!
! $Header$
!
      SUBROUTINE prather (q,w,masse,pbaru,pbarv,nt,dt)
      IMPLICIT NONE

c=======================================================================
c   Adaptation LMDZ:  A.Armengaud (LGGE)
c   ----------------
c
c   ************************************************
c   Transport des traceurs par la methode de prather
c   Ref : 
c
c   ************************************************
c   q,w,pext,pbaru et pbarv : arguments d'entree  pour le s-pg
c
c=======================================================================


!-----------------------------------------------------------------------
!   INCLUDE 'dimensions.h'
!
!   dimensions.h contient les dimensions du modele
!   ndm est tel que iim=2**ndm
!-----------------------------------------------------------------------

      INTEGER iim,jjm,llm,ndm

      PARAMETER (iim= 128,jjm=96,llm=64,ndm=1)

!-----------------------------------------------------------------------
!
! $Header$
!
!
!  ATTENTION!!!!: ce fichier include est compatible format fixe/format libre
!                 veillez  n'utiliser que des ! pour les commentaires
!                 et  bien positionner les & des lignes de continuation
!                 (les placer en colonne 6 et en colonne 73)
!
!
!-----------------------------------------------------------------------
!   INCLUDE 'paramet.h'

      INTEGER  iip1,iip2,iip3,jjp1,llmp1,llmp2,llmm1
      INTEGER  kftd,ip1jm,ip1jmp1,ip1jmi1,ijp1llm
      INTEGER  ijmllm,mvar
      INTEGER jcfil,jcfllm

      PARAMETER( iip1= iim+1,iip2=iim+2,iip3=iim+3                       &
     &    ,jjp1=jjm+1-1/jjm)
      PARAMETER( llmp1 = llm+1,  llmp2 = llm+2, llmm1 = llm-1 )
      PARAMETER( kftd  = iim/2 -ndm )
      PARAMETER( ip1jm  = iip1*jjm,  ip1jmp1= iip1*jjp1 )
      PARAMETER( ip1jmi1= ip1jm - iip1 )
      PARAMETER( ijp1llm= ip1jmp1 * llm, ijmllm= ip1jm * llm )
      PARAMETER( mvar= ip1jmp1*( 2*llm+1) + ijmllm )
      PARAMETER( jcfil=jjm/2+5, jcfllm=jcfil*llm )

!-----------------------------------------------------------------------
!
! $Id: comconst.h 1437 2010-09-30 08:29:10Z emillour $
!
!-----------------------------------------------------------------------
! INCLUDE comconst.h

      COMMON/comconsti/im,jm,lllm,imp1,jmp1,lllmm1,lllmp1,lcl,          &
     &                 iflag_top_bound,mode_top_bound
      COMMON/comconstr/dtvr,daysec,                                     &
     & pi,dtphys,dtdiss,rad,r,kappa,cotot,unsim,g,omeg                  &
     & ,dissip_fac_mid,dissip_fac_up,dissip_deltaz,dissip_hdelta        &
     & ,dissip_pupstart  ,tau_top_bound,                                &
     & daylen,molmass, ihf
      COMMON/cpdetvenus/cpp,nu_venus,t0_venus

      INTEGER im,jm,lllm,imp1,jmp1,lllmm1,lllmp1,lcl
      REAL dtvr ! dynamical time step (in s)
      REAL daysec !length (in s) of a standard day
      REAL pi    ! something like 3.14159....
      REAL dtphys ! (s) time step for the physics
      REAL dtdiss ! (s) time step for the dissipation
      REAL rad ! (m) radius of the planet
      REAL r ! Reduced Gas constant r=R/mu
             ! with R=8.31.. J.K-1.mol-1, mu: mol mass of atmosphere (kg/mol)
      REAL cpp   ! Cp
      REAL kappa ! kappa=R/Cp 
      REAL cotot
      REAL unsim ! = 1./iim
      REAL g ! (m/s2) gravity
      REAL omeg ! (rad/s) rotation rate of the planet
! Dissipation factors, for Earth model:
      REAL dissip_factz,dissip_zref !dissip_deltaz
! Dissipation factors, for other planets:
      REAL dissip_fac_mid,dissip_fac_up,dissip_deltaz,dissip_hdelta
      REAL dissip_pupstart
      INTEGER iflag_top_bound,mode_top_bound
      REAL tau_top_bound
      REAL daylen ! length of solar day, in 'standard' day length
      REAL molmass ! (g/mol) molar mass of the atmosphere

      REAL nu_venus,t0_venus ! coeffs needed for Cp(T), Venus atmosphere
      REAL ihf  ! (W/m2) intrinsic heat flux for giant planets


!-----------------------------------------------------------------------
!
! $Id: comvert.h 1654 2012-09-24 15:07:18Z aslmd $
!
!-----------------------------------------------------------------------
!   INCLUDE 'comvert.h'

      COMMON/comvertr/ap(llm+1),bp(llm+1),presnivs(llm),dpres(llm),     &
     &               pa,preff,nivsigs(llm),nivsig(llm+1),               &
     &               aps(llm),bps(llm),scaleheight,pseudoalt(llm)

      common/comverti/disvert_type, pressure_exner

      real ap     ! hybrid pressure contribution at interlayers
      real bp     ! hybrid sigma contribution at interlayer
      real presnivs ! (reference) pressure at mid-layers
      real dpres
      real pa     ! reference pressure (Pa) at which hybrid coordinates
                  ! become purely pressure
      real preff  ! reference surface pressure (Pa)
      real nivsigs
      real nivsig
      real aps    ! hybrid pressure contribution at mid-layers
      real bps    ! hybrid sigma contribution at mid-layers
      real scaleheight ! atmospheric (reference) scale height (km)
      real pseudoalt ! pseudo-altitude of model levels (km), based on presnivs(),
                     ! preff and scaleheight

      integer disvert_type ! type of vertical discretization:
                           ! 1: Earth (default for planet_type==earth),
                           !     automatic generation
                           ! 2: Planets (default for planet_type!=earth),
                           !     using 'z2sig.def' (or 'esasig.def) file

      logical pressure_exner
!     compute pressure inside layers using Exner function, else use mean
!     of pressure values at interfaces

 !-----------------------------------------------------------------------
!
! $Header$
!
!CDK comgeom2
      COMMON/comgeom/                                                   &
     & cu(iip1,jjp1),cv(iip1,jjm),unscu2(iip1,jjp1),unscv2(iip1,jjm)  , &
     & aire(iip1,jjp1),airesurg(iip1,jjp1),aireu(iip1,jjp1)           , &
     & airev(iip1,jjm),unsaire(iip1,jjp1),apoln,apols                 , &
     & unsairez(iip1,jjm),airuscv2(iip1,jjm),airvscu2(iip1,jjm)       , &
     & aireij1(iip1,jjp1),aireij2(iip1,jjp1),aireij3(iip1,jjp1)       , &
     & aireij4(iip1,jjp1),alpha1(iip1,jjp1),alpha2(iip1,jjp1)         , &
     & alpha3(iip1,jjp1),alpha4(iip1,jjp1),alpha1p2(iip1,jjp1)        , &
     & alpha1p4(iip1,jjp1),alpha2p3(iip1,jjp1),alpha3p4(iip1,jjp1)    , &
     & fext(iip1,jjm),constang(iip1,jjp1), rlatu(jjp1),rlatv(jjm),      &
     & rlonu(iip1),rlonv(iip1),cuvsurcv(iip1,jjm),cvsurcuv(iip1,jjm)  , &
     & cvusurcu(iip1,jjp1),cusurcvu(iip1,jjp1)                        , &
     & cuvscvgam1(iip1,jjm),cuvscvgam2(iip1,jjm),cvuscugam1(iip1,jjp1), &
     & cvuscugam2(iip1,jjp1),cvscuvgam(iip1,jjm),cuscvugam(iip1,jjp1) , &
     & unsapolnga1,unsapolnga2,unsapolsga1,unsapolsga2                , &
     & unsair_gam1(iip1,jjp1),unsair_gam2(iip1,jjp1)                  , &
     & unsairz_gam(iip1,jjm),aivscu2gam(iip1,jjm),aiuscv2gam(iip1,jjm)  &
     & , xprimu(iip1),xprimv(iip1)


      REAL                                                               &
     & cu,cv,unscu2,unscv2,aire,airesurg,aireu,airev,apoln,apols,unsaire &
     & ,unsairez,airuscv2,airvscu2,aireij1,aireij2,aireij3,aireij4     , &
     & alpha1,alpha2,alpha3,alpha4,alpha1p2,alpha1p4,alpha2p3,alpha3p4 , &
     & fext,constang,rlatu,rlatv,rlonu,rlonv,cuvscvgam1,cuvscvgam2     , &
     & cvuscugam1,cvuscugam2,cvscuvgam,cuscvugam,unsapolnga1           , &
     & unsapolnga2,unsapolsga1,unsapolsga2,unsair_gam1,unsair_gam2     , &
     & unsairz_gam,aivscu2gam,aiuscv2gam,cuvsurcv,cvsurcuv,cvusurcu    , &
     & cusurcvu,xprimu,xprimv

c   Arguments:
c   ----------
      INTEGER iq,nt
      REAL pbaru( ip1jmp1,llm ),pbarv( ip1jm,llm )
      REAL masse(iip1,jjp1,llm)
      REAL q( iip1,jjp1,llm,0:9)
      REAL w( ip1jmp1,llm )
      integer ordre,ilim

c   Local:
c   ------
      LOGICAL limit
      real zq(iip1,jjp1,llm)
      REAL sm ( iip1,jjp1, llm )
      REAL s0( iip1,jjp1,llm ),  sx( iip1,jjp1,llm )
      REAL sy( iip1,jjp1,llm ),  sz( iip1,jjp1,llm )
      REAL sxx( iip1,jjp1,llm)
      REAL sxy( iip1,jjp1,llm)
      REAL sxz( iip1,jjp1,llm)
      REAL syy( iip1,jjp1,llm )
      REAL syz( iip1,jjp1,llm )
      REAL szz( iip1,jjp1,llm ),zz
      INTEGER i,j,l,indice
      real sxn(iip1),sxs(iip1)

      real sinlon(iip1),sinlondlon(iip1)
      real coslon(iip1),coslondlon(iip1)
      real qmin,qmax
      save qmin,qmax
      save sinlon,coslon,sinlondlon,coslondlon
      real dyn1,dyn2,dys1,dys2,qpn,qps,dqzpn,dqzps
      real masn,mass
c
      REAL      SSUM
      integer ismax,ismin
      EXTERNAL  SSUM, convflu,ismin,ismax
      logical first
      save first
      EXTERNAL advxp,advyp,advzp 


      data first/.true./
      data qmin,qmax/-1.e33,1.e33/


c==========================================================================
c==========================================================================
c     MODIFICATION POUR PAS DE TEMPS ADAPTATIF, dtvr remplace par dt
c==========================================================================
c==========================================================================
      REAL dt
c==========================================================================
      limit = .TRUE.
 
      if(first) then
         print*,'SCHEMA PRATHER'
         first=.false.
         do i=2,iip1
            coslon(i)=cos(rlonv(i))
            sinlon(i)=sin(rlonv(i))
            coslondlon(i)=coslon(i)*(rlonu(i)-rlonu(i-1))/pi
            sinlondlon(i)=sinlon(i)*(rlonu(i)-rlonu(i-1))/pi
         enddo
         coslon(1)=coslon(iip1)
         coslondlon(1)=coslondlon(iip1)
         sinlon(1)=sinlon(iip1)
         sinlondlon(1)=sinlondlon(iip1)

        DO l = 1,llm
        DO j = 1,jjp1
        DO i = 1,iip1
        q( i,j,l,1 )=0.
        q( i,j,l,2)=0.
        q( i,j,l,3)=0.
        q( i,j,l,4)=0.
        q( i,j,l,5)=0.
        q( i,j,l,6)=0.
        q( i,j,l,7)=0.
        q( i,j,l,8)=0.
        q( i,j,l,9)=0.
        ENDDO
        ENDDO
        ENDDO
      endif
c   Fin modif Fred

c *** On calcule la masse d'air en kg

       DO l = 1,llm
        DO j = 1,jjp1
         DO i = 1,iip1
         sm( i,j,llm+1-l ) =masse(i,j,l)
         ENDDO
        ENDDO
       ENDDO

c *** q contient les qqtes de traceur avant l'advection 

c *** Affectation des tableaux S a partir de Q
 
       DO l = 1,llm
        DO j = 1,jjp1
         DO i = 1,iip1
       s0( i,j,l) = q ( i,j,llm+1-l,0 )*sm(i,j,l)
       sx( i,j,l) = q( i,j,llm+1-l,1 )*sm(i,j,l)
       sy( i,j,l) = q( i,j,llm+1-l,2)*sm(i,j,l)
       sz( i,j,l) = q( i,j,llm+1-l,3)*sm(i,j,l)
       sxx( i,j,l) = q( i,j,llm+1-l,4)*sm(i,j,l)
       sxy( i,j,l) = q( i,j,llm+1-l,5)*sm(i,j,l)
       sxz( i,j,l) = q( i,j,llm+1-l,6)*sm(i,j,l)
       syy( i,j,l) = q( i,j,llm+1-l,7)*sm(i,j,l)
       syz( i,j,l) = q( i,j,llm+1-l,8)*sm(i,j,l)
       szz( i,j,l) = q( i,j,llm+1-l,9)*sm(i,j,l)
         ENDDO
        ENDDO
       ENDDO
c *** Appel des subroutines d'advection en X, en Y et en Z
c *** Advection avec "time-splitting"
      
c-----------------------------------------------------------
       do indice =1,nt
       call advxp( limit,0.5*dt,pbaru,sm,s0,sx,sy,sz
     .             ,sxx,sxy,sxz,syy,syz,szz,1 )
        end do
        do l=1,llm
        do i=1,iip1
        sy(i,1,l)=0.
        sy(i,jjp1,l)=0.
        enddo
        enddo
c---------------------------------------------------------
       call advyp( limit,.5*dt*nt,pbarv,sm,s0,sx,sy,sz
     .             ,sxx,sxy,sxz,syy,syz,szz,1 )
c---------------------------------------------------------

c---------------------------------------------------------
       do j=1,jjp1
          do i=1,iip1
             sz(i,j,1)=0.
             sz(i,j,llm)=0.
             sxz(i,j,1)=0.
             sxz(i,j,llm)=0.
             syz(i,j,1)=0.
             syz(i,j,llm)=0.
             szz(i,j,1)=0.
             szz(i,j,llm)=0.
          enddo
       enddo
       call advzp( limit,dt*nt,w,sm,s0,sx,sy,sz 
     .             ,sxx,sxy,sxz,syy,syz,szz,1 )
        do l=1,llm
        do i=1,iip1
        sy(i,1,l)=0.
        sy(i,jjp1,l)=0.
        enddo
        enddo

c---------------------------------------------------------

c---------------------------------------------------------
       call advyp( limit,.5*dt*nt,pbarv,sm,s0,sx,sy,sz
     .             ,sxx,sxy,sxz,syy,syz,szz,1 )
c---------------------------------------------------------
       DO l = 1,llm
        DO j = 1,jjp1
             s0( iip1,j,l)=s0( 1,j,l )
             sx( iip1,j,l)=sx( 1,j,l )
             sy( iip1,j,l)=sy( 1,j,l )
             sz( iip1,j,l)=sz( 1,j,l )
             sxx( iip1,j,l)=sxx( 1,j,l )
             sxy( iip1,j,l)=sxy( 1,j,l) 
             sxz( iip1,j,l)=sxz( 1,j,l )
             syy( iip1,j,l)=syy( 1,j,l )
             syz( iip1,j,l)=syz( 1,j,l)
             szz( iip1,j,l)=szz( 1,j,l )
        ENDDO
       ENDDO
       do indice=1,nt
       call advxp( limit,0.5*dt,pbaru,sm,s0,sx,sy,sz
     .             ,sxx,sxy,sxz,syy,syz,szz,1 )
        end do
c---------------------------------------------------------
c---------------------------------------------------------
c ***   On repasse les S dans la variable qpr
c ***   On repasse les S dans la variable q directement 14/10/94

       DO  l = 1,llm
        DO  j = 1,jjp1
         DO  i = 1,iip1
      q( i,j,llm+1-l,0 )=s0( i,j,l )/sm(i,j,l)
      q( i,j,llm+1-l,1 ) = sx( i,j,l )/sm(i,j,l)
      q( i,j,llm+1-l,2 ) = sy( i,j,l )/sm(i,j,l)
      q( i,j,llm+1-l,3 ) = sz( i,j,l )/sm(i,j,l)
      q( i,j,llm+1-l,4 ) = sxx( i,j,l )/sm(i,j,l)
      q( i,j,llm+1-l,5 ) = sxy( i,j,l )/sm(i,j,l)
      q( i,j,llm+1-l,6 ) = sxz( i,j,l )/sm(i,j,l)
      q( i,j,llm+1-l,7 ) = syy( i,j,l )/sm(i,j,l)
      q( i,j,llm+1-l,8 ) = syz( i,j,l )/sm(i,j,l)
      q( i,j,llm+1-l,9 ) = szz( i,j,l )/sm(i,j,l)
      ENDDO
      ENDDO
      ENDDO

c---------------------------------------------------------
c      go to  777
c   filtrages aux poles

c Traitements specifiques au pole

c   filtrages aux poles
         DO l=1,llm
c   filtrages aux poles
         masn=ssum(iim,sm(1,1,l),1)
         mass=ssum(iim,sm(1,jjp1,l),1)
         qpn=ssum(iim,s0(1,1,l),1)/masn
         qps=ssum(iim,s0(1,jjp1,l),1)/mass
         dqzpn=ssum(iim,sz(1,1,l),1)/masn
         dqzps=ssum(iim,sz(1,jjp1,l),1)/mass
         do i=1,iip1
          q( i,1,llm+1-l,3)=dqzpn
          q( i,jjp1,llm+1-l,3)=dqzps
          q( i,1,llm+1-l,0)=qpn
          q( i,jjp1,llm+1-l,0)=qps
         enddo
c       enddo
c         print*,'qpn',qpn,'qps',qps
c          print*,'dqzpn',dqzpn,'dqzps',dqzps
c       enddo
           dyn1=0.
           dys1=0.
           dyn2=0.
           dys2=0.
        do i=1,iim
        zz=s0(i,2,l)/sm(i,2,l)-q(i,1,llm+1-l,0)
        dyn1=dyn1+sinlondlon(i)*zz
        dyn2=dyn2+coslondlon(i)*zz
        zz=q(i,jjp1,llm+1-l,0)-s0(i,jjm,l)/sm(i,jjm,l)
        dys1=dys1+sinlondlon(i)*zz
        dys2=dys2+coslondlon(i)*zz
        enddo
         do i=1,iim
         q(i,1,llm+1-l,2)=
     $   (sinlon(i)*dyn1+coslon(i)*dyn2)/2.
         q(i,1,llm+1-l,0)=q(i,1,llm+1-l,0)
     $          +q(i,1,llm+1-l,2)
         q(i,jjp1,llm+1-l,2)=
     $   (sinlon(i)*dys1+coslon(i)*dys2)/2.
         q(i,jjp1,llm+1-l,0)=q(i,jjp1,llm+1-l,0)
     $      -q(i,jjp1,llm+1-l,2)
         enddo
      q(iip1,1,llm+1-l,0)=q(1,1,llm+1-l,0)
      q(iip1,jjp1,llm+1-l,0)=q(1,jjp1,llm+1-l,0)
      do i=1,iim
      sxn(i)=q(i+1,1,llm+1-l,0)-q(i,1,llm+1-l,0)
      sxs(i)=q(i+1,jjp1,llm+1-l,0)-q(i,jjp1,llm+1-l,0)
      enddo
      sxn(iip1)=sxn(1)
      sxs(iip1)=sxs(1)
      do i=1,iim
      q(i+1,1,llm+1-l,1)=0.25*(sxn(i)+sxn(i+1))
      q(i+1,jjp1,llm+1-l,1)=0.25*(sxs(i)+sxs(i+1))
      END DO
      q(1,1,llm+1-l,1)=q(iip1,1,llm+1-l,1)
      q(1,jjp1,llm+1-l,1)=
     $   q(iip1,jjp1,llm+1-l,1)
        enddo
         do l=1,llm
           do i=1,iim
            q( i,1,llm+1-l,4)=0.
            q( i,jjp1,llm+1-l,4)=0.
            q( i,1,llm+1-l,5)=0.
            q( i,jjp1,llm+1-l,5)=0.
            q( i,1,llm+1-l,6)=0.
            q( i,jjp1,llm+1-l,6)=0.
            q( i,1,llm+1-l,7)=0.
            q( i,jjp1,llm+1-l,7)=0.
            q( i,1,llm+1-l,8)=0.
            q( i,jjp1,llm+1-l,8)=0.
            q( i,1,llm+1-l,9)=0.
            q( i,jjp1,llm+1-l,9)=0.
          enddo
         ENDDO

777      continue
c
c   bouclage en longitude
      do l=1,llm
      do j=1,jjp1
      q(iip1,j,l,0)=q(1,j,l,0)
      q(iip1,j,llm+1-l,0)=q(1,j,llm+1-l,0)
      q(iip1,j,llm+1-l,1)=q(1,j,llm+1-l,1)
      q(iip1,j,llm+1-l,2)=q(1,j,llm+1-l,2)
      q(iip1,j,llm+1-l,3)=q(1,j,llm+1-l,3)
      q(iip1,j,llm+1-l,4)=q(1,j,llm+1-l,4)
      q(iip1,j,llm+1-l,5)=q(1,j,llm+1-l,5)
      q(iip1,j,llm+1-l,6)=q(1,j,llm+1-l,6)
      q(iip1,j,llm+1-l,7)=q(1,j,llm+1-l,7)
      q(iip1,j,llm+1-l,8)=q(1,j,llm+1-l,8)
      q(iip1,j,llm+1-l,9)=q(1,j,llm+1-l,9)
      enddo
      enddo
        DO l = 1,llm
    	 DO j = 2,jjm
           DO i = 1,iip1
         IF (q(i,j,l,0).lt.0.)  THEN
         PRINT*,'------------ BIP-----------' 
         PRINT*,'S0(',i,j,l,')=',q(i,j,l,0),
     $          q(i,j-1,l,0)
         PRINT*,'SX(',i,j,l,')=',q(i,j,l,1)
         PRINT*,'SY(',i,j,l,')=',q(i,j,l,2),
     $   q(i,j-1,l,2)   
         PRINT*,'SZ(',i,j,l,')=',q(i,j,l,3)
c    		     PRINT*,' PBL EN SORTIE D'' ADVZP'
                     q(i,j,l,0)=0.
c                  STOP
               ENDIF
           ENDDO
         ENDDO
         do j=1,jjp1,jjm
         do i=1,iip1
               IF (q(i,j,l,0).lt.0.)  THEN
               PRINT*,'------------ BIP 2-----------'
         PRINT*,'S0(',i,j,l,')=',q(i,j,l,0)
         PRINT*,'SX(',i,j,l,')=',q(i,j,l,1)
         PRINT*,'SY(',i,j,l,')=',q(i,j,l,2)
         PRINT*,'SZ(',i,j,l,')=',q(i,j,l,3)

                     q(i,j,l,0)=0.
c                  STOP
               ENDIF
         enddo
         enddo
        ENDDO
      RETURN
      END