| Directory: | ./ |
|---|---|
| File: | phys/clouds_gno.f90 |
| Date: | 2022-01-11 19:19:34 |
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| 1 | |||
| 2 | ! $Header$ | ||
| 3 | |||
| 4 | |||
| 5 | ! ================================================================================ | ||
| 6 | |||
| 7 | 240 | SUBROUTINE clouds_gno(klon, nd, r, rs, qsub, ptconv, ratqsc, cldf) | |
| 8 | IMPLICIT NONE | ||
| 9 | |||
| 10 | ! -------------------------------------------------------------------------------- | ||
| 11 | |||
| 12 | ! Inputs: | ||
| 13 | |||
| 14 | ! ND----------: Number of vertical levels | ||
| 15 | ! R--------ND-: Domain-averaged mixing ratio of total water | ||
| 16 | ! RS-------ND-: Mean saturation humidity mixing ratio within the gridbox | ||
| 17 | ! QSUB-----ND-: Mixing ratio of condensed water within clouds associated | ||
| 18 | ! with SUBGRID-SCALE condensation processes (here, it is | ||
| 19 | ! predicted by the convection scheme) | ||
| 20 | ! Outputs: | ||
| 21 | |||
| 22 | ! PTCONV-----ND-: Point convectif = TRUE | ||
| 23 | ! RATQSC-----ND-: Largeur normalisee de la distribution | ||
| 24 | ! CLDF-----ND-: Fraction nuageuse | ||
| 25 | |||
| 26 | ! -------------------------------------------------------------------------------- | ||
| 27 | |||
| 28 | |||
| 29 | INTEGER klon, nd | ||
| 30 | REAL r(klon, nd), rs(klon, nd), qsub(klon, nd) | ||
| 31 | LOGICAL ptconv(klon, nd) | ||
| 32 | REAL ratqsc(klon, nd) | ||
| 33 | REAL cldf(klon, nd) | ||
| 34 | |||
| 35 | ! -- parameters controlling the iteration: | ||
| 36 | ! -- nmax : maximum nb of iterations (hopefully never reached) | ||
| 37 | ! -- epsilon : accuracy of the numerical resolution | ||
| 38 | ! -- vmax : v-value above which we use an asymptotic expression for | ||
| 39 | ! ERF(v) | ||
| 40 | |||
| 41 | INTEGER nmax | ||
| 42 | PARAMETER (nmax=10) | ||
| 43 | 480 | REAL epsilon, vmax0, vmax(klon) | |
| 44 | PARAMETER (epsilon=0.02, vmax0=2.0) | ||
| 45 | |||
| 46 | REAL min_mu, min_q | ||
| 47 | PARAMETER (min_mu=1.E-12, min_q=1.E-12) | ||
| 48 | |||
| 49 | INTEGER i, k, n, m | ||
| 50 | 480 | REAL mu(klon), qsat, delta(klon), beta(klon) | |
| 51 | REAL zu2, zv2 | ||
| 52 | 480 | REAL xx(klon), aux(klon), coeff, block | |
| 53 | REAL dist, fprime, det | ||
| 54 | REAL pi, u, v, erfcu, erfcv | ||
| 55 | REAL xx1, xx2 | ||
| 56 | REAL erf, hsqrtlog_2, v2 | ||
| 57 | REAL sqrtpi, sqrt2, zx1, zx2, exdel | ||
| 58 | ! lconv = true si le calcul a converge (entre autre si qsub < min_q) | ||
| 59 | 240 | LOGICAL lconv(klon) | |
| 60 | |||
| 61 | ! cdir arraycomb | ||
| 62 |
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9313440 | cldf(1:klon, 1:nd) = 0.0 ! cym |
| 63 |
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9313440 | ratqsc(1:klon, 1:nd) = 0.0 |
| 64 |
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9313440 | ptconv(1:klon, 1:nd) = .FALSE. |
| 65 | ! cdir end arraycomb | ||
| 66 | |||
| 67 | pi = acos(-1.) | ||
| 68 | sqrtpi = sqrt(pi) | ||
| 69 | sqrt2 = sqrt(2.) | ||
| 70 | hsqrtlog_2 = 0.5*sqrt(log(2.)) | ||
| 71 | |||
| 72 |
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9600 | DO k = 1, nd |
| 73 | |||
| 74 |
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9313200 | DO i = 1, klon ! vector |
| 75 | 9303840 | mu(i) = r(i, k) | |
| 76 | 9303840 | mu(i) = max(mu(i), min_mu) | |
| 77 | 9303840 | qsat = rs(i, k) | |
| 78 | 9303840 | qsat = max(qsat, min_mu) | |
| 79 | 9303840 | delta(i) = log(mu(i)/qsat) | |
| 80 | ! enddo ! vector | ||
| 81 | |||
| 82 | |||
| 83 | ! *** There is no subgrid-scale condensation; *** | ||
| 84 | ! *** the scheme becomes equivalent to an "all-or-nothing" *** | ||
| 85 | ! *** large-scale condensation scheme. *** | ||
| 86 | |||
| 87 | |||
| 88 | |||
| 89 | ! *** Some condensation is produced at the subgrid-scale *** | ||
| 90 | ! *** *** | ||
| 91 | ! *** PDF = generalized log-normal distribution (GNO) *** | ||
| 92 | ! *** (k<0 because a lower bound is considered for the PDF) *** | ||
| 93 | ! *** *** | ||
| 94 | ! *** -> Determine x (the parameter k of the GNO PDF) such *** | ||
| 95 | ! *** that the contribution of subgrid-scale processes to *** | ||
| 96 | ! *** the in-cloud water content is equal to QSUB(K) *** | ||
| 97 | ! *** (equations (13), (14), (15) + Appendix B of the paper) *** | ||
| 98 | ! *** *** | ||
| 99 | ! *** Here, an iterative method is used for this purpose *** | ||
| 100 | ! *** (other numerical methods might be more efficient) *** | ||
| 101 | ! *** *** | ||
| 102 | ! *** NB: the "error function" is called ERF *** | ||
| 103 | ! *** (ERF in double precision) *** | ||
| 104 | |||
| 105 | |||
| 106 | ! On commence par eliminer les cas pour lesquels on n'a pas | ||
| 107 | ! suffisamment d'eau nuageuse. | ||
| 108 | |||
| 109 | ! do i=1,klon ! vector | ||
| 110 | |||
| 111 |
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9313200 | IF (qsub(i,k)<min_q) THEN |
| 112 | 8784770 | ptconv(i, k) = .FALSE. | |
| 113 | 8784770 | ratqsc(i, k) = 0. | |
| 114 | 8784770 | lconv(i) = .TRUE. | |
| 115 | |||
| 116 | ! Rien on a deja initialise | ||
| 117 | |||
| 118 | ELSE | ||
| 119 | |||
| 120 | 519070 | lconv(i) = .FALSE. | |
| 121 | 519070 | vmax(i) = vmax0 | |
| 122 | |||
| 123 | 519070 | beta(i) = qsub(i, k)/mu(i) + exp(-min(0.0,delta(i))) | |
| 124 | |||
| 125 | ! -- roots of equation v > vmax: | ||
| 126 | |||
| 127 | 519070 | det = delta(i) + vmax(i)*vmax(i) | |
| 128 |
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519070 | IF (det<=0.0) vmax(i) = vmax0 + 1.0 |
| 129 | 519070 | det = delta(i) + vmax(i)*vmax(i) | |
| 130 | |||
| 131 |
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519070 | IF (det<=0.) THEN |
| 132 | ✗ | xx(i) = -0.0001 | |
| 133 | ELSE | ||
| 134 | 519070 | zx1 = -sqrt2*vmax(i) | |
| 135 | 519070 | zx2 = sqrt(1.0+delta(i)/(vmax(i)*vmax(i))) | |
| 136 | 519070 | xx1 = zx1*(1.0-zx2) | |
| 137 | 519070 | xx2 = zx1*(1.0+zx2) | |
| 138 | 519070 | xx(i) = 1.01*xx1 | |
| 139 |
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519070 | IF (xx1>=0.0) xx(i) = 0.5*xx2 |
| 140 | END IF | ||
| 141 |
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519070 | IF (delta(i)<0.) xx(i) = -hsqrtlog_2 |
| 142 | |||
| 143 | END IF | ||
| 144 | |||
| 145 | END DO ! vector | ||
| 146 | |||
| 147 | ! ---------------------------------------------------------------------- | ||
| 148 | ! Debut des nmax iterations pour trouver la solution. | ||
| 149 | ! ---------------------------------------------------------------------- | ||
| 150 | |||
| 151 |
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103200 | DO n = 1, nmax |
| 152 | |||
| 153 |
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93141360 | DO i = 1, klon ! vector |
| 154 |
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93132000 | IF (.NOT. lconv(i)) THEN |
| 155 | |||
| 156 | 1386142 | u = delta(i)/(xx(i)*sqrt2) + xx(i)/(2.*sqrt2) | |
| 157 | 1386142 | v = delta(i)/(xx(i)*sqrt2) - xx(i)/(2.*sqrt2) | |
| 158 | 1386142 | v2 = v*v | |
| 159 | |||
| 160 |
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1386142 | IF (v>vmax(i)) THEN |
| 161 | |||
| 162 |
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228372 | IF (abs(u)>vmax(i) .AND. delta(i)<0.) THEN |
| 163 | |||
| 164 | ! -- use asymptotic expression of erf for u and v large: | ||
| 165 | ! ( -> analytic solution for xx ) | ||
| 166 | 202775 | exdel = beta(i)*exp(delta(i)) | |
| 167 | 202775 | aux(i) = 2.0*delta(i)*(1.-exdel)/(1.+exdel) | |
| 168 |
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202775 | IF (aux(i)<0.) THEN |
| 169 | ! print*,'AUX(',i,',',k,')<0',aux(i),delta(i),beta(i) | ||
| 170 | ✗ | aux(i) = 0. | |
| 171 | END IF | ||
| 172 | 202775 | xx(i) = -sqrt(aux(i)) | |
| 173 | 202775 | block = exp(-v*v)/v/sqrtpi | |
| 174 | dist = 0.0 | ||
| 175 | 202775 | fprime = 1.0 | |
| 176 | |||
| 177 | ELSE | ||
| 178 | |||
| 179 | ! -- erfv -> 1.0, use an asymptotic expression of erfv for v | ||
| 180 | ! large: | ||
| 181 | |||
| 182 | 25597 | erfcu = 1.0 - erf(u) | |
| 183 | ! !!! ATTENTION : rajout d'un seuil pour l'exponentiel | ||
| 184 | 25597 | aux(i) = sqrtpi*erfcu*exp(min(v2,100.)) | |
| 185 | 25597 | coeff = 1.0 - 0.5/(v2) + 0.75/(v2*v2) | |
| 186 | 25597 | block = coeff*exp(-v2)/v/sqrtpi | |
| 187 | 25597 | dist = v*aux(i)/coeff - beta(i) | |
| 188 | 25597 | fprime = 2.0/xx(i)*(v2)*(exp(-delta(i))-u*aux(i)/coeff)/coeff | |
| 189 | |||
| 190 | END IF ! ABS(u) | ||
| 191 | |||
| 192 | ELSE | ||
| 193 | |||
| 194 | ! -- general case: | ||
| 195 | |||
| 196 | 1157770 | erfcu = 1.0 - erf(u) | |
| 197 | 1157770 | erfcv = 1.0 - erf(v) | |
| 198 | block = erfcv | ||
| 199 | 1157770 | dist = erfcu/erfcv - beta(i) | |
| 200 | 1157770 | zu2 = u*u | |
| 201 | zv2 = v2 | ||
| 202 |
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1157770 | IF (zu2>20. .OR. zv2>20.) THEN |
| 203 | ! print*,'ATTENTION !!! xx(',i,') =', xx(i) | ||
| 204 | ! print*,'ATTENTION !!! klon,ND,R,RS,QSUB,PTCONV,RATQSC,CLDF', | ||
| 205 | ! .klon,ND,R(i,k),RS(i,k),QSUB(i,k),PTCONV(i,k),RATQSC(i,k), | ||
| 206 | ! .CLDF(i,k) | ||
| 207 | ! print*,'ATTENTION !!! zu2 zv2 =',zu2(i),zv2(i) | ||
| 208 | zu2 = 20. | ||
| 209 | zv2 = 20. | ||
| 210 | fprime = 0. | ||
| 211 | ELSE | ||
| 212 | fprime = 2./sqrtpi/xx(i)/(erfcv*erfcv)* & | ||
| 213 | 1157770 | (erfcv*v*exp(-zu2)-erfcu*u*exp(-zv2)) | |
| 214 | END IF | ||
| 215 | END IF ! x | ||
| 216 | |||
| 217 | ! -- test numerical convergence: | ||
| 218 | |||
| 219 | ! if (beta(i).lt.1.e-10) then | ||
| 220 | ! print*,'avant test ',i,k,lconv(i),u(i),v(i),beta(i) | ||
| 221 | ! stop | ||
| 222 | ! endif | ||
| 223 |
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1386142 | IF (abs(fprime)<1.E-11) THEN |
| 224 | ! print*,'avant test fprime<.e-11 ' | ||
| 225 | ! s ,i,k,lconv(i),u(i),v(i),beta(i),fprime(i) | ||
| 226 | ! print*,'klon,ND,R,RS,QSUB', | ||
| 227 | ! s klon,ND,R(i,k),rs(i,k),qsub(i,k) | ||
| 228 | ✗ | fprime = sign(1.E-11, fprime) | |
| 229 | END IF | ||
| 230 | |||
| 231 | |||
| 232 |
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1386142 | IF (abs(dist/beta(i))<epsilon) THEN |
| 233 | ! print*,'v-u **2',(v(i)-u(i))**2 | ||
| 234 | ! print*,'exp v-u **2',exp((v(i)-u(i))**2) | ||
| 235 | 519070 | ptconv(i, k) = .TRUE. | |
| 236 | 519070 | lconv(i) = .TRUE. | |
| 237 | ! borne pour l'exponentielle | ||
| 238 | 519070 | ratqsc(i, k) = min(2.*(v-u)*(v-u), 20.) | |
| 239 | 519070 | ratqsc(i, k) = sqrt(exp(ratqsc(i,k))-1.) | |
| 240 | 519070 | cldf(i, k) = 0.5*block | |
| 241 | ELSE | ||
| 242 | 867072 | xx(i) = xx(i) - dist/fprime | |
| 243 | END IF | ||
| 244 | ! print*,'apres test ',i,k,lconv(i) | ||
| 245 | |||
| 246 | END IF ! lconv | ||
| 247 | END DO ! vector | ||
| 248 | |||
| 249 | ! ---------------------------------------------------------------------- | ||
| 250 | ! Fin des nmax iterations pour trouver la solution. | ||
| 251 | END DO ! n | ||
| 252 | ! ---------------------------------------------------------------------- | ||
| 253 | |||
| 254 | |||
| 255 | END DO | ||
| 256 | ! K | ||
| 257 | 240 | RETURN | |
| 258 | END SUBROUTINE clouds_gno | ||
| 259 | |||
| 260 | |||
| 261 | |||
| 262 |