!> @file spectra_mod.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 1997-2016 Leibniz Universitaet Hannover !--------------------------------------------------------------------------------! ! ! Current revisions: ! ----------------- ! ! ! Former revisions: ! ----------------- ! $Id: spectra_mod.f90 1834 2016-04-07 14:34:20Z hellstea $ ! ! 1833 2016-04-07 14:23:03Z raasch ! file renamed, reading the spectra_par NAMELIST moved from package_parin to ! here ! ! 1815 2016-04-06 13:49:59Z raasch ! bugfix: preprocessor directives included for the non-parallel case ! ! 1808 2016-04-05 19:44:00Z raasch ! MPI module used by default on all machines ! ! 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 spectra_mod USE kinds PRIVATE CHARACTER (LEN=2), DIMENSION(10) :: spectra_direction = 'x' CHARACTER (LEN=10), DIMENSION(10) :: data_output_sp = ' ' INTEGER(iwp) :: average_count_sp = 0 INTEGER(iwp) :: dosp_time_count = 0 INTEGER(iwp) :: n_sp_x = 0, n_sp_y = 0 INTEGER(iwp) :: comp_spectra_level(100) = 999999 LOGICAL :: calculate_spectra = .FALSE. !< internal switch that spectra are calculated LOGICAL :: spectra_initialized = .FALSE. !< internal switch that spectra related quantities are initialized REAL(wp) :: averaging_interval_sp = 9999999.9_wp !< averaging interval for spectra output REAL(wp) :: dt_dosp = 9999999.9_wp !< time interval for spectra output REAL(wp) :: skip_time_dosp = 9999999.9_wp !< no output of spectra data before this interval has passed REAL(wp), DIMENSION(:), ALLOCATABLE :: var_d REAL(wp), DIMENSION(:,:,:), ALLOCATABLE :: spectrum_x, spectrum_y 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 INTERFACE spectra_check_parameters MODULE PROCEDURE spectra_check_parameters END INTERFACE spectra_check_parameters INTERFACE spectra_header MODULE PROCEDURE spectra_header END INTERFACE spectra_header INTERFACE spectra_init MODULE PROCEDURE spectra_init END INTERFACE spectra_init INTERFACE spectra_parin MODULE PROCEDURE spectra_parin END INTERFACE spectra_parin PUBLIC average_count_sp, averaging_interval_sp, calc_spectra, & calculate_spectra, comp_spectra_level, data_output_sp, & dosp_time_count, dt_dosp, n_sp_x, n_sp_y, plot_spectra_level, & skip_time_dosp, spectra_check_parameters, spectra_direction, & spectra_header, spectra_init, spectra_parin, spectrum_x, & spectrum_y, var_d CONTAINS !------------------------------------------------------------------------------! ! Description: ! ------------ !> Parin for &spectra_par for calculating spectra !------------------------------------------------------------------------------! SUBROUTINE spectra_parin USE control_parameters, & ONLY: dt_data_output IMPLICIT NONE CHARACTER (LEN=80) :: line !< dummy string that contains the current & !< line of the parameter file NAMELIST /spectra_par/ averaging_interval_sp, comp_spectra_level, & data_output_sp, dt_dosp, skip_time_dosp, & spectra_direction ! !-- Position the namelist-file at the beginning (it was already opened in !-- parin), search for the namelist-group of the package and position the !-- file at this line. line = ' ' ! !-- Try to find the spectra package REWIND ( 11 ) line = ' ' DO WHILE ( INDEX( line, '&spectra_par' ) == 0 ) READ ( 11, '(A)', END=10 ) line ENDDO BACKSPACE ( 11 ) ! !-- Read namelist READ ( 11, spectra_par ) ! !-- Default setting of dt_dosp here (instead of check_parameters), because !-- its current value is needed in init_pegrid IF ( dt_dosp == 9999999.9_wp ) dt_dosp = dt_data_output ! !-- Set general switch that spectra shall be calculated calculate_spectra = .TRUE. 10 CONTINUE END SUBROUTINE spectra_parin !------------------------------------------------------------------------------! ! Description: ! ------------ !> Initialization of spectra related variables !------------------------------------------------------------------------------! SUBROUTINE spectra_init USE indices, & ONLY: nx, ny, nzb, nzt IMPLICIT NONE IF ( spectra_initialized ) RETURN IF ( dt_dosp /= 9999999.9_wp ) THEN ALLOCATE( spectrum_x( 1:nx/2, 1:10, 1:10 ), & spectrum_y( 1:ny/2, 1:10, 1:10 ) ) spectrum_x = 0.0_wp spectrum_y = 0.0_wp ALLOCATE( var_d(nzb:nzt+1) ) var_d = 0.0_wp ENDIF spectra_initialized = .TRUE. END SUBROUTINE spectra_init !------------------------------------------------------------------------------! ! Description: ! ------------ !> Check spectra related quantities !------------------------------------------------------------------------------! SUBROUTINE spectra_check_parameters USE control_parameters, & ONLY: averaging_interval, message_string, skip_time_data_output IMPLICIT NONE ! !-- Check the average interval IF ( averaging_interval_sp == 9999999.9_wp ) THEN averaging_interval_sp = averaging_interval ENDIF IF ( averaging_interval_sp > dt_dosp ) THEN WRITE( message_string, * ) 'averaging_interval_sp = ', & averaging_interval_sp, ' must be <= dt_dosp = ', dt_dosp CALL message( 'spectra_check_parameters', 'PA0087', 1, 2, 0, 6, 0 ) ENDIF ! !-- Set the default skip time interval for data output, if necessary IF ( skip_time_dosp == 9999999.9_wp ) & skip_time_dosp = skip_time_data_output END SUBROUTINE spectra_check_parameters !------------------------------------------------------------------------------! ! Description: ! ------------ !> Header output for spectra !> !> @todo Output of netcdf data format and compression level !------------------------------------------------------------------------------! SUBROUTINE spectra_header ( io ) USE control_parameters, & ONLY: dt_averaging_input_pr ! USE netcdf_interface, & ! ONLY: netcdf_data_format_string, netcdf_deflate IMPLICIT NONE CHARACTER (LEN=40) :: output_format !< internal string INTEGER(iwp) :: i !< internal counter INTEGER(iwp), INTENT(IN) :: io !< Unit of the output file ! !-- Spectra output IF ( dt_dosp /= 9999999.9_wp ) THEN WRITE ( io, 1 ) ! output_format = netcdf_data_format_string ! IF ( netcdf_deflate == 0 ) THEN ! WRITE ( io, 2 ) output_format ! ELSE ! WRITE ( io, 3 ) TRIM( output_format ), netcdf_deflate ! ENDIF WRITE ( io, 2 ) 'see profiles or other quantities' WRITE ( io, 4 ) dt_dosp IF ( skip_time_dosp /= 0.0_wp ) WRITE ( io, 5 ) skip_time_dosp WRITE ( io, 6 ) ( data_output_sp(i), i = 1,10 ), & ( spectra_direction(i), i = 1,10 ), & ( comp_spectra_level(i), i = 1,100 ), & averaging_interval_sp, dt_averaging_input_pr ENDIF 1 FORMAT (' Spectra:') 2 FORMAT (' Output format: ',A/) 3 FORMAT (' Output format: ',A, ' compressed with level: ',I1/) 4 FORMAT (' Output every ',F7.1,' s'/) 5 FORMAT (' No output during initial ',F8.2,' s') 6 FORMAT (' Arrays: ', 10(A5,',')/ & ' Directions: ', 10(A5,',')/ & ' height levels k = ', 20(I3,',')/ & ' ', 20(I3,',')/ & ' ', 20(I3,',')/ & ' ', 20(I3,',')/ & ' ', 19(I3,','),I3,'.'/ & ' Time averaged over ', F7.1, ' s,' / & ' Profiles for the time averaging are taken every ', & F6.1,' s') END SUBROUTINE spectra_header SUBROUTINE calc_spectra USE arrays_3d, & ONLY: d, tend USE control_parameters, & ONLY: 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 spectra related quantities CALL spectra_init ! !-- 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( __parallel ) #if defined( __mpifh ) INCLUDE "mpif.h" #else USE MPI #endif #endif USE pegrid, & ONLY: collective_wait, comm2d, ierr USE statistics, & ONLY: hom 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( __parallel ) #if defined( __mpifh ) INCLUDE "mpif.h" #else USE MPI #endif #endif USE pegrid, & ONLY: comm2d, ierr, myid 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( __parallel ) #if defined( __mpifh ) INCLUDE "mpif.h" #else USE MPI #endif #endif USE pegrid, & ONLY: comm2d, ierr, myid 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 spectra_mod