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module CLOUDS_GNO_m |
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IMPLICIT NONE |
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contains |
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SUBROUTINE CLOUDS_GNO(klon, ND, R, RS, QSUB, PTCONV, RATQSC, CLDF) |
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! From LMDZ4/libf/phylmd/clouds_gno.F, version 1.2, 2004/11/09 16:55:40 |
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use numer_rec_95, only: nr_erf |
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|
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! Inputs: |
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|
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! ND : Number of vertical levels |
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! R ND: Domain-averaged mixing ratio of total water |
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! RS ND: Mean saturation humidity mixing ratio within the gridbox |
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|
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! QSUB ND: Mixing ratio of condensed water within clouds associated |
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! with SUBGRID-SCALE condensation processes (here, it is |
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! predicted by the convection scheme) |
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|
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! Outputs: |
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|
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! PTCONV ND: Point convectif = TRUE |
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! RATQSC ND: Largeur normalisee de la distribution |
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! CLDF ND: Fraction nuageuse |
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|
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INTEGER klon, ND |
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REAL R(klon, ND), RS(klon, ND), QSUB(klon, ND) |
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LOGICAL PTCONV(klon, ND) |
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REAL RATQSC(klon, ND) |
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REAL CLDF(klon, ND) |
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|
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! parameters controlling the iteration: |
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! nmax : maximum nb of iterations (hopefully never reached) |
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! epsilon : accuracy of the numerical resolution |
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! vmax : v-value above which we use an asymptotic expression for ERF(v) |
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|
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INTEGER nmax |
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PARAMETER ( nmax = 10) |
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REAL epsilon, vmax0, vmax(klon) |
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PARAMETER ( epsilon = 0.02, vmax0 = 2.0 ) |
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|
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REAL min_mu, min_Q |
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PARAMETER ( min_mu = 1.e-12, min_Q=1.e-12 ) |
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INTEGER i, K, n |
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REAL mu(klon), qsat(klon), delta(klon), beta(klon) |
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real zu2(klon), zv2(klon) |
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REAL xx(klon), aux(klon), coeff(klon), block(klon) |
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REAL dist(klon), fprime(klon), det(klon) |
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REAL pi, u(klon), v(klon), erfcu(klon), erfcv(klon) |
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REAL xx1(klon), xx2(klon) |
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real sqrtpi, sqrt2, zx1, zx2, exdel |
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! lconv = true si le calcul a converge (entre autres si qsub < min_q) |
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LOGICAL lconv(klon) |
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|
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!-------------------------------------------------------------- |
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|
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cldf(:, :)=0.0 |
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|
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pi = ACOS(-1.) |
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sqrtpi=sqrt(pi) |
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sqrt2=sqrt(2.) |
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|
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ptconv=.false. |
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ratqsc=0. |
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|
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loop_vertical: DO K = 1, ND |
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do i=1, klon |
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mu(i) = R(i, K) |
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mu(i) = MAX(mu(i), min_mu) |
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qsat(i) = RS(i, K) |
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qsat(i) = MAX(qsat(i), min_mu) |
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delta(i) = log(mu(i)/qsat(i)) |
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enddo |
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|
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! There is no subgrid-scale condensation; the scheme becomes |
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! equivalent to an "all-or-nothing" large-scale condensation |
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! scheme. |
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|
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! Some condensation is produced at the subgrid-scale |
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! |
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! PDF = generalized log-normal distribution (GNO) |
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! (k<0 because a lower bound is considered for the PDF) |
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! |
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! -> Determine x (the parameter k of the GNO PDF) such that the |
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! contribution of subgrid-scale processes to the in-cloud water |
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! content is equal to QSUB(K) (equations (13), (14), (15) + |
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! Appendix B of the paper) |
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! |
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! Here, an iterative method is used for this purpose (other |
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! numerical methods might be more efficient) |
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! |
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! NB: the "error function" is called ERF (ERF in double |
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! precision) |
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|
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! On commence par eliminer les cas pour lesquels on n'a pas |
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! suffisamment d'eau nuageuse. |
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do i=1, klon |
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IF ( QSUB(i, K) .lt. min_Q ) THEN |
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ptconv(i, k)=.false. |
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ratqsc(i, k)=0. |
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lconv(i) = .true. |
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ELSE |
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lconv(i) = .FALSE. |
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vmax(i) = vmax0 |
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beta(i) = QSUB(i, K)/mu(i) + EXP( -MIN(0.0, delta(i)) ) |
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! roots of equation v > vmax: |
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det(i) = delta(i) + vmax(i)**2. |
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if (det(i).LE.0.0) vmax(i) = vmax0 + 1.0 |
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det(i) = delta(i) + vmax(i)**2. |
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if (det(i).LE.0.) then |
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xx(i) = -0.0001 |
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else |
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zx1=-sqrt2*vmax(i) |
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zx2=SQRT(1.0+delta(i)/(vmax(i)**2.)) |
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xx1(i)=zx1*(1.0-zx2) |
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xx2(i)=zx1*(1.0+zx2) |
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xx(i) = 1.01 * xx1(i) |
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if ( xx1(i) .GE. 0.0 ) xx(i) = 0.5*xx2(i) |
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endif |
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if (delta(i).LT.0.) xx(i) = -0.5*SQRT(log(2.)) |
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ENDIF |
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enddo |
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|
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! Debut des nmax iterations pour trouver la solution. |
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DO n = 1, nmax |
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loop_horizontal: do i = 1, klon |
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test_lconv: if (.not.lconv(i)) then |
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u(i) = delta(i)/(xx(i)*sqrt2) + xx(i)/(2.*sqrt2) |
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v(i) = delta(i)/(xx(i)*sqrt2) - xx(i)/(2.*sqrt2) |
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IF ( v(i) .GT. vmax(i) ) THEN |
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IF ( ABS(u(i)) .GT. vmax(i) .AND. delta(i) .LT. 0. ) THEN |
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! use asymptotic expression of erf for u and v large: |
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! ( -> analytic solution for xx ) |
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exdel=beta(i)*EXP(delta(i)) |
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aux(i) = 2.0*delta(i)*(1.-exdel) /(1.+exdel) |
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if (aux(i).lt.0.) then |
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aux(i)=0. |
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endif |
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xx(i) = -SQRT(aux(i)) |
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block(i) = EXP(-v(i)*v(i)) / v(i) / sqrtpi |
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dist(i) = 0.0 |
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fprime(i) = 1.0 |
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ELSE |
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! erfv -> 1.0, use an asymptotic expression of |
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! erfv for v large: |
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|
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erfcu(i) = 1.0-NR_ERF(u(i)) |
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! Attention : ajout d'un seuil pour l'exponentielle |
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aux(i) = sqrtpi*erfcu(i)*EXP(min(v(i)*v(i), 80.)) |
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coeff(i) = 1.0 - 1./2./(v(i)**2.) + 3./4./(v(i)**4.) |
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block(i) = coeff(i) * EXP(-v(i)*v(i)) / v(i) / sqrtpi |
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dist(i) = v(i) * aux(i) / coeff(i) - beta(i) |
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fprime(i) = 2.0 / xx(i) * (v(i)**2.) & |
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* ( coeff(i)*EXP(-delta(i)) - u(i) * aux(i) ) & |
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/ coeff(i) / coeff(i) |
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ENDIF |
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ELSE |
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! general case: |
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|
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erfcu(i) = 1.0-NR_ERF(u(i)) |
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erfcv(i) = 1.0-NR_ERF(v(i)) |
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block(i) = erfcv(i) |
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dist(i) = erfcu(i) / erfcv(i) - beta(i) |
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zu2(i)=u(i)*u(i) |
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zv2(i)=v(i)*v(i) |
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if(zu2(i).gt.20..or. zv2(i).gt.20.) then |
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zu2(i)=20. |
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zv2(i)=20. |
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fprime(i) = 0. |
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else |
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fprime(i) = 2. /sqrtpi /xx(i) /erfcv(i)**2. & |
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* ( erfcv(i)*v(i)*EXP(-zu2(i)) & |
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- erfcu(i)*u(i)*EXP(-zv2(i)) ) |
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endif |
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ENDIF |
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! test numerical convergence: |
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if ( ABS(dist(i)/beta(i)) .LT. epsilon ) then |
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ptconv(i, K) = .TRUE. |
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lconv(i)=.true. |
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! borne pour l'exponentielle |
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ratqsc(i, k)=min(2.*(v(i)-u(i))**2, 20.) |
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ratqsc(i, k)=sqrt(exp(ratqsc(i, k))-1.) |
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CLDF(i, K) = 0.5 * block(i) |
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else |
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xx(i) = xx(i) - dist(i)/fprime(i) |
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endif |
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endif test_lconv |
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enddo loop_horizontal |
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ENDDO |
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end DO loop_vertical |
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|
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END SUBROUTINE CLOUDS_GNO |
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end module CLOUDS_GNO_m |
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