#include "cppdefs.h" MODULE step3d_t_mod #if !defined TS_FIXED && (defined NONLINEAR && defined SOLVE3D) ! !svn $Id: step3d_t.F 1054 2021-03-06 19:47:12Z arango $ !======================================================================= ! Copyright (c) 2002-2021 The ROMS/TOMS Group ! ! Licensed under a MIT/X style license ! ! See License_ROMS.txt Hernan G. Arango ! !========================================== Alexander F. Shchepetkin === ! ! ! This routine time-steps tracer equations. Notice that advective ! ! and diffusive terms are time-stepped differently. It applies the ! ! corrector time-step for horizontal/vertical advection, vertical ! ! diffusion, nudging if necessary, and lateral boundary conditions. ! ! ! ! A different horizontal/vertical advection scheme is allowed for ! ! each tracer. If the MPDATA or HSIMT monotonic scheme, it is applied ! ! to both horizontal and vertical advective fluxes. ! ! ! ! Notice that at input the tracer arrays have: ! ! ! ! t(:,:,:,nnew,:) m Tunits n+1 horizontal/vertical diffusion ! ! terms plus source/sink terms ! ! (biology, sediment), if any ! ! ! ! t(:,:,:,3 ,:) Tunits n+1/2 advective terms and vertical ! ! diffusion predictor step ! ! ! !======================================================================= ! implicit none ! PRIVATE PUBLIC :: step3d_t ! CONTAINS ! !*********************************************************************** SUBROUTINE step3d_t (ng, tile) !*********************************************************************** ! USE mod_param # ifdef DIAGNOSTICS_TS USE mod_diags # endif USE mod_grid USE mod_mixing USE mod_ocean USE mod_stepping ! ! Imported variable declarations. ! integer, intent(in) :: ng, tile ! ! Local variable declarations. ! character (len=*), parameter :: MyFile = & & __FILE__ ! # include "tile.h" ! # ifdef PROFILE CALL wclock_on (ng, iNLM, 35, __LINE__, MyFile) # endif CALL step3d_t_tile (ng, tile, & & LBi, UBi, LBj, UBj, & & IminS, ImaxS, JminS, JmaxS, & & nrhs(ng), nstp(ng), nnew(ng), & # ifdef MASKING & GRID(ng) % rmask, & & GRID(ng) % umask, & & GRID(ng) % vmask, & # endif # ifdef WET_DRY & GRID(ng) % rmask_wet, & & GRID(ng) % umask_wet, & & GRID(ng) % vmask_wet, & # endif & GRID(ng) % omn, & & GRID(ng) % om_u, & & GRID(ng) % om_v, & & GRID(ng) % on_u, & & GRID(ng) % on_v, & & GRID(ng) % pm, & & GRID(ng) % pn, & & GRID(ng) % Hz, & & GRID(ng) % Huon, & & GRID(ng) % Hvom, & & GRID(ng) % z_r, & & MIXING(ng) % Akt, & & OCEAN(ng) % W, & # if defined FLOATS && defined FLOAT_VWALK & MIXING(ng) % dAktdz, & # endif # ifdef DIAGNOSTICS_TS & DIAGS(ng) % DiaTwrk, & # endif & OCEAN(ng) % t) # ifdef PROFILE CALL wclock_off (ng, iNLM, 35, __LINE__, MyFile) # endif ! RETURN END SUBROUTINE step3d_t ! !*********************************************************************** SUBROUTINE step3d_t_tile (ng, tile, & & LBi, UBi, LBj, UBj, & & IminS, ImaxS, JminS, JmaxS, & & nrhs, nstp, nnew, & # ifdef MASKING & rmask, umask, vmask, & # endif # ifdef WET_DRY & rmask_wet, umask_wet, vmask_wet, & # endif & omn, om_u, om_v, on_u, on_v, & & pm, pn, & & Hz, Huon, Hvom, & & z_r, & & Akt, & & W, & # if defined FLOATS && defined FLOAT_VWALK & dAktdz, & # endif # ifdef DIAGNOSTICS_TS & DiaTwrk, & # endif & t) !*********************************************************************** ! USE mod_param USE mod_clima USE mod_ncparam # if defined NESTING && !defined ONE_WAY USE mod_nesting # endif USE mod_scalars USE mod_sources ! USE exchange_3d_mod, ONLY : exchange_r3d_tile # ifdef DISTRIBUTE USE mp_exchange_mod, ONLY : mp_exchange3d USE mp_exchange_mod, ONLY : mp_exchange4d # endif USE mpdata_adiff_mod # ifdef NESTING USE nesting_mod, ONLY : bry_fluxes # endif USE t3dbc_mod, ONLY : 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 ! # ifdef ASSUMED_SHAPE # ifdef MASKING real(r8), intent(in) :: rmask(LBi:,LBj:) real(r8), intent(in) :: umask(LBi:,LBj:) real(r8), intent(in) :: vmask(LBi:,LBj:) # endif # ifdef WET_DRY real(r8), intent(in) :: rmask_wet(LBi:,LBj:) real(r8), intent(in) :: umask_wet(LBi:,LBj:) real(r8), intent(in) :: vmask_wet(LBi:,LBj:) # endif real(r8), intent(in) :: omn(LBi:,LBj:) real(r8), intent(in) :: om_u(LBi:,LBj:) real(r8), intent(in) :: om_v(LBi:,LBj:) real(r8), intent(in) :: on_u(LBi:,LBj:) real(r8), intent(in) :: on_v(LBi:,LBj:) real(r8), intent(in) :: pm(LBi:,LBj:) real(r8), intent(in) :: pn(LBi:,LBj:) real(r8), intent(in) :: Hz(LBi:,LBj:,:) real(r8), intent(in) :: Huon(LBi:,LBj:,:) real(r8), intent(in) :: Hvom(LBi:,LBj:,:) real(r8), intent(in) :: z_r(LBi:,LBj:,:) # ifdef SUN real(r8), intent(in) :: Akt(LBi:UBi,LBj:UBj,0:N(ng),NAT) # else real(r8), intent(in) :: Akt(LBi:,LBj:,0:,:) # endif real(r8), intent(in) :: W(LBi:,LBj:,0:) # ifdef DIAGNOSTICS_TS real(r8), intent(inout) :: DiaTwrk(LBi:,LBj:,:,:,:) # endif # ifdef SUN real(r8), intent(inout) :: t(LBi:UBi,LBj:UBj,N(ng),3,NT(ng)) # else real(r8), intent(inout) :: t(LBi:,LBj:,:,:,:) # endif # if defined FLOATS && defined FLOAT_VWALK real(r8), intent(out) :: dAktdz(LBi:,LBj:,:) # endif # else # 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 # ifdef WET_DRY real(r8), intent(in) :: rmask_wet(LBi:UBi,LBj:UBj) real(r8), intent(in) :: umask_wet(LBi:UBi,LBj:UBj) real(r8), intent(in) :: vmask_wet(LBi:UBi,LBj:UBj) # endif real(r8), intent(in) :: omn(LBi:UBi,LBj:UBj) real(r8), intent(in) :: om_u(LBi:UBi,LBj:UBj) real(r8), intent(in) :: om_v(LBi:UBi,LBj:UBj) real(r8), intent(in) :: on_u(LBi:UBi,LBj:UBj) real(r8), intent(in) :: on_v(LBi:UBi,LBj:UBj) real(r8), intent(in) :: pm(LBi:UBi,LBj:UBj) real(r8), intent(in) :: pn(LBi:UBi,LBj:UBj) real(r8), intent(in) :: Hz(LBi:UBi,LBj:UBj,N(ng)) real(r8), intent(in) :: Huon(LBi:UBi,LBj:UBj,N(ng)) real(r8), intent(in) :: Hvom(LBi:UBi,LBj:UBj,N(ng)) real(r8), intent(in) :: z_r(LBi:UBi,LBj:UBj,N(ng)) real(r8), intent(in) :: Akt(LBi:UBi,LBj:UBj,0:N(ng),NAT) real(r8), intent(in) :: W(LBi:UBi,LBj:UBj,0:N(ng)) # ifdef DIAGNOSTICS_TS real(r8), intent(inout) :: DiaTwrk(LBi:UBi,LBj:UBj,N(ng),NT(ng), & & NDT) # endif real(r8), intent(inout) :: t(LBi:UBi,LBj:UBj,N(ng),3,NT(ng)) # if defined FLOATS && defined FLOAT_VWALK real(r8), intent(out) :: dAktdz(LBi:UBi,LBj:UBj,N(ng)) # endif # endif ! ! Local variable declarations. ! logical :: LapplySrc, Lhsimt, Lmpdata ! # ifdef NESTING integer :: ILB, IUB, JLB, JUB integer :: dg, cr, rg # endif integer :: IminT, ImaxT, JminT, JmaxT integer :: Isrc, Jsrc integer :: i, ic, ii, is, itrc, j, jj, k, ltrc # if defined AGE_MEAN && defined T_PASSIVE integer :: iage # endif # ifdef DIAGNOSTICS_TS integer :: idiag # endif real(r8) :: eps = 1.0E-16_r8 real(r8) :: eps1 = 1.0E-12_r8 real(r8) :: cff, cff1, cff2, cff3 real(r8) :: betaL, betaR, betaD, betaU real(r8) :: rL, rR, rD, rU, rkaL, rkaR, rkaD, rkaU real(r8) :: a1, b1, sw, sw_eta, sw_xi real(r8), dimension(IminS:ImaxS) :: gradX, KaX, oKaX real(r8), dimension(JminS:JmaxS) :: gradE, KaE, oKaE real(r8), dimension(0:N(ng)) :: gradZ, KaZ, oKaZ real(r8), dimension(IminS:ImaxS,0:N(ng)) :: CF real(r8), dimension(IminS:ImaxS,0:N(ng)) :: BC real(r8), dimension(IminS:ImaxS,0:N(ng)) :: DC real(r8), dimension(IminS:ImaxS,0:N(ng)) :: FC 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,N(ng)) :: oHz # ifdef DIAGNOSTICS_TS real(r8), allocatable :: Dhadv(:,:,:) real(r8), allocatable :: Dvadv(:,:,:,:) # endif real(r8), allocatable :: Ta(:,:,:,:) real(r8), allocatable :: Ua(:,:,:) real(r8), allocatable :: Va(:,:,:) real(r8), allocatable :: Wa(:,:,:) # include "set_bounds.h" # ifdef NESTING ! ! Notice that the trace flux boundary arrays are dimensioned with the ! global dimensions of grid to facilitate processing. ! ILB=BOUNDS(ng)%LBi(-1) IUB=BOUNDS(ng)%UBi(-1) JLB=BOUNDS(ng)%LBj(-1) JUB=BOUNDS(ng)%UBj(-1) # endif ! !----------------------------------------------------------------------- ! Time-step horizontal advection term. !----------------------------------------------------------------------- ! Lhsimt =ANY(Hadvection(:,ng)%HSIMT).and. & & ANY(Vadvection(:,ng)%HSIMT) Lmpdata=ANY(Hadvection(:,ng)%MPDATA).and. & & ANY(Vadvection(:,ng)%MPDATA) ! ! Allocate local arrays for MPDATA. ! IF (Lmpdata) THEN # ifdef DIAGNOSTICS_TS IF (.not.allocated(Dhadv)) THEN allocate ( Dhadv(IminS:ImaxS,JminS:JmaxS,3) ) Dhadv=0.0_r8 END IF IF (.not.allocated(Dvadv)) THEN allocate ( Dvadv(IminS:ImaxS,JminS:JmaxS,N(ng),NT(ng)) ) Dvadv=0.0_r8 END IF # endif IF (.not.allocated(Ta)) THEN allocate ( Ta(IminS:ImaxS,JminS:JmaxS,N(ng),NT(ng)) ) Ta=0.0_r8 END IF IF (.not.allocated(Ua)) THEN allocate ( Ua(IminS:ImaxS,JminS:JmaxS,N(ng)) ) Ua=0.0_r8 END IF IF (.not.allocated(Va)) THEN allocate ( Va(IminS:ImaxS,JminS:JmaxS,N(ng)) ) Va=0.0_r8 END IF IF (.not.allocated(Wa)) THEN allocate ( Wa(IminS:ImaxS,JminS:JmaxS,0:N(ng)) ) Wa=0.0_r8 END IF END IF ! ! Compute reciprocal thickness, 1/Hz. ! IF (Lmpdata.or.Lhsimt) THEN DO k=1,N(ng) DO j=Jstrm2,Jendp2 DO i=Istrm2,Iendp2 oHz(i,j,k)=1.0_r8/Hz(i,j,k) END DO END DO END DO ELSE DO k=1,N(ng) DO j=Jstr,Jend DO i=Istr,Iend oHz(i,j,k)=1.0_r8/Hz(i,j,k) END DO END DO END DO END IF ! ! Horizontal tracer advection. It is possible to have a different ! advection schme for each tracer. ! T_LOOP1 : DO itrc=1,NT(ng) ! ! The MPDATA and HSIMT algorithms requires a three-point footprint, so ! exchange boundary data on t(:,:,:,nnew,:) so other processes computed ! earlier (horizontal diffusion, biology, or sediment) are accounted. ! IF ((Hadvection(itrc,ng)%MPDATA).or. & & (Hadvection(itrc,ng)%HSIMT)) THEN IF (EWperiodic(ng).or.NSperiodic(ng)) THEN CALL exchange_r3d_tile (ng, tile, & & LBi, UBi, LBj, UBj, 1, N(ng), & & t(:,:,:,nnew,itrc)) END IF # ifdef DISTRIBUTE CALL mp_exchange3d (ng, tile, iNLM, 1, & & LBi, UBi, LBj, UBj, 1, N(ng), & & NghostPoints, & & EWperiodic(ng), NSperiodic(ng), & & t(:,:,:,nnew,itrc)) # endif END IF ! ! Compute horizontal tracer advection fluxes. ! K_LOOP : DO k=1,N(ng) ! HADV_FLUX : IF (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,3,itrc)+ & & t(i ,j,k,3,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,3,itrc)+ & & t(i,j ,k,3,itrc)) END DO END DO ! ELSE IF (Hadvection(itrc,ng)%MPDATA) THEN ! ! First-order, upstream differences horizontal advective fluxes. ! DO j=JstrVm2,Jendp2i DO i=IstrUm2,Iendp3 cff1=MAX(Huon(i,j,k),0.0_r8) cff2=MIN(Huon(i,j,k),0.0_r8) FX(i,j)=cff1*t(i-1,j,k,3,itrc)+ & & cff2*t(i ,j,k,3,itrc) END DO END DO DO j=JstrVm2,Jendp3 DO i=IstrUm2,Iendp2i cff1=MAX(Hvom(i,j,k),0.0_r8) cff2=MIN(Hvom(i,j,k),0.0_r8) FE(i,j)=cff1*t(i,j-1,k,3,itrc)+ & & cff2*t(i,j ,k,3,itrc) END DO END DO ! ELSE IF (Hadvection(itrc,ng)%HSIMT) THEN ! ! Third High-order Spatial Interpolation at the Middle Temporal level ! (HSIMT; Wu and Zhu, 2010) with a Total Variation Diminishing (TVD) ! limiter horizontal advection fluxes. ! ! Hui Wu and Jianrong Zhu, 2010: Advection scheme with 3rd high-order ! spatial interpolation at the middle temporal level and its ! application to saltwater intrusion in the Changjiang Estuary, ! Ocean Modelling 33, 33-51, doi:10.1016/j.ocemod.2009.12.001 ! DO j=Jstr,Jend DO i=IstrU-1,Iendp2 cff=0.125_r8*(pm(i-1,j)+pm(i,j))*(pn(i-1,j)+pn(i,j))* & & dt(ng) cff1=cff*(oHz(i-1,j,k)+oHz(i,j,k)) gradX(i)=t(i,j,k,3,itrc)-t(i-1,j,k,3,itrc) KaX(i)=1.0_r8-ABS(Huon(i,j,k)*cff1) # ifdef MASKING gradX(i)=gradX(i)*umask(i,j) KaX(i)=KaX(i)*umask(i,j) # endif END DO IF (.not.EWperiodic(ng)) THEN IF (DOMAIN(ng)%Western_Edge(tile)) THEN IF (Huon(Istr,j,k).ge.0.0_r8) THEN gradX(Istr-1)=0.0_r8 KaX(Istr-1)=0.0_r8 END IF END IF IF (DOMAIN(ng)%Eastern_Edge(tile)) THEN IF (Huon(Iend+1,j,k).lt.0.0_r8) THEN gradX(Iend+2)=0.0_r8 KaX(Iend+2)=0.0_r8 END IF END IF END IF DO i=Istr,Iend+1 IF (KaX(i).le.eps1) THEN oKaX(i)=0.0_r8 ELSE oKaX(i)=1.0_r8/MAX(KaX(i),eps1) END IF IF (Huon(i,j,k).ge.0.0_r8) THEN IF (ABS(gradX(i)).le.eps1) THEN rL=0.0_r8 rkaL=0.0_r8 ELSE rL=gradX(i-1)/gradX(i) rkaL=KaX(i-1)*oKaX(i) END IF a1= cc1*KaX(i)+cc2-cc3*oKaX(i) b1=-cc1*KaX(i)+cc2+cc3*oKaX(i) betaL=a1+b1*rL cff=0.5_r8*MAX(0.0_r8, & & MIN(2.0_r8, 2.0_r8*rL*rkaL, betaL))* & & gradX(i)*KaX(i) # ifdef MASKING ii=MAX(i-2,0) cff=cff*rmask(ii,j) # endif sw_xi=t(i-1,j,k,3,itrc)+cff ELSE IF (ABS(gradX(i)).le.eps1) THEN rR=0.0_r8 rkaR=0.0_r8 ELSE rR=gradX(i+1)/gradX(i) rkaR=KaX(i+1)*oKaX(i) END IF a1= cc1*KaX(i)+cc2-cc3*oKaX(i) b1=-cc1*KaX(i)+cc2+cc3*oKaX(i) betaR=a1+b1*rR cff=0.5_r8*MAX(0.0_r8, & & MIN(2.0_r8, 2.0_r8*rR*rkaR, betaR))* & & gradX(i)*KaX(i) # ifdef MASKING ii=MIN(i+1,Lm(ng)+1) cff=cff*rmask(ii,j) # endif sw_xi=t(i,j,k,3,itrc)-cff END IF FX(i,j)=sw_xi*Huon(i,j,k) END DO END DO ! DO i=Istr,Iend DO j=JstrV-1,Jendp2 cff=0.125_r8*(pn(i,j)+pn(i,j-1))*(pm(i,j)+pm(i,j-1))* & & dt(ng) cff1=cff*(oHz(i,j,k)+oHz(i,j-1,k)) gradE(j)=t(i,j,k,3,itrc)-t(i,j-1,k,3,itrc) KaE(j)=1.0_r8-ABS(Hvom(i,j,k)*cff1) # ifdef MASKING gradE(j)=gradE(j)*vmask(i,j) KaE(j)=KaE(j)*vmask(i,j) # endif END DO IF (.not.NSperiodic(ng)) THEN IF (DOMAIN(ng)%Southern_Edge(tile)) THEN IF (Hvom(i,Jstr,k).ge.0.0_r8) THEN gradE(Jstr-1)=0.0_r8 KaE(Jstr-1)=0.0_r8 END IF END IF IF (DOMAIN(ng)%Northern_Edge(tile)) THEN IF (Hvom(i,Jend+1,k).lt.0.0_r8) THEN gradE(Jend+2)=0.0_r8 KaE(Jend+2)=0.0_r8 END IF END IF END IF DO j=Jstr,Jend+1 IF (KaE(j).le.eps1) THEN oKaE(j)=0.0_r8 ELSE oKaE(j)=1.0_r8/MAX(KaE(j),eps1) END IF IF (Hvom(i,j,k).ge.0.0_r8) THEN IF (ABS(gradE(j)).le.eps1) THEN rD=0.0_r8 rkaD=0.0_r8 ELSE rD=gradE(j-1)/gradE(j) rkaD=KaE(j-1)*oKaE(j) END IF a1= cc1*KaE(j)+cc2-cc3*oKaE(j) b1=-cc1*KaE(j)+cc2+cc3*oKaE(j) betaD=a1+b1*rD cff=0.5_r8*MAX(0.0_r8, & & MIN(2.0_r8, 2.0_r8*rD*rkaD, betaD))* & & gradE(j)*KaE(j) # ifdef MASKING jj=MAX(j-2,0) cff=cff*rmask(i,jj) # endif sw_eta=t(i,j-1,k,3,itrc)+cff ELSE IF (ABS(gradE(j)).le.eps1) THEN rU=0.0_r8 rkaU=0.0_r8 ELSE rU=gradE(j+1)/gradE(j) rkaU=KaE(j+1)*oKaE(j) END IF a1= cc1*KaE(j)+cc2-cc3*oKaE(j) b1=-cc1*KaE(j)+cc2+cc3*oKaE(j) betaU=a1+b1*rU cff=0.5*MAX(0.0_r8, & & MIN(2.0_r8, 2.0_r8*rU*rkaU, betaU))* & & gradE(j)*KaE(j) # ifdef MASKING jj=MIN(j+1,Mm(ng)+1) cff=cff*rmask(i,jj) # endif sw_eta=t(i,j,k,3,itrc)-cff END IF FE(i,j)=sw_eta*Hvom(i,j,k) END DO END DO ! ELSE IF ((Hadvection(itrc,ng)%AKIMA4).or. & & (Hadvection(itrc,ng)%CENTERED4).or. & & (Hadvection(itrc,ng)%SPLIT_U3).or. & & (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,3,itrc)- & & t(i-1,j,k,3,itrc) # ifdef MASKING FX(i,j)=FX(i,j)*umask(i,j) # endif 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) 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) END DO END IF END IF ! DO j=Jstr,Jend DO i=Istr-1,Iend+1 IF (Hadvection(itrc,ng)%UPSTREAM3) THEN curv(i,j)=FX(i+1,j)-FX(i,j) ELSE IF (Hadvection(itrc,ng)%AKIMA4) THEN cff=2.0_r8*FX(i+1,j)*FX(i,j) IF (cff.gt.eps) THEN grad(i,j)=cff/(FX(i+1,j)+FX(i,j)) ELSE grad(i,j)=0.0_r8 END IF ELSE IF ((Hadvection(itrc,ng)%CENTERED4).or. & & (Hadvection(itrc,ng)%SPLIT_U3)) THEN grad(i,j)=0.5_r8*(FX(i+1,j)+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 (Hadvection(itrc,ng)%UPSTREAM3) THEN FX(i,j)=Huon(i,j,k)*0.5_r8* & & (t(i-1,j,k,3,itrc)+ & & t(i ,j,k,3,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)) ELSE IF ((Hadvection(itrc,ng)%AKIMA4).or. & & (Hadvection(itrc,ng)%CENTERED4).or. & & (Hadvection(itrc,ng)%SPLIT_U3)) THEN FX(i,j)=Huon(i,j,k)*0.5_r8* & & (t(i-1,j,k,3,itrc)+ & & t(i ,j,k,3,itrc)- & & cff2*(grad(i ,j)- & & 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,3,itrc)- & & t(i,j-1,k,3,itrc) # ifdef MASKING FE(i,j)=FE(i,j)*vmask(i,j) # endif 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) 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) END DO END IF END IF ! DO j=Jstr-1,Jend+1 DO i=Istr,Iend IF (Hadvection(itrc,ng)%UPSTREAM3) THEN curv(i,j)=FE(i,j+1)-FE(i,j) ELSE IF (Hadvection(itrc,ng)%AKIMA4) THEN cff=2.0_r8*FE(i,j+1)*FE(i,j) IF (cff.gt.eps) THEN grad(i,j)=cff/(FE(i,j+1)+FE(i,j)) ELSE grad(i,j)=0.0_r8 END IF ELSE IF ((Hadvection(itrc,ng)%CENTERED4).or. & & (Hadvection(itrc,ng)%SPLIT_U3)) THEN grad(i,j)=0.5_r8*(FE(i,j+1)+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 (Hadvection(itrc,ng)%UPSTREAM3) THEN FE(i,j)=Hvom(i,j,k)*0.5_r8* & & (t(i,j-1,k,3,itrc)+ & & t(i,j ,k,3,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)) ELSE IF ((Hadvection(itrc,ng)%AKIMA4).or. & & (Hadvection(itrc,ng)%CENTERED4).or. & & (Hadvection(itrc,ng)%SPLIT_U3)) THEN FE(i,j)=Hvom(i,j,k)*0.5_r8* & & (t(i,j-1,k,3,itrc)+ & & t(i,j ,k,3,itrc)- & & cff2*(grad(i,j )- & & 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. ! IF (LuvSrc(ng)) THEN DO is=1,Nsrc(ng) Isrc=SOURCES(ng)%Isrc(is) Jsrc=SOURCES(ng)%Jsrc(is) IF (INT(SOURCES(ng)%Dsrc(is)).eq.0) THEN IF ((Hadvection(itrc,ng)%MPDATA).or. & & (Hadvection(itrc,ng)%HSIMT)) THEN LapplySrc=(IstrUm2.le.Isrc).and. & & (Isrc.le.Iendp3).and. & & (JstrVm2.le.Jsrc).and. & & (Jsrc.le.Jendp2i) ELSE LapplySrc=(Istr.le.Isrc).and. & & (Isrc.le.Iend+1).and. & & (Jstr.le.Jsrc).and. & & (Jsrc.le.Jend) END IF IF (LapplySrc) THEN IF (LtracerSrc(itrc,ng)) THEN FX(Isrc,Jsrc)=Huon(Isrc,Jsrc,k)* & & SOURCES(ng)%Tsrc(is,k,itrc) # ifdef MASKING ELSE IF ((rmask(Isrc ,Jsrc).eq.0.0_r8).and. & & (rmask(Isrc-1,Jsrc).eq.1.0_r8)) THEN FX(Isrc,Jsrc)=Huon(Isrc,Jsrc,k)* & & t(Isrc-1,Jsrc,k,3,itrc) ELSE IF ((rmask(Isrc ,Jsrc).eq.1.0_r8).and. & & (rmask(Isrc-1,Jsrc).eq.0.0_r8)) THEN FX(Isrc,Jsrc)=Huon(Isrc,Jsrc,k)* & & t(Isrc ,Jsrc,k,3,itrc) END IF # endif END IF END IF ELSE IF (INT(SOURCES(ng)%Dsrc(is)).eq.1) THEN IF ((Hadvection(itrc,ng)%MPDATA).or. & & (Hadvection(itrc,ng)%HSIMT)) THEN LapplySrc=(IstrUm2.le.Isrc).and. & & (Isrc.le.Iendp2i).and. & & (JstrVm2.le.Jsrc).and. & & (Jsrc.le.Jendp3) ELSE LapplySrc=(Istr.le.Isrc).and. & & (Isrc.le.Iend).and. & & (Jstr.le.Jsrc).and. & & (Jsrc.le.Jend+1) END IF IF (LapplySrc) THEN IF (LtracerSrc(itrc,ng)) THEN FE(Isrc,Jsrc)=Hvom(Isrc,Jsrc,k)* & & SOURCES(ng)%Tsrc(is,k,itrc) # ifdef MASKING ELSE IF ((rmask(Isrc,Jsrc ).eq.0.0_r8).and. & & (rmask(Isrc,Jsrc-1).eq.1.0_r8)) THEN FE(Isrc,Jsrc)=Hvom(Isrc,Jsrc,k)* & & t(Isrc,Jsrc-1,k,3,itrc) ELSE IF ((rmask(Isrc,Jsrc ).eq.1.0_r8).and. & & (rmask(Isrc,Jsrc-1).eq.0.0_r8)) THEN FE(Isrc,Jsrc)=Hvom(Isrc,Jsrc,k)* & & t(Isrc,Jsrc ,k,3,itrc) END IF # endif END IF END IF END IF END DO END IF # if defined NESTING && !defined ONE_WAY ! ! If refinement grids, extract tracer horizontal advection fluxes ! (Hz*u*T/n, Hz*v*T/m) at the grid contact boundary (physical ! domain perimeter) to be used in two-way nesting. ! IF (RefinedGrid(ng)) THEN DO cr=1,Ncontact dg=Rcontact(cr)%donor_grid rg=Rcontact(cr)%receiver_grid IF (ng.eq.rg) THEN CALL bry_fluxes (dg, rg, cr, iNLM, tile, & & IminS, ImaxS, JminS, JmaxS, & & ILB, IUB, JLB, JUB, & & dt(ng), FX, FE, & & BRY_CONTACT(iwest, cr)%Tflux(:,k,itrc), & & BRY_CONTACT(ieast, cr)%Tflux(:,k,itrc), & & BRY_CONTACT(isouth,cr)%Tflux(:,k,itrc), & & BRY_CONTACT(inorth,cr)%Tflux(:,k,itrc)) END IF END DO END IF # endif ! ! If MPDATA, time-step horizontal advection for intermediate diffusive ! tracer, Ta (m Tunits). ! HADV_STEPPING : IF (Hadvection(itrc,ng)%MPDATA) THEN DO j=JstrVm2,Jendp2i DO i=IstrUm2,Iendp2i cff=dt(ng)*pm(i,j)*pn(i,j) cff1=cff*(FX(i+1,j)-FX(i,j)) cff2=cff*(FE(i,j+1)-FE(i,j)) cff3=cff1+cff2 Ta(i,j,k,itrc)=t(i,j,k,nnew,itrc)-cff3 # ifdef DIAGNOSTICS_TS Dhadv(i,j,iTxadv)=-cff1 Dhadv(i,j,iTyadv)=-cff2 Dhadv(i,j,iThadv)=-cff3 # endif END DO END DO # ifdef DIAGNOSTICS_TS ! DO j=Jstr,Jend DO i=Istr,Iend DiaTwrk(i,j,k,itrc,iTxadv)=Dhadv(i,j,iTxadv) DiaTwrk(i,j,k,itrc,iTyadv)=Dhadv(i,j,iTyadv) DiaTwrk(i,j,k,itrc,iThadv)=Dhadv(i,j,iThadv) END DO END DO # endif ! ! OTHERWISE, time-step horizontal advection term. Advective fluxes ! have units of Tunits m3/s. The new tracer has units of m Tunits. ! ELSE DO j=Jstr,Jend DO i=Istr,Iend cff=dt(ng)*pm(i,j)*pn(i,j) cff1=cff*(FX(i+1,j)-FX(i,j)) cff2=cff*(FE(i,j+1)-FE(i,j)) cff3=cff1+cff2 t(i,j,k,nnew,itrc)=t(i,j,k,nnew,itrc)-cff3 # ifdef DIAGNOSTICS_TS DiaTwrk(i,j,k,itrc,iTxadv)=-cff1 DiaTwrk(i,j,k,itrc,iTyadv)=-cff2 DiaTwrk(i,j,k,itrc,iThadv)=-cff3 # endif END DO END DO END IF HADV_STEPPING END DO K_LOOP END DO T_LOOP1 ! !----------------------------------------------------------------------- ! Time-step vertical advection term. !----------------------------------------------------------------------- ! T_LOOP2 : DO itrc=1,NT(ng) IF (Vadvection(itrc,ng)%MPDATA) THEN JminT=JstrVm2 JmaxT=Jendp2i ELSE JminT=Jstr JmaxT=Jend END IF ! J_LOOP1 : DO j=JminT,JmaxT ! start pipelined J-loop ! VADV_FLUX : IF (Vadvection(itrc,ng)%SPLINES) THEN ! ! Build conservative parabolic splines for the vertical derivatives ! "FC" of the tracer. Then, the interfacial "FC" values are ! converted to vertical advective flux (Tunits m3/s). ! DO i=Istr,Iend # ifdef NEUMANN FC(i,0)=1.5_r8*t(i,j,1,3,itrc) CF(i,1)=0.5_r8 # else FC(i,0)=2.0_r8*t(i,j,1,3,itrc) CF(i,1)=1.0_r8 # endif 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+1,3,itrc)+ & & Hz(i,j,k+1)*t(i,j,k ,3,itrc))- & & Hz(i,j,k+1)*FC(i,k-1)) END DO END DO DO i=Istr,Iend # ifdef NEUMANN FC(i,N(ng))=(3.0_r8*t(i,j,N(ng),3,itrc)-FC(i,N(ng)-1))/ & & (2.0_r8-CF(i,N(ng))) # else FC(i,N(ng))=(2.0_r8*t(i,j,N(ng),3,itrc)-FC(i,N(ng)-1))/ & & (1.0_r8-CF(i,N(ng))) # endif 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) 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 (Vadvection(itrc,ng)%AKIMA4) THEN ! ! Fourth-order, Akima vertical advective flux (Tunits m3/s). ! DO k=1,N(ng)-1 DO i=Istr,Iend FC(i,k)=t(i,j,k+1,3,itrc)- & & t(i,j,k ,3,itrc) END DO END DO DO i=Istr,Iend FC(i,0)=FC(i,1) FC(i,N(ng))=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) IF (cff.gt.eps) THEN CF(i,k)=cff/(FC(i,k)+FC(i,k-1)) ELSE 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 ,3,itrc)+ & & t(i,j,k+1,3,itrc)- & & cff1*(CF(i,k+1)-CF(i,k))) END DO END DO DO i=Istr,Iend # ifdef SED_MORPH FC(i,0)=W(i,j,0)*t(i,j,1,3,itrc) # else FC(i,0)=0.0_r8 # endif FC(i,N(ng))=0.0_r8 END DO ! ELSE IF (Vadvection(itrc,ng)%CENTERED2) THEN ! ! Second-order, central differences vertical advective flux ! (Tunits m3/s). ! DO k=1,N(ng)-1 DO i=Istr,Iend FC(i,k)=W(i,j,k)* & & 0.5_r8*(t(i,j,k ,3,itrc)+ & & t(i,j,k+1,3,itrc)) END DO END DO DO i=Istr,Iend # ifdef SED_MORPH FC(i,0)=W(i,j,0)*t(i,j,1,3,itrc) # else FC(i,0)=0.0_r8 # endif FC(i,N(ng))=0.0_r8 END DO ! ELSE IF (Vadvection(itrc,ng)%MPDATA) THEN ! ! First_order, upstream differences vertical advective flux ! (Tunits m3/s). ! DO i=IstrUm2,Iendp2i DO k=1,N(ng)-1 cff1=MAX(W(i,j,k),0.0_r8) cff2=MIN(W(i,j,k),0.0_r8) FC(i,k)=cff1*t(i,j,k ,3,itrc)+ & & cff2*t(i,j,k+1,3,itrc) END DO # ifdef SED_MORPH FC(i,0)=W(i,j,0)*t(i,j,1,3,itrc) # else FC(i,0)=0.0_r8 # endif FC(i,N(ng))=0.0_r8 END DO ! ELSE IF (Vadvection(itrc,ng)%HSIMT) THEN ! ! Third High-order Spatial Interpolation at the Middle Temporal level ! (HSIMT; Wu and Zhu, 2010) with a Total Variation Diminishing (TVD) ! limiter vertical advection flux (Tunits m3/s). ! DO i=Istr,Iend KaZ(0)=0.0_r8 oKaZ(0)=0.0_r8 gradZ(0)=0.0_r8 DO k=1,N(ng)-1 cff=pm(i,j)*pn(i,j)*dt(ng) KaZ(k)=1.0_r8-ABS(cff*W(i,j,k)/ & & (z_r(i,j,k+1)-z_r(i,j,k))) oKaZ(k)=1.0_r8/KaZ(k) gradZ(k)=t(i,j,k+1,3,itrc)-t(i,j,k,3,itrc) END DO KaZ(N(ng))=0.0_r8 okaZ(N(ng))=0.0_r8 gradZ(N(ng))=0.0_r8 ! DO k=1,N(ng)-1 IF ((k.eq.1).and.(W(i,j,k).ge.0.0_r8)) THEN FC(i,k)=W(i,j,k)*t(i,j,k,3,itrc) ELSE IF ((k.eq.N(ng)-1).and.(W(i,j,k).lt.0.0_r8)) THEN FC(i,k)=W(i,j,k)*t(i,j,k+1,3,itrc) ELSE IF (W(i,j,k).ge.0) THEN IF (ABS(gradZ(k)).le.eps1) THEN rD=0.0_r8 rkaD=0.0_r8 ELSE rD=gradZ(k-1)/gradZ(k) rkaD=KaZ(k-1)*oKaZ(k) END IF a1= cc1*KaZ(k)+cc2-cc3*oKaZ(k) b1=-cc1*KaZ(k)+cc2+cc3*oKaZ(k) betaD=a1+b1*rD cff=0.5_r8*MAX(0.0_r8, & & MIN(2.0_r8, 2.0_r8*rD*rkaD, betaD))* & & gradZ(k)*KaZ(k) sw=t(i,j,k,3,itrc)+cff ELSE IF (ABS(gradZ(k)).le.eps1) THEN rU=0.0_r8 rkaU=0.0_r8 ELSE rU=gradZ(k+1)/gradZ(k) rkaU=KaZ(k+1)*oKaZ(k) END IF a1= cc1*KaZ(k)+cc2-cc3*oKaZ(k) b1=-cc1*KaZ(k)+cc2+cc3*oKaZ(k) betaU=a1+b1*rU cff=0.5_r8*MAX(0.0_r8, & & MIN(2.0_r8, 2.0_r8*rU*rkaU, betaU))* & & gradZ(k)*KaZ(k) sw=t(i,j,k+1,3,itrc)-cff END IF FC(i,k)=W(i,j,k)*sw END IF END DO # ifdef SED_MORPH FC(i,0)=W(i,j,0)*t(i,j,1,3,itrc) # else FC(i,0)=0.0_r8 # endif FC(i,N(ng))=0.0_r8 END DO ! ELSE IF ((Vadvection(itrc,ng)%CENTERED4).or. & & (Vadvection(itrc,ng)%SPLIT_U3)) THEN ! ! Fourth-order, central differences vertical advective flux ! (Tunits m3/s). ! 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 ,3,itrc)+ & & t(i,j,k+1,3,itrc))- & & cff3*(t(i,j,k-1,3,itrc)+ & & t(i,j,k+2,3,itrc))) END DO END DO DO i=Istr,Iend # ifdef SED_MORPH FC(i,0)=W(i,j,0)*2.0_r8* & & (cff2*t(i,j,1,3,itrc)- & & cff3*t(i,j,2,3,itrc)) # else FC(i,0)=0.0_r8 # endif FC(i,1)=W(i,j,1)* & & (cff1*t(i,j,1,3,itrc)+ & & cff2*t(i,j,2,3,itrc)- & & cff3*t(i,j,3,3,itrc)) FC(i,N(ng)-1)=W(i,j,N(ng)-1)* & & (cff1*t(i,j,N(ng) ,3,itrc)+ & & cff2*t(i,j,N(ng)-1,3,itrc)- & & cff3*t(i,j,N(ng)-2,3,itrc)) FC(i,N(ng))=0.0_r8 END DO END IF VADV_FLUX ! ! If MPDATA and cell-centered point source (LwSrc), augment the ! intermediate tracer, Ta, with the tracer divergence. For other ! advection schemes LwSrc is applied after the vertical advection ! is completed (J. Wilkin). ! IF (LwSrc(ng)) THEN IF (Hadvection(itrc,ng)%MPDATA) THEN DO is=1,Nsrc(ng) IF (INT(SOURCES(ng)%Dsrc(is)).eq.2) THEN 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)).and. & & (j.eq.Jsrc)) THEN DO k=1,N(ng) cff=dt(ng)*pm(i,j)*pn(i,j) IF (LtracerSrc(itrc,ng)) THEN cff3=SOURCES(ng)%Tsrc(is,k,itrc) ELSE cff3=t(Isrc,Jsrc,k,3,itrc) END IF Ta(Isrc,Jsrc,k,itrc)=Ta(Isrc,Jsrc,k,itrc)+ & & cff*SOURCES(ng)%Qsrc(is,k)* & & cff3 END DO END IF END IF END DO END IF END IF ! ! If MPDATA, time-step vertical advection for intermediate diffusive ! tracer, Ta (Tunits). # ifdef DIAGNOSTICS_TS ! Convert units of tracer diagnostic terms to Tunits. # endif ! VADV_STEPPING : IF (Vadvection(itrc,ng)%MPDATA) THEN DO i=IstrUm2,Iendp2i CF(i,0)=dt(ng)*pm(i,j)*pn(i,j) END DO DO k=1,N(ng) DO i=IstrUm2,Iendp2i cff1=CF(i,0)*(FC(i,k)-FC(i,k-1)) Ta(i,j,k,itrc)=(Ta(i,j,k,itrc)-cff1)*oHz(i,j,k) # ifdef DIAGNOSTICS_TS Dvadv(i,j,k,itrc)=-cff1 # endif END DO END DO ! ! OTHERWISE, time-step vertical advection term (m Tunits, or Tunits if ! conservative, parabolic splines diffusion). # ifdef DIAGNOSTICS_TS ! Convert units of tracer diagnostic terms to Tunits. # endif ! ELSE DO i=Istr,Iend CF(i,0)=dt(ng)*pm(i,j)*pn(i,j) END DO DO k=1,N(ng) DO i=Istr,Iend cff1=CF(i,0)*(FC(i,k)-FC(i,k-1)) t(i,j,k,nnew,itrc)=t(i,j,k,nnew,itrc)-cff1 # ifdef SPLINES_VDIFF t(i,j,k,nnew,itrc)=t(i,j,k,nnew,itrc)*oHz(i,j,k) # endif # ifdef DIAGNOSTICS_TS DiaTwrk(i,j,k,itrc,iTvadv)=-cff1 DO idiag=1,NDT DiaTwrk(i,j,k,itrc,idiag)=DiaTwrk(i,j,k,itrc,idiag)* & & oHz(i,j,k) END DO # endif END DO END DO END IF VADV_STEPPING END DO J_LOOP1 END DO T_LOOP2 ! !----------------------------------------------------------------------- ! Compute anti-diffusive velocities to corrected advected tracers ! using MPDATA recursive method. Notice that pipelined J-loop ended. !----------------------------------------------------------------------- ! T_LOOP3 : DO itrc=1,NT(ng) MPDATA : IF ((Hadvection(itrc,ng)%MPDATA).and. & & (Vadvection(itrc,ng)%MPDATA)) THEN CALL mpdata_adiff_tile (ng, tile, & & LBi, UBi, LBj, UBj, & & IminS, ImaxS, JminS, JmaxS, & # ifdef MASKING & rmask, umask, vmask, & # endif # ifdef WET_DRY & rmask_wet, umask_wet, vmask_wet, & # endif & pm, pn, omn, om_u, on_v, & & z_r, oHz, & & Huon, Hvom, W, & & t(:,:,:,3,itrc), & & Ta(:,:,:,itrc), Ua, Va, Wa) ! ! Compute anti-diffusive corrected advection fluxes. ! DO k=1,N(ng) DO j=Jstr,Jend DO i=Istr,Iend+1 cff1=MAX(Ua(i,j,k),0.0_r8) cff2=MIN(Ua(i,j,k),0.0_r8) FX(i,j)=(cff1*Ta(i-1,j,k,itrc)+ & & cff2*Ta(i ,j,k,itrc))* & & 0.5_r8*(Hz(i,j,k)+Hz(i-1,j,k))*on_u(i,j) END DO END DO DO j=Jstr,Jend+1 DO i=Istr,Iend cff1=MAX(Va(i,j,k),0.0_r8) cff2=MIN(Va(i,j,k),0.0_r8) FE(i,j)=(cff1*Ta(i,j-1,k,itrc)+ & & cff2*Ta(i,j ,k,itrc))* & & 0.5_r8*(Hz(i,j,k)+Hz(i,j-1,k))*om_v(i,j) END DO END DO ! ! Time-step corrected horizontal advection (Tunits m). ! DO j=Jstr,Jend DO i=Istr,Iend cff=dt(ng)*pm(i,j)*pn(i,j) cff1=cff*(FX(i+1,j)-FX(i,j)) cff2=cff*(FE(i,j+1)-FE(i,j)) cff3=cff1+cff2 t(i,j,k,nnew,itrc)=Ta(i,j,k,itrc)*Hz(i,j,k)-cff3 # ifdef DIAGNOSTICS_TS DiaTwrk(i,j,k,itrc,iTxadv)=DiaTwrk(i,j,k,itrc,iTxadv)- & & cff1 DiaTwrk(i,j,k,itrc,iTyadv)=DiaTwrk(i,j,k,itrc,iTyadv)- & & cff2 DiaTwrk(i,j,k,itrc,iThadv)=DiaTwrk(i,j,k,itrc,iThadv)- & & cff3 # endif END DO END DO END DO ! ! Compute anti-diffusive corrected vertical advection flux. ! DO j=Jstr,Jend DO k=1,N(ng)-1 DO i=Istr,Iend cff1=MAX(Wa(i,j,k),0.0_r8) cff2=MIN(Wa(i,j,k),0.0_r8) FC(i,k)=cff1*Ta(i,j,k ,itrc)+ & & cff2*Ta(i,j,k+1,itrc) END DO END DO DO i=Istr,Iend FC(i,0)=0.0_r8 FC(i,N(ng))=0.0_r8 END DO ! ! Time-step corrected vertical advection (Tunits). # ifdef DIAGNOSTICS_TS ! Convert units of tracer diagnostic terms to Tunits. # endif ! DO i=Istr,Iend CF(i,0)=dt(ng)*pm(i,j)*pn(i,j) END DO DO k=1,N(ng) DO i=Istr,Iend cff1=CF(i,0)*(FC(i,k)-FC(i,k-1)) t(i,j,k,nnew,itrc)=t(i,j,k,nnew,itrc)-cff1 # ifdef DIAGNOSTICS_TS DiaTwrk(i,j,k,itrc,iTvadv)=Dvadv(i,j,k,itrc)- & & cff1 DO idiag=1,NDT DiaTwrk(i,j,k,itrc,idiag)=DiaTwrk(i,j,k,itrc,idiag)* & & oHz(i,j,k) END DO # endif END DO END DO END DO END IF MPDATA END DO T_LOOP3 ! !----------------------------------------------------------------------- ! Add tracer divergence due to cell-centered (LwSrc) point sources. !----------------------------------------------------------------------- ! ! When LTracerSrc is .true. the inflowing concentration is Tsrc. ! When LtracerSrc is .false. we add tracer mass to compensate for the ! added volume to keep the receiving cell concentration unchanged. ! J. Levin (Jupiter Intelligence Inc.) and J. Wilkin ! IF (LwSrc(ng)) THEN DO itrc=1,NT(ng) IF (.not.((Hadvection(itrc,ng)%MPDATA).and. & & (Vadvection(itrc,ng)%MPDATA))) THEN DO is=1,Nsrc(ng) IF (INT(SOURCES(ng)%Dsrc(is)).eq.2) THEN 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 DO k=1,N(ng) cff=dt(ng)*pm(i,j)*pn(i,j) # ifdef SPLINES_VDIFF cff=cff*oHz(Isrc,Jsrc,k) # endif IF (LtracerSrc(itrc,ng)) THEN cff3=SOURCES(ng)%Tsrc(is,k,itrc) ELSE cff3=t(Isrc,Jsrc,k,3,itrc) END IF t(Isrc,Jsrc,k,nnew,itrc)=t(Isrc,Jsrc,k,nnew,itrc)+ & & cff*SOURCES(ng)%Qsrc(is,k)*& & cff3 END DO END IF END IF END DO END IF END DO END IF ! !----------------------------------------------------------------------- ! Time-step vertical diffusion term. !----------------------------------------------------------------------- ! J_LOOP2 : DO j=Jstr,Jend ! start pipelined J-loop DO itrc=1,NT(ng) ltrc=MIN(NAT,itrc) # ifdef SPLINES_VDIFF IF (.not.((Hadvection(itrc,ng)%MPDATA).and. & & (Vadvection(itrc,ng)%MPDATA))) THEN ! ! Use conservative, parabolic spline reconstruction of vertical ! diffusion derivatives. Then, time step vertical diffusion term ! implicitly. ! cff1=1.0_r8/6.0_r8 DO k=1,N(ng)-1 DO i=Istr,Iend FC(i,k)=cff1*Hz(i,j,k )- & & dt(ng)*Akt(i,j,k-1,ltrc)*oHz(i,j,k ) CF(i,k)=cff1*Hz(i,j,k+1)- & & dt(ng)*Akt(i,j,k+1,ltrc)*oHz(i,j,k+1) END DO END DO DO i=Istr,Iend CF(i,0)=0.0_r8 DC(i,0)=0.0_r8 END DO ! ! LU decomposition and forward substitution. ! 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))+ & & dt(ng)*Akt(i,j,k,ltrc)*(oHz(i,j,k)+oHz(i,j,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*(t(i,j,k+1,nnew,itrc)-t(i,j,k,nnew,itrc)- & & FC(i,k)*DC(i,k-1)) END DO END DO ! ! Backward substitution. ! DO i=Istr,Iend 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) END DO END DO ! DO k=1,N(ng) DO i=Istr,Iend DC(i,k)=DC(i,k)*Akt(i,j,k,ltrc) cff1=dt(ng)*oHz(i,j,k)*(DC(i,k)-DC(i,k-1)) t(i,j,k,nnew,itrc)=t(i,j,k,nnew,itrc)+cff1 # ifdef DIAGNOSTICS_TS DiaTwrk(i,j,k,itrc,iTvdif)=DiaTwrk(i,j,k,itrc,iTvdif)+ & & cff1 # endif END DO END DO ELSE # endif ! ! Compute off-diagonal coefficients FC [lambda*dt*Akt/Hz] for the ! implicit vertical diffusion terms at future time step, located ! at horizontal RHO-points and vertical W-points. ! Also set FC at the top and bottom levels. ! cff=-dt(ng)*lambda DO k=1,N(ng)-1 DO i=Istr,Iend cff1=1.0_r8/(z_r(i,j,k+1)-z_r(i,j,k)) FC(i,k)=cff*cff1*Akt(i,j,k,ltrc) END DO END DO DO i=Istr,Iend FC(i,0)=0.0_r8 FC(i,N(ng))=0.0_r8 END DO ! ! Compute diagonal matrix coefficients BC and load right-hand-side ! terms for the tracer equation into DC. ! 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)=t(i,j,k,nnew,itrc) END DO END DO ! ! Solve the tridiagonal system. ! 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. ! DO i=Istr,Iend # ifdef DIAGNOSTICS_TS cff1=t(i,j,N(ng),nnew,itrc)*oHz(i,j,N(ng)) # endif 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)) t(i,j,N(ng),nnew,itrc)=DC(i,N(ng)) # ifdef DIAGNOSTICS_TS DiaTwrk(i,j,N(ng),itrc,iTvdif)= & & DiaTwrk(i,j,N(ng),itrc,iTvdif)+ & & t(i,j,N(ng),nnew,itrc)-cff1 # endif END DO DO k=N(ng)-1,1,-1 DO i=Istr,Iend # ifdef DIAGNOSTICS_TS cff1=t(i,j,k,nnew,itrc)*oHz(i,j,k) # endif DC(i,k)=DC(i,k)-CF(i,k)*DC(i,k+1) t(i,j,k,nnew,itrc)=DC(i,k) # ifdef DIAGNOSTICS_TS DiaTwrk(i,j,k,itrc,iTvdif)=DiaTwrk(i,j,k,itrc,iTvdif)+ & & t(i,j,k,nnew,itrc)-cff1 # endif END DO END DO # ifdef SPLINES_VDIFF END IF # endif END DO END DO J_LOOP2 # if defined AGE_MEAN && defined T_PASSIVE ! !----------------------------------------------------------------------- ! If inert passive tracer and Mean Age, compute age concentration (even ! inert index) forced by the right-hand-side term that is concentration ! of an associated conservative passive tracer (odd inert index). Mean ! Age is age concentration divided by conservative passive tracer ! concentration. Code implements NPT/2 mean age tracer pairs. ! ! Implemented and tested by W.G. Zhang and J. Wilkin. See following ! reference for details. ! ! Zhang et al. (2010): Simulation of water age and residence time in ! the New York Bight, JPO, 40,965-982, doi:10.1175/2009JPO4249.1 !----------------------------------------------------------------------- ! DO itrc=1,NPT,2 iage=inert(itrc+1) ! even inert tracer index DO k=1,N(ng) DO j=Jstr,Jend DO i=Istr,Iend IF ((Hadvection(inert(itrc),ng)%MPDATA).and. & & (Vadvection(inert(itrc),ng)%MPDATA)) THEN t(i,j,k,nnew,iage)=t(i,j,k,nnew,iage)+ & & dt(ng)*t(i,j,k,nnew,inert(itrc)) ELSE t(i,j,k,nnew,iage)=t(i,j,k,nnew,iage)+ & & dt(ng)*t(i,j,k,3,inert(itrc)) END IF END DO END DO END DO END DO # endif ! !----------------------------------------------------------------------- ! Apply lateral boundary conditions and, if appropriate, nudge ! to tracer data and apply Land/Sea mask. !----------------------------------------------------------------------- ! ! Initialize tracer counter index. The "tclm" array is only allocated ! to the NTCLM fields that need to be processed. This is done to ! reduce memory. ! ic=0 ! DO itrc=1,NT(ng) ! ! Set compact reduced memory tracer index for nudging coefficients and ! climatology arrays. ! IF (LtracerCLM(itrc,ng).and.LnudgeTCLM(itrc,ng)) THEN ic=ic+1 END IF ! ! Set lateral boundary conditions. ! CALL t3dbc_tile (ng, tile, itrc, ic, & & LBi, UBi, LBj, UBj, N(ng), NT(ng), & & IminS, ImaxS, JminS, JmaxS, & & nstp, nnew, & & t) ! ! Nudge towards tracer climatology. ! IF (LtracerCLM(itrc,ng).and.LnudgeTCLM(itrc,ng)) THEN DO k=1,N(ng) DO j=JstrR,JendR DO i=IstrR,IendR t(i,j,k,nnew,itrc)=t(i,j,k,nnew,itrc)+ & & dt(ng)* & & CLIMA(ng)%Tnudgcof(i,j,k,ic)* & & (CLIMA(ng)%tclm(i,j,k,ic)- & & t(i,j,k,nnew,itrc)) END DO END DO END DO END IF # ifdef MASKING ! ! Apply Land/Sea mask. ! DO k=1,N(ng) DO j=JstrR,JendR DO i=IstrR,IendR t(i,j,k,nnew,itrc)=t(i,j,k,nnew,itrc)*rmask(i,j) END DO END DO END DO # endif # ifdef DIAGNOSTICS_TS ! ! Compute time-rate-of-change diagnostic term. ! DO k=1,N(ng) DO j=JstrR,JendR DO i=IstrR,IendR DiaTwrk(i,j,k,itrc,iTrate)=t(i,j,k,nnew,itrc)- & & DiaTwrk(i,j,k,itrc,iTrate) !! DiaTwrk(i,j,k,itrc,iTrate)=t(i,j,k,nnew,itrc)- & !! & t(i,j,k,nstp,itrc) END DO END DO END DO # endif ! ! Apply periodic boundary conditions. ! IF (EWperiodic(ng).or.NSperiodic(ng)) THEN CALL exchange_r3d_tile (ng, tile, & & LBi, UBi, LBj, UBj, 1, N(ng), & & t(:,:,:,nnew,itrc)) END IF END DO # ifdef DISTRIBUTE ! ! Exchange boundary data. ! CALL mp_exchange4d (ng, tile, iNLM, 1, & & LBi, UBi, LBj, UBj, 1, N(ng), 1, NT(ng), & & NghostPoints, & & EWperiodic(ng), NSperiodic(ng), & & t(:,:,:,nnew,:)) # endif # if defined FLOATS && defined FLOAT_VWALK ! !----------------------------------------------------------------------- ! Compute vertical gradient in vertical T-diffusion coefficient for ! floats random walk. !----------------------------------------------------------------------- ! DO j=JstrR,JendR DO i=IstrR,IendR DO k=1,N(ng) dAktdz(i,j,k)=(Akt(i,j,k,1)-Akt(i,j,k-1,1))/Hz(i,j,k) END DO END DO END DO ! ! Apply periodic boundary conditions. ! IF (EWperiodic(ng).or.NSperiodic(ng)) THEN CALL exchange_r3d_tile (ng, tile, & & LBi, UBi, LBj, UBj, 1, N(ng), & & dAktdz) END IF # ifdef DISTRIBUTE CALL mp_exchange3d (ng, tile, iNLM, 1, & & LBi, UBi, LBj, UBj, 1, N(ng), & & NghostPoints, & & EWperiodic(ng), NSperiodic(ng), & & dAktdz) # endif # endif ! !----------------------------------------------------------------------- ! If applicable, deallocate local arrays. !----------------------------------------------------------------------- ! IF (Lmpdata) THEN # ifdef DIAGNOSTICS_TS IF (allocated(Dhadv)) deallocate (Dhadv) IF (allocated(Dvadv)) deallocate (Dvadv) # endif IF (allocated(Ta)) deallocate (Ta) IF (allocated(Ua)) deallocate (Ua) IF (allocated(Va)) deallocate (Va) IF (allocated(Wa)) deallocate (Wa) END IF ! RETURN END SUBROUTINE step3d_t_tile #endif END MODULE step3d_t_mod