SUBROUTINE time_integration

!--------------------------------------------------------------------------------!
! This file is part of PALM.
!
! PALM is free software: you can redistribute it and/or modify it under the terms
! of the GNU General Public License as published by the Free Software Foundation,
! either version 3 of the License, or (at your option) any later version.
!
! PALM is distributed in the hope that it will be useful, but WITHOUT ANY
! WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
! A PARTICULAR PURPOSE.  See the GNU General Public License for more details.
!
! You should have received a copy of the GNU General Public License along with
! PALM. If not, see <http://www.gnu.org/licenses/>.
!
! Copyright 1997-2012  Leibniz University Hannover
!--------------------------------------------------------------------------------!
!
! Current revisions:
! ------------------
! host update of arrays before timestep is called
!
! Former revisions:
! -----------------
! $Id: time_integration.f90 1221 2013-09-10 08:59:13Z raasch $
!
! 1179 2013-06-14 05:57:58Z raasch
! mean profiles for reference state are only calculated if required,
! small bugfix for background communication
!
! 1171 2013-05-30 11:27:45Z raasch
! split of prognostic_equations deactivated (comment lines), for the time being
!
! 1128 2013-04-12 06:19:32Z raasch
! asynchronous transfer of ghost point data realized for acc-optimized version:
! prognostic_equations are first called two times for those points required for
! the left-right and north-south exchange, respectively, and then for the
! remaining points,
! those parts requiring global communication moved from prognostic_equations to
! here
!
! 1115 2013-03-26 18:16:16Z hoffmann
! calculation of qr and nr is restricted to precipitation
!
! 1113 2013-03-10 02:48:14Z raasch
! GPU-porting of boundary conditions,
! openACC directives updated
! formal parameter removed from routine boundary_conds
!
! 1111 2013-03-08 23:54:10Z raasch
! +internal timestep counter for cpu statistics added,
! openACC directives updated
!
! 1092 2013-02-02 11:24:22Z raasch
! unused variables removed
!
! 1065 2012-11-22 17:42:36Z hoffmann
! exchange of diss (dissipation rate) in case of turbulence = .TRUE. added
!
! 1053 2012-11-13 17:11:03Z hoffmann
! exchange of ghost points for nr, qr added
!
! 1036 2012-10-22 13:43:42Z raasch
! code put under GPL (PALM 3.9)
!
! 1019 2012-09-28 06:46:45Z raasch
! non-optimized version of prognostic_equations removed
!
! 1015 2012-09-27 09:23:24Z raasch
! +call of prognostic_equations_acc
!
! 1001 2012-09-13 14:08:46Z raasch
! all actions concerning leapfrog- and upstream-spline-scheme removed
!
! 849 2012-03-15 10:35:09Z raasch
! advec_particles renamed lpm, first_call_advec_particles renamed first_call_lpm
!
! 825 2012-02-19 03:03:44Z raasch
! wang_collision_kernel renamed wang_kernel
!
! 790 2011-11-29 03:11:20Z raasch
! exchange of ghostpoints for array diss
!
! 707 2011-03-29 11:39:40Z raasch
! bc_lr/ns replaced by bc_lr/ns_cyc, calls of exchange_horiz are modified,
! adaption to sloping surface
!
! 667  2010-12-23 12:06:00Z suehring/gryschka
! Calls of exchange_horiz are modified.
! Adaption to slooping surface.
!
! 449 2010-02-02 11:23:59Z raasch
! Bugfix: exchange of ghost points for prho included
!
! 410 2009-12-04 17:05:40Z letzel
! masked data output
!
! 388 2009-09-23 09:40:33Z raasch
! Using prho instead of rho in diffusvities.
! Coupling with independent precursor runs.
! Bugfix: output of particle time series only if particle advection is switched
!         on
!
! 151 2008-03-07 13:42:18Z raasch
! inflow turbulence is imposed by calling new routine inflow_turbulence
!
! 108 2007-08-24 15:10:38Z letzel
! Call of new routine surface_coupler,
! presure solver is called after the first Runge-Kutta substep instead of the
! last in case that call_psolver_at_all_substeps = .F.; for this case, the
! random perturbation has to be added to the velocity fields also after the
! first substep
!
! 97 2007-06-21 08:23:15Z raasch
! diffusivities is called with argument rho in case of ocean runs,
! new argument pt_/prho_reference in calls of diffusivities,
! ghostpoint exchange for salinity and density
!
! 87 2007-05-22 15:46:47Z raasch
! var_hom renamed pr_palm
!
! 75 2007-03-22 09:54:05Z raasch
! Move call of user_actions( 'after_integration' ) below increment of times
! and counters,
! calls of prognostic_equations_.. changed to .._noopt, .._cache, and
! .._vector, these calls are now controlled by switch loop_optimization,
! uxrp, vynp eliminated, 2nd+3rd argument removed from exchange horiz,
! moisture renamed humidity
!
! RCS Log replace by Id keyword, revision history cleaned up
!
! Revision 1.8  2006/08/22 14:16:05  raasch
! Disturbances are imposed only for the last Runge-Kutta-substep
!
! Revision 1.2  2004/04/30 13:03:40  raasch
! decalpha-specific warning removed, routine name changed to time_integration,
! particle advection is carried out only once during the intermediate steps,
! impulse_advec renamed momentum_advec
!
! Revision 1.1  1997/08/11 06:19:04  raasch
! Initial revision
!
!
! Description:
! ------------
! Integration in time of the model equations, statistical analysis and graphic
! output
!------------------------------------------------------------------------------!

    USE advec_ws
    USE arrays_3d
    USE averaging
    USE buoyancy_mod
    USE control_parameters
    USE cpulog
#if defined( __dvrp_graphics )
    USE DVRP
#endif
    USE grid_variables
    USE indices
    USE interaction_droplets_ptq_mod
    USE interfaces
    USE particle_attributes
    USE pegrid
    USE production_e_mod
    USE prognostic_equations_mod
    USE statistics
    USE user_actions_mod

    IMPLICIT NONE

    CHARACTER (LEN=9) ::  time_to_string

!
!-- At the beginning of a simulation determine the time step as well as
!-- determine and print out the run control parameters
    IF ( simulated_time == 0.0 )  CALL timestep

    CALL run_control


!
!-- Data exchange between coupled models in case that a call has been omitted 
!-- at the end of the previous run of a job chain.
    IF ( coupling_mode /= 'uncoupled'  .AND.  run_coupled )  THEN
!
!--    In case of model termination initiated by the local model the coupler 
!--    must not be called because this would again cause an MPI hang. 
       DO WHILE ( time_coupling >= dt_coupling .AND. terminate_coupled == 0 )
          CALL surface_coupler
          time_coupling = time_coupling - dt_coupling
       ENDDO
       IF (time_coupling == 0.0 .AND. time_since_reference_point < dt_coupling)&
       THEN
          time_coupling = time_since_reference_point
       ENDIF
    ENDIF


#if defined( __dvrp_graphics )
!
!-- Time measurement with dvrp software  
    CALL DVRP_LOG_EVENT( 2, current_timestep_number )
#endif

!
!-- Start of the time loop
    DO  WHILE ( simulated_time < end_time  .AND.  .NOT. stop_dt  .AND. &
                .NOT. terminate_run )

       CALL cpu_log( log_point_s(10), 'timesteps', 'start' )

!
!--    Determine size of next time step
       IF ( simulated_time /= 0.0 )  THEN
          !$acc update host( kh, km, u, v, w )
          CALL timestep
       ENDIF

!
!--    Execute the user-defined actions
       CALL user_actions( 'before_timestep' )

!
!--    Start of intermediate step loop
       intermediate_timestep_count = 0
       DO  WHILE ( intermediate_timestep_count < &
                   intermediate_timestep_count_max )

          intermediate_timestep_count = intermediate_timestep_count + 1

!
!--       Set the steering factors for the prognostic equations which depend
!--       on the timestep scheme
          CALL timestep_scheme_steering

!
!--       Calculate those variables needed in the tendency terms which need
!--       global communication
          IF ( .NOT. use_single_reference_value  .AND. &
               .NOT. use_initial_profile_as_reference )  THEN
!
!--          Horizontally averaged profiles to be used as reference state in
!--          buoyancy terms (WARNING: only the respective last call of
!--          calc_mean_profile defines the reference state!)
             IF ( .NOT. neutral )  CALL calc_mean_profile( pt, 4 )
             IF ( ocean         )  CALL calc_mean_profile( rho, 64 )
             IF ( humidity      )  CALL calc_mean_profile( vpt, 44 )
          ENDIF

          IF ( .NOT. constant_diffusion )  CALL production_e_init
          IF ( ( ws_scheme_mom .OR. ws_scheme_sca )  .AND.  &
               intermediate_timestep_count == 1 )  CALL ws_statistics

!
!--       Solve the prognostic equations. A fast cache optimized version with
!--       only one single loop is used in case of Piascek-Williams advection
!--       scheme. NEC vector machines use a different version, because
!--       in the other versions a good vectorization is prohibited due to
!--       inlining problems.
          IF ( loop_optimization == 'cache' )  THEN
             CALL prognostic_equations_cache
          ELSEIF ( loop_optimization == 'vector' )  THEN
             CALL prognostic_equations_vector
          ELSEIF ( loop_optimization == 'acc' )  THEN
             i_left  = nxl;         i_right = nxr
             j_south = nys;         j_north = nyn
             CALL prognostic_equations_acc

!             i_left  = nxl;         i_right = nxl+nbgp-1
!             j_south = nys;         j_north = nyn
!             CALL prognostic_equations_acc
!             i_left  = nxr-nbgp+1;  i_right = nxr
!             j_south = nys;         j_north = nyn
!             CALL prognostic_equations_acc

!
!--          Exchange of ghost points (lateral boundary conditions)
             IF ( background_communication )  THEN

                CALL cpu_log( log_point(26), 'exchange-horiz-progn', 'start' )
                
                send_receive = 'lr'
                sendrecv_in_background = .TRUE.
                req          = 0
                req_count    = 0

                IF ( numprocs == 1 )  THEN    ! workaround for single-core GPU runs
                   on_device = .TRUE.         ! to be removed after complete porting
                ELSE                          ! of ghost point exchange
                   !$acc update host( e_p, pt_p, u_p, v_p, w_p )
                ENDIF

                CALL exchange_horiz( u_p, nbgp )
                CALL exchange_horiz( v_p, nbgp )
                CALL exchange_horiz( w_p, nbgp )
                CALL exchange_horiz( pt_p, nbgp )
                IF ( .NOT. constant_diffusion )  CALL exchange_horiz( e_p, nbgp )
                IF ( ocean )  THEN
                   CALL exchange_horiz( sa_p, nbgp )
                   CALL exchange_horiz( rho, nbgp )
                  CALL exchange_horiz( prho, nbgp )
                ENDIF
                IF (humidity  .OR.  passive_scalar)  THEN
                   CALL exchange_horiz( q_p, nbgp )
                   IF ( cloud_physics .AND. icloud_scheme == 0 )  THEN
                      CALL exchange_horiz( qr_p, nbgp )
                      CALL exchange_horiz( nr_p, nbgp )
                   ENDIF
                ENDIF
                IF ( cloud_droplets )  THEN
                   CALL exchange_horiz( ql, nbgp )
                   CALL exchange_horiz( ql_c, nbgp )
                   CALL exchange_horiz( ql_v, nbgp )
                   CALL exchange_horiz( ql_vp, nbgp )
                ENDIF
                IF ( wang_kernel  .OR.  turbulence )  CALL exchange_horiz( diss, nbgp )

                IF ( numprocs == 1 )  THEN    ! workaround for single-core GPU runs
                   on_device = .FALSE.        ! to be removed after complete porting
                ELSE                          ! of ghost point exchange
                   !$acc update device( e_p, pt_p, u_p, v_p, w_p )
                ENDIF

                sendrecv_in_background = .FALSE.

                CALL cpu_log( log_point(26), 'exchange-horiz-progn', 'pause' )

             ENDIF

!             i_left  = nxl+nbgp;    i_right = nxr-nbgp
!             j_south = nys;         j_north = nys+nbgp-1
!             CALL prognostic_equations_acc
!             i_left  = nxl+nbgp;    i_right = nxr-nbgp
!             j_south = nyn-nbgp+1;  j_north = nyn
!             CALL prognostic_equations_acc

             IF ( background_communication )  THEN
                CALL cpu_log( log_point(41), 'exchange-horiz-wait', 'start' )
#if defined( __parallel )
                CALL MPI_WAITALL( req_count, req, wait_stat, ierr )
#endif
                CALL cpu_log( log_point(41), 'exchange-horiz-wait', 'pause' )

                CALL cpu_log( log_point(26), 'exchange-horiz-progn', 'continue' )

                send_receive = 'ns'
                sendrecv_in_background = .TRUE.
                req          = 0
                req_count    = 0

                IF ( numprocs == 1 )  THEN    ! workaround for single-core GPU runs
                   on_device = .TRUE.         ! to be removed after complete porting
                ELSE                          ! of ghost point exchange
                   !$acc update host( e_p, pt_p, u_p, v_p, w_p )
                ENDIF

                CALL exchange_horiz( u_p, nbgp )
                CALL exchange_horiz( v_p, nbgp )
                CALL exchange_horiz( w_p, nbgp )
                CALL exchange_horiz( pt_p, nbgp )
                IF ( .NOT. constant_diffusion )  CALL exchange_horiz( e_p, nbgp )
                IF ( ocean )  THEN
                   CALL exchange_horiz( sa_p, nbgp )
                   CALL exchange_horiz( rho, nbgp )
                  CALL exchange_horiz( prho, nbgp )
                ENDIF
                IF (humidity  .OR.  passive_scalar)  THEN
                   CALL exchange_horiz( q_p, nbgp )
                   IF ( cloud_physics .AND. icloud_scheme == 0 )  THEN
                      CALL exchange_horiz( qr_p, nbgp )
                      CALL exchange_horiz( nr_p, nbgp )
                   ENDIF
                ENDIF
                IF ( cloud_droplets )  THEN
                   CALL exchange_horiz( ql, nbgp )
                   CALL exchange_horiz( ql_c, nbgp )
                   CALL exchange_horiz( ql_v, nbgp )
                   CALL exchange_horiz( ql_vp, nbgp )
                ENDIF
                IF ( wang_kernel  .OR.  turbulence )  CALL exchange_horiz( diss, nbgp )

                IF ( numprocs == 1 )  THEN    ! workaround for single-core GPU runs
                   on_device = .FALSE.        ! to be removed after complete porting
                ELSE                          ! of ghost point exchange
                   !$acc update device( e_p, pt_p, u_p, v_p, w_p )
                ENDIF

                sendrecv_in_background = .FALSE.

                CALL cpu_log( log_point(26), 'exchange-horiz-progn', 'stop' )

             ENDIF

!             i_left  = nxl+nbgp;    i_right = nxr-nbgp
!             j_south = nys+nbgp;    j_north = nyn-nbgp
!             CALL prognostic_equations_acc

             IF ( background_communication )  THEN
                CALL cpu_log( log_point(41), 'exchange-horiz-wait', 'continue' )
#if defined( __parallel )
                CALL MPI_WAITALL( req_count, req, wait_stat, ierr )
#endif
                send_receive = 'al'
                CALL cpu_log( log_point(41), 'exchange-horiz-wait', 'stop' )
             ENDIF

          ENDIF

!
!--       Particle transport/physics with the Lagrangian particle model
!--       (only once during intermediate steps, because it uses an Euler-step)
!--       ### particle model should be moved before prognostic_equations, in order
!--       to regard droplet interactions directly
          IF ( particle_advection  .AND.                         &
               simulated_time >= particle_advection_start  .AND. &
               intermediate_timestep_count == 1 )  THEN
             CALL lpm
             first_call_lpm = .FALSE.
          ENDIF

!
!--       Interaction of droplets with temperature and specific humidity.
!--       Droplet condensation and evaporation is calculated within
!--       advec_particles.
          IF ( cloud_droplets  .AND.  &
               intermediate_timestep_count == intermediate_timestep_count_max )&
          THEN
             CALL interaction_droplets_ptq
          ENDIF

!
!--       Exchange of ghost points (lateral boundary conditions)
          IF ( .NOT. background_communication )  THEN

             CALL cpu_log( log_point(26), 'exchange-horiz-progn', 'start' )

             IF ( numprocs == 1 )  THEN    ! workaround for single-core GPU runs
                on_device = .TRUE.         ! to be removed after complete porting
             ELSE                          ! of ghost point exchange
                !$acc update host( e_p, pt_p, u_p, v_p, w_p )
             ENDIF

             CALL exchange_horiz( u_p, nbgp )
             CALL exchange_horiz( v_p, nbgp )
             CALL exchange_horiz( w_p, nbgp )
             CALL exchange_horiz( pt_p, nbgp )
             IF ( .NOT. constant_diffusion )  CALL exchange_horiz( e_p, nbgp )
             IF ( ocean )  THEN
                CALL exchange_horiz( sa_p, nbgp )
                CALL exchange_horiz( rho, nbgp )
                CALL exchange_horiz( prho, nbgp )
             ENDIF
             IF (humidity  .OR.  passive_scalar)  THEN
                CALL exchange_horiz( q_p, nbgp )
                IF ( cloud_physics .AND. icloud_scheme == 0  .AND.  &
                     precipitation )  THEN
                   CALL exchange_horiz( qr_p, nbgp )
                   CALL exchange_horiz( nr_p, nbgp )
                ENDIF
             ENDIF
             IF ( cloud_droplets )  THEN
                CALL exchange_horiz( ql, nbgp )
                CALL exchange_horiz( ql_c, nbgp )
                CALL exchange_horiz( ql_v, nbgp )
                CALL exchange_horiz( ql_vp, nbgp )
             ENDIF
             IF ( wang_kernel  .OR.  turbulence )  CALL exchange_horiz( diss, nbgp )

             IF ( numprocs == 1 )  THEN    ! workaround for single-core GPU runs
                on_device = .FALSE.        ! to be removed after complete porting
             ELSE                          ! of ghost point exchange
                !$acc update device( e_p, pt_p, u_p, v_p, w_p )
             ENDIF

             CALL cpu_log( log_point(26), 'exchange-horiz-progn', 'stop' )

          ENDIF

!
!--       Boundary conditions for the prognostic quantities (except of the
!--       velocities at the outflow in case of a non-cyclic lateral wall)
          CALL boundary_conds

!
!--       Swap the time levels in preparation for the next time step.
          CALL swap_timelevel

!
!--       Temperature offset must be imposed at cyclic boundaries in x-direction
!--       when a sloping surface is used
          IF ( sloping_surface )  THEN
             IF ( nxl ==  0 )  pt(:,:,nxlg:nxl-1) = pt(:,:,nxlg:nxl-1) - &
                                                    pt_slope_offset
             IF ( nxr == nx )  pt(:,:,nxr+1:nxrg) = pt(:,:,nxr+1:nxrg) + &
                                                    pt_slope_offset
          ENDIF

!
!--       Impose a turbulent inflow using the recycling method
          IF ( turbulent_inflow )  CALL  inflow_turbulence

!
!--       Impose a random perturbation on the horizontal velocity field
          IF ( create_disturbances  .AND.                                      &
               ( call_psolver_at_all_substeps  .AND.                           &
               intermediate_timestep_count == intermediate_timestep_count_max )&
          .OR. ( .NOT. call_psolver_at_all_substeps  .AND.                     &
               intermediate_timestep_count == 1 ) )                            &
          THEN
             time_disturb = time_disturb + dt_3d
             IF ( time_disturb >= dt_disturb )  THEN
                !$acc update host( u, v )
                IF ( numprocs == 1 )  on_device = .FALSE.  ! workaround, remove later
                IF ( hom(nzb+5,1,pr_palm,0) < disturbance_energy_limit )  THEN
                   CALL disturb_field( nzb_u_inner, tend, u )
                   CALL disturb_field( nzb_v_inner, tend, v )
                ELSEIF ( .NOT. bc_lr_cyc  .OR.  .NOT. bc_ns_cyc )  THEN
!
!--                Runs with a non-cyclic lateral wall need perturbations
!--                near the inflow throughout the whole simulation
                   dist_range = 1
                   CALL disturb_field( nzb_u_inner, tend, u )
                   CALL disturb_field( nzb_v_inner, tend, v )
                   dist_range = 0
                ENDIF
                IF ( numprocs == 1 )  on_device = .TRUE.  ! workaround, remove later
                !$acc update device( u, v )
                time_disturb = time_disturb - dt_disturb
             ENDIF
          ENDIF

!
!--       Reduce the velocity divergence via the equation for perturbation
!--       pressure.
          IF ( intermediate_timestep_count == 1  .OR. &
                call_psolver_at_all_substeps )  THEN
             CALL pres
          ENDIF

!
!--       If required, compute liquid water content
          IF ( cloud_physics )  THEN
             CALL calc_liquid_water_content
             !$acc update device( ql )
          ENDIF
! 
!--       If required, compute virtual potential temperature 
          IF ( humidity )  THEN 
             CALL compute_vpt 
             !$acc update device( vpt ) 
          ENDIF 
!
!--       Compute the diffusion quantities
          IF ( .NOT. constant_diffusion )  THEN

!
!--          First the vertical fluxes in the Prandtl layer are being computed
             IF ( prandtl_layer )  THEN
                CALL cpu_log( log_point(19), 'prandtl_fluxes', 'start' )
                CALL prandtl_fluxes
                CALL cpu_log( log_point(19), 'prandtl_fluxes', 'stop' )
             ENDIF
!
!--          Compute the diffusion coefficients
             CALL cpu_log( log_point(17), 'diffusivities', 'start' )
             IF ( .NOT. humidity ) THEN
                IF ( ocean )  THEN
                   CALL diffusivities( prho, prho_reference )
                ELSE
                   CALL diffusivities( pt, pt_reference )
                ENDIF
             ELSE
                CALL diffusivities( vpt, pt_reference )
             ENDIF
             CALL cpu_log( log_point(17), 'diffusivities', 'stop' )

          ENDIF

       ENDDO   ! Intermediate step loop

!
!--    Increase simulation time and output times
       nr_timesteps_this_run      = nr_timesteps_this_run + 1
       current_timestep_number    = current_timestep_number + 1
       simulated_time             = simulated_time   + dt_3d
       simulated_time_chr         = time_to_string( simulated_time )
       time_since_reference_point = simulated_time - coupling_start_time

       IF ( simulated_time >= skip_time_data_output_av )  THEN
          time_do_av         = time_do_av       + dt_3d
       ENDIF
       IF ( simulated_time >= skip_time_do2d_xy )  THEN
          time_do2d_xy       = time_do2d_xy     + dt_3d
       ENDIF
       IF ( simulated_time >= skip_time_do2d_xz )  THEN
          time_do2d_xz       = time_do2d_xz     + dt_3d
       ENDIF
       IF ( simulated_time >= skip_time_do2d_yz )  THEN
          time_do2d_yz       = time_do2d_yz     + dt_3d
       ENDIF
       IF ( simulated_time >= skip_time_do3d    )  THEN
          time_do3d          = time_do3d        + dt_3d
       ENDIF
       DO  mid = 1, masks
          IF ( simulated_time >= skip_time_domask(mid) )  THEN
             time_domask(mid)= time_domask(mid) + dt_3d
          ENDIF
       ENDDO
       time_dvrp          = time_dvrp        + dt_3d
       IF ( simulated_time >= skip_time_dosp )  THEN
          time_dosp       = time_dosp        + dt_3d
       ENDIF
       time_dots          = time_dots        + dt_3d
       IF ( .NOT. first_call_lpm )  THEN
          time_dopts      = time_dopts       + dt_3d
       ENDIF
       IF ( simulated_time >= skip_time_dopr )  THEN
          time_dopr       = time_dopr        + dt_3d
       ENDIF
       time_dopr_listing          = time_dopr_listing        + dt_3d
       time_run_control   = time_run_control + dt_3d

!
!--    Data exchange between coupled models
       IF ( coupling_mode /= 'uncoupled'  .AND.  run_coupled )  THEN
          time_coupling = time_coupling + dt_3d

!
!--       In case of model termination initiated by the local model 
!--       (terminate_coupled > 0), the coupler must be skipped because it would 
!--       cause an MPI intercomminucation hang.
!--       If necessary, the coupler will be called at the beginning of the 
!--       next restart run.
          DO WHILE ( time_coupling >= dt_coupling .AND. terminate_coupled == 0 )
             CALL surface_coupler
             time_coupling = time_coupling - dt_coupling
          ENDDO
       ENDIF

!
!--    Execute user-defined actions
       CALL user_actions( 'after_integration' )

!
!--    If Galilei transformation is used, determine the distance that the
!--    model has moved so far
       IF ( galilei_transformation )  THEN
          advected_distance_x = advected_distance_x + u_gtrans * dt_3d
          advected_distance_y = advected_distance_y + v_gtrans * dt_3d
       ENDIF

!
!--    Check, if restart is necessary (because cpu-time is expiring or
!--    because it is forced by user) and set stop flag
!--    This call is skipped if the remote model has already initiated a restart.
       IF ( .NOT. terminate_run )  CALL check_for_restart

!
!--    Carry out statistical analysis and output at the requested output times.
!--    The MOD function is used for calculating the output time counters (like
!--    time_dopr) in order to regard a possible decrease of the output time
!--    interval in case of restart runs

!
!--    Set a flag indicating that so far no statistics have been created
!--    for this time step
       flow_statistics_called = .FALSE.

!
!--    If required, call flow_statistics for averaging in time
       IF ( averaging_interval_pr /= 0.0  .AND.  &
            ( dt_dopr - time_dopr ) <= averaging_interval_pr  .AND.  &
            simulated_time >= skip_time_dopr )  THEN
          time_dopr_av = time_dopr_av + dt_3d
          IF ( time_dopr_av >= dt_averaging_input_pr )  THEN
             do_sum = .TRUE.
             time_dopr_av = MOD( time_dopr_av, &
                                    MAX( dt_averaging_input_pr, dt_3d ) )
          ENDIF
       ENDIF
       IF ( do_sum )  CALL flow_statistics

!
!--    Sum-up 3d-arrays for later output of time-averaged 2d/3d/masked data
       IF ( averaging_interval /= 0.0  .AND.                                &
            ( dt_data_output_av - time_do_av ) <= averaging_interval  .AND. &
            simulated_time >= skip_time_data_output_av )                    &
       THEN
          time_do_sla = time_do_sla + dt_3d
          IF ( time_do_sla >= dt_averaging_input )  THEN
             CALL sum_up_3d_data
             average_count_3d = average_count_3d + 1
             time_do_sla = MOD( time_do_sla, MAX( dt_averaging_input, dt_3d ) )
          ENDIF
       ENDIF

!
!--    Calculate spectra for time averaging
       IF ( averaging_interval_sp /= 0.0  .AND.  &
            ( dt_dosp - time_dosp ) <= averaging_interval_sp  .AND.  &
            simulated_time >= skip_time_dosp )  THEN
          time_dosp_av = time_dosp_av + dt_3d
          IF ( time_dosp_av >= dt_averaging_input_pr )  THEN
             CALL calc_spectra
             time_dosp_av = MOD( time_dosp_av, &
                                 MAX( dt_averaging_input_pr, dt_3d ) )
          ENDIF
       ENDIF

!
!--    Computation and output of run control parameters.
!--    This is also done whenever perturbations have been imposed
       IF ( time_run_control >= dt_run_control  .OR.                     &
            timestep_scheme(1:5) /= 'runge'  .OR.  disturbance_created ) &
       THEN
          CALL run_control
          IF ( time_run_control >= dt_run_control )  THEN
             time_run_control = MOD( time_run_control, &
                                     MAX( dt_run_control, dt_3d ) )
          ENDIF
       ENDIF

!
!--    Profile output (ASCII) on file
       IF ( time_dopr_listing >= dt_dopr_listing )  THEN
          CALL print_1d
          time_dopr_listing = MOD( time_dopr_listing, MAX( dt_dopr_listing, &
                                                           dt_3d ) )
       ENDIF

!
!--    Graphic output for PROFIL
       IF ( time_dopr >= dt_dopr )  THEN
          IF ( dopr_n /= 0 )  CALL data_output_profiles
          time_dopr = MOD( time_dopr, MAX( dt_dopr, dt_3d ) )
          time_dopr_av = 0.0    ! due to averaging (see above)
       ENDIF

!
!--    Graphic output for time series
       IF ( time_dots >= dt_dots )  THEN
          CALL data_output_tseries
          time_dots = MOD( time_dots, MAX( dt_dots, dt_3d ) )
       ENDIF

!
!--    Output of spectra (formatted for use with PROFIL), in case of no
!--    time averaging, spectra has to be calculated before
       IF ( time_dosp >= dt_dosp )  THEN
          IF ( average_count_sp == 0 )  CALL calc_spectra
          CALL data_output_spectra
          time_dosp = MOD( time_dosp, MAX( dt_dosp, dt_3d ) )
       ENDIF

!
!--    2d-data output (cross-sections)
       IF ( time_do2d_xy >= dt_do2d_xy )  THEN
          CALL data_output_2d( 'xy', 0 )
          time_do2d_xy = MOD( time_do2d_xy, MAX( dt_do2d_xy, dt_3d ) )
       ENDIF
       IF ( time_do2d_xz >= dt_do2d_xz )  THEN
          CALL data_output_2d( 'xz', 0 )
          time_do2d_xz = MOD( time_do2d_xz, MAX( dt_do2d_xz, dt_3d ) )
       ENDIF
       IF ( time_do2d_yz >= dt_do2d_yz )  THEN
          CALL data_output_2d( 'yz', 0 )
          time_do2d_yz = MOD( time_do2d_yz, MAX( dt_do2d_yz, dt_3d ) )
       ENDIF

!
!--    3d-data output (volume data)
       IF ( time_do3d >= dt_do3d )  THEN
          CALL data_output_3d( 0 )
          time_do3d = MOD( time_do3d, MAX( dt_do3d, dt_3d ) )
       ENDIF

!
!--    masked data output
       DO  mid = 1, masks
          IF ( time_domask(mid) >= dt_domask(mid) )  THEN
             CALL data_output_mask( 0 )
             time_domask(mid) = MOD( time_domask(mid),  &
                                     MAX( dt_domask(mid), dt_3d ) )
          ENDIF
       ENDDO

!
!--    Output of time-averaged 2d/3d/masked data
       IF ( time_do_av >= dt_data_output_av )  THEN
          CALL average_3d_data
          CALL data_output_2d( 'xy', 1 )
          CALL data_output_2d( 'xz', 1 )
          CALL data_output_2d( 'yz', 1 )
          CALL data_output_3d( 1 )
          DO  mid = 1, masks
             CALL data_output_mask( 1 )
          ENDDO
          time_do_av = MOD( time_do_av, MAX( dt_data_output_av, dt_3d ) )
       ENDIF

!
!--    Output of particle time series
       IF ( particle_advection )  THEN
          IF ( time_dopts >= dt_dopts  .OR. &
               ( simulated_time >= particle_advection_start  .AND. &
                 first_call_lpm ) )  THEN
             CALL data_output_ptseries
             time_dopts = MOD( time_dopts, MAX( dt_dopts, dt_3d ) )
          ENDIF
       ENDIF

!
!--    Output of dvrp-graphics (isosurface, particles, slicer)
#if defined( __dvrp_graphics )
       CALL DVRP_LOG_EVENT( -2, current_timestep_number-1 )
#endif
       IF ( time_dvrp >= dt_dvrp )  THEN
          CALL data_output_dvrp
          time_dvrp = MOD( time_dvrp, MAX( dt_dvrp, dt_3d ) )
       ENDIF
#if defined( __dvrp_graphics )
       CALL DVRP_LOG_EVENT( 2, current_timestep_number )
#endif

!
!--    If required, set the heat flux for the next time step at a random value
       IF ( constant_heatflux  .AND.  random_heatflux )  CALL disturb_heatflux

!
!--    Execute user-defined actions
       CALL user_actions( 'after_timestep' )

       CALL cpu_log( log_point_s(10), 'timesteps', 'stop' )


    ENDDO   ! time loop

#if defined( __dvrp_graphics )
    CALL DVRP_LOG_EVENT( -2, current_timestep_number )
#endif

 END SUBROUTINE time_integration