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