| 1 | ! |
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| 2 | ! $Header$ |
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| 3 | ! |
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| 4 | !C |
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| 5 | !C================================================================================ |
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| 6 | !C |
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| 7 | SUBROUTINE CLOUDS_GNO(klon,ND,R,RS,QSUB,PTCONV,RATQSC,CLDF) |
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| 8 | IMPLICIT NONE |
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| 9 | !C |
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| 10 | !C-------------------------------------------------------------------------------- |
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| 11 | !C |
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| 12 | !C Inputs: |
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| 13 | !C |
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| 14 | !C ND----------: Number of vertical levels |
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| 15 | !C R--------ND-: Domain-averaged mixing ratio of total water |
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| 16 | !C RS-------ND-: Mean saturation humidity mixing ratio within the gridbox |
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| 17 | !C QSUB-----ND-: Mixing ratio of condensed water within clouds associated |
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| 18 | !C with SUBGRID-SCALE condensation processes (here, it is |
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| 19 | !C predicted by the convection scheme) |
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| 20 | !C Outputs: |
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| 21 | !C |
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| 22 | !C PTCONV-----ND-: Point convectif = TRUE |
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| 23 | !C RATQSC-----ND-: Largeur normalisee de la distribution |
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| 24 | !C CLDF-----ND-: Fraction nuageuse |
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| 25 | !C |
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| 26 | !C-------------------------------------------------------------------------------- |
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| 27 | |
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| 28 | |
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| 29 | INTEGER klon,ND |
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| 30 | REAL R(klon,ND), RS(klon,ND), QSUB(klon,ND) |
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| 31 | LOGICAL PTCONV(klon,ND) |
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| 32 | REAL RATQSC(klon,ND) |
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| 33 | REAL CLDF(klon,ND) |
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| 34 | |
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| 35 | !c -- parameters controlling the iteration: |
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| 36 | !c -- nmax : maximum nb of iterations (hopefully never reached) |
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| 37 | !c -- epsilon : accuracy of the numerical resolution |
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| 38 | !c -- vmax : v-value above which we use an asymptotic expression for ERF(v) |
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| 39 | |
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| 40 | INTEGER nmax |
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| 41 | PARAMETER ( nmax = 10) |
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| 42 | REAL epsilon, vmax0, vmax(klon) |
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| 43 | PARAMETER ( epsilon = 0.02, vmax0 = 2.0 ) |
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| 44 | |
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| 45 | REAL min_mu, min_Q |
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| 46 | PARAMETER ( min_mu = 1.e-12, min_Q=1.e-12 ) |
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| 47 | INTEGER i,K, n, m |
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| 48 | REAL mu(klon), qsat, delta(klon), beta(klon) |
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| 49 | real zu2,zv2 |
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| 50 | REAL xx(klon), aux(klon), coeff, block |
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| 51 | REAL dist, fprime, det |
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| 52 | REAL pi, u, v, erfcu, erfcv |
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| 53 | REAL xx1, xx2 |
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| 54 | real erf,hsqrtlog_2,v2 |
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| 55 | real sqrtpi,sqrt2,zx1,zx2,exdel |
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| 56 | !c lconv = true si le calcul a converge (entre autre si qsub < min_q) |
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| 57 | LOGICAL lconv(klon) |
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| 58 | |
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| 59 | !cdir arraycomb |
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| 60 | cldf (1:klon,1:ND)=0.0 ! cym |
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| 61 | ratqsc(1:klon,1:ND)=0.0 |
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| 62 | ptconv(1:klon,1:ND)=.false. |
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| 63 | !cdir end arraycomb |
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| 64 | |
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| 65 | pi = ACOS(-1.) |
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| 66 | sqrtpi=sqrt(pi) |
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| 67 | sqrt2=sqrt(2.) |
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| 68 | hsqrtlog_2=0.5*SQRT(log(2.)) |
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| 69 | |
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| 70 | DO 500 K = 1, ND |
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| 71 | |
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| 72 | do i=1,klon ! vector |
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| 73 | mu(i) = R(i,K) |
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| 74 | mu(i) = MAX(mu(i),min_mu) |
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| 75 | qsat = RS(i,K) |
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| 76 | qsat = MAX(qsat,min_mu) |
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| 77 | delta(i) = log(mu(i)/qsat) |
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| 78 | !c enddo ! vector |
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| 79 | |
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| 80 | !C |
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| 81 | !C *** There is no subgrid-scale condensation; *** |
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| 82 | !C *** the scheme becomes equivalent to an "all-or-nothing" *** |
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| 83 | !C *** large-scale condensation scheme. *** |
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| 84 | !C |
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| 85 | |
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| 86 | !C |
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| 87 | !C *** Some condensation is produced at the subgrid-scale *** |
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| 88 | !C *** *** |
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| 89 | !C *** PDF = generalized log-normal distribution (GNO) *** |
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| 90 | !C *** (k<0 because a lower bound is considered for the PDF) *** |
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| 91 | !C *** *** |
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| 92 | !C *** -> Determine x (the parameter k of the GNO PDF) such *** |
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| 93 | !C *** that the contribution of subgrid-scale processes to *** |
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| 94 | !C *** the in-cloud water content is equal to QSUB(K) *** |
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| 95 | !C *** (equations (13), (14), (15) + Appendix B of the paper) *** |
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| 96 | !C *** *** |
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| 97 | !C *** Here, an iterative method is used for this purpose *** |
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| 98 | !C *** (other numerical methods might be more efficient) *** |
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| 99 | !C *** *** |
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| 100 | !C *** NB: the "error function" is called ERF *** |
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| 101 | !C *** (ERF in double precision) *** |
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| 102 | !C |
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| 103 | |
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| 104 | !c On commence par eliminer les cas pour lesquels on n'a pas |
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| 105 | !c suffisamment d'eau nuageuse. |
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| 106 | |
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| 107 | !c do i=1,klon ! vector |
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| 108 | |
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| 109 | IF ( QSUB(i,K) .lt. min_Q ) THEN |
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| 110 | ptconv(i,k)=.false. |
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| 111 | ratqsc(i,k)=0. |
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| 112 | lconv(i) = .true. |
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| 113 | |
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| 114 | !c Rien on a deja initialise |
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| 115 | |
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| 116 | ELSE |
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| 117 | |
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| 118 | lconv(i) = .FALSE. |
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| 119 | vmax(i) = vmax0 |
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| 120 | |
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| 121 | beta(i) = QSUB(i,K)/mu(i) + EXP( -MIN(0.0,delta(i)) ) |
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| 122 | |
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| 123 | !c -- roots of equation v > vmax: |
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| 124 | |
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| 125 | det = delta(i) + vmax(i)*vmax(i) |
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| 126 | if (det.LE.0.0) vmax(i) = vmax0 + 1.0 |
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| 127 | det = delta(i) + vmax(i)*vmax(i) |
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| 128 | |
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| 129 | if (det.LE.0.) then |
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| 130 | xx(i) = -0.0001 |
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| 131 | else |
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| 132 | zx1=-sqrt2*vmax(i) |
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| 133 | zx2=SQRT(1.0+delta(i)/(vmax(i)*vmax(i))) |
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| 134 | xx1=zx1*(1.0-zx2) |
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| 135 | xx2=zx1*(1.0+zx2) |
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| 136 | xx(i) = 1.01 * xx1 |
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| 137 | if ( xx1 .GE. 0.0 ) xx(i) = 0.5*xx2 |
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| 138 | endif |
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| 139 | if (delta(i).LT.0.) xx(i) = -hsqrtlog_2 |
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| 140 | |
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| 141 | ENDIF |
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| 142 | |
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| 143 | enddo ! vector |
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| 144 | |
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| 145 | !c---------------------------------------------------------------------- |
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| 146 | !c Debut des nmax iterations pour trouver la solution. |
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| 147 | !c---------------------------------------------------------------------- |
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| 148 | |
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| 149 | DO n = 1, nmax |
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| 150 | |
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| 151 | do i=1,klon ! vector |
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| 152 | if (.not.lconv(i)) then |
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| 153 | |
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| 154 | u = delta(i)/(xx(i)*sqrt2) + xx(i)/(2.*sqrt2) |
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| 155 | v = delta(i)/(xx(i)*sqrt2) - xx(i)/(2.*sqrt2) |
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| 156 | v2 = v*v |
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| 157 | |
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| 158 | IF ( v .GT. vmax(i) ) THEN |
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| 159 | |
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| 160 | IF ( ABS(u) .GT. vmax(i) & |
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| 161 | & .AND. delta(i) .LT. 0. ) THEN |
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| 162 | |
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| 163 | !c -- use asymptotic expression of erf for u and v large: |
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| 164 | !c ( -> analytic solution for xx ) |
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| 165 | exdel=beta(i)*EXP(delta(i)) |
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| 166 | aux(i) = 2.0*delta(i)*(1.-exdel) & |
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| 167 | & /(1.+exdel) |
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| 168 | if (aux(i).lt.0.) then |
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| 169 | !c print*,'AUX(',i,',',k,')<0',aux(i),delta(i),beta(i) |
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| 170 | aux(i)=0. |
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| 171 | endif |
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| 172 | xx(i) = -SQRT(aux(i)) |
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| 173 | block = EXP(-v*v) / v / sqrtpi |
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| 174 | dist = 0.0 |
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| 175 | fprime = 1.0 |
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| 176 | |
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| 177 | ELSE |
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| 178 | |
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| 179 | !c -- erfv -> 1.0, use an asymptotic expression of erfv for v large: |
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| 180 | |
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| 181 | erfcu = 1.0-ERF(u) |
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| 182 | !c !!! ATTENTION : rajout d'un seuil pour l'exponentiel |
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| 183 | aux(i) = sqrtpi*erfcu*EXP(min(v2,100.)) |
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| 184 | coeff = 1.0 - 0.5/(v2) + 0.75/(v2*v2) |
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| 185 | block = coeff * EXP(-v2) / v / sqrtpi |
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| 186 | dist = v * aux(i) / coeff - beta(i) |
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| 187 | fprime = 2.0 / xx(i) * (v2) & |
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| 188 | & * ( EXP(-delta(i)) - u * aux(i) / coeff ) & |
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| 189 | & / coeff |
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| 190 | |
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| 191 | ENDIF ! ABS(u) |
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| 192 | |
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| 193 | ELSE |
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| 194 | |
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| 195 | !c -- general case: |
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| 196 | |
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| 197 | erfcu = 1.0-ERF(u) |
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| 198 | erfcv = 1.0-ERF(v) |
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| 199 | block = erfcv |
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| 200 | dist = erfcu / erfcv - beta(i) |
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| 201 | zu2=u*u |
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| 202 | zv2=v2 |
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| 203 | if(zu2.gt.20..or. zv2.gt.20.) then |
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| 204 | !c print*,'ATTENTION !!! xx(',i,') =', xx(i) |
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| 205 | !c print*,'ATTENTION !!! klon,ND,R,RS,QSUB,PTCONV,RATQSC,CLDF', |
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| 206 | !c .klon,ND,R(i,k),RS(i,k),QSUB(i,k),PTCONV(i,k),RATQSC(i,k), |
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| 207 | !c .CLDF(i,k) |
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| 208 | !c print*,'ATTENTION !!! zu2 zv2 =',zu2(i),zv2(i) |
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| 209 | zu2=20. |
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| 210 | zv2=20. |
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| 211 | fprime = 0. |
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| 212 | else |
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| 213 | fprime = 2. /sqrtpi /xx(i) /(erfcv*erfcv) & |
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| 214 | & * ( erfcv*v*EXP(-zu2) & |
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| 215 | & - erfcu*u*EXP(-zv2) ) |
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| 216 | endif |
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| 217 | ENDIF ! x |
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| 218 | |
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| 219 | !c -- test numerical convergence: |
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| 220 | |
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| 221 | ! if (beta(i).lt.1.e-10) then |
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| 222 | ! print*,'avant test ',i,k,lconv(i),u(i),v(i),beta(i) |
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| 223 | ! stop |
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| 224 | ! endif |
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| 225 | if (abs(fprime).lt.1.e-11) then |
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| 226 | ! print*,'avant test fprime<.e-11 ' |
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| 227 | ! s ,i,k,lconv(i),u(i),v(i),beta(i),fprime(i) |
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| 228 | ! print*,'klon,ND,R,RS,QSUB', |
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| 229 | ! s klon,ND,R(i,k),rs(i,k),qsub(i,k) |
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| 230 | fprime=sign(1.e-11,fprime) |
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| 231 | endif |
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| 232 | |
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| 233 | |
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| 234 | if ( ABS(dist/beta(i)) .LT. epsilon ) then |
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| 235 | !c print*,'v-u **2',(v(i)-u(i))**2 |
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| 236 | !c print*,'exp v-u **2',exp((v(i)-u(i))**2) |
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| 237 | ptconv(i,K) = .TRUE. |
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| 238 | lconv(i)=.true. |
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| 239 | !c borne pour l'exponentielle |
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| 240 | ratqsc(i,k)=min(2.*(v-u)*(v-u),20.) |
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| 241 | ratqsc(i,k)=sqrt(exp(ratqsc(i,k))-1.) |
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| 242 | CLDF(i,K) = 0.5 * block |
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| 243 | else |
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| 244 | xx(i) = xx(i) - dist/fprime |
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| 245 | endif |
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| 246 | !c print*,'apres test ',i,k,lconv(i) |
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| 247 | |
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| 248 | endif ! lconv |
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| 249 | enddo ! vector |
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| 250 | |
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| 251 | !c---------------------------------------------------------------------- |
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| 252 | !c Fin des nmax iterations pour trouver la solution. |
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| 253 | ENDDO ! n |
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| 254 | !c---------------------------------------------------------------------- |
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| 255 | |
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| 256 | 500 CONTINUE ! K |
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| 257 | |
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| 258 | RETURN |
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| 259 | END SUBROUTINE CLOUDS_GNO |
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| 260 | |
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| 261 | |
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| 262 | |
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