fxhyp_m.F90

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module fxhyp_m

  IMPLICIT NONE

contains

  SUBROUTINE fxhyp(xprimm025, rlonv, xprimv, rlonu, xprimu, xprimp025)

    ! From LMDZ4/libf/dyn3d/fxhyp.F, version 1.2, 2005/06/03 09:11:32
    ! Author: P. Le Van, from formulas by R. Sadourny

    ! Calcule les longitudes et dérivées dans la grille du GCM pour
    ! une fonction f(x) à dérivée tangente hyperbolique.

    ! Il vaut mieux avoir : grossismx \times dzoom < pi

    ! Le premier point scalaire pour une grille regulière (grossismx =
    ! 1., taux=0., clon=0.) est à - 180 degrés.

    use arth_m, only: arth
    use invert_zoom_x_m, only: invert_zoom_x, nmax
    use nrtype, only: pi, pi_d, twopi, twopi_d, k8
    use principal_cshift_m, only: principal_cshift

    include "dimensions.h"
    ! for iim

    include "serre.h"
    ! for clon, grossismx, dzoomx, taux

    REAL, intent(out):: xprimm025(:), rlonv(:), xprimv(:) ! (iim + 1)
    real, intent(out):: rlonu(:), xprimu(:), xprimp025(:) ! (iim + 1)

    ! Local:
    real rlonm025(iim + 1), rlonp025(iim + 1)
    REAL dzoom, step
    real d_rlonv(iim)
    REAL(K8) xtild(0:2 * nmax)
    REAL(K8) fhyp(nmax:2 * nmax), ffdx, beta, Xprimt(0:2 * nmax)
    REAL(K8) Xf(0:2 * nmax), xxpr(2 * nmax)
    REAL(K8) fa, fb
    INTEGER i, is2
    REAL(K8) xmoy, fxm

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

    print *, "Call sequence information: fxhyp"

    test_iim: if (iim==1) then
       rlonv(1)=0.
       rlonu(1)=pi
       rlonv(2)=rlonv(1)+twopi
       rlonu(2)=rlonu(1)+twopi

       xprimm025(:)=1.
       xprimv(:)=1.
       xprimu(:)=1.
       xprimp025(:)=1.
    else test_iim
       test_grossismx: if (grossismx == 1.) then
          step = twopi / iim

          xprimm025(:iim) = step
          xprimp025(:iim) = step
          xprimv(:iim) = step
          xprimu(:iim) = step

          rlonv(:iim) = arth(- pi + clon / 180. * pi, step, iim)
          rlonm025(:iim) = rlonv(:iim) - 0.25 * step
          rlonp025(:iim) = rlonv(:iim) + 0.25 * step
          rlonu(:iim) = rlonv(:iim) + 0.5 * step
       else test_grossismx
          dzoom = dzoomx * twopi_d
          xtild = arth(- pi_d, pi_d / nmax, 2 * nmax + 1)

          ! Compute fhyp:
          DO i = nmax, 2 * nmax
             fa = taux * (dzoom / 2. - xtild(i))
             fb = xtild(i) * (pi_d - xtild(i))

             IF (200. * fb < - fa) THEN
                fhyp(i) = - 1.
             ELSE IF (200. * fb < fa) THEN
                fhyp(i) = 1.
             ELSE
                IF (abs(fa) < 1e-13 .AND. abs(fb) < 1e-13) THEN
                   IF (200. * fb + fa < 1e-10) THEN
                      fhyp(i) = - 1.
                   ELSE IF (200. * fb - fa < 1e-10) THEN
                      fhyp(i) = 1.
                   END IF
                ELSE
                   fhyp(i) = tanh(fa / fb)
                END IF
             END IF

             IF (xtild(i) == 0.) fhyp(i) = 1.
             IF (xtild(i) == pi_d) fhyp(i) = -1.
          END DO

          ! Calcul de beta 

          ffdx = 0.

          DO i = nmax + 1, 2 * nmax
             xmoy = 0.5 * (xtild(i-1) + xtild(i))
             fa = taux * (dzoom / 2. - xmoy)
             fb = xmoy * (pi_d - xmoy)

             IF (200. * fb < - fa) THEN
                fxm = - 1.
             ELSE IF (200. * fb < fa) THEN
                fxm = 1.
             ELSE
                IF (abs(fa) < 1e-13 .AND. abs(fb) < 1e-13) THEN
                   IF (200. * fb + fa < 1e-10) THEN
                      fxm = - 1.
                   ELSE IF (200. * fb - fa < 1e-10) THEN
                      fxm = 1.
                   END IF
                ELSE
                   fxm = tanh(fa / fb)
                END IF
             END IF

             IF (xmoy == 0.) fxm = 1.
             IF (xmoy == pi_d) fxm = -1.

             ffdx = ffdx + fxm * (xtild(i) - xtild(i-1))
          END DO

          print *, "ffdx = ", ffdx
          beta = (grossismx * ffdx - pi_d) / (ffdx - pi_d)
          print *, "beta = ", beta

          IF (2. * beta - grossismx <= 0.) THEN
             print *, 'Bad choice of grossismx, taux, dzoomx.'
             print *, 'Decrease dzoomx or grossismx.'
             stop 1
          END IF

          ! calcul de Xprimt 
          xprimt(nmax:2 * nmax) = beta + (grossismx - beta) * fhyp
          xprimt(:nmax - 1) = xprimt(2 * nmax:nmax + 1:- 1)

          ! Calcul de Xf

          DO i = nmax + 1, 2 * nmax
             xmoy = 0.5 * (xtild(i-1) + xtild(i))
             fa = taux * (dzoom / 2. - xmoy)
             fb = xmoy * (pi_d - xmoy)

             IF (200. * fb < - fa) THEN
                fxm = - 1.
             ELSE IF (200. * fb < fa) THEN
                fxm = 1.
             ELSE
                fxm = tanh(fa / fb)
             END IF

             IF (xmoy == 0.) fxm = 1.
             IF (xmoy == pi_d) fxm = -1.
             xxpr(i) = beta + (grossismx - beta) * fxm
          END DO

          xxpr(:nmax) = xxpr(2 * nmax:nmax + 1:- 1)

          xf(0) = - pi_d

          DO i=1, 2 * nmax - 1
             xf(i) = xf(i-1) + xxpr(i) * (xtild(i) - xtild(i-1))
          END DO

          xf(2 * nmax) = pi_d

          call invert_zoom_x(xf, xtild, xprimt, rlonm025(:iim), &
               xprimm025(:iim), xuv = - 0.25_k8)
          call invert_zoom_x(xf, xtild, xprimt, rlonv(:iim), xprimv(:iim), &
               xuv = 0._k8)
          call invert_zoom_x(xf, xtild, xprimt, rlonu(:iim), xprimu(:iim), &
               xuv = 0.5_k8)
          call invert_zoom_x(xf, xtild, xprimt, rlonp025(:iim), &
               xprimp025(:iim), xuv = 0.25_k8)
       end if test_grossismx

       is2 = 0

       IF (minval(rlonm025(:iim)) < - pi - 0.1 &
            .or. maxval(rlonm025(:iim)) > pi + 0.1) THEN
          IF (clon <= 0.) THEN
             is2 = 1

             do while (rlonm025(is2) < - pi .and. is2 < iim)
                is2 = is2 + 1
             end do

             if (rlonm025(is2) < - pi) then
                print *, 'Rlonm025 plus petit que - pi !'
                stop 1
             end if
          ELSE
             is2 = iim

             do while (rlonm025(is2) > pi .and. is2 > 1)
                is2 = is2 - 1
             end do

             if (rlonm025(is2) > pi) then
                print *, 'Rlonm025 plus grand que pi !'
                stop 1
             end if
          END IF
       END IF

       call principal_cshift(is2, rlonm025, xprimm025)
       call principal_cshift(is2, rlonv, xprimv)
       call principal_cshift(is2, rlonu, xprimu)
       call principal_cshift(is2, rlonp025, xprimp025)

       forall (i = 1: iim) d_rlonv(i) = rlonv(i + 1) - rlonv(i)
       print *, "Minimum longitude step:", minval(d_rlonv) * 180. / pi, &
            "degrees"
       print *, "Maximum longitude step:", maxval(d_rlonv) * 180. / pi, &
            "degrees"

       ! Check that rlonm025 <= rlonv <= rlonp025 <= rlonu:
       DO i = 1, iim + 1
          IF (rlonp025(i) < rlonv(i)) THEN
             print *, 'rlonp025(', i, ') = ', rlonp025(i)
             print *, "< rlonv(", i, ") = ", rlonv(i)
             stop 1
          END IF

          IF (rlonv(i) < rlonm025(i)) THEN 
             print *, 'rlonv(', i, ') = ', rlonv(i)
             print *, "< rlonm025(", i, ") = ", rlonm025(i)
             stop 1
          END IF

          IF (rlonp025(i) > rlonu(i)) THEN
             print *, 'rlonp025(', i, ') = ', rlonp025(i)
             print *, "> rlonu(", i, ") = ", rlonu(i)
             stop 1
          END IF
       END DO
    end if test_iim

  END SUBROUTINE fxhyp

end module fxhyp_m