!> @synthetic_turbulence_generator_mod.f90
!------------------------------------------------------------------------------!
! This file is part of PALM-4U.
!
! PALM-4U 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-4U 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 2017 Leibniz Universitaet Hannover
!------------------------------------------------------------------------------!
!
! Current revisions:
! -----------------
! 
! 
! Former revisions:
! -----------------
! $Id: synthetic_turbulence_generator_mod.f90 2259 2017-06-08 09:09:11Z hoffmann $
! Initial revision
!
! 
!
! Authors:
! --------
! @author Tobias Gronemeier, Atsushi Inagaki, Micha Gryschka, Christoph Knigge
!
!
! Description:
! ------------
!> The module generates turbulence at the inflow boundary based on a method by
!> Xie and Castro (2008) utilizing a Lund rotation (Lund, 1998) and a mass-flux
!> correction by Kim et al. (2013).
!> The turbulence is correlated based on length scales in y- and z-direction and
!> a time scale for each velocity component. The profiles of length and time
!> scales, mean u, v, w, e and pt, and all components of the Reynolds stress
!> tensor are read from file STG_PROFILES.
!>
!> @todo test restart
!>       enable cyclic_fill
!>       implement turbulence generation for e and pt
!> @note <Enter notes on the module>
!> @bug  Height information from input file is not used. Profiles from input
!>       must match with current PALM grid.
!>       Transformation of length scales to number of gridpoints does not
!>       consider grid stretching.
!>       In case of restart, velocity seeds differ from precursor run if a11,
!>       a22, or a33 are zero.
!------------------------------------------------------------------------------!
 MODULE synthetic_turbulence_generator_mod


    USE arrays_3d,                                                             &
        ONLY:  mean_inflow_profiles, u, v, w

    USE constants,                                                             &
        ONLY:  pi

    USE control_parameters,                                                    &
        ONLY:  initializing_actions, message_string,                           &
               synthetic_turbulence_generator

    USE cpulog,                                                                &
        ONLY:  cpu_log, log_point, log_point_s

    USE indices,                                                               &
        ONLY:  nbgp, nzb, nzt, nyng, nysg

    USE kinds

    USE MPI

    USE pegrid,                                                                &
        ONLY:  comm1dx, comm1dy, comm2d, id_inflow, ierr, myidx, pdims

    USE transpose_indices,                                                     &
        ONLY: nzb_x, nzt_x


    IMPLICIT NONE

    LOGICAL :: velocity_seed_initialized = .FALSE.           !< true after first call of stg_main
    LOGICAL :: use_synthetic_turbulence_generator = .FALSE.  !< switch to use synthetic turbulence generator

    INTEGER(iwp) :: stg_type_yz        !< MPI type for full z range
    INTEGER(iwp) :: stg_type_yz_small  !< MPI type for small z range
    INTEGER(iwp) :: merg               !< maximum length scale (in gp)
    INTEGER(iwp) :: mergp              !< merg + nbgp

    REAL(wp) :: mc_factor    !< mass flux correction factor

    INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: displs      !< displacement for MPI_GATHERV
    INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: recv_count  !< receive count for MPI_GATHERV
    INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nuy         !< length scale of u in y direction (in gp)
    INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nuz         !< length scale of u in z direction (in gp)
    INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nvy         !< length scale of v in y direction (in gp)
    INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nvz         !< length scale of v in z direction (in gp)
    INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nwy         !< length scale of w in y direction (in gp)
    INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nwz         !< length scale of w in z direction (in gp)

    INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: seed        !< seed of random number for rn-generator

    REAL(wp), DIMENSION(:), ALLOCATABLE :: a11             !< coefficient for Lund rotation
    REAL(wp), DIMENSION(:), ALLOCATABLE :: a21             !< coefficient for Lund rotation
    REAL(wp), DIMENSION(:), ALLOCATABLE :: a22             !< coefficient for Lund rotation
    REAL(wp), DIMENSION(:), ALLOCATABLE :: a31             !< coefficient for Lund rotation
    REAL(wp), DIMENSION(:), ALLOCATABLE :: a32             !< coefficient for Lund rotation
    REAL(wp), DIMENSION(:), ALLOCATABLE :: a33             !< coefficient for Lund rotation
    REAL(wp), DIMENSION(:), ALLOCATABLE :: tu              !< Lagrangian time scale of u
    REAL(wp), DIMENSION(:), ALLOCATABLE :: tv              !< Lagrangian time scale of v
    REAL(wp), DIMENSION(:), ALLOCATABLE :: tw              !< Lagrangian time scale of w

    REAL(wp), DIMENSION(:,:), ALLOCATABLE :: buy           !< filter function for u in y direction
    REAL(wp), DIMENSION(:,:), ALLOCATABLE :: buz           !< filter function for u in z direction
    REAL(wp), DIMENSION(:,:), ALLOCATABLE :: bvy           !< filter function for v in y direction
    REAL(wp), DIMENSION(:,:), ALLOCATABLE :: bvz           !< filter function for v in z direction
    REAL(wp), DIMENSION(:,:), ALLOCATABLE :: bwy           !< filter function for w in y direction
    REAL(wp), DIMENSION(:,:), ALLOCATABLE :: bwz           !< filter function for w in z direction
    REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fu            !< velocity seed for u
    REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fuo           !< velocity seed for u with new random number
    REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fv            !< velocity seed for v
    REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fvo           !< velocity seed for v with new random number
    REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fw            !< velocity seed for w
    REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fwo           !< velocity seed for w with new random number


!
!-- PALM interfaces:
!-- Input parameter checks to be done in check_parameters
    INTERFACE stg_check_parameters
       MODULE PROCEDURE stg_check_parameters
    END INTERFACE stg_check_parameters

!
!-- Calculate filter functions
    INTERFACE stg_filter_func
       MODULE PROCEDURE stg_filter_func
    END INTERFACE stg_filter_func

!
!-- Generate velocity seeds
    INTERFACE stg_generate_seed_yz
       MODULE PROCEDURE stg_generate_seed_yz
    END INTERFACE stg_generate_seed_yz

!
!-- Output of information to the header file
    INTERFACE stg_header
       MODULE PROCEDURE stg_header
    END INTERFACE stg_header

!
!-- Initialization actions
    INTERFACE stg_init
       MODULE PROCEDURE stg_init
    END INTERFACE stg_init

!
!-- Main procedure of synth. turb. gen.
    INTERFACE stg_main
       MODULE PROCEDURE stg_main
    END INTERFACE stg_main

!
!-- Reading of NAMELIST parameters
    INTERFACE stg_parin
       MODULE PROCEDURE stg_parin
    END INTERFACE stg_parin

!
!-- Reading of parameters for restart runs
    INTERFACE stg_read_restart_data
       MODULE PROCEDURE stg_read_restart_data
    END INTERFACE stg_read_restart_data

!
!-- Writing of binary output for restart runs
    INTERFACE stg_write_restart_data
       MODULE PROCEDURE stg_write_restart_data
    END INTERFACE stg_write_restart_data

    SAVE

    PRIVATE

!
!-- Public interfaces
    PUBLIC  stg_check_parameters, stg_header, stg_init, stg_main, stg_parin,   &
            stg_read_restart_data, stg_write_restart_data

!
!-- Public variables
    PUBLIC  use_synthetic_turbulence_generator


 CONTAINS


!------------------------------------------------------------------------------!
! Description:
! ------------
!> Check parameters routine for synthetic turbulence generator
!------------------------------------------------------------------------------!
 SUBROUTINE stg_check_parameters


    USE control_parameters,                                                    &
        ONLY:  bc_lr, bc_ns, turbulent_inflow


    IMPLICIT NONE

    IF ( use_synthetic_turbulence_generator )  THEN

       IF ( INDEX( initializing_actions, 'set_constant_profiles' ) == 0  .AND. &
            INDEX( initializing_actions, 'read_restart_data' ) == 0 )  THEN
          message_string = 'Using synthetic turbulence generator ' //          &
                           'requires &initializing_actions = '            //   &
                           '"set_constant_profiles" or "read_restart_data"'
          CALL message( 'stg_check_parameters', 'PA0015', 1, 2, 0, 6, 0 )
       ENDIF

       IF ( bc_lr /= 'dirichlet/radiation' )  THEN
          message_string = 'Using synthetic turbulence generator ' //          &
                           'requires &bc_lr = "dirichlet/radiation"'
          CALL message( 'stg_check_parameters', 'PA0035', 1, 2, 0, 6, 0 )
       ENDIF
       IF ( bc_ns /= 'cyclic' )  THEN
          message_string = 'Using synthetic turbulence generator ' //          &
                           'requires &bc_ns = "cyclic"'
          CALL message( 'stg_check_parameters', 'PA0037', 1, 2, 0, 6, 0 )
       ENDIF
       IF ( turbulent_inflow )  THEN
          message_string = 'Using synthetic turbulence generator ' //          &
                           'in combination &with turbulent_inflow = .T. ' //   &
                           'is not allowed'
          CALL message( 'stg_check_parameters', 'PA0039', 1, 2, 0, 6, 0 )
       ENDIF

    ENDIF

 END SUBROUTINE stg_check_parameters


!------------------------------------------------------------------------------!
! Description:
! ------------
!> Header output for synthetic turbulence generator
!------------------------------------------------------------------------------!
 SUBROUTINE stg_header ( io )


    IMPLICIT NONE

    INTEGER(iwp), INTENT(IN) ::  io   !< Unit of the output file

!
!-- Write synthetic turbulence generator Header
    WRITE( io, 1 )
    IF ( use_synthetic_turbulence_generator )  THEN
       WRITE( io, 2 )
    ELSE
       WRITE( io, 3 )
    ENDIF

1   FORMAT (//' Synthetic turbulence generator information:'/                  &
              ' ------------------------------------------'/)
2   FORMAT ('    synthetic turbulence generator switched on')
3   FORMAT ('    synthetic turbulence generator switched off')

 END SUBROUTINE stg_header


!------------------------------------------------------------------------------!
! Description:
! ------------
!> Initialization of the synthetic turbulence generator
!------------------------------------------------------------------------------!
 SUBROUTINE stg_init


    USE arrays_3d,                                                             &
        ONLY:  u_init, v_init

    USE control_parameters,                                                    &
        ONLY:  coupling_char, dz, e_init

    USE grid_variables,                                                        &
        ONLY:  ddy


    IMPLICIT NONE

    INTEGER(KIND=MPI_ADDRESS_KIND) :: extent !< extent of new MPI type
    INTEGER(KIND=MPI_ADDRESS_KIND) :: tob=0  !< dummy variable

    INTEGER(iwp) :: j                        !> loop index
    INTEGER(iwp) :: k                        !< index
    INTEGER(iwp) :: newtype                  !< dummy MPI type
    INTEGER(iwp) :: realsize                 !< size of REAL variables
    INTEGER(iwp) :: nseed                    !< dimension of random number seed
    INTEGER(iwp) :: startseed = 1234567890   !< start seed for random number generator

!
!-- Dummy variables used for reading profiles
    REAL(wp) :: d1      !< u profile
    REAL(wp) :: d2      !< v profile
    REAL(wp) :: d3      !< w profile
    REAL(wp) :: d5      !< e profile
    REAL(wp) :: d11     !< vertical interpolation for a11
    REAL(wp) :: d21     !< vertical interpolation for a21
    REAL(wp) :: d22     !< vertical interpolation for a22
    REAL(wp) :: luy     !< length scale for u in y direction
    REAL(wp) :: luz     !< length scale for u in z direction
    REAL(wp) :: lvy     !< length scale for v in y direction
    REAL(wp) :: lvz     !< length scale for v in z direction
    REAL(wp) :: lwy     !< length scale for w in y direction
    REAL(wp) :: lwz     !< length scale for w in z direction
    REAL(wp) :: zz      !< height

    REAL(wp),DIMENSION(nzb:nzt+1) :: r11  !< Reynolds parameter
    REAL(wp),DIMENSION(nzb:nzt+1) :: r21  !< Reynolds parameter
    REAL(wp),DIMENSION(nzb:nzt+1) :: r22  !< Reynolds parameter
    REAL(wp),DIMENSION(nzb:nzt+1) :: r31  !< Reynolds parameter
    REAL(wp),DIMENSION(nzb:nzt+1) :: r32  !< Reynolds parameter
    REAL(wp),DIMENSION(nzb:nzt+1) :: r33  !< Reynolds parameter


#if defined( __parallel )
    CALL MPI_BARRIER( comm2d, ierr )
#endif

    CALL  cpu_log( log_point(57), 'synthetic_turbulence_gen', 'start' )

    IF ( .NOT. ALLOCATED( mean_inflow_profiles ) )                             &
       ALLOCATE( mean_inflow_profiles(nzb:nzt+1,5) )

    ALLOCATE ( a11(nzb:nzt+1), a21(nzb:nzt+1), a22(nzb:nzt+1),                 &
               a31(nzb:nzt+1), a32(nzb:nzt+1), a33(nzb:nzt+1),                 &
               nuy(nzb:nzt+1), nuz(nzb:nzt+1), nvy(nzb:nzt+1),                 &
               nvz(nzb:nzt+1), nwy(nzb:nzt+1), nwz(nzb:nzt+1),                 &
               tu(nzb:nzt+1),  tv(nzb:nzt+1),  tw(nzb:nzt+1)   )

!
!-- Define MPI type used in stg_generate_seed_yz to gather vertical splitted
!-- velocity seeds
    CALL MPI_TYPE_SIZE( MPI_REAL, realsize, ierr )
    extent = 1 * realsize

    ! stg_type_yz: yz-slice with vertical bounds nzb:nzt+1
    CALL MPI_TYPE_CREATE_SUBARRAY( 2, [nzt-nzb+2,nyng-nysg+1],                 &
            [1,nyng-nysg+1], [0,0], MPI_ORDER_FORTRAN, MPI_REAL, newtype, ierr )
    CALL MPI_TYPE_CREATE_RESIZED( newtype, tob, extent, stg_type_yz, ierr )
    CALL MPI_TYPE_COMMIT( stg_type_yz, ierr )
    CALL MPI_TYPE_FREE( newtype, ierr )

    ! stg_type_yz_small: yz-slice with vertical bounds nzb_x:nzt_x+1
    CALL MPI_TYPE_CREATE_SUBARRAY( 2, [nzt_x-nzb_x+2,nyng-nysg+1],             &
            [1,nyng-nysg+1], [0,0], MPI_ORDER_FORTRAN, MPI_REAL, newtype, ierr )
    CALL MPI_TYPE_CREATE_RESIZED( newtype, tob, extent, stg_type_yz_small, ierr )
    CALL MPI_TYPE_COMMIT( stg_type_yz_small, ierr )
    CALL MPI_TYPE_FREE( newtype, ierr )

    ! receive count and displacement for MPI_GATHERV in stg_generate_seed_yz
    ALLOCATE( recv_count(pdims(1)), displs(pdims(1)) )

    recv_count           = nzt_x-nzb_x + 1
    recv_count(pdims(1)) = recv_count(pdims(1)) + 1

    DO  j = 1, pdims(1)
       displs(j) = 0 + (nzt_x-nzb_x+1) * (j-1)
    ENDDO

!
!-- Define seed of random number
    CALL RANDOM_SEED()
    CALL RANDOM_SEED( size=nseed )
    ALLOCATE( seed(1:nseed) )
    DO  j = 1, nseed
       seed(j) = startseed + j
    ENDDO
    CALL RANDOM_SEED(put=seed)

!
!-- Read inflow profile
!-- Height levels of profiles in input profile is as follows:
!-- zu: luy, luz, tu, lvy, lvz, tv, r11, r21, r22, d1, d2, d5
!-- zw: lwy, lwz, tw, r31, r32, r33, d3
!-- WARNING: zz is not used at the moment
    OPEN( 24, FILE='STG_PROFILES'//TRIM( coupling_char ), STATUS='OLD',        &
                   FORM='FORMATTED')

    ! Skip header
    READ( 24, * )

    DO  k = nzb, nzt+1
       READ( 24, * ) zz, luy, luz, tu(k), lvy, lvz, tv(k), lwy, lwz, tw(k),    &
                     r11(k), r21(k), r22(k), r31(k), r32(k), r33(k),           &
                     d1, d2, d3, d5

!
!--    Convert length scales from meter to number of grid points
       nuy(k) = INT( luy * ddy )
       nuz(k) = INT( luz / dz  )
       nvy(k) = INT( lvy * ddy )
       nvz(k) = INT( lvz / dz  )
       nwy(k) = INT( lwy * ddy )
       nwz(k) = INT( lwz / dz  )

!
!--    Save Mean inflow profiles
       IF ( TRIM( initializing_actions ) /= 'read_restart_data' ) THEN
          mean_inflow_profiles(k,1) = d1
          mean_inflow_profiles(k,2) = d2
         !  mean_inflow_profiles(k,4) = d4
          mean_inflow_profiles(k,5) = d5
       ENDIF
    ENDDO

    CLOSE(24)

!
!--    Assign initial profiles
    u_init = mean_inflow_profiles(:,1)
    v_init = mean_inflow_profiles(:,2)
   !  pt_init = mean_inflow_profiles(:,4)
    e_init = MAXVAL( mean_inflow_profiles(:,5) )

!
!-- Calculate coefficient matrix from Reynolds stress tensor (Lund rotation)
    DO  k = nzb, nzt+1
       IF ( r11(k) > 0.0_wp )  THEN
          a11(k) = SQRT( r11(k) )
          a21(k) = r21(k) / a11(k)
       ELSE
          a11(k) = 0.0_wp
          a21(k) = 0.0_wp
       ENDIF

       a22(k) = r22(k) - a21(k)**2
       IF ( a22(k) > 0.0_wp )  THEN
          a22(k) = SQRT( a22(k) )
          a32(k) = ( r32(k) - a21(k) * a31(k) ) / a22(k)
       ELSE
          a22(k) = 0.0_wp
          a32(k) = 0.0_wp
       ENDIF

!
!--    a31, a32, a33 must be calculated with interpolated a11, a21, a22 (d11,
!--    d21, d22) because of different vertical grid
       IF ( k .le. nzt )  THEN
          d11 = 0.5_wp * ( r11(k) + r11(k+1) )
          IF ( d11 > 0.0_wp )  THEN
             d11 = SQRT( d11 )
             d21 = ( 0.5_wp * ( r21(k) + r21(k+1) ) ) / d11
             a31(k) = r31(k) / d11
          ELSE
             d21 = 0.0_wp
             a31(k) = 0.0_wp
          ENDIF

          d22 = 0.5_wp * ( r22(k) + r22(k+1) ) - d21 ** 2
          IF ( d22 > 0.0_wp )  THEN
             a32(k) = ( r32(k) - d21 * a31(k) ) / SQRT( d22 )
          ELSE
             a32(k) = 0.0_wp
          ENDIF

          a33(k) = r33(k) - a31(k) ** 2 - a32(k) ** 2
          IF ( a33(k) > 0.0_wp )  THEN
             a33(k) = SQRT( a33(k) )
          ELSE
             a33(k) = 0.0_wp
          ENDIF
       ELSE
          a31(k) = a31(k-1)
          a32(k) = a32(k-1)
          a33(k) = a33(k-1)
       ENDIF

    ENDDO

!
!-- Define the size of the filter functions and allocate them.
    merg = 0

    ! arrays must be large enough to cover the largest length scale
    DO  k = nzb, nzt+1
       j = MAX( ABS(nuy(k)), ABS(nuz(k)), &
                ABS(nvy(k)), ABS(nvz(k)), &
                ABS(nwy(k)), ABS(nwz(k))  )
       IF ( j > merg )  merg = j
    ENDDO

    merg  = 2 * merg
    mergp = merg + nbgp

    ALLOCATE ( buy(-merg:merg,nzb:nzt+1), buz(-merg:merg,nzb:nzt+1), &
               bvy(-merg:merg,nzb:nzt+1), bvz(-merg:merg,nzb:nzt+1), &
               bwy(-merg:merg,nzb:nzt+1), bwz(-merg:merg,nzb:nzt+1)  )

!
!-- Allocate velocity seeds
    ALLOCATE ( fu( nzb:nzt+1,nysg:nyng), fuo(nzb:nzt+1,nysg:nyng), &
               fv( nzb:nzt+1,nysg:nyng), fvo(nzb:nzt+1,nysg:nyng), &
               fw( nzb:nzt+1,nysg:nyng), fwo(nzb:nzt+1,nysg:nyng)  )

    fu  = 0._wp
    fuo = 0._wp
    fv  = 0._wp
    fvo = 0._wp
    fw  = 0._wp
    fwo = 0._wp

!
!-- Create filter functions
    CALL stg_filter_func( nuy, buy ) !filter uy
    CALL stg_filter_func( nuz, buz ) !filter uz
    CALL stg_filter_func( nvy, bvy ) !filter vy
    CALL stg_filter_func( nvz, bvz ) !filter vz
    CALL stg_filter_func( nwy, bwy ) !filter wy
    CALL stg_filter_func( nwz, bwz ) !filter wz

#if defined( __parallel )
    CALL MPI_BARRIER( comm2d, ierr )
#endif

!
!--    In case of restart, calculate velocity seeds fu, fv, fw from former
!      time step.
!      Bug: fu, fv, fw are different in those heights where a11, a22, a33
!           are 0 compared to the prerun. This is mostly for k=nzt+1.
    IF ( TRIM( initializing_actions ) == 'read_restart_data' )  THEN
       IF ( myidx == id_inflow )  THEN
          DO  j = nysg, nyng
             DO  k = nzb, nzt+1

                IF  ( a11(k) .NE. 0._wp ) THEN
                fu(k,j) = ( u(k,j,-1) / mc_factor -                    &
                            mean_inflow_profiles(k,1) ) / a11(k)
                ELSE
                   fu(k,j) = 0._wp
                ENDIF

                IF  ( a22(k) .NE. 0._wp ) THEN
                fv(k,j) = ( v(k,j,-1) / mc_factor - a21(k) * fu(k,j) - &
                            mean_inflow_profiles(k,2) ) / a22(k)
                ELSE
                   fv(k,j) = 0._wp
                ENDIF

                IF  ( a33(k) .NE. 0._wp ) THEN
                fw(k,j) = ( w(k,j,-1) / mc_factor - a31(k) * fu(k,j) - &
                            a32(k) * fv(k,j) ) / a33(k)
                ELSE
                   fw = 0._wp
                ENDIF

             ENDDO
          ENDDO
       ENDIF
    ENDIF

    CALL  cpu_log( log_point(57), 'synthetic_turbulence_gen', 'stop' )

 END SUBROUTINE stg_init


!------------------------------------------------------------------------------!
! Description:
! ------------
!> Calculate filter function bxx from length scale nxx following Eg.9 and 10
!> (Xie and Castro, 2008)
!------------------------------------------------------------------------------!
 SUBROUTINE stg_filter_func( nxx, bxx )


    IMPLICIT NONE

    INTEGER(iwp) :: k         !< loop index
    INTEGER(iwp) :: n_k       !< length scale nXX in height k
    INTEGER(iwp) :: n_k2      !< n_k * 2
    INTEGER(iwp) :: nf        !< index for length scales

    REAL(wp) :: bdenom        !< denominator for filter functions bXX
    REAL(wp) :: qsi = 1.0_wp  !< minimization factor

    INTEGER(iwp), DIMENSION(:) :: nxx(nzb:nzt+1)           !< length scale (in gp)

    REAL(wp), DIMENSION(:,:) :: bxx(-merg:merg,nzb:nzt+1)  !< filter function


    bxx = 0.0_wp

    DO  k = nzb, nzt+1
       bdenom = 0.0_wp
       n_k    = nxx(k)
       IF ( n_k /= 0 )  THEN
          n_k2 = n_k * 2

!
!--       ( Eq.10 )^2
          DO  nf = -n_k2, n_k2
             bdenom = bdenom + EXP( -qsi * pi * ABS(nf) / n_k )**2
          ENDDO

!
!--       ( Eq.9 )
          bdenom = SQRT( bdenom )
          DO  nf = -n_k2, n_k2
             bxx(nf,k) = EXP( -qsi * pi * ABS(nf) / n_k ) / bdenom
          ENDDO
       ENDIF
    ENDDO

END SUBROUTINE stg_filter_func


!------------------------------------------------------------------------------!
! Description:
! ------------
!> Parin for &stg_par for synthetic turbulence generator
!------------------------------------------------------------------------------!
 SUBROUTINE stg_parin


    IMPLICIT NONE

    CHARACTER (LEN=80) ::  line   !< dummy string that contains the current line of the parameter file


    NAMELIST /stg_par/   use_synthetic_turbulence_generator

    line = ' '

!
!-- Try to find stg package
    REWIND ( 11 )
    line = ' '
    DO WHILE ( INDEX( line, '&stg_par' ) == 0 )
       READ ( 11, '(A)', END=10 )  line
    ENDDO
    BACKSPACE ( 11 )

!
!-- Read namelist
    READ ( 11, stg_par )

!
!-- Set flag that indicates that the synthetic turbulence generator is switched
!-- on
    synthetic_turbulence_generator = .TRUE.

 10 CONTINUE

 END SUBROUTINE stg_parin


!------------------------------------------------------------------------------!
! Description:
! ------------
!> This routine reads the respective restart data.
!------------------------------------------------------------------------------!
 SUBROUTINE stg_read_restart_data


    IMPLICIT NONE

    CHARACTER (LEN=30) ::  variable_chr  !< dummy variable to read string


    READ ( 13 )  variable_chr
    DO  WHILE ( TRIM( variable_chr ) /= '*** end stg module ***' )

       SELECT CASE ( TRIM( variable_chr ) )

          CASE ( 'use_synthetic_turbulence_generator ' )
             READ ( 13 )  use_synthetic_turbulence_generator
          CASE ( 'mc_factor' )
             READ ( 13 )  mc_factor

       END SELECT

       READ ( 13 )  variable_chr

    ENDDO

 END SUBROUTINE stg_read_restart_data


!------------------------------------------------------------------------------!
! Description:
! ------------
!> This routine writes the respective restart data.
!------------------------------------------------------------------------------!
 SUBROUTINE stg_write_restart_data


    IMPLICIT NONE

    WRITE ( 14 )  'use_synthetic_turbulence_generator '
    WRITE ( 14 )  use_synthetic_turbulence_generator
    WRITE ( 14 )  'mc_factor           '
    WRITE ( 14 )  mc_factor

    WRITE ( 14 )  '*** end stg module ***            '

END SUBROUTINE stg_write_restart_data


!------------------------------------------------------------------------------!
! Description:
! ------------
!> Create turbulent inflow fields for u, v, w with prescribed length scales and
!> Reynolds stress tensor after a method of Xie and Castro (2008), modified
!> following suggestions of Kim et al. (2013), and using a Lund rotation
!> (Lund, 1998).
!------------------------------------------------------------------------------!
 SUBROUTINE stg_main


    USE arrays_3d,                                                             &
        ONLY:  dzw

    USE control_parameters,                                                    &
        ONLY:  dt_3d, intermediate_timestep_count, simulated_time,             &
               volume_flow_initial

    USE indices,                                                               &
        ONLY:  nyn, nys

    USE statistics,                                                            &
        ONLY:  weight_substep


    IMPLICIT NONE

    INTEGER(iwp) :: j           !< loop index in y-direction
    INTEGER(iwp) :: k           !< loop index in z-direction

    REAL(wp) :: dt_stg          !< wheighted subtimestep
    REAL(wp) :: mc_factor_l     !< local mass flux correction factor

    REAL(wp), DIMENSION(nzb:nzt+1,nysg:nyng,5,nbgp) :: inflow_dist !< disturbance for inflow profiles


    CALL  cpu_log( log_point(57), 'synthetic_turbulence_gen', 'start' )

!
!-- Calculate time step which is needed for filter functions
    dt_stg = dt_3d * weight_substep(intermediate_timestep_count)

!
!-- Initial value of fu, fv, fw
    IF ( simulated_time == 0.0_wp .AND. .NOT. velocity_seed_initialized )  THEN
       CALL stg_generate_seed_yz( nuy, nuz, buy, buz, fu )
       CALL stg_generate_seed_yz( nvy, nvz, bvy, bvz, fv )
       CALL stg_generate_seed_yz( nwy, nwz, bwy, bwz, fw )
       velocity_seed_initialized = .TRUE.
    ENDIF
!
!-- New set of fu, fv, fw
    CALL stg_generate_seed_yz( nuy, nuz, buy, buz, fuo )
    CALL stg_generate_seed_yz( nvy, nvz, bvy, bvz, fvo )
    CALL stg_generate_seed_yz( nwy, nwz, bwy, bwz, fwo )

    IF ( myidx == id_inflow )  THEN

       DO  j = nysg, nyng
          DO  k = nzb, nzt + 1
!
!--          Update fu, fv, fw following Eq. 14 of Xie and Castro (2008)
             IF ( tu(k) == 0.0_wp )  THEN
                fu(k,j) = fuo(k,j)
             ELSE
                fu(k,j) = fu(k,j) * EXP( -pi * dt_stg * 0.5_wp / tu(k) ) +     &
                         fuo(k,j) * SQRT( 1.0_wp - EXP( -pi * dt_stg / tu(k) ) )
             ENDIF

             IF ( tv(k) == 0.0_wp )  THEN
                fv(k,j) = fvo(k,j)
             ELSE
                fv(k,j) = fv(k,j) * EXP( -pi * dt_stg * 0.5_wp / tv(k) ) +     &
                         fvo(k,j) * SQRT( 1.0_wp - EXP( -pi * dt_stg / tv(k) ) )
             ENDIF

             IF ( tw(k) == 0.0_wp )  THEN
                fw(k,j) = fwo(k,j)
             ELSE
                fw(k,j) = fw(k,j) * EXP( -pi * dt_stg * 0.5_wp / tw(k) ) +     &
                         fwo(k,j) * SQRT( 1.0_wp - EXP( -pi * dt_stg / tw(k) ) )
             ENDIF
!
!--          Lund rotation following Eq. 17 in Xie and Castro (2008).
!--          Additional factors are added to improve the variance of v and w
             IF( k == 0 )  THEN
                inflow_dist(k,j,1,1) = 0.0_wp
                inflow_dist(k,j,2,1) = 0.0_wp
                inflow_dist(k,j,3,1) = 0.0_wp
                inflow_dist(k,j,4,1) = 0.0_wp
                inflow_dist(k,j,5,1) = 0.0_wp
             ELSE
                inflow_dist(k,j,1,1) = a11(k) * fu(k,j)
                !experimental test of 1.2
                inflow_dist(k,j,2,1) = ( SQRT( a22(k) / MAXVAL(a22) )          &
                                         * 1.2_wp )                            &
                                       * (   a21(k) * fu(k,j)                  &
                                           + a22(k) * fv(k,j) )
                inflow_dist(k,j,3,1) = ( SQRT(a33(k) / MAXVAL(a33) )           &
                                         * 1.3_wp )                            &
                                       * (   a31(k) * fu(k,j)                  &
                                           + a32(k) * fv(k,j)                  &
                                           + a33(k) * fw(k,j) )
                ! Calculation for pt and e not yet implemented
                inflow_dist(k,j,4,1) = 0.0_wp
                inflow_dist(k,j,5,1) = 0.0_wp
             ENDIF

          ENDDO
       ENDDO

!
!--    Mass flux correction following Kim et al. (2013)
!--    This correction factor insures that the mass flux is preserved at the
!--    inflow boundary
       mc_factor_l = 0.0_wp
       mc_factor   = 0.0_wp
       DO  j = nys, nyn
          DO  k = nzb+1, nzt
             mc_factor_l = mc_factor_l + dzw(k)  *                             &
                           ( mean_inflow_profiles(k,1) + inflow_dist(k,j,1,1) )
          ENDDO
       ENDDO

#if defined( __parallel )
       CALL MPI_ALLREDUCE( mc_factor_l, mc_factor,  &
                           1, MPI_REAL, MPI_SUM, comm1dy, ierr )
#else
       mc_factor = mc_factor_l
#endif

       mc_factor = volume_flow_initial(1) / mc_factor

!
!--    Add disturbance at the inflow
       DO  j = nysg, nyng
          DO  k = nzb, nzt+1
              u(k,j,-nbgp+1:0) = ( mean_inflow_profiles(k,1) +                 &
                                   inflow_dist(k,j,1,1)      ) * mc_factor
              v(k,j,-nbgp:-1)  = ( mean_inflow_profiles(k,2) +                 &
                                   inflow_dist(k,j,2,1)      ) * mc_factor
              w(k,j,-nbgp:-1)  =   inflow_dist(k,j,3,1)        * mc_factor
          ENDDO
       ENDDO

    ENDIF

    CALL  cpu_log( log_point(57), 'synthetic_turbulence_gen', 'stop' )

 END SUBROUTINE stg_main


!------------------------------------------------------------------------------!
! Description:
! ------------
!> Generate a set of random number rand_it wich is equal on each PE
!> and calculate the velocity seed f_n.
!> f_n is splitted in vertical direction by the number of PEs in x-direction and
!> and each PE calculates a vertical subsection of f_n. At the the end, all
!> parts are collected to form the full array.
!------------------------------------------------------------------------------!
 SUBROUTINE stg_generate_seed_yz( n_y, n_z, b_y, b_z, f_n )


    USE indices,                                                               &
        ONLY: ny


    IMPLICIT NONE

    INTEGER(iwp) :: j           !< loop index in y-direction
    INTEGER(iwp) :: jj          !< loop index in y-direction
    INTEGER(iwp) :: k           !< loop index in z-direction
    INTEGER(iwp) :: kk          !< loop index in z-direction
    INTEGER(iwp) :: send_count  !< send count for MPI_GATHERV

    INTEGER(iwp), DIMENSION(nzb:nzt+1) :: n_y    !< length scale in y-direction
    INTEGER(iwp), DIMENSION(nzb:nzt+1) :: n_z    !< length scale in z-direction
    INTEGER(iwp), DIMENSION(nzb:nzt+1) :: n_y2   !< n_y*2
    INTEGER(iwp), DIMENSION(nzb:nzt+1) :: n_z2   !< n_z*2

    REAL(wp) :: nyz_inv         !< inverse of number of grid points in yz-slice
    REAL(wp) :: rand_av         !< average of random number
    REAL(wp) :: rand_sigma_inv  !< inverse of stdev of random number

    REAL(wp), DIMENSION(-merg:merg,nzb:nzt+1)    :: b_y     !< filter func in y-dir
    REAL(wp), DIMENSION(-merg:merg,nzb:nzt+1)    :: b_z     !< filter func in z-dir
    REAL(wp), DIMENSION(nzb_x:nzt_x+1,nysg:nyng) :: f_n_l   !<  local velocity seed
    REAL(wp), DIMENSION(nzb:nzt+1,nysg:nyng)     :: f_n     !<  velocity seed
    REAL(wp), DIMENSION(:,:), ALLOCATABLE        :: rand_it !<  random number


!
!-- Generate random numbers using a seed generated in stg_init.
!-- The set of random numbers are modified to have an average of 0 and
!-- unit variance.
    ALLOCATE( rand_it(nzb-mergp:nzt+1+mergp,-mergp:ny+mergp) )

    rand_av        = 0.0_wp
    rand_sigma_inv = 0.0_wp
    nyz_inv        = 1.0_wp / REAL( ( nzt+1 - nzb+1 ) * ( ny+1 ), KIND=wp )

    DO  j = 0, ny
       DO  k = nzb, nzt+1
          CALL RANDOM_NUMBER( rand_it(k,j) )
          rand_av = rand_av + rand_it(k,j)
       ENDDO
    ENDDO

    rand_av = rand_av * nyz_inv

    DO  j = 0, ny
       DO  k = nzb, nzt+1
          rand_it(k,j)   = rand_it(k,j) - rand_av
          rand_sigma_inv = rand_sigma_inv + rand_it(k,j) ** 2
       ENDDO
    ENDDO

    rand_sigma_inv = 1.0_wp / SQRT(rand_sigma_inv * nyz_inv)

    DO  j = 0, ny
       DO  k = nzb, nzt+1
          rand_it(k,j) = rand_it(k,j) * rand_sigma_inv
       ENDDO
    ENDDO

!
!-- Periodic fill of random number in space
    DO  j = 0, ny
       DO  k = 1, mergp
          rand_it(nzb  -k,j) = rand_it(nzt+2-k,j)    ! bottom margin
          rand_it(nzt+1+k,j) = rand_it(nzb+k-1,j)    ! top margin
       ENDDO
    ENDDO
    DO  j = 1, mergp
       DO  k = nzb-mergp, nzt+1+mergp
          rand_it(k,  -j) = rand_it(k,ny-j+1)        ! south margin
          rand_it(k,ny+j) = rand_it(k,   j-1)        ! north margin
       ENDDO
    ENDDO

!
!-- Generate velocity seed following Eq.6 of Xie and Castro (2008)
    n_y2 = n_y * 2
    n_z2 = n_z * 2
    f_n_l  = 0.0_wp

    DO  j = nysg, nyng
       DO  k = nzb_x, nzt_x+1
          DO  jj = -n_y2(k), n_y2(k)
             DO  kk = -n_z2(k), n_z2(k)
                f_n_l(k,j) = f_n_l(k,j)                                        &
                           + b_y(jj,k) * b_z(kk,k) * rand_it(k+kk,j+jj)
             ENDDO
          ENDDO
       ENDDO
    ENDDO

    DEALLOCATE( rand_it )

!
!-- Gather velocity seeds of full subdomain
    send_count = nzt_x - nzb_x + 1
    IF ( nzt_x == nzt )  send_count = send_count + 1

#if defined( __parallel )
    CALL MPI_GATHERV( f_n_l(nzb_x,nysg), send_count, stg_type_yz_small,        &
                      f_n(nzb+1,nysg), recv_count, displs, stg_type_yz,        &
                      id_inflow, comm1dx, ierr )
#else
    f_n(nzb+1:nzt+1,nysg:nyng) = f_n_l(nzb_x:nzt_x+1,nysg:nyng)
#endif


 END SUBROUTINE stg_generate_seed_yz

 END MODULE synthetic_turbulence_generator_mod