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module fxhyp_m |
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IMPLICIT NONE |
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|
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contains |
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SUBROUTINE fxhyp(xprimm025, rlonv, xprimv, rlonu, xprimu, xprimp025) |
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! From LMDZ4/libf/dyn3d/fxhyp.F, version 1.2, 2005/06/03 09:11:32 |
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! Author: P. Le Van, from formulas by R. Sadourny |
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|
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! Calcule les longitudes et dérivées dans la grille du GCM pour |
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! une fonction f(x) à dérivée tangente hyperbolique. |
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|
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! On doit avoir grossismx \times dzoomx < pi (radians) |
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|
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USE dimens_m, ONLY: iim |
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use nr_util, only: pi_d, twopi_d |
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use serre, only: clon, grossismx, dzoomx, taux |
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|
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REAL, intent(out):: xprimm025(:), rlonv(:), xprimv(:) ! (iim + 1) |
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real, intent(out):: rlonu(:), xprimu(:), xprimp025(:) ! (iim + 1) |
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|
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! Local: |
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|
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DOUBLE PRECISION champmin, champmax |
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real rlonm025(iim + 1), rlonp025(iim + 1) |
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INTEGER, PARAMETER:: nmax = 30000, nmax2 = 2*nmax |
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|
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LOGICAL, PARAMETER:: scal180 = .TRUE. |
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! scal180 = .TRUE. si on veut avoir le premier point scalaire pour |
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! une grille reguliere (grossismx = 1., taux=0., clon=0.) a |
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! -180. degres. sinon scal180 = .FALSE. |
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|
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REAL dzoom |
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DOUBLE PRECISION xlon(iim + 1), xprimm(iim + 1), xuv |
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DOUBLE PRECISION xtild(0:nmax2) |
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DOUBLE PRECISION fhyp(0:nmax2), ffdx, beta, Xprimt(0:nmax2) |
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DOUBLE PRECISION Xf(0:nmax2), xxpr(0:nmax2) |
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DOUBLE PRECISION xvrai(iim + 1), xxprim(iim + 1) |
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DOUBLE PRECISION my_eps, xzoom, fa, fb |
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DOUBLE PRECISION Xf1, Xfi, a0, a1, a2, a3, xi2 |
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INTEGER i, it, ik, iter, ii, idif, ii1, ii2 |
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DOUBLE PRECISION xi, xo1, xmoy, xlon2, fxm, Xprimin |
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DOUBLE PRECISION decalx |
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INTEGER, save:: is2 |
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|
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!---------------------------------------------------------------------- |
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|
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my_eps = 1e-3 |
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xzoom = clon * pi_d / 180. |
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|
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IF (grossismx == 1. .AND. scal180) THEN |
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decalx = 1. |
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else |
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decalx = 0.75 |
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END IF |
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|
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IF (dzoomx < 1.) THEN |
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dzoom = dzoomx * twopi_d |
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ELSE IF (dzoomx < 25.) THEN |
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print *, "Le paramètre dzoomx pour fxhyp est trop petit. " & |
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// "L'augmenter et relancer." |
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STOP 1 |
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ELSE |
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dzoom = dzoomx * pi_d / 180. |
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END IF |
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|
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print *, 'dzoom (rad):', dzoom |
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|
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DO i = 0, nmax2 |
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xtild(i) = - pi_d + REAL(i) * twopi_d / nmax2 |
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END DO |
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|
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DO i = nmax, nmax2 |
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fa = taux* (dzoom / 2. - xtild(i)) |
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fb = xtild(i) * (pi_d - xtild(i)) |
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|
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IF (200.* fb < - fa) THEN |
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fhyp(i) = - 1. |
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ELSE IF (200. * fb < fa) THEN |
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fhyp(i) = 1. |
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ELSE |
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IF (ABS(fa) < 1e-13.AND.ABS(fb) < 1e-13) THEN |
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IF (200.*fb + fa < 1e-10) THEN |
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fhyp(i) = - 1. |
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ELSE IF (200.*fb - fa < 1e-10) THEN |
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fhyp(i) = 1. |
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END IF |
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ELSE |
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fhyp(i) = TANH(fa / fb) |
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END IF |
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END IF |
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|
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IF (xtild(i) == 0.) fhyp(i) = 1. |
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IF (xtild(i) == pi_d) fhyp(i) = -1. |
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END DO |
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|
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! Calcul de beta |
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|
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ffdx = 0. |
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|
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DO i = nmax + 1, nmax2 |
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xmoy = 0.5 * (xtild(i-1) + xtild(i)) |
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fa = taux* (dzoom / 2. - xmoy) |
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fb = xmoy * (pi_d - xmoy) |
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IF (200.* fb < - fa) THEN |
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fxm = - 1. |
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ELSE IF (200. * fb < fa) THEN |
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fxm = 1. |
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ELSE |
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IF (ABS(fa) < 1e-13.AND.ABS(fb) < 1e-13) THEN |
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IF (200.*fb + fa < 1e-10) THEN |
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fxm = - 1. |
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ELSE IF (200.*fb - fa < 1e-10) THEN |
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fxm = 1. |
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END IF |
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ELSE |
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fxm = TANH(fa / fb) |
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END IF |
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END IF |
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|
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IF (xmoy == 0.) fxm = 1. |
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IF (xmoy == pi_d) fxm = -1. |
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ffdx = ffdx + fxm * (xtild(i) - xtild(i-1)) |
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END DO |
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beta = (grossismx * ffdx - pi_d) / (ffdx - pi_d) |
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|
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IF (2. * beta - grossismx <= 0.) THEN |
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print *, 'Attention ! La valeur beta calculée dans fxhyp est mauvaise.' |
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print *, 'Modifier les valeurs de grossismx, taux ou dzoomx et relancer.' |
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STOP 1 |
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END IF |
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|
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! calcul de Xprimt |
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|
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DO i = nmax, nmax2 |
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Xprimt(i) = beta + (grossismx - beta) * fhyp(i) |
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END DO |
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|
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DO i = nmax + 1, nmax2 |
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Xprimt(nmax2 - i) = Xprimt(i) |
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END DO |
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|
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! Calcul de Xf |
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|
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Xf(0) = - pi_d |
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DO i = nmax + 1, nmax2 |
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xmoy = 0.5 * (xtild(i-1) + xtild(i)) |
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fa = taux* (dzoom / 2. - xmoy) |
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fb = xmoy * (pi_d - xmoy) |
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|
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IF (200.* fb < - fa) THEN |
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fxm = - 1. |
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ELSE IF (200. * fb < fa) THEN |
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fxm = 1. |
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ELSE |
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fxm = TANH(fa / fb) |
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END IF |
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|
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IF (xmoy == 0.) fxm = 1. |
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IF (xmoy == pi_d) fxm = -1. |
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xxpr(i) = beta + (grossismx - beta) * fxm |
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END DO |
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DO i = nmax + 1, nmax2 |
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xxpr(nmax2-i + 1) = xxpr(i) |
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END DO |
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DO i=1, nmax2 |
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Xf(i) = Xf(i-1) + xxpr(i) * (xtild(i) - xtild(i-1)) |
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END DO |
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|
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! xuv = 0. si calcul aux points scalaires |
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! xuv = 0.5 si calcul aux points U |
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|
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loop_ik: DO ik = 1, 4 |
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IF (ik == 1) THEN |
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xuv = -0.25 |
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ELSE IF (ik == 2) THEN |
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xuv = 0. |
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ELSE IF (ik == 3) THEN |
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xuv = 0.50 |
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ELSE IF (ik == 4) THEN |
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xuv = 0.25 |
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END IF |
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|
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xo1 = 0. |
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|
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ii1=1 |
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ii2=iim |
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IF (ik == 1.and.grossismx == 1.) THEN |
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ii1 = 2 |
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ii2 = iim + 1 |
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END IF |
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DO i = ii1, ii2 |
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xlon2 = - pi_d + (REAL(i) + xuv - decalx) * twopi_d / REAL(iim) |
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Xfi = xlon2 |
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|
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it = nmax2 |
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do while (xfi < xf(it) .and. it >= 1) |
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it = it - 1 |
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end do |
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! Calcul de Xf(xi) |
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|
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xi = xtild(it) |
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|
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IF (it == nmax2) THEN |
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it = nmax2 -1 |
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Xf(it + 1) = pi_d |
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END IF |
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|
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! Appel de la routine qui calcule les coefficients a0, a1, |
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! a2, a3 d'un polynome de degre 3 qui passe par les points |
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! (Xf(it), xtild(it)) et (Xf(it + 1), xtild(it + 1)) |
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|
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CALL coefpoly(Xf(it), Xf(it + 1), Xprimt(it), Xprimt(it + 1), & |
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xtild(it), xtild(it + 1), a0, a1, a2, a3) |
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Xf1 = Xf(it) |
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Xprimin = a1 + 2.* a2 * xi + 3.*a3 * xi *xi |
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|
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iter = 1 |
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|
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do |
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xi = xi - (Xf1 - Xfi) / Xprimin |
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IF (ABS(xi - xo1) <= my_eps .or. iter == 300) exit |
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xo1 = xi |
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xi2 = xi * xi |
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Xf1 = a0 + a1 * xi + a2 * xi2 + a3 * xi2 * xi |
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Xprimin = a1 + 2.* a2 * xi + 3.* a3 * xi2 |
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end DO |
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|
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if (ABS(xi - xo1) > my_eps) then |
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! iter == 300 |
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print *, 'Pas de solution.' |
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print *, i, xlon2 |
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STOP 1 |
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end if |
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|
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xxprim(i) = twopi_d / (REAL(iim) * Xprimin) |
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xvrai(i) = xi + xzoom |
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end DO |
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|
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IF (ik == 1 .and. grossismx == 1.) THEN |
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xvrai(1) = xvrai(iim + 1)-twopi_d |
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xxprim(1) = xxprim(iim + 1) |
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END IF |
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|
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DO i = 1, iim |
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xlon(i) = xvrai(i) |
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xprimm(i) = xxprim(i) |
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END DO |
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|
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DO i = 1, iim -1 |
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IF (xvrai(i + 1) < xvrai(i)) THEN |
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print *, 'Problème avec rlonu(', i + 1, & |
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') plus petit que rlonu(', i, ')' |
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STOP 1 |
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END IF |
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END DO |
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|
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! Réorganisation des longitudes pour les avoir entre - pi et pi |
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|
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champmin = 1e12 |
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champmax = -1e12 |
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DO i = 1, iim |
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champmin = MIN(champmin, xvrai(i)) |
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champmax = MAX(champmax, xvrai(i)) |
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END DO |
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|
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IF (.not. (champmin >= -pi_d - 0.1 .and. champmax <= pi_d + 0.1)) THEN |
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print *, 'Reorganisation des longitudes pour avoir entre - pi', & |
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' et pi ' |
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|
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IF (xzoom <= 0.) THEN |
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IF (ik == 1) THEN |
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i = 1 |
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|
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do while (xvrai(i) < - pi_d .and. i < iim) |
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i = i + 1 |
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end do |
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|
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if (xvrai(i) < - pi_d) then |
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print *, 'Xvrai plus petit que - pi !' |
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STOP 1 |
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end if |
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|
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is2 = i |
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END IF |
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|
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IF (is2.NE. 1) THEN |
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DO ii = is2, iim |
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xlon(ii-is2 + 1) = xvrai(ii) |
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xprimm(ii-is2 + 1) = xxprim(ii) |
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END DO |
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DO ii = 1, is2 -1 |
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xlon(ii + iim-is2 + 1) = xvrai(ii) + twopi_d |
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xprimm(ii + iim-is2 + 1) = xxprim(ii) |
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END DO |
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END IF |
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ELSE |
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IF (ik == 1) THEN |
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i = iim |
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|
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do while (xvrai(i) > pi_d .and. i > 1) |
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i = i - 1 |
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end do |
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|
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if (xvrai(i) > pi_d) then |
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print *, 'Xvrai plus grand que pi !' |
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STOP 1 |
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end if |
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|
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is2 = i |
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END IF |
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|
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idif = iim -is2 |
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|
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DO ii = 1, is2 |
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xlon(ii + idif) = xvrai(ii) |
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xprimm(ii + idif) = xxprim(ii) |
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END DO |
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|
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DO ii = 1, idif |
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xlon(ii) = xvrai(ii + is2) - twopi_d |
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xprimm(ii) = xxprim(ii + is2) |
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END DO |
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END IF |
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END IF |
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|
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! Fin de la reorganisation |
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|
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xlon(iim + 1) = xlon(1) + twopi_d |
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xprimm(iim + 1) = xprimm(1) |
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|
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DO i = 1, iim + 1 |
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xvrai(i) = xlon(i)*180. / pi_d |
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END DO |
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|
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IF (ik == 1) THEN |
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DO i = 1, iim + 1 |
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rlonm025(i) = xlon(i) |
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xprimm025(i) = xprimm(i) |
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END DO |
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ELSE IF (ik == 2) THEN |
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rlonv = xlon |
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xprimv = xprimm |
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ELSE IF (ik == 3) THEN |
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DO i = 1, iim + 1 |
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rlonu(i) = xlon(i) |
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xprimu(i) = xprimm(i) |
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END DO |
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ELSE IF (ik == 4) THEN |
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DO i = 1, iim + 1 |
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rlonp025(i) = xlon(i) |
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xprimp025(i) = xprimm(i) |
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END DO |
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END IF |
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end DO loop_ik |
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|
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print * |
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|
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DO i = 1, iim |
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xlon(i) = rlonv(i + 1) - rlonv(i) |
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END DO |
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champmin = 1e12 |
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champmax = -1e12 |
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DO i = 1, iim |
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champmin = MIN(champmin, xlon(i)) |
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champmax = MAX(champmax, xlon(i)) |
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END DO |
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champmin = champmin * 180. / pi_d |
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champmax = champmax * 180. / pi_d |
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|
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DO i = 1, iim + 1 |
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IF (rlonp025(i) < rlonv(i)) THEN |
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print *, ' Attention ! rlonp025 < rlonv', i |
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STOP 1 |
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END IF |
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|
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IF (rlonv(i) < rlonm025(i)) THEN |
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print *, ' Attention ! rlonm025 > rlonv', i |
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STOP 1 |
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END IF |
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|
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IF (rlonp025(i) > rlonu(i)) THEN |
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print *, ' Attention ! rlonp025 > rlonu', i |
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STOP 1 |
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END IF |
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END DO |
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|
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print *, ' Longitudes ' |
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print 3, champmin, champmax |
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|
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3 Format(1x, ' Au centre du zoom, la longueur de la maille est', & |
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' d environ ', f0.2, ' degres ', /, & |
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' alors que la maille en dehors de la zone du zoom est ', & |
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"d'environ", f0.2, ' degres ') |
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|
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END SUBROUTINE fxhyp |
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|
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end module fxhyp_m |
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