| 1 | module fyhyp_m |
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| 2 | |
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| 3 | IMPLICIT NONE |
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| 4 | |
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| 5 | contains |
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| 6 | |
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| 7 | SUBROUTINE fyhyp(rlatu, yyprimu, rlatv, rlatu2, yprimu2, rlatu1, yprimu1) |
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| 8 | |
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| 9 | ! From LMDZ4/libf/dyn3d/fyhyp.F, version 1.2, 2005/06/03 09:11:32 |
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| 10 | |
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| 11 | ! Author: P. Le Van, from analysis by R. Sadourny |
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| 12 | |
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| 13 | ! Calcule les latitudes et dérivées dans la grille du GCM pour une |
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| 14 | ! fonction f(y) à dérivée tangente hyperbolique. |
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| 15 | |
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| 16 | ! Il vaut mieux avoir : grossismy * dzoom < pi / 2 |
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| 17 | |
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| 18 | use coefpoly_m, only: coefpoly |
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| 19 | use nrtype, only: k8 |
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| 20 | use serre_mod, only: clat, grossismy, dzoomy, tauy |
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| 21 | |
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| 22 | include "dimensions.h" |
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| 23 | ! for jjm |
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| 24 | |
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| 25 | REAL, intent(out):: rlatu(jjm + 1), yyprimu(jjm + 1) |
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| 26 | REAL, intent(out):: rlatv(jjm) |
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| 27 | real, intent(out):: rlatu2(jjm), yprimu2(jjm), rlatu1(jjm), yprimu1(jjm) |
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| 28 | |
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| 29 | ! Local: |
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| 30 | |
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| 31 | REAL(K8) champmin, champmax |
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| 32 | INTEGER, PARAMETER:: nmax=30000, nmax2=2*nmax |
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| 33 | REAL dzoom ! distance totale de la zone du zoom (en radians) |
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| 34 | REAL(K8) ylat(jjm + 1), yprim(jjm + 1) |
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| 35 | REAL(K8) yuv |
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| 36 | REAL(K8), save:: yt(0:nmax2) |
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| 37 | REAL(K8) fhyp(0:nmax2), beta |
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| 38 | REAL(K8), save:: ytprim(0:nmax2) |
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| 39 | REAL(K8) fxm(0:nmax2) |
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| 40 | REAL(K8), save:: yf(0:nmax2) |
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| 41 | REAL(K8) yypr(0:nmax2) |
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| 42 | REAL(K8) yvrai(jjm + 1), yprimm(jjm + 1), ylatt(jjm + 1) |
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| 43 | REAL(K8) pi, pis2, epsilon, y0, pisjm |
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| 44 | REAL(K8) yo1, yi, ylon2, ymoy, yprimin |
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| 45 | REAL(K8) yfi, yf1, ffdy |
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| 46 | REAL(K8) ypn, deply, y00 |
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| 47 | SAVE y00, deply |
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| 48 | |
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| 49 | INTEGER i, j, it, ik, iter, jlat |
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| 50 | INTEGER jpn, jjpn |
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| 51 | SAVE jpn |
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| 52 | REAL(K8) a0, a1, a2, a3, yi2, heavyy0, heavyy0m |
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| 53 | REAL(K8) fa(0:nmax2), fb(0:nmax2) |
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| 54 | REAL y0min, y0max |
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| 55 | |
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| 56 | REAL(K8) heavyside |
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| 57 | |
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| 58 | !------------------------------------------------------------------- |
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| 59 | |
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| 60 | print *, "Call sequence information: fyhyp" |
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| 61 | |
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| 62 | pi = 2.*asin(1.) |
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| 63 | pis2 = pi/2. |
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| 64 | pisjm = pi/real(jjm) |
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| 65 | epsilon = 1e-3 |
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| 66 | y0 = clat*pi/180. |
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| 67 | dzoom = dzoomy*pi |
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| 68 | print *, 'yzoom(rad), grossismy, tauy, dzoom (rad):' |
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| 69 | print *, y0, grossismy, tauy, dzoom |
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| 70 | |
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| 71 | DO i = 0, nmax2 |
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| 72 | yt(i) = -pis2 + real(i)*pi/nmax2 |
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| 73 | END DO |
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| 74 | |
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| 75 | heavyy0m = heavyside(-y0) |
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| 76 | heavyy0 = heavyside(y0) |
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| 77 | y0min = 2.*y0*heavyy0m - pis2 |
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| 78 | y0max = 2.*y0*heavyy0 + pis2 |
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| 79 | |
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| 80 | fa = 999.999 |
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| 81 | fb = 999.999 |
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| 82 | |
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| 83 | DO i = 0, nmax2 |
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| 84 | IF (yt(i)<y0) THEN |
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| 85 | fa(i) = tauy*(yt(i)-y0 + dzoom/2.) |
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| 86 | fb(i) = (yt(i)-2.*y0*heavyy0m + pis2)*(y0-yt(i)) |
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| 87 | ELSE IF (yt(i)>y0) THEN |
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| 88 | fa(i) = tauy*(y0-yt(i) + dzoom/2.) |
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| 89 | fb(i) = (2.*y0*heavyy0-yt(i) + pis2)*(yt(i)-y0) |
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| 90 | END IF |
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| 91 | |
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| 92 | IF (200.*fb(i)<-fa(i)) THEN |
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| 93 | fhyp(i) = -1. |
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| 94 | ELSE IF (200.*fb(i)<fa(i)) THEN |
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| 95 | fhyp(i) = 1. |
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| 96 | ELSE |
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| 97 | fhyp(i) = tanh(fa(i)/fb(i)) |
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| 98 | END IF |
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| 99 | |
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| 100 | IF (yt(i)==y0) fhyp(i) = 1. |
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| 101 | IF (yt(i)==y0min .OR. yt(i)==y0max) fhyp(i) = -1. |
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| 102 | END DO |
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| 103 | |
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| 104 | ! Calcul de beta |
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| 105 | |
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| 106 | ffdy = 0. |
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| 107 | |
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| 108 | DO i = 1, nmax2 |
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| 109 | ymoy = 0.5*(yt(i-1) + yt(i)) |
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| 110 | IF (ymoy<y0) THEN |
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| 111 | fa(i) = tauy*(ymoy-y0 + dzoom/2.) |
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| 112 | fb(i) = (ymoy-2.*y0*heavyy0m + pis2)*(y0-ymoy) |
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| 113 | ELSE IF (ymoy>y0) THEN |
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| 114 | fa(i) = tauy*(y0-ymoy + dzoom/2.) |
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| 115 | fb(i) = (2.*y0*heavyy0-ymoy + pis2)*(ymoy-y0) |
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| 116 | END IF |
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| 117 | |
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| 118 | IF (200.*fb(i)<-fa(i)) THEN |
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| 119 | fxm(i) = -1. |
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| 120 | ELSE IF (200.*fb(i)<fa(i)) THEN |
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| 121 | fxm(i) = 1. |
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| 122 | ELSE |
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| 123 | fxm(i) = tanh(fa(i)/fb(i)) |
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| 124 | END IF |
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| 125 | IF (ymoy==y0) fxm(i) = 1. |
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| 126 | IF (ymoy==y0min .OR. yt(i)==y0max) fxm(i) = -1. |
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| 127 | ffdy = ffdy + fxm(i)*(yt(i)-yt(i-1)) |
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| 128 | END DO |
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| 129 | |
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| 130 | beta = (grossismy*ffdy-pi)/(ffdy-pi) |
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| 131 | |
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| 132 | IF (2. * beta - grossismy <= 0.) THEN |
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| 133 | print *, 'Attention ! La valeur beta calculee dans la routine fyhyp ' & |
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| 134 | // 'est mauvaise. Modifier les valeurs de grossismy, tauy ou ' & |
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| 135 | // 'dzoomy et relancer.' |
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| 136 | STOP 1 |
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| 137 | END IF |
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| 138 | |
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| 139 | ! calcul de Ytprim |
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| 140 | |
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| 141 | DO i = 0, nmax2 |
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| 142 | ytprim(i) = beta + (grossismy-beta)*fhyp(i) |
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| 143 | END DO |
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| 144 | |
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| 145 | ! Calcul de Yf |
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| 146 | |
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| 147 | yf(0) = -pis2 |
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| 148 | DO i = 1, nmax2 |
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| 149 | yypr(i) = beta + (grossismy-beta)*fxm(i) |
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| 150 | END DO |
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| 151 | |
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| 152 | DO i = 1, nmax2 |
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| 153 | yf(i) = yf(i-1) + yypr(i)*(yt(i)-yt(i-1)) |
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| 154 | END DO |
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| 155 | |
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| 156 | ! yuv = 0. si calcul des latitudes aux pts. U |
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| 157 | ! yuv = 0.5 si calcul des latitudes aux pts. V |
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| 158 | |
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| 159 | loop_ik: DO ik = 1, 4 |
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| 160 | IF (ik==1) THEN |
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| 161 | yuv = 0. |
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| 162 | jlat = jjm + 1 |
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| 163 | ELSE IF (ik==2) THEN |
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| 164 | yuv = 0.5 |
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| 165 | jlat = jjm |
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| 166 | ELSE IF (ik==3) THEN |
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| 167 | yuv = 0.25 |
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| 168 | jlat = jjm |
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| 169 | ELSE IF (ik==4) THEN |
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| 170 | yuv = 0.75 |
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| 171 | jlat = jjm |
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| 172 | END IF |
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| 173 | |
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| 174 | yo1 = 0. |
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| 175 | DO j = 1, jlat |
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| 176 | yo1 = 0. |
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| 177 | ylon2 = -pis2 + pisjm*(real(j) + yuv-1.) |
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| 178 | yfi = ylon2 |
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| 179 | |
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| 180 | it = nmax2 |
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| 181 | DO while (it >= 1 .and. yfi < yf(it)) |
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| 182 | it = it - 1 |
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| 183 | END DO |
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| 184 | |
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| 185 | yi = yt(it) |
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| 186 | IF (it==nmax2) THEN |
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| 187 | it = nmax2 - 1 |
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| 188 | yf(it + 1) = pis2 |
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| 189 | END IF |
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| 190 | |
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| 191 | ! Interpolation entre yi(it) et yi(it + 1) pour avoir Y(yi) |
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| 192 | ! et Y'(yi) |
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| 193 | |
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| 194 | CALL coefpoly(yf(it), yf(it + 1), ytprim(it), ytprim(it + 1), & |
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| 195 | yt(it), yt(it + 1), a0, a1, a2, a3) |
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| 196 | |
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| 197 | yf1 = yf(it) |
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| 198 | yprimin = a1 + 2.*a2*yi + 3.*a3*yi*yi |
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| 199 | |
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| 200 | iter = 1 |
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| 201 | DO |
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| 202 | yi = yi - (yf1-yfi)/yprimin |
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| 203 | IF (abs(yi-yo1)<=epsilon .or. iter == 300) exit |
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| 204 | yo1 = yi |
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| 205 | yi2 = yi*yi |
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| 206 | yf1 = a0 + a1*yi + a2*yi2 + a3*yi2*yi |
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| 207 | yprimin = a1 + 2.*a2*yi + 3.*a3*yi2 |
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| 208 | END DO |
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| 209 | if (abs(yi-yo1) > epsilon) then |
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| 210 | print *, 'Pas de solution.', j, ylon2 |
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| 211 | STOP 1 |
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| 212 | end if |
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| 213 | |
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| 214 | yprimin = a1 + 2.*a2*yi + 3.*a3*yi*yi |
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| 215 | yprim(j) = pi/(jjm*yprimin) |
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| 216 | yvrai(j) = yi |
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| 217 | END DO |
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| 218 | |
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| 219 | DO j = 1, jlat - 1 |
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| 220 | IF (yvrai(j + 1)<yvrai(j)) THEN |
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| 221 | print *, 'Problème avec rlat(', j + 1, ') plus petit que rlat(', & |
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| 222 | j, ')' |
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| 223 | STOP 1 |
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| 224 | END IF |
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| 225 | END DO |
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| 226 | |
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| 227 | print *, 'Reorganisation des latitudes pour avoir entre - pi/2 et pi/2' |
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| 228 | |
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| 229 | IF (ik==1) THEN |
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| 230 | ypn = pis2 |
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| 231 | DO j = jjm + 1, 1, -1 |
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| 232 | IF (yvrai(j)<=ypn) exit |
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| 233 | END DO |
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| 234 | |
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| 235 | jpn = j |
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| 236 | y00 = yvrai(jpn) |
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| 237 | deply = pis2 - y00 |
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| 238 | END IF |
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| 239 | |
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| 240 | DO j = 1, jjm + 1 - jpn |
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| 241 | ylatt(j) = -pis2 - y00 + yvrai(jpn + j-1) |
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| 242 | yprimm(j) = yprim(jpn + j-1) |
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| 243 | END DO |
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| 244 | |
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| 245 | jjpn = jpn |
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| 246 | IF (jlat==jjm) jjpn = jpn - 1 |
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| 247 | |
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| 248 | DO j = 1, jjpn |
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| 249 | ylatt(j + jjm + 1-jpn) = yvrai(j) + deply |
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| 250 | yprimm(j + jjm + 1-jpn) = yprim(j) |
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| 251 | END DO |
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| 252 | |
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| 253 | ! Fin de la reorganisation |
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| 254 | |
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| 255 | DO j = 1, jlat |
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| 256 | ylat(j) = ylatt(jlat + 1-j) |
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| 257 | yprim(j) = yprimm(jlat + 1-j) |
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| 258 | END DO |
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| 259 | |
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| 260 | DO j = 1, jlat |
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| 261 | yvrai(j) = ylat(j)*180./pi |
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| 262 | END DO |
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| 263 | |
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| 264 | IF (ik==1) THEN |
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| 265 | DO j = 1, jjm + 1 |
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| 266 | rlatu(j) = ylat(j) |
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| 267 | yyprimu(j) = yprim(j) |
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| 268 | END DO |
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| 269 | ELSE IF (ik==2) THEN |
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| 270 | DO j = 1, jjm |
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| 271 | rlatv(j) = ylat(j) |
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| 272 | END DO |
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| 273 | ELSE IF (ik==3) THEN |
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| 274 | DO j = 1, jjm |
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| 275 | rlatu2(j) = ylat(j) |
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| 276 | yprimu2(j) = yprim(j) |
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| 277 | END DO |
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| 278 | ELSE IF (ik==4) THEN |
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| 279 | DO j = 1, jjm |
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| 280 | rlatu1(j) = ylat(j) |
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| 281 | yprimu1(j) = yprim(j) |
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| 282 | END DO |
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| 283 | END IF |
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| 284 | END DO loop_ik |
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| 285 | |
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| 286 | DO j = 1, jjm |
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| 287 | ylat(j) = rlatu(j) - rlatu(j + 1) |
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| 288 | END DO |
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| 289 | champmin = 1e12 |
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| 290 | champmax = -1e12 |
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| 291 | DO j = 1, jjm |
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| 292 | champmin = min(champmin, ylat(j)) |
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| 293 | champmax = max(champmax, ylat(j)) |
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| 294 | END DO |
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| 295 | champmin = champmin*180./pi |
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| 296 | champmax = champmax*180./pi |
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| 297 | |
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| 298 | DO j = 1, jjm |
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| 299 | IF (rlatu1(j) <= rlatu2(j)) THEN |
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| 300 | print *, 'Attention ! rlatu1 < rlatu2 ', rlatu1(j), rlatu2(j), j |
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| 301 | STOP 13 |
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| 302 | ENDIF |
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| 303 | |
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| 304 | IF (rlatu2(j) <= rlatu(j+1)) THEN |
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| 305 | print *, 'Attention ! rlatu2 < rlatup1 ', rlatu2(j), rlatu(j+1), j |
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| 306 | STOP 14 |
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| 307 | ENDIF |
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| 308 | |
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| 309 | IF (rlatu(j) <= rlatu1(j)) THEN |
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| 310 | print *, ' Attention ! rlatu < rlatu1 ', rlatu(j), rlatu1(j), j |
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| 311 | STOP 15 |
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| 312 | ENDIF |
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| 313 | |
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| 314 | IF (rlatv(j) <= rlatu2(j)) THEN |
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| 315 | print *, ' Attention ! rlatv < rlatu2 ', rlatv(j), rlatu2(j), j |
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| 316 | STOP 16 |
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| 317 | ENDIF |
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| 318 | |
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| 319 | IF (rlatv(j) >= rlatu1(j)) THEN |
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| 320 | print *, ' Attention ! rlatv > rlatu1 ', rlatv(j), rlatu1(j), j |
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| 321 | STOP 17 |
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| 322 | ENDIF |
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| 323 | |
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| 324 | IF (rlatv(j) >= rlatu(j)) THEN |
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| 325 | print *, ' Attention ! rlatv > rlatu ', rlatv(j), rlatu(j), j |
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| 326 | STOP 18 |
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| 327 | ENDIF |
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| 328 | ENDDO |
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| 329 | |
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| 330 | print *, 'Latitudes' |
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| 331 | print 3, champmin, champmax |
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| 332 | |
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| 333 | 3 Format(1x, ' Au centre du zoom, la longueur de la maille est', & |
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| 334 | ' d environ ', f0.2, ' degres ', /, & |
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| 335 | ' alors que la maille en dehors de la zone du zoom est ', & |
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| 336 | "d'environ ", f0.2, ' degres ') |
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| 337 | |
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| 338 | END SUBROUTINE fyhyp |
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| 339 | |
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| 340 | end module fyhyp_m |
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