source: LMDZ6/branches/Amaury_dev/libf/phylmd/hbtm_mod.F90 @ 5143

module hbtm_mod

  IMPLICIT NONE

CONTAINS

  SUBROUTINE hbtm(knon, paprs, pplay, t2m, t10m, q2m, q10m, ustar, wstar, &
          flux_t, flux_q, u, v, t, q, pblh, cape, eauliq, ctei, pblt, therm, &
          trmb1, trmb2, trmb3, plcl)
    USE dimphy
    USE lmdz_YOETHF
    USE lmdz_fcttre, ONLY: foeew, foede, qsats, qsatl, dqsats, dqsatl, thermcep

    ! ***************************************************************
    ! *                                                             *
    ! * HBTM2   D'apres Holstag&Boville et Troen&Mahrt              *
    ! *                 JAS 47              BLM                     *
    ! * Algorithme These Anne Mathieu                               *
    ! * Critere d'Entrainement Peter Duynkerke (JAS 50)             *
    ! * written by  : Anne MATHIEU & Alain LAHELLEC, 22/11/99       *
    ! * features : implem. exces Mathieu                            *
    ! ***************************************************************
    ! * mods : decembre 99 passage th a niveau plus bas. voir fixer *
    ! * la prise du th a z/Lambda = -.2 (max Ray)                   *
    ! * Autre algo : entrainement ~ Theta+v =cste mais comment=>The?*
    ! * on peut fixer q a .7qsat(cf non adiab)=>T2 et The2          *
    ! * voir aussi //KE pblh = niveau The_e ou l = env.             *
    ! ***************************************************************
    ! * fin therm a la HBTM passage a forme Mathieu 12/09/2001      *
    ! ***************************************************************
    ! *


    ! AM Fev 2003
    ! Adaptation a LMDZ version couplee

    ! Pour le moment on fait passer en argument les grdeurs de surface :
    ! flux, t,q2m, t,q10m, on va utiliser systematiquement les grdeurs a 2m ms
    ! on garde la possibilite de changer si besoin est (jusqu'a present la
    ! forme de HB avec le 1er niveau modele etait conservee)

    include "YOMCST.h"
    REAL rlvcp, reps
    ! Arguments:

    INTEGER knon ! nombre de points a calculer
    ! AM
    REAL t2m(klon), t10m(klon) ! temperature a 2 et 10m
    REAL q2m(klon), q10m(klon) ! q a 2 et 10m
    REAL ustar(klon)
    REAL wstar(klon) ! w*, convective velocity scale
    REAL paprs(klon, klev + 1) ! pression a inter-couche (Pa)
    REAL pplay(klon, klev) ! pression au milieu de couche (Pa)
    REAL flux_t(klon, klev), flux_q(klon, klev) ! Flux
    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)
    ! AM      REAL cd_h(klon) ! coefficient de friction au sol pour chaleur
    ! AM      REAL cd_m(klon) ! coefficient de friction au sol pour vitesse

    INTEGER isommet
    ! um      PARAMETER (isommet=klev) ! limite max sommet pbl
    REAL, PARAMETER :: vk = 0.35 ! Von Karman => passer a .41 ! cf U.Olgstrom
    REAL, PARAMETER :: ricr = 0.4
    REAL, PARAMETER :: fak = 8.5 ! b calcul du Prandtl et de dTetas
    REAL, PARAMETER :: fakn = 7.2 ! a
    REAL, PARAMETER :: onet = 1.0 / 3.0
    REAL, PARAMETER :: t_coup = 273.15
    REAL, PARAMETER :: zkmin = 0.01
    REAL, PARAMETER :: betam = 15.0 ! pour Phim / h dans la S.L stable
    REAL, PARAMETER :: betah = 15.0

    REAL, PARAMETER :: betas = 5.0
    ! Phit dans la S.L. stable (mais 2 formes / z/OBL<>1

    REAL, PARAMETER :: sffrac = 0.1 ! S.L. = z/h < .1
    REAL, PARAMETER :: usmin = 1.E-12
    REAL, PARAMETER :: binm = betam * sffrac
    REAL, PARAMETER :: binh = betah * sffrac
    REAL, PARAMETER :: ccon = fak * sffrac * vk
    REAL, PARAMETER :: b1 = 70., b2 = 20.
    REAL, PARAMETER :: zref = 2. ! Niveau de ref a 2m peut eventuellement
    ! etre choisi a 10m
    REAL q_star, t_star
    REAL b212, b2sr ! Lambert correlations T' q' avec T* q*

    REAL z(klon, klev)
    ! AM      REAL pcfm(klon,klev), pcfh(klon,klev)
    INTEGER i, k, j
    REAL zxt
    ! AM      REAL zxt, zxq, zxu, zxv, zxmod, taux, tauy
    ! AM      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 rhino(klon, klev) ! bulk Richardon no. mais en Theta_v
    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
    LOGICAL omegafl(klon) ! flag de prolongerment cape pour pt Omega
    REAL pblh(klon)
    REAL pblt(klon)
    REAL plcl(klon)
    ! AM      REAL cgh(klon,2:klev) ! counter-gradient term for heat [K/m]
    ! AM      REAL cgq(klon,2:klev) ! counter-gradient term for constituents
    ! AM      REAL cgs(klon,2:klev) ! counter-gradient star (cg/flux)
    REAL unsobklen(klon) ! Monin-Obukhov lengh
    ! AM      REAL ztvd, ztvu,
    REAL zdu2
    REAL, INTENT(OUT) :: therm(:) ! (klon) thermal virtual temperature excess
    REAL trmb1(klon), trmb2(klon), trmb3(klon)
    ! Algorithme thermique
    REAL s(klon, klev) ! [P/Po]^Kappa milieux couches
    REAL th_th(klon) ! potential temperature of thermal
    REAL the_th(klon) ! equivalent potential temperature of thermal
    REAL qt_th(klon) ! total water  of thermal
    REAL tbef(klon) ! T thermique niveau precedent
    REAL qsatbef(klon)
    LOGICAL zsat(klon) ! le thermique est sature
    REAL cape(klon) ! Cape du thermique
    REAL kape(klon) ! Cape locale
    REAL eauliq(klon) ! Eau liqu integr du thermique
    REAL ctei(klon) ! Critere d'instab d'entrainmt des nuages de CL
    REAL the1, the2, aa, bb, zthvd, zthvu, xintpos, qqsat
    ! IM 091204 BEG
    REAL a1, a2, a3
    ! IM 091204 END
    REAL xhis, rnum, denom, th1, th2, thv1, thv2, ql2
    REAL dqsat_dt, qsat2, qt1, q2, t1, t2, xnull, delt_the
    REAL delt_qt, delt_2, quadsat, spblh, reduc

    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*wstar/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 zm(klon) ! current level height
    REAL zp(klon) ! current level height + one level up
    REAL zcor, zdelta, zcvm5
    ! AM      REAL zxqs
    REAL fac, pblmin, zmzp, term

    ! initialisations (Anne)
    isommet = klev
    th_th(:) = 0.
    q_star = 0
    t_star = 0
    therm = 0.

    b212 = sqrt(b1 * b2)
    b2sr = sqrt(b2)

    ! ============================================================
    ! Fonctions thermo implicites
    ! ============================================================
    ! +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
    ! Tetens : pression partielle de vap d'eau e_sat(T)
    ! =================================================
    ! ++ e_sat(T) = r2*exp( r3*(T-Tf)/(T-r4) ) id a r2*FOEWE
    ! ++ avec :
    ! ++ Tf = 273.16 K  (Temp de fusion de la glace)
    ! ++ r2 = 611.14 Pa
    ! ++ r3 = 17.269 (liquide) 21.875 (solide) adim
    ! ++ r4 = 35.86             7.66           Kelvin
    ! ++  q_sat = eps*e_sat/(p-(1-eps)*e_sat)
    ! ++ derivé :
    ! ++ =========
    ! ++                   r3*(Tf-r4)*q_sat(T,p)
    ! ++ d_qsat_dT = --------------------------------
    ! ++             (T-r4)^2*( 1-(1-eps)*e_sat(T)/p )
    ! ++ pour zcvm5=Lv, c'est FOEDE
    ! ++ Rq :(1.-REPS)*esarg/Parg id a RETV*Qsat
    ! ------------------------------------------------------------------

    ! Initialisation
    rlvcp = rlvtt / rcpd
    reps = rd / rv


    ! DO i = 1, klon
    ! pcfh(i,1) = cd_h(i)
    ! pcfm(i,1) = cd_m(i)
    ! ENDDO
    ! 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
    ! ENDDO
    ! ENDDO

    ! Calculer les hauteurs de chaque couche
    ! (geopotentielle Int_dp/ro = Int_[Rd.T.dp/p] z = geop/g)
    ! pourquoi ne pas utiliser Phi/RG ?
    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
      s(i, 1) = (pplay(i, 1) / paprs(i, 1))**rkappa
    END DO
    ! s(k) = [pplay(k)/ps]^kappa
    ! + + + + + + + + + pplay  <-> s(k)   t  dp=pplay(k-1)-pplay(k)

    ! -----------------  paprs <-> sig(k)

    ! + + + + + + + + + pplay  <-> s(k-1)


    ! + + + + + + + + + pplay  <-> s(1)   t  dp=paprs-pplay   z(1)

    ! -----------------  paprs <-> sig(1)

    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
        s(i, k) = (pplay(i, k) / paprs(i, 1))**rkappa
      END DO
    END DO
    ! ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
    ! ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
    ! +++  Determination des grandeurs de surface  +++++++++++++++++++++
    ! ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
    ! ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
    DO i = 1, knon
      ! AM         IF (thermcep) THEN
      ! AM           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))
      ! AM           zxqs= r2es * FOEEW(tsol(i),zdelta)/paprs(i,1)
      ! AM           zxqs=MIN(0.5,zxqs)
      ! AM           zcor=1./(1.-retv*zxqs)
      ! AM           zxqs=zxqs*zcor
      ! AM         ELSE
      ! AM           IF (tsol(i).LT.t_coup) THEN
      ! AM              zxqs = qsats(tsol(i)) / paprs(i,1)
      ! AM           ELSE
      ! AM              zxqs = qsatl(tsol(i)) / paprs(i,1)
      ! AM           ENDIF
      ! AM         ENDIF
      ! niveau de reference bulk; mais ici, c,a pourrait etre le niveau de ref
      ! du thermique
      ! AM        zx_alf1 = 1.0
      ! AM        zx_alf2 = 1.0 - zx_alf1
      ! AM        zxt = (t(i,1)+z(i,1)*RG/RCPD/(1.+RVTMP2*q(i,1)))
      ! AM     .        *(1.+RETV*q(i,1))*zx_alf1
      ! AM     .      + (t(i,2)+z(i,2)*RG/RCPD/(1.+RVTMP2*q(i,2)))
      ! AM     .        *(1.+RETV*q(i,2))*zx_alf2
      ! AM        zxu = u(i,1)*zx_alf1+u(i,2)*zx_alf2
      ! AM        zxv = v(i,1)*zx_alf1+v(i,2)*zx_alf2
      ! AM        zxq = q(i,1)*zx_alf1+q(i,2)*zx_alf2
      ! AM
      ! AMAM           zxu = u10m(i)
      ! AMAM           zxv = v10m(i)
      ! AMAM           zxmod = 1.0+SQRT(zxu**2+zxv**2)
      ! AM Niveau de ref choisi a 2m
      zxt = t2m(i)

      ! ***************************************************
      ! attention, il doit s'agir de <w'theta'>
      ! ;Calcul de tcls virtuel et de w'theta'virtuel
      ! ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
      ! tcls=tcls*(1+.608*qcls)

      ! ;Pour avoir w'theta',
      ! ; il faut diviser par ro.Cp
      ! Cp=Cpd*(1+0.84*qcls)
      ! fcs=fcs/(ro_surf*Cp)
      ! ;On transforme w'theta' en w'thetav'
      ! Lv=(2.501-0.00237*(tcls-273.15))*1.E6
      ! xle=xle/(ro_surf*Lv)
      ! fcsv=fcs+.608*xle*tcls
      ! ***************************************************
      ! AM        khfs(i) = (tsol(i)*(1.+RETV*q(i,1))-zxt) *zxmod*cd_h(i)
      ! AM        kqfs(i) = (zxqs-zxq) *zxmod*cd_h(i) * beta(i)
      ! AM
      ! dif khfs est deja w't'_v / heatv(i) = khfs(i) + RETV*zxt*kqfs(i)
      ! AM calcule de Ro = paprs(i,1)/Rd zxt
      ! AM convention >0 vers le bas ds lmdz
      khfs(i) = -flux_t(i, 1) * zxt * rd / (rcpd * paprs(i, 1))
      kqfs(i) = -flux_q(i, 1) * zxt * rd / (paprs(i, 1))
      ! AM   verifier que khfs et kqfs sont bien de la forme w'l'
      heatv(i) = khfs(i) + 0.608 * zxt * kqfs(i)
      ! a comparer aussi aux sorties de clqh : flux_T/RoCp et flux_q/RoLv
      ! AM        heatv(i) = khfs(i)
      ! AM ustar est en entree
      ! AM        taux = zxu *zxmod*cd_m(i)
      ! AM        tauy = zxv *zxmod*cd_m(i)
      ! AM        ustar(i) = SQRT(taux**2+tauy**2)
      ! AM        ustar(i) = MAX(SQRT(ustar(i)),0.01)
      ! Theta et qT du thermique sans exces (interpolin vers surf)
      ! chgt de niveau du thermique (jeudi 30/12/1999)
      ! (interpolation lineaire avant integration phi_h)
      ! AM        qT_th(i) = zxqs*beta(i) + 4./z(i,1)*(q(i,1)-zxqs*beta(i))
      ! AM        qT_th(i) = max(qT_th(i),q(i,1))
      qt_th(i) = q2m(i)
      ! n The_th restera la Theta du thermique sans exces jusqu'a 2eme calcul
      ! n reste a regler convention P) pour Theta
      ! The_th(i) = tsol(i) + 4./z(i,1)*(t(i,1)-tsol(i))
      ! -                      + RLvCp*qT_th(i)
      ! AM        Th_th(i) = tsol(i) + 4./z(i,1)*(t(i,1)-tsol(i))
      th_th(i) = t2m(i)
    END DO

    DO i = 1, knon
      rhino(i, 1) = 0.0 ! Global Richardson
      check(i) = .TRUE.
      pblh(i) = z(i, 1) ! on initialise pblh a l'altitude du 1er niveau
      plcl(i) = 6000.
      ! Lambda = -u*^3 / (alpha.g.kvon.<w'Theta'v>
      unsobklen(i) = -rg * vk * heatv(i) / (t(i, 1) * max(ustar(i), usmin)**3)
      trmb1(i) = 0.
      trmb2(i) = 0.
      trmb3(i) = 0.
    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.
    ! (bonne idee Nu de separer le Ric et l'exces de temp du thermique)
    ! ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
    fac = 100.0
    DO k = 2, isommet
      DO i = 1, knon
        IF (check(i)) THEN
          ! pourquoi / niveau 1 (au lieu du sol) et le terme en u*^2 ?
          ! test     zdu2 =
          ! (u(i,k)-u(i,1))**2+(v(i,k)-v(i,1))**2+fac*ustar(i)**2
          zdu2 = u(i, k)**2 + v(i, k)**2
          zdu2 = max(zdu2, 1.0E-20)
          ! Theta_v environnement
          zthvd = t(i, k) / s(i, k) * (1. + retv * q(i, k))

          ! therm Theta_v sans exces (avec hypothese fausse de H&B, sinon,
          ! passer par Theta_e et virpot)
          ! zthvu=t(i,1)/s(i,1)*(1.+RETV*q(i,1))
          ! AM         zthvu = Th_th(i)*(1.+RETV*q(i,1))
          zthvu = th_th(i) * (1. + retv * qt_th(i))
          ! Le Ri par Theta_v
          ! AM         rhino(i,k) = (z(i,k)-z(i,1))*RG*(zthvd-zthvu)
          ! AM     .               /(zdu2*0.5*(zthvd+zthvu))
          ! AM On a nveau de ref a 2m ???
          rhino(i, k) = (z(i, k) - zref) * rg * (zthvd - zthvu) / (zdu2 * 0.5&
                  * (zthvd + zthvu))

          IF (rhino(i, k)>=ricr) THEN
            pblh(i) = z(i, k - 1) + (z(i, k - 1) - z(i, k)) * (ricr - rhino(i, k - 1))&
                    / (rhino(i, k - 1) - rhino(i, k))
            ! test04
            pblh(i) = pblh(i) + 100.
            pblt(i) = t(i, k - 1) + (t(i, k) - t(i, k - 1)) * (pblh(i) - z(i, k - 1))&
                    / (z(i, k) - z(i, k - 1))
            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) * unsobklen(i))**onet
        ! ***************************************************
        ! Wm ? et W* ? c'est la formule pour z/h < .1
        ! ;Calcul de w* ;;
        ! ;;;;;;;;;;;;;;;;
        ! w_star=((g/tcls)*fcsv*z(ind))^(1/3.) [ou prendre la premiere approx
        ! de h)
        ! ;; CALCUL DE wm ;;
        ! ;;;;;;;;;;;;;;;;;;
        ! ; Ici on considerera que l'on est dans la couche de surf jusqu'a
        ! 100 m
        ! ; On prend svt couche de surface=0.1*h mais on ne connait pas h
        ! ;;;;;;;;;;;Dans la couche de surface
        ! if (z(ind) le 20) then begin
        ! Phim=(1.-15.*(z(ind)/L))^(-1/3.)
        ! wm=u_star/Phim
        ! ;;;;;;;;;;;En dehors de la couche de surface
        ! END IF ELSE IF (z(ind) gt 20) then begin
        ! wm=(u_star^3+c1*w_star^3)^(1/3.)
        ! END IF
        ! ***************************************************
        wm(i) = ustar(i) * phiminv(i)
        ! ===================================================================
        ! valeurs de Dominique Lambert de la campagne SEMAPHORE :
        ! <T'^2> = 100.T*^2; <q'^2> = 20.q*^2 a 10m
        ! <Tv'^2> = (1+1.2q).100.T* + 1.2Tv.sqrt(20*100).T*.q* +
        ! (.608*Tv)^2*20.q*^2;
        ! et dTetavS = sqrt(<Tv'^2>) ainsi calculee.
        ! avec : T*=<w'T'>_s/w* et q*=<w'q'>/w*
        ! !!! on peut donc utiliser w* pour les fluctuations <-> Lambert
        ! (leur corellation pourrait dependre de beta par ex)
        ! if fcsv(i,j) gt 0 then begin
        ! dTetavs=b1*(1.+2.*.608*q_10(i,j))*(fcs(i,j)/wm(i,j))^2+$
        ! (.608*Thetav_10(i,j))^2*b2*(xle(i,j)/wm(i,j))^2+$
        ! 2.*.608*thetav_10(i,j)*sqrt(b1*b2)*(xle(i,j)/wm(i,j))*(fcs(i,j)
        ! /wm(i,j))
        ! dqs=b2*(xle(i,j)/wm(i,j))^2
        ! theta_s(i,j)=thetav_10(i,j)+sqrt(dTetavs)
        ! q_s(i,j)=q_10(i,j)+sqrt(dqs)
        ! END IF else begin
        ! Theta_s(i,j)=thetav_10(i,j)
        ! q_s(i,j)=q_10(i,j)
        ! endelse
        ! ===================================================================

        ! HBTM        therm(i) = heatv(i)*fak/wm(i)
        ! forme Mathieu :
        q_star = kqfs(i) / wm(i)
        t_star = khfs(i) / wm(i)
        ! IM 091204 BEG
        IF (1==0) THEN
          IF (t_star<0. .OR. q_star<0.) THEN
            PRINT *, 'i t_star q_star khfs kqfs wm', i, t_star, q_star, &
                    khfs(i), kqfs(i), wm(i)
          END IF
        END IF
        ! IM 091204 END
        ! AM Nveau cde ref 2m =>
        ! AM        therm(i) = sqrt( b1*(1.+2.*RETV*q(i,1))*t_star**2
        ! AM     +             + (RETV*T(i,1))**2*b2*q_star**2
        ! AM     +             + 2.*RETV*T(i,1)*b212*q_star*t_star
        ! AM     +                 )
        ! IM 091204 BEG
        a1 = b1 * (1. + 2. * retv * qt_th(i)) * t_star**2
        a2 = (retv * th_th(i))**2 * b2 * q_star * q_star
        a3 = 2. * retv * th_th(i) * b212 * q_star * t_star
        aa = a1 + a2 + a3
        IF (1==0) THEN
          IF (aa<0.) THEN
            PRINT *, 'i a1 a2 a3 aa', i, a1, a2, a3, aa
            PRINT *, 'i qT_th Th_th t_star q_star RETV b1 b2 b212', i, &
                    qt_th(i), th_th(i), t_star, q_star, retv, b1, b2, b212
          END IF
        END IF
        ! IM 091204 END
        therm(i) = sqrt(b1 * (1. + 2. * retv * qt_th(i)) * t_star**2 + (retv * th_th(&
                i))**2 * b2 * q_star * q_star &  ! IM 101204  +             +
                ! 2.*RETV*Th_th(i)*b212*q_star*t_star
                + max(0., 2. * retv * th_th(i) * b212 * q_star * t_star))

        ! Theta et qT du thermique (forme H&B) avec exces
        ! (attention, on ajoute therm(i) qui est virtuelle ...)
        ! pourquoi pas sqrt(b1)*t_star ?
        ! dqs = b2sr*kqfs(i)/wm(i)
        qt_th(i) = qt_th(i) + b2sr * q_star
        ! new on differre le calcul de Theta_e
        ! The_th(i) = The_th(i) + therm(i) + RLvCp*qT_th(i)
        ! ou:    The_th(i) = The_th(i) + sqrt(b1)*khfs(i)/wm(i) +
        ! RLvCp*qT_th(i)
        rhino(i, 1) = 0.0
      END IF
    END DO

    ! +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
    ! ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
    ! ++ Improve pblh estimate for unstable conditions using the +++++++
    ! ++          convective temperature excess :                +++++++
    ! ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
    ! +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++

    DO k = 2, isommet
      DO i = 1, knon
        IF (check(i)) THEN
          ! test     zdu2 =
          ! (u(i,k)-u(i,1))**2+(v(i,k)-v(i,1))**2+fac*ustar(i)**2
          zdu2 = u(i, k)**2 + v(i, k)**2
          zdu2 = max(zdu2, 1.0E-20)
          ! Theta_v environnement
          zthvd = t(i, k) / s(i, k) * (1. + retv * q(i, k))

          ! et therm Theta_v (avec hypothese de constance de H&B,
          ! zthvu=(t(i,1)+therm(i))/s(i,1)*(1.+RETV*q(i,1))
          zthvu = th_th(i) * (1. + retv * qt_th(i)) + therm(i)


          ! Le Ri par Theta_v
          ! AM Niveau de ref 2m
          ! AM         rhino(i,k) = (z(i,k)-z(i,1))*RG*(zthvd-zthvu)
          ! AM     .               /(zdu2*0.5*(zthvd+zthvu))
          rhino(i, k) = (z(i, k) - zref) * rg * (zthvd - zthvu) / (zdu2 * 0.5&
                  * (zthvd + zthvu))

          IF (rhino(i, k)>=ricr) THEN
            pblh(i) = z(i, k - 1) + (z(i, k - 1) - z(i, k)) * (ricr - rhino(i, k - 1))&
                    / (rhino(i, k - 1) - rhino(i, k))
            ! test04
            pblh(i) = pblh(i) + 100.
            pblt(i) = t(i, k - 1) + (t(i, k) - t(i, k - 1)) * (pblh(i) - z(i, k - 1))&
                    / (z(i, k) - z(i, k - 1))
            check(i) = .FALSE.
            ! IM 170305 BEG
            IF (1==0) THEN
              ! debug print -120;34       -34-        58 et    0;26 wamp
              IF (i==950 .OR. i==192 .OR. i==624 .OR. i==118) THEN
                PRINT *, ' i,Th_th,Therm,qT :', i, th_th(i), therm(i), &
                        qt_th(i)
                q_star = kqfs(i) / wm(i)
                t_star = khfs(i) / wm(i)
                PRINT *, 'q* t*, b1,b2,b212 ', q_star, t_star, &
                        b1 * (1. + 2. * retv * qt_th(i)) * t_star**2, &
                        (retv * th_th(i))**2 * b2 * q_star**2, 2. * retv * th_th(i)&
                        * b212 * q_star * t_star
                PRINT *, 'zdu2 ,100.*ustar(i)**2', zdu2, fac * ustar(i)**2
              END IF
            END IF !(1.EQ.0) THEN
            ! IM 170305 END
            ! q_star = kqfs(i)/wm(i)
            ! t_star = khfs(i)/wm(i)
            ! trmb1(i) = b1*(1.+2.*RETV*q(i,1))*t_star**2
            ! trmb2(i) = (RETV*T(i,1))**2*b2*q_star**2
            ! Omega now   trmb3(i) = 2.*RETV*T(i,1)*b212*q_star*t_star
          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

    ! 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)
      ! par exemple :
      pblt(i) = t(i, 2) + (t(i, 3) - t(i, 2)) * (pblh(i) - z(i, 2)) / (z(i, 3) - z(i, 2))
    END DO

    ! ********************************************************************
    ! pblh is now available; do preparation for diffusivity calculation :
    ! ********************************************************************
    DO i = 1, knon
      check(i) = .TRUE.
      zsat(i) = .FALSE.
      ! omegafl utilise pour prolongement CAPE
      omegafl(i) = .FALSE.
      cape(i) = 0.
      kape(i) = 0.
      eauliq(i) = 0.
      ctei(i) = 0.
      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.
      ! *** Rq: les formule sont prises dans leur forme CS ***
      IF (unstbl(i)) THEN
        ! AM Niveau de ref du thermique
        ! AM          zxt=(t(i,1)-z(i,1)*0.5*RG/RCPD/(1.+RVTMP2*q(i,1)))
        ! AM     .         *(1.+RETV*q(i,1))
        zxt = (th_th(i) - zref * 0.5 * rg / rcpd / (1. + rvtmp2 * qt_th(i))) * &
                (1. + retv * qt_th(i))
        phiminv(i) = (1. - binm * pblh(i) * unsobklen(i))**onet
        phihinv(i) = sqrt(1. - binh * pblh(i) * unsobklen(i))
        wm(i) = ustar(i) * phiminv(i)
        fak2(i) = wm(i) * pblh(i) * vk
        wstar(i) = (heatv(i) * rg * pblh(i) / zxt)**onet
        fak3(i) = fakn * wstar(i) / wm(i)
      ELSE
        wstar(i) = 0.
      END IF
      ! Computes Theta_e for thermal (all cases : to be modified)
      ! attention ajout therm(i) = virtuelle
      the_th(i) = th_th(i) + therm(i) + rlvcp * qt_th(i)
      ! ou:    The_th(i) = Th_th(i) + sqrt(b1)*khfs(i)/wm(i) + RLvCp*qT_th(i)
    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))
          ! debug
          ! if (i.EQ.1864) THEN
          ! PRINT*,'i,pblh(1864),obklen(1864)',i,pblh(i),obklen(i)
          ! END IF

          zh(i) = zmzp / pblh(i)
          zl(i) = zmzp * unsobklen(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
      ! PRINT*,'fin calcul niveaux'

      ! 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
      ! PRINT*,'fin counter-gradient terms zero'

      ! 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
      ! PRINT*,'fin counter-gradient terms non zero'

      ! For all unstable layers, compute diffusivities and ctrgrad ter m

      ! DO i = 1, knon
      ! IF (unslev(i)) THEN
      ! pcfm(i,k) = pblk(i)
      ! pcfh(i,k) = pblk(i)/pr(i)
      ! etc cf original
      ! ENDIF
      ! ENDDO

      ! For all layers, compute integral info and CTEI

      DO i = 1, knon
        IF (check(i) .OR. omegafl(i)) THEN
          IF (.NOT. zsat(i)) THEN
            ! Th2 = The_th(i) - RLvCp*qT_th(i)
            th2 = th_th(i)
            t2 = th2 * s(i, k)
            ! thermodyn functions
            zdelta = max(0., sign(1., rtt - t2))
            qqsat = r2es * foeew(t2, zdelta) / pplay(i, k)
            qqsat = min(0.5, qqsat)
            zcor = 1. / (1. - retv * qqsat)
            qqsat = qqsat * zcor

            IF (qqsat<qt_th(i)) THEN
              ! on calcule lcl
              IF (k==2) THEN
                plcl(i) = z(i, k)
              ELSE
                plcl(i) = z(i, k - 1) + (z(i, k - 1) - z(i, k)) * (qt_th(i)&
                        - qsatbef(i)) / (qsatbef(i) - qqsat)
              END IF
              zsat(i) = .TRUE.
              tbef(i) = t2
            END IF

            qsatbef(i) = qqsat ! bug dans la version orig ???
          END IF
          ! amn ???? cette ligne a deja ete faite normalement ?
        END IF
        ! PRINT*,'hbtm2 i,k=',i,k
      END DO
    END DO ! end of level loop
    ! IM 170305 BEG
    IF (1==0) THEN
      PRINT *, 'hbtm2  ok'
    END IF !(1.EQ.0) THEN
    ! IM 170305 END

  END SUBROUTINE hbtm

END MODULE hbtm_mod