!> @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 .
!
! Copyright 1997-2014 Leibniz Universitaet Hannover
!--------------------------------------------------------------------------------!
!
! Current revisions:
! -----------------
!
!
! Former revisions:
! -----------------
! $Id: spectrum.f90 1787 2016-03-08 06:57:00Z maronga $
!
! 1786 2016-03-08 05:49:27Z raasch
! 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
!
! 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 ^2566^25692s>->2 ', &
'k ^2236 ^2566^25692s>->2 ', &
'k ^2236 ^2566^25692s>->2 ', &
'k ^2236 ^2566^2569<^1185(k) in m>2s>->2', &
'k ^2236 ^2566^25692s>->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