| 1 | ! $Id: disvert.F90 2153 2014-11-24 15:18:11Z aborella $ |
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| 2 | |
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| 3 | SUBROUTINE disvert() |
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| 4 | |
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| 5 | #ifdef CPP_IOIPSL |
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| 6 | use ioipsl, only: getin |
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| 7 | #else |
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| 8 | USE ioipsl_getincom, only: getin |
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| 9 | #endif |
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| 10 | use new_unit_m, only: new_unit |
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| 11 | use assert_m, only: assert |
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| 12 | |
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| 13 | IMPLICIT NONE |
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| 14 | |
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| 15 | include "dimensions.h" |
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| 16 | include "paramet.h" |
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| 17 | include "comvert.h" |
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| 18 | include "comconst.h" |
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| 19 | include "iniprint.h" |
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| 20 | include "logic.h" |
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| 21 | |
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| 22 | !------------------------------------------------------------------------------- |
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| 23 | ! Purpose: Vertical distribution functions for LMDZ. |
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| 24 | ! Triggered by the levels number llm. |
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| 25 | !------------------------------------------------------------------------------- |
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| 26 | ! Read in "comvert.h": |
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| 27 | |
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| 28 | ! pa !--- vertical coordinate is close to a PRESSURE COORDINATE FOR P |
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| 29 | ! < 0.3 * pa (relative variation of p on a model level is < 0.1 %) |
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| 30 | |
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| 31 | ! preff !--- REFERENCE PRESSURE (101325 Pa) |
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| 32 | ! Written in "comvert.h": |
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| 33 | ! ap(llm+1), bp(llm+1) !--- Ap, Bp HYBRID COEFFICIENTS AT INTERFACES |
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| 34 | ! aps(llm), bps(llm) !--- Ap, Bp HYBRID COEFFICIENTS AT MID-LAYERS |
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| 35 | ! dpres(llm) !--- PRESSURE DIFFERENCE FOR EACH LAYER |
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| 36 | ! presnivs(llm) !--- PRESSURE AT EACH MID-LAYER |
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| 37 | ! scaleheight !--- VERTICAL SCALE HEIGHT (Earth: 8kms) |
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| 38 | ! nivsig(llm+1) !--- SIGMA INDEX OF EACH LAYER INTERFACE |
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| 39 | ! nivsigs(llm) !--- SIGMA INDEX OF EACH MID-LAYER |
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| 40 | !------------------------------------------------------------------------------- |
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| 41 | ! Local variables: |
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| 42 | REAL sig(llm+1), dsig(llm) |
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| 43 | REAL sig0(llm+1), zz(llm+1) |
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| 44 | REAL zk, zkm1, dzk1, dzk2, z, k0, k1 |
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| 45 | |
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| 46 | INTEGER l, unit |
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| 47 | REAL dsigmin |
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| 48 | REAL vert_scale,vert_dzmin,vert_dzlow,vert_z0low,vert_dzmid,vert_z0mid,vert_h_mid,vert_dzhig,vert_z0hig,vert_h_hig |
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| 49 | |
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| 50 | REAL alpha, beta, deltaz |
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| 51 | REAL x |
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| 52 | character(len=*),parameter :: modname="disvert" |
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| 53 | |
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| 54 | character(len=24):: vert_sampling |
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| 55 | ! (allowed values are "param", "tropo", "strato" and "read") |
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| 56 | |
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| 57 | !----------------------------------------------------------------------- |
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| 58 | |
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| 59 | WRITE(lunout,*) TRIM(modname)//" starts" |
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| 60 | |
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| 61 | ! default scaleheight is 8km for earth |
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| 62 | scaleheight=8. |
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| 63 | |
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| 64 | vert_sampling = merge("strato", "tropo ", ok_strato) ! default value |
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| 65 | call getin('vert_sampling', vert_sampling) |
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| 66 | WRITE(lunout,*) TRIM(modname)//' vert_sampling = ' // vert_sampling |
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| 67 | if (llm==39 .and. vert_sampling=="strato") then |
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| 68 | dsigmin=0.3 ! Vieille option par défaut pour CMIP5 |
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| 69 | else |
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| 70 | dsigmin=1. |
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| 71 | endif |
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| 72 | call getin('dsigmin', dsigmin) |
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| 73 | WRITE(LUNOUT,*) trim(modname), 'Discretisation verticale DSIGMIN=',dsigmin |
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| 74 | |
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| 75 | |
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| 76 | select case (vert_sampling) |
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| 77 | case ("param") |
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| 78 | ! On lit les options dans sigma.def: |
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| 79 | OPEN(99, file='sigma.def', status='old', form='formatted') |
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| 80 | READ(99, *) scaleheight ! hauteur d'echelle 8. |
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| 81 | READ(99, *) deltaz ! epaiseur de la premiere couche 0.04 |
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| 82 | READ(99, *) beta ! facteur d'acroissement en haut 1.3 |
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| 83 | READ(99, *) k0 ! nombre de couches dans la transition surf |
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| 84 | READ(99, *) k1 ! nombre de couches dans la transition haute |
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| 85 | CLOSE(99) |
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| 86 | alpha=deltaz/(llm*scaleheight) |
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| 87 | write(lunout, *)trim(modname),':scaleheight, alpha, k0, k1, beta', & |
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| 88 | scaleheight, alpha, k0, k1, beta |
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| 89 | |
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| 90 | alpha=deltaz/tanh(1./k0)*2. |
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| 91 | zkm1=0. |
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| 92 | sig(1)=1. |
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| 93 | do l=1, llm |
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| 94 | sig(l+1)=(cosh(l/k0))**(-alpha*k0/scaleheight) & |
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| 95 | *exp(-alpha/scaleheight*tanh((llm-k1)/k0) & |
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| 96 | *beta**(l-(llm-k1))/log(beta)) |
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| 97 | zk=-scaleheight*log(sig(l+1)) |
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| 98 | |
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| 99 | dzk1=alpha*tanh(l/k0) |
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| 100 | dzk2=alpha*tanh((llm-k1)/k0)*beta**(l-(llm-k1))/log(beta) |
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| 101 | write(lunout, *)l, sig(l+1), zk, zk-zkm1, dzk1, dzk2 |
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| 102 | zkm1=zk |
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| 103 | enddo |
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| 104 | |
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| 105 | sig(llm+1)=0. |
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| 106 | |
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| 107 | bp(: llm) = EXP(1. - 1. / sig(: llm)**2) |
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| 108 | bp(llmp1) = 0. |
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| 109 | |
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| 110 | ap = pa * (sig - bp) |
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| 111 | case("sigma") |
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| 112 | DO l = 1, llm |
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| 113 | x = 2*asin(1.) * (l - 0.5) / (llm + 1) |
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| 114 | dsig(l) = dsigmin + 7.0 * SIN(x)**2 |
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| 115 | ENDDO |
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| 116 | dsig = dsig / sum(dsig) |
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| 117 | sig(llm+1) = 0. |
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| 118 | DO l = llm, 1, -1 |
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| 119 | sig(l) = sig(l+1) + dsig(l) |
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| 120 | ENDDO |
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| 121 | |
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| 122 | bp(1)=1. |
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| 123 | bp(2: llm) = sig(2:llm) |
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| 124 | bp(llmp1) = 0. |
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| 125 | ap(:)=0. |
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| 126 | case("tropo") |
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| 127 | DO l = 1, llm |
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| 128 | x = 2*asin(1.) * (l - 0.5) / (llm + 1) |
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| 129 | dsig(l) = dsigmin + 7.0 * SIN(x)**2 |
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| 130 | ENDDO |
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| 131 | dsig = dsig / sum(dsig) |
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| 132 | sig(llm+1) = 0. |
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| 133 | DO l = llm, 1, -1 |
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| 134 | sig(l) = sig(l+1) + dsig(l) |
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| 135 | ENDDO |
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| 136 | |
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| 137 | bp(1)=1. |
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| 138 | bp(2: llm) = EXP(1. - 1. / sig(2: llm)**2) |
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| 139 | bp(llmp1) = 0. |
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| 140 | |
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| 141 | ap(1)=0. |
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| 142 | ap(2: llm + 1) = pa * (sig(2: llm + 1) - bp(2: llm + 1)) |
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| 143 | case("strato") |
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| 144 | DO l = 1, llm |
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| 145 | x = 2*asin(1.) * (l - 0.5) / (llm + 1) |
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| 146 | dsig(l) =(dsigmin + 7. * SIN(x)**2) & |
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| 147 | *(0.5*(1.-tanh(1.*(x-asin(1.))/asin(1.))))**2 |
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| 148 | ENDDO |
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| 149 | dsig = dsig / sum(dsig) |
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| 150 | sig(llm+1) = 0. |
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| 151 | DO l = llm, 1, -1 |
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| 152 | sig(l) = sig(l+1) + dsig(l) |
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| 153 | ENDDO |
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| 154 | |
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| 155 | bp(1)=1. |
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| 156 | bp(2: llm) = EXP(1. - 1. / sig(2: llm)**2) |
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| 157 | bp(llmp1) = 0. |
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| 158 | |
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| 159 | ap(1)=0. |
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| 160 | ap(2: llm + 1) = pa * (sig(2: llm + 1) - bp(2: llm + 1)) |
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| 161 | case("strato_correct") |
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| 162 | !================================================================== |
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| 163 | ! Fredho 2014/05/18, Saint-Louis du Senegal |
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| 164 | ! Cette version de la discretisation strato est corrige au niveau |
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| 165 | ! du passage des sig aux ap, bp |
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| 166 | ! la version precedente donne un coude dans l'epaisseur des couches |
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| 167 | ! vers la tropopause |
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| 168 | !================================================================== |
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| 169 | |
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| 170 | |
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| 171 | DO l = 1, llm |
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| 172 | x = 2*asin(1.) * (l - 0.5) / (llm + 1) |
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| 173 | dsig(l) =(dsigmin + 7. * SIN(x)**2) & |
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| 174 | *(0.5*(1.-tanh(1.*(x-asin(1.))/asin(1.))))**2 |
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| 175 | ENDDO |
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| 176 | dsig = dsig / sum(dsig) |
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| 177 | sig0(llm+1) = 0. |
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| 178 | DO l = llm, 1, -1 |
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| 179 | sig0(l) = sig0(l+1) + dsig(l) |
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| 180 | ENDDO |
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| 181 | sig=racinesig(sig0) |
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| 182 | |
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| 183 | bp(1)=1. |
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| 184 | bp(2:llm)=EXP(1.-1./sig(2: llm)**2) |
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| 185 | bp(llmp1)=0. |
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| 186 | |
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| 187 | ap(1)=0. |
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| 188 | ap(2:llm)=pa*(sig(2:llm)-bp(2:llm)) |
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| 189 | ap(llm+1)=0. |
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| 190 | |
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| 191 | CASE("strato_custom0") |
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| 192 | !======================================================= |
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| 193 | ! Version Transitoire |
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| 194 | ! custumize strato distribution with specific alpha & beta values and function |
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| 195 | ! depending on llm (experimental and temporary)! |
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| 196 | SELECT CASE (llm) |
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| 197 | CASE(55) |
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| 198 | alpha=0.45 |
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| 199 | beta=4.0 |
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| 200 | CASE(63) |
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| 201 | alpha=0.45 |
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| 202 | beta=5.0 |
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| 203 | CASE(71) |
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| 204 | alpha=3.05 |
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| 205 | beta=65. |
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| 206 | CASE(79) |
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| 207 | alpha=3.20 |
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| 208 | ! alpha=2.05 ! FLOTT 79 (PLANTE) |
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| 209 | beta=70. |
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| 210 | END SELECT |
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| 211 | ! Or used values provided by user in def file: |
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| 212 | CALL getin("strato_alpha",alpha) |
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| 213 | CALL getin("strato_beta",beta) |
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| 214 | |
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| 215 | ! Build geometrical distribution |
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| 216 | scaleheight=7. |
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| 217 | zz(1)=0. |
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| 218 | IF (llm==55.OR.llm==63) THEN |
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| 219 | DO l=1,llm |
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| 220 | z=zz(l)/scaleheight |
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| 221 | zz(l+1)=zz(l)+0.03+z*1.5*(1.-TANH(z-0.5))+alpha*(1.+TANH(z-1.5)) & |
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| 222 | +5.0*EXP((l-llm)/beta) |
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| 223 | ENDDO |
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| 224 | ELSEIF (llm==71) THEN !.OR.llm==79) THEN ! FLOTT 79 (PLANTE) |
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| 225 | DO l=1,llm |
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| 226 | z=zz(l) |
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| 227 | zz(l+1)=zz(l)+0.02+0.88*TANH(z/2.5)+alpha*(1.+TANH((z-beta)/15.)) |
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| 228 | ENDDO |
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| 229 | ELSEIF (llm==79) THEN |
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| 230 | DO l=1,llm |
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| 231 | z=zz(l) |
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| 232 | zz(l+1)=zz(l)+0.02+0.80*TANH(z/3.8)+alpha*(1+TANH((z-beta)/17.)) & |
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| 233 | +0.03*TANH(z/.25) |
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| 234 | ENDDO |
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| 235 | ENDIF ! of IF (llm==55.OR.llm==63) ... |
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| 236 | |
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| 237 | |
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| 238 | ! Build sigma distribution |
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| 239 | sig0=EXP(-zz(:)/scaleheight) |
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| 240 | sig0(llm+1)=0. |
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| 241 | ! sig=ridders(sig0) |
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| 242 | sig=racinesig(sig0) |
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| 243 | |
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| 244 | ! Compute ap() and bp() |
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| 245 | bp(1)=1. |
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| 246 | bp(2:llm)=EXP(1.-1./sig(2:llm)**2) |
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| 247 | bp(llm+1)=0. |
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| 248 | ap=pa*(sig-bp) |
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| 249 | |
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| 250 | CASE("strato_custom") |
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| 251 | !=================================================================== |
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| 252 | ! David Cugnet, François Lott, Lionel Guez, Ehouoarn Millour, Fredho |
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| 253 | ! 2014/05 |
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| 254 | ! custumize strato distribution |
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| 255 | ! Al the parameter are given in km assuming a given scalehigh |
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| 256 | vert_scale=7. ! scale hight |
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| 257 | vert_dzmin=0.02 ! width of first layer |
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| 258 | vert_dzlow=1. ! dz in the low atmosphere |
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| 259 | vert_z0low=8. ! height at which resolution recches dzlow |
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| 260 | vert_dzmid=3. ! dz in the mid atmsophere |
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| 261 | vert_z0mid=70. ! height at which resolution recches dzmid |
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| 262 | vert_h_mid=20. ! width of the transition |
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| 263 | vert_dzhig=11. ! dz in the high atmsophere |
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| 264 | vert_z0hig=80. ! height at which resolution recches dz |
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| 265 | vert_h_hig=20. ! width of the transition |
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| 266 | !=================================================================== |
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| 267 | |
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| 268 | call getin('vert_scale',vert_scale) |
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| 269 | call getin('vert_dzmin',vert_dzmin) |
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| 270 | call getin('vert_dzlow',vert_dzlow) |
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| 271 | call getin('vert_z0low',vert_z0low) |
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| 272 | CALL getin('vert_dzmid',vert_dzmid) |
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| 273 | CALL getin('vert_z0mid',vert_z0mid) |
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| 274 | call getin('vert_h_mid',vert_h_mid) |
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| 275 | call getin('vert_dzhig',vert_dzhig) |
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| 276 | call getin('vert_z0hig',vert_z0hig) |
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| 277 | call getin('vert_h_hig',vert_h_hig) |
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| 278 | |
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| 279 | scaleheight=vert_scale ! for consistency with further computations |
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| 280 | ! Build geometrical distribution |
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| 281 | zz(1)=0. |
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| 282 | DO l=1,llm |
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| 283 | z=zz(l) |
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| 284 | zz(l+1)=zz(l)+vert_dzmin+vert_dzlow*TANH(z/vert_z0low)+ & |
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| 285 | & (vert_dzmid-vert_dzlow)* & |
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| 286 | & (TANH((z-vert_z0mid)/vert_h_mid)-TANH((-vert_z0mid)/vert_h_mid)) & |
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| 287 | & +(vert_dzhig-vert_dzmid-vert_dzlow)* & |
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| 288 | & (TANH((z-vert_z0hig)/vert_h_hig)-TANH((-vert_z0hig)/vert_h_hig)) |
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| 289 | ENDDO |
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| 290 | |
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| 291 | |
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| 292 | !=================================================================== |
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| 293 | ! Comment added Fredho 2014/05/18, Saint-Louis, Senegal |
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| 294 | ! From approximate z to ap, bp, so that p=ap+bp*p0 and p/p0=exp(-z/H) |
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| 295 | ! sig0 is p/p0 |
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| 296 | ! sig is an intermediate distribution introduce to estimate bp |
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| 297 | ! 1. sig0=exp(-z/H) |
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| 298 | ! 2. inversion of sig0=(1-pa/p0)*sig+(1-pa/p0)*exp(1-1/sig**2) |
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| 299 | ! 3. bp=exp(1-1/sig**2) |
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| 300 | ! 4. ap deduced from the combination of 2 and 3 so that sig0=ap/p0+bp |
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| 301 | !=================================================================== |
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| 302 | |
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| 303 | sig0=EXP(-zz(:)/vert_scale) |
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| 304 | sig0(llm+1)=0. |
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| 305 | sig=racinesig(sig0) |
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| 306 | bp(1)=1. |
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| 307 | bp(2:llm)=EXP(1.-1./sig(2:llm)**2) |
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| 308 | bp(llm+1)=0. |
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| 309 | ap=pa*(sig-bp) |
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| 310 | |
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| 311 | case("read") |
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| 312 | ! Read "ap" and "bp". First line is skipped (title line). "ap" |
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| 313 | ! should be in Pa. First couple of values should correspond to |
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| 314 | ! the surface, that is : "bp" should be in descending order. |
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| 315 | call new_unit(unit) |
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| 316 | open(unit, file="hybrid.txt", status="old", action="read", & |
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| 317 | position="rewind") |
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| 318 | read(unit, fmt=*) ! skip title line |
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| 319 | do l = 1, llm + 1 |
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| 320 | read(unit, fmt=*) ap(l), bp(l) |
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| 321 | end do |
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| 322 | close(unit) |
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| 323 | call assert(ap(1) == 0., ap(llm + 1) == 0., bp(1) == 1., & |
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| 324 | bp(llm + 1) == 0., "disvert: bad ap or bp values") |
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| 325 | case default |
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| 326 | call abort_gcm("disvert", 'Wrong value for "vert_sampling"', 1) |
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| 327 | END select |
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| 328 | |
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| 329 | DO l=1, llm |
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| 330 | nivsigs(l) = REAL(l) |
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| 331 | ENDDO |
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| 332 | |
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| 333 | DO l=1, llmp1 |
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| 334 | nivsig(l)= REAL(l) |
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| 335 | ENDDO |
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| 336 | |
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| 337 | write(lunout, *) trim(modname),': BP ' |
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| 338 | write(lunout, *) bp |
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| 339 | write(lunout, *) trim(modname),': AP ' |
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| 340 | write(lunout, *) ap |
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| 341 | |
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| 342 | write(lunout, *) 'Niveaux de pressions approximatifs aux centres des' |
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| 343 | write(lunout, *)'couches calcules pour une pression de surface =', preff |
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| 344 | write(lunout, *) 'et altitudes equivalentes pour une hauteur d echelle de ' |
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| 345 | write(lunout, *) scaleheight,' km' |
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| 346 | DO l = 1, llm |
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| 347 | dpres(l) = bp(l) - bp(l+1) |
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| 348 | presnivs(l) = 0.5 *( ap(l)+bp(l)*preff + ap(l+1)+bp(l+1)*preff ) |
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| 349 | write(lunout, *)'PRESNIVS(', l, ')=', presnivs(l), ' Z ~ ', & |
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| 350 | log(preff/presnivs(l))*scaleheight & |
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| 351 | , ' DZ ~ ', scaleheight*log((ap(l)+bp(l)*preff)/ & |
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| 352 | max(ap(l+1)+bp(l+1)*preff, 1.e-10)) |
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| 353 | ENDDO |
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| 354 | |
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| 355 | write(lunout, *) trim(modname),': PRESNIVS ' |
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| 356 | write(lunout, *) presnivs |
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| 357 | |
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| 358 | CONTAINS |
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| 359 | |
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| 360 | !------------------------------------------------------------------------------- |
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| 361 | ! |
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| 362 | FUNCTION ridders(sig) RESULT(sg) |
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| 363 | ! |
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| 364 | !------------------------------------------------------------------------------- |
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| 365 | IMPLICIT NONE |
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| 366 | !------------------------------------------------------------------------------- |
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| 367 | ! Purpose: Search for s solving (Pa/Preff)*s+(1-Pa/Preff)*EXP(1-1./s**2)=sg |
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| 368 | ! Notes: Uses Ridders' method, quite robust. Initial bracketing: 0<=sg<=1. |
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| 369 | ! Reference: Ridders, C. F. J. "A New Algorithm for Computing a Single Root of a |
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| 370 | ! Real Continuous Function" IEEE Trans. Circuits Systems 26, 979-980, 1979 |
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| 371 | !------------------------------------------------------------------------------- |
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| 372 | ! Arguments: |
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| 373 | REAL, INTENT(IN) :: sig(:) |
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| 374 | REAL :: sg(SIZE(sig)) |
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| 375 | !------------------------------------------------------------------------------- |
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| 376 | ! Local variables: |
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| 377 | INTEGER :: it, ns, maxit |
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| 378 | REAL :: c1, c2, x1, x2, x3, x4, f1, f2, f3, f4, s, xx, distrib |
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| 379 | !------------------------------------------------------------------------------- |
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| 380 | ns=SIZE(sig); maxit=9999 |
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| 381 | c1=Pa/Preff; c2=1.-c1 |
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| 382 | DO l=1,ns |
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| 383 | xx=HUGE(1.) |
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| 384 | x1=0.0; f1=distrib(x1,c1,c2,sig(l)) |
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| 385 | x2=1.0; f2=distrib(x2,c1,c2,sig(l)) |
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| 386 | DO it=1,maxit |
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| 387 | x3=0.5*(x1+x2); f3=distrib(x3,c1,c2,sig(l)) |
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| 388 | s=SQRT(f3**2-f1*f2); IF(s==0.) EXIT |
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| 389 | x4=x3+(x3-x1)*(SIGN(1.,f1-f2)*f3/s); IF(ABS(10.*LOG(x4-xx))<=1E-5) EXIT |
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| 390 | xx=x4; f4=distrib(x4,c1,c2,sig(l)); IF(f4==0.) EXIT |
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| 391 | IF(SIGN(f3,f4)/=f3) THEN; x1=x3; f1=f3; x2=xx; f2=f4 |
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| 392 | ELSE IF(SIGN(f1,f4)/=f1) THEN; x2=xx; f2=f4 |
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| 393 | ELSE IF(SIGN(f2,f4)/=f2) THEN; x1=xx; f1=f4 |
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| 394 | ELSE; CALL abort_gcm("ridders",'Algorithm failed (which is odd...') |
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| 395 | END IF |
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| 396 | IF(ABS(10.*LOG(ABS(x2-x1)))<=1E-5) EXIT !--- ERROR ON SIG <= 0.01m |
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| 397 | END DO |
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| 398 | IF(it==maxit+1) WRITE(lunout,'(a,i3)')'WARNING in ridder: failed to converg& |
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| 399 | &e for level ',l |
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| 400 | sg(l)=xx |
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| 401 | END DO |
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| 402 | sg(1)=1.; sg(ns)=0. |
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| 403 | |
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| 404 | END FUNCTION ridders |
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| 405 | |
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| 406 | FUNCTION racinesig(sig) RESULT(sg) |
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| 407 | ! |
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| 408 | !------------------------------------------------------------------------------- |
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| 409 | IMPLICIT NONE |
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| 410 | !------------------------------------------------------------------------------- |
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| 411 | ! Fredho 2014/05/18 |
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| 412 | ! Purpose: Search for s solving (Pa/Preff)*sg+(1-Pa/Preff)*EXP(1-1./sg**2)=s |
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| 413 | ! Notes: Uses Newton Raphson search |
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| 414 | !------------------------------------------------------------------------------- |
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| 415 | ! Arguments: |
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| 416 | REAL, INTENT(IN) :: sig(:) |
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| 417 | REAL :: sg(SIZE(sig)) |
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| 418 | !------------------------------------------------------------------------------- |
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| 419 | ! Local variables: |
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| 420 | INTEGER :: it, ns, maxit |
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| 421 | REAL :: c1, c2, x1, x2, x3, x4, f1, f2, f3, f4, s, xx, distrib |
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| 422 | !------------------------------------------------------------------------------- |
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| 423 | ns=SIZE(sig); maxit=100 |
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| 424 | c1=Pa/Preff; c2=1.-c1 |
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| 425 | DO l=2,ns-1 |
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| 426 | sg(l)=sig(l) |
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| 427 | DO it=1,maxit |
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| 428 | f1=exp(1-1./sg(l)**2)*(1.-c1) |
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| 429 | sg(l)=sg(l)-(c1*sg(l)+f1-sig(l))/(c1+2*f1*sg(l)**(-3)) |
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| 430 | ENDDO |
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| 431 | ! print*,'SSSSIG ',sig(l),sg(l),c1*sg(l)+exp(1-1./sg(l)**2)*(1.-c1) |
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| 432 | ENDDO |
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| 433 | sg(1)=1.; sg(ns)=0. |
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| 434 | |
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| 435 | END FUNCTION racinesig |
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| 436 | |
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| 437 | |
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| 438 | |
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| 439 | |
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| 440 | END SUBROUTINE disvert |
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| 441 | |
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| 442 | !------------------------------------------------------------------------------- |
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| 443 | |
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| 444 | FUNCTION distrib(x,c1,c2,x0) RESULT(res) |
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| 445 | ! |
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| 446 | !------------------------------------------------------------------------------- |
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| 447 | ! Arguments: |
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| 448 | REAL, INTENT(IN) :: x, c1, c2, x0 |
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| 449 | REAL :: res |
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| 450 | !------------------------------------------------------------------------------- |
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| 451 | res=c1*x+c2*EXP(1-1/(x**2))-x0 |
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| 452 | |
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| 453 | END FUNCTION distrib |
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| 454 | |
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| 455 | |
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