#include "cppdefs.h" MODULE rhs3d_mod #if defined NONLINEAR && defined SOLVE3D ! !svn $Id: rhs3d.F 409 2009-11-18 20:39:05Z 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 subroutine evaluates right-hand-side terms for 3D momentum ! ! and tracers equations. ! ! ! !======================================================================= ! implicit none PRIVATE PUBLIC :: rhs3d CONTAINS ! !*********************************************************************** SUBROUTINE rhs3d (ng, tile) !*********************************************************************** ! USE mod_param # ifdef CLIMATOLOGY USE mod_clima # endif USE mod_coupling # if defined DIAGNOSTICS_TS || defined DIAGNOSTICS_UV USE mod_diags # endif USE mod_forces USE mod_grid # ifdef NEARSHORE_MELLOR USE mod_mixing # endif # if defined ASSIMILATION || defined NUDGING USE mod_obs # endif USE mod_ocean USE mod_stepping ! USE pre_step3d_mod, ONLY : pre_step3d USE prsgrd_mod, ONLY : prsgrd # ifndef TS_FIXED # ifdef TS_DIF2 USE t3dmix_mod, ONLY : t3dmix2 # endif # ifdef TS_DIF4 USE t3dmix_mod, ONLY : t3dmix4 # endif # endif # ifdef UV_VIS2 USE uv3dmix_mod, ONLY : uv3dmix2 # endif # ifdef UV_VIS4 USE uv3dmix_mod, ONLY : uv3dmix4 # endif ! ! Imported variable declarations. ! integer, intent(in) :: ng, tile ! ! Local variable declarations. ! # include "tile.h" ! !----------------------------------------------------------------------- ! Initialize computations for new time step of the 3D primitive ! variables. !----------------------------------------------------------------------- ! CALL pre_step3d (ng, tile) ! !----------------------------------------------------------------------- ! Compute baroclinic pressure gradient. !----------------------------------------------------------------------- ! CALL prsgrd (ng, tile) # ifndef TS_FIXED # ifdef TS_DIF2 ! !----------------------------------------------------------------------- ! Compute horizontal harmonic mixing of tracer type variables. !----------------------------------------------------------------------- ! CALL t3dmix2 (ng, tile) # endif # ifdef TS_DIF4 ! !----------------------------------------------------------------------- ! Compute horizontal biharmonic mixing of tracer type variables. !----------------------------------------------------------------------- ! CALL t3dmix4 (ng, tile) # endif # endif ! !----------------------------------------------------------------------- ! Compute right-hand-side terms for the 3D momentum equations. !----------------------------------------------------------------------- ! # ifdef PROFILE CALL wclock_on (ng, iNLM, 21) # endif CALL rhs3d_tile (ng, tile, & & LBi, UBi, LBj, UBj, & & IminS, ImaxS, JminS, JmaxS, & & nrhs(ng), & & GRID(ng) % Hz, & & GRID(ng) % Huon, & & GRID(ng) % Hvom, & # if defined CURVGRID && defined UV_ADV & GRID(ng) % dmde, & & GRID(ng) % dndx, & # endif & GRID(ng) % fomn, & & GRID(ng) % om_u, & & GRID(ng) % om_v, & & GRID(ng) % on_u, & & GRID(ng) % on_v, & & GRID(ng) % pm, & & GRID(ng) % pn, & & FORCES(ng) % bustr, & & FORCES(ng) % bvstr, & & FORCES(ng) % sustr, & & FORCES(ng) % svstr, & # ifdef M3CLM_NUDGING & CLIMA(ng) % M3nudgcof, & & CLIMA(ng) % uclm, & & CLIMA(ng) % vclm, & # endif # if defined NUDGING_UVsur || defined NUDGING_UV & OBS(ng) % EobsUV, & & OBS(ng) % Uobs, & & OBS(ng) % Vobs, & # endif & OCEAN(ng) % u, & & OCEAN(ng) % v, & & OCEAN(ng) % W, & # ifdef NEARSHORE_MELLOR & OCEAN(ng) % u_stokes, & & OCEAN(ng) % v_stokes, & & OCEAN(ng) % rulag3d, & & OCEAN(ng) % rvlag3d, & & MIXING(ng) % rustr3d, & & MIXING(ng) % rvstr3d, & # endif & COUPLING(ng) % rufrc, & & COUPLING(ng) % rvfrc, & # ifdef DIAGNOSTICS_UV & DIAGS(ng) % DiaRUfrc, & & DIAGS(ng) % DiaRVfrc, & & DIAGS(ng) % DiaRU, & & DIAGS(ng) % DiaRV, & # endif & OCEAN(ng) % ru, & & OCEAN(ng) % rv) # ifdef PROFILE CALL wclock_off (ng, iNLM, 21) # endif # ifdef UV_VIS2 ! !----------------------------------------------------------------------- ! Compute horizontal, harmonic mixing of momentum. !----------------------------------------------------------------------- ! CALL uv3dmix2 (ng, tile) # endif # ifdef UV_VIS4 ! !----------------------------------------------------------------------- ! Compute horizontal, biharmonic mixing of momentum. !----------------------------------------------------------------------- ! CALL uv3dmix4 (ng, tile) # endif RETURN END SUBROUTINE rhs3d ! !*********************************************************************** SUBROUTINE rhs3d_tile (ng, tile, & & LBi, UBi, LBj, UBj, & & IminS, ImaxS, JminS, JmaxS, & & nrhs, & & Hz, Huon, Hvom, & # if defined CURVGRID && defined UV_ADV & dmde, dndx, & # endif & fomn, & & om_u, om_v, on_u, on_v, pm, pn, & & bustr, bvstr, & & sustr, svstr, & # ifdef M3CLM_NUDGING & M3nudgcof, uclm, vclm, & # endif # if defined NUDGING_UVsur || defined NUDGING_UV & EobsUV, Uobs, Vobs, & # endif & u, v, W, & # ifdef NEARSHORE_MELLOR & u_stokes, v_stokes, & & rulag3d, rvlag3d, & & rustr3d, rvstr3d, & # endif & rufrc, rvfrc, & # ifdef DIAGNOSTICS_UV & DiaRUfrc, DiaRVfrc, & & DiaRU, DiaRV, & # endif & ru, rv) !*********************************************************************** ! USE mod_param USE mod_scalars ! ! 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 ! # ifdef ASSUMED_SHAPE real(r8), intent(in) :: Hz(LBi:,LBj:,:) real(r8), intent(in) :: Huon(LBi:,LBj:,:) real(r8), intent(in) :: Hvom(LBi:,LBj:,:) # if defined CURVGRID && defined UV_ADV real(r8), intent(in) :: dmde(LBi:,LBj:) real(r8), intent(in) :: dndx(LBi:,LBj:) # endif real(r8), intent(in) :: fomn(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) :: bustr(LBi:,LBj:) real(r8), intent(in) :: bvstr(LBi:,LBj:) real(r8), intent(in) :: sustr(LBi:,LBj:) real(r8), intent(in) :: svstr(LBi:,LBj:) # ifdef M3CLM_NUDGING real(r8), intent(in) :: M3nudgcof(LBi:,LBj:) real(r8), intent(in) :: uclm(LBi:,LBj:,:) real(r8), intent(in) :: vclm(LBi:,LBj:,:) # endif # if defined NUDGING_UVsur || defined NUDGING_UV real(r8), intent(in) :: EobsUV(LBi:,LBj:,:) real(r8), intent(in) :: Uobs(LBi:,LBj:,:) real(r8), intent(in) :: Vobs(LBi:,LBj:,:) # endif real(r8), intent(in) :: u(LBi:,LBj:,:,:) real(r8), intent(in) :: v(LBi:,LBj:,:,:) real(r8), intent(in) :: W(LBi:,LBj:,0:) # ifdef NEARSHORE_MELLOR real(r8), intent(in) :: u_stokes(LBi:,LBj:,:) real(r8), intent(in) :: v_stokes(LBi:,LBj:,:) real(r8), intent(in) :: rulag3d(LBi:,LBj:,:) real(r8), intent(in) :: rvlag3d(LBi:,LBj:,:) real(r8), intent(in) :: rustr3d(LBi:,LBj:,:) real(r8), intent(in) :: rvstr3d(LBi:,LBj:,:) # endif real(r8), intent(inout) :: ru(LBi:,LBj:,0:,:) real(r8), intent(inout) :: rv(LBi:,LBj:,0:,:) # ifdef DIAGNOSTICS_UV real(r8), intent(inout) :: DiaRUfrc(LBi:,LBj:,:,:) real(r8), intent(inout) :: DiaRVfrc(LBi:,LBj:,:,:) real(r8), intent(inout) :: DiaRU(LBi:,LBj:,:,:,:) real(r8), intent(inout) :: DiaRV(LBi:,LBj:,:,:,:) # endif real(r8), intent(out) :: rufrc(LBi:,LBj:) real(r8), intent(out) :: rvfrc(LBi:,LBj:) # else 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)) # if defined CURVGRID && defined UV_ADV real(r8), intent(in) :: dmde(LBi:UBi,LBj:UBj) real(r8), intent(in) :: dndx(LBi:UBi,LBj:UBj) # endif real(r8), intent(in) :: fomn(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) :: bustr(LBi:UBi,LBj:UBj) real(r8), intent(in) :: bvstr(LBi:UBi,LBj:UBj) real(r8), intent(in) :: sustr(LBi:UBi,LBj:UBj) real(r8), intent(in) :: svstr(LBi:UBi,LBj:UBj) # ifdef M3CLM_NUDGING real(r8), intent(in) :: M3nudgcof(LBi:UBi,LBj:UBj) real(r8), intent(in) :: uclm(LBi:UBi,LBj:UBj,N(ng)) real(r8), intent(in) :: vclm(LBi:UBi,LBj:UBj,N(ng)) # endif # if defined NUDGING_UVsur || defined NUDGING_UV real(r8), intent(in) :: EobsUV(LBi:UBi,LBj:UBj,N(ng)) real(r8), intent(in) :: Uobs(LBi:UBi,LBj:UBj,N(ng)) real(r8), intent(in) :: Vobs(LBi:UBi,LBj:UBj,N(ng)) # endif real(r8), intent(in) :: u(LBi:UBi,LBj:UBj,N(ng),2) real(r8), intent(in) :: v(LBi:UBi,LBj:UBj,N(ng),2) real(r8), intent(in) :: W(LBi:UBi,LBj:UBj,0:N(ng)) # ifdef NEARSHORE_MELLOR real(r8), intent(in) :: u_stokes(LBi:UBi,LBj:UBj,N(ng)) real(r8), intent(in) :: v_stokes(LBi:UBi,LBj:UBj,N(ng)) real(r8), intent(in) :: rulag3d(LBi:UBi,LBj:UBj,N(ng)) real(r8), intent(in) :: rvlag3d(LBi:UBi,LBj:UBj,N(ng)) real(r8), intent(in) :: rustr3d(LBi:UBi,LBj:UBj,N(ng)) real(r8), intent(in) :: rvstr3d(LBi:UBi,LBj:UBj,N(ng)) # endif real(r8), intent(inout) :: ru(LBi:UBi,LBj:UBj,0:N(ng),2) real(r8), intent(inout) :: rv(LBi:UBi,LBj:UBj,0:N(ng),2) # ifdef DIAGNOSTICS_UV real(r8), intent(inout) :: DiaRUfrc(LBi:UBi,LBj:UBj,3,NDM2d-1) real(r8), intent(inout) :: DiaRVfrc(LBi:UBi,LBj:UBj,3,NDM2d-1) 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(out) :: rufrc(LBi:UBi,LBj:UBj) real(r8), intent(out) :: rvfrc(LBi:UBi,LBj:UBj) # 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, j, k real(r8), parameter :: Gadv = -0.25_r8 real(r8) :: cff, cff1, cff2, cff3, cff4 real(r8) :: fac, fac1, fac2 real(r8), dimension(IminS:ImaxS,0:N(ng)) :: CF real(r8), dimension(IminS:ImaxS,0:N(ng)) :: DC real(r8), dimension(IminS:ImaxS,0:N(ng)) :: FC real(r8), dimension(IminS:ImaxS,JminS:JmaxS) :: Huee real(r8), dimension(IminS:ImaxS,JminS:JmaxS) :: Huxx real(r8), dimension(IminS:ImaxS,JminS:JmaxS) :: Hvee real(r8), dimension(IminS:ImaxS,JminS:JmaxS) :: Hvxx real(r8), dimension(IminS:ImaxS,JminS:JmaxS) :: UFx real(r8), dimension(IminS:ImaxS,JminS:JmaxS) :: UFe real(r8), dimension(IminS:ImaxS,JminS:JmaxS) :: Uwrk real(r8), dimension(IminS:ImaxS,JminS:JmaxS) :: VFx real(r8), dimension(IminS:ImaxS,JminS:JmaxS) :: VFe real(r8), dimension(IminS:ImaxS,JminS:JmaxS) :: Vwrk real(r8), dimension(IminS:ImaxS,JminS:JmaxS) :: uee real(r8), dimension(IminS:ImaxS,JminS:JmaxS) :: uxx real(r8), dimension(IminS:ImaxS,JminS:JmaxS) :: vee real(r8), dimension(IminS:ImaxS,JminS:JmaxS) :: vxx real(r8), dimension(IminS:ImaxS,JminS:JmaxS) :: wrk # include "set_bounds.h" # ifdef BODYFORCE ! !----------------------------------------------------------------------- ! Apply surface stress as a bodyforce: determine the thickness (m) ! of the surface layer; then add in surface stress as a bodyfoce. !----------------------------------------------------------------------- ! # ifdef DIAGNOSTICS_UV DO k=1,N(ng) DO j=Jstr,Jend DO i=Istr,Iend DiaRU(i,j,k,M3vvis)=0.0_r8 DiaRV(i,j,k,M3vvis)=0.0_r8 END DO END DO END DO DO j=Jstr,Jend DO i=IstrU,Iend DiaRUfrc(i,j,3,M2sstr)=0.0_r8 DiaRUfrc(i,j,3,M2bstr)=0.0_r8 END DO END DO DO j=JstrV,Jend DO i=Istr,Iend DiaRVfrc(i,j,3,M2sstr)=0.0_r8 DiaRVfrc(i,j,3,M2bstr)=0.0_r8 END DO END DO # endif DO j=JstrV-1,Jend DO i=IstrU-1,Iend wrk(i,j)=0.0_r8 END DO END DO DO k=N(ng),levsfrc(ng),-1 DO j=JstrV-1,Jend DO i=IstrU-1,Iend wrk(i,j)=wrk(i,j)+Hz(i,j,k) END DO END DO END DO DO j=Jstr,Jend DO i=IstrU,Iend cff=0.25_r8*(pm(i-1,j)+pm(i,j))* & & (pn(i-1,j)+pn(i,j)) cff1=1.0_r8/(cff*(wrk(i-1,j)+wrk(i,j))) Uwrk(i,j)=sustr(i,j)*cff1 END DO END DO DO j=JstrV,Jend DO i=Istr,Iend cff=0.25*(pm(i,j-1)+pm(i,j))* & & (pn(i,j-1)+pn(i,j)) cff1=1.0_r8/(cff*(wrk(i,j-1)+wrk(i,j))) Vwrk(i,j)=svstr(i,j)*cff1 END DO END DO DO k=levsfrc(ng),N(ng) DO j=Jstr,Jend DO i=IstrU,Iend cff=Uwrk(i,j)*(Hz(i ,j,k)+ & & Hz(i-1,j,k)) ru(i,j,k,nrhs)=ru(i,j,k,nrhs)+cff # ifdef DIAGNOSTICS_UV DiaRU(i,j,k,nrhs,M3vvis)=DiaRU(i,j,k,nrhs,M3vvis)+cff DiaRUfrc(i,j,3,M2sstr)=DiaRUfrc(i,j,3,M2sstr)+cff # endif END DO END DO DO j=JstrV,Jend DO i=Istr,Iend cff=Vwrk(i,j)*(Hz(i,j ,k)+ & & Hz(i,j-1,k)) rv(i,j,k,nrhs)=rv(i,j,k,nrhs)+cff # ifdef DIAGNOSTICS_UV DiaRV(i,j,k,nrhs,M3vvis)=DiaRV(i,j,k,nrhs,M3vvis)+cff DiaRVfrc(i,j,3,M2sstr)=DiaRVfrc(i,j,3,M2sstr)+cff # endif END DO END DO END DO ! ! Apply bottom stress as a bodyforce: determine the thickness (m) ! of the bottom layer; then add in bottom stress as a bodyfoce. ! DO j=JstrV-1,Jend DO i=IstrU-1,Iend wrk(i,j)=0.0_r8 END DO END DO DO k=1,levbfrc(ng) DO j=JstrV-1,Jend DO i=IstrU-1,Iend wrk(i,j)=wrk(i,j)+Hz(i,j,k) END DO END DO END DO DO j=Jstr,Jend DO i=IstrU,Iend cff=0.25_r8*(pm (i-1,j)+pm (i,j))* & & (pn (i-1,j)+pn (i,j)) cff1=1.0_r8/(cff*(wrk(i-1,j)+wrk(i,j))) Uwrk(i,j)=bustr(i,j)*cff1 END DO END DO DO j=JstrV,Jend DO i=Istr,Iend cff=0.25_r8*(pm (i,j-1)+pm (i,j))* & & (pn (i,j-1)+pn (i,j)) cff1=1.0_r8/(cff*(wrk(i,j-1)+wrk(i,j))) Vwrk(i,j)=bvstr(i,j)*cff1 END DO END DO DO k=1,levbfrc(ng) DO j=Jstr,Jend DO i=IstrU,Iend cff=Uwrk(i,j)*(Hz(i ,j,k)+ & & Hz(i-1,j,k)) ru(i,j,k,nrhs)=ru(i,j,k,nrhs)-cff # ifdef DIAGNOSTICS_UV DiaRU(i,j,k,nrhs,M3vvis)=DiaRU(i,j,k,nrhs,M3vvis)-cff DiaRUfrc(i,j,3,M2bstr)=DiaRUfrc(i,j,3,M2bstr)-cff # endif END DO END DO DO j=JstrV,Jend DO i=Istr,Iend cff=Vwrk(i,j)*(Hz(i,j ,k)+ & & Hz(i,j-1,k)) rv(i,j,k,nrhs)=rv(i,j,k,nrhs)-cff # ifdef DIAGNOSTICS_UV DiaRV(i,j,k,nrhs,M3vvis)=DiaRV(i,j,k,nrhs,M3vvis)-cff DiaRVfrc(i,j,3,M2bstr)=DiaRVfrc(i,j,3,M2bstr)-cff # endif END DO END DO END DO # endif ! K_LOOP : DO k=1,N(ng) # if defined UV_COR || (defined CURVGRID && defined UV_ADV) ! !----------------------------------------------------------------------- ! Add in Coriolis and curvilinear transformation terms, if any. !----------------------------------------------------------------------- ! DO j=JstrV-1,Jend DO i=IstrU-1,Iend cff=0.5_r8*Hz(i,j,k)*( & # ifdef UV_COR & fomn(i,j) & # endif # if (defined CURVGRID && defined UV_ADV) & +0.5_r8*((v(i,j ,k,nrhs)+ & # ifdef NEARSHORE_MELLOR & v_stokes(i,j ,k)+ & & v_stokes(i,j+1,k)+ & # endif & v(i,j+1,k,nrhs))*dndx(i,j)- & & (u(i ,j,k,nrhs)+ & # ifdef NEARSHORE_MELLOR & u_stokes(i ,j,k)+ & & u_stokes(i+1,j,k)+ & # endif & u(i+1,j,k,nrhs))*dmde(i,j)) & # endif & ) UFx(i,j)=cff*(v(i,j ,k,nrhs)+ & # ifdef NEARSHORE_MELLOR & v_stokes(i,j ,k)+ & & v_stokes(i,j+1,k)+ & # endif & v(i,j+1,k,nrhs)) VFe(i,j)=cff*(u(i ,j,k,nrhs)+ & # ifdef NEARSHORE_MELLOR & u_stokes(i ,j,k)+ & & u_stokes(i+1,j,k)+ & # endif & u(i+1,j,k,nrhs)) # ifdef DIAGNOSTICS_UV # ifdef UV_COR Uwrk(i,j)=0.5_r8*Hz(i,j,k)*fomn(i,j)* & & (v(i,j ,k,nrhs)+ & # ifdef NEARSHORE_MELLOR & v_stokes(i,j ,k)+ & & v_stokes(i,j+1,k)+ & # endif & v(i,j+1,k,nrhs)) Vwrk(i,j)=0.5_r8*Hz(i,j,k)*fomn(i,j)* & & (u(i ,j,k,nrhs)+ & # ifdef NEARSHORE_MELLOR & u_stokes(i ,j,k)+ & & u_stokes(i+1,j,k)+ & # endif & u(i+1,j,k,nrhs)) # else Uwrk(i,j)=0.0_r8 Vwrk(i,j)=0.0_r8 # endif # endif END DO END DO DO j=Jstr,Jend DO i=IstrU,Iend cff1=0.5_r8*(UFx(i,j)+UFx(i-1,j)) ru(i,j,k,nrhs)=ru(i,j,k,nrhs)+cff1 # ifdef DIAGNOSTICS_UV cff2=0.5_r8*(Uwrk(i,j)+Uwrk(i-1,j)) # ifdef UV_COR DiaRU(i,j,k,nrhs,M3fcor)=cff2 # endif # if defined UV_ADV && defined CURVGRID DiaRU(i,j,k,nrhs,M3hadv)=cff1-cff2 # endif # endif END DO END DO DO j=JstrV,Jend DO i=Istr,Iend cff1=0.5_r8*(VFe(i,j)+VFe(i,j-1)) rv(i,j,k,nrhs)=rv(i,j,k,nrhs)-cff1 # ifdef DIAGNOSTICS_UV cff2=0.5_r8*(Vwrk(i,j)+Vwrk(i,j-1)) # ifdef UV_COR DiaRV(i,j,k,nrhs,M3fcor)=-cff2 # endif # if defined UV_ADV && defined CURVGRID DiaRV(i,j,k,nrhs,M3hadv)=-cff1+cff2 # endif # endif END DO END DO # endif # ifdef M3CLM_NUDGING ! !----------------------------------------------------------------------- ! Add in nudging of 3D momentum climatology. !----------------------------------------------------------------------- ! DO j=Jstr,Jend DO i=IstrU,Iend cff=0.25_r8*(M3nudgcof(i-1,j)+M3nudgcof(i,j))* & & om_u(i,j)*on_u(i,j) ru(i,j,k,nrhs)=ru(i,j,k,nrhs)+ & & cff*(Hz(i-1,j,k)+Hz(i,j,k))* & & (uclm(i,j,k)-u(i,j,k,nrhs)) END DO END DO DO j=JstrV,Jend DO i=Istr,Iend cff=0.25_r8*(M3nudgcof(i,j-1)+M3nudgcof(i,j))* & & om_v(i,j)*on_v(i,j) rv(i,j,k,nrhs)=rv(i,j,k,nrhs)+ & & cff*(Hz(i,j-1,k)+Hz(i,j,k))* & & (vclm(i,j,k)-v(i,j,k,nrhs)) END DO END DO # endif # if defined NUDGING_UVsur || defined NUDGING_UV ! !----------------------------------------------------------------------- ! Assimilate horizontal currents observations via nudging. !----------------------------------------------------------------------- ! ! Notice that the nondimensional error variance "EobsUV" is flipped, ! so a value of unity represents unavailable data. ! IF (update_UV(ng)) THEN DO j=Jstr,Jend DO i=IstrU,Iend cff=MIN(1.0_r8,MAX(0.0_r8,0.5_r8*(EobsUV(i-1,j,k)+ & & EobsUV(i ,j,k)))) cff=M3nudass(ng)*(1.0_r8-cff) ru(i,j,k,nrhs)=ru(i,j,k,nrhs)+ & & cff*0.5_r8*(Hz(i,j,k)+Hz(i-1,j,k))* & & (Uobs(i,j,k)-u(i,j,k,nrhs))* & & om_u(i,j)*on_u(i,j) END DO END DO DO j=JstrV,Jend DO i=Istr,Iend cff=MIN(1.0_r8,MAX(0.0_r8,0.5_r8*(EobsUV(i,j-1,k)+ & & EobsUV(i,j ,k)))) cff=M3nudass(ng)*(1.0_r8-cff) rv(i,j,k,nrhs)=rv(i,j,k,nrhs)+ & & cff*0.5_r8*(Hz(i,j-1,k)+Hz(i,j,k))* & & (Vobs(i,j,k)-v(i,j,k,nrhs))* & & om_v(i,j)*on_v(i,j) END DO END DO END IF # endif # ifdef UV_ADV ! !----------------------------------------------------------------------- ! Add in horizontal advection of momentum. !----------------------------------------------------------------------- ! ! Compute diagonal [UFx,VFe] and off-diagonal [UFe,VFx] components ! of tensor of momentum flux due to horizontal advection. ! # ifdef UV_C2ADVECTION ! ! Second-order, centered differences advection. ! DO j=Jstr,Jend DO i=IstrU-1,Iend UFx(i,j)=0.25_r8*(u(i ,j,k,nrhs)+ & # ifdef NEARSHORE_MELLOR & u_stokes(i ,j,k)+ & & u_stokes(i+1,j,k)+ & # endif & u(i+1,j,k,nrhs))* & & (Huon(i ,j,k)+ & & Huon(i+1,j,k)) END DO END DO DO j=Jstr,Jend+1 DO i=IstrU,Iend UFe(i,j)=0.25_r8*(u(i,j-1,k,nrhs)+ & # ifdef NEARSHORE_MELLOR & u_stokes(i,j-1,k)+ & & u_stokes(i,j ,k)+ & # endif & u(i,j ,k,nrhs))* & & (Hvom(i-1,j,k)+ & & Hvom(i ,j,k)) END DO END DO DO j=JstrV,Jend DO i=Istr,Iend+1 VFx(i,j)=0.25_r8*(v(i-1,j,k,nrhs)+ & # ifdef NEARSHORE_MELLOR & v_stokes(i-1,j,k)+ & & v_stokes(i ,j,k)+ & # endif & v(i ,j,k,nrhs))* & & (Huon(i,j-1,k)+ & & Huon(i,j ,k)) END DO END DO DO j=JstrV-1,Jend DO i=Istr,Iend VFe(i,j)=0.25_r8*(v(i,j ,k,nrhs)+ & # ifdef NEARSHORE_MELLOR & v_stokes(i,j ,k)+ & & v_stokes(i,j+1,k)+ & # endif & v(i,j+1,k,nrhs))* & & (Hvom(i,j ,k)+ & & Hvom(i,j+1,k)) END DO END DO # else # ifdef EW_PERIODIC # define IU_RANGE IstrU-1,Iend+1 # else # define IU_RANGE MAX(IstrU-1,2),MIN(Iend+1,Lm(ng)) # endif DO j=Jstr,Jend DO i=IU_RANGE uxx(i,j)=u(i-1,j,k,nrhs)-2.0_r8*u(i,j,k,nrhs)+ & # ifdef NEARSHORE_MELLOR & u_stokes(i-1,j,k)-2.0_r8*u_stokes(i,j,k)+ & & u_stokes(i+1,j,k)+ & # endif & u(i+1,j,k,nrhs) Huxx(i,j)=Huon(i-1,j,k)-2.0_r8*Huon(i,j,k)+Huon(i+1,j,k) END DO END DO # undef IU_RANGE # ifndef EW_PERIODIC IF (WESTERN_EDGE) THEN DO j=Jstr,Jend uxx (Istr,j)=uxx (Istr+1,j) Huxx(Istr,j)=Huxx(Istr+1,j) END DO END IF IF (EASTERN_EDGE) THEN DO j=Jstr,Jend uxx (Iend+1,j)=uxx (Iend,j) Huxx(Iend+1,j)=Huxx(Iend,j) END DO END IF # endif # ifdef UV_C4ADVECTION ! ! Fourth-order, centered differences u-momentum horizontal advection. ! cff=1.0_r8/6.0_r8 DO j=Jstr,Jend DO i=IstrU-1,Iend UFx(i,j)=0.25_r8*(u(i ,j,k,nrhs)+ & # ifdef NEARSHORE_MELLOR & u_stokes(i ,j,k)+ & & u_stokes(i+1,j,k)+ & # endif & u(i+1,j,k,nrhs)- & & cff*(uxx (i ,j)+ & & uxx (i+1,j)))* & & (Huon(i ,j,k)+ & & Huon(i+1,j,k)- & & cff*(Huxx(i ,j)+ & & Huxx(i+1,j))) END DO END DO # else ! ! Third-order, upstream bias u-momentum advection with velocity ! dependent hyperdiffusion. ! DO j=Jstr,Jend DO i=IstrU-1,Iend cff1=u(i ,j,k,nrhs)+ & # ifdef NEARSHORE_MELLOR & u_stokes(i ,j,k)+ & & u_stokes(i+1,j,k)+ & # endif & u(i+1,j,k,nrhs) IF (cff1.gt.0.0_r8) THEN cff=uxx(i,j) ELSE cff=uxx(i+1,j) END IF UFx(i,j)=0.25_r8*(cff1+Gadv*cff)* & & (Huon(i ,j,k)+ & & Huon(i+1,j,k)+ & & Gadv*0.5_r8*(Huxx(i ,j)+ & & Huxx(i+1,j))) END DO END DO # endif # ifdef NS_PERIODIC # define JU_RANGE Jstr-1,Jend+1 # else # define JU_RANGE MAX(Jstr-1,1),MIN(Jend+1,Mm(ng)) # endif DO j=JU_RANGE DO i=IstrU,Iend uee(i,j)=u(i,j-1,k,nrhs)-2.0_r8*u(i,j,k,nrhs)+ & # ifdef NEARSHORE_MELLOR & u_stokes(i,j-1,k)-2.0_r8*u_stokes(i,j,k)+ & & u_stokes(i,j+1,k)+ & # endif & u(i,j+1,k,nrhs) END DO END DO # undef JU_RANGE # ifndef NS_PERIODIC IF (SOUTHERN_EDGE) THEN DO i=IstrU,Iend uee(i,Jstr-1)=uee(i,Jstr) END DO END IF IF (NORTHERN_EDGE) THEN DO i=IstrU,Iend uee(i,Jend+1)=uee(i,Jend) END DO END IF # endif DO j=Jstr,Jend+1 DO i=IstrU-1,Iend Hvxx(i,j)=Hvom(i-1,j,k)-2.0_r8*Hvom(i,j,k)+Hvom(i+1,j,k) END DO END DO # ifdef UV_C4ADVECTION cff=1.0_r8/6.0_r8 DO j=Jstr,Jend+1 DO i=IstrU,Iend UFe(i,j)=0.25_r8*(u(i,j ,k,nrhs)+ & # ifdef NEARSHORE_MELLOR & u_stokes(i,j ,k)+ & & u_stokes(i,j-1,k)+ & # endif & u(i,j-1,k,nrhs)- & & cff*(uee (i,j )+ & & uee (i,j-1)))* & & (Hvom(i ,j,k)+ & & Hvom(i-1,j,k)- & & cff*(Hvxx(i ,j)+ & & Hvxx(i-1,j))) END DO END DO # else DO j=Jstr,Jend+1 DO i=IstrU,Iend cff1=u(i,j ,k,nrhs)+ & # ifdef NEARSHORE_MELLOR & u_stokes(i,j ,k)+ & & u_stokes(i,j-1,k)+ & # endif & u(i,j-1,k,nrhs) cff2=Hvom(i,j,k)+Hvom(i-1,j,k) IF (cff2.gt.0.0_r8) THEN cff=uee(i,j-1) ELSE cff=uee(i,j) END IF UFe(i,j)=0.25_r8*(cff1+Gadv*cff)* & & (cff2+Gadv*0.5_r8*(Hvxx(i ,j)+ & & Hvxx(i-1,j))) END DO END DO # endif # ifdef EW_PERIODIC # define IV_RANGE Istr-1,Iend+1 # else # define IV_RANGE MAX(Istr-1,1),MIN(Iend+1,Lm(ng)) # endif DO j=JstrV,Jend DO i=IV_RANGE vxx(i,j)=v(i-1,j,k,nrhs)-2.0_r8*v(i,j,k,nrhs)+ & # ifdef NEARSHORE_MELLOR & v_stokes(i-1,j,k)-2.0_r8*v_stokes(i,j,k)+ & & v_stokes(i+1,j,k)+ & # endif & v(i+1,j,k,nrhs) END DO END DO # undef IV_RANGE # ifndef EW_PERIODIC IF (WESTERN_EDGE) THEN DO j=JstrV,Jend vxx(Istr-1,j)=vxx(Istr,j) END DO END IF IF (EASTERN_EDGE) THEN DO j=JstrV,Jend vxx(Iend+1,j)=vxx(Iend,j) END DO END IF # endif DO j=JstrV-1,Jend DO i=Istr,Iend+1 Huee(i,j)=Huon(i,j-1,k)-2.0_r8*Huon(i,j,k)+Huon(i,j+1,k) END DO END DO # ifdef UV_C4ADVECTION ! ! Fourth-order, centered differences v-momentum horizontal advection. ! cff=1.0_r8/6.0_r8 DO j=JstrV,Jend DO i=Istr,Iend+1 VFx(i,j)=0.25_r8*(v(i ,j,k,nrhs)+ & # ifdef NEARSHORE_MELLOR & v_stokes(i ,j,k)+ & & v_stokes(i-1,j,k)+ & # endif & v(i-1,j,k,nrhs)- & & cff*(vxx (i ,j)+ & & vxx (i-1,j)))* & & (Huon(i,j ,k)+ & & Huon(i,j-1,k)- & & cff*(Huee(i,j )+ & & Huee(i,j-1))) END DO END DO # else ! ! Third-order, upstream bias v-momentum advection with velocity ! dependent hyperdiffusion. ! DO j=JstrV,Jend DO i=Istr,Iend+1 cff1=v(i ,j,k,nrhs)+ & # ifdef NEARSHORE_MELLOR & v_stokes(i ,j,k)+ & & v_stokes(i-1,j,k)+ & # endif & v(i-1,j,k,nrhs) cff2=Huon(i,j,k)+Huon(i,j-1,k) IF (cff2.gt.0.0_r8) THEN cff=vxx(i-1,j) ELSE cff=vxx(i,j) END IF VFx(i,j)=0.25_r8*(cff1+Gadv*cff)* & & (cff2+Gadv*0.5_r8*(Huee(i,j )+ & & Huee(i,j-1))) END DO END DO # endif # ifdef NS_PERIODIC # define JV_RANGE JstrV-1,Jend+1 # else # define JV_RANGE MAX(JstrV-1,2),MIN(Jend+1,Mm(ng)) # endif DO j=JV_RANGE DO i=Istr,Iend vee(i,j)=v(i,j-1,k,nrhs)-2.0_r8*v(i,j,k,nrhs)+ & # ifdef NEARSHORE_MELLOR & v_stokes(i,j-1,k)-2.0_r8*v_stokes(i,j,k)+ & & v_stokes(i,j+1,k)+ & # endif & v(i,j+1,k,nrhs) Hvee(i,j)=Hvom(i,j-1,k)-2.0_r8*Hvom(i,j,k)+Hvom(i,j+1,k) END DO END DO # undef JV_RANGE # ifndef NS_PERIODIC IF (SOUTHERN_EDGE) THEN DO i=Istr,Iend vee (i,Jstr)=vee (i,Jstr+1) Hvee(i,Jstr)=Hvee(i,Jstr+1) END DO END IF IF (NORTHERN_EDGE) THEN DO i=Istr,Iend vee (i,Jend+1)=vee (i,Jend) Hvee(i,Jend+1)=Hvee(i,Jend) END DO END IF # endif # ifdef UV_C4ADVECTION cff=1.0_r8/6.0_r8 DO j=JstrV-1,Jend DO i=Istr,Iend VFe(i,j)=0.25_r8*(v(i,j ,k,nrhs)+ & # ifdef NEARSHORE_MELLOR & v_stokes(i,j ,k)+ & & v_stokes(i,j+1,k)+ & # endif & v(i,j+1,k,nrhs)- & & cff*(vee (i,j )+ & & vee (i,j+1)))* & & (Hvom(i,j ,k)+ & & Hvom(i,j+1,k)- & & cff*(Hvee(i,j )+ & & Hvee(i,j+1))) END DO END DO # else DO j=JstrV-1,Jend DO i=Istr,Iend cff1=v(i,j ,k,nrhs)+ & # ifdef NEARSHORE_MELLOR & v_stokes(i,j ,k)+ & & v_stokes(i,j+1,k)+ & # endif & v(i,j+1,k,nrhs) IF (cff1.gt.0.0_r8) THEN cff=vee(i,j) ELSE cff=vee(i,j+1) END IF VFe(i,j)=0.25_r8*(cff1+Gadv*cff)* & & (Hvom(i,j ,k)+ & & Hvom(i,j+1,k)+ & & Gadv*0.5_r8*(Hvee(i,j )+ & & Hvee(i,j+1))) END DO END DO # endif # endif ! ! Add in horizontal advection. ! DO j=Jstr,Jend DO i=IstrU,Iend cff=UFx(i,j)-UFx(i-1,j)+ & & UFe(i,j+1)-UFe(i,j) ru(i,j,k,nrhs)=ru(i,j,k,nrhs)-cff # ifdef DIAGNOSTICS_UV # ifdef CURVGRID DiaRU(i,j,k,nrhs,M3hadv)=DiaRU(i,j,k,nrhs,M3hadv)-cff # else DiaRU(i,j,k,nrhs,M3hadv)=-cff # endif # endif END DO END DO DO j=JstrV,Jend DO i=Istr,Iend cff=VFx(i+1,j)-VFx(i,j)+ & & VFe(i,j)-VFe(i,j-1) rv(i,j,k,nrhs)=rv(i,j,k,nrhs)-cff # ifdef DIAGNOSTICS_UV # ifdef CURVGRID DiaRV(i,j,k,nrhs,M3hadv)=DiaRV(i,j,k,nrhs,M3hadv)-cff # else DiaRV(i,j,k,nrhs,M3hadv)=-cff # endif # endif END DO END DO # endif # ifdef NEARSHORE_MELLOR ! !----------------------------------------------------------------------- ! Add in radiation stress terms. Convert stresses to m4/s2. !----------------------------------------------------------------------- ! DO j=Jstr,Jend DO i=IstrU,Iend ru(i,j,k,nrhs)=ru(i,j,k,nrhs)- & & rustr3d(i,j,k)*om_u(i,j)*on_u(i,j)- & & rulag3d(i,j,k) END DO END DO DO j=JstrV,Jend DO i=Istr,Iend rv(i,j,k,nrhs)=rv(i,j,k,nrhs)- & & rvstr3d(i,j,k)*om_v(i,j)*on_v(i,j)- & & rvlag3d(i,j,k) END DO END DO # endif END DO K_LOOP ! J_LOOP : DO j=Jstr,Jend # ifdef UV_ADV ! !----------------------------------------------------------------------- ! Add in vertical advection. !----------------------------------------------------------------------- ! # ifdef UV_SADVECTION ! ! Construct conservative parabolic splines for the vertical ! derivatives "CF" of u-momentum. ! cff1=9.0_r8/16.0_r8 cff2=1.0_r8/16.0_r8 DO k=1,N(ng) DO i=IstrU,Iend DC(i,k)=cff1*(Hz(i ,j,k)+ & & Hz(i-1,j,k))- & & cff2*(Hz(i+1,j,k)+ & & Hz(i-2,j,k)) END DO END DO DO i=IstrU,Iend FC(i,0)=0.0_r8 CF(i,0)=0.0_r8 END DO DO k=1,N(ng)-1 DO i=IstrU,Iend cff=1.0_r8/(2.0_r8*DC(i,k+1)+DC(i,k)*(2.0_r8-FC(i,k-1))) FC(i,k)=cff*DC(i,k+1) CF(i,k)=cff*(6.0_r8*(u(i,j,k+1,nrhs)- & # ifdef NEARSHORE_MELLOR & u_stokes(i,j,k )+ & & u_stokes(i,j,k+1)- & # endif & u(i,j,k ,nrhs))- & & DC(i,k)*CF(i,k-1)) END DO END DO DO i=IstrU,Iend CF(i,N(ng))=0.0_r8 END DO DO k=N(ng)-1,1,-1 DO i=IstrU,Iend CF(i,k)=CF(i,k)-FC(i,k)*CF(i,k+1) END DO END DO ! ! Compute spline-interpolated, vertical advective u-momentum flux. ! cff3=1.0_r8/3.0_r8 cff4=1.0_r8/6.0_r8 DO k=1,N(ng)-1 DO i=IstrU,Iend FC(i,k)=(cff1*(W(i ,j,k)+ & & W(i-1,j,k))- & & cff2*(W(i+1,j,k)+ & & W(i-2,j,k)))* & & (u(i,j,k,nrhs)+ & # ifdef NEARSHORE_MELLOR & u_stokes(i,j,k)+ & # endif & DC(i,k)*(cff3*CF(i,k )+ & & cff4*CF(i,k-1))) END DO END DO DO i=IstrU,Iend FC(i,N(ng))=0.0_r8 FC(i,0)=0.0_r8 END DO # elif defined UV_C2ADVECTION DO k=1,N(ng)-1 DO i=IstrU,Iend FC(i,k)=0.25_r8*(u(i,j,k ,nrhs)+ & # ifdef NEARSHORE_MELLOR & u_stokes(i,j,k )+ & & u_stokes(i,j,k+1)+ & # endif & u(i,j,k+1,nrhs))* & & (W(i ,j,k)+ & & W(i-1,j,k)) END DO END DO DO i=IstrU,Iend # ifdef SED_MORPH # ifdef NEARSHORE_MELLOR FC(i,0)=0.5_r8*(u(i,j,1,nrhs)+u_stokes(i,j,1))* & & (W(i ,j,0)+ & & W(i-1,j,0)) # else FC(i,0)=0.5_r8*u(i,j,1,nrhs)* & & (W(i ,j,0)+ & & W(i-1,j,0)) # endif # else FC(i,0)=0.0_r8 # endif FC(i,N(ng))=0.0_r8 END DO # elif defined UV_C4ADVECTION cff1=9.0_r8/32.0_r8 cff2=1.0_r8/32.0_r8 DO k=2,N(ng)-2 DO i=IstrU,Iend FC(i,k)=(cff1*(u(i,j,k ,nrhs)+ & # ifdef NEARSHORE_MELLOR & u_stokes(i,j,k )+ & & u_stokes(i,j,k+1)+ & # endif & u(i,j,k+1,nrhs))- & & cff2*(u(i,j,k-1,nrhs)+ & # ifdef NEARSHORE_MELLOR & u_stokes(i,j,k-1)+ & & u_stokes(i,j,k+2)+ & # endif & u(i,j,k+2,nrhs)))* & & (W(i ,j,k)+ & & W(i-1,j,k)) END DO END DO DO i=IstrU,Iend FC(i,N(ng))=0.0_r8 FC(i,N(ng)-1)=(cff1*(u(i,j,N(ng)-1,nrhs)+ & # ifdef NEARSHORE_MELLOR & u_stokes(i,j,N(ng)-1)+ & & u_stokes(i,j,N(ng) )+ & # endif & u(i,j,N(ng) ,nrhs))- & & cff2*(u(i,j,N(ng)-2,nrhs)+ & # ifdef NEARSHORE_MELLOR & u_stokes(i,j,N(ng)-2)+ & & u_stokes(i,j,N(ng) )+ & # endif & u(i,j,N(ng) ,nrhs)))* & & (W(i ,j,N(ng)-1)+ & & W(i-1,j,N(ng)-1)) FC(i,1)=(cff1*(u(i,j,1,nrhs)+ & # ifdef NEARSHORE_MELLOR & u_stokes(i,j,1)+ & & u_stokes(i,j,2)+ & # endif & u(i,j,2,nrhs))- & & cff2*(u(i,j,1,nrhs)+ & # ifdef NEARSHORE_MELLOR & u_stokes(i,j,1)+ & & u_stokes(i,j,3)+ & # endif & u(i,j,3,nrhs)))* & & (W(i ,j,1)+ & & W(i-1,j,1)) # ifdef SED_MORPH # ifdef NEARSHORE_MELLOR FC(i,0)=2.0_r8* & & (cff1*(u(i,j,1,nrhs)+u_stokes(i,j,1))- & & cff2*(u(i,j,2,nrhs)+u_stokes(i,j,2)))* & & (W(i ,j,0)+ & & W(i-1,j,0)) # else FC(i,0)=2.0_r8* & & (cff1*u(i,j,1,nrhs)- & & cff2*u(i,j,2,nrhs))* & & (W(i ,j,0)+ & & W(i-1,j,0)) # endif # else FC(i,0)=0.0_r8 # endif END DO # else cff1=9.0_r8/16.0_r8 cff2=1.0_r8/16.0_r8 DO k=2,N(ng)-2 DO i=IstrU,Iend FC(i,k)=(cff1*(u(i,j,k ,nrhs)+ & # ifdef NEARSHORE_MELLOR & u_stokes(i,j,k )+ & & u_stokes(i,j,k+1)+ & # endif & u(i,j,k+1,nrhs))- & & cff2*(u(i,j,k-1,nrhs)+ & # ifdef NEARSHORE_MELLOR & u_stokes(i,j,k-1)+ & & u_stokes(i,j,k+2)+ & # endif & u(i,j,k+2,nrhs)))* & & (cff1*(W(i ,j,k)+ & & W(i-1,j,k))- & & cff2*(W(i+1,j,k)+ & & W(i-2,j,k))) END DO END DO DO i=IstrU,Iend FC(i,N(ng))=0.0_r8 FC(i,N(ng)-1)=(cff1*(u(i,j,N(ng)-1,nrhs)+ & # ifdef NEARSHORE_MELLOR & u_stokes(i,j,N(ng)-1)+ & & u_stokes(i,j,N(ng) )+ & # endif & u(i,j,N(ng) ,nrhs))- & & cff2*(u(i,j,N(ng)-2,nrhs)+ & # ifdef NEARSHORE_MELLOR & u_stokes(i,j,N(ng)-2)+ & & u_stokes(i,j,N(ng) )+ & # endif & u(i,j,N(ng) ,nrhs)))* & & (cff1*(W(i ,j,N(ng)-1)+ & & W(i-1,j,N(ng)-1))- & & cff2*(W(i+1,j,N(ng)-1)+ & & W(i-2,j,N(ng)-1))) FC(i,1)=(cff1*(u(i,j,1,nrhs)+ & # ifdef NEARSHORE_MELLOR & u_stokes(i,j,1)+ & & u_stokes(i,j,2)+ & # endif & u(i,j,2,nrhs))- & & cff2*(u(i,j,1,nrhs)+ & # ifdef NEARSHORE_MELLOR & u_stokes(i,j,1)+ & & u_stokes(i,j,3)+ & # endif & u(i,j,3,nrhs)))* & & (cff1*(W(i ,j,1)+ & & W(i-1,j,1))- & & cff2*(W(i+1,j,1)+ & & W(i-2,j,1))) # ifdef SED_MORPH # ifdef NEARSHORE_MELLOR FC(i,0)=2.0_r8* & & (cff1*(u(i,j,1,nrhs)+u_stokes(i,j,1))- & & cff2*(u(i,j,2,nrhs)+u_stokes(i,j,2)))* & & (cff1*(W(i ,j,0)+ & & W(i-1,j,0))- & & cff2*(W(i+1,j,0)+ & & W(i-2,j,0))) # else FC(i,0)=2.0_r8* & & (cff1*u(i,j,1,nrhs)- & & cff2*u(i,j,2,nrhs))* & & (cff1*(W(i ,j,0)+ & & W(i-1,j,0))- & & cff2*(W(i+1,j,0)+ & & W(i-2,j,0))) # endif # else FC(i,0)=0.0_r8 # endif END DO # endif DO k=1,N(ng) DO i=IstrU,Iend cff=FC(i,k)-FC(i,k-1) ru(i,j,k,nrhs)=ru(i,j,k,nrhs)-cff # ifdef DIAGNOSTICS_UV DiaRU(i,j,k,nrhs,M3vadv)=-cff # endif END DO END DO IF (j.ge.JstrV) THEN # ifdef UV_SADVECTION ! ! Construct conservative parabolic splines for the vertical ! derivatives "CF" of v-momentum. ! cff1=9.0_r8/16.0_r8 cff2=1.0_r8/16.0_r8 DO k=1,N(ng) DO i=Istr,Iend DC(i,k)=(cff1*(Hz(i,j ,k)+ & & Hz(i,j-1,k))- & & cff2*(Hz(i,j+1,k)+ & & Hz(i,j-2,k))) END DO END DO DO i=Istr,Iend FC(i,0)=0.0_r8 CF(i,0)=0.0_r8 END DO DO k=1,N(ng)-1 DO i=Istr,Iend cff=1.0_r8/(2.0_r8*DC(i,k+1)+DC(i,k)*(2.0_r8-FC(i,k-1))) FC(i,k)=cff*DC(i,k+1) CF(i,k)=cff*(6.0_r8*(v(i,j,k+1,nrhs)- & # ifdef NEARSHORE_MELLOR & v_stokes(i,j,k )+ & & v_stokes(i,j,k+1)- & # endif & v(i,j,k ,nrhs))- & & DC(i,k)*CF(i,k-1)) END DO END DO DO i=Istr,Iend CF(i,N(ng))=0.0_r8 END DO DO k=N(ng)-1,1,-1 DO i=Istr,Iend CF(i,k)=CF(i,k)-FC(i,k)*CF(i,k+1) END DO END DO ! ! Compute spline-interpolated, vertical advective v-momentum flux. ! cff3=1.0_r8/3.0_r8 cff4=1.0_r8/6.0_r8 DO k=1,N(ng)-1 DO i=Istr,Iend FC(i,k)=(cff1*(W(i,j ,k)+ & & W(i,j-1,k))- & & cff2*(W(i,j+1,k)+ & & W(i,j-2,k)))* & & (v(i,j,k,nrhs)+ & # ifdef NEARSHORE_MELLOR & v_stokes(i,j,k)+ & # endif & DC(i,k)*(cff3*CF(i,k )+ & & cff4*CF(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 UV_C2ADVECTION ! ! Second-order, centered differences vertical advection. ! DO k=1,N(ng)-1 DO i=Istr,Iend FC(i,k)=0.25_r8*(v(i,j,k ,nrhs)+ & # ifdef NEARSHORE_MELLOR & v_stokes(i,j,k )+ & & v_stokes(i,j,k+1)+ & # endif & v(i,j,k+1,nrhs))* & & (W(i,j ,k)+ & & W(i,j-1,k)) END DO END DO DO i=Istr,Iend # ifdef SED_MORPH # ifdef NEARSHORE_MELLOR FC(i,0)=0.5_r8*(v(i,j,1,nrhs)+v_stokes(i,j,1))* & & (W(i,j ,0)+ & & W(i,j-1,0)) # else FC(i,0)=0.5_r8*v(i,j,1,nrhs)* & & (W(i,j ,0)+ & & W(i,j-1,0)) # endif # else FC(i,0)=0.0_r8 # endif FC(i,N(ng))=0.0_r8 END DO # elif defined UV_C4ADVECTION ! ! Forth-order, centered differences vertical advection. ! cff1=9.0_r8/32.0_r8 cff2=1.0_r8/32.0_r8 DO k=2,N(ng)-2 DO i=Istr,Iend FC(i,k)=(cff1*(v(i,j,k ,nrhs)+ & # ifdef NEARSHORE_MELLOR & v_stokes(i,j,k )+ & & v_stokes(i,j,k+1)+ & # endif & v(i,j,k+1,nrhs))- & & cff2*(v(i,j,k-1,nrhs)+ & # ifdef NEARSHORE_MELLOR & v_stokes(i,j,k-1)+ & & v_stokes(i,j,k+2)+ & # endif & v(i,j,k+2,nrhs)))* & & (W(i,j ,k)+ & & W(i,j-1,k)) END DO END DO DO i=Istr,Iend FC(i,N(ng))=0.0_r8 FC(i,N(ng)-1)=(cff1*(v(i,j,N(ng)-1,nrhs)+ & # ifdef NEARSHORE_MELLOR & v_stokes(i,j,N(ng)-1)+ & & v_stokes(i,j,N(ng) )+ & # endif & v(i,j,N(ng) ,nrhs))- & & cff2*(v(i,j,N(ng)-2,nrhs)+ & # ifdef NEARSHORE_MELLOR & v_stokes(i,j,N(ng)-2)+ & & v_stokes(i,j,N(ng) )+ & # endif & v(i,j,N(ng) ,nrhs)))* & & (W(i,j ,N(ng)-1)+ & & W(i,j-1,N(ng)-1)) FC(i,1)=(cff1*(v(i,j,1,nrhs)+ & # ifdef NEARSHORE_MELLOR & v_stokes(i,j,1)+ & & v_stokes(i,j,2)+ & # endif & v(i,j,2,nrhs))- & & cff2*(v(i,j,1,nrhs)+ & # ifdef NEARSHORE_MELLOR & v_stokes(i,j,1)+ & & v_stokes(i,j,3)+ & # endif & v(i,j,3,nrhs)))* & & (W(i,j ,1)+ & & W(i,j-1,1)) # ifdef SED_MORPH # ifdef NEARSHORE_MELLOR FC(i,0)=2.0_r8* & & (cff1*(v(i,j,1,nrhs)+v_stokes(i,j,1))- & & cff2*(v(i,j,2,nrhs)+v_stokes(i,j,2)))* & & (W(i,j ,0)+ & & W(i,j-1,0)) # else FC(i,0)=2.0_r8* & & (cff1*v(i,j,1,nrhs)- & & cff2*v(i,j,2,nrhs))* & & (W(i,j ,0)+ & & W(i,j-1,0)) # endif # else FC(i,0)=0.0_r8 # endif END DO # else cff1=9.0_r8/16.0_r8 cff2=1.0_r8/16.0_r8 DO k=2,N(ng)-2 DO i=Istr,Iend FC(i,k)=(cff1*(v(i,j,k ,nrhs)+ & # ifdef NEARSHORE_MELLOR & v_stokes(i,j,k )+ & & v_stokes(i,j,k+1)+ & # endif & v(i,j,k+1,nrhs))- & & cff2*(v(i,j,k-1,nrhs)+ & # ifdef NEARSHORE_MELLOR & v_stokes(i,j,k-1)+ & & v_stokes(i,j,k+2)+ & # endif & v(i,j,k+2,nrhs)))* & & (cff1*(W(i,j ,k)+ & & W(i,j-1,k))- & & cff2*(W(i,j+1,k)+ & & W(i,j-2,k))) END DO END DO DO i=Istr,Iend FC(i,N(ng))=0.0_r8 FC(i,N(ng)-1)=(cff1*(v(i,j,N(ng)-1,nrhs)+ & # ifdef NEARSHORE_MELLOR & v_stokes(i,j,N(ng)-1)+ & & v_stokes(i,j,N(ng) )+ & # endif & v(i,j,N(ng) ,nrhs))- & & cff2*(v(i,j,N(ng)-2,nrhs)+ & # ifdef NEARSHORE_MELLOR & v_stokes(i,j,N(ng)-2)+ & & v_stokes(i,j,N(ng) )+ & # endif & v(i,j,N(ng) ,nrhs)))* & & (cff1*(W(i,j ,N(ng)-1)+ & & W(i,j-1,N(ng)-1))- & & cff2*(W(i,j+1,N(ng)-1)+ & & W(i,j-2,N(ng)-1))) FC(i,1)=(cff1*(v(i,j,1,nrhs)+ & # ifdef NEARSHORE_MELLOR & v_stokes(i,j,1)+ & & v_stokes(i,j,2)+ & # endif & v(i,j,2,nrhs))- & & cff2*(v(i,j,1,nrhs)+ & # ifdef NEARSHORE_MELLOR & v_stokes(i,j,1)+ & & v_stokes(i,j,3)+ & # endif & v(i,j,3,nrhs)))* & & (cff1*(W(i,j ,1)+ & & W(i,j-1,1))- & & cff2*(W(i,j+1,1)+ & & W(i,j-2,1))) # ifdef SED_MORPH # ifdef NEARSHORE_MELLOR FC(i,0)=2.0_r8* & & (cff1*(v(i,j,1,nrhs)+v_stokes(i,j,1))- & & cff2*(v(i,j,2,nrhs)+v_stokes(i,j,2)))* & & (cff1*(W(i,j ,0)+ & & W(i,j-1,0))- & & cff2*(W(i,j+1,0)+ & & W(i,j-2,0))) # else FC(i,0)=2.0_r8* & & (cff1*v(i,j,1,nrhs)- & & cff2*v(i,j,2,nrhs))* & & (cff1*(W(i,j ,0)+ & & W(i,j-1,0))- & & cff2*(W(i,j+1,0)+ & & W(i,j-2,0))) # endif # else FC(i,0)=0.0_r8 # endif END DO # endif DO k=1,N(ng) DO i=Istr,Iend cff=FC(i,k)-FC(i,k-1) rv(i,j,k,nrhs)=rv(i,j,k,nrhs)-cff # ifdef DIAGNOSTICS_UV DiaRV(i,j,k,nrhs,M3vadv)=-cff # endif END DO END DO END IF # endif ! !----------------------------------------------------------------------- ! Compute forcing term for the 2D momentum equations. !----------------------------------------------------------------------- ! ! Vertically integrate baroclinic right-hand-side terms. If not ! body force stresses, add in the difference between surface and ! bottom stresses. ! DO i=IstrU,Iend rufrc(i,j)=ru(i,j,1,nrhs) # ifdef DIAGNOSTICS_UV DiaRUfrc(i,j,3,M2pgrd)=DiaRU(i,j,1,nrhs,M3pgrd) # ifdef UV_COR DiaRUfrc(i,j,3,M2fcor)=DiaRU(i,j,1,nrhs,M3fcor) # endif # ifdef UV_ADV DiaRUfrc(i,j,3,M2hadv)=DiaRU(i,j,1,nrhs,M3hadv) # endif # ifdef NEARSHORE_MELLOR DiaRUfrc(i,j,3,M2hrad)=DiaRU(i,j,1,nrhs,M3hrad) # endif # if defined UV_VIS2 || defined UV_VIS4 DiaRUfrc(i,j,3,M2hvis)=0.0_r8 # endif # ifdef BODYFORCE !! DiaRUfrc(i,j,3,M2strs)=DiaRU(i,j,1,nrhs,M3vvis) # endif # endif END DO DO k=2,N(ng) DO i=IstrU,Iend rufrc(i,j)=rufrc(i,j)+ru(i,j,k,nrhs) # ifdef DIAGNOSTICS_UV DiaRUfrc(i,j,3,M2pgrd)=DiaRUfrc(i,j,3,M2pgrd)+ & & DiaRU(i,j,k,nrhs,M3pgrd) # ifdef UV_COR DiaRUfrc(i,j,3,M2fcor)=DiaRUfrc(i,j,3,M2fcor)+ & & DiaRU(i,j,k,nrhs,M3fcor) # endif # ifdef UV_ADV DiaRUfrc(i,j,3,M2hadv)=DiaRUfrc(i,j,3,M2hadv)+ & & DiaRU(i,j,k,nrhs,M3hadv) # endif # ifdef NEARSHORE_MELLOR DiaRUfrc(i,j,3,M2hrad)=DiaRUfrc(i,j,3,M2hrad)+ & & DiaRU(i,j,k,nrhs,M3hrad) # endif # ifdef BODYFORCE !! DiaRUfrc(i,j,3,M2strs)=DiaRUfrc(i,j,3,M2strs)+ & !! & DiaRU(i,j,k,nrhs,M3vvis) # endif # endif END DO END DO # ifndef BODYFORCE DO i=IstrU,Iend cff=om_u(i,j)*on_u(i,j) cff1= sustr(i,j)*cff cff2=-bustr(i,j)*cff rufrc(i,j)=rufrc(i,j)+cff1+cff2 # ifdef DIAGNOSTICS_UV DiaRUfrc(i,j,3,M2sstr)=cff1 DiaRUfrc(i,j,3,M2bstr)=cff2 # endif END DO # endif IF (j.ge.JstrV) THEN DO i=Istr,Iend rvfrc(i,j)=rv(i,j,1,nrhs) # ifdef DIAGNOSTICS_UV DiaRVfrc(i,j,3,M2pgrd)=DiaRV(i,j,1,nrhs,M3pgrd) # ifdef UV_COR DiaRVfrc(i,j,3,M2fcor)=DiaRV(i,j,1,nrhs,M3fcor) # endif # ifdef UV_ADV DiaRVfrc(i,j,3,M2hadv)=DiaRV(i,j,1,nrhs,M3hadv) # endif # ifdef NEARSHORE_MELLOR DiaRVfrc(i,j,3,M2hrad)=DiaRV(i,j,1,nrhs,M3hrad) # endif # if defined UV_VIS2 || defined UV_VIS4 DiaRVfrc(i,j,3,M2hvis)=0.0_r8 # endif # ifdef BODYFORCE ! DiaRVfrc(i,j,3,M2strs)=DiaRV(i,j,1,nrhs,M3vvis) # endif # endif END DO DO k=2,N(ng) DO i=Istr,Iend rvfrc(i,j)=rvfrc(i,j)+rv(i,j,k,nrhs) # ifdef DIAGNOSTICS_UV DiaRVfrc(i,j,3,M2pgrd)=DiaRVfrc(i,j,3,M2pgrd)+ & & DiaRV(i,j,k,nrhs,M3pgrd) # ifdef UV_COR DiaRVfrc(i,j,3,M2fcor)=DiaRVfrc(i,j,3,M2fcor)+ & & DiaRV(i,j,k,nrhs,M3fcor) # endif # ifdef UV_ADV DiaRVfrc(i,j,3,M2hadv)=DiaRVfrc(i,j,3,M2hadv)+ & & DiaRV(i,j,k,nrhs,M3hadv) # endif # ifdef NEARSHORE_MELLOR DiaRVfrc(i,j,3,M2hrad)=DiaRVfrc(i,j,3,M2hrad)+ & & DiaRV(i,j,k,nrhs,M3hrad) # endif # ifdef BODYFORCE !! DiaRVfrc(i,j,3,M2strs)=DiaRVfrc(i,j,3,M2strs)+ & !! & DiaRV(i,j,k,nrhs,M3vvis) # endif # endif END DO END DO # ifndef BODYFORCE DO i=Istr,Iend cff=om_v(i,j)*on_v(i,j) cff1= svstr(i,j)*cff cff2=-bvstr(i,j)*cff rvfrc(i,j)=rvfrc(i,j)+cff1+cff2 # ifdef DIAGNOSTICS_UV DiaRVfrc(i,j,3,M2sstr)=cff1 DiaRVfrc(i,j,3,M2bstr)=cff2 # endif END DO # endif END IF END DO J_LOOP RETURN END SUBROUTINE rhs3d_tile #endif END MODULE rhs3d_mod