source: palm/trunk/SOURCE/time_integration_spinup.f90 @ 3719

Last change on this file since 3719 was 3719, checked in by kanani, 3 years ago

Correct and clean-up cpu_logs, some overlapping counts (chemistry_model_mod, disturb_heatflux, large_scale_forcing_nudging_mod, ocean_mod, palm, prognostic_equations, synthetic_turbulence_generator_mod, time_integration, time_integration_spinup, turbulence_closure_mod)

  • Property svn:keywords set to Id
File size: 21.7 KB
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1!> @file time_integration_spinup.f90
2!------------------------------------------------------------------------------!
3! This file is part of the PALM model system.
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 1997-2019 Leibniz Universitaet Hannover
18!------------------------------------------------------------------------------!
19!
20! Current revisions:
21! ------------------
22!
23!
24! Former revisions:
25! -----------------
26! $Id: time_integration_spinup.f90 3719 2019-02-06 13:10:18Z kanani $
27! Removed log_point(19,54,74,50,75), since they count together with same log
28! points in time_integration, impossible to separate the contributions.
29! Instead, the entire spinup gets an individual log_point in palm.f90
30!
31! 3655 2019-01-07 16:51:22Z knoop
32! Removed call to calculation of near air (10 cm) potential temperature (now in
33! surface layer fluxes)
34!
35! 3467 2018-10-30 19:05:21Z suehring
36! call to material_heat_model now with check if spinup runs (rvtils)
37!
38! 3337 2018-10-12 15:17:09Z kanani
39! (from branch resler)
40! Add pt1 initialization
41!
42! 3274 2018-09-24 15:42:55Z knoop
43! Modularization of all bulk cloud physics code components
44!
45! 3241 2018-09-12 15:02:00Z raasch
46! unused variables removed
47!
48! 2983 2018-04-18 10:43:40Z suehring
49! Revise limitation of wall-adjacent velocity.
50!
51! 2934 2018-03-26 19:13:22Z suehring
52! Synchronize parent and child models after spinup.
53!
54! 2881 2018-03-13 16:24:40Z maronga
55! Added flag for switching on/off calculation of soil moisture
56!
57! 2818 2018-02-19 16:42:36Z maronga
58! Velocity components near walls/ground are now set to the profiles stored in
59! u_init and v_init. Activated soil moisture calculation during spinup.
60!
61! 2782 2018-02-02 11:51:10Z maronga
62! Bugfix and re-activation of homogeneous setting of velocity components
63! during spinup
64!
65! 2758 2018-01-17 12:55:21Z suehring
66! Comment out homogeneous setting of wind velocity as this will lead to zero
67! friction velocity and cause problems in MOST relationships.
68!
69! 2728 2018-01-09 07:03:53Z maronga
70! Set velocity componenets to homogeneous values during spinup
71!
72! 2724 2018-01-05 12:12:38Z maronga
73! Use dt_spinup for all active components during spinup
74!
75! 2723 2018-01-05 09:27:03Z maronga
76! Bugfix: array rad_sw_in no longer exists and is thus removed from RUN_CONTROL
77! output.
78! Added output of XY and 3D data during spinup.
79! Bugfix: time step in LSM and USM was set to dt_3d instead of dt_spinup
80!
81! 2718 2018-01-02 08:49:38Z maronga
82! Corrected "Former revisions" section
83!
84! 2696 2017-12-14 17:12:51Z kanani
85! Change in file header (GPL part)
86! Added radiation interactions (moved from USM) (MS)
87!
88! 2544 2017-10-13 18:09:32Z maronga
89! Date and time quantities are now read from date_and_time_mod
90!
91! 2299 2017-06-29 10:14:38Z maronga
92! Call of soil model adjusted to avoid prognostic equation for soil moisture
93! during spinup.
94! Better representation of diurnal cycle of near-surface temperature.
95! Excluded prognostic equation for soil moisture during spinup.
96! Added output of run control data for spinup.
97!
98! 2297 2017-06-28 14:35:57Z scharf
99! bugfixes
100!
101! 2296 2017-06-28 07:53:56Z maronga
102! Initial revision
103!
104!
105! Description:
106! ------------
107!> Integration in time of the non-atmospheric model components such as land
108!> surface model and urban surface model
109!------------------------------------------------------------------------------!
110 SUBROUTINE time_integration_spinup
111 
112    USE arrays_3d,                                                             &
113        ONLY:  pt, pt_p, u, u_init, v, v_init
114
115    USE control_parameters,                                                    &
116        ONLY:  averaging_interval_pr, calc_soil_moisture_during_spinup,        &
117               constant_diffusion, constant_flux_layer, coupling_start_time,   &
118               data_output_during_spinup, dopr_n, do_sum,                      &
119               dt_averaging_input_pr, dt_dopr, dt_dots, dt_do2d_xy, dt_do3d,   &
120               dt_spinup, dt_3d, humidity, intermediate_timestep_count,        &
121               intermediate_timestep_count_max, land_surface,                  &
122               simulated_time, simulated_time_chr, skip_time_dopr,             &
123               skip_time_do2d_xy, skip_time_do3d, spinup_pt_amplitude,         &
124               spinup_pt_mean, spinup_time, timestep_count, time_dopr,         &
125               time_dopr_av, time_dots, time_do2d_xy, time_do3d,               &
126               time_run_control, time_since_reference_point, urban_surface
127
128    USE cpulog,                                                                &
129        ONLY:  cpu_log, log_point, log_point_s
130
131    USE date_and_time_mod,                                                     &
132        ONLY: day_of_year_init, time_utc_init
133
134    USE indices,                                                               &
135        ONLY:  nbgp, nzb, nzt, nysg, nyng, nxlg, nxrg
136
137
138    USE land_surface_model_mod,                                                &
139        ONLY:  lsm_energy_balance, lsm_soil_model, lsm_swap_timelevel
140    USE pegrid
141
142    USE pmc_interface,                                                         &
143        ONLY:  nested_run
144
145    USE kinds
146
147    USE radiation_model_mod,                                                   &
148        ONLY:  force_radiation_call, radiation, radiation_control,             &
149               radiation_interaction, radiation_interactions, time_radiation
150
151    USE statistics,                                                            &
152        ONLY:  flow_statistics_called
153
154    USE surface_layer_fluxes_mod,                                              &
155        ONLY:  surface_layer_fluxes
156
157    USE surface_mod,                                                           &
158        ONLY :  surf_lsm_h, surf_lsm_v, surf_usm_h,    &
159                surf_usm_v
160
161    USE urban_surface_mod,                                                     &
162        ONLY:  usm_material_heat_model, usm_material_model,                    &
163               usm_surface_energy_balance, usm_swap_timelevel,                 &
164               usm_green_heat_model
165
166
167
168
169    IMPLICIT NONE
170
171    CHARACTER (LEN=9) ::  time_to_string          !<
172 
173    INTEGER(iwp) ::  i !< running index
174    INTEGER(iwp) ::  j !< running index
175    INTEGER(iwp) ::  k !< running index
176    INTEGER(iwp) ::  l !< running index
177    INTEGER(iwp) ::  m !< running index
178
179    INTEGER(iwp) :: current_timestep_number_spinup = 0  !< number if timestep during spinup
180 
181    LOGICAL :: run_control_header_spinup = .FALSE.  !< flag parameter for steering whether the header information must be output
182
183    REAL(wp) ::  pt_spinup   !< temporary storage of temperature
184    REAL(wp) ::  dt_save     !< temporary storage for time step
185                 
186    REAL(wp), DIMENSION(:,:,:), ALLOCATABLE ::  pt_save  !< temporary storage of temperature
187    REAL(wp), DIMENSION(:,:,:), ALLOCATABLE ::  u_save   !< temporary storage of u wind component
188    REAL(wp), DIMENSION(:,:,:), ALLOCATABLE ::  v_save   !< temporary storage of v wind component
189
190
191!
192!-- Save 3D arrays because they are to be changed for spinup purpose
193    ALLOCATE( pt_save(nzb:nzt+1,nysg:nyng,nxlg:nxrg) )
194    ALLOCATE( u_save(nzb:nzt+1,nysg:nyng,nxlg:nxrg) )
195    ALLOCATE( v_save(nzb:nzt+1,nysg:nyng,nxlg:nxrg) )
196
197    CALL exchange_horiz( pt, nbgp )   
198    CALL exchange_horiz( u,  nbgp ) 
199    CALL exchange_horiz( v,  nbgp ) 
200 
201    pt_save = pt
202    u_save  = u
203    v_save  = v
204
205!
206!-- Set the same wall-adjacent velocity to all grid points. The sign of the
207!-- original velocity field must be preserved because the surface schemes crash
208!-- otherwise. The precise reason is still unknown. A minimum velocity of 0.1
209!-- m/s is used to maintain turbulent transfer at the surface.
210    IF ( land_surface )  THEN
211       DO  m = 1, surf_lsm_h%ns
212          i   = surf_lsm_h%i(m)           
213          j   = surf_lsm_h%j(m)
214          k   = surf_lsm_h%k(m)
215          u(k,j,i) = SIGN(1.0_wp,u_init(k)) * MAX( ABS( u_init(k) ),0.1_wp)
216          v(k,j,i) = SIGN(1.0_wp,v_init(k)) * MAX( ABS( v_init(k) ),0.1_wp)
217       ENDDO
218
219       DO  l = 0, 3
220          DO  m = 1, surf_lsm_v(l)%ns
221             i   = surf_lsm_v(l)%i(m)           
222             j   = surf_lsm_v(l)%j(m)
223             k   = surf_lsm_v(l)%k(m)
224             u(k,j,i) = SIGN(1.0_wp,u_init(k)) * MAX( ABS( u_init(k) ),0.1_wp)
225             v(k,j,i) = SIGN(1.0_wp,v_init(k)) * MAX( ABS( v_init(k) ),0.1_wp)
226          ENDDO
227       ENDDO
228    ENDIF
229
230    IF ( urban_surface )  THEN
231       DO  m = 1, surf_usm_h%ns
232          i   = surf_usm_h%i(m)           
233          j   = surf_usm_h%j(m)
234          k   = surf_usm_h%k(m)
235          u(k,j,i) = SIGN(1.0_wp,u_init(k)) * MAX( ABS( u_init(k) ),0.1_wp)
236          v(k,j,i) = SIGN(1.0_wp,v_init(k)) * MAX( ABS( v_init(k) ),0.1_wp)
237       ENDDO
238
239       DO  l = 0, 3
240          DO  m = 1, surf_usm_v(l)%ns
241             i   = surf_usm_v(l)%i(m)           
242             j   = surf_usm_v(l)%j(m)
243             k   = surf_usm_v(l)%k(m)
244             u(k,j,i) = SIGN(1.0_wp,u_init(k)) * MAX( ABS( u_init(k) ),0.1_wp)
245             v(k,j,i) = SIGN(1.0_wp,v_init(k)) * MAX( ABS( v_init(k) ),0.1_wp)
246          ENDDO
247       ENDDO
248    ENDIF
249
250    CALL exchange_horiz( u,  nbgp )
251    CALL exchange_horiz( v,  nbgp )
252
253    dt_save = dt_3d
254    dt_3d   = dt_spinup
255
256    CALL location_message( 'starting spinup-sequence', .TRUE. )
257!
258!-- Start of the time loop
259    DO  WHILE ( simulated_time < spinup_time )
260
261       CALL cpu_log( log_point_s(15), 'timesteps spinup', 'start' )
262   
263!
264!--    Start of intermediate step loop
265       intermediate_timestep_count = 0
266       DO  WHILE ( intermediate_timestep_count < &
267                   intermediate_timestep_count_max )
268
269          intermediate_timestep_count = intermediate_timestep_count + 1
270
271!
272!--       Set the steering factors for the prognostic equations which depend
273!--       on the timestep scheme
274          CALL timestep_scheme_steering
275
276
277!
278!--       Estimate a near-surface air temperature based on the position of the
279!--       sun and user input about mean temperature and amplitude. The time is
280!--       shifted by one hour to simulate a lag between air temperature and
281!--       incoming radiation
282          pt_spinup = spinup_pt_mean + spinup_pt_amplitude                     &
283             * solar_angle (time_utc_init + time_since_reference_point - 3600.0)
284
285!
286!--       Map air temperature to all grid points in the vicinity of a surface
287!--       element
288          IF ( land_surface )  THEN
289             DO  m = 1, surf_lsm_h%ns
290                i   = surf_lsm_h%i(m)           
291                j   = surf_lsm_h%j(m)
292                k   = surf_lsm_h%k(m)
293                pt(k,j,i) = pt_spinup
294             ENDDO
295
296             DO  l = 0, 3
297                DO  m = 1, surf_lsm_v(l)%ns
298                   i   = surf_lsm_v(l)%i(m)           
299                   j   = surf_lsm_v(l)%j(m)
300                   k   = surf_lsm_v(l)%k(m)
301                   pt(k,j,i) = pt_spinup
302                ENDDO
303             ENDDO
304          ENDIF
305
306          IF ( urban_surface )  THEN
307             DO  m = 1, surf_usm_h%ns
308                i   = surf_usm_h%i(m)           
309                j   = surf_usm_h%j(m)
310                k   = surf_usm_h%k(m)
311                pt(k,j,i) = pt_spinup
312                !!!!!!!!!!!!!!!!HACK!!!!!!!!!!!!!
313                surf_usm_h%pt1 = pt_spinup
314                !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
315             ENDDO
316
317             DO  l = 0, 3
318                DO  m = 1, surf_usm_v(l)%ns
319                   i   = surf_usm_v(l)%i(m)           
320                   j   = surf_usm_v(l)%j(m)
321                   k   = surf_usm_v(l)%k(m)
322                   pt(k,j,i) = pt_spinup
323                   !!!!!!!!!!!!!!!!HACK!!!!!!!!!!!!!
324                   surf_usm_v(l)%pt1 = pt_spinup
325                   !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
326                ENDDO
327             ENDDO
328          ENDIF
329
330          CALL exchange_horiz( pt,  nbgp )   
331
332
333!
334!--       Swap the time levels in preparation for the next time step.
335          timestep_count = timestep_count + 1
336     
337          IF ( land_surface )  THEN
338              CALL lsm_swap_timelevel ( 0 )
339          ENDIF
340
341          IF ( urban_surface )  THEN
342             CALL usm_swap_timelevel ( 0 )
343          ENDIF
344
345          IF ( land_surface )  THEN
346             CALL lsm_swap_timelevel ( MOD( timestep_count, 2) )
347          ENDIF
348
349          IF ( urban_surface )  THEN
350             CALL usm_swap_timelevel ( MOD( timestep_count, 2) )
351          ENDIF
352         
353!
354!--       If required, compute virtual potential temperature
355          IF ( humidity )  THEN
356             CALL compute_vpt
357          ENDIF
358
359!
360!--       Compute the diffusion quantities
361          IF ( .NOT. constant_diffusion )  THEN
362
363!
364!--          First the vertical (and horizontal) fluxes in the surface
365!--          (constant flux) layer are computed
366             IF ( constant_flux_layer )  THEN
367                CALL surface_layer_fluxes
368             ENDIF
369
370!
371!--          If required, solve the energy balance for the surface and run soil
372!--          model. Call for horizontal as well as vertical surfaces.
373!--          The prognostic equation for soil moisure is switched off
374             IF ( land_surface )  THEN
375
376!
377!--             Call for horizontal upward-facing surfaces
378                CALL lsm_energy_balance( .TRUE., -1 )
379                CALL lsm_soil_model( .TRUE., -1, calc_soil_moisture_during_spinup )
380!
381!--             Call for northward-facing surfaces
382                CALL lsm_energy_balance( .FALSE., 0 )
383                CALL lsm_soil_model( .FALSE., 0, calc_soil_moisture_during_spinup )
384!
385!--             Call for southward-facing surfaces
386                CALL lsm_energy_balance( .FALSE., 1 )
387                CALL lsm_soil_model( .FALSE., 1, calc_soil_moisture_during_spinup )
388!
389!--             Call for eastward-facing surfaces
390                CALL lsm_energy_balance( .FALSE., 2 )
391                CALL lsm_soil_model( .FALSE., 2, calc_soil_moisture_during_spinup )
392!
393!--             Call for westward-facing surfaces
394                CALL lsm_energy_balance( .FALSE., 3 )
395                CALL lsm_soil_model( .FALSE., 3, calc_soil_moisture_during_spinup )
396
397             ENDIF
398
399!
400!--          If required, solve the energy balance for urban surfaces and run
401!--          the material heat model
402             IF (urban_surface) THEN
403
404                CALL usm_surface_energy_balance( .TRUE. )
405                IF ( usm_material_model )  THEN
406                   CALL usm_green_heat_model
407                   CALL usm_material_heat_model( .TRUE. )
408                ENDIF
409
410             ENDIF
411
412          ENDIF
413
414!
415!--       If required, calculate radiative fluxes and heating rates
416          IF ( radiation .AND. intermediate_timestep_count                     &
417               == intermediate_timestep_count_max )  THEN
418
419               time_radiation = time_radiation + dt_3d
420
421             IF ( time_radiation >= dt_3d .OR. force_radiation_call )          &
422             THEN
423
424                IF ( .NOT. force_radiation_call )  THEN
425                   time_radiation = time_radiation - dt_3d
426                ENDIF
427
428                CALL radiation_control
429
430                IF ( radiation_interactions )  THEN
431                   CALL radiation_interaction
432                ENDIF
433             ENDIF
434          ENDIF
435
436       ENDDO   ! Intermediate step loop
437
438!
439!--    Increase simulation time and output times
440       current_timestep_number_spinup = current_timestep_number_spinup + 1
441       simulated_time             = simulated_time   + dt_3d
442       simulated_time_chr         = time_to_string( simulated_time )
443       time_since_reference_point = simulated_time - coupling_start_time
444
445       IF ( data_output_during_spinup )  THEN
446          IF ( simulated_time >= skip_time_do2d_xy )  THEN
447             time_do2d_xy       = time_do2d_xy     + dt_3d
448          ENDIF
449          IF ( simulated_time >= skip_time_do3d    )  THEN
450             time_do3d          = time_do3d        + dt_3d
451          ENDIF
452          time_dots          = time_dots        + dt_3d
453          IF ( simulated_time >= skip_time_dopr )  THEN
454             time_dopr       = time_dopr        + dt_3d
455          ENDIF
456          time_run_control   = time_run_control + dt_3d
457
458!
459!--       Carry out statistical analysis and output at the requested output times.
460!--       The MOD function is used for calculating the output time counters (like
461!--       time_dopr) in order to regard a possible decrease of the output time
462!--       interval in case of restart runs
463
464!
465!--       Set a flag indicating that so far no statistics have been created
466!--       for this time step
467          flow_statistics_called = .FALSE.
468
469!
470!--       If required, call flow_statistics for averaging in time
471          IF ( averaging_interval_pr /= 0.0_wp  .AND.                          &
472             ( dt_dopr - time_dopr ) <= averaging_interval_pr  .AND.           &
473             simulated_time >= skip_time_dopr )  THEN
474             time_dopr_av = time_dopr_av + dt_3d
475             IF ( time_dopr_av >= dt_averaging_input_pr )  THEN
476                do_sum = .TRUE.
477                time_dopr_av = MOD( time_dopr_av,                              &
478                               MAX( dt_averaging_input_pr, dt_3d ) )
479             ENDIF
480          ENDIF
481          IF ( do_sum )  CALL flow_statistics
482
483!
484!--       Output of profiles
485          IF ( time_dopr >= dt_dopr )  THEN
486             IF ( dopr_n /= 0 )  CALL data_output_profiles
487             time_dopr = MOD( time_dopr, MAX( dt_dopr, dt_3d ) )
488             time_dopr_av = 0.0_wp    ! due to averaging (see above)
489          ENDIF
490
491!
492!--       Output of time series
493          IF ( time_dots >= dt_dots )  THEN
494             CALL data_output_tseries
495             time_dots = MOD( time_dots, MAX( dt_dots, dt_3d ) )
496          ENDIF
497
498!
499!--       2d-data output (cross-sections)
500          IF ( time_do2d_xy >= dt_do2d_xy )  THEN
501             CALL data_output_2d( 'xy', 0 )
502             time_do2d_xy = MOD( time_do2d_xy, MAX( dt_do2d_xy, dt_3d ) )
503          ENDIF
504
505!
506!--       3d-data output (volume data)
507          IF ( time_do3d >= dt_do3d )  THEN
508             CALL data_output_3d( 0 )
509             time_do3d = MOD( time_do3d, MAX( dt_do3d, dt_3d ) )
510          ENDIF
511
512
513       ENDIF
514
515!
516!--    Computation and output of run control parameters.
517!--    This is also done whenever perturbations have been imposed
518!        IF ( time_run_control >= dt_run_control  .OR.                           &
519!             timestep_scheme(1:5) /= 'runge'  .OR.  disturbance_created )       &
520!        THEN
521!           CALL run_control
522!           IF ( time_run_control >= dt_run_control )  THEN
523!              time_run_control = MOD( time_run_control,                         &
524!                                      MAX( dt_run_control, dt_3d ) )
525!           ENDIF
526!        ENDIF
527
528       CALL cpu_log( log_point_s(15), 'timesteps spinup', 'stop' )
529
530
531!
532!--    Run control output
533       IF ( myid == 0 )  THEN
534!
535!--       If necessary, write header
536          IF ( .NOT. run_control_header_spinup )  THEN
537             CALL check_open( 15 )
538             WRITE ( 15, 100 )
539             run_control_header_spinup = .TRUE.
540          ENDIF
541!
542!--       Write some general information about the spinup in run control file
543          WRITE ( 15, 101 )  current_timestep_number_spinup, simulated_time_chr, dt_3d, pt_spinup
544!
545!--       Write buffer contents to disc immediately
546          FLUSH( 15 )
547       ENDIF
548
549
550
551    ENDDO   ! time loop
552
553!
554!-- Write back saved arrays to the 3D arrays
555    pt   = pt_save
556    pt_p = pt_save
557    u    = u_save
558    v    = v_save
559
560!
561!-- Reset time step
562    dt_3d = dt_save
563
564    DEALLOCATE(pt_save)
565    DEALLOCATE(u_save)
566    DEALLOCATE(v_save)
567
568#if defined( __parallel )
569    IF ( nested_run )  CALL MPI_BARRIER( MPI_COMM_WORLD, ierr )
570#endif
571
572    CALL location_message( 'finished spinup-sequence', .TRUE. )
573
574
575!
576!-- Formats
577100 FORMAT (///'Spinup control output:'/  &
578            '--------------------------------'// &
579            'ITER.  HH:MM:SS    DT   PT(z_MO)'/   &
580            '--------------------------------')
581101 FORMAT (I5,2X,A9,1X,F6.2,3X,F6.2,2X,F6.2)
582
583 CONTAINS
584
585!
586!-- Returns the cosine of the solar zenith angle at a given time. This routine
587!-- is similar to that for calculation zenith (see radiation_model_mod.f90)
588    FUNCTION solar_angle( local_time ) 
589
590       USE basic_constants_and_equations_mod,                                  &
591       ONLY:  pi
592     
593       USE kinds
594
595       USE radiation_model_mod,                                                &
596           ONLY:  decl_1, decl_2, decl_3, lat, lon
597
598       IMPLICIT NONE
599
600
601       REAL(wp) ::  solar_angle     !< cosine of the solar zenith angle
602
603       REAL(wp) ::  day             !< day of the year
604       REAL(wp) ::  declination     !< solar declination angle
605       REAL(wp) ::  hour_angle      !< solar hour angle
606       REAL(wp) ::  time_utc        !< current time in UTC
607       REAL(wp), INTENT(IN) :: local_time
608!
609!--    Calculate current day and time based on the initial values and simulation
610!--    time
611
612       day = day_of_year_init + INT(FLOOR( local_time / 86400.0_wp ), KIND=iwp)
613       time_utc = MOD(local_time, 86400.0_wp)
614
615
616!
617!--    Calculate solar declination and hour angle   
618       declination = ASIN( decl_1 * SIN(decl_2 * REAL(day, KIND=wp) - decl_3) )
619       hour_angle  = 2.0_wp * pi * (time_utc / 86400.0_wp) + lon - pi
620
621!
622!--    Calculate cosine of solar zenith angle
623       solar_angle = SIN(lat) * SIN(declination) + COS(lat) * COS(declination) &
624                     * COS(hour_angle)
625
626
627    END FUNCTION solar_angle
628
629
630 END SUBROUTINE time_integration_spinup
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