source: palm/trunk/SOURCE/calc_spectra.f90 @ 1511

 SUBROUTINE calc_spectra

!--------------------------------------------------------------------------------!
! 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 1997-2014 Leibniz Universitaet Hannover
!--------------------------------------------------------------------------------!
!
! Current revisions:
! -----------------
! Bugfix concerning spectra normalization
! 
! Former revisions:
! -----------------
! $Id: calc_spectra.f90 1511 2014-12-16 15:54:16Z suehring $
!
! 1431 2014-07-15 14:47:17Z suehring
! Wavenumber-integrated spectra coincide with respective variance. 
! 
! 1342 2014-03-26 17:04:47Z kanani
! REAL constants defined as wp-kinds
!
! 1324 2014-03-21 09:13:16Z suehring
! Bugfix: nzb_x, nzb_yd, nyn_x, nyn_x, nzt_x, nzt_yd belong to transpose_indices 
!
! 1320 2014-03-20 08:40:49Z raasch
! ONLY-attribute added to USE-statements,
! kind-parameters added to all INTEGER and REAL declaration statements,
! kinds are defined in new module kinds,
! revision history before 2012 removed,
! comment fields (!:) to be used for variable explanations added to
! all variable declaration statements
!
! 1318 2014-03-17 13:35:16Z raasch
! module interfaces removed
!
! 1216 2013-08-26 09:31:42Z raasch
! resorting of array moved to separate routine resort_for_zx,
! one argument removed from the transpose_..d routines
!
! 1120 2013-04-05 15:11:35Z raasch
! bugfix: calls of fft_x|y replaced by fft_x|y_1d
!
! 1036 2012-10-22 13:43:42Z raasch
! code put under GPL (PALM 3.9)
!
! 1003 2012-09-14 14:35:53Z raasch
! adjustment of array tend for cases with unequal subdomain sizes removed
!
! Revision 1.1  2001/01/05 15:08:07  raasch
! Initial revision
!
!
! Description:
! ------------
! Calculate horizontal spectra along x and y. 
! ATTENTION: 1d-decomposition along y still needs improvement, because in that
!            case the gridpoint number along z still depends on the PE number
!            because transpose_xz has to be used (and possibly also
!            transpose_zyd needs modification).
!------------------------------------------------------------------------------!

#if defined( __spectra )
    USE arrays_3d,                                                             &
        ONLY:  d, tend

    USE control_parameters,                                                    &
        ONLY:  average_count_sp, bc_lr_cyc, bc_ns_cyc, message_string, psolver

    USE cpulog,                                                                &
        ONLY:  cpu_log, log_point

    USE fft_xy,                                                                &
        ONLY:  fft_init

    USE indices,                                                               &
        ONLY:  nxl, nxr, nyn, nys, nzb, nzt

    USE kinds

    USE pegrid

    USE spectrum,                                                              &
        ONLY:  data_output_sp, spectra_direction


    IMPLICIT NONE

    INTEGER(iwp) ::  m  !:
    INTEGER(iwp) ::  pr !:


    CALL cpu_log( log_point(30), 'calc_spectra', 'start' )

!
!-- Initialize ffts
    CALL fft_init

!
!-- Reallocate array d in required size
    IF ( psolver == 'multigrid' )  THEN
       DEALLOCATE( d )
       ALLOCATE( d(nzb+1:nzt,nys:nyn,nxl:nxr) )
    ENDIF

    m = 1
    DO WHILE ( data_output_sp(m) /= ' '  .AND.  m <= 10 )
!
!--    Transposition from z --> x  ( y --> x in case of a 1d-decomposition
!--    along x)
       IF ( INDEX( spectra_direction(m), 'x' ) /= 0 )  THEN

!
!--       Calculation of spectra works for cyclic boundary conditions only
          IF ( .NOT. bc_lr_cyc )  THEN

             message_string = 'non-cyclic lateral boundaries along x do not'// &
                              '& allow calculation of spectra along x'
             CALL message( 'calc_spectra', 'PA0160', 1, 2, 0, 6, 0 )
          ENDIF

          CALL preprocess_spectra( m, pr )

#if defined( __parallel )
          IF ( pdims(2) /= 1 )  THEN
             CALL resort_for_zx( d, tend )
             CALL transpose_zx( tend, d )
          ELSE
             CALL transpose_yxd( d, d )
          ENDIF
          CALL calc_spectra_x( d, pr, m )
#else
          message_string = 'sorry, calculation of spectra in non parallel ' // &
                           'mode& is still not realized'
          CALL message( 'calc_spectra', 'PA0161', 1, 2, 0, 6, 0 )      
#endif

       ENDIF

!
!--    Transposition from z --> y (d is rearranged only in case of a
!--    1d-decomposition along x)
       IF ( INDEX( spectra_direction(m), 'y' ) /= 0 )  THEN

!
!--       Calculation of spectra works for cyclic boundary conditions only
          IF ( .NOT. bc_ns_cyc )  THEN
             IF ( myid == 0 )  THEN
                message_string = 'non-cyclic lateral boundaries along y do' // &
                                 ' not & allow calculation of spectra along y' 
                CALL message( 'calc_spectra', 'PA0162', 1, 2, 0, 6, 0 )
             ENDIF
             CALL local_stop
          ENDIF

          CALL preprocess_spectra( m, pr )

#if defined( __parallel )
          CALL transpose_zyd( d, d )
          CALL calc_spectra_y( d, pr, m )
#else
          message_string = 'sorry, calculation of spectra in non parallel' //  &
                           'mode& is still not realized'
          CALL message( 'calc_spectra', 'PA0161', 1, 2, 0, 6, 0 )
#endif

       ENDIF

!
!--    Increase counter for next spectrum
       m = m + 1
          
    ENDDO

!
!-- Increase counter for averaging process in routine plot_spectra
    average_count_sp = average_count_sp + 1

    CALL cpu_log( log_point(30), 'calc_spectra', 'stop' )

#endif
 END SUBROUTINE calc_spectra


#if defined( __spectra )
 SUBROUTINE preprocess_spectra( m, pr )

    USE arrays_3d,                                                             &
        ONLY:  d, pt, q, u, v, w

    USE indices,                                                               &
        ONLY:  ngp_2dh, nxl, nxr, nyn, nys, nzb, nzt

    USE kinds

    USE pegrid

    USE spectrum,                                                              &
        ONLY:  data_output_sp

    USE statistics,                                                            &
        ONLY:  hom, var_d


    IMPLICIT NONE

    INTEGER(iwp) :: i  !:
    INTEGER(iwp) :: j  !:
    INTEGER(iwp) :: k  !:
    INTEGER(iwp) :: m  !:
    INTEGER(iwp) :: pr !:

    REAL(wp), DIMENSION(nzb:nzt+1) :: var_d_l

    SELECT CASE ( TRIM( data_output_sp(m) ) )
          
    CASE ( 'u' )
       pr = 1
       d(nzb+1:nzt,nys:nyn,nxl:nxr) = u(nzb+1:nzt,nys:nyn,nxl:nxr)
       
    CASE ( 'v' )
       pr = 2
       d(nzb+1:nzt,nys:nyn,nxl:nxr) = v(nzb+1:nzt,nys:nyn,nxl:nxr)
       
    CASE ( 'w' )
       pr = 3
       d(nzb+1:nzt,nys:nyn,nxl:nxr) = w(nzb+1:nzt,nys:nyn,nxl:nxr)
       
    CASE ( 'pt' )
       pr = 4
       d(nzb+1:nzt,nys:nyn,nxl:nxr) = pt(nzb+1:nzt,nys:nyn,nxl:nxr)
       
    CASE ( 'q' )
       pr = 41
       d(nzb+1:nzt,nys:nyn,nxl:nxr) = q(nzb+1:nzt,nys:nyn,nxl:nxr)
       
    CASE DEFAULT
!
!--    The DEFAULT case is reached either if the parameter data_output_sp(m)
!--    contains a wrong character string or if the user has coded a special
!--    case in the user interface. There, the subroutine user_spectra 
!--    checks which of these two conditions applies.
       CALL user_spectra( 'preprocess', m, pr )
          
    END SELECT

!
!-- Subtract horizontal mean from the array, for which spectra have to be
!-- calculated
    var_d_l(:) = 0.0_wp
    DO  i = nxl, nxr
       DO  j = nys, nyn
          DO  k = nzb+1, nzt
             d(k,j,i)   = d(k,j,i) - hom(k,1,pr,0)
             var_d_l(k) = var_d_l(k) + d(k,j,i) * d(k,j,i)
          ENDDO
       ENDDO
    ENDDO
!
!-- Compute total variance from local variances
    var_d(:) = 0.0_wp
#if defined( __parallel ) 
    IF ( collective_wait )  CALL MPI_BARRIER( comm2d, ierr )
    CALL MPI_ALLREDUCE( var_d_l(0), var_d(0), nzt+1-nzb, MPI_REAL,   &
                        MPI_SUM, comm2d, ierr )
#else
    var_d(:) = var_d_l(:)
#endif
    var_d(:) = var_d(:) / ngp_2dh(0)

 END SUBROUTINE preprocess_spectra


 SUBROUTINE calc_spectra_x( ddd, pr, m )

    USE arrays_3d,                                                             &
        ONLY:  

    USE control_parameters,                                                    &
        ONLY:  fft_method

    USE fft_xy,                                                                &
        ONLY:  fft_x_1d

    USE grid_variables,                                                        &
        ONLY:  dx

    USE indices,                                                               &
        ONLY:  nx, ny

    USE kinds

    USE pegrid

    USE spectrum,                                                              &
        ONLY:  comp_spectra_level, n_sp_x

    USE statistics,                                                            &
        ONLY:  spectrum_x, var_d

    USE transpose_indices,                                                     &
        ONLY:  nyn_x, nys_x, nzb_x, nzt_x


    IMPLICIT NONE

    INTEGER(iwp) ::  i         !:
    INTEGER(iwp) ::  ishape(1) !:
    INTEGER(iwp) ::  j         !:
    INTEGER(iwp) ::  k         !:
    INTEGER(iwp) ::  m         !:
    INTEGER(iwp) ::  n         !:
    INTEGER(iwp) ::  pr        !:

    REAL(wp) ::  exponent     !:
    REAL(wp) ::  sum_spec_dum !: wavenumber-integrated spectrum
    
    REAL(wp), DIMENSION(0:nx) ::  work !:
    
    REAL(wp), DIMENSION(0:nx/2) ::  sums_spectra_l !:
    
    REAL(wp), DIMENSION(0:nx/2,100) ::  sums_spectra !:
    
    REAL(wp), DIMENSION(0:nx,nys_x:nyn_x,nzb_x:nzt_x) ::  ddd !:

!
!-- Exponent for geometric average
    exponent = 1.0_wp / ( ny + 1.0_wp )

!
!-- Loop over all levels defined by the user
    n = 1
    DO WHILE ( comp_spectra_level(n) /= 999999  .AND.  n <= 100 )

       k = comp_spectra_level(n)

!
!--    Calculate FFT only if the corresponding level is situated on this PE
       IF ( k >= nzb_x  .AND.  k <= nzt_x )  THEN
          
          DO  j = nys_x, nyn_x

             work = ddd(0:nx,j,k)
             CALL fft_x_1d( work, 'forward' )

             ddd(0,j,k) = dx * work(0)**2
             DO  i = 1, nx/2
                ddd(i,j,k) = dx * ( work(i)**2 + work(nx+1-i)**2 )
             ENDDO

          ENDDO

!
!--       Local sum and geometric average of these spectra
!--       (WARNING: no global sum should be performed, because floating
!--       point overflow may occur)
          DO  i = 0, nx/2

             sums_spectra_l(i) = 1.0_wp
             DO  j = nys_x, nyn_x
                sums_spectra_l(i) = sums_spectra_l(i) * ddd(i,j,k)**exponent
             ENDDO

          ENDDO
          
       ELSE

          sums_spectra_l = 1.0_wp

       ENDIF

!
!--    Global sum of spectra on PE0 (from where they are written on file) 
       sums_spectra(:,n) = 0.0_wp
#if defined( __parallel )   
       CALL MPI_BARRIER( comm2d, ierr )  ! Necessary?
       CALL MPI_REDUCE( sums_spectra_l(0), sums_spectra(0,n), nx/2+1,          &
                        MPI_REAL, MPI_PROD, 0, comm2d, ierr )
#else
       sums_spectra(:,n) = sums_spectra_l
#endif
!
!--    Normalize spectra by variance
       sum_spec_dum = SUM( sums_spectra(:,n) )
       IF ( sum_spec_dum /= 0.0_wp )  THEN
          sums_spectra(:,n) = sums_spectra(:,n) * var_d(k) / sum_spec_dum
       ENDIF
       n = n + 1

    ENDDO
    n = n - 1

    IF ( myid == 0 )  THEN
!
!--    Sum of spectra for later averaging (see routine data_output_spectra)
       DO  i = 1, nx/2
          DO k = 1, n
             spectrum_x(i,k,m) = spectrum_x(i,k,m) + sums_spectra(i,k)
          ENDDO
       ENDDO

    ENDIF
!
!-- n_sp_x is needed by data_output_spectra_x
    n_sp_x = n

 END SUBROUTINE calc_spectra_x


 SUBROUTINE calc_spectra_y( ddd, pr, m )

    USE arrays_3d,                                                             &
        ONLY:  

    USE control_parameters,                                                    &
        ONLY:  fft_method

    USE fft_xy,                                                                &
        ONLY:  fft_y_1d

    USE grid_variables,                                                        &
        ONLY:  dy

    USE indices,                                                               &
        ONLY:  nx, ny

    USE kinds

    USE pegrid

    USE spectrum,                                                              &
        ONLY:  comp_spectra_level, n_sp_y

    USE statistics,                                                            &
        ONLY:  spectrum_y, var_d

    USE transpose_indices,                                                     &
        ONLY:  nxl_yd, nxr_yd, nzb_yd, nzt_yd


    IMPLICIT NONE

    INTEGER(iwp) ::  i         !:
    INTEGER(iwp) ::  j         !:
    INTEGER(iwp) ::  jshape(1) !:
    INTEGER(iwp) ::  k         !:
    INTEGER(iwp) ::  m         !:
    INTEGER(iwp) ::  n         !:
    INTEGER(iwp) ::  pr        !:

    REAL(wp) ::  exponent !:
    REAL(wp) ::  sum_spec_dum !: wavenumber-integrated spectrum
    
    REAL(wp), DIMENSION(0:ny) ::  work !:
    
    REAL(wp), DIMENSION(0:ny/2) ::  sums_spectra_l !:
    
    REAL(wp), DIMENSION(0:ny/2,100) ::  sums_spectra !:
    
    REAL(wp), DIMENSION(0:ny,nxl_yd:nxr_yd,nzb_yd:nzt_yd) :: ddd !:


!
!-- Exponent for geometric average
    exponent = 1.0_wp / ( nx + 1.0_wp )

!
!-- Loop over all levels defined by the user
    n = 1
    DO WHILE ( comp_spectra_level(n) /= 999999  .AND.  n <= 100 )

       k = comp_spectra_level(n)

!
!--    Calculate FFT only if the corresponding level is situated on this PE
       IF ( k >= nzb_yd  .AND.  k <= nzt_yd )  THEN
          
          DO  i = nxl_yd, nxr_yd

             work = ddd(0:ny,i,k)
             CALL fft_y_1d( work, 'forward' )

             ddd(0,i,k) = dy * work(0)**2
             DO  j = 1, ny/2
                ddd(j,i,k) = dy * ( work(j)**2 + work(ny+1-j)**2 )
             ENDDO

          ENDDO

!
!--       Local sum and geometric average of these spectra
!--       (WARNING: no global sum should be performed, because floating
!--       point overflow may occur)
          DO  j = 0, ny/2

             sums_spectra_l(j) = 1.0_wp
             DO  i = nxl_yd, nxr_yd
                sums_spectra_l(j) = sums_spectra_l(j) * ddd(j,i,k)**exponent
             ENDDO

          ENDDO
          
       ELSE

          sums_spectra_l = 1.0_wp

       ENDIF

!
!--    Global sum of spectra on PE0 (from where they are written on file) 
       sums_spectra(:,n) = 0.0_wp
#if defined( __parallel )   
       CALL MPI_BARRIER( comm2d, ierr )  ! Necessary?
       CALL MPI_REDUCE( sums_spectra_l(0), sums_spectra(0,n), ny/2+1,          &
                        MPI_REAL, MPI_PROD, 0, comm2d, ierr )
#else
       sums_spectra(:,n) = sums_spectra_l
#endif
!
!--    Normalize spectra by variance
       sum_spec_dum = SUM( sums_spectra(:,n) )
       IF ( SUM(sums_spectra(:,n)) /= 0.0_wp )  THEN
          sums_spectra(:,n) = sums_spectra(:,n) * var_d(k) / SUM(sums_spectra(:,n))
       ENDIF
       n = n + 1

    ENDDO
    n = n - 1


    IF ( myid == 0 )  THEN
!
!--    Sum of spectra for later averaging (see routine data_output_spectra)
       DO  j = 1, ny/2
          DO k = 1, n
             spectrum_y(j,k,m) = spectrum_y(j,k,m) + sums_spectra(j,k)
          ENDDO
       ENDDO

    ENDIF

!
!-- n_sp_y is needed by data_output_spectra_y
    n_sp_y = n

 END SUBROUTINE calc_spectra_y
#endif