MODULE lmdz_wake

! $Id: lmdz_wake.F90 5103 2024-07-23 13:29:36Z abarral $

CONTAINS

SUBROUTINE wake(klon,klev,znatsurf, p, ph, pi, dtime, &
                tb0, qb0, omgb, &
                dtdwn, dqdwn, amdwn, amup, dta, dqa, wgen, &
                sigd_con, Cin, &
                deltatw, deltaqw, sigmaw, asigmaw, wdens, awdens, &                  ! state variables           
                dth, hw, wape, fip, gfl, &
                dtls, dqls, ktopw, omgbdth, dp_omgb, tx, qx, &
                dtke, dqke, omg, dp_deltomg, wkspread, cstar, &
                d_deltat_gw, &                                                      ! tendencies
                d_deltatw2, d_deltaqw2, d_sigmaw2, d_asigmaw2, d_wdens2, d_awdens2)             ! tendencies


  ! **************************************************************
  ! *
  ! WAKE                                                        *
  ! retour a un Pupper fixe                                *
  ! *
  ! written by   :  GRANDPEIX Jean-Yves   09/03/2000            *
  ! modified by :   ROEHRIG Romain        01/29/2007            *
  ! **************************************************************


  USE lmdz_wake_ini , ONLY: wake_ini
  USE lmdz_wake_ini , ONLY: prt_level,epsim1,RG,RD
  USE lmdz_wake_ini , ONLY: stark, wdens_ref, coefgw, alpk, wk_pupper
  USE lmdz_wake_ini , ONLY: crep_upper, crep_sol, tau_cv, rzero, aa0, flag_wk_check_trgl
  USE lmdz_wake_ini , ONLY: ok_bug_gfl
  USE lmdz_wake_ini , ONLY: iflag_wk_act, iflag_wk_check_trgl, iflag_wk_pop_dyn, wdensinit, wdensthreshold
  USE lmdz_wake_ini , ONLY: sigmad, hwmin, wapecut, cstart, sigmaw_max, dens_rate, epsilon_loc
  USE lmdz_wake_ini , ONLY: iflag_wk_profile
  USE lmdz_wake_ini , ONLY: smallestreal,wk_nsub


  IMPLICIT NONE
  ! ============================================================================


  ! But : Decrire le comportement des poches froides apparaissant dans les
  ! grands systemes convectifs, et fournir l'energie disponible pour
  ! le declenchement de nouvelles colonnes convectives.

  ! State variables : 
  ! deltatw    : temperature difference between wake and off-wake regions
  ! deltaqw    : specific humidity difference between wake and off-wake regions
  ! sigmaw     : fractional area covered by wakes.
  ! asigmaw    : fractional area covered by active wakes.
  ! wdens      : number of wakes per unit area
  ! awdens     : number of active wakes per unit area

  ! Variable de sortie :

  ! wape : WAke Potential Energy
  ! fip  : Front Incident Power (W/m2) - ALP
  ! gfl  : Gust Front Length per unit area (m-1)
  ! dtls : large scale temperature tendency due to wake
  ! dqls : large scale humidity tendency due to wake
  ! hw   : wake top hight (given by hw*deltatw(1)/2=wape)
  ! dp_omgb : vertical gradient of large scale omega
  ! awdens  : densite de poches actives
  ! wdens   : densite de poches
  ! omgbdth: flux of Delta_Theta transported by LS omega
  ! dtKE   : differential heating (wake - unpertubed)
  ! dqKE   : differential moistening (wake - unpertubed)
  ! omg    : Delta_omg =vertical velocity diff. wake-undist. (Pa/s)
  ! dp_deltomg  : vertical gradient of omg (s-1)
  ! wkspread  : spreading term in d_t_wake and d_q_wake
  ! deltatw     : updated temperature difference (T_w-T_u).
  ! deltaqw     : updated humidity difference (q_w-q_u).
  ! sigmaw      : updated wake fractional area.
  ! asigmaw     : updated active wake fractional area.
  ! d_deltat_gw : delta T tendency due to GW

  ! Variables d'entree :

  ! aire : aire de la maille
  ! tb0  : horizontal average of temperature  (K)
  ! qb0  : horizontal average of humidity   (kg/kg)
  ! omgb : vitesse verticale moyenne sur la maille (Pa/s)
  ! dtdwn: source de chaleur due aux descentes (K/s)
  ! dqdwn: source d'humidite due aux descentes (kg/kg/s)
  ! dta  : source de chaleur due courants satures et detrain  (K/s)
  ! dqa  : source d'humidite due aux courants satures et detra (kg/kg/s)
  ! wgen : number of wakes generated per unit area and per sec (/m^2/s)
  ! amdwn: flux de masse total des descentes, par unite de
  !        surface de la maille (kg/m2/s)
  ! amup : flux de masse total des ascendances, par unite de
  !        surface de la maille (kg/m2/s)
  ! sigd_con: 
  ! Cin  : convective inhibition
  ! p    : pressions aux milieux des couches (Pa)
  ! ph   : pressions aux interfaces (Pa)
  ! pi  : (p/p_0)**kapa (adim)
  ! dtime: increment temporel (s)

  ! Variables internes :

  ! rho  : mean density at P levels
  ! rhoh : mean density at Ph levels
  ! tb   : mean temperature | may change within
  ! qb   : mean humidity    | sub-time-stepping
  ! thb  : mean potential temperature
  ! thx  : potential temperature in (x) area
  ! tx   : temperature  in (x) area
  ! qx   : humidity in (x) area
  ! dp_omgb: vertical gradient og LS omega
  ! omgbw  : wake average vertical omega
  ! dp_omgbw: vertical gradient of omgbw
  ! omgbdq : flux of Delta_q transported by LS omega
  ! dth  : potential temperature diff. wake-undist.
  ! th1  : first pot. temp. for vertical advection (=thx)
  ! th2  : second pot. temp. for vertical advection (=thw)
  ! q1   : first humidity for vertical advection
  ! q2   : second humidity for vertical advection
  ! d_deltatw   : redistribution term for deltatw
  ! d_deltaqw   : redistribution term for deltaqw
  ! deltatw0   : initial deltatw 
  ! deltaqw0   : initial deltaqw 
  ! hw0    : wake top hight (defined as the altitude at which deltatw=0)
  ! amflux : horizontal mass flux through wake boundary
  ! wdens_ref: initial number of wakes per unit area (3D) or per
  !            unit length (2D), at the beginning of each time step
  ! Tgw    : 1 sur la periode de onde de gravite
  ! Cgw    : vitesse de propagation de onde de gravite
  ! LL     : distance between 2 wakes

  ! -------------------------------------------------------------------------
  ! Declaration de variables
  ! -------------------------------------------------------------------------


  ! Arguments en entree
  ! --------------------

  INTEGER, INTENT(IN) :: klon,klev
  INTEGER, DIMENSION (klon),        INTENT(IN)          :: znatsurf
  REAL, DIMENSION (klon, klev),     INTENT(IN)          :: p, pi
  REAL, DIMENSION (klon, klev+1),   INTENT(IN)          :: ph
  REAL, DIMENSION (klon, klev),     INTENT(IN)          :: omgb
  REAL,                             INTENT(IN)          :: dtime
  REAL, DIMENSION (klon, klev),     INTENT(IN)          :: tb0, qb0
  REAL, DIMENSION (klon, klev),     INTENT(IN)          :: dtdwn, dqdwn
  REAL, DIMENSION (klon, klev),     INTENT(IN)          :: amdwn, amup
  REAL, DIMENSION (klon, klev),     INTENT(IN)          :: dta, dqa
  REAL, DIMENSION (klon),           INTENT(IN)          :: wgen
  REAL, DIMENSION (klon),           INTENT(IN)          :: sigd_con
  REAL, DIMENSION (klon),           INTENT(IN)          :: Cin

  ! Input/Output
  ! State variables
  REAL, DIMENSION (klon, klev),     INTENT(INOUT)       :: deltatw, deltaqw
  REAL, DIMENSION (klon),           INTENT(INOUT)       :: sigmaw
  REAL, DIMENSION (klon),           INTENT(INOUT)       :: asigmaw
  REAL, DIMENSION (klon),           INTENT(INOUT)       :: wdens
  REAL, DIMENSION (klon),           INTENT(INOUT)       :: awdens

  ! Sorties
  ! --------

  REAL, DIMENSION (klon, klev),     INTENT(OUT)         :: dth
  REAL, DIMENSION (klon, klev),     INTENT(OUT)         :: tx, qx
  REAL, DIMENSION (klon, klev),     INTENT(OUT)         :: dtls, dqls
  REAL, DIMENSION (klon, klev),     INTENT(OUT)         :: dtke, dqke
  REAL, DIMENSION (klon, klev),     INTENT(OUT)         :: wkspread    !  unused (jyg)
  REAL, DIMENSION (klon, klev),     INTENT(OUT)         :: omgbdth, omg
  REAL, DIMENSION (klon, klev),     INTENT(OUT)         :: dp_omgb, dp_deltomg
  REAL, DIMENSION (klon),           INTENT(OUT)         :: hw, wape, fip, gfl, cstar
  INTEGER, DIMENSION (klon),        INTENT(OUT)         :: ktopw
  ! Tendencies of state variables (2 is appended to the names of fields which are the cumul of fields 
  !                                 computed at each sub-timestep; e.g. d_wdens2 is the cumul of d_wdens)
  REAL, DIMENSION (klon, klev),     INTENT(OUT)         :: d_deltat_gw
  REAL, DIMENSION (klon, klev),     INTENT(OUT)         :: d_deltatw2, d_deltaqw2
  REAL, DIMENSION (klon),           INTENT(OUT)         :: d_sigmaw2, d_asigmaw2, d_wdens2, d_awdens2

  ! Variables internes
  ! -------------------

  ! Variables a fixer

  REAL                                                  :: delta_t_min
  REAL                                                  :: dtimesub
  REAL                                                  :: wdens0
  ! IM 080208
  LOGICAL, DIMENSION (klon)                             :: gwake

  ! Variables de sauvegarde
  REAL, DIMENSION (klon, klev)                          :: deltatw0
  REAL, DIMENSION (klon, klev)                          :: deltaqw0
  REAL, DIMENSION (klon, klev)                          :: tb, qb

  ! Variables liees a la dynamique de population 1
  REAL, DIMENSION(klon)                                 :: act
  REAL, DIMENSION(klon)                                 :: rad_wk, tau_wk_inv
  REAL, DIMENSION(klon)                                 :: f_shear
  REAL, DIMENSION(klon)                                 :: drdt
  
  ! Variables liees a la dynamique de population 2
  REAL, DIMENSION(klon)                                 :: cont_fact  
  
  ! Variables liees a la dynamique de population 3
  REAL, DIMENSION(klon)                                 :: arad_wk, irad_wk
  
!!  REAL, DIMENSION(klon)                                 :: d_sig_gen, d_sig_death, d_sig_col
  REAL, DIMENSION(klon)                                 :: wape1_act, wape2_act
  LOGICAL, DIMENSION (klon)                             :: kill_wake
  REAL                                                  :: drdt_pos
  REAL                                                  :: tau_wk_inv_min
  ! Some components of the tendencies of state variables  
  REAL, DIMENSION (klon)                                :: d_sig_gen2, d_sig_death2, d_sig_col2, d_sig_spread2, d_sig_bnd2
  REAL, DIMENSION (klon)                                :: d_asig_death2, d_asig_aicol2, d_asig_iicol2, d_asig_spread2, d_asig_bnd2
  REAL, DIMENSION (klon)                                :: d_dens_gen2, d_dens_death2, d_dens_col2, d_dens_bnd2
  REAL, DIMENSION (klon)                                :: d_adens_death2, d_adens_icol2, d_adens_acol2, d_adens_bnd2

  ! Variables pour les GW
  REAL, DIMENSION (klon)                                :: ll
  REAL, DIMENSION (klon, klev)                          :: n2
  REAL, DIMENSION (klon, klev)                          :: cgw
  REAL, DIMENSION (klon, klev)                          :: tgw

  ! Variables liees au calcul de hw
  REAL, DIMENSION (klon)                                :: ptop
  REAL, DIMENSION (klon)                                :: sum_dth
  REAL, DIMENSION (klon)                                :: dthmin
  REAL, DIMENSION (klon)                                :: z, dz, hw0
  INTEGER, DIMENSION (klon)                             :: ktop, kupper

  ! Variables liees au test de la forme triangulaire du profil de Delta_theta
  REAL, DIMENSION (klon)                                :: sum_half_dth
  REAL, DIMENSION (klon)                                :: dz_half

  ! Sub-timestep tendencies and related variables
  REAL, DIMENSION (klon, klev)                          :: d_deltatw, d_deltaqw
  REAL, DIMENSION (klon, klev)                          :: d_tb, d_qb
  REAL, DIMENSION (klon)                                :: d_wdens, d_awdens, d_sigmaw, d_asigmaw 
  REAL, DIMENSION (klon)                                :: d_sig_gen, d_sig_death, d_sig_col, d_sig_spread, d_sig_bnd
  REAL, DIMENSION (klon)                                :: d_asig_death, d_asig_aicol, d_asig_iicol, d_asig_spread, d_asig_bnd
  REAL, DIMENSION (klon)                                :: d_dens_gen, d_dens_death, d_dens_col, d_dens_bnd
  REAL, DIMENSION (klon)                                :: d_adens_death, d_adens_icol, d_adens_acol, d_adens_bnd
  REAL, DIMENSION (klon)                                :: agfl              !! gust front length of active wakes
                                                                             !!  per unit area
  REAL, DIMENSION (klon)                                :: alpha, alpha_tot
  REAL, DIMENSION (klon)                                :: q0_min, q1_min
  LOGICAL, DIMENSION (klon)                             :: wk_adv, ok_qx_qw

  ! Autres variables internes
  INTEGER                                               ::isubstep, k, i, igout

  REAL                                                  :: wdensmin

  REAL                                                  :: sigmaw_targ
  REAL                                                  :: wdens_targ
  REAL                                                  :: d_sigmaw_targ
  REAL                                                  :: d_wdens_targ

  REAL, DIMENSION (klon)                                :: sum_thx, sum_tx, sum_qx, sum_thvx
  REAL, DIMENSION (klon)                                :: sum_dq
  REAL, DIMENSION (klon)                                :: sum_dtdwn, sum_dqdwn
  REAL, DIMENSION (klon)                                :: av_thx, av_tx, av_qx, av_thvx
  REAL, DIMENSION (klon)                                :: av_dth, av_dq
  REAL, DIMENSION (klon)                                :: av_dtdwn, av_dqdwn

  REAL, DIMENSION (klon, klev)                          :: rho
  REAL, DIMENSION (klon, klev+1)                        :: rhoh
  REAL, DIMENSION (klon, klev)                          :: zh
  REAL, DIMENSION (klon, klev+1)                        :: zhh

  REAL, DIMENSION (klon, klev)                          :: thb, thx

  REAL, DIMENSION (klon, klev)                          :: omgbw
  REAL, DIMENSION (klon)                                :: pupper
  REAL, DIMENSION (klon)                                :: omgtop
  REAL, DIMENSION (klon, klev)                          :: dp_omgbw
  REAL, DIMENSION (klon)                                :: ztop, dztop
  REAL, DIMENSION (klon, klev)                          :: alpha_up

  REAL, DIMENSION (klon)                                :: rre1, rre2
  REAL                                                  :: rrd1, rrd2
  REAL, DIMENSION (klon, klev)                          :: th1, th2, q1, q2
  REAL, DIMENSION (klon, klev)                          :: d_th1, d_th2, d_dth
  REAL, DIMENSION (klon, klev)                          :: d_q1, d_q2, d_dq
  REAL, DIMENSION (klon, klev)                          :: omgbdq

  REAL, DIMENSION (klon)                                :: ff, gg
  REAL, DIMENSION (klon)                                :: wape2, cstar2, heff
                                                        
  REAL, DIMENSION (klon, klev)                          :: crep
                                                        
  REAL, DIMENSION (klon, klev)                          :: ppi

  ! cc nrlmd
  REAL, DIMENSION (klon)                                :: death_rate
!!  REAL, DIMENSION (klon)                                :: nat_rate
  REAL, DIMENSION (klon, klev)                          :: entr
  REAL, DIMENSION (klon, klev)                          :: detr

  REAL, DIMENSION(klon)                                 :: sigmaw_in, asigmaw_in ! pour les prints
  REAL, DIMENSION(klon)                                 :: wdens_in, awdens_in   ! pour les prints

!!!  LOGICAL                                               :: phys_sub=.TRUE.
  LOGICAL                                               :: phys_sub=.FALSE.

  LOGICAL                                               :: first_call=.TRUE.


  !!-- variables liees au nouveau calcul de ptop et hw
  REAL, DIMENSION (klon, klev)                          :: int_dth
  REAL, DIMENSION (klon, klev)                          :: zzz, dzzz
  REAL                                                  :: epsil
  REAL, DIMENSION (klon)                                :: ptop1
  INTEGER, DIMENSION (klon)                             :: ktop1
  REAL, DIMENSION (klon)                                :: omega
  REAL, DIMENSION (klon)                                :: h_zzz

!PRINT*,'WAKE LJYFz'

  ! -------------------------------------------------------------------------
  ! Initialisations
  ! -------------------------------------------------------------------------
  ! ALON = 3.e5
  ! alon = 1.E6

  !  Provisionnal; to be suppressed when f_shear is parameterized
  f_shear(:) = 1.       ! 0. for strong shear, 1. for weak shear

  ! Configuration de coefgw,stark,wdens (22/02/06 by YU Jingmei)

  ! coefgw : Coefficient pour les ondes de gravite
  ! stark : Coefficient k dans Cstar=k*sqrt(2*WAPE)
  ! wdens : Densite surfacique de poche froide
  ! -------------------------------------------------------------------------

  ! cc nrlmd      coefgw=10
  ! coefgw=1
  ! wdens0 = 1.0/(alon**2)
  ! cc nrlmd      wdens = 1.0/(alon**2)
  ! cc nrlmd      stark = 0.50
  ! CRtest
  ! cc nrlmd      alpk=0.1
  ! alpk = 1.0
  ! alpk = 0.5
  ! alpk = 0.05

 igout = klon/2+1/klon

!   sub-time-stepping parameters
  dtimesub = dtime/wk_nsub

IF (first_call) THEN
!!#define IOPHYS_WK
#undef IOPHYS_WK
#ifdef IOPHYS_WK
  IF (phys_sub) THEN
    CALL iophys_ini(dtimesub)
  ELSE
    CALL iophys_ini(dtime)
  ENDIF
#endif
  first_call = .FALSE.
ENDIF   !(first_call)

 IF (iflag_wk_pop_dyn == 0) THEN
  ! Initialisation de toutes des densites a wdens_ref.
  ! Les densites peuvent evoluer si les poches debordent
  ! (voir au tout debut de la boucle sur les substeps)
  !jyg<
  !!  wdens(:) = wdens_ref
   DO i = 1,klon
     wdens(i) = wdens_ref(znatsurf(i)+1)
   ENDDO 
  !>jyg
 ENDIF  ! (iflag_wk_pop_dyn == 0)

 IF (iflag_wk_pop_dyn >=1) THEN
   IF (iflag_wk_pop_dyn == 3) THEN
     wdensmin = wdensthreshold
   ELSE
     wdensmin = wdensinit
   ENDIF
 ENDIF

  ! PRINT*,'stark',stark
  ! PRINT*,'alpk',alpk
  ! PRINT*,'wdens',wdens
  ! PRINT*,'coefgw',coefgw
  ! cc
  ! Minimum value for |T_wake - T_undist|. Used for wake top definition
  ! -------------------------------------------------------------------------

   delta_t_min = 0.2

  ! 1. - Save initial values, initialize tendencies, initialize output fields
  ! ------------------------------------------------------------------------

!jyg<
!!  DO k = 1, klev
!!    DO i = 1, klon
!!      ppi(i, k) = pi(i, k)
!!      deltatw0(i, k) = deltatw(i, k)
!!      deltaqw0(i, k) = deltaqw(i, k)
!!      tb(i, k) = tb0(i, k)
!!      qb(i, k) = qb0(i, k)
!!      dtls(i, k) = 0.
!!      dqls(i, k) = 0.
!!      d_deltat_gw(i, k) = 0.
!!      d_tb(i, k) = 0.
!!      d_qb(i, k) = 0.
!!      d_deltatw(i, k) = 0.
!!      d_deltaqw(i, k) = 0.
!!      ! IM 060508 beg
!!      d_deltatw2(i, k) = 0.
!!      d_deltaqw2(i, k) = 0.
!!      ! IM 060508 end
!!    END DO
!!  END DO
      ppi(:,:) = pi(:,:)
      deltatw0(:,:) = deltatw(:,:)
      deltaqw0(:,:) = deltaqw(:,:)
      tb(:,:) = tb0(:,:)
      qb(:,:) = qb0(:,:)
      dtls(:,:) = 0.
      dqls(:,:) = 0.
      d_deltat_gw(:,:) = 0.
      d_tb(:,:) = 0.
      d_qb(:,:) = 0.
      d_deltatw(:,:) = 0.
      d_deltaqw(:,:) = 0.
      d_deltatw2(:,:) = 0.
      d_deltaqw2(:,:) = 0.

      d_sig_gen2(:)   = 0.
      d_sig_death2(:) = 0.
      d_sig_col2(:)   = 0.
      d_sig_spread2(:)= 0.
      d_asig_death2(:) = 0.
      d_asig_iicol2(:) = 0.
      d_asig_aicol2(:) = 0.
      d_asig_spread2(:)= 0.
      d_asig_bnd2(:) = 0.
      d_asigmaw2(:) = 0.

      d_dens_gen2(:)   = 0.
      d_dens_death2(:) = 0.
      d_dens_col2(:)   = 0.
      d_dens_bnd2(:) = 0.
      d_wdens2(:) = 0.
      d_adens_bnd2(:) = 0.
      d_awdens2(:) = 0.
      d_adens_death2(:) = 0.
      d_adens_icol2(:) = 0.
      d_adens_acol2(:) = 0.

      IF (iflag_wk_act == 0) THEN
        act(:) = 0.
      ELSEIF (iflag_wk_act == 1) THEN
        act(:) = 1.
      ENDIF

!!  DO i = 1, klon
!!   sigmaw_in(i) = sigmaw(i)
!!  END DO
   sigmaw_in(:)  = sigmaw(:)
   asigmaw_in(:) = asigmaw(:)
!>jyg

  IF (iflag_wk_pop_dyn >= 1) THEN
    awdens_in(:) = awdens(:)
    wdens_in(:) = wdens(:)
!!    wdens(:) = wdens(:) + wgen(:)*dtime
!!    d_wdens2(:) = wgen(:)*dtime
!!  ELSE
  ENDIF  ! (iflag_wk_pop_dyn >= 1)


  ! sigmaw1=sigmaw
  ! IF (sigd_con.GT.sigmaw1) THEN
  ! PRINT*, 'sigmaw,sigd_con', sigmaw, sigd_con
  ! ENDIF
  IF (iflag_wk_pop_dyn >= 1) THEN
    DO i = 1, klon
      d_dens_gen2(i)   = 0.
      d_dens_death2(i) = 0.
      d_dens_col2(i)   = 0.
      d_awdens2(i) = 0.
      IF (wdens(i) < wdensthreshold) THEN
  !!      wdens_targ = max(wdens(i),wdensmin)
        wdens_targ = max(wdens(i),wdensinit)
        d_dens_bnd2(i) = wdens_targ - wdens(i)
        d_wdens2(i) = wdens_targ - wdens(i)
        wdens(i) = wdens_targ
      ELSE
        d_dens_bnd2(i) = 0.
        d_wdens2(i) = 0.
      ENDIF  !! (wdens(i) < wdensthreshold)
    END DO
    IF (iflag_wk_pop_dyn >= 2) THEN
      DO i = 1, klon  
        IF (awdens(i) < wdensthreshold) THEN
!!          wdens_targ = min(max(awdens(i),wdensmin),wdens(i))
            wdens_targ = min(max(awdens(i),wdensinit),wdens(i))
            d_adens_bnd2(i) = wdens_targ - awdens(i)
            d_awdens2(i) = wdens_targ - awdens(i)
            awdens(i) = wdens_targ
        ELSE
            wdens_targ = min(awdens(i), wdens(i))
            d_adens_bnd2(i) = wdens_targ - awdens(i)
            d_awdens2(i) = wdens_targ - awdens(i)
            awdens(i) = wdens_targ
        ENDIF
      END DO
    ENDIF ! (iflag_wk_pop_dyn >= 2)
  ELSE  
    DO i = 1, klon
      d_awdens2(i) = 0.
      d_wdens2(i) = 0.
    END DO
  ENDIF  ! (iflag_wk_pop_dyn >= 1)

  DO i = 1, klon
    sigmaw_targ = min(max(sigmaw(i), sigmad),0.99)
    d_sig_bnd2(i) = sigmaw_targ - sigmaw(i)
    d_sigmaw2(i) = sigmaw_targ - sigmaw(i)
    sigmaw(i) = sigmaw_targ
  END DO

  IF (iflag_wk_pop_dyn == 3) THEN
     DO i = 1, klon  
        IF ((wdens(i)-awdens(i)) <= smallestreal) THEN
          sigmaw_targ = sigmaw(i)
        ELSE
          sigmaw_targ = min(max(asigmaw(i),sigmad),sigmaw(i))
        ENDIF
        d_asig_bnd2(i) = sigmaw_targ - asigmaw(i)
        d_asigmaw2(i) = sigmaw_targ - asigmaw(i)
        asigmaw(i) = sigmaw_targ
     END DO
  ENDIF ! (iflag_wk_pop_dyn == 3)

  wape(:) = 0.
  wape2(:) = 0.
  d_sigmaw(:) = 0.
  d_asigmaw(:) = 0.
  ktopw(:) = 0

!<jyg
dth(:,:) = 0.
tx(:,:) = 0.
qx(:,:) = 0.
dtke(:,:) = 0.
dqke(:,:) = 0.
wkspread(:,:) = 0.
omgbdth(:,:) = 0.
omg(:,:) = 0.
dp_omgb(:,:) = 0.
dp_deltomg(:,:) = 0.
hw(:) = 0.
wape(:) = 0.
fip(:) = 0.
gfl(:) = 0.
cstar(:) = 0.
ktopw(:) = 0

!  Vertical advection local variables
omgbw(:,:) = 0.
omgtop(:) = 0
dp_omgbw(:,:) = 0.
omgbdq(:,:) = 0.

!>jyg

  IF (prt_level>=10) THEN
    PRINT *, 'wake-1, sigmaw(igout) ', sigmaw(igout)
    PRINT *, 'wake-1, deltatw(igout,k) ', (k,deltatw(igout,k), k=1,klev)
    PRINT *, 'wake-1, deltaqw(igout,k) ', (k,deltaqw(igout,k), k=1,klev)
    PRINT *, 'wake-1, dowwdraughts, amdwn(igout,k) ', (k,amdwn(igout,k), k=1,klev)
    PRINT *, 'wake-1, dowwdraughts, dtdwn(igout,k) ', (k,dtdwn(igout,k), k=1,klev)
    PRINT *, 'wake-1, dowwdraughts, dqdwn(igout,k) ', (k,dqdwn(igout,k), k=1,klev)
    PRINT *, 'wake-1, updraughts, amup(igout,k) ', (k,amup(igout,k), k=1,klev)
    PRINT *, 'wake-1, updraughts, dta(igout,k) ', (k,dta(igout,k), k=1,klev)
    PRINT *, 'wake-1, updraughts, dqa(igout,k) ', (k,dqa(igout,k), k=1,klev)
  ENDIF

  ! 2. - Prognostic part
  ! --------------------


  ! 2.1 - Undisturbed area and Wake integrals
  ! ---------------------------------------------------------

  DO i = 1, klon
    z(i) = 0.
    ktop(i) = 0
    kupper(i) = 0
    sum_thx(i) = 0.
    sum_tx(i) = 0.
    sum_qx(i) = 0.
    sum_thvx(i) = 0.
    sum_dth(i) = 0.
    sum_dq(i) = 0.
    sum_dtdwn(i) = 0.
    sum_dqdwn(i) = 0.

    av_thx(i) = 0.
    av_tx(i) = 0.
    av_qx(i) = 0.
    av_thvx(i) = 0.
    av_dth(i) = 0.
    av_dq(i) = 0.
    av_dtdwn(i) = 0.
    av_dqdwn(i) = 0.
  END DO

  ! Distance between wakes
  DO i = 1, klon
    ll(i) = (1-sqrt(sigmaw(i)))/sqrt(wdens(i))
  END DO
  ! Potential temperatures and humidity
  ! ----------------------------------------------------------
  DO k = 1, klev
    DO i = 1, klon
      ! write(*,*)'wake 1',i,k,RD,tb(i,k)
      rho(i, k) = p(i, k)/(RD*tb(i,k))
      ! write(*,*)'wake 2',rho(i,k)
      IF (k==1) THEN
        ! write(*,*)'wake 3',i,k,rd,tb(i,k)
        rhoh(i, k) = ph(i, k)/(RD*tb(i,k))
        ! write(*,*)'wake 4',i,k,rd,tb(i,k)
        zhh(i, k) = 0
      ELSE
        ! write(*,*)'wake 5',rd,(tb(i,k)+tb(i,k-1))
        rhoh(i, k) = ph(i, k)*2./(RD*(tb(i,k)+tb(i,k-1)))
        ! write(*,*)'wake 6',(-rhoh(i,k)*RG)+zhh(i,k-1)
        zhh(i, k) = (ph(i,k)-ph(i,k-1))/(-rhoh(i,k)*RG) + zhh(i, k-1)
      END IF
      ! write(*,*)'wake 7',ppi(i,k)
      thb(i, k) = tb(i, k)/ppi(i, k)
      thx(i, k) = (tb(i,k)-deltatw(i,k)*sigmaw(i))/ppi(i, k)
      tx(i, k) = tb(i, k) - deltatw(i, k)*sigmaw(i)
      qx(i, k) = qb(i, k) - deltaqw(i, k)*sigmaw(i)
      ! write(*,*)'wake 8',(RD*(tb(i,k)+deltatw(i,k)))
      dth(i, k) = deltatw(i, k)/ppi(i, k)
    END DO
  END DO

  DO k = 1, klev - 1
    DO i = 1, klon
      IF (k==1) THEN
        n2(i, k) = 0
      ELSE
        n2(i, k) = amax1(0., -RG**2/thb(i,k)*rho(i,k)*(thb(i,k+1)-thb(i,k-1))/ &
                             (p(i,k+1)-p(i,k-1)))
      END IF
      zh(i, k) = (zhh(i,k)+zhh(i,k+1))/2

      cgw(i, k) = sqrt(n2(i,k))*zh(i, k)
      tgw(i, k) = coefgw*cgw(i, k)/ll(i)
    END DO
  END DO

  DO i = 1, klon
    n2(i, klev) = 0
    zh(i, klev) = 0
    cgw(i, klev) = 0
    tgw(i, klev) = 0
  END DO

  
  ! Choose an integration bound well above wake top
  ! -----------------------------------------------------------------

  ! Determine Wake top pressure (Ptop) from buoyancy integral
  ! --------------------------------------------------------

   Do i=1, klon
       wk_adv(i) = .True.
   Enddo
   Call pkupper (klon, klev, ptop, ph, p, pupper, kupper, &
                    dth, hw0, rho, delta_t_min, &
                    ktop, wk_adv, h_zzz, ptop1, ktop1)
 
   !!print'("pkupper APPEL ",7i6)',0,int(ptop/100.),int(ptop1/100.),int(pupper/100.),ktop,ktop1,kupper
   
   IF (prt_level>=10) THEN
     PRINT *, 'wake-3, ktop(igout), kupper(igout) ', ktop(igout), kupper(igout)
  ENDIF

  ! -5/ Set deltatw & deltaqw to 0 above kupper

  DO k = 1, klev
    DO i = 1, klon
      IF (k>=kupper(i)) THEN
        deltatw(i, k) = 0.
        deltaqw(i, k) = 0.
        d_deltatw2(i,k) = -deltatw0(i,k)
        d_deltaqw2(i,k) = -deltaqw0(i,k)
      END IF
    END DO
  END DO


  ! Vertical gradient of LS omega

  DO k = 1, klev
    DO i = 1, klon
      IF (k<=kupper(i)) THEN
        dp_omgb(i, k) = (omgb(i,k+1)-omgb(i,k))/(ph(i,k+1)-ph(i,k))
      END IF
    END DO
  END DO

  ! Integrals (and wake top level number)
  ! --------------------------------------

  ! Initialize sum_thvx to 1st level virt. pot. temp.

  DO i = 1, klon
    z(i) = 1.
    dz(i) = 1.
    sum_thvx(i) = thx(i, 1)*(1.+epsim1*qx(i,1))*dz(i)
    sum_dth(i) = 0.
  END DO

  DO k = 1, klev
    DO i = 1, klon
      dz(i) = -(amax1(ph(i,k+1),ptop(i))-ph(i,k))/(rho(i,k)*RG)
      IF (dz(i)>0) THEN
              ! LJYF : ecriture pas sympa avec un tableau z(i) qui n'est pas utilise come tableau
        z(i) = z(i) + dz(i)
        sum_thx(i) = sum_thx(i) + thx(i, k)*dz(i)
        sum_tx(i) = sum_tx(i) + tx(i, k)*dz(i)
        sum_qx(i) = sum_qx(i) + qx(i, k)*dz(i)
        sum_thvx(i) = sum_thvx(i) + thx(i, k)*(1.+epsim1*qx(i,k))*dz(i)
        sum_dth(i) = sum_dth(i) + dth(i, k)*dz(i)
        sum_dq(i) = sum_dq(i) + deltaqw(i, k)*dz(i)
        sum_dtdwn(i) = sum_dtdwn(i) + dtdwn(i, k)*dz(i)
        sum_dqdwn(i) = sum_dqdwn(i) + dqdwn(i, k)*dz(i)
      END IF
    END DO
  END DO

  DO i = 1, klon
    hw0(i) = z(i)
  END DO


  ! 2.1 - WAPE and mean forcing computation
  ! ---------------------------------------

  ! ---------------------------------------

  ! Means

  DO i = 1, klon
    av_thx(i) = sum_thx(i)/hw0(i)
    av_tx(i) = sum_tx(i)/hw0(i)
    av_qx(i) = sum_qx(i)/hw0(i)
    av_thvx(i) = sum_thvx(i)/hw0(i)
    ! av_thve = sum_thve/hw0
    av_dth(i) = sum_dth(i)/hw0(i)
    av_dq(i) = sum_dq(i)/hw0(i)
    av_dtdwn(i) = sum_dtdwn(i)/hw0(i)
    av_dqdwn(i) = sum_dqdwn(i)/hw0(i)

    wape(i) = -RG*hw0(i)*(av_dth(i)+ &
        epsim1*(av_thx(i)*av_dq(i)+av_dth(i)*av_qx(i)+av_dth(i)*av_dq(i)))/av_thvx(i)

  END DO
#ifdef IOPHYS_WK
  IF (.not.phys_sub) CALL iophys_ecrit('wape_a',1,'wape_a','J/kg',wape)
#endif

  ! 2.2 Prognostic variable update
  ! ------------------------------

  ! Filter out bad wakes

  DO k = 1, klev
    DO i = 1, klon
      IF (wape(i)<0.) THEN
        deltatw(i, k) = 0.
        deltaqw(i, k) = 0.
        dth(i, k) = 0.
        d_deltatw2(i,k) = -deltatw0(i,k)
        d_deltaqw2(i,k) = -deltaqw0(i,k)
      END IF
    END DO
  END DO

  DO i = 1, klon
    IF (wape(i)<0.) THEN
!!      sigmaw(i) = amax1(sigmad, sigd_con(i))
      sigmaw_targ = max(sigmad, sigd_con(i))
      d_sig_bnd2(i) = d_sig_bnd2(i) + sigmaw_targ - sigmaw(i)
      d_sigmaw2(i) = d_sigmaw2(i) + sigmaw_targ - sigmaw(i)
      sigmaw(i) = sigmaw_targ
    ENDIF  !!  (wape(i)<0.)
  ENDDO

  IF (iflag_wk_pop_dyn == 3) THEN
    DO i = 1, klon
      IF (wape(i)<0.) THEN
        sigmaw_targ = max(sigmad, sigd_con(i))
        d_asig_bnd2(i) = d_asig_bnd2(i) + sigmaw_targ - asigmaw(i)
        d_asigmaw2(i) = d_asigmaw2(i) + sigmaw_targ - asigmaw(i)
        asigmaw(i) = sigmaw_targ
      ENDIF  !!  (wape(i)<0.)
    ENDDO
  ENDIF  !!  (iflag_wk_pop_dyn == 3)

  DO i = 1, klon
    IF (wape(i)<0.) THEN
      wape(i) = 0.
      cstar(i) = 0.
      hw(i) = hwmin
      fip(i) = 0.
      gwake(i) = .FALSE.
    ELSE
      hw(i) = hw0(i)
      cstar(i) = stark*sqrt(2.*wape(i))
      gwake(i) = .TRUE.
    END IF
  END DO

  ! Check qx and qw positivity
  ! --------------------------
  DO i = 1, klon
    q0_min(i) = min((qb(i,1)-sigmaw(i)*deltaqw(i,1)),  &
                    (qb(i,1)+(1.-sigmaw(i))*deltaqw(i,1)))
  END DO
  DO k = 2, klev
    DO i = 1, klon
      q1_min(i) = min((qb(i,k)-sigmaw(i)*deltaqw(i,k)), &
                      (qb(i,k)+(1.-sigmaw(i))*deltaqw(i,k)))
      IF (q1_min(i)<=q0_min(i)) THEN
        q0_min(i) = q1_min(i)
      END IF
    END DO
  END DO

  DO i = 1, klon
    ok_qx_qw(i) = q0_min(i) >= 0.
    alpha(i) = 1.
    alpha_tot(i) = 1.
  END DO

  IF (prt_level>=10) THEN
    PRINT *, 'wake-4, sigmaw(igout), cstar(igout), wape(igout), ktop(igout) ', &
                      sigmaw(igout), cstar(igout), wape(igout), ktop(igout)
  ENDIF


  ! C -----------------------------------------------------------------
  ! Sub-time-stepping
  ! -----------------

!    wk_nsub and dtimesub definitions moved to begining of routine.
!!  wk_nsub = 10
!!  dtimesub = dtime/wk_nsub

  
  ! ------------------------------------------------------------------------
  ! ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
  ! ------------------------------------------------------------------------

  DO isubstep = 1, wk_nsub

  ! ------------------------------------------------------------------------
    ! wk_adv is the logical flag enabling wake evolution in the time advance
    ! loop
    DO i = 1, klon
      wk_adv(i) = ok_qx_qw(i) .AND. alpha(i) >= 1.
    END DO
    IF (prt_level>=10) THEN
      PRINT *, 'wake-4.1, isubstep,wk_adv(igout),cstar(igout),wape(igout), ptop(igout) ', &
                          isubstep,wk_adv(igout),cstar(igout),wape(igout), ptop(igout)
     
    ENDIF

    ! cc nrlmd   Ajout d'un recalcul de wdens dans le cas d'un entrainement
    ! negatif de ktop a kupper --------
    ! cc           On calcule pour cela une densite wdens0 pour laquelle on
    ! aurait un entrainement nul ---
    !jyg<
    ! Dans la configuration avec wdens prognostique, il s'agit d'un cas ou 
    ! les poches sont insuffisantes pour accueillir tout le flux de masse 
    ! des descentes unsaturees. Nous faisons alors l'hypothese que la 
    ! convection profonde cree directement de nouvelles poches, sans passer 
    ! par les thermiques. La nouvelle valeur de wdens est alors imposee.

    DO i = 1, klon
      ! c       print *,' isubstep,wk_adv(i),cstar(i),wape(i) ',
      ! c     $           isubstep,wk_adv(i),cstar(i),wape(i)
      IF (wk_adv(i) .AND. cstar(i)>0.01) THEN
        IF ( iflag_wk_profile == 0 ) THEN
           omg(i, kupper(i)+1)=-RG*amdwn(i, kupper(i)+1)/sigmaw(i) + &
                               RG*amup(i, kupper(i)+1)/(1.-sigmaw(i))
        ELSE
           omg(i, kupper(i)+1)=0.
        ENDIF
        wdens0 = (sigmaw(i)/(4.*3.14))* &
          ((1.-sigmaw(i))*omg(i,kupper(i)+1)/((ph(i,1)-pupper(i))*cstar(i)))**(2)
        IF (prt_level >= 10) THEN
             PRINT*,'omg(i,kupper(i)+1),wdens0,wdens(i),cstar(i), ph(i,1)-pupper(i)', &
                     omg(i,kupper(i)+1),wdens0,wdens(i),cstar(i), ph(i,1)-pupper(i)
        ENDIF
        IF (wdens(i)<=wdens0*1.1) THEN
          IF (iflag_wk_pop_dyn >= 1) THEN
             d_dens_bnd2(i) = d_dens_bnd2(i) + wdens0 - wdens(i)
             d_wdens2(i) = d_wdens2(i) + wdens0 - wdens(i)
          ENDIF
          wdens(i) = wdens0
        END IF
      END IF
    END DO

    IF (iflag_wk_pop_dyn == 0 .AND. ok_bug_gfl) THEN
!!--------------------------------------------------------
!!Bug : computing gfl and rad_wk before changing sigmaw
!!      This bug exists only for iflag_wk_pop_dyn=0. Otherwise, gfl and rad_wk 
!!      are computed within  wake_popdyn
!!--------------------------------------------------------
      DO i = 1, klon
        IF (wk_adv(i)) THEN
          gfl(i) = 2.*sqrt(3.14*wdens(i)*sigmaw(i))
          rad_wk(i) = sqrt(sigmaw(i)/(3.14*wdens(i)))
        END IF
      END DO
    ENDIF   ! (iflag_wk_pop_dyn == 0 .AND. ok_bug_gfl)
!!--------------------------------------------------------

    DO i = 1, klon
      IF (wk_adv(i)) THEN
        sigmaw_targ = min(sigmaw(i), sigmaw_max)
        d_sig_bnd2(i) = d_sig_bnd2(i) + sigmaw_targ - sigmaw(i)
        d_sigmaw2(i)  = d_sigmaw2(i)  + sigmaw_targ - sigmaw(i)
        sigmaw(i) = sigmaw_targ
      END IF
    END DO

    IF (iflag_wk_pop_dyn == 0 .AND. .NOT.ok_bug_gfl) THEN
!!--------------------------------------------------------
!!Fix : computing gfl and rad_wk after changing sigmaw
!!--------------------------------------------------------
      DO i = 1, klon
        IF (wk_adv(i)) THEN
          gfl(i) = 2.*sqrt(3.14*wdens(i)*sigmaw(i))
          rad_wk(i) = sqrt(sigmaw(i)/(3.14*wdens(i)))
        END IF
      END DO
    ENDIF   ! (iflag_wk_pop_dyn == 0 .AND. .NOT.ok_bug_gfl)
!!--------------------------------------------------------

    IF (iflag_wk_pop_dyn >= 1) THEN
  !  The variable "death_rate" is significant only when iflag_wk_pop_dyn = 0.
  !  Here, it has to be set to zero.
      death_rate(:) = 0.
    ENDIF
  
    IF (iflag_wk_pop_dyn >= 3) THEN
      DO i = 1, klon
        IF (wk_adv(i)) THEN
         sigmaw_targ = min(asigmaw(i), sigmaw_max)
         d_asig_bnd2(i) = d_asig_bnd2(i) + sigmaw_targ - asigmaw(i)
         d_asigmaw2(i)  = d_asigmaw2(i)  + sigmaw_targ - asigmaw(i)
         asigmaw(i) = sigmaw_targ
        ENDIF
      ENDDO
    ENDIF
  
!!--------------------------------------------------------
!!--------------------------------------------------------
    IF (iflag_wk_pop_dyn == 1) THEN

     CALL wake_popdyn_1 (klon, klev, dtime, cstar, tau_wk_inv, wgen, wdens, awdens, sigmaw, &
                  wdensmin, &
                  dtimesub, gfl, rad_wk, f_shear, drdt_pos, &
                  d_awdens, d_wdens, d_sigmaw, &
                  iflag_wk_act, wk_adv, cin, wape, &
                  drdt, &
                  d_dens_gen, d_dens_death, d_dens_col, d_dens_bnd, &
                  d_sig_gen, d_sig_death, d_sig_col, d_sig_spread, d_sig_bnd, &
                  d_wdens_targ, d_sigmaw_targ)
                      
    
!!--------------------------------------------------------
    ELSEIF (iflag_wk_pop_dyn == 2) THEN

     CALL wake_popdyn_2 ( klon, klev, wk_adv, dtimesub, wgen, &
                             wdensmin, &
                             sigmaw, wdens, awdens, &   !! state variables
                             gfl, cstar, cin, wape, rad_wk, &
                             d_sigmaw, d_wdens, d_awdens, &  !! tendencies                              
                             cont_fact, &
                             d_sig_gen, d_sig_death, d_sig_col, d_sig_spread, d_sig_bnd, &
                             d_dens_gen, d_dens_death, d_dens_col, d_dens_bnd, &
                             d_adens_death, d_adens_icol, d_adens_acol, d_adens_bnd )
sigmaw=sigmaw-d_sigmaw
wdens=wdens-d_wdens
awdens=awdens-d_awdens

!!--------------------------------------------------------
    ELSEIF (iflag_wk_pop_dyn == 3) THEN
#ifdef IOPHYS_WK
    IF (phys_sub) THEN
     CALL iophys_ecrit('ptop',1,'ptop','Pa',ptop)
     CALL iophys_ecrit('sigmaw',1,'sigmaw','',sigmaw)
     CALL iophys_ecrit('asigmaw',1,'asigmaw','',asigmaw)
     CALL iophys_ecrit('wdens',1,'wdens','1/m2',wdens)
     CALL iophys_ecrit('awdens',1,'awdens','1/m2',awdens)
     CALL iophys_ecrit('rad_wk',1,'rad_wk','m',rad_wk)
     CALL iophys_ecrit('arad_wk',1,'arad_wk','m',arad_wk)
     CALL iophys_ecrit('irad_wk',1,'irad_wk','m',irad_wk)
    ENDIF
#endif

     CALL wake_popdyn_3 ( klon, klev, phys_sub, wk_adv, dtimesub, wgen, &
                             wdensmin, &
                             sigmaw, asigmaw, wdens, awdens, &   !! state variables
                             gfl, agfl, cstar, cin, wape, &
                             rad_wk, arad_wk, irad_wk, &
                             d_sigmaw, d_asigmaw, d_wdens, d_awdens, &  !! tendencies                              
                             d_sig_gen, d_sig_death, d_sig_col, d_sig_spread, d_sig_bnd, &
                             d_asig_death, d_asig_aicol, d_asig_iicol, d_asig_spread, d_asig_bnd, &
                             d_dens_gen, d_dens_death, d_dens_col, d_dens_bnd, &
                             d_adens_death, d_adens_icol, d_adens_acol, d_adens_bnd )
sigmaw=sigmaw-d_sigmaw
asigmaw=asigmaw-d_asigmaw
wdens=wdens-d_wdens
awdens=awdens-d_awdens
   
!!--------------------------------------------------------
    ELSEIF (iflag_wk_pop_dyn == 0) THEN
    
    ! cc nrlmd

      DO i = 1, klon
        IF (wk_adv(i)) THEN

          ! cc nrlmd          Introduction du taux de mortalite des poches et
          ! test sur sigmaw_max=0.4
          ! cc         d_sigmaw(i) = gfl(i)*Cstar(i)*dtimesub
          IF (sigmaw(i)>=sigmaw_max) THEN
            death_rate(i) = gfl(i)*cstar(i)/sigmaw(i)
          ELSE
            death_rate(i) = 0.
          END IF
    
          d_sigmaw(i) = gfl(i)*cstar(i)*dtimesub - death_rate(i)*sigmaw(i)* &
            dtimesub
          ! $              - nat_rate(i)*sigmaw(i)*dtimesub
          ! c        PRINT*, 'd_sigmaw(i),sigmaw(i),gfl(i),Cstar(i),wape(i),
          ! c     $  death_rate(i),ktop(i),kupper(i)',
          ! c     $	         d_sigmaw(i),sigmaw(i),gfl(i),Cstar(i),wape(i),
          ! c     $  death_rate(i),ktop(i),kupper(i)
    
          ! sigmaw(i) =sigmaw(i) + gfl(i)*Cstar(i)*dtimesub
          ! sigmaw(i) =min(sigmaw(i),0.99)     !!!!!!!!
          ! wdens = wdens0/(10.*sigmaw)
          ! sigmaw =max(sigmaw,sigd_con)
          ! sigmaw =max(sigmaw,sigmad)
        END IF
      END DO

    ENDIF   !  (iflag_wk_pop_dyn == 1) ... ELSEIF (iflag_wk_pop_dyn == 0)
!!--------------------------------------------------------
!!--------------------------------------------------------

#ifdef IOPHYS_WK
    IF (phys_sub) THEN
     CALL iophys_ecrit('wdensa',1,'wdensa','m',wdens)
     CALL iophys_ecrit('awdensa',1,'awdensa','m',awdens)
     CALL iophys_ecrit('sigmawa',1,'sigmawa','m',sigmaw)
     CALL iophys_ecrit('asigmawa',1,'asigmawa','m',asigmaw)
    ENDIF
#endif
    ! calcul de la difference de vitesse verticale poche - zone non perturbee
    ! IM 060208 differences par rapport au code initial; init. a 0 dp_deltomg
    ! IM 060208 et omg sur les niveaux de 1 a klev+1, alors que avant l'on definit
    ! IM 060208 au niveau k=1...
    !JYG 161013 Correction : maintenant omg est dimensionne a klev.
    DO k = 1, klev
      DO i = 1, klon
        IF (wk_adv(i)) THEN !!! nrlmd
          dp_deltomg(i, k) = 0.
        END IF
      END DO
    END DO
    DO k = 1, klev
      DO i = 1, klon
        IF (wk_adv(i)) THEN !!! nrlmd
          omg(i, k) = 0.
        END IF
      END DO
    END DO

    DO i = 1, klon
      IF (wk_adv(i)) THEN
        z(i) = 0.
        omg(i, 1) = 0.
        dp_deltomg(i, 1) = -(gfl(i)*cstar(i))/(sigmaw(i)*(1-sigmaw(i)))
      END IF
    END DO

    DO k = 2, klev
      DO i = 1, klon
        IF (wk_adv(i) .AND. k<=ktop(i)) THEN
          dz(i) = -(ph(i,k)-ph(i,k-1))/(rho(i,k-1)*RG)
          z(i) = z(i) + dz(i)
          dp_deltomg(i, k) = dp_deltomg(i, 1)
          omg(i, k) = dp_deltomg(i, 1)*z(i)
        END IF
      END DO
    END DO

    DO i = 1, klon
      IF (wk_adv(i)) THEN
        dztop(i) = -(ptop(i)-ph(i,ktop(i)))/(rho(i,ktop(i))*RG)
        ztop(i) = z(i) + dztop(i)
        omgtop(i) = dp_deltomg(i, 1)*ztop(i)
      END IF
    END DO

    IF (prt_level>=10) THEN
      PRINT *, 'wake-4.2, omg(igout,k) ', (k,omg(igout,k), k=1,klev)
      PRINT *, 'wake-4.2, omgtop(igout), ptop(igout), ktop(igout) ', &
                          omgtop(igout), ptop(igout), ktop(igout)
    ENDIF

    ! -----------------
    ! From m/s to Pa/s
    ! -----------------

    DO i = 1, klon
      IF (wk_adv(i)) THEN
        omgtop(i) = -rho(i, ktop(i))*RG*omgtop(i)
!! LJYF        dp_deltomg(i, 1) = omgtop(i)/(ptop(i)-ph(i,1))
        dp_deltomg(i, 1) = omgtop(i)/min(ptop(i)-ph(i,1),-smallestreal)
      END IF
    END DO

    DO k = 1, klev
      DO i = 1, klon
        IF (wk_adv(i) .AND. k<=ktop(i)) THEN
          omg(i, k) = -rho(i, k)*RG*omg(i, k)
          dp_deltomg(i, k) = dp_deltomg(i, 1)
        END IF
      END DO
    END DO

    ! raccordement lineaire de omg de ptop a pupper

    DO i = 1, klon
      IF (wk_adv(i) .AND. kupper(i)>ktop(i)) THEN
        IF ( iflag_wk_profile == 0 ) THEN
           omg(i, kupper(i)+1) =-RG*amdwn(i, kupper(i)+1)/sigmaw(i) + &
          RG*amup(i, kupper(i)+1)/(1.-sigmaw(i))
        ELSE
           omg(i, kupper(i)+1) = 0.
        ENDIF
        dp_deltomg(i, kupper(i)) = (omgtop(i)-omg(i,kupper(i)+1))/ &
          (ptop(i)-pupper(i))
      END IF
    END DO

    ! c      DO i=1,klon
    ! c        PRINT*,'Pente entre 0 et kupper (reference)'
    ! c     $   	,omg(i,kupper(i)+1)/(pupper(i)-ph(i,1))
    ! c        PRINT*,'Pente entre ktop et kupper'
    ! c     $  	,(omg(i,kupper(i)+1)-omgtop(i))/(pupper(i)-ptop(i))
    ! c      ENDDO
    ! c
    DO k = 1, klev
      DO i = 1, klon
        IF (wk_adv(i) .AND. k>ktop(i) .AND. k<=kupper(i)) THEN
          dp_deltomg(i, k) = dp_deltomg(i, kupper(i))
          omg(i, k) = omgtop(i) + (ph(i,k)-ptop(i))*dp_deltomg(i, kupper(i))
        END IF
      END DO
    END DO
!!    print *,'omg(igout,k) ', (k,omg(igout,k),k=1,klev)
    ! cc nrlmd
    ! c      DO i=1,klon
    ! c      PRINT*,'deltaw_ktop,deltaw_conv',omgtop(i),omg(i,kupper(i)+1)
    ! c      END DO
    ! cc


    ! --    Compute wake average vertical velocity omgbw


    DO k = 1, klev
      DO i = 1, klon
        IF (wk_adv(i)) THEN
          omgbw(i, k) = omgb(i, k) + (1.-sigmaw(i))*omg(i, k)
        END IF
      END DO
    END DO
    ! --    and its vertical gradient dp_omgbw

    DO k = 1, klev-1
      DO i = 1, klon
        IF (wk_adv(i)) THEN
          dp_omgbw(i, k) = (omgbw(i,k+1)-omgbw(i,k))/(ph(i,k+1)-ph(i,k))
        END IF
      END DO
    END DO
    DO i = 1, klon
      IF (wk_adv(i)) THEN
          dp_omgbw(i, klev) = 0.
      END IF
    END DO

    ! --    Upstream coefficients for omgb velocity
    ! --    (alpha_up(k) is the coefficient of the value at level k)
    ! --    (1-alpha_up(k) is the coefficient of the value at level k-1)
    DO k = 1, klev
      DO i = 1, klon
        IF (wk_adv(i)) THEN
          alpha_up(i, k) = 0.
          IF (omgb(i,k)>0.) alpha_up(i, k) = 1.
        END IF
      END DO
    END DO

    ! Matrix expressing [The,deltatw] from  [Th1,Th2]

    DO i = 1, klon
      IF (wk_adv(i)) THEN
        rre1(i) = 1. - sigmaw(i)
        rre2(i) = sigmaw(i)
      END IF
    END DO
    rrd1 = -1.
    rrd2 = 1.

    ! --    Get [Th1,Th2], dth and [q1,q2]

    DO k = 1, klev
      DO i = 1, klon
        IF (wk_adv(i) .AND. k<=kupper(i)+1) THEN
          dth(i, k) = deltatw(i, k)/ppi(i, k)
          th1(i, k) = thb(i, k) - sigmaw(i)*dth(i, k) ! undisturbed area
          th2(i, k) = thb(i, k) + (1.-sigmaw(i))*dth(i, k) ! wake
          q1(i, k) = qb(i, k) - sigmaw(i)*deltaqw(i, k) ! undisturbed area
          q2(i, k) = qb(i, k) + (1.-sigmaw(i))*deltaqw(i, k) ! wake
        END IF
      END DO
    END DO

    DO i = 1, klon
      IF (wk_adv(i)) THEN !!! nrlmd
        d_th1(i, 1) = 0.
        d_th2(i, 1) = 0.
        d_dth(i, 1) = 0.
        d_q1(i, 1) = 0.
        d_q2(i, 1) = 0.
        d_dq(i, 1) = 0.
      END IF
    END DO

    DO k = 2, klev
      DO i = 1, klon
        IF (wk_adv(i) .AND. k<=kupper(i)+1) THEN
          d_th1(i, k) = th1(i, k-1) - th1(i, k)
          d_th2(i, k) = th2(i, k-1) - th2(i, k)
          d_dth(i, k) = dth(i, k-1) - dth(i, k)
          d_q1(i, k) = q1(i, k-1) - q1(i, k)
          d_q2(i, k) = q2(i, k-1) - q2(i, k)
          d_dq(i, k) = deltaqw(i, k-1) - deltaqw(i, k)
        END IF
      END DO
    END DO

    DO i = 1, klon
      IF (wk_adv(i)) THEN
        omgbdth(i, 1) = 0.
        omgbdq(i, 1) = 0.
      END IF
    END DO

    DO k = 2, klev
      DO i = 1, klon
        IF (wk_adv(i) .AND. k<=kupper(i)+1) THEN !   loop on interfaces
          omgbdth(i, k) = omgb(i, k)*(dth(i,k-1)-dth(i,k))
          omgbdq(i, k) = omgb(i, k)*(deltaqw(i,k-1)-deltaqw(i,k))
        END IF
      END DO
    END DO

!!    IF (prt_level>=10) THEN
    IF (prt_level>=10 .and. wk_adv(igout)) THEN
      PRINT *, 'wake-4.3, th1(igout,k) ', (k,th1(igout,k), k=1,kupper(igout))
      PRINT *, 'wake-4.3, th2(igout,k) ', (k,th2(igout,k), k=1,kupper(igout))
      PRINT *, 'wake-4.3, dth(igout,k) ', (k,dth(igout,k), k=1,kupper(igout))
      PRINT *, 'wake-4.3, omgbdth(igout,k) ', (k,omgbdth(igout,k), k=1,kupper(igout))
    ENDIF

    ! -----------------------------------------------------------------
    DO k = 1, klev-1
      DO i = 1, klon
        IF (wk_adv(i) .AND. k<=kupper(i)-1) THEN
          ! -----------------------------------------------------------------

          ! Compute redistribution (advective) term

          d_deltatw(i, k) = dtimesub/(ph(i,k)-ph(i,k+1))* &
            (rrd1*omg(i,k)*sigmaw(i)*d_th1(i,k) - &
             rrd2*omg(i,k+1)*(1.-sigmaw(i))*d_th2(i,k+1)- &
             (1.-alpha_up(i,k))*omgbdth(i,k)- &
             alpha_up(i,k+1)*omgbdth(i,k+1))*ppi(i, k)
!           PRINT*,'d_d,k_ptop_provis(i)eltatw=', k, d_deltatw(i,k)

          d_deltaqw(i, k) = dtimesub/(ph(i,k)-ph(i,k+1))* &
            (rrd1*omg(i,k)*sigmaw(i)*d_q1(i,k)- &
             rrd2*omg(i,k+1)*(1.-sigmaw(i))*d_q2(i,k+1)- &
             (1.-alpha_up(i,k))*omgbdq(i,k)- &
             alpha_up(i,k+1)*omgbdq(i,k+1))
!           PRINT*,'d_deltaqw=', k, d_deltaqw(i,k)

          ! and increment large scale tendencies




          ! C
          ! -----------------------------------------------------------------
          d_tb(i, k) = dtimesub*((rre1(i)*omg(i,k)*sigmaw(i)*d_th1(i,k)- &
                                  rre2(i)*omg(i,k+1)*(1.-sigmaw(i))*d_th2(i,k+1))/ &
                                 (ph(i,k)-ph(i,k+1)) &
                                 -sigmaw(i)*(1.-sigmaw(i))*dth(i,k)*(omg(i,k)-omg(i,k+1))/ &
                                 (ph(i,k)-ph(i,k+1)) )*ppi(i, k)

          d_qb(i, k) = dtimesub*((rre1(i)*omg(i,k)*sigmaw(i)*d_q1(i,k)- &
                                  rre2(i)*omg(i,k+1)*(1.-sigmaw(i))*d_q2(i,k+1))/ &
                                 (ph(i,k)-ph(i,k+1)) &
                                 -sigmaw(i)*(1.-sigmaw(i))*deltaqw(i,k)*(omg(i,k)-omg(i,k+1))/ &
                                 (ph(i,k)-ph(i,k+1)) )
        ELSE IF (wk_adv(i) .AND. k==kupper(i)) THEN
          d_tb(i, k) = dtimesub*(rre1(i)*omg(i,k)*sigmaw(i)*d_th1(i,k)/(ph(i,k)-ph(i,k+1)))*ppi(i, k)

          d_qb(i, k) = dtimesub*(rre1(i)*omg(i,k)*sigmaw(i)*d_q1(i,k)/(ph(i,k)-ph(i,k+1)))

        END IF
        ! cc
      END DO
    END DO
    ! ------------------------------------------------------------------

    IF (prt_level>=10) THEN
      PRINT *, 'wake-4.3, d_deltatw(igout,k) ', (k,d_deltatw(igout,k), k=1,klev)
      PRINT *, 'wake-4.3, d_deltaqw(igout,k) ', (k,d_deltaqw(igout,k), k=1,klev)
    ENDIF

    ! Increment state variables
!jyg<
    IF (iflag_wk_pop_dyn >= 1) THEN
      DO k = 1, klev
        DO i = 1, klon
          IF (wk_adv(i) .AND. k<=kupper(i)) THEN
            detr(i,k) = - d_sig_death(i) - d_sig_col(i)      
            entr(i,k) = d_sig_gen(i)
          ENDIF
        ENDDO
      ENDDO
      ELSE  ! (iflag_wk_pop_dyn >= 1)
      DO k = 1, klev
        DO i = 1, klon
          IF (wk_adv(i) .AND. k<=kupper(i)) THEN
            detr(i, k) = 0.
   
            entr(i, k) = 0.
          ENDIF
        ENDDO
      ENDDO
    ENDIF  ! (iflag_wk_pop_dyn >= 1)

    

    DO k = 1, klev
      DO i = 1, klon
        ! cc nrlmd       IF( wk_adv(i) .AND. k .LE. kupper(i)-1) THEN
        IF (wk_adv(i) .AND. k<=kupper(i)) THEN
          ! cc



          ! Coefficient de repartition

          crep(i, k) = crep_sol*(ph(i,kupper(i))-ph(i,k))/ &
            (ph(i,kupper(i))-ph(i,1))
          crep(i, k) = crep(i, k) + crep_upper*(ph(i,1)-ph(i,k))/ &
            (ph(i,1)-ph(i,kupper(i)))


          ! Reintroduce compensating subsidence term.

          ! dtKE(k)=(dtdwn(k)*Crep(k))/sigmaw
          ! dtKE(k)=dtKE(k)-(dtdwn(k)*(1-Crep(k))+dta(k))
          ! .                   /(1-sigmaw)
          ! dqKE(k)=(dqdwn(k)*Crep(k))/sigmaw
          ! dqKE(k)=dqKE(k)-(dqdwn(k)*(1-Crep(k))+dqa(k))
          ! .                   /(1-sigmaw)

          ! dtKE(k)=(dtdwn(k)*Crep(k)+(1-Crep(k))*dta(k))/sigmaw
          ! dtKE(k)=dtKE(k)-(dtdwn(k)*(1-Crep(k))+dta(k)*Crep(k))
          ! .                   /(1-sigmaw)
          ! dqKE(k)=(dqdwn(k)*Crep(k)+(1-Crep(k))*dqa(k))/sigmaw
          ! dqKE(k)=dqKE(k)-(dqdwn(k)*(1-Crep(k))+dqa(k)*Crep(k))
          ! .                   /(1-sigmaw)

          dtke(i, k) = (dtdwn(i,k)/sigmaw(i)-dta(i,k)/(1.-sigmaw(i)))
          dqke(i, k) = (dqdwn(i,k)/sigmaw(i)-dqa(i,k)/(1.-sigmaw(i)))
          ! PRINT*,'dtKE= ',dtKE(i,k),' dqKE= ',dqKE(i,k)

          ! cc nrlmd          Prise en compte du taux de mortalite
          ! cc               Definitions de entr, detr
!jyg<
!!            detr(i, k) = 0.
!!   
!!            entr(i, k) = detr(i, k) + gfl(i)*cstar(i) + &
!!              sigmaw(i)*(1.-sigmaw(i))*dp_deltomg(i, k)
!!
            entr(i, k) = entr(i,k) + gfl(i)*cstar(i) + &
                         sigmaw(i)*(1.-sigmaw(i))*dp_deltomg(i, k)   
!>jyg
            wkspread(i, k) = (entr(i,k)-detr(i,k))/sigmaw(i)

          ! cc        wkspread(i,k) =
          ! (1.-sigmaw(i))*dp_deltomg(i,k)+gfl(i)*Cstar(i)/
          ! cc     $  sigmaw(i)


          ! ajout d'un effet onde de gravite -Tgw(k)*deltatw(k) 03/02/06 YU
          ! Jingmei

          ! write(lunout,*)'wake.F ',i,k, dtimesub,d_deltat_gw(i,k),
          ! &  Tgw(i,k),deltatw(i,k)
          d_deltat_gw(i, k) = d_deltat_gw(i, k) - tgw(i, k)*deltatw(i, k)* &
            dtimesub
          ! write(lunout,*)'wake.F ',i,k, dtimesub,d_deltatw(i,k)
          ff(i) = d_deltatw(i, k)/dtimesub

          ! Sans GW

          ! deltatw(k)=deltatw(k)+dtimesub*(ff+dtKE(k)-wkspread(k)*deltatw(k))

          ! GW formule 1

          ! deltatw(k) = deltatw(k)+dtimesub*
          ! $         (ff+dtKE(k) - wkspread(k)*deltatw(k)-Tgw(k)*deltatw(k))

          ! GW formule 2

          IF (dtimesub*tgw(i,k)<1.E-10) THEN
            d_deltatw(i, k) = dtimesub*(ff(i)+dtke(i,k) - & 
               entr(i,k)*deltatw(i,k)/sigmaw(i) - &
               (death_rate(i)*sigmaw(i)+detr(i,k))*deltatw(i,k)/(1.-sigmaw(i)) - & ! cc
               tgw(i,k)*deltatw(i,k) )
          ELSE
            d_deltatw(i, k) = 1/tgw(i, k)*(1-exp(-dtimesub*tgw(i,k)))* &
               (ff(i)+dtke(i,k) - &
                entr(i,k)*deltatw(i,k)/sigmaw(i) - &
                (death_rate(i)*sigmaw(i)+detr(i,k))*deltatw(i,k)/(1.-sigmaw(i)) - &
                tgw(i,k)*deltatw(i,k) )
          END IF

          dth(i, k) = deltatw(i, k)/ppi(i, k)

          gg(i) = d_deltaqw(i, k)/dtimesub

          d_deltaqw(i, k) = dtimesub*(gg(i)+dqke(i,k) - & 
            entr(i,k)*deltaqw(i,k)/sigmaw(i) - &
            (death_rate(i)*sigmaw(i)+detr(i,k))*deltaqw(i,k)/(1.-sigmaw(i)))
          ! cc

          ! cc nrlmd
          ! cc       d_deltatw2(i,k)=d_deltatw2(i,k)+d_deltatw(i,k)
          ! cc       d_deltaqw2(i,k)=d_deltaqw2(i,k)+d_deltaqw(i,k)
          ! cc
        END IF
      END DO
    END DO


    ! Scale tendencies so that water vapour remains positive in w and x.

    CALL wake_vec_modulation(klon, klev, wk_adv, epsilon_loc, qb, d_qb, deltaqw, &
      d_deltaqw, sigmaw, d_sigmaw, alpha)

    ! Alpha_tot = Product of all the alpha's
    DO i = 1, klon
      IF (wk_adv(i)) THEN
        alpha_tot(i) = alpha_tot(i)*alpha(i)    
      END IF
    END DO

    ! cc nrlmd
    ! c      PRINT*,'alpha'
    ! c      do i=1,klon
    ! c         PRINT*,alpha(i)
    ! c      END DO
    ! cc
    DO k = 1, klev
      DO i = 1, klon
        IF (wk_adv(i) .AND. k<=kupper(i)) THEN
          d_tb(i, k) = alpha(i)*d_tb(i, k)
          d_qb(i, k) = alpha(i)*d_qb(i, k)
          d_deltatw(i, k) = alpha(i)*d_deltatw(i, k)
          d_deltaqw(i, k) = alpha(i)*d_deltaqw(i, k)
          d_deltat_gw(i, k) = alpha(i)*d_deltat_gw(i, k)
        END IF
      END DO
    END DO
    DO i = 1, klon
      IF (wk_adv(i)) THEN
        d_sigmaw(i) = alpha(i)*d_sigmaw(i)
      END IF
    END DO

    ! Update large scale variables and wake variables
    ! IM 060208 manque DO i + remplace DO k=1,kupper(i)
    ! IM 060208     DO k = 1,kupper(i)
    DO k = 1, klev
      DO i = 1, klon
        IF (wk_adv(i) .AND. k<=kupper(i)) THEN
          dtls(i, k) = dtls(i, k) + d_tb(i, k)
          dqls(i, k) = dqls(i, k) + d_qb(i, k)
          ! cc nrlmd
          d_deltatw2(i, k) = d_deltatw2(i, k) + d_deltatw(i, k)
          d_deltaqw2(i, k) = d_deltaqw2(i, k) + d_deltaqw(i, k)
          ! cc
        END IF
      END DO
    END DO
    DO k = 1, klev
      DO i = 1, klon
        IF (wk_adv(i) .AND. k<=kupper(i)) THEN
          tb(i, k) = tb0(i, k) + dtls(i, k)
          qb(i, k) = qb0(i, k) + dqls(i, k)
          thb(i, k) = tb(i, k)/ppi(i, k)
          deltatw(i, k) = deltatw(i, k) + d_deltatw(i, k)
          deltaqw(i, k) = deltaqw(i, k) + d_deltaqw(i, k)
          dth(i, k) = deltatw(i, k)/ppi(i, k)
          ! c      PRINT*,'k,qx,qw',k,qb(i,k)-sigmaw(i)*deltaqw(i,k)
          ! c     $        ,qb(i,k)+(1-sigmaw(i))*deltaqw(i,k)
        END IF
      END DO
    END DO

    DO i = 1, klon
      IF (wk_adv(i)) THEN
        sigmaw(i) = sigmaw(i) + d_sigmaw(i)
        d_sigmaw2(i) = d_sigmaw2(i) + d_sigmaw(i)
      END IF
    END DO
!jyg<
    IF (iflag_wk_pop_dyn >= 1) THEN
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! sigmaw !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!  Cumulatives
      DO i = 1, klon
        IF (wk_adv(i)) THEN
          d_sig_gen2(i)   = d_sig_gen2(i)   + d_sig_gen(i)
          d_sig_death2(i) = d_sig_death2(i) + d_sig_death(i)
          d_sig_col2(i)   = d_sig_col2(i)   + d_sig_col(i)
          d_sig_spread2(i)= d_sig_spread2(i)+ d_sig_spread(i)
          d_sig_bnd2(i)   = d_sig_bnd2(i)   + d_sig_bnd(i)
        END IF
      END DO
!  Bounds
      DO i = 1, klon
        IF (wk_adv(i)) THEN
          sigmaw_targ = max(sigmaw(i),sigmad)
          d_sig_bnd2(i) = d_sig_bnd2(i) + sigmaw_targ - sigmaw(i)
          d_sigmaw2(i) = d_sigmaw2(i) + sigmaw_targ - sigmaw(i)
          sigmaw(i) = sigmaw_targ
        END IF
      END DO
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! wdens  !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!  Cumulatives
      DO i = 1, klon
        IF (wk_adv(i)) THEN
          wdens(i) = wdens(i) + d_wdens(i)
          d_wdens2(i) = d_wdens2(i) + d_wdens(i)
          d_dens_gen2(i)   = d_dens_gen2(i)   + d_dens_gen(i)
          d_dens_death2(i) = d_dens_death2(i) + d_dens_death(i)
          d_dens_col2(i)   = d_dens_col2(i)   + d_dens_col(i)
          d_dens_bnd2(i)   = d_dens_bnd2(i)   + d_dens_bnd(i)
        END IF
      END DO
!  Bounds
      DO i = 1, klon
        IF (wk_adv(i)) THEN
          wdens_targ = max(wdens(i),wdensmin)
          d_dens_bnd2(i) = d_dens_bnd2(i) + wdens_targ - wdens(i)
          d_wdens2(i) = d_wdens2(i) + wdens_targ - wdens(i)
          wdens(i) = wdens_targ
        END IF
      END DO
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! awdens !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!  Cumulatives
      DO i = 1, klon
        IF (wk_adv(i)) THEN
          awdens(i) = awdens(i) + d_awdens(i)
          d_awdens2(i) = d_awdens2(i) + d_awdens(i)
        END IF
      END DO
!  Bounds
      DO i = 1, klon
        IF (wk_adv(i)) THEN
          wdens_targ = min( max(awdens(i),0.), wdens(i) )
          d_adens_bnd2(i) = d_adens_bnd2(i) + wdens_targ - awdens(i)
          d_awdens2(i) = d_awdens2(i) + wdens_targ - awdens(i)
          awdens(i) = wdens_targ
        END IF
      END DO

      IF (iflag_wk_pop_dyn >= 2) THEN
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! awdens again for iflag_wk_pop_dyn >= 2!!!!!!
!  Cumulatives
        DO i = 1, klon
           IF (wk_adv(i)) THEN
               d_adens_death2(i)   = d_adens_death2(i)   + d_adens_death(i)
               d_adens_icol2(i)   = d_adens_icol2(i)   + d_adens_icol(i)
               d_adens_acol2(i)   = d_adens_acol2(i)   + d_adens_acol(i)
               d_adens_bnd2(i)   = d_adens_bnd2(i)   + d_adens_bnd(i)          
           END IF
        END DO
!  Bounds
        DO i = 1, klon
           IF (wk_adv(i)) THEN
               wdens_targ = min( max(awdens(i),0.), wdens(i) )
               d_adens_bnd2(i) = d_adens_bnd2(i) + wdens_targ - awdens(i)
               awdens(i) = wdens_targ
           END IF
        END DO

        IF (iflag_wk_pop_dyn == 3) THEN
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! asigmaw for iflag_wk_pop_dyn = 3!!!!!!
!  Cumulatives
          DO i = 1, klon
             IF (wk_adv(i)) THEN
                 asigmaw(i) = asigmaw(i) + d_asigmaw(i)
                 d_asigmaw2(i) = d_asigmaw2(i) + d_asigmaw(i)
                 d_asig_death2(i)   = d_asig_death2(i)   + d_asig_death(i)
                 d_asig_spread2(i)  = d_asig_spread2(i)  + d_asig_spread(i)
                 d_asig_iicol2(i)   = d_asig_iicol2(i)   + d_asig_iicol(i)
                 d_asig_aicol2(i)   = d_asig_aicol2(i)   + d_asig_aicol(i)
                 d_asig_bnd2(i)     = d_asig_bnd2(i)     + d_asig_bnd(i)          
             END IF
          END DO
!  Bounds
          DO i = 1, klon
             IF (wk_adv(i)) THEN
   !   asigmaw lower bound set to sigmad/2 in order to allow asigmaw values lower than sigmad.
   !!             sigmaw_targ = min(max(asigmaw(i),sigmad),sigmaw(i))
                sigmaw_targ = min(max(asigmaw(i),sigmad/2.),sigmaw(i))
                d_asig_bnd2(i) = d_asig_bnd2(i) + sigmaw_targ - asigmaw(i)
                d_asigmaw2(i) = d_asigmaw2(i) + sigmaw_targ - asigmaw(i)
                asigmaw(i) = sigmaw_targ
             END IF
          END DO

#ifdef IOPHYS_WK
    IF (phys_sub) THEN
     CALL iophys_ecrit('wdensb',1,'wdensb','m',wdens)
     CALL iophys_ecrit('awdensb',1,'awdensb','m',awdens)
     CALL iophys_ecrit('sigmawb',1,'sigmawb','m',sigmaw)
     CALL iophys_ecrit('asigmawb',1,'asigmawb','m',asigmaw)

     CALL iophys_ecrit('d_wdens2',1,'d_wdens2','',d_wdens2)
     CALL iophys_ecrit('d_dens_gen2',1,'d_dens_gen2','',d_dens_gen2)
     CALL iophys_ecrit('d_dens_death2',1,'d_dens_death2','',d_dens_death2)
     CALL iophys_ecrit('d_dens_col2',1,'d_dens_col2','',d_dens_col2)
     CALL iophys_ecrit('d_dens_bnd2',1,'d_dens_bnd2','',d_dens_bnd2)

     CALL iophys_ecrit('d_awdens2',1,'d_awdens2','',d_awdens2)
     CALL iophys_ecrit('d_adens_death2',1,'d_adens_death2','',d_adens_death2)
     CALL iophys_ecrit('d_adens_icol2',1,'d_adens_icol2','',d_adens_icol2)
     CALL iophys_ecrit('d_adens_acol2',1,'d_adens_acol2','',d_adens_acol2)
     CALL iophys_ecrit('d_adens_bnd2',1,'d_adens_bnd2','',d_adens_bnd2)

     CALL iophys_ecrit('d_sigmaw2',1,'d_sigmaw2','',d_sigmaw2)
     CALL iophys_ecrit('d_sig_gen2',1,'d_sig_gen2','m',d_sig_gen2)
     CALL iophys_ecrit('d_sig_spread2',1,'d_sig_spread2','',d_sig_spread2)
     CALL iophys_ecrit('d_sig_col2',1,'d_sig_col2','',d_sig_col2)
     CALL iophys_ecrit('d_sig_death2',1,'d_sig_death2','',d_sig_death2)
     CALL iophys_ecrit('d_sig_bnd2',1,'d_sig_bnd2','',d_sig_bnd2)

     CALL iophys_ecrit('d_asigmaw2',1,'d_asigmaw2','',d_asigmaw2)
     CALL iophys_ecrit('d_asig_spread2',1,'d_asig_spread2','m',d_asig_spread2)
     CALL iophys_ecrit('d_asig_aicol2',1,'d_asig_aicol2','m',d_asig_aicol2)
     CALL iophys_ecrit('d_asig_iicol2',1,'d_asig_iicol2','m',d_asig_iicol2)
     CALL iophys_ecrit('d_asig_death2',1,'d_asig_death2','m',d_asig_death2)
     CALL iophys_ecrit('d_asig_bnd2',1,'d_asig_bnd2','m',d_asig_bnd2)
    ENDIF
#endif
        ENDIF ! (iflag_wk_pop_dyn == 3)
      ENDIF ! (iflag_wk_pop_dyn >= 2)
    ENDIF  ! (iflag_wk_pop_dyn >= 1)



   Call pkupper (klon, klev, ptop, ph, p, pupper, kupper, &
                    dth, hw, rho, delta_t_min, &
                    ktop, wk_adv, h_zzz, ptop1, ktop1)
   !! print'("pkupper APPEL ",7i6)',isubstep,int(ptop/100.),int(ptop1/100.),int(pupper/100.),ktop,ktop1,kupper

    ! 5/ Set deltatw & deltaqw to 0 above kupper

    DO k = 1, klev
      DO i = 1, klon
        IF (wk_adv(i) .AND. k>=kupper(i)) THEN
          deltatw(i, k) = 0.
          deltaqw(i, k) = 0.
          d_deltatw2(i,k) = -deltatw0(i,k)
          d_deltaqw2(i,k) = -deltaqw0(i,k)
        END IF
      END DO
    END DO


    ! -------------Cstar computation---------------------------------
    DO i = 1, klon
      IF (wk_adv(i)) THEN !!! nrlmd
        sum_thx(i) = 0.
        sum_tx(i) = 0.
        sum_qx(i) = 0.
        sum_thvx(i) = 0.
        sum_dth(i) = 0.
        sum_dq(i) = 0.
        sum_dtdwn(i) = 0.
        sum_dqdwn(i) = 0.

        av_thx(i) = 0.
        av_tx(i) = 0.
        av_qx(i) = 0.
        av_thvx(i) = 0.
        av_dth(i) = 0.
        av_dq(i) = 0.
        av_dtdwn(i) = 0.
        av_dqdwn(i) = 0.
      END IF
    END DO

    ! Integrals (and wake top level number)
    ! --------------------------------------

    ! Initialize sum_thvx to 1st level virt. pot. temp.

    DO i = 1, klon
      IF (wk_adv(i)) THEN !!! nrlmd
        z(i) = 1.
        dz(i) = 1.
        sum_thvx(i) = thx(i, 1)*(1.+epsim1*qx(i,1))*dz(i)
        sum_dth(i) = 0.
      END IF
    END DO

    DO k = 1, klev
      DO i = 1, klon
        IF (wk_adv(i)) THEN !!! nrlmd
          dz(i) = -(max(ph(i,k+1),ptop(i))-ph(i,k))/(rho(i,k)*RG)
          IF (dz(i)>0) THEN
            z(i) = z(i) + dz(i)
            sum_thx(i) = sum_thx(i) + thx(i, k)*dz(i)
            sum_tx(i) = sum_tx(i) + tx(i, k)*dz(i)
            sum_qx(i) = sum_qx(i) + qx(i, k)*dz(i)
            sum_thvx(i) = sum_thvx(i) + thx(i, k)*(1.+epsim1*qx(i,k))*dz(i)
            sum_dth(i) = sum_dth(i) + dth(i, k)*dz(i)
            sum_dq(i) = sum_dq(i) + deltaqw(i, k)*dz(i)
            sum_dtdwn(i) = sum_dtdwn(i) + dtdwn(i, k)*dz(i)
            sum_dqdwn(i) = sum_dqdwn(i) + dqdwn(i, k)*dz(i)
          END IF
        END IF
      END DO
    END DO

    DO i = 1, klon
      IF (wk_adv(i)) THEN !!! nrlmd
        hw0(i) = z(i)
      END IF
    END DO


    ! - WAPE and mean forcing computation
    ! ---------------------------------------

    ! ---------------------------------------

    ! Means

    DO i = 1, klon
      IF (wk_adv(i)) THEN !!! nrlmd
        av_thx(i) = sum_thx(i)/hw0(i)
        av_tx(i) = sum_tx(i)/hw0(i)
        av_qx(i) = sum_qx(i)/hw0(i)
        av_thvx(i) = sum_thvx(i)/hw0(i)
        av_dth(i) = sum_dth(i)/hw0(i)
        av_dq(i) = sum_dq(i)/hw0(i)
        av_dtdwn(i) = sum_dtdwn(i)/hw0(i)
        av_dqdwn(i) = sum_dqdwn(i)/hw0(i)

        wape(i) = -RG*hw0(i)*(av_dth(i)+epsim1*(av_thx(i)*av_dq(i) + &
                              av_dth(i)*av_qx(i)+av_dth(i)*av_dq(i)))/av_thvx(i)
      END IF
    END DO


    ! Filter out bad wakes

    DO k = 1, klev
      DO i = 1, klon
        IF (wk_adv(i)) THEN !!! nrlmd
          IF (wape(i)<0.) THEN
            deltatw(i, k) = 0.
            deltaqw(i, k) = 0.
            dth(i, k) = 0.
            d_deltatw2(i,k) = -deltatw0(i,k)
            d_deltaqw2(i,k) = -deltaqw0(i,k)
          END IF
        END IF
      END DO
    END DO

    DO i = 1, klon
      IF (wk_adv(i)) THEN !!! nrlmd
        IF (wape(i)<0.) THEN
          wape(i) = 0.
          cstar(i) = 0.
          hw(i) = hwmin
!jyg<
!!          sigmaw(i) = max(sigmad, sigd_con(i))
          sigmaw_targ = max(sigmad, sigd_con(i))
          d_sig_bnd2(i) = d_sig_bnd2(i) + sigmaw_targ - sigmaw(i)
          d_sigmaw2(i) = d_sigmaw2(i) + sigmaw_targ - sigmaw(i)
          sigmaw(i) = sigmaw_targ

          d_asig_bnd2(i) = d_asig_bnd2(i) + sigmaw_targ - asigmaw(i)
          d_asigmaw2(i) = d_asigmaw2(i) + sigmaw_targ - asigmaw(i)
          asigmaw(i) = sigmaw_targ
!>jyg
          fip(i) = 0.
          gwake(i) = .FALSE.
        ELSE
          cstar(i) = stark*sqrt(2.*wape(i))
          gwake(i) = .TRUE.
        END IF
      END IF
    END DO

  ! ------------------------------------------------------------------------

  END DO   ! isubstep end sub-timestep loop

  ! ------------------------------------------------------------------------
  ! ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
  ! ------------------------------------------------------------------------

#ifdef IOPHYS_WK
    IF (.not.phys_sub) CALL iophys_ecrit('wape_b',1,'wape_b','J/kg',wape)
#endif
  IF (prt_level>=10) THEN
    PRINT *, 'wake-5, sigmaw(igout), cstar(igout), wape(igout), ptop(igout) ', &
                      sigmaw(igout), cstar(igout), wape(igout), ptop(igout)
  ENDIF


  ! ----------------------------------------------------------
  ! Determine wake final state; recompute wape, cstar, ktop;
  ! filter out bad wakes.
  ! ----------------------------------------------------------

  ! 2.1 - Undisturbed area and Wake integrals
  ! ---------------------------------------------------------

  DO i = 1, klon
    ! cc nrlmd       if (wk_adv(i)) then !!! nrlmd
    IF (ok_qx_qw(i)) THEN
      ! cc
      z(i) = 0.
      sum_thx(i) = 0.
      sum_tx(i) = 0.
      sum_qx(i) = 0.
      sum_thvx(i) = 0.
      sum_dth(i) = 0.
      sum_half_dth(i) = 0.
      sum_dq(i) = 0.
      sum_dtdwn(i) = 0.
      sum_dqdwn(i) = 0.

      av_thx(i) = 0.
      av_tx(i) = 0.
      av_qx(i) = 0.
      av_thvx(i) = 0.
      av_dth(i) = 0.
      av_dq(i) = 0.
      av_dtdwn(i) = 0.
      av_dqdwn(i) = 0.

      dthmin(i) = -delta_t_min
    END IF
  END DO
  ! Potential temperatures and humidity
  ! ----------------------------------------------------------

  DO k = 1, klev
    DO i = 1, klon
      ! cc nrlmd       IF ( wk_adv(i)) THEN
      IF (ok_qx_qw(i)) THEN
        ! cc
        rho(i, k) = p(i, k)/(RD*tb(i,k))
        IF (k==1) THEN
          rhoh(i, k) = ph(i, k)/(RD*tb(i,k))
          zhh(i, k) = 0
        ELSE
          rhoh(i, k) = ph(i, k)*2./(RD*(tb(i,k)+tb(i,k-1)))
          zhh(i, k) = (ph(i,k)-ph(i,k-1))/(-rhoh(i,k)*RG) + zhh(i, k-1)
        END IF
        thb(i, k) = tb(i, k)/ppi(i, k)
        thx(i, k) = (tb(i,k)-deltatw(i,k)*sigmaw(i))/ppi(i, k)
        tx(i, k) = tb(i, k) - deltatw(i, k)*sigmaw(i)
        qx(i, k) = qb(i, k) - deltaqw(i, k)*sigmaw(i)
        dth(i, k) = deltatw(i, k)/ppi(i, k)
      END IF
    END DO
  END DO

  ! Integrals (and wake top level number)
  ! -----------------------------------------------------------

  ! Initialize sum_thvx to 1st level virt. pot. temp.

  DO i = 1, klon
    ! cc nrlmd       IF ( wk_adv(i)) THEN
    IF (ok_qx_qw(i)) THEN
      ! cc
      z(i) = 1.
      dz(i) = 1.
      dz_half(i) = 1.
      sum_thvx(i) = thx(i, 1)*(1.+epsim1*qx(i,1))*dz(i)
      sum_dth(i) = 0.
    END IF
  END DO

  DO k = 1, klev
    DO i = 1, klon
      ! cc nrlmd       IF ( wk_adv(i)) THEN
      IF (ok_qx_qw(i)) THEN
        ! cc
        dz(i) = -(amax1(ph(i,k+1),ptop(i))-ph(i,k))/(rho(i,k)*RG)
        dz_half(i) = -(amax1(ph(i,k+1),0.5*(ptop(i)+ph(i,1)))-ph(i,k))/(rho(i,k)*RG)
        IF (dz(i)>0) THEN
          z(i) = z(i) + dz(i)
          sum_thx(i) = sum_thx(i) + thx(i, k)*dz(i)
          sum_tx(i) = sum_tx(i) + tx(i, k)*dz(i)
          sum_qx(i) = sum_qx(i) + qx(i, k)*dz(i)
          sum_thvx(i) = sum_thvx(i) + thx(i, k)*(1.+epsim1*qx(i,k))*dz(i)
          sum_dth(i) = sum_dth(i) + dth(i, k)*dz(i)
          sum_dq(i) = sum_dq(i) + deltaqw(i, k)*dz(i)
          sum_dtdwn(i) = sum_dtdwn(i) + dtdwn(i, k)*dz(i)
          sum_dqdwn(i) = sum_dqdwn(i) + dqdwn(i, k)*dz(i)

          dthmin(i) = min(dthmin(i), dth(i,k))
        END IF
        IF (dz_half(i)>0) THEN
          sum_half_dth(i) = sum_half_dth(i) + dth(i, k)*dz_half(i)
        END IF
      END IF
    END DO
  END DO

  DO i = 1, klon
    ! cc nrlmd       IF ( wk_adv(i)) THEN
    IF (ok_qx_qw(i)) THEN
      ! cc
      hw0(i) = z(i)
    END IF
  END DO

  ! - WAPE and mean forcing computation
  ! -------------------------------------------------------------

  ! Means

  DO i = 1, klon
    ! cc nrlmd       IF ( wk_adv(i)) THEN
    IF (ok_qx_qw(i)) THEN
      ! cc
      av_thx(i) = sum_thx(i)/hw0(i)
      av_tx(i) = sum_tx(i)/hw0(i)
      av_qx(i) = sum_qx(i)/hw0(i)
      av_thvx(i) = sum_thvx(i)/hw0(i)
      av_dth(i) = sum_dth(i)/hw0(i)
      av_dq(i) = sum_dq(i)/hw0(i)
      av_dtdwn(i) = sum_dtdwn(i)/hw0(i)
      av_dqdwn(i) = sum_dqdwn(i)/hw0(i)

      wape2(i) = -RG*hw0(i)*(av_dth(i)+epsim1*(av_thx(i)*av_dq(i) + &
                             av_dth(i)*av_qx(i)+av_dth(i)*av_dq(i)))/av_thvx(i)
    END IF
  END DO
#ifdef IOPHYS_WK
  IF (.not.phys_sub) CALL iophys_ecrit('wape2_a',1,'wape2_a','J/kg',wape2)
#endif


  ! Prognostic variable update
  ! ------------------------------------------------------------

  ! Filter out bad wakes

  IF (iflag_wk_check_trgl>=1) THEN
    ! Check triangular shape of dth profile
    DO i = 1, klon
      IF (ok_qx_qw(i)) THEN
        !! print *,'wake, hw0(i), dthmin(i) ', hw0(i), dthmin(i)
        !! print *,'wake, 2.*sum_dth(i)/(hw0(i)*dthmin(i)) ', &
        !!                2.*sum_dth(i)/(hw0(i)*dthmin(i))
        !! print *,'wake, sum_half_dth(i), sum_dth(i) ', &
        !!                sum_half_dth(i), sum_dth(i)
        IF ((hw0(i) < 1.) .or. (dthmin(i) >= -delta_t_min) ) THEN
          wape2(i) = -1.
          !! print *,'wake, rej 1'
        ELSE IF (iflag_wk_check_trgl==1.AND.abs(2.*sum_dth(i)/(hw0(i)*dthmin(i)) - 1.) > 0.5) THEN
          wape2(i) = -1.
          !! print *,'wake, rej 2'
        ELSE IF (abs(sum_half_dth(i)) < 0.5*abs(sum_dth(i)) ) THEN
          wape2(i) = -1.
          !! print *,'wake, rej 3'
        END IF
      END IF
    END DO
  END IF
#ifdef IOPHYS_WK
  IF (.not.phys_sub) CALL iophys_ecrit('wape2_b',1,'wape2_b','J/kg',wape2)
#endif


  DO k = 1, klev
    DO i = 1, klon
      ! cc nrlmd        IF ( wk_adv(i) .AND. wape2(i) .LT. 0.) THEN
      IF (ok_qx_qw(i) .AND. wape2(i)<0.) THEN
        ! cc
        deltatw(i, k) = 0.
        deltaqw(i, k) = 0.
        dth(i, k) = 0.
        d_deltatw2(i,k) = -deltatw0(i,k)
        d_deltaqw2(i,k) = -deltaqw0(i,k)
      END IF
    END DO
  END DO


  DO i = 1, klon
    ! cc nrlmd       IF ( wk_adv(i)) THEN
    IF (ok_qx_qw(i)) THEN
      ! cc
      IF (wape2(i)<0.) THEN
        wape2(i) = 0.
        cstar2(i) = 0.
        hw(i) = hwmin
!jyg<
!!      sigmaw(i) = amax1(sigmad, sigd_con(i))
      sigmaw_targ = max(sigmad, sigd_con(i))
      d_sig_bnd2(i) = d_sig_bnd2(i) + sigmaw_targ - sigmaw(i)
      d_sigmaw2(i) = d_sigmaw2(i) + sigmaw_targ - sigmaw(i)
      sigmaw(i) = sigmaw_targ

      d_asig_bnd2(i) = d_asig_bnd2(i) + sigmaw_targ - asigmaw(i)
      d_asigmaw2(i) = d_asigmaw2(i) + sigmaw_targ - asigmaw(i)
      asigmaw(i) = sigmaw_targ
!>jyg
        fip(i) = 0.
        gwake(i) = .FALSE.
      ELSE
        IF (prt_level>=10) PRINT *, 'wape2>0'
        cstar2(i) = stark*sqrt(2.*wape2(i))
        gwake(i) = .TRUE.
      END IF
#ifdef IOPHYS_WK
  IF (.not.phys_sub) CALL iophys_ecrit('cstar2',1,'cstar2','J/kg',cstar2)
#endif
    END IF  ! (ok_qx_qw(i))
  END DO

  DO i = 1, klon
    ! cc nrlmd       IF ( wk_adv(i)) THEN
    IF (ok_qx_qw(i)) THEN
      ! cc
      ktopw(i) = ktop(i)
    END IF
  END DO

  DO i = 1, klon
    ! cc nrlmd       IF ( wk_adv(i)) THEN
    IF (ok_qx_qw(i)) THEN
      ! cc
      IF (ktopw(i)>0 .AND. gwake(i)) THEN

        ! jyg1     Utilisation d'un h_efficace constant ( ~ feeding layer)
        ! cc       heff = 600.
        ! Utilisation de la hauteur hw
        ! c       heff = 0.7*hw
        heff(i) = hw(i)

        fip(i) = 0.5*rho(i, ktopw(i))*cstar2(i)**3*heff(i)*2* &
          sqrt(sigmaw(i)*wdens(i)*3.14)
        fip(i) = alpk*fip(i)
        ! jyg2
      ELSE
        fip(i) = 0.
      END IF
    END IF
  END DO
    IF (iflag_wk_pop_dyn >= 3) THEN
#ifdef IOPHYS_WK
      IF (.not.phys_sub) THEN
       CALL iophys_ecrit('fip',1,'fip','J/kg',fip)
       CALL iophys_ecrit('hw',1,'hw','J/kg',hw)
       CALL iophys_ecrit('ptop',1,'ptop','J/kg',ptop)
       CALL iophys_ecrit('wdens',1,'wdens','J/kg',wdens)
       CALL iophys_ecrit('awdens',1,'awdens','m',awdens)
       CALL iophys_ecrit('sigmaw',1,'sigmaw','m',sigmaw)
       CALL iophys_ecrit('asigmaw',1,'asigmaw','m',asigmaw)

       CALL iophys_ecrit('rad_wk',1,'rad_wk','J/kg',rad_wk)
       CALL iophys_ecrit('arad_wk',1,'arad_wk','J/kg',arad_wk)
       CALL iophys_ecrit('irad_wk',1,'irad_wk','J/kg',irad_wk)

       CALL iophys_ecrit('d_wdens2',1,'d_wdens2','',d_wdens2)
       CALL iophys_ecrit('d_dens_gen2',1,'d_dens_gen2','',d_dens_gen2)
       CALL iophys_ecrit('d_dens_death2',1,'d_dens_death2','',d_dens_death2)
       CALL iophys_ecrit('d_dens_col2',1,'d_dens_col2','',d_dens_col2)
       CALL iophys_ecrit('d_dens_bnd2',1,'d_dens_bnd2','',d_dens_bnd2)

       CALL iophys_ecrit('d_awdens2',1,'d_awdens2','',d_awdens2)
       CALL iophys_ecrit('d_adens_death2',1,'d_adens_death2','',d_adens_death2)
       CALL iophys_ecrit('d_adens_icol2',1,'d_adens_icol2','',d_adens_icol2)
       CALL iophys_ecrit('d_adens_acol2',1,'d_adens_acol2','',d_adens_acol2)
       CALL iophys_ecrit('d_adens_bnd2',1,'d_adens_bnd2','',d_adens_bnd2)

       CALL iophys_ecrit('d_sigmaw2',1,'d_sigmaw2','',d_sigmaw2)
       CALL iophys_ecrit('d_sig_gen2',1,'d_sig_gen2','m',d_sig_gen2)
       CALL iophys_ecrit('d_sig_spread2',1,'d_sig_spread2','',d_sig_spread2)
       CALL iophys_ecrit('d_sig_col2',1,'d_sig_col2','',d_sig_col2)
       CALL iophys_ecrit('d_sig_death2',1,'d_sig_death2','',d_sig_death2)
       CALL iophys_ecrit('d_sig_bnd2',1,'d_sig_bnd2','',d_sig_bnd2)

       CALL iophys_ecrit('d_asigmaw2',1,'d_asigmaw2','',d_asigmaw2)
       CALL iophys_ecrit('d_asig_spread2',1,'d_asig_spread2','m',d_asig_spread2)
       CALL iophys_ecrit('d_asig_aicol2',1,'d_asig_aicol2','m',d_asig_aicol2)
       CALL iophys_ecrit('d_asig_iicol2',1,'d_asig_iicol2','m',d_asig_iicol2)
       CALL iophys_ecrit('d_asig_death2',1,'d_asig_death2','m',d_asig_death2)
       CALL iophys_ecrit('d_asig_bnd2',1,'d_asig_bnd2','m',d_asig_bnd2)
      ENDIF  ! (.not.phys_sub)
#endif
    ENDIF  ! (iflag_wk_pop_dyn >= 3)
  ! Limitation de sigmaw

  ! cc nrlmd
  ! DO i=1,klon
  ! IF (OK_qx_qw(i)) THEN
  ! IF (sigmaw(i).GE.sigmaw_max) sigmaw(i)=sigmaw_max
  ! ENDIF
  ! ENDDO
  ! cc

  !jyg<
  IF (iflag_wk_pop_dyn >= 1) THEN
    DO i = 1, klon
      kill_wake(i) = ((wape(i)>=wape2(i)) .AND. (wape2(i)<=wapecut)) .OR. (ktopw(i)<=2) .OR. &
          .NOT. ok_qx_qw(i) .OR. (wdens(i) < wdensthreshold)
!!          .NOT. ok_qx_qw(i) .OR. (wdens(i) < 2.*wdensmin)
    ENDDO
  ELSE  ! (iflag_wk_pop_dyn >= 1)
    DO i = 1, klon
      kill_wake(i) = ((wape(i)>=wape2(i)) .AND. (wape2(i)<=wapecut)) .OR. (ktopw(i)<=2) .OR. &
          .NOT. ok_qx_qw(i)
    ENDDO
  ENDIF  ! (iflag_wk_pop_dyn >= 1)
  !>jyg

  DO k = 1, klev
    DO i = 1, klon
!!jyg      IF (((wape(i)>=wape2(i)) .AND. (wape2(i)<=wapecut)) .OR. (ktopw(i)<=2) .OR. &
!!jyg          .NOT. ok_qx_qw(i)) THEN
      IF (kill_wake(i)) THEN
        ! cc
        dtls(i, k) = 0.
        dqls(i, k) = 0.
        deltatw(i, k) = 0.
        deltaqw(i, k) = 0.
        d_deltatw2(i,k) = -deltatw0(i,k)
        d_deltaqw2(i,k) = -deltaqw0(i,k)
      END IF  ! (kill_wake(i))
    END DO
  END DO

  DO i = 1, klon
!!jyg    IF (((wape(i)>=wape2(i)) .AND. (wape2(i)<=wapecut)) .OR. (ktopw(i)<=2) .OR. &
!!jyg        .NOT. ok_qx_qw(i)) THEN
      IF (kill_wake(i)) THEN
      ktopw(i) = 0
      wape(i) = 0.
      cstar(i) = 0.
!!jyg   Outside SUBROUTINE "Wake" hw, wdens sigmaw and asigmaw are zero when there are no wakes
!!      hw(i) = hwmin                       !jyg
!!      sigmaw(i) = sigmad                  !jyg
      hw(i) = 0.                            !jyg
      fip(i) = 0.

!!      sigmaw(i) = 0.                        !jyg
      sigmaw_targ = 0.
      d_sig_bnd2(i) = d_sig_bnd2(i) + sigmaw_targ - sigmaw(i)
!!      d_sigmaw2(i) = d_sigmaw2(i) + sigmaw_targ - sigmaw(i)
      d_sigmaw2(i) = sigmaw_targ - sigmaw_in(i)      ! _in = correction jyg 20220124
      sigmaw(i) = sigmaw_targ

      IF (iflag_wk_pop_dyn >= 3) THEN
        sigmaw_targ = 0.
        d_asig_bnd2(i) = d_asig_bnd2(i) + sigmaw_targ - asigmaw(i)
!!        d_sigmaw2(i) = d_sigmaw2(i) + sigmaw_targ - sigmaw(i)
        d_asigmaw2(i) = sigmaw_targ - asigmaw_in(i)      ! _in = correction jyg 20220124
        asigmaw(i) = sigmaw_targ
      ELSE
        asigmaw(i) = 0.
      ENDIF ! (iflag_wk_pop_dyn >= 3)

      IF (iflag_wk_pop_dyn >= 1) THEN
!!        awdens(i) = 0.
!!        wdens(i) = 0.
        wdens_targ = 0.
        d_dens_bnd2(i) = d_dens_bnd2(i) + wdens_targ - wdens(i)
!!        d_wdens2(i) = wdens_targ - wdens(i)
        d_wdens2(i) = wdens_targ - wdens_in(i)      ! jyg 20220916
        wdens(i) = wdens_targ
        wdens_targ = 0.
!!jyg: bug fix : the d_adens_bnd2 computation must be before the update of awdens.
        IF (iflag_wk_pop_dyn >= 2) THEN
            d_adens_bnd2(i) = d_adens_bnd2(i) + wdens_targ - awdens(i)
        ENDIF ! (iflag_wk_pop_dyn >= 2)
!!        d_awdens2(i) = wdens_targ - awdens(i)
        d_awdens2(i) = wdens_targ - awdens_in(i)    ! jyg 20220916
        awdens(i) = wdens_targ
!!        IF (iflag_wk_pop_dyn == 2) THEN
!!            d_adens_bnd2(i) = d_adens_bnd2(i) + wdens_targ - awdens(i)
!!        ENDIF ! (iflag_wk_pop_dyn == 2)
      ENDIF  ! (iflag_wk_pop_dyn >= 1)
    ELSE  ! (kill_wake(i))
      wape(i) = wape2(i)
      cstar(i) = cstar2(i)
    END IF  ! (kill_wake(i))
    ! c        PRINT*,'wape wape2 ktopw OK_qx_qw =',
    ! c     $          wape(i),wape2(i),ktopw(i),OK_qx_qw(i)
  END DO

  IF (prt_level>=10) THEN
    PRINT *, 'wake-6, wape wape2 ktopw OK_qx_qw =', &
                      wape(igout),wape2(igout),ktopw(igout),OK_qx_qw(igout)
  ENDIF
#ifdef IOPHYS_WK
  IF (.not.phys_sub) CALL iophys_ecrit('wape_c',1,'wape_c','J/kg',wape)
#endif


  ! -----------------------------------------------------------------
  ! Get back to tendencies per second

  DO k = 1, klev
    DO i = 1, klon

      ! cc nrlmd        IF ( wk_adv(i) .AND. k .LE. kupper(i)) THEN
!jyg<
!!      IF (ok_qx_qw(i) .AND. k<=kupper(i)) THEN
      IF (ok_qx_qw(i)) THEN
!>jyg
        ! cc
        dtls(i, k) = dtls(i, k)/dtime
        dqls(i, k) = dqls(i, k)/dtime
        d_deltatw2(i, k) = d_deltatw2(i, k)/dtime
        d_deltaqw2(i, k) = d_deltaqw2(i, k)/dtime
        d_deltat_gw(i, k) = d_deltat_gw(i, k)/dtime
        ! c      PRINT*,'k,dqls,omg,entr,detr',k,dqls(i,k),omg(i,k),entr(i,k)
        ! c     $         ,death_rate(i)*sigmaw(i)
      END IF
    END DO
  END DO
!jyg<
  IF (iflag_wk_pop_dyn >= 1) THEN
    DO i = 1, klon
        IF (ok_qx_qw(i)) THEN
      d_sig_gen2(i) = d_sig_gen2(i)/dtime
      d_sig_death2(i) = d_sig_death2(i)/dtime
      d_sig_col2(i) = d_sig_col2(i)/dtime
      d_sig_spread2(i) = d_sig_spread2(i)/dtime
      d_sig_bnd2(i) = d_sig_bnd2(i)/dtime
      d_sigmaw2(i) = d_sigmaw2(i)/dtime

      d_dens_gen2(i) = d_dens_gen2(i)/dtime
      d_dens_death2(i) = d_dens_death2(i)/dtime
      d_dens_col2(i) = d_dens_col2(i)/dtime
      d_dens_bnd2(i) = d_dens_bnd2(i)/dtime
      d_awdens2(i) = d_awdens2(i)/dtime
      d_wdens2(i) = d_wdens2(i)/dtime
        ENDIF
    ENDDO
    IF (iflag_wk_pop_dyn >= 2) THEN
      DO i = 1, klon
        IF (ok_qx_qw(i)) THEN
        d_adens_death2(i) = d_adens_death2(i)/dtime
        d_adens_icol2(i) = d_adens_icol2(i)/dtime
        d_adens_acol2(i) = d_adens_acol2(i)/dtime
        d_adens_bnd2(i) = d_adens_bnd2(i)/dtime
        ENDIF
      ENDDO
      IF (iflag_wk_pop_dyn == 3) THEN
       DO i = 1, klon
          IF (ok_qx_qw(i)) THEN
        d_asig_death2(i)  = d_asig_death2(i)/dtime
        d_asig_iicol2(i)  = d_asig_iicol2(i)/dtime
        d_asig_aicol2(i)  = d_asig_aicol2(i)/dtime
        d_asig_spread2(i) = d_asig_spread2(i)/dtime
        d_asig_bnd2(i) = d_asig_bnd2(i)/dtime
          ENDIF
       ENDDO
      ENDIF ! (iflag_wk_pop_dyn == 3)  
    ENDIF ! (iflag_wk_pop_dyn >= 2)  
  ENDIF  ! (iflag_wk_pop_dyn >= 1)
 
!>jyg

 RETURN
END SUBROUTINE wake

SUBROUTINE wake_vec_modulation(nlon, nl, wk_adv, epsilon_loc, qb, d_qb, deltaqw, &
    d_deltaqw, sigmaw, d_sigmaw, alpha)
  ! ------------------------------------------------------
  ! Dtermination du coefficient alpha tel que les tendances
  ! corriges alpha*d_G, pour toutes les grandeurs G, correspondent
  ! a une humidite positive dans la zone (x) et dans la zone (w).
  ! ------------------------------------------------------
  IMPLICIT NONE

  ! Input
  REAL qb(nlon, nl), d_qb(nlon, nl)
  REAL deltaqw(nlon, nl), d_deltaqw(nlon, nl)
  REAL sigmaw(nlon), d_sigmaw(nlon)
  LOGICAL wk_adv(nlon)
  INTEGER nl, nlon
  ! Output
  REAL alpha(nlon)
  ! Internal variables
  REAL zeta(nlon, nl)
  REAL alpha1(nlon)
  REAL x, a, b, c, discrim
  REAL epsilon_loc
  INTEGER i,k

  DO k = 1, nl
    DO i = 1, nlon
      IF (wk_adv(i)) THEN
        IF ((deltaqw(i,k)+d_deltaqw(i,k))>=0.) THEN
          zeta(i, k) = 0.
        ELSE
          zeta(i, k) = 1.
        END IF
      END IF
    END DO
    DO i = 1, nlon
      IF (wk_adv(i)) THEN
        x = qb(i, k) + (zeta(i,k)-sigmaw(i))*deltaqw(i, k) + d_qb(i, k) + &
          (zeta(i,k)-sigmaw(i))*d_deltaqw(i, k) - d_sigmaw(i) * &
          (deltaqw(i,k)+d_deltaqw(i,k))
        a = -d_sigmaw(i)*d_deltaqw(i, k)
        b = d_qb(i, k) + (zeta(i,k)-sigmaw(i))*d_deltaqw(i, k) - &
          deltaqw(i, k)*d_sigmaw(i)
        c = qb(i, k) + (zeta(i,k)-sigmaw(i))*deltaqw(i, k) + epsilon_loc
        discrim = b*b - 4.*a*c
        ! PRINT*, 'x, a, b, c, discrim', x, a, b, c, discrim
        IF (a+b>=0.) THEN !! Condition suffisante pour la positivite de ovap
          alpha1(i) = 1.
        ELSE
          IF (x>=0.) THEN
            alpha1(i) = 1.
          ELSE
            IF (a>0.) THEN
              alpha1(i) = 0.9*min( (2.*c)/(-b+sqrt(discrim)),  &
                                   (-b+sqrt(discrim))/(2.*a) )
            ELSE IF (a==0.) THEN
              alpha1(i) = 0.9*(-c/b)
            ELSE
              ! PRINT*,'a,b,c discrim',a,b,c discrim
              alpha1(i) = 0.9*max( (2.*c)/(-b+sqrt(discrim)),  &
                                   (-b+sqrt(discrim))/(2.*a))
            END IF
          END IF
        END IF
        alpha(i) = min(alpha(i), alpha1(i))
      END IF
    END DO
  END DO

  RETURN
END SUBROUTINE wake_vec_modulation



SUBROUTINE pkupper (klon, klev, ptop, ph, p, pupper, kupper, &
                    dth, hw_, rho, delta_t_min_in, &
                    ktop, wk_adv, h_zzz, ptop1, ktop1)

USE lmdz_wake_ini , ONLY: wk_pupper
USE lmdz_wake_ini , ONLY: RG
USE lmdz_wake_ini , ONLY: hwmin
USE lmdz_wake_ini , ONLY: iflag_wk_new_ptop, wk_delta_t_min, wk_frac_int_delta_t
USE lmdz_wake_ini , ONLY: wk_int_delta_t_min

IMPLICIT NONE

INTEGER,                              INTENT(IN) :: klon,klev
REAL,       DIMENSION (klon,klev+1) , INTENT(IN) :: ph, p
REAL,       DIMENSION (klon,klev+1) , INTENT(IN) :: rho
LOGICAL,    DIMENSION (klon)        , INTENT(IN) :: wk_adv
REAL,       DIMENSION (klon,klev+1) , INTENT(IN) :: dth
REAL,                                 INTENT(IN) :: delta_t_min_in


REAL,       DIMENSION (klon)  , INTENT(OUT)        :: hw_
REAL,       DIMENSION (klon)  , INTENT(OUT)        :: ptop
INTEGER,    DIMENSION (klon)  , INTENT(OUT)        :: Ktop
REAL,       DIMENSION (klon)  , INTENT(OUT)        :: pupper
INTEGER,    DIMENSION (klon)  , INTENT(OUT)        :: kupper
REAL,       DIMENSION (klon)  , INTENT(OUT)        :: h_zzz       !!
REAL,       DIMENSION (klon)  , INTENT(OUT)        :: Ptop1      !!
INTEGER,    DIMENSION (klon)  , INTENT(OUT)        :: ktop1      !!

INTEGER :: i,k

LOGICAL,    DIMENSION (klon)       :: wk_active
REAL                               :: delta_t_min
REAL,     DIMENSION (klon)         :: dthmin
REAL,     DIMENSION (klon)         :: ptop_provis,ptop_new
REAL,     DIMENSION (klon)         :: z, dz
REAL,     DIMENSION (klon)         :: sum_dth

INTEGER,     DIMENSION (klon)                     :: k_ptop_provis
REAL,     DIMENSION (klon)                     :: zk_ptop_provis
REAL,     DIMENSION (klon)                        :: omega        !!
REAL,     DIMENSION (klon,klev+1)                 :: int_dth      !! 
REAL,     DIMENSION (klon,klev+1)                 :: dzz          !!
REAL,     DIMENSION (klon,klev+1)                 :: zzz          !!
REAL,     DIMENSION (klon)                 :: frac_int_dth          !!
REAL                                              :: ddd!!


INTEGER, SAVE :: ipas=0



!INTEGER, SAVE :: compte=0

! LJYF : a priori z, dz sum_dth sont aussi des variables internes
! Les eliminer apres verification convergence numerique

!compte=compte+1
!PRINT*,'compte=',compte

    ! Determine Ptop from buoyancy integral
    ! ---------------------------------------

    ! -     1/ Pressure of the level where dth changes sign.
    !PRINT*,'WAKE LJYF'


IF (iflag_wk_new_ptop==0) then
    delta_t_min=delta_t_min_in
else
    delta_t_min=wk_delta_t_min
END IF

    DO i = 1, klon
        ptop_provis(i) = ph(i, 1)
        k_ptop_provis(i) = 1
    END DO

    DO k = 2, klev
      DO i = 1, klon
        IF (wk_adv(i) .AND. ptop_provis(i)==ph(i,1) .AND. &
! LJYF changer :           dth(i,k)>=-delta_t_min .AND. dth(i,k-1)<-delta_t_min) THEN
            dth(i,k)>-delta_t_min .AND. dth(i,k-1)<-delta_t_min) THEN
          ptop_provis(i) = ((dth(i,k)+delta_t_min)*p(i,k-1) - &
                            (dth(i,k-1)+delta_t_min)*p(i,k))/(dth(i,k)-dth(i,k-1))
          k_ptop_provis(i) = k
        END IF
      END DO
    END DO



    ! -     2/ dth integral

    DO i = 1, klon
      IF (wk_adv(i)) THEN !!! nrlmd
        sum_dth(i) = 0.
        dthmin(i) = -delta_t_min
        z(i) = 0.
      END IF
    END DO

    DO k = 1, klev
      DO i = 1, klon
        IF (wk_adv(i)) THEN
          dz(i) = -(amax1(ph(i,k+1),ptop_provis(i))-ph(i,k))/(rho(i,k)*RG)
          IF (dz(i)>0) THEN
            z(i) = z(i) + dz(i)
            sum_dth(i) = sum_dth(i) + dth(i, k)*dz(i)
            dthmin(i) = amin1(dthmin(i), dth(i,k))
          END IF
        END IF
      END DO
    END DO

    ! -     3/ height of triangle with area= sum_dth and base = dthmin

    DO i = 1, klon
      IF (wk_adv(i)) THEN
        hw_(i) = 2.*sum_dth(i)/amin1(dthmin(i), -0.5)
        hw_(i) = amax1(hwmin, hw_(i))
      END IF
    END DO

    ! -     4/ now, get Ptop

    DO i = 1, klon
      IF (wk_adv(i)) THEN !!! nrlmd
        ktop(i) = 0
        z(i) = 0.
      END IF
    END DO

    DO k = 1, klev
      DO i = 1, klon
        IF (wk_adv(i)) THEN
          dz(i) = amin1(-(ph(i,k+1)-ph(i,k))/(rho(i,k)*RG), hw_(i)-z(i))
          IF (dz(i)>0) THEN
            z(i) = z(i) + dz(i)
            ptop(i) = ph(i, k) - rho(i, k)*RG*dz(i)
            ktop(i) = k
          END IF
        END IF
      END DO
    END DO

    ! 4.5/Correct ktop and ptop

    DO i = 1, klon
        ptop_new(i) = ptop(i)
    END DO

    DO k = klev, 2, -1
      DO i = 1, klon
        ! IM v3JYG; IF (k .GE. ktop(i)
        IF (wk_adv(i) .AND. k<=ktop(i) .AND. ptop_new(i)==ptop(i) .AND. &
! LJYF changer :           dth(i,k)>=-delta_t_min .AND. dth(i,k-1)<-delta_t_min) THEN
            dth(i,k)>=-delta_t_min .AND. dth(i,k-1)<-delta_t_min) THEN
          ptop_new(i) = ((dth(i,k)+delta_t_min)*p(i,k-1) - &
                         (dth(i,k-1)+delta_t_min)*p(i,k))/(dth(i,k)-dth(i,k-1))
        END IF
      END DO
    END DO


    DO i = 1, klon
        ptop(i) = ptop_new(i)
    END DO

    DO k = klev, 1, -1
      DO i = 1, klon
        IF (wk_adv(i)) THEN !!! nrlmd
          IF (ph(i,k+1)<ptop(i)) ktop(i) = k
        END IF
      END DO
    END DO
  
!  IF (prt_level>=10) THEN
!    PRINT *, 'wake-3, ktop(igout), kupper(igout) ', ktop(igout), kupper(igout)
!  ENDIF

    ! -----------------------------------------------------------------------
    ! nouveau calcul de hw et ptop
    ! -----------------------------------------------------------------------
!if (iflag_wk_new_ptop>0) then
DO i=1,klon
   ptop1(i)=ph(i,1)
   ktop1(i)=1
   h_zzz(i)=0.
END DO
    
IF (iflag_wk_new_ptop/=0) THEN
    
    int_dth(1:klon,1:klev+1)=0.
    DO i = 1, klon
       IF (wk_adv(i)) THEN 
          int_dth(i,1) = 0.
      END IF
    END DO
    
    if (abs(iflag_wk_new_ptop) == 1 ) then
        DO k = 2, klev+1
           Do i = 1, klon
              IF (wk_adv(i)) THEN
                 if (k<=k_ptop_provis(i)) then
                      ddd=dth(i,k-1)*(ph(i,k-1) - max(ptop_provis(i),ph(i,k)))
                      !ddd=dth(i,k-1)*(ph(i,k-1) - ph(i,k))
                 else
                      ddd=0.
                 endif             
                 int_dth(i,k) = int_dth(i,k-1) + ddd
              !ELSE
              !   int_dth(i,k) = 0.
              END IF
           END DO
        END DO
    else
        k_ptop_provis(:)=klev+1
        dthmin(:)=dth(:,1)
        ! calcul de l'int??grale de dT * dP jusqu'au dernier
        ! niveau avec dT<0. (en s'assurant qu'on a bien un 
        ! dT negatif plus bas)
        DO k = 1, klev
           DO i = 1, klon
              dthmin(i)=min(dthmin(i),dth(i,k))
              ddd=dth(i,k)*(ph(i,k)-ph(i,k+1))
              if (dthmin(i)<0.) then
                  if (k>=k_ptop_provis(i)) then
                      ddd=0.
                  else if (dth(i,k)>=0.) then
                      ddd=0.
                      k_ptop_provis(i)=k+1
                  endif
              endif
              int_dth(i,k+1) = int_dth(i,k)+ ddd
           ENDDO
        ENDDO

        DO i = 1, klon
           if ( k_ptop_provis(i)==klev+1 .or. .not. wk_adv(i)) then
                k_ptop_provis(i)=1
           endif
        ENDDO
    endif ! (abs(iflag_wk_new_ptop) == 1 )
   ! PRINT*, 'xxx, int_dth', (k,int_dth(1,k),k=1,klev)
   ! PRINT*, 'xxx, k_ptop_provis', k_ptop_provis(1)
   

 
    ! On se limite ?? des poches avec integrale dT * dp < -wk_int_delta_t_min
    do i=1,klon
          if (int_dth(i,k_ptop_provis(i)) > -wk_int_delta_t_min .or. k_ptop_provis(i)==1) then
          !if (1==0) then
             wk_active(i)=.FALSE.
             ptop(i)=ph(i,1)
             ktop(i)=1
             hw_(i)=0.
          else
             wk_active(i)=wk_adv(i)
          endif
    enddo

    DO i=1,klon
       IF (wk_active(i)) THEN
        frac_int_dth(i)=wk_frac_int_delta_t*int_dth(i,k_ptop_provis(i))
       ENDIF
    ENDDO
    DO k = 1,klev
       DO i =1, klon
!         PRINT*,ipas,'yyy ',k,int_dth(i,k),frac_int_dth(i)
          IF (wk_active(i)) THEN
            IF (int_dth(i,k)>=frac_int_dth(i)) THEN
              ktop1(i) = min(k, k_ptop_provis(i))
              !ktop1(i) = k
              !PRINT*,ipas,'yyy ktop1= ',ktop1
            ENDIF
          ENDIF
       END DO
    END DO
    !PRINT*, 'LAMINE'
    
    DO i = 1, klon
       IF (wk_active(i)) THEN
           !PRINT*, ipas,'xxx1, int_dth(i,ktop1(i)), frac_int_dth(i), int_dth(i,ktop1(i)+1) ',ktop1
           ddd=int_dth(i,ktop1(i)+1)-int_dth(i,ktop1(i))
           if (ddd==0.) then
              omega(i)=0.
           else
              omega(i) = (frac_int_dth(i) - int_dth(i,ktop1(i)))/ddd
           endif
           !! PRINT*,'OMEGA ',omega(i)
       END IF
    END DO
    
    !! PRINT*, 'xxx'
    DO i = 1, klon
       IF (wk_active(i)) THEN
      ! PRINT*, 'xxx, int_dth(i,ktop1(i)), frac_int_dth(i), int_dth(i,ktop1(i)+1) ', &
      !               int_dth(i,ktop1(i)), frac_int_dth(i), int_dth(i,ktop1(i)+1)
      ! PRINT*, 'xxx, omega(i), ph(i,ktop1(i)), ph(i,ktop1(i)+1) ',  &
      !e               omega(i), ph(i,ktop1(i)), ph(i,ktop1(i)+1)
          ptop1(i) = min((1 - omega(i))*ph(i,ktop1(i)) + omega(i)*ph(i,ktop1(i)+1), ph(i,1))
      END IF
    END DO
    
    DO i=1, klon
       IF (wk_active(i)) THEN 
           zzz(i, 1) = 0
       END IF
     END DO
    DO k = 1, klev
       DO i = 1, klon 
           IF (wk_active(i)) THEN         
              dzz(i,k) = (ph(i,k) - ph(i,k+1))/(rho(i,k)*RG)
              zzz(i,k+1) = zzz(i,k) + dzz(i,k)
           END IF
       END DO
    END DO
    
    DO i =1, klon
       IF (wk_active(i)) THEN
           h_zzz(i) = max((1- omega(i))*zzz(i,ktop1(i)) + omega(i)*zzz(i,ktop1(i)+1), hwmin)
       END IF
    END DO


ENDIF ! (iflag_wk_new_ptop/=0)

!if (iflag_wk_new_ptop==2) then
IF (iflag_wk_new_ptop>0) THEN 
   do i=1,klon
      ptop(i)=ptop1(i)
      ktop(i)=ktop1(i)
      hw_(i)=h_zzz(i)
   enddo

!endif
ENDIF

 kupper = 0
 
IF (wk_pupper<1.) THEN
 ! Choose an integration bound well above wake top
  ! -----------------------------------------------------------------

  ! Pupper = 50000.  ! melting level
  ! Pupper = 60000.
  ! Pupper = 80000.  ! essais pour case_e
  DO i = 1, klon
  !  pupper(i) = 0.6*ph(i, 1)
    pupper(i) = wk_pupper*ph(i, 1)
    pupper(i) = max(pupper(i), 45000.)
    ! cc        Pupper(i) = 60000.
  END DO

ELSE
  DO i=1, klon
     ! pupper(i) = wk_pupper*ptop(i)+(1.-wk_pupper)*ph(i, 1) 
     !  pupper(i) = min( wk_pupper*ptop(i)+(1.-wk_pupper)*ph(i, 1) , ptop(i)-50.) 
      pupper(i) = min( wk_pupper*ptop(i)+(1.-wk_pupper)*ph(i, 1) , ptop(i)-5000.) 
  END DO
END IF
 
  ! -5/ Determination de kupper

  DO k = klev, 1, -1
    DO i = 1, klon
      IF (ph(i,k+1)<pupper(i)) kupper(i) = k
    END DO
  END DO

  ! On evite kupper = 1 et kupper = klev
  DO i = 1, klon
    kupper(i) = max(kupper(i), 2)
    kupper(i) = min(kupper(i), klev-1)
  END DO 
  !---------- FIN nouveau calcul hw et ptop -------------------------------------

IF (iflag_wk_new_ptop==999) THEN
    DO i = 1, klon
    hw_(i)=0.
    ptop(i)=ph(i,1)
    Ktop(i)=1
    pupper(i)=ph(i,2)
    kupper(i)=2
    h_zzz(i)=0.
    Ptop1(i)=ph(i,1)
    ENDDO
ENDIF

zk_ptop_provis=k_ptop_provis

    RETURN
END SUBROUTINE pkupper


SUBROUTINE wake_popdyn_1(klon, klev, dtime, cstar, tau_wk_inv, wgen, wdens, awdens, sigmaw, &
                  wdensmin, &
                  dtimesub, gfl, rad_wk, f_shear, drdt_pos, &
                  d_awdens, d_wdens, d_sigmaw, &
                  iflag_wk_act, wk_adv, cin, wape, &
                  drdt, &
                  d_dens_gen, d_dens_death, d_dens_col, d_dens_bnd, &
                  d_sig_gen, d_sig_death, d_sig_col, d_sig_spread, d_sig_bnd, &
                  d_wdens_targ, d_sigmaw_targ)
                

  USE lmdz_wake_ini , ONLY: wake_ini
  USE lmdz_wake_ini , ONLY: prt_level,RG
  USE lmdz_wake_ini , ONLY: stark, wdens_ref
  USE lmdz_wake_ini , ONLY: tau_cv, rzero, aa0
!!  USE lmdz_wake_ini , ONLY: iflag_wk_pop_dyn, wdensmin
  USE lmdz_wake_ini , ONLY: iflag_wk_pop_dyn
  USE lmdz_wake_ini , ONLY: sigmad, cstart, sigmaw_max
  
IMPLICIT NONE

  INTEGER, INTENT(IN)                                   :: klon,klev
  LOGICAL, DIMENSION (klon),        INTENT(IN)          :: wk_adv
  REAL,                             INTENT(IN)          :: dtime
  REAL,                             INTENT(IN)          :: dtimesub
  REAL,                             INTENT(IN)          :: wdensmin
  REAL, DIMENSION (klon),           INTENT(IN)          :: wgen
  REAL, DIMENSION (klon),           INTENT(IN)          :: wdens
  REAL, DIMENSION (klon),           INTENT(IN)          :: awdens
  REAL, DIMENSION (klon),           INTENT(IN)          :: sigmaw
  REAL, DIMENSION (klon),           INTENT(IN)          :: cstar
  REAL, DIMENSION (klon),           INTENT(IN)          :: cin, wape
  REAL, DIMENSION (klon),           INTENT(IN)          :: f_shear
  INTEGER,                          INTENT(IN)          :: iflag_wk_act

  ! Tendencies of state variables (2 is appended to the names of fields which are the cumul of fields 
  !                                 computed at each sub-timestep; e.g. d_wdens2 is the cumul of d_wdens)
  REAL, DIMENSION (klon),           INTENT(OUT)         :: rad_wk
  REAL, DIMENSION (klon),           INTENT(OUT)         :: gfl
  REAL, DIMENSION (klon),           INTENT(OUT)         :: d_sigmaw, d_awdens, d_wdens
  REAL, DIMENSION (klon),           INTENT(OUT)         :: drdt
  ! Some components of the tendencies of state variables  
  REAL, DIMENSION (klon),           INTENT(OUT)         :: d_sig_gen, d_sig_death, d_sig_col, d_sig_bnd
  REAL, DIMENSION (klon),           INTENT(OUT)         :: d_sig_spread
  REAL, DIMENSION (klon),           INTENT(OUT)         :: d_dens_gen, d_dens_death, d_dens_col, d_dens_bnd
  REAL,                             INTENT(OUT)         :: d_wdens_targ, d_sigmaw_targ
 
  
  REAL                                                  :: delta_t_min
  INTEGER                                               :: i, k
  REAL                                                  :: wdens0
  ! IM 080208
  LOGICAL, DIMENSION (klon)                             :: gwake
  
   ! Variables liees a la dynamique de population
  REAL, DIMENSION(klon)                                 :: act
  REAL, DIMENSION(klon)                                 :: tau_wk_inv
  REAL, DIMENSION(klon)                                 :: wape1_act, wape2_act
  LOGICAL, DIMENSION (klon)                             :: kill_wake
  REAL                                                  :: drdt_pos
  REAL                                                  :: tau_wk_inv_min
  
     

      IF (iflag_wk_act == 0) THEN
        act(:) = 0.
      ELSEIF (iflag_wk_act == 1) THEN
        act(:) = 1.
      ELSEIF (iflag_wk_act ==2) THEN
      DO i = 1, klon
        IF (wk_adv(i)) THEN
          wape1_act(i) = abs(cin(i))
          wape2_act(i) = 2.*wape1_act(i) + 1.
          act(i) = min(1., max(0., (wape(i)-wape1_act(i)) / (wape2_act(i)-wape1_act(i)) ))
        ENDIF  ! (wk_adv(i))
      ENDDO
      ENDIF  ! (iflag_wk_act ==2)

      DO i = 1, klon
        IF (wk_adv(i)) THEN
          rad_wk(i) = max( sqrt(sigmaw(i)/(3.14*wdens(i))) , rzero)
          gfl(i)  = 2.*sqrt(3.14*wdens(i)*sigmaw(i))
        END IF
      END DO

      DO i = 1, klon
        IF (wk_adv(i)) THEN
!!          tau_wk(i) = max(rad_wk(i)/(3.*cstar(i))*((cstar(i)/cstart)**1.5 - 1), 100.)
          tau_wk_inv(i) = max( (3.*cstar(i))/(rad_wk(i)*((cstar(i)/cstart)**1.5 - 1)), 0.)
          tau_wk_inv_min = min(tau_wk_inv(i), 1./dtimesub)
          drdt(i) = (cstar(i) - wgen(i)*(sigmaw(i)/wdens(i)-aa0)/gfl(i)) / &
                    (1 + 2*f_shear(i)*(2.*sigmaw(i)-aa0*wdens(i)) - 2.*sigmaw(i))
!!                    (1 - 2*sigmaw(i)*(1.-f_shear(i)))
          drdt_pos=max(drdt(i),0.)

!!          d_wdens(i) = ( wgen(i)*(1.+2.*(sigmaw(i)-sigmad)) &
!!                     - wdens(i)*tau_wk_inv_min &
!!                     - 2.*gfl(i)*wdens(i)*Cstar(i) )*dtimesub
!jyg+mlt<
          d_awdens(i) = ( wgen(i) - (1./tau_cv)*(awdens(i) - act(i)*wdens(i)) )*dtimesub
          d_dens_gen(i) = wgen(i)
          d_dens_death(i) = - (wdens(i)-awdens(i))*tau_wk_inv_min 
          d_dens_col(i) =  -2.*wdens(i)*gfl(i)*drdt_pos 
          d_dens_gen(i) =  d_dens_gen(i)*dtimesub
          d_dens_death(i) = d_dens_death(i)*dtimesub
          d_dens_col(i) =  d_dens_col(i)*dtimesub 

          d_wdens(i) = d_dens_gen(i)+d_dens_death(i)+d_dens_col(i)
!!          d_wdens(i) = ( wgen(i) - (wdens(i)-awdens(i))*tau_wk_inv_min -  &
!!                         2.*wdens(i)*gfl(i)*drdt_pos )*dtimesub
!>jyg+mlt

!jyg<
          d_wdens_targ = max(d_wdens(i), wdensmin-wdens(i))
!!          d_dens_bnd(i) = d_dens_bnd(i) + d_wdens_targ - d_wdens(i)
          d_dens_bnd(i) = d_wdens_targ - d_wdens(i)
          d_wdens(i) = d_wdens_targ
!!          d_wdens(i) = max(d_wdens(i), wdensmin-wdens(i))
!>jyg

!jyg+mlt<
!!          d_sigmaw(i) = ( (1.-2*f_shear(i)*sigmaw(i))*(gfl(i)*Cstar(i)+wgen(i)*sigmad/wdens(i)) &
!!                      + 2.*f_shear(i)*wgen(i)*sigmaw(i)**2/wdens(i) &
!!                      - sigmaw(i)*tau_wk_inv_min )*dtimesub
          d_sig_gen(i) = wgen(i)*aa0
          d_sig_death(i) = - sigmaw(i)*(1.-awdens(i)/wdens(i))*tau_wk_inv_min
!!        
          
          d_sig_col(i) = - 2*f_shear(i)*sigmaw(i)*gfl(i)*drdt_pos
          d_sig_col(i) = - 2*f_shear(i)*(2.*sigmaw(i)-wdens(i)*aa0)*gfl(i)*drdt_pos
          d_sig_spread(i) = gfl(i)*cstar(i)
          d_sig_gen(i) =  d_sig_gen(i)*dtimesub
          d_sig_death(i) = d_sig_death(i)*dtimesub
          d_sig_col(i) =  d_sig_col(i)*dtimesub 
          d_sig_spread(i) =  d_sig_spread(i)*dtimesub 
          d_sigmaw(i) =  d_sig_gen(i) + d_sig_death(i) + d_sig_col(i) + d_sig_spread(i)
!>jyg+mlt

!jyg<
          d_sigmaw_targ = max(d_sigmaw(i), sigmad-sigmaw(i))
!!          d_sig_bnd(i) = d_sig_bnd(i) + d_sigmaw_targ - d_sigmaw(i)
!!          d_sig_bnd_provis(i) = d_sigmaw_targ - d_sigmaw(i)
          d_sig_bnd(i) = d_sigmaw_targ - d_sigmaw(i)
          d_sigmaw(i) = d_sigmaw_targ
!!          d_sigmaw(i) = max(d_sigmaw(i), sigmad-sigmaw(i))
!>jyg
        ENDIF
      ENDDO

      IF (prt_level >= 10) THEN
        print *,'wake, cstar(1), cstar(1)/cstart, rad_wk(1), tau_wk_inv(1), drdt(1) ', &
                       cstar(1), cstar(1)/cstart, rad_wk(1), tau_wk_inv(1), drdt(1)
        print *,'wake, wdens(1), awdens(1), act(1), d_awdens(1) ', &
                       wdens(1), awdens(1), act(1), d_awdens(1)
        print *,'wake, wgen, -(wdens-awdens)*tau_wk_inv, -2.*wdens*gfl*drdt_pos, d_wdens ', &
                       wgen(1), -(wdens(1)-awdens(1))*tau_wk_inv(1), -2.*wdens(1)*gfl(1)*drdt_pos, d_wdens(1)
        print *,'wake, d_sig_gen(1), d_sig_death(1), d_sig_col(1), d_sigmaw(1) ', &
                       d_sig_gen(1), d_sig_death(1), d_sig_col(1), d_sigmaw(1)
      ENDIF
    
    RETURN 
    END SUBROUTINE wake_popdyn_1
    
    SUBROUTINE wake_popdyn_2 ( klon, klev, wk_adv, dtimesub, wgen, &
                             wdensmin, &
                             sigmaw, wdens, awdens, &   !! states variables
                             gfl, cstar, cin, wape, rad_wk, &
                             d_sigmaw, d_wdens, d_awdens, &  !! tendences 
                             cont_fact, &
                             d_sig_gen, d_sig_death, d_sig_col, d_sig_spread, d_sig_bnd, &
                             d_dens_gen, d_dens_death, d_dens_col, d_dens_bnd, &
                             d_adens_death, d_adens_icol, d_adens_acol, d_adens_bnd )
                             
                                             

  USE lmdz_wake_ini , ONLY: wake_ini
  USE lmdz_wake_ini , ONLY: prt_level,RG
  USE lmdz_wake_ini , ONLY: stark, wdens_ref
  USE lmdz_wake_ini , ONLY: tau_cv, rzero, aa0
!!  USE lmdz_wake_ini , ONLY: iflag_wk_pop_dyn, wdensmin
  USE lmdz_wake_ini , ONLY: iflag_wk_pop_dyn
  USE lmdz_wake_ini , ONLY: sigmad, cstart, sigmaw_max
  
IMPLICIT NONE

  INTEGER, INTENT(IN)                                   :: klon,klev
  LOGICAL, DIMENSION (klon),        INTENT(IN)          :: wk_adv
  REAL,                             INTENT(IN)          :: dtimesub
  REAL,                             INTENT(IN)          :: wdensmin
  REAL, DIMENSION (klon),           INTENT(IN)          :: wgen      !! B = birth rate of wakes
  REAL, DIMENSION (klon),           INTENT(INOUT)       :: sigmaw    !! sigma = fractional area of wakes 
  REAL, DIMENSION (klon),           INTENT(INOUT)       :: wdens     !! D = number of wakes per unit area 
  REAL, DIMENSION (klon),           INTENT(INOUT)       :: awdens    !! A = number of active wakes per unit area
  REAL, DIMENSION (klon),           INTENT(IN)          :: cstar     !! C* = spreading velocity of wakes
  REAL, DIMENSION (klon),           INTENT(IN)          :: cin, wape  ! RM : A Faire disparaitre

  REAL, DIMENSION (klon),           INTENT(OUT)         :: rad_wk    !! r = wake radius
  REAL, DIMENSION (klon),           INTENT(OUT)         :: gfl       !! Lg = gust front lenght per unit area
  REAL, DIMENSION (klon),           INTENT(OUT)         :: d_sigmaw, d_wdens, d_awdens
  REAL, DIMENSION (klon),           INTENT(OUT)         :: cont_fact  !! RM facteur de contact = 2 pi * rad * C*
  ! Some components of the tendencies of state variables  
  REAL, DIMENSION (klon),           INTENT(OUT)         :: d_sig_gen, d_sig_death, d_sig_col, d_sig_spread, d_sig_bnd
  REAL, DIMENSION (klon),           INTENT(OUT)         :: d_dens_gen, d_dens_death, d_dens_col, d_dens_bnd
  REAL, DIMENSION (klon),           INTENT(OUT)         :: d_adens_death, d_adens_icol, d_adens_acol, d_adens_bnd


!! internal variables
  
  INTEGER                                               :: i, k
  REAL, DIMENSION (klon)                                :: tau_wk_inv      !! tau = life time of wakes
  REAL                                                  :: tau_wk_inv_min
  REAL, DIMENSION (klon)                                :: tau_prime       !! tau_prime = life time of actives wakes
  REAL                                                  :: d_wdens_targ, d_sigmaw_targ
  

!! Equations
!! dD/dt = B - (D-A)/tau - f D^2
!! dA/dt = B - A/tau_prime + f (D-A)^2 - f A^2
!! dsigma/dt = B a0 - sigma/D (D-A)/tau + Lg C* - f (D-A)^2 (sigma/D-a0)
!!
!! f = 2 (B (a0-sigma/D) + Lg C*) / (2 (D-A)^2 (2 sigma/D-a0) + D (1-2 sigma))


      DO i = 1, klon
        IF (wk_adv(i)) THEN
          rad_wk(i) = max( sqrt(sigmaw(i)/(3.14*wdens(i))) , rzero)
          gfl(i)  = 2.*sqrt(3.14*wdens(i)*sigmaw(i))
        END IF
      END DO


      DO i = 1, klon
        IF (wk_adv(i)) THEN
!!          tau_wk(i) = max(rad_wk(i)/(3.*cstar(i))*((cstar(i)/cstart)**1.5 - 1), 100.)
          tau_wk_inv(i) = max( (3.*cstar(i))/(rad_wk(i)*((cstar(i)/cstart)**1.5 - 1)), 0.)
          tau_wk_inv_min = min(tau_wk_inv(i), 1./dtimesub)
          tau_prime(i) = tau_cv
!!          cont_fact(i) = 2.*(wgen(i)*(aa0-sigmaw(i)/wdens(i)) + gfl(i)*cstar(i)) / &
!!                             (2.*(wdens(i)-awdens(i))**2*(2.*sigmaw(i)/wdens(i) - aa0) + wdens(i)*(1.-2.*sigmaw(i)))
!!          cont_fact(i) = 2.*3.14*rad_wk(i)*cstar(i)     ! bug
!!          cont_fact(i) = 4.*3.14*rad_wk(i)*cstar(i)
          cont_fact(i) = 2.*gfl(i)*cstar(i)/wdens(i)

          d_sig_gen(i) = wgen(i)*aa0
          d_sig_death(i) = - sigmaw(i)*(1.-awdens(i)/wdens(i))*tau_wk_inv_min
          d_sig_col(i) = - cont_fact(i)*(wdens(i)-awdens(i))**2*(2.*sigmaw(i)/wdens(i)-aa0)
          d_sig_spread(i) = gfl(i)*cstar(i)

          d_sig_gen(i) =  d_sig_gen(i)*dtimesub
          d_sig_death(i) = d_sig_death(i)*dtimesub
          d_sig_col(i) =  d_sig_col(i)*dtimesub 
          d_sig_spread(i) =  d_sig_spread(i)*dtimesub 
          d_sigmaw(i) =  d_sig_gen(i) + d_sig_death(i) + d_sig_col(i) + d_sig_spread(i)

         
          d_sigmaw_targ = max(d_sigmaw(i), sigmad-sigmaw(i))
!!          d_sig_bnd(i) = d_sig_bnd(i) + d_sigmaw_targ - d_sigmaw(i)
!!          d_sig_bnd_provis(i) = d_sigmaw_targ - d_sigmaw(i)
          d_sig_bnd(i) = d_sigmaw_targ - d_sigmaw(i)
          d_sigmaw(i) = d_sigmaw_targ
!!          d_sigmaw(i) = max(d_sigmaw(i), sigmad-sigmaw(i))
         
         
          d_dens_gen(i) = wgen(i)
          d_dens_death(i) = - (wdens(i)-awdens(i))*tau_wk_inv_min 
          d_dens_col(i) =  - cont_fact(i)*wdens(i)**2

          d_dens_gen(i) =  d_dens_gen(i)*dtimesub
          d_dens_death(i) = d_dens_death(i)*dtimesub
          d_dens_col(i) =  d_dens_col(i)*dtimesub 
          d_wdens(i) = d_dens_gen(i) + d_dens_death(i) + d_dens_col(i)


          d_adens_death(i) = -awdens(i)/tau_prime(i)
          d_adens_icol(i) = cont_fact(i)*(wdens(i)-awdens(i))**2
          d_adens_acol(i) = - cont_fact(i)*awdens(i)**2

          d_adens_death(i) =  d_adens_death(i)*dtimesub
          d_adens_icol(i) =   d_adens_icol(i)*dtimesub
          d_adens_acol(i) =   d_adens_acol(i)*dtimesub
          d_awdens(i) =   d_dens_gen(i) + d_adens_death(i) + d_adens_icol(i) + d_adens_acol(i)     
            
!!
          d_wdens_targ = max(d_wdens(i), wdensmin-wdens(i))
!!          d_dens_bnd(i) = d_dens_bnd(i) + d_wdens_targ - d_wdens(i)
          d_dens_bnd(i) = d_wdens_targ - d_wdens(i)
          d_wdens(i) = d_wdens_targ
          
          d_wdens_targ = min(max(d_awdens(i),-awdens(i)), wdens(i)-awdens(i))
!!          d_dens_bnd(i) = d_dens_bnd(i) + d_wdens_targ - d_wdens(i)
          d_adens_bnd(i) = d_wdens_targ - d_awdens(i)
          d_awdens(i) = d_wdens_targ



        ENDIF
      ENDDO

      IF (prt_level >= 10) THEN
        print *,'wake, cstar(1), cstar(1)/cstart, rad_wk(1), tau_wk_inv(1), cont_fact(1) ', &
                       cstar(1), cstar(1)/cstart, rad_wk(1), tau_wk_inv(1), cont_fact(1)
        print *,'wake, wdens(1), awdens(1), d_awdens(1) ', &
                       wdens(1), awdens(1), d_awdens(1)
        print *,'wake, d_sig_gen(1), d_sig_death(1), d_sig_col(1), d_sigmaw(1) ', &
                       d_sig_gen(1), d_sig_death(1), d_sig_col(1), d_sigmaw(1)
      ENDIF
sigmaw=sigmaw+d_sigmaw
wdens=wdens+d_wdens
awdens=awdens+d_awdens

    RETURN 
    END SUBROUTINE wake_popdyn_2  
  
    SUBROUTINE wake_popdyn_3 ( klon, klev, phys_sub, wk_adv, dtimesub, wgen, &
                             wdensmin, &
                             sigmaw, asigmaw, wdens, awdens, &                       !! state variables
                             gfl, agfl, cstar, cin, wape, &
                             rad_wk, arad_wk, irad_wk, &
                             d_sigmaw, d_asigmaw, d_wdens, d_awdens, &               !! tendencies 
                             d_sig_gen, d_sig_death, d_sig_col, d_sig_spread, d_sig_bnd, &
                             d_asig_death, d_asig_aicol, d_asig_iicol, d_asig_spread, d_asig_bnd, &
                             d_dens_gen, d_dens_death, d_dens_col, d_dens_bnd, &
                             d_adens_death, d_adens_icol, d_adens_acol, d_adens_bnd )
                             
                                             

  USE lmdz_wake_ini , ONLY: wake_ini
  USE lmdz_wake_ini , ONLY: prt_level,RG
  USE lmdz_wake_ini , ONLY: stark, wdens_ref
  USE lmdz_wake_ini , ONLY: tau_cv, rzero, aa0
!!  USE lmdz_wake_ini , ONLY: iflag_wk_pop_dyn, wdensmin
  USE lmdz_wake_ini , ONLY: iflag_wk_pop_dyn
  USE lmdz_wake_ini , ONLY: sigmad, cstart, sigmaw_max
  USE lmdz_wake_ini , ONLY: smallestreal
  
IMPLICIT NONE

  INTEGER, INTENT(IN)                                   :: klon,klev
  LOGICAL,                          INTENT(IN)          :: phys_sub 
  LOGICAL, DIMENSION (klon),        INTENT(IN)          :: wk_adv
  REAL,                             INTENT(IN)          :: dtimesub
  REAL,                             INTENT(IN)          :: wdensmin
  REAL, DIMENSION (klon),           INTENT(IN)          :: wgen      !! B = birth rate of wakes
  REAL, DIMENSION (klon),           INTENT(INOUT)       :: sigmaw    !! sigma = fractional area of wakes 
  REAL, DIMENSION (klon),           INTENT(INOUT)       :: asigmaw   !! sigma = fractional area of active wakes 
  REAL, DIMENSION (klon),           INTENT(INOUT)       :: wdens     !! D = number of wakes per unit area 
  REAL, DIMENSION (klon),           INTENT(INOUT)       :: awdens    !! A = number of active wakes per unit area
  REAL, DIMENSION (klon),           INTENT(IN)          :: cstar     !! C* = spreading velocity of wakes
  REAL, DIMENSION (klon),           INTENT(IN)          :: cin, wape  ! RM : A Faire disparaitre

  REAL, DIMENSION (klon),           INTENT(OUT)         :: rad_wk    !! r = mean wake radius
  REAL, DIMENSION (klon),           INTENT(OUT)         :: arad_wk    !! r_A = wake radius of active wakes
  REAL, DIMENSION (klon),           INTENT(OUT)         :: irad_wk    !! r_I = wake radius of inactive wakes
  REAL, DIMENSION (klon),           INTENT(OUT)         :: gfl       !! Lg = gust front length per unit area
  REAL, DIMENSION (klon),           INTENT(OUT)         :: agfl      !! LgA = gust front length of active wakes
                                                                     !!  per unit area
  REAL, DIMENSION (klon),           INTENT(OUT)         :: d_sigmaw, d_asigmaw, d_wdens, d_awdens
  ! Some components of the tendencies of state variables  
  REAL, DIMENSION (klon),           INTENT(OUT)         :: d_sig_gen, d_sig_death, d_sig_col, d_sig_spread, d_sig_bnd
  REAL, DIMENSION (klon),           INTENT(OUT)         :: d_asig_death, d_asig_aicol, d_asig_iicol, d_asig_spread, d_asig_bnd
  REAL, DIMENSION (klon),           INTENT(OUT)         :: d_dens_gen, d_dens_death, d_dens_col, d_dens_bnd
  REAL, DIMENSION (klon),           INTENT(OUT)         :: d_adens_death, d_adens_acol, d_adens_icol, d_adens_bnd


!! internal variables
  
  INTEGER                                               :: i, k
  REAL, DIMENSION (klon)                                :: iwdens, isigmaw !! inactive wake density and fractional area
!!  REAL, DIMENSION (klon)                                :: d_arad, d_irad
  REAL, DIMENSION (klon)                                :: igfl            !! LgI = gust front length of inactive wakes
                                                                           !!  per unit area
  REAL, DIMENSION (klon)                                :: s_wk            !! mean area of individual wakes
  REAL, DIMENSION (klon)                                :: as_wk           !! mean area of individual active wakes
  REAL, DIMENSION (klon)                                :: is_wk           !! mean area of individual inactive wakes
  REAL, DIMENSION (klon)                                :: tau_wk_inv      !! tau = life time of wakes
  REAL                                                  :: tau_wk_inv_min
  REAL, DIMENSION (klon)                                :: tau_prime       !! tau_prime = life time of actives wakes
  REAL                                                  :: d_wdens_targ, d_sigmaw_targ


!! Equations
!! ---------
!! Gust fronts:
!! Lg_A = 2 pi r_A A
!! Lg_I = 2 pi r_I I
!! Lg   = 2 pi r   D
!!
!! Areas:
!! s = pi r^2
!! s_A = pi r_A^2
!! s_I = pi r_I^2
!!
!! Life expectancy:
!! tau_I = 3 C* ((C*/C*t)^3/2 - 1) / r_I
!!
!! Time deratives:
!! dD/dt = B - (D-A)/tau_I - 2 Lg C* D
!! dA/dt = B - A/tau_A     + 2 Lg_I C* (D-A) - 2 Lg_A C* A
!! dsigma/dt = B a0 - sigma_I/tau_I + Lg C* - 2 Lg_I C* (D-A) (2 s_I - a0)
!! dsigma_A/dt = B a0 - sigma_A/tau_A + Lg_A C* + (Lg_A I + Lg_I A) C* s_I + 2 Lg_I C* I a0
!!

      DO i = 1, klon
        IF (wk_adv(i)) THEN
         iwdens(i) = wdens(i) - awdens(i)
         isigmaw(i) = sigmaw(i) - asigmaw(i)

         arad_wk(i) = max( sqrt(asigmaw(i)/(3.14*awdens(i))) , rzero)
         irad_wk(i) = max( sqrt((sigmaw(i)-asigmaw(i))/  &
                           (3.14*max(smallestreal,(wdens(i)-awdens(i))))), rzero)
         rad_wk(i) = (awdens(i)*arad_wk(i)+(wdens(i)-awdens(i))*irad_wk(i))/wdens(i)

         s_wk(i) = 3.14*rad_wk(i)**2
         as_wk(i) = 3.14*arad_wk(i)**2
         is_wk(i) = 3.14*irad_wk(i)**2

         gfl(i)  = 2.*sqrt(3.14*wdens(i)*sigmaw(i))
         agfl(i) = 2.*sqrt(3.14*awdens(i)*asigmaw(i))
         igfl(i) = gfl(i) - agfl(i)
        ENDIF
      ENDDO


      DO i = 1, klon
        IF (wk_adv(i)) THEN
          tau_wk_inv(i) = max( (3.*cstar(i))/(irad_wk(i)*((cstar(i)/cstart)**1.5 - 1)), 0.)
          tau_wk_inv_min = min(tau_wk_inv(i), 1./dtimesub)
          tau_prime(i) = tau_cv

          d_sig_gen(i) = wgen(i)*aa0
          d_sig_death(i) = - isigmaw(i)*tau_wk_inv_min
          d_sig_col(i) = - 2.*igfl(i)*cstar(i)*iwdens(i)*(2.*is_wk(i)-aa0)
          d_sig_spread(i) = gfl(i)*cstar(i)

          d_sig_gen(i) =  d_sig_gen(i)*dtimesub
          d_sig_death(i) = d_sig_death(i)*dtimesub
          d_sig_col(i) =  d_sig_col(i)*dtimesub 
          d_sig_spread(i) =  d_sig_spread(i)*dtimesub 
          d_sigmaw(i) =  d_sig_gen(i) + d_sig_death(i) + d_sig_col(i) + d_sig_spread(i)
#ifdef IOPHYS_WK
          IF (phys_sub) CALL iophys_ecrit('d_sigmaw0',1,'d_sigmaw0','',d_sigmaw)
#endif

         
          d_sigmaw_targ = max(d_sigmaw(i), sigmad-sigmaw(i))
!!          d_sig_bnd(i) = d_sig_bnd(i) + d_sigmaw_targ - d_sigmaw(i)
!!          d_sig_bnd_provis(i) = d_sigmaw_targ - d_sigmaw(i)
          d_sig_bnd(i) = d_sigmaw_targ - d_sigmaw(i)
          d_sigmaw(i) = d_sigmaw_targ
!!          d_sigmaw(i) = max(d_sigmaw(i), sigmad-sigmaw(i))
#ifdef IOPHYS_WK
          IF (phys_sub) THEN
             CALL iophys_ecrit('tauwk_inv',1,'tau_wk_inv_min','',tau_wk_inv_min)
             CALL iophys_ecrit('d_sigmaw',1,'d_sigmaw','',d_sigmaw)
             CALL iophys_ecrit('d_sig_gen',1,'d_sig_gen','',d_sig_gen)
             CALL iophys_ecrit('d_sig_death',1,'d_sig_death','',d_sig_death)
             CALL iophys_ecrit('d_sig_col',1,'d_sig_col','',d_sig_col)
             CALL iophys_ecrit('d_sig_spread',1,'d_sig_spread','',d_sig_spread)
             CALL iophys_ecrit('d_sig_bnd',1,'d_sig_bnd','',d_sig_bnd)
          ENDIF
#endif
          d_asig_death(i) = - asigmaw(i)/tau_prime(i)
          d_asig_aicol(i) = (agfl(i)*iwdens(i) + igfl(i)*awdens(i))*cstar(i)*is_wk(i)
          d_asig_iicol(i) = 2.*igfl(i)*cstar(i)*iwdens(i)*aa0
          d_asig_spread(i) = agfl(i)*cstar(i)

          d_asig_death(i) = d_asig_death(i)*dtimesub
          d_asig_aicol(i) =  d_asig_aicol(i)*dtimesub 
          d_asig_iicol(i) =  d_asig_iicol(i)*dtimesub 
          d_asig_spread(i) =  d_asig_spread(i)*dtimesub 
          d_asigmaw(i) =  d_sig_gen(i) + d_asig_death(i) + d_asig_aicol(i) + d_asig_iicol(i) + d_asig_spread(i)
#ifdef IOPHYS_WK
          IF (phys_sub) CALL iophys_ecrit('d_asigmaw0',1,'d_asigmaw0','',d_asigmaw)
#endif

          d_sigmaw_targ = min(max(d_asigmaw(i),-asigmaw(i)), sigmaw(i)-asigmaw(i))
!!          d_dens_bnd(i) = d_dens_bnd(i) + d_sigmaw_targ - d_sigmaw(i)
          d_asig_bnd(i) = d_sigmaw_targ - d_asigmaw(i)
          d_asigmaw(i) = d_sigmaw_targ
#ifdef IOPHYS_WK
          IF (phys_sub) THEN
             CALL iophys_ecrit('d_asigmaw',1,'d_asigmaw','',d_asigmaw)
             CALL iophys_ecrit('d_asig_death',1,'d_asig_death','',d_asig_death)
             CALL iophys_ecrit('d_asig_aicol',1,'d_asig_aicol','',d_asig_aicol)
             CALL iophys_ecrit('d_asig_iicol',1,'d_asig_iicol','',d_asig_iicol)
             CALL iophys_ecrit('d_asig_spread',1,'d_asig_spread','',d_asig_spread)
             CALL iophys_ecrit('d_asig_bnd',1,'d_asig_bnd','',d_asig_bnd)
          ENDIF
#endif
          d_dens_gen(i) = wgen(i)
          d_dens_death(i) = - iwdens(i)*tau_wk_inv_min 
          d_dens_col(i) =  - 2.*gfl(i)*cstar(i)*wdens(i)

          d_dens_gen(i) =  d_dens_gen(i)*dtimesub
          d_dens_death(i) = d_dens_death(i)*dtimesub
          d_dens_col(i) =  d_dens_col(i)*dtimesub 
          d_wdens(i) = d_dens_gen(i) + d_dens_death(i) + d_dens_col(i)
!!
          d_wdens_targ = max(d_wdens(i), wdensmin-wdens(i))
!!          d_dens_bnd(i) = d_dens_bnd(i) + d_wdens_targ - d_wdens(i)
          d_dens_bnd(i) = d_wdens_targ - d_wdens(i)
          d_wdens(i) = d_wdens_targ
#ifdef IOPHYS_WK
    IF (phys_sub) THEN 
        CALL iophys_ecrit('d_wdens',1,'d_wdens','',d_wdens)
        CALL iophys_ecrit('d_dens_gen',1,'d_dens_gen','',d_dens_gen)
        CALL iophys_ecrit('d_dens_death',1,'d_dens_death','',d_dens_death)
        CALL iophys_ecrit('d_dens_col',1,'d_dens_col','',d_dens_col)
    ENDIF
#endif

          d_adens_death(i) = -awdens(i)/tau_prime(i)
          d_adens_icol(i) =   2.*igfl(i)*cstar(i)*iwdens(i)
          d_adens_acol(i)  = - 2.*agfl(i)*cstar(i)*awdens(i)

          d_adens_death(i) =  d_adens_death(i)*dtimesub
          d_adens_icol(i) =   d_adens_icol(i)*dtimesub
          d_adens_acol(i)  =   d_adens_acol(i)*dtimesub
          d_awdens(i) =   d_dens_gen(i) + d_adens_death(i) + d_adens_icol(i) + d_adens_acol(i)     
#ifdef IOPHYS_WK
    IF (phys_sub) THEN 
        CALL iophys_ecrit('d_awdens',1,'d_awdens','',d_awdens)
        CALL iophys_ecrit('d_adens_death',1,'d_adens_death','',d_adens_death)
        CALL iophys_ecrit('d_adens_icol',1,'d_adens_icol','',d_adens_icol)
        CALL iophys_ecrit('d_adens_acol',1,'d_adens_acol','',d_adens_acol)
    ENDIF
#endif
          d_wdens_targ = min(max(d_awdens(i),-awdens(i)), wdens(i)-awdens(i))
!!          d_dens_bnd(i) = d_dens_bnd(i) + d_wdens_targ - d_wdens(i)
          d_adens_bnd(i) = d_wdens_targ - d_awdens(i)
          d_awdens(i) = d_wdens_targ

!!          d_irad(i) = (d_sigmaw(i)-d_asigmaw(i)-isigmaw(i)*(d_wdens(i)-awdens(i))/iwdens(i)) / &
!!                      max(smallestreal,(2.*3.14*iwdens(i)*irad_wk(i)))
!!          d_arad(i) = (d_asigmaw(i)-asigmaw(i)*d_awdens(i)/awdens(i)) / &
!!                      max(smallestreal,(2.*3.14*awdens(i)*arad_wk(i)))
!!          d_irad(i) = d_irad(i)*dtimesub
!!          d_arad(i) = d_arad(i)*dtimesub
!!          CALL iophys_ecrit('d_irad',1,'d_irad','m',d_irad)
!!          CALL iophys_ecrit('d_airad',1,'d_arad','m',d_arad)
!!
        ENDIF
      ENDDO

      IF (prt_level >= 10) THEN
        print *,'wake, cstar(1), cstar(1)/cstart, rad_wk(1), tau_wk_inv(1), gfl(1) ', &
                       cstar(1), cstar(1)/cstart, rad_wk(1), tau_wk_inv(1), gfl(1)
        print *,'wake, wdens(1), awdens(1), d_awdens(1) ', &
                       wdens(1), awdens(1), d_awdens(1)
        print *,'wake, d_sig_gen(1), d_sig_death(1), d_sig_col(1), d_sigmaw(1) ', &
                       d_sig_gen(1), d_sig_death(1), d_sig_col(1), d_sigmaw(1)
      ENDIF
sigmaw=sigmaw+d_sigmaw
asigmaw=asigmaw+d_asigmaw
wdens=wdens+d_wdens
awdens=awdens+d_awdens

    RETURN 
    END SUBROUTINE wake_popdyn_3  

END MODULE lmdz_wake
