source: LMDZ6/branches/Amaury_dev/libf/phylmd/nonlocal.F90 @ 5157

! $Header$

! ======================================================================
SUBROUTINE nonlocal(knon, paprs, pplay, tsol, beta, u, v, t, q, cd_h, cd_m, &
        pcfh, pcfm, cgh, cgq)
  USE dimphy
  USE lmdz_yoethf

  USE lmdz_yomcst

  IMPLICIT NONE
 INCLUDE "FCTTRE.h"
  ! ======================================================================
  ! 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

  ! 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

END SUBROUTINE nonlocal