#include "cppdefs.h" MODULE pre_step3d_mod #if defined NONLINEAR && defined SOLVE3D # define NEUMANN ! !svn $Id: pre_step3d.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 subroutine initialize computations for new time step of the ! ! 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". ! ! ! !======================================================================= ! implicit none ! PRIVATE PUBLIC :: pre_step3d ! CONTAINS ! !*********************************************************************** SUBROUTINE pre_step3d (ng, tile) !*********************************************************************** ! USE mod_param # ifdef DIAGNOSTICS USE mod_diags # endif 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 = & & __FILE__ ! # include "tile.h" ! # ifdef PROFILE CALL wclock_on (ng, iNLM, 22, __LINE__, MyFile) # endif CALL pre_step3d_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, & # if defined SOLAR_SOURCE && defined WET_DRY & GRID(ng) % rmask_wet, & # endif # endif & GRID(ng) % pm, & & GRID(ng) % pn, & & GRID(ng) % Hz, & & GRID(ng) % Huon, & & GRID(ng) % Hvom, & & GRID(ng) % z_r, & & GRID(ng) % z_w, & & FORCES(ng) % btflx, & & FORCES(ng) % bustr, & & FORCES(ng) % bvstr, & & FORCES(ng) % stflx, & & FORCES(ng) % sustr, & & FORCES(ng) % svstr, & # ifdef SOLAR_SOURCE & FORCES(ng) % srflx, & # endif & MIXING(ng) % Akt, & & MIXING(ng) % Akv, & # ifdef LMD_NONLOCAL & MIXING(ng) % ghats, & # endif & OCEAN(ng) % W, & & OCEAN(ng) % ru, & & OCEAN(ng) % rv, & # ifdef DIAGNOSTICS_TS & DIAGS(ng) % DiaTwrk, & # endif # ifdef DIAGNOSTICS_UV & DIAGS(ng) % DiaU3wrk, & & DIAGS(ng) % DiaV3wrk, & & DIAGS(ng) % DiaRU, & & DIAGS(ng) % DiaRV, & # endif & OCEAN(ng) % t, & & OCEAN(ng) % u, & & OCEAN(ng) % v) # ifdef PROFILE CALL wclock_off (ng, iNLM, 22, __LINE__, MyFile) # endif ! RETURN END SUBROUTINE pre_step3d ! !*********************************************************************** SUBROUTINE pre_step3d_tile (ng, tile, & & LBi, UBi, LBj, UBj, & & IminS, ImaxS, JminS, JmaxS, & & nrhs, nstp, nnew, & # ifdef MASKING & rmask, umask, vmask, & # if defined SOLAR_SOURCE && defined WET_DRY & rmask_wet, & # endif # endif & pm, pn, & & Hz, Huon, Hvom, & & z_r, z_w, & & btflx, bustr, bvstr, & & stflx, sustr, svstr, & # ifdef SOLAR_SOURCE & srflx, & # endif & Akt, Akv, & # ifdef LMD_NONLOCAL & ghats, & # endif & W, & & ru, rv, & # ifdef DIAGNOSTICS_TS & DiaTwrk, & # endif # ifdef DIAGNOSTICS_UV & DiaU3wrk, DiaV3wrk, & & DiaRU, DiaRV, & # endif & t, u, v) !*********************************************************************** ! USE mod_param USE mod_scalars USE mod_sources ! USE exchange_3d_mod, ONLY : exchange_r3d_tile # ifdef DISTRIBUTE USE mp_exchange_mod, ONLY : mp_exchange4d # 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:) # if defined SOLAR_SOURCE && defined WET_DRY real(r8), intent(in) :: rmask_wet(LBi:,LBj:) # endif # endif 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) :: btflx(LBi:,LBj:,:) real(r8), intent(in) :: bustr(LBi:,LBj:) real(r8), intent(in) :: bvstr(LBi:,LBj:) real(r8), intent(in) :: stflx(LBi:,LBj:,:) real(r8), intent(in) :: sustr(LBi:,LBj:) real(r8), intent(in) :: svstr(LBi:,LBj:) # ifdef SOLAR_SOURCE real(r8), intent(in) :: srflx(LBi:,LBj:) # endif # 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) :: Akv(LBi:,LBj:,0:) # ifdef LMD_NONLOCAL real(r8), intent(in) :: ghats(LBi:,LBj:,0:,:) # endif real(r8), intent(in) :: W(LBi:,LBj:,0:) real(r8), intent(in) :: ru(LBi:,LBj:,0:,:) real(r8), intent(in) :: rv(LBi:,LBj:,0:,:) # ifdef DIAGNOSTICS_TS real(r8), intent(inout) :: DiaTwrk(LBi:,LBj:,:,:,:) # endif # ifdef DIAGNOSTICS_UV real(r8), intent(inout) :: DiaU3wrk(LBi:,LBj:,:,:) real(r8), intent(inout) :: DiaV3wrk(LBi:,LBj:,:,:) real(r8), intent(inout) :: DiaRU(LBi:,LBj:,:,:,:) real(r8), intent(inout) :: DiaRV(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 real(r8), intent(inout) :: u(LBi:,LBj:,:,:) real(r8), intent(inout) :: v(LBi:,LBj:,:,:) # 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) # if defined SOLAR_SOURCE && defined WET_DRY real(r8), intent(in) :: rmask_wet(LBi:UBi,LBj:UBj) # endif # endif 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) :: z_w(LBi:UBi,LBj:UBj,0:N(ng)) real(r8), intent(in) :: btflx(LBi:UBi,LBj:UBj,NT(ng)) real(r8), intent(in) :: bustr(LBi:UBi,LBj:UBj) real(r8), intent(in) :: bvstr(LBi:UBi,LBj:UBj) real(r8), intent(in) :: stflx(LBi:UBi,LBj:UBj,NT(ng)) real(r8), intent(in) :: sustr(LBi:UBi,LBj:UBj) real(r8), intent(in) :: svstr(LBi:UBi,LBj:UBj) # ifdef SOLAR_SOURCE real(r8), intent(in) :: srflx(LBi:UBi,LBj:UBj) # endif real(r8), intent(in) :: Akt(LBi:UBi,LBj:UBj,0:N(ng),NAT) real(r8), intent(in) :: Akv(LBi:UBi,LBj:UBj,0:N(ng)) # ifdef LMD_NONLOCAL real(r8), intent(in) :: ghats(LBi:UBi,LBj:UBj,0:N(ng),NAT) # endif real(r8), intent(in) :: W(LBi:UBi,LBj:UBj,0:N(ng)) real(r8), intent(in) :: ru(LBi:UBi,LBj:UBj,0:N(ng),2) real(r8), intent(in) :: rv(LBi:UBi,LBj:UBj,0:N(ng),2) # ifdef DIAGNOSTICS_TS real(r8), intent(inout) :: DiaTwrk(LBi:UBi,LBj:UBj,N(ng),NT(ng), & & NDT) # endif # ifdef DIAGNOSTICS_UV real(r8), intent(inout) :: DiaU3wrk(LBi:UBi,LBj:UBj,N(ng),NDM3d) real(r8), intent(inout) :: DiaV3wrk(LBi:UBi,LBj:UBj,N(ng),NDM3d) real(r8), intent(inout) :: DiaRU(LBi:UBi,LBj:UBj,N(ng),2,NDrhs) real(r8), intent(inout) :: DiaRV(LBi:UBi,LBj:UBj,N(ng),2,NDrhs) # endif real(r8), intent(inout) :: t(LBi:UBi,LBj:UBj,N(ng),3,NT(ng)) real(r8), intent(inout) :: u(LBi:UBi,LBj:UBj,N(ng),2) real(r8), intent(inout) :: v(LBi:UBi,LBj:UBj,N(ng),2) # endif ! ! Local variable declarations. ! integer :: Isrc, Jsrc integer :: i, ic, indx, is, itrc, j, k, ltrc # if defined AGE_MEAN && defined T_PASSIVE integer :: iage # endif # if defined DIAGNOSTICS_TS || defined DIAGNOSTICS_UV integer :: idiag # endif real(r8), parameter :: eps = 1.0E-16_r8 real(r8) :: cff, cff1, cff2, cff3, 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 # ifdef SOLAR_SOURCE real(r8), dimension(IminS:ImaxS,JminS:JmaxS,0:N(ng)) :: swdk # endif 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 # include "set_bounds.h" # ifndef TS_FIXED ! !======================================================================= ! Tracer equation(s). !======================================================================= # ifdef SOLAR_SOURCE ! ! 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) END DO END DO CALL lmd_swfrac_tile (ng, tile, & & LBi, UBi, LBj, UBj, & & IminS, ImaxS, JminS, JmaxS, & & -1.0_r8, FX, FE) DO j=Jstr,Jend DO i=Istr,Iend swdk(i,j,k)=FE(i,j) END DO END DO END DO # endif ! !----------------------------------------------------------------------- ! 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 (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)) 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)) END DO END DO ! ELSE IF ((Hadvection(itrc,ng)%MPDATA).or. & & (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) FX(i,j)=cff1*t(i-1,j,k,nstp,itrc)+ & & cff2*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) FE(i,j)=cff1*t(i,j-1,k,nstp,itrc)+ & & cff2*t(i,j ,k,nstp,itrc) 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,nstp,itrc)- & & t(i-1,j,k,nstp,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,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)) 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,nstp,itrc)+ & & t(i ,j,k,nstp,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,nstp,itrc)- & & t(i,j-1,k,nstp,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,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)) 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,nstp,itrc)+ & & t(i,j ,k,nstp,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 (((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) ELSE FX(Isrc,Jsrc)=0.0_r8 END IF ELSEIF (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) ELSE FE(Isrc,Jsrc)=0.0_r8 END IF END IF END IF END DO END IF ! ! Time-step horizontal advection (m Tunits). ! IF ((Hadvection(itrc,ng)%MPDATA).or. & & (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)) END DO END DO END DO K_LOOP END DO T_LOOP1 # 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). ! Implemented and tested by W.G. Zhang and J. Wilkin. (m Tunits) ! DO itrc=1,NPT,2 IF (.not.((Hadvection(inert(itrc),ng)%MPDATA).or. & & (Hadvection(inert(itrc),ng)%HSIMT))) THEN IF (iic(ng).eq.ntfirst(ng)) THEN cff=0.5_r8*dt(ng) ELSE Gamma=1.0_r8/6.0_r8 cff=(1.0_r8-Gamma)*dt(ng) END IF iage=inert(itrc+1) ! even inert tracer index DO k=1,N(ng) DO j=Jstr,Jend DO i=Istr,Iend t(i,j,k,3,iage)=t(i,j,k,3,iage)+ & & cff*Hz(i,j,k)* & & t(i,j,k,nnew,inert(itrc)) END DO END DO END DO END IF END DO # endif ! !----------------------------------------------------------------------- ! 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 (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. ! DO i=Istr,Iend # ifdef NEUMANN FC(i,0)=1.5_r8*t(i,j,1,nstp,itrc) CF(i,1)=0.5_r8 # else FC(i,0)=2.0_r8*t(i,j,1,nstp,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,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 # ifdef NEUMANN 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))) # else FC(i,N(ng))=(2.0_r8*t(i,j,N(ng),nstp,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. ! 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) 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 ,nstp,itrc)+ & & t(i,j,k+1,nstp,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,nstp,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. ! 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)) END DO END DO DO i=Istr,Iend # ifdef SED_MORPH FC(i,0)=W(i,j,0)*t(i,j,1,nstp,itrc) # else FC(i,0)=0.0_r8 # endif FC(i,N(ng))=0.0_r8 END DO ! ELSE IF ((Vadvection(itrc,ng)%MPDATA).or. & & (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) FC(i,k)=cff1*t(i,j,k ,nstp,itrc)+ & & cff2*t(i,j,k+1,nstp,itrc) END DO END DO DO i=Istr,Iend # ifdef SED_MORPH FC(i,0)=W(i,j,0)*t(i,j,1,nstp,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. ! 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))) 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,nstp,itrc)- & & cff3*t(i,j,2,nstp,itrc)) # else FC(i,0)=0.0_r8 # endif 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)) 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)) 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)))) END DO END DO ! ! Time-step vertical advection of tracers (Tunits). Impose artificial ! continuity equation. ! 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))) 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)) FC(i,k)=cff3*cff*Akt(i,j,k,ltrc)* & & (t(i,j,k+1,nstp,itrc)- & & t(i,j,k ,nstp,itrc)) END DO END DO # ifdef LMD_NONLOCAL ! ! Add in the nonlocal transport flux for unstable (convective) ! forcing conditions into matrix FC when using the Large et al. ! KPP scheme. The nonlocal transport is only applied to active ! tracers. ! IF (itrc.le.NAT) THEN DO k=1,N(ng)-1 DO i=Istr,Iend FC(i,k)=FC(i,k)- & & dt(ng)*Akt(i,j,k,itrc)*ghats(i,j,k,itrc) END DO END DO END IF # endif # ifdef SOLAR_SOURCE ! ! 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)* & # ifdef WET_DRY & rmask_wet(i,j)* & # endif & swdk(i,j,k) END DO END DO END IF # endif ! ! Apply bottom and surface tracer flux conditions. ! DO i=Istr,Iend FC(i,0)=dt(ng)*btflx(i,j,itrc) FC(i,N(ng))=dt(ng)*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) cff2=FC(i,k)-FC(i,k-1) t(i,j,k,nnew,itrc)=cff1+cff2 # ifdef DIAGNOSTICS_TS DiaTwrk(i,j,k,itrc,iTrate)=cff1 DiaTwrk(i,j,k,itrc,iTvdif)=cff2 # endif END DO END DO END DO END DO # endif /* !TS_FIXED */ ! !======================================================================= ! 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 )) 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)) END DO END DO ! ! Apply bottom and surface stresses, if so is prescribed. ! DO i=IstrU,Iend # ifdef BODYFORCE FC(i,0)=0.0_r8 FC(i,N(ng))=0.0_r8 # else FC(i,0)=dt(ng)*bustr(i,j) FC(i,N(ng))=dt(ng)*sustr(i,j) # endif 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)) cff2=FC(i,k)-FC(i,k-1) u(i,j,k,nnew)=cff1+cff2 # ifdef DIAGNOSTICS_UV DO idiag=1,M3pgrd DiaU3wrk(i,j,k,idiag)=0.0_r8 END DO DiaU3wrk(i,j,k,M3vvis)=cff2 DiaU3wrk(i,j,k,M3rate)=cff1 # endif 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)) cff2=FC(i,k)-FC(i,k-1) cff3=0.5_r8*DC(i,0) u(i,j,k,nnew)=cff1- & & cff3*ru(i,j,k,indx)+ & & cff2 # ifdef DIAGNOSTICS_UV DO idiag=1,M3pgrd DiaU3wrk(i,j,k,idiag)=-cff3*DiaRU(i,j,k,indx,idiag) END DO DiaU3wrk(i,j,k,M3vvis)=cff2 # ifdef BODYFORCE DiaU3wrk(i,j,k,M3vvis)=DiaU3wrk(i,j,k,M3vvis)- & & cff3*DiaRU(i,j,k,indx,M3vvis) # endif DiaU3wrk(i,j,k,M3rate)=cff1 # endif 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)) cff4=FC(i,k)-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 # ifdef DIAGNOSTICS_UV DO idiag=1,M3pgrd DiaU3wrk(i,j,k,idiag)=DC(i,0)* & & (cff1*DiaRU(i,j,k,nrhs,idiag)- & & cff2*DiaRU(i,j,k,indx,idiag)) END DO DiaU3wrk(i,j,k,M3vvis)=cff4 # ifdef BODYFORCE DiaU3wrk(i,j,k,M3vvis)=DiaU3wrk(i,j,k,M3vvis)+ & & DC(i,0)* & & (cff1*DiaRU(i,j,k,nrhs,M3vvis)- & & cff2*DiaRU(i,j,k,indx,M3vvis)) # endif DiaU3wrk(i,j,k,M3rate)=cff3 # endif 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 )) 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)) END DO END DO ! ! Apply bottom and surface stresses, if so is prescribed. ! DO i=Istr,Iend # ifdef BODYFORCE FC(i,0)=0.0_r8 FC(i,N(ng))=0.0_r8 # else FC(i,0)=dt(ng)*bvstr(i,j) FC(i,N(ng))=dt(ng)*svstr(i,j) # endif 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)) cff2=FC(i,k)-FC(i,k-1) v(i,j,k,nnew)=cff1+cff2 # ifdef DIAGNOSTICS_UV DO idiag=1,M3pgrd DiaV3wrk(i,j,k,idiag)=0.0_r8 END DO DiaV3wrk(i,j,k,M3vvis)=cff2 DiaV3wrk(i,j,k,M3rate)=cff1 # endif 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)) cff2=FC(i,k)-FC(i,k-1) cff3=0.5_r8*DC(i,0) v(i,j,k,nnew)=cff1- & & cff3*rv(i,j,k,indx)+ & & cff2 # ifdef DIAGNOSTICS_UV DO idiag=1,M3pgrd DiaV3wrk(i,j,k,idiag)=-cff3*DiaRV(i,j,k,indx,idiag) END DO DiaV3wrk(i,j,k,M3vvis)=cff2 # ifdef BODYFORCE DiaV3wrk(i,j,k,M3vvis)=DiaV3wrk(i,j,k,M3vvis)- & & cff3*DiaRV(i,j,k,indx,M3vvis) # endif DiaV3wrk(i,j,k,M3rate)=cff1 # endif 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)) cff4=FC(i,k)-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 # ifdef DIAGNOSTICS_UV DO idiag=1,M3pgrd DiaV3wrk(i,j,k,idiag)=DC(i,0)* & & (cff1*DiaRV(i,j,k,nrhs,idiag)- & & cff2*DiaRV(i,j,k,indx,idiag)) END DO DiaV3wrk(i,j,k,M3vvis)=cff4 # ifdef BODYFORCE DiaV3wrk(i,j,k,M3vvis)=DiaV3wrk(i,j,k,M3vvis)+ & & DC(i,0)* & & (cff1*DiaRV(i,j,k,nrhs,M3vvis)- & & cff2*DiaRV(i,j,k,indx,M3vvis)) # endif DiaV3wrk(i,j,k,M3rate)=cff3 # endif END DO END DO END IF END IF END DO J_LOOP2 # ifndef TS_FIXED ! !======================================================================= ! 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) IF (EWperiodic(ng).or.NSperiodic(ng)) THEN CALL exchange_r3d_tile (ng, tile, & & LBi, UBi, LBj, UBj, 1, N(ng), & & t(:,:,:,3,itrc)) END IF END DO # ifdef DISTRIBUTE CALL mp_exchange4d (ng, tile, iNLM, 1, & & LBi, UBi, LBj, UBj, 1, N(ng), 1, NT(ng), & & NghostPoints, & & EWperiodic(ng), NSperiodic(ng), & & t(:,:,:,3,:)) # endif # endif ! RETURN END SUBROUTINE pre_step3d_tile #endif END MODULE pre_step3d_mod