c c $Header$ c SUBROUTINE fyhyp ( yzoomdeg, grossism, dzoom,tau , , rrlatu,yyprimu,rrlatv,yyprimv,rlatu2,yprimu2,rlatu1,yprimu1 ) cc ... Version du 01/04/2001 .... IMPLICIT NONE c c ... Auteur : P. Le Van ... c c ....... d'apres formulations de R. Sadourny ....... c c Calcule les latitudes et derivees dans la grille du GCM pour une c fonction f(y) a tangente hyperbolique . c c grossism etant le grossissement ( = 2 si 2 fois, = 3 si 3 fois , etc) c dzoom etant la distance totale de la zone du zoom ( en radians ) c tau la raideur de la transition de l'interieur a l'exterieur du zoom c c c N.B : Il vaut mieux avoir : grossism * dzoom < pi/2 (radians) ,en lati. c ******************************************************************** c c #include "dimensions.h" #include "paramet.h" INTEGER nmax , nmax2 PARAMETER ( nmax = 30000, nmax2 = 2*nmax ) c c c ....... arguments d'entree ....... c REAL yzoomdeg, grossism,dzoom,tau c ( rentres par run.def ) c ....... arguments de sortie ....... c REAL rrlatu(jjp1), yyprimu(jjp1),rrlatv(jjm), yyprimv(jjm), , rlatu1(jjm), yprimu1(jjm), rlatu2(jjm), yprimu2(jjm) c c ..... champs locaux ..... c REAL*8 ylat(jjp1), yprim(jjp1) REAL*8 yuv REAL*8 yt(0:nmax2) REAL*8 fhyp(0:nmax2),beta,Ytprim(0:nmax2),fxm(0:nmax2) SAVE Ytprim, yt,Yf REAL*8 Yf(0:nmax2),yypr(0:nmax2) REAL*8 yvrai(jjp1), yprimm(jjp1),ylatt(jjp1) REAL*8 pi,depi,pis2,epsilon,y0,pisjm REAL*8 yo1,yi,ylon2,ymoy,Yprimin,champmin,champmax REAL*8 yfi,Yf1,ffdy REAL*8 ypn,deply,y00 SAVE y00, deply INTEGER i,j,it,ik,iter,jlat INTEGER jpn,jjpn SAVE jpn REAL*8 a0,a1,a2,a3,yi2,heavyy0,heavyy0m REAL*8 fa(0:nmax2),fb(0:nmax2) REAL y0min,y0max REAL*8 heavyside EXTERNAL heavyside pi = 2. * ASIN(1.) depi = 2. * pi pis2 = pi/2. pisjm = pi/ FLOAT(jjm) epsilon = 1.e-3 y0 = yzoomdeg * pi/180. IF( dzoom.LT.1.) THEN dzoom = dzoom * pi ELSEIF( dzoom.LT. 12. ) THEN WRITE(6,*) ' Le param. dzoomy pour fyhyp est trop petit ! L aug ,menter et relancer ! ' STOP 1 ELSE dzoom = dzoom * pi/180. ENDIF WRITE(6,*) ' yzoom ,dzoomy (radians),tau',y0,dzoom,tau DO i = 0, nmax2 yt(i) = - pis2 + FLOAT(i)* pi /nmax2 ENDDO heavyy0m = heavyside( -y0 ) heavyy0 = heavyside( y0 ) y0min = 2.*y0*heavyy0m - pis2 y0max = 2.*y0*heavyy0 + pis2 DO i = 0, nmax2 IF( yt(i).LT.y0 ) THEN fa (i) = tau* (yt(i)-y0+dzoom/2. ) fb(i) = (yt(i)-2.*y0*heavyy0m +pis2) * ( y0 - yt(i) ) ELSEIF ( yt(i).GT.y0 ) THEN fa(i) = tau *(y0-yt(i)+dzoom/2. ) fb(i) = (2.*y0*heavyy0 -yt(i)+pis2) * ( yt(i) - y0 ) ENDIF IF( 200.* fb(i) .LT. - fa(i) ) THEN fhyp ( i) = - 1. ELSEIF( 200. * fb(i) .LT. fa(i) ) THEN fhyp ( i) = 1. ELSE fhyp(i) = TANH ( fa(i)/fb(i) ) ENDIF IF( yt(i).EQ.y0 ) fhyp(i) = 1. IF(yt(i).EQ. y0min. OR.yt(i).EQ. y0max ) fhyp(i) = -1. ENDDO cc .... Calcul de beta .... c ffdy = 0. DO i = 1, nmax2 ymoy = 0.5 * ( yt(i-1) + yt( i ) ) IF( ymoy.LT.y0 ) THEN fa(i)= tau * ( ymoy-y0+dzoom/2.) fb(i) = (ymoy-2.*y0*heavyy0m +pis2) * ( y0 - ymoy ) ELSEIF ( ymoy.GT.y0 ) THEN fa(i)= tau * ( y0-ymoy+dzoom/2. ) fb(i) = (2.*y0*heavyy0 -ymoy+pis2) * ( ymoy - y0 ) ENDIF IF( 200.* fb(i) .LT. - fa(i) ) THEN fxm ( i) = - 1. ELSEIF( 200. * fb(i) .LT. fa(i) ) THEN fxm ( i) = 1. ELSE fxm(i) = TANH ( fa(i)/fb(i) ) ENDIF IF( ymoy.EQ.y0 ) fxm(i) = 1. IF (ymoy.EQ. y0min. OR.yt(i).EQ. y0max ) fxm(i) = -1. ffdy = ffdy + fxm(i) * ( yt(i) - yt(i-1) ) ENDDO beta = ( grossism * ffdy - pi ) / ( ffdy - pi ) IF( 2.*beta - grossism.LE. 0.) THEN WRITE(6,*) ' ** Attention ! La valeur beta calculee dans la rou ,tine fyhyp est mauvaise ! ' WRITE(6,*)'Modifier les valeurs de grossismy ,tauy ou dzoomy', , ' et relancer ! *** ' CALL ABORT ENDIF c c ..... calcul de Ytprim ..... c DO i = 0, nmax2 Ytprim(i) = beta + ( grossism - beta ) * fhyp(i) ENDDO c ..... Calcul de Yf ........ Yf(0) = - pis2 DO i = 1, nmax2 yypr(i) = beta + ( grossism - beta ) * fxm(i) ENDDO DO i=1,nmax2 Yf(i) = Yf(i-1) + yypr(i) * ( yt(i) - yt(i-1) ) ENDDO c **************************************************************** c c ..... yuv = 0. si calcul des latitudes aux pts. U ..... c ..... yuv = 0.5 si calcul des latitudes aux pts. V ..... c c DO 5000 ik = 1,4 IF( ik.EQ.1 ) THEN yuv = 0. jlat = jjm + 1 ELSE IF ( ik.EQ.2 ) THEN yuv = 0.5 jlat = jjm ELSE IF ( ik.EQ.3 ) THEN yuv = 0.25 jlat = jjm ELSE IF ( ik.EQ.4 ) THEN yuv = 0.75 jlat = jjm ENDIF c yo1 = 0. DO 1500 j = 1,jlat yo1 = 0. ylon2 = - pis2 + pisjm * ( FLOAT(j) + yuv -1.) yfi = ylon2 c DO 250 it = nmax2,0,-1 IF( yfi.GE.Yf(it)) GO TO 350 250 CONTINUE it = 0 350 CONTINUE yi = yt(it) IF(it.EQ.nmax2) THEN it = nmax2 -1 Yf(it+1) = pis2 ENDIF c ................................................................. c .... Interpolation entre yi(it) et yi(it+1) pour avoir Y(yi) c ..... et Y'(yi) ..... c ................................................................. CALL coefpoly ( Yf(it),Yf(it+1),Ytprim(it), Ytprim(it+1), , yt(it),yt(it+1) , a0,a1,a2,a3 ) Yf1 = Yf(it) Yprimin = a1 + 2.* a2 * yi + 3.*a3 * yi *yi DO 500 iter = 1,300 yi = yi - ( Yf1 - yfi )/ Yprimin IF( ABS(yi-yo1).LE.epsilon) GO TO 550 yo1 = yi yi2 = yi * yi Yf1 = a0 + a1 * yi + a2 * yi2 + a3 * yi2 * yi Yprimin = a1 + 2.* a2 * yi + 3.* a3 * yi2 500 CONTINUE WRITE(6,*) ' Pas de solution ***** ',j,ylon2,iter STOP 2 550 CONTINUE c Yprimin = a1 + 2.* a2 * yi + 3.* a3 * yi* yi yprim(j) = pi / ( jjm * Yprimin ) yvrai(j) = yi 1500 CONTINUE DO j = 1, jlat -1 IF( yvrai(j+1). LT. yvrai(j) ) THEN WRITE(6,*) ' PBS. avec rlat(',j+1,') plus petit que rlat(',j, , ')' STOP 3 ENDIF ENDDO WRITE(6,18) WRITE(6,*) 'Reorganisation des latitudes pour avoir entre - pi/2' , ,' et pi/2 ' c IF( ik.EQ.1 ) THEN ypn = pis2 DO j = jlat,1,-1 IF( yvrai(j).LE. ypn ) GO TO 1502 ENDDO 1502 CONTINUE jpn = j y00 = yvrai(jpn) deply = pis2 - y00 ENDIF DO j = 1, jjm +1 - jpn ylatt (j) = -pis2 - y00 + yvrai(jpn+j-1) yprimm(j) = yprim(jpn+j-1) ENDDO jjpn = jpn IF( jlat.EQ. jjm ) jjpn = jpn -1 DO j = 1,jjpn ylatt (j + jjm+1 -jpn) = yvrai(j) + deply yprimm(j + jjm+1 -jpn) = yprim(j) ENDDO c *********** Fin de la reorganisation ************* c 1600 CONTINUE DO j = 1, jlat ylat(j) = ylatt( jlat +1 -j ) yprim(j) = yprimm( jlat +1 -j ) ENDDO DO j = 1, jlat yvrai(j) = ylat(j)*180./pi ENDDO IF( ik.EQ.1 ) THEN WRITE(6,18) WRITE(6,*) ' YLAT en U apres ( en deg. ) ' WRITE(6,68) (yvrai(j),j=1,jlat) cc WRITE(6,*) ' YPRIM ' cc WRITE(6,445) ( yprim(j),j=1,jlat) DO j = 1, jlat rrlatu(j) = ylat( j ) yyprimu(j) = yprim( j ) ENDDO ELSE IF ( ik.EQ. 2 ) THEN WRITE(6,18) WRITE(6,*) ' YLAT en V apres ( en deg. ) ' WRITE(6,68) (yvrai(j),j=1,jlat) cc WRITE(6,*)' YPRIM ' cc WRITE(6,445) ( yprim(j),j=1,jlat) DO j = 1, jlat rrlatv(j) = ylat( j ) yyprimv(j) = yprim( j ) ENDDO ELSE IF ( ik.EQ. 3 ) THEN WRITE(6,18) WRITE(6,*) ' YLAT en U + 0.75 apres ( en deg. ) ' WRITE(6,68) (yvrai(j),j=1,jlat) cc WRITE(6,*) ' YPRIM ' cc WRITE(6,445) ( yprim(j),j=1,jlat) DO j = 1, jlat rlatu2(j) = ylat( j ) yprimu2(j) = yprim( j ) ENDDO ELSE IF ( ik.EQ. 4 ) THEN WRITE(6,18) WRITE(6,*) ' YLAT en U + 0.25 apres ( en deg. ) ' WRITE(6,68)(yvrai(j),j=1,jlat) cc WRITE(6,*) ' YPRIM ' cc WRITE(6,68) ( yprim(j),j=1,jlat) DO j = 1, jlat rlatu1(j) = ylat( j ) yprimu1(j) = yprim( j ) ENDDO ENDIF 5000 CONTINUE c c ..... fin de la boucle do 5000 ..... DO j = 1, jjm ylat(j) = rrlatu(j) - rrlatu(j+1) ENDDO champmin = 1.e12 champmax = -1.e12 DO j = 1, jjm champmin = MIN( champmin, ylat(j) ) champmax = MAX( champmax, ylat(j) ) ENDDO champmin = champmin * 180./pi champmax = champmax * 180./pi WRITE(6,18) WRITE(6,*) ' Latitudes ' WRITE(6,18) WRITE(6,3) champmin, champmax WRITE(6,*) ' Si cette derniere est trop lache , modifiez les par ,ametres grossism , tau , dzoom pour Y et repasser ! ' WRITE(6,18) c 3 Format(1x, ' Au centre du zoom , la longueur de la maille est', , ' d environ ',f8.2 ,' degres ', , ' alors que la maille en dehors de la zone du zoom est d environ , ', f8.2,' degres ' ) 18 FORMAT(/) 68 FORMAT(1x,7f9.2) RETURN END