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  • !MNH_LIC Copyright 1994-2020 CNRS, Meteo-France and Universite Paul Sabatier
    !MNH_LIC This is part of the Meso-NH software governed by the CeCILL-C licence
    !MNH_LIC version 1. See LICENSE, CeCILL-C_V1-en.txt and CeCILL-C_V1-fr.txt
    !MNH_LIC for details. version 1.
    !-----------------------------------------------------------------
    !     ####################
          MODULE MODI_CONTRAV
    !     ####################
    !
    INTERFACE
    !
          SUBROUTINE CONTRAV(HLBCX,HLBCY,PRUT,PRVT,PRWT,PDXX,PDYY,PDZZ,PDZX,PDZY,  &
                             PRUCT,PRVCT,PRWCT,KADV_ORDER                       )
    !
    !
    CHARACTER (LEN=4), DIMENSION(2), INTENT(IN) :: HLBCX  ! X direction LBC type
    CHARACTER (LEN=4), DIMENSION(2), INTENT(IN) :: HLBCY  ! Y direction LBC type                         
    REAL, DIMENSION(:,:,:),  INTENT(IN)    ::  PRUT       ! Cartesian comp along x
    REAL, DIMENSION(:,:,:),  INTENT(IN)    ::  PRVT       ! Cartesian comp along y
    REAL, DIMENSION(:,:,:),  INTENT(IN)    ::  PRWT       ! Cartesian comp along z
    REAL, DIMENSION(:,:,:),  INTENT(IN)    ::  PDXX       ! Metric coefficients
    REAL, DIMENSION(:,:,:),  INTENT(IN)    ::  PDYY       ! Metric coefficients
    REAL, DIMENSION(:,:,:),  INTENT(IN)    ::  PDZZ       ! Metric coefficients
    REAL, DIMENSION(:,:,:),  INTENT(IN)    ::  PDZX       ! Metric coefficients
    REAL, DIMENSION(:,:,:),  INTENT(IN)    ::  PDZY       ! Metric coefficients
    REAL, DIMENSION(:,:,:),  INTENT(OUT)   ::  PRUCT      ! Contrav comp along x-bar
    REAL, DIMENSION(:,:,:),  INTENT(OUT)   ::  PRVCT      ! Contrav comp along y-bar
    REAL, DIMENSION(:,:,:),  INTENT(OUT)   ::  PRWCT      ! Contrav comp along z-bar
    INTEGER,                 INTENT(IN)    ::  KADV_ORDER ! Order of the advection scheme
    !
    END SUBROUTINE CONTRAV
    !
    #ifdef MNH_OPENACC
          SUBROUTINE CONTRAV_DEVICE(HLBCX,HLBCY,PRUT,PRVT,PRWT,PDXX,PDYY,PDZZ,PDZX,PDZY,  &
                             PRUCT,PRVCT,PRWCT,KADV_ORDER,Z1,Z2,ODATA_ON_DEVICE     )
    !
    !
    CHARACTER (LEN=4), DIMENSION(2), INTENT(IN) :: HLBCX  ! X direction LBC type
    CHARACTER (LEN=4), DIMENSION(2), INTENT(IN) :: HLBCY  ! Y direction LBC type
    REAL, DIMENSION(:,:,:),  INTENT(IN)    ::  PRUT       ! Cartesian comp along x
    REAL, DIMENSION(:,:,:),  INTENT(IN)    ::  PRVT       ! Cartesian comp along y
    REAL, DIMENSION(:,:,:),  INTENT(IN)    ::  PRWT       ! Cartesian comp along z
    REAL, DIMENSION(:,:,:),  INTENT(IN)    ::  PDXX       ! Metric coefficients
    REAL, DIMENSION(:,:,:),  INTENT(IN)    ::  PDYY       ! Metric coefficients
    REAL, DIMENSION(:,:,:),  INTENT(IN)    ::  PDZZ       ! Metric coefficients
    
    REAL, DIMENSION(:,:,:),  INTENT(INOUT) ::  PDZX       ! Metric coefficients
    REAL, DIMENSION(:,:,:),  INTENT(INOUT) ::  PDZY       ! Metric coefficients
    
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    REAL, DIMENSION(:,:,:),  INTENT(OUT)   ::  PRUCT      ! Contrav comp along x-bar
    REAL, DIMENSION(:,:,:),  INTENT(OUT)   ::  PRVCT      ! Contrav comp along y-bar
    REAL, DIMENSION(:,:,:),  INTENT(OUT)   ::  PRWCT      ! Contrav comp along z-bar
    INTEGER,                 INTENT(IN)    ::  KADV_ORDER ! Order of the advection scheme
    REAL, DIMENSION(:,:,:),  INTENT(OUT)   :: Z1,Z2       ! Work arrays
    LOGICAL, OPTIONAL,       INTENT(IN)    :: ODATA_ON_DEVICE ! Is some of the data on the accelerator device
    !
    !
    END SUBROUTINE CONTRAV_DEVICE
    #endif
    !
    END INTERFACE
    !
    END MODULE MODI_CONTRAV 
    !
    !
    !
    !     ##############################################################
          SUBROUTINE CONTRAV(HLBCX,HLBCY,PRUT,PRVT,PRWT,PDXX,PDYY,PDZZ,PDZX,PDZY,  &
                             PRUCT,PRVCT,PRWCT,KADV_ORDER                        )
    !     ##############################################################
    !
    !!****  *CONTRAV * - computes the contravariant components from the
    !!       cartesian components
    !!
    !!    PURPOSE
    !!    -------
    !       This routine computes the contravariant components of vector
    !     defined by its cartesian components (U,V,W) , using the following
    !     formulae:
    !     UC = U / DXX
    !     VC = V / DYY
    !               (     ----------x    ----------y )  
    !               (           ---z           ---z  )
    !           1   (            U              V    )
    !     WC = ---  ( W - DZX * ---    - DZY * ---   )
    !          DZZ  (           DXX            DYY   )
    !
    !  
    !       In the no-topography case, WC = W / DZZ
    !
    !
    !!**  METHOD
    !!    ------
    !!      We employ the Shuman operators to compute the averages. The metric
    !!    coefficients PDXX, PDYY, PDZX, PDZY, PDZZ are dummy arguments
    !!
    !!
    !!    EXTERNAL 
    !!    --------
    !!
    !!
    !!    IMPLICIT ARGUMENTS
    !!    ------------------
    !!
    !!      Module MODD_CONF   : contains configuration variable 
    !!           LFLAT : Logical for topography
    !!                  = .TRUE.  if Zs = 0 (Flat terrain)
    !!
    !!    REFERENCE
    !!    ---------
    !!      Book2 of documentation (subroutine CONTRAV)
    !!
    !!
    !!    AUTHOR
    !!    ------
    !!      J.L. Redelsperger     * CNRM *
    !!	J.-P. Pinty      * Laboratoire d'Aerologie*
    !!
    !!    MODIFICATIONS
    !!    -------------
    !!      Original   27/07/94
    !!      Corrections 3/08/94 (by J.P. Lafore)
    !!      Corrections 17/10/94 (by J.P. Lafore) WC modified for w-advection
    !!      Corrections 19/01/11 (by J.P. Pinty) WC 4th order
    !!      Corrections 28/03/11 (by V.Masson) // of WC 4th order
    !!      J.Escobar 21/03/2013: for HALOK comment all NHALO=1 test
    !  P. Wautelet 20/05/2019: add name argument to ADDnFIELD_ll + new ADD4DFIELD_ll subroutine
    !----------------------------------------------------------------------------
    !
    !*       0.    DECLARATIONS
    !              ------------
    USE MODD_CONF
    USE MODD_PARAMETERS
    USE MODD_GRID_n, ONLY: XZZ
    !
    USE MODD_ARGSLIST_ll, ONLY : HALO2LIST_ll
    USE MODE_ll
    !
    USE MODI_GET_HALO
    !
    USE MODE_MPPDB
    !
    IMPLICIT NONE
    !
    !*       0.1   declarations of arguments    
    !
    CHARACTER (LEN=4), DIMENSION(2), INTENT(IN) :: HLBCX ! X direction LBC type
    CHARACTER (LEN=4), DIMENSION(2), INTENT(IN) :: HLBCY ! Y direction LBC type
    !
    REAL, DIMENSION(:,:,:),  INTENT(IN)    ::  PRUT     ! Cartesian comp along x
    REAL, DIMENSION(:,:,:),  INTENT(IN)    ::  PRVT     ! Cartesian comp along y
    REAL, DIMENSION(:,:,:),  INTENT(IN)    ::  PRWT     ! Cartesian comp along z
    !
    REAL, DIMENSION(:,:,:),  INTENT(IN)    ::  PDXX     ! Metric coefficients
    REAL, DIMENSION(:,:,:),  INTENT(IN)    ::  PDYY     ! Metric coefficients
    REAL, DIMENSION(:,:,:),  INTENT(IN)    ::  PDZZ     ! Metric coefficients
    REAL, DIMENSION(:,:,:),  INTENT(IN)    ::  PDZX     ! Metric coefficients
    REAL, DIMENSION(:,:,:),  INTENT(IN)    ::  PDZY     ! Metric coefficients
    !
    !
    REAL, DIMENSION(:,:,:),  INTENT(OUT)   ::  PRUCT    ! Contrav comp along x-bar
    REAL, DIMENSION(:,:,:),  INTENT(OUT)   ::  PRVCT    ! Contrav comp along y-bar
    REAL, DIMENSION(:,:,:),  INTENT(OUT)   ::  PRWCT    ! Contrav comp along z-bar
    INTEGER,                 INTENT(IN)    ::  KADV_ORDER ! Order of the advection scheme
    !
    !
    !*       0.2   declarations of local variables
    !              
    REAL, DIMENSION(SIZE(PDXX,1),SIZE(PDXX,2),SIZE(PDXX,3)):: Z1,Z2
    INTEGER :: IIB,IIE,IJB,IJE,IKB,IKE
    INTEGER :: IIU, IJU, IKU
    INTEGER:: IW,IE,IS,IN   ! Coordinate of forth order diffusion area
    !
    TYPE(LIST_ll),      POINTER :: TZFIELD_U, TZFIELD_V, TZFIELD_DZX, TZFIELD_DZY
    TYPE(HALO2LIST_ll), POINTER :: TZHALO2_U, TZHALO2_V, TZHALO2_DZX, TZHALO2_DZY
    INTEGER                     :: IINFO_ll
    !-----------------------------------------------------------------------
    !
    !*       1.    Compute the horizontal contravariant components
    !              -----------------------------------------------
    !
    IF (MPPDB_INITIALIZED) THEN
      !Check all IN arrays
      CALL MPPDB_CHECK(PRUT,"CONTRAV beg:PRUT")
      CALL MPPDB_CHECK(PRVT,"CONTRAV beg:PRVT")
      CALL MPPDB_CHECK(PRWT,"CONTRAV beg:PRWT")
      CALL MPPDB_CHECK(PDXX,"CONTRAV beg:PDXX")
      CALL MPPDB_CHECK(PDYY,"CONTRAV beg:PDYY")
      CALL MPPDB_CHECK(PDZZ,"CONTRAV beg:PDZZ")
      CALL MPPDB_CHECK(PDZX,"CONTRAV beg:PDZX")
      CALL MPPDB_CHECK(PDZY,"CONTRAV beg:PDZY")
    END IF
    !
    IIU= SIZE(PDXX,1)
    IJU= SIZE(PDXX,2)
    IKU= SIZE(PDXX,3)
    !
    CALL GET_INDICE_ll( IIB,IJB,IIE,IJE)
    !
    IKB=1+JPVEXT
    IKE=IKU - JPVEXT
    !
    PRUCT(:,:,:) = PRUT(:,:,:) / PDXX(:,:,:)
    PRVCT(:,:,:) = PRVT(:,:,:) / PDYY(:,:,:)
    !
    IF (KADV_ORDER == 4 ) THEN
     IF( .NOT. LFLAT) THEN 
      NULLIFY(TZFIELD_U)
      NULLIFY(TZFIELD_V)
      CALL ADD3DFIELD_ll( TZFIELD_U, PRUCT, 'CONTRAV::PRUCT' )
      CALL ADD3DFIELD_ll( TZFIELD_V, PRVCT, 'CONTRAV::PRVCT' )
      CALL UPDATE_HALO_ll(TZFIELD_U,IINFO_ll)
      CALL UPDATE_HALO_ll(TZFIELD_V,IINFO_ll)
    !!$ IF( NHALO==1 ) THEN 
      NULLIFY(TZFIELD_DZX)
      NULLIFY(TZFIELD_DZY)
      CALL ADD3DFIELD_ll( TZFIELD_DZX, PDZX, 'CONTRAV::PDZX' )
      CALL ADD3DFIELD_ll( TZFIELD_DZY, PDZY, 'CONTRAV::PDZY' )
      NULLIFY(TZHALO2_U)
      NULLIFY(TZHALO2_V)
      NULLIFY(TZHALO2_DZX)
      NULLIFY(TZHALO2_DZY)
      CALL INIT_HALO2_ll(TZHALO2_U,1,IIU,IJU,IKU)
      CALL INIT_HALO2_ll(TZHALO2_V,1,IIU,IJU,IKU)
      CALL INIT_HALO2_ll(TZHALO2_DZX,1,IIU,IJU,IKU)
      CALL INIT_HALO2_ll(TZHALO2_DZY,1,IIU,IJU,IKU)
      CALL UPDATE_HALO2_ll(TZFIELD_U, TZHALO2_U, IINFO_ll)
      CALL UPDATE_HALO2_ll(TZFIELD_V, TZHALO2_V, IINFO_ll)
      CALL UPDATE_HALO2_ll(TZFIELD_DZX, TZHALO2_DZX, IINFO_ll)
      CALL UPDATE_HALO2_ll(TZFIELD_DZY, TZHALO2_DZY, IINFO_ll)
    !!$ END IF
     END IF
    END IF
    !
    !
    !*       2.    Compute the vertical contravariant components (flat case)
    !              ------------------------------------
    !
    IF (LFLAT) THEN
      PRWCT(:,:,:) = PRWT(:,:,:) / PDZZ(:,:,:)
      RETURN
    END IF
    !
    !*       3.    Compute the vertical contravariant components (general case)
    !              ------------------------------------
    !
    Z1 = 0.
    Z2 = 0.
    !
    IF (KADV_ORDER == 2 ) THEN
    !
      Z1(IIB:IIE,:,IKB:IKE+1)=                                             &
          (PRUCT(IIB:IIE,:,IKB:IKE+1)+PRUCT(IIB:IIE,:,IKB-1:IKE) )         &
           *PDZX(IIB:IIE,:,IKB:IKE+1) *0.25                                &
         +(PRUCT(IIB+1:IIE+1,:,IKB:IKE+1)+PRUCT(IIB+1:IIE+1,:,IKB-1:IKE) ) &
           *PDZX(IIB+1:IIE+1,:,IKB:IKE+1) *0.25   
                            
      Z2(:,IJB:IJE,IKB:IKE+1)=                                             &
          (PRVCT(:,IJB:IJE,IKB:IKE+1)+PRVCT(:,IJB:IJE,IKB-1:IKE) )         &
           *PDZY(:,IJB:IJE,IKB:IKE+1) *0.25                                &
         +(PRVCT(:,IJB+1:IJE+1,IKB:IKE+1)+PRVCT(:,IJB+1:IJE+1,IKB-1:IKE) ) &
           *PDZY(:,IJB+1:IJE+1,IKB:IKE+1) *0.25   
      PRWCT=0.             
      PRWCT(IIB:IIE,IJB:IJE,IKB:IKE+1) =                 &
          (   PRWT(IIB:IIE,IJB:IJE,IKB:IKE+1)            &
            - Z1(IIB:IIE,IJB:IJE,IKB:IKE+1)              &
            - Z2(IIB:IIE,IJB:IJE,IKB:IKE+1)              &
          ) / PDZZ(IIB:IIE,IJB:IJE,IKB:IKE+1)  
    !
    ELSE IF (KADV_ORDER == 4 ) THEN
    !
    !!$   IF (NHALO == 1) THEN
          IF ( LWEST_ll() .AND. HLBCX(1)/='CYCL' ) THEN
             IW=IIB+2 -1
          ELSE
             IW=IIB+1 -1
          END IF
          IE=IIE-1
    !!$   ELSE
    !!$      IF (LWEST_ll()) THEN
    !!$         IW=IIB+1
    !!$      ELSE
    !!$         IW=IIB
    !!$      END IF
    !!$      IF (LEAST_ll() .AND. HLBCX(2)/='CYCL' ) THEN
    !!$         IE=IIE-1
    !!$      ELSE
    !!$         IE=IIE
    !!$      END IF
    !!$   END IF
       !
    !!$   IF(NHALO == 1) THEN
          IF ( LSOUTH_ll() .AND. HLBCY(1)/='CYCL' ) THEN
             IS=IJB+2 -1
          ELSE
             IS=IJB+1 -1
          END IF
          IN=IJE-1
    !!$   ELSE
    !!$      IF (LSOUTH_ll()) THEN
    !!$         IS=IJB+1
    !!$      ELSE
    !!$         IS=IJB
    !!$      END IF
    !!$      IF (LNORTH_ll() .AND. HLBCY(2)/='CYCL' ) THEN
    !!$         IN=IJE-1
    !!$      ELSE
    !!$         IN=IJE
    !!$      END IF
    !!$   END IF
       !
       !
       !*       3.1    interior of the process subdomain
    !
    !
       Z1(IW:IE,:,IKB:IKE+1)=                                               &
           7.0*( (PRUCT(IW:IE,:,IKB:IKE+1)+PRUCT(IW:IE,:,IKB-1:IKE)) &
                *( 9.0*PDZX(IW:IE,:,IKB:IKE+1)-(PDZX(IW+1:IE+1,:,IKB:IKE+1) &
                      +PDZX(IW:IE,:,IKB:IKE+1)+PDZX(IW-1:IE-1,:,IKB:IKE+1))/3.0)/8.0 * 0.5 &
               +(PRUCT(IW+1:IE+1,:,IKB:IKE+1)+PRUCT(IW+1:IE+1,:,IKB-1:IKE)) &
                *( 9.0*PDZX(IW+1:IE+1,:,IKB:IKE+1)-(PDZX(IW+2:IE+2,:,IKB:IKE+1) &
                      +PDZX(IW+1:IE+1,:,IKB:IKE+1)+PDZX(IW:IE,:,IKB:IKE+1))/3.0)/8.0 * 0.5 )/12.0 &
              -( (PRUCT(IW-1:IE-1,:,IKB:IKE+1)+PRUCT(IW-1:IE-1,:,IKB-1:IKE)) &
                *PDZX(IW-1:IE-1,:,IKB:IKE+1) *0.5 &
                +(PRUCT(IW+2:IE+2,:,IKB:IKE+1)+PRUCT(IW+2:IE+2,:,IKB-1:IKE)) &
                *PDZX(IW+2:IE+2,:,IKB:IKE+1) *0.5)/12.0
    
    !
       Z2(:,IS:IN,IKB:IKE+1)=                                               &
           7.0*( (PRVCT(:,IS:IN,IKB:IKE+1)+PRVCT(:,IS:IN,IKB-1:IKE)) &
                *( 9.0*PDZY(:,IS:IN,IKB:IKE+1)-(PDZY(:,IS+1:IN+1,IKB:IKE+1) &
                      +PDZY(:,IS:IN,IKB:IKE+1)+PDZY(:,IS-1:IN-1,IKB:IKE+1))/3.0)/8.0 * 0.5 &
               +(PRVCT(:,IS+1:IN+1,IKB:IKE+1)+PRVCT(:,IS+1:IN+1,IKB-1:IKE)) &
                *( 9.0*PDZY(:,IS+1:IN+1,IKB:IKE+1)-(PDZY(:,IS+2:IN+2,IKB:IKE+1) &
                      +PDZY(:,IS+1:IN+1,IKB:IKE+1)+PDZY(:,IS:IN,IKB:IKE+1))/3.0)/8.0 * 0.5 )/12.0 &
              -( (PRVCT(:,IS-1:IN-1,IKB:IKE+1)+PRVCT(:,IS-1:IN-1,IKB-1:IKE)) &
                *PDZY(:,IS-1:IN-1,IKB:IKE+1) *0.5 &
                +(PRVCT(:,IS+2:IN+2,IKB:IKE+1)+PRVCT(:,IS+2:IN+2,IKB-1:IKE)) &
                *PDZY(:,IS+2:IN+2,IKB:IKE+1) *0.5)/12.0
    !
    !*       3.2    limits of the process subdomain (inside the whole domain or in cyclic conditions)
    !
    !!$  IF (NHALO==1) THEN
    
       Z1(IIE,:,IKB:IKE+1)=                                               &
           7.0*( (PRUCT(IIE,:,IKB:IKE+1)+PRUCT(IIE,:,IKB-1:IKE)) &
                *( 9.0*PDZX(IIE,:,IKB:IKE+1)-(PDZX(IIE+1,:,IKB:IKE+1) &
                      +PDZX(IIE,:,IKB:IKE+1)+PDZX(IIE-1,:,IKB:IKE+1))/3.0)/8.0 * 0.5 &
               +(PRUCT(IIE+1,:,IKB:IKE+1)+PRUCT(IIE+1,:,IKB-1:IKE)) &
                *( 9.0*PDZX(IIE+1,:,IKB:IKE+1)-(TZHALO2_DZX%HALO2%EAST(:,IKB:IKE+1) &
                      +PDZX(IIE+1,:,IKB:IKE+1)+PDZX(IIE,:,IKB:IKE+1))/3.0)/8.0 * 0.5 )/12.0 &
              -( (PRUCT(IIE-1,:,IKB:IKE+1)+PRUCT(IIE-1,:,IKB-1:IKE)) &
                *PDZX(IIE-1,:,IKB:IKE+1) *0.5 &
                +(TZHALO2_U%HALO2%EAST(:,IKB:IKE+1)+TZHALO2_U%HALO2%EAST(:,IKB-1:IKE)) &
                *TZHALO2_DZX%HALO2%EAST(:,IKB:IKE+1) *0.5)/12.0
    !
       Z2(:,IJE,IKB:IKE+1)=                                               &
           7.0*( (PRVCT(:,IJE,IKB:IKE+1)+PRVCT(:,IJE,IKB-1:IKE)) &
                *( 9.0*PDZY(:,IJE,IKB:IKE+1)-(PDZY(:,IJE+1,IKB:IKE+1) &
                      +PDZY(:,IJE,IKB:IKE+1)+PDZY(:,IJE-1,IKB:IKE+1))/3.0)/8.0 * 0.5 &
               +(PRVCT(:,IJE+1,IKB:IKE+1)+PRVCT(:,IJE+1,IKB-1:IKE)) &
                *( 9.0*PDZY(:,IJE+1,IKB:IKE+1)-(TZHALO2_DZY%HALO2%NORTH(:,IKB:IKE+1) &
                      +PDZY(:,IJE+1,IKB:IKE+1)+PDZY(:,IJE,IKB:IKE+1))/3.0)/8.0 * 0.5 )/12.0 &
              -( (PRVCT(:,IJE-1,IKB:IKE+1)+PRVCT(:,IJE-1,IKB-1:IKE)) &
                *PDZY(:,IJE-1,IKB:IKE+1) *0.5 &
                +(TZHALO2_V%HALO2%NORTH(:,IKB:IKE+1)+TZHALO2_V%HALO2%NORTH(:,IKB-1:IKE)) &
                *TZHALO2_DZY%HALO2%NORTH(:,IKB:IKE+1) *0.5)/12.0
    !!$  END IF
    !
    !*       3.3    non-CYCLIC CASE IN THE X DIRECTION: 2nd order case
    !
      IF (HLBCX(1)/='CYCL' .AND. LWEST_ll()) THEN
    !
       Z1(IIB,:,IKB:IKE+1)=                                     &
           (PRUCT(IIB,:,IKB:IKE+1)+PRUCT(IIB,:,IKB-1:IKE) )     &
            *PDZX(IIB,:,IKB:IKE+1) *0.25                        &
          +(PRUCT(IIB+1,:,IKB:IKE+1)+PRUCT(IIB+1,:,IKB-1:IKE) ) &
            *PDZX(IIB+1,:,IKB:IKE+1) *0.25   
      END IF
    !
      IF (HLBCX(2)/='CYCL' .AND. LEAST_ll()) THEN
    !
       Z1(IIE,:,IKB:IKE+1)=                                     &
           (PRUCT(IIE,:,IKB:IKE+1)+PRUCT(IIE,:,IKB-1:IKE) )     &
            *PDZX(IIE,:,IKB:IKE+1) *0.25                        &
          +(PRUCT(IIE+1,:,IKB:IKE+1)+PRUCT(IIE+1,:,IKB-1:IKE) ) &
            *PDZX(IIE+1,:,IKB:IKE+1) *0.25   
      END IF
    !
    !*       3.4    non-CYCLIC CASE IN THE Y DIRECTION: 2nd order case
    !
      IF (HLBCY(1)/='CYCL' .AND. LSOUTH_ll()) THEN
    !
       Z2(:,IJB,IKB:IKE+1)=                                     &
           (PRVCT(:,IJB,IKB:IKE+1)+PRVCT(:,IJB,IKB-1:IKE) )     &
            *PDZY(:,IJB,IKB:IKE+1) *0.25                        &
          +(PRVCT(:,IJB+1,IKB:IKE+1)+PRVCT(:,IJB+1,IKB-1:IKE) ) &
            *PDZY(:,IJB+1,IKB:IKE+1) *0.25   
    !
      END IF
    !
      IF (HLBCY(2)/='CYCL' .AND. LNORTH_ll()) THEN
    !
       Z2(:,IJE,IKB:IKE+1)=                                     &
           (PRVCT(:,IJE,IKB:IKE+1)+PRVCT(:,IJE,IKB-1:IKE) )     &
            *PDZY(:,IJE,IKB:IKE+1) *0.25                        &
          +(PRVCT(:,IJE+1,IKB:IKE+1)+PRVCT(:,IJE+1,IKB-1:IKE) ) &
            *PDZY(:,IJE+1,IKB:IKE+1) *0.25   
    !
      END IF
    !
    !*       3.5    Vertical contyravariant wind
    !
    !
    !!$  CALL GET_HALO(Z1)
    !!$  CALL GET_HALO(Z2)
    !!$
    !!$  CALL MPPDB_CHECK3DM("contrav ::Z1/Z2/ PDZZ",PRECISION,Z1,Z2,PDZZ)                    
      PRWCT=0.             
      PRWCT(IIB:IIE,IJB:IJE,IKB:IKE+1) =                 &
         (   PRWT(IIB:IIE,IJB:IJE,IKB:IKE+1)            &
           - Z1(IIB:IIE,IJB:IJE,IKB:IKE+1)              &
           - Z2(IIB:IIE,IJB:IJE,IKB:IKE+1)              &
         ) / PDZZ(IIB:IIE,IJB:IJE,IKB:IKE+1)  
    !
    END IF
    !
    PRWCT(:,:,1) = - PRWCT(:,:,3)     ! Mirror hypothesis
    !
    IF (KADV_ORDER == 4 ) THEN
      CALL CLEANLIST_ll(TZFIELD_U)
      CALL CLEANLIST_ll(TZFIELD_V)
    !!$  IF (NHALO==1) THEN
        CALL CLEANLIST_ll(TZFIELD_DZX)
        CALL CLEANLIST_ll(TZFIELD_DZY)
        CALL DEL_HALO2_ll(TZHALO2_U)
        CALL DEL_HALO2_ll(TZHALO2_V)
        CALL DEL_HALO2_ll(TZHALO2_DZX)
        CALL DEL_HALO2_ll(TZHALO2_DZY)
    !!$  END IF
    END IF
    !-----------------------------------------------------------------------
    IF (MPPDB_INITIALIZED) THEN
      !Check all OUT arrays
      CALL MPPDB_CHECK(PRUCT,"CONTRAV end:PRUCT")
      CALL MPPDB_CHECK(PRVCT,"CONTRAV end:PRVCT")
      CALL MPPDB_CHECK(PRWCT,"CONTRAV end:PRWCT")
    END IF
    !
    END SUBROUTINE CONTRAV
    !
    #ifdef MNH_OPENACC
    !     ##############################################################
          SUBROUTINE CONTRAV_DEVICE(HLBCX,HLBCY,PRUT,PRVT,PRWT,PDXX,PDYY,PDZZ,PDZX,PDZY,  &
                             PRUCT,PRVCT,PRWCT,KADV_ORDER,Z1,Z2,ODATA_ON_DEVICE     )
    !     ##############################################################
    !
    !!****  *CONTRAV * - computes the contravariant components from the
    !!       cartesian components
    !!
    !!    PURPOSE
    !!    -------
    !       This routine computes the contravariant components of vector
    !     defined by its cartesian components (U,V,W) , using the following
    !     formulae:
    !     UC = U / DXX
    !     VC = V / DYY
    !               (     ----------x    ----------y )  
    !               (           ---z           ---z  )
    !           1   (            U              V    )
    !     WC = ---  ( W - DZX * ---    - DZY * ---   )
    !          DZZ  (           DXX            DYY   )
    !
    !  
    !       In the no-topography case, WC = W / DZZ
    !
    !
    !!**  METHOD
    !!    ------
    !!      We employ the Shuman operators to compute the averages. The metric
    !!    coefficients PDXX, PDYY, PDZX, PDZY, PDZZ are dummy arguments
    !!
    !!
    !!    EXTERNAL 
    !!    --------
    !!      MXF, MYF, MZM         : Shuman functions (mean operators)
    !!       
    !!      Module MODI_SHUMAN    : Interface for Shuman functions   
    !!
    !!
    !!    IMPLICIT ARGUMENTS
    !!    ------------------
    !!
    !!      Module MODD_CONF   : contains configuration variable 
    !!           LFLAT : Logical for topography
    !!                  = .TRUE.  if Zs = 0 (Flat terrain)
    !!
    !!    REFERENCE
    !!    ---------
    !!      Book2 of documentation (subroutine CONTRAV)
    !!
    !!
    !!    AUTHOR
    !!    ------
    !!      J.L. Redelsperger     * CNRM *
    !!	J.-P. Pinty      * Laboratoire d'Aerologie*
    !!
    !!    MODIFICATIONS
    !!    -------------
    !!      Original   27/07/94
    !!      Corrections 3/08/94 (by J.P. Lafore)
    !!      Corrections 17/10/94 (by J.P. Lafore) WC modified for w-advection
    !!      Corrections 19/01/11 (by J.P. Pinty) WC 4th order
    !!      Corrections 28/03/11 (by V.Masson) // of WC 4th order
    !!      J.Escobar 21/03/2013: for HALOK comment all NHALO=1 test
    !  P. Wautelet 26/06/2019: optimisation for GPU + improve readability
    !----------------------------------------------------------------------------
    !
    !*       0.    DECLARATIONS
    !              ------------
    USE MODD_ARGSLIST_ll, ONLY: HALO2LIST_ll
    USE MODD_CONF
    USE MODD_GRID_n,      ONLY: XZZ
    USE MODD_PARAMETERS
    !
    USE MODE_ll
    USE MODE_MPPDB
    #ifdef MNH_OPENACC
    use mode_msg
    #endif
    !
    USE MODI_GET_HALO
    USE MODI_SHUMAN
    !
    IMPLICIT NONE
    !
    !*       0.1   declarations of arguments    
    !
    CHARACTER (LEN=4), DIMENSION(2), INTENT(IN) :: HLBCX ! X direction LBC type
    CHARACTER (LEN=4), DIMENSION(2), INTENT(IN) :: HLBCY ! Y direction LBC type
    !
    REAL, DIMENSION(:,:,:),  INTENT(IN)    ::  PRUT     ! Cartesian comp along x
    REAL, DIMENSION(:,:,:),  INTENT(IN)    ::  PRVT     ! Cartesian comp along y
    REAL, DIMENSION(:,:,:),  INTENT(IN)    ::  PRWT     ! Cartesian comp along z
    !
    REAL, DIMENSION(:,:,:),  INTENT(IN)    ::  PDXX     ! Metric coefficients
    REAL, DIMENSION(:,:,:),  INTENT(IN)    ::  PDYY     ! Metric coefficients
    REAL, DIMENSION(:,:,:),  INTENT(IN)    ::  PDZZ     ! Metric coefficients
    
    REAL, DIMENSION(:,:,:),  INTENT(INOUT) ::  PDZX     ! Metric coefficients
    REAL, DIMENSION(:,:,:),  INTENT(INOUT) ::  PDZY     ! Metric coefficients
    
    !
    !
    REAL, DIMENSION(:,:,:),  INTENT(OUT)   ::  PRUCT    ! Contrav comp along x-bar
    REAL, DIMENSION(:,:,:),  INTENT(OUT)   ::  PRVCT    ! Contrav comp along y-bar
    REAL, DIMENSION(:,:,:),  INTENT(OUT)   ::  PRWCT    ! Contrav comp along z-bar
    INTEGER,                 INTENT(IN)    ::  KADV_ORDER ! Order of the advection scheme
    REAL, DIMENSION(:,:,:),  INTENT(OUT)   :: Z1,Z2       ! Work arrays
    LOGICAL,   OPTIONAL,     INTENT(IN)    :: ODATA_ON_DEVICE ! Is some of the data on the accelerator device
    !
    !
    !*       0.2   declarations of local variables
    !
    integer                             :: ji, jj, jk
    INTEGER                             :: IIB, IIE, IJB, IJE, IKB, IKE
    INTEGER                             :: IIU, IJU, IKU
    INTEGER                             :: IW, IE, IS, IN   ! Coordinate of fourth order diffusion area
    INTEGER                             :: IINFO_ll
    LOGICAL                             :: GDATA_ON_DEVICE
    real                                :: ZTMP1, ZTMP2 ! Intermediate work variables
    REAL,   DIMENSION(:,:), POINTER , CONTIGUOUS :: ZU_EAST, ZV_NORTH, ZDZX_EAST, ZDZY_NORTH
    TYPE(LIST_ll),          POINTER     :: TZFIELD_U, TZFIELD_V, TZFIELD_DZX, TZFIELD_DZY
    
    TYPE(HALO2LIST_ll), SAVE, POINTER  :: TZHALO2_U, TZHALO2_V, TZHALO2_DZX, TZHALO2_DZY
    LOGICAL , SAVE :: GFIRST_CALL_CONTRAV_DEVICE = .TRUE.
    
    !$acc data present( PRUT, PRVT, PRWT, PDXX, PDYY, PDZZ, PDZX, PDZY, PRUCT, PRVCT, PRWCT, Z1, Z2 )
    
    IF ( PRESENT(ODATA_ON_DEVICE) ) THEN
      GDATA_ON_DEVICE = ODATA_ON_DEVICE
    ELSE
      GDATA_ON_DEVICE = .FALSE.
    END IF
    !-----------------------------------------------------------------------
    !
    !*       1.    Compute the horizontal contravariant components
    !              -----------------------------------------------
    !
    IF (MPPDB_INITIALIZED) THEN
      !Check all IN arrays
      CALL MPPDB_CHECK(PRUT,"CONTRAV beg:PRUT")
      CALL MPPDB_CHECK(PRVT,"CONTRAV beg:PRVT")
      CALL MPPDB_CHECK(PRWT,"CONTRAV beg:PRWT")
      CALL MPPDB_CHECK(PDXX,"CONTRAV beg:PDXX")
      CALL MPPDB_CHECK(PDYY,"CONTRAV beg:PDYY")
      CALL MPPDB_CHECK(PDZZ,"CONTRAV beg:PDZZ")
      CALL MPPDB_CHECK(PDZX,"CONTRAV beg:PDZX")
      CALL MPPDB_CHECK(PDZY,"CONTRAV beg:PDZY")
    END IF
    !
    IIU= SIZE(PDXX,1)
    IJU= SIZE(PDXX,2)
    IKU= SIZE(PDXX,3)
    !
    
    GWEST  = ( HLBCX(1) /= 'CYCL' .AND. LWEST_ll() )
    GEAST  = ( HLBCX(2) /= 'CYCL' .AND. LEAST_ll() )
    GSOUTH = ( HLBCY(1) /= 'CYCL' .AND. LSOUTH_ll() )
    GNORTH = ( HLBCY(2) /= 'CYCL' .AND. LNORTH_ll() )
    !
    
    CALL GET_INDICE_ll( IIB,IJB,IIE,IJE)
    !
    IKB=1+JPVEXT
    IKE=IKU - JPVEXT
    !
    IF (GDATA_ON_DEVICE) THEN
    !PW TODO:remplacer (ailleurs aussi...) 1/PDXX... par PINV_PDXX (fait pour la turbulence...) cfr MNH/turb_hor_splt.f90
    !$acc kernels
      PRUCT(:,:,:) = PRUT(:,:,:) / PDXX(:,:,:)
      PRVCT(:,:,:) = PRVT(:,:,:) / PDYY(:,:,:)
    !$acc end kernels
    !$acc update self(PRUCT,PRVCT)
    ELSE
      PRUCT(:,:,:) = PRUT(:,:,:) / PDXX(:,:,:)
      PRVCT(:,:,:) = PRVT(:,:,:) / PDYY(:,:,:)
    END IF
    !
    IF (KADV_ORDER == 4 ) THEN
     IF( .NOT. LFLAT) THEN 
    !!$  NULLIFY(TZFIELD_U)
    !!$  NULLIFY(TZFIELD_V)
    !!$  CALL ADD3DFIELD_ll( TZFIELD_U, PRUCT, 'CONTRAV::PRUCT' )
    !!$  CALL ADD3DFIELD_ll( TZFIELD_V, PRVCT, 'CONTRAV::PRVCT' )
    !!$  CALL UPDATE_HALO_ll(TZFIELD_U,IINFO_ll)
    !!$  CALL UPDATE_HALO_ll(TZFIELD_V,IINFO_ll)
    !!$ !!$ IF( NHALO==1 ) THEN 
    !!$  NULLIFY(TZFIELD_DZX)
    !!$  NULLIFY(TZFIELD_DZY)
    !!$  CALL ADD3DFIELD_ll( TZFIELD_DZX, PDZX, 'CONTRAV::PDZX' )
    !!$  CALL ADD3DFIELD_ll( TZFIELD_DZY, PDZY, 'CONTRAV::PDZY' )
    
        IF ( GFIRST_CALL_CONTRAV_DEVICE ) THEN
           GFIRST_CALL_CONTRAV_DEVICE = .FALSE.
           NULLIFY(TZHALO2_U)
           NULLIFY(TZHALO2_V)
           NULLIFY(TZHALO2_DZX)
           NULLIFY(TZHALO2_DZY)
           CALL INIT_HALO2_ll(TZHALO2_U,1,IIU,IJU,IKU)
           CALL INIT_HALO2_ll(TZHALO2_V,1,IIU,IJU,IKU)
           CALL INIT_HALO2_ll(TZHALO2_DZX,1,IIU,IJU,IKU)
           CALL INIT_HALO2_ll(TZHALO2_DZY,1,IIU,IJU,IKU)
        END IF
    
    !!$  CALL UPDATE_HALO2_ll(TZFIELD_U, TZHALO2_U, IINFO_ll)
    !!$  CALL UPDATE_HALO2_ll(TZFIELD_V, TZHALO2_V, IINFO_ll)
    !!$  CALL UPDATE_HALO2_ll(TZFIELD_DZX, TZHALO2_DZX, IINFO_ll)
    !!$  CALL UPDATE_HALO2_ll(TZFIELD_DZY, TZHALO2_DZY, IINFO_ll)
      !
    
      CALL GET_HALO2_DF(PRUCT,TZHALO2_U,'CONTRAV::PRUCT')
      CALL GET_HALO2_DF(PRVCT,TZHALO2_V,'CONTRAV::PRVCT')
      CALL GET_HALO2_DF(PDZX,TZHALO2_DZX,'CONTRAV::PDZX')
      CALL GET_HALO2_DF(PDZY,TZHALO2_DZY,'CONTRAV::PDZY')
    
      
    !!$!$acc update device(PRUCT,PRVCT)
    !!$ !!$ END IF
    !
      !PW: necessary because pointers does not work with OpenACC (PGI 16.1)
    !!$  ALLOCATE(ZU_EAST(IJU,IKU),ZV_NORTH(IIU,IKU),ZDZX_EAST(IJU,IKU),ZDZY_NORTH(IIU,IKU))
    !!$  !$acc enter data create( zu_east, zv_north, zdzx_east, zdzy_north )
    !!$  !$acc kernels
      ZU_EAST => TZHALO2_U%HALO2%EAST
      ZDZX_EAST => TZHALO2_DZX%HALO2%EAST
      ZV_NORTH => TZHALO2_V%HALO2%NORTH
      ZDZY_NORTH => TZHALO2_DZY%HALO2%NORTH
    !!$  !$acc end kernels
    !!$!$acc update device(ZU_EAST,ZV_NORTH,ZDZX_EAST,ZDZY_NORTH)
     END IF
    END IF
    !
    !
    !*       2.    Compute the vertical contravariant components (flat case)
    !              ------------------------------------
    !
    FLAT: IF (LFLAT) THEN
      IF (GDATA_ON_DEVICE) THEN
    !$acc kernels
        PRWCT(:,:,:) = PRWT(:,:,:) / PDZZ(:,:,:)
    !$acc end kernels
    !$acc update self(PRWCT)
      ELSE
        PRWCT(:,:,:) = PRWT(:,:,:) / PDZZ(:,:,:)
      END IF
    ELSE
    !
    !*       3.    Compute the vertical contravariant components (general case)
    !              ------------------------------------
    !
    ! Z1(:,:,:) = 0.
    
    !
    IF (KADV_ORDER == 2 ) THEN
    #ifdef MNH_OPENACC
      call Print_msg( NVERB_WARNING, 'GEN', 'CONTRAV', 'OpenACC: KADV_ORDER=2 and LFLAT=.TRUE. not yet tested' )
    #endif
    
      do concurrent (ji=iib:iie,jj=1:iju,jk=ikb:ike+1)
         Z1(ji, jj, jk ) =   ( PRUCT(ji,     jj, jk ) + PRUCT(ji,     jj, jk - 1 ) ) * PDZX (ji,     jj, jk ) * 0.25 &
                           + ( PRUCT(ji + 1, jj, jk ) + PRUCT(ji + 1, jj, jk - 1 ) ) * PDZX (ji + 1, jj, jk ) * 0.25
    
      do concurrent (ji=1:iiu,jj=ijb:ije,jk=ikb:ike+1)
         Z2(ji, jj, jk ) =   ( PRVCT(ji, jj,     jk) + PRVCT( ji, jj,    jk - 1) ) * PDZY(ji, jj,     jk) * 0.25 &
                           + ( PRVCT(ji, jj + 1, jk) + PRVCT( ji, jj + 1,jk - 1) ) * PDZY(ji, jj + 1, jk) * 0.25
    
      do concurrent (ji=iib:iie,jj=ijb:ije,jk=ikb:ike+1)
         PRWCT(ji ,jj, jk ) = ( PRWT(ji ,jj, jk ) - Z1(ji ,jj, jk ) - Z2(ji ,jj, jk ) ) / PDZZ(ji ,jj, jk )
    
    ELSE IF (KADV_ORDER == 4 ) THEN
    !
    !!$   IF (NHALO == 1) THEN
    
             IW=IIB+2 -1
          ELSE
             IW=IIB+1 -1
          END IF
          IE=IIE-1
    !!$   ELSE
    !!$      IF (LWEST_ll()) THEN
    !!$         IW=IIB+1
    !!$      ELSE
    !!$         IW=IIB
    !!$      END IF
    !!$      IF (LEAST_ll() .AND. HLBCX(2)/='CYCL' ) THEN
    !!$         IE=IIE-1
    !!$      ELSE
    !!$         IE=IIE
    !!$      END IF
    !!$   END IF
       !
    !!$   IF(NHALO == 1) THEN
    
             IS=IJB+2 -1
          ELSE
             IS=IJB+1 -1
          END IF
          IN=IJE-1
    !!$   ELSE
    !!$      IF (LSOUTH_ll()) THEN
    !!$         IS=IJB+1
    !!$      ELSE
    !!$         IS=IJB
    !!$      END IF
    !!$      IF (LNORTH_ll() .AND. HLBCY(2)/='CYCL' ) THEN
    !!$         IN=IJE-1
    !!$      ELSE
    !!$         IN=IJE
    !!$      END IF
    !!$   END IF
       !
       !
       !*       3.1    interior of the process subdomain
    
    !
    !
    !PW: OpenACC remarks: *computing only ztmp2 and reusing it at next iteration works
    !                      but ji loop can not be collapsed -> 10x slower on GPU
    !                     *ztmp1 and ztmp2 are not necessary but improve readability (no impact on performance)
    !$acc loop independent collapse(3) private(ztmp1, ztmp2)
    
      do concurrent(ji=IW:IE,jj=1:iju,jk=IKB:IKE+1)
    
            ztmp1 = ( 9.0 * PDZX(ji,   jj, jk ) - ( PDZX(ji+1, jj, jk ) + PDZX(ji,   jj, jk ) + PDZX(ji-1, jj, jk ) ) / 3.0 ) / 16.0
            ztmp2 = ( 9.0 * PDZX(ji+1, jj, jk ) - ( PDZX(ji+2, jj, jk ) + PDZX(ji+1, jj, jk ) + PDZX(ji,   jj, jk ) ) / 3.0 ) / 16.0
            Z1(ji, jj, jk ) =  7.0 * (  ( PRUCT(ji,   jj, jk ) + PRUCT(ji,   jj, jk-1 ) ) * ztmp1                        &
                                      + ( PRUCT(ji+1, jj, jk ) + PRUCT(ji+1, jj, jk-1 ) ) * ztmp2               ) / 12.0 &
                             - 0.5 * (  ( PRUCT(ji-1, jj, jk ) + PRUCT(ji-1, jj, jk-1 ) ) * PDZX(ji-1, jj, jk)           &
                                      + ( PRUCT(ji+2, jj, jk ) + PRUCT(ji+2, jj, jk-1 ) ) * PDZX(ji+2, jj, jk)  ) / 12.0
      end do
    !
    !$acc loop independent collapse(3)
    
      do concurrent(ji=1:iiu,jj=is:in,jk=IKB:IKE+1)
    
            ztmp1 = ( 9.0 * PDZY(ji, jj,   jk ) - ( PDZY(ji, jj+1, jk ) + PDZY(ji, jj,   jk ) + PDZY(ji, jj-1, jk ) ) / 3.0 ) / 16.0
            ztmp2 = ( 9.0 * PDZY(ji, jj+1, jk ) - ( PDZY(ji, jj+2, jk ) + PDZY(ji, jj+1, jk ) + PDZY(ji, jj,   jk ) ) / 3.0 ) / 16.0
            Z2(ji, jj, jk ) =  7.0 * (  ( PRVCT(ji, jj,   jk ) + PRVCT(ji, jj,   jk-1 ) ) * ztmp1                         &
                                      + ( PRVCT(ji, jj+1, jk ) + PRVCT(ji, jj+1, jk-1 ) ) * ztmp2                ) / 12.0 &
                             - 0.5 * (  ( PRVCT(ji, jj-1, jk ) + PRVCT(ji, jj-1, jk-1 ) ) * PDZY(ji, jj-1, jk )           &
                                      + ( PRVCT(ji, jj+2, jk ) + PRVCT(ji, jj+2, jk-1 ) ) * PDZY(ji, jj+2, jk )  ) / 12.0
      end do
    
    !
    !*       3.2    limits of the process subdomain (inside the whole domain or in cyclic conditions)
    !
    !!$  IF (NHALO==1) THEN
    
    !$acc parallel loop independent collapse(2) async
        do concurrent(jj=1:iju,jk=IKB:IKE+1)
    
          ztmp1 = ( 9.0 * PDZX(IIE,   jj, jk ) - ( PDZX(IIE+1, jj, jk ) + PDZX(IIE,   jj, jk ) + PDZX(IIE-1, jj, jk ) ) / 3.0 ) / 16.0
          ztmp2 = ( 9.0 * PDZX(IIE+1, jj, jk ) - ( ZDZX_EAST(jj, jk )   + PDZX(IIE+1, jj, jk ) + PDZX(IIE,   jj, jk ) ) / 3.0 ) / 16.0
          Z1(IIE, jj, jk ) =  7.0 * (  ( PRUCT(IIE,   jj, jk ) + PRUCT(IIE,   jj, jk-1 ) ) * ztmp1                        &
                                     + ( PRUCT(IIE+1, jj, jk ) + PRUCT(IIE+1, jj, jk-1 ) ) * ztmp2               ) / 12.0 &
                            - 0.5 * (  ( PRUCT(IIE-1, jj, jk ) + PRUCT(IIE-1, jj, jk-1 ) ) * PDZX(IIE-1, jj, jk)          &
                                     + ( ZU_EAST     (jj, jk ) + ZU_EAST     (jj, jk-1 ) ) * ZDZX_EAST  (jj, jk)  ) / 12.0
        end do
    !
    
    !$acc parallel loop independent collapse(2) async
        do concurrent(ji=1:iiu,jk=IKB:IKE+1)
    
          ztmp1 = ( 9.0 * PDZY(ji, IJE,   jk) - ( PDZY      (ji, IJE+1, jk) + PDZY(ji, IJE,   jk) + PDZY(ji, IJE-1, jk) ) / 3.0 ) / 16.0
          ztmp2 = ( 9.0 * PDZY(ji, IJE+1, jk) - ( ZDZY_NORTH(ji,        jk) + PDZY(ji, IJE+1, jk) + PDZY(ji, IJE,   jk) ) / 3.0 ) / 16.0
          Z2(ji, IJE, jk ) =  7.0 * (  ( PRVCT   (ji, IJE,   jk ) + PRVCT   (ji, IJE,   jk-1 ) ) * ztmp1                               &
                                     + ( PRVCT   (ji, IJE+1, jk ) + PRVCT   (ji, IJE+1, jk-1 ) ) * ztmp2                      ) / 12.0 &
                            - 0.5 * (  ( PRVCT   (ji, IJE-1, jk ) + PRVCT   (ji, IJE-1, jk-1 ) ) * PDZY      (ji, IJE-1, jk )          &
                                     + ( ZV_NORTH(ji,        jk ) + ZV_NORTH(ji,        jk-1 ) ) * ZDZY_NORTH(ji,        jk ) ) / 12.0
    
    !!$  END IF
    !
    !*       3.3    non-CYCLIC CASE IN THE X DIRECTION: 2nd order case
    !
    
        Z1(IIB, :, IKB:IKE+1 ) =  ( PRUCT(IIB,   :, IKB:IKE+1 ) + PRUCT(IIB,   :, IKB-1:IKE ) ) * PDZX(IIB,   :, IKB:IKE+1 ) * 0.25 &
                                + ( PRUCT(IIB+1, :, IKB:IKE+1 ) + PRUCT(IIB+1, :, IKB-1:IKE ) ) * PDZX(IIB+1, :, IKB:IKE+1 ) * 0.25
    
        Z1(IIE, :, IKB:IKE+1 ) =  ( PRUCT(IIE,   :, IKB:IKE+1 ) + PRUCT(IIE,   :, IKB-1:IKE ) ) * PDZX(IIE,   :, IKB:IKE+1 ) * 0.25 &
                                + ( PRUCT(IIE+1, :, IKB:IKE+1 ) + PRUCT(IIE+1, :, IKB-1:IKE ) ) * PDZX(IIE+1, :, IKB:IKE+1 ) * 0.25
    
    !
    !*       3.4    non-CYCLIC CASE IN THE Y DIRECTION: 2nd order case
    !
    
        Z2(:, IJB, IKB:IKE+1 ) =  ( PRVCT(:, IJB,   IKB:IKE+1 ) + PRVCT(:, IJB,   IKB-1:IKE ) ) * PDZY(:, IJB,   IKB:IKE+1 ) * 0.25 &
                                + ( PRVCT(:, IJB+1, IKB:IKE+1 ) + PRVCT(:, IJB+1, IKB-1:IKE ) ) * PDZY(:, IJB+1, IKB:IKE+1 ) * 0.25
    
        Z2(:, IJE, IKB:IKE+1 ) =  ( PRVCT(:, IJE,   IKB:IKE+1 ) + PRVCT(:, IJE,   IKB-1:IKE ) ) * PDZY(:, IJE,   IKB:IKE+1 ) * 0.25 &
                                + ( PRVCT(:, IJE+1, IKB:IKE+1 ) + PRVCT(:, IJE+1, IKB-1:IKE ) ) * PDZY(:, IJE+1, IKB:IKE+1 ) * 0.25
    
    !!$  CALL GET_HALO(Z1)
    !!$  CALL GET_HALO(Z2)
    !!$
    !!$  CALL MPPDB_CHECK3DM("contrav_device ::Z1/Z2/ PDZZ",PRECISION,Z1,Z2,PDZZ)
      PRWCT(:,:,:)=0.
    !$acc loop independent collapse(3)
    
      do concurrent (ji=iib:iie,jj=ijb:ije,jk=ikb:ike+1)
    
            PRWCT(ji ,jj, jk ) = ( PRWT(ji ,jj, jk ) - Z1(ji ,jj, jk ) - Z2(ji ,jj, jk ) ) / PDZZ(ji ,jj, jk )
      end do
    
    PRWCT(:,:,1) = - PRWCT(:,:,3)     ! Mirror hypothesis
    !$acc end kernels
    !$acc update self(PRWCT)
    !
    IF (KADV_ORDER == 4 ) THEN
    !!$!$acc exit data delete( zu_east, zv_north, zdzx_east, zdzy_north )
    !!$  DEALLOCATE(ZU_EAST,ZV_NORTH,ZDZX_EAST,ZDZY_NORTH)
    !!$  CALL CLEANLIST_ll(TZFIELD_U)
    !!$  CALL CLEANLIST_ll(TZFIELD_V)
    !!$ !!$  IF (NHALO==1) THEN
    !!$    CALL CLEANLIST_ll(TZFIELD_DZX)
    !!$    CALL CLEANLIST_ll(TZFIELD_DZY)
    
    !!$    CALL DEL_HALO2_ll(TZHALO2_U)
    !!$    CALL DEL_HALO2_ll(TZHALO2_V)
    !!$    CALL DEL_HALO2_ll(TZHALO2_DZX)
    !!$    CALL DEL_HALO2_ll(TZHALO2_DZY)
    
    !!$ !!$  END IF
    END IF
    
    END IF FLAT
    !-----------------------------------------------------------------------
    IF (MPPDB_INITIALIZED) THEN
      !Check all OUT arrays
      CALL MPPDB_CHECK(PRUCT,"CONTRAV end:PRUCT")
      CALL MPPDB_CHECK(PRVCT,"CONTRAV end:PRVCT")
      CALL MPPDB_CHECK(PRWCT,"CONTRAV end:PRWCT")
    END IF
    
    !$acc end data
    
    END SUBROUTINE CONTRAV_DEVICE
    #endif