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! |
module fxhyp_m |
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! $Header: /home/cvsroot/LMDZ4/libf/dyn3d/fxhyp.F,v 1.2 2005/06/03 09:11:32 fairhead Exp $ |
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! |
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c |
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c |
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SUBROUTINE fxhyp ( xzoomdeg,grossism,dzooma,tau , |
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, rlonm025,xprimm025,rlonv,xprimv,rlonu,xprimu,rlonp025,xprimp025, |
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, champmin,champmax ) |
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c Auteur : P. Le Van |
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use dimens_m |
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use paramet_m |
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IMPLICIT NONE |
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c Calcule les longitudes et derivees dans la grille du GCM pour une |
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c fonction f(x) a tangente hyperbolique . |
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c |
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c grossism etant le grossissement ( = 2 si 2 fois, = 3 si 3 fois,etc.) |
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c dzoom etant la distance totale de la zone du zoom |
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c tau la raideur de la transition de l'interieur a l'exterieur du zoom |
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c |
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c On doit avoir grossism x dzoom < pi ( radians ) , en longitude. |
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c ******************************************************************** |
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INTEGER nmax, nmax2 |
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PARAMETER ( nmax = 30000, nmax2 = 2*nmax ) |
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c |
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LOGICAL scal180 |
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PARAMETER ( scal180 = .TRUE. ) |
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c scal180 = .TRUE. si on veut avoir le premier point scalaire pour |
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c une grille reguliere ( grossism = 1.,tau=0.,clon=0. ) a -180. degres. |
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c sinon scal180 = .FALSE. |
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c ...... arguments d'entree ....... |
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c |
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REAL xzoomdeg,dzooma,tau,grossism |
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c ...... arguments de sortie ...... |
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REAL rlonm025(iip1),xprimm025(iip1),rlonv(iip1),xprimv(iip1), |
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, rlonu(iip1),xprimu(iip1),rlonp025(iip1),xprimp025(iip1) |
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c .... variables locales .... |
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c |
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REAL dzoom |
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DOUBLE PRECISION xlon(iip1),xprimm(iip1),xuv |
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DOUBLE PRECISION xtild(0:nmax2) |
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DOUBLE PRECISION fhyp(0:nmax2),ffdx,beta,Xprimt(0:nmax2) |
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DOUBLE PRECISION Xf(0:nmax2),xxpr(0:nmax2) |
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DOUBLE PRECISION xvrai(iip1),xxprim(iip1) |
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DOUBLE PRECISION pi,depi,epsilon,xzoom,fa,fb |
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DOUBLE PRECISION Xf1, Xfi , a0,a1,a2,a3,xi2 |
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INTEGER i,it,ik,iter,ii,idif,ii1,ii2 |
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DOUBLE PRECISION xi,xo1,xmoy,xlon2,fxm,Xprimin |
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DOUBLE PRECISION champmin,champmax,decalx |
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INTEGER is2 |
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SAVE is2 |
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DOUBLE PRECISION heavyside |
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pi = 2. * ASIN(1.) |
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depi = 2. * pi |
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epsilon = 1.e-3 |
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xzoom = xzoomdeg * pi/180. |
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c |
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decalx = .75 |
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IF( grossism.EQ.1..AND.scal180 ) THEN |
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decalx = 1. |
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ENDIF |
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WRITE(6,*) 'FXHYP scal180,decalx', scal180,decalx |
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c |
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IF( dzooma.LT.1.) THEN |
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dzoom = dzooma * depi |
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ELSEIF( dzooma.LT. 25. ) THEN |
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WRITE(6,*) ' Le param. dzoomx pour fxhyp est trop petit ! L aug |
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,menter et relancer ! ' |
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STOP 1 |
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ELSE |
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dzoom = dzooma * pi/180. |
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ENDIF |
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WRITE(6,*) ' xzoom( rad.),grossism,tau,dzoom (radians)' |
IMPLICIT NONE |
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WRITE(6,24) xzoom,grossism,tau,dzoom |
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DO i = 0, nmax2 |
contains |
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xtild(i) = - pi + FLOAT(i) * depi /nmax2 |
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ENDDO |
SUBROUTINE fxhyp(xprimm025, rlonv, xprimv, rlonu, xprimu, xprimp025) |
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DO i = nmax, nmax2 |
! From LMDZ4/libf/dyn3d/fxhyp.F, version 1.2, 2005/06/03 09:11:32 |
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! Author: P. Le Van, from formulas by R. Sadourny |
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fa = tau* ( dzoom/2. - xtild(i) ) |
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fb = xtild(i) * ( pi - xtild(i) ) |
! Calcule les longitudes et dérivées dans la grille du GCM pour |
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! une fonction x_f(\tilde x) à dérivée tangente hyperbolique. |
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IF( 200.* fb .LT. - fa ) THEN |
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fhyp ( i) = - 1. |
! Il vaut mieux avoir : grossismx \times delta < pi |
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ELSEIF( 200. * fb .LT. fa ) THEN |
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fhyp ( i) = 1. |
! Le premier point scalaire pour une grille regulière (grossismx = |
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ELSE |
! 1) avec clon = 0 est à - 180 degrés. |
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IF( ABS(fa).LT.1.e-13.AND.ABS(fb).LT.1.e-13) THEN |
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IF( 200.*fb + fa.LT.1.e-10 ) THEN |
USE dimens_m, ONLY: iim |
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fhyp ( i ) = - 1. |
use dynetat0_m, only: clon, grossismx, dzoomx, taux |
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ELSEIF( 200.*fb - fa.LT.1.e-10 ) THEN |
use invert_zoom_x_m, only: invert_zoom_x, nmax |
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fhyp ( i ) = 1. |
use nr_util, only: pi, pi_d, twopi, twopi_d, arth |
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ENDIF |
use principal_cshift_m, only: principal_cshift |
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ELSE |
use tanh_cautious_m, only: tanh_cautious |
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fhyp ( i ) = TANH ( fa/fb ) |
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ENDIF |
REAL, intent(out):: xprimm025(:), rlonv(:), xprimv(:) ! (iim + 1) |
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ENDIF |
real, intent(out):: rlonu(:), xprimu(:), xprimp025(:) ! (iim + 1) |
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IF ( xtild(i).EQ. 0. ) fhyp(i) = 1. |
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IF ( xtild(i).EQ. pi ) fhyp(i) = -1. |
! Local: |
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real rlonm025(iim + 1), rlonp025(iim + 1), d_rlonv(iim) |
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ENDDO |
REAL delta, step |
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DOUBLE PRECISION, dimension(0:nmax):: xtild, fhyp, G, Xf, ffdx |
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cc .... Calcul de beta .... |
DOUBLE PRECISION beta |
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INTEGER i, is2 |
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ffdx = 0. |
DOUBLE PRECISION xmoy(nmax), fxm(nmax) |
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DO i = nmax +1,nmax2 |
!---------------------------------------------------------------------- |
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xmoy = 0.5 * ( xtild(i-1) + xtild( i ) ) |
print *, "Call sequence information: fxhyp" |
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fa = tau* ( dzoom/2. - xmoy ) |
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fb = xmoy * ( pi - xmoy ) |
if (grossismx == 1.) then |
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step = twopi / iim |
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IF( 200.* fb .LT. - fa ) THEN |
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fxm = - 1. |
xprimm025(:iim) = step |
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ELSEIF( 200. * fb .LT. fa ) THEN |
xprimp025(:iim) = step |
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fxm = 1. |
xprimv(:iim) = step |
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ELSE |
xprimu(:iim) = step |
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IF( ABS(fa).LT.1.e-13.AND.ABS(fb).LT.1.e-13) THEN |
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IF( 200.*fb + fa.LT.1.e-10 ) THEN |
rlonv(:iim) = arth(- pi + clon, step, iim) |
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fxm = - 1. |
rlonm025(:iim) = rlonv(:iim) - 0.25 * step |
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ELSEIF( 200.*fb - fa.LT.1.e-10 ) THEN |
rlonp025(:iim) = rlonv(:iim) + 0.25 * step |
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fxm = 1. |
rlonu(:iim) = rlonv(:iim) + 0.5 * step |
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ENDIF |
else |
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ELSE |
delta = dzoomx * twopi_d |
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fxm = TANH ( fa/fb ) |
xtild = arth(0d0, pi_d / nmax, nmax + 1) |
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ENDIF |
forall (i = 1:nmax) xmoy(i) = 0.5d0 * (xtild(i-1) + xtild(i)) |
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ENDIF |
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! Compute fhyp: |
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IF ( xmoy.EQ. 0. ) fxm = 1. |
fhyp(1:nmax - 1) = tanh_cautious(taux * (delta / 2d0 & |
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IF ( xmoy.EQ. pi ) fxm = -1. |
- xtild(1:nmax - 1)), xtild(1:nmax - 1) & |
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* (pi_d - xtild(1:nmax - 1))) |
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ffdx = ffdx + fxm * ( xtild(i) - xtild(i-1) ) |
fhyp(0) = 1d0 |
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fhyp(nmax) = -1d0 |
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ENDDO |
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fxm = tanh_cautious(taux * (delta / 2d0 - xmoy), xmoy * (pi_d - xmoy)) |
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beta = ( grossism * ffdx - pi ) / ( ffdx - pi ) |
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! Compute \int_0 ^{\tilde x} F: |
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IF( 2.*beta - grossism.LE. 0.) THEN |
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WRITE(6,*) ' ** Attention ! La valeur beta calculee dans la rou |
ffdx(0) = 0d0 |
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,tine fxhyp est mauvaise ! ' |
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WRITE(6,*)'Modifier les valeurs de grossismx ,tau ou dzoomx ', |
DO i = 1, nmax |
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, ' et relancer ! *** ' |
ffdx(i) = ffdx(i - 1) + fxm(i) * (xtild(i) - xtild(i-1)) |
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STOP 1 |
END DO |
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ENDIF |
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c |
print *, "ffdx(nmax) = ", ffdx(nmax) |
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c ..... calcul de Xprimt ..... |
beta = (pi_d - grossismx * ffdx(nmax)) / (pi_d - ffdx(nmax)) |
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c |
print *, "beta = ", beta |
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DO i = nmax, nmax2 |
IF (2d0 * beta - grossismx <= 0d0) THEN |
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Xprimt(i) = beta + ( grossism - beta ) * fhyp(i) |
print *, 'Bad choice of grossismx, taux, dzoomx.' |
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ENDDO |
print *, 'Decrease dzoomx or grossismx.' |
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c |
STOP 1 |
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DO i = nmax+1, nmax2 |
END IF |
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Xprimt( nmax2 - i ) = Xprimt( i ) |
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ENDDO |
G = beta + (grossismx - beta) * fhyp |
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c |
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Xf(:nmax - 1) = beta * xtild(:nmax - 1) + (grossismx - beta) & |
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c ..... Calcul de Xf ........ |
* ffdx(:nmax - 1) |
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Xf(nmax) = pi_d |
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Xf(0) = - pi |
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call invert_zoom_x(xf, xtild, G, rlonm025(:iim), xprimm025(:iim), & |
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DO i = nmax +1, nmax2 |
xuv = - 0.25d0) |
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call invert_zoom_x(xf, xtild, G, rlonv(:iim), xprimv(:iim), xuv = 0d0) |
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xmoy = 0.5 * ( xtild(i-1) + xtild( i ) ) |
call invert_zoom_x(xf, xtild, G, rlonu(:iim), xprimu(:iim), xuv = 0.5d0) |
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fa = tau* ( dzoom/2. - xmoy ) |
call invert_zoom_x(xf, xtild, G, rlonp025(:iim), xprimp025(:iim), & |
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fb = xmoy * ( pi - xmoy ) |
xuv = 0.25d0) |
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end if |
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IF( 200.* fb .LT. - fa ) THEN |
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fxm = - 1. |
is2 = 0 |
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ELSEIF( 200. * fb .LT. fa ) THEN |
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fxm = 1. |
IF (MINval(rlonm025(:iim)) < - pi - 0.1 & |
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.or. MAXval(rlonm025(:iim)) > pi + 0.1) THEN |
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IF (clon <= 0.) THEN |
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is2 = 1 |
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do while (rlonm025(is2) < - pi .and. is2 < iim) |
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is2 = is2 + 1 |
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end do |
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if (rlonm025(is2) < - pi) then |
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print *, 'Rlonm025 plus petit que - pi !' |
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STOP 1 |
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end if |
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ELSE |
ELSE |
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fxm = TANH ( fa/fb ) |
is2 = iim |
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ENDIF |
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do while (rlonm025(is2) > pi .and. is2 > 1) |
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is2 = is2 - 1 |
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end do |
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if (rlonm025(is2) > pi) then |
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print *, 'Rlonm025 plus grand que pi !' |
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STOP 1 |
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end if |
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END IF |
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END IF |
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call principal_cshift(is2, rlonm025, xprimm025) |
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call principal_cshift(is2, rlonv, xprimv) |
| 131 |
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call principal_cshift(is2, rlonu, xprimu) |
| 132 |
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call principal_cshift(is2, rlonp025, xprimp025) |
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forall (i = 1: iim) d_rlonv(i) = rlonv(i + 1) - rlonv(i) |
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print *, "Minimum longitude step:", MINval(d_rlonv) * 180. / pi, "degrees" |
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print *, "Maximum longitude step:", MAXval(d_rlonv) * 180. / pi, "degrees" |
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! Check that rlonm025 <= rlonv <= rlonp025 <= rlonu: |
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DO i = 1, iim + 1 |
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IF (rlonp025(i) < rlonv(i)) THEN |
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print *, 'rlonp025(', i, ') = ', rlonp025(i) |
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print *, "< rlonv(", i, ") = ", rlonv(i) |
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STOP 1 |
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END IF |
| 145 |
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IF (rlonv(i) < rlonm025(i)) THEN |
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print *, 'rlonv(', i, ') = ', rlonv(i) |
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print *, "< rlonm025(", i, ") = ", rlonm025(i) |
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STOP 1 |
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END IF |
| 151 |
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IF (rlonp025(i) > rlonu(i)) THEN |
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print *, 'rlonp025(', i, ') = ', rlonp025(i) |
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print *, "> rlonu(", i, ") = ", rlonu(i) |
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STOP 1 |
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END IF |
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END DO |
| 158 |
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IF ( xmoy.EQ. 0. ) fxm = 1. |
END SUBROUTINE fxhyp |
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IF ( xmoy.EQ. pi ) fxm = -1. |
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xxpr(i) = beta + ( grossism - beta ) * fxm |
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ENDDO |
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DO i = nmax+1, nmax2 |
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xxpr(nmax2-i+1) = xxpr(i) |
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ENDDO |
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DO i=1,nmax2 |
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Xf(i) = Xf(i-1) + xxpr(i) * ( xtild(i) - xtild(i-1) ) |
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ENDDO |
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c ***************************************************************** |
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c |
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c ..... xuv = 0. si calcul aux pts scalaires ........ |
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c ..... xuv = 0.5 si calcul aux pts U ........ |
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c |
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WRITE(6,18) |
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c |
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DO 5000 ik = 1, 4 |
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IF( ik.EQ.1 ) THEN |
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xuv = -0.25 |
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ELSE IF ( ik.EQ.2 ) THEN |
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xuv = 0. |
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ELSE IF ( ik.EQ.3 ) THEN |
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xuv = 0.50 |
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ELSE IF ( ik.EQ.4 ) THEN |
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xuv = 0.25 |
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ENDIF |
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xo1 = 0. |
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ii1=1 |
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ii2=iim |
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IF(ik.EQ.1.and.grossism.EQ.1.) THEN |
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ii1 = 2 |
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ii2 = iim+1 |
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ENDIF |
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DO 1500 i = ii1, ii2 |
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xlon2 = - pi + (FLOAT(i) + xuv - decalx) * depi / FLOAT(iim) |
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Xfi = xlon2 |
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c |
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DO 250 it = nmax2,0,-1 |
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IF( Xfi.GE.Xf(it)) GO TO 350 |
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250 CONTINUE |
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it = 0 |
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350 CONTINUE |
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c ...... Calcul de Xf(xi) ...... |
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c |
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xi = xtild(it) |
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IF(it.EQ.nmax2) THEN |
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it = nmax2 -1 |
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Xf(it+1) = pi |
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ENDIF |
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c ..................................................................... |
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c |
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c Appel de la routine qui calcule les coefficients a0,a1,a2,a3 d'un |
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c polynome de degre 3 qui passe par les points (Xf(it),xtild(it) ) |
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c et (Xf(it+1),xtild(it+1) ) |
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CALL coefpoly ( Xf(it),Xf(it+1),Xprimt(it),Xprimt(it+1), |
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, xtild(it),xtild(it+1), a0, a1, a2, a3 ) |
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Xf1 = Xf(it) |
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Xprimin = a1 + 2.* a2 * xi + 3.*a3 * xi *xi |
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DO 500 iter = 1,300 |
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xi = xi - ( Xf1 - Xfi )/ Xprimin |
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IF( ABS(xi-xo1).LE.epsilon) GO TO 550 |
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xo1 = xi |
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xi2 = xi * xi |
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Xf1 = a0 + a1 * xi + a2 * xi2 + a3 * xi2 * xi |
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Xprimin = a1 + 2.* a2 * xi + 3.* a3 * xi2 |
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500 CONTINUE |
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WRITE(6,*) ' Pas de solution ***** ',i,xlon2,iter |
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STOP 6 |
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550 CONTINUE |
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xxprim(i) = depi/ ( FLOAT(iim) * Xprimin ) |
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xvrai(i) = xi + xzoom |
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1500 CONTINUE |
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IF(ik.EQ.1.and.grossism.EQ.1.) THEN |
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xvrai(1) = xvrai(iip1)-depi |
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xxprim(1) = xxprim(iip1) |
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ENDIF |
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DO i = 1 , iim |
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xlon(i) = xvrai(i) |
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xprimm(i) = xxprim(i) |
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ENDDO |
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DO i = 1, iim -1 |
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IF( xvrai(i+1). LT. xvrai(i) ) THEN |
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WRITE(6,*) ' PBS. avec rlonu(',i+1,') plus petit que rlonu(',i, |
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, ')' |
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STOP 7 |
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ENDIF |
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ENDDO |
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c |
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c ... Reorganisation des longitudes pour les avoir entre - pi et pi .. |
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c ........................................................................ |
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champmin = 1.e12 |
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champmax = -1.e12 |
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DO i = 1, iim |
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champmin = MIN( champmin,xvrai(i) ) |
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champmax = MAX( champmax,xvrai(i) ) |
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ENDDO |
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IF(champmin .GE.-pi-0.10.and.champmax.LE.pi+0.10 ) THEN |
|
|
GO TO 1600 |
|
|
ELSE |
|
|
WRITE(6,*) 'Reorganisation des longitudes pour avoir entre - pi', |
|
|
, ' et pi ' |
|
|
c |
|
|
IF( xzoom.LE.0.) THEN |
|
|
IF( ik.EQ. 1 ) THEN |
|
|
DO i = 1, iim |
|
|
IF( xvrai(i).GE. - pi ) GO TO 80 |
|
|
ENDDO |
|
|
WRITE(6,*) ' PBS. 1 ! Xvrai plus petit que - pi ! ' |
|
|
STOP 8 |
|
|
80 CONTINUE |
|
|
is2 = i |
|
|
ENDIF |
|
|
|
|
|
IF( is2.NE. 1 ) THEN |
|
|
DO ii = is2 , iim |
|
|
xlon (ii-is2+1) = xvrai(ii) |
|
|
xprimm(ii-is2+1) = xxprim(ii) |
|
|
ENDDO |
|
|
DO ii = 1 , is2 -1 |
|
|
xlon (ii+iim-is2+1) = xvrai(ii) + depi |
|
|
xprimm(ii+iim-is2+1) = xxprim(ii) |
|
|
ENDDO |
|
|
ENDIF |
|
|
ELSE |
|
|
IF( ik.EQ.1 ) THEN |
|
|
DO i = iim,1,-1 |
|
|
IF( xvrai(i).LE. pi ) GO TO 90 |
|
|
ENDDO |
|
|
WRITE(6,*) ' PBS. 2 ! Xvrai plus grand que pi ! ' |
|
|
STOP 9 |
|
|
90 CONTINUE |
|
|
is2 = i |
|
|
ENDIF |
|
|
idif = iim -is2 |
|
|
DO ii = 1, is2 |
|
|
xlon (ii+idif) = xvrai(ii) |
|
|
xprimm(ii+idif) = xxprim(ii) |
|
|
ENDDO |
|
|
DO ii = 1, idif |
|
|
xlon (ii) = xvrai (ii+is2) - depi |
|
|
xprimm(ii) = xxprim(ii+is2) |
|
|
ENDDO |
|
|
ENDIF |
|
|
ENDIF |
|
|
c |
|
|
c ......... Fin de la reorganisation ............................ |
|
|
|
|
|
1600 CONTINUE |
|
|
|
|
|
|
|
|
xlon ( iip1) = xlon(1) + depi |
|
|
xprimm( iip1 ) = xprimm (1 ) |
|
|
|
|
|
DO i = 1, iim+1 |
|
|
xvrai(i) = xlon(i)*180./pi |
|
|
ENDDO |
|
|
|
|
|
IF( ik.EQ.1 ) THEN |
|
|
c WRITE(6,*) ' XLON aux pts. V-0.25 apres ( en deg. ) ' |
|
|
c WRITE(6,18) |
|
|
c WRITE(6,68) xvrai |
|
|
c WRITE(6,*) ' XPRIM k ',ik |
|
|
c WRITE(6,566) xprimm |
|
|
|
|
|
DO i = 1,iim +1 |
|
|
rlonm025(i) = xlon( i ) |
|
|
xprimm025(i) = xprimm(i) |
|
|
ENDDO |
|
|
ELSE IF( ik.EQ.2 ) THEN |
|
|
c WRITE(6,18) |
|
|
c WRITE(6,*) ' XLON aux pts. V apres ( en deg. ) ' |
|
|
c WRITE(6,68) xvrai |
|
|
c WRITE(6,*) ' XPRIM k ',ik |
|
|
c WRITE(6,566) xprimm |
|
|
|
|
|
DO i = 1,iim + 1 |
|
|
rlonv(i) = xlon( i ) |
|
|
xprimv(i) = xprimm(i) |
|
|
ENDDO |
|
|
|
|
|
ELSE IF( ik.EQ.3) THEN |
|
|
c WRITE(6,18) |
|
|
c WRITE(6,*) ' XLON aux pts. U apres ( en deg. ) ' |
|
|
c WRITE(6,68) xvrai |
|
|
c WRITE(6,*) ' XPRIM ik ',ik |
|
|
c WRITE(6,566) xprimm |
|
|
|
|
|
DO i = 1,iim + 1 |
|
|
rlonu(i) = xlon( i ) |
|
|
xprimu(i) = xprimm(i) |
|
|
ENDDO |
|
|
|
|
|
ELSE IF( ik.EQ.4 ) THEN |
|
|
c WRITE(6,18) |
|
|
c WRITE(6,*) ' XLON aux pts. V+0.25 apres ( en deg. ) ' |
|
|
c WRITE(6,68) xvrai |
|
|
c WRITE(6,*) ' XPRIM ik ',ik |
|
|
c WRITE(6,566) xprimm |
|
|
|
|
|
DO i = 1,iim + 1 |
|
|
rlonp025(i) = xlon( i ) |
|
|
xprimp025(i) = xprimm(i) |
|
|
ENDDO |
|
|
|
|
|
ENDIF |
|
|
|
|
|
5000 CONTINUE |
|
|
c |
|
|
WRITE(6,18) |
|
|
c |
|
|
c ........... fin de la boucle do 5000 ............ |
|
|
|
|
|
DO i = 1, iim |
|
|
xlon(i) = rlonv(i+1) - rlonv(i) |
|
|
ENDDO |
|
|
champmin = 1.e12 |
|
|
champmax = -1.e12 |
|
|
DO i = 1, iim |
|
|
champmin = MIN( champmin, xlon(i) ) |
|
|
champmax = MAX( champmax, xlon(i) ) |
|
|
ENDDO |
|
|
champmin = champmin * 180./pi |
|
|
champmax = champmax * 180./pi |
|
|
|
|
|
18 FORMAT(/) |
|
|
24 FORMAT(2x,'Parametres xzoom,gross,tau ,dzoom pour fxhyp ',4f8.3) |
|
|
68 FORMAT(1x,7f9.2) |
|
|
566 FORMAT(1x,7f9.4) |
|
| 160 |
|
|
| 161 |
RETURN |
end module fxhyp_m |
|
END |
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