MODULE tl_uv3dmix2_mod
!
!git $Id$
!svn $Id: tl_uv3dmix2_geo.h 1151 2023-02-09 03:08:53Z arango $
!================================================== Hernan G. Arango ===
! Copyright (c) 2002-2023 The ROMS/TOMS Group Andrew M. Moore !
! Licensed under a MIT/X style license !
! See License_ROMS.md !
!=======================================================================
! !
! This routine computes tangent linear harmonic mixing of momentum, !
! rotated along geopotentials, from the horizontal divergence of !
! the stress tensor. A transverse isotropy is assumed so the stress !
! tensor is split into vertical and horizontal subtensors. !
! !
! Reference: !
! !
! Wajsowicz, R.C, 1993: A consistent formulation of the !
! anisotropic stress tensor for use in models of the !
! large-scale ocean circulation, JCP, 105, 333-338. !
! !
! Sadourny, R. and K. Maynard, 1997: Formulations of !
! lateral diffusion in geophysical fluid dynamics !
! models, In Numerical Methods of Atmospheric and !
! Oceanic Modelling. Lin, Laprise, and Ritchie, !
! Eds., NRC Research Press, 547-556. !
! !
! Griffies, S.M. and R.W. Hallberg, 2000: Biharmonic !
! friction with a Smagorinsky-like viscosity for !
! use in large-scale eddy-permitting ocean models, !
! Monthly Weather Rev., 128, 8, 2935-2946. !
! !
!=======================================================================
!
implicit none
!
PRIVATE
PUBLIC tl_uv3dmix2
!
CONTAINS
!
!***********************************************************************
SUBROUTINE tl_uv3dmix2 (ng, tile)
!***********************************************************************
!
USE mod_param
USE mod_coupling
#ifdef DIAGNOSTICS_UV
!! USE mod_diags
#endif
USE mod_grid
USE mod_mixing
USE mod_ocean
USE mod_stepping
!
! Imported variable declarations.
!
integer, intent(in) :: ng, tile
!
! Local variable declarations.
!
character (len=*), parameter :: MyFile = &
& __FILE__
!
#include "tile.h"
!
#ifdef PROFILE
CALL wclock_on (ng, iTLM, 31, __LINE__, MyFile)
#endif
CALL tl_uv3dmix2_geo_tile (ng, tile, &
& LBi, UBi, LBj, UBj, &
& IminS, ImaxS, JminS, JmaxS, &
& nrhs(ng), nnew(ng), &
#ifdef MASKING
& GRID(ng) % pmask, &
& GRID(ng) % rmask, &
& GRID(ng) % umask, &
& GRID(ng) % vmask, &
#endif
& GRID(ng) % om_p, &
& GRID(ng) % om_r, &
& GRID(ng) % om_u, &
& GRID(ng) % om_v, &
& GRID(ng) % on_p, &
& GRID(ng) % on_r, &
& GRID(ng) % on_u, &
& GRID(ng) % on_v, &
& GRID(ng) % pm, &
& GRID(ng) % pn, &
& GRID(ng) % Hz, &
& GRID(ng) % tl_Hz, &
& GRID(ng) % z_r, &
& GRID(ng) % tl_z_r, &
#ifdef VISC_3DCOEF
& MIXING(ng) % visc3d_r, &
& MIXING(ng) % tl_visc3d_r, &
#else
& MIXING(ng) % visc2_p, &
& MIXING(ng) % visc2_r, &
#endif
#ifdef DIAGNOSTICS_UV
!! & DIAGS(ng) % DiaRUfrc, &
!! & DIAGS(ng) % DiaRVfrc, &
!! & DIAGS(ng) % DiaU3wrk, &
!! & DIAGS(ng) % DiaV3wrk, &
#endif
& OCEAN(ng) % u, &
& OCEAN(ng) % v, &
& OCEAN(ng) % tl_u, &
& OCEAN(ng) % tl_v, &
& COUPLING(ng) % tl_rufrc, &
& COUPLING(ng) % tl_rvfrc)
#ifdef PROFILE
CALL wclock_off (ng, iTLM, 31, __LINE__, MyFile)
#endif
!
RETURN
END SUBROUTINE tl_uv3dmix2
!
!***********************************************************************
SUBROUTINE tl_uv3dmix2_geo_tile (ng, tile, &
& LBi, UBi, LBj, UBj, &
& IminS, ImaxS, JminS, JmaxS, &
& nrhs, nnew, &
#ifdef MASKING
& pmask, rmask, umask, vmask, &
#endif
& om_p, om_r, om_u, om_v, &
& on_p, on_r, on_u, on_v, &
& pm, pn, &
& Hz, tl_Hz, &
& z_r, tl_z_r, &
#ifdef VISC_3DCOEF
& visc3d_r, tl_visc3d_r, &
#else
& visc2_p, visc2_r, &
#endif
#ifdef DIAGNOSTICS_UV
!! & DiaRUfrc, DiaRVfrc, &
!! & DiaU3wrk, DiaV3wrk, &
#endif
& u, v, &
& tl_u, tl_v, &
& tl_rufrc, tl_rvfrc)
!***********************************************************************
!
USE mod_param
USE mod_scalars
!
! Imported variable declarations.
!
integer, intent(in) :: ng, tile
integer, intent(in) :: LBi, UBi, LBj, UBj
integer, intent(in) :: IminS, ImaxS, JminS, JmaxS
integer, intent(in) :: nrhs, nnew
#ifdef ASSUMED_SHAPE
# ifdef MASKING
real(r8), intent(in) :: pmask(LBi:,LBj:)
real(r8), intent(in) :: rmask(LBi:,LBj:)
real(r8), intent(in) :: umask(LBi:,LBj:)
real(r8), intent(in) :: vmask(LBi:,LBj:)
# endif
real(r8), intent(in) :: om_p(LBi:,LBj:)
real(r8), intent(in) :: om_r(LBi:,LBj:)
real(r8), intent(in) :: om_u(LBi:,LBj:)
real(r8), intent(in) :: om_v(LBi:,LBj:)
real(r8), intent(in) :: on_p(LBi:,LBj:)
real(r8), intent(in) :: on_r(LBi:,LBj:)
real(r8), intent(in) :: on_u(LBi:,LBj:)
real(r8), intent(in) :: on_v(LBi:,LBj:)
real(r8), intent(in) :: pm(LBi:,LBj:)
real(r8), intent(in) :: pn(LBi:,LBj:)
real(r8), intent(in) :: Hz(LBi:,LBj:,:)
real(r8), intent(in) :: tl_Hz(LBi:,LBj:,:)
real(r8), intent(in) :: z_r(LBi:,LBj:,:)
real(r8), intent(in) :: tl_z_r(LBi:,LBj:,:)
# ifdef VISC_3DCOEF
real(r8), intent(in) :: visc3d_r(LBi:,LBj:,:)
# else
real(r8), intent(in) :: visc2_p(LBi:,LBj:)
real(r8), intent(in) :: visc2_r(LBi:,LBj:)
# endif
real(r8), intent(in) :: u(LBi:,LBj:,:,:)
real(r8), intent(in) :: v(LBi:,LBj:,:,:)
# ifdef DIAGNOSTICS_UV
!! real(r8), intent(inout) :: DiaRUfrc(LBi:,LBj:,:,:)
!! real(r8), intent(inout) :: DiaRVfrc(LBi:,LBj:,:,:)
!! real(r8), intent(inout) :: DiaU3wrk(LBi:,LBj:,:,:)
!! real(r8), intent(inout) :: DiaV3wrk(LBi:,LBj:,:,:)
# endif
real(r8), intent(inout) :: tl_rufrc(LBi:,LBj:)
real(r8), intent(inout) :: tl_rvfrc(LBi:,LBj:)
real(r8), intent(inout) :: tl_u(LBi:,LBj:,:,:)
real(r8), intent(inout) :: tl_v(LBi:,LBj:,:,:)
# ifdef VISC_3DCOEF
real(r8), intent(inout) :: tl_visc3d_r(LBi:,LBj:,:)
# endif
#else
# ifdef MASKING
real(r8), intent(in) :: pmask(LBi:UBi,LBj:UBj)
real(r8), intent(in) :: rmask(LBi:UBi,LBj:UBj)
real(r8), intent(in) :: umask(LBi:UBi,LBj:UBj)
real(r8), intent(in) :: vmask(LBi:UBi,LBj:UBj)
# endif
real(r8), intent(in) :: om_p(LBi:UBi,LBj:UBj)
real(r8), intent(in) :: om_r(LBi:UBi,LBj:UBj)
real(r8), intent(in) :: om_u(LBi:UBi,LBj:UBj)
real(r8), intent(in) :: om_v(LBi:UBi,LBj:UBj)
real(r8), intent(in) :: on_p(LBi:UBi,LBj:UBj)
real(r8), intent(in) :: on_r(LBi:UBi,LBj:UBj)
real(r8), intent(in) :: on_u(LBi:UBi,LBj:UBj)
real(r8), intent(in) :: on_v(LBi:UBi,LBj:UBj)
real(r8), intent(in) :: pm(LBi:UBi,LBj:UBj)
real(r8), intent(in) :: pn(LBi:UBi,LBj:UBj)
real(r8), intent(in) :: Hz(LBi:UBi,LBj:UBj,N(ng))
real(r8), intent(in) :: tl_Hz(LBi:UBi,LBj:UBj,N(ng))
real(r8), intent(in) :: z_r(LBi:UBi,LBj:UBj,N(ng))
real(r8), intent(in) :: tl_z_r(LBi:UBi,LBj:UBj,N(ng))
# ifdef VISC_3DCOEF
real(r8), intent(in) :: visc3d_r(LBi:UBi,LBj:UBj,N(ng))
# else
real(r8), intent(in) :: visc2_p(LBi:UBi,LBj:UBj)
real(r8), intent(in) :: visc2_r(LBi:UBi,LBj:UBj)
# endif
real(r8), intent(in) :: u(LBi:UBi,LBj:UBj,N(ng),2)
real(r8), intent(in) :: v(LBi:UBi,LBj:UBj,N(ng),2)
# ifdef DIAGNOSTICS_UV
!! real(r8), intent(inout) :: DiaRUfrc(LBi:UBi,LBj:UBj,3,NDM2d-1)
!! real(r8), intent(inout) :: DiaRVfrc(LBi:UBi,LBj:UBj,3,NDM2d-1)
!! real(r8), intent(inout) :: DiaU3wrk(LBi:UBi,LBj:UBj,N(ng),NDM3d)
!! real(r8), intent(inout) :: DiaV3wrk(LBi:UBi,LBj:UBj,N(ng),NDM3d)
# endif
real(r8), intent(inout) :: tl_rufrc(LBi:UBi,LBj:UBj)
real(r8), intent(inout) :: tl_rvfrc(LBi:UBi,LBj:UBj)
real(r8), intent(inout) :: tl_u(LBi:UBi,LBj:UBj,N(ng),2)
real(r8), intent(inout) :: tl_v(LBi:UBi,LBj:UBj,N(ng),2)
# ifdef VISC_3DCOEF
real(r8), intent(inout) :: tl_visc3d_r(LBi:UBi,LBj:UBj,N(ng))
# endif
#endif
!
! Local variable declarations.
!
integer :: i, j, k, k1, k2
real(r8) :: cff, fac1, fac2, pm_p, pn_p
real(r8) :: cff1, cff2, cff3, cff4
real(r8) :: cff5, cff6, cff7, cff8
real(r8) :: dmUdz, dnUdz, dmVdz, dnVdz
#ifdef VISC_3DCOEF
real(r8) :: visc_p
real(r8) :: tl_fac1, tl_fac2, tl_visc_p
#endif
real(r8) :: tl_cff
real(r8) :: tl_cff1, tl_cff2, tl_cff3, tl_cff4
real(r8) :: tl_cff5, tl_cff6, tl_cff7, tl_cff8
real(r8) :: tl_dmUdz, tl_dnUdz, tl_dmVdz, tl_dnVdz
real(r8), dimension(IminS:ImaxS,JminS:JmaxS) :: UFx
real(r8), dimension(IminS:ImaxS,JminS:JmaxS) :: VFe
real(r8), dimension(IminS:ImaxS,JminS:JmaxS) :: tl_UFe
real(r8), dimension(IminS:ImaxS,JminS:JmaxS) :: tl_UFx
real(r8), dimension(IminS:ImaxS,JminS:JmaxS) :: tl_VFe
real(r8), dimension(IminS:ImaxS,JminS:JmaxS) :: tl_VFx
real(r8), dimension(IminS:ImaxS,JminS:JmaxS,2) :: dmUde
real(r8), dimension(IminS:ImaxS,JminS:JmaxS,2) :: dmVde
real(r8), dimension(IminS:ImaxS,JminS:JmaxS,2) :: dnUdx
real(r8), dimension(IminS:ImaxS,JminS:JmaxS,2) :: dnVdx
real(r8), dimension(IminS:ImaxS,JminS:JmaxS,2) :: dUdz
real(r8), dimension(IminS:ImaxS,JminS:JmaxS,2) :: dVdz
real(r8), dimension(IminS:ImaxS,JminS:JmaxS,2) :: dZde_p
real(r8), dimension(IminS:ImaxS,JminS:JmaxS,2) :: dZde_r
real(r8), dimension(IminS:ImaxS,JminS:JmaxS,2) :: dZdx_p
real(r8), dimension(IminS:ImaxS,JminS:JmaxS,2) :: dZdx_r
real(r8), dimension(IminS:ImaxS,JminS:JmaxS,2) :: tl_UFse
real(r8), dimension(IminS:ImaxS,JminS:JmaxS,2) :: tl_UFsx
real(r8), dimension(IminS:ImaxS,JminS:JmaxS,2) :: tl_VFse
real(r8), dimension(IminS:ImaxS,JminS:JmaxS,2) :: tl_VFsx
real(r8), dimension(IminS:ImaxS,JminS:JmaxS,2) :: tl_dmUde
real(r8), dimension(IminS:ImaxS,JminS:JmaxS,2) :: tl_dmVde
real(r8), dimension(IminS:ImaxS,JminS:JmaxS,2) :: tl_dnUdx
real(r8), dimension(IminS:ImaxS,JminS:JmaxS,2) :: tl_dnVdx
real(r8), dimension(IminS:ImaxS,JminS:JmaxS,2) :: tl_dUdz
real(r8), dimension(IminS:ImaxS,JminS:JmaxS,2) :: tl_dVdz
real(r8), dimension(IminS:ImaxS,JminS:JmaxS,2) :: tl_dZde_p
real(r8), dimension(IminS:ImaxS,JminS:JmaxS,2) :: tl_dZde_r
real(r8), dimension(IminS:ImaxS,JminS:JmaxS,2) :: tl_dZdx_p
real(r8), dimension(IminS:ImaxS,JminS:JmaxS,2) :: tl_dZdx_r
#include "set_bounds.h"
!
!-----------------------------------------------------------------------
! Compute horizontal harmonic viscosity along geopotential surfaces.
!-----------------------------------------------------------------------
!
! Compute horizontal and vertical gradients. Notice the recursive
! blocking sequence. The vertical placement of the gradients is:
!
! dZdx_r, dZde_r, dnUdx, dmVde(:,:,k1) k rho-points
! dZdx_r, dZde_r, dnUdx, dmVde(:,:,k2) k+1 rho-points
! dZdx_p, dZde_p, dnVdx, dmUde(:,:,k1) k psi-points
! dZdx_p, dZde_p, dnVdx, dmUde(:,:,k2) k+1 psi-points
! UFse, UFsx, dUdz(:,:,k1) k-1/2 WU-points
! UFse, UFsx, dUdz(:,:,k2) k+1/2 WU-points
! VFse, VFsx, dVdz(:,:,k1) k-1/2 WV-points
! VFse, VFsx, dVdz(:,:,k2) k+1/2 WV-points
!
k2=1
K_LOOP : DO k=0,N(ng)
k1=k2
k2=3-k1
IF (k.lt.N(ng)) THEN
!
! Compute slopes (nondimensional) at RHO- and PSI-points.
!
DO j=Jstr-1,Jend+1
DO i=IstrU-1,Iend+1
cff=0.5_r8*(pm(i-1,j)+pm(i,j))
#ifdef MASKING
cff=cff*umask(i,j)
#endif
UFx(i,j)=cff*(z_r(i ,j,k+1)- &
& z_r(i-1,j,k+1))
tl_UFx(i,j)=cff*(tl_z_r(i ,j,k+1)- &
& tl_z_r(i-1,j,k+1))
END DO
END DO
DO j=JstrV-1,Jend+1
DO i=Istr-1,Iend+1
cff=0.5_r8*(pn(i,j-1)+pn(i,j))
#ifdef MASKING
cff=cff*vmask(i,j)
#endif
VFe(i,j)=cff*(z_r(i,j ,k+1)- &
& z_r(i,j-1,k+1))
tl_VFe(i,j)=cff*(tl_z_r(i,j ,k+1)- &
& tl_z_r(i,j-1,k+1))
END DO
END DO
!
DO j=Jstr,Jend+1
DO i=Istr,Iend+1
dZdx_p(i,j,k2)=0.5_r8*(UFx(i,j-1)+ &
& UFx(i,j ))
tl_dZdx_p(i,j,k2)=0.5_r8*(tl_UFx(i,j-1)+ &
& tl_UFx(i,j ))
dZde_p(i,j,k2)=0.5_r8*(VFe(i-1,j)+ &
& VFe(i ,j))
tl_dZde_p(i,j,k2)=0.5_r8*(tl_VFe(i-1,j)+ &
& tl_VFe(i ,j))
END DO
END DO
DO j=JstrV-1,Jend
DO i=IstrU-1,Iend
dZdx_r(i,j,k2)=0.5_r8*(UFx(i ,j)+ &
& UFx(i+1,j))
tl_dZdx_r(i,j,k2)=0.5_r8*(tl_UFx(i ,j)+ &
& tl_UFx(i+1,j))
dZde_r(i,j,k2)=0.5_r8*(VFe(i,j )+ &
& VFe(i,j+1))
tl_dZde_r(i,j,k2)=0.5_r8*(tl_VFe(i,j )+ &
& tl_VFe(i,j+1))
END DO
END DO
!
! Compute momentum horizontal (1/m/s) and vertical (1/s) gradients.
!
DO j=JstrV-1,Jend
DO i=IstrU-1,Iend
cff=0.5_r8*pm(i,j)
#ifdef MASKING
cff=cff*rmask(i,j)
#endif
dnUdx(i,j,k2)=cff*((pn(i ,j)+pn(i+1,j))* &
& u(i+1,j,k+1,nrhs)- &
& (pn(i-1,j)+pn(i ,j))* &
& u(i ,j,k+1,nrhs))
tl_dnUdx(i,j,k2)=cff*((pn(i ,j)+pn(i+1,j))* &
& tl_u(i+1,j,k+1,nrhs)- &
& (pn(i-1,j)+pn(i ,j))* &
& tl_u(i ,j,k+1,nrhs))
END DO
END DO
DO j=Jstr,Jend+1
DO i=Istr,Iend+1
cff=0.125_r8*(pn(i-1,j )+pn(i,j )+ &
& pn(i-1,j-1)+pn(i,j-1))
#ifdef MASKING
cff=cff*pmask(i,j)
#endif
dmUde(i,j,k2)=cff*((pm(i-1,j )+pm(i,j ))* &
& u(i,j ,k+1,nrhs)- &
& (pm(i-1,j-1)+pm(i,j-1))* &
& u(i,j-1,k+1,nrhs))
tl_dmUde(i,j,k2)=cff*((pm(i-1,j )+pm(i,j ))* &
& tl_u(i,j ,k+1,nrhs)- &
& (pm(i-1,j-1)+pm(i,j-1))* &
& tl_u(i,j-1,k+1,nrhs))
END DO
END DO
DO j=Jstr,Jend+1
DO i=Istr,Iend+1
cff=0.125_r8*(pm(i-1,j )+pm(i,j )+ &
& pm(i-1,j-1)+pm(i,j-1))
#ifdef MASKING
cff=cff*pmask(i,j)
#endif
dnVdx(i,j,k2)=cff*((pn(i ,j-1)+pn(i ,j))* &
& v(i ,j,k+1,nrhs)- &
& (pn(i-1,j-1)+pn(i-1,j))* &
& v(i-1,j,k+1,nrhs))
tl_dnVdx(i,j,k2)=cff*((pn(i ,j-1)+pn(i ,j))* &
& tl_v(i ,j,k+1,nrhs)- &
& (pn(i-1,j-1)+pn(i-1,j))* &
& tl_v(i-1,j,k+1,nrhs))
END DO
END DO
DO j=JstrV-1,Jend
DO i=IstrU-1,Iend
cff=0.5_r8*pn(i,j)
#ifdef MASKING
cff=cff*rmask(i,j)
#endif
dmVde(i,j,k2)=cff*((pm(i,j )+pm(i,j+1))* &
& v(i,j+1,k+1,nrhs)- &
& (pm(i,j-1)+pm(i,j ))* &
& v(i,j ,k+1,nrhs))
tl_dmVde(i,j,k2)=cff*((pm(i,j )+pm(i,j+1))* &
& tl_v(i,j+1,k+1,nrhs)- &
& (pm(i,j-1)+pm(i,j ))* &
& tl_v(i,j ,k+1,nrhs))
END DO
END DO
END IF
IF ((k.eq.0).or.(k.eq.N(ng))) THEN
DO j=Jstr-1,Jend+1
DO i=IstrU-1,Iend+1
dUdz(i,j,k2)=0.0_r8
tl_dUdz(i,j,k2)=0.0_r8
END DO
END DO
DO j=JstrV-1,Jend+1
DO i=Istr-1,Iend+1
dVdz(i,j,k2)=0.0_r8
tl_dVdz(i,j,k2)=0.0_r8
END DO
END DO
DO j=Jstr,Jend
DO i=IstrU,Iend
!^ UFsx(i,j,k2)=0.0_r8
!^
tl_UFsx(i,j,k2)=0.0_r8
!^ UFse(i,j,k2)=0.0_r8
!^
tl_UFse(i,j,k2)=0.0_r8
END DO
END DO
DO j=JstrV,Jend
DO i=Istr,Iend
!^ VFsx(i,j,k2)=0.0_r8
!^
tl_VFsx(i,j,k2)=0.0_r8
!^ VFse(i,j,k2)=0.0_r8
!^
tl_VFse(i,j,k2)=0.0_r8
END DO
END DO
ELSE
DO j=Jstr-1,Jend+1
DO i=IstrU-1,Iend+1
cff=1.0_r8/(0.5_r8*(z_r(i-1,j,k+1)-z_r(i-1,j,k)+ &
& z_r(i ,j,k+1)-z_r(i ,j,k)))
tl_cff=-cff*cff*(0.5_r8*(tl_z_r(i-1,j,k+1)- &
& tl_z_r(i-1,j,k )+ &
& tl_z_r(i ,j,k+1)- &
& tl_z_r(i ,j,k )))
dUdz(i,j,k2)=cff*(u(i,j,k+1,nrhs)- &
& u(i,j,k ,nrhs))
tl_dUdz(i,j,k2)=tl_cff*(u(i,j,k+1,nrhs)- &
& u(i,j,k ,nrhs))+ &
& cff*(tl_u(i,j,k+1,nrhs)- &
& tl_u(i,j,k ,nrhs))
END DO
END DO
DO j=JstrV-1,Jend+1
DO i=Istr-1,Iend+1
cff=1.0_r8/(0.5_r8*(z_r(i,j-1,k+1)-z_r(i,j-1,k)+ &
& z_r(i,j ,k+1)-z_r(i,j ,k)))
tl_cff=-cff*cff*(0.5_r8*(tl_z_r(i,j-1,k+1)- &
& tl_z_r(i,j-1,k )+ &
& tl_z_r(i,j ,k+1)- &
& tl_z_r(i,j ,k )))
dVdz(i,j,k2)=cff*(v(i,j,k+1,nrhs)- &
& v(i,j,k ,nrhs))
tl_dVdz(i,j,k2)=tl_cff*(v(i,j,k+1,nrhs)- &
& v(i,j,k ,nrhs))+ &
& cff*(tl_v(i,j,k+1,nrhs)- &
& tl_v(i,j,k ,nrhs))
END DO
END DO
END IF
!
! Compute components of the rotated viscous flux (m5/s2) along
! geopotential surfaces in the XI- and ETA-directions.
!
IF (k.gt.0) THEN
DO j=JstrV-1,Jend
DO i=IstrU-1,Iend
cff1=MIN(dZdx_r(i,j,k1),0.0_r8)
cff2=MAX(dZdx_r(i,j,k1),0.0_r8)
cff3=MIN(dZde_r(i,j,k1),0.0_r8)
cff4=MAX(dZde_r(i,j,k1),0.0_r8)
tl_cff1=(0.5_r8+SIGN(0.5_r8,-dZdx_r(i,j,k1)))* &
& tl_dZdx_r(i,j,k1)
tl_cff2=(0.5_r8+SIGN(0.5_r8, dZdx_r(i,j,k1)))* &
& tl_dZdx_r(i,j,k1)
tl_cff3=(0.5_r8+SIGN(0.5_r8,-dZde_r(i,j,k1)))* &
& tl_dZde_r(i,j,k1)
tl_cff4=(0.5_r8+SIGN(0.5_r8, dZde_r(i,j,k1)))* &
& tl_dZde_r(i,j,k1)
#ifdef VISC_3DCOEF
cff=Hz(i,j,k)* &
& (on_r(i,j)*(dnUdx(i,j,k1)- &
& 0.5_r8*pn(i,j)* &
& (cff1*(dUdz(i ,j,k1)+ &
& dUdz(i+1,j,k2))+ &
& cff2*(dUdz(i ,j,k2)+ &
& dUdz(i+1,j,k1))))- &
& om_r(i,j)*(dmVde(i,j,k1)- &
& 0.5_r8*pm(i,j)* &
& (cff3*(dVdz(i,j ,k1)+ &
& dVdz(i,j+1,k2))+ &
& cff4*(dVdz(i,j ,k2)+ &
& dVdz(i,j+1,k1)))))
#else
!^ cff=Hz(i,j,k)* &
!^ & (on_r(i,j)*(dnUdx(i,j,k1)- &
!^ & 0.5_r8*pn(i,j)* &
!^ & (cff1*(dUdz(i ,j,k1)+ &
!^ & dUdz(i+1,j,k2))+ &
!^ & cff2*(dUdz(i ,j,k2)+ &
!^ & dUdz(i+1,j,k1))))- &
!^ & om_r(i,j)*(dmVde(i,j,k1)- &
!^ & 0.5_r8*pm(i,j)* &
!^ & (cff3*(dVdz(i,j ,k1)+ &
!^ & dVdz(i,j+1,k2))+ &
!^ & cff4*(dVdz(i,j ,k2)+ &
!^ & dVdz(i,j+1,k1)))))
!^
#endif
tl_cff=tl_Hz(i,j,k)* &
& (on_r(i,j)*(dnUdx(i,j,k1)- &
& 0.5_r8*pn(i,j)* &
& (cff1*(dUdz(i ,j,k1)+ &
& dUdz(i+1,j,k2))+ &
& cff2*(dUdz(i ,j,k2)+ &
& dUdz(i+1,j,k1))))- &
& om_r(i,j)*(dmVde(i,j,k1)- &
& 0.5_r8*pm(i,j)* &
& (cff3*(dVdz(i,j ,k1)+ &
& dVdz(i,j+1,k2))+ &
& cff4*(dVdz(i,j ,k2)+ &
& dVdz(i,j+1,k1)))))+ &
& Hz(i,j,k)* &
& (on_r(i,j)*(tl_dnUdx(i,j,k1)- &
& 0.5_r8*pn(i,j)* &
& (tl_cff1*(dUdz(i ,j,k1)+ &
& dUdz(i+1,j,k2))+ &
& cff1*(tl_dUdz(i ,j,k1)+ &
& tl_dUdz(i+1,j,k2))+ &
& tl_cff2*(dUdz(i ,j,k2)+ &
& dUdz(i+1,j,k1))+ &
& cff2*(tl_dUdz(i ,j,k2)+ &
& tl_dUdz(i+1,j,k1))))- &
& om_r(i,j)*(tl_dmVde(i,j,k1)- &
& 0.5_r8*pm(i,j)* &
& (tl_cff3*(dVdz(i,j ,k1)+ &
& dVdz(i,j+1,k2))+ &
& cff3*(tl_dVdz(i,j ,k1)+ &
& tl_dVdz(i,j+1,k2))+ &
& tl_cff4*(dVdz(i,j ,k2)+ &
& dVdz(i,j+1,k1))+ &
& cff4*(tl_dVdz(i,j ,k2)+ &
& tl_dVdz(i,j+1,k1)))))
#ifdef MASKING
# ifdef VISC_3DCOEF
cff=cff*rmask(i,j)
# else
!^ cff=cff*rmask(i,j)
!^
# endif
tl_cff=tl_cff*rmask(i,j)
#endif
#ifdef VISC_3DCOEF
!^ UFx(i,j)=on_r(i,j)*on_r(i,j)*visc3d_r(i,j,k)*cff
!^
tl_UFx(i,j)=on_r(i,j)*on_r(i,j)* &
& (tl_visc3d_r(i,j,k)*cff+ &
& visc3d_r(i,j,k)*tl_cff)
!^ VFe(i,j)=om_r(i,j)*om_r(i,j)*visc3d_r(i,j,k)*cff
!^
tl_VFe(i,j)=om_r(i,j)*om_r(i,j)* &
& (tl_visc3d_r(i,j,k)*cff+ &
& visc3d_r(i,j,k)*tl_cff)
#else
!^ UFx(i,j)=on_r(i,j)*on_r(i,j)*visc2_r(i,j)*cff
!^
tl_UFx(i,j)=on_r(i,j)*on_r(i,j)*visc2_r(i,j)*tl_cff
!^ VFe(i,j)=om_r(i,j)*om_r(i,j)*visc2_r(i,j)*cff
!^
tl_VFe(i,j)=om_r(i,j)*om_r(i,j)*visc2_r(i,j)*tl_cff
#endif
END DO
END DO
DO j=Jstr,Jend+1
DO i=Istr,Iend+1
pm_p=0.25_r8*(pm(i-1,j-1)+pm(i-1,j)+ &
& pm(i ,j-1)+pm(i ,j))
pn_p=0.25_r8*(pn(i-1,j-1)+pn(i-1,j)+ &
& pn(i ,j-1)+pn(i ,j))
cff1=MIN(dZdx_p(i,j,k1),0.0_r8)
cff2=MAX(dZdx_p(i,j,k1),0.0_r8)
cff3=MIN(dZde_p(i,j,k1),0.0_r8)
cff4=MAX(dZde_p(i,j,k1),0.0_r8)
tl_cff1=(0.5_r8+SIGN(0.5_r8,-dZdx_p(i,j,k1)))* &
& tl_dZdx_p(i,j,k1)
tl_cff2=(0.5_r8+SIGN(0.5_r8, dZdx_p(i,j,k1)))* &
& tl_dZdx_p(i,j,k1)
tl_cff3=(0.5_r8+SIGN(0.5_r8,-dZde_p(i,j,k1)))* &
& tl_dZde_p(i,j,k1)
tl_cff4=(0.5_r8+SIGN(0.5_r8, dZde_p(i,j,k1)))* &
& tl_dZde_p(i,j,k1)
#ifdef VISC_3DCOEF
cff=0.25_r8* &
& (Hz(i-1,j ,k)+Hz(i,j ,k)+ &
& Hz(i-1,j-1,k)+Hz(i,j-1,k))* &
& (on_p(i,j)*(dnVdx(i,j,k1)- &
& 0.5_r8*pn_p* &
& (cff1*(dVdz(i-1,j,k1)+ &
& dVdz(i ,j,k2))+ &
& cff2*(dVdz(i-1,j,k2)+ &
& dVdz(i ,j,k1))))+ &
& om_p(i,j)*(dmUde(i,j,k1)- &
& 0.5_r8*pm_p* &
& (cff3*(dUdz(i,j-1,k1)+ &
& dUdz(i,j ,k2))+ &
& cff4*(dUdz(i,j-1,k2)+ &
& dUdz(i,j ,k1)))))
#else
!^ cff=0.25_r8* &
!^ & (Hz(i-1,j ,k)+Hz(i,j ,k)+ &
!^ & Hz(i-1,j-1,k)+Hz(i,j-1,k))* &
!^ & (on_p(i,j)*(dnVdx(i,j,k1)- &
!^ & 0.5_r8*pn_p* &
!^ & (cff1*(dVdz(i-1,j,k1)+ &
!^ & dVdz(i ,j,k2))+ &
!^ & cff2*(dVdz(i-1,j,k2)+ &
!^ & dVdz(i ,j,k1))))+ &
!^ & om_p(i,j)*(dmUde(i,j,k1)- &
!^ & 0.5_r8*pm_p* &
!^ & (cff3*(dUdz(i,j-1,k1)+ &
!^ & dUdz(i,j ,k2))+ &
!^ & cff4*(dUdz(i,j-1,k2)+ &
!^ & dUdz(i,j ,k1)))))
!^
#endif
tl_cff=0.25_r8* &
& ((tl_Hz(i-1,j ,k)+tl_Hz(i,j ,k)+ &
& tl_Hz(i-1,j-1,k)+tl_Hz(i,j-1,k))* &
& (on_p(i,j)*(dnVdx(i,j,k1)- &
& 0.5_r8*pn_p* &
& (cff1*(dVdz(i-1,j,k1)+ &
& dVdz(i ,j,k2))+ &
& cff2*(dVdz(i-1,j,k2)+ &
& dVdz(i ,j,k1))))+ &
& om_p(i,j)*(dmUde(i,j,k1)- &
& 0.5_r8*pm_p* &
& (cff3*(dUdz(i,j-1,k1)+ &
& dUdz(i,j ,k2))+ &
& cff4*(dUdz(i,j-1,k2)+ &
& dUdz(i,j ,k1)))))+ &
& (Hz(i-1,j ,k)+Hz(i,j ,k)+ &
& Hz(i-1,j-1,k)+Hz(i,j-1,k))* &
& (on_p(i,j)*(tl_dnVdx(i,j,k1)- &
& 0.5_r8*pn_p* &
& (tl_cff1*(dVdz(i-1,j,k1)+ &
& dVdz(i ,j,k2))+ &
& cff1*(tl_dVdz(i-1,j,k1)+ &
& tl_dVdz(i ,j,k2))+ &
& tl_cff2*(dVdz(i-1,j,k2)+ &
& dVdz(i ,j,k1))+ &
& cff2*(tl_dVdz(i-1,j,k2)+ &
& tl_dVdz(i ,j,k1))))+ &
& om_p(i,j)*(tl_dmUde(i,j,k1)- &
& 0.5_r8*pm_p* &
& (tl_cff3*(dUdz(i,j-1,k1)+ &
& dUdz(i,j ,k2))+ &
& cff3*(tl_dUdz(i,j-1,k1)+ &
& tl_dUdz(i,j ,k2))+ &
& tl_cff4*(dUdz(i,j-1,k2)+ &
& dUdz(i,j ,k1))+ &
& cff4*(tl_dUdz(i,j-1,k2)+ &
& tl_dUdz(i,j ,k1))))))
#ifdef MASKING
# ifdef VISC_3DCOEF
cff=cff*pmask(i,j)
# else
!^ cff=cff*pmask(i,j)
!^
# endif
tl_cff=tl_cff*pmask(i,j)
#endif
#ifdef VISC_3DCOEF
visc_p=0.25_r8* &
& (visc3d_r(i-1,j-1,k)+visc3d_r(i-1,j,k)+ &
& visc3d_r(i ,j-1,k)+visc3d_r(i ,j,k))
tl_visc_p=0.25_r8* &
& (tl_visc3d_r(i-1,j-1,k)+tl_visc3d_r(i-1,j,k)+ &
& tl_visc3d_r(i ,j-1,k)+tl_visc3d_r(i ,j,k))
!^ UFe(i,j)=om_p(i,j)*om_p(i,j)*visc_p*cff
!^
tl_UFe(i,j)=om_p(i,j)*om_p(i,j)* &
& (tl_visc_p*cff+visc_p*tl_cff)
!^ VFx(i,j)=on_p(i,j)*on_p(i,j)*visc_p*cff
!^
tl_VFx(i,j)=on_p(i,j)*on_p(i,j)* &
& (tl_visc_p*cff+visc_p*tl_cff)
#else
!^ UFe(i,j)=om_p(i,j)*om_p(i,j)*visc2_p(i,j)*cff
!^
tl_UFe(i,j)=om_p(i,j)*om_p(i,j)*visc2_p(i,j)*tl_cff
!^ VFx(i,j)=on_p(i,j)*on_p(i,j)*visc2_p(i,j)*cff
!^
tl_VFx(i,j)=on_p(i,j)*on_p(i,j)*visc2_p(i,j)*tl_cff
#endif
END DO
END DO
!
! Compute vertical flux (m2/s2) due to sloping terrain-following
! surfaces.
!
IF (k.lt.N(ng)) THEN
DO j=Jstr,Jend
DO i=IstrU,Iend
#ifdef VISC_3DCOEF
cff=0.125_r8* &
& (visc3d_r(i-1,j,k )+visc3d_r(i,j,k )+ &
& visc3d_r(i-1,j,k+1)+visc3d_r(i,j,k+1))
tl_cff=0.125_r8* &
& (tl_visc3d_r(i-1,j,k )+tl_visc3d_r(i,j,k )+ &
& tl_visc3d_r(i-1,j,k+1)+tl_visc3d_r(i,j,k+1))
fac1=cff*on_u(i,j)
tl_fac1=tl_cff*on_u(i,j)
fac2=cff*om_u(i,j)
tl_fac2=tl_cff*om_u(i,j)
#else
cff=0.25_r8*(visc2_r(i-1,j)+visc2_r(i,j))
fac1=cff*on_u(i,j)
fac2=cff*om_u(i,j)
#endif
cff=0.5_r8*(pn(i-1,j)+pn(i,j))
dnUdz=cff*dUdz(i,j,k2)
tl_dnUdz=cff*tl_dUdz(i,j,k2)
dnVdz=cff*0.25_r8*(dVdz(i-1,j+1,k2)+ &
& dVdz(i ,j+1,k2)+ &
& dVdz(i-1,j ,k2)+ &
& dVdz(i ,j ,k2))
tl_dnVdz=cff*0.25_r8*(tl_dVdz(i-1,j+1,k2)+ &
& tl_dVdz(i ,j+1,k2)+ &
& tl_dVdz(i-1,j ,k2)+ &
& tl_dVdz(i ,j ,k2))
cff=0.5_r8*(pm(i-1,j)+pm(i,j))
dmUdz=cff*dUdz(i,j,k2)
tl_dmUdz=cff*tl_dUdz(i,j,k2)
dmVdz=cff*0.25_r8*(dVdz(i-1,j+1,k2)+ &
& dVdz(i ,j+1,k2)+ &
& dVdz(i-1,j ,k2)+ &
& dVdz(i ,j ,k2))
tl_dmVdz=cff*0.25_r8*(tl_dVdz(i-1,j+1,k2)+ &
& tl_dVdz(i ,j+1,k2)+ &
& tl_dVdz(i-1,j ,k2)+ &
& tl_dVdz(i ,j ,k2))
cff1=MIN(dZdx_r(i-1,j,k1),0.0_r8)
cff2=MIN(dZdx_r(i ,j,k2),0.0_r8)
cff3=MAX(dZdx_r(i-1,j,k2),0.0_r8)
cff4=MAX(dZdx_r(i ,j,k1),0.0_r8)
tl_cff1=(0.5_r8+SIGN(0.5_r8,-dZdx_r(i-1,j,k1)))* &
& tl_dZdx_r(i-1,j,k1)
tl_cff2=(0.5_r8+SIGN(0.5_r8,-dZdx_r(i ,j,k2)))* &
& tl_dZdx_r(i ,j,k2)
tl_cff3=(0.5_r8+SIGN(0.5_r8, dZdx_r(i-1,j,k2)))* &
& tl_dZdx_r(i-1,j,k2)
tl_cff4=(0.5_r8+SIGN(0.5_r8, dZdx_r(i ,j,k1)))* &
& tl_dZdx_r(i ,j,k1)
!^ UFsx(i,j,k2)=fac1* &
!^ & (cff1*(cff1*dnUdz-dnUdx(i-1,j,k1))+ &
!^ & cff2*(cff2*dnUdz-dnUdx(i ,j,k2))+ &
!^ & cff3*(cff3*dnUdz-dnUdx(i-1,j,k2))+ &
!^ & cff4*(cff4*dnUdz-dnUdx(i ,j,k1)))
!^
tl_UFsx(i,j,k2)=fac1* &
& (tl_cff1*(cff1*dnUdz-dnUdx(i-1,j,k1))+ &
& tl_cff2*(cff2*dnUdz-dnUdx(i ,j,k2))+ &
& tl_cff3*(cff3*dnUdz-dnUdx(i-1,j,k2))+ &
& tl_cff4*(cff4*dnUdz-dnUdx(i ,j,k1))+ &
& cff1*(tl_cff1*dnUdz+cff1*tl_dnUdz- &
& tl_dnUdx(i-1,j,k1))+ &
& cff2*(tl_cff2*dnUdz+cff2*tl_dnUdz- &
& tl_dnUdx(i ,j,k2))+ &
& cff3*(tl_cff3*dnUdz+cff3*tl_dnUdz- &
& tl_dnUdx(i-1,j,k2))+ &
& cff4*(tl_cff4*dnUdz+cff4*tl_dnUdz- &
& tl_dnUdx(i ,j,k1)))
#ifdef VISC_3DCOEF
tl_UFsx(i,j,k2)=tl_UFsx(i,j,k2)+ &
& tl_fac1* &
& (cff1*(cff1*dnUdz-dnUdx(i-1,j,k1))+ &
& cff2*(cff2*dnUdz-dnUdx(i ,j,k2))+ &
& cff3*(cff3*dnUdz-dnUdx(i-1,j,k2))+ &
& cff4*(cff4*dnUdz-dnUdx(i ,j,k1)))
#endif
cff1=MIN(dZde_p(i,j ,k1),0.0_r8)
cff2=MIN(dZde_p(i,j+1,k2),0.0_r8)
cff3=MAX(dZde_p(i,j ,k2),0.0_r8)
cff4=MAX(dZde_p(i,j+1,k1),0.0_r8)
tl_cff1=(0.5_r8+SIGN(0.5_r8,-dZde_p(i,j ,k1)))* &
& tl_dZde_p(i,j ,k1)
tl_cff2=(0.5_r8+SIGN(0.5_r8,-dZde_p(i,j+1,k2)))* &
& tl_dZde_p(i,j+1,k2)
tl_cff3=(0.5_r8+SIGN(0.5_r8, dZde_p(i,j ,k2)))* &
& tl_dZde_p(i,j ,k2)
tl_cff4=(0.5_r8+SIGN(0.5_r8, dZde_p(i,j+1,k1)))* &
& tl_dZde_p(i,j+1,k1)
!^ UFse(i,j,k2)=fac2* &
!^ & (cff1*(cff1*dmUdz-dmUde(i,j ,k1))+ &
!^ & cff2*(cff2*dmUdz-dmUde(i,j+1,k2))+ &
!^ & cff3*(cff3*dmUdz-dmUde(i,j ,k2))+ &
!^ & cff4*(cff4*dmUdz-dmUde(i,j+1,k1)))
!^
tl_UFse(i,j,k2)=fac2* &
& (tl_cff1*(cff1*dmUdz-dmUde(i,j ,k1))+ &
& tl_cff2*(cff2*dmUdz-dmUde(i,j+1,k2))+ &
& tl_cff3*(cff3*dmUdz-dmUde(i,j ,k2))+ &
& tl_cff4*(cff4*dmUdz-dmUde(i,j+1,k1))+ &
& cff1*(tl_cff1*dmUdz+cff1*tl_dmUdz- &
& tl_dmUde(i,j ,k1))+ &
& cff2*(tl_cff2*dmUdz+cff2*tl_dmUdz- &
& tl_dmUde(i,j+1,k2))+ &
& cff3*(tl_cff3*dmUdz+cff3*tl_dmUdz- &
& tl_dmUde(i,j ,k2))+ &
& cff4*(tl_cff4*dmUdz+cff4*tl_dmUdz- &
& tl_dmUde(i,j+1,k1)))
#ifdef VISC_3DCOEF
tl_UFse(i,j,k2)=tl_UFse(i,j,k2)+ &
& tl_fac2* &
& (cff1*(cff1*dmUdz-dmUde(i,j ,k1))+ &
& cff2*(cff2*dmUdz-dmUde(i,j+1,k2))+ &
& cff3*(cff3*dmUdz-dmUde(i,j ,k2))+ &
& cff4*(cff4*dmUdz-dmUde(i,j+1,k1)))
#endif
cff1=MIN(dZde_p(i,j ,k1),0.0_r8)
cff2=MIN(dZde_p(i,j+1,k2),0.0_r8)
cff3=MAX(dZde_p(i,j ,k2),0.0_r8)
cff4=MAX(dZde_p(i,j+1,k1),0.0_r8)
cff5=MIN(dZdx_p(i,j ,k1),0.0_r8)
cff6=MIN(dZdx_p(i,j+1,k2),0.0_r8)
cff7=MAX(dZdx_p(i,j ,k2),0.0_r8)
cff8=MAX(dZdx_p(i,j+1,k1),0.0_r8)
tl_cff1=(0.5_r8+SIGN(0.5_r8,-dZde_p(i,j ,k1)))* &
& tl_dZde_p(i,j ,k1)
tl_cff2=(0.5_r8+SIGN(0.5_r8,-dZde_p(i,j+1,k2)))* &
& tl_dZde_p(i,j+1,k2)
tl_cff3=(0.5_r8+SIGN(0.5_r8, dZde_p(i,j ,k2)))* &
& tl_dZde_p(i,j ,k2)
tl_cff4=(0.5_r8+SIGN(0.5_r8, dZde_p(i,j+1,k1)))* &
& tl_dZde_p(i,j+1,k1)
tl_cff5=(0.5_r8+SIGN(0.5_r8,-dZdx_p(i,j ,k1)))* &
& tl_dZdx_p(i,j ,k1)
tl_cff6=(0.5_r8+SIGN(0.5_r8,-dZdx_p(i,j+1,k2)))* &
& tl_dZdx_p(i,j+1,k2)
tl_cff7=(0.5_r8+SIGN(0.5_r8, dZdx_p(i,j ,k2)))* &
& tl_dZdx_p(i,j ,k2)
tl_cff8=(0.5_r8+SIGN(0.5_r8, dZdx_p(i,j+1,k1)))* &
& tl_dZdx_p(i,j+1,k1)
!^ UFsx(i,j,k2)=UFsx(i,j,k2)+ &
!^ & fac1* &
!^ & (cff1*(cff5*dnVdz-dnVdx(i,j ,k1))+ &
!^ & cff2*(cff6*dnVdz-dnVdx(i,j+1,k2))+ &
!^ & cff3*(cff7*dnVdz-dnVdx(i,j ,k2))+ &
!^ & cff4*(cff8*dnVdz-dnVdx(i,j+1,k1)))
!^
tl_UFsx(i,j,k2)=tl_UFsx(i,j,k2)+ &
& fac1* &
& (tl_cff1*(cff5*dnVdz-dnVdx(i,j ,k1))+ &
& tl_cff2*(cff6*dnVdz-dnVdx(i,j+1,k2))+ &
& tl_cff3*(cff7*dnVdz-dnVdx(i,j ,k2))+ &
& tl_cff4*(cff8*dnVdz-dnVdx(i,j+1,k1))+ &
& cff1*(tl_cff5*dnVdz+cff5*tl_dnVdz- &
& tl_dnVdx(i,j ,k1))+ &
& cff2*(tl_cff6*dnVdz+cff6*tl_dnVdz- &
& tl_dnVdx(i,j+1,k2))+ &
& cff3*(tl_cff7*dnVdz+cff7*tl_dnVdz- &
& tl_dnVdx(i,j ,k2))+ &
& cff4*(tl_cff8*dnVdz+cff8*tl_dnVdz- &
& tl_dnVdx(i,j+1,k1)))
#ifdef VISC_3DCOEF
tl_UFsx(i,j,k2)=tl_UFsx(i,j,k2)+ &
& tl_fac1* &
& (cff1*(cff5*dnVdz-dnVdx(i,j ,k1))+ &
& cff2*(cff6*dnVdz-dnVdx(i,j+1,k2))+ &
& cff3*(cff7*dnVdz-dnVdx(i,j ,k2))+ &
& cff4*(cff8*dnVdz-dnVdx(i,j+1,k1)))
#endif
cff1=MIN(dZdx_r(i-1,j,k1),0.0_r8)
cff2=MIN(dZdx_r(i ,j,k2),0.0_r8)
cff3=MAX(dZdx_r(i-1,j,k2),0.0_r8)
cff4=MAX(dZdx_r(i ,j,k1),0.0_r8)
cff5=MIN(dZde_r(i-1,j,k1),0.0_r8)
cff6=MIN(dZde_r(i ,j,k2),0.0_r8)
cff7=MAX(dZde_r(i-1,j,k2),0.0_r8)
cff8=MAX(dZde_r(i ,j,k1),0.0_r8)
tl_cff1=(0.5_r8+SIGN(0.5_r8,-dZdx_r(i-1,j,k1)))* &
& tl_dZdx_r(i-1,j,k1)
tl_cff2=(0.5_r8+SIGN(0.5_r8,-dZdx_r(i ,j,k2)))* &
& tl_dZdx_r(i ,j,k2)
tl_cff3=(0.5_r8+SIGN(0.5_r8, dZdx_r(i-1,j,k2)))* &
& tl_dZdx_r(i-1,j,k2)
tl_cff4=(0.5_r8+SIGN(0.5_r8, dZdx_r(i ,j,k1)))* &
& tl_dZdx_r(i ,j,k1)
tl_cff5=(0.5_r8+SIGN(0.5_r8,-dZde_r(i-1,j,k1)))* &
& tl_dZde_r(i-1,j,k1)
tl_cff6=(0.5_r8+SIGN(0.5_r8,-dZde_r(i ,j,k2)))* &
& tl_dZde_r(i ,j,k2)
tl_cff7=(0.5_r8+SIGN(0.5_r8, dZde_r(i-1,j,k2)))* &
& tl_dZde_r(i-1,j,k2)
tl_cff8=(0.5_r8+SIGN(0.5_r8, dZde_r(i ,j,k1)))* &
& tl_dZde_r(i ,j,k1)
!^ UFse(i,j,k2)=UFse(i,j,k2)- &
!^ & fac2* &
!^ & (cff1*(cff5*dmVdz-dmVde(i-1,j,k1))+ &
!^ & cff2*(cff6*dmVdz-dmVde(i ,j,k2))+ &
!^ & cff3*(cff7*dmVdz-dmVde(i-1,j,k2))+ &
!^ & cff4*(cff8*dmVdz-dmVde(i ,j,k1)))
!^
tl_UFse(i,j,k2)=tl_UFse(i,j,k2)- &
& fac2* &
& (tl_cff1*(cff5*dmVdz-dmVde(i-1,j,k1))+ &
& tl_cff2*(cff6*dmVdz-dmVde(i ,j,k2))+ &
& tl_cff3*(cff7*dmVdz-dmVde(i-1,j,k2))+ &
& tl_cff4*(cff8*dmVdz-dmVde(i ,j,k1))+ &
& cff1*(tl_cff5*dmVdz+cff5*tl_dmVdz- &
& tl_dmVde(i-1,j,k1))+ &
& cff2*(tl_cff6*dmVdz+cff6*tl_dmVdz- &
& tl_dmVde(i ,j,k2))+ &
& cff3*(tl_cff7*dmVdz+cff7*tl_dmVdz- &
& tl_dmVde(i-1,j,k2))+ &
& cff4*(tl_cff8*dmVdz+cff8*tl_dmVdz- &
& tl_dmVde(i ,j,k1)))
#ifdef VISC_3DCOEF
tl_UFse(i,j,k2)=tl_UFse(i,j,k2)- &
& tl_fac2* &
& (cff1*(cff5*dmVdz-dmVde(i-1,j,k1))+ &
& cff2*(cff6*dmVdz-dmVde(i ,j,k2))+ &
& cff3*(cff7*dmVdz-dmVde(i-1,j,k2))+ &
& cff4*(cff8*dmVdz-dmVde(i ,j,k1)))
#endif
END DO
END DO
!
DO j=JstrV,Jend
DO i=Istr,Iend
#ifdef VISC_3DCOEF
cff=0.125_r8* &
& (visc3d_r(i,j-1,k )+visc3d_r(i,j,k )+ &
& visc3d_r(i,j-1,k+1)+visc3d_r(i,j,k+1))
tl_cff=0.125_r8* &
& (tl_visc3d_r(i,j-1,k )+tl_visc3d_r(i,j,k )+ &
& tl_visc3d_r(i,j-1,k+1)+tl_visc3d_r(i,j,k+1))
fac1=cff*on_v(i,j)
tl_fac1=tl_cff*on_v(i,j)
fac2=cff*om_v(i,j)
tl_fac2=tl_cff*om_v(i,j)
#else
cff=0.25_r8*(visc2_r(i,j-1)+visc2_r(i,j))
fac1=cff*on_v(i,j)
fac2=cff*om_v(i,j)
#endif
cff=0.5_r8*(pn(i,j-1)+pn(i,j))
dnUdz=cff*0.25_r8*(dUdz(i ,j ,k2)+ &
& dUdz(i+1,j ,k2)+ &
& dUdz(i ,j-1,k2)+ &
& dUdz(i+1,j-1,k2))
tl_dnUdz=cff*0.25_r8*(tl_dUdz(i ,j ,k2)+ &
& tl_dUdz(i+1,j ,k2)+ &
& tl_dUdz(i ,j-1,k2)+ &
& tl_dUdz(i+1,j-1,k2))
dnVdz=cff*dVdz(i,j,k2)
tl_dnVdz=cff*tl_dVdz(i,j,k2)
cff=0.5_r8*(pm(i,j-1)+pm(i,j))
dmUdz=cff*0.25_r8*(dUdz(i ,j ,k2)+ &
& dUdz(i+1,j ,k2)+ &
& dUdz(i ,j-1,k2)+ &
& dUdz(i+1,j-1,k2))
tl_dmUdz=cff*0.25_r8*(tl_dUdz(i ,j ,k2)+ &
& tl_dUdz(i+1,j ,k2)+ &
& tl_dUdz(i ,j-1,k2)+ &
& tl_dUdz(i+1,j-1,k2))
dmVdz=cff*dVdz(i,j,k2)
tl_dmVdz=cff*tl_dVdz(i,j,k2)
cff1=MIN(dZdx_p(i ,j,k1),0.0_r8)
cff2=MIN(dZdx_p(i+1,j,k2),0.0_r8)
cff3=MAX(dZdx_p(i ,j,k2),0.0_r8)
cff4=MAX(dZdx_p(i+1,j,k1),0.0_r8)
tl_cff1=(0.5_r8+SIGN(0.5_r8,-dZdx_p(i ,j,k1)))* &
& tl_dZdx_p(i ,j,k1)
tl_cff2=(0.5_r8+SIGN(0.5_r8,-dZdx_p(i+1,j,k2)))* &
& tl_dZdx_p(i+1,j,k2)
tl_cff3=(0.5_r8+SIGN(0.5_r8, dZdx_p(i ,j,k2)))* &
& tl_dZdx_p(i ,j,k2)
tl_cff4=(0.5_r8+SIGN(0.5_r8, dZdx_p(i+1,j,k1)))* &
& tl_dZdx_p(i+1,j,k1)
!^ VFsx(i,j,k2)=fac1* &
!^ & (cff1*(cff1*dnVdz-dnVdx(i ,j,k1))+ &
!^ & cff2*(cff2*dnVdz-dnVdx(i+1,j,k2))+ &
!^ & cff3*(cff3*dnVdz-dnVdx(i ,j,k2))+ &
!^ & cff4*(cff4*dnVdz-dnVdx(i+1,j,k1)))
!^
tl_VFsx(i,j,k2)=fac1* &
& (tl_cff1*(cff1*dnVdz-dnVdx(i ,j,k1))+ &
& tl_cff2*(cff2*dnVdz-dnVdx(i+1,j,k2))+ &
& tl_cff3*(cff3*dnVdz-dnVdx(i ,j,k2))+ &
& tl_cff4*(cff4*dnVdz-dnVdx(i+1,j,k1))+ &
& cff1*(tl_cff1*dnVdz+cff1*tl_dnVdz- &
& tl_dnVdx(i ,j,k1))+ &
& cff2*(tl_cff2*dnVdz+cff2*tl_dnVdz- &
& tl_dnVdx(i+1,j,k2))+ &
& cff3*(tl_cff3*dnVdz+cff3*tl_dnVdz- &
& tl_dnVdx(i ,j,k2))+ &
& cff4*(tl_cff4*dnVdz+cff4*tl_dnVdz- &
& tl_dnVdx(i+1,j,k1)))
#ifdef VISC_3DCOEF
tl_VFsx(i,j,k2)=tl_VFsx(i,j,k2)+ &
& tl_fac1* &
& (cff1*(cff1*dnVdz-dnVdx(i ,j,k1))+ &
& cff2*(cff2*dnVdz-dnVdx(i+1,j,k2))+ &
& cff3*(cff3*dnVdz-dnVdx(i ,j,k2))+ &
& cff4*(cff4*dnVdz-dnVdx(i+1,j,k1)))
#endif
cff1=MIN(dZde_r(i,j-1,k1),0.0_r8)
cff2=MIN(dZde_r(i,j ,k2),0.0_r8)
cff3=MAX(dZde_r(i,j-1,k2),0.0_r8)
cff4=MAX(dZde_r(i,j ,k1),0.0_r8)
tl_cff1=(0.5_r8+SIGN(0.5_r8,-dZde_r(i,j-1,k1)))* &
& tl_dZde_r(i,j-1,k1)
tl_cff2=(0.5_r8+SIGN(0.5_r8,-dZde_r(i,j ,k2)))* &
& tl_dZde_r(i,j ,k2)
tl_cff3=(0.5_r8+SIGN(0.5_r8, dZde_r(i,j-1,k2)))* &
& tl_dZde_r(i,j-1,k2)
tl_cff4=(0.5_r8+SIGN(0.5_r8, dZde_r(i,j ,k1)))* &
& tl_dZde_r(i,j ,k1)
!^ VFse(i,j,k2)=fac2* &
!^ & (cff1*(cff1*dmVdz-dmVde(i,j-1,k1))+ &
!^ & cff2*(cff2*dmVdz-dmVde(i,j ,k2))+ &
!^ & cff3*(cff3*dmVdz-dmVde(i,j-1,k2))+ &
!^ & cff4*(cff4*dmVdz-dmVde(i,j ,k1)))
!^
tl_VFse(i,j,k2)=fac2* &
& (tl_cff1*(cff1*dmVdz-dmVde(i,j-1,k1))+ &
& tl_cff2*(cff2*dmVdz-dmVde(i,j ,k2))+ &
& tl_cff3*(cff3*dmVdz-dmVde(i,j-1,k2))+ &
& tl_cff4*(cff4*dmVdz-dmVde(i,j ,k1))+ &
& cff1*(tl_cff1*dmVdz+cff1*tl_dmVdz- &
& tl_dmVde(i,j-1,k1))+ &
& cff2*(tl_cff2*dmVdz+cff2*tl_dmVdz- &
& tl_dmVde(i,j ,k2))+ &
& cff3*(tl_cff3*dmVdz+cff3*tl_dmVdz- &
& tl_dmVde(i,j-1,k2))+ &
& cff4*(tl_cff4*dmVdz+cff4*tl_dmVdz- &
& tl_dmVde(i,j ,k1)))
#ifdef VISC_3DCOEF
tl_VFse(i,j,k2)=tl_VFse(i,j,k2)+ &
& tl_fac2* &
& (cff1*(cff1*dmVdz-dmVde(i,j-1,k1))+ &
& cff2*(cff2*dmVdz-dmVde(i,j ,k2))+ &
& cff3*(cff3*dmVdz-dmVde(i,j-1,k2))+ &
& cff4*(cff4*dmVdz-dmVde(i,j ,k1)))
#endif
cff1=MIN(dZde_r(i,j-1,k1),0.0_r8)
cff2=MIN(dZde_r(i,j ,k2),0.0_r8)
cff3=MAX(dZde_r(i,j-1,k2),0.0_r8)
cff4=MAX(dZde_r(i,j ,k1),0.0_r8)
cff5=MIN(dZdx_r(i,j-1,k1),0.0_r8)
cff6=MIN(dZdx_r(i,j ,k2),0.0_r8)
cff7=MAX(dZdx_r(i,j-1,k2),0.0_r8)
cff8=MAX(dZdx_r(i,j ,k1),0.0_r8)
tl_cff1=(0.5_r8+SIGN(0.5_r8,-dZde_r(i,j-1,k1)))* &
& tl_dZde_r(i,j-1,k1)
tl_cff2=(0.5_r8+SIGN(0.5_r8,-dZde_r(i,j ,k2)))* &
& tl_dZde_r(i,j ,k2)
tl_cff3=(0.5_r8+SIGN(0.5_r8, dZde_r(i,j-1,k2)))* &
& tl_dZde_r(i,j-1,k2)
tl_cff4=(0.5_r8+SIGN(0.5_r8, dZde_r(i,j ,k1)))* &
& tl_dZde_r(i,j ,k1)
tl_cff5=(0.5_r8+SIGN(0.5_r8,-dZdx_r(i,j-1,k1)))* &
& tl_dZdx_r(i,j-1,k1)
tl_cff6=(0.5_r8+SIGN(0.5_r8,-dZdx_r(i,j ,k2)))* &
& tl_dZdx_r(i,j ,k2)
tl_cff7=(0.5_r8+SIGN(0.5_r8, dZdx_r(i,j-1,k2)))* &
& tl_dZdx_r(i,j-1,k2)
tl_cff8=(0.5_r8+SIGN(0.5_r8, dZdx_r(i,j ,k1)))* &
& tl_dZdx_r(i,j ,k1)
!^ VFsx(i,j,k2)=VFsx(i,j,k2)- &
!^ & fac1* &
!^ & (cff1*(cff5*dnUdz-dnUdx(i,j-1,k1))+ &
!^ & cff2*(cff6*dnUdz-dnUdx(i,j ,k2))+ &
!^ & cff3*(cff7*dnUdz-dnUdx(i,j-1,k2))+ &
!^ & cff4*(cff8*dnUdz-dnUdx(i,j ,k1)))
!^
tl_VFsx(i,j,k2)=tl_VFsx(i,j,k2)- &
& fac1* &
& (tl_cff1*(cff5*dnUdz-dnUdx(i,j-1,k1))+ &
& tl_cff2*(cff6*dnUdz-dnUdx(i,j ,k2))+ &
& tl_cff3*(cff7*dnUdz-dnUdx(i,j-1,k2))+ &
& tl_cff4*(cff8*dnUdz-dnUdx(i,j ,k1))+ &
& cff1*(tl_cff5*dnUdz+cff5*tl_dnUdz- &
& tl_dnUdx(i,j-1,k1))+ &
& cff2*(tl_cff6*dnUdz+cff6*tl_dnUdz- &
& tl_dnUdx(i,j ,k2))+ &
& cff3*(tl_cff7*dnUdz+cff7*tl_dnUdz- &
& tl_dnUdx(i,j-1,k2))+ &
& cff4*(tl_cff8*dnUdz+cff8*tl_dnUdz- &
& tl_dnUdx(i,j ,k1)))
#ifdef VISC_3DCOEF
tl_VFsx(i,j,k2)=tl_VFsx(i,j,k2)- &
& tl_fac1* &
& (cff1*(cff5*dnUdz-dnUdx(i,j-1,k1))+ &
& cff2*(cff6*dnUdz-dnUdx(i,j ,k2))+ &
& cff3*(cff7*dnUdz-dnUdx(i,j-1,k2))+ &
& cff4*(cff8*dnUdz-dnUdx(i,j ,k1)))
#endif
cff1=MIN(dZdx_p(i ,j,k1),0.0_r8)
cff2=MIN(dZdx_p(i+1,j,k2),0.0_r8)
cff3=MAX(dZdx_p(i ,j,k2),0.0_r8)
cff4=MAX(dZdx_p(i+1,j,k1),0.0_r8)
cff5=MIN(dZde_p(i ,j,k1),0.0_r8)
cff6=MIN(dZde_p(i+1,j,k2),0.0_r8)
cff7=MAX(dZde_p(i ,j,k2),0.0_r8)
cff8=MAX(dZde_p(i+1,j,k1),0.0_r8)
tl_cff1=(0.5_r8+SIGN(0.5_r8,-dZdx_p(i ,j,k1)))* &
& tl_dZdx_p(i ,j,k1)
tl_cff2=(0.5_r8+SIGN(0.5_r8,-dZdx_p(i+1,j,k2)))* &
& tl_dZdx_p(i+1,j,k2)
tl_cff3=(0.5_r8+SIGN(0.5_r8, dZdx_p(i ,j,k2)))* &
& tl_dZdx_p(i ,j,k2)
tl_cff4=(0.5_r8+SIGN(0.5_r8, dZdx_p(i+1,j,k1)))* &
& tl_dZdx_p(i+1,j,k1)
tl_cff5=(0.5_r8+SIGN(0.5_r8,-dZde_p(i ,j,k1)))* &
& tl_dZde_p(i ,j,k1)
tl_cff6=(0.5_r8+SIGN(0.5_r8,-dZde_p(i+1,j,k2)))* &
& tl_dZde_p(i+1,j,k2)
tl_cff7=(0.5_r8+SIGN(0.5_r8, dZde_p(i ,j,k2)))* &
& tl_dZde_p(i ,j,k2)
tl_cff8=(0.5_r8+SIGN(0.5_r8, dZde_p(i+1,j,k1)))* &
& tl_dZde_p(i+1,j,k1)
!^ VFse(i,j,k2)=VFse(i,j,k2)+ &
!^ & fac2* &
!^ & (cff1*(cff5*dmUdz-dmUde(i ,j,k1))+ &
!^ & cff2*(cff6*dmUdz-dmUde(i+1,j,k2))+ &
!^ & cff3*(cff7*dmUdz-dmUde(i ,j,k2))+ &
!^ & cff4*(cff8*dmUdz-dmUde(i+1,j,k1)))
!^
tl_VFse(i,j,k2)=tl_VFse(i,j,k2)+ &
& fac2* &
& (tl_cff1*(cff5*dmUdz-dmUde(i ,j,k1))+ &
& tl_cff2*(cff6*dmUdz-dmUde(i+1,j,k2))+ &
& tl_cff3*(cff7*dmUdz-dmUde(i ,j,k2))+ &
& tl_cff4*(cff8*dmUdz-dmUde(i+1,j,k1))+ &
& cff1*(tl_cff5*dmUdz+cff5*tl_dmUdz- &
& tl_dmUde(i ,j,k1))+ &
& cff2*(tl_cff6*dmUdz+cff6*tl_dmUdz- &
& tl_dmUde(i+1,j,k2))+ &
& cff3*(tl_cff7*dmUdz+cff7*tl_dmUdz- &
& tl_dmUde(i ,j,k2))+ &
& cff4*(tl_cff8*dmUdz+cff8*tl_dmUdz- &
& tl_dmUde(i+1,j,k1)))
#ifdef VISC_3DCOEF
tl_VFse(i,j,k2)=tl_VFse(i,j,k2)+ &
& tl_fac2* &
& (cff1*(cff5*dmUdz-dmUde(i ,j,k1))+ &
& cff2*(cff6*dmUdz-dmUde(i+1,j,k2))+ &
& cff3*(cff7*dmUdz-dmUde(i ,j,k2))+ &
& cff4*(cff8*dmUdz-dmUde(i+1,j,k1)))
#endif
END DO
END DO
END IF
!
! Time-step harmonic, geopotential viscosity term. Notice that
! momentum at this stage is HzU and HzV and has m2/s units. Add
! contribution for barotropic forcing terms.
#ifdef DIAGNOSTICS_UV
!! The rotated vertical term cannot be split from the horizontal
!! terms because of the 2D/3D momentum coupling.
#endif
!
DO j=Jstr,Jend
DO i=IstrU,Iend
cff=dt(ng)*0.25_r8*(pm(i-1,j)+pm(i,j))*(pn(i-1,j)+pn(i,j))
!^ cff1=0.5_r8*(pn(i-1,j)+pn(i,j))*(UFx(i,j )-UFx(i-1,j))
!^
tl_cff1=0.5_r8*(pn(i-1,j)+pn(i,j))* &
& (tl_UFx(i,j )-tl_UFx(i-1,j))
!^ cff2=0.5_r8*(pm(i-1,j)+pm(i,j))*(UFe(i,j+1)-UFe(i ,j))
!^
tl_cff2=0.5_r8*(pm(i-1,j)+pm(i,j))* &
& (tl_UFe(i,j+1)-tl_UFe(i ,j))
!^ cff3=UFsx(i,j,k2)-UFsx(i,j,k1)
!^
tl_cff3=tl_UFsx(i,j,k2)-tl_UFsx(i,j,k1)
!^ cff4=UFse(i,j,k2)-UFse(i,j,k1)
!^
tl_cff4=tl_UFse(i,j,k2)-tl_UFse(i,j,k1)
!^ cff5=cff*(cff1+cff2)
!^
tl_cff5=cff*(tl_cff1+tl_cff2)
!^ cff6=dt(ng)*(cff3+cff4)
!^
tl_cff6=dt(ng)*(tl_cff3+tl_cff4)
!^ rufrc(i,j)=rufrc(i,j)+cff1+cff2+cff3+cff4
!^
tl_rufrc(i,j)=tl_rufrc(i,j)+ &
& tl_cff1+tl_cff2+tl_cff3+tl_cff4
!^ u(i,j,k,nnew)=u(i,j,k,nnew)+cff5+cff6
!^
tl_u(i,j,k,nnew)=tl_u(i,j,k,nnew)+tl_cff5+tl_cff6
#ifdef DIAGNOSTICS_UV
!! DiaRUfrc(i,j,3,M2hvis)=DiaRUfrc(i,j,3,M2hvis)+cff1+cff2+ &
!! & cff3+cff4
!! DiaRUfrc(i,j,3,M2xvis)=DiaRUfrc(i,j,3,M2xvis)+cff1+cff3
!! DiaRUfrc(i,j,3,M2yvis)=DiaRUfrc(i,j,3,M2yvis)+cff2+cff4
!! DiaU3wrk(i,j,k,M3hvis)=cff5+cff6
!! DiaU3wrk(i,j,k,M3xvis)=cff*cff1+dt(ng)*cff3
!! DiaU3wrk(i,j,k,M3yvis)=cff*cff2+dt(ng)*cff4
#endif
END DO
END DO
DO j=JstrV,Jend
DO i=Istr,Iend
cff=dt(ng)*0.25_r8*(pm(i,j)+pm(i,j-1))*(pn(i,j)+pn(i,j-1))
!^ cff1=0.5_r8*(pn(i,j-1)+pn(i,j))*(VFx(i+1,j)-VFx(i,j ))
!^
tl_cff1=0.5_r8*(pn(i,j-1)+pn(i,j))* &
& (tl_VFx(i+1,j)-tl_VFx(i,j ))
!^ cff2=0.5_r8*(pm(i,j-1)+pm(i,j))*(VFe(i ,j)-VFe(i,j-1))
!^
tl_cff2=0.5_r8*(pm(i,j-1)+pm(i,j))* &
& (tl_VFe(i ,j)-tl_VFe(i,j-1))
!^ cff3=VFsx(i,j,k2)-VFsx(i,j,k1)
!^
tl_cff3=tl_VFsx(i,j,k2)-tl_VFsx(i,j,k1)
!^ cff4=VFse(i,j,k2)-VFse(i,j,k1)
!^
tl_cff4=tl_VFse(i,j,k2)-tl_VFse(i,j,k1)
!^ cff5=cff*(cff1-cff2)
!^
tl_cff5=cff*(tl_cff1-tl_cff2)
!^ cff6=dt(ng)*(cff3+cff4)
!^
tl_cff6=dt(ng)*(tl_cff3+tl_cff4)
!^ rvfrc(i,j)=rvfrc(i,j)+cff1-cff2+cff3+cff4
!^
tl_rvfrc(i,j)=tl_rvfrc(i,j)+ &
& tl_cff1-tl_cff2+tl_cff3+tl_cff4
!^ v(i,j,k,nnew)=v(i,j,k,nnew)+cff5+cff6
!^
tl_v(i,j,k,nnew)=tl_v(i,j,k,nnew)+tl_cff5+tl_cff6
#ifdef DIAGNOSTICS_UV
!! DiaRVfrc(i,j,3,M2hvis)=DiaRVfrc(i,j,3,M2hvis)+cff1-cff2+ &
!! & cff3+cff4
!! DiaRVfrc(i,j,3,M2xvis)=DiaRVfrc(i,j,3,M2xvis)+cff1+cff3
!! DiaRVfrc(i,j,3,M2yvis)=DiaRVfrc(i,j,3,M2yvis)-cff2+cff4
!! DiaV3wrk(i,j,k,M3hvis)=cff5+cff6
!! DiaV3wrk(i,j,k,M3xvis)= cff*cff1+dt(ng)*cff3
!! DiaV3wrk(i,j,k,M3yvis)=-cff*cff2+dt(ng)*cff4
#endif
END DO
END DO
END IF
END DO K_LOOP
!
RETURN
END SUBROUTINE tl_uv3dmix2_geo_tile
END MODULE tl_uv3dmix2_mod