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! $Header$ |
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! ====================================================================== |
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SUBROUTINE nonlocal(knon, paprs, pplay, tsol, beta, u, v, t, q, cd_h, cd_m, & |
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pcfh, pcfm, cgh, cgq) |
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USE dimphy |
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IMPLICIT NONE |
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! ====================================================================== |
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! Laurent Li (LMD/CNRS), le 30 septembre 1998 |
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! Couche limite non-locale. Adaptation du code du CCM3. |
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! Code non teste, donc a ne pas utiliser. |
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! ====================================================================== |
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! Nonlocal scheme that determines eddy diffusivities based on a |
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! diagnosed boundary layer height and a turbulent velocity scale. |
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! Also countergradient effects for heat and moisture are included. |
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! For more information, see Holtslag, A.A.M., and B.A. Boville, 1993: |
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! Local versus nonlocal boundary-layer diffusion in a global climate |
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! model. J. of Climate, vol. 6, 1825-1842. |
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! ====================================================================== |
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include "YOMCST.h" |
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! Arguments: |
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INTEGER knon ! nombre de points a calculer |
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REAL tsol(klon) ! temperature du sol (K) |
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REAL beta(klon) ! efficacite d'evaporation (entre 0 et 1) |
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REAL paprs(klon, klev+1) ! pression a inter-couche (Pa) |
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REAL pplay(klon, klev) ! pression au milieu de couche (Pa) |
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REAL u(klon, klev) ! vitesse U (m/s) |
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REAL v(klon, klev) ! vitesse V (m/s) |
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REAL t(klon, klev) ! temperature (K) |
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REAL q(klon, klev) ! vapeur d'eau (kg/kg) |
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REAL cd_h(klon) ! coefficient de friction au sol pour chaleur |
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REAL cd_m(klon) ! coefficient de friction au sol pour vitesse |
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INTEGER isommet |
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REAL vk |
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PARAMETER (vk=0.40) |
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REAL ricr |
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PARAMETER (ricr=0.4) |
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REAL fak |
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PARAMETER (fak=8.5) |
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REAL fakn |
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PARAMETER (fakn=7.2) |
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REAL onet |
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PARAMETER (onet=1.0/3.0) |
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REAL t_coup |
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PARAMETER (t_coup=273.15) |
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REAL zkmin |
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PARAMETER (zkmin=0.01) |
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REAL betam |
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PARAMETER (betam=15.0) |
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REAL betah |
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PARAMETER (betah=15.0) |
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REAL betas |
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PARAMETER (betas=5.0) |
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REAL sffrac |
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PARAMETER (sffrac=0.1) |
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REAL binm |
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PARAMETER (binm=betam*sffrac) |
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REAL binh |
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PARAMETER (binh=betah*sffrac) |
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REAL ccon |
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PARAMETER (ccon=fak*sffrac*vk) |
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REAL z(klon, klev) |
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REAL pcfm(klon, klev), pcfh(klon, klev) |
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INTEGER i, k |
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REAL zxt, zxq, zxu, zxv, zxmod, taux, tauy |
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REAL zx_alf1, zx_alf2 ! parametres pour extrapolation |
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REAL khfs(klon) ! surface kinematic heat flux [mK/s] |
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REAL kqfs(klon) ! sfc kinematic constituent flux [m/s] |
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REAL heatv(klon) ! surface virtual heat flux |
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REAL ustar(klon) |
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REAL rino(klon, klev) ! bulk Richardon no. from level to ref lev |
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LOGICAL unstbl(klon) ! pts w/unstbl pbl (positive virtual ht flx) |
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LOGICAL stblev(klon) ! stable pbl with levels within pbl |
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LOGICAL unslev(klon) ! unstbl pbl with levels within pbl |
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LOGICAL unssrf(klon) ! unstb pbl w/lvls within srf pbl lyr |
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LOGICAL unsout(klon) ! unstb pbl w/lvls in outer pbl lyr |
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LOGICAL check(klon) ! True=>chk if Richardson no.>critcal |
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REAL pblh(klon) |
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REAL cgh(klon, 2:klev) ! counter-gradient term for heat [K/m] |
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REAL cgq(klon, 2:klev) ! counter-gradient term for constituents |
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REAL cgs(klon, 2:klev) ! counter-gradient star (cg/flux) |
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REAL obklen(klon) |
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REAL ztvd, ztvu, zdu2 |
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REAL therm(klon) ! thermal virtual temperature excess |
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REAL phiminv(klon) ! inverse phi function for momentum |
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REAL phihinv(klon) ! inverse phi function for heat |
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REAL wm(klon) ! turbulent velocity scale for momentum |
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REAL fak1(klon) ! k*ustar*pblh |
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REAL fak2(klon) ! k*wm*pblh |
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REAL fak3(klon) ! fakn*wstr/wm |
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REAL pblk(klon) ! level eddy diffusivity for momentum |
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REAL pr(klon) ! Prandtl number for eddy diffusivities |
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REAL zl(klon) ! zmzp / Obukhov length |
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REAL zh(klon) ! zmzp / pblh |
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REAL zzh(klon) ! (1-(zmzp/pblh))**2 |
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REAL wstr(klon) ! w*, convective velocity scale |
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REAL zm(klon) ! current level height |
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REAL zp(klon) ! current level height + one level up |
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REAL zcor, zdelta, zcvm5, zxqs |
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REAL fac, pblmin, zmzp, term |
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include "YOETHF.h" |
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include "FCTTRE.h" |
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! Initialisation |
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isommet = klev |
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DO i = 1, klon |
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pcfh(i, 1) = cd_h(i) |
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pcfm(i, 1) = cd_m(i) |
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END DO |
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DO k = 2, klev |
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DO i = 1, klon |
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pcfh(i, k) = zkmin |
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pcfm(i, k) = zkmin |
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cgs(i, k) = 0.0 |
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cgh(i, k) = 0.0 |
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cgq(i, k) = 0.0 |
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END DO |
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END DO |
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! Calculer les hauteurs de chaque couche |
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DO i = 1, knon |
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z(i, 1) = rd*t(i, 1)/(0.5*(paprs(i,1)+pplay(i,1)))*(paprs(i,1)-pplay(i,1) & |
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)/rg |
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END DO |
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DO k = 2, klev |
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DO i = 1, knon |
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z(i, k) = z(i, k-1) + rd*0.5*(t(i,k-1)+t(i,k))/paprs(i, k)*(pplay(i,k-1 & |
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)-pplay(i,k))/rg |
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END DO |
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END DO |
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DO i = 1, knon |
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IF (thermcep) THEN |
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zdelta = max(0., sign(1.,rtt-tsol(i))) |
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zcvm5 = r5les*rlvtt*(1.-zdelta) + r5ies*rlstt*zdelta |
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zcvm5 = zcvm5/rcpd/(1.0+rvtmp2*q(i,1)) |
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zxqs = r2es*foeew(tsol(i), zdelta)/paprs(i, 1) |
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zxqs = min(0.5, zxqs) |
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zcor = 1./(1.-retv*zxqs) |
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zxqs = zxqs*zcor |
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ELSE |
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IF (tsol(i)<t_coup) THEN |
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zxqs = qsats(tsol(i))/paprs(i, 1) |
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ELSE |
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zxqs = qsatl(tsol(i))/paprs(i, 1) |
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END IF |
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END IF |
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zx_alf1 = 1.0 |
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zx_alf2 = 1.0 - zx_alf1 |
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zxt = (t(i,1)+z(i,1)*rg/rcpd/(1.+rvtmp2*q(i,1)))*(1.+retv*q(i,1))*zx_alf1 & |
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+ (t(i,2)+z(i,2)*rg/rcpd/(1.+rvtmp2*q(i,2)))*(1.+retv*q(i,2))*zx_alf2 |
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zxu = u(i, 1)*zx_alf1 + u(i, 2)*zx_alf2 |
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zxv = v(i, 1)*zx_alf1 + v(i, 2)*zx_alf2 |
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zxq = q(i, 1)*zx_alf1 + q(i, 2)*zx_alf2 |
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zxmod = 1.0 + sqrt(zxu**2+zxv**2) |
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khfs(i) = (tsol(i)*(1.+retv*q(i,1))-zxt)*zxmod*cd_h(i) |
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kqfs(i) = (zxqs-zxq)*zxmod*cd_h(i)*beta(i) |
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heatv(i) = khfs(i) + 0.61*zxt*kqfs(i) |
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taux = zxu*zxmod*cd_m(i) |
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tauy = zxv*zxmod*cd_m(i) |
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ustar(i) = sqrt(taux**2+tauy**2) |
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ustar(i) = max(sqrt(ustar(i)), 0.01) |
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END DO |
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DO i = 1, knon |
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rino(i, 1) = 0.0 |
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check(i) = .TRUE. |
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pblh(i) = z(i, 1) |
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obklen(i) = -t(i, 1)*ustar(i)**3/(rg*vk*heatv(i)) |
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END DO |
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! PBL height calculation: |
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! Search for level of pbl. Scan upward until the Richardson number between |
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! the first level and the current level exceeds the "critical" value. |
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fac = 100.0 |
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DO k = 1, isommet |
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DO i = 1, knon |
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IF (check(i)) THEN |
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zdu2 = (u(i,k)-u(i,1))**2 + (v(i,k)-v(i,1))**2 + fac*ustar(i)**2 |
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zdu2 = max(zdu2, 1.0E-20) |
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ztvd = (t(i,k)+z(i,k)*0.5*rg/rcpd/(1.+rvtmp2*q(i, & |
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k)))*(1.+retv*q(i,k)) |
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ztvu = (t(i,1)-z(i,k)*0.5*rg/rcpd/(1.+rvtmp2*q(i, & |
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1)))*(1.+retv*q(i,1)) |
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rino(i, k) = (z(i,k)-z(i,1))*rg*(ztvd-ztvu)/(zdu2*0.5*(ztvd+ztvu)) |
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IF (rino(i,k)>=ricr) THEN |
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pblh(i) = z(i, k-1) + (z(i,k-1)-z(i,k))*(ricr-rino(i,k-1))/(rino(i, & |
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k-1)-rino(i,k)) |
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check(i) = .FALSE. |
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END IF |
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END IF |
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END DO |
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END DO |
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! Set pbl height to maximum value where computation exceeds number of |
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! layers allowed |
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DO i = 1, knon |
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IF (check(i)) pblh(i) = z(i, isommet) |
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END DO |
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! Improve estimate of pbl height for the unstable points. |
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! Find unstable points (sensible heat flux is upward): |
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DO i = 1, knon |
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IF (heatv(i)>0.) THEN |
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unstbl(i) = .TRUE. |
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check(i) = .TRUE. |
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ELSE |
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unstbl(i) = .FALSE. |
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check(i) = .FALSE. |
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END IF |
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END DO |
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! For the unstable case, compute velocity scale and the |
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! convective temperature excess: |
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DO i = 1, knon |
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IF (check(i)) THEN |
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phiminv(i) = (1.-binm*pblh(i)/obklen(i))**onet |
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wm(i) = ustar(i)*phiminv(i) |
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therm(i) = heatv(i)*fak/wm(i) |
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rino(i, 1) = 0.0 |
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END IF |
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END DO |
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! Improve pblh estimate for unstable conditions using the |
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! convective temperature excess: |
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DO k = 1, isommet |
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DO i = 1, knon |
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IF (check(i)) THEN |
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zdu2 = (u(i,k)-u(i,1))**2 + (v(i,k)-v(i,1))**2 + fac*ustar(i)**2 |
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zdu2 = max(zdu2, 1.0E-20) |
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ztvd = (t(i,k)+z(i,k)*0.5*rg/rcpd/(1.+rvtmp2*q(i, & |
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k)))*(1.+retv*q(i,k)) |
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ztvu = (t(i,1)+therm(i)-z(i,k)*0.5*rg/rcpd/(1.+rvtmp2*q(i, & |
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1)))*(1.+retv*q(i,1)) |
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rino(i, k) = (z(i,k)-z(i,1))*rg*(ztvd-ztvu)/(zdu2*0.5*(ztvd+ztvu)) |
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IF (rino(i,k)>=ricr) THEN |
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pblh(i) = z(i, k-1) + (z(i,k-1)-z(i,k))*(ricr-rino(i,k-1))/(rino(i, & |
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k-1)-rino(i,k)) |
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check(i) = .FALSE. |
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END IF |
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END IF |
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END DO |
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END DO |
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! Set pbl height to maximum value where computation exceeds number of |
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! layers allowed |
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DO i = 1, knon |
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IF (check(i)) pblh(i) = z(i, isommet) |
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END DO |
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! Points for which pblh exceeds number of pbl layers allowed; |
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! set to maximum |
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DO i = 1, knon |
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IF (check(i)) pblh(i) = z(i, isommet) |
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END DO |
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! PBL height must be greater than some minimum mechanical mixing depth |
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! Several investigators have proposed minimum mechanical mixing depth |
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! relationships as a function of the local friction velocity, u*. We |
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! make use of a linear relationship of the form h = c u* where c=700. |
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! The scaling arguments that give rise to this relationship most often |
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! represent the coefficient c as some constant over the local coriolis |
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! parameter. Here we make use of the experimental results of Koracin |
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! and Berkowicz (1988) [BLM, Vol 43] for wich they recommend 0.07/f |
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! where f was evaluated at 39.5 N and 52 N. Thus we use a typical mid |
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! latitude value for f so that c = 0.07/f = 700. |
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DO i = 1, knon |
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pblmin = 700.0*ustar(i) |
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pblh(i) = max(pblh(i), pblmin) |
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END DO |
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! pblh is now available; do preparation for diffusivity calculation: |
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DO i = 1, knon |
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pblk(i) = 0.0 |
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fak1(i) = ustar(i)*pblh(i)*vk |
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! Do additional preparation for unstable cases only, set temperature |
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! and moisture perturbations depending on stability. |
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IF (unstbl(i)) THEN |
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zxt = (t(i,1)-z(i,1)*0.5*rg/rcpd/(1.+rvtmp2*q(i,1)))*(1.+retv*q(i,1)) |
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phiminv(i) = (1.-binm*pblh(i)/obklen(i))**onet |
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phihinv(i) = sqrt(1.-binh*pblh(i)/obklen(i)) |
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wm(i) = ustar(i)*phiminv(i) |
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fak2(i) = wm(i)*pblh(i)*vk |
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wstr(i) = (heatv(i)*rg*pblh(i)/zxt)**onet |
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fak3(i) = fakn*wstr(i)/wm(i) |
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END IF |
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END DO |
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! Main level loop to compute the diffusivities and |
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! counter-gradient terms: |
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DO k = 2, isommet |
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! Find levels within boundary layer: |
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DO i = 1, knon |
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unslev(i) = .FALSE. |
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stblev(i) = .FALSE. |
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zm(i) = z(i, k-1) |
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zp(i) = z(i, k) |
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IF (zkmin==0.0 .AND. zp(i)>pblh(i)) zp(i) = pblh(i) |
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IF (zm(i)<pblh(i)) THEN |
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zmzp = 0.5*(zm(i)+zp(i)) |
328 |
|
|
zh(i) = zmzp/pblh(i) |
329 |
|
|
zl(i) = zmzp/obklen(i) |
330 |
|
|
zzh(i) = 0. |
331 |
|
|
IF (zh(i)<=1.0) zzh(i) = (1.-zh(i))**2 |
332 |
|
|
|
333 |
|
|
! stblev for points zm < plbh and stable and neutral |
334 |
|
|
! unslev for points zm < plbh and unstable |
335 |
|
|
|
336 |
|
|
IF (unstbl(i)) THEN |
337 |
|
|
unslev(i) = .TRUE. |
338 |
|
|
ELSE |
339 |
|
|
stblev(i) = .TRUE. |
340 |
|
|
END IF |
341 |
|
|
END IF |
342 |
|
|
END DO |
343 |
|
|
|
344 |
|
|
! Stable and neutral points; set diffusivities; counter-gradient |
345 |
|
|
! terms zero for stable case: |
346 |
|
|
|
347 |
|
|
DO i = 1, knon |
348 |
|
|
IF (stblev(i)) THEN |
349 |
|
|
IF (zl(i)<=1.) THEN |
350 |
|
|
pblk(i) = fak1(i)*zh(i)*zzh(i)/(1.+betas*zl(i)) |
351 |
|
|
ELSE |
352 |
|
|
pblk(i) = fak1(i)*zh(i)*zzh(i)/(betas+zl(i)) |
353 |
|
|
END IF |
354 |
|
|
pcfm(i, k) = pblk(i) |
355 |
|
|
pcfh(i, k) = pcfm(i, k) |
356 |
|
|
END IF |
357 |
|
|
END DO |
358 |
|
|
|
359 |
|
|
! unssrf, unstable within surface layer of pbl |
360 |
|
|
! unsout, unstable within outer layer of pbl |
361 |
|
|
|
362 |
|
|
DO i = 1, knon |
363 |
|
|
unssrf(i) = .FALSE. |
364 |
|
|
unsout(i) = .FALSE. |
365 |
|
|
IF (unslev(i)) THEN |
366 |
|
|
IF (zh(i)<sffrac) THEN |
367 |
|
|
unssrf(i) = .TRUE. |
368 |
|
|
ELSE |
369 |
|
|
unsout(i) = .TRUE. |
370 |
|
|
END IF |
371 |
|
|
END IF |
372 |
|
|
END DO |
373 |
|
|
|
374 |
|
|
! Unstable for surface layer; counter-gradient terms zero |
375 |
|
|
|
376 |
|
|
DO i = 1, knon |
377 |
|
|
IF (unssrf(i)) THEN |
378 |
|
|
term = (1.-betam*zl(i))**onet |
379 |
|
|
pblk(i) = fak1(i)*zh(i)*zzh(i)*term |
380 |
|
|
pr(i) = term/sqrt(1.-betah*zl(i)) |
381 |
|
|
END IF |
382 |
|
|
END DO |
383 |
|
|
|
384 |
|
|
! Unstable for outer layer; counter-gradient terms non-zero: |
385 |
|
|
|
386 |
|
|
DO i = 1, knon |
387 |
|
|
IF (unsout(i)) THEN |
388 |
|
|
pblk(i) = fak2(i)*zh(i)*zzh(i) |
389 |
|
|
cgs(i, k) = fak3(i)/(pblh(i)*wm(i)) |
390 |
|
|
cgh(i, k) = khfs(i)*cgs(i, k) |
391 |
|
|
pr(i) = phiminv(i)/phihinv(i) + ccon*fak3(i)/fak |
392 |
|
|
cgq(i, k) = kqfs(i)*cgs(i, k) |
393 |
|
|
END IF |
394 |
|
|
END DO |
395 |
|
|
|
396 |
|
|
! For all unstable layers, set diffusivities |
397 |
|
|
|
398 |
|
|
DO i = 1, knon |
399 |
|
|
IF (unslev(i)) THEN |
400 |
|
|
pcfm(i, k) = pblk(i) |
401 |
|
|
pcfh(i, k) = pblk(i)/pr(i) |
402 |
|
|
END IF |
403 |
|
|
END DO |
404 |
|
|
END DO ! end of level loop |
405 |
|
|
|
406 |
|
|
RETURN |
407 |
|
|
END SUBROUTINE nonlocal |