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SUBROUTINE inifilr |
module inifilr_m |
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! From filtrez/inifilr.F,v 1.1.1.1 2004/05/19 12:53:09 |
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! H. Upadhyaya, O.Sharma |
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! This routine computes the eigenfunctions of the laplacien |
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! on the stretched grid, and the filtering coefficients |
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! We designate: |
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! eignfn eigenfunctions of the discrete laplacien |
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! eigenvl eigenvalues |
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! jfiltn indexof the last scalar line filtered in NH |
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! jfilts index of the first line filtered in SH |
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! modfrst index of the mode from where modes are filtered |
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! modemax maximum number of modes ( im ) |
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! coefil filtering coefficients ( lamda_max*cos(rlat)/lamda ) |
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! sdd SQRT( dx ) |
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! the modes are filtered from modfrst to modemax |
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USE dimens_m |
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USE paramet_m |
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USE logic |
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USE comgeom |
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USE serre |
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USE parafilt |
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USE coefils |
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IMPLICIT NONE |
IMPLICIT NONE |
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REAL dlonu(iim), dlatu(jjm) |
INTEGER jfiltnu, jfiltnv |
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REAL rlamda(iim), eignvl(iim) |
! index of the last line filtered in northern hemisphere at rlat[uv] |
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! latitudes |
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REAL lamdamax, pi, cof |
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INTEGER i, j, modemax, imx, k, kf, ii |
integer jfiltsu, jfiltsv |
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REAL dymin, dxmin, colat0 |
! index of the first line filtered in southern hemisphere at |
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REAL eignft(iim,iim), coff |
! rlat[uv] latitudes |
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EXTERNAL inifgn |
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! Filtre pour les champs situes sur la grille scalaire (longitudes |
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!----------------------------------------------------------- |
! rlonv, latitudes rlatu) : |
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real, pointer:: matriceun(:, :, :) ! (iim, iim, jfiltnu - 1) |
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real, pointer:: matriceus(:, :, :) ! (iim, iim, jjm - jfiltsu + 1) |
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pi = 2.*asin(1.) |
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! Filtre pour les champs situes sur la grille scalaire (longitudes |
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DO i = 1, iim |
! rlonv, latitudes rlatu), pour le filtre inverse : |
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dlonu(i) = xprimu(i) |
real, pointer:: matrinvn(:, :, :) ! (iim, iim, jfiltnu - 1) |
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END DO |
real, pointer:: matrinvs(:, :, :) ! (iim, iim, jjm - jfiltsu + 1) |
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CALL inifgn(eignvl) |
! Filtre pour les champs situes sur la grille de la vorticit\'e |
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! (longitudes rlonu, latitudes rlatv) |
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PRINT *, ' EIGNVL ' |
real, pointer:: matricevn(:, :, :) ! (iim, iim, jfiltnv) matrice |
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PRINT 250, eignvl |
real, pointer:: matricevs(:, :, :) ! (iim, iim, jjm - jfiltsv + 1) |
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250 FORMAT (1X,5E13.6) |
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contains |
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! compute eigenvalues and eigenfunctions |
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SUBROUTINE inifilr |
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!................................................................. |
! From filtrez/inifilr.F, version 1.1.1.1, 2004/05/19 12:53:09 |
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! H. Upadhyaya, O. Sharma |
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! compute the filtering coefficients for scalar lines and |
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! meridional wind v-lines |
! This procedure computes the filtering coefficients for scalar |
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! lines and meridional wind v lines. The modes are filtered from |
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! we filter all those latitude lines where coefil < 1 |
! modfrst to iim. We filter all those latitude lines where coefil |
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! NO FILTERING AT POLES |
! < 1. No filtering at poles. colat0 is to be used when alpha |
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! (stretching coefficient) is set equal to zero for the regular |
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! colat0 is to be used when alpha (stretching coefficient) |
! grid case. |
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! is set equal to zero for the regular grid case |
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USE dimens_m, ONLY : iim, jjm |
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! ....... Calcul de colat0 ......... |
USE dynetat0_m, ONLY : rlatu, rlatv, xprimu, grossismx |
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! ..... colat0 = minimum de ( 0.5, min dy/ min dx ) ... |
use inifgn_m, only: inifgn |
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use inifilr_hemisph_m, only: inifilr_hemisph |
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use jumble, only: new_unit |
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DO j = 1, jjm |
use nr_util, only: pi, ifirstloc, assert |
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dlatu(j) = rlatu(j) - rlatu(j+1) |
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END DO |
! Local: |
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dxmin = dlonu(1) |
REAL dlatu(jjm) |
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DO i = 2, iim |
REAL rlamda(2:iim) ! > 0, in descending order |
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dxmin = min(dxmin,dlonu(i)) |
real eignvl(iim) ! eigenvalues (<= 0) sorted in descending order |
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END DO |
INTEGER j, unit |
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dymin = dlatu(1) |
REAL colat0 ! > 0 |
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DO j = 2, jjm |
integer j1 ! index of negative latitude closest to the equator |
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dymin = min(dymin,dlatu(j)) |
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END DO |
real eignfnu(iim, iim), eignfnv(iim, iim) |
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! eigenvectors of the discrete second derivative with respect to |
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! longitude, at rlon[uv] longitudes |
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colat0 = min(0.5,dymin/dxmin) |
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!----------------------------------------------------------- |
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IF ( .NOT. fxyhypb .AND. ysinus) THEN |
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colat0 = 0.6 |
print *, "Call sequence information: inifilr" |
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! ...... a revoir pour ysinus ! ....... |
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alphax = 0. |
CALL inifgn(eignvl, eignfnu, eignfnv) |
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END IF |
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! Calcul de colat0 |
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PRINT 50, colat0, alphax |
forall (j = 1:jjm) dlatu(j) = rlatu(j) - rlatu(j + 1) |
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50 FORMAT (/15X,' Inifilr colat0 alphax ',2E16.7) |
colat0 = min(0.5, minval(dlatu) / minval(xprimu(:iim))) |
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PRINT *, 'colat0 = ', colat0 |
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IF (alphax==1.) THEN |
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PRINT *, ' Inifilr alphax doit etre < a 1. Corriger ' |
rlamda = iim / pi / colat0 * grossismx / sqrt(- eignvl(2: iim)) |
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STOP 1 |
print *, "1 / rlamda(iim) = ", 1. / rlamda(iim) |
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END IF |
! This is demonstrated in the notes but just to be sure: |
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call assert(rlamda(iim) * colat0 >= 1. - 2. * epsilon(0.), & |
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lamdamax = iim/(pi*colat0*(1.-alphax)) |
"inifilr rlamda(iim) * colat0") |
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DO i = 2, iim |
call new_unit(unit) |
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rlamda(i) = lamdamax/sqrt(abs(eignvl(i))) |
open(unit, file = "modfrst.csv", status = "replace", action = "write") |
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END DO |
write(unit, fmt = *) '"rlat (degrees)" modfrst' ! title line |
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j1 = ifirstloc(rlatu <= 0.) |
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DO j = 1, jjm |
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DO i = 1, iim |
call inifilr_hemisph(rlatu(j1 - 1:2:- 1), rlamda, unit, eignfnv, jfiltnu, & |
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coefilu(i,j) = 0.0 |
matriceun, matrinvn) |
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coefilv(i,j) = 0.0 |
jfiltnu = j1 - jfiltnu |
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coefilu2(i,j) = 0.0 |
matriceun = matriceun(:, :, jfiltnu - 1:1:- 1) |
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coefilv2(i,j) = 0.0 |
matrinvn = matrinvn(:, :, jfiltnu - 1:1:- 1) |
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end DO |
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END DO |
call inifilr_hemisph(- rlatu(j1:jjm), rlamda, unit, eignfnv, jfiltsu, & |
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matriceus, matrinvs) |
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jfiltsu = j1 - 1 + jfiltsu |
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! ... Determination de jfiltnu,jfiltnv,jfiltsu,jfiltsv .... |
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! ......................................................... |
j1 = ifirstloc(rlatv <= 0.) |
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modemax = iim |
call inifilr_hemisph(rlatv(j1 - 1:1:- 1), rlamda, unit, eignfnu, jfiltnv, & |
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matricevn) |
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!ccc imx = modemax - 4 * (modemax/iim) |
jfiltnv = j1 - jfiltnv |
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matricevn = matricevn(:, :, jfiltnv:1:- 1) |
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imx = iim |
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call inifilr_hemisph(- rlatv(j1:jjm), rlamda, unit, eignfnu, jfiltsv, & |
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PRINT *, ' TRUNCATION AT ', imx |
matricevs) |
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jfiltsv = j1 - 1 + jfiltsv |
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DO j = 2, jjm/2 + 1 |
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cof = cos(rlatu(j))/colat0 |
close(unit) |
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IF (cof<1.) THEN |
PRINT *, 'jfiltnu =', jfiltnu |
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IF (rlamda(imx)*cos(rlatu(j))<1.) jfiltnu = j |
PRINT *, 'jfiltsu =', jfiltsu |
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END IF |
PRINT *, 'jfiltnv =', jfiltnv |
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PRINT *, 'jfiltsv =', jfiltsv |
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cof = cos(rlatu(jjp1-j+1))/colat0 |
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IF (cof<1.) THEN |
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IF (rlamda(imx)*cos(rlatu(jjp1-j+1))<1.) jfiltsu = jjp1 - j + 1 |
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END IF |
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END DO |
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DO j = 1, jjm/2 |
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cof = cos(rlatv(j))/colat0 |
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IF (cof<1.) THEN |
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IF (rlamda(imx)*cos(rlatv(j))<1.) jfiltnv = j |
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END IF |
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cof = cos(rlatv(jjm-j+1))/colat0 |
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IF (cof<1.) THEN |
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IF (rlamda(imx)*cos(rlatv(jjm-j+1))<1.) jfiltsv = jjm - j + 1 |
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END IF |
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END DO |
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IF (jfiltnu<=0) jfiltnu = 1 |
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IF (jfiltnu>jjm/2+1) THEN |
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PRINT *, ' jfiltnu en dehors des valeurs acceptables ', jfiltnu |
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STOP 1 |
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END IF |
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IF (jfiltsu<=0) jfiltsu = 1 |
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IF (jfiltsu>jjm+1) THEN |
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PRINT *, ' jfiltsu en dehors des valeurs acceptables ', jfiltsu |
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STOP 1 |
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END IF |
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IF (jfiltnv<=0) jfiltnv = 1 |
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IF (jfiltnv>jjm/2) THEN |
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PRINT *, ' jfiltnv en dehors des valeurs acceptables ', jfiltnv |
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STOP 1 |
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END IF |
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IF (jfiltsv<=0) jfiltsv = 1 |
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IF (jfiltsv>jjm) THEN |
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PRINT *, ' jfiltsv en dehors des valeurs acceptables ', jfiltsv |
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STOP 1 |
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END IF |
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PRINT *, ' jfiltnv jfiltsv jfiltnu jfiltsu ', jfiltnv, jfiltsv, jfiltnu, & |
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jfiltsu |
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! ... Determination de coefilu,coefilv,n=modfrstu,modfrstv .... |
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!................................................................ |
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DO j = 1, jjm |
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modfrstu(j) = iim |
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modfrstv(j) = iim |
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END DO |
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DO j = 2, jfiltnu |
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DO k = 2, modemax |
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cof = rlamda(k)*cos(rlatu(j)) |
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IF (cof<1.) GO TO 82 |
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end DO |
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cycle |
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82 modfrstu(j) = k |
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kf = modfrstu(j) |
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DO k = kf, modemax |
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cof = rlamda(k)*cos(rlatu(j)) |
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coefilu(k,j) = cof - 1. |
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coefilu2(k,j) = cof*cof - 1. |
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end DO |
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END DO |
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DO j = 1, jfiltnv |
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DO k = 2, modemax |
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cof = rlamda(k)*cos(rlatv(j)) |
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IF (cof<1.) GO TO 87 |
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end DO |
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cycle |
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87 modfrstv(j) = k |
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kf = modfrstv(j) |
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DO k = kf, modemax |
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cof = rlamda(k)*cos(rlatv(j)) |
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coefilv(k,j) = cof - 1. |
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coefilv2(k,j) = cof*cof - 1. |
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end DO |
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end DO |
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DO j = jfiltsu, jjm |
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DO k = 2, modemax |
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cof = rlamda(k)*cos(rlatu(j)) |
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IF (cof<1.) GO TO 92 |
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end DO |
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cycle |
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92 modfrstu(j) = k |
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kf = modfrstu(j) |
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DO k = kf, modemax |
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cof = rlamda(k)*cos(rlatu(j)) |
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coefilu(k,j) = cof - 1. |
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coefilu2(k,j) = cof*cof - 1. |
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end DO |
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end DO |
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DO j = jfiltsv, jjm |
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DO k = 2, modemax |
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cof = rlamda(k)*cos(rlatv(j)) |
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IF (cof<1.) GO TO 97 |
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end DO |
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cycle |
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97 modfrstv(j) = k |
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kf = modfrstv(j) |
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DO k = kf, modemax |
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cof = rlamda(k)*cos(rlatv(j)) |
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coefilv(k,j) = cof - 1. |
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coefilv2(k,j) = cof*cof - 1. |
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end DO |
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END DO |
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IF (jfiltnv>=jjm/2 .OR. jfiltnu>=jjm/2) THEN |
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IF (jfiltnv==jfiltsv) jfiltsv = 1 + jfiltnv |
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IF (jfiltnu==jfiltsu) jfiltsu = 1 + jfiltnu |
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PRINT *, 'jfiltnv jfiltsv jfiltnu jfiltsu', jfiltnv, jfiltsv, jfiltnu, & |
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jfiltsu |
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END IF |
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PRINT *, ' Modes premiers v ' |
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PRINT 334, modfrstv |
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PRINT *, ' Modes premiers u ' |
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PRINT 334, modfrstu |
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IF (nfilun<jfiltnu) THEN |
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PRINT *, ' le parametre nfilun utilise pour la matrice ', & |
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' matriceun est trop petit ! ' |
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PRINT *, 'Le changer dans parafilt.h et le mettre a ', jfiltnu |
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PRINT *, 'Pour information, nfilun,nfilus,nfilvn,nfilvs ', & |
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'doivent etre egaux successivement a ', jfiltnu, jjm - jfiltsu + 1, & |
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jfiltnv, jjm - jfiltsv + 1 |
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STOP 1 |
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END IF |
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IF (nfilun>jfiltnu+2) THEN |
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PRINT *, ' le parametre nfilun utilise pour la matrice ', & |
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' matriceun est trop grand ! Gachis de memoire ! ' |
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PRINT *, 'Le changer dans parafilt.h et le mettre a ', jfiltnu |
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PRINT *, 'Pour information, nfilun,nfilus,nfilvn,nfilvs ', & |
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'doivent etre egaux successivement a ', jfiltnu, jjm - jfiltsu + 1, & |
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jfiltnv, jjm - jfiltsv + 1 |
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END IF |
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IF (nfilus<jjm-jfiltsu+1) THEN |
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PRINT *, ' le parametre nfilus utilise pour la matrice ', & |
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' matriceus est trop petit ! ' |
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PRINT *, ' Le changer dans parafilt.h et le mettre a ', & |
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jjm - jfiltsu + 1 |
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PRINT *, ' Pour information , nfilun,nfilus,nfilvn,nfilvs ', & |
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'doivent etre egaux successivement a ', jfiltnu, jjm - jfiltsu + 1, & |
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jfiltnv, jjm - jfiltsv + 1 |
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STOP 1 |
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END IF |
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IF (nfilus>jjm-jfiltsu+3) THEN |
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PRINT *, ' le parametre nfilus utilise pour la matrice ', & |
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' matriceus est trop grand ! ' |
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PRINT *, ' Le changer dans parafilt.h et le mettre a ', & |
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jjm - jfiltsu + 1 |
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PRINT *, ' Pour information , nfilun,nfilus,nfilvn,nfilvs ', & |
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'doivent etre egaux successivement a ', jfiltnu, jjm - jfiltsu + 1, & |
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jfiltnv, jjm - jfiltsv + 1 |
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END IF |
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IF (nfilvn<jfiltnv) THEN |
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PRINT *, ' le parametre nfilvn utilise pour la matrice ', & |
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' matricevn est trop petit ! ' |
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PRINT *, 'Le changer dans parafilt.h et le mettre a ', jfiltnv |
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PRINT *, ' Pour information , nfilun,nfilus,nfilvn,nfilvs ', & |
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'doivent etre egaux successivement a ', jfiltnu, jjm - jfiltsu + 1, & |
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jfiltnv, jjm - jfiltsv + 1 |
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STOP 1 |
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END IF |
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IF (nfilvn>jfiltnv+2) THEN |
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PRINT *, ' le parametre nfilvn utilise pour la matrice ', & |
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' matricevn est trop grand ! Gachis de memoire ! ' |
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PRINT *, 'Le changer dans parafilt.h et le mettre a ', jfiltnv |
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PRINT *, ' Pour information , nfilun,nfilus,nfilvn,nfilvs ', & |
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'doivent etre egaux successivement a ', jfiltnu, jjm - jfiltsu + 1, & |
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jfiltnv, jjm - jfiltsv + 1 |
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END IF |
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IF (nfilvs<jjm-jfiltsv+1) THEN |
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PRINT *, ' le parametre nfilvs utilise pour la matrice ', & |
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' matricevs est trop petit ! Le changer dans parafilt.h ' |
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PRINT *, ' Le changer dans parafilt.h et le mettre a ', & |
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jjm - jfiltsv + 1 |
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PRINT *, ' Pour information , nfilun,nfilus,nfilvn,nfilvs ', & |
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'doivent etre egaux successivement a ', jfiltnu, jjm - jfiltsu + 1, & |
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jfiltnv, jjm - jfiltsv + 1 |
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STOP 1 |
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END IF |
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IF (nfilvs>jjm-jfiltsv+3) THEN |
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PRINT *, ' le parametre nfilvs utilise pour la matrice ', & |
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' matricevs est trop grand ! Gachis de memoire ! ' |
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PRINT *, ' Le changer dans parafilt.h et le mettre a ', & |
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jjm - jfiltsv + 1 |
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PRINT *, ' Pour information , nfilun,nfilus,nfilvn,nfilvs ', & |
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'doivent etre egaux successivement a ', jfiltnu, jjm - jfiltsu + 1, & |
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jfiltnv, jjm - jfiltsv + 1 |
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END IF |
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! ... Calcul de la matrice filtre 'matriceu' pour les champs situes |
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! sur la grille scalaire ........ |
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DO j = 2, jfiltnu |
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DO i = 1, iim |
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coff = coefilu(i,j) |
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IF (i<modfrstu(j)) coff = 0. |
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DO k = 1, iim |
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eignft(i,k) = eignfnv(k,i)*coff |
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END DO |
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END DO |
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DO k = 1, iim |
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DO i = 1, iim |
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matriceun(i,k,j) = 0.0 |
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DO ii = 1, iim |
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matriceun(i,k,j) = matriceun(i,k,j) + eignfnv(i,ii)*eignft(ii,k) |
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END DO |
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END DO |
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END DO |
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END DO |
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DO j = jfiltsu, jjm |
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DO i = 1, iim |
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coff = coefilu(i,j) |
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IF (i<modfrstu(j)) coff = 0. |
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DO k = 1, iim |
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eignft(i,k) = eignfnv(k,i)*coff |
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END DO |
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END DO |
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DO k = 1, iim |
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DO i = 1, iim |
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matriceus(i,k,j-jfiltsu+1) = 0.0 |
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DO ii = 1, iim |
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matriceus(i,k,j-jfiltsu+1) = matriceus(i,k,j-jfiltsu+1) + & |
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eignfnv(i,ii)*eignft(ii,k) |
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END DO |
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END DO |
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END DO |
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END DO |
|
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! ................................................................... |
|
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|
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! ... Calcul de la matrice filtre 'matricev' pour les champs situes |
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! sur la grille de V ou de Z ........ |
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! ................................................................... |
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DO j = 1, jfiltnv |
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DO i = 1, iim |
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coff = coefilv(i,j) |
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IF (i<modfrstv(j)) coff = 0. |
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DO k = 1, iim |
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eignft(i,k) = eignfnu(k,i)*coff |
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END DO |
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END DO |
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DO k = 1, iim |
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DO i = 1, iim |
|
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matricevn(i,k,j) = 0.0 |
|
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DO ii = 1, iim |
|
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matricevn(i,k,j) = matricevn(i,k,j) + eignfnu(i,ii)*eignft(ii,k) |
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END DO |
|
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END DO |
|
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END DO |
|
|
|
|
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END DO |
|
|
|
|
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DO j = jfiltsv, jjm |
|
|
|
|
|
DO i = 1, iim |
|
|
coff = coefilv(i,j) |
|
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IF (i<modfrstv(j)) coff = 0. |
|
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DO k = 1, iim |
|
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eignft(i,k) = eignfnu(k,i)*coff |
|
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END DO |
|
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END DO |
|
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DO k = 1, iim |
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DO i = 1, iim |
|
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matricevs(i,k,j-jfiltsv+1) = 0.0 |
|
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DO ii = 1, iim |
|
|
matricevs(i,k,j-jfiltsv+1) = matricevs(i,k,j-jfiltsv+1) + & |
|
|
eignfnu(i,ii)*eignft(ii,k) |
|
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END DO |
|
|
END DO |
|
|
END DO |
|
|
|
|
|
END DO |
|
|
|
|
|
! ................................................................... |
|
|
|
|
|
! ... Calcul de la matrice filtre 'matrinv' pour les champs situes |
|
|
! sur la grille scalaire , pour le filtre inverse ........ |
|
|
! ................................................................... |
|
|
|
|
|
DO j = 2, jfiltnu |
|
|
|
|
|
DO i = 1, iim |
|
|
coff = coefilu(i,j)/(1.+coefilu(i,j)) |
|
|
IF (i<modfrstu(j)) coff = 0. |
|
|
DO k = 1, iim |
|
|
eignft(i,k) = eignfnv(k,i)*coff |
|
|
END DO |
|
|
END DO |
|
|
DO k = 1, iim |
|
|
DO i = 1, iim |
|
|
matrinvn(i,k,j) = 0.0 |
|
|
DO ii = 1, iim |
|
|
matrinvn(i,k,j) = matrinvn(i,k,j) + eignfnv(i,ii)*eignft(ii,k) |
|
|
END DO |
|
|
END DO |
|
|
END DO |
|
|
|
|
|
END DO |
|
|
|
|
|
DO j = jfiltsu, jjm |
|
|
|
|
|
DO i = 1, iim |
|
|
coff = coefilu(i,j)/(1.+coefilu(i,j)) |
|
|
IF (i<modfrstu(j)) coff = 0. |
|
|
DO k = 1, iim |
|
|
eignft(i,k) = eignfnv(k,i)*coff |
|
|
END DO |
|
|
END DO |
|
|
DO k = 1, iim |
|
|
DO i = 1, iim |
|
|
matrinvs(i,k,j-jfiltsu+1) = 0.0 |
|
|
DO ii = 1, iim |
|
|
matrinvs(i,k,j-jfiltsu+1) = matrinvs(i,k,j-jfiltsu+1) + & |
|
|
eignfnv(i,ii)*eignft(ii,k) |
|
|
END DO |
|
|
END DO |
|
|
END DO |
|
|
|
|
|
END DO |
|
| 111 |
|
|
| 112 |
334 FORMAT (1X,24I3) |
END SUBROUTINE inifilr |
| 113 |
|
|
| 114 |
END SUBROUTINE inifilr |
end module inifilr_m |
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