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source: palm/trunk/SOURCE/prognostic_equations.f90 @ 2076

Last change on this file since 2076 was 2032, checked in by knoop, 8 years ago
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[1873]	1	!> @file prognostic_equations.f90
[2000]	2	!------------------------------------------------------------------------------!
[1875]	3	! This file is part of PALM.
	4	!
[2000]	5	! PALM is free software: you can redistribute it and/or modify it under the
	6	! terms of the GNU General Public License as published by the Free Software
	7	! Foundation, either version 3 of the License, or (at your option) any later
	8	! version.
[1875]	9	!
	10	! PALM is distributed in the hope that it will be useful, but WITHOUT ANY
	11	! WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	12	! A PARTICULAR PURPOSE. See the GNU General Public License for more details.
	13	!
	14	! You should have received a copy of the GNU General Public License along with
	15	! PALM. If not, see <http://www.gnu.org/licenses/>.
	16	!
	17	! Copyright 1997-2016 Leibniz Universitaet Hannover
[2000]	18	!------------------------------------------------------------------------------!
[1875]	19	!
	20	! Current revisions:
	21	! ------------------
[1827]	22	!
[2032]	23	!
[1875]	24	! Former revisions:
	25	! -----------------
	26	! $Id: prognostic_equations.f90 2032 2016-10-21 15:13:51Z raasch $
	27	!
[2032]	28	! 2031 2016-10-21 15:11:58Z knoop
	29	! renamed variable rho to rho_ocean
	30	!
[2012]	31	! 2011 2016-09-19 17:29:57Z kanani
	32	! Flag urban_surface is now defined in module control_parameters.
	33	!
[2008]	34	! 2007 2016-08-24 15:47:17Z kanani
	35	! Added pt tendency calculation based on energy balance at urban surfaces
	36	! (new urban surface model)
	37	!
[2001]	38	! 2000 2016-08-20 18:09:15Z knoop
	39	! Forced header and separation lines into 80 columns
	40	!
[1977]	41	! 1976 2016-07-27 13:28:04Z maronga
	42	! Simplied calls to radiation model
	43	!
[1961]	44	! 1960 2016-07-12 16:34:24Z suehring
	45	! Separate humidity and passive scalar
	46	!
[1917]	47	! 1914 2016-05-26 14:44:07Z witha
	48	! Added calls for wind turbine model
	49	!
[1874]	50	! 1873 2016-04-18 14:50:06Z maronga
	51	! Module renamed (removed _mod)
	52	!
[1851]	53	! 1850 2016-04-08 13:29:27Z maronga
	54	! Module renamed
	55	!
[1827]	56	! 1826 2016-04-07 12:01:39Z maronga
[1875]	57	! Renamed canopy model calls.
	58	!
	59	! 1822 2016-04-07 07:49:42Z hoffmann
	60	! Kessler microphysics scheme moved to microphysics.
	61	!
	62	! 1757 2016-02-22 15:49:32Z maronga
	63	!
	64	! 1691 2015-10-26 16:17:44Z maronga
	65	! Added optional model spin-up without radiation / land surface model calls.
	66	! Formatting corrections.
	67	!
	68	! 1682 2015-10-07 23:56:08Z knoop
	69	! Code annotations made doxygen readable
	70	!
	71	! 1585 2015-04-30 07:05:52Z maronga
	72	! Added call for temperature tendency calculation due to radiative flux divergence
	73	!
	74	! 1517 2015-01-07 19:12:25Z hoffmann
	75	! advec_s_bc_mod addded, since advec_s_bc is now a module
	76	!
	77	! 1496 2014-12-02 17:25:50Z maronga
	78	! Renamed "radiation" -> "cloud_top_radiation"
	79	!
	80	! 1484 2014-10-21 10:53:05Z kanani
	81	! Changes due to new module structure of the plant canopy model:
	82	! parameters cthf and plant_canopy moved to module plant_canopy_model_mod.
	83	! Removed double-listing of use_upstream_for_tke in ONLY-list of module
	84	! control_parameters
	85	!
	86	! 1409 2014-05-23 12:11:32Z suehring
	87	! Bugfix: i_omp_start changed for advec_u_ws at left inflow and outflow boundary.
	88	! This ensures that left-hand side fluxes are also calculated for nxl in that
	89	! case, even though the solution at nxl is overwritten in boundary_conds()
	90	!
	91	! 1398 2014-05-07 11:15:00Z heinze
	92	! Rayleigh-damping for horizontal velocity components changed: instead of damping
	93	! against ug and vg, damping against u_init and v_init is used to allow for a
	94	! homogenized treatment in case of nudging
	95	!
	96	! 1380 2014-04-28 12:40:45Z heinze
	97	! Change order of calls for scalar prognostic quantities:
	98	! ls_advec -> nudging -> subsidence since initial profiles
	99	!
	100	! 1374 2014-04-25 12:55:07Z raasch
	101	! missing variables added to ONLY lists
	102	!
	103	! 1365 2014-04-22 15:03:56Z boeske
	104	! Calls of ls_advec for large scale advection added,
	105	! subroutine subsidence is only called if use_subsidence_tendencies = .F.,
	106	! new argument ls_index added to the calls of subsidence
	107	! +ls_index
	108	!
	109	! 1361 2014-04-16 15:17:48Z hoffmann
	110	! Two-moment microphysics moved to the start of prognostic equations. This makes
	111	! the 3d arrays for tend_q, tend_qr, tend_pt and tend_pt redundant.
	112	! Additionally, it is allowed to call the microphysics just once during the time
	113	! step (not at each sub-time step).
	114	!
	115	! Two-moment cloud physics added for vector and accelerator optimization.
	116	!
	117	! 1353 2014-04-08 15:21:23Z heinze
	118	! REAL constants provided with KIND-attribute
	119	!
	120	! 1337 2014-03-25 15:11:48Z heinze
	121	! Bugfix: REAL constants provided with KIND-attribute
	122	!
	123	! 1332 2014-03-25 11:59:43Z suehring
	124	! Bugfix: call advec_ws or advec_pw for TKE only if NOT use_upstream_for_tke
	125	!
	126	! 1330 2014-03-24 17:29:32Z suehring
	127	! In case of SGS-particle velocity advection of TKE is also allowed with
	128	! dissipative 5th-order scheme.
	129	!
	130	! 1320 2014-03-20 08:40:49Z raasch
	131	! ONLY-attribute added to USE-statements,
	132	! kind-parameters added to all INTEGER and REAL declaration statements,
	133	! kinds are defined in new module kinds,
	134	! old module precision_kind is removed,
	135	! revision history before 2012 removed,
	136	! comment fields (!:) to be used for variable explanations added to
	137	! all variable declaration statements
	138	!
	139	! 1318 2014-03-17 13:35:16Z raasch
	140	! module interfaces removed
	141	!
	142	! 1257 2013-11-08 15:18:40Z raasch
	143	! openacc loop vector clauses removed, independent clauses added
	144	!
	145	! 1246 2013-11-01 08:59:45Z heinze
	146	! enable nudging also for accelerator version
	147	!
	148	! 1241 2013-10-30 11:36:58Z heinze
	149	! usage of nudging enabled (so far not implemented for accelerator version)
	150	!
	151	! 1179 2013-06-14 05:57:58Z raasch
	152	! two arguments removed from routine buoyancy, ref_state updated on device
	153	!
	154	! 1128 2013-04-12 06:19:32Z raasch
	155	! those parts requiring global communication moved to time_integration,
	156	! loop index bounds in accelerator version replaced by i_left, i_right, j_south,
	157	! j_north
	158	!
	159	! 1115 2013-03-26 18:16:16Z hoffmann
	160	! optimized cloud physics: calculation of microphysical tendencies transfered
	161	! to microphysics.f90; qr and nr are only calculated if precipitation is required
	162	!
	163	! 1111 2013-03-08 23:54:10Z raasch
	164	! update directives for prognostic quantities removed
	165	!
	166	! 1106 2013-03-04 05:31:38Z raasch
	167	! small changes in code formatting
	168	!
	169	! 1092 2013-02-02 11:24:22Z raasch
	170	! unused variables removed
	171	!
	172	! 1053 2012-11-13 17:11:03Z hoffmann
	173	! implementation of two new prognostic equations for rain drop concentration (nr)
	174	! and rain water content (qr)
	175	!
	176	! currently, only available for cache loop optimization
	177	!
	178	! 1036 2012-10-22 13:43:42Z raasch
	179	! code put under GPL (PALM 3.9)
	180	!
	181	! 1019 2012-09-28 06:46:45Z raasch
	182	! non-optimized version of prognostic_equations removed
	183	!
	184	! 1015 2012-09-27 09:23:24Z raasch
	185	! new branch prognostic_equations_acc
	186	! OpenACC statements added + code changes required for GPU optimization
	187	!
	188	! 1001 2012-09-13 14:08:46Z raasch
	189	! all actions concerning leapfrog- and upstream-spline-scheme removed
	190	!
	191	! 978 2012-08-09 08:28:32Z fricke
	192	! km_damp_x and km_damp_y removed in calls of diffusion_u and diffusion_v
	193	! add ptdf_x, ptdf_y for damping the potential temperature at the inflow
	194	! boundary in case of non-cyclic lateral boundaries
	195	! Bugfix: first thread index changes for WS-scheme at the inflow
	196	!
	197	! 940 2012-07-09 14:31:00Z raasch
	198	! temperature equation can be switched off
	199	!
	200	! Revision 1.1 2000/04/13 14:56:27 schroeter
	201	! Initial revision
	202	!
	203	!
	204	! Description:
	205	! ------------
	206	!> Solving the prognostic equations.
	207	!------------------------------------------------------------------------------!
	208	MODULE prognostic_equations_mod
	209
	210
	211
	212	USE arrays_3d, &
	213	ONLY: diss_l_e, diss_l_nr, diss_l_pt, diss_l_q, diss_l_qr, &
[1960]	214	diss_l_s, diss_l_sa, diss_s_e, diss_s_nr, diss_s_pt, diss_s_q, &
	215	diss_s_qr, diss_s_s, diss_s_sa, e, e_p, flux_s_e, flux_s_nr, &
	216	flux_s_pt, flux_s_q, flux_s_qr, flux_s_s, flux_s_sa, flux_l_e, &
	217	flux_l_nr, flux_l_pt, flux_l_q, flux_l_qr, flux_l_s, flux_l_sa, &
	218	nr, nr_p, nrsws, nrswst, pt, ptdf_x, ptdf_y, pt_init, pt_p, &
	219	prho, q, q_init, q_p, qsws, qswst, qr, qr_p, qrsws, qrswst, rdf,&
[2031]	220	rdf_sc, ref_state, rho_ocean, s, s_init, s_p, sa, sa_init, sa_p, &
[1960]	221	saswsb, saswst, shf, ssws, sswst, tend, &
	222	te_m, tnr_m, tpt_m, tq_m, tqr_m, ts_m, tsa_m, tswst, tu_m, tv_m,&
[1875]	223	tw_m, u, ug, u_init, u_p, v, vg, vpt, v_init, v_p, w, w_p
	224
	225	USE control_parameters, &
	226	ONLY: call_microphysics_at_all_substeps, cloud_physics, &
	227	cloud_top_radiation, constant_diffusion, dp_external, &
	228	dp_level_ind_b, dp_smooth_factor, dpdxy, dt_3d, humidity, &
	229	inflow_l, intermediate_timestep_count, &
	230	intermediate_timestep_count_max, large_scale_forcing, &
	231	large_scale_subsidence, microphysics_seifert, &
	232	microphysics_sat_adjust, neutral, nudging, ocean, outflow_l, &
	233	outflow_s, passive_scalar, prho_reference, prho_reference, &
	234	prho_reference, pt_reference, pt_reference, pt_reference, &
	235	scalar_advec, scalar_advec, simulated_time, sloping_surface, &
[2011]	236	timestep_scheme, tsc, urban_surface, use_subsidence_tendencies, &
[1875]	237	use_upstream_for_tke, wall_heatflux, &
	238	wall_nrflux, wall_qflux, wall_qflux, wall_qflux, wall_qrflux, &
[1960]	239	wall_salinityflux, wall_sflux, ws_scheme_mom, ws_scheme_sca
[1875]	240
	241	USE cpulog, &
	242	ONLY: cpu_log, log_point
	243
	244	USE eqn_state_seawater_mod, &
	245	ONLY: eqn_state_seawater
	246
	247	USE indices, &
	248	ONLY: i_left, i_right, j_north, j_south, nxl, nxlu, nxr, nyn, nys, &
	249	nysv, nzb_s_inner, nzb_u_inner, nzb_v_inner, nzb_w_inner, nzt
	250
	251	USE advec_ws, &
	252	ONLY: advec_s_ws, advec_s_ws_acc, advec_u_ws, advec_u_ws_acc, &
	253	advec_v_ws, advec_v_ws_acc, advec_w_ws, advec_w_ws_acc
	254
	255	USE advec_s_bc_mod, &
	256	ONLY: advec_s_bc
	257
	258	USE advec_s_pw_mod, &
	259	ONLY: advec_s_pw
	260
	261	USE advec_s_up_mod, &
	262	ONLY: advec_s_up
	263
	264	USE advec_u_pw_mod, &
	265	ONLY: advec_u_pw
	266
	267	USE advec_u_up_mod, &
	268	ONLY: advec_u_up
	269
	270	USE advec_v_pw_mod, &
	271	ONLY: advec_v_pw
	272
	273	USE advec_v_up_mod, &
	274	ONLY: advec_v_up
	275
	276	USE advec_w_pw_mod, &
	277	ONLY: advec_w_pw
	278
	279	USE advec_w_up_mod, &
	280	ONLY: advec_w_up
	281
	282	USE buoyancy_mod, &
	283	ONLY: buoyancy, buoyancy_acc
	284
	285	USE calc_radiation_mod, &
	286	ONLY: calc_radiation
	287
	288	USE coriolis_mod, &
	289	ONLY: coriolis, coriolis_acc
	290
	291	USE diffusion_e_mod, &
	292	ONLY: diffusion_e, diffusion_e_acc
	293
	294	USE diffusion_s_mod, &
	295	ONLY: diffusion_s, diffusion_s_acc
	296
	297	USE diffusion_u_mod, &
	298	ONLY: diffusion_u, diffusion_u_acc
	299
	300	USE diffusion_v_mod, &
	301	ONLY: diffusion_v, diffusion_v_acc
	302
	303	USE diffusion_w_mod, &
	304	ONLY: diffusion_w, diffusion_w_acc
	305
	306	USE kinds
	307
	308	USE ls_forcing_mod, &
	309	ONLY: ls_advec
	310
	311	USE microphysics_mod, &
	312	ONLY: microphysics_control
	313
	314	USE nudge_mod, &
	315	ONLY: nudge
	316
	317	USE plant_canopy_model_mod, &
	318	ONLY: cthf, plant_canopy, pcm_tendency
	319
	320	USE production_e_mod, &
	321	ONLY: production_e, production_e_acc
	322
	323	USE radiation_model_mod, &
[1976]	324	ONLY: radiation, radiation_tendency, &
[1875]	325	skip_time_do_radiation
	326
	327	USE statistics, &
	328	ONLY: hom
	329
	330	USE subsidence_mod, &
	331	ONLY: subsidence
	332
[2007]	333	USE urban_surface_mod, &
[2011]	334	ONLY: usm_wall_heat_flux
[2007]	335
[1875]	336	USE user_actions_mod, &
	337	ONLY: user_actions
	338
[1914]	339	USE wind_turbine_model_mod, &
	340	ONLY: wind_turbine, wtm_tendencies
[1875]	341
[1914]	342
[1875]	343	PRIVATE
	344	PUBLIC prognostic_equations_cache, prognostic_equations_vector, &
	345	prognostic_equations_acc
	346
	347	INTERFACE prognostic_equations_cache
	348	MODULE PROCEDURE prognostic_equations_cache
	349	END INTERFACE prognostic_equations_cache
	350
	351	INTERFACE prognostic_equations_vector
	352	MODULE PROCEDURE prognostic_equations_vector
	353	END INTERFACE prognostic_equations_vector
	354
	355	INTERFACE prognostic_equations_acc
	356	MODULE PROCEDURE prognostic_equations_acc
	357	END INTERFACE prognostic_equations_acc
	358
	359
	360	CONTAINS
	361
	362
	363	!------------------------------------------------------------------------------!
	364	! Description:
	365	! ------------
	366	!> Version with one optimized loop over all equations. It is only allowed to
	367	!> be called for the Wicker and Skamarock or Piascek-Williams advection scheme.
	368	!>
	369	!> Here the calls of most subroutines are embedded in two DO loops over i and j,
	370	!> so communication between CPUs is not allowed (does not make sense) within
	371	!> these loops.
	372	!>
	373	!> (Optimized to avoid cache missings, i.e. for Power4/5-architectures.)
	374	!------------------------------------------------------------------------------!
	375
	376	SUBROUTINE prognostic_equations_cache
	377
	378
	379	IMPLICIT NONE
	380
	381	INTEGER(iwp) :: i !<
	382	INTEGER(iwp) :: i_omp_start !<
	383	INTEGER(iwp) :: j !<
	384	INTEGER(iwp) :: k !<
	385	INTEGER(iwp) :: omp_get_thread_num !<
	386	INTEGER(iwp) :: tn = 0 !<
	387
	388	LOGICAL :: loop_start !<
	389
	390
	391	!
	392	!-- Time measurement can only be performed for the whole set of equations
	393	CALL cpu_log( log_point(32), 'all progn.equations', 'start' )
	394
	395	!
	396	!-- Loop over all prognostic equations
	397	!$OMP PARALLEL private (i,i_omp_start,j,k,loop_start,tn)
	398
	399	!$ tn = omp_get_thread_num()
	400	loop_start = .TRUE.
	401	!$OMP DO
	402	DO i = nxl, nxr
	403
	404	!
	405	!-- Store the first loop index. It differs for each thread and is required
	406	!-- later in advec_ws
	407	IF ( loop_start ) THEN
	408	loop_start = .FALSE.
	409	i_omp_start = i
	410	ENDIF
	411
	412	DO j = nys, nyn
	413	!
	414	!-- If required, calculate cloud microphysics
	415	IF ( cloud_physics .AND. .NOT. microphysics_sat_adjust .AND. &
	416	( intermediate_timestep_count == 1 .OR. &
	417	call_microphysics_at_all_substeps ) &
	418	) THEN
	419	CALL microphysics_control( i, j )
	420	ENDIF
	421	!
	422	!-- Tendency terms for u-velocity component
	423	IF ( .NOT. outflow_l .OR. i > nxl ) THEN
	424
	425	tend(:,j,i) = 0.0_wp
	426	IF ( timestep_scheme(1:5) == 'runge' ) THEN
	427	IF ( ws_scheme_mom ) THEN
	428	CALL advec_u_ws( i, j, i_omp_start, tn )
	429	ELSE
	430	CALL advec_u_pw( i, j )
	431	ENDIF
	432	ELSE
	433	CALL advec_u_up( i, j )
	434	ENDIF
	435	CALL diffusion_u( i, j )
	436	CALL coriolis( i, j, 1 )
	437	IF ( sloping_surface .AND. .NOT. neutral ) THEN
	438	CALL buoyancy( i, j, pt, 1 )
	439	ENDIF
	440
	441	!
	442	!-- Drag by plant canopy
	443	IF ( plant_canopy ) CALL pcm_tendency( i, j, 1 )
	444
	445	!
	446	!-- External pressure gradient
	447	IF ( dp_external ) THEN
	448	DO k = dp_level_ind_b+1, nzt
	449	tend(k,j,i) = tend(k,j,i) - dpdxy(1) * dp_smooth_factor(k)
	450	ENDDO
	451	ENDIF
	452
	453	!
	454	!-- Nudging
	455	IF ( nudging ) CALL nudge( i, j, simulated_time, 'u' )
	456
[1914]	457	!
	458	!-- Forces by wind turbines
	459	IF ( wind_turbine ) CALL wtm_tendencies( i, j, 1 )
	460
[1875]	461	CALL user_actions( i, j, 'u-tendency' )
	462	!
	463	!-- Prognostic equation for u-velocity component
	464	DO k = nzb_u_inner(j,i)+1, nzt
	465	u_p(k,j,i) = u(k,j,i) + dt_3d * ( tsc(2) * tend(k,j,i) + &
	466	tsc(3) * tu_m(k,j,i) ) &
	467	- tsc(5) * rdf(k) * ( u(k,j,i) - u_init(k) )
	468	ENDDO
	469
	470	!
	471	!-- Calculate tendencies for the next Runge-Kutta step
	472	IF ( timestep_scheme(1:5) == 'runge' ) THEN
	473	IF ( intermediate_timestep_count == 1 ) THEN
	474	DO k = nzb_u_inner(j,i)+1, nzt
	475	tu_m(k,j,i) = tend(k,j,i)
	476	ENDDO
	477	ELSEIF ( intermediate_timestep_count < &
	478	intermediate_timestep_count_max ) THEN
	479	DO k = nzb_u_inner(j,i)+1, nzt
	480	tu_m(k,j,i) = -9.5625_wp * tend(k,j,i) + 5.3125_wp * tu_m(k,j,i)
	481	ENDDO
	482	ENDIF
	483	ENDIF
	484
	485	ENDIF
	486
	487	!
	488	!-- Tendency terms for v-velocity component
	489	IF ( .NOT. outflow_s .OR. j > nys ) THEN
	490
	491	tend(:,j,i) = 0.0_wp
	492	IF ( timestep_scheme(1:5) == 'runge' ) THEN
	493	IF ( ws_scheme_mom ) THEN
	494	CALL advec_v_ws( i, j, i_omp_start, tn )
	495	ELSE
	496	CALL advec_v_pw( i, j )
	497	ENDIF
	498	ELSE
	499	CALL advec_v_up( i, j )
	500	ENDIF
	501	CALL diffusion_v( i, j )
	502	CALL coriolis( i, j, 2 )
	503
	504	!
	505	!-- Drag by plant canopy
	506	IF ( plant_canopy ) CALL pcm_tendency( i, j, 2 )
	507
	508	!
	509	!-- External pressure gradient
	510	IF ( dp_external ) THEN
	511	DO k = dp_level_ind_b+1, nzt
	512	tend(k,j,i) = tend(k,j,i) - dpdxy(2) * dp_smooth_factor(k)
	513	ENDDO
	514	ENDIF
	515
	516	!
	517	!-- Nudging
	518	IF ( nudging ) CALL nudge( i, j, simulated_time, 'v' )
	519
[1914]	520	!
	521	!-- Forces by wind turbines
	522	IF ( wind_turbine ) CALL wtm_tendencies( i, j, 2 )
	523
[1875]	524	CALL user_actions( i, j, 'v-tendency' )
	525	!
	526	!-- Prognostic equation for v-velocity component
	527	DO k = nzb_v_inner(j,i)+1, nzt
	528	v_p(k,j,i) = v(k,j,i) + dt_3d * ( tsc(2) * tend(k,j,i) + &
	529	tsc(3) * tv_m(k,j,i) ) &
	530	- tsc(5) * rdf(k) * ( v(k,j,i) - v_init(k) )
	531	ENDDO
	532
	533	!
	534	!-- Calculate tendencies for the next Runge-Kutta step
	535	IF ( timestep_scheme(1:5) == 'runge' ) THEN
	536	IF ( intermediate_timestep_count == 1 ) THEN
	537	DO k = nzb_v_inner(j,i)+1, nzt
	538	tv_m(k,j,i) = tend(k,j,i)
	539	ENDDO
	540	ELSEIF ( intermediate_timestep_count < &
	541	intermediate_timestep_count_max ) THEN
	542	DO k = nzb_v_inner(j,i)+1, nzt
	543	tv_m(k,j,i) = -9.5625_wp * tend(k,j,i) + 5.3125_wp * tv_m(k,j,i)
	544	ENDDO
	545	ENDIF
	546	ENDIF
	547
	548	ENDIF
	549
	550	!
	551	!-- Tendency terms for w-velocity component
	552	tend(:,j,i) = 0.0_wp
	553	IF ( timestep_scheme(1:5) == 'runge' ) THEN
	554	IF ( ws_scheme_mom ) THEN
	555	CALL advec_w_ws( i, j, i_omp_start, tn )
	556	ELSE
	557	CALL advec_w_pw( i, j )
	558	END IF
	559	ELSE
	560	CALL advec_w_up( i, j )
	561	ENDIF
	562	CALL diffusion_w( i, j )
	563	CALL coriolis( i, j, 3 )
	564
	565	IF ( .NOT. neutral ) THEN
	566	IF ( ocean ) THEN
[2031]	567	CALL buoyancy( i, j, rho_ocean, 3 )
[1875]	568	ELSE
	569	IF ( .NOT. humidity ) THEN
	570	CALL buoyancy( i, j, pt, 3 )
	571	ELSE
	572	CALL buoyancy( i, j, vpt, 3 )
	573	ENDIF
	574	ENDIF
	575	ENDIF
	576
	577	!
	578	!-- Drag by plant canopy
	579	IF ( plant_canopy ) CALL pcm_tendency( i, j, 3 )
	580
[1914]	581	!
	582	!-- Forces by wind turbines
	583	IF ( wind_turbine ) CALL wtm_tendencies( i, j, 3 )
	584
[1875]	585	CALL user_actions( i, j, 'w-tendency' )
	586
	587	!
	588	!-- Prognostic equation for w-velocity component
	589	DO k = nzb_w_inner(j,i)+1, nzt-1
	590	w_p(k,j,i) = w(k,j,i) + dt_3d * ( tsc(2) * tend(k,j,i) + &
	591	tsc(3) * tw_m(k,j,i) ) &
	592	- tsc(5) * rdf(k) * w(k,j,i)
	593	ENDDO
	594
	595	!
	596	!-- Calculate tendencies for the next Runge-Kutta step
	597	IF ( timestep_scheme(1:5) == 'runge' ) THEN
	598	IF ( intermediate_timestep_count == 1 ) THEN
	599	DO k = nzb_w_inner(j,i)+1, nzt-1
	600	tw_m(k,j,i) = tend(k,j,i)
	601	ENDDO
	602	ELSEIF ( intermediate_timestep_count < &
	603	intermediate_timestep_count_max ) THEN
	604	DO k = nzb_w_inner(j,i)+1, nzt-1
	605	tw_m(k,j,i) = -9.5625_wp * tend(k,j,i) + 5.3125_wp * tw_m(k,j,i)
	606	ENDDO
	607	ENDIF
	608	ENDIF
	609
	610	!
	611	!-- If required, compute prognostic equation for potential temperature
	612	IF ( .NOT. neutral ) THEN
	613	!
	614	!-- Tendency terms for potential temperature
	615	tend(:,j,i) = 0.0_wp
	616	IF ( timestep_scheme(1:5) == 'runge' ) THEN
	617	IF ( ws_scheme_sca ) THEN
	618	CALL advec_s_ws( i, j, pt, 'pt', flux_s_pt, diss_s_pt, &
	619	flux_l_pt, diss_l_pt, i_omp_start, tn )
	620	ELSE
	621	CALL advec_s_pw( i, j, pt )
	622	ENDIF
	623	ELSE
	624	CALL advec_s_up( i, j, pt )
	625	ENDIF
	626	CALL diffusion_s( i, j, pt, shf, tswst, wall_heatflux )
	627
	628	!
[2007]	629	!-- Tendency pt from wall heat flux from urban surface
	630	IF ( urban_surface ) THEN
	631	CALL usm_wall_heat_flux( i, j )
	632	ENDIF
	633
	634	!
[1875]	635	!-- If required compute heating/cooling due to long wave radiation
	636	!-- processes
	637	IF ( cloud_top_radiation ) THEN
	638	CALL calc_radiation( i, j )
	639	ENDIF
	640
	641	!
	642	!-- Consideration of heat sources within the plant canopy
	643	IF ( plant_canopy .AND. cthf /= 0.0_wp ) THEN
	644	CALL pcm_tendency( i, j, 4 )
	645	ENDIF
	646
	647	!
	648	!-- Large scale advection
	649	IF ( large_scale_forcing ) THEN
	650	CALL ls_advec( i, j, simulated_time, 'pt' )
	651	ENDIF
	652
	653	!
	654	!-- Nudging
	655	IF ( nudging ) CALL nudge( i, j, simulated_time, 'pt' )
	656
	657	!
	658	!-- If required, compute effect of large-scale subsidence/ascent
	659	IF ( large_scale_subsidence .AND. &
	660	.NOT. use_subsidence_tendencies ) THEN
	661	CALL subsidence( i, j, tend, pt, pt_init, 2 )
	662	ENDIF
	663
	664	!
	665	!-- If required, add tendency due to radiative heating/cooling
[1976]	666	IF ( radiation .AND. &
[1875]	667	simulated_time > skip_time_do_radiation ) THEN
	668	CALL radiation_tendency ( i, j, tend )
	669	ENDIF
	670
	671
	672	CALL user_actions( i, j, 'pt-tendency' )
	673
	674	!
	675	!-- Prognostic equation for potential temperature
	676	DO k = nzb_s_inner(j,i)+1, nzt
	677	pt_p(k,j,i) = pt(k,j,i) + dt_3d * ( tsc(2) * tend(k,j,i) + &
	678	tsc(3) * tpt_m(k,j,i) ) &
	679	- tsc(5) * ( pt(k,j,i) - pt_init(k) ) *&
	680	( rdf_sc(k) + ptdf_x(i) + ptdf_y(j) )
	681	ENDDO
	682
	683	!
	684	!-- Calculate tendencies for the next Runge-Kutta step
	685	IF ( timestep_scheme(1:5) == 'runge' ) THEN
	686	IF ( intermediate_timestep_count == 1 ) THEN
	687	DO k = nzb_s_inner(j,i)+1, nzt
	688	tpt_m(k,j,i) = tend(k,j,i)
	689	ENDDO
	690	ELSEIF ( intermediate_timestep_count < &
	691	intermediate_timestep_count_max ) THEN
	692	DO k = nzb_s_inner(j,i)+1, nzt
	693	tpt_m(k,j,i) = -9.5625_wp * tend(k,j,i) + &
	694	5.3125_wp * tpt_m(k,j,i)
	695	ENDDO
	696	ENDIF
	697	ENDIF
	698
	699	ENDIF
	700
	701	!
	702	!-- If required, compute prognostic equation for salinity
	703	IF ( ocean ) THEN
	704
	705	!
	706	!-- Tendency-terms for salinity
	707	tend(:,j,i) = 0.0_wp
	708	IF ( timestep_scheme(1:5) == 'runge' ) &
	709	THEN
	710	IF ( ws_scheme_sca ) THEN
	711	CALL advec_s_ws( i, j, sa, 'sa', flux_s_sa, &
	712	diss_s_sa, flux_l_sa, diss_l_sa, i_omp_start, tn )
	713	ELSE
	714	CALL advec_s_pw( i, j, sa )
	715	ENDIF
	716	ELSE
	717	CALL advec_s_up( i, j, sa )
	718	ENDIF
	719	CALL diffusion_s( i, j, sa, saswsb, saswst, wall_salinityflux )
	720
	721	CALL user_actions( i, j, 'sa-tendency' )
	722
	723	!
	724	!-- Prognostic equation for salinity
	725	DO k = nzb_s_inner(j,i)+1, nzt
	726	sa_p(k,j,i) = sa(k,j,i) + dt_3d * ( tsc(2) * tend(k,j,i) + &
	727	tsc(3) * tsa_m(k,j,i) ) &
	728	- tsc(5) * rdf_sc(k) * &
	729	( sa(k,j,i) - sa_init(k) )
	730	IF ( sa_p(k,j,i) < 0.0_wp ) sa_p(k,j,i) = 0.1_wp * sa(k,j,i)
	731	ENDDO
	732
	733	!
	734	!-- Calculate tendencies for the next Runge-Kutta step
	735	IF ( timestep_scheme(1:5) == 'runge' ) THEN
	736	IF ( intermediate_timestep_count == 1 ) THEN
	737	DO k = nzb_s_inner(j,i)+1, nzt
	738	tsa_m(k,j,i) = tend(k,j,i)
	739	ENDDO
	740	ELSEIF ( intermediate_timestep_count < &
	741	intermediate_timestep_count_max ) THEN
	742	DO k = nzb_s_inner(j,i)+1, nzt
	743	tsa_m(k,j,i) = -9.5625_wp * tend(k,j,i) + &
	744	5.3125_wp * tsa_m(k,j,i)
	745	ENDDO
	746	ENDIF
	747	ENDIF
	748
	749	!
	750	!-- Calculate density by the equation of state for seawater
	751	CALL eqn_state_seawater( i, j )
	752
	753	ENDIF
	754
	755	!
[1960]	756	!-- If required, compute prognostic equation for total water content
	757	IF ( humidity ) THEN
[1875]	758
	759	!
	760	!-- Tendency-terms for total water content / scalar
	761	tend(:,j,i) = 0.0_wp
	762	IF ( timestep_scheme(1:5) == 'runge' ) &
	763	THEN
	764	IF ( ws_scheme_sca ) THEN
	765	CALL advec_s_ws( i, j, q, 'q', flux_s_q, &
	766	diss_s_q, flux_l_q, diss_l_q, i_omp_start, tn )
	767	ELSE
	768	CALL advec_s_pw( i, j, q )
	769	ENDIF
	770	ELSE
	771	CALL advec_s_up( i, j, q )
	772	ENDIF
	773	CALL diffusion_s( i, j, q, qsws, qswst, wall_qflux )
	774
	775	!
[1960]	776	!-- Sink or source of humidity due to canopy elements
[1875]	777	IF ( plant_canopy ) CALL pcm_tendency( i, j, 5 )
	778
	779	!
	780	!-- Large scale advection
	781	IF ( large_scale_forcing ) THEN
	782	CALL ls_advec( i, j, simulated_time, 'q' )
	783	ENDIF
	784
	785	!
	786	!-- Nudging
	787	IF ( nudging ) CALL nudge( i, j, simulated_time, 'q' )
	788
	789	!
	790	!-- If required compute influence of large-scale subsidence/ascent
	791	IF ( large_scale_subsidence .AND. &
	792	.NOT. use_subsidence_tendencies ) THEN
	793	CALL subsidence( i, j, tend, q, q_init, 3 )
	794	ENDIF
	795
	796	CALL user_actions( i, j, 'q-tendency' )
	797
	798	!
	799	!-- Prognostic equation for total water content / scalar
	800	DO k = nzb_s_inner(j,i)+1, nzt
	801	q_p(k,j,i) = q(k,j,i) + dt_3d * ( tsc(2) * tend(k,j,i) + &
	802	tsc(3) * tq_m(k,j,i) ) &
	803	- tsc(5) * rdf_sc(k) * &
	804	( q(k,j,i) - q_init(k) )
	805	IF ( q_p(k,j,i) < 0.0_wp ) q_p(k,j,i) = 0.1_wp * q(k,j,i)
	806	ENDDO
	807
	808	!
	809	!-- Calculate tendencies for the next Runge-Kutta step
	810	IF ( timestep_scheme(1:5) == 'runge' ) THEN
	811	IF ( intermediate_timestep_count == 1 ) THEN
	812	DO k = nzb_s_inner(j,i)+1, nzt
	813	tq_m(k,j,i) = tend(k,j,i)
	814	ENDDO
	815	ELSEIF ( intermediate_timestep_count < &
	816	intermediate_timestep_count_max ) THEN
	817	DO k = nzb_s_inner(j,i)+1, nzt
	818	tq_m(k,j,i) = -9.5625_wp * tend(k,j,i) + &
	819	5.3125_wp * tq_m(k,j,i)
	820	ENDDO
	821	ENDIF
	822	ENDIF
	823
	824	!
	825	!-- If required, calculate prognostic equations for rain water content
	826	!-- and rain drop concentration
	827	IF ( cloud_physics .AND. microphysics_seifert ) THEN
	828	!
	829	!-- Calculate prognostic equation for rain water content
	830	tend(:,j,i) = 0.0_wp
	831	IF ( timestep_scheme(1:5) == 'runge' ) &
	832	THEN
	833	IF ( ws_scheme_sca ) THEN
	834	CALL advec_s_ws( i, j, qr, 'qr', flux_s_qr, &
	835	diss_s_qr, flux_l_qr, diss_l_qr, &
	836	i_omp_start, tn )
	837	ELSE
	838	CALL advec_s_pw( i, j, qr )
	839	ENDIF
	840	ELSE
	841	CALL advec_s_up( i, j, qr )
	842	ENDIF
	843	CALL diffusion_s( i, j, qr, qrsws, qrswst, wall_qrflux )
	844
	845	!
	846	!-- Prognostic equation for rain water content
	847	DO k = nzb_s_inner(j,i)+1, nzt
	848	qr_p(k,j,i) = qr(k,j,i) + dt_3d * ( tsc(2) * tend(k,j,i) + &
	849	tsc(3) * tqr_m(k,j,i) ) &
	850	- tsc(5) * rdf_sc(k) * qr(k,j,i)
	851	IF ( qr_p(k,j,i) < 0.0_wp ) qr_p(k,j,i) = 0.0_wp
	852	ENDDO
	853	!
	854	!-- Calculate tendencies for the next Runge-Kutta step
	855	IF ( timestep_scheme(1:5) == 'runge' ) THEN
	856	IF ( intermediate_timestep_count == 1 ) THEN
	857	DO k = nzb_s_inner(j,i)+1, nzt
	858	tqr_m(k,j,i) = tend(k,j,i)
	859	ENDDO
	860	ELSEIF ( intermediate_timestep_count < &
	861	intermediate_timestep_count_max ) THEN
	862	DO k = nzb_s_inner(j,i)+1, nzt
	863	tqr_m(k,j,i) = -9.5625_wp * tend(k,j,i) + &
	864	5.3125_wp * tqr_m(k,j,i)
	865	ENDDO
	866	ENDIF
	867	ENDIF
	868
	869	!
	870	!-- Calculate prognostic equation for rain drop concentration.
	871	tend(:,j,i) = 0.0_wp
	872	IF ( timestep_scheme(1:5) == 'runge' ) THEN
	873	IF ( ws_scheme_sca ) THEN
	874	CALL advec_s_ws( i, j, nr, 'nr', flux_s_nr, &
	875	diss_s_nr, flux_l_nr, diss_l_nr, &
	876	i_omp_start, tn )
	877	ELSE
	878	CALL advec_s_pw( i, j, nr )
	879	ENDIF
	880	ELSE
	881	CALL advec_s_up( i, j, nr )
	882	ENDIF
	883	CALL diffusion_s( i, j, nr, nrsws, nrswst, wall_nrflux )
	884
	885	!
	886	!-- Prognostic equation for rain drop concentration
	887	DO k = nzb_s_inner(j,i)+1, nzt
	888	nr_p(k,j,i) = nr(k,j,i) + dt_3d * ( tsc(2) * tend(k,j,i) + &
	889	tsc(3) * tnr_m(k,j,i) ) &
	890	- tsc(5) * rdf_sc(k) * nr(k,j,i)
	891	IF ( nr_p(k,j,i) < 0.0_wp ) nr_p(k,j,i) = 0.0_wp
	892	ENDDO
	893	!
	894	!-- Calculate tendencies for the next Runge-Kutta step
	895	IF ( timestep_scheme(1:5) == 'runge' ) THEN
	896	IF ( intermediate_timestep_count == 1 ) THEN
	897	DO k = nzb_s_inner(j,i)+1, nzt
	898	tnr_m(k,j,i) = tend(k,j,i)
	899	ENDDO
	900	ELSEIF ( intermediate_timestep_count < &
	901	intermediate_timestep_count_max ) THEN
	902	DO k = nzb_s_inner(j,i)+1, nzt
	903	tnr_m(k,j,i) = -9.5625_wp * tend(k,j,i) + &
	904	5.3125_wp * tnr_m(k,j,i)
	905	ENDDO
	906	ENDIF
	907	ENDIF
	908
	909	ENDIF
	910
	911	ENDIF
[1960]	912
	913	!
	914	!-- If required, compute prognostic equation for scalar
	915	IF ( passive_scalar ) THEN
	916	!
	917	!-- Tendency-terms for total water content / scalar
	918	tend(:,j,i) = 0.0_wp
	919	IF ( timestep_scheme(1:5) == 'runge' ) &
	920	THEN
	921	IF ( ws_scheme_sca ) THEN
	922	CALL advec_s_ws( i, j, s, 's', flux_s_s, &
	923	diss_s_s, flux_l_s, diss_l_s, i_omp_start, tn )
	924	ELSE
	925	CALL advec_s_pw( i, j, s )
	926	ENDIF
	927	ELSE
	928	CALL advec_s_up( i, j, s )
	929	ENDIF
	930	CALL diffusion_s( i, j, s, ssws, sswst, wall_sflux )
[1875]	931
	932	!
[1960]	933	!-- Sink or source of scalar concentration due to canopy elements
	934	IF ( plant_canopy ) CALL pcm_tendency( i, j, 7 )
	935
	936	!
	937	!-- Large scale advection, still need to be extended for scalars
	938	! IF ( large_scale_forcing ) THEN
	939	! CALL ls_advec( i, j, simulated_time, 's' )
	940	! ENDIF
	941
	942	!
	943	!-- Nudging, still need to be extended for scalars
	944	! IF ( nudging ) CALL nudge( i, j, simulated_time, 's' )
	945
	946	!
	947	!-- If required compute influence of large-scale subsidence/ascent.
	948	!-- Note, the last argument is of no meaning in this case, as it is
	949	!-- only used in conjunction with large_scale_forcing, which is to
	950	!-- date not implemented for scalars.
	951	IF ( large_scale_subsidence .AND. &
	952	.NOT. use_subsidence_tendencies .AND. &
	953	.NOT. large_scale_forcing ) THEN
	954	CALL subsidence( i, j, tend, s, s_init, 3 )
	955	ENDIF
	956
	957	CALL user_actions( i, j, 's-tendency' )
	958
	959	!
	960	!-- Prognostic equation for scalar
	961	DO k = nzb_s_inner(j,i)+1, nzt
	962	s_p(k,j,i) = s(k,j,i) + dt_3d * ( tsc(2) * tend(k,j,i) + &
	963	tsc(3) * ts_m(k,j,i) ) &
	964	- tsc(5) * rdf_sc(k) * &
	965	( s(k,j,i) - s_init(k) )
	966	IF ( s_p(k,j,i) < 0.0_wp ) s_p(k,j,i) = 0.1_wp * s(k,j,i)
	967	ENDDO
	968
	969	!
	970	!-- Calculate tendencies for the next Runge-Kutta step
	971	IF ( timestep_scheme(1:5) == 'runge' ) THEN
	972	IF ( intermediate_timestep_count == 1 ) THEN
	973	DO k = nzb_s_inner(j,i)+1, nzt
	974	ts_m(k,j,i) = tend(k,j,i)
	975	ENDDO
	976	ELSEIF ( intermediate_timestep_count < &
	977	intermediate_timestep_count_max ) THEN
	978	DO k = nzb_s_inner(j,i)+1, nzt
	979	ts_m(k,j,i) = -9.5625_wp * tend(k,j,i) + &
	980	5.3125_wp * ts_m(k,j,i)
	981	ENDDO
	982	ENDIF
	983	ENDIF
	984
	985	ENDIF
	986	!
[1875]	987	!-- If required, compute prognostic equation for turbulent kinetic
	988	!-- energy (TKE)
	989	IF ( .NOT. constant_diffusion ) THEN
	990
	991	!
	992	!-- Tendency-terms for TKE
	993	tend(:,j,i) = 0.0_wp
	994	IF ( timestep_scheme(1:5) == 'runge' &
	995	.AND. .NOT. use_upstream_for_tke ) THEN
	996	IF ( ws_scheme_sca ) THEN
	997	CALL advec_s_ws( i, j, e, 'e', flux_s_e, diss_s_e, &
	998	flux_l_e, diss_l_e , i_omp_start, tn )
	999	ELSE
	1000	CALL advec_s_pw( i, j, e )
	1001	ENDIF
	1002	ELSE
	1003	CALL advec_s_up( i, j, e )
	1004	ENDIF
	1005	IF ( .NOT. humidity ) THEN
	1006	IF ( ocean ) THEN
	1007	CALL diffusion_e( i, j, prho, prho_reference )
	1008	ELSE
	1009	CALL diffusion_e( i, j, pt, pt_reference )
	1010	ENDIF
	1011	ELSE
	1012	CALL diffusion_e( i, j, vpt, pt_reference )
	1013	ENDIF
	1014	CALL production_e( i, j )
	1015
	1016	!
	1017	!-- Additional sink term for flows through plant canopies
	1018	IF ( plant_canopy ) CALL pcm_tendency( i, j, 6 )
	1019
	1020	CALL user_actions( i, j, 'e-tendency' )
	1021
	1022	!
	1023	!-- Prognostic equation for TKE.
	1024	!-- Eliminate negative TKE values, which can occur due to numerical
	1025	!-- reasons in the course of the integration. In such cases the old
	1026	!-- TKE value is reduced by 90%.
	1027	DO k = nzb_s_inner(j,i)+1, nzt
	1028	e_p(k,j,i) = e(k,j,i) + dt_3d * ( tsc(2) * tend(k,j,i) + &
	1029	tsc(3) * te_m(k,j,i) )
	1030	IF ( e_p(k,j,i) < 0.0_wp ) e_p(k,j,i) = 0.1_wp * e(k,j,i)
	1031	ENDDO
	1032
	1033	!
	1034	!-- Calculate tendencies for the next Runge-Kutta step
	1035	IF ( timestep_scheme(1:5) == 'runge' ) THEN
	1036	IF ( intermediate_timestep_count == 1 ) THEN
	1037	DO k = nzb_s_inner(j,i)+1, nzt
	1038	te_m(k,j,i) = tend(k,j,i)
	1039	ENDDO
	1040	ELSEIF ( intermediate_timestep_count < &
	1041	intermediate_timestep_count_max ) THEN
	1042	DO k = nzb_s_inner(j,i)+1, nzt
	1043	te_m(k,j,i) = -9.5625_wp * tend(k,j,i) + &
	1044	5.3125_wp * te_m(k,j,i)
	1045	ENDDO
	1046	ENDIF
	1047	ENDIF
	1048
	1049	ENDIF ! TKE equation
	1050
	1051	ENDDO
	1052	ENDDO
	1053	!$OMP END PARALLEL
	1054
	1055	CALL cpu_log( log_point(32), 'all progn.equations', 'stop' )
	1056
	1057
	1058	END SUBROUTINE prognostic_equations_cache
	1059
	1060
	1061	!------------------------------------------------------------------------------!
	1062	! Description:
	1063	! ------------
	1064	!> Version for vector machines
	1065	!------------------------------------------------------------------------------!
	1066
	1067	SUBROUTINE prognostic_equations_vector
	1068
	1069
	1070	IMPLICIT NONE
	1071
	1072	INTEGER(iwp) :: i !<
	1073	INTEGER(iwp) :: j !<
	1074	INTEGER(iwp) :: k !<
	1075
	1076	REAL(wp) :: sbt !<
	1077
	1078
	1079	!
	1080	!-- If required, calculate cloud microphysical impacts
	1081	IF ( cloud_physics .AND. .NOT. microphysics_sat_adjust .AND. &
	1082	( intermediate_timestep_count == 1 .OR. &
	1083	call_microphysics_at_all_substeps ) &
	1084	) THEN
	1085	CALL cpu_log( log_point(51), 'microphysics', 'start' )
	1086	CALL microphysics_control
	1087	CALL cpu_log( log_point(51), 'microphysics', 'stop' )
	1088	ENDIF
	1089
	1090	!
	1091	!-- u-velocity component
	1092	CALL cpu_log( log_point(5), 'u-equation', 'start' )
	1093
	1094	tend = 0.0_wp
	1095	IF ( timestep_scheme(1:5) == 'runge' ) THEN
	1096	IF ( ws_scheme_mom ) THEN
	1097	CALL advec_u_ws
	1098	ELSE
	1099	CALL advec_u_pw
	1100	ENDIF
	1101	ELSE
	1102	CALL advec_u_up
	1103	ENDIF
	1104	CALL diffusion_u
	1105	CALL coriolis( 1 )
	1106	IF ( sloping_surface .AND. .NOT. neutral ) THEN
	1107	CALL buoyancy( pt, 1 )
	1108	ENDIF
	1109
	1110	!
	1111	!-- Drag by plant canopy
	1112	IF ( plant_canopy ) CALL pcm_tendency( 1 )
	1113
	1114	!
	1115	!-- External pressure gradient
	1116	IF ( dp_external ) THEN
	1117	DO i = nxlu, nxr
	1118	DO j = nys, nyn
	1119	DO k = dp_level_ind_b+1, nzt
	1120	tend(k,j,i) = tend(k,j,i) - dpdxy(1) * dp_smooth_factor(k)
	1121	ENDDO
	1122	ENDDO
	1123	ENDDO
	1124	ENDIF
	1125
	1126	!
	1127	!-- Nudging
	1128	IF ( nudging ) CALL nudge( simulated_time, 'u' )
	1129
[1914]	1130	!
	1131	!-- Forces by wind turbines
	1132	IF ( wind_turbine ) CALL wtm_tendencies( 1 )
	1133
[1875]	1134	CALL user_actions( 'u-tendency' )
	1135
	1136	!
	1137	!-- Prognostic equation for u-velocity component
	1138	DO i = nxlu, nxr
	1139	DO j = nys, nyn
	1140	DO k = nzb_u_inner(j,i)+1, nzt
	1141	u_p(k,j,i) = u(k,j,i) + dt_3d * ( tsc(2) * tend(k,j,i) + &
	1142	tsc(3) * tu_m(k,j,i) ) &
	1143	- tsc(5) * rdf(k) * ( u(k,j,i) - u_init(k) )
	1144	ENDDO
	1145	ENDDO
	1146	ENDDO
	1147
	1148	!
	1149	!-- Calculate tendencies for the next Runge-Kutta step
	1150	IF ( timestep_scheme(1:5) == 'runge' ) THEN
	1151	IF ( intermediate_timestep_count == 1 ) THEN
	1152	DO i = nxlu, nxr
	1153	DO j = nys, nyn
	1154	DO k = nzb_u_inner(j,i)+1, nzt
	1155	tu_m(k,j,i) = tend(k,j,i)
	1156	ENDDO
	1157	ENDDO
	1158	ENDDO
	1159	ELSEIF ( intermediate_timestep_count < &
	1160	intermediate_timestep_count_max ) THEN
	1161	DO i = nxlu, nxr
	1162	DO j = nys, nyn
	1163	DO k = nzb_u_inner(j,i)+1, nzt
	1164	tu_m(k,j,i) = -9.5625_wp * tend(k,j,i) + 5.3125_wp * tu_m(k,j,i)
	1165	ENDDO
	1166	ENDDO
	1167	ENDDO
	1168	ENDIF
	1169	ENDIF
	1170
	1171	CALL cpu_log( log_point(5), 'u-equation', 'stop' )
	1172
	1173	!
	1174	!-- v-velocity component
	1175	CALL cpu_log( log_point(6), 'v-equation', 'start' )
	1176
	1177	tend = 0.0_wp
	1178	IF ( timestep_scheme(1:5) == 'runge' ) THEN
	1179	IF ( ws_scheme_mom ) THEN
	1180	CALL advec_v_ws
	1181	ELSE
	1182	CALL advec_v_pw
	1183	END IF
	1184	ELSE
	1185	CALL advec_v_up
	1186	ENDIF
	1187	CALL diffusion_v
	1188	CALL coriolis( 2 )
	1189
	1190	!
	1191	!-- Drag by plant canopy
	1192	IF ( plant_canopy ) CALL pcm_tendency( 2 )
	1193
	1194	!
	1195	!-- External pressure gradient
	1196	IF ( dp_external ) THEN
	1197	DO i = nxl, nxr
	1198	DO j = nysv, nyn
	1199	DO k = dp_level_ind_b+1, nzt
	1200	tend(k,j,i) = tend(k,j,i) - dpdxy(2) * dp_smooth_factor(k)
	1201	ENDDO
	1202	ENDDO
	1203	ENDDO
	1204	ENDIF
	1205
	1206	!
	1207	!-- Nudging
	1208	IF ( nudging ) CALL nudge( simulated_time, 'v' )
	1209
[1914]	1210	!
	1211	!-- Forces by wind turbines
	1212	IF ( wind_turbine ) CALL wtm_tendencies( 2 )
	1213
[1875]	1214	CALL user_actions( 'v-tendency' )
	1215
	1216	!
	1217	!-- Prognostic equation for v-velocity component
	1218	DO i = nxl, nxr
	1219	DO j = nysv, nyn
	1220	DO k = nzb_v_inner(j,i)+1, nzt
	1221	v_p(k,j,i) = v(k,j,i) + dt_3d * ( tsc(2) * tend(k,j,i) + &
	1222	tsc(3) * tv_m(k,j,i) ) &
	1223	- tsc(5) * rdf(k) * ( v(k,j,i) - v_init(k) )
	1224	ENDDO
	1225	ENDDO
	1226	ENDDO
	1227
	1228	!
	1229	!-- Calculate tendencies for the next Runge-Kutta step
	1230	IF ( timestep_scheme(1:5) == 'runge' ) THEN
	1231	IF ( intermediate_timestep_count == 1 ) THEN
	1232	DO i = nxl, nxr
	1233	DO j = nysv, nyn
	1234	DO k = nzb_v_inner(j,i)+1, nzt
	1235	tv_m(k,j,i) = tend(k,j,i)
	1236	ENDDO
	1237	ENDDO
	1238	ENDDO
	1239	ELSEIF ( intermediate_timestep_count < &
	1240	intermediate_timestep_count_max ) THEN
	1241	DO i = nxl, nxr
	1242	DO j = nysv, nyn
	1243	DO k = nzb_v_inner(j,i)+1, nzt
	1244	tv_m(k,j,i) = -9.5625_wp * tend(k,j,i) + 5.3125_wp * tv_m(k,j,i)
	1245	ENDDO
	1246	ENDDO
	1247	ENDDO
	1248	ENDIF
	1249	ENDIF
	1250
	1251	CALL cpu_log( log_point(6), 'v-equation', 'stop' )
	1252
	1253	!
	1254	!-- w-velocity component
	1255	CALL cpu_log( log_point(7), 'w-equation', 'start' )
	1256
	1257	tend = 0.0_wp
	1258	IF ( timestep_scheme(1:5) == 'runge' ) THEN
	1259	IF ( ws_scheme_mom ) THEN
	1260	CALL advec_w_ws
	1261	ELSE
	1262	CALL advec_w_pw
	1263	ENDIF
	1264	ELSE
	1265	CALL advec_w_up
	1266	ENDIF
	1267	CALL diffusion_w
	1268	CALL coriolis( 3 )
	1269
	1270	IF ( .NOT. neutral ) THEN
	1271	IF ( ocean ) THEN
[2031]	1272	CALL buoyancy( rho_ocean, 3 )
[1875]	1273	ELSE
	1274	IF ( .NOT. humidity ) THEN
	1275	CALL buoyancy( pt, 3 )
	1276	ELSE
	1277	CALL buoyancy( vpt, 3 )
	1278	ENDIF
	1279	ENDIF
	1280	ENDIF
	1281
	1282	!
	1283	!-- Drag by plant canopy
	1284	IF ( plant_canopy ) CALL pcm_tendency( 3 )
	1285
[1914]	1286	!
	1287	!-- Forces by wind turbines
	1288	IF ( wind_turbine ) CALL wtm_tendencies( 3 )
	1289
[1875]	1290	CALL user_actions( 'w-tendency' )
	1291
	1292	!
	1293	!-- Prognostic equation for w-velocity component
	1294	DO i = nxl, nxr
	1295	DO j = nys, nyn
	1296	DO k = nzb_w_inner(j,i)+1, nzt-1
	1297	w_p(k,j,i) = w(k,j,i) + dt_3d * ( tsc(2) * tend(k,j,i) + &
	1298	tsc(3) * tw_m(k,j,i) ) &
	1299	- tsc(5) * rdf(k) * w(k,j,i)
	1300	ENDDO
	1301	ENDDO
	1302	ENDDO
	1303
	1304	!
	1305	!-- Calculate tendencies for the next Runge-Kutta step
	1306	IF ( timestep_scheme(1:5) == 'runge' ) THEN
	1307	IF ( intermediate_timestep_count == 1 ) THEN
	1308	DO i = nxl, nxr
	1309	DO j = nys, nyn
	1310	DO k = nzb_w_inner(j,i)+1, nzt-1
	1311	tw_m(k,j,i) = tend(k,j,i)
	1312	ENDDO
	1313	ENDDO
	1314	ENDDO
	1315	ELSEIF ( intermediate_timestep_count < &
	1316	intermediate_timestep_count_max ) THEN
	1317	DO i = nxl, nxr
	1318	DO j = nys, nyn
	1319	DO k = nzb_w_inner(j,i)+1, nzt-1
	1320	tw_m(k,j,i) = -9.5625_wp * tend(k,j,i) + 5.3125_wp * tw_m(k,j,i)
	1321	ENDDO
	1322	ENDDO
	1323	ENDDO
	1324	ENDIF
	1325	ENDIF
	1326
	1327	CALL cpu_log( log_point(7), 'w-equation', 'stop' )
	1328
	1329
	1330	!
	1331	!-- If required, compute prognostic equation for potential temperature
	1332	IF ( .NOT. neutral ) THEN
	1333
	1334	CALL cpu_log( log_point(13), 'pt-equation', 'start' )
	1335
	1336	!
	1337	!-- pt-tendency terms with communication
	1338	sbt = tsc(2)
	1339	IF ( scalar_advec == 'bc-scheme' ) THEN
	1340
	1341	IF ( timestep_scheme(1:5) /= 'runge' ) THEN
	1342	!
	1343	!-- Bott-Chlond scheme always uses Euler time step. Thus:
	1344	sbt = 1.0_wp
	1345	ENDIF
	1346	tend = 0.0_wp
	1347	CALL advec_s_bc( pt, 'pt' )
	1348
	1349	ENDIF
	1350
	1351	!
	1352	!-- pt-tendency terms with no communication
	1353	IF ( scalar_advec /= 'bc-scheme' ) THEN
	1354	tend = 0.0_wp
	1355	IF ( timestep_scheme(1:5) == 'runge' ) THEN
	1356	IF ( ws_scheme_sca ) THEN
	1357	CALL advec_s_ws( pt, 'pt' )
	1358	ELSE
	1359	CALL advec_s_pw( pt )
	1360	ENDIF
	1361	ELSE
	1362	CALL advec_s_up( pt )
	1363	ENDIF
	1364	ENDIF
	1365
	1366	CALL diffusion_s( pt, shf, tswst, wall_heatflux )
	1367
	1368	!
[2007]	1369	!-- Tendency pt from wall heat flux from urban surface
	1370	IF ( urban_surface ) THEN
	1371	CALL usm_wall_heat_flux
	1372	ENDIF
	1373
	1374	!
[1875]	1375	!-- If required compute heating/cooling due to long wave radiation processes
	1376	IF ( cloud_top_radiation ) THEN
	1377	CALL calc_radiation
	1378	ENDIF
	1379
	1380	!
	1381	!-- Consideration of heat sources within the plant canopy
	1382	IF ( plant_canopy .AND. ( cthf /= 0.0_wp ) ) THEN
	1383	CALL pcm_tendency( 4 )
	1384	ENDIF
	1385
	1386	!
	1387	!-- Large scale advection
	1388	IF ( large_scale_forcing ) THEN
	1389	CALL ls_advec( simulated_time, 'pt' )
	1390	ENDIF
	1391
	1392	!
	1393	!-- Nudging
	1394	IF ( nudging ) CALL nudge( simulated_time, 'pt' )
	1395
	1396	!
	1397	!-- If required compute influence of large-scale subsidence/ascent
	1398	IF ( large_scale_subsidence .AND. &
	1399	.NOT. use_subsidence_tendencies ) THEN
	1400	CALL subsidence( tend, pt, pt_init, 2 )
	1401	ENDIF
	1402
	1403	!
	1404	!-- If required, add tendency due to radiative heating/cooling
[1976]	1405	IF ( radiation .AND. &
[1875]	1406	simulated_time > skip_time_do_radiation ) THEN
	1407	CALL radiation_tendency ( tend )
	1408	ENDIF
	1409
	1410	CALL user_actions( 'pt-tendency' )
	1411
	1412	!
	1413	!-- Prognostic equation for potential temperature
	1414	DO i = nxl, nxr
	1415	DO j = nys, nyn
	1416	DO k = nzb_s_inner(j,i)+1, nzt
	1417	pt_p(k,j,i) = pt(k,j,i) + dt_3d * ( sbt * tend(k,j,i) + &
	1418	tsc(3) * tpt_m(k,j,i) ) &
	1419	- tsc(5) * ( pt(k,j,i) - pt_init(k) ) *&
	1420	( rdf_sc(k) + ptdf_x(i) + ptdf_y(j) )
	1421	ENDDO
	1422	ENDDO
	1423	ENDDO
	1424
	1425	!
	1426	!-- Calculate tendencies for the next Runge-Kutta step
	1427	IF ( timestep_scheme(1:5) == 'runge' ) THEN
	1428	IF ( intermediate_timestep_count == 1 ) THEN
	1429	DO i = nxl, nxr
	1430	DO j = nys, nyn
	1431	DO k = nzb_s_inner(j,i)+1, nzt
	1432	tpt_m(k,j,i) = tend(k,j,i)
	1433	ENDDO
	1434	ENDDO
	1435	ENDDO
	1436	ELSEIF ( intermediate_timestep_count < &
	1437	intermediate_timestep_count_max ) THEN
	1438	DO i = nxl, nxr
	1439	DO j = nys, nyn
	1440	DO k = nzb_s_inner(j,i)+1, nzt
	1441	tpt_m(k,j,i) = -9.5625_wp * tend(k,j,i) + &
	1442	5.3125_wp * tpt_m(k,j,i)
	1443	ENDDO
	1444	ENDDO
	1445	ENDDO
	1446	ENDIF
	1447	ENDIF
	1448
	1449	CALL cpu_log( log_point(13), 'pt-equation', 'stop' )
	1450
	1451	ENDIF
	1452
	1453	!
	1454	!-- If required, compute prognostic equation for salinity
	1455	IF ( ocean ) THEN
	1456
	1457	CALL cpu_log( log_point(37), 'sa-equation', 'start' )
	1458
	1459	!
	1460	!-- sa-tendency terms with communication
	1461	sbt = tsc(2)
	1462	IF ( scalar_advec == 'bc-scheme' ) THEN
	1463
	1464	IF ( timestep_scheme(1:5) /= 'runge' ) THEN
	1465	!
	1466	!-- Bott-Chlond scheme always uses Euler time step. Thus:
	1467	sbt = 1.0_wp
	1468	ENDIF
	1469	tend = 0.0_wp
	1470	CALL advec_s_bc( sa, 'sa' )
	1471
	1472	ENDIF
	1473
	1474	!
	1475	!-- sa-tendency terms with no communication
	1476	IF ( scalar_advec /= 'bc-scheme' ) THEN
	1477	tend = 0.0_wp
	1478	IF ( timestep_scheme(1:5) == 'runge' ) THEN
	1479	IF ( ws_scheme_sca ) THEN
	1480	CALL advec_s_ws( sa, 'sa' )
	1481	ELSE
	1482	CALL advec_s_pw( sa )
	1483	ENDIF
	1484	ELSE
	1485	CALL advec_s_up( sa )
	1486	ENDIF
	1487	ENDIF
	1488
	1489	CALL diffusion_s( sa, saswsb, saswst, wall_salinityflux )
	1490
	1491	CALL user_actions( 'sa-tendency' )
	1492
	1493	!
	1494	!-- Prognostic equation for salinity
	1495	DO i = nxl, nxr
	1496	DO j = nys, nyn
	1497	DO k = nzb_s_inner(j,i)+1, nzt
	1498	sa_p(k,j,i) = sa(k,j,i) + dt_3d * ( sbt * tend(k,j,i) + &
	1499	tsc(3) * tsa_m(k,j,i) ) &
	1500	- tsc(5) * rdf_sc(k) * &
	1501	( sa(k,j,i) - sa_init(k) )
	1502	IF ( sa_p(k,j,i) < 0.0_wp ) sa_p(k,j,i) = 0.1_wp * sa(k,j,i)
	1503	ENDDO
	1504	ENDDO
	1505	ENDDO
	1506
	1507	!
	1508	!-- Calculate tendencies for the next Runge-Kutta step
	1509	IF ( timestep_scheme(1:5) == 'runge' ) THEN
	1510	IF ( intermediate_timestep_count == 1 ) THEN
	1511	DO i = nxl, nxr
	1512	DO j = nys, nyn
	1513	DO k = nzb_s_inner(j,i)+1, nzt
	1514	tsa_m(k,j,i) = tend(k,j,i)
	1515	ENDDO
	1516	ENDDO
	1517	ENDDO
	1518	ELSEIF ( intermediate_timestep_count < &
	1519	intermediate_timestep_count_max ) THEN
	1520	DO i = nxl, nxr
	1521	DO j = nys, nyn
	1522	DO k = nzb_s_inner(j,i)+1, nzt
	1523	tsa_m(k,j,i) = -9.5625_wp * tend(k,j,i) + &
	1524	5.3125_wp * tsa_m(k,j,i)
	1525	ENDDO
	1526	ENDDO
	1527	ENDDO
	1528	ENDIF
	1529	ENDIF
	1530
	1531	CALL cpu_log( log_point(37), 'sa-equation', 'stop' )
	1532
	1533	!
	1534	!-- Calculate density by the equation of state for seawater
	1535	CALL cpu_log( log_point(38), 'eqns-seawater', 'start' )
	1536	CALL eqn_state_seawater
	1537	CALL cpu_log( log_point(38), 'eqns-seawater', 'stop' )
	1538
	1539	ENDIF
	1540
	1541	!
[1960]	1542	!-- If required, compute prognostic equation for total water content
	1543	IF ( humidity ) THEN
[1875]	1544
[1960]	1545	CALL cpu_log( log_point(29), 'q-equation', 'start' )
[1875]	1546
	1547	!
	1548	!-- Scalar/q-tendency terms with communication
	1549	sbt = tsc(2)
	1550	IF ( scalar_advec == 'bc-scheme' ) THEN
	1551
	1552	IF ( timestep_scheme(1:5) /= 'runge' ) THEN
	1553	!
	1554	!-- Bott-Chlond scheme always uses Euler time step. Thus:
	1555	sbt = 1.0_wp
	1556	ENDIF
	1557	tend = 0.0_wp
	1558	CALL advec_s_bc( q, 'q' )
	1559
	1560	ENDIF
	1561
	1562	!
	1563	!-- Scalar/q-tendency terms with no communication
	1564	IF ( scalar_advec /= 'bc-scheme' ) THEN
	1565	tend = 0.0_wp
	1566	IF ( timestep_scheme(1:5) == 'runge' ) THEN
	1567	IF ( ws_scheme_sca ) THEN
	1568	CALL advec_s_ws( q, 'q' )
	1569	ELSE
	1570	CALL advec_s_pw( q )
	1571	ENDIF
	1572	ELSE
	1573	CALL advec_s_up( q )
	1574	ENDIF
	1575	ENDIF
	1576
	1577	CALL diffusion_s( q, qsws, qswst, wall_qflux )
	1578
	1579	!
[1960]	1580	!-- Sink or source of humidity due to canopy elements
[1875]	1581	IF ( plant_canopy ) CALL pcm_tendency( 5 )
	1582
	1583	!
	1584	!-- Large scale advection
	1585	IF ( large_scale_forcing ) THEN
	1586	CALL ls_advec( simulated_time, 'q' )
	1587	ENDIF
	1588
	1589	!
	1590	!-- Nudging
	1591	IF ( nudging ) CALL nudge( simulated_time, 'q' )
	1592
	1593	!
	1594	!-- If required compute influence of large-scale subsidence/ascent
	1595	IF ( large_scale_subsidence .AND. &
	1596	.NOT. use_subsidence_tendencies ) THEN
	1597	CALL subsidence( tend, q, q_init, 3 )
	1598	ENDIF
	1599
	1600	CALL user_actions( 'q-tendency' )
	1601
	1602	!
[1960]	1603	!-- Prognostic equation for total water content
[1875]	1604	DO i = nxl, nxr
	1605	DO j = nys, nyn
	1606	DO k = nzb_s_inner(j,i)+1, nzt
	1607	q_p(k,j,i) = q(k,j,i) + dt_3d * ( sbt * tend(k,j,i) + &
	1608	tsc(3) * tq_m(k,j,i) ) &
	1609	- tsc(5) * rdf_sc(k) * &
	1610	( q(k,j,i) - q_init(k) )
	1611	IF ( q_p(k,j,i) < 0.0_wp ) q_p(k,j,i) = 0.1_wp * q(k,j,i)
	1612	ENDDO
	1613	ENDDO
	1614	ENDDO
	1615
	1616	!
	1617	!-- Calculate tendencies for the next Runge-Kutta step
	1618	IF ( timestep_scheme(1:5) == 'runge' ) THEN
	1619	IF ( intermediate_timestep_count == 1 ) THEN
	1620	DO i = nxl, nxr
	1621	DO j = nys, nyn
	1622	DO k = nzb_s_inner(j,i)+1, nzt
	1623	tq_m(k,j,i) = tend(k,j,i)
	1624	ENDDO
	1625	ENDDO
	1626	ENDDO
	1627	ELSEIF ( intermediate_timestep_count < &
	1628	intermediate_timestep_count_max ) THEN
	1629	DO i = nxl, nxr
	1630	DO j = nys, nyn
	1631	DO k = nzb_s_inner(j,i)+1, nzt
	1632	tq_m(k,j,i) = -9.5625_wp * tend(k,j,i) + 5.3125_wp * tq_m(k,j,i)
	1633	ENDDO
	1634	ENDDO
	1635	ENDDO
	1636	ENDIF
	1637	ENDIF
	1638
[1960]	1639	CALL cpu_log( log_point(29), 'q-equation', 'stop' )
[1875]	1640
	1641	!
	1642	!-- If required, calculate prognostic equations for rain water content
	1643	!-- and rain drop concentration
	1644	IF ( cloud_physics .AND. microphysics_seifert ) THEN
	1645
	1646	CALL cpu_log( log_point(52), 'qr-equation', 'start' )
	1647
	1648	!
	1649	!-- Calculate prognostic equation for rain water content
	1650	sbt = tsc(2)
	1651	IF ( scalar_advec == 'bc-scheme' ) THEN
	1652
	1653	IF ( timestep_scheme(1:5) /= 'runge' ) THEN
	1654	!
	1655	!-- Bott-Chlond scheme always uses Euler time step. Thus:
	1656	sbt = 1.0_wp
	1657	ENDIF
	1658	tend = 0.0_wp
	1659	CALL advec_s_bc( qr, 'qr' )
	1660
	1661	ENDIF
	1662
	1663	!
	1664	!-- qr-tendency terms with no communication
	1665	IF ( scalar_advec /= 'bc-scheme' ) THEN
	1666	tend = 0.0_wp
	1667	IF ( timestep_scheme(1:5) == 'runge' ) THEN
	1668	IF ( ws_scheme_sca ) THEN
	1669	CALL advec_s_ws( qr, 'qr' )
	1670	ELSE
	1671	CALL advec_s_pw( qr )
	1672	ENDIF
	1673	ELSE
	1674	CALL advec_s_up( qr )
	1675	ENDIF
	1676	ENDIF
	1677
	1678	CALL diffusion_s( qr, qrsws, qrswst, wall_qrflux )
	1679
	1680	CALL user_actions( 'qr-tendency' )
	1681
	1682	!
	1683	!-- Prognostic equation for rain water content
	1684	DO i = nxl, nxr
	1685	DO j = nys, nyn
	1686	DO k = nzb_s_inner(j,i)+1, nzt
	1687	qr_p(k,j,i) = qr(k,j,i) + dt_3d * ( sbt * tend(k,j,i) + &
	1688	tsc(3) * tqr_m(k,j,i) ) &
	1689	- tsc(5) * rdf_sc(k) * qr(k,j,i)
	1690	IF ( qr_p(k,j,i) < 0.0_wp ) qr_p(k,j,i) = 0.0_wp
	1691	ENDDO
	1692	ENDDO
	1693	ENDDO
	1694
	1695	!
	1696	!-- Calculate tendencies for the next Runge-Kutta step
	1697	IF ( timestep_scheme(1:5) == 'runge' ) THEN
	1698	IF ( intermediate_timestep_count == 1 ) THEN
	1699	DO i = nxl, nxr
	1700	DO j = nys, nyn
	1701	DO k = nzb_s_inner(j,i)+1, nzt
	1702	tqr_m(k,j,i) = tend(k,j,i)
	1703	ENDDO
	1704	ENDDO
	1705	ENDDO
	1706	ELSEIF ( intermediate_timestep_count < &
	1707	intermediate_timestep_count_max ) THEN
	1708	DO i = nxl, nxr
	1709	DO j = nys, nyn
	1710	DO k = nzb_s_inner(j,i)+1, nzt
	1711	tqr_m(k,j,i) = -9.5625_wp * tend(k,j,i) + 5.3125_wp * &
	1712	tqr_m(k,j,i)
	1713	ENDDO
	1714	ENDDO
	1715	ENDDO
	1716	ENDIF
	1717	ENDIF
	1718
	1719	CALL cpu_log( log_point(52), 'qr-equation', 'stop' )
	1720	CALL cpu_log( log_point(53), 'nr-equation', 'start' )
	1721
	1722	!
	1723	!-- Calculate prognostic equation for rain drop concentration
	1724	sbt = tsc(2)
	1725	IF ( scalar_advec == 'bc-scheme' ) THEN
	1726
	1727	IF ( timestep_scheme(1:5) /= 'runge' ) THEN
	1728	!
	1729	!-- Bott-Chlond scheme always uses Euler time step. Thus:
	1730	sbt = 1.0_wp
	1731	ENDIF
	1732	tend = 0.0_wp
	1733	CALL advec_s_bc( nr, 'nr' )
	1734
	1735	ENDIF
	1736
	1737	!
	1738	!-- nr-tendency terms with no communication
	1739	IF ( scalar_advec /= 'bc-scheme' ) THEN
	1740	tend = 0.0_wp
	1741	IF ( timestep_scheme(1:5) == 'runge' ) THEN
	1742	IF ( ws_scheme_sca ) THEN
	1743	CALL advec_s_ws( nr, 'nr' )
	1744	ELSE
	1745	CALL advec_s_pw( nr )
	1746	ENDIF
	1747	ELSE
	1748	CALL advec_s_up( nr )
	1749	ENDIF
	1750	ENDIF
	1751
	1752	CALL diffusion_s( nr, nrsws, nrswst, wall_nrflux )
	1753
	1754	!
	1755	!-- Prognostic equation for rain drop concentration
	1756	DO i = nxl, nxr
	1757	DO j = nys, nyn
	1758	DO k = nzb_s_inner(j,i)+1, nzt
	1759	nr_p(k,j,i) = nr(k,j,i) + dt_3d * ( sbt * tend(k,j,i) + &
	1760	tsc(3) * tnr_m(k,j,i) ) &
	1761	- tsc(5) * rdf_sc(k) * nr(k,j,i)
	1762	IF ( nr_p(k,j,i) < 0.0_wp ) nr_p(k,j,i) = 0.0_wp
	1763	ENDDO
	1764	ENDDO
	1765	ENDDO
	1766
	1767	!
	1768	!-- Calculate tendencies for the next Runge-Kutta step
	1769	IF ( timestep_scheme(1:5) == 'runge' ) THEN
	1770	IF ( intermediate_timestep_count == 1 ) THEN
	1771	DO i = nxl, nxr
	1772	DO j = nys, nyn
	1773	DO k = nzb_s_inner(j,i)+1, nzt
	1774	tnr_m(k,j,i) = tend(k,j,i)
	1775	ENDDO
	1776	ENDDO
	1777	ENDDO
	1778	ELSEIF ( intermediate_timestep_count < &
	1779	intermediate_timestep_count_max ) THEN
	1780	DO i = nxl, nxr
	1781	DO j = nys, nyn
	1782	DO k = nzb_s_inner(j,i)+1, nzt
	1783	tnr_m(k,j,i) = -9.5625_wp * tend(k,j,i) + 5.3125_wp * &
	1784	tnr_m(k,j,i)
	1785	ENDDO
	1786	ENDDO
	1787	ENDDO
	1788	ENDIF
	1789	ENDIF
	1790
	1791	CALL cpu_log( log_point(53), 'nr-equation', 'stop' )
	1792
	1793	ENDIF
	1794
	1795	ENDIF
[1960]	1796	!
	1797	!-- If required, compute prognostic equation for scalar
	1798	IF ( passive_scalar ) THEN
[1875]	1799
[1960]	1800	CALL cpu_log( log_point(66), 's-equation', 'start' )
	1801
[1875]	1802	!
[1960]	1803	!-- Scalar/q-tendency terms with communication
	1804	sbt = tsc(2)
	1805	IF ( scalar_advec == 'bc-scheme' ) THEN
	1806
	1807	IF ( timestep_scheme(1:5) /= 'runge' ) THEN
	1808	!
	1809	!-- Bott-Chlond scheme always uses Euler time step. Thus:
	1810	sbt = 1.0_wp
	1811	ENDIF
	1812	tend = 0.0_wp
	1813	CALL advec_s_bc( s, 's' )
	1814
	1815	ENDIF
	1816
	1817	!
	1818	!-- Scalar/q-tendency terms with no communication
	1819	IF ( scalar_advec /= 'bc-scheme' ) THEN
	1820	tend = 0.0_wp
	1821	IF ( timestep_scheme(1:5) == 'runge' ) THEN
	1822	IF ( ws_scheme_sca ) THEN
	1823	CALL advec_s_ws( s, 's' )
	1824	ELSE
	1825	CALL advec_s_pw( s )
	1826	ENDIF
	1827	ELSE
	1828	CALL advec_s_up( s )
	1829	ENDIF
	1830	ENDIF
	1831
	1832	CALL diffusion_s( s, ssws, sswst, wall_sflux )
	1833
	1834	!
	1835	!-- Sink or source of humidity due to canopy elements
	1836	IF ( plant_canopy ) CALL pcm_tendency( 7 )
	1837
	1838	!
	1839	!-- Large scale advection. Not implemented for scalars so far.
	1840	! IF ( large_scale_forcing ) THEN
	1841	! CALL ls_advec( simulated_time, 'q' )
	1842	! ENDIF
	1843
	1844	!
	1845	!-- Nudging. Not implemented for scalars so far.
	1846	! IF ( nudging ) CALL nudge( simulated_time, 'q' )
	1847
	1848	!
	1849	!-- If required compute influence of large-scale subsidence/ascent.
	1850	!-- Not implemented for scalars so far.
	1851	IF ( large_scale_subsidence .AND. &
	1852	.NOT. use_subsidence_tendencies .AND. &
	1853	.NOT. large_scale_forcing ) THEN
	1854	CALL subsidence( tend, s, s_init, 3 )
	1855	ENDIF
	1856
	1857	CALL user_actions( 's-tendency' )
	1858
	1859	!
	1860	!-- Prognostic equation for total water content
	1861	DO i = nxl, nxr
	1862	DO j = nys, nyn
	1863	DO k = nzb_s_inner(j,i)+1, nzt
	1864	s_p(k,j,i) = s(k,j,i) + dt_3d * ( sbt * tend(k,j,i) + &
	1865	tsc(3) * ts_m(k,j,i) ) &
	1866	- tsc(5) * rdf_sc(k) * &
	1867	( s(k,j,i) - s_init(k) )
	1868	IF ( s_p(k,j,i) < 0.0_wp ) s_p(k,j,i) = 0.1_wp * s(k,j,i)
	1869	ENDDO
	1870	ENDDO
	1871	ENDDO
	1872
	1873	!
	1874	!-- Calculate tendencies for the next Runge-Kutta step
	1875	IF ( timestep_scheme(1:5) == 'runge' ) THEN
	1876	IF ( intermediate_timestep_count == 1 ) THEN
	1877	DO i = nxl, nxr
	1878	DO j = nys, nyn
	1879	DO k = nzb_s_inner(j,i)+1, nzt
	1880	ts_m(k,j,i) = tend(k,j,i)
	1881	ENDDO
	1882	ENDDO
	1883	ENDDO
	1884	ELSEIF ( intermediate_timestep_count < &
	1885	intermediate_timestep_count_max ) THEN
	1886	DO i = nxl, nxr
	1887	DO j = nys, nyn
	1888	DO k = nzb_s_inner(j,i)+1, nzt
	1889	ts_m(k,j,i) = -9.5625_wp * tend(k,j,i) + 5.3125_wp * ts_m(k,j,i)
	1890	ENDDO
	1891	ENDDO
	1892	ENDDO
	1893	ENDIF
	1894	ENDIF
	1895
	1896	CALL cpu_log( log_point(66), 's-equation', 'stop' )
	1897
	1898	ENDIF
	1899	!
[1875]	1900	!-- If required, compute prognostic equation for turbulent kinetic
	1901	!-- energy (TKE)
	1902	IF ( .NOT. constant_diffusion ) THEN
	1903
	1904	CALL cpu_log( log_point(16), 'tke-equation', 'start' )
	1905
	1906	sbt = tsc(2)
	1907	IF ( .NOT. use_upstream_for_tke ) THEN
	1908	IF ( scalar_advec == 'bc-scheme' ) THEN
	1909
	1910	IF ( timestep_scheme(1:5) /= 'runge' ) THEN
	1911	!
	1912	!-- Bott-Chlond scheme always uses Euler time step. Thus:
	1913	sbt = 1.0_wp
	1914	ENDIF
	1915	tend = 0.0_wp
	1916	CALL advec_s_bc( e, 'e' )
	1917
	1918	ENDIF
	1919	ENDIF
	1920
	1921	!
	1922	!-- TKE-tendency terms with no communication
	1923	IF ( scalar_advec /= 'bc-scheme' .OR. use_upstream_for_tke ) THEN
	1924	IF ( use_upstream_for_tke ) THEN
	1925	tend = 0.0_wp
	1926	CALL advec_s_up( e )
	1927	ELSE
	1928	tend = 0.0_wp
	1929	IF ( timestep_scheme(1:5) == 'runge' ) THEN
	1930	IF ( ws_scheme_sca ) THEN
	1931	CALL advec_s_ws( e, 'e' )
	1932	ELSE
	1933	CALL advec_s_pw( e )
	1934	ENDIF
	1935	ELSE
	1936	CALL advec_s_up( e )
	1937	ENDIF
	1938	ENDIF
	1939	ENDIF
	1940
	1941	IF ( .NOT. humidity ) THEN
	1942	IF ( ocean ) THEN
	1943	CALL diffusion_e( prho, prho_reference )
	1944	ELSE
	1945	CALL diffusion_e( pt, pt_reference )
	1946	ENDIF
	1947	ELSE
	1948	CALL diffusion_e( vpt, pt_reference )
	1949	ENDIF
	1950
	1951	CALL production_e
	1952
	1953	!
	1954	!-- Additional sink term for flows through plant canopies
	1955	IF ( plant_canopy ) CALL pcm_tendency( 6 )
	1956	CALL user_actions( 'e-tendency' )
	1957
	1958	!
	1959	!-- Prognostic equation for TKE.
	1960	!-- Eliminate negative TKE values, which can occur due to numerical
	1961	!-- reasons in the course of the integration. In such cases the old TKE
	1962	!-- value is reduced by 90%.
	1963	DO i = nxl, nxr
	1964	DO j = nys, nyn
	1965	DO k = nzb_s_inner(j,i)+1, nzt
	1966	e_p(k,j,i) = e(k,j,i) + dt_3d * ( sbt * tend(k,j,i) + &
	1967	tsc(3) * te_m(k,j,i) )
	1968	IF ( e_p(k,j,i) < 0.0_wp ) e_p(k,j,i) = 0.1_wp * e(k,j,i)
	1969	ENDDO
	1970	ENDDO
	1971	ENDDO
	1972
	1973	!
	1974	!-- Calculate tendencies for the next Runge-Kutta step
	1975	IF ( timestep_scheme(1:5) == 'runge' ) THEN
	1976	IF ( intermediate_timestep_count == 1 ) THEN
	1977	DO i = nxl, nxr
	1978	DO j = nys, nyn
	1979	DO k = nzb_s_inner(j,i)+1, nzt
	1980	te_m(k,j,i) = tend(k,j,i)
	1981	ENDDO
	1982	ENDDO
	1983	ENDDO
	1984	ELSEIF ( intermediate_timestep_count < &
	1985	intermediate_timestep_count_max ) THEN
	1986	DO i = nxl, nxr
	1987	DO j = nys, nyn
	1988	DO k = nzb_s_inner(j,i)+1, nzt
	1989	te_m(k,j,i) = -9.5625_wp * tend(k,j,i) + 5.3125_wp * te_m(k,j,i)
	1990	ENDDO
	1991	ENDDO
	1992	ENDDO
	1993	ENDIF
	1994	ENDIF
	1995
	1996	CALL cpu_log( log_point(16), 'tke-equation', 'stop' )
	1997
	1998	ENDIF
	1999
	2000	END SUBROUTINE prognostic_equations_vector
	2001
	2002
	2003	!------------------------------------------------------------------------------!
	2004	! Description:
	2005	! ------------
	2006	!> Version for accelerator boards
	2007	!------------------------------------------------------------------------------!
	2008
	2009	SUBROUTINE prognostic_equations_acc
	2010
	2011
	2012	IMPLICIT NONE
	2013
	2014	INTEGER(iwp) :: i !<
	2015	INTEGER(iwp) :: j !<
	2016	INTEGER(iwp) :: k !<
	2017	INTEGER(iwp) :: runge_step !<
	2018
	2019	REAL(wp) :: sbt !<
	2020
	2021	!
	2022	!-- Set switch for intermediate Runge-Kutta step
	2023	runge_step = 0
	2024	IF ( timestep_scheme(1:5) == 'runge' ) THEN
	2025	IF ( intermediate_timestep_count == 1 ) THEN
	2026	runge_step = 1
	2027	ELSEIF ( intermediate_timestep_count < &
	2028	intermediate_timestep_count_max ) THEN
	2029	runge_step = 2
	2030	ENDIF
	2031	ENDIF
	2032
	2033	!
	2034	!-- If required, calculate cloud microphysical impacts (two-moment scheme)
	2035	IF ( cloud_physics .AND. .NOT. microphysics_sat_adjust .AND. &
	2036	( intermediate_timestep_count == 1 .OR. &
	2037	call_microphysics_at_all_substeps ) &
	2038	) THEN
	2039	CALL cpu_log( log_point(51), 'microphysics', 'start' )
	2040	CALL microphysics_control
	2041	CALL cpu_log( log_point(51), 'microphysics', 'stop' )
	2042	ENDIF
	2043
	2044	!
	2045	!-- u-velocity component
	2046	!++ Statistics still not completely ported to accelerators
	2047	!$acc update device( hom, ref_state )
	2048	CALL cpu_log( log_point(5), 'u-equation', 'start' )
	2049
	2050	IF ( timestep_scheme(1:5) == 'runge' ) THEN
	2051	IF ( ws_scheme_mom ) THEN
	2052	CALL advec_u_ws_acc
	2053	ELSE
	2054	tend = 0.0_wp ! to be removed later??
	2055	CALL advec_u_pw
	2056	ENDIF
	2057	ELSE
	2058	CALL advec_u_up
	2059	ENDIF
	2060	CALL diffusion_u_acc
	2061	CALL coriolis_acc( 1 )
	2062	IF ( sloping_surface .AND. .NOT. neutral ) THEN
	2063	CALL buoyancy( pt, 1 )
	2064	ENDIF
	2065
	2066	!
	2067	!-- Drag by plant canopy
	2068	IF ( plant_canopy ) CALL pcm_tendency( 1 )
	2069
	2070	!
	2071	!-- External pressure gradient
	2072	IF ( dp_external ) THEN
	2073	DO i = i_left, i_right
	2074	DO j = j_south, j_north
	2075	DO k = dp_level_ind_b+1, nzt
	2076	tend(k,j,i) = tend(k,j,i) - dpdxy(1) * dp_smooth_factor(k)
	2077	ENDDO
	2078	ENDDO
	2079	ENDDO
	2080	ENDIF
	2081
	2082	!
	2083	!-- Nudging
	2084	IF ( nudging ) CALL nudge( simulated_time, 'u' )
	2085
[1914]	2086	!
	2087	!-- Forces by wind turbines
	2088	IF ( wind_turbine ) CALL wtm_tendencies( 1 )
	2089
[1875]	2090	CALL user_actions( 'u-tendency' )
	2091
	2092	!
	2093	!-- Prognostic equation for u-velocity component
	2094	!$acc kernels present( nzb_u_inner, rdf, tend, tu_m, u, u_init, u_p )
	2095	!$acc loop independent
	2096	DO i = i_left, i_right
	2097	!$acc loop independent
	2098	DO j = j_south, j_north
	2099	!$acc loop independent
	2100	DO k = 1, nzt
	2101	IF ( k > nzb_u_inner(j,i) ) THEN
	2102	u_p(k,j,i) = u(k,j,i) + dt_3d * ( tsc(2) * tend(k,j,i) + &
	2103	tsc(3) * tu_m(k,j,i) ) &
	2104	- tsc(5) * rdf(k) * ( u(k,j,i) - u_init(k) )
	2105	!
	2106	!-- Tendencies for the next Runge-Kutta step
	2107	IF ( runge_step == 1 ) THEN
	2108	tu_m(k,j,i) = tend(k,j,i)
	2109	ELSEIF ( runge_step == 2 ) THEN
	2110	tu_m(k,j,i) = -9.5625_wp * tend(k,j,i) + 5.3125_wp * tu_m(k,j,i)
	2111	ENDIF
	2112	ENDIF
	2113	ENDDO
	2114	ENDDO
	2115	ENDDO
	2116	!$acc end kernels
	2117
	2118	CALL cpu_log( log_point(5), 'u-equation', 'stop' )
	2119
	2120	!
	2121	!-- v-velocity component
	2122	CALL cpu_log( log_point(6), 'v-equation', 'start' )
	2123
	2124	IF ( timestep_scheme(1:5) == 'runge' ) THEN
	2125	IF ( ws_scheme_mom ) THEN
	2126	CALL advec_v_ws_acc
	2127	ELSE
	2128	tend = 0.0_wp ! to be removed later??
	2129	CALL advec_v_pw
	2130	END IF
	2131	ELSE
	2132	CALL advec_v_up
	2133	ENDIF
	2134	CALL diffusion_v_acc
	2135	CALL coriolis_acc( 2 )
	2136
	2137	!
	2138	!-- Drag by plant canopy
	2139	IF ( plant_canopy ) CALL pcm_tendency( 2 )
	2140
	2141	!
	2142	!-- External pressure gradient
	2143	IF ( dp_external ) THEN
	2144	DO i = i_left, i_right
	2145	DO j = j_south, j_north
	2146	DO k = dp_level_ind_b+1, nzt
	2147	tend(k,j,i) = tend(k,j,i) - dpdxy(2) * dp_smooth_factor(k)
	2148	ENDDO
	2149	ENDDO
	2150	ENDDO
	2151	ENDIF
	2152
	2153	!
	2154	!-- Nudging
	2155	IF ( nudging ) CALL nudge( simulated_time, 'v' )
	2156
[1914]	2157	!
	2158	!-- Forces by wind turbines
	2159	IF ( wind_turbine ) CALL wtm_tendencies( 2 )
	2160
[1875]	2161	CALL user_actions( 'v-tendency' )
	2162
	2163	!
	2164	!-- Prognostic equation for v-velocity component
	2165	!$acc kernels present( nzb_v_inner, rdf, tend, tv_m, v, v_init, v_p )
	2166	!$acc loop independent
	2167	DO i = i_left, i_right
	2168	!$acc loop independent
	2169	DO j = j_south, j_north
	2170	!$acc loop independent
	2171	DO k = 1, nzt
	2172	IF ( k > nzb_v_inner(j,i) ) THEN
	2173	v_p(k,j,i) = v(k,j,i) + dt_3d * ( tsc(2) * tend(k,j,i) + &
	2174	tsc(3) * tv_m(k,j,i) ) &
	2175	- tsc(5) * rdf(k) * ( v(k,j,i) - v_init(k) )
	2176	!
	2177	!-- Tendencies for the next Runge-Kutta step
	2178	IF ( runge_step == 1 ) THEN
	2179	tv_m(k,j,i) = tend(k,j,i)
	2180	ELSEIF ( runge_step == 2 ) THEN
	2181	tv_m(k,j,i) = -9.5625_wp * tend(k,j,i) + 5.3125_wp * tv_m(k,j,i)
	2182	ENDIF
	2183	ENDIF
	2184	ENDDO
	2185	ENDDO
	2186	ENDDO
	2187	!$acc end kernels
	2188
	2189	CALL cpu_log( log_point(6), 'v-equation', 'stop' )
	2190
	2191	!
	2192	!-- w-velocity component
	2193	CALL cpu_log( log_point(7), 'w-equation', 'start' )
	2194
	2195	IF ( timestep_scheme(1:5) == 'runge' ) THEN
	2196	IF ( ws_scheme_mom ) THEN
	2197	CALL advec_w_ws_acc
	2198	ELSE
	2199	tend = 0.0_wp ! to be removed later??
	2200	CALL advec_w_pw
	2201	ENDIF
	2202	ELSE
	2203	CALL advec_w_up
	2204	ENDIF
	2205	CALL diffusion_w_acc
	2206	CALL coriolis_acc( 3 )
	2207
	2208	IF ( .NOT. neutral ) THEN
	2209	IF ( ocean ) THEN
[2031]	2210	CALL buoyancy( rho_ocean, 3 )
[1875]	2211	ELSE
	2212	IF ( .NOT. humidity ) THEN
	2213	CALL buoyancy_acc( pt, 3 )
	2214	ELSE
	2215	CALL buoyancy( vpt, 3 )
	2216	ENDIF
	2217	ENDIF
	2218	ENDIF
	2219
	2220	!
	2221	!-- Drag by plant canopy
	2222	IF ( plant_canopy ) CALL pcm_tendency( 3 )
	2223
[1914]	2224	!
	2225	!-- Forces by wind turbines
	2226	IF ( wind_turbine ) CALL wtm_tendencies( 3 )
	2227
[1875]	2228	CALL user_actions( 'w-tendency' )
	2229
	2230	!
	2231	!-- Prognostic equation for w-velocity component
	2232	!$acc kernels present( nzb_w_inner, rdf, tend, tw_m, w, w_p )
	2233	!$acc loop independent
	2234	DO i = i_left, i_right
	2235	!$acc loop independent
	2236	DO j = j_south, j_north
	2237	!$acc loop independent
	2238	DO k = 1, nzt-1
	2239	IF ( k > nzb_w_inner(j,i) ) THEN
	2240	w_p(k,j,i) = w(k,j,i) + dt_3d * ( tsc(2) * tend(k,j,i) + &
	2241	tsc(3) * tw_m(k,j,i) ) &
	2242	- tsc(5) * rdf(k) * w(k,j,i)
	2243	!
	2244	!-- Tendencies for the next Runge-Kutta step
	2245	IF ( runge_step == 1 ) THEN
	2246	tw_m(k,j,i) = tend(k,j,i)
	2247	ELSEIF ( runge_step == 2 ) THEN
	2248	tw_m(k,j,i) = -9.5625_wp * tend(k,j,i) + 5.3125_wp * tw_m(k,j,i)
	2249	ENDIF
	2250	ENDIF
	2251	ENDDO
	2252	ENDDO
	2253	ENDDO
	2254	!$acc end kernels
	2255
	2256	CALL cpu_log( log_point(7), 'w-equation', 'stop' )
	2257
	2258
	2259	!
	2260	!-- If required, compute prognostic equation for potential temperature
	2261	IF ( .NOT. neutral ) THEN
	2262
	2263	CALL cpu_log( log_point(13), 'pt-equation', 'start' )
	2264
	2265	!
	2266	!-- pt-tendency terms with communication
	2267	sbt = tsc(2)
	2268	IF ( scalar_advec == 'bc-scheme' ) THEN
	2269
	2270	IF ( timestep_scheme(1:5) /= 'runge' ) THEN
	2271	!
	2272	!-- Bott-Chlond scheme always uses Euler time step. Thus:
	2273	sbt = 1.0_wp
	2274	ENDIF
	2275	tend = 0.0_wp
	2276	CALL advec_s_bc( pt, 'pt' )
	2277
	2278	ENDIF
	2279
	2280	!
	2281	!-- pt-tendency terms with no communication
	2282	IF ( scalar_advec /= 'bc-scheme' ) THEN
	2283	tend = 0.0_wp
	2284	IF ( timestep_scheme(1:5) == 'runge' ) THEN
	2285	IF ( ws_scheme_sca ) THEN
	2286	CALL advec_s_ws_acc( pt, 'pt' )
	2287	ELSE
	2288	tend = 0.0_wp ! to be removed later??
	2289	CALL advec_s_pw( pt )
	2290	ENDIF
	2291	ELSE
	2292	CALL advec_s_up( pt )
	2293	ENDIF
	2294	ENDIF
	2295
	2296	CALL diffusion_s_acc( pt, shf, tswst, wall_heatflux )
	2297
	2298	!
[2007]	2299	!-- Tendency pt from wall heat flux from urban surface
	2300	IF ( urban_surface ) THEN
	2301	CALL usm_wall_heat_flux
	2302	ENDIF
	2303
	2304	!
[1875]	2305	!-- If required compute heating/cooling due to long wave radiation processes
	2306	IF ( cloud_top_radiation ) THEN
	2307	CALL calc_radiation
	2308	ENDIF
	2309
	2310	!
	2311	!-- Consideration of heat sources within the plant canopy
	2312	IF ( plant_canopy .AND. ( cthf /= 0.0_wp ) ) THEN
	2313	CALL pcm_tendency( 4 )
	2314	ENDIF
	2315
	2316	!
	2317	!-- Large scale advection
	2318	IF ( large_scale_forcing ) THEN
	2319	CALL ls_advec( simulated_time, 'pt' )
	2320	ENDIF
	2321
	2322	!
	2323	!-- Nudging
	2324	IF ( nudging ) CALL nudge( simulated_time, 'pt' )
	2325
	2326	!
	2327	!-- If required compute influence of large-scale subsidence/ascent
	2328	IF ( large_scale_subsidence .AND. &
	2329	.NOT. use_subsidence_tendencies ) THEN
	2330	CALL subsidence( tend, pt, pt_init, 2 )
	2331	ENDIF
	2332
[1976]	2333	IF ( radiation .AND. &
[1875]	2334	simulated_time > skip_time_do_radiation ) THEN
	2335	CALL radiation_tendency ( tend )
	2336	ENDIF
	2337
	2338	CALL user_actions( 'pt-tendency' )
	2339
	2340	!
	2341	!-- Prognostic equation for potential temperature
	2342	!$acc kernels present( nzb_s_inner, rdf_sc, ptdf_x, ptdf_y, pt_init ) &
	2343	!$acc present( tend, tpt_m, pt, pt_p )
	2344	!$acc loop independent
	2345	DO i = i_left, i_right
	2346	!$acc loop independent
	2347	DO j = j_south, j_north
	2348	!$acc loop independent
	2349	DO k = 1, nzt
	2350	IF ( k > nzb_s_inner(j,i) ) THEN
	2351	pt_p(k,j,i) = pt(k,j,i) + dt_3d * ( sbt * tend(k,j,i) + &
	2352	tsc(3) * tpt_m(k,j,i) ) &
	2353	- tsc(5) * ( pt(k,j,i) - pt_init(k) ) *&
	2354	( rdf_sc(k) + ptdf_x(i) + ptdf_y(j) )
	2355	!
	2356	!-- Tendencies for the next Runge-Kutta step
	2357	IF ( runge_step == 1 ) THEN
	2358	tpt_m(k,j,i) = tend(k,j,i)
	2359	ELSEIF ( runge_step == 2 ) THEN
	2360	tpt_m(k,j,i) = -9.5625_wp * tend(k,j,i) + 5.3125_wp * tpt_m(k,j,i)
	2361	ENDIF
	2362	ENDIF
	2363	ENDDO
	2364	ENDDO
	2365	ENDDO
	2366	!$acc end kernels
	2367
	2368	CALL cpu_log( log_point(13), 'pt-equation', 'stop' )
	2369
	2370	ENDIF
	2371
	2372	!
	2373	!-- If required, compute prognostic equation for salinity
	2374	IF ( ocean ) THEN
	2375
	2376	CALL cpu_log( log_point(37), 'sa-equation', 'start' )
	2377
	2378	!
	2379	!-- sa-tendency terms with communication
	2380	sbt = tsc(2)
	2381	IF ( scalar_advec == 'bc-scheme' ) THEN
	2382
	2383	IF ( timestep_scheme(1:5) /= 'runge' ) THEN
	2384	!
	2385	!-- Bott-Chlond scheme always uses Euler time step. Thus:
	2386	sbt = 1.0_wp
	2387	ENDIF
	2388	tend = 0.0_wp
	2389	CALL advec_s_bc( sa, 'sa' )
	2390
	2391	ENDIF
	2392
	2393	!
	2394	!-- sa-tendency terms with no communication
	2395	IF ( scalar_advec /= 'bc-scheme' ) THEN
	2396	tend = 0.0_wp
	2397	IF ( timestep_scheme(1:5) == 'runge' ) THEN
	2398	IF ( ws_scheme_sca ) THEN
	2399	CALL advec_s_ws( sa, 'sa' )
	2400	ELSE
	2401	CALL advec_s_pw( sa )
	2402	ENDIF
	2403	ELSE
	2404	CALL advec_s_up( sa )
	2405	ENDIF
	2406	ENDIF
	2407
	2408	CALL diffusion_s( sa, saswsb, saswst, wall_salinityflux )
	2409
	2410	CALL user_actions( 'sa-tendency' )
	2411
	2412	!
	2413	!-- Prognostic equation for salinity
	2414	DO i = i_left, i_right
	2415	DO j = j_south, j_north
	2416	DO k = nzb_s_inner(j,i)+1, nzt
	2417	sa_p(k,j,i) = sa(k,j,i) + dt_3d * ( sbt * tend(k,j,i) + &
	2418	tsc(3) * tsa_m(k,j,i) ) &
	2419	- tsc(5) * rdf_sc(k) * &
	2420	( sa(k,j,i) - sa_init(k) )
	2421	IF ( sa_p(k,j,i) < 0.0_wp ) sa_p(k,j,i) = 0.1_wp * sa(k,j,i)
	2422	!
	2423	!-- Tendencies for the next Runge-Kutta step
	2424	IF ( runge_step == 1 ) THEN
	2425	tsa_m(k,j,i) = tend(k,j,i)
	2426	ELSEIF ( runge_step == 2 ) THEN
	2427	tsa_m(k,j,i) = -9.5625_wp * tend(k,j,i) + 5.3125_wp * tsa_m(k,j,i)
	2428	ENDIF
	2429	ENDDO
	2430	ENDDO
	2431	ENDDO
	2432
	2433	CALL cpu_log( log_point(37), 'sa-equation', 'stop' )
	2434
	2435	!
	2436	!-- Calculate density by the equation of state for seawater
	2437	CALL cpu_log( log_point(38), 'eqns-seawater', 'start' )
	2438	CALL eqn_state_seawater
	2439	CALL cpu_log( log_point(38), 'eqns-seawater', 'stop' )
	2440
	2441	ENDIF
	2442
	2443	!
[1960]	2444	!-- If required, compute prognostic equation for total water content
	2445	IF ( humidity ) THEN
[1875]	2446
[1960]	2447	CALL cpu_log( log_point(29), 'q-equation', 'start' )
[1875]	2448
	2449	!
	2450	!-- Scalar/q-tendency terms with communication
	2451	sbt = tsc(2)
	2452	IF ( scalar_advec == 'bc-scheme' ) THEN
	2453
	2454	IF ( timestep_scheme(1:5) /= 'runge' ) THEN
	2455	!
	2456	!-- Bott-Chlond scheme always uses Euler time step. Thus:
	2457	sbt = 1.0_wp
	2458	ENDIF
	2459	tend = 0.0_wp
	2460	CALL advec_s_bc( q, 'q' )
	2461
	2462	ENDIF
	2463
	2464	!
	2465	!-- Scalar/q-tendency terms with no communication
	2466	IF ( scalar_advec /= 'bc-scheme' ) THEN
	2467	tend = 0.0_wp
	2468	IF ( timestep_scheme(1:5) == 'runge' ) THEN
	2469	IF ( ws_scheme_sca ) THEN
	2470	CALL advec_s_ws( q, 'q' )
	2471	ELSE
	2472	CALL advec_s_pw( q )
	2473	ENDIF
	2474	ELSE
	2475	CALL advec_s_up( q )
	2476	ENDIF
	2477	ENDIF
	2478
	2479	CALL diffusion_s( q, qsws, qswst, wall_qflux )
	2480
	2481	!
	2482	!-- Sink or source of scalar concentration due to canopy elements
	2483	IF ( plant_canopy ) CALL pcm_tendency( 5 )
	2484
	2485	!
	2486	!-- Large scale advection
	2487	IF ( large_scale_forcing ) THEN
	2488	CALL ls_advec( simulated_time, 'q' )
	2489	ENDIF
	2490
	2491	!
	2492	!-- Nudging
	2493	IF ( nudging ) CALL nudge( simulated_time, 'q' )
	2494
	2495	!
	2496	!-- If required compute influence of large-scale subsidence/ascent
	2497	IF ( large_scale_subsidence .AND. &
	2498	.NOT. use_subsidence_tendencies ) THEN
	2499	CALL subsidence( tend, q, q_init, 3 )
	2500	ENDIF
	2501
	2502	CALL user_actions( 'q-tendency' )
	2503
	2504	!
	2505	!-- Prognostic equation for total water content / scalar
	2506	DO i = i_left, i_right
	2507	DO j = j_south, j_north
	2508	DO k = nzb_s_inner(j,i)+1, nzt
	2509	q_p(k,j,i) = q(k,j,i) + dt_3d * ( sbt * tend(k,j,i) + &
	2510	tsc(3) * tq_m(k,j,i) ) &
	2511	- tsc(5) * rdf_sc(k) * &
	2512	( q(k,j,i) - q_init(k) )
	2513	IF ( q_p(k,j,i) < 0.0_wp ) q_p(k,j,i) = 0.1_wp * q(k,j,i)
	2514	!
	2515	!-- Tendencies for the next Runge-Kutta step
	2516	IF ( runge_step == 1 ) THEN
	2517	tq_m(k,j,i) = tend(k,j,i)
	2518	ELSEIF ( runge_step == 2 ) THEN
	2519	tq_m(k,j,i) = -9.5625_wp * tend(k,j,i) + 5.3125_wp * tq_m(k,j,i)
	2520	ENDIF
	2521	ENDDO
	2522	ENDDO
	2523	ENDDO
	2524
[1960]	2525	CALL cpu_log( log_point(29), 'q-equation', 'stop' )
[1875]	2526
	2527	!
	2528	!-- If required, calculate prognostic equations for rain water content
	2529	!-- and rain drop concentration
	2530	IF ( cloud_physics .AND. microphysics_seifert ) THEN
	2531
	2532	CALL cpu_log( log_point(52), 'qr-equation', 'start' )
	2533	!
	2534	!-- qr-tendency terms with communication
	2535	sbt = tsc(2)
	2536	IF ( scalar_advec == 'bc-scheme' ) THEN
	2537
	2538	IF ( timestep_scheme(1:5) /= 'runge' ) THEN
	2539	!
	2540	!-- Bott-Chlond scheme always uses Euler time step. Thus:
	2541	sbt = 1.0_wp
	2542	ENDIF
	2543	tend = 0.0_wp
	2544	CALL advec_s_bc( qr, 'qr' )
	2545
	2546	ENDIF
	2547
	2548	!
	2549	!-- qr-tendency terms with no communication
	2550	IF ( scalar_advec /= 'bc-scheme' ) THEN
	2551	tend = 0.0_wp
	2552	IF ( timestep_scheme(1:5) == 'runge' ) THEN
	2553	IF ( ws_scheme_sca ) THEN
	2554	CALL advec_s_ws( qr, 'qr' )
	2555	ELSE
	2556	CALL advec_s_pw( qr )
	2557	ENDIF
	2558	ELSE
	2559	CALL advec_s_up( qr )
	2560	ENDIF
	2561	ENDIF
	2562
	2563	CALL diffusion_s( qr, qrsws, qrswst, wall_qrflux )
	2564
	2565	!
	2566	!-- Prognostic equation for rain water content
	2567	DO i = i_left, i_right
	2568	DO j = j_south, j_north
	2569	DO k = nzb_s_inner(j,i)+1, nzt
	2570	qr_p(k,j,i) = qr(k,j,i) + dt_3d * ( sbt * tend(k,j,i) + &
	2571	tsc(3) * tqr_m(k,j,i) ) &
	2572	- tsc(5) * rdf_sc(k) * qr(k,j,i)
	2573	IF ( qr_p(k,j,i) < 0.0_wp ) qr_p(k,j,i) = 0.0_wp
	2574	!
	2575	!-- Tendencies for the next Runge-Kutta step
	2576	IF ( runge_step == 1 ) THEN
	2577	tqr_m(k,j,i) = tend(k,j,i)
	2578	ELSEIF ( runge_step == 2 ) THEN
	2579	tqr_m(k,j,i) = -9.5625_wp * tend(k,j,i) + 5.3125_wp * &
	2580	tqr_m(k,j,i)
	2581	ENDIF
	2582	ENDDO
	2583	ENDDO
	2584	ENDDO
	2585
	2586	CALL cpu_log( log_point(52), 'qr-equation', 'stop' )
	2587	CALL cpu_log( log_point(53), 'nr-equation', 'start' )
	2588
	2589	!
	2590	!-- nr-tendency terms with communication
	2591	sbt = tsc(2)
	2592	IF ( scalar_advec == 'bc-scheme' ) THEN
	2593
	2594	IF ( timestep_scheme(1:5) /= 'runge' ) THEN
	2595	!
	2596	!-- Bott-Chlond scheme always uses Euler time step. Thus:
	2597	sbt = 1.0_wp
	2598	ENDIF
	2599	tend = 0.0_wp
	2600	CALL advec_s_bc( nr, 'nr' )
	2601
	2602	ENDIF
	2603
	2604	!
	2605	!-- nr-tendency terms with no communication
	2606	IF ( scalar_advec /= 'bc-scheme' ) THEN
	2607	tend = 0.0_wp
	2608	IF ( timestep_scheme(1:5) == 'runge' ) THEN
	2609	IF ( ws_scheme_sca ) THEN
	2610	CALL advec_s_ws( nr, 'nr' )
	2611	ELSE
	2612	CALL advec_s_pw( nr )
	2613	ENDIF
	2614	ELSE
	2615	CALL advec_s_up( nr )
	2616	ENDIF
	2617	ENDIF
	2618
	2619	CALL diffusion_s( nr, nrsws, nrswst, wall_nrflux )
	2620
	2621	!
	2622	!-- Prognostic equation for rain drop concentration
	2623	DO i = i_left, i_right
	2624	DO j = j_south, j_north
	2625	DO k = nzb_s_inner(j,i)+1, nzt
	2626	nr_p(k,j,i) = nr(k,j,i) + dt_3d * ( sbt * tend(k,j,i) + &
	2627	tsc(3) * tnr_m(k,j,i) ) &
	2628	- tsc(5) * rdf_sc(k) * nr(k,j,i)
	2629	IF ( nr_p(k,j,i) < 0.0_wp ) nr_p(k,j,i) = 0.0_wp
	2630	!
	2631	!-- Tendencies for the next Runge-Kutta step
	2632	IF ( runge_step == 1 ) THEN
	2633	tnr_m(k,j,i) = tend(k,j,i)
	2634	ELSEIF ( runge_step == 2 ) THEN
	2635	tnr_m(k,j,i) = -9.5625_wp * tend(k,j,i) + 5.3125_wp * &
	2636	tnr_m(k,j,i)
	2637	ENDIF
	2638	ENDDO
	2639	ENDDO
	2640	ENDDO
	2641
	2642	CALL cpu_log( log_point(53), 'nr-equation', 'stop' )
	2643
	2644	ENDIF
	2645
	2646	ENDIF
	2647
	2648	!
[1960]	2649	!-- If required, compute prognostic equation for scalar
	2650	IF ( passive_scalar ) THEN
	2651
	2652	CALL cpu_log( log_point(66), 's-equation', 'start' )
	2653
	2654	!
	2655	!-- Scalar/q-tendency terms with communication
	2656	sbt = tsc(2)
	2657	IF ( scalar_advec == 'bc-scheme' ) THEN
	2658
	2659	IF ( timestep_scheme(1:5) /= 'runge' ) THEN
	2660	!
	2661	!-- Bott-Chlond scheme always uses Euler time step. Thus:
	2662	sbt = 1.0_wp
	2663	ENDIF
	2664	tend = 0.0_wp
	2665	CALL advec_s_bc( s, 's' )
	2666
	2667	ENDIF
	2668
	2669	!
	2670	!-- Scalar/q-tendency terms with no communication
	2671	IF ( scalar_advec /= 'bc-scheme' ) THEN
	2672	tend = 0.0_wp
	2673	IF ( timestep_scheme(1:5) == 'runge' ) THEN
	2674	IF ( ws_scheme_sca ) THEN
	2675	CALL advec_s_ws( s, 's' )
	2676	ELSE
	2677	CALL advec_s_pw( s )
	2678	ENDIF
	2679	ELSE
	2680	CALL advec_s_up( s )
	2681	ENDIF
	2682	ENDIF
	2683
	2684	CALL diffusion_s( s, ssws, sswst, wall_sflux )
	2685
	2686	!
	2687	!-- Sink or source of scalar concentration due to canopy elements
	2688	IF ( plant_canopy ) CALL pcm_tendency( 7 )
	2689
	2690	!
	2691	!-- Large scale advection. Not implemented so far.
	2692	! IF ( large_scale_forcing ) THEN
	2693	! CALL ls_advec( simulated_time, 's' )
	2694	! ENDIF
	2695
	2696	!
	2697	!-- Nudging. Not implemented so far.
	2698	! IF ( nudging ) CALL nudge( simulated_time, 's' )
	2699
	2700	!
	2701	!-- If required compute influence of large-scale subsidence/ascent.
	2702	!-- Not implemented so far.
	2703	IF ( large_scale_subsidence .AND. &
	2704	.NOT. use_subsidence_tendencies .AND. &
	2705	.NOT. large_scale_forcing ) THEN
	2706	CALL subsidence( tend, s, s_init, 3 )
	2707	ENDIF
	2708
	2709	CALL user_actions( 's-tendency' )
	2710
	2711	!
	2712	!-- Prognostic equation for total water content / scalar
	2713	DO i = i_left, i_right
	2714	DO j = j_south, j_north
	2715	DO k = nzb_s_inner(j,i)+1, nzt
	2716	s_p(k,j,i) = s(k,j,i) + dt_3d * ( sbt * tend(k,j,i) + &
	2717	tsc(3) * ts_m(k,j,i) ) &
	2718	- tsc(5) * rdf_sc(k) * &
	2719	( s(k,j,i) - s_init(k) )
	2720	IF ( s_p(k,j,i) < 0.0_wp ) s_p(k,j,i) = 0.1_wp * s(k,j,i)
	2721	!
	2722	!-- Tendencies for the next Runge-Kutta step
	2723	IF ( runge_step == 1 ) THEN
	2724	ts_m(k,j,i) = tend(k,j,i)
	2725	ELSEIF ( runge_step == 2 ) THEN
	2726	ts_m(k,j,i) = -9.5625_wp * tend(k,j,i) + 5.3125_wp * ts_m(k,j,i)
	2727	ENDIF
	2728	ENDDO
	2729	ENDDO
	2730	ENDDO
	2731
	2732	CALL cpu_log( log_point(66), 's-equation', 'stop' )
	2733
	2734	ENDIF
	2735	!
[1875]	2736	!-- If required, compute prognostic equation for turbulent kinetic
	2737	!-- energy (TKE)
	2738	IF ( .NOT. constant_diffusion ) THEN
	2739
	2740	CALL cpu_log( log_point(16), 'tke-equation', 'start' )
	2741
	2742	sbt = tsc(2)
	2743	IF ( .NOT. use_upstream_for_tke ) THEN
	2744	IF ( scalar_advec == 'bc-scheme' ) THEN
	2745
	2746	IF ( timestep_scheme(1:5) /= 'runge' ) THEN
	2747	!
	2748	!-- Bott-Chlond scheme always uses Euler time step. Thus:
	2749	sbt = 1.0_wp
	2750	ENDIF
	2751	tend = 0.0_wp
	2752	CALL advec_s_bc( e, 'e' )
	2753
	2754	ENDIF
	2755	ENDIF
	2756
	2757	!
	2758	!-- TKE-tendency terms with no communication
	2759	IF ( scalar_advec /= 'bc-scheme' .OR. use_upstream_for_tke ) THEN
	2760	IF ( use_upstream_for_tke ) THEN
	2761	tend = 0.0_wp
	2762	CALL advec_s_up( e )
	2763	ELSE
	2764	IF ( timestep_scheme(1:5) == 'runge' ) THEN
	2765	IF ( ws_scheme_sca ) THEN
	2766	CALL advec_s_ws_acc( e, 'e' )
	2767	ELSE
	2768	tend = 0.0_wp ! to be removed later??
	2769	CALL advec_s_pw( e )
	2770	ENDIF
	2771	ELSE
	2772	tend = 0.0_wp ! to be removed later??
	2773	CALL advec_s_up( e )
	2774	ENDIF
	2775	ENDIF
	2776	ENDIF
	2777
	2778	IF ( .NOT. humidity ) THEN
	2779	IF ( ocean ) THEN
	2780	CALL diffusion_e( prho, prho_reference )
	2781	ELSE
	2782	CALL diffusion_e_acc( pt, pt_reference )
	2783	ENDIF
	2784	ELSE
	2785	CALL diffusion_e( vpt, pt_reference )
	2786	ENDIF
	2787
	2788	CALL production_e_acc
	2789
	2790	!
	2791	!-- Additional sink term for flows through plant canopies
	2792	IF ( plant_canopy ) CALL pcm_tendency( 6 )
	2793	CALL user_actions( 'e-tendency' )
	2794
	2795	!
	2796	!-- Prognostic equation for TKE.
	2797	!-- Eliminate negative TKE values, which can occur due to numerical
	2798	!-- reasons in the course of the integration. In such cases the old TKE
	2799	!-- value is reduced by 90%.
	2800	!$acc kernels present( e, e_p, nzb_s_inner, tend, te_m )
	2801	!$acc loop independent
	2802	DO i = i_left, i_right
	2803	!$acc loop independent
	2804	DO j = j_south, j_north
	2805	!$acc loop independent
	2806	DO k = 1, nzt
	2807	IF ( k > nzb_s_inner(j,i) ) THEN
	2808	e_p(k,j,i) = e(k,j,i) + dt_3d * ( sbt * tend(k,j,i) + &
	2809	tsc(3) * te_m(k,j,i) )
	2810	IF ( e_p(k,j,i) < 0.0_wp ) e_p(k,j,i) = 0.1_wp * e(k,j,i)
	2811	!
	2812	!-- Tendencies for the next Runge-Kutta step
	2813	IF ( runge_step == 1 ) THEN
	2814	te_m(k,j,i) = tend(k,j,i)
	2815	ELSEIF ( runge_step == 2 ) THEN
	2816	te_m(k,j,i) = -9.5625_wp * tend(k,j,i) + 5.3125_wp * te_m(k,j,i)
	2817	ENDIF
	2818	ENDIF
	2819	ENDDO
	2820	ENDDO
	2821	ENDDO
	2822	!$acc end kernels
	2823
	2824	CALL cpu_log( log_point(16), 'tke-equation', 'stop' )
	2825
	2826	ENDIF
	2827
	2828	END SUBROUTINE prognostic_equations_acc
	2829
	2830
	2831	END MODULE prognostic_equations_mod

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