:,2) ! v
	229	hom(:,1,4,sr) = sums(:,4) ! pt
	230
	231	!
	232	!-- Humidity and cloud parameters
	233	IF ( moisture ) THEN
	234	sums(:,44) = sums(:,44) / ngp_2dh_outer(:,sr)
	235	sums(:,41) = sums(:,41) / ngp_2dh_outer(:,sr)
	236	hom(:,1,44,sr) = sums(:,44) ! vpt
	237	hom(:,1,41,sr) = sums(:,41) ! qv (q)
	238	IF ( cloud_physics ) THEN
	239	sums(:,42) = sums(:,42) / ngp_2dh_outer(:,sr)
	240	sums(:,43) = sums(:,43) / ngp_2dh_outer(:,sr)
	241	hom(:,1,42,sr) = sums(:,42) ! qv
	242	hom(:,1,43,sr) = sums(:,43) ! pt
	243	ENDIF
	244	ENDIF
	245
	246	!
	247	!-- Passive scalar
	248	IF ( passive_scalar ) hom(:,1,41,sr) = sums(:,41) / ngp_2dh_outer(:,sr)
	249
	250	!
	251	!-- Horizontally averaged profiles of the remaining prognostic variables,
	252	!-- variances, the total and the perturbation energy (single values in last
	253	!-- column of sums_l) and some diagnostic quantities.
	254	!-- NOTE: for simplicity, nzb_s_outer is used below, although strictly
	255	!-- ---- speaking the following k-loop would have to be split up and
	256	!-- rearranged according to the staggered grid.
	257	tn = 0
	258	#if defined( __lcmuk )
	259	!$OMP PARALLEL PRIVATE( i, j, k, pts, sums_ll, sums_l_eper, sums_l_etot, &
	260	!$OMP tn, ust, ust2, u2, vst, vst2, v2, w2 )
	261	tn = omp_get_thread_num()
	262	#else
	263	!$OMP PARALLEL PRIVATE( i, j, k, pts, sums_ll, sums_l_eper, sums_l_etot, tn, ust, ust2, u2, vst, vst2, v2, w2 )
	264	!$ tn = omp_get_thread_num()
	265	#endif
	266	!$OMP DO
	267	DO i = nxl, nxr
	268	DO j = nys, nyn
	269	sums_l_etot = 0.0
	270	sums_l_eper = 0.0
	271	DO k = nzb_s_outer(j,i), nzt+1
	272	u2 = u(k,j,i)**2
	273	v2 = v(k,j,i)**2
	274	w2 = w(k,j,i)**2
	275	ust2 = ( u(k,j,i) - hom(k,1,1,sr) )**2
	276	vst2 = ( v(k,j,i) - hom(k,1,2,sr) )**2
	277	!
	278	!-- Prognostic and diagnostic variables
	279	sums_l(k,3,tn) = sums_l(k,3,tn) + w(k,j,i) * rmask(j,i,sr)
	280	sums_l(k,8,tn) = sums_l(k,8,tn) + e(k,j,i) * rmask(j,i,sr)
	281	sums_l(k,9,tn) = sums_l(k,9,tn) + km(k,j,i) * rmask(j,i,sr)
	282	sums_l(k,10,tn) = sums_l(k,10,tn) + kh(k,j,i) * rmask(j,i,sr)
	283	sums_l(k,40,tn) = sums_l(k,40,tn) + p(k,j,i)
	284
	285	!
	286	!-- Variances
	287	sums_l(k,30,tn) = sums_l(k,30,tn) + ust2 * rmask(j,i,sr)
	288	sums_l(k,31,tn) = sums_l(k,31,tn) + vst2 * rmask(j,i,sr)
	289	sums_l(k,32,tn) = sums_l(k,32,tn) + w2 * rmask(j,i,sr)
	290	sums_l(k,33,tn) = sums_l(k,33,tn) + &
	291	( pt(k,j,i)-hom(k,1,4,sr) )*2 rmask(j,i,sr)
	292	!
	293	!-- Higher moments
	294	!-- (Computation of the skewness of w further below)
	295	sums_l(k,38,tn) = sums_l(k,38,tn) + w(k,j,i) * w2 * &
	296	rmask(j,i,sr)
	297	!
	298	!-- Perturbation energy
	299	sums_l(k,34,tn) = sums_l(k,34,tn) + 0.5 * ( ust2 + vst2 + w2 ) &
	300	* rmask(j,i,sr)
	301	sums_l_etot = sums_l_etot + &
	302	0.5 * ( u2 + v2 + w2 ) * rmask(j,i,sr)
	303	sums_l_eper = sums_l_eper + &
	304	0.5 * ( ust2+vst2+w2 ) * rmask(j,i,sr)
	305	ENDDO
	306	!
	307	!-- Total and perturbation energy for the total domain (being
	308	!-- collected in the last column of sums_l). Summation of these
	309	!-- quantities is seperated from the previous loop in order to
	310	!-- allow vectorization of that loop.
	311	sums_l(nzb+4,var_sum,tn) = sums_l(nzb+4,var_sum,tn) + sums_l_etot
	312	sums_l(nzb+5,var_sum,tn) = sums_l(nzb+5,var_sum,tn) + sums_l_eper
	313	!
	314	!-- 2D-arrays (being collected in the last column of sums_l)
	315	sums_l(nzb,var_sum,tn) = sums_l(nzb,var_sum,tn) + &
	316	us(j,i) * rmask(j,i,sr)
	317	sums_l(nzb+1,var_sum,tn) = sums_l(nzb+1,var_sum,tn) + &
	318	usws(j,i) * rmask(j,i,sr)
	319	sums_l(nzb+2,var_sum,tn) = sums_l(nzb+2,var_sum,tn) + &
	320	vsws(j,i) * rmask(j,i,sr)
	321	sums_l(nzb+3,var_sum,tn) = sums_l(nzb+3,var_sum,tn) + &
	322	ts(j,i) * rmask(j,i,sr)
	323	ENDDO
	324	ENDDO
	325
	326	!
	327	!-- Horizontally averaged profiles of the vertical fluxes
	328	!$OMP DO
	329	DO i = nxl, nxr
	330	DO j = nys, nyn
	331	!
	332	!-- Subgridscale fluxes (without Prandtl layer from k=nzb,
	333	!-- oterwise from k=nzb+1)
	334	!-- NOTE: for simplicity, nzb_diff_s_outer is used below, although
	335	!-- ---- strictly speaking the following k-loop would have to be
	336	!-- split up according to the staggered grid.
	337	DO k = nzb_diff_s_outer(j,i)-1, nzt
	338	!
	339	!-- Momentum flux w"u"
	340	sums_l(k,12,tn) = sums_l(k,12,tn) - 0.25 * ( &
	341	km(k,j,i)+km(k+1,j,i)+km(k,j,i-1)+km(k+1,j,i-1) &
	342	) * ( &
	343	( u(k+1,j,i) - u(k,j,i) ) * ddzu(k+1) &
	344	+ ( w(k,j,i) - w(k,j,i-1) ) * ddx &
	345	) * rmask(j,i,sr)
	346	!
	347	!-- Momentum flux w"v"
	348	sums_l(k,14,tn) = sums_l(k,14,tn) - 0.25 * ( &
	349	km(k,j,i)+km(k+1,j,i)+km(k,j-1,i)+km(k+1,j-1,i) &
	350	) * ( &
	351	( v(k+1,j,i) - v(k,j,i) ) * ddzu(k+1) &
	352	+ ( w(k,j,i) - w(k,j-1,i) ) * ddy &
	353	) * rmask(j,i,sr)
[19]	354	ENDDO
	355
	356	DO k = nzb_diff_s_outer(j,i)-1, nzt_diff
[1]	357	!
	358	!-- Heat flux w"pt"
	359	sums_l(k,16,tn) = sums_l(k,16,tn) &
	360	- 0.5 * ( kh(k,j,i) + kh(k+1,j,i) ) &
	361	* ( pt(k+1,j,i) - pt(k,j,i) ) &
	362	* ddzu(k+1) * rmask(j,i,sr)
	363
	364
	365	!
	366	!-- Buoyancy flux, water flux (humidity flux) w"q"
	367	IF ( moisture ) THEN
	368	sums_l(k,45,tn) = sums_l(k,45,tn) &
	369	- 0.5 * ( kh(k,j,i) + kh(k+1,j,i) ) &
	370	* ( vpt(k+1,j,i) - vpt(k,j,i) ) &
	371	* ddzu(k+1) * rmask(j,i,sr)
	372	sums_l(k,48,tn) = sums_l(k,48,tn) &
	373	- 0.5 * ( kh(k,j,i) + kh(k+1,j,i) ) &
	374	* ( q(k+1,j,i) - q(k,j,i) ) &
	375	* ddzu(k+1) * rmask(j,i,sr)
	376	IF ( cloud_physics ) THEN
	377	sums_l(k,51,tn) = sums_l(k,51,tn) &
	378	- 0.5 * ( kh(k,j,i) + kh(k+1,j,i) ) &
	379	* ( ( q(k+1,j,i) - ql(k+1,j,i) )&
	380	- ( q(k,j,i) - ql(k,j,i) ) ) &
	381	* ddzu(k+1) * rmask(j,i,sr)
	382	ENDIF
	383	ENDIF
	384
	385	!
	386	!-- Passive scalar flux
	387	IF ( passive_scalar ) THEN
	388	sums_l(k,48,tn) = sums_l(k,48,tn) &
	389	- 0.5 * ( kh(k,j,i) + kh(k+1,j,i) ) &
	390	* ( q(k+1,j,i) - q(k,j,i) ) &
	391	* ddzu(k+1) * rmask(j,i,sr)
	392	ENDIF
	393
	394	ENDDO
	395
	396	!
	397	!-- Subgridscale fluxes in the Prandtl layer
	398	IF ( use_surface_fluxes ) THEN
	399	sums_l(nzb,12,tn) = sums_l(nzb,12,tn) + &
	400	usws(j,i) * rmask(j,i,sr) ! w"u"
	401	sums_l(nzb,14,tn) = sums_l(nzb,14,tn) + &
	402	vsws(j,i) * rmask(j,i,sr) ! w"v"
	403	sums_l(nzb,16,tn) = sums_l(nzb,16,tn) + &
	404	shf(j,i) * rmask(j,i,sr) ! w"pt"
	405	sums_l(nzb,58,tn) = sums_l(nzb,58,tn) + &
	406	0.0 * rmask(j,i,sr) ! u"pt"
	407	sums_l(nzb,61,tn) = sums_l(nzb,61,tn) + &
	408	0.0 * rmask(j,i,sr) ! v"pt"
	409	IF ( moisture ) THEN
	410	sums_l(nzb,48,tn) = sums_l(nzb,48,tn) + &
	411	qsws(j,i) * rmask(j,i,sr) ! w"q" (w"qv")
	412	IF ( cloud_physics ) THEN
	413	sums_l(nzb,45,tn) = sums_l(nzb,45,tn) + ( &
	414	( 1.0 + 0.61 * q(nzb,j,i) ) * &
	415	shf(j,i) + 0.61 * pt(nzb,j,i) * &
	416	qsws(j,i) &
	417	)
	418	!
	419	!-- Formula does not work if ql(nzb) /= 0.0
	420	sums_l(nzb,51,tn) = sums_l(nzb,51,tn) + & ! w"q" (w"qv")
	421	qsws(j,i) * rmask(j,i,sr)
	422	ENDIF
	423	ENDIF
	424	IF ( passive_scalar ) THEN
	425	sums_l(nzb,48,tn) = sums_l(nzb,48,tn) + &
	426	qsws(j,i) * rmask(j,i,sr) ! w"q" (w"qv")
	427	ENDIF
	428	ENDIF
	429
	430	!
[19]	431	!-- Subgridscale fluxes at the top surface
	432	IF ( use_top_fluxes ) THEN
	433	sums_l(nzt,16,tn) = sums_l(nzt,16,tn) + &
	434	tswst(j,i) * rmask(j,i,sr) ! w"pt"
	435	sums_l(nzt,58,tn) = sums_l(nzt,58,tn) + &
	436	0.0 * rmask(j,i,sr) ! u"pt"
	437	sums_l(nzt,61,tn) = sums_l(nzt,61,tn) + &
	438	0.0 * rmask(j,i,sr) ! v"pt"
	439	IF ( moisture ) THEN
	440	sums_l(nzt,48,tn) = sums_l(nzt,48,tn) + &
	441	qswst(j,i) * rmask(j,i,sr) ! w"q" (w"qv")
	442	IF ( cloud_physics ) THEN
	443	sums_l(nzt,45,tn) = sums_l(nzt,45,tn) + ( &
	444	( 1.0 + 0.61 * q(nzt,j,i) ) * &
	445	tswst(j,i) + 0.61 * pt(nzt,j,i) * &
	446	qsws(j,i) &
	447	)
	448	!
	449	!-- Formula does not work if ql(nzb) /= 0.0
	450	sums_l(nzt,51,tn) = sums_l(nzt,51,tn) + & ! w"q" (w"qv")
	451	qswst(j,i) * rmask(j,i,sr)
	452	ENDIF
	453	ENDIF
	454	IF ( passive_scalar ) THEN
	455	sums_l(nzt,48,tn) = sums_l(nzt,48,tn) + &
	456	qswst(j,i) * rmask(j,i,sr) ! w"q" (w"qv")
	457	ENDIF
	458	ENDIF
	459
	460	!
[1]	461	!-- Resolved fluxes (can be computed for all horizontal points)
	462	!-- NOTE: for simplicity, nzb_s_outer is used below, although strictly
	463	!-- ---- speaking the following k-loop would have to be split up and
	464	!-- rearranged according to the staggered grid.
	465	DO k = nzb_s_outer(j,i), nzt
	466	ust = 0.5 * ( u(k,j,i) - hom(k,1,1,sr) + &
	467	u(k+1,j,i) - hom(k+1,1,1,sr) )
	468	vst = 0.5 * ( v(k,j,i) - hom(k,1,2,sr) + &
	469	v(k+1,j,i) - hom(k+1,1,2,sr) )
	470	pts = 0.5 * ( pt(k,j,i) - hom(k,1,4,sr) + &
	471	pt(k+1,j,i) - hom(k+1,1,4,sr) )
	472	!
	473	!-- Momentum flux wu
	474	sums_l(k,13,tn) = sums_l(k,13,tn) + 0.5 * &
	475	( w(k,j,i-1) + w(k,j,i) ) &
	476	* ust * rmask(j,i,sr)
	477	!
	478	!-- Momentum flux wv
	479	sums_l(k,15,tn) = sums_l(k,15,tn) + 0.5 * &
	480	( w(k,j-1,i) + w(k,j,i) ) &
	481	* vst * rmask(j,i,sr)
	482	!
	483	!-- Heat flux wpt
	484	!-- The following formula (comment line, not executed) does not
	485	!-- work if applied to subregions
	486	! sums_l(k,17,tn) = sums_l(k,17,tn) + 0.5 * &
	487	! ( pt(k,j,i)+pt(k+1,j,i) ) &
	488	! * w(k,j,i) * rmask(j,i,sr)
	489	sums_l(k,17,tn) = sums_l(k,17,tn) + pts * w(k,j,i) * &
	490	rmask(j,i,sr)
	491	!
	492	!-- Higher moments
	493	sums_l(k,35,tn) = sums_l(k,35,tn) + pts * w(k,j,i)*2 &
	494	rmask(j,i,sr)
	495	sums_l(k,36,tn) = sums_l(k,36,tn) + pts*2 w(k,j,i) * &
	496	rmask(j,i,sr)
	497
	498	!
	499	!-- Buoyancy flux, water flux, humidity flux and liquid water
	500	!-- content
	501	IF ( moisture ) THEN
	502	pts = 0.5 * ( vpt(k,j,i) - hom(k,1,44,sr) + &
	503	vpt(k+1,j,i) - hom(k+1,1,44,sr) )
	504	sums_l(k,46,tn) = sums_l(k,46,tn) + pts * w(k,j,i) * &
	505	rmask(j,i,sr)
	506	pts = 0.5 * ( q(k,j,i) - hom(k,1,41,sr) + &
	507	q(k+1,j,i) - hom(k+1,1,41,sr) )
	508	sums_l(k,49,tn) = sums_l(k,49,tn) + pts * w(k,j,i) * &
	509	rmask(j,i,sr)
	510	IF ( cloud_physics .OR. cloud_droplets ) THEN
	511	pts = 0.5 * &
	512	( ( q(k,j,i) - ql(k,j,i) ) - hom(k,1,42,sr) &
	513	+ ( q(k+1,j,i) - ql(k+1,j,i) ) - hom(k+1,1,42,sr) )
	514	sums_l(k,52,tn) = sums_l(k,52,tn) + pts * w(k,j,i) * &
	515	rmask(j,i,sr)
	516	sums_l(k,54,tn) = sums_l(k,54,tn) + ql(k,j,i) * &
	517	rmask(j,i,sr)
	518	ENDIF
	519	ENDIF
	520
	521	!
	522	!-- Passive scalar flux
	523	IF ( passive_scalar ) THEN
	524	pts = 0.5 * ( q(k,j,i) - hom(k,1,41,sr) + &
	525	q(k+1,j,i) - hom(k+1,1,41,sr) )
	526	sums_l(k,49,tn) = sums_l(k,49,tn) + pts * w(k,j,i) * &
	527	rmask(j,i,sr)
	528	ENDIF
	529
	530	!
	531	!-- Energy flux we
	532	sums_l(k,37,tn) = sums_l(k,37,tn) + w(k,j,i) * 0.5 * &
	533	( ust2 + vst2 + w(k,j,i)**2 )&
	534	* rmask(j,i,sr)
	535
	536	ENDDO
	537	ENDDO
	538	ENDDO
	539
	540	!
	541	!-- Divergence of vertical flux of resolved scale energy and pressure
	542	!-- fluctuations. First calculate the products, then the divergence.
	543	!-- Calculation is time consuming. Do it only, if profiles shall be plotted.
	544	IF ( hom(nzb+1,2,55,0) /= 0.0 ) THEN
	545
	546	sums_ll = 0.0 ! local array
	547
	548	!$OMP DO
	549	DO i = nxl, nxr
	550	DO j = nys, nyn
	551	DO k = nzb_s_outer(j,i)+1, nzt
	552
	553	sums_ll(k,1) = sums_ll(k,1) + 0.5 * w(k,j,i) * ( &
	554	( 0.25 * ( u(k,j,i)+u(k+1,j,i)+u(k,j,i+1)+u(k+1,j,i+1) &
	555	- 2.0 * ( hom(k,1,1,sr) + hom(k+1,1,1,sr) ) &
	556	) )**2 &
	557	+ ( 0.25 * ( v(k,j,i)+v(k+1,j,i)+v(k,j+1,i)+v(k+1,j+1,i) &
	558	- 2.0 * ( hom(k,1,2,sr) + hom(k+1,1,2,sr) ) &
	559	) )**2 &
	560	+ w(k,j,i)**2 )
	561
	562	sums_ll(k,2) = sums_ll(k,2) + 0.5 * w(k,j,i) &
	563	* ( p(k,j,i) + p(k+1,j,i) )
	564
	565	ENDDO
	566	ENDDO
	567	ENDDO
	568	sums_ll(0,1) = 0.0 ! because w is zero at the bottom
	569	sums_ll(nzt+1,1) = 0.0
	570	sums_ll(0,2) = 0.0
	571	sums_ll(nzt+1,2) = 0.0
	572
	573	DO k = nzb_s_outer(j,i)+1, nzt
	574	sums_l(k,55,tn) = ( sums_ll(k,1) - sums_ll(k-1,1) ) * ddzw(k)
	575	sums_l(k,56,tn) = ( sums_ll(k,2) - sums_ll(k-1,2) ) * ddzw(k)
	576	ENDDO
	577	sums_l(nzb,55,tn) = sums_l(nzb+1,55,tn)
	578	sums_l(nzb,56,tn) = sums_l(nzb+1,56,tn)
	579
	580	ENDIF
	581
	582	!
	583	!-- Divergence of vertical flux of SGS TKE
	584	IF ( hom(nzb+1,2,57,0) /= 0.0 ) THEN
	585
	586	!$OMP DO
	587	DO i = nxl, nxr
	588	DO j = nys, nyn
	589	DO k = nzb_s_outer(j,i)+1, nzt
	590
	591	sums_l(k,57,tn) = sums_l(k,57,tn) + ( &
	592	(km(k,j,i)+km(k+1,j,i)) * (e(k+1,j,i)-e(k,j,i)) * ddzu(k+1) &
	593	- (km(k-1,j,i)+km(k,j,i)) * (e(k,j,i)-e(k-1,j,i)) * ddzu(k) &
	594	) * ddzw(k)
	595
	596	ENDDO
	597	ENDDO
	598	ENDDO
	599	sums_l(nzb,57,tn) = sums_l(nzb+1,57,tn)
	600
	601	ENDIF
	602
	603	!
	604	!-- Horizontal heat fluxes (subgrid, resolved, total).
	605	!-- Do it only, if profiles shall be plotted.
	606	IF ( hom(nzb+1,2,58,0) /= 0.0 ) THEN
	607
	608	!$OMP DO
	609	DO i = nxl, nxr
	610	DO j = nys, nyn
	611	DO k = nzb_s_outer(j,i)+1, nzt
	612	!
	613	!-- Subgrid horizontal heat fluxes u"pt", v"pt"
	614	sums_l(k,58,tn) = sums_l(k,58,tn) - 0.5 * &
	615	( kh(k,j,i) + kh(k,j,i-1) ) &
	616	* ( pt(k,j,i-1) - pt(k,j,i) ) &
	617	* ddx * rmask(j,i,sr)
	618	sums_l(k,61,tn) = sums_l(k,61,tn) - 0.5 * &
	619	( kh(k,j,i) + kh(k,j-1,i) ) &
	620	* ( pt(k,j-1,i) - pt(k,j,i) ) &
	621	* ddy * rmask(j,i,sr)
	622	!
	623	!-- Resolved horizontal heat fluxes upt, vpt
	624	sums_l(k,59,tn) = sums_l(k,59,tn) + &
	625	( u(k,j,i) - hom(k,1,1,sr) ) &
	626	* 0.5 * ( pt(k,j,i-1) - hom(k,1,4,sr) + &
	627	pt(k,j,i) - hom(k,1,4,sr) )
	628	pts = 0.5 * ( pt(k,j-1,i) - hom(k,1,4,sr) + &
	629	pt(k,j,i) - hom(k,1,4,sr) )
	630	sums_l(k,62,tn) = sums_l(k,62,tn) + &
	631	( v(k,j,i) - hom(k,1,2,sr) ) &
	632	* 0.5 * ( pt(k,j-1,i) - hom(k,1,4,sr) + &
	633	pt(k,j,i) - hom(k,1,4,sr) )
	634	ENDDO
	635	ENDDO
	636	ENDDO
	637	!
	638	!-- Fluxes at the surface must be zero (e.g. due to the Prandtl-layer)
	639	sums(nzb,58) = 0.0
	640	sums(nzb,59) = 0.0
	641	sums(nzb,60) = 0.0
	642	sums(nzb,61) = 0.0
	643	sums(nzb,62) = 0.0
	644	sums(nzb,63) = 0.0
	645
	646	ENDIF
	647	!$OMP END PARALLEL
	648
	649	!
	650	!-- Summation of thread sums
	651	IF ( threads_per_task > 1 ) THEN
	652	DO i = 1, threads_per_task-1
	653	sums_l(:,3,0) = sums_l(:,3,0) + sums_l(:,3,i)
	654	sums_l(:,4:40,0) = sums_l(:,4:40,0) + sums_l(:,4:40,i)
	655	sums_l(:,45:var_sum,0) = sums_l(:,45:var_sum,0) + &
	656	sums_l(:,45:var_sum,i)
	657	ENDDO
	658	ENDIF
	659
	660	#if defined( __parallel )
	661	!
	662	!-- Compute total sum from local sums
	663	CALL MPI_ALLREDUCE( sums_l(nzb,1,0), sums(nzb,1), ngp_sums, MPI_REAL, &
	664	MPI_SUM, comm2d, ierr )
	665	#else
	666	sums = sums_l(:,:,0)
	667	#endif
	668
	669	!
	670	!-- Final values are obtained by division by the total number of grid points
	671	!-- used for summation. After that store profiles.
	672	!-- Profiles:
	673	DO k = nzb, nzt+1
	674	sums(k,:var_sum-2) = sums(k,:var_sum-2) / ngp_2dh_outer(k,sr)
	675	ENDDO
	676	!-- Upstream-parts
	677	sums(nzb:nzb+11,var_sum-1) = sums(nzb:nzb+11,var_sum-1) / ngp_3d(sr)
	678	!-- u* and so on
	679	!-- As sums(nzb:nzb+3,var_sum) are full 2D arrays (us, usws, vsws, ts) whose
	680	!-- size is always ( nx + 1 ) * ( ny + 1 ), defined at the first grid layer
	681	!-- above the topography, they are being divided by ngp_2dh(sr)
	682	sums(nzb:nzb+3,var_sum) = sums(nzb:nzb+3,var_sum) / &
	683	ngp_2dh(sr)
	684	!-- eges, e*
	685	sums(nzb+4:nzb+5,var_sum) = sums(nzb+4:nzb+5,var_sum) / &
	686	ngp_3d_inner(sr)
	687	!-- Old and new divergence
	688	sums(nzb+9:nzb+10,var_sum) = sums(nzb+9:nzb+10,var_sum) / &
	689	ngp_3d_inner(sr)
	690
	691	!
	692	!-- Collect horizontal average in hom.
	693	!-- Compute deduced averages (e.g. total heat flux)
	694	hom(:,1,3,sr) = sums(:,3) ! w
	695	hom(:,1,8,sr) = sums(:,8) ! e profiles 5-7 are initial profiles
	696	hom(:,1,9,sr) = sums(:,9) ! km
	697	hom(:,1,10,sr) = sums(:,10) ! kh
	698	hom(:,1,11,sr) = sums(:,11) ! l
	699	hom(:,1,12,sr) = sums(:,12) ! w"u"
	700	hom(:,1,13,sr) = sums(:,13) ! wu
	701	hom(:,1,14,sr) = sums(:,14) ! w"v"
	702	hom(:,1,15,sr) = sums(:,15) ! wv
	703	hom(:,1,16,sr) = sums(:,16) ! w"pt"
	704	hom(:,1,17,sr) = sums(:,17) ! wpt
	705	hom(:,1,18,sr) = sums(:,16) + sums(:,17) ! wpt
	706	hom(:,1,19,sr) = sums(:,12) + sums(:,13) ! wu
	707	hom(:,1,20,sr) = sums(:,14) + sums(:,15) ! wv
	708	hom(:,1,21,sr) = sums(:,21) ! wptBC
	709	hom(:,1,22,sr) = sums(:,16) + sums(:,21) ! wptBC
	710	! profiles 23-29 left empty for initial
	711	! profiles
	712	hom(:,1,30,sr) = sums(:,30) ! u*2
	713	hom(:,1,31,sr) = sums(:,31) ! v*2
	714	hom(:,1,32,sr) = sums(:,32) ! w*2
	715	hom(:,1,33,sr) = sums(:,33) ! pt*2
	716	hom(:,1,34,sr) = sums(:,34) ! e*
	717	hom(:,1,35,sr) = sums(:,35) ! w2pt
	718	hom(:,1,36,sr) = sums(:,36) ! wpt2
	719	hom(:,1,37,sr) = sums(:,37) ! we
	720	hom(:,1,38,sr) = sums(:,38) ! w*3
	721	hom(:,1,39,sr) = sums(:,38) / ( sums(:,32) + 1E-20 )**1.5 ! Sw
	722	hom(:,1,40,sr) = sums(:,40) ! p
	723	hom(:,1,45,sr) = sums(:,45) ! w"q"
	724	hom(:,1,46,sr) = sums(:,46) ! wvpt
	725	hom(:,1,47,sr) = sums(:,45) + sums(:,46) ! wvpt
	726	hom(:,1,48,sr) = sums(:,48) ! w"q" (w"qv")
	727	hom(:,1,49,sr) = sums(:,49) ! wq (wqv)
	728	hom(:,1,50,sr) = sums(:,48) + sums(:,49) ! wq (wqv)
	729	hom(:,1,51,sr) = sums(:,51) ! w"qv"
	730	hom(:,1,52,sr) = sums(:,52) ! wqv
	731	hom(:,1,53,sr) = sums(:,52) + sums(:,51) ! wq (wqv)
	732	hom(:,1,54,sr) = sums(:,54) ! ql
	733	hom(:,1,55,sr) = sums(:,55) ! wuu*/dz
	734	hom(:,1,56,sr) = sums(:,56) ! wp/dz
	735	hom(:,1,57,sr) = sums(:,57) ! w"e/dz
	736	hom(:,1,58,sr) = sums(:,58) ! u"pt"
	737	hom(:,1,59,sr) = sums(:,59) ! upt
	738	hom(:,1,60,sr) = sums(:,58) + sums(:,59) ! upt_t
	739	hom(:,1,61,sr) = sums(:,61) ! v"pt"
	740	hom(:,1,62,sr) = sums(:,62) ! vpt
	741	hom(:,1,63,sr) = sums(:,61) + sums(:,62) ! vpt_t
	742
	743	hom(:,1,var_hom-1,sr) = sums(:,var_sum-1)
	744	! upstream-parts u_x, u_y, u_z, v_x,
	745	! v_y, usw. (in last but one profile)
	746	hom(:,1,var_hom,sr) = sums(:,var_sum)
	747	! u, w'u', w'v', t (in last profile)
	748
	749	!
	750	!-- Determine the boundary layer height using two different schemes.
	751	!-- First scheme: Starting from the Earth's surface, look for the first
	752	!-- relative minimum of the total heat flux. The corresponding height is
	753	!-- accepted as the boundary layer height, if it is less than 1.5 times the
	754	!-- height where the heat flux becomes negative for the first time.
	755	!-- NOTE: This criterion is still capable of improving!
	756	z_i(1) = 0.0
	757	first = .TRUE.
	758	DO k = nzb, nzt-1
	759	IF ( first .AND. hom(k,1,18,sr) < 0.0 ) THEN
	760	first = .FALSE.
	761	height = zw(k)
	762	ENDIF
	763	IF ( hom(k,1,18,sr) < 0.0 .AND. &
	764	hom(k+1,1,18,sr) > hom(k,1,18,sr) ) THEN
	765	IF ( zw(k) < 1.5 * height ) THEN
	766	z_i(1) = zw(k)
	767	ELSE
	768	z_i(1) = height
	769	ENDIF
	770	EXIT
	771	ENDIF
	772	ENDDO
	773
	774	!
	775	!-- Second scheme: Starting from the top model boundary, look for the first
	776	!-- characteristic kink in the temperature profile, where the originally
	777	!-- stable stratification notably weakens.
	778	z_i(2) = 0.0
	779	DO k = nzt-1, nzb+1, -1
	780	IF ( ( hom(k+1,1,4,sr) - hom(k,1,4,sr) ) > &
	781	2.0 * ( hom(k,1,4,sr) - hom(k-1,1,4,sr) ) ) THEN
	782	z_i(2) = zu(k)
	783	EXIT
	784	ENDIF
	785	ENDDO
	786
	787	hom(nzb+6,1,var_hom,sr) = z_i(1)
	788	hom(nzb+7,1,var_hom,sr) = z_i(2)
	789
	790	!
	791	!-- Computation of both the characteristic vertical velocity and
	792	!-- the characteristic convective boundary layer temperature.
	793	!-- The horizontal average at nzb+1 is input for the average temperature.
	794	IF ( hom(nzb,1,18,sr) > 0.0 .AND. z_i(1) /= 0.0 ) THEN
	795	hom(nzb+8,1,var_hom,sr) = ( g / hom(nzb+1,1,4,sr) * &
	796	hom(nzb,1,18,sr) * z_i(1) )**0.333333333
	797	!-- so far this only works if Prandtl layer is used
	798	hom(nzb+11,1,var_hom,sr) = hom(nzb,1,16,sr) / hom(nzb+8,1,var_hom,sr)
	799	ELSE
	800	hom(nzb+8,1,var_hom,sr) = 0.0
	801	hom(nzb+11,1,var_hom,sr) = 0.0
	802	ENDIF
	803
[48]	804	!
	805	!-- Collect the time series quantities
	806	ts_value(1,sr) = hom(nzb+4,1,var_hom,sr) ! E
	807	ts_value(2,sr) = hom(nzb+5,1,var_hom,sr) ! E*
	808	ts_value(3,sr) = dt_3d
	809	ts_value(4,sr) = hom(nzb,1,var_hom,sr) ! u*
	810	ts_value(5,sr) = hom(nzb+3,1,var_hom,sr) ! th*
	811	ts_value(6,sr) = u_max
	812	ts_value(7,sr) = v_max
	813	ts_value(8,sr) = w_max
	814	ts_value(9,sr) = hom(nzb+10,1,var_sum,sr) ! new divergence
	815	ts_value(10,sr) = hom(nzb+9,1,var_hom,sr) ! old Divergence
	816	ts_value(11,sr) = hom(nzb+6,1,var_hom,sr) ! z_i(1)
	817	ts_value(12,sr) = hom(nzb+7,1,var_hom,sr) ! z_i(2)
	818	ts_value(13,sr) = hom(nzb+8,1,var_hom,sr) ! w*
	819	ts_value(14,sr) = hom(nzb,1,16,sr) ! w'pt' at k=0
	820	ts_value(15,sr) = hom(nzb+1,1,16,sr) ! w'pt' at k=1
	821	ts_value(16,sr) = hom(nzb+1,1,18,sr) ! wpt at k=1
	822	ts_value(17,sr) = hom(nzb,1,4,sr) ! pt(0)
	823	ts_value(18,sr) = hom(nzb+1,1,4,sr) ! pt(zp)
	824	ts_value(19,sr) = hom(nzb+9,1,var_hom-1,sr) ! splptx
	825	ts_value(20,sr) = hom(nzb+10,1,var_hom-1,sr) ! splpty
	826	ts_value(21,sr) = hom(nzb+11,1,var_hom-1,sr) ! splptz
	827	IF ( ts_value(5,sr) /= 0.0 ) THEN
	828	ts_value(22,sr) = ts_value(4,sr)**2 / &
	829	( kappa * g * ts_value(5,sr) / ts_value(18,sr) ) ! L
	830	ELSE
	831	ts_value(22,sr) = 10000.0
	832	ENDIF
[1]	833
	834	!
[48]	835	!-- Calculate additional statistics provided by the user interface
	836	CALL user_statistics( sr )
[1]	837
[48]	838	ENDDO ! loop of the subregions
	839
[1]	840	!
	841	!-- If required, sum up horizontal averages for subsequent time averaging
	842	IF ( do_sum ) THEN
	843	IF ( average_count_pr == 0 ) hom_sum = 0.0
	844	hom_sum = hom_sum + hom(:,1,:,:)
	845	average_count_pr = average_count_pr + 1
	846	do_sum = .FALSE.
	847	ENDIF
	848
	849	!
	850	!-- Set flag for other UPs (e.g. output routines, but also buoyancy).
	851	!-- This flag is reset after each time step in time_integration.
	852	flow_statistics_called = .TRUE.
	853
	854	CALL cpu_log( log_point(10), 'flow_statistics', 'stop' )
	855
	856
	857	END SUBROUTINE flow_statistics
	858
	859
	860

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