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source: palm/trunk/SOURCE/prognostic_equations.f90 @ 2232

Last change on this file since 2232 was 2232, checked in by suehring, 7 years ago
Adjustments according new topography and surface-modelling concept implemented
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1	!> @file prognostic_equations.f90
2	!------------------------------------------------------------------------------!
3	! This file is part of PALM.
4	!
5	! PALM is free software: you can redistribute it and/or modify it under the
6	! terms of the GNU General Public License as published by the Free Software
7	! Foundation, either version 3 of the License, or (at your option) any later
8	! version.
9	!
10	! PALM is distributed in the hope that it will be useful, but WITHOUT ANY
11	! WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
12	! A PARTICULAR PURPOSE. See the GNU General Public License for more details.
13	!
14	! You should have received a copy of the GNU General Public License along with
15	! PALM. If not, see <http://www.gnu.org/licenses/>.
16	!
17	! Copyright 1997-2017 Leibniz Universitaet Hannover
18	!------------------------------------------------------------------------------!
19	!
20	! Current revisions:
21	! ------------------
22	! Adjutst to new surface-type structure. Remove call for usm_wall_heat_flux,
23	! which is realized directly in diffusion_s now.
24	!
25	! Former revisions:
26	! -----------------
27	! $Id: prognostic_equations.f90 2232 2017-05-30 17:47:52Z suehring $
28	!
29	! 2192 2017-03-22 04:14:10Z raasch
30	! Bugfix for misplaced and missing openMP directives from r2155
31	!
32	! 2155 2017-02-21 09:57:40Z hoffmann
33	! Bugfix in the calculation of microphysical quantities on ghost points.
34	!
35	! 2118 2017-01-17 16:38:49Z raasch
36	! OpenACC version of subroutine removed
37	!
38	! 2031 2016-10-21 15:11:58Z knoop
39	! renamed variable rho to rho_ocean
40	!
41	! 2011 2016-09-19 17:29:57Z kanani
42	! Flag urban_surface is now defined in module control_parameters.
43	!
44	! 2007 2016-08-24 15:47:17Z kanani
45	! Added pt tendency calculation based on energy balance at urban surfaces
46	! (new urban surface model)
47	!
48	! 2000 2016-08-20 18:09:15Z knoop
49	! Forced header and separation lines into 80 columns
50	!
51	! 1976 2016-07-27 13:28:04Z maronga
52	! Simplied calls to radiation model
53	!
54	! 1960 2016-07-12 16:34:24Z suehring
55	! Separate humidity and passive scalar
56	!
57	! 1914 2016-05-26 14:44:07Z witha
58	! Added calls for wind turbine model
59	!
60	! 1873 2016-04-18 14:50:06Z maronga
61	! Module renamed (removed _mod)
62	!
63	! 1850 2016-04-08 13:29:27Z maronga
64	! Module renamed
65	!
66	! 1826 2016-04-07 12:01:39Z maronga
67	! Renamed canopy model calls.
68	!
69	! 1822 2016-04-07 07:49:42Z hoffmann
70	! Kessler microphysics scheme moved to microphysics.
71	!
72	! 1757 2016-02-22 15:49:32Z maronga
73	!
74	! 1691 2015-10-26 16:17:44Z maronga
75	! Added optional model spin-up without radiation / land surface model calls.
76	! Formatting corrections.
77	!
78	! 1682 2015-10-07 23:56:08Z knoop
79	! Code annotations made doxygen readable
80	!
81	! 1585 2015-04-30 07:05:52Z maronga
82	! Added call for temperature tendency calculation due to radiative flux divergence
83	!
84	! 1517 2015-01-07 19:12:25Z hoffmann
85	! advec_s_bc_mod addded, since advec_s_bc is now a module
86	!
87	! 1496 2014-12-02 17:25:50Z maronga
88	! Renamed "radiation" -> "cloud_top_radiation"
89	!
90	! 1484 2014-10-21 10:53:05Z kanani
91	! Changes due to new module structure of the plant canopy model:
92	! parameters cthf and plant_canopy moved to module plant_canopy_model_mod.
93	! Removed double-listing of use_upstream_for_tke in ONLY-list of module
94	! control_parameters
95	!
96	! 1409 2014-05-23 12:11:32Z suehring
97	! Bugfix: i_omp_start changed for advec_u_ws at left inflow and outflow boundary.
98	! This ensures that left-hand side fluxes are also calculated for nxl in that
99	! case, even though the solution at nxl is overwritten in boundary_conds()
100	!
101	! 1398 2014-05-07 11:15:00Z heinze
102	! Rayleigh-damping for horizontal velocity components changed: instead of damping
103	! against ug and vg, damping against u_init and v_init is used to allow for a
104	! homogenized treatment in case of nudging
105	!
106	! 1380 2014-04-28 12:40:45Z heinze
107	! Change order of calls for scalar prognostic quantities:
108	! ls_advec -> nudging -> subsidence since initial profiles
109	!
110	! 1374 2014-04-25 12:55:07Z raasch
111	! missing variables added to ONLY lists
112	!
113	! 1365 2014-04-22 15:03:56Z boeske
114	! Calls of ls_advec for large scale advection added,
115	! subroutine subsidence is only called if use_subsidence_tendencies = .F.,
116	! new argument ls_index added to the calls of subsidence
117	! +ls_index
118	!
119	! 1361 2014-04-16 15:17:48Z hoffmann
120	! Two-moment microphysics moved to the start of prognostic equations. This makes
121	! the 3d arrays for tend_q, tend_qr, tend_pt and tend_pt redundant.
122	! Additionally, it is allowed to call the microphysics just once during the time
123	! step (not at each sub-time step).
124	!
125	! Two-moment cloud physics added for vector and accelerator optimization.
126	!
127	! 1353 2014-04-08 15:21:23Z heinze
128	! REAL constants provided with KIND-attribute
129	!
130	! 1337 2014-03-25 15:11:48Z heinze
131	! Bugfix: REAL constants provided with KIND-attribute
132	!
133	! 1332 2014-03-25 11:59:43Z suehring
134	! Bugfix: call advec_ws or advec_pw for TKE only if NOT use_upstream_for_tke
135	!
136	! 1330 2014-03-24 17:29:32Z suehring
137	! In case of SGS-particle velocity advection of TKE is also allowed with
138	! dissipative 5th-order scheme.
139	!
140	! 1320 2014-03-20 08:40:49Z raasch
141	! ONLY-attribute added to USE-statements,
142	! kind-parameters added to all INTEGER and REAL declaration statements,
143	! kinds are defined in new module kinds,
144	! old module precision_kind is removed,
145	! revision history before 2012 removed,
146	! comment fields (!:) to be used for variable explanations added to
147	! all variable declaration statements
148	!
149	! 1318 2014-03-17 13:35:16Z raasch
150	! module interfaces removed
151	!
152	! 1257 2013-11-08 15:18:40Z raasch
153	! openacc loop vector clauses removed, independent clauses added
154	!
155	! 1246 2013-11-01 08:59:45Z heinze
156	! enable nudging also for accelerator version
157	!
158	! 1241 2013-10-30 11:36:58Z heinze
159	! usage of nudging enabled (so far not implemented for accelerator version)
160	!
161	! 1179 2013-06-14 05:57:58Z raasch
162	! two arguments removed from routine buoyancy, ref_state updated on device
163	!
164	! 1128 2013-04-12 06:19:32Z raasch
165	! those parts requiring global communication moved to time_integration,
166	! loop index bounds in accelerator version replaced by i_left, i_right, j_south,
167	! j_north
168	!
169	! 1115 2013-03-26 18:16:16Z hoffmann
170	! optimized cloud physics: calculation of microphysical tendencies transfered
171	! to microphysics.f90; qr and nr are only calculated if precipitation is required
172	!
173	! 1111 2013-03-08 23:54:10Z raasch
174	! update directives for prognostic quantities removed
175	!
176	! 1106 2013-03-04 05:31:38Z raasch
177	! small changes in code formatting
178	!
179	! 1092 2013-02-02 11:24:22Z raasch
180	! unused variables removed
181	!
182	! 1053 2012-11-13 17:11:03Z hoffmann
183	! implementation of two new prognostic equations for rain drop concentration (nr)
184	! and rain water content (qr)
185	!
186	! currently, only available for cache loop optimization
187	!
188	! 1036 2012-10-22 13:43:42Z raasch
189	! code put under GPL (PALM 3.9)
190	!
191	! 1019 2012-09-28 06:46:45Z raasch
192	! non-optimized version of prognostic_equations removed
193	!
194	! 1015 2012-09-27 09:23:24Z raasch
195	! new branch prognostic_equations_acc
196	! OpenACC statements added + code changes required for GPU optimization
197	!
198	! 1001 2012-09-13 14:08:46Z raasch
199	! all actions concerning leapfrog- and upstream-spline-scheme removed
200	!
201	! 978 2012-08-09 08:28:32Z fricke
202	! km_damp_x and km_damp_y removed in calls of diffusion_u and diffusion_v
203	! add ptdf_x, ptdf_y for damping the potential temperature at the inflow
204	! boundary in case of non-cyclic lateral boundaries
205	! Bugfix: first thread index changes for WS-scheme at the inflow
206	!
207	! 940 2012-07-09 14:31:00Z raasch
208	! temperature equation can be switched off
209	!
210	! Revision 1.1 2000/04/13 14:56:27 schroeter
211	! Initial revision
212	!
213	!
214	! Description:
215	! ------------
216	!> Solving the prognostic equations.
217	!------------------------------------------------------------------------------!
218	MODULE prognostic_equations_mod
219
220
221
222	USE arrays_3d, &
223	ONLY: diss_l_e, diss_l_nr, diss_l_pt, diss_l_q, diss_l_qr, &
224	diss_l_s, diss_l_sa, diss_s_e, diss_s_nr, diss_s_pt, diss_s_q, &
225	diss_s_qr, diss_s_s, diss_s_sa, e, e_p, flux_s_e, flux_s_nr, &
226	flux_s_pt, flux_s_q, flux_s_qr, flux_s_s, flux_s_sa, flux_l_e, &
227	flux_l_nr, flux_l_pt, flux_l_q, flux_l_qr, flux_l_s, flux_l_sa, &
228	nr, nr_p, pt, ptdf_x, ptdf_y, pt_init, pt_p, &
229	prho, q, q_init, q_p, qr, qr_p, rdf, &
230	rdf_sc, ref_state, rho_ocean, s, s_init, s_p, sa, sa_init, sa_p,&
231	tend, te_m, tnr_m, tpt_m, tq_m, tqr_m, ts_m, tsa_m, tu_m, tv_m, &
232	tw_m, u, ug, u_init, u_p, v, vg, vpt, v_init, v_p, w, w_p
233
234	USE control_parameters, &
235	ONLY: call_microphysics_at_all_substeps, cloud_physics, &
236	cloud_top_radiation, constant_diffusion, dp_external, &
237	dp_level_ind_b, dp_smooth_factor, dpdxy, dt_3d, humidity, &
238	inflow_l, intermediate_timestep_count, &
239	intermediate_timestep_count_max, large_scale_forcing, &
240	large_scale_subsidence, microphysics_seifert, &
241	microphysics_sat_adjust, neutral, nudging, ocean, outflow_l, &
242	outflow_s, passive_scalar, prho_reference, prho_reference, &
243	prho_reference, pt_reference, pt_reference, pt_reference, &
244	scalar_advec, scalar_advec, simulated_time, sloping_surface, &
245	timestep_scheme, tsc, use_subsidence_tendencies, &
246	use_upstream_for_tke, ws_scheme_mom, ws_scheme_sca
247
248	USE cpulog, &
249	ONLY: cpu_log, log_point
250
251	USE eqn_state_seawater_mod, &
252	ONLY: eqn_state_seawater
253
254	USE indices, &
255	ONLY: nxl, nxlg, nxlu, nxr, nxrg, nyn, nyng, nys, nysg, nysv, nzb, &
256	nzt, wall_flags_0
257
258	USE advec_ws, &
259	ONLY: advec_s_ws, advec_u_ws, advec_v_ws, advec_w_ws
260
261	USE advec_s_bc_mod, &
262	ONLY: advec_s_bc
263
264	USE advec_s_pw_mod, &
265	ONLY: advec_s_pw
266
267	USE advec_s_up_mod, &
268	ONLY: advec_s_up
269
270	USE advec_u_pw_mod, &
271	ONLY: advec_u_pw
272
273	USE advec_u_up_mod, &
274	ONLY: advec_u_up
275
276	USE advec_v_pw_mod, &
277	ONLY: advec_v_pw
278
279	USE advec_v_up_mod, &
280	ONLY: advec_v_up
281
282	USE advec_w_pw_mod, &
283	ONLY: advec_w_pw
284
285	USE advec_w_up_mod, &
286	ONLY: advec_w_up
287
288	USE buoyancy_mod, &
289	ONLY: buoyancy
290
291	USE calc_radiation_mod, &
292	ONLY: calc_radiation
293
294	USE coriolis_mod, &
295	ONLY: coriolis
296
297	USE diffusion_e_mod, &
298	ONLY: diffusion_e
299
300	USE diffusion_s_mod, &
301	ONLY: diffusion_s
302
303	USE diffusion_u_mod, &
304	ONLY: diffusion_u
305
306	USE diffusion_v_mod, &
307	ONLY: diffusion_v
308
309	USE diffusion_w_mod, &
310	ONLY: diffusion_w
311
312	USE kinds
313
314	USE ls_forcing_mod, &
315	ONLY: ls_advec
316
317	USE microphysics_mod, &
318	ONLY: microphysics_control
319
320	USE nudge_mod, &
321	ONLY: nudge
322
323	USE plant_canopy_model_mod, &
324	ONLY: cthf, plant_canopy, pcm_tendency
325
326	USE production_e_mod, &
327	ONLY: production_e
328
329	USE radiation_model_mod, &
330	ONLY: radiation, radiation_tendency, &
331	skip_time_do_radiation
332
333	USE statistics, &
334	ONLY: hom
335
336	USE subsidence_mod, &
337	ONLY: subsidence
338
339	USE user_actions_mod, &
340	ONLY: user_actions
341
342	USE surface_mod, &
343	ONLY : surf_def_h, surf_def_v, surf_lsm_h, surf_lsm_v, surf_usm_h, &
344	surf_usm_v
345
346	USE wind_turbine_model_mod, &
347	ONLY: wind_turbine, wtm_tendencies
348
349
350	PRIVATE
351	PUBLIC prognostic_equations_cache, prognostic_equations_vector
352
353	INTERFACE prognostic_equations_cache
354	MODULE PROCEDURE prognostic_equations_cache
355	END INTERFACE prognostic_equations_cache
356
357	INTERFACE prognostic_equations_vector
358	MODULE PROCEDURE prognostic_equations_vector
359	END INTERFACE prognostic_equations_vector
360
361
362	CONTAINS
363
364
365	!------------------------------------------------------------------------------!
366	! Description:
367	! ------------
368	!> Version with one optimized loop over all equations. It is only allowed to
369	!> be called for the Wicker and Skamarock or Piascek-Williams advection scheme.
370	!>
371	!> Here the calls of most subroutines are embedded in two DO loops over i and j,
372	!> so communication between CPUs is not allowed (does not make sense) within
373	!> these loops.
374	!>
375	!> (Optimized to avoid cache missings, i.e. for Power4/5-architectures.)
376	!------------------------------------------------------------------------------!
377
378	SUBROUTINE prognostic_equations_cache
379
380
381	IMPLICIT NONE
382
383	INTEGER(iwp) :: i !<
384	INTEGER(iwp) :: i_omp_start !<
385	INTEGER(iwp) :: j !<
386	INTEGER(iwp) :: k !<
387	INTEGER(iwp) :: omp_get_thread_num !<
388	INTEGER(iwp) :: tn = 0 !<
389
390	LOGICAL :: loop_start !<
391
392
393	!
394	!-- Time measurement can only be performed for the whole set of equations
395	CALL cpu_log( log_point(32), 'all progn.equations', 'start' )
396
397	!
398	!-- If required, calculate cloud microphysics
399	IF ( cloud_physics .AND. .NOT. microphysics_sat_adjust .AND. &
400	( intermediate_timestep_count == 1 .OR. &
401	call_microphysics_at_all_substeps ) ) &
402	THEN
403	!$OMP PARALLEL private (i,j)
404	!$OMP DO
405	!$OMP PARALLEL PRIVATE (i, j)
406	!$OMP DO
407	DO i = nxlg, nxrg
408	DO j = nysg, nyng
409	CALL microphysics_control( i, j )
410	ENDDO
411	ENDDO
412	!$OMP END PARALLEL
413	!$OMP END PARALLEL
414	ENDIF
415
416	!
417	!-- Loop over all prognostic equations
418	!$OMP PARALLEL private (i,i_omp_start,j,k,loop_start,tn)
419
420	!$ tn = omp_get_thread_num()
421	loop_start = .TRUE.
422
423	!$OMP DO
424	DO i = nxl, nxr
425
426	!
427	!-- Store the first loop index. It differs for each thread and is required
428	!-- later in advec_ws
429	IF ( loop_start ) THEN
430	loop_start = .FALSE.
431	i_omp_start = i
432	ENDIF
433
434	DO j = nys, nyn
435	!
436	!-- Tendency terms for u-velocity component
437	IF ( .NOT. outflow_l .OR. i > nxl ) THEN
438
439	tend(:,j,i) = 0.0_wp
440	IF ( timestep_scheme(1:5) == 'runge' ) THEN
441	IF ( ws_scheme_mom ) THEN
442	CALL advec_u_ws( i, j, i_omp_start, tn )
443	ELSE
444	CALL advec_u_pw( i, j )
445	ENDIF
446	ELSE
447	CALL advec_u_up( i, j )
448	ENDIF
449	CALL diffusion_u( i, j )
450	CALL coriolis( i, j, 1 )
451	IF ( sloping_surface .AND. .NOT. neutral ) THEN
452	CALL buoyancy( i, j, pt, 1 )
453	ENDIF
454
455	!
456	!-- Drag by plant canopy
457	IF ( plant_canopy ) CALL pcm_tendency( i, j, 1 )
458
459	!
460	!-- External pressure gradient
461	IF ( dp_external ) THEN
462	DO k = dp_level_ind_b+1, nzt
463	tend(k,j,i) = tend(k,j,i) - dpdxy(1) * dp_smooth_factor(k)
464	ENDDO
465	ENDIF
466
467	!
468	!-- Nudging
469	IF ( nudging ) CALL nudge( i, j, simulated_time, 'u' )
470
471	!
472	!-- Forces by wind turbines
473	IF ( wind_turbine ) CALL wtm_tendencies( i, j, 1 )
474
475	CALL user_actions( i, j, 'u-tendency' )
476	!
477	!-- Prognostic equation for u-velocity component
478	DO k = nzb+1, nzt
479
480	u_p(k,j,i) = u(k,j,i) + ( dt_3d * &
481	( tsc(2) * tend(k,j,i) + &
482	tsc(3) * tu_m(k,j,i) ) &
483	- tsc(5) * rdf(k) &
484	* ( u(k,j,i) - u_init(k) ) &
485	) * MERGE( 1.0_wp, 0.0_wp, &
486	BTEST( wall_flags_0(k,j,i), 1 )&
487	)
488	ENDDO
489
490	!
491	!-- Calculate tendencies for the next Runge-Kutta step
492	IF ( timestep_scheme(1:5) == 'runge' ) THEN
493	IF ( intermediate_timestep_count == 1 ) THEN
494	DO k = nzb+1, nzt
495	tu_m(k,j,i) = tend(k,j,i)
496	ENDDO
497	ELSEIF ( intermediate_timestep_count < &
498	intermediate_timestep_count_max ) THEN
499	DO k = nzb+1, nzt
500	tu_m(k,j,i) = -9.5625_wp * tend(k,j,i) &
501	+ 5.3125_wp * tu_m(k,j,i)
502	ENDDO
503	ENDIF
504	ENDIF
505
506	ENDIF
507
508	!
509	!-- Tendency terms for v-velocity component
510	IF ( .NOT. outflow_s .OR. j > nys ) THEN
511
512	tend(:,j,i) = 0.0_wp
513	IF ( timestep_scheme(1:5) == 'runge' ) THEN
514	IF ( ws_scheme_mom ) THEN
515	CALL advec_v_ws( i, j, i_omp_start, tn )
516	ELSE
517	CALL advec_v_pw( i, j )
518	ENDIF
519	ELSE
520	CALL advec_v_up( i, j )
521	ENDIF
522	CALL diffusion_v( i, j )
523	CALL coriolis( i, j, 2 )
524
525	!
526	!-- Drag by plant canopy
527	IF ( plant_canopy ) CALL pcm_tendency( i, j, 2 )
528
529	!
530	!-- External pressure gradient
531	IF ( dp_external ) THEN
532	DO k = dp_level_ind_b+1, nzt
533	tend(k,j,i) = tend(k,j,i) - dpdxy(2) * dp_smooth_factor(k)
534	ENDDO
535	ENDIF
536
537	!
538	!-- Nudging
539	IF ( nudging ) CALL nudge( i, j, simulated_time, 'v' )
540
541	!
542	!-- Forces by wind turbines
543	IF ( wind_turbine ) CALL wtm_tendencies( i, j, 2 )
544
545	CALL user_actions( i, j, 'v-tendency' )
546	!
547	!-- Prognostic equation for v-velocity component
548	DO k = nzb+1, nzt
549	v_p(k,j,i) = v(k,j,i) + ( dt_3d * &
550	( tsc(2) * tend(k,j,i) + &
551	tsc(3) * tv_m(k,j,i) ) &
552	- tsc(5) * rdf(k) &
553	* ( v(k,j,i) - v_init(k) )&
554	) * MERGE( 1.0_wp, 0.0_wp, &
555	BTEST( wall_flags_0(k,j,i), 2 )&
556	)
557	ENDDO
558
559	!
560	!-- Calculate tendencies for the next Runge-Kutta step
561	IF ( timestep_scheme(1:5) == 'runge' ) THEN
562	IF ( intermediate_timestep_count == 1 ) THEN
563	DO k = nzb+1, nzt
564	tv_m(k,j,i) = tend(k,j,i)
565	ENDDO
566	ELSEIF ( intermediate_timestep_count < &
567	intermediate_timestep_count_max ) THEN
568	DO k = nzb+1, nzt
569	tv_m(k,j,i) = -9.5625_wp * tend(k,j,i) &
570	+ 5.3125_wp * tv_m(k,j,i)
571	ENDDO
572	ENDIF
573	ENDIF
574
575	ENDIF
576
577	!
578	!-- Tendency terms for w-velocity component
579	tend(:,j,i) = 0.0_wp
580	IF ( timestep_scheme(1:5) == 'runge' ) THEN
581	IF ( ws_scheme_mom ) THEN
582	CALL advec_w_ws( i, j, i_omp_start, tn )
583	ELSE
584	CALL advec_w_pw( i, j )
585	END IF
586	ELSE
587	CALL advec_w_up( i, j )
588	ENDIF
589	CALL diffusion_w( i, j )
590	CALL coriolis( i, j, 3 )
591
592	IF ( .NOT. neutral ) THEN
593	IF ( ocean ) THEN
594	CALL buoyancy( i, j, rho_ocean, 3 )
595	ELSE
596	IF ( .NOT. humidity ) THEN
597	CALL buoyancy( i, j, pt, 3 )
598	ELSE
599	CALL buoyancy( i, j, vpt, 3 )
600	ENDIF
601	ENDIF
602	ENDIF
603
604	!
605	!-- Drag by plant canopy
606	IF ( plant_canopy ) CALL pcm_tendency( i, j, 3 )
607
608	!
609	!-- Forces by wind turbines
610	IF ( wind_turbine ) CALL wtm_tendencies( i, j, 3 )
611
612	CALL user_actions( i, j, 'w-tendency' )
613	!
614	!-- Prognostic equation for w-velocity component
615	DO k = nzb+1, nzt-1
616	w_p(k,j,i) = w(k,j,i) + ( dt_3d * &
617	( tsc(2) * tend(k,j,i) + &
618	tsc(3) * tw_m(k,j,i) ) &
619	- tsc(5) * rdf(k) * w(k,j,i) &
620	) * MERGE( 1.0_wp, 0.0_wp, &
621	BTEST( wall_flags_0(k,j,i), 3 )&
622	)
623	ENDDO
624
625	!
626	!-- Calculate tendencies for the next Runge-Kutta step
627	IF ( timestep_scheme(1:5) == 'runge' ) THEN
628	IF ( intermediate_timestep_count == 1 ) THEN
629	DO k = nzb+1, nzt-1
630	tw_m(k,j,i) = tend(k,j,i)
631	ENDDO
632	ELSEIF ( intermediate_timestep_count < &
633	intermediate_timestep_count_max ) THEN
634	DO k = nzb+1, nzt-1
635	tw_m(k,j,i) = -9.5625_wp * tend(k,j,i) &
636	+ 5.3125_wp * tw_m(k,j,i)
637	ENDDO
638	ENDIF
639	ENDIF
640
641	!
642	!-- If required, compute prognostic equation for potential temperature
643	IF ( .NOT. neutral ) THEN
644	!
645	!-- Tendency terms for potential temperature
646	tend(:,j,i) = 0.0_wp
647	IF ( timestep_scheme(1:5) == 'runge' ) THEN
648	IF ( ws_scheme_sca ) THEN
649	CALL advec_s_ws( i, j, pt, 'pt', flux_s_pt, diss_s_pt, &
650	flux_l_pt, diss_l_pt, i_omp_start, tn )
651	ELSE
652	CALL advec_s_pw( i, j, pt )
653	ENDIF
654	ELSE
655	CALL advec_s_up( i, j, pt )
656	ENDIF
657	CALL diffusion_s( i, j, pt, &
658	surf_def_h(0)%shf, surf_def_h(1)%shf, &
659	surf_def_h(2)%shf, &
660	surf_lsm_h%shf, surf_usm_h%shf, &
661	surf_def_v(0)%shf, surf_def_v(1)%shf, &
662	surf_def_v(2)%shf, surf_def_v(3)%shf, &
663	surf_lsm_v(0)%shf, surf_lsm_v(1)%shf, &
664	surf_lsm_v(2)%shf, surf_lsm_v(3)%shf, &
665	surf_usm_v(0)%shf, surf_usm_v(1)%shf, &
666	surf_usm_v(2)%shf, surf_usm_v(3)%shf )
667	!
668	!-- If required compute heating/cooling due to long wave radiation
669	!-- processes
670	IF ( cloud_top_radiation ) THEN
671	CALL calc_radiation( i, j )
672	ENDIF
673
674	!
675	!-- Consideration of heat sources within the plant canopy
676	IF ( plant_canopy .AND. cthf /= 0.0_wp ) THEN
677	CALL pcm_tendency( i, j, 4 )
678	ENDIF
679
680	!
681	!-- Large scale advection
682	IF ( large_scale_forcing ) THEN
683	CALL ls_advec( i, j, simulated_time, 'pt' )
684	ENDIF
685
686	!
687	!-- Nudging
688	IF ( nudging ) CALL nudge( i, j, simulated_time, 'pt' )
689
690	!
691	!-- If required, compute effect of large-scale subsidence/ascent
692	IF ( large_scale_subsidence .AND. &
693	.NOT. use_subsidence_tendencies ) THEN
694	CALL subsidence( i, j, tend, pt, pt_init, 2 )
695	ENDIF
696
697	!
698	!-- If required, add tendency due to radiative heating/cooling
699	IF ( radiation .AND. &
700	simulated_time > skip_time_do_radiation ) THEN
701	CALL radiation_tendency ( i, j, tend )
702	ENDIF
703
704
705	CALL user_actions( i, j, 'pt-tendency' )
706	!
707	!-- Prognostic equation for potential temperature
708	DO k = nzb+1, nzt
709	pt_p(k,j,i) = pt(k,j,i) + ( dt_3d * &
710	( tsc(2) * tend(k,j,i) + &
711	tsc(3) * tpt_m(k,j,i) ) &
712	- tsc(5) &
713	* ( pt(k,j,i) - pt_init(k) ) &
714	* ( rdf_sc(k) + ptdf_x(i) &
715	+ ptdf_y(j) ) &
716	) &
717	* MERGE( 1.0_wp, 0.0_wp, &
718	BTEST( wall_flags_0(k,j,i), 0 )&
719	)
720	ENDDO
721
722	!
723	!-- Calculate tendencies for the next Runge-Kutta step
724	IF ( timestep_scheme(1:5) == 'runge' ) THEN
725	IF ( intermediate_timestep_count == 1 ) THEN
726	DO k = nzb+1, nzt
727	tpt_m(k,j,i) = tend(k,j,i)
728	ENDDO
729	ELSEIF ( intermediate_timestep_count < &
730	intermediate_timestep_count_max ) THEN
731	DO k = nzb+1, nzt
732	tpt_m(k,j,i) = -9.5625_wp * tend(k,j,i) + &
733	5.3125_wp * tpt_m(k,j,i)
734	ENDDO
735	ENDIF
736	ENDIF
737
738	ENDIF
739
740	!
741	!-- If required, compute prognostic equation for salinity
742	IF ( ocean ) THEN
743
744	!
745	!-- Tendency-terms for salinity
746	tend(:,j,i) = 0.0_wp
747	IF ( timestep_scheme(1:5) == 'runge' ) &
748	THEN
749	IF ( ws_scheme_sca ) THEN
750	CALL advec_s_ws( i, j, sa, 'sa', flux_s_sa, &
751	diss_s_sa, flux_l_sa, diss_l_sa, i_omp_start, tn )
752	ELSE
753	CALL advec_s_pw( i, j, sa )
754	ENDIF
755	ELSE
756	CALL advec_s_up( i, j, sa )
757	ENDIF
758	CALL diffusion_s( i, j, sa, &
759	surf_def_h(0)%sasws, surf_def_h(1)%sasws, &
760	surf_def_h(2)%sasws, &
761	surf_lsm_h%sasws, surf_usm_h%sasws, &
762	surf_def_v(0)%sasws, surf_def_v(1)%sasws, &
763	surf_def_v(2)%sasws, surf_def_v(3)%sasws, &
764	surf_lsm_v(0)%sasws, surf_lsm_v(1)%sasws, &
765	surf_lsm_v(2)%sasws, surf_lsm_v(3)%sasws, &
766	surf_usm_v(0)%sasws, surf_usm_v(1)%sasws, &
767	surf_usm_v(2)%sasws, surf_usm_v(3)%sasws )
768
769	CALL user_actions( i, j, 'sa-tendency' )
770
771	!
772	!-- Prognostic equation for salinity
773	DO k = nzb+1, nzt
774	sa_p(k,j,i) = sa(k,j,i) + ( dt_3d * &
775	( tsc(2) * tend(k,j,i) + &
776	tsc(3) * tsa_m(k,j,i) ) &
777	- tsc(5) * rdf_sc(k) &
778	* ( sa(k,j,i) - sa_init(k) )&
779	) * MERGE( 1.0_wp, 0.0_wp, &
780	BTEST( wall_flags_0(k,j,i), 0 )&
781	)
782	IF ( sa_p(k,j,i) < 0.0_wp ) sa_p(k,j,i) = 0.1_wp * sa(k,j,i)
783	ENDDO
784
785	!
786	!-- Calculate tendencies for the next Runge-Kutta step
787	IF ( timestep_scheme(1:5) == 'runge' ) THEN
788	IF ( intermediate_timestep_count == 1 ) THEN
789	DO k = nzb+1, nzt
790	tsa_m(k,j,i) = tend(k,j,i)
791	ENDDO
792	ELSEIF ( intermediate_timestep_count < &
793	intermediate_timestep_count_max ) THEN
794	DO k = nzb+1, nzt
795	tsa_m(k,j,i) = -9.5625_wp * tend(k,j,i) + &
796	5.3125_wp * tsa_m(k,j,i)
797	ENDDO
798	ENDIF
799	ENDIF
800
801	!
802	!-- Calculate density by the equation of state for seawater
803	CALL eqn_state_seawater( i, j )
804
805	ENDIF
806
807	!
808	!-- If required, compute prognostic equation for total water content
809	IF ( humidity ) THEN
810
811	!
812	!-- Tendency-terms for total water content / scalar
813	tend(:,j,i) = 0.0_wp
814	IF ( timestep_scheme(1:5) == 'runge' ) &
815	THEN
816	IF ( ws_scheme_sca ) THEN
817	CALL advec_s_ws( i, j, q, 'q', flux_s_q, &
818	diss_s_q, flux_l_q, diss_l_q, i_omp_start, tn )
819	ELSE
820	CALL advec_s_pw( i, j, q )
821	ENDIF
822	ELSE
823	CALL advec_s_up( i, j, q )
824	ENDIF
825	CALL diffusion_s( i, j, q, &
826	surf_def_h(0)%qsws, surf_def_h(1)%qsws, &
827	surf_def_h(2)%qsws, &
828	surf_lsm_h%qsws, surf_usm_h%qsws, &
829	surf_def_v(0)%qsws, surf_def_v(1)%qsws, &
830	surf_def_v(2)%qsws, surf_def_v(3)%qsws, &
831	surf_lsm_v(0)%qsws, surf_lsm_v(1)%qsws, &
832	surf_lsm_v(2)%qsws, surf_lsm_v(3)%qsws, &
833	surf_usm_v(0)%qsws, surf_usm_v(1)%qsws, &
834	surf_usm_v(2)%qsws, surf_usm_v(3)%qsws )
835
836	!
837	!-- Sink or source of humidity due to canopy elements
838	IF ( plant_canopy ) CALL pcm_tendency( i, j, 5 )
839
840	!
841	!-- Large scale advection
842	IF ( large_scale_forcing ) THEN
843	CALL ls_advec( i, j, simulated_time, 'q' )
844	ENDIF
845
846	!
847	!-- Nudging
848	IF ( nudging ) CALL nudge( i, j, simulated_time, 'q' )
849
850	!
851	!-- If required compute influence of large-scale subsidence/ascent
852	IF ( large_scale_subsidence .AND. &
853	.NOT. use_subsidence_tendencies ) THEN
854	CALL subsidence( i, j, tend, q, q_init, 3 )
855	ENDIF
856
857	CALL user_actions( i, j, 'q-tendency' )
858
859	!
860	!-- Prognostic equation for total water content / scalar
861	DO k = nzb+1, nzt
862	q_p(k,j,i) = q(k,j,i) + ( dt_3d * &
863	( tsc(2) * tend(k,j,i) + &
864	tsc(3) * tq_m(k,j,i) ) &
865	- tsc(5) * rdf_sc(k) * &
866	( q(k,j,i) - q_init(k) ) &
867	) &
868	* MERGE( 1.0_wp, 0.0_wp, &
869	BTEST( wall_flags_0(k,j,i), 0 )&
870	)
871	IF ( q_p(k,j,i) < 0.0_wp ) q_p(k,j,i) = 0.1_wp * q(k,j,i)
872	ENDDO
873
874	!
875	!-- Calculate tendencies for the next Runge-Kutta step
876	IF ( timestep_scheme(1:5) == 'runge' ) THEN
877	IF ( intermediate_timestep_count == 1 ) THEN
878	DO k = nzb+1, nzt
879	tq_m(k,j,i) = tend(k,j,i)
880	ENDDO
881	ELSEIF ( intermediate_timestep_count < &
882	intermediate_timestep_count_max ) THEN
883	DO k = nzb+1, nzt
884	tq_m(k,j,i) = -9.5625_wp * tend(k,j,i) + &
885	5.3125_wp * tq_m(k,j,i)
886	ENDDO
887	ENDIF
888	ENDIF
889
890	!
891	!-- If required, calculate prognostic equations for rain water content
892	!-- and rain drop concentration
893	IF ( cloud_physics .AND. microphysics_seifert ) THEN
894	!
895	!-- Calculate prognostic equation for rain water content
896	tend(:,j,i) = 0.0_wp
897	IF ( timestep_scheme(1:5) == 'runge' ) &
898	THEN
899	IF ( ws_scheme_sca ) THEN
900	CALL advec_s_ws( i, j, qr, 'qr', flux_s_qr, &
901	diss_s_qr, flux_l_qr, diss_l_qr, &
902	i_omp_start, tn )
903	ELSE
904	CALL advec_s_pw( i, j, qr )
905	ENDIF
906	ELSE
907	CALL advec_s_up( i, j, qr )
908	ENDIF
909	CALL diffusion_s( i, j, qr, &
910	surf_def_h(0)%qrsws, surf_def_h(1)%qrsws, &
911	surf_def_h(2)%qrsws, &
912	surf_lsm_h%qrsws, surf_usm_h%qrsws, &
913	surf_def_v(0)%qrsws, surf_def_v(1)%qrsws, &
914	surf_def_v(2)%qrsws, surf_def_v(3)%qrsws, &
915	surf_lsm_v(0)%qrsws, surf_lsm_v(1)%qrsws, &
916	surf_lsm_v(2)%qrsws, surf_lsm_v(3)%qrsws, &
917	surf_usm_v(0)%qrsws, surf_usm_v(1)%qrsws, &
918	surf_usm_v(2)%qrsws, surf_usm_v(3)%qrsws )
919
920	!
921	!-- Prognostic equation for rain water content
922	DO k = nzb+1, nzt
923	qr_p(k,j,i) = qr(k,j,i) + ( dt_3d * &
924	( tsc(2) * tend(k,j,i) + &
925	tsc(3) * tqr_m(k,j,i) )&
926	- tsc(5) * rdf_sc(k) &
927	* qr(k,j,i) &
928	) &
929	* MERGE( 1.0_wp, 0.0_wp, &
930	BTEST( wall_flags_0(k,j,i), 0 )&
931	)
932	IF ( qr_p(k,j,i) < 0.0_wp ) qr_p(k,j,i) = 0.0_wp
933	ENDDO
934	!
935	!-- Calculate tendencies for the next Runge-Kutta step
936	IF ( timestep_scheme(1:5) == 'runge' ) THEN
937	IF ( intermediate_timestep_count == 1 ) THEN
938	DO k = nzb+1, nzt
939	tqr_m(k,j,i) = tend(k,j,i)
940	ENDDO
941	ELSEIF ( intermediate_timestep_count < &
942	intermediate_timestep_count_max ) THEN
943	DO k = nzb+1, nzt
944	tqr_m(k,j,i) = -9.5625_wp * tend(k,j,i) + &
945	5.3125_wp * tqr_m(k,j,i)
946	ENDDO
947	ENDIF
948	ENDIF
949
950	!
951	!-- Calculate prognostic equation for rain drop concentration.
952	tend(:,j,i) = 0.0_wp
953	IF ( timestep_scheme(1:5) == 'runge' ) THEN
954	IF ( ws_scheme_sca ) THEN
955	CALL advec_s_ws( i, j, nr, 'nr', flux_s_nr, &
956	diss_s_nr, flux_l_nr, diss_l_nr, &
957	i_omp_start, tn )
958	ELSE
959	CALL advec_s_pw( i, j, nr )
960	ENDIF
961	ELSE
962	CALL advec_s_up( i, j, nr )
963	ENDIF
964	CALL diffusion_s( i, j, nr, &
965	surf_def_h(0)%nrsws, surf_def_h(1)%nrsws, &
966	surf_def_h(2)%nrsws, &
967	surf_lsm_h%nrsws, surf_usm_h%nrsws, &
968	surf_def_v(0)%nrsws, surf_def_v(1)%nrsws, &
969	surf_def_v(2)%nrsws, surf_def_v(3)%nrsws, &
970	surf_lsm_v(0)%nrsws, surf_lsm_v(1)%nrsws, &
971	surf_lsm_v(2)%nrsws, surf_lsm_v(3)%nrsws, &
972	surf_usm_v(0)%nrsws, surf_usm_v(1)%nrsws, &
973	surf_usm_v(2)%nrsws, surf_usm_v(3)%nrsws )
974
975	!
976	!-- Prognostic equation for rain drop concentration
977	DO k = nzb+1, nzt
978	nr_p(k,j,i) = nr(k,j,i) + ( dt_3d * &
979	( tsc(2) * tend(k,j,i) + &
980	tsc(3) * tnr_m(k,j,i) )&
981	- tsc(5) * rdf_sc(k) &
982	* nr(k,j,i) &
983	) &
984	* MERGE( 1.0_wp, 0.0_wp, &
985	BTEST( wall_flags_0(k,j,i), 0 )&
986	)
987	IF ( nr_p(k,j,i) < 0.0_wp ) nr_p(k,j,i) = 0.0_wp
988	ENDDO
989	!
990	!-- Calculate tendencies for the next Runge-Kutta step
991	IF ( timestep_scheme(1:5) == 'runge' ) THEN
992	IF ( intermediate_timestep_count == 1 ) THEN
993	DO k = nzb+1, nzt
994	tnr_m(k,j,i) = tend(k,j,i)
995	ENDDO
996	ELSEIF ( intermediate_timestep_count < &
997	intermediate_timestep_count_max ) THEN
998	DO k = nzb+1, nzt
999	tnr_m(k,j,i) = -9.5625_wp * tend(k,j,i) + &
1000	5.3125_wp * tnr_m(k,j,i)
1001	ENDDO
1002	ENDIF
1003	ENDIF
1004
1005	ENDIF
1006
1007	ENDIF
1008
1009	!
1010	!-- If required, compute prognostic equation for scalar
1011	IF ( passive_scalar ) THEN
1012	!
1013	!-- Tendency-terms for total water content / scalar
1014	tend(:,j,i) = 0.0_wp
1015	IF ( timestep_scheme(1:5) == 'runge' ) &
1016	THEN
1017	IF ( ws_scheme_sca ) THEN
1018	CALL advec_s_ws( i, j, s, 's', flux_s_s, &
1019	diss_s_s, flux_l_s, diss_l_s, i_omp_start, tn )
1020	ELSE
1021	CALL advec_s_pw( i, j, s )
1022	ENDIF
1023	ELSE
1024	CALL advec_s_up( i, j, s )
1025	ENDIF
1026	CALL diffusion_s( i, j, s, &
1027	surf_def_h(0)%ssws, surf_def_h(1)%ssws, &
1028	surf_def_h(2)%ssws, &
1029	surf_lsm_h%ssws, surf_usm_h%ssws, &
1030	surf_def_v(0)%ssws, surf_def_v(1)%ssws, &
1031	surf_def_v(2)%ssws, surf_def_v(3)%ssws, &
1032	surf_lsm_v(0)%ssws, surf_lsm_v(1)%ssws, &
1033	surf_lsm_v(2)%ssws, surf_lsm_v(3)%ssws, &
1034	surf_usm_v(0)%ssws, surf_usm_v(1)%ssws, &
1035	surf_usm_v(2)%ssws, surf_usm_v(3)%ssws )
1036
1037	!
1038	!-- Sink or source of scalar concentration due to canopy elements
1039	IF ( plant_canopy ) CALL pcm_tendency( i, j, 7 )
1040
1041	!
1042	!-- Large scale advection, still need to be extended for scalars
1043	! IF ( large_scale_forcing ) THEN
1044	! CALL ls_advec( i, j, simulated_time, 's' )
1045	! ENDIF
1046
1047	!
1048	!-- Nudging, still need to be extended for scalars
1049	! IF ( nudging ) CALL nudge( i, j, simulated_time, 's' )
1050
1051	!
1052	!-- If required compute influence of large-scale subsidence/ascent.
1053	!-- Note, the last argument is of no meaning in this case, as it is
1054	!-- only used in conjunction with large_scale_forcing, which is to
1055	!-- date not implemented for scalars.
1056	IF ( large_scale_subsidence .AND. &
1057	.NOT. use_subsidence_tendencies .AND. &
1058	.NOT. large_scale_forcing ) THEN
1059	CALL subsidence( i, j, tend, s, s_init, 3 )
1060	ENDIF
1061
1062	CALL user_actions( i, j, 's-tendency' )
1063
1064	!
1065	!-- Prognostic equation for scalar
1066	DO k = nzb+1, nzt
1067	s_p(k,j,i) = s(k,j,i) + ( dt_3d * &
1068	( tsc(2) * tend(k,j,i) + &
1069	tsc(3) * ts_m(k,j,i) ) &
1070	- tsc(5) * rdf_sc(k) &
1071	* ( s(k,j,i) - s_init(k) )&
1072	) &
1073	* MERGE( 1.0_wp, 0.0_wp, &
1074	BTEST( wall_flags_0(k,j,i), 0 )&
1075	)
1076	IF ( s_p(k,j,i) < 0.0_wp ) s_p(k,j,i) = 0.1_wp * s(k,j,i)
1077	ENDDO
1078
1079	!
1080	!-- Calculate tendencies for the next Runge-Kutta step
1081	IF ( timestep_scheme(1:5) == 'runge' ) THEN
1082	IF ( intermediate_timestep_count == 1 ) THEN
1083	DO k = nzb+1, nzt
1084	ts_m(k,j,i) = tend(k,j,i)
1085	ENDDO
1086	ELSEIF ( intermediate_timestep_count < &
1087	intermediate_timestep_count_max ) THEN
1088	DO k = nzb+1, nzt
1089	ts_m(k,j,i) = -9.5625_wp * tend(k,j,i) + &
1090	5.3125_wp * ts_m(k,j,i)
1091	ENDDO
1092	ENDIF
1093	ENDIF
1094
1095	ENDIF
1096	!
1097	!-- If required, compute prognostic equation for turbulent kinetic
1098	!-- energy (TKE)
1099	IF ( .NOT. constant_diffusion ) THEN
1100
1101	!
1102	!-- Tendency-terms for TKE
1103	tend(:,j,i) = 0.0_wp
1104	IF ( timestep_scheme(1:5) == 'runge' &
1105	.AND. .NOT. use_upstream_for_tke ) THEN
1106	IF ( ws_scheme_sca ) THEN
1107	CALL advec_s_ws( i, j, e, 'e', flux_s_e, diss_s_e, &
1108	flux_l_e, diss_l_e , i_omp_start, tn )
1109	ELSE
1110	CALL advec_s_pw( i, j, e )
1111	ENDIF
1112	ELSE
1113	CALL advec_s_up( i, j, e )
1114	ENDIF
1115	IF ( .NOT. humidity ) THEN
1116	IF ( ocean ) THEN
1117	CALL diffusion_e( i, j, prho, prho_reference )
1118	ELSE
1119	CALL diffusion_e( i, j, pt, pt_reference )
1120	ENDIF
1121	ELSE
1122	CALL diffusion_e( i, j, vpt, pt_reference )
1123	ENDIF
1124	CALL production_e( i, j )
1125
1126	!
1127	!-- Additional sink term for flows through plant canopies
1128	IF ( plant_canopy ) CALL pcm_tendency( i, j, 6 )
1129
1130	CALL user_actions( i, j, 'e-tendency' )
1131
1132	!
1133	!-- Prognostic equation for TKE.
1134	!-- Eliminate negative TKE values, which can occur due to numerical
1135	!-- reasons in the course of the integration. In such cases the old
1136	!-- TKE value is reduced by 90%.
1137	DO k = nzb+1, nzt
1138	e_p(k,j,i) = e(k,j,i) + ( dt_3d * &
1139	( tsc(2) * tend(k,j,i) + &
1140	tsc(3) * te_m(k,j,i) ) &
1141	) &
1142	* MERGE( 1.0_wp, 0.0_wp, &
1143	BTEST( wall_flags_0(k,j,i), 0 )&
1144	)
1145	IF ( e_p(k,j,i) < 0.0_wp ) e_p(k,j,i) = 0.1_wp * e(k,j,i)
1146	ENDDO
1147
1148	!
1149	!-- Calculate tendencies for the next Runge-Kutta step
1150	IF ( timestep_scheme(1:5) == 'runge' ) THEN
1151	IF ( intermediate_timestep_count == 1 ) THEN
1152	DO k = nzb+1, nzt
1153	te_m(k,j,i) = tend(k,j,i)
1154	ENDDO
1155	ELSEIF ( intermediate_timestep_count < &
1156	intermediate_timestep_count_max ) THEN
1157	DO k = nzb+1, nzt
1158	te_m(k,j,i) = -9.5625_wp * tend(k,j,i) + &
1159	5.3125_wp * te_m(k,j,i)
1160	ENDDO
1161	ENDIF
1162	ENDIF
1163
1164	ENDIF ! TKE equation
1165
1166	ENDDO
1167	ENDDO
1168	!$OMP END PARALLEL
1169
1170
1171
1172
1173	CALL cpu_log( log_point(32), 'all progn.equations', 'stop' )
1174
1175
1176	END SUBROUTINE prognostic_equations_cache
1177
1178
1179	!------------------------------------------------------------------------------!
1180	! Description:
1181	! ------------
1182	!> Version for vector machines
1183	!------------------------------------------------------------------------------!
1184
1185	SUBROUTINE prognostic_equations_vector
1186
1187
1188	IMPLICIT NONE
1189
1190	INTEGER(iwp) :: i !<
1191	INTEGER(iwp) :: j !<
1192	INTEGER(iwp) :: k !<
1193
1194	REAL(wp) :: sbt !<
1195
1196
1197	!
1198	!-- If required, calculate cloud microphysical impacts
1199	IF ( cloud_physics .AND. .NOT. microphysics_sat_adjust .AND. &
1200	( intermediate_timestep_count == 1 .OR. &
1201	call_microphysics_at_all_substeps ) &
1202	) THEN
1203	CALL cpu_log( log_point(51), 'microphysics', 'start' )
1204	CALL microphysics_control
1205	CALL cpu_log( log_point(51), 'microphysics', 'stop' )
1206	ENDIF
1207
1208	!
1209	!-- u-velocity component
1210	CALL cpu_log( log_point(5), 'u-equation', 'start' )
1211
1212	tend = 0.0_wp
1213	IF ( timestep_scheme(1:5) == 'runge' ) THEN
1214	IF ( ws_scheme_mom ) THEN
1215	CALL advec_u_ws
1216	ELSE
1217	CALL advec_u_pw
1218	ENDIF
1219	ELSE
1220	CALL advec_u_up
1221	ENDIF
1222	CALL diffusion_u
1223	CALL coriolis( 1 )
1224	IF ( sloping_surface .AND. .NOT. neutral ) THEN
1225	CALL buoyancy( pt, 1 )
1226	ENDIF
1227
1228	!
1229	!-- Drag by plant canopy
1230	IF ( plant_canopy ) CALL pcm_tendency( 1 )
1231
1232	!
1233	!-- External pressure gradient
1234	IF ( dp_external ) THEN
1235	DO i = nxlu, nxr
1236	DO j = nys, nyn
1237	DO k = dp_level_ind_b+1, nzt
1238	tend(k,j,i) = tend(k,j,i) - dpdxy(1) * dp_smooth_factor(k)
1239	ENDDO
1240	ENDDO
1241	ENDDO
1242	ENDIF
1243
1244	!
1245	!-- Nudging
1246	IF ( nudging ) CALL nudge( simulated_time, 'u' )
1247
1248	!
1249	!-- Forces by wind turbines
1250	IF ( wind_turbine ) CALL wtm_tendencies( 1 )
1251
1252	CALL user_actions( 'u-tendency' )
1253
1254	!
1255	!-- Prognostic equation for u-velocity component
1256	DO i = nxlu, nxr
1257	DO j = nys, nyn
1258	DO k = nzb+1, nzt
1259	u_p(k,j,i) = u(k,j,i) + ( dt_3d * ( tsc(2) * tend(k,j,i) + &
1260	tsc(3) * tu_m(k,j,i) ) &
1261	- tsc(5) * rdf(k) * &
1262	( u(k,j,i) - u_init(k) ) &
1263	) * MERGE( 1.0_wp, 0.0_wp, &
1264	BTEST( wall_flags_0(k,j,i), 1 ) &
1265	)
1266	ENDDO
1267	ENDDO
1268	ENDDO
1269
1270	!
1271	!-- Calculate tendencies for the next Runge-Kutta step
1272	IF ( timestep_scheme(1:5) == 'runge' ) THEN
1273	IF ( intermediate_timestep_count == 1 ) THEN
1274	DO i = nxlu, nxr
1275	DO j = nys, nyn
1276	DO k = nzb+1, nzt
1277	tu_m(k,j,i) = tend(k,j,i)
1278	ENDDO
1279	ENDDO
1280	ENDDO
1281	ELSEIF ( intermediate_timestep_count < &
1282	intermediate_timestep_count_max ) THEN
1283	DO i = nxlu, nxr
1284	DO j = nys, nyn
1285	DO k = nzb+1, nzt
1286	tu_m(k,j,i) = -9.5625_wp * tend(k,j,i) &
1287	+ 5.3125_wp * tu_m(k,j,i)
1288	ENDDO
1289	ENDDO
1290	ENDDO
1291	ENDIF
1292	ENDIF
1293
1294	CALL cpu_log( log_point(5), 'u-equation', 'stop' )
1295
1296	!
1297	!-- v-velocity component
1298	CALL cpu_log( log_point(6), 'v-equation', 'start' )
1299
1300	tend = 0.0_wp
1301	IF ( timestep_scheme(1:5) == 'runge' ) THEN
1302	IF ( ws_scheme_mom ) THEN
1303	CALL advec_v_ws
1304	ELSE
1305	CALL advec_v_pw
1306	END IF
1307	ELSE
1308	CALL advec_v_up
1309	ENDIF
1310	CALL diffusion_v
1311	CALL coriolis( 2 )
1312
1313	!
1314	!-- Drag by plant canopy
1315	IF ( plant_canopy ) CALL pcm_tendency( 2 )
1316
1317	!
1318	!-- External pressure gradient
1319	IF ( dp_external ) THEN
1320	DO i = nxl, nxr
1321	DO j = nysv, nyn
1322	DO k = dp_level_ind_b+1, nzt
1323	tend(k,j,i) = tend(k,j,i) - dpdxy(2) * dp_smooth_factor(k)
1324	ENDDO
1325	ENDDO
1326	ENDDO
1327	ENDIF
1328
1329	!
1330	!-- Nudging
1331	IF ( nudging ) CALL nudge( simulated_time, 'v' )
1332
1333	!
1334	!-- Forces by wind turbines
1335	IF ( wind_turbine ) CALL wtm_tendencies( 2 )
1336
1337	CALL user_actions( 'v-tendency' )
1338
1339	!
1340	!-- Prognostic equation for v-velocity component
1341	DO i = nxl, nxr
1342	DO j = nysv, nyn
1343	DO k = nzb+1, nzt
1344	v_p(k,j,i) = v(k,j,i) + ( dt_3d * ( tsc(2) * tend(k,j,i) + &
1345	tsc(3) * tv_m(k,j,i) ) &
1346	- tsc(5) * rdf(k) * &
1347	( v(k,j,i) - v_init(k) ) &
1348	) * MERGE( 1.0_wp, 0.0_wp, &
1349	BTEST( wall_flags_0(k,j,i), 2 )&
1350	)
1351	ENDDO
1352	ENDDO
1353	ENDDO
1354
1355	!
1356	!-- Calculate tendencies for the next Runge-Kutta step
1357	IF ( timestep_scheme(1:5) == 'runge' ) THEN
1358	IF ( intermediate_timestep_count == 1 ) THEN
1359	DO i = nxl, nxr
1360	DO j = nysv, nyn
1361	DO k = nzb+1, nzt
1362	tv_m(k,j,i) = tend(k,j,i)
1363	ENDDO
1364	ENDDO
1365	ENDDO
1366	ELSEIF ( intermediate_timestep_count < &
1367	intermediate_timestep_count_max ) THEN
1368	DO i = nxl, nxr
1369	DO j = nysv, nyn
1370	DO k = nzb+1, nzt
1371	tv_m(k,j,i) = -9.5625_wp * tend(k,j,i) &
1372	+ 5.3125_wp * tv_m(k,j,i)
1373	ENDDO
1374	ENDDO
1375	ENDDO
1376	ENDIF
1377	ENDIF
1378
1379	CALL cpu_log( log_point(6), 'v-equation', 'stop' )
1380
1381	!
1382	!-- w-velocity component
1383	CALL cpu_log( log_point(7), 'w-equation', 'start' )
1384
1385	tend = 0.0_wp
1386	IF ( timestep_scheme(1:5) == 'runge' ) THEN
1387	IF ( ws_scheme_mom ) THEN
1388	CALL advec_w_ws
1389	ELSE
1390	CALL advec_w_pw
1391	ENDIF
1392	ELSE
1393	CALL advec_w_up
1394	ENDIF
1395	CALL diffusion_w
1396	CALL coriolis( 3 )
1397
1398	IF ( .NOT. neutral ) THEN
1399	IF ( ocean ) THEN
1400	CALL buoyancy( rho_ocean, 3 )
1401	ELSE
1402	IF ( .NOT. humidity ) THEN
1403	CALL buoyancy( pt, 3 )
1404	ELSE
1405	CALL buoyancy( vpt, 3 )
1406	ENDIF
1407	ENDIF
1408	ENDIF
1409
1410	!
1411	!-- Drag by plant canopy
1412	IF ( plant_canopy ) CALL pcm_tendency( 3 )
1413
1414	!
1415	!-- Forces by wind turbines
1416	IF ( wind_turbine ) CALL wtm_tendencies( 3 )
1417
1418	CALL user_actions( 'w-tendency' )
1419
1420	!
1421	!-- Prognostic equation for w-velocity component
1422	DO i = nxl, nxr
1423	DO j = nys, nyn
1424	DO k = nzb+1, nzt-1
1425	w_p(k,j,i) = w(k,j,i) + ( dt_3d * ( tsc(2) * tend(k,j,i) + &
1426	tsc(3) * tw_m(k,j,i) ) &
1427	- tsc(5) * rdf(k) * w(k,j,i) &
1428	) * MERGE( 1.0_wp, 0.0_wp, &
1429	BTEST( wall_flags_0(k,j,i), 3 )&
1430	)
1431	ENDDO
1432	ENDDO
1433	ENDDO
1434
1435	!
1436	!-- Calculate tendencies for the next Runge-Kutta step
1437	IF ( timestep_scheme(1:5) == 'runge' ) THEN
1438	IF ( intermediate_timestep_count == 1 ) THEN
1439	DO i = nxl, nxr
1440	DO j = nys, nyn
1441	DO k = nzb+1, nzt-1
1442	tw_m(k,j,i) = tend(k,j,i)
1443	ENDDO
1444	ENDDO
1445	ENDDO
1446	ELSEIF ( intermediate_timestep_count < &
1447	intermediate_timestep_count_max ) THEN
1448	DO i = nxl, nxr
1449	DO j = nys, nyn
1450	DO k = nzb+1, nzt-1
1451	tw_m(k,j,i) = -9.5625_wp * tend(k,j,i) &
1452	+ 5.3125_wp * tw_m(k,j,i)
1453	ENDDO
1454	ENDDO
1455	ENDDO
1456	ENDIF
1457	ENDIF
1458
1459	CALL cpu_log( log_point(7), 'w-equation', 'stop' )
1460
1461
1462	!
1463	!-- If required, compute prognostic equation for potential temperature
1464	IF ( .NOT. neutral ) THEN
1465
1466	CALL cpu_log( log_point(13), 'pt-equation', 'start' )
1467
1468	!
1469	!-- pt-tendency terms with communication
1470	sbt = tsc(2)
1471	IF ( scalar_advec == 'bc-scheme' ) THEN
1472
1473	IF ( timestep_scheme(1:5) /= 'runge' ) THEN
1474	!
1475	!-- Bott-Chlond scheme always uses Euler time step. Thus:
1476	sbt = 1.0_wp
1477	ENDIF
1478	tend = 0.0_wp
1479	CALL advec_s_bc( pt, 'pt' )
1480
1481	ENDIF
1482
1483	!
1484	!-- pt-tendency terms with no communication
1485	IF ( scalar_advec /= 'bc-scheme' ) THEN
1486	tend = 0.0_wp
1487	IF ( timestep_scheme(1:5) == 'runge' ) THEN
1488	IF ( ws_scheme_sca ) THEN
1489	CALL advec_s_ws( pt, 'pt' )
1490	ELSE
1491	CALL advec_s_pw( pt )
1492	ENDIF
1493	ELSE
1494	CALL advec_s_up( pt )
1495	ENDIF
1496	ENDIF
1497
1498	CALL diffusion_s( pt, &
1499	surf_def_h(0)%shf, surf_def_h(1)%shf, &
1500	surf_def_h(2)%shf, &
1501	surf_lsm_h%shf, surf_usm_h%shf, &
1502	surf_def_v(0)%shf, surf_def_v(1)%shf, &
1503	surf_def_v(2)%shf, surf_def_v(3)%shf, &
1504	surf_lsm_v(0)%shf, surf_lsm_v(1)%shf, &
1505	surf_lsm_v(2)%shf, surf_lsm_v(3)%shf, &
1506	surf_usm_v(0)%shf, surf_usm_v(1)%shf, &
1507	surf_usm_v(2)%shf, surf_usm_v(3)%shf )
1508	!
1509	!-- If required compute heating/cooling due to long wave radiation processes
1510	IF ( cloud_top_radiation ) THEN
1511	CALL calc_radiation
1512	ENDIF
1513
1514	!
1515	!-- Consideration of heat sources within the plant canopy
1516	IF ( plant_canopy .AND. ( cthf /= 0.0_wp ) ) THEN
1517	CALL pcm_tendency( 4 )
1518	ENDIF
1519
1520	!
1521	!-- Large scale advection
1522	IF ( large_scale_forcing ) THEN
1523	CALL ls_advec( simulated_time, 'pt' )
1524	ENDIF
1525
1526	!
1527	!-- Nudging
1528	IF ( nudging ) CALL nudge( simulated_time, 'pt' )
1529
1530	!
1531	!-- If required compute influence of large-scale subsidence/ascent
1532	IF ( large_scale_subsidence .AND. &
1533	.NOT. use_subsidence_tendencies ) THEN
1534	CALL subsidence( tend, pt, pt_init, 2 )
1535	ENDIF
1536
1537	!
1538	!-- If required, add tendency due to radiative heating/cooling
1539	IF ( radiation .AND. &
1540	simulated_time > skip_time_do_radiation ) THEN
1541	CALL radiation_tendency ( tend )
1542	ENDIF
1543
1544	CALL user_actions( 'pt-tendency' )
1545
1546	!
1547	!-- Prognostic equation for potential temperature
1548	DO i = nxl, nxr
1549	DO j = nys, nyn
1550	DO k = nzb+1, nzt
1551	pt_p(k,j,i) = pt(k,j,i) + ( dt_3d * ( sbt * tend(k,j,i) + &
1552	tsc(3) * tpt_m(k,j,i) ) &
1553	- tsc(5) * &
1554	( pt(k,j,i) - pt_init(k) ) *&
1555	( rdf_sc(k) + ptdf_x(i) + ptdf_y(j) )&
1556	) &
1557	* MERGE( 1.0_wp, 0.0_wp, &
1558	BTEST( wall_flags_0(k,j,i), 0 ) &
1559	)
1560	ENDDO
1561	ENDDO
1562	ENDDO
1563
1564	!
1565	!-- Calculate tendencies for the next Runge-Kutta step
1566	IF ( timestep_scheme(1:5) == 'runge' ) THEN
1567	IF ( intermediate_timestep_count == 1 ) THEN
1568	DO i = nxl, nxr
1569	DO j = nys, nyn
1570	DO k = nzb+1, nzt
1571	tpt_m(k,j,i) = tend(k,j,i)
1572	ENDDO
1573	ENDDO
1574	ENDDO
1575	ELSEIF ( intermediate_timestep_count < &
1576	intermediate_timestep_count_max ) THEN
1577	DO i = nxl, nxr
1578	DO j = nys, nyn
1579	DO k = nzb+1, nzt
1580	tpt_m(k,j,i) = -9.5625_wp * tend(k,j,i) + &
1581	5.3125_wp * tpt_m(k,j,i)
1582	ENDDO
1583	ENDDO
1584	ENDDO
1585	ENDIF
1586	ENDIF
1587
1588	CALL cpu_log( log_point(13), 'pt-equation', 'stop' )
1589
1590	ENDIF
1591
1592	!
1593	!-- If required, compute prognostic equation for salinity
1594	IF ( ocean ) THEN
1595
1596	CALL cpu_log( log_point(37), 'sa-equation', 'start' )
1597
1598	!
1599	!-- sa-tendency terms with communication
1600	sbt = tsc(2)
1601	IF ( scalar_advec == 'bc-scheme' ) THEN
1602
1603	IF ( timestep_scheme(1:5) /= 'runge' ) THEN
1604	!
1605	!-- Bott-Chlond scheme always uses Euler time step. Thus:
1606	sbt = 1.0_wp
1607	ENDIF
1608	tend = 0.0_wp
1609	CALL advec_s_bc( sa, 'sa' )
1610
1611	ENDIF
1612
1613	!
1614	!-- sa-tendency terms with no communication
1615	IF ( scalar_advec /= 'bc-scheme' ) THEN
1616	tend = 0.0_wp
1617	IF ( timestep_scheme(1:5) == 'runge' ) THEN
1618	IF ( ws_scheme_sca ) THEN
1619	CALL advec_s_ws( sa, 'sa' )
1620	ELSE
1621	CALL advec_s_pw( sa )
1622	ENDIF
1623	ELSE
1624	CALL advec_s_up( sa )
1625	ENDIF
1626	ENDIF
1627
1628	CALL diffusion_s( sa, &
1629	surf_def_h(0)%sasws, surf_def_h(1)%sasws, &
1630	surf_def_h(2)%sasws, &
1631	surf_lsm_h%sasws, surf_usm_h%sasws, &
1632	surf_def_v(0)%sasws, surf_def_v(1)%sasws, &
1633	surf_def_v(2)%sasws, surf_def_v(3)%sasws, &
1634	surf_lsm_v(0)%sasws, surf_lsm_v(1)%sasws, &
1635	surf_lsm_v(2)%sasws, surf_lsm_v(3)%sasws, &
1636	surf_usm_v(0)%sasws, surf_usm_v(1)%sasws, &
1637	surf_usm_v(2)%sasws, surf_usm_v(3)%sasws )
1638
1639	CALL user_actions( 'sa-tendency' )
1640
1641	!
1642	!-- Prognostic equation for salinity
1643	DO i = nxl, nxr
1644	DO j = nys, nyn
1645	DO k = nzb+1, nzt
1646	sa_p(k,j,i) = sa(k,j,i) + ( dt_3d * ( sbt * tend(k,j,i) + &
1647	tsc(3) * tsa_m(k,j,i) ) &
1648	- tsc(5) * rdf_sc(k) * &
1649	( sa(k,j,i) - sa_init(k) ) &
1650	) &
1651	* MERGE( 1.0_wp, 0.0_wp, &
1652	BTEST( wall_flags_0(k,j,i), 0 ) &
1653	)
1654	IF ( sa_p(k,j,i) < 0.0_wp ) sa_p(k,j,i) = 0.1_wp * sa(k,j,i)
1655	ENDDO
1656	ENDDO
1657	ENDDO
1658
1659	!
1660	!-- Calculate tendencies for the next Runge-Kutta step
1661	IF ( timestep_scheme(1:5) == 'runge' ) THEN
1662	IF ( intermediate_timestep_count == 1 ) THEN
1663	DO i = nxl, nxr
1664	DO j = nys, nyn
1665	DO k = nzb+1, nzt
1666	tsa_m(k,j,i) = tend(k,j,i)
1667	ENDDO
1668	ENDDO
1669	ENDDO
1670	ELSEIF ( intermediate_timestep_count < &
1671	intermediate_timestep_count_max ) THEN
1672	DO i = nxl, nxr
1673	DO j = nys, nyn
1674	DO k = nzb+1, nzt
1675	tsa_m(k,j,i) = -9.5625_wp * tend(k,j,i) + &
1676	5.3125_wp * tsa_m(k,j,i)
1677	ENDDO
1678	ENDDO
1679	ENDDO
1680	ENDIF
1681	ENDIF
1682
1683	CALL cpu_log( log_point(37), 'sa-equation', 'stop' )
1684
1685	!
1686	!-- Calculate density by the equation of state for seawater
1687	CALL cpu_log( log_point(38), 'eqns-seawater', 'start' )
1688	CALL eqn_state_seawater
1689	CALL cpu_log( log_point(38), 'eqns-seawater', 'stop' )
1690
1691	ENDIF
1692
1693	!
1694	!-- If required, compute prognostic equation for total water content
1695	IF ( humidity ) THEN
1696
1697	CALL cpu_log( log_point(29), 'q-equation', 'start' )
1698
1699	!
1700	!-- Scalar/q-tendency terms with communication
1701	sbt = tsc(2)
1702	IF ( scalar_advec == 'bc-scheme' ) THEN
1703
1704	IF ( timestep_scheme(1:5) /= 'runge' ) THEN
1705	!
1706	!-- Bott-Chlond scheme always uses Euler time step. Thus:
1707	sbt = 1.0_wp
1708	ENDIF
1709	tend = 0.0_wp
1710	CALL advec_s_bc( q, 'q' )
1711
1712	ENDIF
1713
1714	!
1715	!-- Scalar/q-tendency terms with no communication
1716	IF ( scalar_advec /= 'bc-scheme' ) THEN
1717	tend = 0.0_wp
1718	IF ( timestep_scheme(1:5) == 'runge' ) THEN
1719	IF ( ws_scheme_sca ) THEN
1720	CALL advec_s_ws( q, 'q' )
1721	ELSE
1722	CALL advec_s_pw( q )
1723	ENDIF
1724	ELSE
1725	CALL advec_s_up( q )
1726	ENDIF
1727	ENDIF
1728
1729	CALL diffusion_s( q, &
1730	surf_def_h(0)%qsws, surf_def_h(1)%qsws, &
1731	surf_def_h(2)%qsws, &
1732	surf_lsm_h%qsws, surf_usm_h%qsws, &
1733	surf_def_v(0)%qsws, surf_def_v(1)%qsws, &
1734	surf_def_v(2)%qsws, surf_def_v(3)%qsws, &
1735	surf_lsm_v(0)%qsws, surf_lsm_v(1)%qsws, &
1736	surf_lsm_v(2)%qsws, surf_lsm_v(3)%qsws, &
1737	surf_usm_v(0)%qsws, surf_usm_v(1)%qsws, &
1738	surf_usm_v(2)%qsws, surf_usm_v(3)%qsws )
1739
1740	!
1741	!-- Sink or source of humidity due to canopy elements
1742	IF ( plant_canopy ) CALL pcm_tendency( 5 )
1743
1744	!
1745	!-- Large scale advection
1746	IF ( large_scale_forcing ) THEN
1747	CALL ls_advec( simulated_time, 'q' )
1748	ENDIF
1749
1750	!
1751	!-- Nudging
1752	IF ( nudging ) CALL nudge( simulated_time, 'q' )
1753
1754	!
1755	!-- If required compute influence of large-scale subsidence/ascent
1756	IF ( large_scale_subsidence .AND. &
1757	.NOT. use_subsidence_tendencies ) THEN
1758	CALL subsidence( tend, q, q_init, 3 )
1759	ENDIF
1760
1761	CALL user_actions( 'q-tendency' )
1762
1763	!
1764	!-- Prognostic equation for total water content
1765	DO i = nxl, nxr
1766	DO j = nys, nyn
1767	DO k = nzb+1, nzt
1768	q_p(k,j,i) = q(k,j,i) + ( dt_3d * ( sbt * tend(k,j,i) + &
1769	tsc(3) * tq_m(k,j,i) ) &
1770	- tsc(5) * rdf_sc(k) * &
1771	( q(k,j,i) - q_init(k) ) &
1772	) * MERGE( 1.0_wp, 0.0_wp, &
1773	BTEST( wall_flags_0(k,j,i), 0 ) &
1774	)
1775	IF ( q_p(k,j,i) < 0.0_wp ) q_p(k,j,i) = 0.1_wp * q(k,j,i)
1776	ENDDO
1777	ENDDO
1778	ENDDO
1779
1780	!
1781	!-- Calculate tendencies for the next Runge-Kutta step
1782	IF ( timestep_scheme(1:5) == 'runge' ) THEN
1783	IF ( intermediate_timestep_count == 1 ) THEN
1784	DO i = nxl, nxr
1785	DO j = nys, nyn
1786	DO k = nzb+1, nzt
1787	tq_m(k,j,i) = tend(k,j,i)
1788	ENDDO
1789	ENDDO
1790	ENDDO
1791	ELSEIF ( intermediate_timestep_count < &
1792	intermediate_timestep_count_max ) THEN
1793	DO i = nxl, nxr
1794	DO j = nys, nyn
1795	DO k = nzb+1, nzt
1796	tq_m(k,j,i) = -9.5625_wp * tend(k,j,i) &
1797	+ 5.3125_wp * tq_m(k,j,i)
1798	ENDDO
1799	ENDDO
1800	ENDDO
1801	ENDIF
1802	ENDIF
1803
1804	CALL cpu_log( log_point(29), 'q-equation', 'stop' )
1805
1806	!
1807	!-- If required, calculate prognostic equations for rain water content
1808	!-- and rain drop concentration
1809	IF ( cloud_physics .AND. microphysics_seifert ) THEN
1810
1811	CALL cpu_log( log_point(52), 'qr-equation', 'start' )
1812
1813	!
1814	!-- Calculate prognostic equation for rain water content
1815	sbt = tsc(2)
1816	IF ( scalar_advec == 'bc-scheme' ) THEN
1817
1818	IF ( timestep_scheme(1:5) /= 'runge' ) THEN
1819	!
1820	!-- Bott-Chlond scheme always uses Euler time step. Thus:
1821	sbt = 1.0_wp
1822	ENDIF
1823	tend = 0.0_wp
1824	CALL advec_s_bc( qr, 'qr' )
1825
1826	ENDIF
1827
1828	!
1829	!-- qr-tendency terms with no communication
1830	IF ( scalar_advec /= 'bc-scheme' ) THEN
1831	tend = 0.0_wp
1832	IF ( timestep_scheme(1:5) == 'runge' ) THEN
1833	IF ( ws_scheme_sca ) THEN
1834	CALL advec_s_ws( qr, 'qr' )
1835	ELSE
1836	CALL advec_s_pw( qr )
1837	ENDIF
1838	ELSE
1839	CALL advec_s_up( qr )
1840	ENDIF
1841	ENDIF
1842
1843	CALL diffusion_s( qr, &
1844	surf_def_h(0)%qrsws, surf_def_h(1)%qrsws, &
1845	surf_def_h(2)%qrsws, &
1846	surf_lsm_h%qrsws, surf_usm_h%qrsws, &
1847	surf_def_v(0)%qrsws, surf_def_v(1)%qrsws, &
1848	surf_def_v(2)%qrsws, surf_def_v(3)%qrsws, &
1849	surf_lsm_v(0)%qrsws, surf_lsm_v(1)%qrsws, &
1850	surf_lsm_v(2)%qrsws, surf_lsm_v(3)%qrsws, &
1851	surf_usm_v(0)%qrsws, surf_usm_v(1)%qrsws, &
1852	surf_usm_v(2)%qrsws, surf_usm_v(3)%qrsws )
1853
1854	!
1855	!-- Prognostic equation for rain water content
1856	DO i = nxl, nxr
1857	DO j = nys, nyn
1858	DO k = nzb+1, nzt
1859	qr_p(k,j,i) = qr(k,j,i) + ( dt_3d * ( sbt * tend(k,j,i) + &
1860	tsc(3) * tqr_m(k,j,i) ) &
1861	- tsc(5) * rdf_sc(k) * &
1862	qr(k,j,i) &
1863	) &
1864	* MERGE( 1.0_wp, 0.0_wp, &
1865	BTEST( wall_flags_0(k,j,i), 0 ) &
1866	)
1867	IF ( qr_p(k,j,i) < 0.0_wp ) qr_p(k,j,i) = 0.0_wp
1868	ENDDO
1869	ENDDO
1870	ENDDO
1871
1872	!
1873	!-- Calculate tendencies for the next Runge-Kutta step
1874	IF ( timestep_scheme(1:5) == 'runge' ) THEN
1875	IF ( intermediate_timestep_count == 1 ) THEN
1876	DO i = nxl, nxr
1877	DO j = nys, nyn
1878	DO k = nzb+1, nzt
1879	tqr_m(k,j,i) = tend(k,j,i)
1880	ENDDO
1881	ENDDO
1882	ENDDO
1883	ELSEIF ( intermediate_timestep_count < &
1884	intermediate_timestep_count_max ) THEN
1885	DO i = nxl, nxr
1886	DO j = nys, nyn
1887	DO k = nzb+1, nzt
1888	tqr_m(k,j,i) = -9.5625_wp * tend(k,j,i) &
1889	+ 5.3125_wp * tqr_m(k,j,i)
1890	ENDDO
1891	ENDDO
1892	ENDDO
1893	ENDIF
1894	ENDIF
1895
1896	CALL cpu_log( log_point(52), 'qr-equation', 'stop' )
1897	CALL cpu_log( log_point(53), 'nr-equation', 'start' )
1898
1899	!
1900	!-- Calculate prognostic equation for rain drop concentration
1901	sbt = tsc(2)
1902	IF ( scalar_advec == 'bc-scheme' ) THEN
1903
1904	IF ( timestep_scheme(1:5) /= 'runge' ) THEN
1905	!
1906	!-- Bott-Chlond scheme always uses Euler time step. Thus:
1907	sbt = 1.0_wp
1908	ENDIF
1909	tend = 0.0_wp
1910	CALL advec_s_bc( nr, 'nr' )
1911
1912	ENDIF
1913
1914	!
1915	!-- nr-tendency terms with no communication
1916	IF ( scalar_advec /= 'bc-scheme' ) THEN
1917	tend = 0.0_wp
1918	IF ( timestep_scheme(1:5) == 'runge' ) THEN
1919	IF ( ws_scheme_sca ) THEN
1920	CALL advec_s_ws( nr, 'nr' )
1921	ELSE
1922	CALL advec_s_pw( nr )
1923	ENDIF
1924	ELSE
1925	CALL advec_s_up( nr )
1926	ENDIF
1927	ENDIF
1928
1929	CALL diffusion_s( nr, &
1930	surf_def_h(0)%nrsws, surf_def_h(1)%nrsws, &
1931	surf_def_h(2)%nrsws, &
1932	surf_lsm_h%nrsws, surf_usm_h%nrsws, &
1933	surf_def_v(0)%nrsws, surf_def_v(1)%nrsws, &
1934	surf_def_v(2)%nrsws, surf_def_v(3)%nrsws, &
1935	surf_lsm_v(0)%nrsws, surf_lsm_v(1)%nrsws, &
1936	surf_lsm_v(2)%nrsws, surf_lsm_v(3)%nrsws, &
1937	surf_usm_v(0)%nrsws, surf_usm_v(1)%nrsws, &
1938	surf_usm_v(2)%nrsws, surf_usm_v(3)%nrsws )
1939
1940	!
1941	!-- Prognostic equation for rain drop concentration
1942	DO i = nxl, nxr
1943	DO j = nys, nyn
1944	DO k = nzb+1, nzt
1945	nr_p(k,j,i) = nr(k,j,i) + ( dt_3d * ( sbt * tend(k,j,i) + &
1946	tsc(3) * tnr_m(k,j,i) ) &
1947	- tsc(5) * rdf_sc(k) * &
1948	nr(k,j,i) &
1949	) &
1950	* MERGE( 1.0_wp, 0.0_wp, &
1951	BTEST( wall_flags_0(k,j,i), 0 ) &
1952	)
1953	IF ( nr_p(k,j,i) < 0.0_wp ) nr_p(k,j,i) = 0.0_wp
1954	ENDDO
1955	ENDDO
1956	ENDDO
1957
1958	!
1959	!-- Calculate tendencies for the next Runge-Kutta step
1960	IF ( timestep_scheme(1:5) == 'runge' ) THEN
1961	IF ( intermediate_timestep_count == 1 ) THEN
1962	DO i = nxl, nxr
1963	DO j = nys, nyn
1964	DO k = nzb+1, nzt
1965	tnr_m(k,j,i) = tend(k,j,i)
1966	ENDDO
1967	ENDDO
1968	ENDDO
1969	ELSEIF ( intermediate_timestep_count < &
1970	intermediate_timestep_count_max ) THEN
1971	DO i = nxl, nxr
1972	DO j = nys, nyn
1973	DO k = nzb+1, nzt
1974	tnr_m(k,j,i) = -9.5625_wp * tend(k,j,i) &
1975	+ 5.3125_wp * tnr_m(k,j,i)
1976	ENDDO
1977	ENDDO
1978	ENDDO
1979	ENDIF
1980	ENDIF
1981
1982	CALL cpu_log( log_point(53), 'nr-equation', 'stop' )
1983
1984	ENDIF
1985
1986	ENDIF
1987	!
1988	!-- If required, compute prognostic equation for scalar
1989	IF ( passive_scalar ) THEN
1990
1991	CALL cpu_log( log_point(66), 's-equation', 'start' )
1992
1993	!
1994	!-- Scalar/q-tendency terms with communication
1995	sbt = tsc(2)
1996	IF ( scalar_advec == 'bc-scheme' ) THEN
1997
1998	IF ( timestep_scheme(1:5) /= 'runge' ) THEN
1999	!
2000	!-- Bott-Chlond scheme always uses Euler time step. Thus:
2001	sbt = 1.0_wp
2002	ENDIF
2003	tend = 0.0_wp
2004	CALL advec_s_bc( s, 's' )
2005
2006	ENDIF
2007
2008	!
2009	!-- Scalar/q-tendency terms with no communication
2010	IF ( scalar_advec /= 'bc-scheme' ) THEN
2011	tend = 0.0_wp
2012	IF ( timestep_scheme(1:5) == 'runge' ) THEN
2013	IF ( ws_scheme_sca ) THEN
2014	CALL advec_s_ws( s, 's' )
2015	ELSE
2016	CALL advec_s_pw( s )
2017	ENDIF
2018	ELSE
2019	CALL advec_s_up( s )
2020	ENDIF
2021	ENDIF
2022
2023	CALL diffusion_s( s, &
2024	surf_def_h(0)%ssws, surf_def_h(1)%ssws, &
2025	surf_def_h(2)%ssws, &
2026	surf_lsm_h%ssws, surf_usm_h%ssws, &
2027	surf_def_v(0)%ssws, surf_def_v(1)%ssws, &
2028	surf_def_v(2)%ssws, surf_def_v(3)%ssws, &
2029	surf_lsm_v(0)%ssws, surf_lsm_v(1)%ssws, &
2030	surf_lsm_v(2)%ssws, surf_lsm_v(3)%ssws, &
2031	surf_usm_v(0)%ssws, surf_usm_v(1)%ssws, &
2032	surf_usm_v(2)%ssws, surf_usm_v(3)%ssws )
2033
2034	!
2035	!-- Sink or source of humidity due to canopy elements
2036	IF ( plant_canopy ) CALL pcm_tendency( 7 )
2037
2038	!
2039	!-- Large scale advection. Not implemented for scalars so far.
2040	! IF ( large_scale_forcing ) THEN
2041	! CALL ls_advec( simulated_time, 'q' )
2042	! ENDIF
2043
2044	!
2045	!-- Nudging. Not implemented for scalars so far.
2046	! IF ( nudging ) CALL nudge( simulated_time, 'q' )
2047
2048	!
2049	!-- If required compute influence of large-scale subsidence/ascent.
2050	!-- Not implemented for scalars so far.
2051	IF ( large_scale_subsidence .AND. &
2052	.NOT. use_subsidence_tendencies .AND. &
2053	.NOT. large_scale_forcing ) THEN
2054	CALL subsidence( tend, s, s_init, 3 )
2055	ENDIF
2056
2057	CALL user_actions( 's-tendency' )
2058
2059	!
2060	!-- Prognostic equation for total water content
2061	DO i = nxl, nxr
2062	DO j = nys, nyn
2063	DO k = nzb+1, nzt
2064	s_p(k,j,i) = s(k,j,i) + ( dt_3d * ( sbt * tend(k,j,i) + &
2065	tsc(3) * ts_m(k,j,i) ) &
2066	- tsc(5) * rdf_sc(k) * &
2067	( s(k,j,i) - s_init(k) ) &
2068	) &
2069	* MERGE( 1.0_wp, 0.0_wp, &
2070	BTEST( wall_flags_0(k,j,i), 0 ) &
2071	)
2072	IF ( s_p(k,j,i) < 0.0_wp ) s_p(k,j,i) = 0.1_wp * s(k,j,i)
2073	ENDDO
2074	ENDDO
2075	ENDDO
2076
2077	!
2078	!-- Calculate tendencies for the next Runge-Kutta step
2079	IF ( timestep_scheme(1:5) == 'runge' ) THEN
2080	IF ( intermediate_timestep_count == 1 ) THEN
2081	DO i = nxl, nxr
2082	DO j = nys, nyn
2083	DO k = nzb+1, nzt
2084	ts_m(k,j,i) = tend(k,j,i)
2085	ENDDO
2086	ENDDO
2087	ENDDO
2088	ELSEIF ( intermediate_timestep_count < &
2089	intermediate_timestep_count_max ) THEN
2090	DO i = nxl, nxr
2091	DO j = nys, nyn
2092	DO k = nzb+1, nzt
2093	ts_m(k,j,i) = -9.5625_wp * tend(k,j,i) &
2094	+ 5.3125_wp * ts_m(k,j,i)
2095	ENDDO
2096	ENDDO
2097	ENDDO
2098	ENDIF
2099	ENDIF
2100
2101	CALL cpu_log( log_point(66), 's-equation', 'stop' )
2102
2103	ENDIF
2104	!
2105	!-- If required, compute prognostic equation for turbulent kinetic
2106	!-- energy (TKE)
2107	IF ( .NOT. constant_diffusion ) THEN
2108
2109	CALL cpu_log( log_point(16), 'tke-equation', 'start' )
2110
2111	sbt = tsc(2)
2112	IF ( .NOT. use_upstream_for_tke ) THEN
2113	IF ( scalar_advec == 'bc-scheme' ) THEN
2114
2115	IF ( timestep_scheme(1:5) /= 'runge' ) THEN
2116	!
2117	!-- Bott-Chlond scheme always uses Euler time step. Thus:
2118	sbt = 1.0_wp
2119	ENDIF
2120	tend = 0.0_wp
2121	CALL advec_s_bc( e, 'e' )
2122
2123	ENDIF
2124	ENDIF
2125
2126	!
2127	!-- TKE-tendency terms with no communication
2128	IF ( scalar_advec /= 'bc-scheme' .OR. use_upstream_for_tke ) THEN
2129	IF ( use_upstream_for_tke ) THEN
2130	tend = 0.0_wp
2131	CALL advec_s_up( e )
2132	ELSE
2133	tend = 0.0_wp
2134	IF ( timestep_scheme(1:5) == 'runge' ) THEN
2135	IF ( ws_scheme_sca ) THEN
2136	CALL advec_s_ws( e, 'e' )
2137	ELSE
2138	CALL advec_s_pw( e )
2139	ENDIF
2140	ELSE
2141	CALL advec_s_up( e )
2142	ENDIF
2143	ENDIF
2144	ENDIF
2145
2146	IF ( .NOT. humidity ) THEN
2147	IF ( ocean ) THEN
2148	CALL diffusion_e( prho, prho_reference )
2149	ELSE
2150	CALL diffusion_e( pt, pt_reference )
2151	ENDIF
2152	ELSE
2153	CALL diffusion_e( vpt, pt_reference )
2154	ENDIF
2155
2156	CALL production_e
2157
2158	!
2159	!-- Additional sink term for flows through plant canopies
2160	IF ( plant_canopy ) CALL pcm_tendency( 6 )
2161	CALL user_actions( 'e-tendency' )
2162
2163	!
2164	!-- Prognostic equation for TKE.
2165	!-- Eliminate negative TKE values, which can occur due to numerical
2166	!-- reasons in the course of the integration. In such cases the old TKE
2167	!-- value is reduced by 90%.
2168	DO i = nxl, nxr
2169	DO j = nys, nyn
2170	DO k = nzb+1, nzt
2171	e_p(k,j,i) = e(k,j,i) + ( dt_3d * ( sbt * tend(k,j,i) + &
2172	tsc(3) * te_m(k,j,i) ) &
2173	) &
2174	* MERGE( 1.0_wp, 0.0_wp, &
2175	BTEST( wall_flags_0(k,j,i), 0 ) &
2176	)
2177	IF ( e_p(k,j,i) < 0.0_wp ) e_p(k,j,i) = 0.1_wp * e(k,j,i)
2178	ENDDO
2179	ENDDO
2180	ENDDO
2181
2182	!
2183	!-- Calculate tendencies for the next Runge-Kutta step
2184	IF ( timestep_scheme(1:5) == 'runge' ) THEN
2185	IF ( intermediate_timestep_count == 1 ) THEN
2186	DO i = nxl, nxr
2187	DO j = nys, nyn
2188	DO k = nzb+1, nzt
2189	te_m(k,j,i) = tend(k,j,i)
2190	ENDDO
2191	ENDDO
2192	ENDDO
2193	ELSEIF ( intermediate_timestep_count < &
2194	intermediate_timestep_count_max ) THEN
2195	DO i = nxl, nxr
2196	DO j = nys, nyn
2197	DO k = nzb+1, nzt
2198	te_m(k,j,i) = -9.5625_wp * tend(k,j,i) &
2199	+ 5.3125_wp * te_m(k,j,i)
2200	ENDDO
2201	ENDDO
2202	ENDDO
2203	ENDIF
2204	ENDIF
2205
2206	CALL cpu_log( log_point(16), 'tke-equation', 'stop' )
2207
2208	ENDIF
2209
2210	END SUBROUTINE prognostic_equations_vector
2211
2212
2213	END MODULE prognostic_equations_mod

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