C $Header: /home/ubuntu/mnt/e9_copy/MITgcm/pkg/generic_advdiff/gad_u3_adv_x.F,v 1.4 2002/01/08 21:43:23 jmc Exp $
C $Name:  $

#include "GAD_OPTIONS.h"

CBOP
C !ROUTINE: GAD_U3_ADV_X

C !INTERFACE: ==========================================================
      SUBROUTINE GAD_U3_ADV_X( 
     I           bi,bj,k,
     I           uTrans,
     I           tracer,
     O           uT,
     I           myThid )

C !DESCRIPTION:
C Calculates the area integrated zonal flux due to advection of a tracer
C using upwind biased third-order interpolation (or the $\kappa=1/3$ scheme):
C \begin{equation*}
C F^x_{adv} = U \overline{ \theta  - \frac{1}{6} \delta_{ii} \theta }^i
C                 + \frac{1}{12} |U| \delta_{iii} \theta
C \end{equation*}
C Near boundaries, mask all the gradients ==> still 3rd O.

C !USES: ===============================================================
      IMPLICIT NONE
#include "SIZE.h"
#include "GRID.h"
#include "GAD.h"

C !INPUT PARAMETERS: ===================================================
C  bi,bj                :: tile indices
C  k                    :: vertical level
C  uTrans               :: zonal volume transport
C  tracer               :: tracer field
C  myThid               :: thread number
      INTEGER bi,bj,k
      _RL uTrans(1-OLx:sNx+OLx,1-OLy:sNy+OLy)
      _RL tracer(1-OLx:sNx+OLx,1-OLy:sNy+OLy)
      INTEGER myThid

C !OUTPUT PARAMETERS: ==================================================
C  uT                   :: zonal advective flux
      _RL uT    (1-OLx:sNx+OLx,1-OLy:sNy+OLy)

C !LOCAL VARIABLES: ====================================================
C  i,j                  :: loop indices
C  Rjm,Rj,Rjp           :: differences at i-1,i,i+1
C  Rjjm,Rjjp            :: second differences at i-1,i
      INTEGER i,j
      _RL Rjm,Rj,Rjp,Rjjm,Rjjp
CEOP

      DO j=1-Oly,sNy+Oly
       uT(1-Olx,j)=0.
       uT(2-Olx,j)=0.
       uT(sNx+Olx,j)=0.
       DO i=1-Olx+2,sNx+Olx-1
        Rjp=(tracer(i+1,j)-tracer(i,j))*maskW(i+1,j,k,bi,bj)
        Rj =(tracer(i,j)-tracer(i-1,j))*maskW(i,j,k,bi,bj)
        Rjm=(tracer(i-1,j)-tracer(i-2,j))*maskW(i-1,j,k,bi,bj)
        Rjjp=Rjp-Rj
        Rjjm=Rj-Rjm
        uT(i,j) = 
     &   uTrans(i,j)*(
     &     Tracer(i,j)+Tracer(i-1,j)-oneSixth*( Rjjp+Rjjm )
     &               )*0.5 _d 0
     &  +ABS( uTrans(i,j) )*0.5 _d 0*oneSixth*( Rjjp-Rjjm )
       ENDDO
      ENDDO

      RETURN
      END