MODULE tl_pre_step3d_mod ! !git $Id$ !svn $Id: tl_pre_step3d.F 1180 2023-07-13 02:42:10Z 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 subroutine initialize computations for new time step of the ! ! tangent linear 3D primitive variables. ! ! ! ! Both n-1 and n-2 time-step contributions of the Adams/Bashforth ! ! scheme are added here to u and v at time index "nnew", since the ! ! right-hand-side arrays ru and rv at n-2 will be overwriten in ! ! subsequent calls to routines within the 3D engine. ! ! ! ! It also computes the time "n" vertical viscosity and diffusion ! ! contributions of the Crank-Nicholson implicit scheme because the ! ! thicknesses "Hz" will be overwriten at the end of the 2D engine ! ! (barotropic mode) computations. ! ! ! ! The actual time step will be carried out in routines "step3d_uv" ! ! and "step3d_t". ! ! ! ! BASIC STATE variables needed: AKt, AKv, Huon, Hvom, Hz, Tsrc, W, ! ! bustr, bvstr, ghats, srflx, sustr, ! ! svstr, t, z_r, z_w ! ! ! !======================================================================= ! implicit none ! PRIVATE PUBLIC :: tl_pre_step3d ! CONTAINS ! !*********************************************************************** SUBROUTINE tl_pre_step3d (ng, tile) !*********************************************************************** ! USE mod_param 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_pre_step3d.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, 22, 69, MyFile) CALL tl_pre_step3d_tile (ng, tile, & & LBi, UBi, LBj, UBj, & & IminS, ImaxS, JminS, JmaxS, & & nrhs(ng), nstp(ng), nnew(ng), & & GRID(ng) % rmask, & & GRID(ng) % umask, & & GRID(ng) % vmask, & & GRID(ng) % pm, & & GRID(ng) % pn, & & GRID(ng) % Hz, & & GRID(ng) % tl_Hz, & & GRID(ng) % Huon, & & GRID(ng) % tl_Huon, & & GRID(ng) % Hvom, & & GRID(ng) % tl_Hvom, & & GRID(ng) % z_r, & & GRID(ng) % tl_z_r, & & GRID(ng) % z_w, & & GRID(ng) % tl_z_w, & & FORCES(ng) % tl_btflx, & & FORCES(ng) % tl_bustr, & & FORCES(ng) % tl_bvstr, & & FORCES(ng) % tl_stflx, & & FORCES(ng) % tl_sustr, & & FORCES(ng) % tl_svstr, & & FORCES(ng) % srflx, & & MIXING(ng) % Akt, & & MIXING(ng) % tl_Akt, & & MIXING(ng) % Akv, & & MIXING(ng) % tl_Akv, & & OCEAN(ng) % W, & & OCEAN(ng) % tl_W, & & OCEAN(ng) % tl_ru, & & OCEAN(ng) % tl_rv, & & OCEAN(ng) % t, & & OCEAN(ng) % tl_t, & & OCEAN(ng) % u, & & OCEAN(ng) % tl_u, & & OCEAN(ng) % v, & & OCEAN(ng) % tl_v) CALL wclock_off (ng, iTLM, 22, 131, MyFile) ! RETURN END SUBROUTINE tl_pre_step3d ! !*********************************************************************** SUBROUTINE tl_pre_step3d_tile (ng, tile, & & LBi, UBi, LBj, UBj, & & IminS, ImaxS, JminS, JmaxS, & & nrhs, nstp, nnew, & & rmask, umask, vmask, & & pm, pn, & & Hz, tl_Hz, & & Huon, tl_Huon, & & Hvom, tl_Hvom, & & z_r, tl_z_r, & & z_w, tl_z_w, & & tl_btflx, tl_bustr, tl_bvstr, & & tl_stflx, tl_sustr, tl_svstr, & & srflx, & & Akt, tl_Akt, & & Akv, tl_Akv, & & W, tl_W, & & tl_ru, tl_rv, & & t, tl_t, & & u, tl_u, & & v, tl_v) !*********************************************************************** ! USE mod_param USE mod_scalars USE mod_sources ! USE exchange_3d_mod, ONLY : exchange_r3d_tile USE mp_exchange_mod, ONLY : mp_exchange4d USE tl_t3dbc_mod, ONLY : tl_t3dbc_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) :: rmask(LBi:,LBj:) real(r8), intent(in) :: umask(LBi:,LBj:) real(r8), intent(in) :: vmask(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) :: Huon(LBi:,LBj:,:) real(r8), intent(in) :: Hvom(LBi:,LBj:,:) real(r8), intent(in) :: z_r(LBi:,LBj:,:) real(r8), intent(in) :: z_w(LBi:,LBj:,0:) real(r8), intent(in) :: srflx(LBi:,LBj:) real(r8), intent(in) :: Akt(LBi:,LBj:,0:,:) real(r8), intent(in) :: Akv(LBi:,LBj:,0:) real(r8), intent(in) :: W(LBi:,LBj:,0:) real(r8), intent(in) :: t(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_Huon(LBi:,LBj:,:) real(r8), intent(in) :: tl_Hvom(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_btflx(LBi:,LBj:,:) real(r8), intent(in) :: tl_bustr(LBi:,LBj:) real(r8), intent(in) :: tl_bvstr(LBi:,LBj:) real(r8), intent(in) :: tl_stflx(LBi:,LBj:,:) real(r8), intent(in) :: tl_sustr(LBi:,LBj:) real(r8), intent(in) :: tl_svstr(LBi:,LBj:) real(r8), intent(in) :: tl_ru(LBi:,LBj:,0:,:) real(r8), intent(in) :: tl_rv(LBi:,LBj:,0:,:) real(r8), intent(in) :: tl_Akt(LBi:,LBj:,0:,:) real(r8), intent(in) :: tl_Akv(LBi:,LBj:,0:) real(r8), intent(in) :: tl_W(LBi:,LBj:,0:) real(r8), intent(inout) :: tl_t(LBi:,LBj:,:,:,:) real(r8), intent(inout) :: tl_u(LBi:,LBj:,:,:) real(r8), intent(inout) :: tl_v(LBi:,LBj:,:,:) ! ! Local variable declarations. ! integer :: Isrc, Jsrc integer :: i, ic, indx, is, itrc, j, k, ltrc real(r8), parameter :: eps = 1.0E-16_r8 real(r8) :: cff, cff1, cff2, cff3, cff4 real(r8) :: tl_cff, tl_cff1, tl_cff2, tl_cff3, tl_cff4 real(r8) :: Gamma 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)) :: FC 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,JminS:JmaxS,0:N(ng)) :: tl_swdk real(r8), dimension(IminS:ImaxS,JminS:JmaxS) :: FE real(r8), dimension(IminS:ImaxS,JminS:JmaxS) :: FX real(r8), dimension(IminS:ImaxS,JminS:JmaxS) :: curv real(r8), dimension(IminS:ImaxS,JminS:JmaxS) :: grad real(r8), dimension(IminS:ImaxS,JminS:JmaxS) :: tl_FE real(r8), dimension(IminS:ImaxS,JminS:JmaxS) :: tl_FX real(r8), dimension(IminS:ImaxS,JminS:JmaxS) :: tl_curv real(r8), dimension(IminS:ImaxS,JminS:JmaxS) :: tl_grad ! !----------------------------------------------------------------------- ! 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 ! !======================================================================= ! Tracer equation(s). !======================================================================= ! ! Compute fraction of the solar shortwave radiation, "swdk" ! (at vertical W-points) penetrating water column. ! DO k=1,N(ng)-1 DO j=Jstr,Jend DO i=Istr,Iend FX(i,j)=z_w(i,j,N(ng))-z_w(i,j,k) tl_FX(i,j)=tl_z_w(i,j,N(ng))-tl_z_w(i,j,k) END DO END DO !^ CALL lmd_swfrac_tile (ng, tile, & !^ & LBi, UBi, LBj, UBj, & !^ & IminS, ImaxS, JminS, JmaxS, & !^ & -1.0_r8, FX, FE) !^ CALL tl_lmd_swfrac_tile (ng, tile, & & LBi, UBi, LBj, UBj, & & IminS, ImaxS, JminS, JmaxS, & & -1.0_r8, FX, tl_FX, tl_FE) DO j=Jstr,Jend DO i=Istr,Iend !^ swdk(i,j,k)=FE(i,j) !^ tl_swdk(i,j,k)=tl_FE(i,j) END DO END DO END DO ! !----------------------------------------------------------------------- ! Compute intermediate tracer at n+1/2 time-step, t(i,j,k,3,itrc). !----------------------------------------------------------------------- ! ! Compute time rate of change of intermediate tracer due to ! horizontal advection. ! T_LOOP1 : DO itrc=1,NT(ng) K_LOOP : DO k=1,N(ng) ! HADV_FLUX : IF (tl_Hadvection(itrc,ng)%CENTERED2) THEN ! ! Second-order, centered differences horizontal advective fluxes. ! DO j=Jstr,Jend DO i=Istr,Iend+1 !^ FX(i,j)=Huon(i,j,k)* & !^ & 0.5_r8*(t(i-1,j,k,nstp,itrc)+ & !^ & t(i ,j,k,nstp,itrc)) !^ tl_FX(i,j)=0.5_r8* & & (tl_Huon(i,j,k)* & & (t(i-1,j,k,nstp,itrc)+ & & t(i ,j,k,nstp,itrc))+ & & Huon(i,j,k)* & & (tl_t(i-1,j,k,nstp,itrc)+ & & tl_t(i ,j,k,nstp,itrc))) END DO END DO DO j=Jstr,Jend+1 DO i=Istr,Iend !^ FE(i,j)=Hvom(i,j,k)* & !^ & 0.5_r8*(t(i,j-1,k,nstp,itrc)+ & !^ & t(i,j ,k,nstp,itrc)) !^ tl_FE(i,j)=0.5_r8* & & (tl_Hvom(i,j,k)* & & (t(i,j-1,k,nstp,itrc)+ & & t(i,j ,k,nstp,itrc))+ & & Hvom(i,j,k)* & & (tl_t(i,j-1,k,nstp,itrc)+ & & tl_t(i,j ,k,nstp,itrc))) END DO END DO ! ELSE IF ((tl_Hadvection(itrc,ng)%MPDATA).or. & & (tl_Hadvection(itrc,ng)%HSIMT)) THEN ! ! First-order, upstream differences horizontal advective fluxes. ! DO j=Jstr,Jend DO i=Istr,Iend+1 cff1=MAX(Huon(i,j,k),0.0_r8) cff2=MIN(Huon(i,j,k),0.0_r8) tl_cff1=(0.5_r8+SIGN(0.5_r8, Huon(i,j,k)))* & & tl_Huon(i,j,k) tl_cff2=(0.5_r8+SIGN(0.5_r8,-Huon(i,j,k)))* & & tl_Huon(i,j,k) !^ FX(i,j)=cff1*t(i-1,j,k,nstp,itrc)+ & !^ & cff2*t(i ,j,k,nstp,itrc) !^ tl_FX(i,j)=tl_cff1*t(i-1,j,k,nstp,itrc)+ & & cff1*tl_t(i-1,j,k,nstp,itrc)+ & & tl_cff2*t(i ,j,k,nstp,itrc)+ & & cff2*tl_t(i ,j,k,nstp,itrc) END DO END DO DO j=Jstr,Jend+1 DO i=Istr,Iend cff1=MAX(Hvom(i,j,k),0.0_r8) cff2=MIN(Hvom(i,j,k),0.0_r8) tl_cff1=(0.5_r8+SIGN(0.5_r8, Hvom(i,j,k)))* & & tl_Hvom(i,j,k) tl_cff2=(0.5_r8+SIGN(0.5_r8,-Hvom(i,j,k)))* & & tl_Hvom(i,j,k) !^ FE(i,j)=cff1*t(i,j-1,k,nstp,itrc)+ & !^ & cff2*t(i,j ,k,nstp,itrc) !^ tl_FE(i,j)=tl_cff1*t(i,j-1,k,nstp,itrc)+ & & cff1*tl_t(i,j-1,k,nstp,itrc)+ & & tl_cff2*t(i,j ,k,nstp,itrc)+ & & cff2*tl_t(i,j ,k,nstp,itrc) END DO END DO ! ELSE IF ((tl_Hadvection(itrc,ng)%AKIMA4).or. & & (tl_Hadvection(itrc,ng)%CENTERED4).or. & & (tl_Hadvection(itrc,ng)%SPLIT_U3).or. & & (tl_Hadvection(itrc,ng)%UPSTREAM3)) THEN ! ! Fourth-order Akima, fourth-order centered differences, or third-order ! upstream-biased horizontal advective fluxes. ! DO j=Jstr,Jend DO i=Istrm1,Iendp2 FX(i,j)=t(i ,j,k,nstp,itrc)- & & t(i-1,j,k,nstp,itrc) tl_FX(i,j)=tl_t(i ,j,k,nstp,itrc)- & & tl_t(i-1,j,k,nstp,itrc) FX(i,j)=FX(i,j)*umask(i,j) tl_FX(i,j)=tl_FX(i,j)*umask(i,j) END DO END DO IF (.not.(CompositeGrid(iwest,ng).or.EWperiodic(ng))) THEN IF (DOMAIN(ng)%Western_Edge(tile)) THEN DO j=Jstr,Jend FX(Istr-1,j)=FX(Istr,j) tl_FX(Istr-1,j)=tl_FX(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 j=Jstr,Jend FX(Iend+2,j)=FX(Iend+1,j) tl_FX(Iend+2,j)=tl_FX(Iend+1,j) END DO END IF END IF ! DO j=Jstr,Jend DO i=Istr-1,Iend+1 IF (tl_Hadvection(itrc,ng)%UPSTREAM3) THEN curv(i,j)=FX(i+1,j)-FX(i,j) tl_curv(i,j)=tl_FX(i+1,j)-tl_FX(i,j) ELSE IF (tl_Hadvection(itrc,ng)%AKIMA4) THEN cff=2.0_r8*FX(i+1,j)*FX(i,j) tl_cff=2.0_r8*(tl_FX(i+1,j)*FX(i,j)+ & & FX(i+1,j)*tl_FX(i,j)) IF (cff.gt.eps) THEN grad(i,j)=cff/(FX(i+1,j)+FX(i,j)) tl_grad(i,j)=((FX(i+1,j)+FX(i,j))*tl_cff- & & cff*(tl_FX(i+1,j)+tl_FX(i,j)))/ & & ((FX(i+1,j)+FX(i,j))* & & (FX(i+1,j)+FX(i,j))) ELSE grad(i,j)=0.0_r8 tl_grad(i,j)=0.0_r8 END IF ELSE IF ((tl_Hadvection(itrc,ng)%CENTERED4).or. & & (tl_Hadvection(itrc,ng)%SPLIT_U3)) THEN grad(i,j)=0.5_r8*(FX(i+1,j)+FX(i,j)) tl_grad(i,j)=0.5_r8*(tl_FX(i+1,j)+tl_FX(i,j)) END IF END DO END DO ! cff1=1.0_r8/6.0_r8 cff2=1.0_r8/3.0_r8 DO j=Jstr,Jend DO i=Istr,Iend+1 IF (tl_Hadvection(itrc,ng)%UPSTREAM3) THEN !^ FX(i,j)=Huon(i,j,k)*0.5_r8* & !^ & (t(i-1,j,k,nstp,itrc)+ & !^ & t(i ,j,k,nstp,itrc))- & !^ & cff1*(curv(i-1,j)*MAX(Huon(i,j,k),0.0_r8)+ & !^ & curv(i ,j)*MIN(Huon(i,j,k),0.0_r8)) !^ tl_FX(i,j)=0.5_r8* & & (tl_Huon(i,j,k)* & & (t(i-1,j,k,nstp,itrc)+ & & t(i ,j,k,nstp,itrc))+ & & Huon(i,j,k)* & & (tl_t(i-1,j,k,nstp,itrc)+ & & tl_t(i ,j,k,nstp,itrc)))- & & cff1* & & (tl_curv(i-1,j)*MAX(Huon(i,j,k),0.0_r8)+ & & curv(i-1,j)* & & (0.5_r8+SIGN(0.5_r8, Huon(i,j,k)))* & & tl_Huon(i,j,k)+ & & tl_curv(i ,j)*MIN(Huon(i,j,k),0.0_r8)+ & & curv(i ,j)* & & (0.5_r8+SIGN(0.5_r8,-Huon(i,j,k)))* & & tl_Huon(i,j,k)) ELSE IF ((tl_Hadvection(itrc,ng)%AKIMA4).or. & & (tl_Hadvection(itrc,ng)%CENTERED4).or. & & (tl_Hadvection(itrc,ng)%SPLIT_U3)) THEN !^ FX(i,j)=Huon(i,j,k)*0.5_r8* & !^ & (t(i-1,j,k,nstp,itrc)+ & !^ & t(i ,j,k,nstp,itrc)- & !^ & cff2*(grad(i ,j)- & !^ & grad(i-1,j))) !^ tl_FX(i,j)=0.5_r8* & & (tl_Huon(i,j,k)* & & (t(i-1,j,k,nstp,itrc)+ & & t(i ,j,k,nstp,itrc)- & & cff2*(grad(i ,j)- & & grad(i-1,j)))+ & & Huon(i,j,k)* & & (tl_t(i-1,j,k,nstp,itrc)+ & & tl_t(i ,j,k,nstp,itrc)- & & cff2*(tl_grad(i ,j)- & & tl_grad(i-1,j)))) END IF END DO END DO ! DO j=Jstrm1,Jendp2 DO i=Istr,Iend FE(i,j)=t(i,j ,k,nstp,itrc)- & & t(i,j-1,k,nstp,itrc) tl_FE(i,j)=tl_t(i,j ,k,nstp,itrc)- & & tl_t(i,j-1,k,nstp,itrc) FE(i,j)=FE(i,j)*vmask(i,j) tl_FE(i,j)=tl_FE(i,j)*vmask(i,j) END DO END DO IF (.not.(CompositeGrid(isouth,ng).or.NSperiodic(ng))) THEN IF (DOMAIN(ng)%Southern_Edge(tile)) THEN DO i=Istr,Iend FE(i,Jstr-1)=FE(i,Jstr) tl_FE(i,Jstr-1)=tl_FE(i,Jstr) END DO END IF END IF IF (.not.(CompositeGrid(inorth,ng).or.NSperiodic(ng))) THEN IF (DOMAIN(ng)%Northern_Edge(tile)) THEN DO i=Istr,Iend FE(i,Jend+2)=FE(i,Jend+1) tl_FE(i,Jend+2)=tl_FE(i,Jend+1) END DO END IF END IF ! DO j=Jstr-1,Jend+1 DO i=Istr,Iend IF (tl_Hadvection(itrc,ng)%UPSTREAM3) THEN curv(i,j)=FE(i,j+1)-FE(i,j) tl_curv(i,j)=tl_FE(i,j+1)-tl_FE(i,j) ELSE IF (tl_Hadvection(itrc,ng)%AKIMA4) THEN cff=2.0_r8*FE(i,j+1)*FE(i,j) tl_cff=2.0_r8*(tl_FE(i,j+1)*FE(i,j)+ & & FE(i,j+1)*tl_FE(i,j)) IF (cff.gt.eps) THEN grad(i,j)=cff/(FE(i,j+1)+FE(i,j)) tl_grad(i,j)=((FE(i,j+1)+FE(i,j))*tl_cff- & & cff*(tl_FE(i,j+1)+tl_FE(i,j)))/ & & ((FE(i,j+1)+FE(i,j))* & & (FE(i,j+1)+FE(i,j))) ELSE grad(i,j)=0.0_r8 tl_grad(i,j)=0.0_r8 END IF ELSE IF ((tl_Hadvection(itrc,ng)%CENTERED4).or. & & (tl_Hadvection(itrc,ng)%SPLIT_U3)) THEN grad(i,j)=0.5_r8*(FE(i,j+1)+FE(i,j)) tl_grad(i,j)=0.5_r8*(tl_FE(i,j+1)+tl_FE(i,j)) END IF END DO END DO ! cff1=1.0_r8/6.0_r8 cff2=1.0_r8/3.0_r8 DO j=Jstr,Jend+1 DO i=Istr,Iend IF (tl_Hadvection(itrc,ng)%UPSTREAM3) THEN !^ FE(i,j)=Hvom(i,j,k)*0.5_r8* & !^ & (t(i,j-1,k,nstp,itrc)+ & !^ & t(i,j ,k,nstp,itrc))- & !^ & cff1*(curv(i,j-1)*MAX(Hvom(i,j,k),0.0_r8)+ & !^ & curv(i,j )*MIN(Hvom(i,j,k),0.0_r8)) !^ tl_FE(i,j)=0.5_r8* & & (tl_Hvom(i,j,k)* & & (t(i,j-1,k,nstp,itrc)+ & & t(i,j ,k,nstp,itrc))+ & & Hvom(i,j,k)* & & (tl_t(i,j-1,k,nstp,itrc)+ & & tl_t(i,j ,k,nstp,itrc)))- & & cff1* & & (tl_curv(i,j-1)*MAX(Hvom(i,j,k),0.0_r8)+ & & curv(i,j-1)* & & (0.5_r8+SIGN(0.5_r8, Hvom(i,j,k)))* & & tl_Hvom(i,j,k)+ & & tl_curv(i,j )*MIN(Hvom(i,j,k),0.0_r8)+ & & curv(i,j )* & & (0.5_r8+SIGN(0.5_r8,-Hvom(i,j,k)))* & & tl_Hvom(i,j,k)) ELSE IF ((tl_Hadvection(itrc,ng)%AKIMA4).or. & & (tl_Hadvection(itrc,ng)%CENTERED4).or. & & (tl_Hadvection(itrc,ng)%SPLIT_U3)) THEN !^ FE(i,j)=Hvom(i,j,k)*0.5_r8* & !^ & (t(i,j-1,k,nstp,itrc)+ & !^ & t(i,j ,k,nstp,itrc)- & !^ & cff2*(grad(i,j )- & !^ & grad(i,j-1))) !^ tl_FE(i,j)=0.5_r8* & & (tl_Hvom(i,j,k)* & & (t(i,j-1,k,nstp,itrc)+ & & t(i,j ,k,nstp,itrc)- & & cff2*(grad(i,j )- & & grad(i,j-1)))+ & & Hvom(i,j,k)* & & (tl_t(i,j-1,k,nstp,itrc)+ & & tl_t(i,j ,k,nstp,itrc)- & & cff2*(tl_grad(i,j )- & & tl_grad(i,j-1)))) END IF END DO END DO END IF HADV_FLUX ! ! Apply tracers point sources to the horizontal advection terms, ! if any. ! ! Dsrc(is) = 0, flow across grid cell u-face (positive or negative) ! Dsrc(is) = 1, flow across grid cell v-face (positive or negative) ! IF (LuvSrc(ng)) THEN DO is=1,Nsrc(ng) Isrc=SOURCES(ng)%Isrc(is) Jsrc=SOURCES(ng)%Jsrc(is) IF (((Istr.le.Isrc).and.(Isrc.le.Iend+1)).and. & & ((Jstr.le.Jsrc).and.(Jsrc.le.Jend+1))) THEN IF (INT(SOURCES(ng)%Dsrc(is)).eq.0) THEN IF (LtracerSrc(itrc,ng)) THEN !^ FX(Isrc,Jsrc)=Huon(Isrc,Jsrc,k)* & !^ & SOURCES(ng)%Tsrc(is,k,itrc) !^ tl_FX(Isrc,Jsrc)=tl_Huon(Isrc,Jsrc,k)* & & SOURCES(ng)%Tsrc(is,k,itrc)+ & & Huon(Isrc,Jsrc,k)* & & SOURCES(ng)%tl_Tsrc(is,k,itrc) ELSE !^ FX(Isrc,Jsrc)=0.0_r8 !^ tl_FX(Isrc,Jsrc)=0.0_r8 END IF ELSE IF (INT(SOURCES(ng)%Dsrc(is)).eq.1) THEN IF (LtracerSrc(itrc,ng)) THEN !^ FE(Isrc,Jsrc)=Hvom(Isrc,Jsrc,k)* & !^ & SOURCES(ng)%Tsrc(is,k,itrc) !^ tl_FE(Isrc,Jsrc)=tl_Hvom(Isrc,Jsrc,k)* & & SOURCES(ng)%Tsrc(is,k,itrc)+ & & Hvom(Isrc,Jsrc,k)* & & SOURCES(ng)%tl_Tsrc(is,k,itrc) ELSE !^ FE(Isrc,Jsrc)=0.0_r8 !^ tl_FE(Isrc,Jsrc)=0.0_r8 END IF END IF END IF END DO END IF ! ! Time-step horizontal advection (m Tunits). ! IF ((tl_Hadvection(itrc,ng)%MPDATA).or. & & (tl_Hadvection(itrc,ng)%HSIMT)) THEN Gamma=0.5_r8 ELSE Gamma=1.0_r8/6.0_r8 END IF IF (iic(ng).eq.ntfirst(ng)) THEN cff=0.5_r8*dt(ng) cff1=1.0_r8 cff2=0.0_r8 ELSE cff=(1.0_r8-Gamma)*dt(ng) cff1=0.5_r8+Gamma cff2=0.5_r8-Gamma END IF DO j=Jstr,Jend DO i=Istr,Iend !^ t(i,j,k,3,itrc)=Hz(i,j,k)*(cff1*t(i,j,k,nstp,itrc)+ & !^ & cff2*t(i,j,k,nnew,itrc))- & !^ & cff*pm(i,j)*pn(i,j)* & !^ & (FX(i+1,j)-FX(i,j)+ & !^ & FE(i,j+1)-FE(i,j)) !^ tl_t(i,j,k,3,itrc)=tl_Hz(i,j,k)* & & (cff1*t(i,j,k,nstp,itrc)+ & & cff2*t(i,j,k,nnew,itrc))+ & & Hz(i,j,k)* & & (cff1*tl_t(i,j,k,nstp,itrc)+ & & cff2*tl_t(i,j,k,nnew,itrc))- & & cff*pm(i,j)*pn(i,j)* & & (tl_FX(i+1,j)-tl_FX(i,j)+ & & tl_FE(i,j+1)-tl_FE(i,j)) END DO END DO END DO K_LOOP END DO T_LOOP1 ! !----------------------------------------------------------------------- ! Compute time rate of change of intermediate tracer due to vertical ! advection. Impose artificial continuity equation. !----------------------------------------------------------------------- ! J_LOOP1 : DO j=Jstr,Jend T_LOOP2 : DO itrc=1,NT(ng) ! VADV_FLUX : IF (tl_Vadvection(itrc,ng)%SPLINES) THEN ! ! Build conservative parabolic splines for the BASIC STATE vertical ! derivatives "FC" of the tracer. ! DO i=Istr,Iend FC(i,0)=1.5_r8*t(i,j,1,nstp,itrc) CF(i,1)=0.5_r8 END DO DO k=1,N(ng)-1 DO i=Istr,Iend cff=1.0_r8/(2.0_r8*Hz(i,j,k)+ & & Hz(i,j,k+1)*(2.0_r8-CF(i,k))) CF(i,k+1)=cff*Hz(i,j,k) FC(i,k)=cff*(3.0_r8*(Hz(i,j,k )*t(i,j,k+1,nstp,itrc)+ & & Hz(i,j,k+1)*t(i,j,k ,nstp,itrc))- & & Hz(i,j,k+1)*FC(i,k-1)) END DO END DO DO i=Istr,Iend FC(i,N(ng))=(3.0_r8*t(i,j,N(ng),nstp,itrc)- & & FC(i,N(ng)-1))/(2.0_r8-CF(i,N(ng))) END DO DO k=N(ng)-1,0,-1 DO i=Istr,Iend FC(i,k)=FC(i,k)-CF(i,k+1)*FC(i,k+1) END DO END DO ! ! Now the tangent linear spline code. ! DO i=Istr,Iend !^ FC(i,0)=1.5_r8*t(i,j,1,nstp,itrc) !^ tl_FC(i,0)=1.5_r8*tl_t(i,j,1,nstp,itrc) CF(i,1)=0.5_r8 END DO DO k=1,N(ng)-1 DO i=Istr,Iend cff=1.0_r8/(2.0_r8*Hz(i,j,k)+ & & Hz(i,j,k+1)*(2.0_r8-CF(i,k))) CF(i,k+1)=cff*Hz(i,j,k) tl_FC(i,k)=cff* & & (3.0_r8*(Hz(i,j,k )* & & tl_t(i,j,k+1,nstp,itrc)+ & & Hz(i,j,k+1)* & & tl_t(i,j,k ,nstp,itrc)+ & & tl_Hz(i,j,k )* & & t(i,j,k+1,nstp,itrc)+ & & tl_Hz(i,j,k+1)* & & t(i,j,k ,nstp,itrc))- & & (tl_Hz(i,j,k+1)*FC(i,k-1)+ & & 2.0_r8*(tl_Hz(i,j,k )+ & & tl_Hz(i,j,k+1))*FC(i,k)+ & & tl_Hz(i,j,k )*FC(i,k+1))- & & Hz(i,j,k+1)*tl_FC(i,k-1)) END DO END DO DO i=Istr,Iend !^ FC(i,N(ng))=(3.0_r8*t(i,j,N(ng),nstp,itrc)- & !^ & FC(i,N(ng)-1))/(2.0_r8-CF(i,N(ng))) !^ tl_FC(i,N(ng))=(3.0_r8*tl_t(i,j,N(ng),nstp,itrc)- & & tl_FC(i,N(ng)-1))/ & & (2.0_r8-CF(i,N(ng))) END DO DO k=N(ng)-1,0,-1 DO i=Istr,Iend !^ FC(i,k)=FC(i,k)-CF(i,k+1)*FC(i,k+1) !^ tl_FC(i,k)=tl_FC(i,k)-CF(i,k+1)*tl_FC(i,k+1) !^ FC(i,k+1)=W(i,j,k+1)*FC(i,k+1) !^ tl_FC(i,k+1)=tl_W(i,j,k+1)*FC(i,k+1)+ & & W(i,j,k+1)*tl_FC(i,k+1) END DO END DO DO i=Istr,Iend !^ FC(i,N(ng))=0.0_r8 !^ tl_FC(i,N(ng))=0.0_r8 !^ FC(i,0)=0.0_r8 !^ tl_FC(i,0)=0.0_r8 END DO ! ! Now complete the computation of the flux array FC. ! DO k=N(ng)-1,0,-1 DO i=Istr,Iend FC(i,k+1)=W(i,j,k+1)*FC(i,k+1) END DO END DO DO i=Istr,Iend FC(i,N(ng))=0.0_r8 FC(i,0)=0.0_r8 END DO ! ELSE IF (tl_Vadvection(itrc,ng)%AKIMA4) THEN ! ! Fourth-order, Akima vertical advective flux. ! DO k=1,N(ng)-1 DO i=Istr,Iend FC(i,k)=t(i,j,k+1,nstp,itrc)- & & t(i,j,k ,nstp,itrc) tl_FC(i,k)=tl_t(i,j,k+1,nstp,itrc)- & & tl_t(i,j,k ,nstp,itrc) END DO END DO DO i=Istr,Iend FC(i,0)=FC(i,1) tl_FC(i,0)=tl_FC(i,1) FC(i,N(ng))=FC(i,N(ng)-1) tl_FC(i,N(ng))=tl_FC(i,N(ng)-1) END DO DO k=1,N(ng) DO i=Istr,Iend cff=2.0_r8*FC(i,k)*FC(i,k-1) tl_cff=2.0_r8*(tl_FC(i,k)*FC(i,k-1)+ & & FC(i,k)*tl_FC(i,k-1)) IF (cff.gt.eps) THEN CF(i,k)=cff/(FC(i,k)+FC(i,k-1)) tl_CF(i,k)=((FC(i,k)+FC(i,k-1))*tl_cff- & & cff*(tl_FC(i,k)+tl_FC(i,k-1)))/ & & ((FC(i,k)+FC(i,k-1))*(FC(i,k)+FC(i,k-1))) ELSE CF(i,k)=0.0_r8 tl_CF(i,k)=0.0_r8 END IF END DO END DO cff1=1.0_r8/3.0_r8 DO k=1,N(ng)-1 DO i=Istr,Iend FC(i,k)=W(i,j,k)* & & 0.5_r8*(t(i,j,k ,nstp,itrc)+ & & t(i,j,k+1,nstp,itrc)- & & cff1*(CF(i,k+1)-CF(i,k))) tl_FC(i,k)=0.5_r8* & & (tl_W(i,j,k)* & & (t(i,j,k ,nstp,itrc)+ & & t(i,j,k+1,nstp,itrc)- & & cff1*(CF(i,k+1)-CF(i,k)))+ & & W(i,j,k)* & & (tl_t(i,j,k ,nstp,itrc)+ & & tl_t(i,j,k+1,nstp,itrc)- & & cff1*(tl_CF(i,k+1)-tl_CF(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 ! ELSE IF (tl_Vadvection(itrc,ng)%CENTERED2) THEN ! ! Second-order, central differences vertical advective flux. ! DO k=1,N(ng)-1 DO i=Istr,Iend FC(i,k)=W(i,j,k)* & & 0.5_r8*(t(i,j,k ,nstp,itrc)+ & & t(i,j,k+1,nstp,itrc)) tl_FC(i,k)=0.5_r8* & & (tl_W(i,j,k)* & & (t(i,j,k ,nstp,itrc)+ & & t(i,j,k+1,nstp,itrc))+ & & W(i,j,k)* & & (tl_t(i,j,k ,nstp,itrc)+ & & tl_t(i,j,k+1,nstp,itrc))) 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 ! ELSE IF ((tl_Vadvection(itrc,ng)%MPDATA).or. & & (tl_Vadvection(itrc,ng)%HSIMT)) THEN ! ! First_order, upstream differences vertical advective flux. ! DO k=1,N(ng)-1 DO i=Istr,Iend cff1=MAX(W(i,j,k),0.0_r8) cff2=MIN(W(i,j,k),0.0_r8) tl_cff1=(0.5_r8+SIGN(0.5_r8, W(i,j,k)))*tl_W(i,j,k) tl_cff2=(0.5_r8+SIGN(0.5_r8,-W(i,j,k)))*tl_W(i,j,k) !^ FC(i,k)=cff1*t(i,j,k ,nstp,itrc)+ & !^ & cff2*t(i,j,k+1,nstp,itrc) !^ tl_FC(i,k)=tl_cff1*t(i,j,k ,nstp,itrc)+ & & cff1*tl_t(i,j,k ,nstp,itrc)+ & & tl_cff2*t(i,j,k+1,nstp,itrc)+ & & cff2*tl_t(i,j,k+1,nstp,itrc) 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 ! ELSE IF ((tl_Vadvection(itrc,ng)%CENTERED4).or. & & (tl_Vadvection(itrc,ng)%SPLIT_U3)) THEN ! ! Fourth-order, central differences vertical advective flux. ! cff1=0.5_r8 cff2=7.0_r8/12.0_r8 cff3=1.0_r8/12.0_r8 DO k=2,N(ng)-2 DO i=Istr,Iend FC(i,k)=W(i,j,k)* & & (cff2*(t(i,j,k ,nstp,itrc)+ & & t(i,j,k+1,nstp,itrc))- & & cff3*(t(i,j,k-1,nstp,itrc)+ & & t(i,j,k+2,nstp,itrc))) tl_FC(i,k)=tl_W(i,j,k)* & & (cff2*(t(i,j,k ,nstp,itrc)+ & & t(i,j,k+1,nstp,itrc))- & & cff3*(t(i,j,k-1,nstp,itrc)+ & & t(i,j,k+2,nstp,itrc)))+ & & W(i,j,k)* & & (cff2*(tl_t(i,j,k ,nstp,itrc)+ & & tl_t(i,j,k+1,nstp,itrc))- & & cff3*(tl_t(i,j,k-1,nstp,itrc)+ & & tl_t(i,j,k+2,nstp,itrc))) END DO END DO DO i=Istr,Iend FC(i,0)=0.0_r8 tl_FC(i,0)=0.0_r8 FC(i,1)=W(i,j,1)* & & (cff1*t(i,j,1,nstp,itrc)+ & & cff2*t(i,j,2,nstp,itrc)- & & cff3*t(i,j,3,nstp,itrc)) tl_FC(i,1)=tl_W(i,j,1)* & & (cff1*t(i,j,1,nstp,itrc)+ & & cff2*t(i,j,2,nstp,itrc)- & & cff3*t(i,j,3,nstp,itrc))+ & & W(i,j,1)* & & (cff1*tl_t(i,j,1,nstp,itrc)+ & & cff2*tl_t(i,j,2,nstp,itrc)- & & cff3*tl_t(i,j,3,nstp,itrc)) FC(i,N(ng)-1)=W(i,j,N(ng)-1)* & & (cff1*t(i,j,N(ng) ,nstp,itrc)+ & & cff2*t(i,j,N(ng)-1,nstp,itrc)- & & cff3*t(i,j,N(ng)-2,nstp,itrc)) tl_FC(i,N(ng)-1)=tl_W(i,j,N(ng)-1)* & & (cff1*t(i,j,N(ng) ,nstp,itrc)+ & & cff2*t(i,j,N(ng)-1,nstp,itrc)- & & cff3*t(i,j,N(ng)-2,nstp,itrc))+ & & W(i,j,N(ng)-1)* & & (cff1*tl_t(i,j,N(ng) ,nstp,itrc)+ & & cff2*tl_t(i,j,N(ng)-1,nstp,itrc)- & & cff3*tl_t(i,j,N(ng)-2,nstp,itrc)) FC(i,N(ng))=0.0_r8 tl_FC(i,N(ng))=0.0_r8 END DO END IF VADV_FLUX ! ! Compute artificial continuity equation and load it into private ! array DC (1/m). It is imposed to preserve tracer constancy. It is ! not the same for all the tracer advection schemes because of the ! Gamma value. ! IF ((Vadvection(itrc,ng)%MPDATA).or. & & (Vadvection(itrc,ng)%HSIMT)) THEN Gamma=0.5_r8 ELSE Gamma=1.0_r8/6.0_r8 END IF IF (iic(ng).eq.ntfirst(ng)) THEN cff=0.5_r8*dt(ng) ELSE cff=(1.0_r8-Gamma)*dt(ng) END IF DO k=1,N(ng) DO i=Istr,Iend DC(i,k)=1.0_r8/(Hz(i,j,k)- & & cff*pm(i,j)*pn(i,j)* & & (Huon(i+1,j,k)-Huon(i,j,k)+ & & Hvom(i,j+1,k)-Hvom(i,j,k)+ & & (W(i,j,k)-W(i,j,k-1)))) tl_DC(i,k)=-DC(i,k)*DC(i,k)* & & (tl_Hz(i,j,k)- & & cff*pm(i,j)*pn(i,j)* & & (tl_Huon(i+1,j,k)-tl_Huon(i,j,k)+ & & tl_Hvom(i,j+1,k)-tl_Hvom(i,j,k)+ & & (tl_W(i,j,k)-tl_W(i,j,k-1)))) END DO END DO ! ! Time-step vertical advection of tracers (Tunits). Impose artificial ! continuity equation. ! ! WARNING: t(:,:,:,3,itrc) at this point should be in units of ! ======= m Tunits. But, t(:,:,:,3,itrc) is read from a BASIC ! STATE file and is in Tunits, so we need to multiply ! by level thickness (Hz). ! DO k=1,N(ng) DO i=Istr,Iend cff1=cff*pm(i,j)*pn(i,j) !^ t(i,j,k,3,itrc)=DC(i,k)* & !^ & (t(i,j,k,3,itrc)- & !^ & cff1*(FC(i,k)-FC(i,k-1))) !^ tl_t(i,j,k,3,itrc)=tl_DC(i,k)* & & (t(i,j,k,3,itrc)*Hz(i,j,k)- & & cff1*(FC(i,k)-FC(i,k-1)))+ & & DC(i,k)* & & (tl_t(i,j,k,3,itrc)- & & cff1*(tl_FC(i,k)-tl_FC(i,k-1))) END DO END DO END DO T_LOOP2 END DO J_LOOP1 ! !----------------------------------------------------------------------- ! Start computation of tracers at n+1 time-step, t(i,j,k,nnew,itrc). !----------------------------------------------------------------------- ! ! Compute vertical diffusive fluxes "FC" of the tracer fields at ! current time step n, and at horizontal RHO-points and vertical ! W-points. Notice that the vertical diffusion coefficients for ! passive tracers is the same as that for salinity (ltrc=NAT). ! DO j=Jstr,Jend cff3=dt(ng)*(1.0_r8-lambda) DO itrc=1,NT(ng) ltrc=MIN(NAT,itrc) DO k=1,N(ng)-1 DO i=Istr,Iend cff=1.0_r8/(z_r(i,j,k+1)-z_r(i,j,k)) tl_cff=-cff*cff*(tl_z_r(i,j,k+1)-tl_z_r(i,j,k)) !^ FC(i,k)=cff3*cff*Akt(i,j,k,ltrc)* & !^ & (t(i,j,k+1,nstp,itrc)- & !^ & t(i,j,k ,nstp,itrc)) !^ tl_FC(i,k)=cff3* & & (cff*(tl_Akt(i,j,k,ltrc)* & & (t(i,j,k+1,nstp,itrc)- & & t(i,j,k ,nstp,itrc))+ & & Akt(i,j,k,ltrc)* & & (tl_t(i,j,k+1,nstp,itrc)- & & tl_t(i,j,k ,nstp,itrc)))+ & & tl_cff*(Akt(i,j,k,ltrc)* & & (t(i,j,k+1,nstp,itrc)- & & t(i,j,k,nstp,itrc)))) END DO END DO ! ! Add in incoming solar radiation at interior W-points using decay ! decay penetration function based on Jerlov water type. ! IF (itrc.eq.itemp) THEN DO k=1,N(ng)-1 DO i=Istr,Iend !^ FC(i,k)=FC(i,k)+ & !^ & dt(ng)*srflx(i,j)* & !^ & swdk(i,j,k) !^ tl_FC(i,k)=tl_FC(i,k)+ & & dt(ng)*srflx(i,j)* & & tl_swdk(i,j,k) END DO END DO END IF ! ! Apply bottom and surface tracer flux conditions. ! DO i=Istr,Iend !^ FC(i,0)=dt(ng)*btflx(i,j,itrc) !^ tl_FC(i,0)=dt(ng)*tl_btflx(i,j,itrc) !^ FC(i,N(ng))=dt(ng)*stflx(i,j,itrc) !^ tl_FC(i,N(ng))=dt(ng)*tl_stflx(i,j,itrc) END DO ! ! Compute new tracer field (m Tunits). ! DO k=1,N(ng) DO i=Istr,Iend cff1=Hz(i,j,k)*t(i,j,k,nstp,itrc) tl_cff1=tl_Hz(i,j,k)*t(i,j,k,nstp,itrc)+ & & Hz(i,j,k)*tl_t(i,j,k,nstp,itrc) cff2=FC(i,k)-FC(i,k-1) tl_cff2=tl_FC(i,k)-tl_FC(i,k-1) !^ t(i,j,k,nnew,itrc)=cff1+cff2 !^ tl_t(i,j,k,nnew,itrc)=tl_cff1+tl_cff2 END DO END DO END DO END DO ! !======================================================================= ! 3D momentum equation in the XI-direction. !======================================================================= ! ! Compute U-component viscous vertical momentum fluxes "FC" at ! current time-step n, and at horizontal U-points and vertical ! W-points. ! J_LOOP2: DO j=Jstr,Jend cff3=dt(ng)*(1.0_r8-lambda) DO k=1,N(ng)-1 DO i=IstrU,Iend cff=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_cff=-cff*cff*(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)=cff3*cff*(u(i,j,k+1,nstp)-u(i,j,k,nstp))* & !^ & (Akv(i,j,k)+Akv(i-1,j,k)) !^ tl_FC(i,k)=cff3* & & (cff*((tl_u(i,j,k+1,nstp)-tl_u(i,j,k,nstp))* & & (Akv(i,j,k)+Akv(i-1,j,k))+ & & (u(i,j,k+1,nstp)-u(i,j,k,nstp))* & & (tl_Akv(i,j,k)+tl_Akv(i-1,j,k)))+ & & tl_cff*(u(i,j,k+1,nstp)-u(i,j,k,nstp))* & & (Akv(i,j,k)+Akv(i-1,j,k))) END DO END DO ! ! Apply bottom and surface stresses, if so is prescribed. ! DO i=IstrU,Iend !^ FC(i,0)=dt(ng)*bustr(i,j) !^ tl_FC(i,0)=dt(ng)*tl_bustr(i,j) !^ FC(i,N(ng))=dt(ng)*sustr(i,j) !^ tl_FC(i,N(ng))=dt(ng)*tl_sustr(i,j) END DO ! ! Compute new U-momentum (m m/s). ! cff=dt(ng)*0.25_r8 DO i=IstrU,Iend DC(i,0)=cff*(pm(i,j)+pm(i-1,j))*(pn(i,j)+pn(i-1,j)) END DO indx=3-nrhs IF (iic(ng).eq.ntfirst(ng)) THEN DO k=1,N(ng) DO i=IstrU,Iend !^ cff1=u(i,j,k,nstp)*0.5_r8*(Hz(i,j,k)+Hz(i-1,j,k)) !^ tl_cff1=0.5_r8*(tl_u(i,j,k,nstp)* & & (Hz(i,j,k)+Hz(i-1,j,k))+ & & u(i,j,k,nstp)* & & (tl_Hz(i,j,k)+tl_Hz(i-1,j,k))) !^ cff2=FC(i,k)-FC(i,k-1) !^ tl_cff2=tl_FC(i,k)-tl_FC(i,k-1) !^ u(i,j,k,nnew)=cff1+cff2 !^ tl_u(i,j,k,nnew)=tl_cff1+tl_cff2 END DO END DO ELSE IF (iic(ng).eq.(ntfirst(ng)+1)) THEN DO k=1,N(ng) DO i=IstrU,Iend !^ cff1=u(i,j,k,nstp)*0.5_r8*(Hz(i,j,k)+Hz(i-1,j,k)) !^ tl_cff1=0.5_r8*(tl_u(i,j,k,nstp)* & & (Hz(i,j,k)+Hz(i-1,j,k))+ & & u(i,j,k,nstp)* & & (tl_Hz(i,j,k)+tl_Hz(i-1,j,k))) !^ cff2=FC(i,k)-FC(i,k-1) !^ tl_cff2=tl_FC(i,k)-tl_FC(i,k-1) cff3=0.5_r8*DC(i,0) !^ u(i,j,k,nnew)=cff1- & !^ & cff3*ru(i,j,k,indx)+ & !^ & cff2 !^ tl_u(i,j,k,nnew)=tl_cff1- & & cff3*tl_ru(i,j,k,indx)+ & & tl_cff2 END DO END DO ELSE cff1= 5.0_r8/12.0_r8 cff2=16.0_r8/12.0_r8 DO k=1,N(ng) DO i=IstrU,Iend !^ cff3=u(i,j,k,nstp)*0.5_r8*(Hz(i,j,k)+Hz(i-1,j,k)) !^ tl_cff3=0.5_r8*(tl_u(i,j,k,nstp)* & & (Hz(i,j,k)+Hz(i-1,j,k))+ & & u(i,j,k,nstp)* & & (tl_Hz(i,j,k)+tl_Hz(i-1,j,k))) !^ cff4=FC(i,k)-FC(i,k-1) !^ tl_cff4=tl_FC(i,k)-tl_FC(i,k-1) !^ u(i,j,k,nnew)=cff3+ & !^ & DC(i,0)*(cff1*ru(i,j,k,nrhs)- & !^ & cff2*ru(i,j,k,indx))+ & !^ & cff4 !^ tl_u(i,j,k,nnew)=tl_cff3+ & & DC(i,0)*(cff1*tl_ru(i,j,k,nrhs)- & & cff2*tl_ru(i,j,k,indx))+ & & tl_cff4 END DO END DO END IF ! !======================================================================= ! 3D momentum equation in the ETA-direction. !======================================================================= ! ! Compute V-component viscous vertical momentum fluxes "FC" at ! current time-step n, and at horizontal V-points and vertical ! W-points. ! IF (j.ge.JstrV) THEN cff3=dt(ng)*(1.0_r8-lambda) DO k=1,N(ng)-1 DO i=Istr,Iend cff=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_cff=-cff*cff*(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)=cff3*cff*(v(i,j,k+1,nstp)-v(i,j,k,nstp))* & !^ & (Akv(i,j,k)+Akv(i,j-1,k)) !^ tl_FC(i,k)=cff3* & & (cff*((tl_v(i,j,k+1,nstp)-tl_v(i,j,k,nstp))* & & (Akv(i,j,k)+Akv(i,j-1,k))+ & & (v(i,j,k+1,nstp)-v(i,j,k,nstp))* & & (tl_Akv(i,j,k)+tl_Akv(i,j-1,k)))+ & & tl_cff*(v(i,j,k+1,nstp)-v(i,j,k,nstp))* & & (Akv(i,j,k)+Akv(i,j-1,k))) END DO END DO ! ! Apply bottom and surface stresses, if so is prescribed. ! DO i=Istr,Iend !^ FC(i,0)=dt(ng)*bvstr(i,j) !^ tl_FC(i,0)=dt(ng)*tl_bvstr(i,j) !^ FC(i,N(ng))=dt(ng)*svstr(i,j) !^ tl_FC(i,N(ng))=dt(ng)*tl_svstr(i,j) END DO ! ! Compute new V-momentum (m m/s). ! cff=dt(ng)*0.25_r8 DO i=Istr,Iend DC(i,0)=cff*(pm(i,j)+pm(i,j-1))*(pn(i,j)+pn(i,j-1)) END DO IF (iic(ng).eq.ntfirst(ng)) THEN DO k=1,N(ng) DO i=Istr,Iend !^ cff1=v(i,j,k,nstp)*0.5_r8*(Hz(i,j,k)+Hz(i,j-1,k)) !^ tl_cff1=0.5_r8*(tl_v(i,j,k,nstp)* & & (Hz(i,j,k)+Hz(i,j-1,k))+ & & v(i,j,k,nstp)* & & (tl_Hz(i,j,k)+tl_Hz(i,j-1,k))) !^ cff2=FC(i,k)-FC(i,k-1) !^ tl_cff2=tl_FC(i,k)-tl_FC(i,k-1) !^ v(i,j,k,nnew)=cff1+cff2 !^ tl_v(i,j,k,nnew)=tl_cff1+tl_cff2 END DO END DO ELSE IF (iic(ng).eq.(ntfirst(ng)+1)) THEN DO k=1,N(ng) DO i=Istr,Iend !^ cff1=v(i,j,k,nstp)*0.5_r8*(Hz(i,j,k)+Hz(i,j-1,k)) !^ tl_cff1=0.5_r8*(tl_v(i,j,k,nstp)* & & (Hz(i,j,k)+Hz(i,j-1,k))+ & & v(i,j,k,nstp)* & & (tl_Hz(i,j,k)+tl_Hz(i,j-1,k))) !^ cff2=FC(i,k)-FC(i,k-1) !^ tl_cff2=tl_FC(i,k)-tl_FC(i,k-1) cff3=0.5_r8*DC(i,0) !^ v(i,j,k,nnew)=cff1- & !^ & cff3*rv(i,j,k,indx)+ & !^ & cff2 !^ tl_v(i,j,k,nnew)=tl_cff1- & & cff3*tl_rv(i,j,k,indx)+ & & tl_cff2 END DO END DO ELSE cff1= 5.0_r8/12.0_r8 cff2=16.0_r8/12.0_r8 DO k=1,N(ng) DO i=Istr,Iend !^ cff3=v(i,j,k,nstp)*0.5_r8*(Hz(i,j,k)+Hz(i,j-1,k)) !^ tl_cff3=0.5_r8*(tl_v(i,j,k,nstp)* & & (Hz(i,j,k)+Hz(i,j-1,k))+ & & v(i,j,k,nstp)* & & (tl_Hz(i,j,k)+tl_Hz(i,j-1,k))) !^ cff4=FC(i,k)-FC(i,k-1) !^ tl_cff4=tl_FC(i,k)-tl_FC(i,k-1) !^ v(i,j,k,nnew)=cff3+ & !^ & DC(i,0)*(cff1*rv(i,j,k,nrhs)- & !^ & cff2*rv(i,j,k,indx))+ & !^ & cff4 !^ tl_v(i,j,k,nnew)=tl_cff3+ & & DC(i,0)*(cff1*tl_rv(i,j,k,nrhs)- & & cff2*tl_rv(i,j,k,indx))+ & & tl_cff4 END DO END DO END IF END IF END DO J_LOOP2 ! !======================================================================= ! Apply intermediate tracers lateral boundary conditions. !======================================================================= ! ic=0 DO itrc=1,NT(ng) IF (LtracerCLM(itrc,ng).and.LnudgeTCLM(itrc,ng)) THEN ic=ic+1 END IF !^ CALL t3dbc_tile (ng, tile, itrc, ic, & !^ & LBi, UBi, LBj, UBj, N(ng), NT(ng), & !^ & IminS, ImaxS, JminS, JmaxS, & !^ & nstp, 3, & !^ & t) !^ CALL tl_t3dbc_tile (ng, tile, itrc, ic, & & LBi, UBi, LBj, UBj, N(ng), NT(ng), & & IminS, ImaxS, JminS, JmaxS, & & nstp, 3, & & tl_t) IF (EWperiodic(ng).or.NSperiodic(ng)) THEN !^ CALL exchange_r3d_tile (ng, tile, & !^ & LBi, UBi, LBj, UBj, 1, N(ng), & !^ & t(:,:,:,3,itrc)) !^ CALL exchange_r3d_tile (ng, tile, & & LBi, UBi, LBj, UBj, 1, N(ng), & & tl_t(:,:,:,3,itrc)) END IF END DO !^ CALL mp_exchange4d (ng, tile, iNLM, 1, & !^ & LBi, UBi, LBj, UBj, 1, N(ng), 1, NT(ng), & !^ & NghostPoints, & !^ & EWperiodic(ng), NSperiodic(ng), & !^ & t(:,:,:,3,:)) !^ CALL mp_exchange4d (ng, tile, iTLM, 1, & & LBi, UBi, LBj, UBj, 1, N(ng), 1, NT(ng), & & NghostPoints, & & EWperiodic(ng), NSperiodic(ng), & & tl_t(:,:,:,3,:)) ! RETURN END SUBROUTINE tl_pre_step3d_tile END MODULE tl_pre_step3d_mod