#include "cppdefs.h"
MODULE tl_conv_bry3d_mod
#if defined TANGENT && defined FOUR_DVAR && defined SOLVE3D && \
defined ADJUST_BOUNDARY
!
!svn $Id: tl_conv_bry3d.F 889 2018-02-10 03:32:52Z arango $
!================================================== Hernan G. Arango ===
! Copyright (c) 2002-2019 The ROMS/TOMS Group Andrew M. Moore !
! Licensed under a MIT/X style license !
! See License_ROMS.txt !
!=======================================================================
! !
! These routines applies the background error covariance to data !
! assimilation fields via the space convolution of the diffusion !
! equation (filter) for 3D state variables. The diffusion filter !
! is solved using an implicit or explicit vertical algorithm. !
! !
! For Gaussian (bell-shaped) correlations, the space convolution !
! of the diffusion operator is an efficient way to estimate the !
! finite domain error covariances. !
! !
! On Input: !
! !
! ng Nested grid number !
! tile Tile partition !
! model Calling model identifier !
! boundary Boundary edge to convolve !
! edge Boundary edges index !
! LBij Lower bound MIN(I,J)-dimension !
! LBij Lower bound MAX(I,J)-dimension !
! LBi I-dimension lower bound !
! UBi I-dimension upper bound !
! LBj J-dimension lower bound !
! UBj J-dimension upper bound !
! LBk K-dimension lower bound !
! UBk K-dimension upper bound !
! Nghost Number of ghost points !
! NHsteps Number of horizontal diffusion integration steps !
! NVsteps Number of vertical diffusion integration steps !
! DTsizeH Horizontal diffusion pseudo time-step size !
! DTsizeV Vertical diffusion pseudo time-step size !
! Kh Horizontal diffusion coefficients !
! Kv Vertical diffusion coefficients !
! tl_A 3D boundary state variable to diffuse !
! !
! On Output: !
! !
! tl_A Convolved 3D boundary state variable !
! !
! Routines: !
! !
! tl_conv_r3d_bry_tile Tangent linear 3D boundary convolution at !
! RHO-points !
! tl_conv_u3d_bry_tile Tangent linear 3D boundary convolution at !
! U-points !
! tl_conv_v3d_bry_tile Tangent linear 3D boundary convolution at !
! V-points !
! !
!=======================================================================
!
implicit none
!
PUBLIC
!
CONTAINS
!
!***********************************************************************
SUBROUTINE tl_conv_r3d_bry_tile (ng, tile, model, boundary, &
& edge, LBij, UBij, &
& LBi, UBi, LBj, UBj, LBk, UBk, &
& IminS, ImaxS, JminS, JmaxS, &
& Nghost, NHsteps, NVsteps, &
& DTsizeH, DTsizeV, &
& Kh, Kv, &
& pm, pn, pmon_u, pnom_v, &
# ifdef MASKING
& rmask, umask, vmask, &
# endif
& Hz, z_r, &
& tl_A)
!***********************************************************************
!
USE mod_param
USE mod_scalars
!
USE bc_bry3d_mod, ONLY: bc_r3d_bry_tile
# ifdef DISTRIBUTE
USE mp_exchange_mod, ONLY : mp_exchange3d_bry
# endif
!
! Imported variable declarations.
!
integer, intent(in) :: ng, tile, model, boundary
integer, intent(in) :: edge(4)
integer, intent(in) :: LBij, UBij
integer, intent(in) :: LBi, UBi, LBj, UBj, LBk, UBk
integer, intent(in) :: IminS, ImaxS, JminS, JmaxS
integer, intent(in) :: Nghost, NHsteps, NVsteps
real(r8), intent(in) :: DTsizeH, DTsizeV
!
# ifdef ASSUMED_SHAPE
real(r8), intent(in) :: pm(LBi:,LBj:)
real(r8), intent(in) :: pn(LBi:,LBj:)
real(r8), intent(in) :: pmon_u(LBi:,LBj:)
real(r8), intent(in) :: pnom_v(LBi:,LBj:)
# ifdef MASKING
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) :: Hz(LBi:,LBj:,:)
real(r8), intent(in) :: z_r(LBi:,LBj:,:)
real(r8), intent(in) :: Kh(LBi:,LBj:)
real(r8), intent(in) :: Kv(LBi:,LBj:,0:)
real(r8), intent(inout) :: tl_A(LBij:,LBk:)
# else
real(r8), intent(in) :: pm(LBi:UBi,LBj:UBj)
real(r8), intent(in) :: pn(LBi:UBi,LBj:UBj)
real(r8), intent(in) :: pmon_u(LBi:UBi,LBj:UBj)
real(r8), intent(in) :: pnom_v(LBi:UBi,LBj:UBj)
# ifdef MASKING
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) :: Hz(LBi:UBi,LBj:UBj,N(ng))
real(r8), intent(in) :: z_r(LBi:UBi,LBj:UBj,N(ng))
real(r8), intent(in) :: Kh(LBi:UBi,LBj:UBj)
real(r8), intent(in) :: Kv(LBi:UBi,LBj:UBj,0:UBk)
real(r8), intent(inout) :: tl_A(LBij:UBij,LBk:UBk)
# endif
!
! Local variable declarations.
!
logical, dimension(4) :: Lconvolve
integer :: Nnew, Nold, Nsav, i, j, k, step
real(r8) :: cff, cff1
real(r8), dimension(LBij:UBij,LBk:UBk,2) :: tl_Awrk
real(r8), dimension(JminS:JmaxS,LBk:UBk) :: tl_FE
real(r8), dimension(IminS:ImaxS,LBk:UBk) :: tl_FX
real(r8), dimension(LBij:UBij) :: Hfac
# ifdef VCONVOLUTION
# ifndef SPLINES_VCONV
real(r8), dimension(LBij:UBij,0:N(ng)) :: FC
# endif
# if !defined IMPLICIT_VCONV || defined SPLINES_VCONV
real(r8), dimension(LBij:UBij,N(ng)) :: oHz
# endif
# if defined IMPLICIT_VCONV || defined SPLINES_VCONV
real(r8), dimension(LBij:UBij,0:N(ng)) :: BC
real(r8), dimension(LBij:UBij,0:N(ng)) :: CF
# ifdef SPLINES_VCONV
real(r8), dimension(LBij:UBij,0:N(ng)) :: FC
# endif
real(r8), dimension(LBij:UBij,0:N(ng)) :: tl_DC
# else
real(r8), dimension(LBij:UBij,0:N(ng)) :: tl_FS
# endif
# endif
# include "set_bounds.h"
!
!-----------------------------------------------------------------------
! Space convolution of the diffusion equation for a 2D state variable
! at RHO-points.
!-----------------------------------------------------------------------
!
Lconvolve(iwest )=DOMAIN(ng)%Western_Edge (tile)
Lconvolve(ieast )=DOMAIN(ng)%Eastern_Edge (tile)
Lconvolve(isouth)=DOMAIN(ng)%Southern_Edge(tile)
Lconvolve(inorth)=DOMAIN(ng)%Northern_Edge(tile)
!
! Compute metrics factors. Notice that "z_r" and "Hz" are assumed to
! be time invariant in the vertical convolution. Scratch array are
! used for efficiency.
!
IF (Lconvolve(boundary)) THEN
IF ((boundary.eq.iwest).or.(boundary.eq.ieast)) THEN
i=edge(boundary)
DO j=Jstr-1,Jend+1
Hfac(j)=DTsizeH*pm(i,j)*pn(i,j)
# ifdef VCONVOLUTION
# ifndef SPLINES_VCONV
FC(j,N(ng))=0.0_r8
DO k=1,N(ng)-1
# ifdef IMPLICIT_VCONV
FC(j,k)=-DTsizeV*Kv(i,j,k)/ &
& (z_r(i,j,k+1)-z_r(i,j,k))
# else
FC(j,k)=DTsizeV*Kv(i,j,k)/ &
& (z_r(i,j,k+1)-z_r(i,j,k))
# endif
END DO
FC(j,0)=0.0_r8
# endif
# if !defined IMPLICIT_VCONV || defined SPLINES_VCONV
DO k=1,N(ng)
oHz(j,k)=1.0_r8/Hz(i,j,k)
END DO
# endif
# endif
END DO
ELSE IF ((boundary.eq.isouth).or.(boundary.eq.inorth)) THEN
j=edge(boundary)
DO i=Istr-1,Iend+1
Hfac(i)=DTsizeH*pm(i,j)*pn(i,j)
# ifdef VCONVOLUTION
# ifndef SPLINES_VCONV
FC(i,N(ng))=0.0_r8
DO k=1,N(ng)-1
# ifdef IMPLICIT_VCONV
FC(i,k)=-DTsizeV*Kv(i,j,k)/ &
& (z_r(i,j,k+1)-z_r(i,j,k))
# else
FC(i,k)=DTsizeV*Kv(i,j,k)/ &
& (z_r(i,j,k+1)-z_r(i,j,k))
# endif
END DO
FC(i,0)=0.0_r8
# endif
# if !defined IMPLICIT_VCONV || defined SPLINES_VCONV
DO k=1,N(ng)
oHz(i,k)=1.0_r8/Hz(i,j,k)
END DO
# endif
# endif
END DO
END IF
END IF
!
! Set integration indices and initial conditions.
!
Nold=1
Nnew=2
!> CALL bc_r3d_bry_tile (ng, tile, boundary, &
!> & LBij, UBij, 1, N(ng), &
!> & A)
!>
CALL bc_r3d_bry_tile (ng, tile, boundary, &
& LBij, UBij, 1, N(ng), &
& tl_A)
# ifdef DISTRIBUTE
!> CALL mp_exchange3d_bry (ng, tile, model, 1, boundary, &
!> & LBij, UBij, 1, N(ng), &
!> & Nghost, &
!> & EWperiodic(ng), NSperiodic(ng), &
!> & A)
!>
CALL mp_exchange3d_bry (ng, tile, model, 1, boundary, &
& LBij, UBij, 1, N(ng), &
& Nghost, &
& EWperiodic(ng), NSperiodic(ng), &
& tl_A)
# endif
IF (Lconvolve(boundary)) THEN
IF ((boundary.eq.iwest).or.(boundary.eq.ieast)) THEN
DO k=1,N(ng)
DO j=Jstr-1,Jend+1
!> Awrk(j,k,Nold)=A(j,k)
!>
tl_Awrk(j,k,Nold)=tl_A(j,k)
END DO
END DO
ELSE IF ((boundary.eq.isouth).or.(boundary.eq.inorth)) THEN
DO k=1,N(ng)
DO i=Istr-1,Iend+1
!> Awrk(i,k,Nold)=A(i,k)
!>
tl_Awrk(i,k,Nold)=tl_A(i,k)
END DO
END DO
END IF
END IF
!
!-----------------------------------------------------------------------
! Integrate horizontal diffusion equation.
!-----------------------------------------------------------------------
!
DO step=1,NHsteps
!
! Compute XI- and ETA-components of diffusive flux.
!
IF (Lconvolve(boundary)) THEN
IF ((boundary.eq.iwest).or.(boundary.eq.ieast)) THEN
i=edge(boundary)
DO k=1,N(ng)
DO j=Jstr,Jend+1
!> FE(j,k)=pnom_v(i,j)*0.5_r8*(Kh(i,j-1)+Kh(i,j))* &
!> & (Awrk(j ,k,Nold)- &
!> & Awrk(j-1,k,Nold))
!>
tl_FE(j,k)=pnom_v(i,j)*0.5_r8*(Kh(i,j-1)+Kh(i,j))* &
& (tl_Awrk(j ,k,Nold)- &
& tl_Awrk(j-1,k,Nold))
# ifdef MASKING
!> FE(j,k)=FE(j,k)*vmask(i,j)
!>
tl_FE(j,k)=tl_FE(j,k)*vmask(i,j)
# endif
END DO
END DO
ELSE IF ((boundary.eq.isouth).or.(boundary.eq.inorth)) THEN
j=edge(boundary)
DO k=1,N(ng)
DO i=Istr,Iend+1
!> FX(i,k)=pmon_u(i,j)*0.5_r8*(Kh(i-1,j)+Kh(i,j))* &
!> & (Awrk(i ,k,Nold)- &
!> & Awrk(i-1,k,Nold))
!>
tl_FX(i,k)=pmon_u(i,j)*0.5_r8*(Kh(i-1,j)+Kh(i,j))* &
& (tl_Awrk(i ,k,Nold)- &
& tl_Awrk(i-1,k,Nold))
# ifdef MASKING
!> FX(i,k)=FX(i,k)*umask(i,j)
!>
tl_FX(i,k)=tl_FX(i,k)*umask(i,j)
# endif
END DO
END DO
END IF
END IF
!
! Time-step horizontal diffusion equation.
!
IF (Lconvolve(boundary)) THEN
IF ((boundary.eq.iwest).or.(boundary.eq.ieast)) THEN
DO k=1,N(ng)
DO j=Jstr,Jend
!> Awrk(j,k,Nnew)=Awrk(j,k,Nold)+ &
!> & Hfac(j)* &
!> & (FE(j+1,k)-FE(j,k))
!>
tl_Awrk(j,k,Nnew)=tl_Awrk(j,k,Nold)+ &
& Hfac(j)* &
& (tl_FE(j+1,k)-tl_FE(j,k))
END DO
END DO
ELSE IF ((boundary.eq.isouth).or.(boundary.eq.inorth)) THEN
DO k=1,N(ng)
DO i=Istr,Iend
!> Awrk(i,k,Nnew)=Awrk(i,k,Nold)+ &
!> & Hfac(i)* &
!> & (FX(i+1,k)-FX(i,k))
!>
tl_Awrk(i,k,Nnew)=tl_Awrk(i,k,Nold)+ &
& Hfac(i)* &
& (tl_FX(i+1,k)-tl_FX(i,k))
END DO
END DO
END IF
END IF
!
! Apply boundary conditions.
!
!> CALL bc_r3d_bry_tile (ng, tile, boundary, &
!> & LBij, UBij, 1, N(ng), &
!> & Awrk(:,:,Nnew))
!>
CALL bc_r3d_bry_tile (ng, tile, boundary, &
& LBij, UBij, 1, N(ng), &
& tl_Awrk(:,:,Nnew))
# ifdef DISTRIBUTE
!> CALL mp_exchange3d_bry (ng, tile, model, 1, boundary, &
!> & LBij, UBij, 1, N(ng), &
!> & Nghost, &
!> & EWperiodic(ng), NSperiodic(ng), &
!> & Awrk(:,:,Nnew))
!>
CALL mp_exchange3d_bry (ng, tile, model, 1, boundary, &
& LBij, UBij, 1, N(ng), &
& Nghost, &
& EWperiodic(ng), NSperiodic(ng), &
& tl_Awrk(:,:,Nnew))
# endif
!
! Update integration indices.
!
Nsav=Nold
Nold=Nnew
Nnew=Nsav
END DO
# ifdef VCONVOLUTION
# ifdef IMPLICIT_VCONV
# ifdef SPLINES_VCONV
!
!-----------------------------------------------------------------------
! Integrate vertical diffusion equation implicitly using parabolic
! splines.
!-----------------------------------------------------------------------
!
DO step=1,NVsteps
!
! Use conservative, parabolic spline reconstruction of vertical
! diffusion derivatives. Then, time step vertical diffusion term
! implicitly.
!
IF (Lconvolve(boundary)) THEN
IF ((boundary.eq.iwest).or.(boundary.eq.ieast)) THEN
i=edge(boundary)
cff1=1.0_r8/6.0_r8
DO j=Jstr,Jend
DO k=1,N(ng)-1
FC(j,k)=cff1*Hz(i,j,k )- &
& DTsizeV*Kv(i,j,k-1)*oHz(j,k )
CF(j,k)=cff1*Hz(i,j,k+1)- &
& DTsizeV*Kv(i,j,k+1)*oHz(j,k+1)
END DO
CF(j,0)=0.0_r8
!> DC(j,0)=0.0_r8
!>
tl_DC(j,0)=0.0_r8
END DO
ELSE IF ((boundary.eq.isouth).or.(boundary.eq.inorth)) THEN
j=edge(boundary)
cff1=1.0_r8/6.0_r8
DO i=Istr,Iend
DO k=1,N(ng)-1
FC(i,k)=cff1*Hz(i,j,k )- &
& DTsizeV*Kv(i,j,k-1)*oHz(i,k )
CF(i,k)=cff1*Hz(i,j,k+1)- &
& DTsizeV*Kv(i,j,k+1)*oHz(i,k+1)
END DO
CF(i,0)=0.0_r8
!> DC(i,0)=0.0_r8
!>
tl_DC(i,0)=0.0_r8
END DO
END IF
!
! LU decomposition and forward substitution.
!
IF ((boundary.eq.iwest).or.(boundary.eq.ieast)) THEN
i=edge(boundary)
cff1=1.0_r8/3.0_r8
DO k=1,N(ng)-1
DO j=Jstr,Jend
BC(j,k)=cff1*(Hz(i,j,k)+Hz(i,j,k+1))+ &
& DTsizeV*Kv(i,j,k)* &
& (oHz(j,k)+oHz(j,k+1))
cff=1.0_r8/(BC(j,k)-FC(j,k)*CF(j,k-1))
CF(j,k)=cff*CF(j,k)
!> DC(j,k)=cff*(Awrk(j,k+1,Nold)- &
!> & Awrk(j,k ,Nold)- &
!> & FC(j,k)*DC(j,k-1))
!>
tl_DC(j,k)=cff*(tl_Awrk(j,k+1,Nold)- &
& tl_Awrk(j,k ,Nold)- &
& FC(j,k)*tl_DC(j,k-1))
END DO
END DO
ELSE IF ((boundary.eq.isouth).or.(boundary.eq.inorth)) THEN
j=edge(boundary)
cff1=1.0_r8/3.0_r8
DO k=1,N(ng)-1
DO i=Istr,Iend
BC(i,k)=cff1*(Hz(i,j,k)+Hz(i,j,k+1))+ &
& DTsizeV*Kv(i,j,k)* &
& (oHz(i,k)+oHz(i,k+1))
cff=1.0_r8/(BC(i,k)-FC(i,k)*CF(i,k-1))
CF(i,k)=cff*CF(i,k)
!> DC(i,k)=cff*(Awrk(i,k+1,Nold)- &
!> & Awrk(i,k ,Nold)- &
!> & FC(i,k)*DC(i,k-1))
!>
tl_DC(i,k)=cff*(tl_Awrk(i,k+1,Nold)- &
& tl_Awrk(i,k ,Nold)- &
& FC(i,k)*tl_DC(i,k-1))
END DO
END DO
END IF
!
! Backward substitution.
!
IF ((boundary.eq.iwest).or.(boundary.eq.ieast)) THEN
i=edge(boundary)
DO j=Jstr,Jend
!> DC(j,N(ng))=0.0_r8
!>
tl_DC(j,N(ng))=0.0_r8
END DO
DO k=N(ng)-1,1,-1
DO j=Jstr,Jend
!> DC(j,k)=DC(j,k)-CF(j,k)*DC(j,k+1)
!>
tl_DC(j,k)=tl_DC(j,k)-CF(j,k)*tl_DC(j,k+1)
END DO
END DO
DO k=1,N(ng)
DO j=Jstr,Jend
!> DC(j,k)=DC(j,k)*Kv(i,j,k)
!>
tl_DC(j,k)=tl_DC(j,k)*Kv(i,j,k)
!> Awrk(j,k,Nnew)=Awrk(j,k,Nold)+ &
!> & DTsizeV*oHz(j,k)* &
!> & (DC(j,k)-DC(j,k-1))
!>
tl_Awrk(j,k,Nnew)=tl_Awrk(j,k,Nold)+ &
& DTsizeV*oHz(j,k)* &
& (tl_DC(j,k)-tl_DC(j,k-1))
END DO
END DO
ELSE IF ((boundary.eq.isouth).or.(boundary.eq.inorth)) THEN
j=edge(boundary)
DO i=Istr,Iend
!> DC(i,N(ng))=0.0_r8
!>
tl_DC(i,N(ng))=0.0_r8
END DO
DO k=N(ng)-1,1,-1
DO i=Istr,Iend
!> DC(i,k)=DC(i,k)-CF(i,k)*DC(i,k+1)
!>
tl_DC(i,k)=tl_DC(i,k)-CF(i,k)*tl_DC(i,k+1)
END DO
END DO
DO k=1,N(ng)
DO i=Istr,Iend
!> DC(i,k)=DC(i,k)*Kv(i,j,k)
!>
tl_DC(i,k)=tl_DC(i,k)*Kv(i,j,k)
!> Awrk(i,k,Nnew)=Awrk(i,k,Nold)+ &
!> & DTsizeV*oHz(i,k)* &
!> & (DC(i,k)-DC(i,k-1))
!>
tl_Awrk(i,k,Nnew)=tl_Awrk(i,k,Nold)+ &
& DTsizeV*oHz(i,k)* &
& (tl_DC(i,k)-tl_DC(i,k-1))
END DO
END DO
END IF
END IF
!
! Update integration indices.
!
Nsav=Nold
Nold=Nnew
Nnew=Nsav
END DO
# else
!
!-----------------------------------------------------------------------
! Integrate vertical diffusion equation implicitly.
!-----------------------------------------------------------------------
!
DO step=1,NVsteps
!
! Compute diagonal matrix coefficients BC and load right-hand-side
! terms for the diffusion equation into DC.
!
IF (Lconvolve(boundary)) THEN
IF ((boundary.eq.iwest).or.(boundary.eq.ieast)) THEN
i=edge(boundary)
DO k=1,N(ng)
DO j=Jstr,Jend
BC(j,k)=Hz(i,j,k)-FC(j,k)-FC(j,k-1)
!> DC(j,k)=Awrk(j,k,Nold)*Hz(i,j,k)
!>
tl_DC(j,k)=tl_Awrk(j,k,Nold)*Hz(i,j,k)
END DO
END DO
ELSE IF ((boundary.eq.isouth).or.(boundary.eq.inorth)) THEN
j=edge(boundary)
DO k=1,N(ng)
DO i=Istr,Iend
BC(i,k)=Hz(i,j,k)-FC(i,k)-FC(i,k-1)
!> DC(i,k)=Awrk(i,k,Nold)*Hz(i,j,k)
!>
tl_DC(i,k)=tl_Awrk(i,k,Nold)*Hz(i,j,k)
END DO
END DO
END IF
!
! Solve the tridiagonal system.
!
IF ((boundary.eq.iwest).or.(boundary.eq.ieast)) THEN
DO j=Jstr,Jend
cff=1.0_r8/BC(j,1)
CF(j,1)=cff*FC(j,1)
!> DC(j,1)=cff*DC(j,1)
!>
tl_DC(j,1)=cff*tl_DC(j,1)
END DO
DO k=2,N(ng)-1
DO j=Jstr,Jend
cff=1.0_r8/(BC(j,k)-FC(j,k-1)*CF(j,k-1))
CF(j,k)=cff*FC(j,k)
!> DC(j,k)=cff*(DC(j,k)-FC(j,k-1)*DC(j,k-1))
!>
tl_DC(j,k)=cff*(tl_DC(j,k)-FC(j,k-1)*tl_DC(j,k-1))
END DO
END DO
ELSE IF ((boundary.eq.isouth).or.(boundary.eq.inorth)) THEN
DO i=Istr,Iend
cff=1.0_r8/BC(i,1)
CF(i,1)=cff*FC(i,1)
!> DC(i,1)=cff*DC(i,1)
!>
tl_DC(i,1)=cff*tl_DC(i,1)
END DO
DO k=2,N(ng)-1
DO i=Istr,Iend
cff=1.0_r8/(BC(i,k)-FC(i,k-1)*CF(i,k-1))
CF(i,k)=cff*FC(i,k)
!> DC(i,k)=cff*(DC(i,k)-FC(i,k-1)*DC(i,k-1))
!>
tl_DC(i,k)=cff*(tl_DC(i,k)-FC(i,k-1)*tl_DC(i,k-1))
END DO
END DO
END IF
!
! Compute new solution by back substitution.
!
IF ((boundary.eq.iwest).or.(boundary.eq.ieast)) THEN
i=edge(boundary)
DO j=Jstr,Jend
!> DC(j,N(ng))=(DC(j,N(ng))- &
!> & FC(j,N(ng)-1)*DC(j,N(ng)-1))/ &
!> & (BC(j,N(ng))- &
!> & FC(j,N(ng)-1)*CF(j,N(ng)-1))
!>
tl_DC(j,N(ng))=(tl_DC(j,N(ng))- &
& FC(j,N(ng)-1)*tl_DC(j,N(ng)-1))/ &
& (BC(j,N(ng))- &
& FC(j,N(ng)-1)*CF(j,N(ng)-1))
!> Awrk(j,N(ng),Nnew)=DC(j,N(ng))
!>
tl_Awrk(j,N(ng),Nnew)=tl_DC(j,N(ng))
# ifdef MASKING
!> Awrk(j,N(ng),Nnew)=Awrk(j,N(ng),Nnew)*rmask(i,j)
!>
tl_Awrk(j,N(ng),Nnew)=tl_Awrk(j,N(ng),Nnew)*rmask(i,j)
# endif
END DO
DO k=N(ng)-1,1,-1
DO j=Jstr,Jend
!> DC(j,k)=DC(j,k)-CF(j,k)*DC(j,k+1)
!>
tl_DC(j,k)=tl_DC(j,k)-CF(j,k)*tl_DC(j,k+1)
!> Awrk(j,k,Nnew)=DC(j,k)
!>
tl_Awrk(j,k,Nnew)=tl_DC(j,k)
# ifdef MASKING
!> Awrk(j,k,Nnew)=Awrk(j,k,Nnew)*rmask(i,j)
!>
tl_Awrk(j,k,Nnew)=tl_Awrk(j,k,Nnew)*rmask(i,j)
# endif
END DO
END DO
ELSE IF ((boundary.eq.isouth).or.(boundary.eq.inorth)) THEN
j=edge(boundary)
DO i=Istr,Iend
!> DC(i,N(ng))=(DC(i,N(ng))- &
!> & FC(i,N(ng)-1)*DC(i,N(ng)-1))/ &
!> & (BC(i,N(ng))- &
!> & FC(i,N(ng)-1)*CF(i,N(ng)-1))
!>
tl_DC(i,N(ng))=(tl_DC(i,N(ng))- &
& FC(i,N(ng)-1)*tl_DC(i,N(ng)-1))/ &
& (BC(i,N(ng))- &
& FC(i,N(ng)-1)*CF(i,N(ng)-1))
!> Awrk(i,N(ng),Nnew)=DC(i,N(ng))
!>
tl_Awrk(i,N(ng),Nnew)=tl_DC(i,N(ng))
# ifdef MASKING
!> Awrk(i,N(ng),Nnew)=Awrk(i,N(ng),Nnew)*rmask(i,j)
!>
tl_Awrk(i,N(ng),Nnew)=tl_Awrk(i,N(ng),Nnew)*rmask(i,j)
# endif
END DO
DO k=N(ng)-1,1,-1
DO i=Istr,Iend
!> DC(i,k)=DC(i,k)-CF(i,k)*DC(i,k+1)
!>
tl_DC(i,k)=tl_DC(i,k)-CF(i,k)*tl_DC(i,k+1)
!> Awrk(i,k,Nnew)=DC(i,k)
!>
tl_Awrk(i,k,Nnew)=tl_DC(i,k)
# ifdef MASKING
!> Awrk(i,k,Nnew)=Awrk(i,k,Nnew)*rmask(i,j)
!>
tl_Awrk(i,k,Nnew)=tl_Awrk(i,k,Nnew)*rmask(i,j)
# endif
END DO
END DO
END IF
END IF
!
! Update integration indices.
!
Nsav=Nold
Nold=Nnew
Nnew=Nsav
END DO
# endif
# else
!
!-----------------------------------------------------------------------
! Integrate vertical diffusion equation explicitly.
!-----------------------------------------------------------------------
!
DO step=1,NVsteps
!
! Compute vertical diffusive flux. Notice that "FC" is assumed to
! be time invariant.
!
IF (Lconvolve(boundary)) THEN
IF ((boundary.eq.iwest).or.(boundary.eq.ieast)) THEN
i=edge(boundary)
DO j=Jstr,Jend
DO k=1,N(ng)-1
!> FS(j,k)=FC(j,k)*(Awrk(j,k+1,Nold)- &
!> & Awrk(j,k ,Nold))
!>
tl_FS(j,k)=FC(j,k)*(tl_Awrk(j,k+1,Nold)- &
& tl_Awrk(j,k ,Nold))
# ifdef MASKING
!> FS(j,k)=FS(j,k)*rmask(i,j)
!>
tl_FS(j,k)=tl_FS(j,k)*rmask(i,j)
# endif
END DO
!> FS(j,0)=0.0_r8
!>
tl_FS(j,0)=0.0_r8
!> FS(j,N(ng))=0.0_r8
!>
tl_FS(j,N(ng))=0.0_r8
END DO
ELSE IF ((boundary.eq.isouth).or.(boundary.eq.inorth)) THEN
j=edge(boundary)
DO i=Istr,Iend
DO k=1,N(ng)-1
!> FS(i,k)=FC(i,k)*(Awrk(i,k+1,Nold)- &
!> & Awrk(i,k ,Nold))
!>
tl_FS(i,k)=FC(i,k)*(tl_Awrk(i,k+1,Nold)- &
& tl_Awrk(i,k ,Nold))
# ifdef MASKING
!> FS(i,k)=FS(i,k)*rmask(i,j)
!>
tl_FS(i,k)=tl_FS(i,k)*rmask(i,j)
# endif
END DO
!> FS(i,0)=0.0_r8
!>
tl_FS(i,0)=0.0_r8
!> FS(i,N(ng))=0.0_r8
!>
tl_FS(i,N(ng))=0.0_r8
END DO
END IF
!
! Time-step vertical diffusive term. Notice that "oHz" is assumed to
! be time invariant.
!
IF ((boundary.eq.iwest).or.(boundary.eq.ieast)) THEN
DO k=1,N(ng)
DO j=Jstr,Jend
!> Awrk(j,k,Nnew)=Awrk(j,k,Nold)+ &
!> & oHz(j,k)*(FS(j,k )- &
!> & FS(j,k-1))
!>
tl_Awrk(j,k,Nnew)=tl_Awrk(j,k,Nold)+ &
& oHz(j,k)*(tl_FS(j,k )- &
& tl_FS(j,k-1))
END DO
END DO
ELSE IF ((boundary.eq.isouth).or.(boundary.eq.inorth)) THEN
DO k=1,N(ng)
DO i=Istr,Iend
!> Awrk(i,k,Nnew)=Awrk(i,k,Nold)+ &
!> & oHz(i,k)*(FS(i,k )- &
!> & FS(i,k-1))
!>
tl_Awrk(i,k,Nnew)=tl_Awrk(i,k,Nold)+ &
& oHz(i,k)*(tl_FS(i,k )- &
& tl_FS(i,k-1))
END DO
END DO
END IF
END IF
!
! Update integration indices.
!
Nsav=Nold
Nold=Nnew
Nnew=Nsav
END DO
# endif
# endif
!
!-----------------------------------------------------------------------
! Load convolved solution.
!-----------------------------------------------------------------------
!
IF (Lconvolve(boundary)) THEN
IF ((boundary.eq.iwest).or.(boundary.eq.ieast)) THEN
DO k=1,N(ng)
DO j=Jstr,Jend
!> A(j,k)=Awrk(j,k,Nold)
!>
tl_A(j,k)=tl_Awrk(j,k,Nold)
END DO
END DO
ELSE IF ((boundary.eq.isouth).or.(boundary.eq.inorth)) THEN
DO k=1,N(ng)
DO i=Istr,Iend
!> A(i,k)=Awrk(i,k,Nold)
!>
tl_A(i,k)=tl_Awrk(i,k,Nold)
END DO
END DO
END IF
END IF
!> CALL bc_r3d_bry_tile (ng, tile, boundary, &
!> & LBij, UBij, 1, N(ng), &
!> & A)
!>
CALL bc_r3d_bry_tile (ng, tile, boundary, &
& LBij, UBij, 1, N(ng), &
& tl_A)
# ifdef DISTRIBUTE
!> CALL mp_exchange3d_bry (ng, tile, model, 1, boundary, &
!> & LBij, UBij, 1, N(ng), &
!> & Nghost, &
!> & EWperiodic(ng), NSperiodic(ng), &
!> & A)
!>
CALL mp_exchange3d_bry (ng, tile, model, 1, boundary, &
& LBij, UBij, 1, N(ng), &
& Nghost, &
& EWperiodic(ng), NSperiodic(ng), &
& tl_A)
# endif
RETURN
END SUBROUTINE tl_conv_r3d_bry_tile
!
!***********************************************************************
SUBROUTINE tl_conv_u3d_bry_tile (ng, tile, model, boundary, &
& edge, LBij, UBij, &
& LBi, UBi, LBj, UBj, LBk, UBk, &
& IminS, ImaxS, JminS, JmaxS, &
& Nghost, NHsteps, NVsteps, &
& DTsizeH, DTsizeV, &
& Kh, Kv, &
& pm, pn, pmon_r, pnom_p, &
# ifdef MASKING
& umask, pmask, &
# endif
& Hz, z_r, &
& tl_A)
!***********************************************************************
!
USE mod_param
USE mod_scalars
!
USE bc_bry3d_mod, ONLY: bc_u3d_bry_tile
# ifdef DISTRIBUTE
USE mp_exchange_mod, ONLY : mp_exchange3d_bry
# endif
!
! Imported variable declarations.
!
integer, intent(in) :: ng, tile, model, boundary
integer, intent(in) :: edge(4)
integer, intent(in) :: LBij, UBij
integer, intent(in) :: LBi, UBi, LBj, UBj, LBk, UBk
integer, intent(in) :: IminS, ImaxS, JminS, JmaxS
integer, intent(in) :: Nghost, NHsteps, NVsteps
real(r8), intent(in) :: DTsizeH, DTsizeV
!
# ifdef ASSUMED_SHAPE
real(r8), intent(in) :: pm(LBi:,LBj:)
real(r8), intent(in) :: pn(LBi:,LBj:)
real(r8), intent(in) :: pmon_r(LBi:,LBj:)
real(r8), intent(in) :: pnom_p(LBi:,LBj:)
# ifdef MASKING
real(r8), intent(in) :: umask(LBi:,LBj:)
real(r8), intent(in) :: pmask(LBi:,LBj:)
# endif
real(r8), intent(in) :: Hz(LBi:,LBj:,:)
real(r8), intent(in) :: z_r(LBi:,LBj:,:)
real(r8), intent(in) :: Kh(LBi:,LBj:)
real(r8), intent(in) :: Kv(LBi:,LBj:,0:)
real(r8), intent(inout) :: tl_A(LBij:,LBk:)
# else
real(r8), intent(in) :: pm(LBi:UBi,LBj:UBj)
real(r8), intent(in) :: pn(LBi:UBi,LBj:UBj)
real(r8), intent(in) :: pmon_r(LBi:UBi,LBj:UBj)
real(r8), intent(in) :: pnom_p(LBi:UBi,LBj:UBj)
# ifdef MASKING
real(r8), intent(in) :: umask(LBi:UBi,LBj:UBj)
real(r8), intent(in) :: pmask(LBi:UBi,LBj:UBj)
# endif
real(r8), intent(in) :: Hz(LBi:UBi,LBj:UBj,N(ng))
real(r8), intent(in) :: z_r(LBi:UBi,LBj:UBj,N(ng))
real(r8), intent(in) :: Kh(LBi:UBi,LBj:UBj)
real(r8), intent(in) :: Kv(LBi:UBi,LBj:UBj,0:UBk)
real(r8), intent(inout) :: tl_A(LBij:UBij,LBk:UBk)
# endif
!
! Local variable declarations.
!
logical, dimension(4) :: Lconvolve
integer :: Nnew, Nold, Nsav, i, j, k, step
real(r8) :: cff, cff1
real(r8), dimension(LBij:UBij,LBk:UBk,2) :: tl_Awrk
real(r8), dimension(JminS:JmaxS,LBk:UBk) :: tl_FE
real(r8), dimension(IminS:ImaxS,LBk:UBk) :: tl_FX
real(r8), dimension(LBij:UBij) :: Hfac
# ifdef VCONVOLUTION
# ifndef SPLINES_VCONV
real(r8), dimension(LBij:UBij,0:N(ng)) :: FC
# endif
# if !defined IMPLICIT_VCONV || defined SPLINES_VCONV
real(r8), dimension(LBij:UBij,N(ng)) :: oHz
# endif
# if defined IMPLICIT_VCONV || defined SPLINES_VCONV
real(r8), dimension(LBij:UBij,0:N(ng)) :: BC
real(r8), dimension(LBij:UBij,0:N(ng)) :: CF
# ifdef SPLINES_VCONV
real(r8), dimension(LBij:UBij,0:N(ng)) :: FC
# endif
real(r8), dimension(LBij:UBij,0:N(ng)) :: tl_DC
# else
real(r8), dimension(LBij:UBij,0:N(ng)) :: tl_FS
# endif
# endif
# include "set_bounds.h"
!
!-----------------------------------------------------------------------
! Space convolution of the diffusion equation for a 2D state variable
! at RHO-points.
!-----------------------------------------------------------------------
!
Lconvolve(iwest )=DOMAIN(ng)%Western_Edge (tile)
Lconvolve(ieast )=DOMAIN(ng)%Eastern_Edge (tile)
Lconvolve(isouth)=DOMAIN(ng)%Southern_Edge(tile)
Lconvolve(inorth)=DOMAIN(ng)%Northern_Edge(tile)
!
! Compute metrics factors. Notice that "z_r" and "Hz" are assumed to
! be time invariant in the vertical convolution. Scratch array are
! used for efficiency.
!
IF (Lconvolve(boundary)) THEN
cff=DTsizeH*0.25_r8
IF ((boundary.eq.iwest).or.(boundary.eq.ieast)) THEN
i=edge(boundary)
DO j=Jstr-1,Jend+1
Hfac(j)=cff*(pm(i-1,j)+pm(i,j))*(pn(i-1,j)+pn(i,j))
# ifdef VCONVOLUTION
# ifndef SPLINES_VCONV
FC(j,N(ng))=0.0_r8
DO k=1,N(ng)-1
# ifdef IMPLICIT_VCONV
FC(j,k)=-DTsizeV*(Kv(i-1,j,k)+Kv(i,j,k))/ &
& (z_r(i-1,j,k+1)+z_r(i,j,k+1)- &
& z_r(i-1,j,k )-z_r(i,j,k ))
# else
FC(j,k)=DTsizeV*(Kv(i-1,j,k)+Kv(i,j,k))/ &
& (z_r(i-1,j,k+1)+z_r(i,j,k+1)- &
& z_r(i-1,j,k )-z_r(i,j,k ))
# endif
END DO
FC(j,0)=0.0_r8
# endif
# if !defined IMPLICIT_VCONV || defined SPLINES_VCONV
DO k=1,N(ng)
oHz(j,k)=2.0_r8/(Hz(i-1,j,k)+Hz(i,j,k))
END DO
# endif
# endif
END DO
ELSE IF ((boundary.eq.isouth).or.(boundary.eq.inorth)) THEN
j=edge(boundary)
DO i=IstrU-1,Iend+1
Hfac(i)=cff*(pm(i-1,j)+pm(i,j))*(pn(i-1,j)+pn(i,j))
# ifdef VCONVOLUTION
# ifndef SPLINES_VCONV
FC(i,N(ng))=0.0_r8
DO k=1,N(ng)-1
# ifdef IMPLICIT_VCONV
FC(i,k)=-DTsizeV*(Kv(i-1,j,k)+Kv(i,j,k))/ &
& (z_r(i-1,j,k+1)+z_r(i,j,k+1)- &
& z_r(i-1,j,k )-z_r(i,j,k ))
# else
FC(i,k)=DTsizeV*(Kv(i-1,j,k)+Kv(i,j,k))/ &
& (z_r(i-1,j,k+1)+z_r(i,j,k+1)- &
& z_r(i-1,j,k )-z_r(i,j,k ))
# endif
END DO
FC(i,0)=0.0_r8
# endif
# if !defined IMPLICIT_VCONV || defined SPLINES_VCONV
DO k=1,N(ng)
oHz(i,k)=2.0_r8/(Hz(i-1,j,k)+Hz(i,j,k))
END DO
# endif
# endif
END DO
END IF
END IF
!
! Set integration indices and initial conditions.
!
Nold=1
Nnew=2
!> CALL bc_u3d_bry_tile (ng, tile, boundary, &
!> & LBij, UBij, 1, N(ng), &
!> & A)
!>
CALL bc_u3d_bry_tile (ng, tile, boundary, &
& LBij, UBij, 1, N(ng), &
& tl_A)
# ifdef DISTRIBUTE
!> CALL mp_exchange3d_bry (ng, tile, model, 1, boundary, &
!> & LBij, UBij, 1, N(ng), &
!> & Nghost, &
!> & EWperiodic(ng), NSperiodic(ng), &
!> & A)
!>
CALL mp_exchange3d_bry (ng, tile, model, 1, boundary, &
& LBij, UBij, 1, N(ng), &
& Nghost, &
& EWperiodic(ng), NSperiodic(ng), &
& tl_A)
# endif
IF (Lconvolve(boundary)) THEN
IF ((boundary.eq.iwest).or.(boundary.eq.ieast)) THEN
DO k=1,N(ng)
DO j=Jstr-1,Jend+1
!> Awrk(j,k,Nold)=A(j,k)
!>
tl_Awrk(j,k,Nold)=tl_A(j,k)
END DO
END DO
ELSE IF ((boundary.eq.isouth).or.(boundary.eq.inorth)) THEN
DO k=1,N(ng)
DO i=IstrU-1,Iend+1
!> Awrk(i,k,Nold)=A(i,k)
!>
tl_Awrk(i,k,Nold)=tl_A(i,k)
END DO
END DO
END IF
END IF
!
!-----------------------------------------------------------------------
! Integrate horizontal diffusion equation.
!-----------------------------------------------------------------------
!
DO step=1,NHsteps
!
! Compute XI- and ETA-components of diffusive flux.
!
IF (Lconvolve(boundary)) THEN
IF ((boundary.eq.iwest).or.(boundary.eq.ieast)) THEN
i=edge(boundary)
DO k=1,N(ng)
DO j=Jstr,Jend+1
!> FE(j,k)=pnom_p(i,j)* &
!> & 0.25_r8*(Kh(i-1,j )+Kh(i,j )+ &
!> & Kh(i-1,j-1)+Kh(i,j-1))* &
!> & (Awrk(j ,k,Nold)- &
!> & Awrk(j-1,k,Nold))
!>
tl_FE(j,k)=pnom_p(i,j)* &
& 0.25_r8*(Kh(i-1,j )+Kh(i,j )+ &
& Kh(i-1,j-1)+Kh(i,j-1))* &
& (tl_Awrk(j ,k,Nold)- &
& tl_Awrk(j-1,k,Nold))
# ifdef MASKING
!> FE(j,k)=FE(j,k)*pmask(i,j)
!>
tl_FE(j,k)=tl_FE(j,k)*pmask(i,j)
# endif
END DO
END DO
ELSE IF ((boundary.eq.isouth).or.(boundary.eq.inorth)) THEN
j=edge(boundary)
DO k=1,N(ng)
DO i=IstrU-1,Iend
!> FX(i,k)=pmon_r(i,j)*Kh(i,j)* &
!> & (Awrk(i+1,k,Nold)- &
!> & Awrk(i ,k,Nold))
!>
tl_FX(i,k)=pmon_r(i,j)*Kh(i,j)* &
& (tl_Awrk(i+1,k,Nold)- &
& tl_Awrk(i ,k,Nold))
END DO
END DO
END IF
!
! Time-step horizontal diffusion equation.
!
IF ((boundary.eq.iwest).or.(boundary.eq.ieast)) THEN
DO k=1,N(ng)
DO j=Jstr,Jend
!> Awrk(j,k,Nnew)=Awrk(j,k,Nold)+ &
!> & Hfac(j)* &
!> & (FE(j+1,k)-FE(j,k))
!>
tl_Awrk(j,k,Nnew)=tl_Awrk(j,k,Nold)+ &
& Hfac(j)* &
& (tl_FE(j+1,k)-tl_FE(j,k))
END DO
END DO
ELSE IF ((boundary.eq.isouth).or.(boundary.eq.inorth)) THEN
DO k=1,N(ng)
DO i=IstrU,Iend
!> Awrk(i,k,Nnew)=Awrk(i,k,Nold)+ &
!> & Hfac(i)* &
!> & (FX(i,k)-FX(i-1,k))
!>
tl_Awrk(i,k,Nnew)=tl_Awrk(i,k,Nold)+ &
& Hfac(i)* &
& (tl_FX(i,k)-tl_FX(i-1,k))
END DO
END DO
END IF
END IF
!
! Apply boundary conditions.
!
!> CALL bc_u3d_bry_tile (ng, tile, boundary, &
!> & LBij, UBij, 1, N(ng), &
!> & Awrk(:,:,Nnew))
!>
CALL bc_u3d_bry_tile (ng, tile, boundary, &
& LBij, UBij, 1, N(ng), &
& tl_Awrk(:,:,Nnew))
# ifdef DISTRIBUTE
!> CALL mp_exchange3d_bry (ng, tile, model, 1, boundary, &
!> & LBij, UBij, 1, N(ng), &
!> & Nghost, &
!> & EWperiodic(ng), NSperiodic(ng), &
!> & Awrk(:,:,Nnew))
!>
CALL mp_exchange3d_bry (ng, tile, model, 1, boundary, &
& LBij, UBij, 1, N(ng), &
& Nghost, &
& EWperiodic(ng), NSperiodic(ng), &
& tl_Awrk(:,:,Nnew))
# endif
!
! Update integration indices.
!
Nsav=Nold
Nold=Nnew
Nnew=Nsav
END DO
# ifdef VCONVOLUTION
# ifdef IMPLICIT_VCONV
# ifdef SPLINES_VCONV
!
!-----------------------------------------------------------------------
! Integrate vertical diffusion equation implicitly using parabolic
! splines.
!-----------------------------------------------------------------------
!
DO step=1,NVsteps
!
! Use conservative, parabolic spline reconstruction of vertical
! diffusion derivatives. Then, time step vertical diffusion term
! implicitly.
!
IF (Lconvolve(boundary)) THEN
IF ((boundary.eq.iwest).or.(boundary.eq.ieast)) THEN
i=edge(boundary)
cff1=0.5_r8*(1.0_r8/6.0_r8)
DO j=Jstr,Jend
DO k=1,N(ng)-1
FC(j,k)=cff1*(Hz(i-1,j,k )+Hz(i,j,k ))- &
& DTsizeV*Kv(i,j,k-1)*oHz(j,k )
CF(j,k)=cff1*(Hz(i-1,j,k+1)+Hz(i,j,k+1))- &
& DTsizeV*Kv(i,j,k+1)*oHz(j,k+1)
END DO
CF(j,0)=0.0_r8
!> DC(j,0)=0.0_r8
!>
tl_DC(j,0)=0.0_r8
END DO
ELSE IF ((boundary.eq.isouth).or.(boundary.eq.inorth)) THEN
j=edge(boundary)
cff1=0.5_r8*(1.0_r8/6.0_r8)
DO i=IstrU,Iend
DO k=1,N(ng)-1
FC(i,k)=cff1*(Hz(i-1,j,k )+Hz(i,j,k ))- &
& DTsizeV*Kv(i,j,k-1)*oHz(i,k )
CF(i,k)=cff1*(Hz(i-1,j,k+1)+Hz(i,j,k+1))- &
& DTsizeV*Kv(i,j,k+1)*oHz(i,k+1)
END DO
CF(i,0)=0.0_r8
!> DC(i,0)=0.0_r8
!>
tl_DC(i,0)=0.0_r8
END DO
END IF
!
! LU decomposition and forward substitution.
!
IF ((boundary.eq.iwest).or.(boundary.eq.ieast)) THEN
i=edge(boundary)
cff1=0.5_r8*(1.0_r8/3.0_r8)
DO k=1,N(ng)-1
DO j=Jstr,Jend
BC(j,k)=cff1*(Hz(i-1,j,k )+Hz(i,j,k )+ &
& Hz(i-1,j,k+1)+Hz(i,j,k+1))+ &
& DTsizeV*Kv(i,j,k)* &
& (oHz(j,k)+oHz(j,k+1))
cff=1.0_r8/(BC(j,k)-FC(j,k)*CF(j,k-1))
CF(j,k)=cff*CF(j,k)
!> DC(j,k)=cff*(Awrk(j,k+1,Nold)- &
!> & Awrk(j,k ,Nold)- &
!> & FC(j,k)*DC(j,k-1))
!>
tl_DC(j,k)=cff*(tl_Awrk(j,k+1,Nold)- &
& tl_Awrk(j,k ,Nold)- &
& FC(j,k)*tl_DC(j,k-1))
END DO
END DO
ELSE IF ((boundary.eq.isouth).or.(boundary.eq.inorth)) THEN
j=edge(boundary)
cff1=0.5_r8*(1.0_r8/3.0_r8)
DO k=1,N(ng)-1
DO i=IstrU,Iend
BC(i,k)=cff1*(Hz(i-1,j,k )+Hz(i,j,k )+ &
& Hz(i-1,j,k+1)+Hz(i,j,k+1))+ &
& DTsizeV*Kv(i,j,k)* &
& (oHz(i,k)+oHz(i,k+1))
cff=1.0_r8/(BC(i,k)-FC(i,k)*CF(i,k-1))
CF(i,k)=cff*CF(i,k)
!> DC(i,k)=cff*(Awrk(i,k+1,Nold)- &
!> & Awrk(i,k ,Nold)- &
!> & FC(i,k)*DC(i,k-1))
!>
tl_DC(i,k)=cff*(tl_Awrk(i,k+1,Nold)- &
& tl_Awrk(i,k ,Nold)- &
& FC(i,k)*tl_DC(i,k-1))
END DO
END DO
END IF
!
! Backward substitution.
!
IF ((boundary.eq.iwest).or.(boundary.eq.ieast)) THEN
i=edge(boundary)
DO j=Jstr,Jend
!> DC(j,N(ng))=0.0_r8
!>
tl_DC(j,N(ng))=0.0_r8
END DO
DO k=N(ng)-1,1,-1
DO j=Jstr,Jend
!> DC(j,k)=DC(j,k)-CF(j,k)*DC(j,k+1)
!>
tl_DC(j,k)=tl_DC(j,k)-CF(j,k)*tl_DC(j,k+1)
END DO
END DO
DO k=1,N(ng)
DO j=Jstr,Jend
!> DC(j,k)=DC(j,k)*Kv(i,j,k)
!>
tl_DC(j,k)=tl_DC(j,k)*Kv(i,j,k)
!> Awrk(j,k,Nnew)=Awrk(j,k,Nold)+ &
!> & DTsizeV*oHz(j,k)* &
!> & (DC(j,k)-DC(j,k-1))
!>
tl_Awrk(j,k,Nnew)=tl_Awrk(j,k,Nold)+ &
& DTsizeV*oHz(j,k)* &
& (tl_DC(j,k)-tl_DC(j,k-1))
END DO
END DO
ELSE IF ((boundary.eq.isouth).or.(boundary.eq.inorth)) THEN
j=edge(boundary)
DO i=IstrU,Iend
!> DC(i,N(ng))=0.0_r8
!>
tl_DC(i,N(ng))=0.0_r8
END DO
DO k=N(ng)-1,1,-1
DO i=IstrU,Iend
!> DC(i,k)=DC(i,k)-CF(i,k)*DC(i,k+1)
!>
tl_DC(i,k)=tl_DC(i,k)-CF(i,k)*tl_DC(i,k+1)
END DO
END DO
DO k=1,N(ng)
DO i=IstrU,Iend
!> DC(i,k)=DC(i,k)*Kv(i,j,k)
!>
tl_DC(i,k)=tl_DC(i,k)*Kv(i,j,k)
!> Awrk(i,k,Nnew)=Awrk(i,k,Nold)+ &
!> & DTsizeV*oHz(i,k)* &
!> & (DC(i,k)-DC(i,k-1))
!>
tl_Awrk(i,k,Nnew)=tl_Awrk(i,k,Nold)+ &
& DTsizeV*oHz(i,k)* &
& (tl_DC(i,k)-tl_DC(i,k-1))
END DO
END DO
END IF
END IF
!
! Update integration indices.
!
Nsav=Nold
Nold=Nnew
Nnew=Nsav
END DO
# else
!
!-----------------------------------------------------------------------
! Integrate vertical diffusion equation implicitly.
!-----------------------------------------------------------------------
!
DO step=1,NVsteps
!
! Compute diagonal matrix coefficients BC and load right-hand-side
! terms for the diffusion equation into DC.
!
IF (Lconvolve(boundary)) THEN
IF ((boundary.eq.iwest).or.(boundary.eq.ieast)) THEN
i=edge(boundary)
DO k=1,N(ng)
DO j=Jstr,Jend
cff=0.5_r8*(Hz(i-1,j,k)+Hz(i,j,k))
BC(j,k)=cff-FC(j,k)-FC(j,k-1)
!> DC(j,k)=Awrk(j,k,Nold)*cff
!>
tl_DC(j,k)=tl_Awrk(j,k,Nold)*cff
END DO
END DO
ELSE IF ((boundary.eq.isouth).or.(boundary.eq.inorth)) THEN
j=edge(boundary)
DO k=1,N(ng)
DO i=IstrU,Iend
cff=0.5_r8*(Hz(i-1,j,k)+Hz(i,j,k))
BC(i,k)=cff-FC(i,k)-FC(i,k-1)
!> DC(i,k)=Awrk(i,k,Nold)*cff
!>
tl_DC(i,k)=tl_Awrk(i,k,Nold)*cff
END DO
END DO
END IF
!
! Solve the tridiagonal system.
!
IF ((boundary.eq.iwest).or.(boundary.eq.ieast)) THEN
DO j=Jstr,Jend
cff=1.0_r8/BC(j,1)
CF(j,1)=cff*FC(j,1)
!> DC(j,1)=cff*DC(j,1)
!>
tl_DC(j,1)=cff*tl_DC(j,1)
END DO
DO k=2,N(ng)-1
DO j=Jstr,Jend
cff=1.0_r8/(BC(j,k)-FC(j,k-1)*CF(j,k-1))
CF(j,k)=cff*FC(j,k)
!> DC(j,k)=cff*(DC(j,k)-FC(j,k-1)*DC(j,k-1))
!>
tl_DC(j,k)=cff*(tl_DC(j,k)-FC(j,k-1)*tl_DC(j,k-1))
END DO
END DO
ELSE IF ((boundary.eq.isouth).or.(boundary.eq.inorth)) THEN
DO i=IstrU,Iend
cff=1.0_r8/BC(i,1)
CF(i,1)=cff*FC(i,1)
!> DC(i,1)=cff*DC(i,1)
!>
tl_DC(i,1)=cff*tl_DC(i,1)
END DO
DO k=2,N(ng)-1
DO i=IstrU,Iend
cff=1.0_r8/(BC(i,k)-FC(i,k-1)*CF(i,k-1))
CF(i,k)=cff*FC(i,k)
!> DC(i,k)=cff*(DC(i,k)-FC(i,k-1)*DC(i,k-1))
!>
tl_DC(i,k)=cff*(tl_DC(i,k)-FC(i,k-1)*tl_DC(i,k-1))
END DO
END DO
END IF
!
! Compute new solution by back substitution.
!
IF ((boundary.eq.iwest).or.(boundary.eq.ieast)) THEN
i=edge(boundary)
DO j=Jstr,Jend
!> DC(j,N(ng))=(DC(j,N(ng))- &
!> & FC(j,N(ng)-1)*DC(j,N(ng)-1))/ &
!> & (BC(j,N(ng))- &
!> & FC(j,N(ng)-1)*CF(j,N(ng)-1))
!>
tl_DC(j,N(ng))=(tl_DC(j,N(ng))- &
& FC(j,N(ng)-1)*tl_DC(j,N(ng)-1))/ &
& (BC(j,N(ng))- &
& FC(j,N(ng)-1)*CF(j,N(ng)-1))
!> Awrk(j,N(ng),Nnew)=DC(j,N(ng))
!>
tl_Awrk(j,N(ng),Nnew)=tl_DC(j,N(ng))
# ifdef MASKING
!> Awrk(j,N(ng),Nnew)=Awrk(j,N(ng),Nnew)*umask(i,j)
!>
tl_Awrk(j,N(ng),Nnew)=tl_Awrk(j,N(ng),Nnew)*umask(i,j)
# endif
END DO
DO k=N(ng)-1,1,-1
DO j=Jstr,Jend
!> DC(j,k)=DC(j,k)-CF(j,k)*DC(j,k+1)
!>
tl_DC(j,k)=tl_DC(j,k)-CF(j,k)*tl_DC(j,k+1)
!> Awrk(j,k,Nnew)=DC(j,k)
!>
tl_Awrk(j,k,Nnew)=tl_DC(j,k)
# ifdef MASKING
!> Awrk(j,k,Nnew)=Awrk(j,k,Nnew)*umask(i,j)
!>
tl_Awrk(j,k,Nnew)=tl_Awrk(j,k,Nnew)*umask(i,j)
# endif
END DO
END DO
ELSE IF ((boundary.eq.isouth).or.(boundary.eq.inorth)) THEN
j=edge(boundary)
DO i=IstrU,Iend
!> DC(i,N(ng))=(DC(i,N(ng))- &
!> & FC(i,N(ng)-1)*DC(i,N(ng)-1))/ &
!> & (BC(i,N(ng))- &
!> & FC(i,N(ng)-1)*CF(i,N(ng)-1))
!>
tl_DC(i,N(ng))=(tl_DC(i,N(ng))- &
& FC(i,N(ng)-1)*tl_DC(i,N(ng)-1))/ &
& (BC(i,N(ng))- &
& FC(i,N(ng)-1)*CF(i,N(ng)-1))
!> Awrk(i,N(ng),Nnew)=DC(i,N(ng))
!>
tl_Awrk(i,N(ng),Nnew)=tl_DC(i,N(ng))
# ifdef MASKING
!> Awrk(i,N(ng),Nnew)=Awrk(i,N(ng),Nnew)*umask(i,j)
!>
tl_Awrk(i,N(ng),Nnew)=tl_Awrk(i,N(ng),Nnew)*umask(i,j)
# endif
END DO
DO k=N(ng)-1,1,-1
DO i=IstrU,Iend
!> DC(i,k)=DC(i,k)-CF(i,k)*DC(i,k+1)
!>
tl_DC(i,k)=tl_DC(i,k)-CF(i,k)*tl_DC(i,k+1)
!> Awrk(i,k,Nnew)=DC(i,k)
!>
tl_Awrk(i,k,Nnew)=tl_DC(i,k)
# ifdef MASKING
!> Awrk(i,k,Nnew)=Awrk(i,k,Nnew)*umask(i,j)
!>
tl_Awrk(i,k,Nnew)=tl_Awrk(i,k,Nnew)*umask(i,j)
# endif
END DO
END DO
END IF
END IF
!
! Update integration indices.
!
Nsav=Nold
Nold=Nnew
Nnew=Nsav
END DO
# endif
# else
!
!-----------------------------------------------------------------------
! Integrate vertical diffusion equation explicitly.
!-----------------------------------------------------------------------
!
DO step=1,NVsteps
!
! Compute vertical diffusive flux. Notice that "FC" is assumed to
! be time invariant.
!
IF (Lconvolve(boundary)) THEN
IF ((boundary.eq.iwest).or.(boundary.eq.ieast)) THEN
i=edge(boundary)
DO j=Jstr,Jend
DO k=1,N(ng)-1
!> FS(j,k)=FC(j,k)*(Awrk(j,k+1,Nold)- &
!> & Awrk(j,k ,Nold))
!>
tl_FS(j,k)=FC(j,k)*(tl_Awrk(j,k+1,Nold)- &
& tl_Awrk(j,k ,Nold))
# ifdef MASKING
!> FS(j,k)=FS(j,k)*umask(i,j)
!>
tl_FS(j,k)=tl_FS(j,k)*umask(i,j)
# endif
END DO
!> FS(j,0)=0.0_r8
!>
tl_FS(j,0)=0.0_r8
!> FS(j,N(ng))=0.0_r8
!>
tl_FS(j,N(ng))=0.0_r8
END DO
ELSE IF ((boundary.eq.isouth).or.(boundary.eq.inorth)) THEN
j=edge(boundary)
DO i=IstrU,Iend
DO k=1,N(ng)-1
!> FS(i,k)=FC(i,k)*(Awrk(i,k+1,Nold)- &
!> & Awrk(i,k ,Nold))
!>
tl_FS(i,k)=FC(i,k)*(tl_Awrk(i,k+1,Nold)- &
& tl_Awrk(i,k ,Nold))
# ifdef MASKING
!> FS(i,k)=FS(i,k)*umask(i,j)
!>
tl_FS(i,k)=tl_FS(i,k)*umask(i,j)
# endif
END DO
!> FS(i,0)=0.0_r8
!>
tl_FS(i,0)=0.0_r8
!> FS(i,N(ng))=0.0_r8
!>
tl_FS(i,N(ng))=0.0_r8
END DO
END IF
!
! Time-step vertical diffusive term. Notice that "oHz" is assumed to
! be time invariant.
!
IF ((boundary.eq.iwest).or.(boundary.eq.ieast)) THEN
DO k=1,N(ng)
DO j=Jstr,Jend
!> Awrk(j,k,Nnew)=Awrk(j,k,Nold)+ &
!> & oHz(j,k)*(FS(j,k )- &
!> & FS(j,k-1))
!>
tl_Awrk(j,k,Nnew)=tl_Awrk(j,k,Nold)+ &
& oHz(j,k)*(tl_FS(j,k )- &
& tl_FS(j,k-1))
END DO
END DO
ELSE IF ((boundary.eq.isouth).or.(boundary.eq.inorth)) THEN
DO k=1,N(ng)
DO i=IstrU,Iend
!> Awrk(i,k,Nnew)=Awrk(i,k,Nold)+ &
!> & oHz(i,k)*(FS(i,k )- &
!> & FS(i,k-1))
!>
tl_Awrk(i,k,Nnew)=tl_Awrk(i,k,Nold)+ &
& oHz(i,k)*(tl_FS(i,k )- &
& tl_FS(i,k-1))
END DO
END DO
END IF
END IF
!
! Update integration indices.
!
Nsav=Nold
Nold=Nnew
Nnew=Nsav
END DO
# endif
# endif
!
!-----------------------------------------------------------------------
! Load convolved solution.
!-----------------------------------------------------------------------
!
IF (Lconvolve(boundary)) THEN
IF ((boundary.eq.iwest).or.(boundary.eq.ieast)) THEN
DO k=1,N(ng)
DO j=Jstr,Jend
!> A(j,k)=Awrk(j,k,Nold)
!>
tl_A(j,k)=tl_Awrk(j,k,Nold)
END DO
END DO
ELSE IF ((boundary.eq.isouth).or.(boundary.eq.inorth)) THEN
DO k=1,N(ng)
DO i=Istr,Iend
!> A(i,k)=Awrk(i,k,Nold)
!>
tl_A(i,k)=tl_Awrk(i,k,Nold)
END DO
END DO
END IF
END IF
!> CALL bc_u3d_bry_tile (ng, tile, boundary, &
!> & LBij, UBij, 1, N(ng), &
!> & A)
!>
CALL bc_u3d_bry_tile (ng, tile, boundary, &
& LBij, UBij, 1, N(ng), &
& tl_A)
# ifdef DISTRIBUTE
!> CALL mp_exchange3d_bry (ng, tile, model, 1, boundary, &
!> & LBij, UBij, 1, N(ng), &
!> & Nghost, &
!> & EWperiodic(ng), NSperiodic(ng), &
!> & A)
!>
CALL mp_exchange3d_bry (ng, tile, model, 1, boundary, &
& LBij, UBij, 1, N(ng), &
& Nghost, &
& EWperiodic(ng), NSperiodic(ng), &
& tl_A)
# endif
RETURN
END SUBROUTINE tl_conv_u3d_bry_tile
!
!***********************************************************************
SUBROUTINE tl_conv_v3d_bry_tile (ng, tile, model, boundary, &
& edge, LBij, UBij, &
& LBi, UBi, LBj, UBj, LBk, UBk, &
& IminS, ImaxS, JminS, JmaxS, &
& Nghost, NHsteps, NVsteps, &
& DTsizeH, DTsizeV, &
& Kh, Kv, &
& pm, pn, pmon_p, pnom_r, &
# ifdef MASKING
& vmask, pmask, &
# endif
& Hz, z_r, &
& tl_A)
!***********************************************************************
!
USE mod_param
USE mod_scalars
!
USE bc_bry3d_mod, ONLY: bc_v3d_bry_tile
# ifdef DISTRIBUTE
USE mp_exchange_mod, ONLY : mp_exchange3d_bry
# endif
!
! Imported variable declarations.
!
integer, intent(in) :: ng, tile, model, boundary
integer, intent(in) :: edge(4)
integer, intent(in) :: LBij, UBij
integer, intent(in) :: LBi, UBi, LBj, UBj, LBk, UBk
integer, intent(in) :: IminS, ImaxS, JminS, JmaxS
integer, intent(in) :: Nghost, NHsteps, NVsteps
real(r8), intent(in) :: DTsizeH, DTsizeV
!
# ifdef ASSUMED_SHAPE
real(r8), intent(in) :: pm(LBi:,LBj:)
real(r8), intent(in) :: pn(LBi:,LBj:)
real(r8), intent(in) :: pmon_p(LBi:,LBj:)
real(r8), intent(in) :: pnom_r(LBi:,LBj:)
# ifdef MASKING
real(r8), intent(in) :: vmask(LBi:,LBj:)
real(r8), intent(in) :: pmask(LBi:,LBj:)
# endif
real(r8), intent(in) :: Hz(LBi:,LBj:,:)
real(r8), intent(in) :: z_r(LBi:,LBj:,:)
real(r8), intent(in) :: Kh(LBi:,LBj:)
real(r8), intent(in) :: Kv(LBi:,LBj:,0:)
real(r8), intent(inout) :: tl_A(LBij:,LBk:)
# else
real(r8), intent(in) :: pm(LBi:UBi,LBj:UBj)
real(r8), intent(in) :: pn(LBi:UBi,LBj:UBj)
real(r8), intent(in) :: pmon_p(LBi:UBi,LBj:UBj)
real(r8), intent(in) :: pnom_r(LBi:UBi,LBj:UBj)
# ifdef MASKING
real(r8), intent(in) :: vmask(LBi:UBi,LBj:UBj)
real(r8), intent(in) :: pmask(LBi:UBi,LBj:UBj)
# endif
real(r8), intent(in) :: Hz(LBi:UBi,LBj:UBj,N(ng))
real(r8), intent(in) :: z_r(LBi:UBi,LBj:UBj,N(ng))
real(r8), intent(in) :: Kh(LBi:UBi,LBj:UBj)
real(r8), intent(in) :: Kv(LBi:UBi,LBj:UBj,0:UBk)
real(r8), intent(inout) :: tl_A(LBij:UBij,LBk:UBk)
# endif
!
! Local variable declarations.
!
logical, dimension(4) :: Lconvolve
integer :: Nnew, Nold, Nsav, i, ib, j, k, step
real(r8) :: cff, cff1
real(r8), dimension(LBij:UBij,LBk:UBk,2) :: tl_Awrk
real(r8), dimension(JminS:JmaxS,LBk:UBk) :: tl_FE
real(r8), dimension(IminS:ImaxS,LBk:UBk) :: tl_FX
real(r8), dimension(LBij:UBij) :: Hfac
# ifdef VCONVOLUTION
# ifndef SPLINES_VCONV
real(r8), dimension(LBij:UBij,0:N(ng)) :: FC
# endif
# if !defined IMPLICIT_VCONV || defined SPLINES_VCONV
real(r8), dimension(LBij:UBij,N(ng)) :: oHz
# endif
# if defined IMPLICIT_VCONV || defined SPLINES_VCONV
real(r8), dimension(LBij:UBij,0:N(ng)) :: BC
real(r8), dimension(LBij:UBij,0:N(ng)) :: CF
# ifdef SPLINES_VCONV
real(r8), dimension(LBij:UBij,0:N(ng)) :: FC
# endif
real(r8), dimension(LBij:UBij,0:N(ng)) :: tl_DC
# else
real(r8), dimension(LBij:UBij,0:N(ng)) :: tl_FS
# endif
# endif
# include "set_bounds.h"
!
!-----------------------------------------------------------------------
! Space convolution of the diffusion equation for a 2D state variable
! at RHO-points.
!-----------------------------------------------------------------------
!
Lconvolve(iwest )=DOMAIN(ng)%Western_Edge (tile)
Lconvolve(ieast )=DOMAIN(ng)%Eastern_Edge (tile)
Lconvolve(isouth)=DOMAIN(ng)%Southern_Edge(tile)
Lconvolve(inorth)=DOMAIN(ng)%Northern_Edge(tile)
!
! Compute metrics factors. Notice that "z_r" and "Hz" are assumed to
! be time invariant in the vertical convolution. Scratch array are
! used for efficiency.
!
IF (Lconvolve(boundary)) THEN
cff=DTsizeH*0.25_r8
IF ((boundary.eq.iwest).or.(boundary.eq.ieast)) THEN
i=edge(boundary)
DO j=JstrV-1,Jend+1
Hfac(j)=cff*(pm(i,j-1)+pm(i,j))*(pn(i,j-1)+pn(i,j))
# ifdef VCONVOLUTION
# ifndef SPLINES_VCONV
FC(j,N(ng))=0.0_r8
DO k=1,N(ng)-1
# ifdef IMPLICIT_VCONV
FC(j,k)=-DTsizeV*(Kv(i,j-1,k)+Kv(i,j,k))/ &
& (z_r(i,j-1,k+1)+z_r(i,j,k+1)- &
& z_r(i,j-1,k )-z_r(i,j,k ))
# else
FC(j,k)=DTsizeV*(Kv(i,j-1,k)+Kv(i,j,k))/ &
& (z_r(i,j-1,k+1)+z_r(i,j,k+1)- &
& z_r(i,j-1,k )-z_r(i,j,k ))
# endif
END DO
FC(j,0)=0.0_r8
# endif
# if !defined IMPLICIT_VCONV || defined SPLINES_VCONV
DO k=1,N(ng)
oHz(j,k)=2.0_r8/(Hz(i,j-1,k)+Hz(i,j,k))
END DO
# endif
# endif
END DO
ELSE IF ((boundary.eq.isouth).or.(boundary.eq.inorth)) THEN
j=edge(boundary)
DO i=Istr-1,Iend+1
Hfac(i)=cff*(pm(i,j-1)+pm(i,j))*(pn(i,j-1)+pn(i,j))
# ifdef VCONVOLUTION
# ifndef SPLINES_VCONV
FC(i,N(ng))=0.0_r8
DO k=1,N(ng)-1
# ifdef IMPLICIT_VCONV
FC(i,k)=-DTsizeV*(Kv(i,j-1,k)+Kv(i,j,k))/ &
& (z_r(i,j-1,k+1)+z_r(i,j,k+1)- &
& z_r(i,j-1,k )-z_r(i,j,k ))
# else
FC(i,k)=DTsizeV*(Kv(i,j-1,k)+Kv(i,j,k))/ &
& (z_r(i,j-1,k+1)+z_r(i,j,k+1)- &
& z_r(i,j-1,k )-z_r(i,j,k ))
# endif
END DO
FC(i,0)=0.0_r8
# endif
# if !defined IMPLICIT_VCONV || defined SPLINES_VCONV
DO k=1,N(ng)
oHz(i,k)=2.0_r8/(Hz(i,j-1,k)+Hz(i,j,k))
END DO
# endif
# endif
END DO
END IF
END IF
!
! Set integration indices and initial conditions.
!
Nold=1
Nnew=2
!> CALL bc_v3d_bry_tile (ng, tile, boundary, &
!> & LBij, UBij, 1, N(ng), &
!> & A)
!>
CALL bc_v3d_bry_tile (ng, tile, boundary, &
& LBij, UBij, 1, N(ng), &
& tl_A)
# ifdef DISTRIBUTE
!> CALL mp_exchange3d_bry (ng, tile, model, 1, boundary, &
!> & LBij, UBij, 1, N(ng), &
!> & Nghost,
!> & EWperiodic(ng), NSperiodic(ng), &
!> & A)
!>
CALL mp_exchange3d_bry (ng, tile, model, 1, boundary, &
& LBij, UBij, 1, N(ng), &
& Nghost, &
& EWperiodic(ng), NSperiodic(ng), &
& tl_A)
# endif
IF (Lconvolve(boundary)) THEN
IF ((boundary.eq.iwest).or.(boundary.eq.ieast)) THEN
DO k=1,N(ng)
DO j=JstrV-1,Jend+1
!> Awrk(j,k,Nold)=A(j,k)
!>
tl_Awrk(j,k,Nold)=tl_A(j,k)
END DO
END DO
ELSE IF ((boundary.eq.isouth).or.(boundary.eq.inorth)) THEN
DO k=1,N(ng)
DO i=Istr-1,Iend+1
!> Awrk(i,k,Nold)=A(i,k)
!>
tl_Awrk(i,k,Nold)=tl_A(i,k)
END DO
END DO
END IF
END IF
!
!-----------------------------------------------------------------------
! Integrate horizontal diffusion equation.
!-----------------------------------------------------------------------
!
DO step=1,NHsteps
!
! Compute XI- and ETA-components of diffusive flux.
!
IF (Lconvolve(boundary)) THEN
IF ((boundary.eq.iwest).or.(boundary.eq.ieast)) THEN
i=edge(boundary)
DO k=1,N(ng)
DO j=JstrV-1,Jend
!> FE(j,k)=pnom_r(i,j)*Kh(i,j)* &
!> & (Awrk(j+1,k,Nold)- &
!> & Awrk(j ,k,Nold))
!>
tl_FE(j,k)=pnom_r(i,j)*Kh(i,j)* &
& (tl_Awrk(j+1,k,Nold)- &
& tl_Awrk(j ,k,Nold))
END DO
END DO
ELSE IF ((boundary.eq.isouth).or.(boundary.eq.inorth)) THEN
j=edge(boundary)
DO k=1,N(ng)
DO i=Istr,Iend+1
!> FX(i,k)=pmon_p(i,j)* &
!> & 0.25_r8*(Kh(i-1,j )+Kh(i,j )+ &
!> & Kh(i-1,j-1)+Kh(i,j-1))* &
!> & (Awrk(i ,k,Nold)- &
!> & Awrk(i-1,k,Nold))
!>
tl_FX(i,k)=pmon_p(i,j)* &
& 0.25_r8*(Kh(i-1,j )+Kh(i,j )+ &
& Kh(i-1,j-1)+Kh(i,j-1))* &
& (tl_Awrk(i ,k,Nold)- &
& tl_Awrk(i-1,k,Nold))
# ifdef MASKING
!> FX(i,k)=FX(i,k)*pmask(i,j)
!>
tl_FX(i,k)=tl_FX(i,k)*pmask(i,j)
# endif
END DO
END DO
END IF
END IF
!
! Time-step horizontal diffusion equation.
!
IF (Lconvolve(boundary)) THEN
IF ((boundary.eq.iwest).or.(boundary.eq.ieast)) THEN
DO k=1,N(ng)
DO j=JstrV,Jend
!> Awrk(j,k,Nnew)=Awrk(j,k,Nold)+ &
!> & Hfac(j)* &
!> & (FE(j,k)-FE(j-1,k))
!>
tl_Awrk(j,k,Nnew)=tl_Awrk(j,k,Nold)+ &
& Hfac(j)* &
& (tl_FE(j,k)-tl_FE(j-1,k))
END DO
END DO
ELSE IF ((boundary.eq.isouth).or.(boundary.eq.inorth)) THEN
DO k=1,N(ng)
DO i=Istr,Iend
!> Awrk(i,k,Nnew)=Awrk(i,k,Nold)+ &
!> & Hfac(i)* &
!> & (FX(i+1,k)-FX(i,k))
!>
tl_Awrk(i,k,Nnew)=tl_Awrk(i,k,Nold)+ &
& Hfac(i)* &
& (tl_FX(i+1,k)-tl_FX(i,k))
END DO
END DO
END IF
END IF
!
! Apply boundary conditions.
!
!> CALL bc_v3d_bry_tile (ng, tile, boundary, &
!> & LBij, UBij, 1, N(ng), &
!> & Awrk(:,:,Nnew))
!>
CALL bc_v3d_bry_tile (ng, tile, boundary, &
& LBij, UBij, 1, N(ng), &
& tl_Awrk(:,:,Nnew))
# ifdef DISTRIBUTE
!> CALL mp_exchange3d_bry (ng, tile, model, 1, boundary, &
!> & LBij, UBij, 1, N(ng), &
!> & Nghost, &
!> & EWperiodic(ng), NSperiodic(ng), &
!> & Awrk(:,:,Nnew))
!>
CALL mp_exchange3d_bry (ng, tile, model, 1, boundary, &
& LBij, UBij, 1, N(ng), &
& Nghost, &
& EWperiodic(ng), NSperiodic(ng), &
& tl_Awrk(:,:,Nnew))
# endif
!
! Update integration indices.
!
Nsav=Nold
Nold=Nnew
Nnew=Nsav
END DO
# ifdef VCONVOLUTION
# ifdef IMPLICIT_VCONV
# ifdef SPLINES_VCONV
!
!-----------------------------------------------------------------------
! Integrate vertical diffusion equation implicitly using parabolic
! splines.
!-----------------------------------------------------------------------
!
DO step=1,NVsteps
!
! Use conservative, parabolic spline reconstruction of vertical
! diffusion derivatives. Then, time step vertical diffusion term
! implicitly.
!
IF (Lconvolve(boundary)) THEN
IF ((boundary.eq.iwest).or.(boundary.eq.ieast)) THEN
i=edge(boundary)
cff1=0.5_r8*(1.0_r8/6.0_r8)
DO j=JstrV,Jend
DO k=1,N(ng)-1
FC(j,k)=cff1*(Hz(i,j-1,k )+Hz(i,j,k ))- &
& DTsizeV*Kv(i,j,k-1)*oHz(j,k )
CF(j,k)=cff1*(Hz(i,j-1,k+1)+Hz(i,j,k+1))- &
& DTsizeV*Kv(i,j,k+1)*oHz(j,k+1)
END DO
CF(j,0)=0.0_r8
!> DC(j,0)=0.0_r8
!>
tl_DC(j,0)=0.0_r8
END DO
ELSE IF ((boundary.eq.isouth).or.(boundary.eq.inorth)) THEN
j=edge(boundary)
cff1=0.5_r8*(1.0_r8/6.0_r8)
DO i=Istr,Iend
DO k=1,N(ng)-1
FC(i,k)=cff1*(Hz(i,j-1,k )+Hz(i,j,k ))- &
& DTsizeV*Kv(i,j,k-1)*oHz(i,k )
CF(i,k)=cff1*(Hz(i,j-1,k+1)+Hz(i,j,k+1))- &
& DTsizeV*Kv(i,j,k+1)*oHz(i,k+1)
END DO
CF(i,0)=0.0_r8
!> DC(i,0)=0.0_r8
!>
tl_DC(i,0)=0.0_r8
END DO
END IF
!
! LU decomposition and forward substitution.
!
IF ((boundary.eq.iwest).or.(boundary.eq.ieast)) THEN
i=edge(boundary)
cff1=0.5_r8*(1.0_r8/3.0_r8)
DO k=1,N(ng)-1
DO j=JstrV,Jend
BC(j,k)=cff1*(Hz(i,j-1,k )+Hz(i,j,k )+ &
& Hz(i,j-1,k+1)+Hz(i,j,k+1))+ &
& DTsizeV*Kv(i,j,k)* &
& (oHz(j,k)+oHz(j,k+1))
cff=1.0_r8/(BC(j,k)-FC(j,k)*CF(j,k-1))
CF(j,k)=cff*CF(j,k)
!> DC(j,k)=cff*(Awrk(j,k+1,Nold)- &
!> & Awrk(j,k ,Nold)- &
!> & FC(j,k)*DC(j,k-1))
!>
tl_DC(j,k)=cff*(tl_Awrk(j,k+1,Nold)- &
& tl_Awrk(j,k ,Nold)- &
& FC(j,k)*tl_DC(j,k-1))
END DO
END DO
ELSE IF ((boundary.eq.isouth).or.(boundary.eq.inorth)) THEN
j=edge(boundary)
cff1=0.5_r8*(1.0_r8/3.0_r8)
DO k=1,N(ng)-1
DO i=Istr,Iend
BC(i,k)=cff1*(Hz(i,j-1,k )+Hz(i,j,k )+ &
& Hz(i,j-1,k+1)+Hz(i,j,k+1))+ &
& DTsizeV*Kv(i,j,k)* &
& (oHz(i,k)+oHz(i,k+1))
cff=1.0_r8/(BC(i,k)-FC(i,k)*CF(i,k-1))
CF(i,k)=cff*CF(i,k)
!> DC(i,k)=cff*(Awrk(i,k+1,Nold)- &
!> & Awrk(i,k ,Nold)- &
!> & FC(i,k)*DC(i,k-1))
!>
tl_DC(i,k)=cff*(tl_Awrk(i,k+1,Nold)- &
& tl_Awrk(i,k ,Nold)- &
& FC(i,k)*tl_DC(i,k-1))
END DO
END DO
END IF
!
! Backward substitution.
!
IF ((boundary.eq.iwest).or.(boundary.eq.ieast)) THEN
i=edge(boundary)
DO j=JstrV,Jend
!> DC(j,N(ng))=0.0_r8
!>
tl_DC(j,N(ng))=0.0_r8
END DO
DO k=N(ng)-1,1,-1
DO j=JstrV,Jend
!> DC(j,k)=DC(j,k)-CF(j,k)*DC(j,k+1)
!>
tl_DC(j,k)=tl_DC(j,k)-CF(j,k)*tl_DC(j,k+1)
END DO
END DO
DO k=1,N(ng)
DO j=JstrV,Jend
!> DC(j,k)=DC(j,k)*Kv(i,j,k)
!>
tl_DC(j,k)=tl_DC(j,k)*Kv(i,j,k)
!> Awrk(j,k,Nnew)=Awrk(j,k,Nold)+ &
!> & DTsizeV*oHz(j,k)* &
!> & (DC(j,k)-DC(j,k-1))
!>
tl_Awrk(j,k,Nnew)=tl_Awrk(j,k,Nold)+ &
& DTsizeV*oHz(j,k)* &
& (tl_DC(j,k)-tl_DC(j,k-1))
END DO
END DO
ELSE IF ((boundary.eq.isouth).or.(boundary.eq.inorth)) THEN
j=edge(boundary)
DO i=Istr,Iend
!> DC(i,N(ng))=0.0_r8
!>
tl_DC(i,N(ng))=0.0_r8
END DO
DO k=N(ng)-1,1,-1
DO i=Istr,Iend
!> DC(i,k)=DC(i,k)-CF(i,k)*DC(i,k+1)
!>
tl_DC(i,k)=tl_DC(i,k)-CF(i,k)*tl_DC(i,k+1)
END DO
END DO
DO k=1,N(ng)
DO i=Istr,Iend
!> DC(i,k)=DC(i,k)*Kv(i,j,k)
!>
tl_DC(i,k)=tl_DC(i,k)*Kv(i,j,k)
!> Awrk(i,k,Nnew)=Awrk(i,k,Nold)+ &
!> & DTsizeV*oHz(i,k)* &
!> & (DC(i,k)-DC(i,k-1))
!>
tl_Awrk(i,k,Nnew)=tl_Awrk(i,k,Nold)+ &
& DTsizeV*oHz(i,k)* &
& (tl_DC(i,k)-tl_DC(i,k-1))
END DO
END DO
END IF
END IF
!
! Update integration indices.
!
Nsav=Nold
Nold=Nnew
Nnew=Nsav
END DO
# else
!
!-----------------------------------------------------------------------
! Integrate vertical diffusion equation implicitly.
!-----------------------------------------------------------------------
!
DO step=1,NVsteps
!
! Compute diagonal matrix coefficients BC and load right-hand-side
! terms for the diffusion equation into DC.
!
IF (Lconvolve(boundary)) THEN
IF ((boundary.eq.iwest).or.(boundary.eq.ieast)) THEN
i=edge(boundary)
DO k=1,N(ng)
DO j=JstrV,Jend
cff=0.5_r8*(Hz(i,j-1,k)+Hz(i,j,k))
BC(j,k)=cff-FC(j,k)-FC(j,k-1)
!> DC(j,k)=Awrk(j,k,Nold)*cff
!>
tl_DC(j,k)=tl_Awrk(j,k,Nold)*cff
END DO
END DO
ELSE IF ((boundary.eq.isouth).or.(boundary.eq.inorth)) THEN
j=edge(boundary)
DO k=1,N(ng)
DO i=Istr,Iend
cff=0.5_r8*(Hz(i,j-1,k)+Hz(i,j,k))
BC(i,k)=cff-FC(i,k)-FC(i,k-1)
!> DC(i,k)=Awrk(i,k,Nold)*cff
!>
tl_DC(i,k)=tl_Awrk(i,k,Nold)*cff
END DO
END DO
END IF
!
! Solve the tridiagonal system.
!
IF ((boundary.eq.iwest).or.(boundary.eq.ieast)) THEN
DO j=JstrV,Jend
cff=1.0_r8/BC(j,1)
CF(j,1)=cff*FC(j,1)
!> DC(j,1)=cff*DC(j,1)
!>
tl_DC(j,1)=cff*tl_DC(j,1)
END DO
DO k=2,N(ng)-1
DO j=JstrV,Jend
cff=1.0_r8/(BC(j,k)-FC(j,k-1)*CF(j,k-1))
CF(j,k)=cff*FC(j,k)
!> DC(j,k)=cff*(DC(j,k)-FC(j,k-1)*DC(j,k-1))
!>
tl_DC(j,k)=cff*(tl_DC(j,k)-FC(j,k-1)*tl_DC(j,k-1))
END DO
END DO
ELSE IF ((boundary.eq.isouth).or.(boundary.eq.inorth)) THEN
DO i=Istr,Iend
cff=1.0_r8/BC(i,1)
CF(i,1)=cff*FC(i,1)
!> DC(i,1)=cff*DC(i,1)
!>
tl_DC(i,1)=cff*tl_DC(i,1)
END DO
DO k=2,N(ng)-1
DO i=Istr,Iend
cff=1.0_r8/(BC(i,k)-FC(i,k-1)*CF(i,k-1))
CF(i,k)=cff*FC(i,k)
!> DC(i,k)=cff*(DC(i,k)-FC(i,k-1)*DC(i,k-1))
!>
tl_DC(i,k)=cff*(tl_DC(i,k)-FC(i,k-1)*tl_DC(i,k-1))
END DO
END DO
END IF
!
! Compute new solution by back substitution.
!
IF ((boundary.eq.iwest).or.(boundary.eq.ieast)) THEN
i=edge(boundary)
DO j=JstrV,Jend
!> DC(j,N(ng))=(DC(j,N(ng))- &
!> & FC(j,N(ng)-1)*DC(j,N(ng)-1))/ &
!> & (BC(j,N(ng))- &
!> & FC(j,N(ng)-1)*CF(j,N(ng)-1))
!>
tl_DC(j,N(ng))=(tl_DC(j,N(ng))- &
& FC(j,N(ng)-1)*tl_DC(j,N(ng)-1))/ &
& (BC(j,N(ng))- &
& FC(j,N(ng)-1)*CF(j,N(ng)-1))
!> Awrk(j,N(ng),Nnew)=DC(j,N(ng))
!>
tl_Awrk(j,N(ng),Nnew)=tl_DC(j,N(ng))
# ifdef MASKING
!> Awrk(j,N(ng),Nnew)=Awrk(j,N(ng),Nnew)*vmask(i,j)
!>
tl_Awrk(j,N(ng),Nnew)=tl_Awrk(j,N(ng),Nnew)*vmask(i,j)
# endif
END DO
DO k=N(ng)-1,1,-1
DO j=JstrV,Jend
!> DC(j,k)=DC(j,k)-CF(j,k)*DC(j,k+1)
!>
tl_DC(j,k)=tl_DC(j,k)-CF(j,k)*tl_DC(j,k+1)
!> Awrk(j,k,Nnew)=DC(j,k)
!>
tl_Awrk(j,k,Nnew)=tl_DC(j,k)
# ifdef MASKING
!> Awrk(j,k,Nnew)=Awrk(j,k,Nnew)*vmask(i,j)
!>
tl_Awrk(j,k,Nnew)=tl_Awrk(j,k,Nnew)*vmask(i,j)
# endif
END DO
END DO
ELSE IF ((boundary.eq.isouth).or.(boundary.eq.inorth)) THEN
j=edge(boundary)
DO i=Istr,Iend
!> DC(i,N(ng))=(DC(i,N(ng))- &
!> & FC(i,N(ng)-1)*DC(i,N(ng)-1))/ &
!> & (BC(i,N(ng))- &
!> & FC(i,N(ng)-1)*CF(i,N(ng)-1))
!>
tl_DC(i,N(ng))=(tl_DC(i,N(ng))- &
& FC(i,N(ng)-1)*tl_DC(i,N(ng)-1))/ &
& (BC(i,N(ng))- &
& FC(i,N(ng)-1)*CF(i,N(ng)-1))
!> Awrk(i,N(ng),Nnew)=DC(i,N(ng))
!>
tl_Awrk(i,N(ng),Nnew)=tl_DC(i,N(ng))
# ifdef MASKING
!> Awrk(i,N(ng),Nnew)=Awrk(i,N(ng),Nnew)*vmask(i,j)
!>
tl_Awrk(i,N(ng),Nnew)=tl_Awrk(i,N(ng),Nnew)*vmask(i,j)
# endif
END DO
DO k=N(ng)-1,1,-1
DO i=Istr,Iend
!> DC(i,k)=DC(i,k)-CF(i,k)*DC(i,k+1)
!>
tl_DC(i,k)=tl_DC(i,k)-CF(i,k)*tl_DC(i,k+1)
!> Awrk(i,k,Nnew)=DC(i,k)
!>
tl_Awrk(i,k,Nnew)=tl_DC(i,k)
# ifdef MASKING
!> Awrk(i,k,Nnew)=Awrk(i,k,Nnew)*vmask(i,j)
!>
tl_Awrk(i,k,Nnew)=tl_Awrk(i,k,Nnew)*vmask(i,j)
# endif
END DO
END DO
END IF
END IF
!
! Update integration indices.
!
Nsav=Nold
Nold=Nnew
Nnew=Nsav
END DO
# endif
# else
!
!-----------------------------------------------------------------------
! Integrate vertical diffusion equation explicitly.
!-----------------------------------------------------------------------
!
DO step=1,NVsteps
!
! Compute vertical diffusive flux. Notice that "FC" is assumed to
! be time invariant.
!
IF (Lconvolve(boundary)) THEN
IF ((boundary.eq.iwest).or.(boundary.eq.ieast)) THEN
i=edge(boundary)
DO j=JstrV,Jend
DO k=1,N(ng)-1
!> FS(j,k)=FC(j,k)*(Awrk(j,k+1,Nold)- &
!> & Awrk(j,k ,Nold))
!>
tl_FS(j,k)=FC(j,k)*(tl_Awrk(j,k+1,Nold)- &
& tl_Awrk(j,k ,Nold))
# ifdef MASKING
!> FS(j,k)=FS(j,k)*vmask(i,j)
!>
tl_FS(j,k)=tl_FS(j,k)*vmask(i,j)
# endif
END DO
!> FS(j,0)=0.0_r8
!>
tl_FS(j,0)=0.0_r8
!> FS(j,N(ng))=0.0_r8
!>
tl_FS(j,N(ng))=0.0_r8
END DO
ELSE IF ((boundary.eq.isouth).or.(boundary.eq.inorth)) THEN
j=edge(boundary)
DO i=Istr,Iend
DO k=1,N(ng)-1
!> FS(i,k)=FC(i,k)*(Awrk(i,k+1,Nold)- &
!> & Awrk(i,k ,Nold))
!>
tl_FS(i,k)=FC(i,k)*(tl_Awrk(i,k+1,Nold)- &
& tl_Awrk(i,k ,Nold))
# ifdef MASKING
!> FS(i,k)=FS(i,k)*vmask(i,j)
!>
tl_FS(i,k)=tl_FS(i,k)*vmask(i,j)
# endif
END DO
!> FS(i,0)=0.0_r8
!>
tl_FS(i,0)=0.0_r8
!> FS(i,N(ng))=0.0_r8
!>
tl_FS(i,N(ng))=0.0_r8
END DO
END IF
!
! Time-step vertical diffusive term. Notice that "oHz" is assumed to
! be time invariant.
!
IF ((boundary.eq.iwest).or.(boundary.eq.ieast)) THEN
DO k=1,N(ng)
DO j=JstrV,Jend
!> Awrk(j,k,Nnew)=Awrk(j,k,Nold)+ &
!> & oHz(j,k)*(FS(j,k )- &
!> & FS(j,k-1))
!>
tl_Awrk(j,k,Nnew)=tl_Awrk(j,k,Nold)+ &
& oHz(j,k)*(tl_FS(j,k )- &
& tl_FS(j,k-1))
END DO
END DO
ELSE IF ((boundary.eq.isouth).or.(boundary.eq.inorth)) THEN
DO k=1,N(ng)
DO i=Istr,Iend
!> Awrk(i,k,Nnew)=Awrk(i,k,Nold)+ &
!> & oHz(i,k)*(FS(i,k )- &
!> & FS(i,k-1))
!>
tl_Awrk(i,k,Nnew)=tl_Awrk(i,k,Nold)+ &
& oHz(i,k)*(tl_FS(i,k )- &
& tl_FS(i,k-1))
END DO
END DO
END IF
END IF
!
! Update integration indices.
!
Nsav=Nold
Nold=Nnew
Nnew=Nsav
END DO
# endif
# endif
!
!-----------------------------------------------------------------------
! Load convolved solution.
!-----------------------------------------------------------------------
!
IF (Lconvolve(boundary)) THEN
IF ((boundary.eq.iwest).or.(boundary.eq.ieast)) THEN
DO k=1,N(ng)
DO j=JstrV,Jend
!> A(j,k)=Awrk(j,k,Nold)
!>
tl_A(j,k)=tl_Awrk(j,k,Nold)
END DO
END DO
ELSE IF ((boundary.eq.isouth).or.(boundary.eq.inorth)) THEN
DO k=1,N(ng)
DO i=Istr,Iend
!> A(i,k)=Awrk(i,k,Nold)
!>
tl_A(i,k)=tl_Awrk(i,k,Nold)
END DO
END DO
END IF
END IF
!> CALL bc_v3d_bry_tile (ng, tile, boundary, &
!> & LBij, UBij, 1, N(ng), &
!> & A)
!>
CALL bc_v3d_bry_tile (ng, tile, boundary, &
& LBij, UBij, 1, N(ng), &
& tl_A)
# ifdef DISTRIBUTE
!> CALL mp_exchange3d_bry (ng, tile, model, 1, boundary, &
!> & LBij, UBij, 1, N(ng), &
!> & Nghost, &
!> & EWperiodic(ng), NSperiodic(ng), &
!> & A)
!>
CALL mp_exchange3d_bry (ng, tile, model, 1, boundary, &
& LBij, UBij, 1, N(ng), &
& Nghost, &
& EWperiodic(ng), NSperiodic(ng), &
& tl_A)
# endif
RETURN
END SUBROUTINE tl_conv_v3d_bry_tile
#endif
END MODULE tl_conv_bry3d_mod