#include "cppdefs.h" MODULE step3d_t_mod #if !defined TS_FIXED && (defined NONLINEAR && defined SOLVE3D) ! !svn $Id: step3d_t.F 412 2009-12-03 20:46:03Z arango $ !======================================================================= ! Copyright (c) 2002-2009 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. ! ! ! !======================================================================= ! implicit none PRIVATE PUBLIC :: step3d_t CONTAINS ! !*********************************************************************** SUBROUTINE step3d_t (ng, tile) !*********************************************************************** ! USE mod_param # ifdef CLIMATOLOGY USE mod_clima # endif # ifdef DIAGNOSTICS USE mod_diags # endif USE mod_grid USE mod_mixing # if defined ASSIMILATION || defined NUDGING USE mod_obs # endif USE mod_ocean # ifdef TS_PSOURCE USE mod_sources # endif USE mod_stepping ! ! Imported variable declarations. ! integer, intent(in) :: ng, tile ! ! Local variable declarations. ! # include "tile.h" ! # ifdef PROFILE CALL wclock_on (ng, iNLM, 35) # endif CALL step3d_t_tile (ng, tile, & & LBi, UBi, LBj, UBj, & & IminS, ImaxS, JminS, JmaxS, & & nrhs(ng), nstp(ng), nnew(ng), & # if defined TS_PSOURCE || defined Q_PSOURCE & Msrc(ng), Nsrc(ng), & & SOURCES(ng) % Isrc, & & SOURCES(ng) % Jsrc, & & SOURCES(ng) % Tsrc, & # endif # ifdef TS_PSOURCE & SOURCES(ng) % Dsrc, & # endif # ifdef Q_PSOURCE & SOURCES(ng) % Qsrc, & # endif # ifdef MASKING & GRID(ng) % rmask, & & GRID(ng) % umask, & & GRID(ng) % vmask, & # endif # ifdef TS_MPDATA # 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, & # endif & GRID(ng) % pm, & & GRID(ng) % pn, & & GRID(ng) % Hz, & & GRID(ng) % Huon, & & GRID(ng) % Hvom, & & GRID(ng) % z_r, & # if defined TCLM_NUDGING && defined TCLIMATOLOGY & CLIMA(ng) % Tnudgcof, & & CLIMA(ng) % tclm, & # endif # if defined NUDGING_SST || defined NUDGING_T & OBS(ng) % EobsT, & & OBS(ng) % Tobs, & # endif & MIXING(ng) % Akt, & # ifdef TS_MPDATA & OCEAN(ng) % u, & & OCEAN(ng) % v, & # endif & 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) # endif RETURN END SUBROUTINE step3d_t ! !*********************************************************************** SUBROUTINE step3d_t_tile (ng, tile, & & LBi, UBi, LBj, UBj, & & IminS, ImaxS, JminS, JmaxS, & & nrhs, nstp, nnew, & # if defined TS_PSOURCE || defined Q_PSOURCE & Msrc, Nsrc, & & Isrc, Jsrc, Tsrc, & # endif # ifdef TS_PSOURCE & Dsrc, & # endif # ifdef Q_PSOURCE & Qsrc, & # endif # ifdef MASKING & rmask, umask, vmask, & # endif # ifdef TS_MPDATA # ifdef WET_DRY & rmask_wet, umask_wet, vmask_wet, & # endif & omn, om_u, om_v, on_u, on_v, & # endif & pm, pn, & & Hz, Huon, Hvom, & & z_r, & # if defined TCLM_NUDGING && defined TCLIMATOLOGY & Tnudgcof, tclm, & # endif # if defined NUDGING_SST || defined NUDGING_T & EobsT, Tobs, & # endif & Akt, & # ifdef TS_MPDATA & u, v, & # endif & W, & # if defined FLOATS && defined FLOAT_VWALK & dAktdz, & # endif # ifdef DIAGNOSTICS_TS & DiaTwrk, & # endif & t) !*********************************************************************** ! USE mod_param USE mod_ncparam USE mod_scalars ! # if defined EW_PERIODIC || defined NS_PERIODIC USE exchange_3d_mod, ONLY : exchange_r3d_tile # endif # ifdef DISTRIBUTE # if defined FLOATS && defined FLOAT_VWALK USE mp_exchange_mod, ONLY : mp_exchange3d # endif USE mp_exchange_mod, ONLY : mp_exchange4d # endif # ifdef TS_MPDATA USE mpdata_adiff_mod # 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 # if defined TS_PSOURCE || defined Q_PSOURCE integer, intent(in) :: Msrc, Nsrc # endif ! # ifdef ASSUMED_SHAPE # if defined TS_PSOURCE || defined Q_PSOURCE integer, intent(in) :: Isrc(:) integer, intent(in) :: Jsrc(:) real(r8), intent(in) :: Tsrc(:,:,:) # endif # ifdef TS_PSOURCE real(r8), intent(in) :: Dsrc(:) # endif # ifdef Q_PSOURCE real(r8), intent(in) :: Qsrc(:,:) # endif # 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 TS_MPDATA # 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:) # endif real(r8), intent(in) :: pm(LBi:,LBj:) real(r8), intent(in) :: pn(LBi:,LBj:) # if defined TCLM_NUDGING && defined TCLIMATOLOGY real(r8), intent(in) :: Tnudgcof(LBi:,LBj:,:) real(r8), intent(in) :: tclm(LBi:,LBj:,:,:) # endif # if defined NUDGING_SST || defined NUDGING_T real(r8), intent(in) :: EobsT(LBi:,LBj:,:,:) real(r8), intent(in) :: Tobs(LBi:,LBj:,:,:) # endif 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 # ifdef TS_MPDATA real(r8), intent(in) :: u(LBi:,LBj:,:,:) real(r8), intent(in) :: v(LBi:,LBj:,:,:) # 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 # if defined TS_PSOURCE || defined Q_PSOURCE integer, intent(in) :: Isrc(Msrc) integer, intent(in) :: Jsrc(Msrc) real(r8), intent(in) :: Tsrc(Msrc,N(ng),NT(ng)) # endif # ifdef TS_PSOURCE real(r8), intent(in) :: Dsrc(Msrc) # endif # ifdef Q_PSOURCE real(r8), intent(in) :: Qsrc(Msrc,N(ng)) # endif # 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 TS_MPDATA # 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) # endif real(r8), intent(in) :: pm(LBi:UBi,LBj:UBj) real(r8), intent(in) :: pn(LBi:UBi,LBj:UBj) # if defined TCLM_NUDGING && defined TCLIMATOLOGY real(r8), intent(in) :: Tnudgcof(LBi:UBi,LBj:UBj,NT(ng)) real(r8), intent(in) :: tclm(LBi:UBi,LBj:UBj,N(ng),NT(ng)) # endif # if defined NUDGING_SST || defined NUDGING_T real(r8), intent(in) :: EobsT(LBi:UBi,LBj:UBj,N(ng),NT(ng)) real(r8), intent(in) :: Tobs(LBi:UBi,LBj:UBj,N(ng),NT(ng)) # endif 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) # ifdef TS_MPDATA real(r8), intent(in) :: u(LBi:UBi,LBj:UBj,N(ng),2) real(r8), intent(in) :: v(LBi:UBi,LBj:UBj,N(ng),2) # endif 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. ! # ifdef DISTRIBUTE # ifdef EW_PERIODIC logical :: EWperiodic=.TRUE. # else logical :: EWperiodic=.FALSE. # endif # ifdef NS_PERIODIC logical :: NSperiodic=.TRUE. # else logical :: NSperiodic=.FALSE. # endif # endif integer :: i, is, itrc, j, k, ltrc integer :: idiag real(r8), parameter :: eps = 1.0E-16_r8 real(r8) :: cff, cff1, cff2, cff3 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 TS_MPDATA real(r8), dimension(IminS:ImaxS,JminS:JmaxS,N(ng),NT(ng)) :: Ta real(r8), dimension(IminS:ImaxS,JminS:JmaxS,N(ng)) :: Ua real(r8), dimension(IminS:ImaxS,JminS:JmaxS,N(ng)) :: Va real(r8), dimension(IminS:ImaxS,JminS:JmaxS,0:N(ng)) :: Wa # endif # include "set_bounds.h" ! !----------------------------------------------------------------------- ! Time-step horizontal advection term. !----------------------------------------------------------------------- ! ! Compute inverse thickness. ! # ifdef TS_MPDATA # ifdef EW_PERIODIC # define I_RANGE Istr-2,Iend+2 # else # define I_RANGE MAX(Istr-2,0),MIN(Iend+2,Lm(ng)+1) # endif # ifdef NS_PERIODIC # define J_RANGE Jstr-2,Jend+2 # else # define J_RANGE MAX(Jstr-2,0),MIN(Jend+2,Mm(ng)+1) # endif # else # define I_RANGE Istr,Iend # define J_RANGE Jstr,Jend # endif DO k=1,N(ng) DO j=J_RANGE DO i=I_RANGE oHz(i,j,k)=1.0_r8/Hz(i,j,k) END DO END DO END DO # undef I_RANGE # undef J_RANGE ! ! Compute horizontal tracer advection fluxes. ! # if defined TS_MPDATA && \ (defined EW_PERIODIC || defined NS_PERIODIC || defined DISTRIBUTE) ! ! The MPDATA algorithm requires a three-point footprint, so exchange ! boundary data on t(:,:,:,3,:) so other processes computed earlier ! (horizontal diffusion, biology, or sediment) are accounted. ! # if defined EW_PERIODIC || defined NS_PERIODIC DO itrc=1,NT(ng) CALL exchange_r3d_tile (ng, tile, & & LBi, UBi, LBj, UBj, 1, N(ng), & & t(:,:,:,3,itrc)) END DO # endif # ifdef DISTRIBUTE CALL mp_exchange4d (ng, tile, iNLM, 1, & & LBi, UBi, LBj, UBj, 1, N(ng), 1, NT(ng), & & NghostPoints, EWperiodic, NSperiodic, & & t(:,:,:,3,:)) # endif # endif T_LOOP : DO itrc=1,NT(ng) K_LOOP : DO k=1,N(ng) # if defined TS_C2HADVECTION ! ! 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 # elif defined TS_MPDATA ! ! First-order, upstream differences horizontal advective fluxes. ! # ifdef EW_PERIODIC # define I_RANGE Istr-2,Iend+3 # else # define I_RANGE MAX(Istr-2,1),MIN(Iend+3,Lm(ng)+1) # endif # ifdef NS_PERIODIC # define J_RANGE Jstr-2,Jend+2 # else # define J_RANGE MAX(Jstr-2,1),MIN(Jend+2,Mm(ng)) # endif DO j=J_RANGE DO i=I_RANGE 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 # undef I_RANGE # undef J_RANGE # ifdef EW_PERIODIC # define I_RANGE Istr-2,Iend+2 # else # define I_RANGE MAX(Istr-2,1),MIN(Iend+2,Lm(ng)) # endif # ifdef NS_PERIODIC # define J_RANGE Jstr-2,Jend+3 # else # define J_RANGE MAX(Jstr-2,1),MIN(Jend+3,Mm(ng)+1) # endif DO j=J_RANGE DO i=I_RANGE 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 # undef I_RANGE # undef J_RANGE # else ! # if defined TS_U3HADVECTION ! Third-order, uptream-biased horizontal advective fluxes. # elif defined TS_A4HADVECTION ! Fourth-order, Akima horizontal advective fluxes. # else ! Fourth-order, centered differences horizontal advective fluxes. # endif ! # ifdef EW_PERIODIC # define I_RANGE Istr-1,Iend+2 # else # define I_RANGE MAX(Istr-1,1),MIN(Iend+2,Lm(ng)+1) # endif DO j=Jstr,Jend DO i=I_RANGE 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 # undef I_RANGE # ifndef EW_PERIODIC IF (WESTERN_EDGE) THEN DO j=Jstr,Jend FX(Istr-1,j)=FX(Istr,j) END DO END IF IF (EASTERN_EDGE) THEN DO j=Jstr,Jend FX(Iend+2,j)=FX(Iend+1,j) END DO END IF # endif ! DO j=Jstr,Jend DO i=Istr-1,Iend+1 # if defined TS_U3HADVECTION curv(i,j)=FX(i+1,j)-FX(i,j) # elif defined TS_A4HADVECTION 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 grad(i,j)=0.5_r8*(FX(i+1,j)+FX(i,j)) # endif 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 # ifdef TS_U3HADVECTION 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 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))) # endif END DO END DO ! # ifdef NS_PERIODIC # define J_RANGE Jstr-1,Jend+2 # else # define J_RANGE MAX(Jstr-1,1),MIN(Jend+2,Mm(ng)+1) # endif DO j=J_RANGE 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 # undef J_RANGE # ifndef NS_PERIODIC IF (SOUTHERN_EDGE) THEN DO i=Istr,Iend FE(i,Jstr-1)=FE(i,Jstr) END DO END IF IF (NORTHERN_EDGE) THEN DO i=Istr,Iend FE(i,Jend+2)=FE(i,Jend+1) END DO END IF # endif ! DO j=Jstr-1,Jend+1 DO i=Istr,Iend # if defined TS_U3HADVECTION curv(i,j)=FE(i,j+1)-FE(i,j) # elif defined TS_A4HADVECTION 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 grad(i,j)=0.5_r8*(FE(i,j+1)+FE(i,j)) # endif 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 # ifdef TS_U3HADVECTION 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 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))) # endif END DO END DO # endif # if defined TS_PSOURCE && !defined Q_PSOURCE ! ! Apply tracers point sources to the horizontal advection terms. ! DO is=1,Nsrc i=Isrc(is) j=Jsrc(is) IF (INT(Dsrc(is)).eq.0) THEN # ifdef TS_MPDATA IF (((Istr-2.le.i).and.(i.le.Iend+2)).and. & & ((Jstr-2.le.j).and.(j.le.Jend+2))) THEN # else IF (((Istr.le.i).and.(i.le.Iend+1)).and. & & ((Jstr.le.j).and.(j.le.Jend))) THEN # endif IF (LtracerSrc(itrc,ng)) THEN FX(i,j)=Huon(i,j,k)*Tsrc(is,k,itrc) # ifdef MASKING ELSE IF ((rmask(i ,j).eq.0.0_r8).and. & & (rmask(i-1,j).eq.1.0_r8)) THEN FX(i,j)=Huon(i,j,k)*t(i-1,j,k,3,itrc) ELSE IF ((rmask(i ,j).eq.1.0_r8).and. & & (rmask(i-1,j).eq.0.0_r8)) THEN FX(i,j)=Huon(i,j,k)*t(i ,j,k,3,itrc) END IF # endif END IF END IF ELSE IF (INT(Dsrc(is)).eq.1) THEN # ifdef TS_MPDATA IF (((Istr-2.le.i).and.(i.le.Iend+2)).and. & & ((Jstr-2.le.j).and.(j.le.Jend+2))) THEN # else IF (((Istr.le.i).and.(i.le.Iend)).and. & & ((Jstr.le.j).and.(j.le.Jend+1))) THEN # endif IF (LtracerSrc(itrc,ng)) THEN FE(i,j)=Hvom(i,j,k)*Tsrc(is,k,itrc) # ifdef MASKING ELSE IF ((rmask(i,j ).eq.0.0_r8).and. & & (rmask(i,j-1).eq.1.0_r8)) THEN FE(i,j)=Hvom(i,j,k)*t(i,j-1,k,3,itrc) ELSE IF ((rmask(i,j ).eq.1.0_r8).and. & & (rmask(i,j-1).eq.0.0_r8)) THEN FE(i,j)=Hvom(i,j,k)*t(i,j ,k,3,itrc) END IF # endif END IF END IF END IF END DO # endif ! ! Time-step horizontal advection term. ! # ifdef TS_MPDATA # ifdef EW_PERIODIC # define I_RANGE Istr-2,Iend+2 # else # define I_RANGE MAX(Istr-2,1),MIN(Iend+2,Lm(ng)) # endif # ifdef NS_PERIODIC # define J_RANGE Jstr-2,Jend+2 # else # define J_RANGE MAX(Jstr-2,1),MIN(Jend+2,Mm(ng)) # endif # else # define I_RANGE Istr,Iend # define J_RANGE Jstr,Jend # endif DO j=J_RANGE DO i=I_RANGE cff=dt(ng)*pm(i,j)*pn(i,j) cff1=cff*(FX(i+1,j)-FX(i,j)+ & & FE(i,j+1)-FE(i,j)) # ifdef TS_MPDATA cff2=Hz(i,j,k)+ & & cff*(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))) ! Hz_old Ta(i,j,k,itrc)=t(i,j,k,3,itrc)*cff2-cff1 # else t(i,j,k,nnew,itrc)=t(i,j,k,nnew,itrc)-cff1 # endif # ifdef DIAGNOSTICS_TS DiaTwrk(i,j,k,itrc,iThadv)=-cff1 # endif END DO END DO END DO K_LOOP END DO T_LOOP ! !----------------------------------------------------------------------- ! Time-step vertical advection term. !----------------------------------------------------------------------- ! DO j=J_RANGE DO itrc=1,NT(ng) # if defined TS_SVADVECTION ! ! Build conservative parabolic splines for the vertical derivatives ! "FC" of the tracer. Then, the interfacial "FC" values are ! converted to vertical advective flux. ! 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 # elif defined TS_A4VADVECTION ! ! Fourth-order, Akima vertical advective flux. ! 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 # elif defined TS_C2VADVECTION ! ! 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 ,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 # elif defined TS_MPDATA ! ! First_order, upstream differences vertical advective flux. ! DO i=I_RANGE 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 ! ! 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 ,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 # endif ! ! Time-step vertical advection term. # ifdef DIAGNOSTICS_TS ! Convert units of tracer diagnostic terms to Tunits. # endif ! DO i=I_RANGE CF(i,0)=dt(ng)*pm(i,j)*pn(i,j) END DO # ifdef Q_PSOURCE ! ! Apply mass point sources - Volume influx. ! DO is=1,Nsrc i=Isrc(is) IF (((IstrR.le.i).and.(i.le.IendR)).and. & & ((JstrR.le.j).and.(j.le.JendR))) THEN IF (j.eq.Jsrc(is)) THEN DO k=1,N(ng) FC(i,k)=FC(i,k)+0.5_r8* & & (Qsrc(is,k )*Tsrc(is,k ,itrc)+ & & Qsrc(is,k+1)*Tsrc(is,k+1,itrc)) END DO END IF END IF END DO # endif DO k=1,N(ng) DO i=I_RANGE cff1=CF(i,0)*(FC(i,k)-FC(i,k-1)) # ifdef TS_MPDATA Ta(i,j,k,itrc)=(Ta(i,j,k,itrc)-cff1)*oHz(i,j,k) # ifdef DIAGNOSTICS_TS DiaTwrk(i,j,k,itrc,iTvadv)=-cff1 # endif # else t(i,j,k,nnew,itrc)=t(i,j,k,nnew,itrc)-cff1 # ifdef SPLINES 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 DiaTwrk(i,j,k,itrc,iThadv)=DiaTwrk(i,j,k,itrc,iThadv)* & & oHz(i,j,k) DiaTwrk(i,j,k,itrc,iTvadv)=DiaTwrk(i,j,k,itrc,iTvadv)* & & oHz(i,j,k) # if defined TS_DIF2 || defined TS_DIF4 DiaTwrk(i,j,k,itrc,iThdif)=DiaTwrk(i,j,k,itrc,iThdif)* & & oHz(i,j,k) # endif DiaTwrk(i,j,k,itrc,iTvdif)=DiaTwrk(i,j,k,itrc,iTvdif)* & & oHz(i,j,k) DiaTwrk(i,j,k,itrc,iTrate)=DiaTwrk(i,j,k,itrc,iTrate)* & & oHz(i,j,k) # endif # endif END DO END DO END DO # ifdef TS_MPDATA END DO ! !----------------------------------------------------------------------- ! Compute anti-diffusive velocities to corrected advected tracers ! using MPDATA recursive method. Notice that pipelined J-loop ended. !----------------------------------------------------------------------- ! DO itrc=1,NT(ng) CALL mpdata_adiff_tile (ng, tile, & & LBi, UBi, LBj, UBj, & & IminS, ImaxS, JminS, JmaxS, & & nrhs, & # 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-difussive 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 cff1=dt(ng)*pm(i,j)*pn(i,j)* & & (FX(i+1,j)-FX(i,j)+ & & FE(i,j+1)-FE(i,j)) t(i,j,k,nnew,itrc)=Ta(i,j,k,itrc)*Hz(i,j,k)-cff1 # ifdef DIAGNOSTICS_TS DiaTwrk(i,j,k,itrc,iThadv)=DiaTwrk(i,j,k,itrc,iThadv)- & & cff1 # endif END DO END DO END DO ! ! Compute anti-difussive 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)=DiaTwrk(i,j,k,itrc,iTvadv)- & & cff1 DiaTwrk(i,j,k,itrc,iThadv)=DiaTwrk(i,j,k,itrc,iThadv)* & & oHz(i,j,k) DiaTwrk(i,j,k,itrc,iTvadv)=DiaTwrk(i,j,k,itrc,iTvadv)* & & oHz(i,j,k) # if defined TS_DIF2 || defined TS_DIF4 DiaTwrk(i,j,k,itrc,iThdif)=DiaTwrk(i,j,k,itrc,iThdif)* & & oHz(i,j,k) # endif DiaTwrk(i,j,k,itrc,iTvdif)=DiaTwrk(i,j,k,itrc,iTvdif)* & & oHz(i,j,k) DiaTwrk(i,j,k,itrc,iTrate)=DiaTwrk(i,j,k,itrc,iTrate)* & & oHz(i,j,k) # endif END DO END DO END DO END DO ! ! Start pipelined J-loop. ! DO j=Jstr,Jend # endif /* TS_MPDATA */ ! !----------------------------------------------------------------------- ! Time-step vertical diffusion term. !----------------------------------------------------------------------- ! DO itrc=1,NT(ng) ltrc=MIN(NAT,itrc) # if defined SPLINES && !defined TS_MPDATA ! ! 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 ! ! 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 # endif END DO END DO ! !----------------------------------------------------------------------- ! Apply lateral boundary conditions and, if appropriate, nudge ! to tracer data and apply Land/Sea mask. !----------------------------------------------------------------------- ! DO itrc=1,NT(ng) ! ! Set lateral boundary conditions. ! CALL t3dbc_tile (ng, tile, itrc, & & LBi, UBi, LBj, UBj, N(ng), NT(ng), & & IminS, ImaxS, JminS, JmaxS, & & nstp, nnew, & & t) # if defined TCLM_NUDGING && defined TCLIMATOLOGY ! ! Nudge towards tracer climatology. ! 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)*Tnudgcof(i,j,itrc)* & & (tclm(i,j,k,itrc)-t(i,j,k,nnew,itrc)) END DO END DO END DO # endif # if defined NUDGING_SST || defined NUDGING_T ! ! Assimilate tracer observations via nudging. ! IF (update_T(itrc,ng)) THEN DO k=1,N(ng) DO j=JstrR,JendR DO i=IstrR,IendR cff=MIN(1.0_r8,MAX(0.0_r8,EobsT(i,j,k,itrc))) cff=dt(ng)*Tnudass(itrc,ng)*(1.0_r8-cff) t(i,j,k,nnew,itrc)=t(i,j,k,nnew,itrc)+ & & cff*(Tobs(i,j,k,itrc)- & & t(i,j,k,nnew,itrc)) END DO END DO END DO END IF # endif # 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 # if defined EW_PERIODIC || defined NS_PERIODIC ! ! Apply periodic boundary conditions. ! CALL exchange_r3d_tile (ng, tile, & & LBi, UBi, LBj, UBj, 1, N(ng), & & t(:,:,:,nnew,itrc)) # endif 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, NSperiodic, & & 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 # if defined EW_PERIODIC || defined NS_PERIODIC ! ! Apply periodic boundary conditions. ! CALL exchange_r3d_tile (ng, tile, & & LBi, UBi, LBj, UBj, 1, N(ng), & & dAktdz) # endif # ifdef DISTRIBUTE CALL mp_exchange3d (ng, tile, iNLM, 1, & & LBi, UBi, LBj, UBj, 1, N(ng), & & NghostPoints, EWperiodic, NSperiodic, & & dAktdz) # endif # endif RETURN END SUBROUTINE step3d_t_tile #endif END MODULE step3d_t_mod