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! Author: P. Le Van, from formulas by R. Sadourny |
! Author: P. Le Van, from formulas by R. Sadourny |
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! Calcule les longitudes et dérivées dans la grille du GCM pour |
! Calcule les longitudes et dérivées dans la grille du GCM pour |
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! une fonction f(x) à dérivée tangente hyperbolique. |
! une fonction x_f(\tilde x) à dérivée tangente hyperbolique. |
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! Il vaut mieux avoir : grossismx \times dzoom < pi |
! Il vaut mieux avoir : grossismx \times delta < pi |
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! Le premier point scalaire pour une grille regulière (grossismx = |
! Le premier point scalaire pour une grille regulière (grossismx = |
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! 1., taux=0., clon=0.) est à - 180 degrés. |
! 1) avec clon = 0 est à - 180 degrés. |
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USE dimens_m, ONLY: iim |
USE dimens_m, ONLY: iim |
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use fxhyp_loop_ik_m, only: fxhyp_loop_ik, nmax |
use dynetat0_m, only: clon, grossismx, dzoomx, taux |
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use invert_zoom_x_m, only: invert_zoom_x, nmax |
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use nr_util, only: pi, pi_d, twopi, twopi_d, arth |
use nr_util, only: pi, pi_d, twopi, twopi_d, arth |
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use principal_cshift_m, only: principal_cshift |
use principal_cshift_m, only: principal_cshift |
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use serre, only: clon, grossismx, dzoomx, taux |
use tanh_cautious_m, only: tanh_cautious |
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REAL, intent(out):: xprimm025(:), rlonv(:), xprimv(:) ! (iim + 1) |
REAL, intent(out):: xprimm025(:) ! (iim + 1) |
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real, intent(out):: rlonu(:), xprimu(:), xprimp025(:) ! (iim + 1) |
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REAL, intent(out):: rlonv(:) ! (iim + 1) |
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! longitudes of points of the "scalar" and "v" grid, in rad |
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REAL, intent(out):: xprimv(:) ! (iim + 1) |
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! 2 pi / iim * (derivative of the longitudinal zoom function)(rlonv) |
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real, intent(out):: rlonu(:) ! (iim + 1) |
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! longitudes of points of the "u" grid, in rad |
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real, intent(out):: xprimu(:) ! (iim + 1) |
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! 2 pi / iim * (derivative of the longitudinal zoom function)(rlonu) |
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real, intent(out):: xprimp025(:) ! (iim + 1) |
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! Local: |
! Local: |
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real rlonm025(iim + 1), rlonp025(iim + 1) |
real rlonm025(iim + 1), rlonp025(iim + 1), d_rlonv(iim) |
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REAL dzoom, step |
REAL delta, h |
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real d_rlonv(iim) |
DOUBLE PRECISION, dimension(0:nmax):: xtild, fhyp, G, Xf, ffdx |
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DOUBLE PRECISION xtild(0:2 * nmax) |
DOUBLE PRECISION beta |
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DOUBLE PRECISION fhyp(nmax:2 * nmax), ffdx, beta, Xprimt(0:2 * nmax) |
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DOUBLE PRECISION Xf(0:2 * nmax), xxpr(2 * nmax) |
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DOUBLE PRECISION fa, fb |
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INTEGER i, is2 |
INTEGER i, is2 |
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DOUBLE PRECISION xmoy, fxm |
DOUBLE PRECISION xmoy(nmax), fxm(nmax) |
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!---------------------------------------------------------------------- |
!---------------------------------------------------------------------- |
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print *, "Call sequence information: fxhyp" |
print *, "Call sequence information: fxhyp" |
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test_grossismx: if (grossismx == 1.) then |
if (grossismx == 1.) then |
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step = twopi / iim |
h = twopi / iim |
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xprimm025(:iim) = step |
xprimm025(:iim) = h |
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xprimp025(:iim) = step |
xprimp025(:iim) = h |
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xprimv(:iim) = step |
xprimv(:iim) = h |
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xprimu(:iim) = step |
xprimu(:iim) = h |
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rlonv(:iim) = arth(- pi + clon, step, iim) |
rlonv(:iim) = arth(- pi + clon, h, iim) |
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rlonm025(:iim) = rlonv(:iim) - 0.25 * step |
rlonm025(:iim) = rlonv(:iim) - 0.25 * h |
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rlonp025(:iim) = rlonv(:iim) + 0.25 * step |
rlonp025(:iim) = rlonv(:iim) + 0.25 * h |
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rlonu(:iim) = rlonv(:iim) + 0.5 * step |
rlonu(:iim) = rlonv(:iim) + 0.5 * h |
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else |
else |
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dzoom = dzoomx * twopi_d |
delta = dzoomx * twopi_d |
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xtild = arth(- pi_d, pi_d / nmax, 2 * nmax + 1) |
xtild = arth(0d0, pi_d / nmax, nmax + 1) |
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forall (i = 1:nmax) xmoy(i) = 0.5d0 * (xtild(i-1) + xtild(i)) |
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! Compute fhyp: |
! Compute fhyp: |
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DO i = nmax, 2 * nmax |
fhyp(1:nmax - 1) = tanh_cautious(taux * (delta / 2d0 & |
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fa = taux * (dzoom / 2. - xtild(i)) |
- xtild(1:nmax - 1)), xtild(1:nmax - 1) & |
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fb = xtild(i) * (pi_d - xtild(i)) |
* (pi_d - xtild(1:nmax - 1))) |
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fhyp(0) = 1d0 |
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IF (200. * fb < - fa) THEN |
fhyp(nmax) = -1d0 |
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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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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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! Calcul de beta |
fxm = tanh_cautious(taux * (delta / 2d0 - xmoy), xmoy * (pi_d - xmoy)) |
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ffdx = 0. |
! Compute \int_0 ^{\tilde x} F: |
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DO i = nmax + 1, 2 * nmax |
ffdx(0) = 0d0 |
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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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IF (xmoy == 0.) fxm = 1. |
DO i = 1, nmax |
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IF (xmoy == pi_d) fxm = -1. |
ffdx(i) = ffdx(i - 1) + fxm(i) * (xtild(i) - xtild(i-1)) |
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ffdx = ffdx + fxm * (xtild(i) - xtild(i-1)) |
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END DO |
END DO |
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print *, "ffdx = ", ffdx |
print *, "ffdx(nmax) = ", ffdx(nmax) |
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beta = (grossismx * ffdx - pi_d) / (ffdx - pi_d) |
beta = (pi_d - grossismx * ffdx(nmax)) / (pi_d - ffdx(nmax)) |
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print *, "beta = ", beta |
print *, "beta = ", beta |
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IF (2. * beta - grossismx <= 0.) THEN |
IF (2d0 * beta - grossismx <= 0d0) THEN |
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print *, 'Bad choice of grossismx, taux, dzoomx.' |
print *, 'Bad choice of grossismx, taux, dzoomx.' |
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print *, 'Decrease dzoomx or grossismx.' |
print *, 'Decrease dzoomx or grossismx.' |
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STOP 1 |
STOP 1 |
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END IF |
END IF |
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! calcul de Xprimt |
G = beta + (grossismx - beta) * fhyp |
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Xprimt(nmax:2 * nmax) = beta + (grossismx - beta) * fhyp |
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xprimt(:nmax - 1) = xprimt(2 * nmax:nmax + 1:- 1) |
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! Calcul de Xf |
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DO i = nmax + 1, 2 * nmax |
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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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fxm = TANH(fa / fb) |
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END IF |
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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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xxpr(:nmax) = xxpr(2 * nmax:nmax + 1:- 1) |
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Xf(0) = - pi_d |
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DO i=1, 2 * nmax - 1 |
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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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Xf(2 * nmax) = pi_d |
Xf(:nmax - 1) = beta * xtild(:nmax - 1) + (grossismx - beta) & |
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* ffdx(:nmax - 1) |
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Xf(nmax) = pi_d |
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call fxhyp_loop_ik(xf, xtild, Xprimt, rlonm025(:iim), xprimm025(:iim), & |
call invert_zoom_x(beta, xf, xtild, G, rlonm025(:iim), xprimm025(:iim), & |
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xuv = - 0.25d0) |
xuv = - 0.25d0) |
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call fxhyp_loop_ik(xf, xtild, Xprimt, rlonv(:iim), xprimv(:iim), & |
call invert_zoom_x(beta, xf, xtild, G, rlonv(:iim), xprimv(:iim), & |
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xuv = 0d0) |
xuv = 0d0) |
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call fxhyp_loop_ik(xf, xtild, Xprimt, rlonu(:iim), xprimu(:iim), & |
call invert_zoom_x(beta, xf, xtild, G, rlonu(:iim), xprimu(:iim), & |
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xuv = 0.5d0) |
xuv = 0.5d0) |
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call fxhyp_loop_ik(xf, xtild, Xprimt, rlonp025(:iim), xprimp025(:iim), & |
call invert_zoom_x(beta, xf, xtild, G, rlonp025(:iim), xprimp025(:iim), & |
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xuv = 0.25d0) |
xuv = 0.25d0) |
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end if test_grossismx |
end if |
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is2 = 0 |
is2 = 0 |
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print *, "Minimum longitude step:", MINval(d_rlonv) * 180. / pi, "degrees" |
print *, "Minimum longitude step:", MINval(d_rlonv) * 180. / pi, "degrees" |
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print *, "Maximum longitude step:", MAXval(d_rlonv) * 180. / pi, "degrees" |
print *, "Maximum longitude step:", MAXval(d_rlonv) * 180. / pi, "degrees" |
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! Check that rlonm025 <= rlonv <= rlonp025 <= rlonu: |
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DO i = 1, iim + 1 |
DO i = 1, iim + 1 |
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IF (rlonp025(i) < rlonv(i)) THEN |
IF (rlonp025(i) < rlonv(i)) THEN |
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print *, 'rlonp025(', i, ') = ', rlonp025(i) |
print *, 'rlonp025(', i, ') = ', rlonp025(i) |