| 1 |
! |
| 2 |
! $Header: /home/cvsroot/LMDZ4/libf/phylmd/clouds_gno.F,v 1.2 2004/11/09 16:55:40 lmdzadmin Exp $ |
| 3 |
! |
| 4 |
C |
| 5 |
C================================================================================ |
| 6 |
C |
| 7 |
SUBROUTINE CLOUDS_GNO(klon,ND,R,RS,QSUB,PTCONV,RATQSC,CLDF) |
| 8 |
IMPLICIT NONE |
| 9 |
C |
| 10 |
C-------------------------------------------------------------------------------- |
| 11 |
C |
| 12 |
C Inputs: |
| 13 |
C |
| 14 |
C ND----------: Number of vertical levels |
| 15 |
C R--------ND-: Domain-averaged mixing ratio of total water |
| 16 |
C RS-------ND-: Mean saturation humidity mixing ratio within the gridbox |
| 17 |
C QSUB-----ND-: Mixing ratio of condensed water within clouds associated |
| 18 |
C with SUBGRID-SCALE condensation processes (here, it is |
| 19 |
C predicted by the convection scheme) |
| 20 |
C Outputs: |
| 21 |
C |
| 22 |
C PTCONV-----ND-: Point convectif = TRUE |
| 23 |
C RATQSC-----ND-: Largeur normalisee de la distribution |
| 24 |
C CLDF-----ND-: Fraction nuageuse |
| 25 |
C |
| 26 |
C-------------------------------------------------------------------------------- |
| 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 |
c -- parameters controlling the iteration: |
| 36 |
c -- nmax : maximum nb of iterations (hopefully never reached) |
| 37 |
c -- epsilon : accuracy of the numerical resolution |
| 38 |
c -- vmax : v-value above which we use an asymptotic expression for ERF(v) |
| 39 |
|
| 40 |
INTEGER nmax |
| 41 |
PARAMETER ( nmax = 10) |
| 42 |
REAL epsilon, vmax0, vmax(klon) |
| 43 |
PARAMETER ( epsilon = 0.02, vmax0 = 2.0 ) |
| 44 |
|
| 45 |
REAL min_mu, min_Q |
| 46 |
PARAMETER ( min_mu = 1.e-12, min_Q=1.e-12 ) |
| 47 |
|
| 48 |
INTEGER i,K, n, m |
| 49 |
REAL mu(klon), qsat(klon), delta(klon), beta(klon) |
| 50 |
real zu2(klon),zv2(klon) |
| 51 |
REAL xx(klon), aux(klon), coeff(klon), block(klon) |
| 52 |
REAL dist(klon), fprime(klon), det(klon) |
| 53 |
REAL pi, u(klon), v(klon), erfcu(klon), erfcv(klon) |
| 54 |
REAL xx1(klon), xx2(klon) |
| 55 |
real erf,kkk |
| 56 |
real sqrtpi,sqrt2,zx1,zx2,exdel |
| 57 |
c lconv = true si le calcul a converge (entre autre si qsub < min_q) |
| 58 |
LOGICAL lconv(klon) |
| 59 |
|
| 60 |
cym |
| 61 |
cldf(:,:)=0.0 |
| 62 |
|
| 63 |
pi = ACOS(-1.) |
| 64 |
sqrtpi=sqrt(pi) |
| 65 |
sqrt2=sqrt(2.) |
| 66 |
|
| 67 |
ptconv=.false. |
| 68 |
ratqsc=0. |
| 69 |
|
| 70 |
|
| 71 |
DO 500 K = 1, ND |
| 72 |
|
| 73 |
do i=1,klon ! vector |
| 74 |
mu(i) = R(i,K) |
| 75 |
mu(i) = MAX(mu(i),min_mu) |
| 76 |
qsat(i) = RS(i,K) |
| 77 |
qsat(i) = MAX(qsat(i),min_mu) |
| 78 |
delta(i) = log(mu(i)/qsat(i)) |
| 79 |
enddo ! vector |
| 80 |
|
| 81 |
C |
| 82 |
C *** There is no subgrid-scale condensation; *** |
| 83 |
C *** the scheme becomes equivalent to an "all-or-nothing" *** |
| 84 |
C *** large-scale condensation scheme. *** |
| 85 |
C |
| 86 |
|
| 87 |
C |
| 88 |
C *** Some condensation is produced at the subgrid-scale *** |
| 89 |
C *** *** |
| 90 |
C *** PDF = generalized log-normal distribution (GNO) *** |
| 91 |
C *** (k<0 because a lower bound is considered for the PDF) *** |
| 92 |
C *** *** |
| 93 |
C *** -> Determine x (the parameter k of the GNO PDF) such *** |
| 94 |
C *** that the contribution of subgrid-scale processes to *** |
| 95 |
C *** the in-cloud water content is equal to QSUB(K) *** |
| 96 |
C *** (equations (13), (14), (15) + Appendix B of the paper) *** |
| 97 |
C *** *** |
| 98 |
C *** Here, an iterative method is used for this purpose *** |
| 99 |
C *** (other numerical methods might be more efficient) *** |
| 100 |
C *** *** |
| 101 |
C *** NB: the "error function" is called ERF *** |
| 102 |
C *** (ERF in double precision) *** |
| 103 |
C |
| 104 |
|
| 105 |
c On commence par eliminer les cas pour lesquels on n'a pas |
| 106 |
c suffisamment d'eau nuageuse. |
| 107 |
|
| 108 |
do i=1,klon ! vector |
| 109 |
|
| 110 |
IF ( QSUB(i,K) .lt. min_Q ) THEN |
| 111 |
ptconv(i,k)=.false. |
| 112 |
ratqsc(i,k)=0. |
| 113 |
lconv(i) = .true. |
| 114 |
|
| 115 |
c Rien on a deja initialise |
| 116 |
|
| 117 |
ELSE |
| 118 |
|
| 119 |
lconv(i) = .FALSE. |
| 120 |
vmax(i) = vmax0 |
| 121 |
|
| 122 |
beta(i) = QSUB(i,K)/mu(i) + EXP( -MIN(0.0,delta(i)) ) |
| 123 |
|
| 124 |
c -- roots of equation v > vmax: |
| 125 |
|
| 126 |
det(i) = delta(i) + vmax(i)**2. |
| 127 |
if (det(i).LE.0.0) vmax(i) = vmax0 + 1.0 |
| 128 |
det(i) = delta(i) + vmax(i)**2. |
| 129 |
|
| 130 |
if (det(i).LE.0.) then |
| 131 |
xx(i) = -0.0001 |
| 132 |
else |
| 133 |
zx1=-sqrt2*vmax(i) |
| 134 |
zx2=SQRT(1.0+delta(i)/(vmax(i)**2.)) |
| 135 |
xx1(i)=zx1*(1.0-zx2) |
| 136 |
xx2(i)=zx1*(1.0+zx2) |
| 137 |
xx(i) = 1.01 * xx1(i) |
| 138 |
if ( xx1(i) .GE. 0.0 ) xx(i) = 0.5*xx2(i) |
| 139 |
endif |
| 140 |
if (delta(i).LT.0.) xx(i) = -0.5*SQRT(log(2.)) |
| 141 |
|
| 142 |
ENDIF |
| 143 |
|
| 144 |
enddo ! vector |
| 145 |
|
| 146 |
c---------------------------------------------------------------------- |
| 147 |
c Debut des nmax iterations pour trouver la solution. |
| 148 |
c---------------------------------------------------------------------- |
| 149 |
|
| 150 |
DO n = 1, nmax |
| 151 |
|
| 152 |
do i=1,klon ! vector |
| 153 |
if (.not.lconv(i)) then |
| 154 |
|
| 155 |
u(i) = delta(i)/(xx(i)*sqrt2) + xx(i)/(2.*sqrt2) |
| 156 |
v(i) = delta(i)/(xx(i)*sqrt2) - xx(i)/(2.*sqrt2) |
| 157 |
|
| 158 |
IF ( v(i) .GT. vmax(i) ) THEN |
| 159 |
|
| 160 |
IF ( ABS(u(i)) .GT. vmax(i) |
| 161 |
: .AND. delta(i) .LT. 0. ) THEN |
| 162 |
|
| 163 |
c -- use asymptotic expression of erf for u and v large: |
| 164 |
c ( -> analytic solution for xx ) |
| 165 |
exdel=beta(i)*EXP(delta(i)) |
| 166 |
aux(i) = 2.0*delta(i)*(1.-exdel) |
| 167 |
: /(1.+exdel) |
| 168 |
if (aux(i).lt.0.) then |
| 169 |
c print*,'AUX(',i,',',k,')<0',aux(i),delta(i),beta(i) |
| 170 |
aux(i)=0. |
| 171 |
endif |
| 172 |
xx(i) = -SQRT(aux(i)) |
| 173 |
block(i) = EXP(-v(i)*v(i)) / v(i) / sqrtpi |
| 174 |
dist(i) = 0.0 |
| 175 |
fprime(i) = 1.0 |
| 176 |
|
| 177 |
ELSE |
| 178 |
|
| 179 |
c -- erfv -> 1.0, use an asymptotic expression of erfv for v large: |
| 180 |
|
| 181 |
erfcu(i) = 1.0-ERF(u(i)) |
| 182 |
c !!! ATTENTION : rajout d'un seuil pour l'exponentiel |
| 183 |
aux(i) = sqrtpi*erfcu(i)*EXP(min(v(i)*v(i),100.)) |
| 184 |
coeff(i) = 1.0 - 1./2./(v(i)**2.) + 3./4./(v(i)**4.) |
| 185 |
block(i) = coeff(i) * EXP(-v(i)*v(i)) / v(i) / sqrtpi |
| 186 |
dist(i) = v(i) * aux(i) / coeff(i) - beta(i) |
| 187 |
fprime(i) = 2.0 / xx(i) * (v(i)**2.) |
| 188 |
: * ( coeff(i)*EXP(-delta(i)) - u(i) * aux(i) ) |
| 189 |
: / coeff(i) / coeff(i) |
| 190 |
|
| 191 |
ENDIF ! ABS(u) |
| 192 |
|
| 193 |
ELSE |
| 194 |
|
| 195 |
c -- general case: |
| 196 |
|
| 197 |
erfcu(i) = 1.0-ERF(u(i)) |
| 198 |
erfcv(i) = 1.0-ERF(v(i)) |
| 199 |
block(i) = erfcv(i) |
| 200 |
dist(i) = erfcu(i) / erfcv(i) - beta(i) |
| 201 |
zu2(i)=u(i)*u(i) |
| 202 |
zv2(i)=v(i)*v(i) |
| 203 |
if(zu2(i).gt.20..or. zv2(i).gt.20.) then |
| 204 |
c print*,'ATTENTION !!! xx(',i,') =', xx(i) |
| 205 |
c print*,'ATTENTION !!! klon,ND,R,RS,QSUB,PTCONV,RATQSC,CLDF', |
| 206 |
c .klon,ND,R(i,k),RS(i,k),QSUB(i,k),PTCONV(i,k),RATQSC(i,k), |
| 207 |
c .CLDF(i,k) |
| 208 |
c print*,'ATTENTION !!! zu2 zv2 =',zu2(i),zv2(i) |
| 209 |
zu2(i)=20. |
| 210 |
zv2(i)=20. |
| 211 |
fprime(i) = 0. |
| 212 |
else |
| 213 |
fprime(i) = 2. /sqrtpi /xx(i) /erfcv(i)**2. |
| 214 |
: * ( erfcv(i)*v(i)*EXP(-zu2(i)) |
| 215 |
: - erfcu(i)*u(i)*EXP(-zv2(i)) ) |
| 216 |
endif |
| 217 |
ENDIF ! x |
| 218 |
|
| 219 |
c -- test numerical convergence: |
| 220 |
|
| 221 |
c print*,'avant test ',i,k,lconv(i),u(i),v(i) |
| 222 |
if ( ABS(dist(i)/beta(i)) .LT. epsilon ) then |
| 223 |
c print*,'v-u **2',(v(i)-u(i))**2 |
| 224 |
c print*,'exp v-u **2',exp((v(i)-u(i))**2) |
| 225 |
ptconv(i,K) = .TRUE. |
| 226 |
lconv(i)=.true. |
| 227 |
c borne pour l'exponentielle |
| 228 |
ratqsc(i,k)=min(2.*(v(i)-u(i))**2,20.) |
| 229 |
ratqsc(i,k)=sqrt(exp(ratqsc(i,k))-1.) |
| 230 |
CLDF(i,K) = 0.5 * block(i) |
| 231 |
else |
| 232 |
xx(i) = xx(i) - dist(i)/fprime(i) |
| 233 |
endif |
| 234 |
c print*,'apres test ',i,k,lconv(i) |
| 235 |
|
| 236 |
endif ! lconv |
| 237 |
enddo ! vector |
| 238 |
|
| 239 |
c---------------------------------------------------------------------- |
| 240 |
c Fin des nmax iterations pour trouver la solution. |
| 241 |
ENDDO ! n |
| 242 |
c---------------------------------------------------------------------- |
| 243 |
|
| 244 |
500 CONTINUE ! K |
| 245 |
|
| 246 |
RETURN |
| 247 |
END |
| 248 |
|
| 249 |
|
| 250 |
|
Parent Directory
| 
Revision Log