source: palm/trunk/SOURCE/prognostic_equations.f90 @ 1050

 MODULE prognostic_equations_mod

!--------------------------------------------------------------------------------!
! 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:
! -----------------
!
!
! Former revisions:
! -----------------
! $Id: prognostic_equations.f90 1037 2012-10-22 14:10:22Z hoffmann $
!
! 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
! new branch prognostic_equations_acc
! OpenACC statements added + code changes required for GPU optimization
!
! 1001 2012-09-13 14:08:46Z raasch
! all actions concerning leapfrog- and upstream-spline-scheme removed
!
! 978 2012-08-09 08:28:32Z fricke
! km_damp_x and km_damp_y removed in calls of diffusion_u and diffusion_v
! add ptdf_x, ptdf_y for damping the potential temperature at the inflow
! boundary in case of non-cyclic lateral boundaries
! Bugfix: first thread index changes for WS-scheme at the inflow
!
! 940 2012-07-09 14:31:00Z raasch
! temperature equation can be switched off
!
! 785 2011-11-28 09:47:19Z raasch
! new factor rdf_sc allows separate Rayleigh damping of scalars
!
! 736 2011-08-17 14:13:26Z suehring
! Bugfix: determination of first thread index i for WS-scheme
!
! 709 2011-03-30 09:31:40Z raasch
! formatting adjustments
!
! 673 2011-01-18 16:19:48Z suehring
! Consideration of the pressure gradient (steered by tsc(4)) during the time 
! integration removed.
!
! 667 2010-12-23 12:06:00Z suehring/gryschka
! Calls of the advection routines with WS5 added.
! Calls of ws_statistics added to set the statistical arrays to zero after each 
! time step.
!
! 531 2010-04-21 06:47:21Z heinze
! add call of subsidence in the equation for humidity / passive scalar
!
! 411 2009-12-11 14:15:58Z heinze
! add call of subsidence in the equation for potential temperature
!
! 388 2009-09-23 09:40:33Z raasch
! prho is used instead of rho in diffusion_e,
! external pressure gradient
!
! 153 2008-03-19 09:41:30Z steinfeld
! add call of plant_canopy_model in the prognostic equation for
! the potential temperature and for the passive scalar
!
! 138 2007-11-28 10:03:58Z letzel
! add call of subroutines that evaluate the canopy drag terms,
! add wall_*flux to parameter list of calls of diffusion_s
!
! 106 2007-08-16 14:30:26Z raasch
! +uswst, vswst as arguments in calls of diffusion_u|v,
! loops for u and v are starting from index nxlu, nysv, respectively (needed
! for non-cyclic boundary conditions)
!
! 97 2007-06-21 08:23:15Z raasch
! prognostic equation for salinity, density is calculated from equation of
! state for seawater and is used for calculation of buoyancy,
! +eqn_state_seawater_mod
! diffusion_e is called with argument rho in case of ocean runs,
! new argument zw in calls of diffusion_e, new argument pt_/prho_reference
! in calls of buoyancy and diffusion_e, calc_mean_pt_profile renamed
! calc_mean_profile
!
! 75 2007-03-22 09:54:05Z raasch
! checking for negative q and limiting for positive values,
! z0 removed from arguments in calls of diffusion_u/v/w, uxrp, vynp eliminated,
! subroutine names changed to .._noopt, .._cache, and .._vector,
! moisture renamed humidity, Bott-Chlond-scheme can be used in the
! _vector-version
!
! 19 2007-02-23 04:53:48Z raasch
! Calculation of e, q, and pt extended for gridpoint nzt,
! handling of given temperature/humidity/scalar fluxes at top surface
!
! RCS Log replace by Id keyword, revision history cleaned up
!
! Revision 1.21  2006/08/04 15:01:07  raasch
! upstream scheme can be forced to be used for tke (use_upstream_for_tke)
! regardless of the timestep scheme used for the other quantities,
! new argument diss in call of diffusion_e
!
! Revision 1.1  2000/04/13 14:56:27  schroeter
! Initial revision
!
!
! Description:
! ------------
! Solving the prognostic equations.
!------------------------------------------------------------------------------!

    USE arrays_3d
    USE control_parameters
    USE cpulog
    USE eqn_state_seawater_mod
    USE grid_variables
    USE indices
    USE interfaces
    USE pegrid
    USE pointer_interfaces
    USE statistics
    USE advec_ws
    USE advec_s_pw_mod
    USE advec_s_up_mod
    USE advec_u_pw_mod
    USE advec_u_up_mod
    USE advec_v_pw_mod
    USE advec_v_up_mod
    USE advec_w_pw_mod
    USE advec_w_up_mod
    USE buoyancy_mod
    USE calc_precipitation_mod
    USE calc_radiation_mod
    USE coriolis_mod
    USE diffusion_e_mod
    USE diffusion_s_mod
    USE diffusion_u_mod
    USE diffusion_v_mod
    USE diffusion_w_mod
    USE impact_of_latent_heat_mod
    USE plant_canopy_model_mod
    USE production_e_mod
    USE subsidence_mod
    USE user_actions_mod


    PRIVATE
    PUBLIC prognostic_equations_cache, prognostic_equations_vector, &
           prognostic_equations_acc

    INTERFACE prognostic_equations_cache
       MODULE PROCEDURE prognostic_equations_cache
    END INTERFACE prognostic_equations_cache

    INTERFACE prognostic_equations_vector
       MODULE PROCEDURE prognostic_equations_vector
    END INTERFACE prognostic_equations_vector

    INTERFACE prognostic_equations_acc
       MODULE PROCEDURE prognostic_equations_acc
    END INTERFACE prognostic_equations_acc


 CONTAINS


 SUBROUTINE prognostic_equations_cache

!------------------------------------------------------------------------------!
! Version with one optimized loop over all equations. It is only allowed to
! be called for the Wicker and Skamarock or Piascek-Williams advection scheme.
!
! Here the calls of most subroutines are embedded in two DO loops over i and j,
! so communication between CPUs is not allowed (does not make sense) within
! these loops.
!
! (Optimized to avoid cache missings, i.e. for Power4/5-architectures.)
!------------------------------------------------------------------------------!

    IMPLICIT NONE

    CHARACTER (LEN=9) ::  time_to_string
    INTEGER ::  i, i_omp_start, j, k, omp_get_thread_num, tn = 0
    LOGICAL ::  loop_start


!
!-- Time measurement can only be performed for the whole set of equations
    CALL cpu_log( log_point(32), 'all progn.equations', 'start' )


!
!-- Calculate those variables needed in the tendency terms which need
!-- global communication
    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 )
    IF ( .NOT. constant_diffusion )  CALL production_e_init
    IF ( ( ws_scheme_mom .OR. ws_scheme_sca )  .AND.  &
         intermediate_timestep_count == 1 )  CALL ws_statistics

!
!-- Loop over all prognostic equations
!$OMP PARALLEL private (i,i_omp_start,j,k,loop_start,tn)

!$  tn = omp_get_thread_num() 
    loop_start = .TRUE.
!$OMP DO
    DO  i = nxl, nxr

!
!--    Store the first loop index. It differs for each thread and is required
!--    later in advec_ws
       IF ( loop_start )  THEN
          loop_start  = .FALSE.
          i_omp_start = i 
       ENDIF
 
       DO  j = nys, nyn
!
!--       Tendency terms for u-velocity component
          IF ( .NOT. outflow_l  .OR.  i > nxl )  THEN

             tend(:,j,i) = 0.0
             IF ( timestep_scheme(1:5) == 'runge' )  THEN
                IF ( ws_scheme_mom )  THEN
                   IF ( ( inflow_l .OR. outflow_l ) .AND. i_omp_start == nxl )  THEN 
                      CALL advec_u_ws( i, j, i_omp_start + 1, tn )
                   ELSE
                      CALL advec_u_ws( i, j, i_omp_start, tn )
                   ENDIF
                ELSE 
                   CALL advec_u_pw( i, j )
                ENDIF 
             ELSE
                CALL advec_u_up( i, j )
             ENDIF
             CALL diffusion_u( i, j )
             CALL coriolis( i, j, 1 )
             IF ( sloping_surface  .AND.  .NOT. neutral )  THEN
                CALL buoyancy( i, j, pt, pt_reference, 1, 4 )
             ENDIF

!
!--          Drag by plant canopy
             IF ( plant_canopy )  CALL plant_canopy_model( i, j, 1 )

!
!--          External pressure gradient
             IF ( dp_external )  THEN
                DO  k = dp_level_ind_b+1, nzt
                   tend(k,j,i) = tend(k,j,i) - dpdxy(1) * dp_smooth_factor(k)
                ENDDO
             ENDIF

             CALL user_actions( i, j, 'u-tendency' )

!
!--          Prognostic equation for u-velocity component
             DO  k = nzb_u_inner(j,i)+1, nzt
                u_p(k,j,i) = u(k,j,i) + dt_3d * ( tsc(2) * tend(k,j,i) +       &
                                                  tsc(3) * tu_m(k,j,i) )       &
                                      - tsc(5) * rdf(k) * ( u(k,j,i) - ug(k) )
             ENDDO

!
!--          Calculate tendencies for the next Runge-Kutta step
             IF ( timestep_scheme(1:5) == 'runge' )  THEN
                IF ( intermediate_timestep_count == 1 )  THEN
                   DO  k = nzb_u_inner(j,i)+1, nzt
                      tu_m(k,j,i) = tend(k,j,i)
                   ENDDO
                ELSEIF ( intermediate_timestep_count < &
                         intermediate_timestep_count_max )  THEN
                   DO  k = nzb_u_inner(j,i)+1, nzt
                      tu_m(k,j,i) = -9.5625 * tend(k,j,i) + 5.3125 * tu_m(k,j,i)
                   ENDDO
                ENDIF
             ENDIF

          ENDIF

!
!--       Tendency terms for v-velocity component
          IF ( .NOT. outflow_s  .OR.  j > nys )  THEN

             tend(:,j,i) = 0.0
             IF ( timestep_scheme(1:5) == 'runge' )  THEN
                IF ( ws_scheme_mom )  THEN
                    CALL advec_v_ws( i, j, i_omp_start, tn )
                ELSE 
                    CALL advec_v_pw( i, j )
                ENDIF
             ELSE
                CALL advec_v_up( i, j )
             ENDIF
             CALL diffusion_v( i, j )
             CALL coriolis( i, j, 2 )

!
!--          Drag by plant canopy
             IF ( plant_canopy )  CALL plant_canopy_model( i, j, 2 )        

!
!--          External pressure gradient
             IF ( dp_external )  THEN
                DO  k = dp_level_ind_b+1, nzt
                   tend(k,j,i) = tend(k,j,i) - dpdxy(2) * dp_smooth_factor(k)
                ENDDO
             ENDIF

             CALL user_actions( i, j, 'v-tendency' )

!
!--          Prognostic equation for v-velocity component
             DO  k = nzb_v_inner(j,i)+1, nzt
                v_p(k,j,i) = v(k,j,i) + dt_3d * ( tsc(2) * tend(k,j,i) +       &
                                                  tsc(3) * tv_m(k,j,i) )       &
                                      - tsc(5) * rdf(k) * ( v(k,j,i) - vg(k) )
             ENDDO

!
!--          Calculate tendencies for the next Runge-Kutta step
             IF ( timestep_scheme(1:5) == 'runge' )  THEN
                IF ( intermediate_timestep_count == 1 )  THEN
                   DO  k = nzb_v_inner(j,i)+1, nzt
                      tv_m(k,j,i) = tend(k,j,i)
                   ENDDO
                ELSEIF ( intermediate_timestep_count < &
                         intermediate_timestep_count_max )  THEN
                   DO  k = nzb_v_inner(j,i)+1, nzt
                      tv_m(k,j,i) = -9.5625 * tend(k,j,i) + 5.3125 * tv_m(k,j,i)
                   ENDDO
                ENDIF
             ENDIF

          ENDIF

!
!--       Tendency terms for w-velocity component
          tend(:,j,i) = 0.0
          IF ( timestep_scheme(1:5) == 'runge' )  THEN
             IF ( ws_scheme_mom )  THEN
                CALL advec_w_ws( i, j, i_omp_start, tn )
             ELSE 
                CALL advec_w_pw( i, j )
             END IF
          ELSE
             CALL advec_w_up( i, j )
          ENDIF
          CALL diffusion_w( i, j )
          CALL coriolis( i, j, 3 )

          IF ( .NOT. neutral )  THEN
             IF ( ocean )  THEN
                CALL buoyancy( i, j, rho, rho_reference, 3, 64 )
             ELSE
                IF ( .NOT. humidity )  THEN
                   CALL buoyancy( i, j, pt, pt_reference, 3, 4 )
                ELSE
                   CALL buoyancy( i, j, vpt, pt_reference, 3, 44 )
                ENDIF
             ENDIF
          ENDIF

!
!--       Drag by plant canopy
          IF ( plant_canopy )  CALL plant_canopy_model( i, j, 3 )

          CALL user_actions( i, j, 'w-tendency' )

!
!--       Prognostic equation for w-velocity component
          DO  k = nzb_w_inner(j,i)+1, nzt-1
             w_p(k,j,i) = w(k,j,i) + dt_3d * ( tsc(2) * tend(k,j,i) +          &
                                               tsc(3) * tw_m(k,j,i) )          &
                                   - tsc(5) * rdf(k) * w(k,j,i)
          ENDDO

!
!--       Calculate tendencies for the next Runge-Kutta step
          IF ( timestep_scheme(1:5) == 'runge' )  THEN
             IF ( intermediate_timestep_count == 1 )  THEN
                DO  k = nzb_w_inner(j,i)+1, nzt-1
                   tw_m(k,j,i) = tend(k,j,i)
                ENDDO
             ELSEIF ( intermediate_timestep_count < &
                      intermediate_timestep_count_max )  THEN
                DO  k = nzb_w_inner(j,i)+1, nzt-1
                   tw_m(k,j,i) = -9.5625 * tend(k,j,i) + 5.3125 * tw_m(k,j,i)
                ENDDO
             ENDIF
          ENDIF

!
!--       If required, compute prognostic equation for potential temperature
          IF ( .NOT. neutral )  THEN
!
!--          Tendency terms for potential temperature
             tend(:,j,i) = 0.0
             IF ( timestep_scheme(1:5) == 'runge' )  THEN
                   IF ( ws_scheme_sca )  THEN
                      CALL advec_s_ws( i, j, pt, 'pt', flux_s_pt, diss_s_pt, &
                                       flux_l_pt, diss_l_pt, i_omp_start, tn )
                   ELSE
                      CALL advec_s_pw( i, j, pt )
                   ENDIF
             ELSE
                CALL advec_s_up( i, j, pt )
             ENDIF
             CALL diffusion_s( i, j, pt, shf, tswst, wall_heatflux )

!
!--          If required compute heating/cooling due to long wave radiation
!--          processes
             IF ( radiation )  THEN
                CALL calc_radiation( i, j )
             ENDIF

!
!--          If required compute impact of latent heat due to precipitation
             IF ( precipitation )  THEN
                CALL impact_of_latent_heat( i, j )
             ENDIF

!
!--          Consideration of heat sources within the plant canopy
             IF ( plant_canopy .AND. ( cthf /= 0.0 ) ) THEN
                CALL plant_canopy_model( i, j, 4 )
             ENDIF

!
!--          If required, compute influence of large-scale subsidence/ascent
             IF ( large_scale_subsidence )  THEN
                CALL subsidence( i, j, tend, pt, pt_init )
             ENDIF


             CALL user_actions( i, j, 'pt-tendency' )

!
!--          Prognostic equation for potential temperature
             DO  k = nzb_s_inner(j,i)+1, nzt
                pt_p(k,j,i) = pt(k,j,i) + dt_3d * ( tsc(2) * tend(k,j,i) +     &
                                                    tsc(3) * tpt_m(k,j,i) )    &
                                        - tsc(5) * ( pt(k,j,i) - pt_init(k) ) *&
                                          ( rdf_sc(k) + ptdf_x(i) + ptdf_y(j) )
             ENDDO

!
!--          Calculate tendencies for the next Runge-Kutta step
             IF ( timestep_scheme(1:5) == 'runge' )  THEN
                IF ( intermediate_timestep_count == 1 )  THEN
                   DO  k = nzb_s_inner(j,i)+1, nzt
                      tpt_m(k,j,i) = tend(k,j,i)
                   ENDDO
                ELSEIF ( intermediate_timestep_count < &
                         intermediate_timestep_count_max )  THEN
                   DO  k = nzb_s_inner(j,i)+1, nzt
                      tpt_m(k,j,i) = -9.5625 * tend(k,j,i) + &
                                      5.3125 * tpt_m(k,j,i)
                   ENDDO
                ENDIF
             ENDIF

          ENDIF

!
!--       If required, compute prognostic equation for salinity
          IF ( ocean )  THEN

!
!--          Tendency-terms for salinity
             tend(:,j,i) = 0.0
             IF ( timestep_scheme(1:5) == 'runge' ) &
             THEN
                IF ( ws_scheme_sca )  THEN
                    CALL advec_s_ws( i, j, sa, 'sa', flux_s_sa,  &
                                diss_s_sa, flux_l_sa, diss_l_sa, i_omp_start, tn  )
                ELSE 
                    CALL advec_s_pw( i, j, sa )
                ENDIF
             ELSE
                CALL advec_s_up( i, j, sa )
             ENDIF
             CALL diffusion_s( i, j, sa, saswsb, saswst, wall_salinityflux )

             CALL user_actions( i, j, 'sa-tendency' )

!
!--          Prognostic equation for salinity
             DO  k = nzb_s_inner(j,i)+1, nzt
                sa_p(k,j,i) = sa(k,j,i) + dt_3d * ( tsc(2) * tend(k,j,i) +     &
                                                    tsc(3) * tsa_m(k,j,i) )    &
                                        - tsc(5) * rdf_sc(k) *                 &
                                          ( sa(k,j,i) - sa_init(k) )
                IF ( sa_p(k,j,i) < 0.0 )  sa_p(k,j,i) = 0.1 * sa(k,j,i)
             ENDDO

!
!--          Calculate tendencies for the next Runge-Kutta step
             IF ( timestep_scheme(1:5) == 'runge' )  THEN
                IF ( intermediate_timestep_count == 1 )  THEN
                   DO  k = nzb_s_inner(j,i)+1, nzt
                      tsa_m(k,j,i) = tend(k,j,i)
                   ENDDO
                ELSEIF ( intermediate_timestep_count < &
                         intermediate_timestep_count_max )  THEN
                   DO  k = nzb_s_inner(j,i)+1, nzt
                      tsa_m(k,j,i) = -9.5625 * tend(k,j,i) + &
                                      5.3125 * tsa_m(k,j,i)
                   ENDDO
                ENDIF
             ENDIF

!
!--          Calculate density by the equation of state for seawater
             CALL eqn_state_seawater( i, j )

          ENDIF

!
!--       If required, compute prognostic equation for total water content /
!--       scalar
          IF ( humidity  .OR.  passive_scalar )  THEN

!
!--          Tendency-terms for total water content / scalar
             tend(:,j,i) = 0.0
             IF ( timestep_scheme(1:5) == 'runge' ) &
             THEN
                IF ( ws_scheme_sca )  THEN
                   CALL advec_s_ws( i, j, q, 'q', flux_s_q, & 
                                diss_s_q, flux_l_q, diss_l_q, i_omp_start, tn )
                ELSE 
                   CALL advec_s_pw( i, j, q )
                ENDIF
             ELSE
                CALL advec_s_up( i, j, q )
             ENDIF
             CALL diffusion_s( i, j, q, qsws, qswst, wall_qflux )
       
!
!--          If required compute decrease of total water content due to
!--          precipitation
             IF ( precipitation )  THEN
                CALL calc_precipitation( i, j )
             ENDIF

!
!--          Sink or source of scalar concentration due to canopy elements
             IF ( plant_canopy ) CALL plant_canopy_model( i, j, 5 )

!--          If required compute influence of large-scale subsidence/ascent
             IF ( large_scale_subsidence )  THEN
                CALL subsidence( i, j, tend, q, q_init )
             ENDIF

             CALL user_actions( i, j, 'q-tendency' )

!
!--          Prognostic equation for total water content / scalar
             DO  k = nzb_s_inner(j,i)+1, nzt
                q_p(k,j,i) = q(k,j,i) + dt_3d * ( tsc(2) * tend(k,j,i) +       &
                                                  tsc(3) * tq_m(k,j,i) )       &
                                      - tsc(5) * rdf_sc(k) *                   &
                                        ( q(k,j,i) - q_init(k) )
                IF ( q_p(k,j,i) < 0.0 )  q_p(k,j,i) = 0.1 * q(k,j,i)
             ENDDO

!
!--          Calculate tendencies for the next Runge-Kutta step
             IF ( timestep_scheme(1:5) == 'runge' )  THEN
                IF ( intermediate_timestep_count == 1 )  THEN
                   DO  k = nzb_s_inner(j,i)+1, nzt
                      tq_m(k,j,i) = tend(k,j,i)
                   ENDDO
                ELSEIF ( intermediate_timestep_count < &
                         intermediate_timestep_count_max )  THEN
                   DO  k = nzb_s_inner(j,i)+1, nzt
                      tq_m(k,j,i) = -9.5625 * tend(k,j,i) + &
                                     5.3125 * tq_m(k,j,i)
                   ENDDO
                ENDIF
             ENDIF

          ENDIF

!
!--       If required, compute prognostic equation for turbulent kinetic 
!--       energy (TKE)
          IF ( .NOT. constant_diffusion )  THEN

!
!--          Tendency-terms for TKE
             tend(:,j,i) = 0.0
             IF ( timestep_scheme(1:5) == 'runge'  &
                 .AND.  .NOT. use_upstream_for_tke )  THEN
                 IF ( ws_scheme_sca )  THEN
                     CALL advec_s_ws( i, j, e, 'e', flux_s_e, diss_s_e, &
                                      flux_l_e, diss_l_e , i_omp_start, tn )
                 ELSE
                     CALL advec_s_pw( i, j, e )
                 ENDIF
             ELSE
                CALL advec_s_up( i, j, e )
             ENDIF
             IF ( .NOT. humidity )  THEN
                IF ( ocean )  THEN
                   CALL diffusion_e( i, j, prho, prho_reference )
                ELSE
                   CALL diffusion_e( i, j, pt, pt_reference )
                ENDIF
             ELSE
                CALL diffusion_e( i, j, vpt, pt_reference )
             ENDIF
             CALL production_e( i, j )

!
!--          Additional sink term for flows through plant canopies
             IF ( plant_canopy )  CALL plant_canopy_model( i, j, 6 ) 

             CALL user_actions( i, j, 'e-tendency' )

!
!--          Prognostic equation for TKE.
!--          Eliminate negative TKE values, which can occur due to numerical
!--          reasons in the course of the integration. In such cases the old
!--          TKE value is reduced by 90%.
             DO  k = nzb_s_inner(j,i)+1, nzt
                e_p(k,j,i) = e(k,j,i) + dt_3d * ( tsc(2) * tend(k,j,i) +       &
                                                  tsc(3) * te_m(k,j,i) )
                IF ( e_p(k,j,i) < 0.0 )  e_p(k,j,i) = 0.1 * e(k,j,i)
             ENDDO

!
!--          Calculate tendencies for the next Runge-Kutta step
             IF ( timestep_scheme(1:5) == 'runge' )  THEN
                IF ( intermediate_timestep_count == 1 )  THEN
                   DO  k = nzb_s_inner(j,i)+1, nzt
                      te_m(k,j,i) = tend(k,j,i)
                   ENDDO
                ELSEIF ( intermediate_timestep_count < &
                         intermediate_timestep_count_max )  THEN
                   DO  k = nzb_s_inner(j,i)+1, nzt
                      te_m(k,j,i) = -9.5625 * tend(k,j,i) + &
                                     5.3125 * te_m(k,j,i)
                   ENDDO
                ENDIF
             ENDIF

          ENDIF   ! TKE equation

       ENDDO
    ENDDO
!$OMP END PARALLEL

    CALL cpu_log( log_point(32), 'all progn.equations', 'stop' )


 END SUBROUTINE prognostic_equations_cache


 SUBROUTINE prognostic_equations_vector

!------------------------------------------------------------------------------!
! Version for vector machines
!------------------------------------------------------------------------------!

    IMPLICIT NONE

    CHARACTER (LEN=9) ::  time_to_string
    INTEGER ::  i, j, k
    REAL    ::  sbt

!
!-- Calculate those variables needed in the tendency terms which need
!-- global communication
    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 )
    IF ( ( ws_scheme_mom .OR. ws_scheme_sca )  .AND.  &
         intermediate_timestep_count == 1 )  CALL ws_statistics

!
!-- u-velocity component
    CALL cpu_log( log_point(5), 'u-equation', 'start' )

    tend = 0.0
    IF ( timestep_scheme(1:5) == 'runge' )  THEN
       IF ( ws_scheme_mom )  THEN
          CALL advec_u_ws
       ELSE
          CALL advec_u_pw
       ENDIF
    ELSE
       CALL advec_u_up
    ENDIF
    CALL diffusion_u
    CALL coriolis( 1 )
    IF ( sloping_surface  .AND.  .NOT. neutral )  THEN
       CALL buoyancy( pt, pt_reference, 1, 4 )
    ENDIF

!
!-- Drag by plant canopy
    IF ( plant_canopy )  CALL plant_canopy_model( 1 )

!
!-- External pressure gradient
    IF ( dp_external )  THEN
       DO  i = nxlu, nxr
          DO  j = nys, nyn
             DO  k = dp_level_ind_b+1, nzt
                tend(k,j,i) = tend(k,j,i) - dpdxy(1) * dp_smooth_factor(k)
             ENDDO
          ENDDO
       ENDDO
    ENDIF

    CALL user_actions( 'u-tendency' )

!
!-- Prognostic equation for u-velocity component
    DO  i = nxlu, nxr
       DO  j = nys, nyn
          DO  k = nzb_u_inner(j,i)+1, nzt
             u_p(k,j,i) = u(k,j,i) + dt_3d * ( tsc(2) * tend(k,j,i) +          &
                                               tsc(3) * tu_m(k,j,i) )          &
                                   - tsc(5) * rdf(k) * ( u(k,j,i) - ug(k) )
          ENDDO
       ENDDO
    ENDDO

!
!-- Calculate tendencies for the next Runge-Kutta step
    IF ( timestep_scheme(1:5) == 'runge' )  THEN
       IF ( intermediate_timestep_count == 1 )  THEN
          DO  i = nxlu, nxr
             DO  j = nys, nyn
                DO  k = nzb_u_inner(j,i)+1, nzt
                   tu_m(k,j,i) = tend(k,j,i)
                ENDDO
             ENDDO
          ENDDO
       ELSEIF ( intermediate_timestep_count < &
                intermediate_timestep_count_max )  THEN
          DO  i = nxlu, nxr
             DO  j = nys, nyn
                DO  k = nzb_u_inner(j,i)+1, nzt
                   tu_m(k,j,i) = -9.5625 * tend(k,j,i) + 5.3125 * tu_m(k,j,i)
                ENDDO
             ENDDO
          ENDDO
       ENDIF
    ENDIF

    CALL cpu_log( log_point(5), 'u-equation', 'stop' )

!
!-- v-velocity component
    CALL cpu_log( log_point(6), 'v-equation', 'start' )

    tend = 0.0
    IF ( timestep_scheme(1:5) == 'runge' )  THEN
       IF ( ws_scheme_mom )  THEN
          CALL advec_v_ws
       ELSE 
          CALL advec_v_pw
       END IF
    ELSE
       CALL advec_v_up
    ENDIF
    CALL diffusion_v
    CALL coriolis( 2 )

!
!-- Drag by plant canopy
    IF ( plant_canopy )  CALL plant_canopy_model( 2 )

!
!-- External pressure gradient
    IF ( dp_external )  THEN
       DO  i = nxl, nxr
          DO  j = nysv, nyn
             DO  k = dp_level_ind_b+1, nzt
                tend(k,j,i) = tend(k,j,i) - dpdxy(2) * dp_smooth_factor(k)
             ENDDO
          ENDDO
       ENDDO
    ENDIF

    CALL user_actions( 'v-tendency' )

!
!-- Prognostic equation for v-velocity component
    DO  i = nxl, nxr
       DO  j = nysv, nyn
          DO  k = nzb_v_inner(j,i)+1, nzt
             v_p(k,j,i) = v(k,j,i) + dt_3d * ( tsc(2) * tend(k,j,i) +          &
                                               tsc(3) * tv_m(k,j,i) )          &
                                   - tsc(5) * rdf(k) * ( v(k,j,i) - vg(k) )
          ENDDO
       ENDDO
    ENDDO

!
!-- Calculate tendencies for the next Runge-Kutta step
    IF ( timestep_scheme(1:5) == 'runge' )  THEN
       IF ( intermediate_timestep_count == 1 )  THEN
          DO  i = nxl, nxr
             DO  j = nysv, nyn
                DO  k = nzb_v_inner(j,i)+1, nzt
                   tv_m(k,j,i) = tend(k,j,i)
                ENDDO
             ENDDO
          ENDDO
       ELSEIF ( intermediate_timestep_count < &
                intermediate_timestep_count_max )  THEN
          DO  i = nxl, nxr
             DO  j = nysv, nyn
                DO  k = nzb_v_inner(j,i)+1, nzt
                   tv_m(k,j,i) = -9.5625 * tend(k,j,i) + 5.3125 * tv_m(k,j,i)
                ENDDO
             ENDDO
          ENDDO
       ENDIF
    ENDIF

    CALL cpu_log( log_point(6), 'v-equation', 'stop' )

!
!-- w-velocity component
    CALL cpu_log( log_point(7), 'w-equation', 'start' )

    tend = 0.0
    IF ( timestep_scheme(1:5) == 'runge' )  THEN
       IF ( ws_scheme_mom )  THEN
          CALL advec_w_ws
       ELSE
          CALL advec_w_pw
       ENDIF
    ELSE
       CALL advec_w_up
    ENDIF
    CALL diffusion_w
    CALL coriolis( 3 )

    IF ( .NOT. neutral )  THEN
       IF ( ocean )  THEN
          CALL buoyancy( rho, rho_reference, 3, 64 )
       ELSE
          IF ( .NOT. humidity )  THEN
             CALL buoyancy( pt, pt_reference, 3, 4 )
          ELSE
             CALL buoyancy( vpt, pt_reference, 3, 44 )
          ENDIF
       ENDIF
    ENDIF

!
!-- Drag by plant canopy
    IF ( plant_canopy )  CALL plant_canopy_model( 3 )

    CALL user_actions( 'w-tendency' )

!
!-- Prognostic equation for w-velocity component
    DO  i = nxl, nxr
       DO  j = nys, nyn
          DO  k = nzb_w_inner(j,i)+1, nzt-1
             w_p(k,j,i) = w(k,j,i) + dt_3d * ( tsc(2) * tend(k,j,i) +          &
                                               tsc(3) * tw_m(k,j,i) )          &
                                   - tsc(5) * rdf(k) * w(k,j,i)
          ENDDO
       ENDDO
    ENDDO

!
!-- Calculate tendencies for the next Runge-Kutta step
    IF ( timestep_scheme(1:5) == 'runge' )  THEN
       IF ( intermediate_timestep_count == 1 )  THEN
          DO  i = nxl, nxr
             DO  j = nys, nyn
                DO  k = nzb_w_inner(j,i)+1, nzt-1
                   tw_m(k,j,i) = tend(k,j,i)
                ENDDO
             ENDDO
          ENDDO
       ELSEIF ( intermediate_timestep_count < &
                intermediate_timestep_count_max )  THEN
          DO  i = nxl, nxr
             DO  j = nys, nyn
                DO  k = nzb_w_inner(j,i)+1, nzt-1
                   tw_m(k,j,i) = -9.5625 * tend(k,j,i) + 5.3125 * tw_m(k,j,i)
                ENDDO
             ENDDO
          ENDDO
       ENDIF
    ENDIF

    CALL cpu_log( log_point(7), 'w-equation', 'stop' )


!
!-- If required, compute prognostic equation for potential temperature
    IF ( .NOT. neutral )  THEN

       CALL cpu_log( log_point(13), 'pt-equation', 'start' )

!
!--    pt-tendency terms with communication
       sbt = tsc(2)
       IF ( scalar_advec == 'bc-scheme' )  THEN

          IF ( timestep_scheme(1:5) /= 'runge' )  THEN
!
!--          Bott-Chlond scheme always uses Euler time step. Thus:
             sbt = 1.0
          ENDIF
          tend = 0.0
          CALL advec_s_bc( pt, 'pt' )

       ENDIF

!
!--    pt-tendency terms with no communication
       IF ( scalar_advec /= 'bc-scheme' )  THEN
          tend = 0.0
          IF ( timestep_scheme(1:5) == 'runge' )  THEN
             IF ( ws_scheme_sca )  THEN
                CALL advec_s_ws( pt, 'pt' )
             ELSE
                CALL advec_s_pw( pt )
             ENDIF
          ELSE
             CALL advec_s_up( pt )
          ENDIF
       ENDIF

       CALL diffusion_s( pt, shf, tswst, wall_heatflux )

!
!--    If required compute heating/cooling due to long wave radiation processes
       IF ( radiation )  THEN
          CALL calc_radiation
       ENDIF

!
!--    If required compute impact of latent heat due to precipitation
       IF ( precipitation )  THEN
          CALL impact_of_latent_heat
       ENDIF

!
!--    Consideration of heat sources within the plant canopy
       IF ( plant_canopy .AND. ( cthf /= 0.0 ) ) THEN
          CALL plant_canopy_model( 4 )
       ENDIF

!
!--    If required compute influence of large-scale subsidence/ascent
       IF ( large_scale_subsidence )  THEN
          CALL subsidence( tend, pt, pt_init )
       ENDIF

       CALL user_actions( 'pt-tendency' )

!
!--    Prognostic equation for potential temperature
       DO  i = nxl, nxr
          DO  j = nys, nyn
             DO  k = nzb_s_inner(j,i)+1, nzt
                pt_p(k,j,i) = pt(k,j,i) + dt_3d * ( sbt * tend(k,j,i) +        &
                                                    tsc(3) * tpt_m(k,j,i) )    &
                                        - tsc(5) * ( pt(k,j,i) - pt_init(k) ) *&
                                          ( rdf_sc(k) + ptdf_x(i) + ptdf_y(j) )
             ENDDO
          ENDDO
       ENDDO

!
!--    Calculate tendencies for the next Runge-Kutta step
       IF ( timestep_scheme(1:5) == 'runge' )  THEN
          IF ( intermediate_timestep_count == 1 )  THEN
             DO  i = nxl, nxr
                DO  j = nys, nyn
                   DO  k = nzb_s_inner(j,i)+1, nzt
                      tpt_m(k,j,i) = tend(k,j,i)
                   ENDDO
                ENDDO
             ENDDO
          ELSEIF ( intermediate_timestep_count < &
                   intermediate_timestep_count_max )  THEN
             DO  i = nxl, nxr
                DO  j = nys, nyn
                   DO  k = nzb_s_inner(j,i)+1, nzt
                      tpt_m(k,j,i) = -9.5625 * tend(k,j,i) + &
                                      5.3125 * tpt_m(k,j,i)
                   ENDDO
                ENDDO
             ENDDO
          ENDIF
       ENDIF

       CALL cpu_log( log_point(13), 'pt-equation', 'stop' )

    ENDIF

!
!-- If required, compute prognostic equation for salinity
    IF ( ocean )  THEN

       CALL cpu_log( log_point(37), 'sa-equation', 'start' )

!
!--    sa-tendency terms with communication
       sbt = tsc(2)
       IF ( scalar_advec == 'bc-scheme' )  THEN

          IF ( timestep_scheme(1:5) /= 'runge' )  THEN
!
!--          Bott-Chlond scheme always uses Euler time step. Thus:
             sbt = 1.0
          ENDIF
          tend = 0.0
          CALL advec_s_bc( sa, 'sa' )

       ENDIF

!
!--    sa-tendency terms with no communication
       IF ( scalar_advec /= 'bc-scheme' )  THEN
          tend = 0.0
          IF ( timestep_scheme(1:5) == 'runge' )  THEN
             IF ( ws_scheme_sca )  THEN
                 CALL advec_s_ws( sa, 'sa' )
             ELSE
                 CALL advec_s_pw( sa )
             ENDIF
          ELSE
             CALL advec_s_up( sa )
          ENDIF
       ENDIF

       CALL diffusion_s( sa, saswsb, saswst, wall_salinityflux )
       
       CALL user_actions( 'sa-tendency' )

!
!--    Prognostic equation for salinity
       DO  i = nxl, nxr
          DO  j = nys, nyn
             DO  k = nzb_s_inner(j,i)+1, nzt
                sa_p(k,j,i) = sa(k,j,i) + dt_3d * ( sbt * tend(k,j,i) +        &
                                                    tsc(3) * tsa_m(k,j,i) )    &
                                        - tsc(5) * rdf_sc(k) *                 &
                                          ( sa(k,j,i) - sa_init(k) )
                IF ( sa_p(k,j,i) < 0.0 )  sa_p(k,j,i) = 0.1 * sa(k,j,i)
             ENDDO
          ENDDO
       ENDDO

!
!--    Calculate tendencies for the next Runge-Kutta step
       IF ( timestep_scheme(1:5) == 'runge' )  THEN
          IF ( intermediate_timestep_count == 1 )  THEN
             DO  i = nxl, nxr
                DO  j = nys, nyn
                   DO  k = nzb_s_inner(j,i)+1, nzt
                      tsa_m(k,j,i) = tend(k,j,i)
                   ENDDO
                ENDDO
             ENDDO
          ELSEIF ( intermediate_timestep_count < &
                   intermediate_timestep_count_max )  THEN
             DO  i = nxl, nxr
                DO  j = nys, nyn
                   DO  k = nzb_s_inner(j,i)+1, nzt
                      tsa_m(k,j,i) = -9.5625 * tend(k,j,i) + &
                                      5.3125 * tsa_m(k,j,i)
                   ENDDO
                ENDDO
             ENDDO
          ENDIF
       ENDIF

       CALL cpu_log( log_point(37), 'sa-equation', 'stop' )

!
!--    Calculate density by the equation of state for seawater
       CALL cpu_log( log_point(38), 'eqns-seawater', 'start' )
       CALL eqn_state_seawater
       CALL cpu_log( log_point(38), 'eqns-seawater', 'stop' )

    ENDIF

!
!-- If required, compute prognostic equation for total water content / scalar
    IF ( humidity  .OR.  passive_scalar )  THEN

       CALL cpu_log( log_point(29), 'q/s-equation', 'start' )

!
!--    Scalar/q-tendency terms with communication
       sbt = tsc(2)
       IF ( scalar_advec == 'bc-scheme' )  THEN

          IF ( timestep_scheme(1:5) /= 'runge' )  THEN
!
!--          Bott-Chlond scheme always uses Euler time step. Thus:
             sbt = 1.0
          ENDIF
          tend = 0.0
          CALL advec_s_bc( q, 'q' )

       ENDIF

!
!--    Scalar/q-tendency terms with no communication
       IF ( scalar_advec /= 'bc-scheme' )  THEN
          tend = 0.0
          IF ( timestep_scheme(1:5) == 'runge' )  THEN
             IF ( ws_scheme_sca )  THEN
                CALL advec_s_ws( q, 'q' )
             ELSE
                CALL advec_s_pw( q )
             ENDIF
          ELSE
             CALL advec_s_up( q )
          ENDIF
       ENDIF

       CALL diffusion_s( q, qsws, qswst, wall_qflux )
       
!
!--    If required compute decrease of total water content due to
!--    precipitation
       IF ( precipitation )  THEN
          CALL calc_precipitation
       ENDIF

!
!--    Sink or source of scalar concentration due to canopy elements
       IF ( plant_canopy ) CALL plant_canopy_model( 5 )
       
!
!--    If required compute influence of large-scale subsidence/ascent
       IF ( large_scale_subsidence )  THEN
         CALL subsidence( tend, q, q_init )
       ENDIF

       CALL user_actions( 'q-tendency' )

!
!--    Prognostic equation for total water content / scalar
       DO  i = nxl, nxr
          DO  j = nys, nyn
             DO  k = nzb_s_inner(j,i)+1, nzt
                q_p(k,j,i) = q(k,j,i) + dt_3d * ( sbt * tend(k,j,i) +          &
                                                  tsc(3) * tq_m(k,j,i) )       &
                                      - tsc(5) * rdf_sc(k) *                   &
                                        ( q(k,j,i) - q_init(k) )
                IF ( q_p(k,j,i) < 0.0 )  q_p(k,j,i) = 0.1 * q(k,j,i)
             ENDDO
          ENDDO
       ENDDO

!
!--    Calculate tendencies for the next Runge-Kutta step
       IF ( timestep_scheme(1:5) == 'runge' )  THEN
          IF ( intermediate_timestep_count == 1 )  THEN
             DO  i = nxl, nxr
                DO  j = nys, nyn
                   DO  k = nzb_s_inner(j,i)+1, nzt
                      tq_m(k,j,i) = tend(k,j,i)
                   ENDDO
                ENDDO
             ENDDO
          ELSEIF ( intermediate_timestep_count < &
                   intermediate_timestep_count_max )  THEN
             DO  i = nxl, nxr
                DO  j = nys, nyn
                   DO  k = nzb_s_inner(j,i)+1, nzt
                      tq_m(k,j,i) = -9.5625 * tend(k,j,i) + 5.3125 * tq_m(k,j,i)
                   ENDDO
                ENDDO
             ENDDO
          ENDIF
       ENDIF

       CALL cpu_log( log_point(29), 'q/s-equation', 'stop' )

    ENDIF

!
!-- If required, compute prognostic equation for turbulent kinetic 
!-- energy (TKE)
    IF ( .NOT. constant_diffusion )  THEN

       CALL cpu_log( log_point(16), 'tke-equation', 'start' )

!
!--    TKE-tendency terms with communication
       CALL production_e_init

       sbt = tsc(2)
       IF ( .NOT. use_upstream_for_tke )  THEN
          IF ( scalar_advec == 'bc-scheme' )  THEN

             IF ( timestep_scheme(1:5) /= 'runge' )  THEN
!
!--             Bott-Chlond scheme always uses Euler time step. Thus:
                sbt = 1.0
             ENDIF
             tend = 0.0
             CALL advec_s_bc( e, 'e' )

          ENDIF
       ENDIF

!
!--    TKE-tendency terms with no communication
       IF ( scalar_advec /= 'bc-scheme'  .OR.  use_upstream_for_tke )  THEN
          IF ( use_upstream_for_tke )  THEN
             tend = 0.0
             CALL advec_s_up( e )
          ELSE
             tend = 0.0
             IF ( timestep_scheme(1:5) == 'runge' )  THEN
                IF ( ws_scheme_sca )  THEN
                   CALL advec_s_ws( e, 'e' )
                ELSE 
                   CALL advec_s_pw( e )
                ENDIF
             ELSE
                CALL advec_s_up( e )
             ENDIF
          ENDIF
       ENDIF

       IF ( .NOT. humidity )  THEN
          IF ( ocean )  THEN
             CALL diffusion_e( prho, prho_reference )
          ELSE
             CALL diffusion_e( pt, pt_reference )
          ENDIF
       ELSE
          CALL diffusion_e( vpt, pt_reference )
       ENDIF

       CALL production_e

!
!--    Additional sink term for flows through plant canopies
       IF ( plant_canopy )  CALL plant_canopy_model( 6 )
       CALL user_actions( 'e-tendency' )

!
!--    Prognostic equation for TKE.
!--    Eliminate negative TKE values, which can occur due to numerical
!--    reasons in the course of the integration. In such cases the old TKE
!--    value is reduced by 90%.
       DO  i = nxl, nxr
          DO  j = nys, nyn
             DO  k = nzb_s_inner(j,i)+1, nzt
                e_p(k,j,i) = e(k,j,i) + dt_3d * ( sbt * tend(k,j,i) +          &
                                                  tsc(3) * te_m(k,j,i) )
                IF ( e_p(k,j,i) < 0.0 )  e_p(k,j,i) = 0.1 * e(k,j,i)
             ENDDO
          ENDDO
       ENDDO

!
!--    Calculate tendencies for the next Runge-Kutta step
       IF ( timestep_scheme(1:5) == 'runge' )  THEN
          IF ( intermediate_timestep_count == 1 )  THEN
             DO  i = nxl, nxr
                DO  j = nys, nyn
                   DO  k = nzb_s_inner(j,i)+1, nzt
                      te_m(k,j,i) = tend(k,j,i)
                   ENDDO
                ENDDO
             ENDDO
          ELSEIF ( intermediate_timestep_count < &
                   intermediate_timestep_count_max )  THEN
             DO  i = nxl, nxr
                DO  j = nys, nyn
                   DO  k = nzb_s_inner(j,i)+1, nzt
                      te_m(k,j,i) = -9.5625 * tend(k,j,i) + 5.3125 * te_m(k,j,i)
                   ENDDO
                ENDDO
             ENDDO
          ENDIF
       ENDIF

       CALL cpu_log( log_point(16), 'tke-equation', 'stop' )

    ENDIF


 END SUBROUTINE prognostic_equations_vector


 SUBROUTINE prognostic_equations_acc

!------------------------------------------------------------------------------!
! Version for accelerator boards
!------------------------------------------------------------------------------!

    IMPLICIT NONE

    CHARACTER (LEN=9) ::  time_to_string
    INTEGER ::  i, j, k, runge_step
    REAL    ::  sbt

!
!-- Set switch for intermediate Runge-Kutta step
    runge_step = 0
    IF ( timestep_scheme(1:5) == 'runge' )  THEN
       IF ( intermediate_timestep_count == 1 )  THEN
          runge_step = 1
       ELSEIF ( intermediate_timestep_count < &
                intermediate_timestep_count_max )  THEN
          runge_step = 2
       ENDIF
    ENDIF

!
!-- Calculate those variables needed in the tendency terms which need
!-- global communication
    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 )
    IF ( ( ws_scheme_mom .OR. ws_scheme_sca )  .AND.  &
         intermediate_timestep_count == 1 )  CALL ws_statistics

!
!-- u-velocity component
!++ Statistics still not ported to accelerators
    !$acc update device( hom )
    CALL cpu_log( log_point(5), 'u-equation', 'start' )

    IF ( timestep_scheme(1:5) == 'runge' )  THEN
       IF ( ws_scheme_mom )  THEN
          CALL advec_u_ws_acc
       ELSE
          tend = 0.0    ! to be removed later??
          CALL advec_u_pw
       ENDIF
    ELSE
       CALL advec_u_up
    ENDIF
    CALL diffusion_u_acc
    CALL coriolis_acc( 1 )
    IF ( sloping_surface  .AND.  .NOT. neutral )  THEN
       CALL buoyancy( pt, pt_reference, 1, 4 )
    ENDIF

!
!-- Drag by plant canopy
    IF ( plant_canopy )  CALL plant_canopy_model( 1 )

!
!-- External pressure gradient
    IF ( dp_external )  THEN
       DO  i = nxlu, nxr
          DO  j = nys, nyn
             DO  k = dp_level_ind_b+1, nzt
                tend(k,j,i) = tend(k,j,i) - dpdxy(1) * dp_smooth_factor(k)
             ENDDO
          ENDDO
       ENDDO
    ENDIF

    CALL user_actions( 'u-tendency' )

!
!-- Prognostic equation for u-velocity component
    !$acc kernels present( nzb_u_inner, rdf, tend, tu_m, u, ug, u_p )
    !$acc loop
    DO  i = nxlu, nxr
       DO  j = nys, nyn
          !$acc loop vector( 32 )
          DO  k = 1, nzt
             IF ( k > nzb_u_inner(j,i) )  THEN
                u_p(k,j,i) = u(k,j,i) + dt_3d * ( tsc(2) * tend(k,j,i) +       &
                                                  tsc(3) * tu_m(k,j,i) )       &
                                      - tsc(5) * rdf(k) * ( u(k,j,i) - ug(k) )
!
!--             Tendencies for the next Runge-Kutta step
                IF ( runge_step == 1 )  THEN
                   tu_m(k,j,i) = tend(k,j,i)
                ELSEIF ( runge_step == 2 )  THEN
                   tu_m(k,j,i) = -9.5625 * tend(k,j,i) + 5.3125 * tu_m(k,j,i)
                ENDIF
             ENDIF
          ENDDO
       ENDDO
    ENDDO
    !$acc end kernels

    CALL cpu_log( log_point(5), 'u-equation', 'stop' )
    !$acc update host( u_p )

!
!-- v-velocity component
    CALL cpu_log( log_point(6), 'v-equation', 'start' )

    IF ( timestep_scheme(1:5) == 'runge' )  THEN
       IF ( ws_scheme_mom )  THEN
          CALL advec_v_ws_acc
       ELSE
          tend = 0.0    ! to be removed later??
          CALL advec_v_pw
       END IF
    ELSE
       CALL advec_v_up
    ENDIF
    CALL diffusion_v_acc
    CALL coriolis_acc( 2 )

!
!-- Drag by plant canopy
    IF ( plant_canopy )  CALL plant_canopy_model( 2 )

!
!-- External pressure gradient
    IF ( dp_external )  THEN
       DO  i = nxl, nxr
          DO  j = nysv, nyn
             DO  k = dp_level_ind_b+1, nzt
                tend(k,j,i) = tend(k,j,i) - dpdxy(2) * dp_smooth_factor(k)
             ENDDO
          ENDDO
       ENDDO
    ENDIF

    CALL user_actions( 'v-tendency' )

!
!-- Prognostic equation for v-velocity component
    !$acc kernels present( nzb_v_inner, rdf, tend, tv_m, v, vg, v_p )
    !$acc loop
    DO  i = nxl, nxr
       DO  j = nysv, nyn
          !$acc loop vector( 32 )
          DO  k = 1, nzt
             IF ( k > nzb_v_inner(j,i) )  THEN
                v_p(k,j,i) = v(k,j,i) + dt_3d * ( tsc(2) * tend(k,j,i) +       &
                                                  tsc(3) * tv_m(k,j,i) )       &
                                      - tsc(5) * rdf(k) * ( v(k,j,i) - vg(k) )
!
!--             Tendencies for the next Runge-Kutta step
                IF ( runge_step == 1 )  THEN
                   tv_m(k,j,i) = tend(k,j,i)
                ELSEIF ( runge_step == 2 )  THEN
                   tv_m(k,j,i) = -9.5625 * tend(k,j,i) + 5.3125 * tv_m(k,j,i)
                ENDIF
             ENDIF
          ENDDO
       ENDDO
    ENDDO
    !$acc end kernels

    CALL cpu_log( log_point(6), 'v-equation', 'stop' )
    !$acc update host( v_p )

!
!-- w-velocity component
    CALL cpu_log( log_point(7), 'w-equation', 'start' )

    IF ( timestep_scheme(1:5) == 'runge' )  THEN
       IF ( ws_scheme_mom )  THEN
          CALL advec_w_ws_acc
       ELSE
          tend = 0.0    ! to be removed later??
          CALL advec_w_pw
       ENDIF
    ELSE
       CALL advec_w_up
    ENDIF
    CALL diffusion_w_acc
    CALL coriolis_acc( 3 )

    IF ( .NOT. neutral )  THEN
       IF ( ocean )  THEN
          CALL buoyancy( rho, rho_reference, 3, 64 )
       ELSE
          IF ( .NOT. humidity )  THEN
             CALL buoyancy_acc( pt, pt_reference, 3, 4 )
          ELSE
             CALL buoyancy( vpt, pt_reference, 3, 44 )
          ENDIF
       ENDIF
    ENDIF

!
!-- Drag by plant canopy
    IF ( plant_canopy )  CALL plant_canopy_model( 3 )

    CALL user_actions( 'w-tendency' )

!
!-- Prognostic equation for w-velocity component
    !$acc kernels present( nzb_w_inner, rdf, tend, tw_m, w, w_p )
    !$acc loop
    DO  i = nxl, nxr
       DO  j = nys, nyn
          !$acc loop vector( 32 )
          DO  k = 1, nzt-1
             IF ( k > nzb_w_inner(j,i) )  THEN
                w_p(k,j,i) = w(k,j,i) + dt_3d * ( tsc(2) * tend(k,j,i) +       &
                                                  tsc(3) * tw_m(k,j,i) )       &
                                      - tsc(5) * rdf(k) * w(k,j,i)
   !
   !--          Tendencies for the next Runge-Kutta step
                IF ( runge_step == 1 )  THEN
                   tw_m(k,j,i) = tend(k,j,i)
                ELSEIF ( runge_step == 2 )  THEN
                   tw_m(k,j,i) = -9.5625 * tend(k,j,i) + 5.3125 * tw_m(k,j,i)
                ENDIF
             ENDIF
          ENDDO
       ENDDO
    ENDDO
    !$acc end kernels

    CALL cpu_log( log_point(7), 'w-equation', 'stop' )
    !$acc update host( w_p )


!
!-- If required, compute prognostic equation for potential temperature
    IF ( .NOT. neutral )  THEN

       CALL cpu_log( log_point(13), 'pt-equation', 'start' )

!
!--    pt-tendency terms with communication
       sbt = tsc(2)
       IF ( scalar_advec == 'bc-scheme' )  THEN

          IF ( timestep_scheme(1:5) /= 'runge' )  THEN
!
!--          Bott-Chlond scheme always uses Euler time step. Thus:
             sbt = 1.0
          ENDIF
          tend = 0.0
          CALL advec_s_bc( pt, 'pt' )

       ENDIF

!
!--    pt-tendency terms with no communication
       IF ( scalar_advec /= 'bc-scheme' )  THEN
          tend = 0.0
          IF ( timestep_scheme(1:5) == 'runge' )  THEN
             IF ( ws_scheme_sca )  THEN
                CALL advec_s_ws_acc( pt, 'pt' )
             ELSE
                tend = 0.0    ! to be removed later??
                CALL advec_s_pw( pt )
             ENDIF
          ELSE
             CALL advec_s_up( pt )
          ENDIF
       ENDIF

       CALL diffusion_s_acc( pt, shf, tswst, wall_heatflux )

!
!--    If required compute heating/cooling due to long wave radiation processes
       IF ( radiation )  THEN
          CALL calc_radiation
       ENDIF

!
!--    If required compute impact of latent heat due to precipitation
       IF ( precipitation )  THEN
          CALL impact_of_latent_heat
       ENDIF

!
!--    Consideration of heat sources within the plant canopy
       IF ( plant_canopy .AND. ( cthf /= 0.0 ) ) THEN
          CALL plant_canopy_model( 4 )
       ENDIF

!
!--    If required compute influence of large-scale subsidence/ascent
       IF ( large_scale_subsidence )  THEN
          CALL subsidence( tend, pt, pt_init )
       ENDIF

       CALL user_actions( 'pt-tendency' )

!
!--    Prognostic equation for potential temperature
       !$acc kernels present( nzb_s_inner, rdf_sc, ptdf_x, ptdf_y, pt_init ) &
       !$acc         present( tend, tpt_m, pt, pt_p )
       !$acc loop
       DO  i = nxl, nxr
          DO  j = nys, nyn
             !$acc loop vector( 32 )
             DO  k = 1, nzt
                IF ( k > nzb_s_inner(j,i) )  THEN
                   pt_p(k,j,i) = pt(k,j,i) + dt_3d * ( sbt * tend(k,j,i) +        &
                                                       tsc(3) * tpt_m(k,j,i) )    &
                                           - tsc(5) * ( pt(k,j,i) - pt_init(k) ) *&
                                             ( rdf_sc(k) + ptdf_x(i) + ptdf_y(j) )
!
!--                Tendencies for the next Runge-Kutta step
                   IF ( runge_step == 1 )  THEN
                      tpt_m(k,j,i) = tend(k,j,i)
                   ELSEIF ( runge_step == 2 )  THEN
                      tpt_m(k,j,i) = -9.5625 * tend(k,j,i) + 5.3125 * tpt_m(k,j,i)
                   ENDIF
                ENDIF
             ENDDO
          ENDDO
       ENDDO
       !$acc end kernels

       CALL cpu_log( log_point(13), 'pt-equation', 'stop' )
       !$acc update host( pt_p )

    ENDIF

!
!-- If required, compute prognostic equation for salinity
    IF ( ocean )  THEN

       CALL cpu_log( log_point(37), 'sa-equation', 'start' )

!
!--    sa-tendency terms with communication
       sbt = tsc(2)
       IF ( scalar_advec == 'bc-scheme' )  THEN

          IF ( timestep_scheme(1:5) /= 'runge' )  THEN
!
!--          Bott-Chlond scheme always uses Euler time step. Thus:
             sbt = 1.0
          ENDIF
          tend = 0.0
          CALL advec_s_bc( sa, 'sa' )

       ENDIF

!
!--    sa-tendency terms with no communication
       IF ( scalar_advec /= 'bc-scheme' )  THEN
          tend = 0.0
          IF ( timestep_scheme(1:5) == 'runge' )  THEN
             IF ( ws_scheme_sca )  THEN
                 CALL advec_s_ws( sa, 'sa' )
             ELSE
                 CALL advec_s_pw( sa )
             ENDIF
          ELSE
             CALL advec_s_up( sa )
          ENDIF
       ENDIF

       CALL diffusion_s( sa, saswsb, saswst, wall_salinityflux )

       CALL user_actions( 'sa-tendency' )

!
!--    Prognostic equation for salinity
       DO  i = nxl, nxr
          DO  j = nys, nyn
             DO  k = nzb_s_inner(j,i)+1, nzt
                sa_p(k,j,i) = sa(k,j,i) + dt_3d * ( sbt * tend(k,j,i) +        &
                                                    tsc(3) * tsa_m(k,j,i) )    &
                                        - tsc(5) * rdf_sc(k) *                 &
                                          ( sa(k,j,i) - sa_init(k) )
                IF ( sa_p(k,j,i) < 0.0 )  sa_p(k,j,i) = 0.1 * sa(k,j,i)
!
!--             Tendencies for the next Runge-Kutta step
                IF ( runge_step == 1 )  THEN
                   tsa_m(k,j,i) = tend(k,j,i)
                ELSEIF ( runge_step == 2 )  THEN
                   tsa_m(k,j,i) = -9.5625 * tend(k,j,i) + 5.3125 * tsa_m(k,j,i)
                ENDIF
             ENDDO
          ENDDO
       ENDDO

       CALL cpu_log( log_point(37), 'sa-equation', 'stop' )

!
!--    Calculate density by the equation of state for seawater
       CALL cpu_log( log_point(38), 'eqns-seawater', 'start' )
       CALL eqn_state_seawater
       CALL cpu_log( log_point(38), 'eqns-seawater', 'stop' )

    ENDIF

!
!-- If required, compute prognostic equation for total water content / scalar
    IF ( humidity  .OR.  passive_scalar )  THEN

       CALL cpu_log( log_point(29), 'q/s-equation', 'start' )

!
!--    Scalar/q-tendency terms with communication
       sbt = tsc(2)
       IF ( scalar_advec == 'bc-scheme' )  THEN

          IF ( timestep_scheme(1:5) /= 'runge' )  THEN
!
!--          Bott-Chlond scheme always uses Euler time step. Thus:
             sbt = 1.0
          ENDIF
          tend = 0.0
          CALL advec_s_bc( q, 'q' )

       ENDIF

!
!--    Scalar/q-tendency terms with no communication
       IF ( scalar_advec /= 'bc-scheme' )  THEN
          tend = 0.0
          IF ( timestep_scheme(1:5) == 'runge' )  THEN
             IF ( ws_scheme_sca )  THEN
                CALL advec_s_ws( q, 'q' )
             ELSE
                CALL advec_s_pw( q )
             ENDIF
          ELSE
             CALL advec_s_up( q )
          ENDIF
       ENDIF

       CALL diffusion_s( q, qsws, qswst, wall_qflux )

!
!--    If required compute decrease of total water content due to
!--    precipitation
       IF ( precipitation )  THEN
          CALL calc_precipitation
       ENDIF

!
!--    Sink or source of scalar concentration due to canopy elements
       IF ( plant_canopy ) CALL plant_canopy_model( 5 )

!
!--    If required compute influence of large-scale subsidence/ascent
       IF ( large_scale_subsidence )  THEN
         CALL subsidence( tend, q, q_init )
       ENDIF

       CALL user_actions( 'q-tendency' )

!
!--    Prognostic equation for total water content / scalar
       DO  i = nxl, nxr
          DO  j = nys, nyn
             DO  k = nzb_s_inner(j,i)+1, nzt
                q_p(k,j,i) = q(k,j,i) + dt_3d * ( sbt * tend(k,j,i) +          &
                                                  tsc(3) * tq_m(k,j,i) )       &
                                      - tsc(5) * rdf_sc(k) *                   &
                                        ( q(k,j,i) - q_init(k) )
                IF ( q_p(k,j,i) < 0.0 )  q_p(k,j,i) = 0.1 * q(k,j,i)
!
!--             Tendencies for the next Runge-Kutta step
                IF ( runge_step == 1 )  THEN
                   tq_m(k,j,i) = tend(k,j,i)
                ELSEIF ( runge_step == 2 )  THEN
                   tq_m(k,j,i) = -9.5625 * tend(k,j,i) + 5.3125 * tq_m(k,j,i)
                ENDIF
             ENDDO
          ENDDO
       ENDDO

       CALL cpu_log( log_point(29), 'q/s-equation', 'stop' )

    ENDIF

!
!-- If required, compute prognostic equation for turbulent kinetic
!-- energy (TKE)
    IF ( .NOT. constant_diffusion )  THEN

       CALL cpu_log( log_point(16), 'tke-equation', 'start' )

!
!--    TKE-tendency terms with communication
       CALL production_e_init

       sbt = tsc(2)
       IF ( .NOT. use_upstream_for_tke )  THEN
          IF ( scalar_advec == 'bc-scheme' )  THEN

             IF ( timestep_scheme(1:5) /= 'runge' )  THEN
!
!--             Bott-Chlond scheme always uses Euler time step. Thus:
                sbt = 1.0
             ENDIF
             tend = 0.0
             CALL advec_s_bc( e, 'e' )

          ENDIF
       ENDIF

!
!--    TKE-tendency terms with no communication
       IF ( scalar_advec /= 'bc-scheme'  .OR.  use_upstream_for_tke )  THEN
          IF ( use_upstream_for_tke )  THEN
             tend = 0.0
             CALL advec_s_up( e )
          ELSE
             IF ( timestep_scheme(1:5) == 'runge' )  THEN
                IF ( ws_scheme_sca )  THEN
                   CALL advec_s_ws_acc( e, 'e' )
                ELSE
                   tend = 0.0    ! to be removed later??
                   CALL advec_s_pw( e )
                ENDIF
             ELSE
                tend = 0.0    ! to be removed later??
                CALL advec_s_up( e )
             ENDIF
          ENDIF
       ENDIF

       IF ( .NOT. humidity )  THEN
          IF ( ocean )  THEN
             CALL diffusion_e( prho, prho_reference )
          ELSE
             CALL diffusion_e_acc( pt, pt_reference )
          ENDIF
       ELSE
          CALL diffusion_e( vpt, pt_reference )
       ENDIF

       CALL production_e_acc

!
!--    Additional sink term for flows through plant canopies
       IF ( plant_canopy )  CALL plant_canopy_model( 6 )
       CALL user_actions( 'e-tendency' )

!
!--    Prognostic equation for TKE.
!--    Eliminate negative TKE values, which can occur due to numerical
!--    reasons in the course of the integration. In such cases the old TKE
!--    value is reduced by 90%.
       !$acc kernels present( e, e_p, nzb_s_inner, tend, te_m )
       !$acc loop
       DO  i = nxl, nxr
          DO  j = nys, nyn
             !$acc loop vector( 32 )
             DO  k = 1, nzt
                IF ( k > nzb_s_inner(j,i) )  THEN
                   e_p(k,j,i) = e(k,j,i) + dt_3d * ( sbt * tend(k,j,i) +          &
                                                     tsc(3) * te_m(k,j,i) )
                   IF ( e_p(k,j,i) < 0.0 )  e_p(k,j,i) = 0.1 * e(k,j,i)
!
!--                Tendencies for the next Runge-Kutta step
                   IF ( runge_step == 1 )  THEN
                      te_m(k,j,i) = tend(k,j,i)
                   ELSEIF ( runge_step == 2 )  THEN
                      te_m(k,j,i) = -9.5625 * tend(k,j,i) + 5.3125 * te_m(k,j,i)
                   ENDIF
                ENDIF
             ENDDO
          ENDDO
       ENDDO
       !$acc end kernels

       CALL cpu_log( log_point(16), 'tke-equation', 'stop' )
       !$acc update host( e_p )

    ENDIF


 END SUBROUTINE prognostic_equations_acc


 END MODULE prognostic_equations_mod