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source: palm/trunk/SOURCE/flow_statistics.f90 @ 15

Last change on this file since 15 was 4, checked in by raasch, 18 years ago
Id keyword set as property for all *.f90 files
Property svn:keywords set to `Id`
File size: 33.5 KB

Rev	Line
[1]	1	SUBROUTINE flow_statistics
	2
	3	!------------------------------------------------------------------------------!
	4	! Actual revisions:
	5	! -----------------
	6	!
	7	!
	8	! Former revisions:
	9	! -----------------
[3]	10	! $Id: flow_statistics.f90 4 2007-02-13 11:33:16Z 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)
	349	!
	350	!-- Heat flux w"pt"
	351	sums_l(k,16,tn) = sums_l(k,16,tn) &
	352	- 0.5 * ( kh(k,j,i) + kh(k+1,j,i) ) &
	353	* ( pt(k+1,j,i) - pt(k,j,i) ) &
	354	* ddzu(k+1) * rmask(j,i,sr)
	355
	356
	357	!
	358	!-- Buoyancy flux, water flux (humidity flux) w"q"
	359	IF ( moisture ) THEN
	360	sums_l(k,45,tn) = sums_l(k,45,tn) &
	361	- 0.5 * ( kh(k,j,i) + kh(k+1,j,i) ) &
	362	* ( vpt(k+1,j,i) - vpt(k,j,i) ) &
	363	* ddzu(k+1) * rmask(j,i,sr)
	364	sums_l(k,48,tn) = sums_l(k,48,tn) &
	365	- 0.5 * ( kh(k,j,i) + kh(k+1,j,i) ) &
	366	* ( q(k+1,j,i) - q(k,j,i) ) &
	367	* ddzu(k+1) * rmask(j,i,sr)
	368	IF ( cloud_physics ) THEN
	369	sums_l(k,51,tn) = sums_l(k,51,tn) &
	370	- 0.5 * ( kh(k,j,i) + kh(k+1,j,i) ) &
	371	* ( ( q(k+1,j,i) - ql(k+1,j,i) )&
	372	- ( q(k,j,i) - ql(k,j,i) ) ) &
	373	* ddzu(k+1) * rmask(j,i,sr)
	374	ENDIF
	375	ENDIF
	376
	377	!
	378	!-- Passive scalar flux
	379	IF ( passive_scalar ) THEN
	380	sums_l(k,48,tn) = sums_l(k,48,tn) &
	381	- 0.5 * ( kh(k,j,i) + kh(k+1,j,i) ) &
	382	* ( q(k+1,j,i) - q(k,j,i) ) &
	383	* ddzu(k+1) * rmask(j,i,sr)
	384	ENDIF
	385
	386	ENDDO
	387
	388	!
	389	!-- Subgridscale fluxes in the Prandtl layer
	390	IF ( use_surface_fluxes ) THEN
	391	sums_l(nzb,12,tn) = sums_l(nzb,12,tn) + &
	392	usws(j,i) * rmask(j,i,sr) ! w"u"
	393	sums_l(nzb,14,tn) = sums_l(nzb,14,tn) + &
	394	vsws(j,i) * rmask(j,i,sr) ! w"v"
	395	sums_l(nzb,16,tn) = sums_l(nzb,16,tn) + &
	396	shf(j,i) * rmask(j,i,sr) ! w"pt"
	397	sums_l(nzb,58,tn) = sums_l(nzb,58,tn) + &
	398	0.0 * rmask(j,i,sr) ! u"pt"
	399	sums_l(nzb,61,tn) = sums_l(nzb,61,tn) + &
	400	0.0 * rmask(j,i,sr) ! v"pt"
	401	IF ( moisture ) THEN
	402	sums_l(nzb,48,tn) = sums_l(nzb,48,tn) + &
	403	qsws(j,i) * rmask(j,i,sr) ! w"q" (w"qv")
	404	IF ( cloud_physics ) THEN
	405	sums_l(nzb,45,tn) = sums_l(nzb,45,tn) + ( &
	406	( 1.0 + 0.61 * q(nzb,j,i) ) * &
	407	shf(j,i) + 0.61 * pt(nzb,j,i) * &
	408	qsws(j,i) &
	409	)
	410	!
	411	!-- Formula does not work if ql(nzb) /= 0.0
	412	sums_l(nzb,51,tn) = sums_l(nzb,51,tn) + & ! w"q" (w"qv")
	413	qsws(j,i) * rmask(j,i,sr)
	414	ENDIF
	415	ENDIF
	416	IF ( passive_scalar ) THEN
	417	sums_l(nzb,48,tn) = sums_l(nzb,48,tn) + &
	418	qsws(j,i) * rmask(j,i,sr) ! w"q" (w"qv")
	419	ENDIF
	420	ENDIF
	421
	422	!
	423	!-- Resolved fluxes (can be computed for all horizontal points)
	424	!-- NOTE: for simplicity, nzb_s_outer is used below, although strictly
	425	!-- ---- speaking the following k-loop would have to be split up and
	426	!-- rearranged according to the staggered grid.
	427	DO k = nzb_s_outer(j,i), nzt
	428	ust = 0.5 * ( u(k,j,i) - hom(k,1,1,sr) + &
	429	u(k+1,j,i) - hom(k+1,1,1,sr) )
	430	vst = 0.5 * ( v(k,j,i) - hom(k,1,2,sr) + &
	431	v(k+1,j,i) - hom(k+1,1,2,sr) )
	432	pts = 0.5 * ( pt(k,j,i) - hom(k,1,4,sr) + &
	433	pt(k+1,j,i) - hom(k+1,1,4,sr) )
	434	!
	435	!-- Momentum flux wu
	436	sums_l(k,13,tn) = sums_l(k,13,tn) + 0.5 * &
	437	( w(k,j,i-1) + w(k,j,i) ) &
	438	* ust * rmask(j,i,sr)
	439	!
	440	!-- Momentum flux wv
	441	sums_l(k,15,tn) = sums_l(k,15,tn) + 0.5 * &
	442	( w(k,j-1,i) + w(k,j,i) ) &
	443	* vst * rmask(j,i,sr)
	444	!
	445	!-- Heat flux wpt
	446	!-- The following formula (comment line, not executed) does not
	447	!-- work if applied to subregions
	448	! sums_l(k,17,tn) = sums_l(k,17,tn) + 0.5 * &
	449	! ( pt(k,j,i)+pt(k+1,j,i) ) &
	450	! * w(k,j,i) * rmask(j,i,sr)
	451	sums_l(k,17,tn) = sums_l(k,17,tn) + pts * w(k,j,i) * &
	452	rmask(j,i,sr)
	453	!
	454	!-- Higher moments
	455	sums_l(k,35,tn) = sums_l(k,35,tn) + pts * w(k,j,i)*2 &
	456	rmask(j,i,sr)
	457	sums_l(k,36,tn) = sums_l(k,36,tn) + pts*2 w(k,j,i) * &
	458	rmask(j,i,sr)
	459
	460	!
	461	!-- Buoyancy flux, water flux, humidity flux and liquid water
	462	!-- content
	463	IF ( moisture ) THEN
	464	pts = 0.5 * ( vpt(k,j,i) - hom(k,1,44,sr) + &
	465	vpt(k+1,j,i) - hom(k+1,1,44,sr) )
	466	sums_l(k,46,tn) = sums_l(k,46,tn) + pts * w(k,j,i) * &
	467	rmask(j,i,sr)
	468	pts = 0.5 * ( q(k,j,i) - hom(k,1,41,sr) + &
	469	q(k+1,j,i) - hom(k+1,1,41,sr) )
	470	sums_l(k,49,tn) = sums_l(k,49,tn) + pts * w(k,j,i) * &
	471	rmask(j,i,sr)
	472	IF ( cloud_physics .OR. cloud_droplets ) THEN
	473	pts = 0.5 * &
	474	( ( q(k,j,i) - ql(k,j,i) ) - hom(k,1,42,sr) &
	475	+ ( q(k+1,j,i) - ql(k+1,j,i) ) - hom(k+1,1,42,sr) )
	476	sums_l(k,52,tn) = sums_l(k,52,tn) + pts * w(k,j,i) * &
	477	rmask(j,i,sr)
	478	sums_l(k,54,tn) = sums_l(k,54,tn) + ql(k,j,i) * &
	479	rmask(j,i,sr)
	480	ENDIF
	481	ENDIF
	482
	483	!
	484	!-- Passive scalar flux
	485	IF ( passive_scalar ) THEN
	486	pts = 0.5 * ( q(k,j,i) - hom(k,1,41,sr) + &
	487	q(k+1,j,i) - hom(k+1,1,41,sr) )
	488	sums_l(k,49,tn) = sums_l(k,49,tn) + pts * w(k,j,i) * &
	489	rmask(j,i,sr)
	490	ENDIF
	491
	492	!
	493	!-- Energy flux we
	494	sums_l(k,37,tn) = sums_l(k,37,tn) + w(k,j,i) * 0.5 * &
	495	( ust2 + vst2 + w(k,j,i)**2 )&
	496	* rmask(j,i,sr)
	497
	498	ENDDO
	499	ENDDO
	500	ENDDO
	501
	502	!
	503	!-- Divergence of vertical flux of resolved scale energy and pressure
	504	!-- fluctuations. First calculate the products, then the divergence.
	505	!-- Calculation is time consuming. Do it only, if profiles shall be plotted.
	506	IF ( hom(nzb+1,2,55,0) /= 0.0 ) THEN
	507
	508	sums_ll = 0.0 ! local array
	509
	510	!$OMP DO
	511	DO i = nxl, nxr
	512	DO j = nys, nyn
	513	DO k = nzb_s_outer(j,i)+1, nzt
	514
	515	sums_ll(k,1) = sums_ll(k,1) + 0.5 * w(k,j,i) * ( &
	516	( 0.25 * ( u(k,j,i)+u(k+1,j,i)+u(k,j,i+1)+u(k+1,j,i+1) &
	517	- 2.0 * ( hom(k,1,1,sr) + hom(k+1,1,1,sr) ) &
	518	) )**2 &
	519	+ ( 0.25 * ( v(k,j,i)+v(k+1,j,i)+v(k,j+1,i)+v(k+1,j+1,i) &
	520	- 2.0 * ( hom(k,1,2,sr) + hom(k+1,1,2,sr) ) &
	521	) )**2 &
	522	+ w(k,j,i)**2 )
	523
	524	sums_ll(k,2) = sums_ll(k,2) + 0.5 * w(k,j,i) &
	525	* ( p(k,j,i) + p(k+1,j,i) )
	526
	527	ENDDO
	528	ENDDO
	529	ENDDO
	530	sums_ll(0,1) = 0.0 ! because w is zero at the bottom
	531	sums_ll(nzt+1,1) = 0.0
	532	sums_ll(0,2) = 0.0
	533	sums_ll(nzt+1,2) = 0.0
	534
	535	DO k = nzb_s_outer(j,i)+1, nzt
	536	sums_l(k,55,tn) = ( sums_ll(k,1) - sums_ll(k-1,1) ) * ddzw(k)
	537	sums_l(k,56,tn) = ( sums_ll(k,2) - sums_ll(k-1,2) ) * ddzw(k)
	538	ENDDO
	539	sums_l(nzb,55,tn) = sums_l(nzb+1,55,tn)
	540	sums_l(nzb,56,tn) = sums_l(nzb+1,56,tn)
	541
	542	ENDIF
	543
	544	!
	545	!-- Divergence of vertical flux of SGS TKE
	546	IF ( hom(nzb+1,2,57,0) /= 0.0 ) THEN
	547
	548	!$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_l(k,57,tn) = sums_l(k,57,tn) + ( &
	554	(km(k,j,i)+km(k+1,j,i)) * (e(k+1,j,i)-e(k,j,i)) * ddzu(k+1) &
	555	- (km(k-1,j,i)+km(k,j,i)) * (e(k,j,i)-e(k-1,j,i)) * ddzu(k) &
	556	) * ddzw(k)
	557
	558	ENDDO
	559	ENDDO
	560	ENDDO
	561	sums_l(nzb,57,tn) = sums_l(nzb+1,57,tn)
	562
	563	ENDIF
	564
	565	!
	566	!-- Horizontal heat fluxes (subgrid, resolved, total).
	567	!-- Do it only, if profiles shall be plotted.
	568	IF ( hom(nzb+1,2,58,0) /= 0.0 ) THEN
	569
	570	!$OMP DO
	571	DO i = nxl, nxr
	572	DO j = nys, nyn
	573	DO k = nzb_s_outer(j,i)+1, nzt
	574	!
	575	!-- Subgrid horizontal heat fluxes u"pt", v"pt"
	576	sums_l(k,58,tn) = sums_l(k,58,tn) - 0.5 * &
	577	( kh(k,j,i) + kh(k,j,i-1) ) &
	578	* ( pt(k,j,i-1) - pt(k,j,i) ) &
	579	* ddx * rmask(j,i,sr)
	580	sums_l(k,61,tn) = sums_l(k,61,tn) - 0.5 * &
	581	( kh(k,j,i) + kh(k,j-1,i) ) &
	582	* ( pt(k,j-1,i) - pt(k,j,i) ) &
	583	* ddy * rmask(j,i,sr)
	584	!
	585	!-- Resolved horizontal heat fluxes upt, vpt
	586	sums_l(k,59,tn) = sums_l(k,59,tn) + &
	587	( u(k,j,i) - hom(k,1,1,sr) ) &
	588	* 0.5 * ( pt(k,j,i-1) - hom(k,1,4,sr) + &
	589	pt(k,j,i) - hom(k,1,4,sr) )
	590	pts = 0.5 * ( pt(k,j-1,i) - hom(k,1,4,sr) + &
	591	pt(k,j,i) - hom(k,1,4,sr) )
	592	sums_l(k,62,tn) = sums_l(k,62,tn) + &
	593	( v(k,j,i) - hom(k,1,2,sr) ) &
	594	* 0.5 * ( pt(k,j-1,i) - hom(k,1,4,sr) + &
	595	pt(k,j,i) - hom(k,1,4,sr) )
	596	ENDDO
	597	ENDDO
	598	ENDDO
	599	!
	600	!-- Fluxes at the surface must be zero (e.g. due to the Prandtl-layer)
	601	sums(nzb,58) = 0.0
	602	sums(nzb,59) = 0.0
	603	sums(nzb,60) = 0.0
	604	sums(nzb,61) = 0.0
	605	sums(nzb,62) = 0.0
	606	sums(nzb,63) = 0.0
	607
	608	ENDIF
	609	!$OMP END PARALLEL
	610
	611	!
	612	!-- Summation of thread sums
	613	IF ( threads_per_task > 1 ) THEN
	614	DO i = 1, threads_per_task-1
	615	sums_l(:,3,0) = sums_l(:,3,0) + sums_l(:,3,i)
	616	sums_l(:,4:40,0) = sums_l(:,4:40,0) + sums_l(:,4:40,i)
	617	sums_l(:,45:var_sum,0) = sums_l(:,45:var_sum,0) + &
	618	sums_l(:,45:var_sum,i)
	619	ENDDO
	620	ENDIF
	621
	622	#if defined( __parallel )
	623	!
	624	!-- Compute total sum from local sums
	625	CALL MPI_ALLREDUCE( sums_l(nzb,1,0), sums(nzb,1), ngp_sums, MPI_REAL, &
	626	MPI_SUM, comm2d, ierr )
	627	#else
	628	sums = sums_l(:,:,0)
	629	#endif
	630
	631	!
	632	!-- Final values are obtained by division by the total number of grid points
	633	!-- used for summation. After that store profiles.
	634	!-- Profiles:
	635	DO k = nzb, nzt+1
	636	sums(k,:var_sum-2) = sums(k,:var_sum-2) / ngp_2dh_outer(k,sr)
	637	ENDDO
	638	!-- Upstream-parts
	639	sums(nzb:nzb+11,var_sum-1) = sums(nzb:nzb+11,var_sum-1) / ngp_3d(sr)
	640	!-- u* and so on
	641	!-- As sums(nzb:nzb+3,var_sum) are full 2D arrays (us, usws, vsws, ts) whose
	642	!-- size is always ( nx + 1 ) * ( ny + 1 ), defined at the first grid layer
	643	!-- above the topography, they are being divided by ngp_2dh(sr)
	644	sums(nzb:nzb+3,var_sum) = sums(nzb:nzb+3,var_sum) / &
	645	ngp_2dh(sr)
	646	!-- eges, e*
	647	sums(nzb+4:nzb+5,var_sum) = sums(nzb+4:nzb+5,var_sum) / &
	648	ngp_3d_inner(sr)
	649	!-- Old and new divergence
	650	sums(nzb+9:nzb+10,var_sum) = sums(nzb+9:nzb+10,var_sum) / &
	651	ngp_3d_inner(sr)
	652
	653	!
	654	!-- Collect horizontal average in hom.
	655	!-- Compute deduced averages (e.g. total heat flux)
	656	hom(:,1,3,sr) = sums(:,3) ! w
	657	hom(:,1,8,sr) = sums(:,8) ! e profiles 5-7 are initial profiles
	658	hom(:,1,9,sr) = sums(:,9) ! km
	659	hom(:,1,10,sr) = sums(:,10) ! kh
	660	hom(:,1,11,sr) = sums(:,11) ! l
	661	hom(:,1,12,sr) = sums(:,12) ! w"u"
	662	hom(:,1,13,sr) = sums(:,13) ! wu
	663	hom(:,1,14,sr) = sums(:,14) ! w"v"
	664	hom(:,1,15,sr) = sums(:,15) ! wv
	665	hom(:,1,16,sr) = sums(:,16) ! w"pt"
	666	hom(:,1,17,sr) = sums(:,17) ! wpt
	667	hom(:,1,18,sr) = sums(:,16) + sums(:,17) ! wpt
	668	hom(:,1,19,sr) = sums(:,12) + sums(:,13) ! wu
	669	hom(:,1,20,sr) = sums(:,14) + sums(:,15) ! wv
	670	hom(:,1,21,sr) = sums(:,21) ! wptBC
	671	hom(:,1,22,sr) = sums(:,16) + sums(:,21) ! wptBC
	672	! profiles 23-29 left empty for initial
	673	! profiles
	674	hom(:,1,30,sr) = sums(:,30) ! u*2
	675	hom(:,1,31,sr) = sums(:,31) ! v*2
	676	hom(:,1,32,sr) = sums(:,32) ! w*2
	677	hom(:,1,33,sr) = sums(:,33) ! pt*2
	678	hom(:,1,34,sr) = sums(:,34) ! e*
	679	hom(:,1,35,sr) = sums(:,35) ! w2pt
	680	hom(:,1,36,sr) = sums(:,36) ! wpt2
	681	hom(:,1,37,sr) = sums(:,37) ! we
	682	hom(:,1,38,sr) = sums(:,38) ! w*3
	683	hom(:,1,39,sr) = sums(:,38) / ( sums(:,32) + 1E-20 )**1.5 ! Sw
	684	hom(:,1,40,sr) = sums(:,40) ! p
	685	hom(:,1,45,sr) = sums(:,45) ! w"q"
	686	hom(:,1,46,sr) = sums(:,46) ! wvpt
	687	hom(:,1,47,sr) = sums(:,45) + sums(:,46) ! wvpt
	688	hom(:,1,48,sr) = sums(:,48) ! w"q" (w"qv")
	689	hom(:,1,49,sr) = sums(:,49) ! wq (wqv)
	690	hom(:,1,50,sr) = sums(:,48) + sums(:,49) ! wq (wqv)
	691	hom(:,1,51,sr) = sums(:,51) ! w"qv"
	692	hom(:,1,52,sr) = sums(:,52) ! wqv
	693	hom(:,1,53,sr) = sums(:,52) + sums(:,51) ! wq (wqv)
	694	hom(:,1,54,sr) = sums(:,54) ! ql
	695	hom(:,1,55,sr) = sums(:,55) ! wuu*/dz
	696	hom(:,1,56,sr) = sums(:,56) ! wp/dz
	697	hom(:,1,57,sr) = sums(:,57) ! w"e/dz
	698	hom(:,1,58,sr) = sums(:,58) ! u"pt"
	699	hom(:,1,59,sr) = sums(:,59) ! upt
	700	hom(:,1,60,sr) = sums(:,58) + sums(:,59) ! upt_t
	701	hom(:,1,61,sr) = sums(:,61) ! v"pt"
	702	hom(:,1,62,sr) = sums(:,62) ! vpt
	703	hom(:,1,63,sr) = sums(:,61) + sums(:,62) ! vpt_t
	704
	705	hom(:,1,var_hom-1,sr) = sums(:,var_sum-1)
	706	! upstream-parts u_x, u_y, u_z, v_x,
	707	! v_y, usw. (in last but one profile)
	708	hom(:,1,var_hom,sr) = sums(:,var_sum)
	709	! u, w'u', w'v', t (in last profile)
	710
	711	!
	712	!-- Determine the boundary layer height using two different schemes.
	713	!-- First scheme: Starting from the Earth's surface, look for the first
	714	!-- relative minimum of the total heat flux. The corresponding height is
	715	!-- accepted as the boundary layer height, if it is less than 1.5 times the
	716	!-- height where the heat flux becomes negative for the first time.
	717	!-- NOTE: This criterion is still capable of improving!
	718	z_i(1) = 0.0
	719	first = .TRUE.
	720	DO k = nzb, nzt-1
	721	IF ( first .AND. hom(k,1,18,sr) < 0.0 ) THEN
	722	first = .FALSE.
	723	height = zw(k)
	724	ENDIF
	725	IF ( hom(k,1,18,sr) < 0.0 .AND. &
	726	hom(k+1,1,18,sr) > hom(k,1,18,sr) ) THEN
	727	IF ( zw(k) < 1.5 * height ) THEN
	728	z_i(1) = zw(k)
	729	ELSE
	730	z_i(1) = height
	731	ENDIF
	732	EXIT
	733	ENDIF
	734	ENDDO
	735
	736	!
	737	!-- Second scheme: Starting from the top model boundary, look for the first
	738	!-- characteristic kink in the temperature profile, where the originally
	739	!-- stable stratification notably weakens.
	740	z_i(2) = 0.0
	741	DO k = nzt-1, nzb+1, -1
	742	IF ( ( hom(k+1,1,4,sr) - hom(k,1,4,sr) ) > &
	743	2.0 * ( hom(k,1,4,sr) - hom(k-1,1,4,sr) ) ) THEN
	744	z_i(2) = zu(k)
	745	EXIT
	746	ENDIF
	747	ENDDO
	748
	749	hom(nzb+6,1,var_hom,sr) = z_i(1)
	750	hom(nzb+7,1,var_hom,sr) = z_i(2)
	751
	752	!
	753	!-- Computation of both the characteristic vertical velocity and
	754	!-- the characteristic convective boundary layer temperature.
	755	!-- The horizontal average at nzb+1 is input for the average temperature.
	756	IF ( hom(nzb,1,18,sr) > 0.0 .AND. z_i(1) /= 0.0 ) THEN
	757	hom(nzb+8,1,var_hom,sr) = ( g / hom(nzb+1,1,4,sr) * &
	758	hom(nzb,1,18,sr) * z_i(1) )**0.333333333
	759	!-- so far this only works if Prandtl layer is used
	760	hom(nzb+11,1,var_hom,sr) = hom(nzb,1,16,sr) / hom(nzb+8,1,var_hom,sr)
	761	ELSE
	762	hom(nzb+8,1,var_hom,sr) = 0.0
	763	hom(nzb+11,1,var_hom,sr) = 0.0
	764	ENDIF
	765
	766	ENDDO ! loop of the subregions
	767
	768	!
	769	!-- Calculate additional statistics provided by the user interface
	770	CALL user_statistics
	771
	772	!
	773	!-- If required, sum up horizontal averages for subsequent time averaging
	774	IF ( do_sum ) THEN
	775	IF ( average_count_pr == 0 ) hom_sum = 0.0
	776	hom_sum = hom_sum + hom(:,1,:,:)
	777	average_count_pr = average_count_pr + 1
	778	do_sum = .FALSE.
	779	ENDIF
	780
	781	!
	782	!-- Set flag for other UPs (e.g. output routines, but also buoyancy).
	783	!-- This flag is reset after each time step in time_integration.
	784	flow_statistics_called = .TRUE.
	785
	786	CALL cpu_log( log_point(10), 'flow_statistics', 'stop' )
	787
	788
	789	END SUBROUTINE flow_statistics
	790
	791
	792

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