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

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