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source: palm/trunk/SOURCE/prognostic_equations.f90 @ 2008

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

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