| [381] | 1 | C |
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| 2 | C================================================================================ |
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| 3 | C |
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| 4 | SUBROUTINE CLOUDS_GNO(klon,ND,R,RS,QSUB,PTCONV,RATQSC,CLDF) |
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| 5 | IMPLICIT NONE |
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| 6 | C |
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| 7 | C-------------------------------------------------------------------------------- |
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| 8 | C |
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| 9 | C Inputs: |
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| 10 | C |
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| 11 | C ND----------: Number of vertical levels |
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| 12 | C R--------ND-: Domain-averaged mixing ratio of total water |
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| 13 | C RS-------ND-: Mean saturation humidity mixing ratio within the gridbox |
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| 14 | C QSUB-----ND-: Mixing ratio of condensed water within clouds associated |
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| 15 | C with SUBGRID-SCALE condensation processes (here, it is |
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| 16 | C predicted by the convection scheme) |
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| 17 | C Outputs: |
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| 18 | C |
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| 19 | C PTCONV-----ND-: Point convectif = TRUE |
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| 20 | C RATQSC-----ND-: Largeur normalisee de la distribution |
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| 21 | C CLDF-----ND-: Fraction nuageuse |
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| 22 | C |
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| 23 | C-------------------------------------------------------------------------------- |
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| 24 | |
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| 25 | |
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| 26 | INTEGER klon,ND |
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| 27 | REAL R(klon,ND), RS(klon,ND), QSUB(klon,ND) |
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| 28 | LOGICAL PTCONV(klon,ND) |
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| 29 | REAL RATQSC(klon,ND) |
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| 30 | REAL CLDF(klon,ND) |
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| 31 | |
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| 32 | c -- parameters controlling the iteration: |
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| 33 | c -- nmax : maximum nb of iterations (hopefully never reached) |
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| 34 | c -- epsilon : accuracy of the numerical resolution |
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| 35 | c -- vmax : v-value above which we use an asymptotic expression for ERF(v) |
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| 36 | |
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| 37 | INTEGER nmax |
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| 38 | PARAMETER ( nmax = 10) |
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| 39 | REAL epsilon, vmax0, vmax(klon) |
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| 40 | PARAMETER ( epsilon = 0.02, vmax0 = 2.0 ) |
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| 41 | |
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| 42 | REAL min_mu, min_Q |
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| 43 | PARAMETER ( min_mu = 1.e-12, min_Q=1.e-12 ) |
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| 44 | |
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| 45 | INTEGER i,K, n, m |
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| 46 | REAL mu(klon), qsat(klon), delta(klon), beta(klon) |
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| 47 | real zu2(klon),zv2(klon) |
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| 48 | REAL xx(klon), aux(klon), coeff(klon), block(klon) |
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| 49 | REAL dist(klon), fprime(klon), det(klon) |
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| [495] | 50 | REAL pi, u(klon), v(klon), erfcu(klon), erfcv(klon) |
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| [381] | 51 | REAL xx1(klon), xx2(klon) |
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| 52 | real erf,kkk |
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| [495] | 53 | real sqrtpi,sqrt2,zx1,zx2,exdel |
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| [381] | 54 | c lconv = true si le calcul a converge (entre autre si qsub < min_q) |
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| 55 | LOGICAL lconv(klon) |
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| 56 | |
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| 57 | |
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| 58 | pi = ACOS(-1.) |
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| [495] | 59 | sqrtpi=sqrt(pi) |
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| 60 | sqrt2=sqrt(2.) |
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| [381] | 61 | |
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| 62 | ptconv=.false. |
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| 63 | ratqsc=0. |
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| [546] | 64 | CLDF = 0. |
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| [381] | 65 | |
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| 66 | DO 500 K = 1, ND |
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| 67 | |
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| 68 | do i=1,klon ! vector |
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| 69 | mu(i) = R(i,K) |
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| 70 | mu(i) = MAX(mu(i),min_mu) |
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| 71 | qsat(i) = RS(i,K) |
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| 72 | qsat(i) = MAX(qsat(i),min_mu) |
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| 73 | delta(i) = log(mu(i)/qsat(i)) |
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| 74 | enddo ! vector |
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| 75 | |
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| 76 | C |
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| 77 | C *** There is no subgrid-scale condensation; *** |
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| 78 | C *** the scheme becomes equivalent to an "all-or-nothing" *** |
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| 79 | C *** large-scale condensation scheme. *** |
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| 80 | C |
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| 81 | |
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| 82 | C |
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| 83 | C *** Some condensation is produced at the subgrid-scale *** |
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| 84 | C *** *** |
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| 85 | C *** PDF = generalized log-normal distribution (GNO) *** |
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| 86 | C *** (k<0 because a lower bound is considered for the PDF) *** |
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| 87 | C *** *** |
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| 88 | C *** -> Determine x (the parameter k of the GNO PDF) such *** |
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| 89 | C *** that the contribution of subgrid-scale processes to *** |
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| 90 | C *** the in-cloud water content is equal to QSUB(K) *** |
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| 91 | C *** (equations (13), (14), (15) + Appendix B of the paper) *** |
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| 92 | C *** *** |
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| 93 | C *** Here, an iterative method is used for this purpose *** |
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| 94 | C *** (other numerical methods might be more efficient) *** |
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| 95 | C *** *** |
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| 96 | C *** NB: the "error function" is called ERF *** |
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| 97 | C *** (ERF in double precision) *** |
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| 98 | C |
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| 99 | |
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| 100 | c On commence par eliminer les cas pour lesquels on n'a pas |
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| 101 | c suffisamment d'eau nuageuse. |
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| 102 | |
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| 103 | do i=1,klon ! vector |
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| 104 | |
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| 105 | IF ( QSUB(i,K) .lt. min_Q ) THEN |
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| 106 | ptconv(i,k)=.false. |
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| 107 | ratqsc(i,k)=0. |
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| 108 | lconv(i) = .true. |
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| 109 | |
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| 110 | c Rien on a deja initialise |
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| 111 | |
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| 112 | ELSE |
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| 113 | |
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| 114 | lconv(i) = .FALSE. |
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| 115 | vmax(i) = vmax0 |
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| 116 | |
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| 117 | beta(i) = QSUB(i,K)/mu(i) + EXP( -MIN(0.0,delta(i)) ) |
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| 118 | |
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| 119 | c -- roots of equation v > vmax: |
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| 120 | |
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| 121 | det(i) = delta(i) + vmax(i)**2. |
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| 122 | if (det(i).LE.0.0) vmax(i) = vmax0 + 1.0 |
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| 123 | det(i) = delta(i) + vmax(i)**2. |
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| 124 | |
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| 125 | if (det(i).LE.0.) then |
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| 126 | xx(i) = -0.0001 |
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| 127 | else |
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| [495] | 128 | zx1=-sqrt2*vmax(i) |
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| 129 | zx2=SQRT(1.0+delta(i)/(vmax(i)**2.)) |
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| 130 | xx1(i)=zx1*(1.0-zx2) |
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| 131 | xx2(i)=zx1*(1.0+zx2) |
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| [381] | 132 | xx(i) = 1.01 * xx1(i) |
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| 133 | if ( xx1(i) .GE. 0.0 ) xx(i) = 0.5*xx2(i) |
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| 134 | endif |
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| 135 | if (delta(i).LT.0.) xx(i) = -0.5*SQRT(log(2.)) |
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| 136 | |
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| 137 | ENDIF |
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| 138 | |
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| 139 | enddo ! vector |
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| 140 | |
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| 141 | c---------------------------------------------------------------------- |
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| 142 | c Debut des nmax iterations pour trouver la solution. |
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| 143 | c---------------------------------------------------------------------- |
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| 144 | |
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| 145 | DO n = 1, nmax |
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| 146 | |
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| 147 | do i=1,klon ! vector |
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| 148 | if (.not.lconv(i)) then |
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| 149 | |
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| [495] | 150 | u(i) = delta(i)/(xx(i)*sqrt2) + xx(i)/(2.*sqrt2) |
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| 151 | v(i) = delta(i)/(xx(i)*sqrt2) - xx(i)/(2.*sqrt2) |
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| [381] | 152 | |
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| 153 | IF ( v(i) .GT. vmax(i) ) THEN |
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| 154 | |
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| 155 | IF ( ABS(u(i)) .GT. vmax(i) |
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| 156 | : .AND. delta(i) .LT. 0. ) THEN |
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| 157 | |
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| 158 | c -- use asymptotic expression of erf for u and v large: |
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| 159 | c ( -> analytic solution for xx ) |
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| [495] | 160 | exdel=beta(i)*EXP(delta(i)) |
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| 161 | aux(i) = 2.0*delta(i)*(1.-exdel) |
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| 162 | : /(1.+exdel) |
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| [381] | 163 | if (aux(i).lt.0.) then |
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| [495] | 164 | c print*,'AUX(',i,',',k,')<0',aux(i),delta(i),beta(i) |
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| [381] | 165 | aux(i)=0. |
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| 166 | endif |
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| 167 | xx(i) = -SQRT(aux(i)) |
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| [495] | 168 | block(i) = EXP(-v(i)*v(i)) / v(i) / sqrtpi |
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| [381] | 169 | dist(i) = 0.0 |
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| 170 | fprime(i) = 1.0 |
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| 171 | |
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| 172 | ELSE |
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| 173 | |
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| 174 | c -- erfv -> 1.0, use an asymptotic expression of erfv for v large: |
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| 175 | |
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| [495] | 176 | erfcu(i) = 1.0-ERF(u(i)) |
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| [381] | 177 | c !!! ATTENTION : rajout d'un seuil pour l'exponentiel |
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| [495] | 178 | aux(i) = sqrtpi*erfcu(i)*EXP(min(v(i)*v(i),100.)) |
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| [381] | 179 | coeff(i) = 1.0 - 1./2./(v(i)**2.) + 3./4./(v(i)**4.) |
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| [495] | 180 | block(i) = coeff(i) * EXP(-v(i)*v(i)) / v(i) / sqrtpi |
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| [381] | 181 | dist(i) = v(i) * aux(i) / coeff(i) - beta(i) |
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| 182 | fprime(i) = 2.0 / xx(i) * (v(i)**2.) |
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| 183 | : * ( coeff(i)*EXP(-delta(i)) - u(i) * aux(i) ) |
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| 184 | : / coeff(i) / coeff(i) |
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| 185 | |
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| 186 | ENDIF ! ABS(u) |
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| 187 | |
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| 188 | ELSE |
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| 189 | |
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| 190 | c -- general case: |
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| 191 | |
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| [495] | 192 | erfcu(i) = 1.0-ERF(u(i)) |
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| 193 | erfcv(i) = 1.0-ERF(v(i)) |
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| 194 | block(i) = erfcv(i) |
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| 195 | dist(i) = erfcu(i) / erfcv(i) - beta(i) |
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| [381] | 196 | zu2(i)=u(i)*u(i) |
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| 197 | zv2(i)=v(i)*v(i) |
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| 198 | if(zu2(i).gt.20..or. zv2(i).gt.20.) then |
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| [495] | 199 | c print*,'ATTENTION !!! xx(',i,') =', xx(i) |
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| 200 | c print*,'ATTENTION !!! klon,ND,R,RS,QSUB,PTCONV,RATQSC,CLDF', |
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| 201 | c .klon,ND,R(i,k),RS(i,k),QSUB(i,k),PTCONV(i,k),RATQSC(i,k), |
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| 202 | c .CLDF(i,k) |
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| 203 | c print*,'ATTENTION !!! zu2 zv2 =',zu2(i),zv2(i) |
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| [381] | 204 | zu2(i)=20. |
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| 205 | zv2(i)=20. |
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| 206 | fprime(i) = 0. |
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| 207 | else |
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| [495] | 208 | fprime(i) = 2. /sqrtpi /xx(i) /erfcv(i)**2. |
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| 209 | : * ( erfcv(i)*v(i)*EXP(-zu2(i)) |
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| 210 | : - erfcu(i)*u(i)*EXP(-zv2(i)) ) |
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| [381] | 211 | endif |
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| 212 | ENDIF ! x |
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| 213 | |
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| 214 | c -- test numerical convergence: |
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| 215 | |
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| 216 | c print*,'avant test ',i,k,lconv(i),u(i),v(i) |
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| 217 | if ( ABS(dist(i)/beta(i)) .LT. epsilon ) then |
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| 218 | c print*,'v-u **2',(v(i)-u(i))**2 |
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| 219 | c print*,'exp v-u **2',exp((v(i)-u(i))**2) |
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| 220 | ptconv(i,K) = .TRUE. |
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| 221 | lconv(i)=.true. |
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| 222 | c borne pour l'exponentielle |
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| 223 | ratqsc(i,k)=min(2.*(v(i)-u(i))**2,20.) |
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| 224 | ratqsc(i,k)=sqrt(exp(ratqsc(i,k))-1.) |
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| 225 | CLDF(i,K) = 0.5 * block(i) |
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| 226 | else |
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| 227 | xx(i) = xx(i) - dist(i)/fprime(i) |
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| 228 | endif |
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| 229 | c print*,'apres test ',i,k,lconv(i) |
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| 230 | |
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| 231 | endif ! lconv |
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| 232 | enddo ! vector |
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| 233 | |
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| 234 | c---------------------------------------------------------------------- |
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| 235 | c Fin des nmax iterations pour trouver la solution. |
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| 236 | ENDDO ! n |
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| 237 | c---------------------------------------------------------------------- |
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| 238 | |
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| 239 | 500 CONTINUE ! K |
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| 240 | |
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| 241 | RETURN |
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| 242 | END |
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| 243 | |
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| 244 | |
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| 245 | |
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