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module inigeom_m |
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|
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IMPLICIT NONE |
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|
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contains |
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|
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SUBROUTINE inigeom |
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|
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! Auteur : P. Le Van |
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|
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! Calcul des élongations cuij1, ..., cuij4, cvij1, ..., cvij4 aux mêmes |
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! endroits que les aires aireij1_2d, ..., aireij4_2d. |
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|
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! Choix entre une fonction "f(y)" à dérivée sinusoïdale ou à |
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! dérivée tangente hyperbolique. Calcul des coefficients cu_2d, |
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! cv_2d, 1. / cu_2d**2, 1. / cv_2d**2. Les coefficients cu_2d et cv_2d |
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! permettent de passer des vitesses naturelles aux vitesses |
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! covariantes et contravariantes, ou vice-versa. |
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|
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! On a : |
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! u(covariant) = cu_2d * u(naturel), u(contravariant) = u(naturel) / cu_2d |
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! v(covariant) = cv_2d * v(naturel), v(contravariant) = v(naturel) / cv_2d |
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|
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! On en tire : |
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! u(covariant) = cu_2d * cu_2d * u(contravariant) |
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! v(covariant) = cv_2d * cv_2d * v(contravariant) |
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|
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! On a l'application (x(X), y(Y)) avec - im / 2 + 1 <= X <= im / 2 |
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! et - jm / 2 <= Y <= jm / 2 |
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|
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! x est la longitude du point en radians. |
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! y est la latitude du point en radians. |
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! |
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! On a : cu_2d(i, j) = rad * cos(y) * dx / dX |
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! cv(j) = rad * dy / dY |
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! aire_2d(i, j) = cu_2d(i, j) * cv(j) |
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! |
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! y, dx / dX, dy / dY calculés aux points concernés. cv, bien que |
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! dépendant de j uniquement, sera ici indicé aussi en i pour un |
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! adressage plus facile en ij. |
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|
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! xprimu et xprimv sont respectivement les valeurs de dx / dX aux |
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! points u et v. yprimu et yprimv sont respectivement les valeurs |
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! de dy / dY aux points u et v. rlatu et rlatv sont respectivement |
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! les valeurs de la latitude aux points u et v. cvu et cv_2d sont |
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! respectivement les valeurs de cv_2d aux points u et v. |
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|
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! cu_2d, cuv, cuscal, cuz sont respectivement les valeurs de cu_2d |
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! aux points u, v, scalaires, et z. Cf. "inigeom.txt". |
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|
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USE comconst, ONLY : g, omeg, rad |
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USE comgeom, ONLY : airesurg_2d, aireu_2d, airev_2d, aire_2d, & |
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alpha1p2_2d, alpha1p4_2d, alpha1_2d, & |
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alpha2p3_2d, alpha2_2d, alpha3p4_2d, alpha3_2d, alpha4_2d, apoln, & |
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apols, constang_2d, cuscvugam_2d, cusurcvu_2d, cuvscvgam1_2d, & |
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cuvscvgam2_2d, cuvsurcv_2d, cu_2d, cvscuvgam_2d, cvsurcuv_2d, & |
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cvuscugam1_2d, cvuscugam2_2d, cvusurcu_2d, cv_2d, fext_2d, rlatu, & |
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rlatv, rlonu, rlonv, unsairez_2d, unsaire_2d, unsairz_gam_2d, & |
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unsair_gam1_2d, unsair_gam2_2d, unsapolnga1, unsapolnga2, & |
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unsapolsga1, unsapolsga2, unscu2_2d, unscv2_2d, xprimu, xprimv |
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USE comdissnew, ONLY : coefdis, nitergdiv, nitergrot, niterh |
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use conf_gcm_m, ONLY : fxyhypb, ysinus |
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USE dimens_m, ONLY : iim, jjm |
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use fxy_m, only: fxy |
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use fxyhyper_m, only: fxyhyper |
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use jumble, only: new_unit |
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use nr_util, only: pi |
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USE paramet_m, ONLY : iip1, jjp1 |
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USE serre, ONLY : alphax, alphay, clat, clon, dzoomx, dzoomy, grossismx, & |
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grossismy, pxo, pyo, taux, tauy, transx, transy |
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|
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! Variables locales |
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|
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INTEGER i, j, itmax, itmay, iter, unit |
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REAL cvu(iip1, jjp1), cuv(iip1, jjm) |
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REAL ai14, ai23, airez, un4rad2 |
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REAL eps, x1, xo1, f, df, xdm, y1, yo1, ydm |
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REAL coslatm, coslatp, radclatm, radclatp |
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REAL, dimension(iip1, jjp1):: cuij1, cuij2, cuij3, cuij4 ! in m |
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REAL, dimension(iip1, jjp1):: cvij1, cvij2, cvij3, cvij4 ! in m |
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REAL rlatu1(jjm), yprimu1(jjm), rlatu2(jjm), yprimu2(jjm) |
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real yprimv(jjm), yprimu(jjp1) |
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REAL gamdi_gdiv, gamdi_grot, gamdi_h |
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REAL rlonm025(iip1), xprimm025(iip1), rlonp025(iip1), xprimp025(iip1) |
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real, dimension(iim + 1, jjm + 1):: aireij1_2d, aireij2_2d, aireij3_2d, & |
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aireij4_2d ! in m2 |
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real airuscv2_2d(iim + 1, jjm) |
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real airvscu2_2d(iim + 1, jjm), aiuscv2gam_2d(iim + 1, jjm) |
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real aivscu2gam_2d(iim + 1, jjm) |
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|
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!------------------------------------------------------------------ |
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|
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PRINT *, 'Call sequence information: inigeom' |
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|
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IF (nitergdiv/=2) THEN |
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gamdi_gdiv = coefdis / (real(nitergdiv)-2.) |
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ELSE |
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gamdi_gdiv = 0. |
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END IF |
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IF (nitergrot/=2) THEN |
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gamdi_grot = coefdis / (real(nitergrot)-2.) |
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ELSE |
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gamdi_grot = 0. |
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END IF |
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IF (niterh/=2) THEN |
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gamdi_h = coefdis / (real(niterh)-2.) |
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ELSE |
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gamdi_h = 0. |
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END IF |
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|
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print *, 'gamdi_gdiv = ', gamdi_gdiv |
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print *, "gamdi_grot = ", gamdi_grot |
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print *, "gamdi_h = ", gamdi_h |
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|
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IF (.NOT. fxyhypb) THEN |
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IF (ysinus) THEN |
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print *, ' Inigeom, Y = Sinus (Latitude) ' |
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! utilisation de f(x, y) avec y = sinus de la latitude |
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CALL fxysinus(rlatu, yprimu, rlatv, yprimv, rlatu1, yprimu1, & |
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rlatu2, yprimu2, rlonu, xprimu, rlonv, xprimv, rlonm025, & |
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xprimm025, rlonp025, xprimp025) |
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ELSE |
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print *, 'Inigeom, Y = Latitude, der. sinusoid .' |
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! utilisation de f(x, y) a tangente sinusoidale, y etant la latit |
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|
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pxo = clon * pi / 180. |
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pyo = 2. * clat * pi / 180. |
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|
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! determination de transx (pour le zoom) par Newton-Raphson |
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|
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itmax = 10 |
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eps = .1E-7 |
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|
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xo1 = 0. |
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DO iter = 1, itmax |
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x1 = xo1 |
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f = x1 + alphax * sin(x1-pxo) |
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df = 1. + alphax * cos(x1-pxo) |
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x1 = x1 - f / df |
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xdm = abs(x1-xo1) |
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IF (xdm<=eps) EXIT |
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xo1 = x1 |
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END DO |
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|
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transx = xo1 |
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|
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itmay = 10 |
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eps = .1E-7 |
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|
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yo1 = 0. |
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DO iter = 1, itmay |
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y1 = yo1 |
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f = y1 + alphay * sin(y1-pyo) |
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df = 1. + alphay * cos(y1-pyo) |
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y1 = y1 - f / df |
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ydm = abs(y1-yo1) |
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IF (ydm<=eps) EXIT |
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yo1 = y1 |
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END DO |
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|
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transy = yo1 |
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|
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CALL fxy(rlatu, yprimu, rlatv, yprimv, rlatu1, yprimu1, rlatu2, & |
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yprimu2, rlonu, xprimu, rlonv, xprimv, rlonm025, xprimm025, & |
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rlonp025, xprimp025) |
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END IF |
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ELSE |
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! Utilisation de fxyhyper, f(x, y) à dérivée tangente hyperbolique |
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print *, 'Inigeom, Y = Latitude, dérivée tangente hyperbolique' |
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CALL fxyhyper(clat, grossismy, dzoomy, tauy, clon, grossismx, dzoomx, & |
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taux, rlatu, yprimu, rlatv, yprimv, rlatu1, yprimu1, rlatu2, & |
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yprimu2, rlonu, xprimu, rlonv, xprimv, rlonm025, xprimm025, & |
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rlonp025, xprimp025) |
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END IF |
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|
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rlatu(1) = pi / 2. |
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rlatu(jjp1) = -rlatu(1) |
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|
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! Calcul aux pôles |
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|
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yprimu(1) = 0. |
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yprimu(jjp1) = 0. |
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|
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un4rad2 = 0.25 * rad * rad |
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|
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! Cf. "inigeom.txt". Calcul des quatre aires élémentaires |
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! aireij1_2d, aireij2_2d, aireij3_2d, aireij4_2d qui entourent |
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! chaque aire_2d(i, j), ainsi que les quatre élongations |
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! élémentaires cuij et les quatre élongations cvij qui sont |
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! calculées aux mêmes endroits que les aireij. |
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|
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coslatm = cos(rlatu1(1)) |
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radclatm = 0.5 * rad * coslatm |
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|
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aireij1_2d(:iim, 1) = 0. |
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aireij2_2d(:iim, 1) = un4rad2 * coslatm * xprimp025(:iim) * yprimu1(1) |
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aireij3_2d(:iim, 1) = un4rad2 * coslatm * xprimm025(:iim) * yprimu1(1) |
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aireij4_2d(:iim, 1) = 0. |
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|
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cuij1(:iim, 1) = 0. |
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cuij2(:iim, 1) = radclatm * xprimp025(:iim) |
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cuij3(:iim, 1) = radclatm * xprimm025(:iim) |
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cuij4(:iim, 1) = 0. |
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|
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cvij1(:iim, 1) = 0. |
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cvij2(:iim, 1) = 0.5 * rad * yprimu1(1) |
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cvij3(:iim, 1) = cvij2(:iim, 1) |
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cvij4(:iim, 1) = 0. |
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|
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do j = 2, jjm |
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coslatm = cos(rlatu1(j)) |
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coslatp = cos(rlatu2(j-1)) |
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radclatp = 0.5 * rad * coslatp |
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radclatm = 0.5 * rad * coslatm |
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ai14 = un4rad2 * coslatp * yprimu2(j-1) |
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ai23 = un4rad2 * coslatm * yprimu1(j) |
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|
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aireij1_2d(:iim, j) = ai14 * xprimp025(:iim) |
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aireij2_2d(:iim, j) = ai23 * xprimp025(:iim) |
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aireij3_2d(:iim, j) = ai23 * xprimm025(:iim) |
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aireij4_2d(:iim, j) = ai14 * xprimm025(:iim) |
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cuij1(:iim, j) = radclatp * xprimp025(:iim) |
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cuij2(:iim, j) = radclatm * xprimp025(:iim) |
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cuij3(:iim, j) = radclatm * xprimm025(:iim) |
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cuij4(:iim, j) = radclatp * xprimm025(:iim) |
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cvij1(:iim, j) = 0.5 * rad * yprimu2(j-1) |
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cvij2(:iim, j) = 0.5 * rad * yprimu1(j) |
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cvij3(:iim, j) = cvij2(:iim, j) |
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cvij4(:iim, j) = cvij1(:iim, j) |
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end do |
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|
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coslatp = cos(rlatu2(jjm)) |
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radclatp = 0.5 * rad * coslatp |
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|
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aireij1_2d(:iim, jjp1) = un4rad2 * coslatp * xprimp025(:iim) * yprimu2(jjm) |
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aireij2_2d(:iim, jjp1) = 0. |
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aireij3_2d(:iim, jjp1) = 0. |
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aireij4_2d(:iim, jjp1) = un4rad2 * coslatp * xprimm025(:iim) * yprimu2(jjm) |
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|
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cuij1(:iim, jjp1) = radclatp * xprimp025(:iim) |
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cuij2(:iim, jjp1) = 0. |
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cuij3(:iim, jjp1) = 0. |
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cuij4(:iim, jjp1) = radclatp * xprimm025(:iim) |
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|
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cvij1(:iim, jjp1) = 0.5 * rad * yprimu2(jjm) |
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cvij2(:iim, jjp1) = 0. |
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cvij3(:iim, jjp1) = 0. |
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cvij4(:iim, jjp1) = cvij1(:iim, jjp1) |
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|
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! Périodicité : |
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|
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cvij1(iip1, :) = cvij1(1, :) |
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cvij2(iip1, :) = cvij2(1, :) |
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cvij3(iip1, :) = cvij3(1, :) |
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cvij4(iip1, :) = cvij4(1, :) |
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|
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cuij1(iip1, :) = cuij1(1, :) |
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cuij2(iip1, :) = cuij2(1, :) |
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cuij3(iip1, :) = cuij3(1, :) |
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cuij4(iip1, :) = cuij4(1, :) |
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|
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aireij1_2d(iip1, :) = aireij1_2d(1, :) |
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aireij2_2d(iip1, :) = aireij2_2d(1, :) |
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aireij3_2d(iip1, :) = aireij3_2d(1, :) |
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aireij4_2d(iip1, :) = aireij4_2d(1, :) |
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|
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DO j = 1, jjp1 |
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DO i = 1, iim |
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aire_2d(i, j) = aireij1_2d(i, j) + aireij2_2d(i, j) & |
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+ aireij3_2d(i, j) + aireij4_2d(i, j) |
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alpha1_2d(i, j) = aireij1_2d(i, j) / aire_2d(i, j) |
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alpha2_2d(i, j) = aireij2_2d(i, j) / aire_2d(i, j) |
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alpha3_2d(i, j) = aireij3_2d(i, j) / aire_2d(i, j) |
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alpha4_2d(i, j) = aireij4_2d(i, j) / aire_2d(i, j) |
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alpha1p2_2d(i, j) = alpha1_2d(i, j) + alpha2_2d(i, j) |
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alpha1p4_2d(i, j) = alpha1_2d(i, j) + alpha4_2d(i, j) |
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alpha2p3_2d(i, j) = alpha2_2d(i, j) + alpha3_2d(i, j) |
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alpha3p4_2d(i, j) = alpha3_2d(i, j) + alpha4_2d(i, j) |
279 |
END DO |
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|
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aire_2d(iip1, j) = aire_2d(1, j) |
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alpha1_2d(iip1, j) = alpha1_2d(1, j) |
283 |
alpha2_2d(iip1, j) = alpha2_2d(1, j) |
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alpha3_2d(iip1, j) = alpha3_2d(1, j) |
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alpha4_2d(iip1, j) = alpha4_2d(1, j) |
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alpha1p2_2d(iip1, j) = alpha1p2_2d(1, j) |
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alpha1p4_2d(iip1, j) = alpha1p4_2d(1, j) |
288 |
alpha2p3_2d(iip1, j) = alpha2p3_2d(1, j) |
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alpha3p4_2d(iip1, j) = alpha3p4_2d(1, j) |
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END DO |
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|
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DO j = 1, jjp1 |
293 |
DO i = 1, iim |
294 |
aireu_2d(i, j) = aireij1_2d(i, j) + aireij2_2d(i, j) + & |
295 |
aireij4_2d(i + 1, j) + aireij3_2d(i + 1, j) |
296 |
unsaire_2d(i, j) = 1. / aire_2d(i, j) |
297 |
unsair_gam1_2d(i, j) = unsaire_2d(i, j)**(-gamdi_gdiv) |
298 |
unsair_gam2_2d(i, j) = unsaire_2d(i, j)**(-gamdi_h) |
299 |
airesurg_2d(i, j) = aire_2d(i, j) / g |
300 |
END DO |
301 |
aireu_2d(iip1, j) = aireu_2d(1, j) |
302 |
unsaire_2d(iip1, j) = unsaire_2d(1, j) |
303 |
unsair_gam1_2d(iip1, j) = unsair_gam1_2d(1, j) |
304 |
unsair_gam2_2d(iip1, j) = unsair_gam2_2d(1, j) |
305 |
airesurg_2d(iip1, j) = airesurg_2d(1, j) |
306 |
END DO |
307 |
|
308 |
DO j = 1, jjm |
309 |
DO i = 1, iim |
310 |
airev_2d(i, j) = aireij2_2d(i, j) + aireij3_2d(i, j) + & |
311 |
aireij1_2d(i, j + 1) + aireij4_2d(i, j + 1) |
312 |
END DO |
313 |
DO i = 1, iim |
314 |
airez = aireij2_2d(i, j) + aireij1_2d(i, j + 1) & |
315 |
+ aireij3_2d(i + 1, j) + aireij4_2d(i + 1, j + 1) |
316 |
unsairez_2d(i, j) = 1. / airez |
317 |
unsairz_gam_2d(i, j) = unsairez_2d(i, j)**(-gamdi_grot) |
318 |
fext_2d(i, j) = airez * sin(rlatv(j)) * 2. * omeg |
319 |
END DO |
320 |
airev_2d(iip1, j) = airev_2d(1, j) |
321 |
unsairez_2d(iip1, j) = unsairez_2d(1, j) |
322 |
fext_2d(iip1, j) = fext_2d(1, j) |
323 |
unsairz_gam_2d(iip1, j) = unsairz_gam_2d(1, j) |
324 |
END DO |
325 |
|
326 |
! Calcul des élongations cu_2d, cv_2d, cvu |
327 |
|
328 |
DO j = 1, jjm |
329 |
DO i = 1, iim |
330 |
cv_2d(i, j) = 0.5 * & |
331 |
(cvij2(i, j) + cvij3(i, j) + cvij1(i, j + 1) + cvij4(i, j + 1)) |
332 |
cvu(i, j) = 0.5 * (cvij1(i, j) + cvij4(i, j) + cvij2(i, j) & |
333 |
+ cvij3(i, j)) |
334 |
cuv(i, j) = 0.5 * (cuij2(i, j) + cuij3(i, j) + cuij1(i, j + 1) & |
335 |
+ cuij4(i, j + 1)) |
336 |
unscv2_2d(i, j) = 1. / cv_2d(i, j)**2 |
337 |
END DO |
338 |
DO i = 1, iim |
339 |
cuvsurcv_2d(i, j) = airev_2d(i, j) * unscv2_2d(i, j) |
340 |
cvsurcuv_2d(i, j) = 1. / cuvsurcv_2d(i, j) |
341 |
cuvscvgam1_2d(i, j) = cuvsurcv_2d(i, j)**(-gamdi_gdiv) |
342 |
cuvscvgam2_2d(i, j) = cuvsurcv_2d(i, j)**(-gamdi_h) |
343 |
cvscuvgam_2d(i, j) = cvsurcuv_2d(i, j)**(-gamdi_grot) |
344 |
END DO |
345 |
cv_2d(iip1, j) = cv_2d(1, j) |
346 |
cvu(iip1, j) = cvu(1, j) |
347 |
unscv2_2d(iip1, j) = unscv2_2d(1, j) |
348 |
cuv(iip1, j) = cuv(1, j) |
349 |
cuvsurcv_2d(iip1, j) = cuvsurcv_2d(1, j) |
350 |
cvsurcuv_2d(iip1, j) = cvsurcuv_2d(1, j) |
351 |
cuvscvgam1_2d(iip1, j) = cuvscvgam1_2d(1, j) |
352 |
cuvscvgam2_2d(iip1, j) = cuvscvgam2_2d(1, j) |
353 |
cvscuvgam_2d(iip1, j) = cvscuvgam_2d(1, j) |
354 |
END DO |
355 |
|
356 |
DO j = 2, jjm |
357 |
DO i = 1, iim |
358 |
cu_2d(i, j) = 0.5 * (cuij1(i, j) + cuij4(i + 1, j) + cuij2(i, j) & |
359 |
+ cuij3(i + 1, j)) |
360 |
unscu2_2d(i, j) = 1. / cu_2d(i, j)**2 |
361 |
cvusurcu_2d(i, j) = aireu_2d(i, j) * unscu2_2d(i, j) |
362 |
cusurcvu_2d(i, j) = 1. / cvusurcu_2d(i, j) |
363 |
cvuscugam1_2d(i, j) = cvusurcu_2d(i, j)**(-gamdi_gdiv) |
364 |
cvuscugam2_2d(i, j) = cvusurcu_2d(i, j)**(-gamdi_h) |
365 |
cuscvugam_2d(i, j) = cusurcvu_2d(i, j)**(-gamdi_grot) |
366 |
END DO |
367 |
cu_2d(iip1, j) = cu_2d(1, j) |
368 |
unscu2_2d(iip1, j) = unscu2_2d(1, j) |
369 |
cvusurcu_2d(iip1, j) = cvusurcu_2d(1, j) |
370 |
cusurcvu_2d(iip1, j) = cusurcvu_2d(1, j) |
371 |
cvuscugam1_2d(iip1, j) = cvuscugam1_2d(1, j) |
372 |
cvuscugam2_2d(iip1, j) = cvuscugam2_2d(1, j) |
373 |
cuscvugam_2d(iip1, j) = cuscvugam_2d(1, j) |
374 |
END DO |
375 |
|
376 |
! Calcul aux pôles |
377 |
|
378 |
cu_2d(:, 1) = 0. |
379 |
unscu2_2d(:, 1) = 0. |
380 |
cvu(:, 1) = 0. |
381 |
|
382 |
cu_2d(:, jjp1) = 0. |
383 |
unscu2_2d(:, jjp1) = 0. |
384 |
cvu(:, jjp1) = 0. |
385 |
|
386 |
DO j = 1, jjm |
387 |
DO i = 1, iim |
388 |
airvscu2_2d(i, j) = airev_2d(i, j) / (cuv(i, j) * cuv(i, j)) |
389 |
aivscu2gam_2d(i, j) = airvscu2_2d(i, j)**(-gamdi_grot) |
390 |
END DO |
391 |
airvscu2_2d(iip1, j) = airvscu2_2d(1, j) |
392 |
aivscu2gam_2d(iip1, j) = aivscu2gam_2d(1, j) |
393 |
END DO |
394 |
|
395 |
DO j = 2, jjm |
396 |
DO i = 1, iim |
397 |
airuscv2_2d(i, j) = aireu_2d(i, j) / (cvu(i, j) * cvu(i, j)) |
398 |
aiuscv2gam_2d(i, j) = airuscv2_2d(i, j)**(-gamdi_grot) |
399 |
END DO |
400 |
airuscv2_2d(iip1, j) = airuscv2_2d(1, j) |
401 |
aiuscv2gam_2d(iip1, j) = aiuscv2gam_2d(1, j) |
402 |
END DO |
403 |
|
404 |
! Calcul des aires aux pôles : |
405 |
|
406 |
apoln = sum(aire_2d(:iim, 1)) |
407 |
apols = sum(aire_2d(:iim, jjp1)) |
408 |
unsapolnga1 = 1. / (apoln**(-gamdi_gdiv)) |
409 |
unsapolsga1 = 1. / (apols**(-gamdi_gdiv)) |
410 |
unsapolnga2 = 1. / (apoln**(-gamdi_h)) |
411 |
unsapolsga2 = 1. / (apols**(-gamdi_h)) |
412 |
|
413 |
! Changement F. Hourdin calcul conservatif pour fext_2d |
414 |
! constang_2d contient le produit a * cos (latitude) * omega |
415 |
|
416 |
DO i = 1, iim |
417 |
constang_2d(i, 1) = 0. |
418 |
END DO |
419 |
DO j = 1, jjm - 1 |
420 |
DO i = 1, iim |
421 |
constang_2d(i, j + 1) = rad * omeg * cu_2d(i, j + 1) & |
422 |
* cos(rlatu(j + 1)) |
423 |
END DO |
424 |
END DO |
425 |
DO i = 1, iim |
426 |
constang_2d(i, jjp1) = 0. |
427 |
END DO |
428 |
|
429 |
! Périodicité en longitude |
430 |
|
431 |
DO j = 1, jjm |
432 |
fext_2d(iip1, j) = fext_2d(1, j) |
433 |
END DO |
434 |
DO j = 1, jjp1 |
435 |
constang_2d(iip1, j) = constang_2d(1, j) |
436 |
END DO |
437 |
|
438 |
call new_unit(unit) |
439 |
open(unit, file="longitude_latitude.txt", status="replace", action="write") |
440 |
write(unit, fmt=*) '"longitudes at V points (degrees)"', rlonv * 180. / pi |
441 |
write(unit, fmt=*) '"latitudes at V points (degrees)"', rlatv * 180. / pi |
442 |
write(unit, fmt=*) '"longitudes at U points (degrees)"', rlonu * 180. / pi |
443 |
write(unit, fmt=*) '"latitudes at U points (degrees)"', rlatu * 180. / pi |
444 |
close(unit) |
445 |
|
446 |
END SUBROUTINE inigeom |
447 |
|
448 |
end module inigeom_m |