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source: palm/trunk/SOURCE/prognostic_equations.f90 @ 1585

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

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