MODULE tl_step3d_uv_mod ! !git $Id$ !svn $Id: tl_step3d_uv.F 1183 2023-07-27 04:20:57Z 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 time-steps the tangent linear horizontal momentum ! ! equations. The vertical viscosity terms are time-stepped using ! ! an implicit algorithm. ! ! ! ! BASIC STATE variables needed: u, v, ru, rv, Akv, ! ! Hz, Huon, Hvom, z_r, z_w, ! ! DU_avg1, DU_avg2, DV_avg1, DV_avg2, ! ! Qsrc ! ! ! !======================================================================= ! implicit none ! PRIVATE PUBLIC :: tl_step3d_uv ! CONTAINS ! !*********************************************************************** SUBROUTINE tl_step3d_uv (ng, tile) !*********************************************************************** ! USE mod_param USE mod_coupling USE mod_forces 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 = & & "ROMS/Tangent/tl_step3d_uv.F" ! integer :: IminS, ImaxS, JminS, JmaxS integer :: LBi, UBi, LBj, UBj, LBij, UBij ! ! Set horizontal starting and ending indices for automatic private ! storage arrays. ! IminS=BOUNDS(ng)%Istr(tile)-3 ImaxS=BOUNDS(ng)%Iend(tile)+3 JminS=BOUNDS(ng)%Jstr(tile)-3 JmaxS=BOUNDS(ng)%Jend(tile)+3 ! ! Determine array lower and upper bounds in the I- and J-directions. ! LBi=BOUNDS(ng)%LBi(tile) UBi=BOUNDS(ng)%UBi(tile) LBj=BOUNDS(ng)%LBj(tile) UBj=BOUNDS(ng)%UBj(tile) ! ! Set array lower and upper bounds for MIN(I,J) directions and ! MAX(I,J) directions. ! LBij=BOUNDS(ng)%LBij UBij=BOUNDS(ng)%UBij ! CALL wclock_on (ng, iTLM, 34, 58, MyFile) CALL tl_step3d_uv_tile (ng, tile, & & LBi, UBi, LBj, UBj, & & IminS, ImaxS, JminS, JmaxS, & & nrhs(ng), nstp(ng), nnew(ng), & & GRID(ng) % umask, & & GRID(ng) % vmask, & & GRID(ng) % om_v, & & GRID(ng) % on_u, & & GRID(ng) % pm, & & GRID(ng) % pn, & & GRID(ng) % Hz, & & GRID(ng) % tl_Hz, & & GRID(ng) % z_r, & & GRID(ng) % tl_z_r, & & GRID(ng) % z_w, & & GRID(ng) % tl_z_w, & & MIXING(ng) % Akv, & & MIXING(ng) % tl_Akv, & & COUPLING(ng) % DU_avg1, & & COUPLING(ng) % tl_DU_avg1, & & COUPLING(ng) % DV_avg1, & & COUPLING(ng) % tl_DV_avg1, & & COUPLING(ng) % DU_avg2, & & COUPLING(ng) % tl_DU_avg2, & & COUPLING(ng) % DV_avg2, & & COUPLING(ng) % tl_DV_avg2, & & OCEAN(ng) % tl_ru, & & OCEAN(ng) % tl_rv, & & OCEAN(ng) % u, & & OCEAN(ng) % tl_u, & & OCEAN(ng) % v, & & OCEAN(ng) % tl_v, & & OCEAN(ng) % tl_ubar, & & OCEAN(ng) % tl_vbar, & & GRID(ng) % Huon, & & GRID(ng) % tl_Huon, & & GRID(ng) % Hvom, & & GRID(ng) % tl_Hvom) CALL wclock_off (ng, iTLM, 34, 125, MyFile) ! RETURN END SUBROUTINE tl_step3d_uv ! !*********************************************************************** SUBROUTINE tl_step3d_uv_tile (ng, tile, & & LBi, UBi, LBj, UBj, & & IminS, ImaxS, JminS, JmaxS, & & nrhs, nstp, nnew, & & umask, vmask, & & om_v, on_u, pm, pn, & & Hz, tl_Hz, & & z_r, tl_z_r, & & z_w, tl_z_w, & & Akv, tl_Akv, & & DU_avg1, tl_DU_avg1, & & DV_avg1, tl_DV_avg1, & & DU_avg2, tl_DU_avg2, & & DV_avg2, tl_DV_avg2, & & tl_ru, tl_rv, & & u, tl_u, & & v, tl_v, & & tl_ubar, tl_vbar, & & Huon, tl_Huon, & & Hvom, tl_Hvom) !*********************************************************************** ! USE mod_param USE mod_ncparam USE mod_scalars USE mod_sources ! USE exchange_2d_mod USE exchange_3d_mod USE mp_exchange_mod, ONLY : mp_exchange2d, mp_exchange3d USE tl_u3dbc_mod, ONLY : tl_u3dbc_tile USE tl_v3dbc_mod, ONLY : tl_v3dbc_tile ! ! 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, nstp, nnew ! real(r8), intent(in) :: umask(LBi:,LBj:) real(r8), intent(in) :: vmask(LBi:,LBj:) real(r8), intent(in) :: om_v(LBi:,LBj:) real(r8), intent(in) :: on_u(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) :: z_r(LBi:,LBj:,:) real(r8), intent(in) :: z_w(LBi:,LBj:,0:) real(r8), intent(in) :: Akv(LBi:,LBj:,0:) real(r8), intent(in) :: DU_avg1(LBi:,LBj:) real(r8), intent(in) :: DV_avg1(LBi:,LBj:) real(r8), intent(in) :: DU_avg2(LBi:,LBj:) real(r8), intent(in) :: DV_avg2(LBi:,LBj:) real(r8), intent(in) :: u(LBi:,LBj:,:,:) real(r8), intent(in) :: v(LBi:,LBj:,:,:) real(r8), intent(in) :: tl_Hz(LBi:,LBj:,:) real(r8), intent(in) :: tl_z_r(LBi:,LBj:,:) real(r8), intent(in) :: tl_z_w(LBi:,LBj:,0:) real(r8), intent(in) :: tl_Akv(LBi:,LBj:,0:) real(r8), intent(in) :: tl_DU_avg1(LBi:,LBj:) real(r8), intent(in) :: tl_DV_avg1(LBi:,LBj:) real(r8), intent(in) :: tl_DU_avg2(LBi:,LBj:) real(r8), intent(in) :: tl_DV_avg2(LBi:,LBj:) real(r8), intent(in) :: tl_ru(LBi:,LBj:,0:,:) real(r8), intent(in) :: tl_rv(LBi:,LBj:,0:,:) real(r8), intent(inout) :: Huon(LBi:,LBj:,:) real(r8), intent(inout) :: Hvom(LBi:,LBj:,:) real(r8), intent(inout) :: tl_u(LBi:,LBj:,:,:) real(r8), intent(inout) :: tl_v(LBi:,LBj:,:,:) real(r8), intent(out) :: tl_ubar(LBi:,LBj:,:) real(r8), intent(out) :: tl_vbar(LBi:,LBj:,:) real(r8), intent(out) :: tl_Huon(LBi:,LBj:,:) real(r8), intent(out) :: tl_Hvom(LBi:,LBj:,:) ! ! Local variable declarations. ! integer :: i, idiag, is, j, k ! real(r8) :: cff, cff1, cff2 real(r8) :: tl_cff, tl_cff1, tl_cff2 ! real(r8), dimension(IminS:ImaxS) :: CF1 real(r8), dimension(IminS:ImaxS) :: FC1 real(r8), dimension(IminS:ImaxS,0:N(ng)) :: AK real(r8), dimension(IminS:ImaxS,0:N(ng)) :: BC real(r8), dimension(IminS:ImaxS,0:N(ng)) :: CF real(r8), dimension(IminS:ImaxS,0:N(ng)) :: DC real(r8), dimension(IminS:ImaxS,0:N(ng)) :: DC1 real(r8), dimension(IminS:ImaxS,0:N(ng)) :: FC real(r8), dimension(IminS:ImaxS,N(ng)) :: Hzk real(r8), dimension(IminS:ImaxS,N(ng)) :: oHz real(r8), dimension(IminS:ImaxS,0:N(ng)) :: tl_AK real(r8), dimension(IminS:ImaxS,0:N(ng)) :: tl_BC real(r8), dimension(IminS:ImaxS,0:N(ng)) :: tl_CF real(r8), dimension(IminS:ImaxS,0:N(ng)) :: tl_DC real(r8), dimension(IminS:ImaxS,0:N(ng)) :: tl_FC real(r8), dimension(IminS:ImaxS,N(ng)) :: tl_Hzk real(r8), dimension(IminS:ImaxS,N(ng)) :: tl_oHz ! ! !----------------------------------------------------------------------- ! Set lower and upper tile bounds and staggered variables bounds for ! this horizontal domain partition. Notice that if tile=-1, it will ! set the values for the global grid. !----------------------------------------------------------------------- ! integer :: Istr, IstrB, IstrP, IstrR, IstrT, IstrM, IstrU integer :: Iend, IendB, IendP, IendR, IendT integer :: Jstr, JstrB, JstrP, JstrR, JstrT, JstrM, JstrV integer :: Jend, JendB, JendP, JendR, JendT integer :: Istrm3, Istrm2, Istrm1, IstrUm2, IstrUm1 integer :: Iendp1, Iendp2, Iendp2i, Iendp3 integer :: Jstrm3, Jstrm2, Jstrm1, JstrVm2, JstrVm1 integer :: Jendp1, Jendp2, Jendp2i, Jendp3 ! Istr =BOUNDS(ng) % Istr (tile) IstrB =BOUNDS(ng) % IstrB (tile) IstrM =BOUNDS(ng) % IstrM (tile) IstrP =BOUNDS(ng) % IstrP (tile) IstrR =BOUNDS(ng) % IstrR (tile) IstrT =BOUNDS(ng) % IstrT (tile) IstrU =BOUNDS(ng) % IstrU (tile) Iend =BOUNDS(ng) % Iend (tile) IendB =BOUNDS(ng) % IendB (tile) IendP =BOUNDS(ng) % IendP (tile) IendR =BOUNDS(ng) % IendR (tile) IendT =BOUNDS(ng) % IendT (tile) Jstr =BOUNDS(ng) % Jstr (tile) JstrB =BOUNDS(ng) % JstrB (tile) JstrM =BOUNDS(ng) % JstrM (tile) JstrP =BOUNDS(ng) % JstrP (tile) JstrR =BOUNDS(ng) % JstrR (tile) JstrT =BOUNDS(ng) % JstrT (tile) JstrV =BOUNDS(ng) % JstrV (tile) Jend =BOUNDS(ng) % Jend (tile) JendB =BOUNDS(ng) % JendB (tile) JendP =BOUNDS(ng) % JendP (tile) JendR =BOUNDS(ng) % JendR (tile) JendT =BOUNDS(ng) % JendT (tile) ! Istrm3 =BOUNDS(ng) % Istrm3 (tile) ! Istr-3 Istrm2 =BOUNDS(ng) % Istrm2 (tile) ! Istr-2 Istrm1 =BOUNDS(ng) % Istrm1 (tile) ! Istr-1 IstrUm2=BOUNDS(ng) % IstrUm2(tile) ! IstrU-2 IstrUm1=BOUNDS(ng) % IstrUm1(tile) ! IstrU-1 Iendp1 =BOUNDS(ng) % Iendp1 (tile) ! Iend+1 Iendp2 =BOUNDS(ng) % Iendp2 (tile) ! Iend+2 Iendp2i=BOUNDS(ng) % Iendp2i(tile) ! Iend+2 interior Iendp3 =BOUNDS(ng) % Iendp3 (tile) ! Iend+3 Jstrm3 =BOUNDS(ng) % Jstrm3 (tile) ! Jstr-3 Jstrm2 =BOUNDS(ng) % Jstrm2 (tile) ! Jstr-2 Jstrm1 =BOUNDS(ng) % Jstrm1 (tile) ! Jstr-1 JstrVm2=BOUNDS(ng) % JstrVm2(tile) ! JstrV-2 JstrVm1=BOUNDS(ng) % JstrVm1(tile) ! JstrV-1 Jendp1 =BOUNDS(ng) % Jendp1 (tile) ! Jend+1 Jendp2 =BOUNDS(ng) % Jendp2 (tile) ! Jend+2 Jendp2i=BOUNDS(ng) % Jendp2i(tile) ! Jend+2 interior Jendp3 =BOUNDS(ng) % Jendp3 (tile) ! Jend+3 ! !----------------------------------------------------------------------- ! Time step momentum equation in the XI-direction. !----------------------------------------------------------------------- ! DO j=Jstr,Jend DO i=IstrU,Iend AK(i,0)=0.5_r8*(Akv(i-1,j,0)+ & & Akv(i ,j,0)) tl_AK(i,0)=0.5_r8*(tl_Akv(i-1,j,0)+ & & tl_Akv(i ,j,0)) DO k=1,N(ng) AK(i,k)=0.5_r8*(Akv(i-1,j,k)+ & & Akv(i ,j,k)) tl_AK(i,k)=0.5_r8*(tl_Akv(i-1,j,k)+ & & tl_Akv(i ,j,k)) Hzk(i,k)=0.5_r8*(Hz(i-1,j,k)+ & & Hz(i ,j,k)) tl_Hzk(i,k)=0.5_r8*(tl_Hz(i-1,j,k)+ & & tl_Hz(i ,j,k)) END DO END DO ! ! Time step right-hand-side terms. ! IF (iic(ng).eq.ntfirst(ng)) THEN cff=0.25_r8*dt(ng) ELSE IF (iic(ng).eq.(ntfirst(ng)+1)) THEN cff=0.25_r8*dt(ng)*3.0_r8/2.0_r8 ELSE cff=0.25_r8*dt(ng)*23.0_r8/12.0_r8 END IF DO i=IstrU,Iend DC(i,0)=cff*(pm(i,j)+pm(i-1,j))*(pn(i,j)+pn(i-1,j)) END DO ! ! The BASIC STATE "u" used below must be in transport units, but "u" ! retrived is in m/s so we multiply by "Hzk". ! DO k=1,N(ng) DO i=IstrU,Iend !^ u(i,j,k,nnew)=u(i,j,k,nnew)+ & !^ & DC(i,0)*ru(i,j,k,nrhs) !^ tl_u(i,j,k,nnew)=tl_u(i,j,k,nnew)+ & & DC(i,0)*tl_ru(i,j,k,nrhs) END DO END DO ! ! Compute off-diagonal coefficients [lambda*dt*Akv/Hz] for the ! implicit vertical viscosity term at horizontal U-points and ! vertical W-points. ! ! NOTE: The original code solves the tridiagonal system A*u=r where ! A is a matrix and u and r are vectors. We need to solve the ! tangent linear of this system which is A*tl_u+tl_A*u=tl_r. ! Here, tl_A*u and tl_r are known, so we must solve for tl_u ! by inverting A*tl_u=tl_r-tl_A*u. ! cff=-lambda*dt(ng)/0.5_r8 DO k=1,N(ng)-1 DO i=IstrU,Iend cff1=1.0_r8/(z_r(i,j,k+1)+z_r(i-1,j,k+1)- & & z_r(i,j,k )-z_r(i-1,j,k )) tl_cff1=-cff1*cff1*(tl_z_r(i,j,k+1)+tl_z_r(i-1,j,k+1)- & & tl_z_r(i,j,k )-tl_z_r(i-1,j,k )) FC(i,k)=cff*cff1*AK(i,k) tl_FC(i,k)=cff*(tl_cff1*AK(i,k)+cff1*tl_AK(i,k)) END DO END DO DO i=IstrU,Iend FC(i,0)=0.0_r8 tl_FC(i,0)=0.0_r8 FC(i,N(ng))=0.0_r8 tl_FC(i,N(ng))=0.0_r8 END DO ! ! Solve the tangent linear tridiagonal system. ! (DC is a tangent linear variable here). ! DO k=1,N(ng) DO i=IstrU,Iend BC(i,k)=Hzk(i,k)-FC(i,k)-FC(i,k-1) tl_BC(i,k)=tl_Hzk(i,k)-tl_FC(i,k)-tl_FC(i,k-1) END DO END DO DO k=2,N(ng)-1 DO i=IstrU,Iend DC(i,k)=tl_u(i,j,k,nnew)- & & (tl_FC(i,k-1)*u(i,j,k-1,nnew)+ & & tl_BC(i,k )*u(i,j,k ,nnew)+ & & tl_FC(i,k )*u(i,j,k+1,nnew)) END DO END DO DO i=IstrU,Iend DC(i,1)=tl_u(i,j,1,nnew)- & & (tl_BC(i,1)*u(i,j,1,nnew)+ & & tl_FC(i,1)*u(i,j,2,nnew)) DC(i,N(ng))=tl_u(i,j,N(ng),nnew)- & & (tl_FC(i,N(ng)-1)*u(i,j,N(ng)-1,nnew)+ & & tl_BC(i,N(ng) )*u(i,j,N(ng) ,nnew)) END DO 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) 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)) END DO END DO ! ! Compute new solution by back substitution. ! (DC is a tangent linear variable here). ! 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)) !^ u(i,j,N(ng),nnew)=DC(i,N(ng)) !^ tl_u(i,j,N(ng),nnew)=DC(i,N(ng)) 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) !^ u(i,j,k,nnew)=DC(i,k) !^ tl_u(i,j,k,nnew)=DC(i,k) END DO END DO ! ! Replace INTERIOR POINTS incorrect vertical mean with more accurate ! barotropic component, ubar=DU_avg1/(D*on_u). Recall that, D=CF(:,0). ! DO i=IstrU,Iend CF(i,0)=Hzk(i,1) tl_CF(i,0)=tl_Hzk(i,1) DC(i,0)=u(i,j,1,nnew)*Hzk(i,1) tl_DC(i,0)=tl_u(i,j,1,nnew)*Hzk(i,1)+ & & u(i,j,1,nnew)*tl_Hzk(i,1) END DO DO k=2,N(ng) DO i=IstrU,Iend CF(i,0)=CF(i,0)+Hzk(i,k) tl_CF(i,0)=tl_CF(i,0)+tl_Hzk(i,k) DC(i,0)=DC(i,0)+u(i,j,k,nnew)*Hzk(i,k) tl_DC(i,0)=tl_DC(i,0)+ & & tl_u(i,j,k,nnew)*Hzk(i,k)+ & & u(i,j,k,nnew)*tl_Hzk(i,k) END DO END DO DO i=IstrU,Iend DC1(i,0)=DC(i,0) ! intermediate cff1=1.0_r8/(CF(i,0)*on_u(i,j)) tl_cff1=-cff1*cff1*tl_CF(i,0)*on_u(i,j) DC(i,0)=(DC(i,0)*on_u(i,j)-DU_avg1(i,j))*cff1 ! recursive tl_DC(i,0)=(tl_DC(i,0)*on_u(i,j)-tl_DU_avg1(i,j))*cff1+ & & (DC1(i,0)*on_u(i,j)-DU_avg1(i,j))*tl_cff1 END DO ! ! Couple and update new solution. ! DO k=1,N(ng) DO i=IstrU,Iend !^ u(i,j,k,nnew)=u(i,j,k,nnew)-DC(i,0) !^ tl_u(i,j,k,nnew)=tl_u(i,j,k,nnew)-tl_DC(i,0) !^ u(i,j,k,nnew)=u(i,j,k,nnew)*umask(i,j) !^ tl_u(i,j,k,nnew)=tl_u(i,j,k,nnew)*umask(i,j) END DO END DO ! !----------------------------------------------------------------------- ! Time step momentum equation in the ETA-direction. !----------------------------------------------------------------------- ! IF (j.ge.JstrV) THEN DO i=Istr,Iend AK(i,0)=0.5_r8*(Akv(i,j-1,0)+ & & Akv(i,j ,0)) tl_AK(i,0)=0.5_r8*(tl_Akv(i,j-1,0)+ & & tl_Akv(i,j ,0)) DO k=1,N(ng) AK(i,k)=0.5_r8*(Akv(i,j-1,k)+ & & Akv(i,j ,k)) tl_AK(i,k)=0.5_r8*(tl_Akv(i,j-1,k)+ & & tl_Akv(i,j ,k)) Hzk(i,k)=0.5_r8*(Hz(i,j-1,k)+ & & Hz(i,j ,k)) tl_Hzk(i,k)=0.5_r8*(tl_Hz(i,j-1,k)+ & & tl_Hz(i,j ,k)) END DO END DO ! ! Time step right-hand-side terms. ! IF (iic(ng).eq.ntfirst(ng)) THEN cff=0.25_r8*dt(ng) ELSE IF (iic(ng).eq.(ntfirst(ng)+1)) THEN cff=0.25_r8*dt(ng)*3.0_r8/2.0_r8 ELSE cff=0.25_r8*dt(ng)*23.0_r8/12.0_r8 END IF DO i=Istr,Iend DC(i,0)=cff*(pm(i,j)+pm(i,j-1))*(pn(i,j)+pn(i,j-1)) END DO ! ! The BASIC STATE "v" used below must be in transport units, but "v" ! retrived is in m/s so we multiply by "Hzk". ! DO k=1,N(ng) DO i=Istr,Iend !^ v(i,j,k,nnew)=v(i,j,k,nnew)+DC(i,0)*rv(i,j,k,nrhs) !^ tl_v(i,j,k,nnew)=tl_v(i,j,k,nnew)+ & & DC(i,0)*tl_rv(i,j,k,nrhs) END DO END DO ! ! Compute off-diagonal coefficients [lambda*dt*Akv/Hz] for the ! implicit vertical viscosity term at horizontal V-points and ! vertical W-points. ! ! NOTE: The original code solves the tridiagonal system A*v=r where ! A is a matrix and v and r are vectors. We need to solve the ! tangent linear of this system which is A*tl_v+tl_A*v=tl_r. ! Here, tl_A*v and tl_r are known, so we must solve for tl_v ! by inverting A*tl_v=tl_r-tl_A*v. ! cff=-lambda*dt(ng)/0.5_r8 DO k=1,N(ng)-1 DO i=Istr,Iend cff1=1.0_r8/(z_r(i,j,k+1)+z_r(i,j-1,k+1)- & & z_r(i,j,k )-z_r(i,j-1,k )) tl_cff1=-cff1*cff1*(tl_z_r(i,j,k+1)+tl_z_r(i,j-1,k+1)- & & tl_z_r(i,j,k )-tl_z_r(i,j-1,k )) FC(i,k)=cff*cff1*AK(i,k) tl_FC(i,k)=cff*(tl_cff1*AK(i,k)+cff1*tl_AK(i,k)) END DO END DO DO i=Istr,Iend FC(i,0)=0.0_r8 tl_FC(i,0)=0.0_r8 FC(i,N(ng))=0.0_r8 tl_FC(i,N(ng))=0.0_r8 END DO ! ! Solve the tangent linear tridiagonal system. ! DO k=1,N(ng) DO i=Istr,Iend BC(i,k)=Hzk(i,k)-FC(i,k)-FC(i,k-1) tl_BC(i,k)=tl_Hzk(i,k)-tl_FC(i,k)-tl_FC(i,k-1) END DO END DO DO k=2,N(ng)-1 DO i=Istr,Iend DC(i,k)=tl_v(i,j,k,nnew)- & & (tl_FC(i,k-1)*v(i,j,k-1,nnew)+ & & tl_BC(i,k )*v(i,j,k ,nnew)+ & & tl_FC(i,k )*v(i,j,k+1,nnew)) END DO END DO DO i=Istr,Iend DC(i,1)=tl_v(i,j,1,nnew)- & & (tl_BC(i,1)*v(i,j,1,nnew)+ & & tl_FC(i,1)*v(i,j,2,nnew)) DC(i,N(ng))=tl_v(i,j,N(ng),nnew)- & & (tl_FC(i,N(ng)-1)*v(i,j,N(ng)-1,nnew)+ & & tl_BC(i,N(ng) )*v(i,j,N(ng) ,nnew)) END DO 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) 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)) END DO END DO ! ! Compute new solution by back substitution. ! (DC is a tangent linear variable here). ! 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)) !^ v(i,j,N(ng),nnew)=DC(i,N(ng)) !^ tl_v(i,j,N(ng),nnew)=DC(i,N(ng)) 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) !^ v(i,j,k,nnew)=DC(i,k) !^ tl_v(i,j,k,nnew)=DC(i,k) END DO END DO ! ! Replace INTERIOR POINTS incorrect vertical mean with more accurate ! barotropic component, vbar=DV_avg1/(D*om_v). Recall that, D=CF(:,0). ! DO i=Istr,Iend CF(i,0)=Hzk(i,1) tl_CF(i,0)=tl_Hzk(i,1) DC(i,0)=v(i,j,1,nnew)*Hzk(i,1) tl_DC(i,0)=tl_v(i,j,1,nnew)*Hzk(i,1)+ & & v(i,j,1,nnew)*tl_Hzk(i,1) END DO DO k=2,N(ng) DO i=Istr,Iend CF(i,0)=CF(i,0)+Hzk(i,k) tl_CF(i,0)=tl_CF(i,0)+tl_Hzk(i,k) DC(i,0)=DC(i,0)+v(i,j,k,nnew)*Hzk(i,k) tl_DC(i,0)=tl_DC(i,0)+ & & tl_v(i,j,k,nnew)*Hzk(i,k)+ & & v(i,j,k,nnew)*tl_Hzk(i,k) END DO END DO DO i=Istr,Iend DC1(i,0)=DC(i,0) ! intermediate cff1=1.0_r8/(CF(i,0)*om_v(i,j)) tl_cff1=-cff1*cff1*tl_CF(i,0)*om_v(i,j) DC(i,0)=(DC(i,0)*om_v(i,j)-DV_avg1(i,j))*cff1 ! recursive tl_DC(i,0)=(tl_DC(i,0)*om_v(i,j)-tl_DV_avg1(i,j))*cff1+ & & (DC1(i,0)*om_v(i,j)-DV_avg1(i,j))*tl_cff1 END DO ! ! Couple and update new solution. ! DO k=1,N(ng) DO i=Istr,Iend !^ v(i,j,k,nnew)=v(i,j,k,nnew)-DC(i,0) !^ tl_v(i,j,k,nnew)=tl_v(i,j,k,nnew)-tl_DC(i,0) !^ v(i,j,k,nnew)=v(i,j,k,nnew)*vmask(i,j) !^ tl_v(i,j,k,nnew)=tl_v(i,j,k,nnew)*vmask(i,j) END DO END DO END IF END DO ! !----------------------------------------------------------------------- ! Set lateral boundary conditions. !----------------------------------------------------------------------- ! !^ CALL u3dbc_tile (ng, tile, & !^ & LBi, UBi, LBj, UBj, N(ng), & !^ & IminS, ImaxS, JminS, JmaxS, & !^ & nstp, nnew, & !^ & u) !^ CALL tl_u3dbc_tile (ng, tile, & & LBi, UBi, LBj, UBj, N(ng), & & IminS, ImaxS, JminS, JmaxS, & & nstp, nnew, & & tl_u) !^ CALL v3dbc_tile (ng, tile, & !^ & LBi, UBi, LBj, UBj, N(ng), & !^ & IminS, ImaxS, JminS, JmaxS, & !^ & nstp, nnew, & !^ & v) !^ CALL tl_v3dbc_tile (ng, tile, & & LBi, UBi, LBj, UBj, N(ng), & & IminS, ImaxS, JminS, JmaxS, & & nstp, nnew, & & tl_v) ! !----------------------------------------------------------------------- ! Apply momentum transport point sources (like river runoff), if any. !----------------------------------------------------------------------- ! IF (LuvSrc(ng)) THEN DO is=1,Nsrc(ng) i=SOURCES(ng)%Isrc(is) j=SOURCES(ng)%Jsrc(is) IF (((IstrR.le.i).and.(i.le.IendR)).and. & & ((JstrR.le.j).and.(j.le.JendR))) THEN IF (INT(SOURCES(ng)%Dsrc(is)).eq.0) THEN DO k=1,N(ng) cff1=1.0_r8/(on_u(i,j)* & & 0.5_r8*(z_w(i-1,j,k)-z_w(i-1,j,k-1)+ & & z_w(i ,j,k)-z_w(i ,j,k-1))) tl_cff1=-cff1*cff1*on_u(i,j)* & & 0.5_r8*(tl_z_w(i-1,j,k)-tl_z_w(i-1,j,k-1)+ & & tl_z_w(i ,j,k)-tl_z_w(i ,j,k-1)) !^ u(i,j,k,nnew)=SOURCES(ng)%Qsrc(is,k)*cff1 !^ tl_u(i,j,k,nnew)=SOURCES(ng)%tl_Qsrc(is,k)*cff1+ & & SOURCES(ng)%Qsrc(is,k)*tl_cff1 END DO ELSE IF (INT(SOURCES(ng)%Dsrc(is)).eq.1) THEN DO k=1,N(ng) cff1=1.0_r8/(om_v(i,j)* & & 0.5_r8*(z_w(i,j-1,k)-z_w(i,j-1,k-1)+ & & z_w(i,j ,k)-z_w(i,j ,k-1))) tl_cff1=-cff1*cff1*om_v(i,j)* & & 0.5_r8*(tl_z_w(i,j-1,k)-tl_z_w(i,j-1,k-1)+ & & tl_z_w(i,j ,k)-tl_z_w(i,j ,k-1)) !^ v(i,j,k,nnew)=SOURCES(ng)%Qsrc(is,k)*cff1 !^ tl_v(i,j,k,nnew)=SOURCES(ng)%tl_Qsrc(is,k)*cff1+ & & SOURCES(ng)%Qsrc(is,k)*tl_cff1 END DO END IF END IF END DO END IF ! !----------------------------------------------------------------------- ! Couple 2D and 3D momentum equations. !----------------------------------------------------------------------- ! ! Couple velocity component in the XI-direction. ! DO j=JstrT,JendT DO i=IstrP,IendT DC(i,0)=0.0_r8 tl_DC(i,0)=0.0_r8 CF(i,0)=0.0_r8 tl_CF(i,0)=0.0_r8 FC(i,0)=0.0_r8 tl_FC(i,0)=0.0_r8 END DO ! ! Compute thicknesses of U-boxes DC(i,1:N), total depth of the water ! column DC(i,0), and incorrect vertical mean CF(i,0). Notice that ! barotropic component is replaced with its fast-time averaged ! values. ! DO k=1,N(ng) DO i=IstrP,IendT cff=0.5_r8*on_u(i,j) DC(i,k)=cff*(Hz(i,j,k)+Hz(i-1,j,k)) tl_DC(i,k)=cff*(tl_Hz(i,j,k)+tl_Hz(i-1,j,k)) DC(i,0)=DC(i,0)+DC(i,k) tl_DC(i,0)=tl_DC(i,0)+tl_DC(i,k) CF(i,0)=CF(i,0)+ & & DC(i,k)*u(i,j,k,nnew) tl_CF(i,0)=tl_CF(i,0)+ & & tl_DC(i,k)*u(i,j,k,nnew)+ & & DC(i,k)*tl_u(i,j,k,nnew) END DO END DO DO i=IstrP,IendT DC1(i,0)=DC(i,0) ! intermediate DC(i,0)=1.0_r8/DC(i,0) ! recursive tl_DC(i,0)=-tl_DC(i,0)/(DC1(i,0)*DC1(i,0)) CF1(i)=CF(i,0) ! intermediate CF(i,0)=DC(i,0)*(CF(i,0)-DU_avg1(i,j)) ! recursive tl_CF(i,0)=tl_DC(i,0)*(CF1(i)-DU_avg1(i,j))+ & & DC(i,0)*(tl_CF(i,0)-tl_DU_avg1(i,j)) !^ ubar(i,j,1)=DC(i,0)*DU_avg1(i,j) !^ tl_ubar(i,j,1)=tl_DC(i,0)*DU_avg1(i,j)+ & & DC(i,0)*tl_DU_avg1(i,j) !^ ubar(i,j,2)=ubar(i,j,1) !^ tl_ubar(i,j,2)=tl_ubar(i,j,1) END DO ! ! Replace only BOUNDARY POINTS incorrect vertical mean with more ! accurate barotropic component, ubar=DU_avg1/(D*on_u). Recall that, ! D=CF(:,0). ! ! NOTE: Only the BOUNDARY POINTS need to be replaced. Avoid redundant ! update in the interior again for computational purposes which ! will not affect the nonlinear code. However, the adjoint ! code is wrong because the interior solution is corrected ! twice. The replacement is avoided if the boundary edge is ! periodic. The J-loop is pipelined, so we need to do a special ! test for the southern and northern domain edges. ! IF (.not.(CompositeGrid(iwest,ng).or.EWperiodic(ng))) THEN IF (DOMAIN(ng)%Western_Edge(tile)) THEN DO k=1,N(ng) !^ u(Istr,j,k,nnew)=u(Istr,j,k,nnew)-CF(Istr,0) !^ tl_u(Istr,j,k,nnew)=tl_u(Istr,j,k,nnew)- & & tl_CF(Istr,0) !^ u(Istr,j,k,nnew)=u(Istr,j,k,nnew)* & !^ & umask(Istr,j) !^ tl_u(Istr,j,k,nnew)=tl_u(Istr,j,k,nnew)* & & umask(Istr,j) END DO END IF END IF ! IF (.not.(CompositeGrid(ieast,ng).or.EWperiodic(ng))) THEN IF (DOMAIN(ng)%Eastern_Edge(tile)) THEN DO k=1,N(ng) !^ u(Iend+1,j,k,nnew)=u(Iend+1,j,k,nnew)-CF(Iend+1,0) !^ tl_u(Iend+1,j,k,nnew)=tl_u(Iend+1,j,k,nnew)- & & tl_CF(Iend+1,0) !^ u(Iend+1,j,k,nnew)=u(Iend+1,j,k,nnew)* & !^ & umask(Iend+1,j) !^ tl_u(Iend+1,j,k,nnew)=tl_u(Iend+1,j,k,nnew)* & & umask(Iend+1,j) END DO END IF END IF ! IF (.not.(CompositeGrid(isouth,ng).or.NSperiodic(ng))) THEN IF (j.eq.0) THEN ! southern boundary DO k=1,N(ng) ! J-loop pipelined DO i=IstrU,Iend !^ u(i,j,k,nnew)=u(i,j,k,nnew)-CF(i,0) !^ tl_u(i,j,k,nnew)=tl_u(i,j,k,nnew)- & & tl_CF(i,0) !^ u(i,j,k,nnew)=u(i,j,k,nnew)*umask(i,j) !^ tl_u(i,j,k,nnew)=tl_u(i,j,k,nnew)* & & umask(i,j) END DO END DO END IF END IF ! IF (.not.(CompositeGrid(inorth,ng).or.NSperiodic(ng))) THEN IF (j.eq.Mm(ng)+1) THEN ! northern boundary DO k=1,N(ng) ! J-loop pipelined DO i=IstrU,Iend !^ u(i,j,k,nnew)=u(i,j,k,nnew)-CF(i,0) !^ tl_u(i,j,k,nnew)=tl_u(i,j,k,nnew)- & & tl_CF(i,0) !^ u(i,j,k,nnew)=u(i,j,k,nnew)*umask(i,j) !^ tl_u(i,j,k,nnew)=tl_u(i,j,k,nnew)* & & umask(i,j) END DO END DO END IF END IF ! ! Compute correct mass flux, Hz*u/n. ! DO k=N(ng),1,-1 DO i=IstrP,IendT Huon(i,j,k)=0.5_r8*(Huon(i,j,k)+u(i,j,k,nnew)*DC(i,k)) tl_Huon(i,j,k)=0.5_r8*(tl_Huon(i,j,k)+ & & tl_u(i,j,k,nnew)*DC(i,k)+ & & u(i,j,k,nnew)*tl_DC(i,k)) FC(i,0)=FC(i,0)+Huon(i,j,k) tl_FC(i,0)=tl_FC(i,0)+tl_Huon(i,j,k) END DO END DO DO i=IstrP,IendT FC1(i)=FC(i,0) ! intermediate FC(i,0)=DC(i,0)*(FC(i,0)-DU_avg2(i,j)) ! recursive tl_FC(i,0)=tl_DC(i,0)*(FC1(i)-DU_avg2(i,j))+ & & DC(i,0)*(tl_FC(i,0)-tl_DU_avg2(i,j)) END DO DO k=1,N(ng) DO i=IstrP,IendT Huon(i,j,k)=Huon(i,j,k)-DC(i,k)*FC(i,0) tl_Huon(i,j,k)=tl_Huon(i,j,k)- & & tl_DC(i,k)*FC(i,0)- & & DC(i,k)*tl_FC(i,0) END DO END DO ! ! Couple velocity component in the ETA-direction. ! IF (j.ge.Jstr) THEN DO i=IstrT,IendT DC(i,0)=0.0_r8 tl_DC(i,0)=0.0_r8 CF(i,0)=0.0_r8 tl_CF(i,0)=0.0_r8 FC(i,0)=0.0_r8 tl_FC(i,0)=0.0_r8 END DO ! ! Compute thicknesses of V-boxes DC(i,1:N), total depth of the water ! column DC(i,0), and incorrect vertical mean CF(i,0). Notice that ! barotropic component is replaced with its fast-time averaged ! values. ! DO k=1,N(ng) DO i=IstrT,IendT cff=0.5_r8*om_v(i,j) DC(i,k)=cff*(Hz(i,j,k)+Hz(i,j-1,k)) tl_DC(i,k)=cff*(tl_Hz(i,j,k)+tl_Hz(i,j-1,k)) DC(i,0)=DC(i,0)+DC(i,k) tl_DC(i,0)=tl_DC(i,0)+tl_DC(i,k) CF(i,0)=CF(i,0)+ & & DC(i,k)*v(i,j,k,nnew) tl_CF(i,0)=tl_CF(i,0)+ & & tl_DC(i,k)*v(i,j,k,nnew)+ & & DC(i,k)*tl_v(i,j,k,nnew) END DO END DO DO i=IstrT,IendT DC1(i,0)=DC(i,0) ! intermediate DC(i,0)=1.0_r8/DC(i,0) ! recursive tl_DC(i,0)=-tl_DC(i,0)/(DC1(i,0)*DC1(i,0)) CF1(i)=CF(i,0) ! intermediate CF(i,0)=DC(i,0)*(CF(i,0)-DV_avg1(i,j)) ! recursive tl_CF(i,0)=tl_DC(i,0)*(CF1(i)-DV_avg1(i,j))+ & & DC(i,0)*(tl_CF(i,0)-tl_DV_avg1(i,j)) !^ vbar(i,j,1)=DC(i,0)*DV_avg1(i,j) !^ tl_vbar(i,j,1)=tl_DC(i,0)*DV_avg1(i,j)+ & & DC(i,0)*tl_DV_avg1(i,j) !^ vbar(i,j,2)=vbar(i,j,1) !^ tl_vbar(i,j,2)=tl_vbar(i,j,1) END DO ! ! Replace only BOUNDARY POINTS incorrect vertical mean with more ! accurate barotropic component, vbar=DV_avg1/(D*om_v). Recall that, ! D=CF(:,0). ! ! NOTE: Only the BOUNDARY POINTS need to be replaced. Avoid redundant ! update in the interior again for computational purposes which ! will not affect the nonlinear code. However, the adjoint ! code is wrong because the interior solution is corrected ! twice. The replacement is avoided if the boundary edge is ! periodic. The J-loop is pipelined, so we need to do a special ! test for the southern and northern domain edges. ! IF (.not.(CompositeGrid(iwest,ng).or.EWperiodic(ng))) THEN IF (DOMAIN(ng)%Western_Edge(tile)) THEN DO k=1,N(ng) !^ v(Istr-1,j,k,nnew)=v(Istr-1,j,k,nnew)-CF(Istr-1,0) !^ tl_v(Istr-1,j,k,nnew)=tl_v(Istr-1,j,k,nnew)- & & tl_CF(Istr-1,0) !^ v(Istr-1,j,k,nnew)=v(Istr-1,j,k,nnew)* & !^ & vmask(Istr-1,j) !^ tl_v(Istr-1,j,k,nnew)=tl_v(Istr-1,j,k,nnew)* & & vmask(Istr-1,j) END DO END IF END IF ! IF (.not.(CompositeGrid(ieast,ng).or.EWperiodic(ng))) THEN IF (DOMAIN(ng)%Eastern_Edge(tile)) THEN DO k=1,N(ng) !^ v(Iend+1,j,k,nnew)=v(Iend+1,j,k,nnew)-CF(Iend+1,0) !^ tl_v(Iend+1,j,k,nnew)=tl_v(Iend+1,j,k,nnew)- & & tl_CF(Iend+1,0) !^ v(Iend+1,j,k,nnew)=v(Iend+1,j,k,nnew)* & !^ & vmask(Iend+1,j) !^ tl_v(Iend+1,j,k,nnew)=tl_v(Iend+1,j,k,nnew)* & & vmask(Iend+1,j) END DO END IF END IF ! IF (.not.(CompositeGrid(isouth,ng).or.NSperiodic(ng))) THEN IF (j.eq.1) THEN ! southern boundary DO k=1,N(ng) ! J-loop pipelined DO i=Istr,Iend !^ v(i,j,k,nnew)=v(i,j,k,nnew)-CF(i,0) !^ tl_v(i,j,k,nnew)=tl_v(i,j,k,nnew)- & & tl_CF(i,0) !^ v(i,j,k,nnew)=v(i,j,k,nnew)* !^ & vmask(i,j) !^ tl_v(i,j,k,nnew)=tl_v(i,j,k,nnew)* & & vmask(i,j) END DO END DO END IF END IF ! IF (.not.(CompositeGrid(inorth,ng).or.NSperiodic(ng))) THEN IF (j.eq.Mm(ng)+1) THEN ! northern boundary DO k=1,N(ng) ! J-loop pipelined DO i=Istr,Iend !^ v(i,j,k,nnew)=v(i,j,k,nnew)-CF(i,0) !^ tl_v(i,j,k,nnew)=tl_v(i,j,k,nnew)- & & tl_CF(i,0) !^ v(i,j,k,nnew)=v(i,j,k,nnew)* & !^ & vmask(i,j) !^ tl_v(i,j,k,nnew)=tl_v(i,j,k,nnew)* & & vmask(i,j) END DO END DO END IF END IF ! ! Compute correct mass flux, Hz*v/m. ! DO k=N(ng),1,-1 DO i=IstrT,IendT Hvom(i,j,k)=0.5_r8*(Hvom(i,j,k)+v(i,j,k,nnew)*DC(i,k)) tl_Hvom(i,j,k)=0.5_r8*(tl_Hvom(i,j,k)+ & & tl_v(i,j,k,nnew)*DC(i,k)+ & & v(i,j,k,nnew)*tl_DC(i,k)) FC(i,0)=FC(i,0)+Hvom(i,j,k) tl_FC(i,0)=tl_FC(i,0)+tl_Hvom(i,j,k) END DO END DO DO i=IstrT,IendT FC1(i)=FC(i,0) ! intermediate FC(i,0)=DC(i,0)*(FC(i,0)-DV_avg2(i,j)) ! recursive tl_FC(i,0)=tl_DC(i,0)*(FC1(i)-DV_avg2(i,j))+ & & DC(i,0)*(tl_FC(i,0)-tl_DV_avg2(i,j)) END DO DO k=1,N(ng) DO i=IstrT,IendT Hvom(i,j,k)=Hvom(i,j,k)-DC(i,k)*FC(i,0) tl_Hvom(i,j,k)=tl_Hvom(i,j,k)- & & tl_DC(i,k)*FC(i,0)- & & DC(i,k)*tl_FC(i,0) END DO END DO END IF END DO ! !----------------------------------------------------------------------- ! Exchange boundary data. !----------------------------------------------------------------------- ! IF (EWperiodic(ng).or.NSperiodic(ng)) THEN !^ CALL exchange_u3d_tile (ng, tile, & !^ & LBi, UBi, LBj, UBj, 1, N(ng), & !^ & u(:,:,:,nnew)) !^ CALL exchange_u3d_tile (ng, tile, & & LBi, UBi, LBj, UBj, 1, N(ng), & & tl_u(:,:,:,nnew)) !^ CALL exchange_v3d_tile (ng, tile, & !^ & LBi, UBi, LBj, UBj, 1, N(ng), & !^ & v(:,:,:,nnew)) !^ CALL exchange_v3d_tile (ng, tile, & & LBi, UBi, LBj, UBj, 1, N(ng), & & tl_v(:,:,:,nnew)) CALL exchange_u3d_tile (ng, tile, & & LBi, UBi, LBj, UBj, 1, N(ng), & & Huon) CALL exchange_u3d_tile (ng, tile, & & LBi, UBi, LBj, UBj, 1, N(ng), & & tl_Huon) CALL exchange_v3d_tile (ng, tile, & & LBi, UBi, LBj, UBj, 1, N(ng), & & Hvom) CALL exchange_v3d_tile (ng, tile, & & LBi, UBi, LBj, UBj, 1, N(ng), & & tl_Hvom) ! DO k=1,2 !^ CALL exchange_u2d_tile (ng, tile, & !^ & LBi, UBi, LBj, UBj, & !^ & ubar(:,:,k)) !^ CALL exchange_u2d_tile (ng, tile, & & LBi, UBi, LBj, UBj, & & tl_ubar(:,:,k)) !^ CALL exchange_v2d_tile (ng, tile, & !^ & LBi, UBi, LBj, UBj, & !^ & vbar(:,:,k)) !^ CALL exchange_v2d_tile (ng, tile, & & LBi, UBi, LBj, UBj, & & tl_vbar(:,:,k)) END DO END IF !^ CALL mp_exchange3d (ng, tile, iNLM, 4, & !^ & LBi, UBi, LBj, UBj, 1, N(ng), & !^ & NghostPoints, & !^ & EWperiodic(ng), NSperiodic(ng), & !^ & u(:,:,:,nnew), v(:,:,:,nnew), & !^ & Huon, Hvom) !^ CALL mp_exchange3d (ng, tile, iTLM, 4, & & LBi, UBi, LBj, UBj, 1, N(ng), & & NghostPoints, & & EWperiodic(ng), NSperiodic(ng), & & tl_u(:,:,:,nnew), tl_v(:,:,:,nnew), & & tl_Huon, tl_Hvom) CALL mp_exchange3d (ng, tile, iTLM, 2, & & LBi, UBi, LBj, UBj, 1, N(ng), & & NghostPoints, & & EWperiodic(ng), NSperiodic(ng), & & Huon, Hvom) ! !^ CALL mp_exchange2d (ng, tile, iNLM, 4, & !^ & LBi, UBi, LBj, UBj, & !^ & NghostPoints, & !^ & EWperiodic(ng), NSperiodic(ng), & !^ & ubar(:,:,1), vbar(:,:,1), & !^ & ubar(:,:,2), vbar(:,:,2)) !^ CALL mp_exchange2d (ng, tile, iTLM, 4, & & LBi, UBi, LBj, UBj, & & NghostPoints, & & EWperiodic(ng), NSperiodic(ng), & & tl_ubar(:,:,1), tl_vbar(:,:,1), & & tl_ubar(:,:,2), tl_vbar(:,:,2)) ! RETURN END SUBROUTINE tl_step3d_uv_tile END MODULE tl_step3d_uv_mod