#include "cppdefs.h" MODULE ad_rhs3d_mod #if defined ADJOINT && defined SOLVE3D ! !svn $Id: ad_rhs3d.F 889 2018-02-10 03:32:52Z arango $ !================================================== Hernan G. Arango === ! Copyright (c) 2002-2019 The ROMS/TOMS Group Andrew M. Moore ! ! Licensed under a MIT/X style license ! ! See License_ROMS.txt ! !======================================================================= ! ! ! This subroutine evaluates adjoint right-hand-side terms for ! ! 3D momentum and tracers equations ! ! ! ! BASIC STATE variables needed: Hz, Huon, HVom, u, v, W, uclm, vclm, ! ! sustr, svstr, bustr, bvstr ! ! ! !======================================================================= ! implicit none PRIVATE PUBLIC :: ad_rhs3d CONTAINS ! !*********************************************************************** SUBROUTINE ad_rhs3d (ng, tile) !*********************************************************************** ! USE mod_param USE mod_coupling # ifdef DIAGNOSTICS_UV USE mod_diags # endif USE mod_forces USE mod_grid # ifdef NEARSHORE_MELLOR USE mod_mixing # endif USE mod_ocean USE mod_stepping # ifdef RPM_RELAXATION USE mod_fourdvar # endif ! USE ad_pre_step3d_mod, ONLY : ad_pre_step3d USE ad_prsgrd_mod, ONLY : ad_prsgrd # ifndef TS_FIXED # ifdef TS_DIF2 USE ad_t3dmix_mod, ONLY : ad_t3dmix2 # endif # ifdef TS_DIF4 USE ad_t3dmix_mod, ONLY : ad_t3dmix4 # endif # endif # ifdef RPM_RELAXATION USE ad_t3drelax_mod, ONLY : ad_t3drelax USE ad_uv3drelax_mod, ONLY : ad_uv3drelax # endif # ifdef UV_VIS2 USE ad_uv3dmix_mod, ONLY : ad_uv3dmix2 # endif # ifdef UV_VIS4 USE ad_uv3dmix_mod, ONLY : ad_uv3dmix4 # endif ! ! Imported variable declarations. ! integer, intent(in) :: ng, tile ! ! Local variable declarations. ! # include "tile.h" # ifdef RPM_RELAXATION ! !----------------------------------------------------------------------- ! Improve stability and convergence of the tangent linear representer ! model 3D momentum by a "diffusive relaxation" to previous Picard ! iteration solution. Only applied in the call to ad_main3d in outer ! loop. !----------------------------------------------------------------------- ! IF (LweakRelax(ng)) THEN CALL ad_uv3drelax (ng, tile) END IF # endif # ifdef UV_VIS4 ! !----------------------------------------------------------------------- ! Compute horizontal, biharmonic mixing of momentum. !----------------------------------------------------------------------- ! CALL ad_uv3dmix4 (ng, tile) # endif # ifdef UV_VIS2 ! !----------------------------------------------------------------------- ! Compute horizontal, harmonic mixing of momentum. !----------------------------------------------------------------------- ! CALL ad_uv3dmix2 (ng, tile) # endif ! !----------------------------------------------------------------------- ! Compute right-hand-side terms for the 3D momentum equations. !----------------------------------------------------------------------- ! # ifdef PROFILE CALL wclock_on (ng, iADM, 21, __LINE__, __FILE__) # endif CALL ad_rhs3d_tile (ng, tile, & & LBi, UBi, LBj, UBj, & & IminS, ImaxS, JminS, JmaxS, & & knew(ng), nrhs(ng), & & GRID(ng) % Hz, & & GRID(ng) % ad_Hz, & & GRID(ng) % Huon, & & GRID(ng) % ad_Huon, & & GRID(ng) % Hvom, & & GRID(ng) % ad_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) % ad_bustr, & & FORCES(ng) % bvstr, & & FORCES(ng) % ad_bvstr, & & FORCES(ng) % sustr, & & FORCES(ng) % ad_sustr, & & FORCES(ng) % svstr, & & FORCES(ng) % ad_svstr, & & OCEAN(ng) % u, & & OCEAN(ng) % ad_u, & & OCEAN(ng) % v, & & OCEAN(ng) % ad_v, & & OCEAN(ng) % W, & & OCEAN(ng) % ad_W, & # ifdef NEARSHORE_MELLOR & OCEAN(ng) % u_stokes, & & OCEAN(ng) % ad_u_stokes, & & OCEAN(ng) % v_stokes, & & OCEAN(ng) % ad_v_stokes, & & OCEAN(ng) % ad_rulag3d, & & OCEAN(ng) % ad_rvlag3d, & & MIXING(ng) % ad_rustr3d, & & MIXING(ng) % ad_rvstr3d, & # endif & COUPLING(ng) % ad_rufrc, & & COUPLING(ng) % ad_rvfrc, & # ifdef DIAGNOSTICS_UV !! & DIAGS(ng) % DiaRUfrc, & !! & DIAGS(ng) % DiaRVfrc, & !! & DIAGS(ng) % DiaRU, & !! & DIAGS(ng) % DiaRV, & # endif & OCEAN(ng) % ad_ru, & & OCEAN(ng) % ad_rv) # ifdef PROFILE CALL wclock_off (ng, iADM, 21, __LINE__, __FILE__) # endif # ifdef RPM_RELAXATION ! !----------------------------------------------------------------------- ! Improve stability and convergence of the tangent linear representer ! model tracer type variables by a "diffusive relaxation" to previous ! Picard iteration solution. Only applied in the call to ad_main3d in ! outer loop. !----------------------------------------------------------------------- ! IF (LweakRelax(ng)) THEN CALL ad_t3drelax (ng, tile) END IF # endif # ifndef TS_FIXED # ifdef TS_DIF4 ! !----------------------------------------------------------------------- ! Compute horizontal biharmonic mixing of tracer type variables. !----------------------------------------------------------------------- ! CALL ad_t3dmix4 (ng, tile) # endif # ifdef TS_DIF2 ! !----------------------------------------------------------------------- ! Compute horizontal harmonic mixing of tracer type variables. !----------------------------------------------------------------------- ! CALL ad_t3dmix2 (ng, tile) # endif # endif ! !----------------------------------------------------------------------- ! Compute baroclinic pressure gradient. !----------------------------------------------------------------------- ! CALL ad_prsgrd (ng, tile) ! !----------------------------------------------------------------------- ! Initialize computations for new time step of the 3D primitive ! variables. !----------------------------------------------------------------------- ! CALL ad_pre_step3d (ng, tile) RETURN END SUBROUTINE ad_rhs3d ! !*********************************************************************** SUBROUTINE ad_rhs3d_tile (ng, tile, & & LBi, UBi, LBj, UBj, & & IminS, ImaxS, JminS, JmaxS, & & knew, nrhs, & & Hz, ad_Hz, & & Huon, ad_Huon, & & Hvom, ad_Hvom, & # if defined CURVGRID && defined UV_ADV & dmde, dndx, & # endif & fomn, & & om_u, om_v, on_u, on_v, pm, pn, & & bustr, ad_bustr, & & bvstr, ad_bvstr, & & sustr, ad_sustr, & & svstr, ad_svstr, & & u, ad_u, & & v, ad_v, & & W, ad_W, & # ifdef NEARSHORE_MELLOR & u_stokes, ad_u_stokes, & & v_stokes, ad_v_stokes, & & ad_rulag3d, ad_rvlag3d, & & ad_rustr3d, ad_rvstr3d, & # endif & ad_rufrc, & & ad_rvfrc, & # ifdef DIAGNOSTICS_UV !! & DiaRUfrc, DiaRVfrc, & !! & DiaRU, DiaRV, & # endif & ad_ru, ad_rv) !*********************************************************************** ! USE mod_param USE mod_clima 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) :: knew, 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:) 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:,:) # endif # 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(inout) :: ad_Hz(LBi:,LBj:,:) real(r8), intent(inout) :: ad_Huon(LBi:,LBj:,:) real(r8), intent(inout) :: ad_Hvom(LBi:,LBj:,:) real(r8), intent(inout) :: ad_bustr(LBi:,LBj:) real(r8), intent(inout) :: ad_bvstr(LBi:,LBj:) real(r8), intent(inout) :: ad_sustr(LBi:,LBj:) real(r8), intent(inout) :: ad_svstr(LBi:,LBj:) real(r8), intent(inout) :: ad_u(LBi:,LBj:,:,:) real(r8), intent(inout) :: ad_v(LBi:,LBj:,:,:) real(r8), intent(inout) :: ad_W(LBi:,LBj:,0:) # ifdef NEARSHORE_MELLOR real(r8), intent(inout) :: ad_u_stokes(LBi:,LBj:,:) real(r8), intent(inout) :: ad_v_stokes(LBi:,LBj:,:) real(r8), intent(inout) :: ad_rulag3d(LBi:,LBj:,:) real(r8), intent(inout) :: ad_rvlag3d(LBi:,LBj:,:) real(r8), intent(inout) :: ad_rustr3d(LBi:,LBj:,:) real(r8), intent(inout) :: ad_rvstr3d(LBi:,LBj:,:) # endif real(r8), intent(inout) :: ad_ru(LBi:,LBj:,0:,:) real(r8), intent(inout) :: ad_rv(LBi:,LBj:,0:,:) real(r8), intent(inout) :: ad_rufrc(LBi:,LBj:) real(r8), intent(inout) :: ad_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) 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)) # endif # 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(inout) :: ad_Hz(LBi:UBi,LBj:UBj,N(ng)) real(r8), intent(inout) :: ad_Huon(LBi:UBi,LBj:UBj,N(ng)) real(r8), intent(inout) :: ad_Hvom(LBi:UBi,LBj:UBj,N(ng)) real(r8), intent(inout) :: ad_bustr(LBi:UBi,LBj:UBj) real(r8), intent(inout) :: ad_bvstr(LBi:UBi,LBj:UBj) real(r8), intent(inout) :: ad_sustr(LBi:UBi,LBj:UBj) real(r8), intent(inout) :: ad_svstr(LBi:UBi,LBj:UBj) real(r8), intent(inout) :: ad_u(LBi:UBi,LBj:UBj,N(ng),2) real(r8), intent(inout) :: ad_v(LBi:UBi,LBj:UBj,N(ng),2) real(r8), intent(inout) :: ad_W(LBi:UBi,LBj:UBj,0:N(ng)) # ifdef NEARSHORE_MELLOR real(r8), intent(inout) :: ad_u_stokes(LBi:UBi,LBj:UBj,N(ng)) real(r8), intent(inout) :: ad_v_stokes(LBi:UBi,LBj:UBj,N(ng)) real(r8), intent(inout) :: ad_rulag3d(LBi:UBi,LBj:UBj,N(ng)) real(r8), intent(inout) :: ad_rvlag3d(LBi:UBi,LBj:UBj,N(ng)) real(r8), intent(inout) :: ad_rustr3d(LBi:UBi,LBj:UBj,N(ng)) real(r8), intent(inout) :: ad_rvstr3d(LBi:UBi,LBj:UBj,N(ng)) # endif real(r8), intent(inout) :: ad_ru(LBi:UBi,LBj:UBj,0:N(ng),2) real(r8), intent(inout) :: ad_rv(LBi:UBi,LBj:UBj,0:N(ng),2) real(r8), intent(inout) :: ad_rufrc(LBi:UBi,LBj:UBj) real(r8), intent(inout) :: ad_rvfrc(LBi:UBi,LBj:UBj) # endif ! ! Local variable declarations. ! integer :: i, j, k real(r8), parameter :: Gadv = -0.25_r8 real(r8) :: cff, cff1, cff2, cff3, cff4 real(r8) :: ad_cff, ad_cff1, ad_cff2, ad_cff3, ad_cff4 real(r8) :: adfac, adfac1, adfac2, adfac3, adfac4, adfac5 real(r8), dimension(IminS:ImaxS,0:N(ng)) :: CF real(r8), dimension(IminS:ImaxS,0:N(ng)) :: DC real(r8), dimension(IminS:ImaxS,0:N(ng)) :: FC real(r8), dimension(IminS:ImaxS,0:N(ng)) :: ad_CF real(r8), dimension(IminS:ImaxS,0:N(ng)) :: ad_DC real(r8), dimension(IminS:ImaxS,0:N(ng)) :: ad_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 real(r8), dimension(IminS:ImaxS,JminS:JmaxS) :: ad_Huee real(r8), dimension(IminS:ImaxS,JminS:JmaxS) :: ad_Huxx real(r8), dimension(IminS:ImaxS,JminS:JmaxS) :: ad_Hvee real(r8), dimension(IminS:ImaxS,JminS:JmaxS) :: ad_Hvxx real(r8), dimension(IminS:ImaxS,JminS:JmaxS) :: ad_UFx real(r8), dimension(IminS:ImaxS,JminS:JmaxS) :: ad_UFe real(r8), dimension(IminS:ImaxS,JminS:JmaxS) :: ad_Uwrk real(r8), dimension(IminS:ImaxS,JminS:JmaxS) :: ad_VFx real(r8), dimension(IminS:ImaxS,JminS:JmaxS) :: ad_VFe real(r8), dimension(IminS:ImaxS,JminS:JmaxS) :: ad_Vwrk real(r8), dimension(IminS:ImaxS,JminS:JmaxS) :: ad_uee real(r8), dimension(IminS:ImaxS,JminS:JmaxS) :: ad_uxx real(r8), dimension(IminS:ImaxS,JminS:JmaxS) :: ad_vee real(r8), dimension(IminS:ImaxS,JminS:JmaxS) :: ad_vxx real(r8), dimension(IminS:ImaxS,JminS:JmaxS) :: ad_wrk # include "set_bounds.h" ! !----------------------------------------------------------------------- ! Initialize adjoint private variables. !----------------------------------------------------------------------- ! ad_cff=0.0_r8 ad_cff1=0.0_r8 ad_cff2=0.0_r8 ad_cff3=0.0_r8 ad_cff4=0.0_r8 DO j=JminS,JmaxS DO i=IminS,ImaxS ad_Huee(i,j)=0.0_r8 ad_Huxx(i,j)=0.0_r8 ad_Hvee(i,j)=0.0_r8 ad_Hvxx(i,j)=0.0_r8 ad_UFx(i,j)=0.0_r8 ad_UFe(i,j)=0.0_r8 ad_VFx(i,j)=0.0_r8 ad_VFe(i,j)=0.0_r8 ad_Uwrk(i,j)=0.0_r8 ad_Vwrk(i,j)=0.0_r8 ad_uee(i,j)=0.0_r8 ad_uxx(i,j)=0.0_r8 ad_vee(i,j)=0.0_r8 ad_vxx(i,j)=0.0_r8 ad_wrk(i,j)=0.0_r8 END DO END DO DO k=0,N(ng) DO i=IminS,ImaxS ad_CF(i,k)=0.0_r8 ad_DC(i,k)=0.0_r8 ad_FC(i,k)=0.0_r8 END DO END DO ! J_LOOP : DO j=Jstr,Jend ! !----------------------------------------------------------------------- ! 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. ! IF (j.ge.JstrV) THEN # ifndef BODYFORCE DO i=Istr,Iend cff=om_v(i,j)*on_v(i,j) # ifdef DIAGNOSTICS_UV !! DiaRVfrc(i,j,3,M2bstr)=cff2 !! DiaRVfrc(i,j,3,M2sstr)=cff1 # endif !> tl_rvfrc(i,j)=tl_rvfrc(i,j)+tl_cff1+tl_cff2 !> ad_cff1=ad_cff1+ad_rvfrc(i,j) ad_cff2=ad_cff2+ad_rvfrc(i,j) !> tl_cff2=-tl_bvstr(i,j)*cff !> ad_bvstr(i,j)=ad_bvstr(i,j)-cff*ad_cff2 ad_cff2=0.0_r8 !> tl_cff1= tl_svstr(i,j)*cff !> ad_svstr(i,j)=ad_svstr(i,j)+cff*ad_cff1 ad_cff1=0.0_r8 END DO # endif DO k=2,N(ng) DO i=Istr,Iend # ifdef DIAGNOSTICS_UV # ifdef BODYFORCE !! DiaRVfrc(i,j,3,M2strs)=DiaRVfrc(i,j,3,M2strs)+ & !! & DiaRV(i,j,k,nrhs,M3vvis) # endif # ifdef NEARSHORE_MELLOR !! DiaRVfrc(i,j,3,M2hrad)=DiaRVfrc(i,j,3,M2hrad)+ & !! & DiaRV(i,j,k,nrhs,M3hrad) # endif # ifdef UV_ADV !! DiaRVfrc(i,j,3,M2hadv)=DiaRVfrc(i,j,3,M2hadv)+ & !! & DiaRV(i,j,k,nrhs,M3hadv) !! DiaRVfrc(i,j,3,M2yadv)=DiaRVfrc(i,j,3,M2yadv)+ & !! & DiaRV(i,j,k,nrhs,M3yadv) !! DiaRVfrc(i,j,3,M2xadv)=DiaRVfrc(i,j,3,M2xadv)+ & !! & DiaRV(i,j,k,nrhs,M3xadv) # endif # ifdef UV_COR !! DiaRVfrc(i,j,3,M2fcor)=DiaRVfrc(i,j,3,M2fcor)+ & !! & DiaRV(i,j,k,nrhs,M3fcor) # endif !! DiaRVfrc(i,j,3,M2pgrd)=DiaRVfrc(i,j,3,M2pgrd)+ & !! & DiaRV(i,j,k,nrhs,M3pgrd) # endif !> tl_rvfrc(i,j)=tl_rvfrc(i,j)+tl_rv(i,j,k,nrhs) !> ad_rv(i,j,k,nrhs)=ad_rv(i,j,k,nrhs)+ad_rvfrc(i,j) END DO END DO DO i=Istr,Iend # ifdef DIAGNOSTICS_UV # ifdef BODYFORCE !! DiaRVfrc(i,j,3,M2strs)=DiaRV(i,j,1,nrhs,M3vvis) # endif # if defined UV_VIS2 || defined UV_VIS4 !! DiaRVfrc(i,j,3,M2yvis)=0.0_r8 !! DiaRVfrc(i,j,3,M2xvis)=0.0_r8 !! DiaRVfrc(i,j,3,M2hvis)=0.0_r8 # endif # ifdef NEARSHORE_MELLOR !! DiaRVfrc(i,j,3,M2hrad)=DiaRV(i,j,1,nrhs,M3hrad) # endif # ifdef UV_ADV !! DiaRVfrc(i,j,3,M2hadv)=DiaRV(i,j,1,nrhs,M3hadv) !! DiaRVfrc(i,j,3,M2yadv)=DiaRV(i,j,1,nrhs,M3yadv) !! DiaRVfrc(i,j,3,M2xadv)=DiaRV(i,j,1,nrhs,M3xadv) # endif # ifdef UV_COR !! DiaRVfrc(i,j,3,M2fcor)=DiaRV(i,j,1,nrhs,M3fcor) # endif !! DiaRVfrc(i,j,3,M2pgrd)=DiaRV(i,j,1,nrhs,M3pgrd) # endif !> tl_rvfrc(i,j)=tl_rv(i,j,1,nrhs) !> ad_rv(i,j,1,nrhs)=ad_rv(i,j,1,nrhs)+ad_rvfrc(i,j) ad_rvfrc(i,j)=0.0_r8 END DO END IF # ifndef BODYFORCE DO i=IstrU,Iend cff=om_u(i,j)*on_u(i,j) # ifdef DIAGNOSTICS_UV !! DiaRUfrc(i,j,3,M2bstr)=cff2 !! DiaRUfrc(i,j,3,M2sstr)=cff1 # endif !> tl_rufrc(i,j)=tl_rufrc(i,j)+tl_cff1+tl_cff2 !> ad_cff1=ad_cff1+ad_rufrc(i,j) ad_cff2=ad_cff2+ad_rufrc(i,j) !> tl_cff2=-tl_bustr(i,j)*cff !> ad_bustr(i,j)=ad_bustr(i,j)-cff*ad_cff2 ad_cff2=0.0_r8 !> tl_cff1= tl_sustr(i,j)*cff !> ad_sustr(i,j)=ad_sustr(i,j)+cff*ad_cff1 ad_cff1=0.0_r8 END DO # endif DO k=2,N(ng) DO i=IstrU,Iend # ifdef DIAGNOSTICS_UV # ifdef BODYFORCE !! DiaRUfrc(i,j,3,M2strs)=DiaRUfrc(i,j,3,M2strs)+ & !! & DiaRU(i,j,k,nrhs,M3vvis) # endif # ifdef NEARSHORE_MELLOR !! DiaRUfrc(i,j,3,M2hrad)=DiaRUfrc(i,j,3,M2hrad)+ & !! & DiaRU(i,j,k,nrhs,M3hrad) # endif # ifdef UV_ADV !! DiaRUfrc(i,j,3,M2hadv)=DiaRUfrc(i,j,3,M2hadv)+ & !! & DiaRU(i,j,k,nrhs,M3hadv) !! DiaRUfrc(i,j,3,M2yadv)=DiaRUfrc(i,j,3,M2yadv)+ & !! & DiaRU(i,j,k,nrhs,M3yadv) !! DiaRUfrc(i,j,3,M2xadv)=DiaRUfrc(i,j,3,M2xadv)+ & !! & DiaRU(i,j,k,nrhs,M3xadv) # endif # ifdef UV_COR !! DiaRUfrc(i,j,3,M2fcor)=DiaRUfrc(i,j,3,M2fcor)+ & !! & DiaRU(i,j,k,nrhs,M3fcor) # endif !! DiaRUfrc(i,j,3,M2pgrd)=DiaRUfrc(i,j,3,M2pgrd)+ & !! & DiaRU(i,j,k,nrhs,M3pgrd) # endif !> tl_rufrc(i,j)=tl_rufrc(i,j)+tl_ru(i,j,k,nrhs) !> ad_ru(i,j,k,nrhs)=ad_ru(i,j,k,nrhs)+ad_rufrc(i,j) END DO END DO DO i=IstrU,Iend # ifdef DIAGNOSTICS_UV # ifdef BODYFORCE !! DiaRUfrc(i,j,3,M2strs)=DiaRU(i,j,1,nrhs,M3vvis) # endif # if defined UV_VIS2 || defined UV_VIS4 !! DiaRUfrc(i,j,3,M2hvis)=0.0_r8 !! DiaRUfrc(i,j,3,M2yvis)=0.0_r8 !! DiaRUfrc(i,j,3,M2xvis)=0.0_r8 # endif # ifdef NEARSHORE_MELLOR !! DiaRUfrc(i,j,3,M2hrad)=DiaRU(i,j,1,nrhs,M3hrad) # endif # ifdef UV_ADV !! DiaRUfrc(i,j,3,M2hadv)=DiaRU(i,j,1,nrhs,M3hadv) !! DiaRUfrc(i,j,3,M2yadv)=DiaRU(i,j,1,nrhs,M3yadv) !! DiaRUfrc(i,j,3,M2xadv)=DiaRU(i,j,1,nrhs,M3xadv) # endif # ifdef UV_COR !! DiaRUfrc(i,j,3,M2fcor)=DiaRU(i,j,1,nrhs,M3fcor) # endif !! DiaRUfrc(i,j,3,M2pgrd)=DiaRU(i,j,1,nrhs,M3pgrd) # endif !> tl_rufrc(i,j)=tl_ru(i,j,1,nrhs) !> ad_ru(i,j,1,nrhs)=ad_ru(i,j,1,nrhs)+ad_rufrc(i,j) ad_rufrc(i,j)=0.0_r8 END DO # ifdef UV_ADV ! !----------------------------------------------------------------------- ! Add in adjoint vertical advection, V-momentum. !----------------------------------------------------------------------- ! IF (j.ge.JstrV) THEN DO k=1,N(ng) DO i=Istr,Iend # ifdef DIAGNOSTICS_UV !! DiaRV(i,j,k,nrhs,M3vadv)=-cff # endif !> tl_rv(i,j,k,nrhs)=tl_rv(i,j,k,nrhs)-tl_cff !> ad_cff=ad_cff-ad_rv(i,j,k,nrhs) !> tl_cff=tl_FC(i,k)-tl_FC(i,k-1) !> ad_FC(i,k-1)=ad_FC(i,k-1)-ad_cff ad_FC(i,k )=ad_FC(i,k )+ad_cff ad_cff=0.0_r8 END DO END DO # ifdef UV_SADVECTION ! ! Apply spline code to BASIC STATE v-momentum which should be in ! units of m/s. CF will be used by the tangent linear spline code. ! 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. ! DO i=Istr,Iend !> tl_FC(i,N(ng))=0.0_r8 !> ad_FC(i,N(ng))=0.0_r8 !> tl_FC(i,0)=0.0_r8 !> ad_FC(i,0)=0.0_r8 END DO cff3=1.0_r8/3.0_r8 cff4=1.0_r8/6.0_r8 DO k=1,N(ng)-1 DO i=Istr,Iend !> tl_FC(i,k)=(cff1*(tl_W(i,j ,k)+ & !> & tl_W(i,j-1,k))- & !> & cff2*(tl_W(i,j+1,k)+ & !> & tl_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)))+ & !> & (cff1*(W(i,j ,k)+ & !> & W(i,j-1,k))- & !> & cff2*(W(i,j+1,k)+ & !> & W(i,j-2,k)))* & !> & (tl_v(i,j,k,nrhs)+ & # ifdef NEARSHORE_MELLOR !> & tl_v_stokes(i,j,k)+ & # endif !> & DC(i,k)*(cff3*tl_CF(i,k )+ & !> & cff4*tl_CF(i,k-1))+ & !> & tl_DC(i,k)*(cff3*CF(i,k )+ & !> & cff4*CF(i,k-1))) !> adfac1=(cff1*(W(i,j ,k)+ & & W(i,j-1,k))- & & cff2*(W(i,j+1,k)+ & & W(i,j-2,k)))*ad_FC(i,k) adfac2=adfac1*DC(i,k) adfac3=(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)))*ad_FC(i,k) adfac4=adfac3*cff1 adfac5=adfac3*cff2 ad_DC(i,k)=ad_DC(i,k)+(cff3*CF(i,k )+ & cff4*CF(i,k-1))*adfac1 ad_CF(i,k-1)=ad_CF(i,k-1)+cff4*adfac2 ad_CF(i,k )=ad_CF(i,k )+cff3*adfac2 ad_v(i,j,k,nrhs)=ad_v(i,j,k,nrhs)+adfac1 # ifdef NEARSHORE_MELLOR ad_v_stokes(i,j,k)=ad_v_stokes(i,j,k)+adfac1 # endif ad_W(i,j-2,k)=ad_W(i,j-2,k)-adfac5 ad_W(i,j-1,k)=ad_W(i,j-1,k)+adfac4 ad_W(i,j ,k)=ad_W(i,j ,k)+adfac4 ad_W(i,j+1,k)=ad_W(i,j+1,k)-adfac5 ad_FC(i,k)=0.0_r8 END DO END DO ! ! Construct adjoint conservative parabolic splines for the vertical ! derivatives "tl_CF" of v-momentum. ! DO k=1,N(ng)-1 ! adjoint back substitution DO i=Istr,Iend !> tl_CF(i,k)=tl_CF(i,k)-FC(i,k)*tl_CF(i,k+1) !> ad_CF(i,k+1)=ad_CF(i,k+1)-FC(i,k)*ad_CF(i,k) END DO END DO DO i=Istr,Iend !> tl_CF(i,N(ng))=0.0_r8 !> ad_CF(i,N(ng))=0.0_r8 END DO ! adjoint LU decomposition DO k=N(ng)-1,1,-1 ! and forward substitution 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))) !> tl_CF(i,k)=cff*(6.0_r8*(tl_v(i,j,k+1,nrhs)- & # ifdef NEARSHORE_MELLOR !> & tl_v_stokes(i,j,k )+ & !> & tl_v_stokes(i,j,k+1)- & # endif !> & tl_v(i,j,k ,nrhs))- & !> & (tl_DC(i,k)*CF(i,k-1)+ & !> & 2.0_r8*(tl_DC(i,k )+ & !> & tl_DC(i,k+1))*CF(i,k)+ & !> & tl_DC(i,k+1)*CF(i,k+1))- & !> & DC(i,k)*tl_CF(i,k-1)) !> adfac=cff*ad_CF(i,k) adfac1=adfac*6.0_r8 ad_CF(i,k-1)=ad_CF(i,k-1)-DC(i,k)*adfac ad_DC(i,k )=ad_DC(i,k )- & & (CF(i,k-1)+2.0_r8*CF(i,k))*adfac ad_DC(i,k+1)=ad_DC(i,k+1)- & & (CF(i,k+1)+2.0_r8*CF(i,k))*adfac ad_v(i,j,k ,nrhs)=ad_v(i,j,k ,nrhs)-adfac1 ad_v(i,j,k+1,nrhs)=ad_v(i,j,k+1,nrhs)+adfac1 # ifdef NEARSHORE_MELLOR ad_v_stokes(i,j,k )=ad_v_stokes(i,j,k )-adfac1 ad_v_stokes(i,j,k+1)=ad_v_stokes(i,j,k+1)+adfac1 # endif ad_CF(i,k)=0.0_r8 END DO END DO DO i=Istr,Iend !> tl_CF(i,0)=0.0_r8 !> ad_CF(i,0)=0.0_r8 END DO cff1=9.0_r8/16.0_r8 cff2=1.0_r8/16.0_r8 DO k=1,N(ng) ! adjoint triadiagonal coefficients DO i=Istr,Iend !> tl_DC(i,k)=(cff1*(tl_Hz(i,j ,k)+ & !> & tl_Hz(i,j-1,k))- & !> & cff2*(tl_Hz(i,j+1,k)+ & !> & tl_Hz(i,j-2,k))) !> adfac1=cff1*ad_DC(i,k) adfac2=cff2*ad_DC(i,k) ad_Hz(i,j-2,k)=ad_Hz(i,j-2,k)-adfac2 ad_Hz(i,j-1,k)=ad_Hz(i,j-1,k)+adfac1 ad_Hz(i,j ,k)=ad_Hz(i,j ,k)+adfac1 ad_Hz(i,j+1,k)=ad_Hz(i,j+1,k)-adfac2 ad_DC(i,k)=0.0 END DO END DO # elif defined UV_C2ADVECTION ! ! Second-order, central differences vertical v-momentum advection. ! DO i=Istr,Iend # ifdef SED_MORPH # ifdef NEARSHORE_MELLOR !> tl_FC(i,0)=0.5_r8* & !> & ((tl_v(i,j,1,nrhs)+tl_v_stokes(i,j,1))* & !> & (W(i,j ,0)+ & !> & W(i,j-1,0))+ & !> & (v(i,j,1,nrhs)+v_stokes(i,j,1))* & !> & (tl_W(i,j ,0)+ & !> & tl_W(i,j-1,0))) !> adfac=0.5_r8*ad_FC(i,0) adfac1=adfac*(W(i,j ,0)+ & & W(i,j-1,0)) adfac2=adfac*(v(i,j,1,nrhs)+v_stokes(i,j,1)) ad_v(i,j,1,nrhs)=ad_v(i,j,1,nrhs)+adfac1 ad_v_stokes(i,j,1)=ad_v_stokes(i,j,1)+adfac1 ad_W(i,j-1,0)=ad_W(i,j-1,0)+adfac2 ad_W(i,j ,0)=ad_W(i,j ,0)+adfac2 ad_FC(i,0)=0.0_r8 # else !> tl_FC(i,0)=0.5_r8* & !> & (tl_v(i,j,1,nrhs)* & !> & (W(i,j ,0)+ & !> & W(i,j-1,0))+ & !> & v(i,j,1,nrhs)* & !> & (tl_W(i,j ,0)+ & !> & tl_W(i,j-1,0))) !> adfac=0.5_r8*ad_FC(i,0) adfac1=adfac*v(i,j,1,nrhs) ad_v(i,j,1,nrhs)=ad_v(i,j,1,nrhs)+ & & (W(i,j ,0)+ & & W(i,j-1,0))*ad_FC(i,0) ad_W(i,j-1,0)=ad_W(i,j-1,0)+adfac1 ad_W(i,j ,0)=ad_W(i,j ,0)+adfac1 ad_FC(i,0)=0.0_r8 # endif # else !> tl_FC(i,0)=0.0_r8 !> ad_FC(i,0)=0.0_r8 # endif !> tl_FC(i,N(ng))=0.0_r8 !> ad_FC(i,N(ng))=0.0_r8 END DO DO k=1,N(ng)-1 DO i=Istr,Iend !> tl_FC(i,k)=0.25_r8*((tl_v(i,j,k ,nrhs)+ & # ifdef NEARSHORE_MELLOR !> & tl_v_stokes(i,j,k )+ & !> & tl_v_stokes(i,j,k+1)+ & # endif !> & tl_v(i,j,k+1,nrhs))* & !> & (W(i,j ,k)+ & !> & W(i,j-1,k))+ & !> & (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))* & !> & (tl_W(i,j ,k)+ & !> & tl_W(i,j-1,k))) !> adfac=0.25_r8*ad_FC(i,k) adfac1=adfac*(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)) adfac2=adfac*(W(i,j ,k)+ & & W(i,j-1,k)) ad_W(i,j-1,k)=ad_W(i,j-1,k)+adfac1 ad_W(i,j ,k)=ad_W(i,j ,k)+adfac1 ad_v(i,j,k ,nrhs)=ad_v(i,j,k ,nrhs)+adfac2 ad_v(i,j,k+1,nrhs)=ad_v(i,j,k+1,nrhs)+adfac2 # ifdef NEARSHORE_MELLOR ad_v_stokes(i,j,k )=ad_v_stokes(i,j,k )+adfac2 ad_v_stokes(i,j,k+1)=ad_v_stokes(i,j,k+1)+adfac2 # endif ad_FC(i,k)=0.0_r8 END DO END DO # elif defined UV_C4ADVECTION ! ! Fourth-order, central differences vertical v-momentum advection. ! cff1=9.0_r8/32.0_r8 cff2=1.0_r8/32.0_r8 DO i=Istr,Iend # ifdef SED_MORPH # ifdef NEARSHORE_MELLOR !> tl_FC(i,0)=2.0_r8* & !> & ((cff1*(tl_v(i,j,1,nrhs)+tl_v_stokes(i,j,1))- & !> & cff2*(tl_v(i,j,2,nrhs)+tl_v_stokes(i,j,2)))* & !> & (W(i,j ,0)+ & !> & W(i,j-1,0))+ & !> & (cff1*(v(i,j,1,nrhs)+v_stokes(i,j,1))- & !> & cff2*(v(i,j,2,nrhs)+v_stokes(i,j,2)))* & !> & (tl_W(i,j ,0)+ & !> & tl_W(i,j-1,0))) !> adfac=2.0_r8*ad_FC(i,0) adfac1=adfac*(W(i,j ,0)+ & & W(i,j-1,0)) adfac2=adfac1*cff1 adfac3=adfac1*cff2 adfac4=adfac* & & (cff1*(v(i,j,1,nrhs)+v_stokes(i,j,1))- & & cff2*(v(i,j,2,nrhs)+v_stokes(i,j,2))) ad_v(i,j,1,nrhs)=ad_v(i,j,1,nrhs)+adfac2 ad_v(i,j,2,nrhs)=ad_v(i,j,2,nrhs)-adfac3 ad_v_stokes(i,j,1)=ad_v_stokes(i,j,1)+adfac2 ad_v_stokes(i,j,2)=ad_v_stokes(i,j,2)-adfac3 ad_W(i,j-1,0)=ad_W(i,j-1,0)+adfac4 ad_W(i,j ,0)=ad_W(i,j ,0)+adfac4 ad_FC(i,0)=0.0_r8 # else !> tl_FC(i,0)=2.0_r8* & !> & ((cff1*tl_v(i,j,1,nrhs)- & !> & cff2*tl_v(i,j,2,nrhs))* & !> & (W(i,j ,0)+ & !> & W(i,j-1,0))+ & !> & (cff1*v(i,j,1,nrhs)- & !> & cff2*v(i,j,2,nrhs))* & !> & (tl_W(i,j ,0)+ & !> & tl_W(i,j-1,0))) !> adfac=2.0_r8*ad_FC(i,0) adfac1=adfac*(W(i,j ,0)+ & & W(i,j-1,0)) adfac2=adfac*(cff1*v(i,j,1,nrhs)- & & cff2*v(i,j,2,nrhs)) ad_v(i,j,1,nrhs)=ad_v(i,j,1,nrhs)+cff1*adfac1 ad_v(i,j,2,nrhs)=ad_v(i,j,2,nrhs)-cff2*adfac1 ad_W(i,j-1,0)=ad_W(i,j-1,0)+adfac2 ad_W(i,j ,0)=ad_W(i,j ,0)+adfac2 ad_FC(i,0)=0.0_r8 # endif # else !> tl_FC(i,0)=0.0_r8 !> ad_FC(i,0)=0.0_r8 # endif !> tl_FC(i,1)=(cff1*(tl_v(i,j,1,nrhs)+ & # ifdef NEARSHORE_MELLOR !> & tl_v_stokes(i,j,1)+ & !> & tl_v_stokes(i,j,2)+ & # endif !> & tl_v(i,j,2,nrhs))- & !> & cff2*(tl_v(i,j,1,nrhs)+ & # ifdef NEARSHORE_MELLOR !> & tl_v_stokes(i,j,1)+ & !> & tl_v_stokes(i,j,3)+ & # endif !> & tl_v(i,j,3,nrhs)))* & !> & (W(i,j ,1)+ & !> & W(i,j-1,1))+ & !> & (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)))* & !> & (tl_W(i,j ,1)+ & !> & tl_W(i,j-1,1)) !> adfac=(W(i,j ,1)+ & & W(i,j-1,1))*ad_FC(i,1) adfac1=adfac*cff1 adfac2=adfac*cff2 adfac3=(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)))*ad_FC(i,1) ad_W(i,j-1,1)=ad_W(i,j-1,1)+adfac3 ad_W(i,j ,1)=ad_W(i,j ,1)+adfac3 ad_v(i,j,1,nrhs)=ad_v(i,j,1,nrhs)+adfac1-adfac2 ad_v(i,j,2,nrhs)=ad_v(i,j,2,nrhs)+adfac1 ad_v(i,j,3,nrhs)=ad_v(i,j,3,nrhs)-adfac2 # ifdef NEARSHORE_MELLOR ad_v_stokes(i,j,1)=ad_v_stokes(i,j,1)+adfac1-adfac2 ad_v_stokes(i,j,2)=ad_v_stokes(i,j,2)+adfac1 ad_v_stokes(i,j,3)=ad_v_stokes(i,j,3)-adfac2 # endif ad_FC(i,1)=0.0_r8 !> tl_FC(i,N(ng)-1)=(cff1*(tl_v(i,j,N(ng)-1,nrhs)+ & # ifdef NEARSHORE_MELLOR !> & tl_v_stokes(i,j,N(ng)-1)+ & !> & tl_v_stokes(i,j,N(ng) )+ & # endif !> & tl_v(i,j,N(ng) ,nrhs))- & !> & cff2*(tl_v(i,j,N(ng)-2,nrhs)+ & # ifdef NEARSHORE_MELLOR !> & tl_v_stokes(i,j,N(ng)-2)+ & !> & tl_v_stokes(i,j,N(ng) )+ & # endif !> & tl_v(i,j,N(ng) ,nrhs)))* & !> & (W(i,j ,N(ng)-1)+ & !> & W(i,j-1,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)))* & !> & (tl_W(i,j ,N(ng)-1)+ & !> & tl_W(i,j-1,N(ng)-1)) !> adfac=(W(i,j ,N(ng)-1)+ & & W(i,j-1,N(ng)-1))*ad_FC(i,N(ng)-1) adfac1=adfac*cff1 adfac2=adfac*cff2 adfac3=(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)))*ad_FC(i,N(ng)-1) ad_W(i,j-1,N(ng)-1)=ad_W(i,j-1,N(ng)-1)+adfac3 ad_W(i,j ,N(ng)-1)=ad_W(i,j ,N(ng)-1)+adfac3 ad_v(i,j,N(ng)-2,nrhs)=ad_v(i,j,N(ng)-2,nrhs)-adfac2 ad_v(i,j,N(ng)-1,nrhs)=ad_v(i,j,N(ng)-1,nrhs)+adfac1 ad_v(i,j,N(ng) ,nrhs)=ad_v(i,j,N(ng) ,nrhs)+adfac1-adfac2 # ifdef NEARSHORE_MELLOR ad_v_stokes(i,j,N(ng)-2)=ad_v_stokes(i,j,N(ng)-2)-adfac2 ad_v_stokes(i,j,N(ng)-1)=ad_v_stokes(i,j,N(ng)-1)+adfac1 ad_v_stokes(i,j,N(ng) )=ad_v_stokes(i,j,N(ng) )+adfac1- & & adfac2 # endif ad_FC(i,N(ng)-1)=0.0_r8 !> tl_FC(i,N(ng))=0.0_r8 !> ad_FC(i,N(ng))=0.0_r8 END DO DO k=2,N(ng)-2 DO i=Istr,Iend !> tl_FC(i,k)=(cff1*(tl_v(i,j,k ,nrhs)+ & # ifdef NEARSHORE_MELLOR !> & tl_v_stokes(i,j,k )+ & !> & tl_v_stokes(i,j,k+1)+ & # endif !> & tl_v(i,j,k+1,nrhs))- & !> & cff2*(tl_v(i,j,k-1,nrhs)+ & # ifdef NEARSHORE_MELLOR !> & tl_v_stokes(i,j,k-1)+ & !> & tl_v_stokes(i,j,k+2)+ & # endif !> & tl_v(i,j,k+2,nrhs)))* & !> & (W(i,j ,k)+ & !> & W(i,j-1,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)))* & !> & (tl_W(i,j ,k)+ & !> & tl_W(i,j-1,k)) !> adfac=(W(i,j ,k)+ & & W(i,j-1,k))*ad_FC(i,k) adfac1=adfac*cff1 adfac2=adfac*cff2 adfac3=(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)))*ad_FC(i,k) ad_W(i,j-1,k)=ad_W(i,j-1,k)+adfac3 ad_W(i,j ,k)=ad_W(i,j ,k)+adfac3 ad_v(i,j,k-1,nrhs)=ad_v(i,j,k-1,nrhs)-adfac2 ad_v(i,j,k ,nrhs)=ad_v(i,j,k ,nrhs)+adfac1 ad_v(i,j,k+1,nrhs)=ad_v(i,j,k+1,nrhs)+adfac1 ad_v(i,j,k+2,nrhs)=ad_v(i,j,k+2,nrhs)-adfac2 # ifdef NEARSHORE_MELLOR ad_v_stokes(i,j,k-1)=ad_v_stokes(i,j,k-1)-adfac2 ad_v_stokes(i,j,k )=ad_v_stokes(i,j,k )+adfac1 ad_v_stokes(i,j,k+1)=ad_v_stokes(i,j,k+1)+adfac1 ad_v_stokes(i,j,k+2)=ad_v_stokes(i,j,k+2)-adfac2 # endif ad_FC(i,k)=0.0_r8 END DO END DO # else ! ! Fourth-order, central differences vertical v-momentum advection. ! cff1=9.0_r8/16.0_r8 cff2=1.0_r8/16.0_r8 DO i=Istr,Iend # ifdef SED_MORPH # ifdef NEARSHORE_MELLOR !> tl_FC(i,0)=2.0_r8* & !> & ((cff1*(tl_v(i,j,1,nrhs)+tl_v_stokes(i,j,1))- & !> & cff2*(tl_v(i,j,2,nrhs)+tl_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)))+ & !> & (cff1*(v(i,j,1,nrhs)+v_stokes(i,j,1))- & !> & cff2*(v(i,j,2,nrhs)+v_stokes(i,j,2)))* & !> & (cff1*(tl_W(i,j ,0)+ & !> & tl_W(i,j-1,0))- & !> & cff2*(tl_W(i,j+1,0)+ & !> & tl_W(i,j-2,0)))) !> adfac=2.0_r8*ad_FC(i,0) adfac1=adfac*(cff1*(W(i,j ,0)+ & & W(i,j-1,0))- & & cff2*(W(i,j+1,0)+ & & W(i,j-2,0))) adfac2=adfac1*cff1 adfac3=adfac1*cff2 adfac4=adfac* & & (cff1*(v(i,j,1,nrhs)+v_stokes(i,j,1))- & & cff2*(v(i,j,2,nrhs)+v_stokes(i,j,2))) ad_v(i,j,1,nrhs)=ad_v(i,j,1,nrhs)+adfac2 ad_v(i,j,2,nrhs)=ad_v(i,j,2,nrhs)-adfac3 ad_v_stokes(i,j,1)=ad_v_stokes(i,j,1)+adfac2 ad_v_stokes(i,j,2)=ad_v_stokes(i,j,2)-adfac3 ad_W(i,j-2,0)=ad_W(i,j-2,0)-cff2*adfac4 ad_W(i,j-1,0)=ad_W(i,j-1,0)+cff1*adfac4 ad_W(i,j ,0)=ad_W(i,j ,0)+cff1*adfac4 ad_W(i,j+1,0)=ad_W(i,j+1,0)-cff2*adfac4 ad_FC(i,0)=0.0_r8 # else !> tl_FC(i,0)=2.0_r8* & !> & ((cff1*tl_v(i,j,1,nrhs)- & !> & cff2*tl_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)))+ & !> & (cff1*v(i,j,1,nrhs)- & !> & cff2*v(i,j,2,nrhs))* & !> & (cff1*(tl_W(i,j ,0)+ & !> & tl_W(i,j-1,0))- & !> & cff2*(tl_W(i,j+1,0)+ & !> & tl_W(i,j-2,0)))) !> adfac=2.0_r8*ad_FC(i,0) adfac1=adfac*(cff1*(W(i,j ,0)+ & & W(i,j-1,0))- & & cff2*(W(i,j+1,0)+ & & W(i,j-2,0))) adfac2=adfac*(cff1*v(i,j,1,nrhs)- & & cff2*v(i,j,2,nrhs)) adfac3=adfac2*cff1 adfac4=adfac2*cff2 ad_v(i,j,1,nrhs)=ad_v(i,j,1,nrhs)+cff1*adfac1 ad_v(i,j,2,nrhs)=ad_v(i,j,2,nrhs)-cff2*adfac1 ad_W(i,j-2,0)=ad_W(i,j-2,0)-adfac4 ad_W(i,j-1,0)=ad_W(i,j-1,0)+adfac3 ad_W(i,j ,0)=ad_W(i,j ,0)+adfac3 ad_W(i,j+1,0)=ad_W(i,j+1,0)-adfac4 ad_FC(i,0)=0.0_r8 # endif # else !> tl_FC(i,0)=0.0_r8 !> ad_FC(i,0)=0.0_r8 # endif !> tl_FC(i,1)=(cff1*(tl_v(i,j,1,nrhs)+ & # ifdef NEARSHORE_MELLOR !> & tl_v_stokes(i,j,1)+ & !> & tl_v_stokes(i,j,2)+ & # endif !> & tl_v(i,j,2,nrhs))- & !> & cff2*(tl_v(i,j,1,nrhs)+ & # ifdef NEARSHORE_MELLOR !> & tl_v_stokes(i,j,1)+ & !> & tl_v_stokes(i,j,3)+ & # endif !> & tl_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)))+ & !> & (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*(tl_W(i,j ,1)+ & !> & tl_W(i,j-1,1))- & !> & cff2*(tl_W(i,j+1,1)+ & !> & tl_W(i,j-2,1))) !> adfac=(cff1*(W(i,j ,1)+ & & W(i,j-1,1))- & & cff2*(W(i,j+1,1)+ & & W(i,j-2,1)))*ad_FC(i,1) adfac1=adfac*cff1 adfac2=adfac*cff2 adfac=(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)))*ad_FC(i,1) adfac3=adfac*cff1 adfac4=adfac*cff2 ad_W(i,j-2,1)=ad_W(i,j-2,1)-adfac4 ad_W(i,j-1,1)=ad_W(i,j-1,1)+adfac3 ad_W(i,j ,1)=ad_W(i,j ,1)+adfac3 ad_W(i,j+1,1)=ad_W(i,j+1,1)-adfac4 ad_v(i,j,1,nrhs)=ad_v(i,j,1,nrhs)+adfac1-adfac2 ad_v(i,j,2,nrhs)=ad_v(i,j,2,nrhs)+adfac1 ad_v(i,j,3,nrhs)=ad_v(i,j,3,nrhs)-adfac2 # ifdef NEARSHORE_MELLOR ad_v_stokes(i,j,1)=ad_v_stokes(i,j,1)+adfac1-adfac2 ad_v_stokes(i,j,2)=ad_v_stokes(i,j,2)+adfac1 ad_v_stokes(i,j,3)=ad_v_stokes(i,j,3)-adfac2 # endif ad_FC(i,1)=0.0_r8 !> tl_FC(i,N(ng)-1)=(cff1*(tl_v(i,j,N(ng)-1,nrhs)+ & # ifdef NEARSHORE_MELLOR !> & tl_v_stokes(i,j,N(ng)-1)+ & !> & tl_v_stokes(i,j,N(ng) )+ & # endif !> & tl_v(i,j,N(ng) ,nrhs))- & !> & cff2*(tl_v(i,j,N(ng)-2,nrhs)+ & # ifdef NEARSHORE_MELLOR !> & tl_v_stokes(i,j,N(ng)-2)+ & !> & tl_v_stokes(i,j,N(ng) )+ & # endif !> & tl_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)))+ & !> & (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*(tl_W(i,j ,N(ng)-1)+ & !> & tl_W(i,j-1,N(ng)-1))- & !> & cff2*(tl_W(i,j+1,N(ng)-1)+ & !> & tl_W(i,j-2,N(ng)-1))) !> adfac=(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)))*ad_FC(i,N(ng)-1) adfac1=adfac*cff1 adfac2=adfac*cff2 adfac=(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)))*ad_FC(i,N(ng)-1) adfac3=adfac*cff1 adfac4=adfac*cff2 ad_W(i,j-2,N(ng)-1)=ad_W(i,j-2,N(ng)-1)-adfac4 ad_W(i,j-1,N(ng)-1)=ad_W(i,j-1,N(ng)-1)+adfac3 ad_W(i,j ,N(ng)-1)=ad_W(i,j ,N(ng)-1)+adfac3 ad_W(i,j+1,N(ng)-1)=ad_W(i,j+1,N(ng)-1)-adfac4 ad_v(i,j,N(ng)-2,nrhs)=ad_v(i,j,N(ng)-2,nrhs)-adfac2 ad_v(i,j,N(ng)-1,nrhs)=ad_v(i,j,N(ng)-1,nrhs)+adfac1 ad_v(i,j,N(ng) ,nrhs)=ad_v(i,j,N(ng) ,nrhs)+adfac1-adfac2 # ifdef NEARSHORE_MELLOR ad_v_stokes(i,j,N(ng)-2)=ad_v_stokes(i,j,N(ng)-2)-adfac2 ad_v_stokes(i,j,N(ng)-1)=ad_v_stokes(i,j,N(ng)-1)+adfac1 ad_v_stokes(i,j,N(ng) )=ad_v_stokes(i,j,N(ng) )+adfac1- & & adfac2 # endif ad_FC(i,N(ng)-1)=0.0_r8 !> tl_FC(i,N(ng))=0.0_r8 !> ad_FC(i,N(ng))=0.0_r8 END DO DO k=2,N(ng)-2 DO i=Istr,Iend !> tl_FC(i,k)=(cff1*(tl_v(i,j,k ,nrhs)+ & # ifdef NEARSHORE_MELLOR !> & tl_v_stokes(i,j,k )+ & !> & tl_v_stokes(i,j,k+1)+ & # endif !> & tl_v(i,j,k+1,nrhs))- & !> & cff2*(tl_v(i,j,k-1,nrhs)+ & # ifdef NEARSHORE_MELLOR !> & tl_v_stokes(i,j,k-1)+ & !> & tl_v_stokes(i,j,k+2)+ & # endif !> & tl_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)))+ & !> & (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*(tl_W(i,j ,k)+ & !> & tl_W(i,j-1,k))- & !> & cff2*(tl_W(i,j+1,k)+ & !> & tl_W(i,j-2,k))) !> adfac=(cff1*(W(i,j ,k)+ & & W(i,j-1,k))- & & cff2*(W(i,j+1,k)+ & & W(i,j-2,k)))*ad_FC(i,k) adfac1=adfac*cff1 adfac2=adfac*cff2 adfac=(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)))*ad_FC(i,k) adfac3=adfac*cff1 adfac4=adfac*cff2 ad_W(i,j-2,k)=ad_W(i,j-2,k)-adfac4 ad_W(i,j-1,k)=ad_W(i,j-1,k)+adfac3 ad_W(i,j ,k)=ad_W(i,j ,k)+adfac3 ad_W(i,j+1,k)=ad_W(i,j+1,k)-adfac4 ad_v(i,j,k-1,nrhs)=ad_v(i,j,k-1,nrhs)-adfac2 ad_v(i,j,k ,nrhs)=ad_v(i,j,k ,nrhs)+adfac1 ad_v(i,j,k+1,nrhs)=ad_v(i,j,k+1,nrhs)+adfac1 ad_v(i,j,k+2,nrhs)=ad_v(i,j,k+2,nrhs)-adfac2 # ifdef NEARSHORE_MELLOR ad_v_stokes(i,j,k-1)=ad_v_stokes(i,j,k-1)-adfac2 ad_v_stokes(i,j,k )=ad_v_stokes(i,j,k )+adfac1 ad_v_stokes(i,j,k+1)=ad_v_stokes(i,j,k+1)+adfac1 ad_v_stokes(i,j,k+2)=ad_v_stokes(i,j,k+2)-adfac2 # endif ad_FC(i,k)=0.0_r8 END DO END DO # endif END IF ! !----------------------------------------------------------------------- ! Add in adjoint vertical advection, U-momentum. !----------------------------------------------------------------------- ! DO k=1,N(ng) DO i=IstrU,Iend # ifdef DIAGNOSTICS_UV !! DiaRU(i,j,k,nrhs,M3vadv)=-cff # endif !> tl_ru(i,j,k,nrhs)=tl_ru(i,j,k,nrhs)-tl_cff !> ad_cff=ad_cff-ad_ru(i,j,k,nrhs) !> tl_cff=tl_FC(i,k)-tl_FC(i,k-1) !> ad_FC(i,k-1)=ad_FC(i,k-1)-ad_cff ad_FC(i,k )=ad_FC(i,k )+ad_cff ad_cff=0.0_r8 END DO END DO # ifdef UV_SADVECTION ! ! Apply spline code to BASIC STATE u-momentum which should be in ! units of m/s. CF will be used by the tangent linear spline code. ! 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. ! DO i=IstrU,Iend !> tl_FC(i,N(ng))=0.0_r8 !> ad_FC(i,N(ng))=0.0_r8 !> tl_FC(i,0)=0.0_r8 !> ad_FC(i,0)=0.0_r8 END DO cff3=1.0_r8/3.0_r8 cff4=1.0_r8/6.0_r8 DO k=1,N(ng)-1 DO i=IstrU,Iend !> tl_FC(i,k)=(cff1*(tl_W(i ,j,k)+ & !> & tl_W(i-1,j,k))- & !> & cff2*(tl_W(i+1,j,k)+ & !> & tl_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)))+ & !> & (cff1*(W(i ,j,k)+ & !> & W(i-1,j,k))- & !> & cff2*(W(i+1,j,k)+ & !> & W(i-2,j,k)))* & !> & (tl_u(i,j,k,nrhs)+ & # ifdef NEARSHORE_MELLOR !> & tl_u_stokes(i,j,k)+ & # endif !> & DC(i,k)*(cff3*tl_CF(i,k )+ & !> & cff4*tl_CF(i,k-1))+ & !> & tl_DC(i,k)*(cff3*CF(i,k )+ & !> & cff4*CF(i,k-1))) !> adfac1=(cff1*(W(i ,j,k)+ & & W(i-1,j,k))- & & cff2*(W(i+1,j,k)+ & & W(i-2,j,k)))*ad_FC(i,k) adfac2=adfac1*DC(i,k) adfac3=(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)))*ad_FC(i,k) adfac4=adfac3*cff1 adfac5=adfac3*cff2 ad_DC(i,k)=ad_DC(i,k)+(cff3*CF(i,k )+ & & cff4*CF(i,k-1))*adfac1 ad_CF(i,k-1)=ad_CF(i,k-1)+cff4*adfac2 ad_CF(i,k )=ad_CF(i,k )+cff3*adfac2 ad_u(i,j,k,nrhs)=ad_u(i,j,k,nrhs)+adfac1 # ifdef NEARSHORE_MELLOR ad_u_stokes(i,j,k)=ad_u_stokes(i,j,k)+adfac1 # endif ad_W(i-2,j,k)=ad_W(i-2,j,k)-adfac5 ad_W(i-1,j,k)=ad_W(i-1,j,k)+adfac4 ad_W(i ,j,k)=ad_W(i ,j,k)+adfac4 ad_W(i+1,j,k)=ad_W(i+1,j,k)-adfac5 ad_FC(i,k)=0.0_r8 END DO END DO ! ! Construct adjoint conservative parabolic splines for the vertical ! derivatives "tl_CF" of u-momentum. ! DO k=1,N(ng)-1 ! adjoint back substitution DO i=IstrU,Iend !> tl_CF(i,k)=tl_CF(i,k)-FC(i,k)*tl_CF(i,k+1) !> ad_CF(i,k+1)=ad_CF(i,k+1)-FC(i,k)*ad_CF(i,k) END DO END DO DO i=IstrU,Iend !> tl_CF(i,N)=0.0_r8 !> ad_CF(i,N)=0.0_r8 END DO ! adjoint LU decomposition DO k=N(ng)-1,1,-1 ! and forward substitution 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))) !> tl_CF(i,k)=cff*(6.0_r8*(tl_u(i,j,k+1,nrhs)- & # ifdef NEARSHORE_MELLOR !> & tl_u_stokes(i,j,k )+ & !> & tl_u_stokes(i,j,k+1)- & # endif !> & tl_u(i,j,k ,nrhs))- & !> & (tl_DC(i,k)*CF(i,k-1)+ & !> & 2.0_r8*(tl_DC(i,k)+tl_DC(i,k+1))*CF(i,k)+ & !> & tl_DC(i,k+1)*CF(i,k+1))- & !> & DC(i,k)*tl_CF(i,k-1)) !> adfac=cff*ad_CF(i,k) adfac1=adfac*6.0_r8 ad_CF(i,k-1)=ad_CF(i,k-1)-DC(i,k)*adfac ad_DC(i,k )=ad_DC(i,k )- & & (CF(i,k-1)+2.0_r8*CF(i,k))*adfac ad_DC(i,k+1)=ad_DC(i,k+1)- & & (CF(i,k+1)+2.0_r8*CF(i,k))*adfac ad_u(i,j,k ,nrhs)=ad_u(i,j,k ,nrhs)-adfac1 ad_u(i,j,k+1,nrhs)=ad_u(i,j,k+1,nrhs)+adfac1 # ifdef NEARSHORE_MELLOR ad_u_stokes(i,j,k )=ad_u_stokes(i,j,k )-adfac1 ad_u_stokes(i,j,k+1)=ad_u_stokes(i,j,k+1)+adfac1 # endif ad_CF(i,k)=0.0_r8 END DO END DO DO i=IstrU,Iend !> tl_CF(i,0)=0.0_r8 !> ad_CF(i,0)=0.0_r8 END DO cff1=9.0_r8/16.0_r8 cff2=1.0_r8/16.0_r8 DO k=1,N(ng) ! adjoint triadiagonal coefficients DO i=IstrU,Iend !> tl_DC(i,k)=cff1*(tl_Hz(i ,j,k)+ & !> & tl_Hz(i-1,j,k))- & !> & cff2*(tl_Hz(i+1,j,k)+ & !> & tl_Hz(i-2,j,k)) !> adfac1=cff1*ad_DC(i,k) adfac2=cff2*ad_DC(i,k) ad_Hz(i-2,j,k)=ad_Hz(i-2,j,k)-adfac2 ad_Hz(i+1,j,k)=ad_Hz(i+1,j,k)-adfac2 ad_Hz(i-1,j,k)=ad_Hz(i-1,j,k)+adfac1 ad_Hz(i ,j,k)=ad_Hz(i ,j,k)+adfac1 ad_DC(i,k)=0.0_r8 END DO END DO # elif defined UV_C2ADVECTION ! ! Second-order, central differences u-momentum vertical advection. ! DO i=IstrU,Iend # ifdef SED_MORPH # ifdef NEARSHORE_MELLOR !> tl_FC(i,0)=0.5_r8* !> & ((tl_u(i,j,1,nrhs)+tl_u_stokes(i,j,1))* & !> & (W(i ,j,0)+ & !> & W(i-1,j,0))+ & !> & (u(i,j,1,nrhs)+u_stokes(i,j,1))* & !> & (tl_W(i ,j,0)+ & !> & tl_W(i-1,j,0))) !> adfac=0.5_r8*ad_FC(i,0) adfac1=adfac*(W(i ,j,0)+ & & W(i-1,j,0)) adfac2=adfac*(u(i,j,1,nrhs)+u_stokes(i,j,1)) ad_u(i,j,1,nrhs)=ad_u(i,j,1,nrhs)+adfac1 ad_u_stokes(i,j,1)=ad_u_stokes(i,j,1)+adfac1 ad_W(i-1,j,0)=ad_W(i-1,j,0)+adfac2 ad_W(i ,j,0)=ad_W(i ,j,0)+adfac2 ad_FC(i,0)=0.0_r8 # else !> tl_FC(i,0)=0.5_r8* & !> & (tl_u(i,j,1,nrhs)* & !> & (W(i ,j,0)+ & !> & W(i-1,j,0))+ & !> & u(i,j,1,nrhs)* & !> & (tl_W(i ,j,0)+ & !> & tl_W(i-1,j,0))) !> adfac=0.5_r8*ad_FC(i,0) adfac1=adfac*u(i,j,1,nrhs) ad_u(i,j,1,nrhs)=ad_u(i,j,1,nrhs)+ & & (W(i ,j,0)+ & & W(i-1,j,0))*adfac ad_W(i-1,j,0)=ad_W(i-1,j,0)+adfac1 ad_W(i ,j,0)=ad_W(i ,j,0)+adfac1 ad_FC(i,0)=0.0_r8 # endif # else !> tl_FC(i,0)=0.0_r8 !> ad_FC(i,0)=0.0_r8 # endif !> tl_FC(i,N(ng))=0.0_r8 !> ad_FC(i,N(ng))=0.0_r8 END DO DO k=1,N(ng)-1 DO i=IstrU,Iend !> tl_FC(i,k)=0.25_r8*((tl_u(i,j,k ,nrhs)+ & # ifdef NEARSHORE_MELLOR !> & tl_u_stokes(i,j,k )+ & !> & tl_u_stokes(i,j,k+1)+ & # endif !> & tl_u(i,j,k+1,nrhs))* & !> & (W(i ,j,k)+ & !> & W(i-1,j,k))+ & !> & (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))* & !> & (tl_W(i ,j,k)+ & !> & tl_W(i-1,j,k))) !> adfac=0.25_r8*ad_FC(i,k) adfac1=adfac*(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)) adfac2=adfac*(W(i ,j,k)+ & & W(i-1,j,k)) ad_W(i-1,j,k)=ad_W(i-1,j,k)+adfac1 ad_W(i ,j,k)=ad_W(i ,j,k)+adfac1 ad_u(i,j,k ,nrhs)=ad_u(i,j,k ,nrhs)+adfac2 ad_u(i,j,k+1,nrhs)=ad_u(i,j,k+1,nrhs)+adfac2 # ifdef NEARSHORE_MELLOR ad_u_stokes(i,j,k )=ad_u_stokes(i,j,k )+adfac2 ad_u_stokes(i,j,k+1)=ad_u_stokes(i,j,k+1)+adfac2 # endif ad_FC(i,k)=0.0_r8 END DO END DO # elif defined UV_C4ADVECTION ! ! Fourth-order, central differences u-momentum vertical advection. ! cff1=9.0_r8/32.0_r8 cff2=1.0_r8/32.0_r8 DO i=IstrU,Iend # ifdef SED_MORPH # ifdef NEARSHORE_MELLOR !> tl_FC(i,0)=2.0_r8* & !> & ((cff1*(tl_u(i,j,1,nrhs)+tl_u_stokes(i,j,1))- & !> & cff2*(tl_u(i,j,2,nrhs)+tl_u_stokes(i,j,2)))* & !> & (W(i ,j,0)+ & !> & W(i-1,j,0))+ & !> & (cff1*(u(i,j,1,nrhs)+u_stokes(i,j,1))- & !> & cff2*(u(i,j,2,nrhs)+u_stokes(i,j,2)))* & !> & (tl_W(i ,j,0)+ & !> & tl_W(i-1,j,0))) !> adfac=2.0_r8*ad_FC(i,0) adfac1=adfac*(W(i ,j,0)+ & & W(i-1,j,0)) adfac2=adfac1*cff1 adfac3=adfac1*cff2 adfac4=adfac* & & (cff1*(u(i,j,1,nrhs)+u_stokes(i,j,1))- & & cff2*(u(i,j,2,nrhs)+u_stokes(i,j,2))) ad_u(i,j,1,nrhs)=ad_u(i,j,1,nrhs)+adfac2 ad_u(i,j,2,nrhs)=ad_u(i,j,2,nrhs)-adfac3 ad_u_stokes(i,j,1)=ad_u_stokes(i,j,1)+adfac2 ad_u_stokes(i,j,2)=ad_u_stokes(i,j,2)-adfac3 ad_W(i-1,j,0)=ad_W(i-1,j,0)+adfac4 ad_W(i ,j,0)=ad_W(i ,j,0)+adfac4 ad_FC(i,0)=0.0_r8 # else !> tl_FC(i,0)=2.0_r8* & !> & ((cff1*tl_u(i,j,1,nrhs)- & !> & cff2*tl_u(i,j,2,nrhs))* & !> & (W(i ,j,0)+ & !> & W(i-1,j,0))+ & !> & (cff1*u(i,j,1,nrhs)- & !> & cff2*u(i,j,2,nrhs))* & !> & (tl_W(i ,j,0)+ & !> & tl_W(i-1,j,0))) !> adfac=2.0_r8*ad_FC(i,0) adfac1=adfac*(W(i ,j,0)+ & & W(i-1,j,0)) adfac2=adfac*(cff1*u(i,j,1,nrhs)- & & cff2*u(i,j,2,nrhs)) ad_u(i,j,1,nrhs)=ad_u(i,j,1,nrhs)+cff1*adfac1 ad_u(i,j,2,nrhs)=ad_u(i,j,2,nrhs)-cff2*adfac1 ad_W(i-1,j,0)=ad_W(i-1,j,0)+adfac2 ad_W(i ,j,0)=ad_W(i ,j,0)+adfac2 ad_FC(i,0)=0.0_r8 # endif # else !> tl_FC(i,0)=0.0_r8 !> ad_FC(i,0)=0.0_r8 # endif !> tl_FC(i,1)=(cff1*(tl_u(i,j,1,nrhs)+ & # ifdef NEARSHORE_MELLOR !> & tl_u_stokes(i,j,1)+ & !> & tl_u_stokes(i,j,2)+ & # endif !> & tl_u(i,j,2,nrhs))- & !> & cff2*(tl_u(i,j,1,nrhs)+ & # ifdef NEARSHORE_MELLOR !> & tl_u_stokes(i,j,1)+ & !> & tl_u_stokes(i,j,3)+ & # endif !> & tl_u(i,j,3,nrhs)))* & !> & (W(i ,j,1)+ & !> & W(i-1,j,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)))* & !> & (tl_W(i ,j,1)+ & !> & tl_W(i-1,j,1)) !> adfac=(W(i ,j,1)+ & & W(i-1,j,1))*ad_FC(i,1) adfac1=adfac*cff1 adfac2=adfac*cff2 adfac3=(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)))*ad_FC(i,1) ad_W(i-1,j,1)=ad_W(i-1,j,1)+adfac3 ad_W(i ,j,1)=ad_W(i ,j,1)+adfac3 ad_u(i,j,1,nrhs)=ad_u(i,j,1,nrhs)+adfac1-adfac2 ad_u(i,j,2,nrhs)=ad_u(i,j,2,nrhs)+adfac1 ad_u(i,j,3,nrhs)=ad_u(i,j,3,nrhs)-adfac2 # ifdef NEARSHORE_MELLOR ad_u_stokes(i,j,1)=ad_u_stokes(i,j,1)+adfac1-adfac2 ad_u_stokes(i,j,2)=ad_u_stokes(i,j,2)+adfac1 ad_u_stokes(i,j,3)=ad_u_stokes(i,j,3)-adfac2 # endif ad_FC(i,1)=0.0_r8 !> tl_FC(i,N(ng)-1)=(cff1*(tl_u(i,j,N(ng)-1,nrhs)+ & # ifdef NEARSHORE_MELLOR !> & tl_u_stokes(i,j,N(ng)-1)+ & !> & tl_u_stokes(i,j,N(ng) )+ & # endif !> & tl_u(i,j,N(ng) ,nrhs))- & !> & cff2*(tl_u(i,j,N(ng)-2,nrhs)+ & # ifdef NEARSHORE_MELLOR !> & tl_u_stokes(i,j,N(ng)-2)+ & !> & tl_u_stokes(i,j,N(ng) )+ & # endif !> & tl_u(i,j,N(ng) ,nrhs)))* & !> & (W(i ,j,N(ng)-1)+ & !> & W(i-1,j,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)))* & !> & (tl_W(i ,j,N(ng)-1)+ & !> & tl_W(i-1,j,N(ng)-1)) !> adfac=(W(i ,j,N(ng)-1)+ & & W(i-1,j,N(ng)-1))*ad_FC(i,N(ng)-1) adfac1=adfac*cff1 adfac2=adfac*cff2 adfac3=(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)))*ad_FC(i,N(ng)-1) ad_W(i ,j,N(ng)-1)=ad_W(i ,j,N(ng)-1)+adfac3 ad_W(i-1,j,N(ng)-1)=ad_W(i-1,j,N(ng)-1)+adfac3 ad_u(i,j,N(ng)-2,nrhs)=ad_u(i,j,N(ng)-2,nrhs)-adfac2 ad_u(i,j,N(ng)-1,nrhs)=ad_u(i,j,N(ng)-1,nrhs)+adfac1 ad_u(i,j,N(ng) ,nrhs)=ad_u(i,j,N(ng) ,nrhs)+adfac1-adfac2 # ifdef NEARSHORE_MELLOR ad_u_stokes(i,j,N(ng)-2)=ad_u_stokes(i,j,N(ng)-2)-adfac2 ad_u_stokes(i,j,N(ng)-1)=ad_u_stokes(i,j,N(ng)-1)+adfac1 ad_u_stokes(i,j,N(ng) )=ad_u_stokes(i,j,N(ng) )+adfac1- & & adfac2 # endif ad_FC(i,N(ng)-1)=0.0_r8 !> tl_FC(i,N(ng))=0.0_r8 !> ad_FC(i,N(ng))=0.0_r8 END DO DO k=2,N(ng)-2 DO i=IstrU,Iend !> tl_FC(i,k)=(cff1*(tl_u(i,j,k ,nrhs)+ & # ifdef NEARSHORE_MELLOR !> & tl_u_stokes(i,j,k )+ & !> & tl_u_stokes(i,j,k+1)+ & # endif !> & tl_u(i,j,k+1,nrhs))- & !> & cff2*(tl_u(i,j,k-1,nrhs)+ & # ifdef NEARSHORE_MELLOR !> & tl_u_stokes(i,j,k-1)+ & !> & tl_u_stokes(i,j,k+2)+ & # endif !> & tl_u(i,j,k+2,nrhs)))* & !> & (W(i ,j,k)+ & !> & W(i-1,j,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)))* & !> & (tl_W(i ,j,k)+ & !> & tl_W(i-1,j,k)) !> adfac=(W(i ,j,k)+ & & W(i-1,j,k))*ad_FC(i,k) adfac1=adfac*cff1 adfac2=adfac*cff2 adfac3=(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)))*ad_FC(i,k) ad_W(i-1,j,k)=ad_W(i-1,j,k)+adfac3 ad_W(i ,j,k)=ad_W(i ,j,k)+adfac3 ad_u(i,j,k-1,nrhs)=ad_u(i,j,k-1,nrhs)-adfac2 ad_u(i,j,k ,nrhs)=ad_u(i,j,k ,nrhs)+adfac1 ad_u(i,j,k+1,nrhs)=ad_u(i,j,k+1,nrhs)+adfac1 ad_u(i,j,k+2,nrhs)=ad_u(i,j,k+2,nrhs)-adfac2 # ifdef NEARSHORE_MELLOR ad_u_stokes(i,j,k-1)=ad_u_stokes(i,j,k-1)-adfac2 ad_u_stokes(i,j,k )=ad_u_stokes(i,j,k )+adfac1 ad_u_stokes(i,j,k+1)=ad_u_stokes(i,j,k+1)+adfac1 ad_u_stokes(i,j,k+2)=ad_u_stokes(i,j,k+2)-adfac2 # endif ad_FC(i,k)=0.0_r8 END DO END DO # else ! ! Fourth-order, central differences u-momentum vertical advection. ! cff1=9.0_r8/16.0_r8 cff2=1.0_r8/16.0_r8 DO i=IstrU,Iend # ifdef SED_MORPH # ifdef NEARSHORE_MELLOR !> tl_FC(i,0)=2.0_r8* & !> & ((cff1*(tl_u(i,j,1,nrhs)+tl_u_stokes(i,j,1))- & !> & cff2*(tl_u(i,j,2,nrhs)+tl_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)))+ & !> & (cff1*(u(i,j,1,nrhs)+u_stokes(i,j,1))- & !> & cff2*(u(i,j,2,nrhs)+u_stokes(i,j,2)))* & !> & (cff1*(tl_W(i ,j,0)+ & !> & tl_W(i-1,j,0))- & !> & cff2*(tl_W(i+1,j,0)+ & !> & tl_W(i-2,j,0)))) !> adfac=2.0_r8*ad_FC(i,0) adfac1=adfac*(cff1*(W(i ,j,0)+ & & W(i-1,j,0))- & & cff2*(W(i+1,j,0)+ & & W(i-2,j,0))) adfac2=adfac1*cff1 adfac3=adfac1*cff2 adfac4=adfac* & & (cff1*(u(i,j,1,nrhs)+u_stokes(i,j,1))- & & cff2*(u(i,j,2,nrhs)+u_stokes(i,j,2))) ad_u(i,j,1,nrhs)=ad_u(i,j,1,nrhs)+adfac2 ad_u(i,j,2,nrhs)=ad_u(i,j,2,nrhs)-adfac3 ad_u_stokes(i,j,1)=ad_u_stokes(i,j,1)+adfac2 ad_u_stokes(i,j,2)=ad_u_stokes(i,j,2)-adfac3 ad_W(i-2,j,0)=ad_W(i-2,j,0)-cff2*adfac4 ad_W(i-1,j,0)=ad_W(i-1,j,0)+cff1*adfac4 ad_W(i ,j,0)=ad_W(i ,j,0)+cff1*adfac4 ad_W(i+1,j,0)=ad_W(i+1,j,0)-cff2*adfac4 ad_FC(i,0)=0.0_r8 # else !> tl_FC(i,0)=2.0_r8* & !> & ((cff1*tl_u(i,j,1,nrhs)- & !> & cff2*tl_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)))+ & !> & (cff1*u(i,j,1,nrhs)- & !> & cff2*u(i,j,2,nrhs))* & !> & (cff1*(tl_W(i ,j,0)+ & !> & tl_W(i-1,j,0))- & !> & cff2*(tl_W(i+1,j,0)+ & !> & tl_W(i-2,j,0)))) !> adfac=2.0_r8*ad_FC(i,0) adfac1=adfac*(cff1*(W(i ,j,0)+ & & W(i-1,j,0))- & & cff2*(W(i+1,j,0)+ & & W(i-2,j,0))) adfac2=adfac*(cff1*u(i,j,1,nrhs)- & & cff2*u(i,j,2,nrhs)) adfac3=adfac2*cff1 adfac4=adfac2*cff2 ad_u(i,j,1,nrhs)=ad_u(i,j,1,nrhs)+cff1*adfac1 ad_u(i,j,2,nrhs)=ad_u(i,j,2,nrhs)-cff2*adfac1 ad_W(i-2,j,0)=ad_W(i-2,j,0)-adfac4 ad_W(i-1,j,0)=ad_W(i-1,j,0)+adfac3 ad_W(i ,j,0)=ad_W(i ,j,0)+adfac3 ad_W(i+1,j,0)=ad_W(i+1,j,0)-adfac4 ad_FC(i,0)=0.0_r8 # endif # else !> tl_FC(i,0)=0.0_r8 !> ad_FC(i,0)=0.0_r8 # endif !> tl_FC(i,1)=(cff1*(tl_u(i,j,1,nrhs)+ & # ifdef NEARSHORE_MELLOR !> & tl_u_stokes(i,j,1)+ & !> & tl_u_stokes(i,j,2)+ & # endif !> & tl_u(i,j,2,nrhs))- & !> & cff2*(tl_u(i,j,1,nrhs)+ & # ifdef NEARSHORE_MELLOR !> & tl_u_stokes(i,j,1)+ & !> & tl_u_stokes(i,j,3)+ & # endif !> & tl_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)))+ & !> & (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*(tl_W(i ,j,1)+ & !> & tl_W(i-1,j,1))- & !> & cff2*(tl_W(i+1,j,1)+ & !> & tl_W(i-2,j,1))) !> adfac=(cff1*(W(i ,j,1)+ & & W(i-1,j,1))- & & cff2*(W(i+1,j,1)+ & & W(i-2,j,1)))*ad_FC(i,1) adfac1=adfac*cff1 adfac2=adfac*cff2 adfac=(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)))*ad_FC(i,1) adfac3=adfac*cff1 adfac4=adfac*cff2 ad_W(i-2,j,1)=ad_W(i-2,j,1)-adfac4 ad_W(i-1,j,1)=ad_W(i-1,j,1)+adfac3 ad_W(i ,j,1)=ad_W(i ,j,1)+adfac3 ad_W(i+1,j,1)=ad_W(i+1,j,1)-adfac4 ad_u(i,j,1,nrhs)=ad_u(i,j,1,nrhs)+adfac1-adfac2 ad_u(i,j,2,nrhs)=ad_u(i,j,2,nrhs)+adfac1 ad_u(i,j,3,nrhs)=ad_u(i,j,3,nrhs)-adfac2 # ifdef NEARSHORE_MELLOR ad_u_stokes(i,j,1)=ad_u_stokes(i,j,1)+adfac1-adfac2 ad_u_stokes(i,j,2)=ad_u_stokes(i,j,2)+adfac1 ad_u_stokes(i,j,3)=ad_u_stokes(i,j,3)-adfac2 # endif ad_FC(i,1)=0.0_r8 !> tl_FC(i,N(ng)-1)=(cff1*(tl_u(i,j,N(ng)-1,nrhs)+ & # ifdef NEARSHORE_MELLOR !> & tl_u_stokes(i,j,N(ng)-1)+ & !> & tl_u_stokes(i,j,N(ng) )+ & # endif !> & tl_u(i,j,N(ng) ,nrhs))- & !> & cff2*(tl_u(i,j,N(ng)-2,nrhs)+ & # ifdef NEARSHORE_MELLOR !> & tl_u_stokes(i,j,N(ng)-2)+ & !> & tl_u_stokes(i,j,N(ng) )+ & # endif !> & tl_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)))+ & !> & (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*(tl_W(i ,j,N(ng)-1)+ & !> & tl_W(i-1,j,N(ng)-1))- & !> & cff2*(tl_W(i+1,j,N(ng)-1)+ & !> & tl_W(i-2,j,N(ng)-1))) !> adfac=(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)))*ad_FC(i,N(ng)-1) adfac1=adfac*cff1 adfac2=adfac*cff2 adfac=(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)))*ad_FC(i,N(ng)-1) adfac3=adfac*cff1 adfac4=adfac*cff2 ad_W(i-2,j,N(ng)-1)=ad_W(i-2,j,N(ng)-1)-adfac4 ad_W(i-1,j,N(ng)-1)=ad_W(i-1,j,N(ng)-1)+adfac3 ad_W(i ,j,N(ng)-1)=ad_W(i ,j,N(ng)-1)+adfac3 ad_W(i+1,j,N(ng)-1)=ad_W(i+1,j,N(ng)-1)-adfac4 ad_u(i,j,N(ng)-2,nrhs)=ad_u(i,j,N(ng)-2,nrhs)-adfac2 ad_u(i,j,N(ng)-1,nrhs)=ad_u(i,j,N(ng)-1,nrhs)+adfac1 ad_u(i,j,N(ng) ,nrhs)=ad_u(i,j,N(ng) ,nrhs)+adfac1-adfac2 # ifdef NEARSHORE_MELLOR ad_u_stokes(i,j,N(ng)-2)=ad_u_stokes(i,j,N(ng)-2)-adfac2 ad_u_stokes(i,j,N(ng)-1)=ad_u_stokes(i,j,N(ng)-1)+adfac1 ad_u_stokes(i,j,N(ng) )=ad_u_stokes(i,j,N(ng) )+adfac1- & & adfac2 # endif ad_FC(i,N(ng)-1)=0.0_r8 !> tl_FC(i,N)=0.0_r8 !> ad_FC(i,N(ng))=0.0_r8 END DO DO k=2,N(ng)-2 DO i=IstrU,Iend !> tl_FC(i,k)=(cff1*(tl_u(i,j,k ,nrhs)+ & # ifdef NEARSHORE_MELLOR !> & tl_u_stokes(i,j,k )+ & !> & tl_u_stokes(i,j,k+1)+ & # endif !> & tl_u(i,j,k+1,nrhs))- & !> & cff2*(tl_u(i,j,k-1,nrhs)+ & # ifdef NEARSHORE_MELLOR !> & tl_u_stokes(i,j,k-1)+ & !> & tl_u_stokes(i,j,k+2)+ & # endif !> & tl_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)))+ & !> & (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*(tl_W(i ,j,k)+ & !> & tl_W(i-1,j,k))- & !> & cff2*(tl_W(i+1,j,k)+ & !> & tl_W(i-2,j,k))) !> adfac=(cff1*(W(i ,j,k)+ & & W(i-1,j,k))- & & cff2*(W(i+1,j,k)+ & & W(i-2,j,k)))*ad_FC(i,k) adfac1=adfac*cff1 adfac2=adfac*cff2 adfac=(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)))*ad_FC(i,k) adfac3=adfac*cff1 adfac4=adfac*cff2 ad_W(i-2,j,k)=ad_W(i-2,j,k)-adfac4 ad_W(i-1,j,k)=ad_W(i-1,j,k)+adfac3 ad_W(i ,j,k)=ad_W(i ,j,k)+adfac3 ad_W(i+1,j,k)=ad_W(i+1,j,k)-adfac4 ad_u(i,j,k-1,nrhs)=ad_u(i,j,k-1,nrhs)-adfac2 ad_u(i,j,k ,nrhs)=ad_u(i,j,k ,nrhs)+adfac1 ad_u(i,j,k+1,nrhs)=ad_u(i,j,k+1,nrhs)+adfac1 ad_u(i,j,k+2,nrhs)=ad_u(i,j,k+2,nrhs)-adfac2 # ifdef NEARSHORE_MELLOR ad_u_stokes(i,j,k-1)=ad_u_stokes(i,j,k-1)-adfac2 ad_u_stokes(i,j,k )=ad_u_stokes(i,j,k )+adfac1 ad_u_stokes(i,j,k+1)=ad_u_stokes(i,j,k+1)+adfac1 ad_u_stokes(i,j,k+2)=ad_u_stokes(i,j,k+2)-adfac2 # endif ad_FC(i,k)=0.0_r8 END DO END DO # endif # endif END DO J_LOOP K_LOOP : DO k=1,N(ng) # ifdef NEARSHORE_MELLOR ! !----------------------------------------------------------------------- ! Add in adjoint radiation stress terms. !----------------------------------------------------------------------- ! DO j=JstrV,Jend DO i=Istr,Iend !> tl_rv(i,j,k,nrhs)=tl_rv(i,j,k,nrhs)- & !> & tl_rvstr3d(i,j,k)*om_v(i,j)*on_v(i,j)- & !> & tl_rvlag3d(i,j,k) !> ad_rvstr3d(i,j,k)=ad_rvstr3d(i,j,k)- & & om_v(i,j)*on_v(i,j)*ad_rv(i,j,k,nrhs) ad_rvlag3d(i,j,k)=ad_rvlag3d(i,j,k)-ad_rv(i,j,k,nrhs) END DO END DO DO j=Jstr,Jend DO i=IstrU,Iend !> tl_ru(i,j,k,nrhs)=tl_ru(i,j,k,nrhs)- & !> & tl_rustr3d(i,j,k)*om_u(i,j)*on_u(i,j)- & !> & tl_rulag3d(i,j,k) !> ad_rustr3d(i,j,k)=ad_rustr3d(i,j,k)- & & om_u(i,j)*on_u(i,j)*ad_ru(i,j,k,nrhs) ad_rulag3d(i,j,k)=ad_rulag3d(i,j,k)-ad_ru(i,j,k,nrhs) END DO END DO # endif # ifdef UV_ADV ! !----------------------------------------------------------------------- ! Add in adjoint horizontal advection of momentum. !----------------------------------------------------------------------- ! ! Add in adjoint horizontal advection. ! DO j=JstrV,Jend DO i=Istr,Iend # ifdef DIAGNOSTICS_UV # ifdef CURVGRID !! DiaRV(i,j,k,nrhs,M3hadv)=DiaRV(i,j,k,nrhs,M3hadv)-cff !! DiaRV(i,j,k,nrhs,M3yadv)=DiaRV(i,j,k,nrhs,M3yadv)-cff2 !! DiaRV(i,j,k,nrhs,M3xadv)=DiaRV(i,j,k,nrhs,M3xadv)-cff1 # else !! DiaRV(i,j,k,nrhs,M3hadv)=-cff !! DiaRV(i,j,k,nrhs,M3yadv)=-cff2 !! DiaRV(i,j,k,nrhs,M3xadv)=-cff1 # endif # endif !> tl_rv(i,j,k,nrhs)=tl_rv(i,j,k,nrhs)-tl_cff !> ad_cff=ad_cff-ad_rv(i,j,k,nrhs) !> tl_cff=tl_cff1+tl_cff2 !> ad_cff1=ad_cff1+ad_cff ad_cff2=ad_cff2+ad_cff ad_cff=0.0_r8 !> tl_cff2=tl_VFe(i,j)-tl_VFe(i,j-1) !> ad_VFe(i,j-1)=ad_VFe(i,j-1)-ad_cff2 ad_VFe(i,j )=ad_VFe(i,j )+ad_cff2 ad_cff2=0.0_r8 !> tl_cff1=tl_VFx(i+1,j)-tl_VFx(i,j) !> ad_VFx(i ,j)=ad_VFx(i ,j)-ad_cff1 ad_VFx(i+1,j)=ad_VFx(i+1,j)+ad_cff1 ad_cff1=0.0_r8 END DO END DO DO j=Jstr,Jend DO i=IstrU,Iend # ifdef DIAGNOSTICS_UV # ifdef CURVGRID !! DiaRU(i,j,k,nrhs,M3hadv)=DiaRU(i,j,k,nrhs,M3hadv)-cff !! DiaRU(i,j,k,nrhs,M3yadv)=DiaRU(i,j,k,nrhs,M3yadv)-cff2 !! DiaRU(i,j,k,nrhs,M3xadv)=DiaRU(i,j,k,nrhs,M3xadv)-cff1 # else !! DiaRU(i,j,k,nrhs,M3hadv)=-cff !! DiaRU(i,j,k,nrhs,M3yadv)=-cff2 !! DiaRU(i,j,k,nrhs,M3xadv)=-cff1 # endif # endif !> tl_ru(i,j,k,nrhs)=tl_ru(i,j,k,nrhs)-tl_cff !> ad_cff=ad_cff-ad_ru(i,j,k,nrhs) !> tl_cff=tl_cff1+tl_cff2 !> ad_cff1=ad_cff1+ad_cff ad_cff2=ad_cff2+ad_cff ad_cff=0.0_r8 !> tl_cff2=tl_UFe(i,j+1)-tl_UFe(i,j) !> ad_UFe(i,j )=ad_UFe(i,j )-ad_cff2 ad_UFe(i,j+1)=ad_UFe(i,j+1)+ad_cff2 ad_cff2=0.0_r8 !> tl_cff1=tl_UFx(i,j)-tl_UFx(i-1,j) !> ad_UFx(i-1,j)=ad_UFx(i-1,j)-ad_cff1 ad_UFx(i ,j)=ad_UFx(i ,j)+ad_cff1 ad_cff1=0.0_r8 END DO END DO # ifdef UV_C2ADVECTION ! ! Second-order, centered differences advection. ! DO j=JstrV-1,Jend DO i=Istr,Iend !> tl_VFe(i,j)=0.25_r8* & !> & ((tl_v(i,j ,k,nrhs)+ & # ifdef NEARSHORE_MELLOR !> & tl_v_stokes(i,j ,k)+ & !> & tl_v_stokes(i,j+1,k)+ & # endif !> & tl_v(i,j+1,k,nrhs))* & !> & (Hvom(i,j ,k)+ & !> & Hvom(i,j+1,k))+ & !> & (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))* & !> & (tl_Hvom(i,j ,k)+ & !> & tl_Hvom(i,j+1,k))) !> adfac=0.25_r8*ad_VFe(i,j) adfac1=adfac*(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)) adfac2=adfac*(Hvom(i,j ,k)+ & & Hvom(i,j+1,k)) ad_Hvom(i,j ,k)=ad_Hvom(i,j ,k)+adfac1 ad_Hvom(i,j+1,k)=ad_Hvom(i,j+1,k)+adfac1 ad_v(i,j ,k,nrhs)=ad_v(i,j ,k,nrhs)+adfac2 ad_v(i,j+1,k,nrhs)=ad_v(i,j+1,k,nrhs)+adfac2 # ifdef NEARSHORE_MELLOR ad_v_stokes(i,j ,k)=ad_v_stokes(i,j ,k)+adfac2 ad_v_stokes(i,j+1,k)=ad_v_stokes(i,j+1,k)+adfac2 # endif ad_VFe(i,j)=0.0_r8 END DO END DO DO j=JstrV,Jend DO i=Istr,Iend+1 !> tl_VFx(i,j)=0.25_r8* & !> & ((tl_v(i-1,j,k,nrhs)+ & # ifdef NEARSHORE_MELLOR !> & tl_v_stokes(i-1,j,k)+ & !> & tl_v_stokes(i ,j,k)+ & # endif !> & tl_v(i ,j,k,nrhs))* & !> & (Huon(i,j-1,k)+ & !> & Huon(i,j ,k))+ & !> & (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))* & !> & (tl_Huon(i,j-1,k)+ & !> & tl_Huon(i,j ,k))) !> adfac=0.25_r8*ad_VFx(i,j) adfac1=adfac*(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)) adfac2=adfac*(Huon(i,j-1,k)+ & & Huon(i,j ,k)) ad_Huon(i,j-1,k)=ad_Huon(i,j-1,k)+adfac1 ad_Huon(i,j ,k)=ad_Huon(i,j ,k)+adfac1 ad_v(i-1,j,k,nrhs)=ad_v(i-1,j,k,nrhs)+adfac2 ad_v(i ,j,k,nrhs)=ad_v(i ,j,k,nrhs)+adfac2 # ifdef NEARSHORE_MELLOR ad_v_stokes(i-1,j,k)=ad_v_stokes(i-1,j,k)+adfac2 ad_v_stokes(i ,j,k)=ad_v_stokes(i ,j,k)+adfac2 # endif ad_VFx(i,j)=0.0_r8 END DO END DO DO j=Jstr,Jend+1 DO i=IstrU,Iend !> tl_UFe(i,j)=0.25_r8* & !> & ((tl_u(i,j-1,k,nrhs)+ & # ifdef NEARSHORE_MELLOR !> & tl_u_stokes(i,j-1,k)+ & !> & tl_u_stokes(i,j ,k)+ & # endif !> & tl_u(i,j ,k,nrhs))* & !> & (Hvom(i-1,j,k)+ & !> & Hvom(i ,j,k))+ & !> & (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))* & !> & (tl_Hvom(i-1,j,k)+ & !> & tl_Hvom(i ,j,k))) !> adfac=0.25_r8*ad_UFe(i,j) adfac1=adfac*(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)) adfac2=adfac*(Hvom(i-1,j,k)+ & & Hvom(i ,j,k)) ad_Hvom(i-1,j,k)=ad_Hvom(i-1,j,k)+adfac1 ad_Hvom(i ,j,k)=ad_Hvom(i ,j,k)+adfac1 ad_u(i,j-1,k,nrhs)=ad_u(i,j-1,k,nrhs)+adfac2 ad_u(i,j ,k,nrhs)=ad_u(i,j ,k,nrhs)+adfac2 # ifdef NEARSHORE_MELLOR ad_u_stokes(i,j-1,k)=ad_u_stokes(i,j-1,k)+adfac2 ad_u_stokes(i,j ,k)=ad_u_stokes(i,j ,k)+adfac2 # endif ad_UFe(i,j)=0.0_r8 END DO END DO DO j=Jstr,Jend DO i=IstrU-1,Iend !> tl_UFx(i,j)=0.25_r8* & !> & ((tl_u(i ,j,k,nrhs)+ & # ifdef NEARSHORE_MELLOR !> & tl_u_stokes(i ,j,k)+ & !> & tl_u_stokes(i+1,j,k)+ & # endif !> & tl_u(i+1,j,k,nrhs))* & !> & (Huon(i ,j,k)+ & !> & Huon(i+1,j,k))+ & !> & (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))* & !> & (tl_Huon(i ,j,k)+ & !> & tl_Huon(i+1,j,k))) !> adfac=0.25_r8*ad_UFx(i,j) adfac1=adfac*(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)) adfac2=adfac*(Huon(i ,j,k)+ & & Huon(i+1,j,k)) ad_Huon(i ,j,k)=ad_Huon(i ,j,k)+adfac1 ad_Huon(i+1,j,k)=ad_Huon(i+1,j,k)+adfac1 ad_u(i ,j,k,nrhs)=ad_u(i ,j,k,nrhs)+adfac2 ad_u(i+1,j,k,nrhs)=ad_u(i+1,j,k,nrhs)+adfac2 # ifdef NEARSHORE_MELLOR ad_u_stokes(i ,j,k)=ad_u_stokes(i ,j,k)+adfac2 ad_u_stokes(i+1,j,k)=ad_u_stokes(i+1,j,k)+adfac2 # endif ad_UFx(i,j)=0.0_r8 END DO END DO # else ! # ifdef UV_C4ADVECTION ! Fourth-order, centered differences v-momentum advection. # else ! Third-order, upstream bias v-momentum advection with velocity ! dependent hyperdiffusion. # endif ! DO j=JstrVm1,Jendp1 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 IF (.not.(CompositeGrid(isouth,ng).or.NSperiodic(ng))) THEN IF (DOMAIN(ng)%Southern_Edge(tile)) THEN DO i=Istr,Iend vee (i,Jstr)=vee (i,Jstr+1) Hvee(i,Jstr)=Hvee(i,Jstr+1) 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 vee (i,Jend+1)=vee (i,Jend) Hvee(i,Jend+1)=Hvee(i,Jend) END DO END IF END IF # ifdef UV_C4ADVECTION cff=1.0_r8/6.0_r8 DO j=JstrV-1,Jend DO i=Istr,Iend !> tl_VFe(i,j)=0.25_r8*((tl_v(i,j ,k,nrhs)+ & # ifdef NEARSHORE_MELLOR !> & tl_v_stokes(i,j ,k)+ & !> & tl_v_stokes(i,j+1,k)+ & # endif !> & tl_v(i,j+1,k,nrhs)- & !> & cff*(tl_vee (i,j )+ & !> & tl_vee (i,j+1)))* & !> & (Hvom(i,j ,k)+ & !> & Hvom(i,j+1,k)- & !> & cff*(Hvee(i,j )+ & !> & Hvee(i,j+1)))+ & !> & (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)))* & !> & (tl_Hvom(i,j ,k)+ & !> & tl_Hvom(i,j+1,k)- & !> & cff*(tl_Hvee(i,j )+ & !> & tl_Hvee(i,j+1)))) !> adfac=0.25_r8*ad_VFe(i,j) adfac1=adfac*(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))) adfac2=adfac1*cff adfac3=adfac*(Hvom(i,j ,k)+ & & Hvom(i,j+1,k)- & & cff*(Hvee(i,j )+ & & Hvee(i,j+1))) adfac4=adfac3*cff ad_Hvom(i,j ,k)=ad_Hvom(i,j ,k)+adfac1 ad_Hvom(i,j+1,k)=ad_Hvom(i,j+1,k)+adfac1 ad_Hvee(i,j )=ad_Hvee(i,j )-adfac2 ad_Hvee(i,j+1)=ad_Hvee(i,j+1)-adfac2 ad_v(i,j ,k,nrhs)=ad_v(i,j ,k,nrhs)+adfac3 ad_v(i,j+1,k,nrhs)=ad_v(i,j+1,k,nrhs)+adfac3 # ifdef NEARSHORE_MELLOR ad_v_stokes(i,j ,k)=ad_v_stokes(i,j ,k)+adfac3 ad_v_stokes(i,j+1,k)=ad_v_stokes(i,j+1,k)+adfac3 # endif ad_vee (i,j )=ad_vee (i,j )-adfac4 ad_vee (i,j+1)=ad_vee (i,j+1)-adfac4 ad_VFe(i,j)=0.0_r8 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 !> tl_VFe(i,j)=0.25_r8* & !> & ((tl_cff1+Gadv*tl_cff)* & !> & (Hvom(i,j ,k)+ & !> & Hvom(i,j+1,k)+ & !> & Gadv*0.5_r8*(Hvee(i,j )+ & !> & Hvee(i,j+1)))+ & !> & (cff1+Gadv*cff)* & !> & (tl_Hvom(i,j ,k)+ & !> & tl_Hvom(i,j+1,k)+ & !> & Gadv*0.5_r8*(tl_Hvee(i,j )+ & !> & tl_Hvee(i,j+1))) !> adfac=0.25_r8*ad_VFe(i,j) adfac1=adfac*(cff1+Gadv*cff) adfac2=adfac1*Gadv*0.5_r8 adfac3=adfac*(Hvom(i,j ,k)+ & & Hvom(i,j+1,k)+ & & Gadv*0.5_r8*(Hvee(i,j )+ & & Hvee(i,j+1))) ad_Hvom(i,j ,k)=ad_Hvom(i,j ,k)+adfac1 ad_Hvom(i,j+1,k)=ad_Hvom(i,j+1,k)+adfac1 ad_Hvee(i,j )=ad_Hvee(i,j )+adfac2 ad_Hvee(i,j+1)=ad_Hvee(i,j+1)+adfac2 ad_cff=ad_cff+Gadv*adfac3 ad_cff1=ad_cff1+adfac3 ad_VFe(i,j)=0.0_r8 IF (cff1.gt.0.0_r8) THEN !> tl_cff=tl_vee(i,j) !> ad_vee(i,j)=ad_vee(i,j)+ad_cff ad_cff=0.0_r8 ELSE !> tl_cff=tl_vee(i,j+1) !> ad_vee(i,j+1)=ad_vee(i,j+1)+ad_cff ad_cff=0.0_r8 END IF !> tl_cff1=tl_v(i,j ,k,nrhs)+ & # ifdef NEARSHORE_MELLOR !> & tl_v_stokes(i,j ,k)+ & !> & tl_v_stokes(i,j+1,k)+ & # endif !> & tl_v(i,j+1,k,nrhs) !> ad_v(i,j ,k,nrhs)=ad_v(i,j ,k,nrhs)+ad_cff1 ad_v(i,j+1,k,nrhs)=ad_v(i,j+1,k,nrhs)+ad_cff1 # ifdef NEARSHORE_MELLOR ad_v_stokes(i,j ,k)=ad_v_stokes(i,j ,k)+ad_cff1 ad_v_stokes(i,j+1,k)=ad_v_stokes(i,j+1,k)+ad_cff1 # endif ad_cff1=0.0_r8 END DO END DO # endif IF (.not.(CompositeGrid(inorth,ng).or.NSperiodic(ng))) THEN IF (DOMAIN(ng)%Northern_Edge(tile)) THEN DO i=Istr,Iend !> tl_Hvee(i,Jend+1)=tl_Hvee(i,Jend) !> ad_Hvee(i,Jend)=ad_Hvee(i,Jend)+ad_Hvee(i,Jend+1) ad_Hvee(i,Jend+1)=0.0_r8 !> tl_vee (i,Jend+1)=tl_vee (i,Jend) !> ad_vee (i,Jend)=ad_vee (i,Jend)+ad_vee (i,Jend+1) ad_vee (i,Jend+1)=0.0_r8 END DO END IF END IF IF (.not.(CompositeGrid(isouth,ng).or.NSperiodic(ng))) THEN IF (DOMAIN(ng)%Southern_Edge(tile)) THEN DO i=Istr,Iend !> tl_Hvee(i,Jstr)=tl_Hvee(i,Jstr+1) !> ad_Hvee(i,Jstr+1)=ad_Hvee(i,Jstr+1)+ad_Hvee(i,Jstr) ad_Hvee(i,Jstr)=0.0_r8 !> tl_vee (i,Jstr)=tl_vee (i,Jstr+1) !> ad_vee (i,Jstr+1)=ad_vee (i,Jstr+1)+ad_vee (i,Jstr) ad_vee (i,Jstr)=0.0_r8 END DO END IF END IF DO j=JstrVm1,Jendp1 DO i=Istr,Iend !> tl_Hvee(i,j)=tl_Hvom(i,j-1,k)-2.0_r8*tl_Hvom(i,j,k)+ & !> & tl_Hvom(i,j+1,k) !> ad_Hvom(i,j-1,k)=ad_Hvom(i,j-1,k)+ad_Hvee(i,j) ad_Hvom(i,j ,k)=ad_Hvom(i,j ,k)-2.0_r8*ad_Hvee(i,j) ad_Hvom(i,j+1,k)=ad_Hvom(i,j+1,k)+ad_Hvee(i,j) ad_Hvee(i,j)=0.0_r8 !> tl_vee(i,j)=tl_v(i,j-1,k,nrhs)-2.0_r8*tl_v(i,j,k,nrhs)+ & # ifdef NEARSHORE_MELLOR !> tl_v_stokes(i,j-1,k)-2.0_r8*tl_v_stokes(i,j,k)+ & !> & tl_v_stokes(i,j+1,k) # endif !> & tl_v(i,j+1,k,nrhs) !> ad_v(i,j-1,k,nrhs)=ad_v(i,j-1,k,nrhs)+ad_vee(i,j) ad_v(i,j ,k,nrhs)=ad_v(i,j ,k,nrhs)-2.0_r8*ad_vee(i,j) ad_v(i,j+1,k,nrhs)=ad_v(i,j+1,k,nrhs)+ad_vee(i,j) # ifdef NEARSHORE_MELLOR ad_v_stokes(i,j-1,k)=ad_v_stokes(i,j-1,k)+ad_vee(i,j) ad_v_stokes(i,j ,k)=ad_v_stokes(i,j ,k)-2.0_r8*ad_vee(i,j) ad_v_stokes(i,j+1,k)=ad_v_stokes(i,j+1,k)+ad_vee(i,j) # endif ad_vee(i,j)=0.0_r8 END DO END DO DO j=JstrV,Jend DO i=Istrm1,Iendp1 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 IF (.not.(CompositeGrid(iwest,ng).or.EWperiodic(ng))) THEN IF (DOMAIN(ng)%Western_Edge(tile)) THEN DO j=JstrV,Jend vxx(Istr-1,j)=vxx(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=JstrV,Jend vxx(Iend+1,j)=vxx(Iend,j) END DO END IF END IF 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 cff=1.0_r8/6.0_r8 DO j=JstrV,Jend DO i=Istr,Iend+1 !> tl_VFx(i,j)=0.25_r8*((tl_v(i ,j,k,nrhs)+ & # ifdef NEARSHORE_MELLOR !> & tl_v_stokes(i ,j,k)+ & !> & tl_v_stokes(i-1,j,k)+ & # endif !> & tl_v(i-1,j,k,nrhs)- & !> & cff*(tl_vxx (i ,j)+ & !> & tl_vxx (i-1,j)))* & !> & (Huon(i,j ,k)+ & !> & Huon(i,j-1,k)- & !> & cff*(Huee(i,j )+ & !> & Huee(i,j-1)))+ & !> & (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)))* & !> & (tl_Huon(i,j ,k)+ & !> & tl_Huon(i,j-1,k)- & !> & cff*(tl_Huee(i,j )+ & !> & tl_Huee(i,j-1)))) !> adfac=0.25_r8*ad_VFx(i,j) adfac1=adfac*(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))) adfac2=adfac1*cff adfac3=adfac*(Huon(i,j ,k)+ & & Huon(i,j-1,k)- & & cff*(Huee(i,j )+ & & Huee(i,j-1))) adfac4=adfac3*cff ad_Huon(i,j-1,k)=ad_Huon(i,j-1,k)+adfac1 ad_Huon(i,j ,k)=ad_Huon(i,j ,k)+adfac1 ad_Huee(i,j )=ad_Huee(i,j )-adfac2 ad_Huee(i,j-1)=ad_Huee(i,j-1)-adfac2 ad_v(i-1,j,k,nrhs)=ad_v(i-1,j,k,nrhs)+adfac3 ad_v(i ,j,k,nrhs)=ad_v(i ,j,k,nrhs)+adfac3 # ifdef NEARSHORE_MELLOR ad_v_stokes(i-1,j,k)=ad_v_stokes(i-1,j,k)+adfac3 ad_v_stokes(i ,j,k)=ad_v_stokes(i ,j,k)+adfac3 # endif ad_vxx (i-1,j)=ad_vxx (i-1,j)-adfac4 ad_vxx (i ,j)=ad_vxx (i ,j)-adfac4 ad_VFx(i,j)=0.0_r8 END DO END DO # else 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 !> tl_VFx(i,j)=0.25_r8* & !> & ((tl_cff1+Gadv*tl_cff)* & !> & (cff2+Gadv*0.5_r8*(Huee(i,j )+ & !> & Huee(i,j-1)))+ & !> & (cff1+Gadv*cff)* & !> & (tl_cff2+Gadv*0.5_r8*(tl_Huee(i,j )+ & !> & tl_Huee(i,j-1)))) !> adfac=0.25_r8*ad_VFx(i,j) adfac1=adfac*(cff1+Gadv*cff) adfac2=adfac1*Gadv*0.5_r8 adfac3=adfac*(cff2+Gadv*0.5_r8*(Huee(i,j )+ & & Huee(i,j-1))) ad_Huee(i,j-1)=ad_Huee(i,j-1)+adfac2 ad_Huee(i,j )=ad_Huee(i,j )+adfac2 ad_cff2=ad_cff2+adfac1 ad_cff1=ad_cff1+adfac3 ad_cff=ad_cff+Gadv*adfac3 ad_VFx(i,j)=0.0_r8 IF (cff2.gt.0.0_r8) THEN !> tl_cff=tl_vxx(i-1,j) !> ad_vxx(i-1,j)=ad_vxx(i-1,j)+ad_cff ad_cff=0.0_r8 ELSE !> tl_cff=tl_vxx(i,j) !> ad_vxx(i,j)=ad_vxx(i,j)+ad_cff ad_cff=0.0_r8 END IF !> tl_cff2=tl_Huon(i,j,k)+tl_Huon(i,j-1,k) !> ad_Huon(i,j-1,k)=ad_Huon(i,j-1,k)+ad_cff2 ad_Huon(i,j ,k)=ad_Huon(i,j ,k)+ad_cff2 ad_cff2=0.0_r8 !> tl_cff1=tl_v(i ,j,k,nrhs)+ & # ifdef NEARSHORE_MELLOR !> & tl_v_stokes(i ,j,k)+ & !> & tl_v_stokes(i-1,j,k)+ & # endif !> & tl_v(i-1,j,k,nrhs) !> ad_v(i-1,j,k,nrhs)=ad_v(i-1,j,k,nrhs)+ad_cff1 ad_v(i ,j,k,nrhs)=ad_v(i ,j,k,nrhs)+ad_cff1 # ifdef NEARSHORE_MELLOR ad_v_stokes(i-1,j,k)=ad_v_stokes(i-1,j,k)+ad_cff1 ad_v_stokes(i ,j,k)=ad_v_stokes(i ,j,k)+ad_cff1 # endif ad_cff1=0.0_r8 END DO END DO # endif DO j=JstrV-1,Jend DO i=Istr,Iend+1 !> tl_Huee(i,j)=tl_Huon(i,j-1,k)-2.0_r8*tl_Huon(i,j,k)+ !> & tl_Huon(i,j+1,k) !> ad_Huon(i,j-1,k)=ad_Huon(i,j-1,k)+ad_Huee(i,j) ad_Huon(i,j ,k)=ad_Huon(i,j ,k)-2.0_r8*ad_Huee(i,j) ad_Huon(i,j+1,k)=ad_Huon(i,j+1,k)+ad_Huee(i,j) ad_Huee(i,j)=0.0_r8 END DO END DO IF (.not.(CompositeGrid(ieast,ng).or.EWperiodic(ng))) THEN IF (DOMAIN(ng)%Eastern_Edge(tile)) THEN DO j=JstrV,Jend !> tl_vxx(Iend+1,j)=tl_vxx(Iend,j) !> ad_vxx(Iend,j)=ad_vxx(Iend,j)+ad_vxx(Iend+1,j) ad_vxx(Iend+1,j)=0.0_r8 END DO END IF END IF IF (.not.(CompositeGrid(iwest,ng).or.EWperiodic(ng))) THEN IF (DOMAIN(ng)%Western_Edge(tile)) THEN DO j=JstrV,Jend !> tl_vxx(Istr-1,j)=tl_vxx(Istr,j) !> ad_vxx(Istr,j)=ad_vxx(Istr,j)+ad_vxx(Istr-1,j) ad_vxx(Istr-1,j)=0.0_r8 END DO END IF END IF DO j=JstrV,Jend DO i=Istrm1,Iendp1 !> tl_vxx(i,j)=tl_v(i-1,j,k,nrhs)-2.0_r8*tl_v(i,j,k,nrhs)+ & # ifdef NEARSHORE_MELLOR !> & tl_v_stokes(i-1,j,k)-2.0_r8*tl_v_stokes(i,j,k)+ & !> & tl_v_stokes(i+1,j,k)+ & # endif !> & tl_v(i+1,j,k,nrhs) !> ad_v(i-1,j,k,nrhs)=ad_v(i-1,j,k,nrhs)+ad_vxx(i,j) ad_v(i ,j,k,nrhs)=ad_v(i ,j,k,nrhs)-2.0_r8*ad_vxx(i,j) ad_v(i+1,j,k,nrhs)=ad_v(i+1,j,k,nrhs)+ad_vxx(i,j) # ifdef NEARSHORE_MELLOR ad_v_stokes(i-1,j,k)=ad_v_stokes(i-1,j,k)+ad_vxx(i,j) ad_v_stokes(i ,j,k)=ad_v_stokes(i ,j,k)-2.0_r8*ad_vxx(i,j) ad_v_stokes(i+1,j,k)=ad_v_stokes(i+1,j,k)+ad_vxx(i,j) # endif ad_vxx(i,j)=0.0_r8 END DO END DO DO j=Jstrm1,Jendp1 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 IF (.not.(CompositeGrid(isouth,ng).or.NSperiodic(ng))) THEN IF (DOMAIN(ng)%Southern_Edge(tile)) THEN DO i=IstrU,Iend uee(i,Jstr-1)=uee(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=IstrU,Iend uee(i,Jend+1)=uee(i,Jend) END DO END IF END IF 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 ! ! Fourth-order, centered differences u-momentum adjoint advection. ! cff=1.0_r8/6.0_r8 DO j=Jstr,Jend+1 DO i=IstrU,Iend !> tl_UFe(i,j)=0.25_r8*((tl_u(i,j ,k,nrhs)+ & # ifdef NEARSHORE_MELLOR !> & tl_u_stokes(i,j ,k)+ & !> & tl_u_stokes(i,j-1,k)+ & # endif !> & tl_u(i,j-1,k,nrhs)- & !> & cff*(tl_uee (i,j )+ & !> & tl_uee (i,j-1)))* & !> & (Hvom(i ,j,k)+ & !> & Hvom(i-1,j,k)- & !> & cff*(Hvxx(i ,j)+ & !> & Hvxx(i-1,j)))+ & !> & (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)))* & !> & (tl_Hvom(i ,j,k)+ & !> & tl_Hvom(i-1,j,k)- & !> & cff*(tl_Hvxx(i ,j)+ & !> & tl_Hvxx(i-1,j)))) !> adfac=0.25_r8*ad_UFe(i,j) adfac1=adfac*(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))) adfac2=adfac1*cff adfac3=adfac*(Hvom(i ,j,k)+ & & Hvom(i-1,j,k)- & & cff*(Hvxx(i ,j)+ & & Hvxx(i-1,j))) adfac4=adfac3*cff ad_Hvom(i-1,j,k)=ad_Hvom(i-1,j,k)+adfac1 ad_Hvom(i ,j,k)=ad_Hvom(i ,j,k)+adfac1 ad_Hvxx(i-1,j)=ad_Hvxx(i-1,j)-adfac2 ad_Hvxx(i ,j)=ad_Hvxx(i ,j)-adfac2 ad_u(i,j-1,k,nrhs)=ad_u(i,j-1,k,nrhs)+adfac3 ad_u(i,j ,k,nrhs)=ad_u(i,j ,k,nrhs)+adfac3 # ifdef NEARSHORE_MELLOR ad_u_stokes(i,j-1,k)=ad_u_stokes(i,j-1,k)+adfac3 ad_u_stokes(i,j ,k)=ad_u_stokes(i,j ,k)+adfac3 # endif ad_uee (i,j-1)=ad_uee (i,j-1)-adfac4 ad_uee (i,j )=ad_uee (i,j )-adfac4 ad_UFe(i,j)=0.0_r8 END DO END DO # else ! ! Third-order, upstream bias u-momentum adjoint advection with velocity ! dependent hyperdiffusion. ! 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 !> tl_UFe(i,j)=0.25_r8* & !> & ((tl_cff1+Gadv*tl_cff)* & !> & (cff2+Gadv*0.5_r8*(Hvxx(i ,j)+ & !> & Hvxx(i-1,j)))+ & !> & (cff1+Gadv*cff)* & !> & (tl_cff2+Gadv*0.5_r8*(tl_Hvxx(i ,j)+ & !> & tl_Hvxx(i-1,j)))) !> adfac=0.25_r8*ad_UFe(i,j) adfac1=adfac*(cff1+Gadv*cff) adfac2=adfac1*Gadv*0.5_r8 adfac3=adfac*(cff2+Gadv*0.5_r8*(Hvxx(i ,j)+ & & Hvxx(i-1,j))) ad_Hvxx(i-1,j)=ad_Hvxx(i-1,j)+adfac2 ad_Hvxx(i ,j)=ad_Hvxx(i ,j)+adfac2 ad_cff2=ad_cff2+adfac1 ad_cff1=ad_cff1+adfac3 ad_cff=ad_cff+Gadv*adfac3 ad_UFe(i,j)=0.0_r8 IF (cff2.gt.0.0_r8) THEN !> tl_cff=tl_uee(i,j-1) !> ad_uee(i,j-1)=ad_uee(i,j-1)+ad_cff ad_cff=0.0_r8 ELSE !> tl_cff=tl_uee(i,j) !> ad_uee(i,j)=ad_uee(i,j)+ad_cff ad_cff=0.0_r8 END IF !> tl_cff2=tl_Hvom(i,j,k)+tl_Hvom(i-1,j,k) !> ad_Hvom(i-1,j,k)=ad_Hvom(i-1,j,k)+ad_cff2 ad_Hvom(i ,j,k)=ad_Hvom(i ,j,k)+ad_cff2 ad_cff2=0.0_r8 !> tl_cff1=tl_u(i,j,k,nrhs)+ & # ifdef NEARSHORE_MELLOR !> & tl_u_stokes(i,j ,k)+ & !> & tl_u_stokes(i,j-1,k)+ & # endif !> & tl_u(i,j-1,k,nrhs) !> ad_u(i,j-1,k,nrhs)=ad_u(i,j-1,k,nrhs)+ad_cff1 ad_u(i,j ,k,nrhs)=ad_u(i,j ,k,nrhs)+ad_cff1 # ifdef NEARSHORE_MELLOR ad_u_stokes(i,j-1,k)=ad_u_stokes(i,j-1,k)+ad_cff1 ad_u_stokes(i,j ,k)=ad_u_stokes(i,j ,k)+ad_cff1 # endif ad_cff1=0.0_r8 END DO END DO # endif DO j=Jstr,Jend+1 DO i=IstrU-1,Iend !> tl_Hvxx(i,j)=tl_Hvom(i-1,j,k)-2.0_r8*tl_Hvom(i,j,k)+ & !> & tl_Hvom(i+1,j,k) !> ad_Hvom(i-1,j,k)=ad_Hvom(i-1,j,k)+ad_Hvxx(i,j) ad_Hvom(i ,j,k)=ad_Hvom(i ,j,k)-2.0_r8*ad_Hvxx(i,j) ad_Hvom(i+1,j,k)=ad_Hvom(i+1,j,k)+ad_Hvxx(i,j) ad_Hvxx(i,j)=0.0_r8 END DO END DO IF (.not.(CompositeGrid(inorth,ng).or.NSperiodic(ng))) THEN IF (DOMAIN(ng)%Northern_Edge(tile)) THEN DO i=IstrU,Iend !> tl_uee(i,Jend+1)=tl_uee(i,Jend) !> ad_uee(i,Jend)=ad_uee(i,Jend)+ad_uee(i,Jend+1) ad_uee(i,Jend+1)=0.0_r8 END DO END IF END IF IF (.not.(CompositeGrid(isouth,ng).or.NSperiodic(ng))) THEN IF (DOMAIN(ng)%Southern_Edge(tile)) THEN DO i=IstrU,Iend !> tl_uee(i,Jstr-1)=tl_uee(i,Jstr) !> ad_uee(i,Jstr)=ad_uee(i,Jstr)+ad_uee(i,Jstr-1) ad_uee(i,Jstr-1)=0.0_r8 END DO END IF END IF DO j=Jstrm1,Jendp1 DO i=IstrU,Iend !> tl_uee(i,j)=tl_u(i,j-1,k,nrhs)-2.0_r8*tl_u(i,j,k,nrhs)+ & # ifdef NEARSHORE_MELLOR !> & tl_u_stokes(i,j-1,k)-2.0_r8*tl_u_stokes(i,j,k)+ & !> & tl_u_stokes(i,j+1,k)+ & # endif !> & tl_u(i,j+1,k,nrhs) !> ad_u(i,j-1,k,nrhs)=ad_u(i,j-1,k,nrhs)+ad_uee(i,j) ad_u(i,j ,k,nrhs)=ad_u(i,j ,k,nrhs)-2.0_r8*ad_uee(i,j) ad_u(i,j+1,k,nrhs)=ad_u(i,j+1,k,nrhs)+ad_uee(i,j) # ifdef NEARSHORE_MELLOR ad_u_stokes(i,j-1,k)=ad_u_stokes(i,j-1,k)+ad_uee(i,j) ad_u_stokes(i,j ,k)=ad_u_stokes(i,j ,k)-2.0_r8*ad_uee(i,j) ad_u_stokes(i,j+1,k)=ad_u_stokes(i,j+1,k)+ad_uee(i,j) # endif ad_uee(i,j)=0.0_r8 END DO END DO DO j=Jstr,Jend DO i=IstrUm1,Iendp1 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 IF (.not.(CompositeGrid(iwest,ng).or.EWperiodic(ng))) THEN IF (DOMAIN(ng)%Western_Edge(tile)) THEN DO j=Jstr,Jend uxx (Istr,j)=uxx (Istr+1,j) Huxx(Istr,j)=Huxx(Istr+1,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 uxx (Iend+1,j)=uxx (Iend,j) Huxx(Iend+1,j)=Huxx(Iend,j) END DO END IF END IF # ifdef UV_C4ADVECTION cff=1.0_r8/6.0_r8 DO j=Jstr,Jend DO i=IstrU-1,Iend !> tl_UFx(i,j)=0.25_r8*((tl_u(i ,j,k,nrhs)+ & # ifdef NEARSHORE_MELLOR !> & tl_u_stokes(i ,j,k)+ & !> & tl_u_stokes(i+1,j,k)+ & # endif !> & tl_u(i+1,j,k,nrhs)- & !> & cff*(tl_uxx (i ,j)+ & !> & tl_uxx (i+1,j)))* & !> & (Huon(i ,j,k)+ & !> & Huon(i+1,j,k)- & !> & cff*(Huxx(i ,j)+ & !> & Huxx(i+1,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)- & !> & cff*(uxx (i ,j)+ & !> & uxx (i+1,j)))* & !> & (tl_Huon(i ,j,k)+ & !> & tl_Huon(i+1,j,k)- & !> & cff*(tl_Huxx(i ,j)+ & !> & tl_Huxx(i+1,j)))) !> adfac=0.25_r8*ad_UFx(i,j) adfac1=adfac*(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))) adfac2=adfac1*cff adfac3=adfac*(Huon(i ,j,k)+ & & Huon(i+1,j,k)- & & cff*(Huxx(i ,j)+ & & Huxx(i+1,j))) adfac4=adfac3*cff ad_Huon(i ,j,k)=ad_Huon(i ,j,k)+adfac1 ad_Huon(i+1,j,k)=ad_Huon(i+1,j,k)+adfac1 ad_Huxx(i ,j)=ad_Huxx(i ,j)-adfac2 ad_Huxx(i+1,j)=ad_Huxx(i+1,j)-adfac2 ad_u(i ,j,k,nrhs)=ad_u(i ,j,k,nrhs)+adfac3 ad_u(i+1,j,k,nrhs)=ad_u(i+1,j,k,nrhs)+adfac3 # ifdef NEARSHORE_MELLOR ad_u_stokes(i ,j,k)=ad_u_stokes(i ,j,k)+adfac3 ad_u_stokes(i+1,j,k)=ad_u_stokes(i+1,j,k)+adfac3 # endif ad_uxx (i ,j)=ad_uxx (i ,j)-adfac4 ad_uxx (i+1,j)=ad_uxx (i+1,j)-adfac4 ad_UFx(i,j)=0.0_r8 END DO END DO # else 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 !> tl_UFx(i,j)=0.25_r8* & !> & ((tl_cff1+Gadv*tl_cff)* & !> & (Huon(i ,j,k)+ & !> & Huon(i+1,j,k)+ & !> & Gadv*0.5_r8*(Huxx(i ,j)+ & !> & Huxx(i+1,j)))+ & !> & (cff1+Gadv*cff)* & !> & (tl_Huon(i ,j,k)+ & !> & tl_Huon(i+1,j,k)+ & !> & Gadv*0.5_r8*(tl_Huxx(i ,j)+ & !> & tl_Huxx(i+1,j)))) !> adfac=0.25_r8*ad_UFx(i,j) adfac1=adfac*(cff1+Gadv*cff) adfac2=adfac1*Gadv*0.5_r8 adfac3=adfac*(Huon(i ,j,k)+ & & Huon(i+1,j,k)+ & & Gadv*0.5_r8*(Huxx(i ,j)+ & & Huxx(i+1,j))) ad_Huon(i ,j,k)=ad_Huon(i ,j,k)+adfac1 ad_Huon(i+1,j,k)=ad_Huon(i+1,j,k)+adfac1 ad_Huxx(i ,j)=ad_Huxx(i ,j)+adfac2 ad_Huxx(i+1,j)=ad_Huxx(i+1,j)+adfac2 ad_cff1=ad_cff1+adfac3 ad_cff=ad_cff+Gadv*adfac3 ad_UFx(i,j)=0.0_r8 IF (cff1.gt.0.0_r8) THEN !> tl_cff=tl_uxx(i,j) !> ad_uxx(i,j)=ad_uxx(i,j)+ad_cff ad_cff=0.0_r8 ELSE !> tl_cff=tl_uxx(i+1,j) !> ad_uxx(i+1,j)=ad_uxx(i+1,j)+ad_cff ad_cff=0.0_r8 END IF !> tl_cff1=tl_u(i ,j,k,nrhs)+ & # ifdef NEARSHORE_MELLOR !> & tl_u_stokes(i ,j,k)+ & !> & tl_u_stokes(i+1,j,k)+ & # endif !> & tl_u(i+1,j,k,nrhs) !> ad_u(i ,j,k,nrhs)=ad_u(i ,j,k,nrhs)+ad_cff1 ad_u(i+1,j,k,nrhs)=ad_u(i+1,j,k,nrhs)+ad_cff1 # ifdef NEARSHORE_MELLOR ad_u_stokes(i ,j,k)=ad_u_stokes(i ,j,k)+ad_cff1 ad_u_stokes(i+1,j,k)=ad_u_stokes(i+1,j,k)+ad_cff1 # endif ad_cff1=0.0_r8 END DO END DO # endif IF (.not.(CompositeGrid(ieast,ng).or.EWperiodic(ng))) THEN IF (DOMAIN(ng)%Eastern_Edge(tile)) THEN DO j=Jstr,Jend !> tl_Huxx(Iend+1,j)=tl_Huxx(Iend,j) !> ad_Huxx(Iend,j)=ad_Huxx(Iend,j)+ad_Huxx(Iend+1,j) ad_Huxx(Iend+1,j)=0.0_r8 !> tl_uxx (Iend+1,j)=tl_uxx (Iend,j) !> ad_uxx (Iend,j)=ad_uxx (Iend,j)+ad_uxx (Iend+1,j) ad_uxx (Iend+1,j)=0.0_r8 END DO END IF END IF IF (.not.(CompositeGrid(iwest,ng).or.EWperiodic(ng))) THEN IF (DOMAIN(ng)%Western_Edge(tile)) THEN DO j=Jstr,Jend !> tl_Huxx(Istr,j)=tl_Huxx(Istr+1,j) !> ad_Huxx(Istr+1,j)=ad_Huxx(Istr+1,j)+ad_Huxx(Istr,j) ad_Huxx(Istr,j)=0.0_r8 !> tl_uxx (Istr,j)=tl_uxx (Istr+1,j) !> ad_uxx (Istr+1,j)=ad_uxx (Istr+1,j)+ad_uxx (Istr,j) ad_uxx (Istr ,j)=0.0_r8 END DO END IF END IF DO j=Jstr,Jend DO i=IstrUm1,Iendp1 !> tl_Huxx(i,j)=tl_Huon(i-1,j,k)-2.0_r8*tl_Huon(i,j,k)+ & !> & tl_Huon(i+1,j,k) !> ad_Huon(i-1,j,k)=ad_Huon(i-1,j,k)+ad_Huxx(i,j) ad_Huon(i ,j,k)=ad_Huon(i ,j,k)-2.0_r8*ad_Huxx(i,j) ad_Huon(i+1,j,k)=ad_Huon(i+1,j,k)+ad_Huxx(i,j) ad_Huxx(i,j)=0.0_r8 !> tl_uxx(i,j)=tl_u(i-1,j,k,nrhs)-2.0_r8*tl_u(i,j,k,nrhs)+ & # ifdef NEARSHORE_MELLOR !> & tl_u_stokes(i-1,j,k)-2.0_r8*tl_u_stokes(i,j,k)+ & !> & tl_u_stokes(i+1,j,k) # endif !> & tl_u(i+1,j,k,nrhs) !> ad_u(i-1,j,k,nrhs)=ad_u(i-1,j,k,nrhs)+ad_uxx (i,j) ad_u(i ,j,k,nrhs)=ad_u(i ,j,k,nrhs)-2.0_r8*ad_uxx (i,j) ad_u(i+1,j,k,nrhs)=ad_u(i+1,j,k,nrhs)+ad_uxx (i,j) # ifdef NEARSHORE_MELLOR ad_u_stokes(i-1,j,k)=ad_u_stokes(i-1,j,k)+ad_uxx (i,j) ad_u_stokes(i ,j,k)=ad_u_stokes(i ,j,k)-2.0_r8*ad_uxx(i,j) ad_u_stokes(i+1,j,k)=ad_u_stokes(i+1,j,k)+ad_uxx (i,j) # endif ad_uxx (i,j)=0.0_r8 END DO END DO # endif # endif ! !----------------------------------------------------------------------- ! Add in nudging of 3D momentum climatology. !----------------------------------------------------------------------- ! IF (LnudgeM3CLM(ng)) THEN DO j=JstrV,Jend DO i=Istr,Iend cff=0.25_r8*(CLIMA(ng)%M3nudgcof(i,j-1,k)+ & & CLIMA(ng)%M3nudgcof(i,j ,k))* & & om_v(i,j)*on_v(i,j) !> tl_rv(i,j,k,nrhs)=tl_rv(i,j,k,nrhs)+ & !> & cff*((Hz(i,j-1,k)+Hz(i,j,k))* & !> & (-tl_v(i,j,k,nrhs))+ & !> & (tl_Hz(i,j-1,k)+tl_Hz(i,j,k))* & !> & (CLIMA(ng)%vclm(i,j,k)- !> & v(i,j,k,nrhs))) !> adfac=cff*ad_rv(i,j,k,nrhs) adfac1=adfac*(CLIMA(ng)%vclm(i,j,k)-v(i,j,k,nrhs)) ad_Hz(i,j-1,k)=ad_Hz(i,j-1,k)+adfac1 ad_Hz(i,j ,k)=ad_Hz(i,j ,k)+adfac1 ad_v(i,j,k,nrhs)=ad_v(i,j,k,nrhs)- & & (Hz(i,j-1,k)+Hz(i,j,k))*adfac END DO END DO DO j=Jstr,Jend DO i=IstrU,Iend cff=0.25_r8*(CLIMA(ng)%M3nudgcof(i-1,j,k)+ & & CLIMA(ng)%M3nudgcof(i ,j,k))* & & om_u(i,j)*on_u(i,j) !> tl_ru(i,j,k,nrhs)=tl_ru(i,j,k,nrhs)+ & !> & cff*((Hz(i-1,j,k)+Hz(i,j,k))* & !> & (-tl_u(i,j,k,nrhs))+ & !> & (tl_Hz(i-1,j,k)+tl_Hz(i,j,k))* & !> & (CLIMA(ng)%uclm(i,j,k)- !> & u(i,j,k,nrhs))) !> adfac=cff*ad_ru(i,j,k,nrhs) adfac1=adfac*(CLIMA(ng)%uclm(i,j,k)-u(i,j,k,nrhs)) ad_Hz(i-1,j,k)=ad_Hz(i-1,j,k)+adfac1 ad_Hz(i ,j,k)=ad_Hz(i ,j,k)+adfac1 ad_u(i,j,k,nrhs)=ad_u(i,j,k,nrhs)- & & (Hz(i-1,j,k)+Hz(i,j,k))*adfac END DO END DO END IF # if defined CURVGRID && defined UV_ADV ! !----------------------------------------------------------------------- ! Add in curvilinear transformation terms. !----------------------------------------------------------------------- ! DO j=JstrV,Jend DO i=Istr,Iend # ifdef DIAGNOSTICS_UV !! DiaRV(i,j,k,nrhs,M3hadv)=-cff1 !! DiaRV(i,j,k,nrhs,M3yadv)=-cff2 !! DiaRV(i,j,k,nrhs,M3xadv)=-cff1+cff2 !! cff2=0.5_r8*(Vwrk(i,j)+Vwrk(i,j-1)) # endif !> tl_rv(i,j,k,nrhs)=tl_rv(i,j,k,nrhs)-tl_cff1 !> ad_cff1=ad_cff1-ad_rv(i,j,k,nrhs) !> tl_cff1=0.5_r8*(tl_VFe(i,j)+tl_VFe(i,j-1)) !> adfac=0.5_r8*ad_cff1 ad_VFe(i,j-1)=ad_VFe(i,j-1)+adfac ad_VFe(i,j )=ad_VFe(i,j )+adfac ad_cff1=0.0_r8 END DO END DO DO j=Jstr,Jend DO i=IstrU,Iend # ifdef DIAGNOSTICS_UV !! DiaRU(i,j,k,nrhs,M3hadv)=cff1 !! DiaRU(i,j,k,nrhs,M3yadv)=cff2 !! DiaRU(i,j,k,nrhs,M3xadv)=cff1-cff2 !! cff2=0.5_r8*(Uwrk(i,j)+Uwrk(i-1,j)) # endif !> tl_ru(i,j,k,nrhs)=tl_ru(i,j,k,nrhs)+tl_cff1 !> ad_cff1=ad_cff1+ad_ru(i,j,k,nrhs) !> tl_cff1=0.5_r8*(tl_UFx(i,j)+tl_UFx(i-1,j)) !> adfac=0.5_r8*ad_cff1 ad_UFx(i-1,j)=ad_UFx(i-1,j)+adfac ad_UFx(i ,j)=ad_UFx(i ,j)+adfac ad_cff1=0.0_r8 END DO END DO DO j=JstrV-1,Jend DO i=IstrU-1,Iend cff1=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)) cff2=0.5_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)) cff3=cff1*dndx(i,j) cff4=cff2*dmde(i,j) cff=Hz(i,j,k)*(cff3-cff4) # if defined DIAGNOSTICS_UV !! Vwrk(i,j)=-cff*cff2 ! v equation, ETA-term !! Uwrk(i,j)=-cff*cff1 ! u equation, ETA-term !! cff=Hz(i,j,k)*cff4 # endif !> tl_VFe(i,j)=tl_cff*cff2+cff*tl_cff2 !> tl_UFx(i,j)=tl_cff*cff1+cff*tl_cff1 !> ad_cff=ad_cff+ & & cff1*ad_UFx(i,j)+ & & cff2*ad_VFe(i,j) ad_cff1=ad_cff1+cff*ad_UFx(i,j) ad_cff2=ad_cff2+cff*ad_VFe(i,j) ad_UFx(i,j)=0.0_r8 ad_VFe(i,j)=0.0_r8 !> tl_cff=tl_Hz(i,j,k)*(cff3-cff4)+ & !> & Hz(i,j,k)*(tl_cff3-tl_cff4) !> adfac=Hz(i,j,k)*ad_cff ad_cff3=ad_cff3+adfac ad_cff4=ad_cff4-adfac ad_Hz(i,j,k)=ad_Hz(i,j,k)+(cff3-cff4)*ad_cff ad_cff=0.0_r8 !> tl_cff4=tl_cff2*dmde(i,j) !> ad_cff2=ad_cff2+dmde(i,j)*ad_cff4 ad_cff4=0.0_r8 !> tl_cff3=tl_cff1*dndx(i,j) !> ad_cff1=ad_cff1+dndx(i,j)*ad_cff3 ad_cff3=0.0_r8 !> tl_cff2=0.5_r8*(tl_u(i ,j,k,nrhs)+ & # ifdef NEARSHORE_MELLOR !> & tl_u_stokes(i ,j,k)+ & !> & tl_u_stokes(i+1,j,k)+ & # endif !> & tl_u(i+1,j,k,nrhs)) !> adfac=0.5_r8*ad_cff2 ad_u(i ,j,k,nrhs)=ad_u(i ,j,k,nrhs)+adfac ad_u(i+1,j,k,nrhs)=ad_u(i+1,j,k,nrhs)+adfac # ifdef NEARSHORE_MELLOR ad_u_stokes(i ,j,k)=ad_u_stokes(i ,j,k)+adfac ad_u_stokes(i+1,j,k)=ad_u_stokes(i+1,j,k)+adfac # endif ad_cff2=0.0_r8 !> tl_cff1=0.5_r8*(tl_v(i,j ,k,nrhs)+ & # ifdef NEARSHORE_MELLOR !> & tl_v_stokes(i,j ,k)+ & !> & tl_v_stokes(i,j+1,k)+ & # endif !> & tl_v(i,j+1,k,nrhs)) !> adfac=0.5_r8*ad_cff1 ad_v(i,j ,k,nrhs)=ad_v(i,j ,k,nrhs)+adfac ad_v(i,j+1,k,nrhs)=ad_v(i,j+1,k,nrhs)+adfac # ifdef NEARSHORE_MELLOR ad_v_stokes(i,j ,k)=ad_v_stokes(i,j ,k)+adfac ad_v_stokes(i,j+1,k)=ad_v_stokes(i,j+1,k)+adfac # endif ad_cff1=0.0_r8 END DO END DO # endif # ifdef UV_COR ! !----------------------------------------------------------------------- ! Add in Coriolis terms. !----------------------------------------------------------------------- ! DO j=JstrV,Jend DO i=Istr,Iend # ifdef DIAGNOSTICS_UV !! DiaRV(i,j,k,nrhs,M3fcor)=-cff1 # endif !> tl_rv(i,j,k,nrhs)=tl_rv(i,j,k,nrhs)-tl_cff1 !> ad_cff1=ad_cff1-ad_rv(i,j,k,nrhs) !> tl_cff1=0.5_r8*(tl_VFe(i,j)+tl_VFe(i,j-1)) !> adfac=0.5_r8*ad_cff1 ad_VFe(i,j-1)=ad_VFe(i,j-1)+adfac ad_VFe(i,j )=ad_VFe(i,j )+adfac ad_cff1=0.0_r8 END DO END DO DO j=Jstr,Jend DO i=IstrU,Iend # ifdef DIAGNOSTICS_UV !! DiaRU(i,j,k,nrhs,M3fcor)=cff1 # endif !> tl_ru(i,j,k,nrhs)=tl_ru(i,j,k,nrhs)+tl_cff1 !> ad_cff1=ad_cff1+ad_ru(i,j,k,nrhs) !> tl_cff1=0.5_r8*(tl_UFx(i,j)+tl_UFx(i-1,j)) !> adfac=0.5_r8*ad_cff1 ad_UFx(i-1,j)=ad_UFx(i-1,j)+adfac ad_UFx(i ,j)=ad_UFx(i ,j)+adfac ad_cff1=0.0_r8 END DO END DO DO j=JstrV-1,Jend DO i=IstrU-1,Iend cff=0.5_r8*Hz(i,j,k)*fomn(i,j) !> tl_VFe(i,j)=tl_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))+ & !> & cff*(tl_u(i ,j,k,nrhs)+ & # ifdef NEARSHORE_MELLOR !> & tl_u_stokes(i ,j,k)+ & !> & tl_u_stokes(i+1,j,k)+ & # endif !> & tl_u(i+1,j,k,nrhs)) !> adfac=cff*ad_VFe(i,j) ad_u(i ,j,k,nrhs)=ad_u(i ,j,k,nrhs)+adfac ad_u(i+1,j,k,nrhs)=ad_u(i+1,j,k,nrhs)+adfac # ifdef NEARSHORE_MELLOR ad_u_stokes(i ,j,k)=ad_u_stokes(i ,j,k)+adfac ad_u_stokes(i+1,j,k)=ad_u_stokes(i+1,j,k)+adfac # endif ad_cff=ad_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))*ad_VFe(i,j) ad_VFe(i,j)=0.0_r8 !> tl_UFx(i,j)=tl_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))+ & !> & cff*(tl_v(i,j ,k,nrhs)+ & # ifdef NEARSHORE_MELLOR !> & tl_v_stokes(i,j ,k)+ & !> & tl_v_stokes(i,j+1,k)+ & # endif !> & tl_v(i,j+1,k,nrhs)) !> adfac=cff*ad_UFx(i,j) ad_v(i,j ,k,nrhs)=ad_v(i,j ,k,nrhs)+adfac ad_v(i,j+1,k,nrhs)=ad_v(i,j+1,k,nrhs)+adfac # ifdef NEARSHORE_MELLOR ad_v_stokes(i,j ,k)=ad_v_stokes(i,j ,k)+adfac ad_v_stokes(i,j+1,k)=ad_v_stokes(i,j+1,k)+adfac # endif ad_cff=ad_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))*ad_UFx(i,j) ad_UFx(i,j)=0.0_r8 !> tl_cff=0.5_r8*tl_Hz(i,j,k)*fomn(i,j) !> ad_Hz(i,j,k)=ad_Hz(i,j,k)+ & & 0.5_r8*fomn(i,j)*ad_cff ad_cff=0.0_r8 END DO END DO # endif END DO K_LOOP # ifdef BODYFORCE ! !----------------------------------------------------------------------- ! Apply adjoint 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 k=1,levbfrc(ng) DO j=JstrV,Jend DO i=Istr,Iend # ifdef DIAGNOSTICS_UV !! DiaRVfrc(i,j,3,M2bstr)=DiaRVfrc(i,j,3,M2bstr)-cff !! DiaRV(i,j,k,nrhs,M3vvis)=DiaRV(i,j,k,nrhs,M3vvis)-cff # endif !> tl_rv(i,j,k,nrhs)=tl_rv(i,j,k,nrhs)-tl_cff !> ad_cff=ad_cff-ad_rv(i,j,k,nrhs) !> tl_cff=tl_Vwrk(i,j)*(Hz(i,j ,k)+ & !> & Hz(i,j-1,k))+ & !> & Vwrk(i,j)*(tl_Hz(i,j ,k)+ & !> & tl_Hz(i,j-1,k)) !> adfac=Vwrk(i,j)*ad_cff ad_Hz(i,j-1,k)=ad_Hz(i,j-1,k)+adfac ad_Hz(i,j ,k)=ad_Hz(i,j ,k)+adfac ad_Vwrk(i,j)=ad_Vwrk(i,j)+(Hz(i,j ,k)+ & Hz(i,j-1,k))*ad_cff ad_cff=0.0_r8 END DO END DO DO j=Jstr,Jend DO i=IstrU,Iend # ifdef DIAGNOSTICS_UV !! DiaRUfrc(i,j,3,M2bstr)=DiaRUfrc(i,j,3,M2bstr)-cff !! DiaRU(i,j,k,nrhs,M3vvis)=DiaRU(i,j,k,nrhs,M3vvis)-cff # endif !> tl_ru(i,j,k,nrhs)=tl_ru(i,j,k,nrhs)-tl_cff !> ad_cff=ad_cff-ad_ru(i,j,k,nrhs) !> tl_cff=tl_Uwrk(i,j)*(Hz(i ,j,k)+ & !> & Hz(i-1,j,k))+ & !> & Uwrk(i,j)*(tl_Hz(i ,j,k)+ & !> & tl_Hz(i-1,j,k)) !> adfac=Uwrk(i,j)*ad_cff ad_Hz(i-1,j,k)=ad_Hz(i-1,j,k)+adfac ad_Hz(i ,j,k)=ad_Hz(i ,j,k)+adfac ad_Uwrk(i,j)=ad_Uwrk(i,j)+(Hz(i ,j,k)+ & & Hz(i-1,j,k))*ad_cff ad_cff=0.0_r8 END DO 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 !> tl_Vwrk(i,j)=tl_bvstr(i,j)*cff1+ & !> & bvstr(i,j)*tl_cff1 !> ad_cff1=ad_cff+bvstr(i,j)*ad_Vwrk(i,j) ad_bvstr(i,j)=tl_bvstr(i,j)+cff1*ad_Vwrk(i,j) ad_Vwrk(i,j)=0.0_r8 !> tl_cff1=-cff1*cff1*cff*(tl_wrk(i,j-1)+tl_wrk(i,j)) !> adfac=-cff1*cff1*cff*ad_cff1 ad_wrk(i,j )=ad_wrk(i,j )+adfac ad_wrk(i,j-1)=ad_wrk(i,j-1)+adfac ad_cff1=0.0_r8 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 !> tl_Uwrk(i,j)=tl_bustr(i,j)*cff1+ & !> & bustr(i,j)*tl_cff1 !> ad_cff1=ad_cff1+bustr(i,j)*ad_Uwrk(i,j) ad_bustr(i,j)=ad_bustr(i,j)+cff1*ad_Uwrk(i,j) ad_Uwrk(i,j)=0.0_r8 !> tl_cff1=-cff1*cff1*cff*(tl_wrk(i-1,j)+tl_wrk(i,j)) !> adfac=-cff1*cff1*cff*ad_cff1 ad_wrk(i-1,j)=ad_wrk(i-1,j)+adfac ad_wrk(i ,j)=ad_wrk(i ,j)+adfac ad_cff=0.0_r8 END DO END DO DO k=1,levbfrc(ng) DO j=JstrV-1,Jend DO i=IstrU-1,Iend !> tl_wrk(i,j)=tl_wrk(i,j)+tl_Hz(i,j,k) !> ad_Hz(i,j,k)=ad_Hz(i,j,k)+ad_wrk(i,j) ad_wrk(i,j)=0.0_r8 END DO END DO END DO DO j=JstrV-1,Jend DO i=IstrU-1,Iend !> tl_wrk(i,j)=0.0_r8 !> ad_wrk(i,j)=0.0_r8 END DO END DO ! !----------------------------------------------------------------------- ! Apply adjoint surface stress as a bodyforce: determine the thickness ! (m) of the surface layer; then add in surface 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=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 k=levsfrc(ng),N(ng) DO j=JstrV,Jend DO i=Istr,Iend # ifdef DIAGNOSTICS_UV !! DiaRVfrc(i,j,3,M2sstr)=DiaRVfrc(i,j,3,M2sstr)+cff !! DiaRV(i,j,k,nrhs,M3vvis)=DiaRV(i,j,k,nrhs,M3vvis)+cff # endif !> tl_rv(i,j,k,nrhs)=tl_rv(i,j,k,nrhs)+tl_cff !> ad_cff=ad_cff+tl_rv(i,j,k,nrhs) !> tl_cff=tl_Vwrk(i,j)*(Hz(i,j ,k)+ & !> & Hz(i,j-1,k))+ & !> & Vwrk(i,j)*(tl_Hz(i,j ,k)+ & !> & tl_Hz(i,j-1,k)) !> adfac=Vwrk(i,j)*ad_cff ad_Hz(i,j-1,k)=ad_Hz(i,j-1,k)+adfac ad_Hz(i,j ,k)=ad_Hz(i,j ,k)+adfac ad_Vwrk(i,j)=ad_Vwrk(i,j)+(Hz(i,j ,k)+ & & Hz(i,j-1,k))*ad_cff ad_cff=0.0_r8 END DO END DO DO j=Jstr,Jend DO i=IstrU,Iend # ifdef DIAGNOSTICS_UV !! DiaRUfrc(i,j,3,M2sstr)=DiaRUfrc(i,j,3,M2sstr)+cff !! DiaRU(i,j,k,nrhs,M3vvis)=DiaRU(i,j,k,nrhs,M3vvis)+cff # endif !> tl_ru(i,j,k,nrhs)=tl_ru(i,j,k,nrhs)+tl_cff !> ad_cff=ad_cff+tl_ru(i,j,k,nrhs) !> tl_cff=tl_Uwrk(i,j)*(Hz(i ,j,k)+ & !> & Hz(i-1,j,k))+ & !> & Uwrk(i,j)*(tl_Hz(i ,j,k)+ & !> & tl_Hz(i-1,j,k)) !> adfac=Uwrk(i,j)*ad_cff ad_Hz(i-1,j,k)=ad_Hz(i-1,j,k)+adfac ad_Hz(i ,j,k)=ad_Hz(i ,j,k)+adfac ad_Uwrk(i,j)=ad_Uwrk(i,j)+(Hz(i ,j,k)+ & & Hz(i-1,j,k))*ad_fac ad_fac=0.0_r8 END DO 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*(tl_wrk(i,j-1)+tl_wrk(i,j))) Vwrk(i,j)=svstr(i,j)*cff1 !> tl_Vwrk(i,j)=tl_svstr(i,j)*cff1+ & !> & svstr(i,j)*tl_cff1 !> ad_cff1=ad_cff1+svstr(i,j)*ad_Vwrk(i,j) ad_svstr(i,j)=ad_svstr(i,j)+cff1*ad_Vwrk(i,j) ad_Vwrk(i,j)=0.0_r8 !> tl_cff1=-cff1*cff1*cff*(tl_wrk(i,j-1)+tl_wrk(i,j)) !> adfac=-cff1*cff1*cff*ad_cff1 ad_wrk(i,j-1)=ad_wrk(i,j-1)+adfac ad_wrk(i,j )=ad_wrk(i,j )+adfac ad_cff1=0.0_r8 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 !> tl_Uwrk(i,j)=tl_sustr(i,j)*cff1+ & !> & sustr(i,j)*tl_cff1 !> ad_cff1=ad_cff1+sustr(i,j)*ad_Uwrk(i,j) ad_sustr(i,j)=ad_sustr(i,j)+cff1*ad_Uwrk(i,j) ad_Uwrk(i,j)=0.0_r8 !> tl_cff1=-cff1*cff1*cff*(tl_wrk(i-1,j)+tl_wrk(i,j)) !> adfac=-cff1*cff1*cff*ad_cff1 ad_wrk(i-1,j)=ad_wrk(i-1,j)+adfac ad_wrk(i ,j)=ad_wrk(i ,j)+adfac ad_cff1=0.0_r8 END DO END DO DO k=N(ng),levsfrc(Ng),-1 DO j=JstrV-1,Jend DO i=IstrU-1,Iend !> tl_wrk(i,j)=tl_wrk(i,j)+tl_Hz(i,j,k) !> ad_Hz(i,j,k)=ad_Hz(i,j,k)+ad_wrk(i,j) ad_wrk(i,j)=0.0_r8 END DO END DO END DO DO j=JstrV-1,Jend DO i=IstrU-1,Iend !> tl_wrk(i,j)=0.0_r8 !> ad_wrk(i,j)=0.0_r8 END DO END DO # ifdef DIAGNOSTICS_UV !! DO j=JstrV,Jend !! DO i=Istr,Iend !! DiaRVfrc(i,j,3,M2bstr)=0.0_r8 !! DiaRVfrc(i,j,3,M2sstr)=0.0_r8 !! END DO !! END DO !! DO j=Jstr,Jend !! DO i=IstrU,Iend !! DiaRUfrc(i,j,3,M2bstr)=0.0_r8 !! DiaRUfrc(i,j,3,M2sstr)=0.0_r8 !! END DO !! END DO !! DO k=1,N(ng) !! DO j=Jstr,Jend !! DO i=Istr,Iend !! DiaRU(i,j,k,nrhs,M3vvis)=0.0_r8 !! DiaRV(i,j,k,nrhs,M3vvis)=0.0_r8 !! END DO !! END DO !! END DO # endif # endif RETURN END SUBROUTINE ad_rhs3d_tile #endif END MODULE ad_rhs3d_mod