source: LMDZ5/trunk/libf/phylmd/nonlocal.F90 @ 1992

! $Header$

! ======================================================================
SUBROUTINE nonlocal(knon, paprs, pplay, tsol, beta, u, v, t, q, cd_h, cd_m, &
    pcfh, pcfm, cgh, cgq)
  USE dimphy
  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.
  ! ======================================================================
  include "YOMCST.h"
  include "iniprint.h"

  ! 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 "YOETHF.h"
  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