trunk/dyn3d/comgeom.f

module comgeom

  use dimens_m, only: iim, jjm

  implicit none

  private iim, jjm

  real cu_2d(iim + 1, jjm + 1), cv_2d(iim + 1, jjm) ! in m
  real cu((iim + 1) * (jjm + 1)), cv((iim + 1) * jjm) ! in m
  equivalence (cu, cu_2d), (cv, cv_2d)

  real unscu2_2d(iim + 1, jjm + 1) ! in m-2
  real unscu2((iim + 1) * (jjm + 1)) ! in m-2
  equivalence (unscu2, unscu2_2d)

  real unscv2_2d(iim + 1, jjm) ! in m-2
  real unscv2((iim + 1) * jjm) ! in m-2
  equivalence (unscv2, unscv2_2d)

  real aire((iim + 1) * (jjm + 1)), aire_2d(iim + 1, jjm + 1) ! in m2
  real airesurg_2d(iim + 1, jjm + 1), airesurg((iim + 1) * (jjm + 1))
  equivalence (aire, aire_2d), (airesurg, airesurg_2d)

  real aireu_2d(iim + 1, jjm + 1) ! in m2
  real aireu((iim + 1) * (jjm + 1)) ! in m2
  equivalence (aireu, aireu_2d)

  real airev((iim + 1) * jjm), airev_2d(iim + 1, jjm) ! in m2
  real unsaire((iim + 1) * (jjm + 1)), unsaire_2d(iim + 1, jjm + 1) ! in m-2
  equivalence (airev, airev_2d), (unsaire, unsaire_2d)

  real apoln, apols ! in m2

  real unsairez_2d(iim + 1, jjm)
  real unsairez((iim + 1) * jjm)
  equivalence (unsairez, unsairez_2d)

  real alpha1_2d(iim + 1, jjm + 1)
  real alpha1((iim + 1) * (jjm + 1))
  equivalence (alpha1, alpha1_2d)

  real alpha2_2d(iim + 1, jjm + 1)         
  real alpha2((iim + 1) * (jjm + 1))
  equivalence (alpha2, alpha2_2d)

  real alpha3_2d(iim + 1, jjm + 1), alpha4_2d(iim + 1, jjm + 1)
  real alpha3((iim + 1) * (jjm + 1)), alpha4((iim + 1) * (jjm + 1))
  equivalence (alpha3, alpha3_2d), (alpha4, alpha4_2d)

  real alpha1p2_2d(iim + 1, jjm + 1)        
  real alpha1p2((iim + 1) * (jjm + 1))
  equivalence (alpha1p2, alpha1p2_2d)

  real alpha1p4_2d(iim + 1, jjm + 1), alpha2p3_2d(iim + 1, jjm + 1)
  real alpha1p4((iim + 1) * (jjm + 1)), alpha2p3((iim + 1) * (jjm + 1))
  equivalence (alpha1p4, alpha1p4_2d), (alpha2p3, alpha2p3_2d)

  real alpha3p4((iim + 1) * (jjm + 1))
  real alpha3p4_2d(iim + 1, jjm + 1)    
  equivalence (alpha3p4, alpha3p4_2d)

  real fext_2d(iim + 1, jjm), constang_2d(iim + 1, jjm + 1)
  real fext((iim + 1) * jjm), constang((iim + 1) * (jjm + 1))
  equivalence (fext, fext_2d), (constang, constang_2d)

  real cuvsurcv_2d(iim + 1, jjm), cvsurcuv_2d(iim + 1, jjm) ! no dimension
  real cuvsurcv((iim + 1) * jjm), cvsurcuv((iim + 1) * jjm) ! no dimension
  equivalence (cuvsurcv, cuvsurcv_2d), (cvsurcuv, cvsurcuv_2d)

  real cvusurcu_2d(iim + 1, jjm + 1), cusurcvu_2d(iim + 1, jjm + 1)
  ! no dimension
  real cvusurcu((iim + 1) * (jjm + 1)), cusurcvu((iim + 1) * (jjm + 1))
  ! no dimension
  equivalence (cvusurcu, cvusurcu_2d), (cusurcvu, cusurcvu_2d)

  real cuvscvgam1_2d(iim + 1, jjm)
  real cuvscvgam1((iim + 1) * jjm)
  equivalence (cuvscvgam1, cuvscvgam1_2d)

  real cuvscvgam2_2d(iim + 1, jjm), cvuscugam1_2d(iim + 1, jjm + 1)
  real cuvscvgam2((iim + 1) * jjm), cvuscugam1((iim + 1) * (jjm + 1))
  equivalence (cuvscvgam2, cuvscvgam2_2d), (cvuscugam1, cvuscugam1_2d)

  real cvuscugam2_2d(iim + 1, jjm + 1), cvscuvgam_2d(iim + 1, jjm)
  real cvuscugam2((iim + 1) * (jjm + 1)), cvscuvgam((iim + 1) * jjm)
  equivalence (cvuscugam2, cvuscugam2_2d), (cvscuvgam, cvscuvgam_2d)

  real cuscvugam((iim + 1) * (jjm + 1))
  real cuscvugam_2d(iim + 1, jjm + 1) 
  equivalence (cuscvugam, cuscvugam_2d)

  real unsapolnga1, unsapolnga2, unsapolsga1, unsapolsga2                

  real unsair_gam1_2d(iim + 1, jjm + 1), unsair_gam2_2d(iim + 1, jjm + 1)
  real unsair_gam1((iim + 1) * (jjm + 1)), unsair_gam2((iim + 1) * (jjm + 1))
  equivalence (unsair_gam1, unsair_gam1_2d), (unsair_gam2, unsair_gam2_2d)

  real unsairz_gam_2d(iim + 1, jjm)
  real unsairz_gam((iim + 1) * jjm)
  equivalence (unsairz_gam, unsairz_gam_2d)

  save

contains

  SUBROUTINE inigeom

    ! Auteur : P. Le Van

    ! Calcul des élongations cuij1, ..., cuij4, cvij1, ..., cvij4 aux mêmes
    ! endroits que les aires aireij1_2d, ..., aireij4_2d.

    ! Fonction "f(y)" à dérivée tangente hyperbolique. Calcul des
    ! coefficients cu_2d, cv_2d, 1. / cu_2d**2, 1. / cv_2d**2. Les
    ! coefficients cu_2d et cv_2d permettent de passer des vitesses
    ! naturelles aux vitesses covariantes et contravariantes, ou
    ! vice-versa.

    ! On a :
    ! u(covariant) = cu_2d * u(naturel), u(contravariant) = u(naturel) / cu_2d
    ! v(covariant) = cv_2d * v(naturel), v(contravariant) = v(naturel) / cv_2d

    ! On en tire : 
    ! u(covariant) = cu_2d * cu_2d * u(contravariant)
    ! v(covariant) = cv_2d * cv_2d * v(contravariant)

    ! On a l'application (x(X), y(Y)) avec - im / 2 + 1 <= X <= im / 2
    ! et - jm / 2 <= Y <= jm / 2

    ! x est la longitude du point en radians.
    ! y est la latitude du point en radians.
    ! 
    ! On a : cu_2d(i, j) = rad * cos(y) * dx / dX
    ! cv(j) = rad * dy / dY
    ! aire_2d(i, j) = cu_2d(i, j) * cv(j)
    ! 
    ! y, dx / dX, dy / dY calculés aux points concernés. cv, bien que
    ! dépendant de j uniquement, sera ici indicé aussi en i pour un
    ! adressage plus facile en ij.

    ! cvu et cv_2d sont respectivement les valeurs de
    ! cv_2d aux points u et v.

    ! cu_2d, cuv, cuscal, cuz sont respectivement les valeurs de cu_2d
    ! aux points u, v, scalaires, et z. Cf. "inigeom.txt".

    USE comconst, ONLY : g, omeg, rad
    USE comdissnew, ONLY : coefdis, nitergdiv, nitergrot, niterh
    use dynetat0_m, only: xprimp025, xprimm025, rlatu1, rlatu2, rlatu, rlatv, &
         yprimu1, yprimu2, rlonu, rlonv
    use jumble, only: new_unit
    use nr_util, only: pi
    USE paramet_m, ONLY : iip1, jjp1

    ! Local:
    INTEGER i, j, unit
    REAL cvu(iip1, jjp1), cuv(iip1, jjm)
    REAL ai14, ai23, airez, un4rad2
    REAL coslatm, coslatp, radclatm, radclatp
    REAL, dimension(iip1, jjp1):: cuij1, cuij2, cuij3, cuij4 ! in m
    REAL, dimension(iip1, jjp1):: cvij1, cvij2, cvij3, cvij4 ! in m
    REAL gamdi_gdiv, gamdi_grot, gamdi_h
    real, dimension(iim + 1, jjm + 1):: aireij1_2d, aireij2_2d, aireij3_2d, &
         aireij4_2d ! in m2
    real airuscv2_2d(iim + 1, jjm) 
    real airvscu2_2d(iim + 1, jjm), aiuscv2gam_2d(iim + 1, jjm) 
    real aivscu2gam_2d(iim + 1, jjm)

    !------------------------------------------------------------------

    PRINT *, 'Call sequence information: inigeom'

    IF (nitergdiv /= 2) THEN
       gamdi_gdiv = coefdis / (nitergdiv - 2)
    ELSE
       gamdi_gdiv = 0.
    END IF

    IF (nitergrot /= 2) THEN
       gamdi_grot = coefdis / (nitergrot - 2)
    ELSE
       gamdi_grot = 0.
    END IF

    IF (niterh /= 2) THEN
       gamdi_h = coefdis / (niterh - 2)
    ELSE
       gamdi_h = 0.
    END IF

    print *, 'gamdi_gdiv = ', gamdi_gdiv
    print *, "gamdi_grot = ", gamdi_grot
    print *, "gamdi_h = ", gamdi_h

    un4rad2 = 0.25 * rad * rad

    ! Cf. "inigeom.txt". Calcul des quatre aires élémentaires
    ! aireij1_2d, aireij2_2d, aireij3_2d, aireij4_2d qui entourent
    ! chaque aire_2d(i, j), ainsi que les quatre élongations
    ! élémentaires cuij et les quatre élongations cvij qui sont
    ! calculées aux mêmes endroits que les aireij.

    coslatm = cos(rlatu1(1))
    radclatm = 0.5 * rad * coslatm

    aireij1_2d(:iim, 1) = 0.
    aireij2_2d(:iim, 1) = un4rad2 * coslatm * xprimp025(:iim) * yprimu1(1)
    aireij3_2d(:iim, 1) = un4rad2 * coslatm * xprimm025(:iim) * yprimu1(1)
    aireij4_2d(:iim, 1) = 0.

    cuij1(:iim, 1) = 0.
    cuij2(:iim, 1) = radclatm * xprimp025(:iim)
    cuij3(:iim, 1) = radclatm * xprimm025(:iim)
    cuij4(:iim, 1) = 0.

    cvij1(:iim, 1) = 0.
    cvij2(:iim, 1) = 0.5 * rad * yprimu1(1)
    cvij3(:iim, 1) = cvij2(:iim, 1)
    cvij4(:iim, 1) = 0.

    do j = 2, jjm
       coslatm = cos(rlatu1(j))
       coslatp = cos(rlatu2(j-1))
       radclatp = 0.5 * rad * coslatp
       radclatm = 0.5 * rad * coslatm
       ai14 = un4rad2 * coslatp * yprimu2(j-1)
       ai23 = un4rad2 * coslatm * yprimu1(j)

       aireij1_2d(:iim, j) = ai14 * xprimp025(:iim)
       aireij2_2d(:iim, j) = ai23 * xprimp025(:iim)
       aireij3_2d(:iim, j) = ai23 * xprimm025(:iim)
       aireij4_2d(:iim, j) = ai14 * xprimm025(:iim)
       cuij1(:iim, j) = radclatp * xprimp025(:iim)
       cuij2(:iim, j) = radclatm * xprimp025(:iim)
       cuij3(:iim, j) = radclatm * xprimm025(:iim)
       cuij4(:iim, j) = radclatp * xprimm025(:iim)
       cvij1(:iim, j) = 0.5 * rad * yprimu2(j-1)
       cvij2(:iim, j) = 0.5 * rad * yprimu1(j)
       cvij3(:iim, j) = cvij2(:iim, j)
       cvij4(:iim, j) = cvij1(:iim, j)
    end do

    coslatp = cos(rlatu2(jjm))
    radclatp = 0.5 * rad * coslatp

    aireij1_2d(:iim, jjp1) = un4rad2 * coslatp * xprimp025(:iim) * yprimu2(jjm)
    aireij2_2d(:iim, jjp1) = 0.
    aireij3_2d(:iim, jjp1) = 0.
    aireij4_2d(:iim, jjp1) = un4rad2 * coslatp * xprimm025(:iim) * yprimu2(jjm)

    cuij1(:iim, jjp1) = radclatp * xprimp025(:iim)
    cuij2(:iim, jjp1) = 0.
    cuij3(:iim, jjp1) = 0.
    cuij4(:iim, jjp1) = radclatp * xprimm025(:iim)

    cvij1(:iim, jjp1) = 0.5 * rad * yprimu2(jjm)
    cvij2(:iim, jjp1) = 0.
    cvij3(:iim, jjp1) = 0.
    cvij4(:iim, jjp1) = cvij1(:iim, jjp1)

    ! Périodicité :

    cvij1(iip1, :) = cvij1(1, :)
    cvij2(iip1, :) = cvij2(1, :)
    cvij3(iip1, :) = cvij3(1, :)
    cvij4(iip1, :) = cvij4(1, :)

    cuij1(iip1, :) = cuij1(1, :)
    cuij2(iip1, :) = cuij2(1, :)
    cuij3(iip1, :) = cuij3(1, :)
    cuij4(iip1, :) = cuij4(1, :)

    aireij1_2d(iip1, :) = aireij1_2d(1, :)
    aireij2_2d(iip1, :) = aireij2_2d(1, :)
    aireij3_2d(iip1, :) = aireij3_2d(1, :)
    aireij4_2d(iip1, :) = aireij4_2d(1, :)

    DO j = 1, jjp1
       DO i = 1, iim
          aire_2d(i, j) = aireij1_2d(i, j) + aireij2_2d(i, j) &
               + aireij3_2d(i, j) + aireij4_2d(i, j)
          alpha1_2d(i, j) = aireij1_2d(i, j) / aire_2d(i, j)
          alpha2_2d(i, j) = aireij2_2d(i, j) / aire_2d(i, j)
          alpha3_2d(i, j) = aireij3_2d(i, j) / aire_2d(i, j)
          alpha4_2d(i, j) = aireij4_2d(i, j) / aire_2d(i, j)
          alpha1p2_2d(i, j) = alpha1_2d(i, j) + alpha2_2d(i, j)
          alpha1p4_2d(i, j) = alpha1_2d(i, j) + alpha4_2d(i, j)
          alpha2p3_2d(i, j) = alpha2_2d(i, j) + alpha3_2d(i, j)
          alpha3p4_2d(i, j) = alpha3_2d(i, j) + alpha4_2d(i, j)
       END DO

       aire_2d(iip1, j) = aire_2d(1, j)
       alpha1_2d(iip1, j) = alpha1_2d(1, j)
       alpha2_2d(iip1, j) = alpha2_2d(1, j)
       alpha3_2d(iip1, j) = alpha3_2d(1, j)
       alpha4_2d(iip1, j) = alpha4_2d(1, j)
       alpha1p2_2d(iip1, j) = alpha1p2_2d(1, j)
       alpha1p4_2d(iip1, j) = alpha1p4_2d(1, j)
       alpha2p3_2d(iip1, j) = alpha2p3_2d(1, j)
       alpha3p4_2d(iip1, j) = alpha3p4_2d(1, j)
    END DO

    DO j = 1, jjp1
       DO i = 1, iim
          aireu_2d(i, j) = aireij1_2d(i, j) + aireij2_2d(i, j) + &
               aireij4_2d(i + 1, j) + aireij3_2d(i + 1, j)
          unsaire_2d(i, j) = 1. / aire_2d(i, j)
          unsair_gam1_2d(i, j) = unsaire_2d(i, j)**(-gamdi_gdiv)
          unsair_gam2_2d(i, j) = unsaire_2d(i, j)**(-gamdi_h)
          airesurg_2d(i, j) = aire_2d(i, j) / g
       END DO
       aireu_2d(iip1, j) = aireu_2d(1, j)
       unsaire_2d(iip1, j) = unsaire_2d(1, j)
       unsair_gam1_2d(iip1, j) = unsair_gam1_2d(1, j)
       unsair_gam2_2d(iip1, j) = unsair_gam2_2d(1, j)
       airesurg_2d(iip1, j) = airesurg_2d(1, j)
    END DO

    DO j = 1, jjm
       DO i = 1, iim
          airev_2d(i, j) = aireij2_2d(i, j) + aireij3_2d(i, j) + &
               aireij1_2d(i, j + 1) + aireij4_2d(i, j + 1)
       END DO
       DO i = 1, iim
          airez = aireij2_2d(i, j) + aireij1_2d(i, j + 1) &
               + aireij3_2d(i + 1, j) + aireij4_2d(i + 1, j + 1)
          unsairez_2d(i, j) = 1. / airez
          unsairz_gam_2d(i, j) = unsairez_2d(i, j)**(-gamdi_grot)
          fext_2d(i, j) = airez * sin(rlatv(j)) * 2. * omeg
       END DO
       airev_2d(iip1, j) = airev_2d(1, j)
       unsairez_2d(iip1, j) = unsairez_2d(1, j)
       fext_2d(iip1, j) = fext_2d(1, j)
       unsairz_gam_2d(iip1, j) = unsairz_gam_2d(1, j)
    END DO

    ! Calcul des élongations cu_2d, cv_2d, cvu 

    DO j = 1, jjm
       DO i = 1, iim
          cv_2d(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_2d(i, j) = 1. / cv_2d(i, j)**2
       END DO
       DO i = 1, iim
          cuvsurcv_2d(i, j) = airev_2d(i, j) * unscv2_2d(i, j)
          cvsurcuv_2d(i, j) = 1. / cuvsurcv_2d(i, j)
          cuvscvgam1_2d(i, j) = cuvsurcv_2d(i, j)**(-gamdi_gdiv)
          cuvscvgam2_2d(i, j) = cuvsurcv_2d(i, j)**(-gamdi_h)
          cvscuvgam_2d(i, j) = cvsurcuv_2d(i, j)**(-gamdi_grot)
       END DO
       cv_2d(iip1, j) = cv_2d(1, j)
       cvu(iip1, j) = cvu(1, j)
       unscv2_2d(iip1, j) = unscv2_2d(1, j)
       cuv(iip1, j) = cuv(1, j)
       cuvsurcv_2d(iip1, j) = cuvsurcv_2d(1, j)
       cvsurcuv_2d(iip1, j) = cvsurcuv_2d(1, j)
       cuvscvgam1_2d(iip1, j) = cuvscvgam1_2d(1, j)
       cuvscvgam2_2d(iip1, j) = cuvscvgam2_2d(1, j)
       cvscuvgam_2d(iip1, j) = cvscuvgam_2d(1, j)
    END DO

    DO j = 2, jjm
       DO i = 1, iim
          cu_2d(i, j) = 0.5 * (cuij1(i, j) + cuij4(i + 1, j) + cuij2(i, j) &
               + cuij3(i + 1, j))
          unscu2_2d(i, j) = 1. / cu_2d(i, j)**2
          cvusurcu_2d(i, j) = aireu_2d(i, j) * unscu2_2d(i, j)
          cusurcvu_2d(i, j) = 1. / cvusurcu_2d(i, j)
          cvuscugam1_2d(i, j) = cvusurcu_2d(i, j)**(-gamdi_gdiv)
          cvuscugam2_2d(i, j) = cvusurcu_2d(i, j)**(-gamdi_h)
          cuscvugam_2d(i, j) = cusurcvu_2d(i, j)**(-gamdi_grot)
       END DO
       cu_2d(iip1, j) = cu_2d(1, j)
       unscu2_2d(iip1, j) = unscu2_2d(1, j)
       cvusurcu_2d(iip1, j) = cvusurcu_2d(1, j)
       cusurcvu_2d(iip1, j) = cusurcvu_2d(1, j)
       cvuscugam1_2d(iip1, j) = cvuscugam1_2d(1, j)
       cvuscugam2_2d(iip1, j) = cvuscugam2_2d(1, j)
       cuscvugam_2d(iip1, j) = cuscvugam_2d(1, j)
    END DO

    ! Calcul aux pôles 

    cu_2d(:, 1) = 0.
    unscu2_2d(:, 1) = 0.
    cvu(:, 1) = 0.

    cu_2d(:, jjp1) = 0.
    unscu2_2d(:, jjp1) = 0.
    cvu(:, jjp1) = 0.

    DO j = 1, jjm
       DO i = 1, iim
          airvscu2_2d(i, j) = airev_2d(i, j) / (cuv(i, j) * cuv(i, j))
          aivscu2gam_2d(i, j) = airvscu2_2d(i, j)**(-gamdi_grot)
       END DO
       airvscu2_2d(iip1, j) = airvscu2_2d(1, j)
       aivscu2gam_2d(iip1, j) = aivscu2gam_2d(1, j)
    END DO

    DO j = 2, jjm
       DO i = 1, iim
          airuscv2_2d(i, j) = aireu_2d(i, j) / (cvu(i, j) * cvu(i, j))
          aiuscv2gam_2d(i, j) = airuscv2_2d(i, j)**(-gamdi_grot)
       END DO
       airuscv2_2d(iip1, j) = airuscv2_2d(1, j)
       aiuscv2gam_2d(iip1, j) = aiuscv2gam_2d(1, j)
    END DO

    ! Calcul des aires aux pôles :

    apoln = sum(aire_2d(:iim, 1))
    apols = sum(aire_2d(:iim, jjp1))
    unsapolnga1 = 1. / (apoln**(-gamdi_gdiv))
    unsapolsga1 = 1. / (apols**(-gamdi_gdiv))
    unsapolnga2 = 1. / (apoln**(-gamdi_h))
    unsapolsga2 = 1. / (apols**(-gamdi_h))

    ! Changement F. Hourdin calcul conservatif pour fext_2d
    ! constang_2d contient le produit a * cos (latitude) * omega

    DO i = 1, iim
       constang_2d(i, 1) = 0.
    END DO
    DO j = 1, jjm - 1
       DO i = 1, iim
          constang_2d(i, j + 1) = rad * omeg * cu_2d(i, j + 1) &
               * cos(rlatu(j + 1))
       END DO
    END DO
    DO i = 1, iim
       constang_2d(i, jjp1) = 0.
    END DO

    ! Périodicité en longitude
    DO j = 1, jjp1
       constang_2d(iip1, j) = constang_2d(1, j)
    END DO

    call new_unit(unit)
    open(unit, file="longitude_latitude.txt", status="replace", action="write")
    write(unit, fmt=*) '"longitudes at V points (degrees)"', rlonv * 180. / pi
    write(unit, fmt=*) '"latitudes at V points (degrees)"', rlatv * 180. / pi
    write(unit, fmt=*) '"longitudes at U points (degrees)"', rlonu * 180. / pi
    write(unit, fmt=*) '"latitudes at U points (degrees)"', rlatu * 180. / pi
    close(unit)

  END SUBROUTINE inigeom

end module comgeom
1	module comgeom
2
3	use dimens_m, only: iim, jjm
4
5	implicit none
6
7	private iim, jjm
8
9	real cu_2d(iim + 1, jjm + 1), cv_2d(iim + 1, jjm) ! in m
10	real cu((iim + 1) * (jjm + 1)), cv((iim + 1) * jjm) ! in m
11	equivalence (cu, cu_2d), (cv, cv_2d)
12
13	real unscu2_2d(iim + 1, jjm + 1) ! in m-2
14	real unscu2((iim + 1) * (jjm + 1)) ! in m-2
15	equivalence (unscu2, unscu2_2d)
16
17	real unscv2_2d(iim + 1, jjm) ! in m-2
18	real unscv2((iim + 1) * jjm) ! in m-2
19	equivalence (unscv2, unscv2_2d)
20
21	real aire((iim + 1) * (jjm + 1)), aire_2d(iim + 1, jjm + 1) ! in m2
22	real airesurg_2d(iim + 1, jjm + 1), airesurg((iim + 1) * (jjm + 1))
23	equivalence (aire, aire_2d), (airesurg, airesurg_2d)
24
25	real aireu_2d(iim + 1, jjm + 1) ! in m2
26	real aireu((iim + 1) * (jjm + 1)) ! in m2
27	equivalence (aireu, aireu_2d)
28
29	real airev((iim + 1) * jjm), airev_2d(iim + 1, jjm) ! in m2
30	real unsaire((iim + 1) * (jjm + 1)), unsaire_2d(iim + 1, jjm + 1) ! in m-2
31	equivalence (airev, airev_2d), (unsaire, unsaire_2d)
32
33	real apoln, apols ! in m2
34
35	real unsairez_2d(iim + 1, jjm)
36	real unsairez((iim + 1) * jjm)
37	equivalence (unsairez, unsairez_2d)
38
39	real alpha1_2d(iim + 1, jjm + 1)
40	real alpha1((iim + 1) * (jjm + 1))
41	equivalence (alpha1, alpha1_2d)
42
43	real alpha2_2d(iim + 1, jjm + 1)
44	real alpha2((iim + 1) * (jjm + 1))
45	equivalence (alpha2, alpha2_2d)
46
47	real alpha3_2d(iim + 1, jjm + 1), alpha4_2d(iim + 1, jjm + 1)
48	real alpha3((iim + 1) * (jjm + 1)), alpha4((iim + 1) * (jjm + 1))
49	equivalence (alpha3, alpha3_2d), (alpha4, alpha4_2d)
50
51	real alpha1p2_2d(iim + 1, jjm + 1)
52	real alpha1p2((iim + 1) * (jjm + 1))
53	equivalence (alpha1p2, alpha1p2_2d)
54
55	real alpha1p4_2d(iim + 1, jjm + 1), alpha2p3_2d(iim + 1, jjm + 1)
56	real alpha1p4((iim + 1) * (jjm + 1)), alpha2p3((iim + 1) * (jjm + 1))
57	equivalence (alpha1p4, alpha1p4_2d), (alpha2p3, alpha2p3_2d)
58
59	real alpha3p4((iim + 1) * (jjm + 1))
60	real alpha3p4_2d(iim + 1, jjm + 1)
61	equivalence (alpha3p4, alpha3p4_2d)
62
63	real fext_2d(iim + 1, jjm), constang_2d(iim + 1, jjm + 1)
64	real fext((iim + 1) * jjm), constang((iim + 1) * (jjm + 1))
65	equivalence (fext, fext_2d), (constang, constang_2d)
66
67	real cuvsurcv_2d(iim + 1, jjm), cvsurcuv_2d(iim + 1, jjm) ! no dimension
68	real cuvsurcv((iim + 1) * jjm), cvsurcuv((iim + 1) * jjm) ! no dimension
69	equivalence (cuvsurcv, cuvsurcv_2d), (cvsurcuv, cvsurcuv_2d)
70
71	real cvusurcu_2d(iim + 1, jjm + 1), cusurcvu_2d(iim + 1, jjm + 1)
72	! no dimension
73	real cvusurcu((iim + 1) * (jjm + 1)), cusurcvu((iim + 1) * (jjm + 1))
74	! no dimension
75	equivalence (cvusurcu, cvusurcu_2d), (cusurcvu, cusurcvu_2d)
76
77	real cuvscvgam1_2d(iim + 1, jjm)
78	real cuvscvgam1((iim + 1) * jjm)
79	equivalence (cuvscvgam1, cuvscvgam1_2d)
80
81	real cuvscvgam2_2d(iim + 1, jjm), cvuscugam1_2d(iim + 1, jjm + 1)
82	real cuvscvgam2((iim + 1) * jjm), cvuscugam1((iim + 1) * (jjm + 1))
83	equivalence (cuvscvgam2, cuvscvgam2_2d), (cvuscugam1, cvuscugam1_2d)
84
85	real cvuscugam2_2d(iim + 1, jjm + 1), cvscuvgam_2d(iim + 1, jjm)
86	real cvuscugam2((iim + 1) * (jjm + 1)), cvscuvgam((iim + 1) * jjm)
87	equivalence (cvuscugam2, cvuscugam2_2d), (cvscuvgam, cvscuvgam_2d)
88
89	real cuscvugam((iim + 1) * (jjm + 1))
90	real cuscvugam_2d(iim + 1, jjm + 1)
91	equivalence (cuscvugam, cuscvugam_2d)
92
93	real unsapolnga1, unsapolnga2, unsapolsga1, unsapolsga2
94
95	real unsair_gam1_2d(iim + 1, jjm + 1), unsair_gam2_2d(iim + 1, jjm + 1)
96	real unsair_gam1((iim + 1) * (jjm + 1)), unsair_gam2((iim + 1) * (jjm + 1))
97	equivalence (unsair_gam1, unsair_gam1_2d), (unsair_gam2, unsair_gam2_2d)
98
99	real unsairz_gam_2d(iim + 1, jjm)
100	real unsairz_gam((iim + 1) * jjm)
101	equivalence (unsairz_gam, unsairz_gam_2d)
102
103	save
104
105	contains
106
107	SUBROUTINE inigeom
108
109	! Auteur : P. Le Van
110
111	! Calcul des élongations cuij1, ..., cuij4, cvij1, ..., cvij4 aux mêmes
112	! endroits que les aires aireij1_2d, ..., aireij4_2d.
113
114	! Fonction "f(y)" à dérivée tangente hyperbolique. Calcul des
115	! coefficients cu_2d, cv_2d, 1. / cu_2d2, 1. / cv_2d2. Les
116	! coefficients cu_2d et cv_2d permettent de passer des vitesses
117	! naturelles aux vitesses covariantes et contravariantes, ou
118	! vice-versa.
119
120	! On a :
121	! u(covariant) = cu_2d * u(naturel), u(contravariant) = u(naturel) / cu_2d
122	! v(covariant) = cv_2d * v(naturel), v(contravariant) = v(naturel) / cv_2d
123
124	! On en tire :
125	! u(covariant) = cu_2d * cu_2d * u(contravariant)
126	! v(covariant) = cv_2d * cv_2d * v(contravariant)
127
128	! On a l'application (x(X), y(Y)) avec - im / 2 + 1 <= X <= im / 2
129	! et - jm / 2 <= Y <= jm / 2
130
131	! x est la longitude du point en radians.
132	! y est la latitude du point en radians.
133	!
134	! On a : cu_2d(i, j) = rad * cos(y) * dx / dX
135	! cv(j) = rad * dy / dY
136	! aire_2d(i, j) = cu_2d(i, j) * cv(j)
137	!
138	! y, dx / dX, dy / dY calculés aux points concernés. cv, bien que
139	! dépendant de j uniquement, sera ici indicé aussi en i pour un
140	! adressage plus facile en ij.
141
142	! cvu et cv_2d sont respectivement les valeurs de
143	! cv_2d aux points u et v.
144
145	! cu_2d, cuv, cuscal, cuz sont respectivement les valeurs de cu_2d
146	! aux points u, v, scalaires, et z. Cf. "inigeom.txt".
147
148	USE comconst, ONLY : g, omeg, rad
149	USE comdissnew, ONLY : coefdis, nitergdiv, nitergrot, niterh
150	use dynetat0_m, only: xprimp025, xprimm025, rlatu1, rlatu2, rlatu, rlatv, &
151	yprimu1, yprimu2, rlonu, rlonv
152	use jumble, only: new_unit
153	use nr_util, only: pi
154	USE paramet_m, ONLY : iip1, jjp1
155
156	! Local:
157	INTEGER i, j, unit
158	REAL cvu(iip1, jjp1), cuv(iip1, jjm)
159	REAL ai14, ai23, airez, un4rad2
160	REAL coslatm, coslatp, radclatm, radclatp
161	REAL, dimension(iip1, jjp1):: cuij1, cuij2, cuij3, cuij4 ! in m
162	REAL, dimension(iip1, jjp1):: cvij1, cvij2, cvij3, cvij4 ! in m
163	REAL gamdi_gdiv, gamdi_grot, gamdi_h
164	real, dimension(iim + 1, jjm + 1):: aireij1_2d, aireij2_2d, aireij3_2d, &
165	aireij4_2d ! in m2
166	real airuscv2_2d(iim + 1, jjm)
167	real airvscu2_2d(iim + 1, jjm), aiuscv2gam_2d(iim + 1, jjm)
168	real aivscu2gam_2d(iim + 1, jjm)
169
170	!------------------------------------------------------------------
171
172	PRINT *, 'Call sequence information: inigeom'
173
174	IF (nitergdiv /= 2) THEN
175	gamdi_gdiv = coefdis / (nitergdiv - 2)
176	ELSE
177	gamdi_gdiv = 0.
178	END IF
179
180	IF (nitergrot /= 2) THEN
181	gamdi_grot = coefdis / (nitergrot - 2)
182	ELSE
183	gamdi_grot = 0.
184	END IF
185
186	IF (niterh /= 2) THEN
187	gamdi_h = coefdis / (niterh - 2)
188	ELSE
189	gamdi_h = 0.
190	END IF
191
192	print *, 'gamdi_gdiv = ', gamdi_gdiv
193	print *, "gamdi_grot = ", gamdi_grot
194	print *, "gamdi_h = ", gamdi_h
195
196	un4rad2 = 0.25 * rad * rad
197
198	! Cf. "inigeom.txt". Calcul des quatre aires élémentaires
199	! aireij1_2d, aireij2_2d, aireij3_2d, aireij4_2d qui entourent
200	! chaque aire_2d(i, j), ainsi que les quatre élongations
201	! élémentaires cuij et les quatre élongations cvij qui sont
202	! calculées aux mêmes endroits que les aireij.
203
204	coslatm = cos(rlatu1(1))
205	radclatm = 0.5 * rad * coslatm
206
207	aireij1_2d(:iim, 1) = 0.
208	aireij2_2d(:iim, 1) = un4rad2 * coslatm * xprimp025(:iim) * yprimu1(1)
209	aireij3_2d(:iim, 1) = un4rad2 * coslatm * xprimm025(:iim) * yprimu1(1)
210	aireij4_2d(:iim, 1) = 0.
211
212	cuij1(:iim, 1) = 0.
213	cuij2(:iim, 1) = radclatm * xprimp025(:iim)
214	cuij3(:iim, 1) = radclatm * xprimm025(:iim)
215	cuij4(:iim, 1) = 0.
216
217	cvij1(:iim, 1) = 0.
218	cvij2(:iim, 1) = 0.5 * rad * yprimu1(1)
219	cvij3(:iim, 1) = cvij2(:iim, 1)
220	cvij4(:iim, 1) = 0.
221
222	do j = 2, jjm
223	coslatm = cos(rlatu1(j))
224	coslatp = cos(rlatu2(j-1))
225	radclatp = 0.5 * rad * coslatp
226	radclatm = 0.5 * rad * coslatm
227	ai14 = un4rad2 * coslatp * yprimu2(j-1)
228	ai23 = un4rad2 * coslatm * yprimu1(j)
229
230	aireij1_2d(:iim, j) = ai14 * xprimp025(:iim)
231	aireij2_2d(:iim, j) = ai23 * xprimp025(:iim)
232	aireij3_2d(:iim, j) = ai23 * xprimm025(:iim)
233	aireij4_2d(:iim, j) = ai14 * xprimm025(:iim)
234	cuij1(:iim, j) = radclatp * xprimp025(:iim)
235	cuij2(:iim, j) = radclatm * xprimp025(:iim)
236	cuij3(:iim, j) = radclatm * xprimm025(:iim)
237	cuij4(:iim, j) = radclatp * xprimm025(:iim)
238	cvij1(:iim, j) = 0.5 * rad * yprimu2(j-1)
239	cvij2(:iim, j) = 0.5 * rad * yprimu1(j)
240	cvij3(:iim, j) = cvij2(:iim, j)
241	cvij4(:iim, j) = cvij1(:iim, j)
242	end do
243
244	coslatp = cos(rlatu2(jjm))
245	radclatp = 0.5 * rad * coslatp
246
247	aireij1_2d(:iim, jjp1) = un4rad2 * coslatp * xprimp025(:iim) * yprimu2(jjm)
248	aireij2_2d(:iim, jjp1) = 0.
249	aireij3_2d(:iim, jjp1) = 0.
250	aireij4_2d(:iim, jjp1) = un4rad2 * coslatp * xprimm025(:iim) * yprimu2(jjm)
251
252	cuij1(:iim, jjp1) = radclatp * xprimp025(:iim)
253	cuij2(:iim, jjp1) = 0.
254	cuij3(:iim, jjp1) = 0.
255	cuij4(:iim, jjp1) = radclatp * xprimm025(:iim)
256
257	cvij1(:iim, jjp1) = 0.5 * rad * yprimu2(jjm)
258	cvij2(:iim, jjp1) = 0.
259	cvij3(:iim, jjp1) = 0.
260	cvij4(:iim, jjp1) = cvij1(:iim, jjp1)
261
262	! Périodicité :
263
264	cvij1(iip1, :) = cvij1(1, :)
265	cvij2(iip1, :) = cvij2(1, :)
266	cvij3(iip1, :) = cvij3(1, :)
267	cvij4(iip1, :) = cvij4(1, :)
268
269	cuij1(iip1, :) = cuij1(1, :)
270	cuij2(iip1, :) = cuij2(1, :)
271	cuij3(iip1, :) = cuij3(1, :)
272	cuij4(iip1, :) = cuij4(1, :)
273
274	aireij1_2d(iip1, :) = aireij1_2d(1, :)
275	aireij2_2d(iip1, :) = aireij2_2d(1, :)
276	aireij3_2d(iip1, :) = aireij3_2d(1, :)
277	aireij4_2d(iip1, :) = aireij4_2d(1, :)
278
279	DO j = 1, jjp1
280	DO i = 1, iim
281	aire_2d(i, j) = aireij1_2d(i, j) + aireij2_2d(i, j) &
282	+ aireij3_2d(i, j) + aireij4_2d(i, j)
283	alpha1_2d(i, j) = aireij1_2d(i, j) / aire_2d(i, j)
284	alpha2_2d(i, j) = aireij2_2d(i, j) / aire_2d(i, j)
285	alpha3_2d(i, j) = aireij3_2d(i, j) / aire_2d(i, j)
286	alpha4_2d(i, j) = aireij4_2d(i, j) / aire_2d(i, j)
287	alpha1p2_2d(i, j) = alpha1_2d(i, j) + alpha2_2d(i, j)
288	alpha1p4_2d(i, j) = alpha1_2d(i, j) + alpha4_2d(i, j)
289	alpha2p3_2d(i, j) = alpha2_2d(i, j) + alpha3_2d(i, j)
290	alpha3p4_2d(i, j) = alpha3_2d(i, j) + alpha4_2d(i, j)
291	END DO
292
293	aire_2d(iip1, j) = aire_2d(1, j)
294	alpha1_2d(iip1, j) = alpha1_2d(1, j)
295	alpha2_2d(iip1, j) = alpha2_2d(1, j)
296	alpha3_2d(iip1, j) = alpha3_2d(1, j)
297	alpha4_2d(iip1, j) = alpha4_2d(1, j)
298	alpha1p2_2d(iip1, j) = alpha1p2_2d(1, j)
299	alpha1p4_2d(iip1, j) = alpha1p4_2d(1, j)
300	alpha2p3_2d(iip1, j) = alpha2p3_2d(1, j)
301	alpha3p4_2d(iip1, j) = alpha3p4_2d(1, j)
302	END DO
303
304	DO j = 1, jjp1
305	DO i = 1, iim
306	aireu_2d(i, j) = aireij1_2d(i, j) + aireij2_2d(i, j) + &
307	aireij4_2d(i + 1, j) + aireij3_2d(i + 1, j)
308	unsaire_2d(i, j) = 1. / aire_2d(i, j)
309	unsair_gam1_2d(i, j) = unsaire_2d(i, j)**(-gamdi_gdiv)
310	unsair_gam2_2d(i, j) = unsaire_2d(i, j)**(-gamdi_h)
311	airesurg_2d(i, j) = aire_2d(i, j) / g
312	END DO
313	aireu_2d(iip1, j) = aireu_2d(1, j)
314	unsaire_2d(iip1, j) = unsaire_2d(1, j)
315	unsair_gam1_2d(iip1, j) = unsair_gam1_2d(1, j)
316	unsair_gam2_2d(iip1, j) = unsair_gam2_2d(1, j)
317	airesurg_2d(iip1, j) = airesurg_2d(1, j)
318	END DO
319
320	DO j = 1, jjm
321	DO i = 1, iim
322	airev_2d(i, j) = aireij2_2d(i, j) + aireij3_2d(i, j) + &
323	aireij1_2d(i, j + 1) + aireij4_2d(i, j + 1)
324	END DO
325	DO i = 1, iim
326	airez = aireij2_2d(i, j) + aireij1_2d(i, j + 1) &
327	+ aireij3_2d(i + 1, j) + aireij4_2d(i + 1, j + 1)
328	unsairez_2d(i, j) = 1. / airez
329	unsairz_gam_2d(i, j) = unsairez_2d(i, j)**(-gamdi_grot)
330	fext_2d(i, j) = airez * sin(rlatv(j)) * 2. * omeg
331	END DO
332	airev_2d(iip1, j) = airev_2d(1, j)
333	unsairez_2d(iip1, j) = unsairez_2d(1, j)
334	fext_2d(iip1, j) = fext_2d(1, j)
335	unsairz_gam_2d(iip1, j) = unsairz_gam_2d(1, j)
336	END DO
337
338	! Calcul des élongations cu_2d, cv_2d, cvu
339
340	DO j = 1, jjm
341	DO i = 1, iim
342	cv_2d(i, j) = 0.5 * &
343	(cvij2(i, j) + cvij3(i, j) + cvij1(i, j + 1) + cvij4(i, j + 1))
344	cvu(i, j) = 0.5 * (cvij1(i, j) + cvij4(i, j) + cvij2(i, j) &
345	+ cvij3(i, j))
346	cuv(i, j) = 0.5 * (cuij2(i, j) + cuij3(i, j) + cuij1(i, j + 1) &
347	+ cuij4(i, j + 1))
348	unscv2_2d(i, j) = 1. / cv_2d(i, j)**2
349	END DO
350	DO i = 1, iim
351	cuvsurcv_2d(i, j) = airev_2d(i, j) * unscv2_2d(i, j)
352	cvsurcuv_2d(i, j) = 1. / cuvsurcv_2d(i, j)
353	cuvscvgam1_2d(i, j) = cuvsurcv_2d(i, j)**(-gamdi_gdiv)
354	cuvscvgam2_2d(i, j) = cuvsurcv_2d(i, j)**(-gamdi_h)
355	cvscuvgam_2d(i, j) = cvsurcuv_2d(i, j)**(-gamdi_grot)
356	END DO
357	cv_2d(iip1, j) = cv_2d(1, j)
358	cvu(iip1, j) = cvu(1, j)
359	unscv2_2d(iip1, j) = unscv2_2d(1, j)
360	cuv(iip1, j) = cuv(1, j)
361	cuvsurcv_2d(iip1, j) = cuvsurcv_2d(1, j)
362	cvsurcuv_2d(iip1, j) = cvsurcuv_2d(1, j)
363	cuvscvgam1_2d(iip1, j) = cuvscvgam1_2d(1, j)
364	cuvscvgam2_2d(iip1, j) = cuvscvgam2_2d(1, j)
365	cvscuvgam_2d(iip1, j) = cvscuvgam_2d(1, j)
366	END DO
367
368	DO j = 2, jjm
369	DO i = 1, iim
370	cu_2d(i, j) = 0.5 * (cuij1(i, j) + cuij4(i + 1, j) + cuij2(i, j) &
371	+ cuij3(i + 1, j))
372	unscu2_2d(i, j) = 1. / cu_2d(i, j)**2
373	cvusurcu_2d(i, j) = aireu_2d(i, j) * unscu2_2d(i, j)
374	cusurcvu_2d(i, j) = 1. / cvusurcu_2d(i, j)
375	cvuscugam1_2d(i, j) = cvusurcu_2d(i, j)**(-gamdi_gdiv)
376	cvuscugam2_2d(i, j) = cvusurcu_2d(i, j)**(-gamdi_h)
377	cuscvugam_2d(i, j) = cusurcvu_2d(i, j)**(-gamdi_grot)
378	END DO
379	cu_2d(iip1, j) = cu_2d(1, j)
380	unscu2_2d(iip1, j) = unscu2_2d(1, j)
381	cvusurcu_2d(iip1, j) = cvusurcu_2d(1, j)
382	cusurcvu_2d(iip1, j) = cusurcvu_2d(1, j)
383	cvuscugam1_2d(iip1, j) = cvuscugam1_2d(1, j)
384	cvuscugam2_2d(iip1, j) = cvuscugam2_2d(1, j)
385	cuscvugam_2d(iip1, j) = cuscvugam_2d(1, j)
386	END DO
387
388	! Calcul aux pôles
389
390	cu_2d(:, 1) = 0.
391	unscu2_2d(:, 1) = 0.
392	cvu(:, 1) = 0.
393
394	cu_2d(:, jjp1) = 0.
395	unscu2_2d(:, jjp1) = 0.
396	cvu(:, jjp1) = 0.
397
398	DO j = 1, jjm
399	DO i = 1, iim
400	airvscu2_2d(i, j) = airev_2d(i, j) / (cuv(i, j) * cuv(i, j))
401	aivscu2gam_2d(i, j) = airvscu2_2d(i, j)**(-gamdi_grot)
402	END DO
403	airvscu2_2d(iip1, j) = airvscu2_2d(1, j)
404	aivscu2gam_2d(iip1, j) = aivscu2gam_2d(1, j)
405	END DO
406
407	DO j = 2, jjm
408	DO i = 1, iim
409	airuscv2_2d(i, j) = aireu_2d(i, j) / (cvu(i, j) * cvu(i, j))
410	aiuscv2gam_2d(i, j) = airuscv2_2d(i, j)**(-gamdi_grot)
411	END DO
412	airuscv2_2d(iip1, j) = airuscv2_2d(1, j)
413	aiuscv2gam_2d(iip1, j) = aiuscv2gam_2d(1, j)
414	END DO
415
416	! Calcul des aires aux pôles :
417
418	apoln = sum(aire_2d(:iim, 1))
419	apols = sum(aire_2d(:iim, jjp1))
420	unsapolnga1 = 1. / (apoln**(-gamdi_gdiv))
421	unsapolsga1 = 1. / (apols**(-gamdi_gdiv))
422	unsapolnga2 = 1. / (apoln**(-gamdi_h))
423	unsapolsga2 = 1. / (apols**(-gamdi_h))
424
425	! Changement F. Hourdin calcul conservatif pour fext_2d
426	! constang_2d contient le produit a * cos (latitude) * omega
427
428	DO i = 1, iim
429	constang_2d(i, 1) = 0.
430	END DO
431	DO j = 1, jjm - 1
432	DO i = 1, iim
433	constang_2d(i, j + 1) = rad * omeg * cu_2d(i, j + 1) &
434	* cos(rlatu(j + 1))
435	END DO
436	END DO
437	DO i = 1, iim
438	constang_2d(i, jjp1) = 0.
439	END DO
440
441	! Périodicité en longitude
442	DO j = 1, jjp1
443	constang_2d(iip1, j) = constang_2d(1, j)
444	END DO
445
446	call new_unit(unit)
447	open(unit, file="longitude_latitude.txt", status="replace", action="write")
448	write(unit, fmt=) '"longitudes at V points (degrees)"', rlonv 180. / pi
449	write(unit, fmt=) '"latitudes at V points (degrees)"', rlatv 180. / pi
450	write(unit, fmt=) '"longitudes at U points (degrees)"', rlonu 180. / pi
451	write(unit, fmt=) '"latitudes at U points (degrees)"', rlatu 180. / pi
452	close(unit)
453
454	END SUBROUTINE inigeom
455
456	end module comgeom