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SUBROUTINE inigeom c c Auteur : P. Le Van c ..................... c c ............ Version du 16/05/97 ........................ c c Calcul des elongations cuij1,.cuij4 , cvij1,..cvij4 aux memes en- c endroits que les aires aireij1,..aireij4 . c Choix entre f(y) a derivee sinusoid. ou a derivee tangente hyperbol. c c IMPLICIT NONE c #include "dimensions.h" #include "paramet.h" #include "comconst.h" #include "comgeom2.h" #include "serre.h" #include "logic.h" c----------------------------------------------------------------------- c .... Variables locales .... c INTEGER i,j,itmax,itmay,iter REAL yv(jjm),yu(jjp1),yprimv(jjm),yprimu(jjp1), * xprimv(iip1),xprimu(iip1),cvu(iip1,jjp1) REAL cuv(iip1,jjm) REAL ai14,ai23,airez,rlatp,rlatm,xprm,xprp,un4rad2,yprp,yprm REAL eps,x1,xo1,f,df,xdm,y1,yo1,ydm REAL coslatm,coslatp,radclatm,radclatp REAL cuij1(iip1,jjp1),cuij2(iip1,jjp1),cuij3(iip1,jjp1), * cuij4(iip1,jjp1) REAL cvij1(iip1,jjp1),cvij2(iip1,jjp1),cvij3(iip1,jjp1), * cvij4(iip1,jjp1) REAL rlonvv(iip1),rlatuu(jjp1) REAL rlatu1(jjm),yprimu1(jjm),rlatu2(jjm),yprimu2(jjm) REAL yyprimu(jjp1),yyprimv(jjm),rrlatu(jjp1),rrlatv(jjm) c---------------------------------------------------------------------- REAL SSUM EXTERNAL SSUM c c #include "fxyprim.h" c c c ------------------------------------------------------------------ c - - c - calcul des coeff. ( cu, cv , 1./cu**2, 1./cv**2 ) - c - - c ------------------------------------------------------------------ c ------------------------------------------------------------------ c c les coef. ( cu, cv ) permettent de passer des vitesses naturelles c aux vitesses covariantes et contravariantes , ou vice-versa ... c c c on a : u (covariant) = cu * u (naturel) , u(contrav)= u(nat)/cu c v (covariant) = cv * v (naturel) , v(contrav)= v(nat)/cv c c on en tire : u(covariant) = cu * cu * u(contravariant) c v(covariant) = cv * cv * v(contravariant) c c c on a l'application ( x(X) , y(Y) ) avec - im/2 +1 < X < im/2 c = = c et - jm/2 < Y < jm/2 c = = c c ................................................... c ................................................... c . x est la longitude du point en radians . c . y est la latitude du point en radians . c . . c . on a : cu(i,j) = rad * COS(y) * dx/dX . c . cv( j ) = rad * dy/dY . c . aire(i,j) = cu(i,j) * cv(j) . c . . c . y, dx/dX, dy/dY calcules aux points concernes . c . . c ................................................... c ................................................... c c c c , c cv , bien que dependant de j uniquement,sera ici indice aussi en i c pour un adressage plus facile en ij . c c c c ************** aux points u et v , ***************** c xprimu et xprimv sont respectivement les valeurs de dx/dX c yprimu et yprimv . . . . . . . . . . . dy/dY c rlatu et rlatv . . . . . . . . . . .la latitude c cvu et cv . . . . . . . . . . . cv c c ************** aux points u, v, scalaires, et z **************** c cu, cuv, cuscal, cuz sont respectiv. les valeurs de cu c c c c Exemple de distribution de variables sur la grille dans le c domaine de travail ( X,Y ) . c ................................................................ c DX=DY= 1 c c c + represente un point scalaire ( p.exp la pression ) c > represente la composante zonale du vent c V represente la composante meridienne du vent c o represente la vorticite c c ---- , car aux poles , les comp.zonales covariantes sont nulles c c c c i -> c c 1 2 3 4 5 6 7 8 c j c v 1 + ---- + ---- + ---- + ---- + ---- + ---- + ---- + -- c c V o V o V o V o V o V o V o V o c c 2 + > + > + > + > + > + > + > + > c c V o V o V o V o V o V o V o V o c c 3 + > + > + > + > + > + > + > + > c c V o V o V o V o V o V o V o V o c c 4 + > + > + > + > + > + > + > + > c c V o V o V o V o V o V o V o V o c c 5 + ---- + ---- + ---- + ---- + ---- + ---- + ---- + -- c c c Ci-dessus, on voit que le nombre de pts.en longitude est egal c a IM = 8 c De meme , le nombre d'intervalles entre les 2 poles est egal c a JM = 4 c c Les points scalaires ( + ) correspondent donc a des valeurs c entieres de i ( 1 a IM ) et de j ( 1 a JM +1 ) . c c Les vents U ( > ) correspondent a des valeurs semi- c entieres de i ( 1+ 0.5 a IM+ 0.5) et entieres de j ( 1 a JM+1) c c Les vents V ( V ) correspondent a des valeurs entieres c de i ( 1 a IM ) et semi-entieres de j ( 1 +0.5 a JM +0.5) c c c PRINT 3 3 FORMAT( // 10x,' .... INIGEOM date du 09/04/97 ..... ', * //5x,' Calcul des elongations cu et cv comme sommes des 4 ' / * 5x,' elong. cuij1, .. 4 , cvij1,.. 4 qui les entourent , aux * '/ 5x,' memes endroits que les aires aireij1,...j4 . ' / ) c c pi = 2.* ASIN(1.) pxo = clon *pi /180. pyo = 2.* clat* pi /180. c c .... determination de transx ( pour le zoom ) par Newton-Raphson ... c itmax = 10 eps = .1e-7 c xo1 = 0. DO 10 iter = 1, itmax x1 = xo1 f = x1+ alphax *SIN(x1-pxo) df = 1.+ alphax *COS(x1-pxo) x1 = x1 - f/df xdm = ABS( x1- xo1 ) IF( xdm.LE.eps )GO TO 11 xo1 = x1 10 CONTINUE 11 CONTINUE c transx = xo1 c ----------------------------------------------------------------- IF( .NOT.fxyhypb ) THEN c c ...... Utilisation de f(y) a derivee sinusoidale ...... c ............................................................ c itmay = 10 eps = .1e-7 C yo1 = 0. DO 15 iter = 1,itmay y1 = yo1 f = y1 + alphay* SIN(y1-pyo) df = 1. + alphay* COS(y1-pyo) y1 = y1 -f/df ydm = ABS(y1-yo1) IF(ydm.LE.eps) GO TO 17 yo1 = y1 15 CONTINUE c 17 CONTINUE transy = yo1 c PRINT *,'transx and transy ',transx,transy c ELSE c c ..... utilisation de fxyhyp , f(y) a derivee tangente hyperbol. c .................................................................. CALL fxyhyp ( clat, rrlatu,yyprimu,rrlatv,yyprimv,rlatu1,yprimu1, * rlatu2,yprimu2 ) ENDIF c c ------------------------------------------------------------------- DO 20 i = 1,iim xprimu (i) = fxprim( FLOAT(i) + 0.5 ) xprimv (i) = fxprim( FLOAT(i) ) 20 CONTINUE xprimu(iip1) = xprimu(1) xprimv(iip1) = xprimv(1) c IF( .NOT.fxyhypb ) THEN c DO 21 j = 2, jjm yu( j ) = fy( FLOAT(j) ) yprimu(j) = fyprim( FLOAT( j ) ) rlatu(j) = yu(j) 21 CONTINUE DO 23 j = 1, jjm yv( j ) = fy( FLOAT(j) + 0.5 ) yprimv(j) = fyprim( FLOAT( j ) + 0.5 ) rlatv(j) = yv(j) 23 CONTINUE c ELSE c DO 24 j = 2, jjm yu( j ) = rrlatu(j) yprimu(j) = yyprimu(j) rlatu(j) = yu(j) 24 CONTINUE DO 25 j = 1, jjm yv( j ) = rrlatv(j) yprimv(j) = yyprimv(j) rlatv(j) = yv(j) 25 CONTINUE c ENDIF c ................................................... c yu(1) = ASIN(1.) yu(jjp1) = - yu(1) rlatu(1) = yu(1) rlatu(jjp1) = yu(jjp1) c c c .... calcul aux poles .... c yprimu(1) = 0. yprimu(jjp1) = 0. c c un4rad2 = 0.25 * rad * rad c c -------------------------------------------------------------------- c -------------------------------------------------------------------- c - - c - calcul des aires ( aire,aireu,airev, 1./aire, 1./airez ) - c - et de fext , force de coriolis extensive . - c - - c -------------------------------------------------------------------- c -------------------------------------------------------------------- c c c c A 1 point scalaire P (i,j) de la grille, reguliere en (X,Y) , sont c affectees 4 aires entourant P , calculees respectivement aux points c ( i + 1/4, j - 1/4 ) : aireij1 (i,j) c ( i + 1/4, j + 1/4 ) : aireij2 (i,j) c ( i - 1/4, j + 1/4 ) : aireij3 (i,j) c ( i - 1/4, j - 1/4 ) : aireij4 (i,j) c c , c Les cotes de chacun de ces 4 carres etant egaux a 1/2 suivant (X,Y). c Chaque aire centree en 1 point scalaire P(i,j) est egale a la somme c des 4 aires aireij1,aireij2,aireij3,aireij4 qui sont affectees au c point (i,j) . c On definit en outre les coefficients alpha comme etant egaux a c (aireij / aire), c.a.d par exp. alpha1(i,j)=aireij1(i,j)/aire(i,j) c c De meme, toute aire centree en 1 point U est egale a la somme des c 4 aires aireij1,aireij2,aireij3,aireij4 entourant le point U . c Idem pour airev, airez . c c On a ,pour chaque maille : dX = dY = 1 c c c . V c c aireij4 . . aireij1 c c U . . P . U c c aireij3 . . aireij2 c c . V c c c c c c .................................................................... c c Calcul des 4 aires elementaires aireij1,aireij2,aireij3,aireij4 c qui entourent chaque aire(i,j) , ainsi que les 4 elongations elemen c taires cuij et les 4 elongat. cvij qui sont calculees aux memes c endroits que les aireij . c c .................................................................... c c ....... do 35 : boucle sur les jjm + 1 latitudes ..... c c DO 35 j = 1, jjp1 c IF ( j. eq. 1 ) THEN c IF( fxyhypb ) THEN yprm = yprimu1(j) rlatm = rlatu1(j) ELSE yprm = fyprim( FLOAT(j) + 0.25 ) rlatm = fy ( FLOAT(j) + 0.25 ) ENDIF c coslatm = COS( rlatm ) radclatm = 0.5* rad * coslatm c DO 30 i = 1, iim xprp = fxprim( FLOAT(i) + 0.25 ) xprm = fxprim( FLOAT(i) - 0.25 ) aireij2( i,1 ) = un4rad2 * coslatm * xprp * yprm aireij3( i,1 ) = un4rad2 * coslatm * xprm * yprm cuij2 ( i,1 ) = radclatm * xprp cuij3 ( i,1 ) = radclatm * xprm cvij2 ( i,1 ) = 0.5* rad * yprm cvij3 ( i,1 ) = cvij2(i,1) 30 CONTINUE c DO i = 1, iim aireij1( i,1 ) = 0. aireij4( i,1 ) = 0. cuij1 ( i,1 ) = 0. cuij4 ( i,1 ) = 0. cvij1 ( i,1 ) = 0. cvij4 ( i,1 ) = 0. ENDDO c END IF c IF ( j. eq. jjp1 ) THEN IF( fxyhypb ) THEN yprp = yprimu2(j-1) rlatp = rlatu2 (j-1) ELSE yprp = fyprim( FLOAT(j) - 0.25 ) rlatp = fy ( FLOAT(j) - 0.25 ) ENDIF c coslatp = COS( rlatp ) radclatp = 0.5* rad * coslatp c DO 31 i = 1,iim xprp = fxprim( FLOAT(i) + 0.25 ) xprm = fxprim( FLOAT(i) - 0.25 ) aireij1( i,jjp1 ) = un4rad2 * coslatp * xprp * yprp aireij4( i,jjp1 ) = un4rad2 * coslatp * xprm * yprp cuij1(i,jjp1) = radclatp * xprp cuij4(i,jjp1) = radclatp * xprm cvij1(i,jjp1) = 0.5 * rad* yprp cvij4(i,jjp1) = cvij1(i,jjp1) 31 CONTINUE c DO i = 1, iim aireij2( i,jjp1 ) = 0. aireij3( i,jjp1 ) = 0. cvij2 ( i,jjp1 ) = 0. cvij3 ( i,jjp1 ) = 0. cuij2 ( i,jjp1 ) = 0. cuij3 ( i,jjp1 ) = 0. ENDDO c END IF c IF ( j .gt. 1 .AND. j .lt. jjp1 ) THEN c IF( fxyhypb ) THEN rlatp = rlatu2 ( j-1 ) yprp = yprimu2( j-1 ) rlatm = rlatu1 ( j ) yprm = yprimu1( j ) ELSE rlatp = fy ( FLOAT(j) - 0.25 ) yprp = fyprim( FLOAT(j) - 0.25 ) rlatm = fy ( FLOAT(j) + 0.25 ) yprm = fyprim( FLOAT(j) + 0.25 ) ENDIF coslatm = COS( rlatm ) coslatp = COS( rlatp ) radclatp = 0.5* rad * coslatp radclatm = 0.5* rad * coslatm c DO 32 i = 1,iim xprp = fxprim( FLOAT(i) + 0.25 ) xprm = fxprim( FLOAT(i) - 0.25 ) ai14 = un4rad2 * coslatp * yprp ai23 = un4rad2 * coslatm * yprm aireij1 ( i,j ) = ai14 * xprp aireij2 ( i,j ) = ai23 * xprp aireij3 ( i,j ) = ai23 * xprm aireij4 ( i,j ) = ai14 * xprm cuij1 ( i,j ) = radclatp * xprp cuij2 ( i,j ) = radclatm * xprp cuij3 ( i,j ) = radclatm * xprm cuij4 ( i,j ) = radclatp * xprm cvij1 ( i,j ) = 0.5* rad * yprp cvij2 ( i,j ) = 0.5* rad * yprm cvij3 ( i,j ) = cvij2(i,j) cvij4 ( i,j ) = cvij1(i,j) 32 CONTINUE c END IF c c ........ periodicite ............ c cvij1 (iip1,j) = cvij1 (1,j) cvij2 (iip1,j) = cvij2 (1,j) cvij3 (iip1,j) = cvij3 (1,j) cvij4 (iip1,j) = cvij4 (1,j) cuij1 (iip1,j) = cuij1 (1,j) cuij2 (iip1,j) = cuij2 (1,j) cuij3 (iip1,j) = cuij3 (1,j) cuij4 (iip1,j) = cuij4 (1,j) aireij1 (iip1,j) = aireij1 (1,j ) aireij2 (iip1,j) = aireij2 (1,j ) aireij3 (iip1,j) = aireij3 (1,j ) aireij4 (iip1,j) = aireij4 (1,j ) 35 CONTINUE c c c ..... Calcul des elongations cu,cv, cvu ......... c DO j = 1, jjm DO i = 1, iim cv(i,j) = 0.5 *( cvij2(i,j)+cvij3(i,j)+cvij1(i,j+1)+cvij4(i,j+1)) cvu(i,j)= 0.5 *( cvij1(i,j)+cvij4(i,j)+cvij2(i,j) +cvij3(i,j) ) cuv(i,j)= 0.5 *( cuij2(i,j)+cuij3(i,j)+cuij1(i,j+1)+cuij4(i,j+1)) unscv2(i,j) = 1./ ( cv(i,j)*cv(i,j) ) ENDDO cv (iip1,j) = cv (1,j) cvu (iip1,j) = cvu (1,j) unscv2 (iip1,j) = unscv2(1,j) cuv (iip1,j) = cuv (1,j) ENDDO DO j = 2, jjm DO i = 1, iim cu(i,j) = 0.5*(cuij1(i,j)+cuij4(i+1,j)+cuij2(i,j)+cuij3(i+1,j)) unscu2(i,j) = 1./ ( cu(i,j) * cu(i,j) ) ENDDO cu (iip1,j) = cu(1,j) unscu2(iip1,j) = unscu2(1,j) ENDDO c c .... calcul aux poles .... c DO i = 1, iip1 cu ( i, 1 ) = 0. unscu2( i, 1 ) = 0. cvu ( i, 1 ) = 0. c cu (i, jjp1) = 0. unscu2(i, jjp1) = 0. cvu (i, jjp1) = 0. ENDDO c c .............................................................. c DO 37 j = 1, jjp1 DO 36 i = 1, iim aire ( i,j ) = aireij1(i,j) + aireij2(i,j) + aireij3(i,j) + * aireij4(i,j) alpha1 ( i,j ) = aireij1(i,j) / aire(i,j) alpha2 ( i,j ) = aireij2(i,j) / aire(i,j) alpha3 ( i,j ) = aireij3(i,j) / aire(i,j) alpha4 ( i,j ) = aireij4(i,j) / aire(i,j) alpha1p2( i,j ) = alpha1 (i,j) + alpha2 (i,j) alpha1p4( i,j ) = alpha1 (i,j) + alpha4 (i,j) alpha2p3( i,j ) = alpha2 (i,j) + alpha3 (i,j) alpha3p4( i,j ) = alpha3 (i,j) + alpha4 (i,j) 36 CONTINUE c c .... Modif P. Le Van ( 4/07/96 ) ..... c aire (iip1,j) = aire (1,j) alpha1 (iip1,j) = alpha1 (1,j) alpha2 (iip1,j) = alpha2 (1,j) alpha3 (iip1,j) = alpha3 (1,j) alpha4 (iip1,j) = alpha4 (1,j) alpha1p2(iip1,j) = alpha1p2(1,j) alpha1p4(iip1,j) = alpha1p4(1,j) alpha2p3(iip1,j) = alpha2p3(1,j) alpha3p4(iip1,j) = alpha3p4(1,j) 37 CONTINUE c DO 42 j = 1,jjp1 DO 41 i = 1,iim unsaire(i,j) = 1./ aire(i,j) aireu (i,j) = aireij1(i,j) + aireij2(i,j) + aireij4(i+1,j) + * aireij3(i+1,j) 41 CONTINUE aireu (iip1,j) = aireu (1,j) unsaire(iip1,j) = unsaire(1,j) 42 CONTINUE c c DO 48 j = 1,jjm c DO i=1,iim airev(i,j) = aireij2(i,j)+ aireij3(i,j)+ aireij1(i,j+1) + * aireij4(i,j+1) airvscu2(i,j) = airev(i,j)/ ( cuv(i,j) * cuv(i,j) ) ENDDO DO i=1,iim airez = aireij2(i,j)+aireij1(i,j+1)+aireij3(i+1,j) + * aireij4(i+1,j+1) unsairez(i,j) = 1./ airez fext (i,j) = airez * SIN(yv(j))* 2.* omeg ENDDO airev (iip1,j) = airev(1,j) airvscu2(iip1,j) = airvscu2(1,j) unsairez(iip1,j) = unsairez(1,j) fext (iip1,j) = fext(1,j) c 48 CONTINUE c c DO j=2,jjm DO i=1,iim airuscv2(i,j) = aireu(i,j)/ ( cvu(i,j) * cvu(i,j) ) ENDDO airuscv2(iip1,j) = airuscv2(1,j) ENDDO c c c calcul des aires aux poles : c ----------------------------- c apoln = SSUM(iim,aire(1,1),1) apols = SSUM(iim,aire(1,jjp1),1) c c----------------------------------------------------------------------- c gtitre='Coriolis version ancienne' c gfichier='fext1' c CALL writestd(fext,iip1*jjm) c c changement F. Hourdin calcul conservatif pour fext c constang contient le produit a * cos ( latitude ) * omega c DO i=1,iim constang(i,1) = 0. ENDDO DO j=1,jjm-1 DO i=1,iim constang(i,j+1) = rad*omeg*cu(i,j+1)*COS(rlatu(j+1)) ENDDO ENDDO DO i=1,iim constang(i,jjp1) = 0. ENDDO c c periodicite en longitude c DO j=1,jjm fext(iip1,j) = fext(1,j) ENDDO DO j=1,jjp1 constang(iip1,j) = constang(1,j) ENDDO c fin du changement c c----------------------------------------------------------------------- c calcul des longitudes: c ---------------------- c DO 60 i=1,iip1 rlonv(i) = fx(FLOAT(i)) rlonu(i) = fx(FLOAT(i)+0.5) 60 CONTINUE c c----------------------------------------------------------------------- c PRINT *,' INIGEOM RLONV ' DO i=1,iip1 rlonvv(i) = rlonv(i)*180./pi ENDDO PRINT 400,rlonvv c PRINT *,' RLATV ' DO i=1,jjm rlatuu(i)=rlatv(i)*180./pi ENDDO PRINT 400,(rlatuu(i),i=1,jjm) c DO i=1,iip1 rlonvv(i)=rlonu(i)*180./pi ENDDO PRINT *,' RLONU ' PRINT 400,rlonvv c PRINT *,' RLATU ' DO i=1,jjp1 rlatuu(i)=rlatu(i)*180./pi ENDDO PRINT 400,(rlatuu(i),i=1,jjp1) c 400 FORMAT(1x,8f8.2) c RETURN END