source: palm/trunk/SOURCE/spectrum.f90 @ 1786

!> @file spectrum.f90
!--------------------------------------------------------------------------------!
! 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:
! -----------------
! routine is modularized, filename renamed from calc_spectra to spectrum,
! privious data module spectrum moved from modules.f90 to here,
! cpp-direktives for spectra removed, immediate return if no spectra levels are
! given
! 
! Former revisions:
! -----------------
! $Id: spectrum.f90 1786 2016-03-08 05:49:27Z raasch $
!
! 1682 2015-10-07 23:56:08Z knoop
! Code annotations made doxygen readable 
!
! 1575 2015-03-27 09:56:27Z raasch
! adjustments for psolver-queries
!
! 1511 2014-12-16 15:54:16Z suehring
! Bugfix concerning spectra normalization
!
! 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).
!------------------------------------------------------------------------------!
 MODULE spectrum

    USE kinds

    PRIVATE

    CHARACTER (LEN=6),  DIMENSION(1:5) ::  header_char = (/ 'PS(u) ', 'PS(v) ',&
                                           'PS(w) ', 'PS(pt)', 'PS(q) ' /)
    CHARACTER (LEN=2),  DIMENSION(10)  ::  spectra_direction = 'x'
    CHARACTER (LEN=10), DIMENSION(10)  ::  data_output_sp  = ' '
    CHARACTER (LEN=25), DIMENSION(1:5) ::  utext_char =                    &
                                           (/ '-power spectrum of u     ', &
                                              '-power spectrum of v     ', &
                                              '-power spectrum of w     ', &
                                              '-power spectrum of ^1185 ', &
                                              '-power spectrum of q     ' /)
    CHARACTER (LEN=39), DIMENSION(1:5) ::  ytext_char =                        &
                                 (/ 'k ^2236 ^2566^2569<u(k) in m>2s>->2    ', &
                                    'k ^2236 ^2566^2569<v(k) in m>2s>->2    ', &
                                    'k ^2236 ^2566^2569<w(k) in m>2s>->2    ', &
                                    'k ^2236 ^2566^2569<^1185(k) in m>2s>->2', &
                                    'k ^2236 ^2566^2569<q(k) in m>2s>->2    ' /)

    INTEGER(iwp) ::  klist_x = 0, klist_y = 0, n_sp_x = 0, n_sp_y = 0

    INTEGER(iwp) ::  comp_spectra_level(100) = 999999,                   &
                     lstyles(100) = (/ 0, 7, 3, 10, 1, 4, 9, 2, 6, 8,    &
                                       0, 7, 3, 10, 1, 4, 9, 2, 6, 8,    &
                                       0, 7, 3, 10, 1, 4, 9, 2, 6, 8,    &
                                       0, 7, 3, 10, 1, 4, 9, 2, 6, 8,    &
                                       0, 7, 3, 10, 1, 4, 9, 2, 6, 8,    &
                                       0, 7, 3, 10, 1, 4, 9, 2, 6, 8,    &
                                       0, 7, 3, 10, 1, 4, 9, 2, 6, 8,    &
                                       0, 7, 3, 10, 1, 4, 9, 2, 6, 8,    &
                                       0, 7, 3, 10, 1, 4, 9, 2, 6, 8,    &
                                       0, 7, 3, 10, 1, 4, 9, 2, 6, 8 /), &
                     plot_spectra_level(100) = 999999

    REAL(wp)    ::  time_to_start_sp = 0.0_wp

    PUBLIC  comp_spectra_level, data_output_sp, header_char, klist_x, klist_y, &
            lstyles, n_sp_x, n_sp_y, plot_spectra_level, spectra_direction,    &
            utext_char, ytext_char

    SAVE

    INTERFACE calc_spectra
       MODULE PROCEDURE calc_spectra
    END INTERFACE calc_spectra

    INTERFACE preprocess_spectra
       MODULE PROCEDURE preprocess_spectra
    END INTERFACE preprocess_spectra

    INTERFACE calc_spectra_x
       MODULE PROCEDURE calc_spectra_x
    END INTERFACE calc_spectra_x

    INTERFACE calc_spectra_y
       MODULE PROCEDURE calc_spectra_y
    END INTERFACE calc_spectra_y

    PUBLIC calc_spectra


 CONTAINS

    SUBROUTINE calc_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,                                                             &
           ONLY:  myid, pdims

       IMPLICIT NONE

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


!
!--    Check if user gave any levels for spectra to be calculated
       IF ( comp_spectra_level(1) == 999999 )  RETURN

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

!
!--    Initialize ffts
       CALL fft_init

!
!--    Reallocate array d in required size
       IF ( psolver(1:9) == '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 paral' //  &
                              'lel 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 spectr' // &
                                    'a 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 paral' //  &
                              'lel 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' )

    END SUBROUTINE calc_spectra


!------------------------------------------------------------------------------!
! Description:
! ------------
!> @todo Missing subroutine description.
!------------------------------------------------------------------------------!
    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

#if defined( __lc )
       USE MPI
#else
       INCLUDE "mpif.h"
#endif
       USE pegrid,                                                             &
           ONLY:  collective_wait, comm2d, ierr

       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


!------------------------------------------------------------------------------!
! Description:
! ------------
!> @todo Missing subroutine description.
!------------------------------------------------------------------------------!
    SUBROUTINE calc_spectra_x( ddd, pr, m )

       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

#if defined( __lc )
       USE MPI
#else
       INCLUDE "mpif.h"
#endif
       USE pegrid,                                                             &
           ONLY:  comm2d, ierr, myid

       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


!------------------------------------------------------------------------------!
! Description:
! ------------
!> @todo Missing subroutine description.
!------------------------------------------------------------------------------!
    SUBROUTINE calc_spectra_y( ddd, pr, m )

       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

#if defined( __lc )
       USE MPI
#else
       INCLUDE "mpif.h"
#endif
       USE pegrid,                                                             &
           ONLY:  comm2d, ierr, myid

       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

 END MODULE spectrum