#define PREDICTOR_2D_STEP (knew.eq.3) #define DEBUG MODULE ad_step2d_mod ! !svn $Id: ad_step2d_FB_LF_AM3.h 277 2023-02-23 19:59:35Z arango $ !======================================================================= ! ! ! It solves adjoint shallow-water primitive equations predictor ! ! (Leap-frog) and corrector (Adams-Moulton) time-stepping engine ! ! with a Forward-Backward feedback. ! ! ! ! The kernel formulation is based on Shchepetkin and McWilliams ! ! (2005), equations (2.38)-(2.39) and (2.40)-(2.41). ! ! ! ! Reference: ! ! ! ! Shchepetkin, A.F. and J.C. McWilliams, 2005: The regional oceanic ! ! modeling system (ROMS): a split-explicit, free-surface, ! ! topography-following-coordinate oceanic model, Ocean Modelling, ! ! 9, 347-404, doi:10.1016/j.ocemod.2004.08.002. ! ! ! !======================================================================= ! USE mod_param USE mod_parallel #ifdef SOLVE3D USE mod_coupling #endif #ifdef DIAGNOSTICS_UV !! USE mod_diags #endif USE mod_forces USE mod_grid #if defined UV_VIS2 || defined UV_VIS4 USE mod_mixing #endif USE mod_ncparam USE mod_scalars USE mod_ocean #if defined SEDIMENT_NOT_YET && defined SED_MORPH_NOT_YET && \ defined SOLVE3D USE mod_sedbed #endif USE mod_sources USE mod_stepping ! USE ad_exchange_2d_mod USE exchange_2d_mod #ifdef DISTRIBUTE USE mp_exchange_mod, ONLY : ad_mp_exchange2d USE mp_exchange_mod, ONLY : mp_exchange2d #endif USE obc_volcons_mod, ONLY : obc_flux_tile, & & set_DUV_bc_tile USE ad_obc_volcons_mod, ONLY : ad_obc_flux_tile, & & ad_set_DUV_bc_tile #ifdef SOLVE3D USE ad_set_depth_mod, ONLY : ad_set_depth #endif USE ad_u2dbc_mod, ONLY : ad_u2dbc_tile USE ad_v2dbc_mod, ONLY : ad_v2dbc_tile USE ad_zetabc_mod, ONLY : ad_zetabc_local #ifdef WET_DRY_NOT_DRY USE wetdry_mod, ONLY : wetdry_tile #endif ! implicit none ! PRIVATE PUBLIC :: ad_step2d ! CONTAINS ! !************************************************************************ SUBROUTINE ad_step2d (ng, tile) !************************************************************************ ! ! Imported variable declarations. ! integer, intent(in) :: ng, tile ! ! Local variable declarations. ! character (len=*), parameter :: MyFile = & & __FILE__ ! #include "tile.h" ! #ifdef PROFILE CALL wclock_on (ng, iADM, 9, __LINE__, MyFile) #endif CALL ad_step2d_tile (ng, tile, & & LBi, UBi, LBj, UBj, & & IminS, ImaxS, JminS, JmaxS, & & kstp(ng), knew(ng), & #ifdef SOLVE3D & nstp(ng), nnew(ng), & #endif #ifdef MASKING & GRID(ng) % pmask, GRID(ng) % rmask, & & GRID(ng) % umask, GRID(ng) % vmask, & #endif #ifdef WET_DRY_NOT_YET & GRID(ng) % pmask_wet, GRID(ng) % pmask_full, & & GRID(ng) % rmask_wet, GRID(ng) % rmask_full, & & GRID(ng) % umask_wet, GRID(ng) % umask_full, & & GRID(ng) % vmask_wet, GRID(ng) % vmask_full, & # ifdef SOLVE3D & GRID(ng) % rmask_wet_avg, & # endif #endif #if (defined UV_COR && !defined SOLVE3D) || defined STEP2D_CORIOLIS & GRID(ng) % fomn, & #endif & GRID(ng) % h, GRID(ng) % ad_h, & & GRID(ng) % om_u, GRID(ng) % om_v, & & GRID(ng) % on_u, GRID(ng) % on_v, & & GRID(ng) % omn, & & GRID(ng) % pm, GRID(ng) % pn, & #if defined CURVGRID && defined UV_ADV && !defined SOLVE3D & GRID(ng) % dndx, GRID(ng) % dmde, & #endif #if defined UV_VIS2 && !defined SOLVE3D & GRID(ng) % pmon_r, GRID(ng) % pnom_r, & & GRID(ng) % pmon_p, GRID(ng) % pnom_p, & & GRID(ng) % om_r, GRID(ng) % on_r, & & GRID(ng) % om_p, GRID(ng) % on_p, & & MIXING(ng) % visc2_p, & & MIXING(ng) % visc2_r, & #endif #if defined SEDIMENT_NOT_YET && defined SED_MORPH_NOT_YET & SEDBED(ng) % ad_bed_thick, & #endif #ifdef WEC_MELLOR & MIXING(ng) % ad_rustr2d, & & MIXING(ng) % ad_rvstr2d, & & OCEAN(ng) % ad_rulag2d, & & OCEAN(ng) % ad_rvlag2d, & & OCEAN(ng) % ubar_stokes, & & OCEAN(ng) % ad_ubar_stokes, & & OCEAN(ng) % vbar_stokes, & & OCEAN(ng) % ad_vbar_stokes, & #endif #if defined TIDE_GENERATING_FORCES && !defined SOLVE3D & OCEAN(ng) % eq_tide, & & OCEAN(ng) % ad_eq_tide, & #endif #ifndef SOLVE3D & FORCES(ng) % sustr, FORCES(ng) % ad_sustr, & & FORCES(ng) % svstr, FORCES(ng) % ad_svstr, & & FORCES(ng) % bustr, FORCES(ng) % ad_bustr, & & FORCES(ng) % bvstr, FORCES(ng) % ad_bvstr, & # ifdef ATM_PRESS & FORCES(ng) % Pair, & # endif #else # ifdef VAR_RHO_2D & COUPLING(ng) % rhoA, & & COUPLING(ng) % ad_rhoA, & & COUPLING(ng) % rhoS, & & COUPLING(ng) % ad_rhoS, & # endif & COUPLING(ng) % ad_DU_avg1, & & COUPLING(ng) % ad_DU_avg2, & & COUPLING(ng) % ad_DV_avg1, & & COUPLING(ng) % ad_DV_avg2, & & COUPLING(ng) % ad_Zt_avg1, & & COUPLING(ng) % rufrc, & & COUPLING(ng) % ad_rufrc, & & COUPLING(ng) % rvfrc, & & COUPLING(ng) % ad_rvfrc, & & COUPLING(ng) % ad_rufrc_bak, & & COUPLING(ng) % ad_rvfrc_bak, & #endif #if defined NESTING && !defined SOLVE3D & OCEAN(ng) % ad_DU_flux, & & OCEAN(ng) % ad_DV_flux, & #endif #ifdef DIAGNOSTICS_UV !! & DIAGS(ng) % DiaU2wrk, DIAGS(ng) % DiaV2wrk, & !! & DIAGS(ng) % DiaRUbar, DIAGS(ng) % DiaRVbar, & # ifdef SOLVE3D !! & DIAGS(ng) % DiaU2int, DIAGS(ng) % DiaV2int, & !! & DIAGS(ng) % DiaRUfrc, DIAGS(ng) % DiaRVfrc, & # endif #endif & OCEAN(ng) % ad_ubar_sol, & & OCEAN(ng) % ad_vbar_sol, & & OCEAN(ng) % ad_zeta_sol, & & OCEAN(ng) % ubar, OCEAN(ng) % ad_ubar, & & OCEAN(ng) % vbar, OCEAN(ng) % ad_vbar, & & OCEAN(ng) % zeta, OCEAN(ng) % ad_zeta) #ifdef PROFILE CALL wclock_off (ng, iADM, 9, __LINE__, MyFile) #endif ! RETURN END SUBROUTINE ad_step2d ! !*********************************************************************** SUBROUTINE ad_step2d_tile (ng, tile, & & LBi, UBi, LBj, UBj, & & IminS, ImaxS, JminS, JmaxS, & & kstp, knew, & #ifdef SOLVE3D & nstp, nnew, & #endif #ifdef MASKING & pmask, rmask, umask, vmask, & #endif #ifdef WET_DRY_NOT_YET & pmask_wet, pmask_full, & & rmask_wet, rmask_full, & & umask_wet, umask_full, & & vmask_wet, vmask_full, & # ifdef SOLVE3D & rmask_wet_avg, & # endif #endif #if (defined UV_COR && !defined SOLVE3D) || defined STEP2D_CORIOLIS & fomn, & #endif & h, ad_h, & & om_u, om_v, on_u, on_v, omn, pm, pn, & #if defined CURVGRID && defined UV_ADV && !defined SOLVE3D & dndx, dmde, & #endif #if defined UV_VIS2 && !defined SOLVE3D & pmon_r, pnom_r, pmon_p, pnom_p, & & om_r, on_r, om_p, on_p, & & visc2_p, visc2_r, & #endif #if defined SEDIMENT_NOT_YET && defined SED_MORPH_NOT_YET & ad_bed_thick, & #endif #ifdef WEC_MELLOR & ad_rustr2d, ad_rvstr2d, & & ad_rulag2d, ad_rvlag2d, & & ubar_stokes, ad_ubar_stokes, & & vbar_stokes, ad_vbar_stokes, & #endif #if defined TIDE_GENERATING_FORCES && !defined SOLVE3D & eq_tide, ad_eq_tide, & #endif #ifndef SOLVE3D & sustr, ad_sustr, & & svstr, ad_svstr, & & bustr, ad_bustr, & & bvstr, ad_bvstr, & # ifdef ATM_PRESS & Pair, & # endif #else # ifdef VAR_RHO_2D & rhoA, ad_rhoA, & & rhoS, ad_rhoS, & # endif & ad_DU_avg1, ad_DU_avg2, & & ad_DV_avg1, ad_DV_avg2, & & ad_Zt_avg1, & & rufrc, ad_rufrc, & & rvfrc, ad_rvfrc, & & ad_rufrc_bak, ad_rvfrc_bak, & #endif #if defined NESTING && !defined SOLVE3D & ad_DU_flux, ad_DV_flux, & #endif #ifdef DIAGNOSTICS_UV !! & DiaU2wrk, DiaV2wrk, & !! & DiaRUbar, DiaRVbar, & # ifdef SOLVE3D !! & DiaU2int, DiaV2int, & !! & DiaRUfrc, DiaRVfrc, & # endif #endif & ad_ubar_sol, & & ad_vbar_sol, & & ad_zeta_sol, & & ubar, ad_ubar, & & vbar, ad_vbar, & & zeta, ad_zeta) !*********************************************************************** ! ! 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 ) :: kstp, knew #ifdef SOLVE3D integer, intent(in ) :: nstp, nnew #endif ! #ifdef ASSUMED_SHAPE # ifdef MASKING real(r8), intent(in ) :: pmask(LBi:,LBj:) real(r8), intent(in ) :: rmask(LBi:,LBj:) real(r8), intent(in ) :: umask(LBi:,LBj:) real(r8), intent(in ) :: vmask(LBi:,LBj:) # endif # if (defined UV_COR && !defined SOLVE3D) || defined STEP2D_CORIOLIS real(r8), intent(in ) :: fomn(LBi:,LBj:) # endif real(r8), intent(in ) :: h(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 ) :: omn(LBi:,LBj:) real(r8), intent(in ) :: pm(LBi:,LBj:) real(r8), intent(in ) :: pn(LBi:,LBj:) # if defined CURVGRID && defined UV_ADV && !defined SOLVE3D real(r8), intent(in ) :: dndx(LBi:,LBj:) real(r8), intent(in ) :: dmde(LBi:,LBj:) # endif real(r8), intent(in ) :: rufrc(LBi:,LBj:) real(r8), intent(in ) :: rvfrc(LBi:,LBj:) # if defined UV_VIS2 && !defined SOLVE3D real(r8), intent(in ) :: pmon_r(LBi:,LBj:) real(r8), intent(in ) :: pnom_r(LBi:,LBj:) real(r8), intent(in ) :: pmon_p(LBi:,LBj:) real(r8), intent(in ) :: pnom_p(LBi:,LBj:) real(r8), intent(in ) :: om_r(LBi:,LBj:) real(r8), intent(in ) :: on_r(LBi:,LBj:) real(r8), intent(in ) :: om_p(LBi:,LBj:) real(r8), intent(in ) :: on_p(LBi:,LBj:) real(r8), intent(in ) :: visc2_p(LBi:,LBj:) real(r8), intent(in ) :: visc2_r(LBi:,LBj:) # endif # if defined SEDIMENT_NOT_YET && defined SED_MORPH_NOT_YET real(r8), intent(inout) :: ad_bed_thick(LBi:,LBj:,:) # endif # ifdef WEC_MELLOR real(r8), intent(in ) :: ubar_stokes(LBi:,LBj:) real(r8), intent(in ) :: vbar_stokes(LBi:,LBj:) # endif # if defined TIDE_GENERATING_FORCES && !defined SOLVE3D real(r8), intent(in ) :: eq_tide(LBi:,LBj:) real(r8), intent(inout) :: ad_eq_tide(LBi:,LBj:) # endif real(r8), intent(in ) :: ubar(LBi:,LBj:,:) real(r8), intent(in ) :: vbar(LBi:,LBj:,:) real(r8), intent(in ) :: zeta(LBi:,LBj:,:) real(r8), intent(inout) :: ad_h(LBi:,LBj:) # ifndef SOLVE3D real(r8), intent(inout) :: ad_sustr(LBi:,LBj:) real(r8), intent(inout) :: ad_svstr(LBi:,LBj:) real(r8), intent(inout) :: ad_bustr(LBi:,LBj:) real(r8), intent(inout) :: ad_bvstr(LBi:,LBj:) # ifdef ATM_PRESS real(r8), intent(inout) :: Pair(LBi:,LBj:) # endif # else # ifdef VAR_RHO_2D real(r8), intent(in ) :: rhoA(LBi:,LBj:) real(r8), intent(in ) :: rhoS(LBi:,LBj:) real(r8), intent(inout) :: ad_rhoA(LBi:,LBj:) real(r8), intent(inout) :: ad_rhoS(LBi:,LBj:) # endif real(r8), intent(inout) :: ad_DU_avg1(LBi:,LBj:) real(r8), intent(inout) :: ad_DU_avg2(LBi:,LBj:) real(r8), intent(inout) :: ad_DV_avg1(LBi:,LBj:) real(r8), intent(inout) :: ad_DV_avg2(LBi:,LBj:) real(r8), intent(inout) :: ad_Zt_avg1(LBi:,LBj:) real(r8), intent(inout) :: ad_rufrc(LBi:,LBj:) real(r8), intent(inout) :: ad_rvfrc(LBi:,LBj:) real(r8), intent(inout) :: ad_rufrc_bak(LBi:,LBj:,:) real(r8), intent(inout) :: ad_rvfrc_bak(LBi:,LBj:,:) # endif # ifdef WEC_MELLOR real(r8), intent(inout) :: ad_rustr2d(LBi:,LBj:) real(r8), intent(inout) :: ad_rvstr2d(LBi:,LBj:) real(r8), intent(inout) :: ad_rulag2d(LBi:,LBj:) real(r8), intent(inout) :: ad_rvlag2d(LBi:,LBj:) real(r8), intent(inout) :: ad_ubar_stokes(LBi:,LBj:) real(r8), intent(inout) :: ad_vbar_stokes(LBi:,LBj:) # endif # ifdef WET_DRY_NOT_YET real(r8), intent(inout) :: pmask_full(LBi:,LBj:) real(r8), intent(inout) :: rmask_full(LBi:,LBj:) real(r8), intent(inout) :: umask_full(LBi:,LBj:) real(r8), intent(inout) :: vmask_full(LBi:,LBj:) real(r8), intent(inout) :: pmask_wet(LBi:,LBj:) real(r8), intent(inout) :: rmask_wet(LBi:,LBj:) real(r8), intent(inout) :: umask_wet(LBi:,LBj:) real(r8), intent(inout) :: vmask_wet(LBi:,LBj:) # ifdef SOLVE3D real(r8), intent(inout) :: rmask_wet_avg(LBi:,LBj:) # endif # endif # ifdef DIAGNOSTICS_UV !! real(r8), intent(inout) :: DiaU2wrk(LBi:,LBj:,:) !! real(r8), intent(inout) :: DiaV2wrk(LBi:,LBj:,:) !! real(r8), intent(inout) :: DiaRUbar(LBi:,LBj:,:,:) !! real(r8), intent(inout) :: DiaRVbar(LBi:,LBj:,:,:) # ifdef SOLVE3D !! real(r8), intent(inout) :: DiaU2int(LBi:,LBj:,:) !! real(r8), intent(inout) :: DiaV2int(LBi:,LBj:,:) !! real(r8), intent(inout) :: DiaRUfrc(LBi:,LBj:,:,:) !! real(r8), intent(inout) :: DiaRVfrc(LBi:,LBj:,:,:) # endif # endif real(r8), intent(inout) :: ad_ubar(LBi:,LBj:,:) real(r8), intent(inout) :: ad_vbar(LBi:,LBj:,:) real(r8), intent(inout) :: ad_zeta(LBi:,LBj:,:) # if defined NESTING && !defined SOLVE3D real(r8), intent(inout) :: ad_DU_flux(LBi:,LBj:) real(r8), intent(inout) :: ad_DV_flux(LBi:,LBj:) # endif real(r8), intent(out ) :: ad_ubar_sol(LBi:,LBj:) real(r8), intent(out ) :: ad_vbar_sol(LBi:,LBj:) real(r8), intent(out ) :: ad_zeta_sol(LBi:,LBj:) #else # ifdef MASKING real(r8), intent(in ) :: pmask(LBi:UBi,LBj:UBj) real(r8), intent(in ) :: rmask(LBi:UBi,LBj:UBj) real(r8), intent(in ) :: umask(LBi:UBi,LBj:UBj) real(r8), intent(in ) :: vmask(LBi:UBi,LBj:UBj) # endif # if (defined UV_COR && !defined SOLVE3D) || defined STEP2D_CORIOLIS real(r8), intent(in ) :: fomn(LBi:UBi,LBj:UBj) # endif real(r8), intent(in ) :: h(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 ) :: omn(LBi:UBi,LBj:UBj) real(r8), intent(in ) :: pm(LBi:UBi,LBj:UBj) real(r8), intent(in ) :: pn(LBi:UBi,LBj:UBj) # if defined CURVGRID && defined UV_ADV && !defined SOLVE3D real(r8), intent(in ) :: dndx(LBi:UBi,LBj:UBj) real(r8), intent(in ) :: dmde(LBi:UBi,LBj:UBj) # endif real(r8), intent(in ) :: rufrc(LBi:UBi,LBj:UBj) real(r8), intent(in ) :: rvfrc(LBi:UBi,LBj:UBj) # if defined UV_VIS2 && !defined SOLVE3D real(r8), intent(in ) :: pmon_r(LBi:UBi,LBj:UBj) real(r8), intent(in ) :: pnom_r(LBi:UBi,LBj:UBj) real(r8), intent(in ) :: pmon_p(LBi:UBi,LBj:UBj) real(r8), intent(in ) :: pnom_p(LBi:UBi,LBj:UBj) real(r8), intent(in ) :: om_r(LBi:UBi,LBj:UBj) real(r8), intent(in ) :: on_r(LBi:UBi,LBj:UBj) real(r8), intent(in ) :: om_p(LBi:UBi,LBj:UBj) real(r8), intent(in ) :: on_p(LBi:UBi,LBj:UBj) real(r8), intent(in ) :: visc2_p(LBi:UBi,LBj:UBj) real(r8), intent(in ) :: visc2_r(LBi:UBi,LBj:UBj) # endif # if defined SEDIMENT_NOT_YET && defined SED_MORPH_NOT_YET real(r8), intent(inout) :: ad_bed_thick(LBi:UBi,LBj:UBj,3) # endif # ifdef WEC_MELLOR real(r8), intent(in ) :: ubar_stokes(LBi:UBi,LBj:UBj) real(r8), intent(in ) :: vbar_stokes(LBi:UBi,LBj:UBj) # endif # if defined TIDE_GENERATING_FORCES && !defined SOLVE3D real(r8), intent(in ) :: eq_tide(LBi:UBi,LBj:UBj) real(r8), intent(in ) :: ad_eq_tide(LBi:UBi,LBj:UBj) # endif real(r8), intent(in ) :: ubar(LBi:UBi,LBj:UBj,:) real(r8), intent(in ) :: vbar(LBi:UBi,LBj:UBj,:) real(r8), intent(in ) :: zeta(LBi:UBi,LBj:UBj,:) real(r8), intent(inout) :: ad_h(LBi:UBi,LBj:UBj) # ifndef SOLVE3D 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_bustr(LBi:UBi,LBj:UBj) real(r8), intent(inout) :: ad_bvstr(LBi:UBi,LBj:UBj) # ifdef ATM_PRESS real(r8), intent(in ) :: Pair(LBi:UBi,LBj:UBj) # endif # else # ifdef VAR_RHO_2D real(r8), intent(in ) :: rhoA(LBi:UBi,LBj:UBj) real(r8), intent(in ) :: rhoS(LBi:UBi,LBj:UBj) real(r8), intent(inout) :: ad_rhoA(LBi:UBi,LBj:UBj) real(r8), intent(inout) :: ad_rhoS(LBi:UBi,LBj:UBj) # endif real(r8), intent(inout) :: ad_DU_avg1(LBi:UBi,LBj:UBj) real(r8), intent(inout) :: ad_DU_avg2(LBi:UBi,LBj:UBj) real(r8), intent(inout) :: ad_DV_avg1(LBi:UBi,LBj:UBj) real(r8), intent(inout) :: ad_DV_avg2(LBi:UBi,LBj:UBj) real(r8), intent(inout) :: ad_Zt_avg1(LBi:UBi,LBj:UBj) real(r8), intent(inout) :: ad_rufrc(LBi:UBi,LBj:UBj) real(r8), intent(inout) :: ad_rvfrc(LBi:UBi,LBj:UBj) real(r8), intent(inout) :: ad_rufrc_bak(LBi:UBi,LBj:UBj,2) real(r8), intent(inout) :: ad_rvfrc_bak(LBi:UBi,LBj:UBj,2) # endif # ifdef WEC_MELLOR real(r8), intent(inout) :: ad_rustr2d(LBi:UBi,LBj:UBj) real(r8), intent(inout) :: ad_rvstr2d(LBi:UBi,LBj:UBj) real(r8), intent(inout) :: ad_rulag2d(LBi:UBi,LBj:UBj) real(r8), intent(inout) :: ad_rvlag2d(LBi:UBi,LBj:UBj) real(r8), intent(inout) :: ad_ubar_stokes(LBi:UBi,LBj:UBj) real(r8), intent(inout) :: ad_vbar_stokes(LBi:UBi,LBj:UBj) # endif # ifdef WET_DRY_NOT_YET real(r8), intent(inout) :: pmask_full(LBi:UBi,LBj:UBj) real(r8), intent(inout) :: rmask_full(LBi:UBi,LBj:UBj) real(r8), intent(inout) :: umask_full(LBi:UBi,LBj:UBj) real(r8), intent(inout) :: vmask_full(LBi:UBi,LBj:UBj) real(r8), intent(inout) :: pmask_wet(LBi:UBi,LBj:UBj) real(r8), intent(inout) :: rmask_wet(LBi:UBi,LBj:UBj) real(r8), intent(inout) :: umask_wet(LBi:UBi,LBj:UBj) real(r8), intent(inout) :: vmask_wet(LBi:UBi,LBj:UBj) # ifdef SOLVE3D real(r8), intent(inout) :: rmask_wet_avg(LBi:UBi,LBj:UBj) # endif # endif # ifdef DIAGNOSTICS_UV !! real(r8), intent(inout) :: DiaU2wrk(LBi:UBi,LBj:UBj,NDM2d) !! real(r8), intent(inout) :: DiaV2wrk(LBi:UBi,LBj:UBj,NDM2d) !! real(r8), intent(inout) :: DiaRUbar(LBi:UBi,LBj:UBj,2,NDM2d-1) !! real(r8), intent(inout) :: DiaRVbar(LBi:UBi,LBj:UBj,2,NDM2d-1) # ifdef SOLVE3D !! real(r8), intent(inout) :: DiaU2int(LBi:UBi,LBj:UBj,NDM2d) !! real(r8), intent(inout) :: DiaV2int(LBi:UBi,LBj:UBj,NDM2d) !! real(r8), intent(inout) :: DiaRUfrc(LBi:UBi,LBj:UBj,3,NDM2d-1) !! real(r8), intent(inout) :: DiaRVfrc(LBi:UBi,LBj:UBj,3,NDM2d-1) # endif # endif real(r8), intent(inout) :: ad_ubar(LBi:UBi,LBj:UBj,:) real(r8), intent(inout) :: ad_vbar(LBi:UBi,LBj:UBj,:) real(r8), intent(inout) :: ad_zeta(LBi:UBi,LBj:UBj,:) # if defined NESTING && !defined SOLVE3D real(r8), intent(inout) :: ad_DU_flux(LBi:UBi,LBj:UBj) real(r8), intent(inout) :: ad_DV_flux(LBi:UBi,LBj:UBj) # endif real(r8), intent(out ) :: ad_ubar_sol(LBi:UBi,LBj:UBj) real(r8), intent(out ) :: ad_vbar_sol(LBi:UBi,LBj:UBj) real(r8), intent(out ) :: ad_zeta_sol(LBi:UBi,LBj:UBj) #endif ! ! Local variable declarations. ! integer :: i, is, j integer :: krhs, kbak #ifdef DIAGNOSTICS_UV integer :: idiag #endif ! real(r8) :: cff, cff1, cff2, cff3, cff4 #ifdef WET_DRY_NOT_YET real(r8) :: cff5, cff6, cff7 #endif real(r8) :: fac, fac1, fac2 real(r8) :: ad_cff, ad_cff1, ad_cff2, ad_cff3, ad_cff4 #ifdef WET_DRY_NOT_YET real(r8) :: ad_cff5, ad_cff6, ad_cff7 #endif real(r8) :: ad_fac, ad_fac1, ad_fac2 real(r8) :: adfac, adfac1, adfac2, adfac3, adfac4, adfac5 ! real(r8), parameter :: IniVal = 0.0_r8 ! #if defined UV_C4ADVECTION && !defined SOLVE3D real(r8), dimension(IminS:ImaxS,JminS:JmaxS) :: Dgrad #endif real(r8), dimension(IminS:ImaxS,JminS:JmaxS) :: Dnew real(r8), dimension(IminS:ImaxS,JminS:JmaxS) :: Drhs #if defined UV_VIS2 && !defined SOLVE3D real(r8), dimension(IminS:ImaxS,JminS:JmaxS) :: Drhs_p #endif real(r8), dimension(IminS:ImaxS,JminS:JmaxS) :: Dstp real(r8), dimension(IminS:ImaxS,JminS:JmaxS) :: DUon real(r8), dimension(IminS:ImaxS,JminS:JmaxS) :: DVom #ifdef WEC_MELLOR real(r8), dimension(IminS:ImaxS,JminS:JmaxS) :: DUSon real(r8), dimension(IminS:ImaxS,JminS:JmaxS) :: DVSom #endif #if defined STEP2D_CORIOLIS || !defined SOLVE3D real(r8), dimension(IminS:ImaxS,JminS:JmaxS) :: UFx real(r8), dimension(IminS:ImaxS,JminS:JmaxS) :: VFe #endif #if !defined SOLVE3D real(r8), dimension(IminS:ImaxS,JminS:JmaxS) :: UFe real(r8), dimension(IminS:ImaxS,JminS:JmaxS) :: VFx #endif #if defined UV_C4ADVECTION && !defined SOLVE3D real(r8), dimension(IminS:ImaxS,JminS:JmaxS) :: grad #endif real(r8), dimension(IminS:ImaxS,JminS:JmaxS) :: rubar real(r8), dimension(IminS:ImaxS,JminS:JmaxS) :: rvbar real(r8), dimension(IminS:ImaxS,JminS:JmaxS) :: rzeta real(r8), dimension(IminS:ImaxS,JminS:JmaxS) :: rzeta2 #if defined VAR_RHO_2D && defined SOLVE3D real(r8), dimension(IminS:ImaxS,JminS:JmaxS) :: rzetaSA #endif real(r8), dimension(IminS:ImaxS,JminS:JmaxS) :: zeta_new real(r8), dimension(IminS:ImaxS,JminS:JmaxS) :: zwrk #ifdef WET_DRY_NOT_YET real(r8), dimension(IminS:ImaxS,JminS:JmaxS) :: wetdry #endif #ifdef DIAGNOSTICS_UV !! real(r8), dimension(IminS:ImaxS,JminS:JmaxS) :: Uwrk !! real(r8), dimension(IminS:ImaxS,JminS:JmaxS) :: Vwrk !! real(r8), dimension(IminS:ImaxS,JminS:JmaxS,NDM2d-1) :: DiaU2rhs !! real(r8), dimension(IminS:ImaxS,JminS:JmaxS,NDM2d-1) :: DiaV2rhs #endif ! #if defined UV_C4ADVECTION && !defined SOLVE3D real(r8), dimension(IminS:ImaxS,JminS:JmaxS) :: ad_Dgrad #endif real(r8), dimension(IminS:ImaxS,JminS:JmaxS) :: ad_Dnew real(r8), dimension(IminS:ImaxS,JminS:JmaxS) :: ad_Drhs #if defined UV_VIS2 && !defined SOLVE3D real(r8), dimension(IminS:ImaxS,JminS:JmaxS) :: ad_Drhs_p #endif real(r8), dimension(IminS:ImaxS,JminS:JmaxS) :: ad_Dstp real(r8), dimension(IminS:ImaxS,JminS:JmaxS) :: ad_DUon real(r8), dimension(IminS:ImaxS,JminS:JmaxS) :: ad_DVom #ifdef WEC_MELLOR real(r8), dimension(IminS:ImaxS,JminS:JmaxS) :: ad_DUSon real(r8), dimension(IminS:ImaxS,JminS:JmaxS) :: ad_DVSom #endif #if defined STEP2D_CORIOLIS || !defined SOLVE3D real(r8), dimension(IminS:ImaxS,JminS:JmaxS) :: ad_UFx real(r8), dimension(IminS:ImaxS,JminS:JmaxS) :: ad_VFe #endif #if !defined SOLVE3D real(r8), dimension(IminS:ImaxS,JminS:JmaxS) :: ad_UFe real(r8), dimension(IminS:ImaxS,JminS:JmaxS) :: ad_VFx #endif #if defined UV_C4ADVECTION && !defined SOLVE3D real(r8), dimension(IminS:ImaxS,JminS:JmaxS) :: ad_grad #endif real(r8), dimension(IminS:ImaxS,JminS:JmaxS) :: ad_rzeta2 #if defined VAR_RHO_2D && defined SOLVE3D real(r8), dimension(IminS:ImaxS,JminS:JmaxS) :: ad_rzetaSA #endif real(r8), dimension(IminS:ImaxS,JminS:JmaxS) :: ad_rzeta real(r8), dimension(IminS:ImaxS,JminS:JmaxS) :: ad_rubar real(r8), dimension(IminS:ImaxS,JminS:JmaxS) :: ad_rvbar real(r8), dimension(IminS:ImaxS,JminS:JmaxS) :: ad_zwrk ! real(r8), allocatable :: ad_zeta_new(:,:) ! ! The following stability limits are obtained empirically using 3/4 ! degree Atlantic model configuration. In all these cases barotropic ! mode time step is about 180...250 seconds, which is much less than ! the inertial period. The maximum stability coefficients turned out ! to be slightly different than predicted by linear theory, although ! all theoretical tendencies agree with the practice. Note the nearly ! 70% gain in stability compared with LF-TR for appropriate ! coefficients (linear theory predicts beta=0.166, epsil=0.84). ! !! real(r8), parameter :: gamma=0.0_r8, & !! & beta =0.0_r8, epsil=0.0_r8 !--> Cu=0.818 !! real(r8), parameter :: gamma=1.0_r8/12.0_r8, & !! & beta =0.0_r8, epsil=0.0_r8 !--> Cu=0.878 !! real(r8), parameter :: gamma=1./12., & !! beta =0.1_r8, epsil=0.6_r8 !--> Cu=1.050 real(r8), parameter :: gamma=0.0_r8, & & beta =0.14_r8, epsil=0.74_r8 !==> Cu=1.341 #include "set_bounds.h" ! !----------------------------------------------------------------------- ! Timestep vertically integrated (barotropic) equations. !----------------------------------------------------------------------- ! ! In the code below it is assumed that variables with time index "krhs" ! are time-centered at step "n" in barotropic time during predictor ! sub-step and "n+1/2" during corrector. ! IF (PREDICTOR_2D_STEP) THEN krhs=kstp ELSE krhs=3 END IF IF (FIRST_2D_STEP) THEN kbak=kstp ! "kbak" is used as "from" ELSE ! time index for LF timestep kbak=3-kstp END IF #ifdef DEBUG ! IF (Master) THEN WRITE (20,10) iic(ng), iif(ng), kbak, krhs, kstp, knew 10 FORMAT (' iic = ',i5.5,' iif = ',i3.3, & & ' kbak = ',i1,' krhs = ',i1,' kstp = ',i1,' knew = ',i1) END IF #endif ! !----------------------------------------------------------------------- ! Initialize adjoint private variables. !----------------------------------------------------------------------- ! ad_cff=IniVal ad_cff1=IniVal ad_cff2=IniVal ad_cff3=IniVal ad_cff4=IniVal ad_fac=IniVal ad_fac1=IniVal ad_fac2=IniVal ! #if defined UV_C4ADVECTION && !defined SOLVE3D ad_Dgrad=IniVal #endif ad_Dnew=IniVal ad_Drhs=IniVal #if defined UV_VIS2 && !defined SOLVE3D ad_Drhs_p=IniVal #endif ad_Dstp=IniVal ad_DUon=IniVal ad_DVom=IniVal #ifdef WEC_MELLOR ad_DUSon=IniVal ad_DVSom=IniVal #endif #if defined STEP2D_CORIOLIS || !defined SOLVE3D ad_UFx=IniVal ad_VFe=IniVal #endif #if !defined SOLVE3D ad_UFe=IniVal ad_VFx=IniVal #endif #if defined UV_C4ADVECTION && !defined SOLVE3D ad_grad=IniVal #endif ad_rzeta2=IniVal #if defined VAR_RHO_2D && defined SOLVE3D ad_rzetaSA=IniVal #endif ad_rzeta=IniVal ad_rubar=IniVal ad_rvbar=IniVal ad_zwrk=IniVal ! !----------------------------------------------------------------------- ! Compute BASIC STATE total depth (m) arrays and vertically ! integerated mass fluxes. !----------------------------------------------------------------------- ! #if defined DISTRIBUTE && !defined NESTING # define IR_RANGE IstrUm2-1,Iendp2 # define JR_RANGE JstrVm2-1,Jendp2 # define IU_RANGE IstrUm1-1,Iendp2 # define JU_RANGE Jstrm1-1,Jendp2 # define IV_RANGE Istrm1-1,Iendp2 # define JV_RANGE JstrVm1-1,Jendp2 #else # define IR_RANGE IstrUm2-1,Iendp2 # define JR_RANGE JstrVm2-1,Jendp2 # define IU_RANGE IstrUm2,Iendp2 # define JU_RANGE JstrVm2-1,Jendp2 # define IV_RANGE IstrUm2-1,Iendp2 # define JV_RANGE JstrVm2,Jendp2 #endif DO j=JR_RANGE DO i=IR_RANGE Drhs(i,j)=zeta(i,j,krhs)+h(i,j) END DO END DO DO j=JU_RANGE DO i=IU_RANGE cff=0.5_r8*on_u(i,j) cff1=cff*(Drhs(i,j)+Drhs(i-1,j)) DUon(i,j)=ubar(i,j,krhs)*cff1 END DO END DO DO j=JV_RANGE DO i=IV_RANGE cff=0.5_r8*om_v(i,j) cff1=cff*(Drhs(i,j)+Drhs(i,j-1)) DVom(i,j)=vbar(i,j,krhs)*cff1 END DO END DO #undef IR_RANGE #undef IU_RANGE #undef IV_RANGE #undef JR_RANGE #undef JU_RANGE #undef JV_RANGE #if defined DISTRIBUTE && \ defined UV_ADV && defined UV_C4ADVECTION && !defined SOLVE3D ! ! In distributed-memory, the I- and J-ranges are different and a ! special exchange is done here to avoid having three ghost points ! for high-order numerical stencils. Notice that a private array is ! passed below to the exchange routine. It also applies periodic ! boundary conditions, if appropriate and no partitions in I- or ! J-directions. ! IF (EWperiodic(ng).or.NSperiodic(ng)) THEN CALL exchange_u2d_tile (ng, tile, & & IminS, ImaxS, JminS, JmaxS, & & DUon) CALL exchange_v2d_tile (ng, tile, & & IminS, ImaxS, JminS, JmaxS, & & DVom) END IF CALL mp_exchange2d (ng, tile, iNLM, 2, & & IminS, ImaxS, JminS, JmaxS, & & NghostPoints, & & EWperiodic(ng), NSperiodic(ng), & & DUon, DVom) #endif ! ! Compute integral mass flux across open boundaries and adjust ! for volume conservation. Compute BASIC STATE value. ! IF (ANY(VolCons(:,ng))) THEN CALL obc_flux_tile (ng, tile, & & LBi, UBi, LBj, UBj, & & IminS, ImaxS, JminS, JmaxS, & & knew, & #ifdef MASKING & umask, vmask, & #endif & h, om_v, on_u, & & ubar, vbar, zeta) ! ! Set vertically integrated mass fluxes DUon and DVom along the open ! boundaries in such a way that the integral volume is conserved. ! CALL set_DUV_bc_tile (ng, tile, & & LBi, UBi, LBj, UBj, & & IminS, ImaxS, JminS, JmaxS, & & krhs, & #ifdef MASKING & umask, vmask, & #endif & om_v, on_u, & & ubar, vbar, & & Drhs, DUon, DVom) END IF ! !----------------------------------------------------------------------- ! Compute BASIC STATE fields associated with pressure gradient and ! time-stepping of adjoint free-surface, "zeta_new". !----------------------------------------------------------------------- ! ! Get background zeta_new from BASIC state. Notice the I- and J-range ! used to avoid calling nonlinear 'zetabc_local' routine. ! DO j=LBj,UBj DO i=LBi,UBi zeta_new(i,j)=zeta(i,j,knew) #ifdef MASKING zeta_new(i,j)=zeta_new(i,j)*rmask(i,j) # ifdef WET_DRY_NOT_YET !^ zeta_new(i,j)=zeta_new(i,j)+ & !^ & (Dcrit(ng)-h(i,j))*(1.0_r8-rmask(i,j)) # endif #endif Dnew(i,j)=h(i,j)+zeta_new(i,j) Dstp(i,j)=h(i,j)+zeta(i,j,kstp) END DO END DO ! ! Notice that the new local free-surface is allocated so it can be ! passed as an argumment to "zetabc_local". An automatic array cannot ! be used here because of weird memory problems. ! allocate ( ad_zeta_new(IminS:ImaxS,JminS:JmaxS) ) ad_zeta_new = 0.0_r8 IF (PREDICTOR_2D_STEP) THEN IF (FIRST_2D_STEP) THEN ! Modified RK2 time step (with cff=dtfast(ng) ! Forward-Backward feedback with #ifdef SOLVE3D cff1=0.0_r8 !==> Forward Euler cff2=1.0_r8 #else cff1=0.333333333333_r8 ! optimally chosen beta=1/3 and cff2=0.666666666667_r8 ! epsilon=2/3, see below) is used #endif cff3=0.0_r8 ! here for the start up. ELSE cff=2.0_r8*dtfast(ng) ! In the code below "zwrk" is cff1=beta ! time-centered at time step "n" cff2=1.0_r8-2.0_r8*beta ! in the case of LF (for all but cff3=beta ! the first time step) END IF ! DO j=JstrV-1,Jend DO i=IstrU-1,Iend !^ fac=cff*pm(i,j)*pn(i,j) !^ zeta_new(i,j)=zeta(i,j,kbak)+ & !^ & fac*(DUon(i,j)-DUon(i+1,j)+ & !^ & DVom(i,j)-DVom(i,j+1)) #ifdef MASKING !^ zeta_new(i,j)=zeta_new(i,j)*rmask(i,j) # ifdef WET_DRY !^ zeta_new(i,j)=zeta_new(i,j)+ & !^ & (Dcrit(ng)-h(i,j))*(1.0_r8-rmask(i,j)) # endif #endif !^ Dnew(i,j)=zeta_new(i,j)+h(i,j) ! using background instead zwrk(i,j)=cff1*zeta_new(i,j)+ & & cff2*zeta(i,j,kstp)+ & & cff3*zeta(i,j,kbak) #if defined VAR_RHO_2D && defined SOLVE3D rzeta(i,j)=(1.0_r8+rhoS(i,j))*zwrk(i,j) rzeta2(i,j)=rzeta(i,j)*zwrk(i,j) rzetaSA(i,j)=zwrk(i,j)*(rhoS(i,j)-rhoA(i,j)) #else rzeta(i,j)=zwrk(i,j) rzeta2(i,j)=zwrk(i,j)*zwrk(i,j) #endif END DO END DO ELSE !--> CORRECTOR STEP IF (FIRST_2D_STEP) THEN cff =0.333333333333_r8 ! Modified RK2 weighting: cff1=0.333333333333_r8 ! here "zwrk" is time- cff2=0.333333333333_r8 ! centered at "n+1/2". cff3=0.0_r8 ELSE cff =1.0_r8-epsil ! zwrk is always time- cff1=(0.5_r8-gamma)*epsil ! centered at n+1/2 cff2=(0.5_r8+2.0_r8*gamma)*epsil ! during corrector sub- cff3=-gamma *epsil ! step. END IF ! DO j=JstrV-1,Jend DO i=IstrU-1,Iend !^ fac=dtfast(ng)*pm(i,j)*pn(i,j) !^ zeta_new(i,j)=zeta(i,j,kstp)+ & !^ & fac*(DUon(i,j)-DUon(i+1,j)+ & !^ & DVom(i,j)-DVom(i,j+1)) #ifdef MASKING !^ zeta_new(i,j)=zeta_new(i,j)*rmask(i,j) #endif !^ Dnew(i,j)=zeta_new(i,j)+h(i,j) ! using background instead zwrk(i,j)=cff *zeta(i,j,krhs)+ & & cff1*zeta_new(i,j)+ & & cff2*zeta(i,j,kstp)+ & & cff3*zeta(i,j,kbak) #if defined VAR_RHO_2D && defined SOLVE3D rzeta(i,j)=(1.0_r8+rhoS(i,j))*zwrk(i,j) rzeta2(i,j)=rzeta(i,j)*zwrk(i,j) rzetaSA(i,j)=zwrk(i,j)*(rhoS(i,j)-rhoA(i,j)) #else rzeta(i,j)=zwrk(i,j) rzeta2(i,j)=zwrk(i,j)*zwrk(i,j) #endif END DO END DO END IF ! !----------------------------------------------------------------------- ! Save adjoint 2D solution at knew index for IO purposes. !----------------------------------------------------------------------- ! #ifdef SOLVE3D IF (iif(ng).eq.nfast(ng)) THEN DO j=JstrR,JendR DO i=IstrR,IendR ad_zeta_sol(i,j)=ad_zeta(i,j,knew) END DO DO i=Istr,IendR ad_ubar_sol(i,j)=ad_ubar(i,j,knew) END DO IF (j.ge.Jstr) THEN DO i=IstrR,IendR ad_vbar_sol(i,j)=ad_vbar(i,j,knew) END DO END IF END DO END IF #else DO j=JstrR,JendR DO i=IstrR,IendR ad_zeta_sol(i,j)=ad_zeta(i,j,knew) END DO DO i=Istr,IendR ad_ubar_sol(i,j)=ad_ubar(i,j,knew) END DO IF (j.ge.Jstr) THEN DO i=IstrR,IendR ad_vbar_sol(i,j)=ad_vbar(i,j,knew) END DO END IF END DO #endif ! !----------------------------------------------------------------------- ! Adjoint of Exchange boundary information. !----------------------------------------------------------------------- ! #ifdef DISTRIBUTE !^ CALL mp_exchange2d (ng, tile, iTLM, 3, & !^ & LBi, UBi, LBj, UBj, & !^ & NghostPoints, & !^ & EWperiodic(ng), NSperiodic(ng), & !^ & tl_zeta(:,:,knew), & !^ & tl_ubar(:,:,knew), & !^ & tl_vbar(:,:,knew)) !^ CALL ad_mp_exchange2d (ng, tile, iADM, 3, & & LBi, UBi, LBj, UBj, & & NghostPoints, & & EWperiodic(ng), NSperiodic(ng), & & ad_zeta(:,:,knew), & & ad_ubar(:,:,knew), & & ad_vbar(:,:,knew)) #endif IF (EWperiodic(ng).or.NSperiodic(ng)) THEN !^ CALL exchange_v2d_tile (ng, tile, & !^ & LBi, UBi, LBj, UBj, & !^ & tl_vbar(:,:,knew)) !^ CALL ad_exchange_v2d_tile (ng, tile, & & LBi, UBi, LBj, UBj, & & ad_vbar(:,:,knew)) !^ CALL exchange_u2d_tile (ng, tile, & !^ & LBi, UBi, LBj, UBj, & !^ & tl_ubar(:,:,knew)) !^ CALL ad_exchange_u2d_tile (ng, tile, & & LBi, UBi, LBj, UBj, & & ad_ubar(:,:,knew)) !^ CALL exchange_r2d_tile (ng, tile, & !^ & LBi, UBi, LBj, UBj, & !^ & tl_zeta(:,:,knew)) !^ CALL ad_exchange_r2d_tile (ng, tile, & & LBi, UBi, LBj, UBj, & & ad_zeta(:,:,knew)) END IF #ifdef WET_DRY_NOT_YET ! !----------------------------------------------------------------------- ! Adjoint of compute new wet/dry masks. !----------------------------------------------------------------------- ! !^ CALL wetdry_tile (ng, tile, & !^ & LBi, UBi, LBj, UBj, & !^ & IminS, ImaxS, JminS, JmaxS, & # ifdef MASKING !^ & pmask, rmask, umask, vmask, & # endif !^ & h, zeta(:,:,knew), & # ifdef SOLVE3D !^ & DU_avg1, DV_avg1, & !^ & rmask_wet_avg, & # endif !^ & pmask_wet, pmask_full, & !^ & rmask_wet, rmask_full, & !^ & umask_wet, umask_full, & !^ & vmask_wet, vmask_full) !^ !^ HGA: Need the TLM code here. !^ #endif #if defined NESTING && !defined SOLVE3D ! !----------------------------------------------------------------------- ! In nesting applications with refinement grids, we need to exchange ! the DU_flux and DV_flux fluxes boundary information for the case ! that a contact point is at a tile partition. Notice that in such ! cases, we need i+1 and j+1 values for spatial/temporal interpolation. !----------------------------------------------------------------------- ! # ifdef DISTRIBUTE !^ CALL mp_exchange2d (ng, tile, iTLM, 2, & !^ & LBi, UBi, LBj, UBj, & !^ & NghostPoints, & !^ & EWperiodic(ng), NSperiodic(ng), & !^ & tl_DU_flux, tl_DV_flux) !^ CALL ad_mp_exchange2d (ng, tile, iADM, 2, & & LBi, UBi, LBj, UBj, & & NghostPoints, & & EWperiodic(ng), NSperiodic(ng), & & ad_DU_flux, ad_DV_flux) ! # endif IF (EWperiodic(ng).or.NSperiodic(ng)) THEN !^ CALL exchange_v2d_tile (ng, tile, & !^ & LBi, UBi, LBj, UBj, & !^ & tl_DV_flux) !^ CALL ad_exchange_v2d_tile (ng, tile, & & LBi, UBi, LBj, UBj, & & ad_DV_flux) !^ CALL exchange_u2d_tile (ng, tile, & !^ & LBi, UBi, LBj, UBj, & !^ & tl_DU_flux) !^ CALL ad_exchange_u2d_tile (ng, tile, & & LBi, UBi, LBj, UBj, & & ad_DU_flux) END IF #endif #ifdef SOLVE3D ! !----------------------------------------------------------------------- ! Adjoint of finalize computation of barotropic mode averages. !----------------------------------------------------------------------- ! ! This procedure starts with filling in boundary rows of total depths ! at the new time step, which is needed to be done only during the ! last barotropic time step, Normally, the computation of averages ! occurs at the beginning of the next predictor step because "DUon" ! and "DVom" are being computed anyway. Strictly speaking, the filling ! the boundaries are necessary only in the case of open boundaries, ! otherwise, the associated fluxes are all zeros. ! IF ((iif(ng).eq.nfast(ng)).and.(knew.lt.3)) THEN # ifdef NESTING ! ! After all fast time steps are completed, apply boundary conditions ! to time averaged fields. ! ! In nesting applications with refinement grids, we need to exchange ! the DU_avg2 and DV_avg2 fluxes boundary information for the case ! that a contact point is at a tile partition. Notice that in such ! cases, we need i+1 and j+1 values for spatial/temporal interpolation. ! # ifdef DISTRIBUTE !^ CALL mp_exchange2d (ng, tile, iTLM, 2, & !^ & LBi, UBi, LBj, UBj, & !^ & NghostPoints, & !^ & EWperiodic(ng), NSperiodic(ng), & !^ & tl_DU_avg2, tl_DV_avg2) !^ CALL ad_mp_exchange2d (ng, tile, iADM, 2, & & LBi, UBi, LBj, UBj, & & NghostPoints, & & EWperiodic(ng), NSperiodic(ng), & & ad_DU_avg2, ad_DV_avg2) !^ CALL mp_exchange2d (ng, tile, iTLM, 3, & !^ & LBi, UBi, LBj, UBj, & !^ & NghostPoints, & !^ & EWperiodic(ng), NSperiodic(ng), & !^ & tl_Zt_avg1, tl_DU_avg1, tl_DV_avg1) !^ CALL ad_mp_exchange2d (ng, tile, iADM, 3, & & LBi, UBi, LBj, UBj, & & NghostPoints, & & EWperiodic(ng), NSperiodic(ng), & & ad_Zt_avg1, ad_DU_avg1, ad_DV_avg1) ! # endif IF (EWperiodic(ng).or.NSperiodic(ng)) THEN !^ CALL exchange_v2d_tile (ng, tile, & !^ & LBi, UBi, LBj, UBj, & !^ & tl_DV_avg2) !^ CALL ad_exchange_v2d_tile (ng, tile, & & LBi, UBi, LBj, UBj, & & ad_DV_avg2) !^ CALL exchange_u2d_tile (ng, tile, & !^ & LBi, UBi, LBj, UBj, & !^ & tl_DU_avg2) !^ CALL ad_exchange_u2d_tile (ng, tile, & & LBi, UBi, LBj, UBj, & & ad_DU_avg2) !^ CALL exchange_v2d_tile (ng, tile, & !^ & LBi, UBi, LBj, UBj, & !^ & tl_DV_avg1) !^ CALL ad_exchange_v2d_tile (ng, tile, & & LBi, UBi, LBj, UBj, & & ad_DV_avg1) !^ CALL exchange_u2d_tile (ng, tile, & !^ & LBi, UBi, LBj, UBj, & !^ & tl_DU_avg1) !^ CALL ad_exchange_u2d_tile (ng, tile, & & LBi, UBi, LBj, UBj, & & ad_DU_avg1) !^ CALL exchange_r2d_tile (ng, tile, & !^ & LBi, UBi, LBj, UBj, & !^ & tl_Zt_avg1) !^ CALL ad_exchange_r2d_tile (ng, tile, & & LBi, UBi, LBj, UBj, & & ad_Zt_avg1) END IF # endif ! ! Adjoint of end of the last 2D time step that replaces the new ! free-surface zeta(:,:,knew) with it fast time-averaged value, ! Zt_avg1. Recall this is state variable is the one that communicates ! with the 3D kernel. Then, compute time-dependent depths. ! cff=weight(1,iif(ng),ng) cff1=0.5*cff ! !^ CALL tl_set_depth (ng, tile, iTLM) !^ CALL ad_set_depth (ng, tile, iADM) ! DO j=JstrR,JendR DO i=IstrR,IendR !^ tl_zeta(i,j,knew)=tl_Zt_avg1(i,j) !^ ad_Zt_avg1(i,j)=ad_Zt_avg1(i,j)+ad_zeta(i,j,knew) ad_zeta(i,j,knew)=0.0_r8 IF (j.ge.Jstr) THEN !^ tl_DV_avg1(i,j)=tl_DV_avg1(i,j)+ & !^ & cff1*om_v(i,j)* & !^ & ((Dnew(i,j)+Dnew(i,j-1))* & !^ & tl_vbar(i,j,knew)+ & !^ & (tl_Dnew(i,j)+tl_Dnew(i,j-1))* & !^ & vbar(i,j,knew)) !^ adfac=cff1*om_v(i,j)*ad_DV_avg1(i,j) adfac1=adfac*vbar(i,j,knew) ad_vbar(i,j,knew)=ad_vbar(i,j,knew)+ & & (Dnew(i,j)+Dnew(i,j-1))*adfac ad_Dnew(i,j-1)=ad_Dnew(i,j-1)+adfac1 ad_Dnew(i,j )=ad_Dnew(i,j )+adfac1 END IF IF (i.ge.Istr) THEN !^ tl_DU_avg1(i,j)=tl_DU_avg1(i,j)+ & !^ & cff1*on_u(i,j)* & !^ & ((Dnew(i,j)+Dnew(i-1,j))* & !^ & tl_ubar(i,j,knew)+ & !^ & (tl_Dnew(i,j)+tl_Dnew(i-1,j))* & !^ & ubar(i,j,knew)) !^ adfac=cff1*on_u(i,j)*ad_DU_avg1(i,j) adfac1=adfac*ubar(i,j,knew) ad_ubar(i,j,knew)=ad_ubar(i,j,knew)+ & & (Dnew(i,j)+Dnew(i-1,j))*adfac ad_Dnew(i-1,j)=ad_Dnew(i-1,j)+adfac1 ad_Dnew(i ,j)=ad_Dnew(i ,j)+adfac1 END IF !^ tl_Zt_avg1(i,j)=tl_Zt_avg1(i,j)+ & !^ & cff*tl_zeta(i,j,knew) !^ ad_zeta(i,j,knew)=ad_zeta(i,j,knew)+cff*ad_Zt_avg1(i,j) END DO END DO ! IF (.not.(CompositeGrid(inorth,ng).or.NSperiodic(ng))) THEN IF (DOMAIN(ng)%Northern_Edge(tile)) THEN DO i=Istr-1,IendR !^ tl_Dnew(i,Jend+1)=tl_h(i,Jend+1)+tl_zeta_new(i,Jend+1) !^ ad_h(i,Jend+1)=ad_h(i,Jend+1)+ & & ad_Dnew(i,Jend+1) ad_zeta_new(i,Jend+1)=ad_zeta_new(i,Jend+1)+ & & ad_Dnew(i,Jend+1) ad_Dnew(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-1,IendR !^ tl_Dnew(i,Jstr-1)=tl_h(i,Jstr-1)+tl_zeta_new(i,Jstr-1) !^ ad_h(i,Jstr-1)=ad_h(i,Jstr-1)+ & & ad_Dnew(i,Jstr-1) ad_zeta_new(i,Jstr-1)=ad_zeta_new(i,Jstr-1)+ & & ad_Dnew(i,Jstr-1) ad_Dnew(i,Jstr-1)=0.0_r8 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-1,JendR !^ tl_Dnew(Iend+1,j)=tl_h(Iend+1,j)+tl_zeta_new(Iend+1,j) !^ ad_h(Iend+1,j)=ad_h(Iend+1,j)+ & & ad_Dnew(Iend+1,j) ad_zeta_new(Iend+1,j)=ad_zeta_new(Iend+1,j)+ & & ad_Dnew(Iend+1,j) ad_Dnew(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-1,JendR !^ tl_Dnew(Istr-1,j)=tl_h(Istr-1,j)+tl_zeta_new(Istr-1,j) !^ ad_h(Istr-1,j)=ad_h(Istr-1,j)+ & & ad_Dnew(Istr-1,j) ad_zeta_new(Istr-1,j)=ad_zeta_new(Istr-1,j)+ & & ad_Dnew(Istr-1,j) ad_Dnew(Istr-1,j)=0.0_r8 END DO END IF END IF END IF #endif ! !----------------------------------------------------------------------- ! Apply momentum transport point sources (like river runoff), if any. ! ! Dsrc(is) = 0, flow across grid cell u-face (positive or negative) ! Dsrc(is) = 1, flow across grid cell v-face (positive or negative) !----------------------------------------------------------------------- ! IF (LuvSrc(ng)) THEN DO is=1,Nsrc(ng) i=SOURCES(ng)%Isrc(is) j=SOURCES(ng)%Jsrc(is) IF (((IstrR.le.i).and.(i.le.IendR)).and. & & ((JstrR.le.j).and.(j.le.JendR))) THEN IF (INT(SOURCES(ng)%Dsrc(is)).eq.0) THEN cff=1.0_r8/(on_u(i,j)* & & 0.5_r8*(Dnew(i-1,j)+Dnew(i,j))) #if defined NESTING && !defined SOLVE3D !^ tl_DU_flux(i,j)=SOURCES(ng)%tl_Qbar(is) !^ SOURCES(ng)%ad_Qbar(is)=SOURCES(ng)%ad_Qbar(is)+ & & ad_DU_flux(i,j) ad_DU_flux(i,j)=0.0_r8 #endif #ifdef SOLVE3D !^ tl_DU_avg1(i,j)=SOURCES(ng)%tl_Qbar(is) !^ SOURCES(ng)%ad_Qbar(is)=SOURCES(ng)%ad_Qbar(is)+ & & ad_DU_avg1(i,j) ad_DU_avg1(i,j)=0.0_r8 #endif !^ tl_ubar(i,j,knew)=SOURCES(ng)%tl_Qbar(is)*cff+ & !^ & SOURCES(ng)%Qbar(is)*tl_cff !^ SOURCES(ng)%ad_Qbar(is)=SOURCES(ng)%ad_Qbar(is)+ & & cff*ad_ubar(i,j,knew) ad_cff=ad_cff+ & & SOURCES(ng)%Qbar(is)*ad_ubar(i,j,knew) ad_ubar(i,j,knew)=0.0_r8 !^ tl_cff=-cff*cff*on_u(i,j)* & !^ & 0.5_r8*(tl_Dnew(i-1,j)+tl_Dnew(i ,j)) !^ adfac=-cff*cff*on_u(i,j)*0.5_r8*ad_cff ad_Dnew(i-1,j)=ad_Dnew(i-1,j)+adfac ad_Dnew(i ,j)=ad_Dnew(i ,j)+adfac ad_cff=0.0_r8 ELSE IF (INT(SOURCES(ng)%Dsrc(is)).eq.1) THEN cff=1.0_r8/(om_v(i,j)* & & 0.5_r8*(Dnew(i,j-1)+Dnew(i,j))) #if defined NESTING && !defined SOLVE3D !^ tl_DV_flux(i,j)=SOURCES(ng)%tl_Qbar(is) !^ SOURCES(ng)%ad_Qbar(is)=SOURCES(ng)%ad_Qbar(is)+ & & ad_DV_flux(i,j) ad_DV_flux(i,j)=0.0_r8 #endif #ifdef SOLVE3D !^ tl_DV_avg1(i,j)=SOURCES(ng)%tl_Qbar(is) !^ SOURCES(ng)%ad_Qbar(is)=SOURCES(ng)%ad_Qbar(is)+ & & ad_DV_avg1(i,j) ad_DV_avg1(i,j)=0.0_r8 #endif !^ tl_vbar(i,j,knew)=SOURCES(ng)%tl_Qbar(is)*cff+ & !^ & SOURCES(ng)%Qbar(is)*tl_cff !^ SOURCES(ng)%ad_Qbar(is)=SOURCES(ng)%ad_Qbar(is)+ & & cff*ad_vbar(i,j,knew) ad_cff=ad_cff+ & & SOURCES(ng)%Qbar(is)*ad_vbar(i,j,knew) ad_vbar(i,j,knew)=0.0_r8 !^ tl_cff=-cff*cff*om_v(i,j)* & !^ & 0.5_r8*(tl_Dnew(i,j-1)+tl_Dnew(i,j)) !^ adfac=-cff*cff*om_v(i,j)*0.5_r8*ad_cff ad_Dnew(i,j-1)=ad_Dnew(i,j-1)+adfac ad_Dnew(i,j )=ad_Dnew(i,j )+adfac ad_cff=0.0_r8 END IF END IF END DO END IF #if defined NESTING && !defined SOLVE3D ! ! Set adjoint barotropic fluxes along physical boundaries. ! IF (.not.(CompositeGrid(inorth,ng).or.NSperiodic(ng))) THEN IF (DOMAIN(ng)%Northern_Edge(tile)) THEN DO i=IstrR,IendR !^ tl_DV_flux(i,Jend+1)=0.5_r8*om_v(i,Jend+1)* & !^ & ((Dnew(i,Jend+1)+ & !^ & Dnew(i,Jend ))* & !^ & tl_vbar(i,Jend+1,knew)+ & !^ & (tl_Dnew(i,Jend+1)+ & !^ & tl_Dnew(i,Jend ))* & !^ & vbar(i,Jend+1,knew)) !^ adfac=0.5_r8*om_v(i,Jend+1)*ad_DV_flux(i,Jend+1) adfac1=adfac1*vbar(i,Jend+1,knew) ad_vbar(i,Jend+1,knew)=ad_vbar(i,Jend+1,knew)+ & & (Dnew(i,Jend+1)+ & & Dnew(i,Jend ))*adfac ad_Dnew(i,Jend )=ad_Dnew(i,Jend )+adfac1 ad_Dnew(i,Jend+1)=ad_Dnew(i,Jend+1)+adfac1 ad_DV_flux(i,Jend+1)=0.0_r8 END DO DO i=IstrU,Iend !^ tl_DU_flux(i,Jend+1)=0.5_r8*on_u(i,Jend+1)* & !^ & ((Dnew(i ,Jend+1)+ & !^ & Dnew(i-1,Jend+1))* & !^ & tl_ubar(i,Jend+1,knew)+ & !^ & (tl_Dnew(i ,Jend+1)+ & !^ & tl_Dnew(i-1,Jend+1))* & !^ & ubar(i,Jend+1,knew)) !^ adfac=0.5_r8*on_u(i,Jend+1)*ad_DU_flux(i,Jend+1) adfac1=adfac*ubar(i,Jend+1,knew) ad_ubar(i,Jend+1,knew)=ad_ubar(i,Jend+1,knew)+ & & (Dnew(i ,Jend+1)+ & & Dnew(i-1,Jend+1))*adfac ad_Dnew(i-1,Jend+1)=ad_Dnew(i-1,Jend+1)+adfac1 ad_Dnew(i ,Jend+1)=ad_Dnew(i ,Jend+1)+adfac1 ad_DU_flux(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=IstrR,IendR !^ tl_DV_flux(i,JstrV-1)=0.5_r8*om_v(i,JstrV-1)* & !^ & ((Dnew(i,JstrV-1)+ & !^ & Dnew(i,JstrV-2))* & !^ & tl_vbar(i,JstrV-1,knew)+ & !^ & (tl_Dnew(i,JstrV-1)+ & !^ & tl_Dnew(i,JstrV-2))* & !^ & vbar(i,JstrV-1,knew)) !^ adfac=0.5_r8*om_v(i,JstrV-1)*ad_DV_flux(i,JstrV-1) adfac1=adfac*vbar(i,JstrV-1,knew) ad_vbar(i,JstrV-1,knew)=ad_vbar(i,JstrV-1,knew)+ & & (Dnew(i,JstrV-1)+ & & Dnew(i,JstrV-2))*adfac ad_Dnew(i,JstrV-2)=ad_Dnew(i,JstrV-2)+adfac1 ad_Dnew(i,JstrV-1)=ad_Dnew(i,JstrV-1)+adfac1 ad_DV_flux(i,JstrV-1)=0.0_r8 END DO DO i=IstrU,Iend !^ tl_DU_flux(i,Jstr-1)=0.5_r8*on_u(i,Jstr-1)* & !^ & ((Dnew(i ,Jstr-1)+ & !^ & Dnew(i-1,Jstr-1))* & !^ & tl_ubar(i,Jstr-1,knew)+ & !^ & (tl_Dnew(i ,Jstr-1)+ & !^ & tl_Dnew(i-1,Jstr-1))* & !^ & ubar(i,Jstr-1,knew)) !^ adfac=0.5_r8*on_u(i,Jstr-1)*ad_DU_flux(i,Jstr-1) adfac1=adfac*ubar(i,Jstr-1,knew) ad_ubar(i,Jstr-1,knew)=ad_ubar(i,Jstr-1,knew)+ & & (Dnew(i ,Jstr-1)+ & & Dnew(i-1,Jstr-1))*adfac ad_Dnew(i-1,Jstr-1)=ad_Dnew(i-1,Jstr-1)+adfac1 ad_Dnew(i ,Jstr-1)=ad_Dnew(i ,Jstr-1)+adfac1 ad_DU_flux(i,Jstr-1)=0.0_r8 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 !^ tl_DV_flux(Iend+1,j)=0.5_r8*om_v(Iend+1,j)* & !^ & ((Dnew(Iend+1,j )+ & !^ & Dnew(Iend+1,j-1))* & !^ & tl_vbar(Iend+1,j,knew)+ & !^ & (tl_Dnew(Iend+1,j )+ & !^ & tl_Dnew(Iend+1,j-1))* & !^ & vbar(Iend+1,j,knew)) !^ adfac=0.5_r8*om_v(Iend+1,j)*ad_DV_flux(Iend+1,j) adfac1=adfac*vbar(Iend+1,j,knew) ad_vbar(Iend+1,j,knew)=ad_vbar(Iend+1,j,knew)+ & & (Dnew(Iend+1,j )+ & & Dnew(Iend+1,j-1))*adfac ad_Dnew(Iend+1,j-1)=ad_Dnew(Iend+1,j-1)+adfac1 ad_Dnew(Iend+1,j )=ad_Dnew(Iend+1,j )+adfac1 ad_DV_flux(Iend+1,j)=0.0_r8 END DO DO j=JstrR,JendR !^ tl_DU_flux(Iend+1,j)=0.5_r8*on_u(Iend+1,j)* & !^ & ((Dnew(Iend+1,j)+ & !^ & Dnew(Iend ,j))* & !^ & tl_ubar(Iend+1,j,knew)+ & !^ & (tl_Dnew(Iend+1,j)+ & !^ & tl_Dnew(Iend ,j))* & !^ & ubar(Iend+1,j,knew)) !^ adfac=0.5_r8*on_u(Iend+1,j)*ad_DU_flux(Iend+1,j) adfac1=adfac*ubar(Iend+1,j,knew) ad_ubar(Iend+1,j,knew)=ad_ubar(Iend+1,j,knew)+ & & (Dnew(Iend+1,j)+ & & Dnew(Iend ,j))*adfac ad_Dnew(Iend ,j)=ad_Dnew(Iend ,j)+adfac1 ad_Dnew(Iend+1,j)=ad_Dnew(Iend+1,j)+adfac1 ad_DU_flux(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_DV_flux(Istr-1,j)=0.5_r8*om_v(Istr-1,j)* & !^ & ((Dnew(Istr-1,j )+ & !^ & Dnew(Istr-1,j-1))* & !^ & tl_vbar(Istr-1,j,knew)+ & !^ & (tl_Dnew(Istr-1,j )+ & !^ & tl_Dnew(Istr-1,j-1))* & !^ & vbar(Istr-1,j,knew)) !^ adfac=0.5_r8*om_v(Istr-1,j)*ad_DV_flux(Istr-1,j) adfac1=adfac*vbar(Istr-1,j,knew) ad_vbar(Istr-1,j,knew)=ad_vbar(Istr-1,j,knew)+ & & (Dnew(Istr-1,j )+ & & Dnew(Istr-1,j-1))*adfac ad_Dnew(Istr-1,j-1)=ad_Dnew(Istr-1,j-1)+adfac1 ad_Dnew(Istr-1,j )=ad_Dnew(Istr-1,j )+adfac1 ad_DV_flux(Istr-1,j)=0.0_r8 END DO DO j=JstrR,JendR !^ tl_DU_flux(IstrU-1,j)=0.5_r8*on_u(IstrU-1,j)* & !^ & ((Dnew(IstrU-1,j)+ & !^ & Dnew(IstrU-2,j))* & !^ & tl_ubar(IstrU-1,j,knew)+ & !^ & (tl_Dnew(IstrU-1,j)+ & !^ & tl_Dnew(IstrU-2,j))* & !^ & ubar(IstrU-1,j,knew)) !^ adfac=0.5_r8*on_u(IstrU-1,j)*ad_DU_flux(IstrU-1,j) adfac1=adfac*ubar(IstrU-1,j,knew) ad_ubar(IstrU-1,j,knew)=ad_ubar(IstrU-1,j,knew)+ & & (Dnew(IstrU-1,j)+ & & Dnew(IstrU-2,j))*adfac ad_Dnew(IstrU-2,j)=ad_Dnew(IstrU-2,j)+adfac1 ad_Dnew(IstrU-1,j)=ad_Dnew(IstrU-1,j)+adfac1 ad_DU_flux(IstrU-1,j)=0.0_r8 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-1,IendR !^ tl_Dnew(i,Jend+1)=tl_h(i,Jend+1)+tl_zeta_new(i,Jend+1) !^ ad_h(i,Jend+1)=ad_h(i,Jend+1)+ & & ad_Dnew(i,Jend+1) ad_zeta_new(i,Jend+1)=ad_zeta_new(i,Jend+1)+ & & ad_Dnew(i,Jend+1) ad_Dnew(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-1,IendR !^ tl_Dnew(i,Jstr-1)=tl_h(i,Jstr-1)+tl_zeta_new(i,Jstr-1) !^ ad_h(i,Jstr-1)=ad_h(i,Jstr-1)+ & & ad_Dnew(i,Jstr-1) ad_zeta_new(i,Jstr-1)=ad_zeta_new(i,Jstr-1)+ & & ad_Dnew(i,Jstr-1) ad_Dnew(i,Jstr-1)=0.0_r8 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-1,JendR !^ tl_Dnew(Iend+1,j)=tl_h(Iend+1,j)+tl_zeta_new(Iend+1,j) !^ ad_h(Iend+1,j)=ad_h(Iend+1,j)+ & & ad_Dnew(Iend+1,j) ad_zeta_new(Iend+1,j)=ad_zeta_new(Iend+1,j)+ & & ad_Dnew(Iend+1,j) ad_Dnew(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-1,JendR !^ tl_Dnew(Istr-1,j)=tl_h(Istr-1,j)+tl_zeta_new(Istr-1,j) !^ ad_h(Istr-1,j)=ad_h(Istr-1,j)+ & & ad_Dnew(Istr-1,j) ad_zeta_new(Istr-1,j)=ad_zeta_new(Istr-1,j)+ & & ad_Dnew(Istr-1,j) ad_Dnew(Istr-1,j)=0.0_r8 END DO END IF END IF #endif ! !======================================================================= ! Adjoint of time step 2D momentum equations. !======================================================================= ! ! Compute integral mass flux across open boundaries and adjust ! for volume conservation. ! IF (ANY(VolCons(:,ng))) THEN !^ CALL tl_obc_flux_tile (ng, tile, & !^ & LBi, UBi, LBj, UBj, & !^ & IminS, ImaxS, JminS, JmaxS, & !^ & knew, & #ifdef MASKING !^ & umask, vmask, & #endif !^ & h, tl_h, om_v, on_u, & !^ & ubar, vbar, zeta, & !^ & tl_ubar, tl_vbar, tl_zeta) !^ CALL ad_obc_flux_tile (ng, tile, & & LBi, UBi, LBj, UBj, & & IminS, ImaxS, JminS, JmaxS, & & knew, & #ifdef MASKING & umask, vmask, & #endif & h, ad_h, om_v, on_u, & & ubar, vbar, zeta, & & ad_ubar, ad_vbar, ad_zeta) END IF ! ! Apply lateral boundary conditions. ! !^ CALL tl_v2dbc_tile (ng, tile, & !^ & LBi, UBi, LBj, UBj, & !^ & IminS, ImaxS, JminS, JmaxS, & !^ & krhs, kstp, knew, & !^ & ubar, vbar, zeta, & !^ & tl_ubar, tl_vbar, tl_zeta) !^ CALL ad_v2dbc_tile (ng, tile, & & LBi, UBi, LBj, UBj, & & IminS, ImaxS, JminS, JmaxS, & & krhs, kstp, knew, & & ubar, vbar, zeta, & & ad_ubar, ad_vbar, ad_zeta) !^ CALL tl_u2dbc_tile (ng, tile, & !^ & LBi, UBi, LBj, UBj, & !^ & IminS, ImaxS, JminS, JmaxS, & !^ & krhs, kstp, knew, & !^ & ubar, vbar, zeta, & !^ & tl_ubar, tl_vbar, tl_zeta) !^ CALL ad_u2dbc_tile (ng, tile, & & LBi, UBi, LBj, UBj, & & IminS, ImaxS, JminS, JmaxS, & & krhs, kstp, knew, & & ubar, vbar, zeta, & & ad_ubar, ad_vbar, ad_zeta) ! ! During the predictor sub-step, once newly computed "ubar" and "vbar" ! become available, interpolate them half-step backward in barotropic ! time (i.e., they end up time-centered at n+1/2) in order to use it ! during subsequent corrector sub-step. ! IF (PREDICTOR_2D_STEP) THEN IF (FIRST_2D_STEP) THEN cff1=0.5_r8*dtfast(ng) cff2=0.5_r8 cff3=0.5_r8 cff4=0.0_r8 ELSE cff1=dtfast(ng) cff2=0.5_r8-gamma cff3=0.5_r8+2.0_r8*gamma cff4=-gamma ENDIF DO j=JstrV,Jend DO i=Istr,Iend cff=cff1*(pm(i,j)+pm(i,j-1))*(pn(i,j)+pn(i,j-1)) fac2=1.0_r8/(Dnew(i,j)+Dnew(i,j-1)) #if defined NESTING && !defined SOLVE3D !^ tl_DV_flux(i,j)=0.5_r8*om_v(i,j)* & !^ & ((Dnew(i,j)+Dnew(i,j-1))* & !^ & tl_vbar(i,j,knew)+ & !^ & (tl_Dnew(i,j)+tl_Dnew(i,j-1))* & !^ & vbar(i,j,knew)) !^ adfac=0.5_r8*om_v(i,j)*ad_DV_flux(i,j) adfac1=adfac*vbar(i,j,knew) ad_vbar(i,j,knew)=ad_vbar(i,j,knew)+ & & (Dnew(i,j)+Dnew(i,j-1))*adfac ad_Dnew(i,j-1)=ad_Dnew(i,j-1)+adfac1 ad_Dnew(i,j )=ad_Dnew(i,j )+adfac1 ad_DV_flux(i,j)=0.0_r8 #endif #ifdef WET_DRY_NOT_YET !^ cff5=ABS(ABS(vmask_wet(i,j))-1.0_r8) !^ cff6=0.5_r8+DSIGN(0.5_r8,vbar(i,j,knew))*vmask_wet(i,j) !^ cff7=0.5_r8*vmask_wet(i,j)*cff5+cff6*(1.0_r8-cff5) !^ vbar(i,j,knew)=vbar(i,j,knew)*cff7 !^ !^ HGA: TLM code needed here. !^ #endif !^ tl_vbar(i,j,knew)=cff2*tl_vbar(i,j,knew)+ & !^ & cff3*tl_vbar(i,j,kstp)+ & !^ & cff4*tl_vbar(i,j,kbak) !^ ad_vbar(i,j,knew)=ad_vbar(i,j,knew)+cff2*ad_vbar(i,j,knew) ad_vbar(i,j,kstp)=ad_vbar(i,j,kstp)+cff3*ad_vbar(i,j,knew) ad_vbar(i,j,kbak)=ad_vbar(i,j,kbak)+cff4*ad_vbar(i,j,knew) ad_vbar(i,j,knew)=0.0_r8 #ifdef MASKING !^ tl_vbar(i,j,knew)=tl_vbar(i,j,knew)*vmask(i,j) !^ ad_vbar(i,j,knew)=ad_vbar(i,j,knew)*vmask(i,j) #endif !^ tl_vbar(i,j,knew)=tl_fac2* & !^ & (vbar(i,j,kbak)* & !^ & (Dstp(i,j)+Dstp(i,j-1))+ & #ifdef SOLVE3D !^ & cff*(rvbar(i,j)+rvfrc(i,j)))+ & #else !^ & cff*rvbar(i,j)+4.0_r8*cff1*svstr(i,j))+ & #endif !^ & fac2* & !^ & (tl_vbar(i,j,kbak)* & !^ & (Dstp(i,j)+Dstp(i,j-1))+ & !^ & vbar(i,j,kbak)* & !^ & (tl_Dstp(i,j)+tl_Dstp(i,j-1))+ & #ifdef SOLVE3D !^ & cff*(tl_rvbar(i,j)+tl_rvfrc(i,j))) #else !^ & cff*tl_rvbar(i,j)+ & !^ & 4.0_r8*cff1*tl_svstr(i,j)) #endif !^ adfac=fac2*ad_vbar(i,j,knew) adfac1=adfac*(Dstp(i,j)+Dstp(i,j-1)) adfac2=adfac*cff adfac3=adfac*vbar(i,j,kbak) ad_vbar(i,j,kbak)=ad_vbar(i,j,kbak)+adfac1 #ifdef SOLVE3D ad_rvbar(i,j)=ad_rvbar(i,j)+adfac2 ad_rvfrc(i,j)=ad_rvfrc(i,j)+adfac2 #else ad_rvbar(i,j)=ad_rvbar(i,j)+adfac2 ad_svstr(i,j)=ad_svstr(i,j)+4.0_r8*cff1*adfac #endif ad_Dstp(i,j-1)=ad_Dstp(i,j-1)+adfac3 ad_Dstp(i,j )=ad_Dstp(i,j )+adfac3 ad_fac2=ad_fac2+ & & ad_vbar(i,j,knew)* & & (vbar(i,j,kbak)* & & (Dstp(i,j)+Dstp(i,j-1))+ & #ifdef SOLVE3D & cff*(rvbar(i,j)+rvfrc(i,j))) #else & cff*rvbar(i,j)+4.0_r8*cff1*svstr(i,j)) #endif ad_vbar(i,j,knew)=0.0_r8 !^ tl_fac2=-fac2*fac2*(tl_Dnew(i,j)+tl_Dnew(i,j-1)) !^ adfac=-fac2*fac2*ad_fac2 ad_Dnew(i,j-1)=ad_Dnew(i,j-1)+adfac ad_Dnew(i,j )=ad_Dnew(i,j )+adfac ad_fac2=0.0_r8 END DO END DO ! DO j=Jstr,Jend DO i=IstrU,Iend cff=cff1*(pm(i,j)+pm(i-1,j))*(pn(i,j)+pn(i-1,j)) fac1=1.0_r8/(Dnew(i,j)+Dnew(i-1,j)) #if defined NESTING && !defined SOLVE3D !^ tl_DU_flux(i,j)=0.5_r8*on_u(i,j)* & !^ & ((Dnew(i,j)+Dnew(i-1,j))* & !^ & tl_ubar(i,j,knew)+ & !^ & (tl_Dnew(i,j)+tl_Dnew(i-1,j))* & !^ & ubar(i,j,knew)) !^ adfac=0.5_r8*on_u(i,j)*ad_DU_flux(i,j) adfac1=adfac*ubar(i,j,knew) ad_ubar(i,j,knew)=ad_ubar(i,j,knew)+ & & (Dnew(i,j)+Dnew(i-1,j))*adfac ad_Dnew(i-1,j)=ad_Dnew(i-1,j)+adfac1 ad_Dnew(i ,j)=ad_Dnew(i ,j)+adfac1 ad_DU_flux(i,j)=0.0_r8 #endif #ifdef WET_DRY_NOT_YET !^ cff5=ABS(ABS(umask_wet(i,j))-1.0_r8) !^ cff6=0.5_r8+DSIGN(0.5_r8,ubar(i,j,knew))*umask_wet(i,j) !^ cff7=0.5_r8*umask_wet(i,j)*cff5+cff6*(1.0_r8-cff5) !^ ubar(i,j,knew)=ubar(i,j,knew)*cff7 !^ !^ HGA: TLM code needed here. !^ #endif !^ tl_ubar(i,j,knew)=cff2*tl_ubar(i,j,knew)+ & !^ & cff3*tl_ubar(i,j,kstp)+ & !^ & cff4*tl_ubar(i,j,kbak) !^ ad_ubar(i,j,knew)=ad_ubar(i,j,knew)+cff2*ad_ubar(i,j,knew) ad_ubar(i,j,kstp)=ad_ubar(i,j,kstp)+cff3*ad_ubar(i,j,knew) ad_ubar(i,j,kbak)=ad_ubar(i,j,kbak)+cff4*ad_ubar(i,j,knew) ad_ubar(i,j,knew)=0.0_r8 #ifdef MASKING !^ tl_ubar(i,j,knew)=tl_ubar(i,j,knew)*umask(i,j) !^ ad_ubar(i,j,knew)=ad_ubar(i,j,knew)*umask(i,j) #endif !^ tl_ubar(i,j,knew)=tl_fac1* & !^ & (ubar(i,j,kbak)* & !^ & (Dstp(i,j)+Dstp(i-1,j))+ & #ifdef SOLVE3D !^ & cff*(rubar(i,j)+rufrc(i,j)))+ & #else !^ & cff*rubar(i,j)+4.0_r8*cff1*sustr(i,j))+ & #endif !^ & fac1* & !^ & (tl_ubar(i,j,kbak)* & !^ & (Dstp(i,j)+Dstp(i-1,j))+ & !^ & ubar(i,j,kbak)* & !^ & (tl_Dstp(i,j)+tl_Dstp(i-1,j))+ & #ifdef SOLVE3D !^ & cff*(tl_rubar(i,j)+tl_rufrc(i,j))) #else !^ & cff*tl_rubar(i,j)+ & !^ & 4.0_r8*cff1*tl_sustr(i,j)) #endif !^ adfac=fac1*ad_ubar(i,j,knew) adfac1=adfac*(Dstp(i,j)+Dstp(i-1,j)) adfac2=adfac*cff adfac3=adfac*ubar(i,j,kbak) ad_ubar(i,j,kbak)=ad_ubar(i,j,kbak)+adfac1 #ifdef SOLVE3D ad_rubar(i,j)=ad_rubar(i,j)+adfac2 ad_rufrc(i,j)=ad_rufrc(i,j)+adfac2 #else ad_rubar(i,j)=ad_rubar(i,j)+adfac2 ad_sustr(i,j)=ad_sustr(i,j)+4.0_r8*cff1*adfac #endif ad_fac1=ad_fac1+ & & ad_ubar(i,j,knew)* & & (ubar(i,j,kbak)* & & (Dstp(i,j)+Dstp(i-1,j))+ & #ifdef SOLVE3D & cff*(rubar(i,j)+rufrc(i,j))) #else & cff*rubar(i,j)+4.0_r8*cff1*sustr(i,j)) #endif ad_ubar(i,j,knew)=0.0_r8 !^ tl_fac1=-fac1*fac1*(tl_Dnew(i,j)+tl_Dnew(i-1,j)) !^ adfac=-fac1*fac1*ad_fac1 ad_Dnew(i-1,j)=ad_Dnew(i-1,j)+adfac ad_Dnew(i ,j)=ad_Dnew(i ,j)+adfac ad_fac1=0.0_r8 END DO END DO ELSE !--> CORRECTOR_2D_STEP DO j=JstrV,Jend DO i=Istr,Iend cff=cff1*(pm(i,j)+pm(i,j-1))*(pn(i,j)+pn(i,j-1)) fac2=1.0_r8/(Dnew(i,j)+Dnew(i,j-1)) #if defined NESTING && !defined SOLVE3D !^ tl_DV_flux(i,j)=0.5_r8*om_v(i,j)* & !^ & ((Dnew(i,j)+Dnew(i,j-1))* & !^ & tl_vbar(i,j,knew)+ & !^ & (tl_Dnew(i,j)+tl_Dnew(i,j-1))* & !^ & vbar(i,j,knew)) !^ adfac=0.5_r8*om_v(i,j)*ad_DV_flux(i,j) adfac1=adfac*vbar(i,j,knew) ad_vbar(i,j,knew)=ad_vbar(i,j,knew)+ & & (Dnew(i,j)+Dnew(i,j-1))*adfac ad_Dnew(i,j-1)=ad_Dnew(i,j-1)+adfac1 ad_Dnew(i,j )=ad_Dnew(i,j )+adfac1 ad_DV_flux(i,j)=0.0_r8 #endif #ifdef WET_DRY_NOT_YET !^ cff5=ABS(ABS(vmask_wet(i,j))-1.0_r8) !^ cff6=0.5_r8+DSIGN(0.5_r8,vbar(i,j,knew))*vmask_wet(i,j) !^ cff7=0.5_r8*vmask_wet(i,j)*cff5+cff6*(1.0_r8-cff5) !^ vbar(i,j,knew)=vbar(i,j,knew)*cff7 !^ !^ HGA: TLM code needed here. !^ #endif #ifdef MASKING !^ tl_vbar(i,j,knew)=tl_vbar(i,j,knew)*vmask(i,j) !^ ad_vbar(i,j,knew)=ad_vbar(i,j,knew)*vmask(i,j) #endif !^ tl_vbar(i,j,knew)=tl_fac2* & !^ & (vbar(i,j,kstp)* & !^ & (Dstp(i,j)+Dstp(i,j-1))+ & #ifdef SOLVE3D !^ & cff*(rvbar(i,j)+rvfrc(i,j)))+ & #else !^ & cff*rvbar(i,j)+4.0_r8*cff1*svstr(i,j))+ & #endif !^ & fac2* & !^ & (tl_vbar(i,j,kstp)* & !^ & (Dstp(i,j)+Dstp(i,j-1))+ & !^ & vbar(i,j,kstp)* & !^ & (tl_Dstp(i,j)+tl_Dstp(i,j-1))+ & #ifdef SOLVE3D !^ & cff*(tl_rvbar(i,j)+tl_rvfrc(i,j))) #else !^ & cff*tl_rvbar(i,j)+ & !^ & 4.0_r8*cff1*svstr(i,j)) #endif !^ adfac=fac2*ad_vbar(i,j,knew) adfac1=adfac*(Dstp(i,j)+Dstp(i,j-1)) adfac2=adfac*cff adfac3=adfac*vbar(i,j,kstp) ad_vbar(i,j,kstp)=ad_vbar(i,j,kstp)+adfac1 #ifdef SOLVE3D ad_rvbar(i,j)=ad_rvbar(i,j)+adfac2 ad_rvfrc(i,j)=ad_rvfrc(i,j)+adfac2 #else ad_rvbar(i,j)=ad_rvbar(i,j)+adfac2 ad_svstr(i,j)=ad_svstr(i,j)+4.0_r8*cff1*adfac #endif ad_Dstp(i,j-1)=ad_Dstp(i,j-1)+adfac3 ad_Dstp(i,j )=ad_Dstp(i,j )+adfac3 ad_fac2=ad_fac2+ & & ad_vbar(i,j,knew)* & & (vbar(i,j,kstp)* & & (Dstp(i,j)+Dstp(i,j-1))+ & #ifdef SOLVE3D & cff*(rvbar(i,j)+rvfrc(i,j))) #else & cff*rvbar(i,j)+4.0_r8*cff1*svstr(i,j)) #endif ad_vbar(i,j,knew)=0.0_r8 !^ tl_fac2=-fac2*fac2*(tl_Dnew(i,j)+tl_Dnew(i,j-1)) !^ adfac=-fac2*fac2*ad_fac2 ad_Dnew(i,j-1)=ad_Dnew(i,j-1)+adfac ad_Dnew(i,j )=ad_Dnew(i,j )+adfac ad_fac2=0.0_r8 END DO END DO ! cff1=0.5_r8*dtfast(ng) DO j=Jstr,Jend DO i=IstrU,Iend cff=cff1*(pm(i,j)+pm(i-1,j))*(pn(i,j)+pn(i-1,j)) fac1=1.0_r8/(Dnew(i,j)+Dnew(i-1,j)) #if defined NESTING && !defined SOLVE3D !^ tl_DU_flux(i,j)=0.5_r8*on_u(i,j)* & !^ & ((Dnew(i,j)+Dnew(i-1,j))* & !^ & tl_ubar(i,j,knew)+ & !^ & (tl_Dnew(i,j)+tl_Dnew(i-1,j))* & !^ & ubar(i,j,knew)) !^ adfac=0.5_r8*on_u(i,j)*ad_DU_flux(i,j) adfac1=adfac*ubar(i,j,knew) ad_ubar(i,j,knew)=ad_ubar(i,j,knew)+ & & (Dnew(i,j)+Dnew(i-1,j))*adfac ad_Dnew(i-1,j)=ad_Dnew(i-1,j)+adfac1 ad_Dnew(i ,j)=ad_Dnew(i ,j)+adfac1 ad_DU_flux(i,j)=0.0_r8 #endif #ifdef WET_DRY_NOT_YET !^ cff5=ABS(ABS(umask_wet(i,j))-1.0_r8) !^ cff6=0.5_r8+DSIGN(0.5_r8,ubar(i,j,knew))*umask_wet(i,j) !^ cff7=0.5_r8*umask_wet(i,j)*cff5+cff6*(1.0_r8-cff5) !^ ubar(i,j,knew)=ubar(i,j,knew)*cff7 !^ !^ HGA: TLM code needed here. !^ #endif #ifdef MASKING !^ tl_ubar(i,j,knew)=tl_ubar(i,j,knew)*umask(i,j) !^ ad_ubar(i,j,knew)=ad_ubar(i,j,knew)*umask(i,j) #endif !^ tl_ubar(i,j,knew)=tl_fac1* & !^ & (ubar(i,j,kstp)* & !^ & (Dstp(i,j)+Dstp(i-1,j))+ & #ifdef SOLVE3D !^ & cff*(rubar(i,j)+rufrc(i,j)))+ & #else !^ & cff*rubar(i,j)+4.0_r8*cff1*sustr(i,j))+ & #endif !^ & fac1* & !^ & (tl_ubar(i,j,kstp)* & !^ & (Dstp(i,j)+Dstp(i-1,j))+ & !^ & ubar(i,j,kstp)* & !^ & (tl_Dstp(i,j)+tl_Dstp(i-1,j))+ & #ifdef SOLVE3D !^ & cff*(tl_rubar(i,j)+tl_rufrc(i,j))) #else !^ & cff*tl_rubar(i,j)+ & !^ & 4.0_r8*cff1*tl_sustr(i,j)) #endif !^ adfac=fac1*ad_ubar(i,j,knew) adfac1=adfac*(Dstp(i,j)+Dstp(i-1,j)) adfac2=adfac*cff adfac3=adfac*ubar(i,j,kstp) ad_ubar(i,j,kstp)=ad_ubar(i,j,kstp)+adfac1 #ifdef SOLVE3D ad_rubar(i,j)=ad_rubar(i,j)+adfac2 ad_rufrc(i,j)=ad_rufrc(i,j)+adfac2 #else ad_rubar(i,j)=ad_rubar(i,j)+adfac2 ad_sustr(i,j)=ad_sustr(i,j)+4.0_r8*cff1*adfac #endif ad_fac1=ad_fac1+ & & ad_ubar(i,j,knew)* & & (ubar(i,j,kstp)* & & (Dstp(i,j)+Dstp(i-1,j))+ & #ifdef SOLVE3D & cff*(rubar(i,j)+rufrc(i,j))) #else & cff*rubar(i,j)+4.0_r8*cff1*sustr(i,j)) #endif ad_ubar(i,j,knew)=0.0_r8 !^ tl_fac1=-fac1*fac1*(Dnew(i,j)+Dnew(i-1,j)) !^ adfac=-fac1*fac1*ad_fac1 ad_Dnew(i-1,j)=ad_Dnew(i-1,j)+adfac ad_Dnew(i ,j)=ad_Dnew(i ,j)+adfac ad_fac1=0.0_r8 END DO END DO END IF ! ! Compute total water column depth. ! IF (FIRST_2D_STEP.or.(.not.PREDICTOR_2D_STEP)) THEN DO j=JstrV-1,Jend DO i=IstrU-1,Iend !^ tl_Dstp(i,j)=tl_h(i,j)+tl_zeta(i,j,kstp) !^ ad_h(i,j)=ad_h(i,j)+ad_Dstp(i,j) ad_zeta(i,j,kstp)=ad_zeta(i,j,kstp)+ad_Dstp(i,j) ad_Dstp(i,j)=0.0_r8 END DO END DO ELSE DO j=JstrV-1,Jend DO i=IstrU-1,Iend !^ tl_Dstp(i,j)=tl_h(i,j)+tl_zeta(i,j,kbak) !^ ad_h(i,j)=ad_h(i,j)+ad_Dstp(i,j) ad_zeta(i,j,kbak)=ad_zeta(i,j,kbak)+ad_Dstp(i,j) ad_Dstp(i,j)=0.0_r8 END DO END DO END IF #ifdef SOLVE3D ! !----------------------------------------------------------------------- ! Coupling between 2D and 3D equations. !----------------------------------------------------------------------- ! ! Before the predictor step of the first barotropic time step, arrays ! "rufrc" and "rvfrc" contain vertical integrals of the 3D RHS terms ! for the momentum equations (including surface and bottom stresses, ! if so prescribed). During the first barotropic time step, convert ! them into forcing terms by subtracting the fast-time "rubar" and ! "rvbar" from them. ! ! These forcing terms are then extrapolated forward in time using ! optimized Adams-Bashforth weights, so that the resultant "rufrc" ! and "rvfrc" are centered effectively at time n+1/2 in baroclinic ! time. ! ! From now on, these newly computed forcing terms remain unchanged ! during the fast time stepping and will be added to "rubar" and ! "rvbar" during all subsequent barotropic time steps. ! ! Thus, the algorithm below is designed for coupling during the 3D ! predictor sub-step. The forcing terms "rufrc" and "rvfrc" are ! computed as instantaneous values at 3D time index "nstp" first and ! then extrapolated half-step forward using AM3-like weights optimized ! for maximum stability (with particular care for startup). ! IF (FIRST_2D_STEP.and.PREDICTOR_2D_STEP) THEN IF (FIRST_TIME_STEP) THEN cff3=0.0_r8 cff2=0.0_r8 cff1=1.0_r8 ELSE IF (FIRST_TIME_STEP+1) THEN cff3=0.0_r8 cff2=-0.5_r8 cff1=1.5_r8 ELSE cff3=0.281105_r8 cff2=-0.5_r8-2.0_r8*cff3 cff1=1.5_r8+cff3 END IF ! DO j=Jstr,Jend DO i=Istr,Iend IF (j.ge.JstrV) THEN # ifdef DIAGNOSTICS_UV !! DiaV2rhs(i,j,M2pgrd)=DiaV2rhs(i,j,M2pgrd)+ & !! & rvbar(i,j) # endif !^ tl_rvbar(i,j)=tl_rvbar(i,j)+ & !^ & cff1*om_v(i,j)* & !^ & ((tl_h(i,j-1)+ & !^ & tl_h(i,j ))* & !^ & (rzeta(i,j-1)- & !^ & rzeta(i,j ))+ & !^ & (h(i,j-1)+ & !^ & h(i,j ))* & !^ & (tl_rzeta(i,j-1)- & !^ & tl_rzeta(i,j ))+ & # if defined VAR_RHO_2D && defined SOLVE3D !^ & (tl_h(i,j-1)- & !^ & tl_h(i,j ))* & !^ & (rzetaSA(i,j-1)+ & !^ & rzetaSA(i,j )+ & !^ & cff2*(rhoA(i,j-1)- & !^ & rhoA(i,j ))* & !^ & (zwrk(i,j-1)- & !^ & zwrk(i,j )))+ & !^ & (h(i,j-1)- & !^ & h(i,j ))* & !^ & (tl_rzetaSA(i,j-1)+ & !^ & tl_rzetaSA(i,j )+ & !^ & cff2*((tl_rhoA(i,j-1)- & !^ & tl_rhoA(i,j ))* & !^ & (zwrk(i,j-1)- & !^ & zwrk(i,j ))+ & !^ & (rhoA(i,j-1)- & !^ & rhoA(i,j ))* & !^ & (tl_zwrk(i,j-1)- & !^ & tl_zwrk(i,j ))))+ & # endif !^ & (tl_rzeta2(i,j-1)- & !^ & tl_rzeta2(i,j ))) !^ adfac=cff1*om_v(i,j)*ad_rvbar(i,j) adfac1=adfac*(rzeta(i,j-1)-rzeta(i,j )) adfac2=adfac*(h(i,j-1)-h(i,j )) ad_h(i,j-1)=ad_h(i,j-1)+adfac1 ad_h(i,j )=ad_h(i,j )+adfac1 ad_rzeta(i,j-1)=ad_rzeta(i,j-1)+adfac2 ad_rzeta(i,j )=ad_rzeta(i,j )-adfac2 ad_rzeta2(i,j-1)=ad_rzeta2(i,j-1)+adfac ad_rzeta2(i,j )=ad_rzeta2(i,j )-adfac # if defined VAR_RHO_2D && defined SOLVE3D adfac3=adfac*(rzetaSA(i,j-1)+ & & rzetaSA(i,j )+ & & cff2*(rhoA(i,j-1)- & & rhoA(i,j ))* & & (zwrk(i,j-1)- & & zwrk(i,j ))) adfac4=adfac2*cff2*(zwrk(i,j-1)-zwrk(i,j)) adfac5=adfac2*cff2*(rhoA(i,j-1)-rhoA(i,j)) ad_h(i,j-1)=ad_h(i,j-1)+adfac3 ad_h(i,j )=ad_h(i,j )-adfac3 ad_rzetaSA(i,j-1)=ad_rzetaSA(i,j-1)+adfac2 ad_rzetaSA(i,j )=ad_rzetaSA(i,j )+adfac2 ad_rhoA(i,j-1)=ad_rhoA(i,j-1)+adfac4 ad_rhoA(i,j )=ad_rhoA(i,j )-adfac4 ad_zwrk(i,j-1)=ad_zwrk(i,j-1)+adfac5 ad_zwrk(i,j )=ad_zwrk(i,j )-adfac5 # endif END IF ! IF (i.ge.IstrU) THEN # ifdef DIAGNOSTICS_UV !! DiaU2rhs(i,j,M2pgrd)=DiaU2rhs(i,j,M2pgrd)+ & !! & rubar(i,j) # endif !^ tl_rubar(i,j)=tl_rubar(i,j)+ & !^ & cff1*on_u(i,j)* & !^ & ((tl_h(i-1,j)+ & !^ & tl_h(i ,j))* & !^ & (rzeta(i-1,j)- & !^ & rzeta(i ,j))+ & !^ & (h(i-1,j)+ & !^ & h(i ,j))* & !^ & (tl_rzeta(i-1,j)- & !^ & tl_rzeta(i ,j))+ & # if defined VAR_RHO_2D && defined SOLVE3D !^ & (tl_h(i-1,j)- & !^ & tl_h(i ,j))* & !^ & (rzetaSA(i-1,j)+ & !^ & rzetaSA(i ,j)+ & !^ & cff2*(rhoA(i-1,j)- & !^ & rhoA(i ,j))* & !^ & (zwrk(i-1,j)- & !^ & zwrk(i ,j)))+ & !^ & (h(i-1,j)- & !^ & h(i ,j))* & !^ & (tl_rzetaSA(i-1,j)+ & !^ & tl_rzetaSA(i ,j)+ & !^ & cff2*((tl_rhoA(i-1,j)- & !^ & tl_rhoA(i ,j))* & !^ & (zwrk(i-1,j)- & !^ & zwrk(i ,j))+ & !^ & (rhoA(i-1,j)- & !^ & rhoA(i ,j))* & !^ & (tl_zwrk(i-1,j)- & !^ & tl_zwrk(i ,j))))+ & # endif !^ & (tl_rzeta2(i-1,j)- & !^ & tl_rzeta2(i ,j))) !^ adfac=cff1*on_u(i,j)*ad_rubar(i,j) adfac1=adfac*(rzeta(i-1,j)-rzeta(i ,j)) adfac2=adfac*(h(i-1,j)+h(i ,j)) ad_h(i-1,j)=ad_h(i-1,j)+adfac1 ad_h(i ,j)=ad_h(i ,j)+adfac1 ad_rzeta(i-1,j)=ad_rzeta(i-1,j)+adfac2 ad_rzeta(i ,j)=ad_rzeta(i ,j)-adfac2 ad_rzeta2(i-1,j)=ad_rzeta2(i-1,j)+adfac ad_rzeta2(i ,j)=ad_rzeta2(i ,j)-adfac # if defined VAR_RHO_2D && defined SOLVE3D adfac3=adfac*(rzetaSA(i-1,j)+ & & rzetaSA(i ,j)+ & & cff2*(rhoA(i-1,j)- & & rhoA(i ,j))* & & (zwrk(i-1,j)- & & zwrk(i ,j))) adfac4=adfac2*cff2*(zwrk(i-1,j)-zwrk(i,j)) adfac5=adfac2*cff2*(rhoA(i-1,j)-rhoA(i,j)) ad_h(i-1,j)=ad_h(i-1,j)+adfac3 ad_h(i ,j)=ad_h(i ,j)-adfac3 ad_rzetaSA(i-1,j)=ad_rzetaSA(i-1,j)+adfac2 ad_rzetaSA(i ,j)=ad_rzetaSA(i ,j)+adfac2 ad_rhoA(i-1,j)=ad_rhoA(i-1,j)+adfac4 ad_rhoA(i ,j)=ad_rhoA(i ,j)-adfac4 ad_zwrk(i-1,j)=ad_zwrk(i-1,j)+adfac5 ad_zwrk(i ,j)=ad_zwrk(i ,j)-adfac5 # endif END IF END DO END DO ! ! Since coupling requires that the pressure gradient term is computed ! using zeta(:,:,kstp) instead of 1/3 toward zeta_new(:,:) as needed ! by generalized RK2 scheme, apply compensation to shift pressure ! gradient terms from "kstp" to 1/3 toward "knew". ! cff1=0.5_r8*g cff2=0.333333333333_r8 cff3=1.666666666666_r8 DO j=JstrV-1,Jend DO i=IstrU-1,Iend # if defined VAR_RHO_2D && defined SOLVE3D !^ tl_rzetaSA(i,j)=tl_zwrk(i,j)* & !^ & (rhoS(i,j)-rhoA(i,j))+ & !^ & zwrk(i,j)* & !^ & (tl_rhoS(i,j)-tl_rhoA(i,j)) !^ adfac=zwrk(i,j)*ad_rzetaSA(i,j) ad_zwrk(i,j)=ad_zwrk(i,j)+ & & (rhoS(i,j)-rhoA(i,j))*ad_rzetaSA(i,j) ad_rhoS(i,j)=ad_rhoS(i,j)+adfac ad_rhoA(i,j)=ad_rhoA(i,j)-adfac ad_rzetaSA(i,j)=0.0_r8 !^ tl_rzeta2(i,j)=tl_rzeta(i,j)* & !^ & (cff2*zeta_new(i,j)+ & !^ & cff3*zeta(i,j,kstp))+ & !^ & rzeta(i,j)* & !^ & (cff2*tl_zeta_new(i,j)+ & !^ & cff3*tl_zeta(i,j,kstp)) !^ adfac=rzeta(i,j)*ad_rzeta2(i,j) ad_rzeta(i,j)=ad_rzeta(i,j)+ & & (cff2*zeta_new(i,j)+ & & cff3*zeta(i,j,kstp))*ad_rzeta2(i,j) ad_zeta_new(i,j)=ad_zeta_new(i,j)+cff2*adfac tl_zeta(i,j,kstp)=tl_zeta(i,j,kstp)+cff3*adfac ad_rzeta2(i,j)=0.0_r8 !^ tl_rzeta(i,j)=(1.0_r8+rhoS(i,j))*tl_zwrk(i,j)+ & !^ & tl_rhoS(i,j)*zwrk(i,j) !^ ad_zwrk(i,j)=ad_zwrk(i,j)+(1.0_r8+rhoS(i,j))*ad_rzeta(i,j) ad_rhoS(i,j)=ad_rhoS(i,j)+zwrk(i,j)*ad_rzeta(i,j) ad_rzeta(i,j)=0.0_r8 # else !^ tl_rzeta2(i,j)=tl_zwrk(i,j)* & !^ & (cff2*zeta_new(i,j)+ & !^ & cff3*zeta(i,j,kstp))+ & !^ & zwrk(i,j)* & !^ & (cff2*tl_zeta_new(i,j)+ & !^ & cff3*tl_zeta(i,j,kstp)) !^ adfac=zwrk(i,j)*ad_rzeta2(i,j) ad_zwrk(i,j)=ad_zwrk(i,j)+ & & (cff2*zeta_new(i,j)+ & & cff3*zeta(i,j,kstp))*ad_rzeta2(i,j) ad_zeta_new(i,j)=ad_zeta_new(i,j)+cff2*adfac ad_zeta(i,j,kstp)=ad_zeta(i,j,kstp)+cff3*adfac3 ad_rzeta2(i,j)=0.0_r8 !^ tl_rzeta(i,j)=tl_zwrk(i,j) !^ ad_zwrk(i,j)=ad_zwrk(i,j)+ad_rzeta(i,j) ad_rzeta(i,j)=0.0_r8 # endif !^ tl_zwrk(i,j)=cff2*(tl_zeta_new(i,j)-tl_zeta(i,j,kstp)) !^ adfac=cff2*ad_zwrk(i,j) ad_zeta_new(i,j)=ad_zeta_new(i,j)+adfac ad_zeta(i,j,kstp)=ad_zeta(i,j,kstp)-adfac ad_zwrk(i,j)=0.0_r8 END DO END DO ! DO j=JstrV,Jend DO i=Istr,Iend !^ tl_rvfrc_bak(i,j,nstp)=tl_cff !^ ad_cff=ad_cff+ad_rvfrc_bak(i,j,nstp) ad_rvfrc_bak(i,j,nstp)=0.0_r8 !^ tl_rvfrc(i,j)=cff1*tl_cff+ & !^ & cff2*tl_rvfrc_bak(i,j,3-nstp)+ & !^ & cff3*tl_rvfrc_bak(i,j,nstp ) !^ ad_cff=ad_cff+cff1*ad_rvfrc(i,j) ad_rvfrc_bak(i,j,3-nstp)=ad_rvfrc_bak(i,j,3-nstp)+ & & cff2*ad_rvfrc(i,j) ad_rvfrc_bak(i,j,nstp )=ad_rvfrc_bak(i,j,nstp )+ & & cff3*ad_rvfrc(i,j) ad_rvfrc(i,j)=0.0_r8 !^ tl_cff=tl_rvfrc(i,j)-tl_rvbar(i,j) !^ ad_rvfrc(i,j)=ad_rvfrc(i,j)+ad_cff ad_rvbar(i,j)=ad_rvbar(i,j)-ad_cff ad_cff=0.0_r8 END DO END DO ! DO j=Jstr,Jend DO i=IstrU,Iend !^ tl_rufrc_bak(i,j,nstp)=tl_cff !^ ad_cff=ad_cff+ad_rufrc_bak(i,j,nstp) ad_rufrc_bak(i,j,nstp)=0.0_r8 !^ tl_rufrc(i,j)=cff1*tl_cff+ & !^ & cff2*tl_rufrc_bak(i,j,3-nstp)+ & !^ & cff3*tl_rufrc_bak(i,j,nstp ) !^ ad_cff=ad_cff+cff1*ad_rufrc(i,j) ad_rufrc_bak(i,j,3-nstp)=ad_rufrc_bak(i,j,3-nstp)+ & & cff2*ad_rufrc(i,j) ad_rufrc_bak(i,j,nstp )=ad_rufrc_bak(i,j,nstp )+ & & cff3*ad_rufrc(i,j) ad_rufrc(i,j)=0.0_r8 !^ tl_cff=tl_rufrc(i,j)-tl_rubar(i,j) !^ ad_rufrc(i,j)=ad_rufrc(i,j)+ad_cff ad_rubar(i,j)=ad_rubar(i,j)-ad_cff ad_cff=0.0_r8 END DO END DO END IF #endif ! !======================================================================= ! Adjoint of compute right-hand-side for the 2D momentum equations. !==============Q========================================================= #ifdef SOLVE3D ! ! Notice that we are suppressing the computation of momentum advection, ! Coriolis, and lateral viscosity terms in 3D Applications because ! these terms are already included in the baroclinic-to-barotropic ! forcing arrays "rufrc" and "rvfrc". It does not mean we are entirely ! omitting them, but it is a choice between recomputing them at every ! barotropic step or keeping them "frozen" during the fast-time ! stepping. # ifdef STEP2D_CORIOLIS ! However, in some coarse grid applications with larger baroclinic ! timestep (say, DT around 20 minutes or larger), adding the Coriolis ! term in the barotropic equations is useful since f*DT is no longer ! small. # endif #endif #ifndef SOLVE3D ! !----------------------------------------------------------------------- ! Add in bottom stress. !----------------------------------------------------------------------- ! DO j=JstrV,Jend DO i=Istr,Iend # ifdef DIAGNOSTICS_UV !! DiaV2rhs(i,j,M2bstr)=-fac # endif !^ tl_rvbar(i,j)=tl_rvbar(i,j)-tl_fac !^ ad_fac=ad_fac-ad_rvbar(i,j) !^ tl_fac=tl_bvstr(i,j)*om_v(i,j)*on_v(i,j) !^ ad_bvstr(i,j)=ad_bvstr(i,j)+ & & om_v(i,j)*on_v(i,j)*ad_fac ad_fac=0.0_r8 END DO END DO DO j=Jstr,Jend DO i=IstrU,Iend # ifdef DIAGNOSTICS_UV !! DiaU2rhs(i,j,M2bstr)=-fac # endif !^ tl_rubar(i,j)=tl_rubar(i,j)-tl_fac !^ ad_fac=ad_fac-tl_rubar(i,j) !^ tl_fac=tl_bustr(i,j)*om_u(i,j)*on_u(i,j) !^ ad_bustr(i,j)=ad_bustr(i,j)+ & & om_u(i,j)*on_u(i,j)*ad_fac END DO END DO #else # ifdef DIAGNOSTICS_UV !! !! Initialize the stress term if no bottom friction is defined. !! !! DO j=Jstr,Jend !! DO i=IstrU,Iend !! DiaU2rhs(i,j,M2bstr)=0.0_r8 !! END DO !! END DO !! DO j=JstrV,Jend !! DO i=Istr,Iend !! DiaV2rhs(i,j,M2bstr)=0.0_r8 !! END DO !! END DO # endif #endif #if defined UV_VIS2 && !defined SOLVE3D ! !----------------------------------------------------------------------- ! Adjoint of add in horizontal harmonic viscosity. !----------------------------------------------------------------------- ! ! Compute BASIC STATE total depth at PSI-points. ! DO j=Jstr,Jend+1 DO i=Istr,Iend+1 Drhs_p(i,j)=0.25_r8*(Drhs(i,j )+Drhs(i-1,j )+ & & Drhs(i,j-1)+Drhs(i-1,j-1)) END DO END DO ! ! Add in harmonic viscosity. ! DO j=Jstr,Jend DO i=Istr,Iend IF (j.ge.JstrV) THEN # if defined DIAGNOSTICS_UV !! DiaV2rhs(i,j,M2hvis)=fac !! DiaV2rhs(i,j,M2xvis)= cff1 !! DiaV2rhs(i,j,M2yvis)=-cff2 # endif !^ tl_rvbar(i,j)=tl_rvbar(i,j)+tl_fac !^ ad_fac=ad_fac+ad_rvbar(i,j) !^ ad_fac=ad_cff1-ad_cff2 !^ ad_cff1=ad_cff1+ad_fac ad_cff2=ad_cff2-ad_fac ad_fac=0.0_r8 !^ tl_cff2=0.5_r8*(pm(i,j-1)+pm(i,j))* & !^ & (tl_VFe(i ,j)-tl_VFe(i,j-1)) !^ adfac=0.5_r8*(pm(i,j-1)+pm(i,j))*ad_cff2 ad_VFe(i,j-1)=ad_VFe(i,j-1)-adfac ad_VFe(i,j )=ad_VFe(i,j )+adfac ad_cff2=0.0_r8 !^ tl_cff1=0.5_r8*(pn(i,j-1)+pn(i,j))* & !^ & (tl_VFx(i+1,j)-tl_VFx(i,j )) !^ adfac=0.5_r8*(pn(i,j-1)+pn(i,j))*ad_cff1 ad_VFx(i ,j)=ad_VFx(i ,j)-adfac ad_VFx(i+1,j)=ad_VFx(i+1,j)+adfac ad_cff1=0.0_r8 END IF ! IF (i.ge.IstrU) THEN # if defined DIAGNOSTICS_UV !! DiaU2rhs(i,j,M2hvis)=fac !! DiaU2rhs(i,j,M2xvis)=cff1 !! DiaU2rhs(i,j,M2yvis)=cff2 # endif !^ tl_rubar(i,j)=tl_rubar(i,j)+tl_fac !^ ad_fac=ad_fac+ad_rubar(i,j) !^ tl_fac=tl_cff1+tl_cff2 !^ ad_cff1=ad_cff1+ad_fac ad_cff2=ad_cff2+ad_fac ad_fac=0.0_r8 !^ tl_cff2=0.5_r8*(pm(i-1,j)+pm(i,j))* & !^ & (tl_UFe(i,j+1)-tl_UFe(i ,j)) !^ adfac=0.5_r8*(pm(i-1,j)+pm(i,j))*ad_cff2 ad_UFe(i,j )=ad_UFe(i,j )-adfac ad_UFe(i,j+1)=ad_UFe(i,j+1)+adfac ad_cff2=0.0_r8 !^ tl_cff1=0.5_r8*(pn(i-1,j)+pn(i,j))* & !^ & (tl_UFx(i,j )-tl_UFx(i-1,j)) !^ adfac=0.5_r8*(pn(i-1,j)+pn(i,j))*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 IF END DO END DO ! ! Compute flux-components of the horizontal divergence of the stress ! tensor (m5/s2) in XI- and ETA-directions. ! DO j=Jstr,Jend+1 DO i=Istr,Iend+1 !^ tl_VFx(i,j)=on_p(i,j)*on_p(i,j)*tl_cff !^ tl_UFe(i,j)=om_p(i,j)*om_p(i,j)*tl_cff !^ ad_cff=ad_cff+ & & on_p(i,j)*on_p(i,j)*ad_VFx(i,j)+ & & om_p(i,j)*om_p(i,j)*ad_UFe(i,j) ad_VFx(i,j)=0.0_r8 ad_UFe(i,j)=0.0_r8 # ifdef WET_DRY_NOT_YET !^ tl_cff=tl_cff*pmask_wet(i,j) !^ ad_cff=ad_cff*pmask_wet(i,j) # endif # ifdef MASKING !^ tl_cff=tl_cff*pmask(i,j !^ ad_cff=ad_cff*pmask(i,j) # endif !^ tl_cff=visc2_p(i,j)*0.5_r8* & !^ & (tl_Drhs_p(i,j)* & !^ & (pmon_p(i,j)* & !^ & ((pn(i ,j-1)+pn(i ,j))*vbar(i ,j,krhs)- & !^ & (pn(i-1,j-1)+pn(i-1,j))*vbar(i-1,j,krhs))+ & !^ & pnom_p(i,j)* & !^ & ((pm(i-1,j )+pm(i,j ))*ubar(i,j ,krhs)- & !^ & (pm(i-1,j-1)+pm(i,j-1))*ubar(i,j-1,krhs)))+ & !^ & Drhs_p(i,j)* & !^ & (pmon_p(i,j)* & !^ & ((pn(i ,j-1)+pn(i ,j))*tl_vbar(i ,j,krhs)- & !^ & (pn(i-1,j-1)+pn(i-1,j))*tl_vbar(i-1,j,krhs))+ & !^ & pnom_p(i,j)* & !^ & ((pm(i-1,j )+pm(i,j ))*tl_ubar(i,j ,krhs)- & !^ & (pm(i-1,j-1)+pm(i,j-1))*tl_ubar(i,j-1,krhs)))) !^ adfac=visc2_p(i,j)*0.5_r8*ad_cff adfac1=adfac*Drhs_p(i,j) adfac2=adfac1*pmon_p(i,j) adfac3=adfac1*pnom_p(i,j) ad_Drhs_p(i,j)=ad_Drhs_p(i,j)+ & & (pmon_p(i,j)* & & ((pn(i ,j-1)+pn(i ,j))*vbar(i ,j,kstp)- & & (pn(i-1,j-1)+pn(i-1,j))*vbar(i-1,j,kstp))+ & & pnom_p(i,j)* & & ((pm(i-1,j )+pm(i,j ))*ubar(i,j ,kstp)- & & (pm(i-1,j-1)+pm(i,j-1))*ubar(i,j-1,kstp)))* & & adfac ad_vbar(i-1,j,kstp)=ad_vbar(i-1,j,kstp)- & & (pn(i-1,j-1)+pn(i-1,j))*adfac2 ad_vbar(i ,j,kstp)=ad_vbar(i ,j,kstp)+ & & (pn(i ,j-1)+pn(i ,j))*adfac2 ad_ubar(i,j-1,kstp)=ad_ubar(i,j-1,kstp)- & & (pm(i-1,j-1)+pm(i,j-1))*adfac3 ad_ubar(i,j ,kstp)=ad_ubar(i,j ,kstp)+ & & (pm(i-1,j )+pm(i,j ))*adfac3 ad_cff=0.0_r8 END DO END DO ! DO j=JstrV-1,Jend DO i=IstrU-1,Iend !^ tl_VFe(i,j)=om_r(i,j)*om_r(i,j)*tl_cff !^ tl_UFx(i,j)=on_r(i,j)*on_r(i,j)*tl_cff !^ ad_cff=ad_cff+ & & om_r(i,j)*om_r(i,j)*ad_VFe(i,j)+ & & on_r(i,j)*on_r(i,j)*ad_UFx(i,j) ad_VFe(i,j)=0.0_r8 ad_UFx(i,j)=0.0_r8 !^ tl_cff=visc2_r(i,j)*0.5_r8* & !^ & (tl_Drhs(i,j)* & !^ & (pmon_r(i,j)* & !^ & ((pn(i ,j)+pn(i+1,j))*ubar(i+1,j,krhs)- & !^ & (pn(i-1,j)+pn(i ,j))*ubar(i ,j,krhs))- & !^ & pnom_r(i,j)* & !^ & ((pm(i,j )+pm(i,j+1))*vbar(i,j+1,krhs)- & !^ & (pm(i,j-1)+pm(i,j ))*vbar(i,j ,krhs)))+ & !^ & Drhs(i,j)* & !^ & (pmon_r(i,j)* & !^ & ((pn(i ,j)+pn(i+1,j))*tl_ubar(i+1,j,krhs)- & !^ & (pn(i-1,j)+pn(i ,j))*tl_ubar(i ,j,krhs))- & !^ & pnom_r(i,j)* & !^ & ((pm(i,j )+pm(i,j+1))*tl_vbar(i,j+1,krhs)- & !^ & (pm(i,j-1)+pm(i,j ))*tl_vbar(i,j ,krhs)))) !^ adfac=visc2_r(i,j)*0.5_r8*ad_cff adfac1=adfac*Drhs(i,j) adfac2=adfac1*pmon_r(i,j) adfac3=adfac1*pnom_r(i,j) ad_Drhs(i,j)=ad_Drhs(i,j)+ & & (pmon_r(i,j)* & & ((pn(i ,j)+pn(i+1,j))*ubar(i+1,j,kstp)- & & (pn(i-1,j)+pn(i ,j))*ubar(i ,j,kstp))- & & pnom_r(i,j)* & & ((pm(i,j )+pm(i,j+1))*vbar(i,j+1,kstp)- & & (pm(i,j-1)+pm(i,j ))*vbar(i,j ,kstp)))* & & adfac ad_ubar(i ,j,kstp)=ad_ubar(i ,j,kstp)- & & (pn(i-1,j)+pn(i ,j))*adfac2 ad_ubar(i+1,j,kstp)=ad_ubar(i+1,j,kstp)+ & & (pn(i ,j)+pn(i+1,j))*adfac2 ad_vbar(i,j ,kstp)=ad_vbar(i,j ,kstp)+ & & (pm(i,j-1)+pm(i,j ))*adfac3 ad_vbar(i,j+1,kstp)=ad_vbar(i,j+1,kstp)- & & (pm(i,j )+pm(i,j+1))*adfac3 ad_cff=0.0_r8 END DO END DO ! ! Compute total depth at PSI-points. ! DO j=Jstr,Jend+1 DO i=Istr,Iend+1 !^ tl_Drhs_p(i,j)=0.25_r8*(tl_Drhs(i,j )+tl_Drhs(i-1,j )+ & !^ & tl_Drhs(i,j-1)+tl_Drhs(i-1,j-1)) !^ adfac=0.25_r8*ad_Drhs_p(i,j) ad_Drhs(i-1,j-1)=ad_Drhs(i-1,j-1)+adfac ad_Drhs(i-1,j )=ad_Drhs(i-1,j )+adfac ad_Drhs(i, j-1)=ad_Drhs(i ,j-1)+adfac ad_Drhs(i ,j )=ad_Drhs(i ,j )+adfac ad_Drhs_p(i,j)=0.0_r8 END DO END DO #endif #if (defined CURVGRID && defined UV_ADV) && !defined SOLVE3D ! !----------------------------------------------------------------------- ! Add in curvilinear transformation terms. !----------------------------------------------------------------------- ! DO j=Jstr,Jend DO i=Istr,Iend IF (j.ge.JstrV) THEN # if defined DIAGNOSTICS_UV !! fac2=0.5_r8*(Vwrk(i,j)+Vwrk(i,j-1)) !! DiaV2rhs(i,j,M2xadv)=DiaV2rhs(i,j,M2xadv)-fac1+fac2 !! DiaV2rhs(i,j,M2yadv)=DiaV2rhs(i,j,M2yadv)-fac2 !! DiaV2rhs(i,j,M2hadv)=DiaV2rhs(i,j,M2hadv)-fac1 # endif !^ tl_rvbar(i,j)=tl_rvbar(i,j)-tl_fac1 !^ ad_fac1=ad_fac1-ad_rvbar(i,j) !^ tl_fac1=0.5_r8*(tl_UFx(i,j)+tl_UFx(i-1,j)) !^ adfac=0.5_r8*ad_fac1 ad_VFe(i,j-1)=ad_VFe(i,j-1)+adfac ad_VFe(i,j )=ad_VFe(i,j )+adfac ad_fac1=0.0_r8 END IF ! IF (i.ge.IstrU) THEN # if defined DIAGNOSTICS_UV !! fac2=0.5_r8*(Uwrk(i,j)+Uwrk(i-1,j)) !! DiaU2rhs(i,j,M2xadv)=DiaU2rhs(i,j,M2xadv)+fac1-fac2 !! DiaU2rhs(i,j,M2yadv)=DiaU2rhs(i,j,M2yadv)+fac2 !! DiaU2rhs(i,j,M2hadv)=DiaU2rhs(i,j,M2hadv)+fac1 # endif !^ tl_rubar(i,j)=tl_rubar(i,j)+tl_fac1 !^ ad_fac1=ad_fac1+ad_rubar(i,j) !^ tl_fac1=0.5_r8*(tl_UFx(i,j)+tl_UFx(i-1,j)) !^ adfac=0.5_r8*ad_fac1 ad_UFx(i-1,j)=ad_UFx(i-1,j)+adfac ad_UFx(i ,j)=ad_UFx(i ,j)+adfac ad_fac1=0.0_r8 END IF END DO END DO ! DO j=JstrV-1,Jend DO i=IstrU-1,Iend cff1=0.5_r8*(vbar(i,j ,krhs)+ & # ifdef WEC_MELLOR & vbar_stokes(i,j )+ & & vbar_stokes(i,j+1)+ & # endif & vbar(i,j+1,krhs)) cff2=0.5_r8*(ubar(i ,j,krhs)+ & # ifdef WEC_MELLOR & ubar_stokes(i ,j)+ & & ubar_stokes(i+1,j)+ & # endif & ubar(i+1,j,krhs)) cff3=cff1*dndx(i,j) cff4=cff2*dmde(i,j) cff=Drhs(i,j)*(cff3-cff4) # if defined DIAGNOSTICS_UV !! cff=Drhs(i,j)*cff4 !! Uwrk(i,j)=-cff*cff1 ! ubar equation, ETA-term !! Vwrk(i,j)=-cff*cff2 ! vbar equation, ETA-term # 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_Drhs(i,j)*(cff3-cff4)+ & !^ & Drhs(i,j)*(tl_cff3-tl_cff4) !^ adfac=Drhs(i,j)*ad_cff ad_cff4=ad_cff4-adfac ad_cff3=ad_cff3+adfac ad_Drhs(i,j)=ad_Drhs(i,j)+(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_ubar(i ,j,krhs)+ & # ifdef WEC_MELLOR !^ & tl_ubar_stokes(i ,j)+ & !^ & tl_ubar_stokes(i+1,j)+ & # endif !^ & tl_ubar(i+1,j,krhs)) !^ adfac=0.5_r8*ad_cff2 ad_ubar(i ,j,krhs)=ad_ubar(i ,j,krhs)+adfac ad_ubar(i+1,j,krhs)=ad_ubar(i+1,j,krhs)+adfac # ifdef WEC_MELLOR ad_ubar_stokes(i ,j)=ad_ubar_stokes(i ,j)+adfac ad_ubar_stokes(i+1,j)=ad_ubar_stokes(i+1,j)+adfac # endif ad_cff2=0.0_r8 !^ tl_cff1=0.5_r8*(tl_vbar(i,j ,krhs)+ & # ifdef WEC_MELLOR !^ & tl_vbar_stokes(i,j )+ & !^ & tl_vbar_stokes(i,j+1)+ & # endif !^ & tl_vbar(i,j+1,krhs)) !^ adfac=0.5_r8*ad_cff1 ad_vbar(i,j ,krhs)=ad_vbar(i,j ,krhs)+adfac ad_vbar(i,j+1,krhs)=ad_vbar(i,j+1,krhs)+adfac # ifdef WEC_MELLOR ad_vbar_stokes(i,j )=ad_vbar_stokes(i,j )+adfac ad_vbar_stokes(i,j+1)=ad_vbar_stokes(i,j+1)+adfac # endif ad_cff1=0.0_r8 END DO END DO #endif #if (defined UV_COR & !defined SOLVE3D) || defined STEP2D_CORIOLIS ! !----------------------------------------------------------------------- ! Add in Coriolis term. !----------------------------------------------------------------------- ! DO j=Jstr,Jend DO i=Istr,Iend IF (j.ge.JstrV) THEN # if defined DIAGNOSTICS_UV !! DiaV2rhs(i,j,M2fcor)=-fac2 # endif !^ tl_rvbar(i,j)=tl_rvbar(i,j)-tl_fac2 !^ ad_fac2=ad_fac2-ad_rvbar(i,j) !^ tl_fac2=0.5_r8*(tl_VFe(i,j)+tl_VFe(i,j-1)) !^ adfac=0.5_r8*ad_fac2 ad_VFe(i,j-1)=ad_VFe(i,j-1)+adfac ad_VFe(i,j )=ad_VFe(i,j )+adfac ad_fac2=0.0_r8 END IF ! IF (i.ge.IstrU) THEN # if defined DIAGNOSTICS_UV !! DiaU2rhs(i,j,M2fcor)=fac1 # endif !^ tl_rubar(i,j)=tl_rubar(i,j)+tl_fac1 !^ ad_fac1=tl_fac1+ad_rubar(i,j) !^ tl_fac1=0.5_r8*(tl_UFx(i,j)+tl_UFx(i-1,j)) !^ adfac=0.5_r8*ad_fac1 ad_UFx(i-1,j)=ad_UFx(i-1,j)+adfac ad_UFx(i ,j)=ad_UFx(i ,j)+adfac ad_fac1=0.0_r8 END IF END DO END DO ! DO j=JstrV-1,Jend DO i=IstrU-1,Iend cff=0.5_r8*Drhs(i,j)*fomn(i,j) !^ tl_VFe(i,j)=tl_cff*(ubar(i ,j,krhs)+ & # ifdef WEC_MELLOR !^ & ubar_stokes(i ,j)+ & !^ & ubar_stokes(i+1,j)+ & # endif !^ & ubar(i+1,j,krhs))+ & !^ & cff*(tl_ubar(i ,j,krhs)+ & # ifdef WEC_MELLOR !^ & tl_ubar_stokes(i ,j)+ & !^ & tl_ubar_stokes(i+1,j)+ & # endif !^ & tl_ubar(i+1,j,krhs)) !^ adfac=cff*ad_VFe(i,j) ad_ubar(i ,j,krhs)=ad_ubar(i ,j,krhs)+adfac ad_ubar(i+1,j,krhs)=ad_ubar(i+1,j,krhs)+adfac # ifdef WEC_MELLOR ad_ubar_stokes(i ,j)=ad_ubar_stokes(i ,j)+adfac ad_ubar_stokes(i+1,j)=ad_ubar_stokes(i+1,j)+adfac # endif ad_cff=ad_cff+ & & (ubar(i ,j,krhs)+ & # ifdef WEC_MELLOR & ubar_stokes(i ,j)+ & & ubar_stokes(i+1,j)+ & # endif & ubar(i+1,j,krhs))*ad_VFe(i,j) ad_VFe(i,j)=0.0_r8 ! !^ tl_UFx(i,j)=tl_cff*(vbar(i,j ,krhs)+ & # ifdef WEC_MELLOR !^ & vbar_stokes(i,j )+ & !^ & vbar_stokes(i,j+1)+ & # endif !^ & vbar(i,j+1,krhs))+ & !^ & cff*(tl_vbar(i,j ,krhs)+ & # ifdef WEC_MELLOR !^ & tl_vbar_stokes(i,j )+ & !^ & tl_vbar_stokes(i,j+1)+ & # endif !^ & tl_vbar(i,j+1,krhs)) !^ adfac=cff*ad_UFx(i,j) ad_vbar(i,j ,krhs)=ad_vbar(i,j ,krhs)+adfac ad_vbar(i,j+1,krhs)=ad_vbar(i,j+1,krhs)+adfac # ifdef WEC_MELLOR ad_vbar_stokes(i,j )=ad_vbar_stokes(i,j )+adfac ad_vbar_stokes(i,j+1)=ad_vbar_stokes(i,j+1)+adfac # endif ad_cff=ad_cff+ & & (vbar(i,j ,krhs)+ & # ifdef WEC_MELLOR & vbar_stokes(i,j )+ & & vbar_stokes(i,j+1)+ & # endif & vbar(i,j+1,krhs))*ad_UFx(i,j) ad_UFx(i,j)=0.0_r8 !^ tl_cff=0.5_r8*tl_Drhs(i,j)*fomn(i,j) !^ ad_Drhs(i,j)=ad_Drhs(i,j)+0.5_r8*fomn(i,j)*ad_cff ad_cff=0.0_r8Q END DO END DO #endif #if defined UV_ADV && !defined SOLVE3D ! !----------------------------------------------------------------------- ! Adjoint of add in horizontal advection of momentum. !----------------------------------------------------------------------- ! ! Add advection to RHS terms. ! DO j=Jstr,Jend DO i=Istr,Iend IF (j.ge.JstrV) THEN # if defined DIAGNOSTICS_UV !! DiaV2rhs(i,j,M2xadv)=-cff1 !! DiaV2rhs(i,j,M2yadv)=-cff2 !! DiaV2rhs(i,j,M2hadv)=-fac # endif !^ tl_rvbar(i,j)=tl_rvbar(i,j)-tl_fac !^ ad_fac=ad_fac-ad_rvbar(i,j) !^ tl_fac=tl_cff1+tl_cff2 !^ ad_cff1=ad_cff1+ad_fac ad_cff2=ad_cff2+ad_fac ad_fac=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 IF ! IF (i.ge.IstrU) THEN # if defined DIAGNOSTICS_UV !! DiaU2rhs(i,j,M2xadv)=-cff1 !! DiaU2rhs(i,j,M2yadv)=-cff2 !! DiaU2rhs(i,j,M2hadv)=-fac # endif !^ tl_rubar(i,j)=tl_rubar(i,j)-tl_fac !^ ad_fac=ad_fac-ad_rubar(i,j) !^ tl_fac=tl_cff1+tl_cff2 !^ ad_cff1=ad_cff1+ad_fac ad_cff2=ad_cff2+ad_fac ad_fac=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 IF END DO END DO # ifdef UV_C2ADVECTION ! ! Second-order, centered differences advection fluxes. ! DO j=JstrV-1,Jend DO i=Istr,Iend !^ tl_VFe(i,j)=0.25_r8* & !^ & ((tl_DVom(i,j)+tl_DVom(i,j+1))* & !^ & (vbar(i,j ,krhs)+ & # ifdef WEC_MELLOR !^ & vbar_stokes(i,j )+ & !^ & vbar_stokes(i,j+1)+ & # endif !^ & vbar(i,j+1,krhs))+ & !^ & (DVom(i,j)+DVom(i,j+1))* & !^ & (tl_vbar(i,j ,krhs)+ & # ifdef WEC_MELLOR !^ & tl_vbar_stokes(i,j )+ & !^ & tl_vbar_stokes(i,j+1)+ & # endif !^ & tl_vbar(i,j+1,krhs))) !^ adfac=0.25_r8*ad_VFe(i,j) adfac1=adfac*(vbar(i,j ,krhs)+ & # ifdef WEC_MELLOR & vbar_stokes(i,j )+ & & vbar_stokes(i,j+1)+ & # endif & vbar(i,j+1,krhs)) adfac2=adfac*(DVom(i,j)+DVom(i,j+1)) ad_DVom(i,j )=ad_DVom(i,j )+adfac1 ad_DVom(i,j+1)=ad_DVom(i,j+1)+adfac1 ad_vbar(i,j ,krhs)=ad_vbar(i,j ,krhs)+adfac2 ad_vbar(i,j+1,krhs)=ad_vbar(i,j+1,krhs)+adfac2 # ifdef WEC_MELLOR ad_vbar_stokes(i,j )=ad_vbar_stokes(i,j )+adfac2 ad_vbar_stokes(i,j+1)=ad_vbar_stokes(i,j+1)+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_DUon(i,j)+tl_DUon(i,j-1))* & !^ & (vbar(i ,j,krhs)+ & # ifdef WEC_MELLOR !^ & vbar_stokes(i ,j)+ & !^ & vbar_stokes(i-1,j)+ & # endif !^ & vbar(i-1,j,krhs))+ & !^ & (DUon(i,j)+DUon(i,j-1))* & !^ & (tl_vbar(i ,j,krhs)+ & # ifdef WEC_MELLOR !^ & tl_vbar_stokes(i ,j)+ & !^ & tl_vbar_stokes(i-1,j)+ & # endif !^ & tl_vbar(i-1,j,krhs))) !^ adfac=0.25_r8*ad_VFx(i,j) adfac1=adfac*(vbar(i ,j,krhs)+ & # ifdef WEC_MELLOR & vbar_stokes(i ,j)+ & & vbar_stokes(i-1,j)+ & # endif & vbar(i-1,j,krhs)) adfac2=adfac*(DUon(i,j)+DUon(i,j-1)) ad_DUon(i,j )=ad_DUon(i,j )+adfac1 ad_DUon(i,j-1)=ad_DUon(i,j-1)+adfac1 ad_vbar(i ,j,krhs)=ad_vbar(i ,j,krhs)+adfac2 ad_vbar(i-1,j,krhs)=ad_vbar(i-1,j,krhs)+adfac2 # ifdef WEC_MELLOR ad_vbar_stokes(i-1,j)=ad_vbar_stokes(i-1,j)+adfac2 ad_vbar_stokes(i ,j)=ad_vbar_stokes(i ,j)+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_DVom(i,j)+tl_DVom(i-1,j))* & !^ & (ubar(i,j ,krhs)+ & # ifdef WEC_MELLOR !^ & ubar_stokes(i,j )+ & !^ & ubar_stokes(i,j-1)+ & # endif !^ & ubar(i,j-1,krhs))+ & !^ & (DVom(i,j)+DVom(i-1,j))* & !^ & (tl_ubar(i,j ,krhs)+ & # ifdef WEC_MELLOR !^ & tl_ubar_stokes(i,j )+ & !^ & tl_ubar_stokes(i,j-1)+ & # endif !^ & tl_ubar(i,j-1,krhs))) !^ adfac=0.25_r8*ad_UFe(i,j) adfac1=adfac*(ubar(i,j ,krhs)+ & # ifdef WEC_MELLOR & ubar_stokes(i,j )+ & & ubar_stokes(i,j-1)+ & # endif & ubar(i,j-1,krhs)) adfac2=adfac*(DVom(i,j)+DVom(i-1,j)) ad_DVom(i ,j)=ad_DVom(i ,j)+adfac1 ad_DVom(i-1,j)=ad_DVom(i-1,j)+adfac1 ad_ubar(i,j ,krhs)=ad_ubar(i,j ,krhs)+adfac2 ad_ubar(i,j-1,krhs)=ad_ubar(i,j-1,krhs)+adfac2 # ifdef WEC_MELLOR ad_ubar_stokes(i,j-1)=ad_ubar_stokes(i,j-1)+adfac2 ad_ubar_stokes(i,j )=ad_ubar_stokes(i,j )+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_DUon(i,j)+tl_DUon(i+1,j))* & !^ & (ubar(i ,j,krhs)+ & # ifdef WEC_MELLOR !^ & ubar_stokes(i ,j)+ & !^ & ubar_stokes(i+1,j)+ & # endif !^ & ubar(i+1,j,krhs))+ & !^ & (DUon(i,j)+DUon(i+1,j))* & !^ & (tl_ubar(i ,j,krhs)+ & # ifdef WEC_MELLOR !^ & tl_ubar_stokes(i ,j)+ & !^ & tl_ubar_stokes(i+1,j)+ & # endif !^ & tl_ubar(i+1,j,krhs))) !^ adfac=0.25_r8*ad_UFx(i,j) adfac1=adfac*(ubar(i ,j,krhs)+ & # ifdef WEC_MELLOR & ubar_stokes(i ,j)+ & & ubar_stokes(i+1,j)+ & # endif & ubar(i+1,j,krhs)) adfac2=adfac*(DUon(i,j)+DUon(i+1,j)) ad_DUon(i ,j)=ad_DUon(i ,j)+adfac1 ad_DUon(i+1,j)=ad_DUon(i+1,j)+adfac1 ad_ubar(i ,j,krhs)=ad_ubar(i ,j,krhs)+adfac2 ad_ubar(i+1,j,krhs)=ad_ubar(i+1,j,krhs)+adfac2 # ifdef WEC_MELLOR ad_ubar_stokes(i ,j)=ad_ubar_stokes(i ,j)+adfac2 ad_ubar_stokes(i+1,j)=ad_ubar_stokes(i+1,j)+adfac2 # endif ad_UFx(i,j)=0.0_r8 END DO END DO # elif defined UV_C4ADVECTION ! ! Fourth-order, centered differences v-momentum advection fluxes. ! DO j=JstrVm1,Jendp1 ! BASIC STATE DO i=Istr,Iend grad (i,j)=vbar(i,j-1,krhs)-2.0_r8*vbar(i,j,krhs)+ & # ifdef WEC_MELLOR & vbar_stokes(i,j-1)-2.0_r8*vbar_stokes(i,j)+ & & vbar_stokes(i,j+1)+ & # endif & vbar(i,j+1,krhs) Dgrad(i,j)=DVom(i,j-1)-2.0_r8*DVom(i,j)+DVom(i,j+1) END DO END DO IF (.not.(CompositeGrid(inorth,ng).or.NSperiodic(ng))) THEN IF (DOMAIN(ng)%Northern_Edge(tile)) THEN DO i=Istr,Iend grad (i,Jend+1)=grad (i,Jend) Dgrad(i,Jend+1)=Dgrad(i,Jend) 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 grad (i,Jstr)=grad (i,Jstr+1) Dgrad(i,Jstr)=Dgrad(i,Jstr+1) END DO END IF END IF ! d/dy(Dvv/m) cff=1.0_r8/6.0_r8 DO j=JstrV-1,Jend DO i=Istr,Iend !^ tl_VFe(i,j)=0.25_r8* & !^ & ((tl_vbar(i,j ,krhs)+ & # ifdef WEC_MELLOR !^ & tl_vbar_stokes(i,j )+ & !^ & tl_vbar_stokes(i,j+1)+ & # endif !^ & tl_vbar(i,j+1,krhs)- & !^ & cff*(tl_grad (i,j)+tl_grad (i,j+1)))* & !^ & (DVom(i,j)+DVom(i,j+1)- & !^ & cff*(Dgrad(i,j)+Dgrad(i,j+1)))+ & !^ & (vbar(i,j ,krhs)+ & # ifdef WEC_MELLOR !^ & vbar_stokes(i,j )+ & !^ & vbar_stokes(i,j+1)+ & # endif !^ & vbar(i,j+1,krhs)- & !^ & cff*(grad (i,j)+grad (i,j+1)))* & !^ & (tl_DVom(i,j)+tl_DVom(i,j+1)- & !^ & cff*(tl_Dgrad(i,j)+tl_Dgrad(i,j+1)))) !^ adfac=0.25_r8*ad_VFe(i,j) adfac1=adfac*(DVom(i,j)+DVom(i,j+1)- & & cff*(Dgrad(i,j)+Dgrad(i,j+1))) adfac2=adfac1*cff adfac3=adfac*(vbar(i,j ,krhs)+ & # ifdef WEC_MELLOR & vbar_stokes(i,j )+ & & vbar_stokes(i,j+1)+ & # endif & vbar(i,j+1,krhs)- & & cff*(grad (i,j)+grad (i,j+1))) adfac4=adfac3*cff ad_vbar(i,j ,krhs)=ad_vbar(i,j ,krhs)+adfac1 ad_vbar(i,j+1,krhs)=ad_vbar(i,j+1,krhs)+adfac1 # ifdef WEC_MELLOR ad_vbar_stokes(i,j )=ad_vbar_stokes(i,j )+adfac1 ad_vbar_stokes(i,j+1)=ad_vbar_stokes(i,j+1)+adfac1 # endif ad_grad (i,j )=ad_grad (i,j )-adfac2 ad_grad (i,j+1)=ad_grad (i,j+1)-adfac2 ad_DVom(i,j )=ad_DVom(i,j )+adfac3 ad_DVom(i,j+1)=ad_DVom(i,j+1)+adfac3 ad_Dgrad(i,j )=ad_Dgrad(i,j )-adfac4 ad_Dgrad(i,j+1)=ad_Dgrad(i,j+1)-adfac4 ad_VFe(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=Istr,Iend !^ tl_Dgrad(i,Jend+1)=tl_Dgrad(i,Jend) !^ ad_Dgrad(i,Jend)=ad_Dgrad(i,Jend)+ad_Dgrad(i,Jend+1) ad_Dgrad(i,Jend+1)=0.0_r8 !^ tl_grad (i,Jend+1)=tl_grad (i,Jend) !^ ad_grad (i,Jend)=ad_grad (i,Jend)+ad_grad (i,Jend+1) ad_grad (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_Dgrad(i,Jstr)=tl_Dgrad(i,Jstr+1) !^ ad_Dgrad(i,Jstr+1)=ad_Dgrad(i,Jstr+1)+ad_Dgrad(i,Jstr) ad_Dgrad(i,Jstr)=0.0_r8 !^ tl_grad (i,Jstr)=tl_grad (i,Jstr+1) !^ ad_grad (i,Jstr+1)=ad_grad (i,Jstr+1)+ad_grad (i,Jstr) ad_grad (i,Jstr)=0.0_r8 END DO END IF END IF DO j=JstrVm1,Jendp1 DO i=Istr,Iend !^ tl_Dgrad(i,j)=tl_DVom(i,j-1)-2.0_r8*tl_DVom(i,j)+ & !^ & tl_DVom(i,j+1) !^ ad_DVom(i,j-1)=ad_DVom(i,j-1)+ad_Dgrad(i,j) ad_DVom(i,j )=ad_DVom(i,j )-2.0_r8*ad_Dgrad(i,j) ad_DVom(i,j+1)=ad_DVom(i,j+1)+ad_Dgrad(i,j) ad_Dgrad(i,j)=0.0_r8 !^ tl_grad(i,j)=tl_vbar(i,j-1,krhs)-2.0_r8*tl_vbar(i,j,krhs)+ & # ifdef WEC_MELLOR !^ & tl_vbar_stokes(i,j-1)-2.0_r8*tl_vbar_stokes(i,j)+& !^ & tl_vbar_stokes(i,j+1)+ & # endif !^ & tl_vbar(i,j+1,krhs) !^ ad_vbar(i,j-1,krhs)=ad_vbar(i,j-1,krhs)+ad_grad(i,j) ad_vbar(i,j ,krhs)=ad_vbar(i,j ,krhs)- & & 2.0_r8*ad_grad(i,j) ad_vbar(i,j+1,krhs)=ad_vbar(i,j+1,krhs)+ad_grad(i,j) # ifdef WEC_MELLOR ad_vbar_stokes(i,j-1)=ad_vbar_stokes(i,j-1)+ad_grad(i,j) ad_vbar_stokes(i,j )=ad_vbar_stokes(i,j )- & & 2.0_r8*ad_grad(i,j) ad_vbar_stokes(i,j+1)=ad_vbar_stokes(i,j+1)+ad_grad(i,j) # endif ad_grad(i,j)=0.0_r8 END DO END DO ! DO j=JstrV,Jend ! BASIC STATE DO i=Istrm1,Iendp1 grad(i,j)=vbar(i-1,j,krhs)-2.0_r8*vbar(i,j,krhs)+ & # ifdef WEC_MELLOR & vbar_stokes(i-1,j)-2.0_r8*vbar_stokes(i,j)+ & & vbar_stokes(i+1,j)+ & # endif & vbar(i+1,j,krhs) END DO END DO IF (.not.(CompositeGrid(iwest,ng).or.EWperiodic(ng))) THEN IF (DOMAIN(ng)%Western_Edge(tile)) THEN DO j=JstrV,Jend grad(Istr-1,j)=grad(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 grad(Iend+1,j)=grad(Iend,j) END DO END IF END IF DO j=JstrV-1,Jend DO i=Istr,Iend+1 Dgrad(i,j)=DUon(i,j-1)-2.0_r8*DUon(i,j)+DUon(i,j+1) END DO END DO ! d/dx(Duv/n) cff=1.0_r8/6.0_r8 DO j=JstrV,Jend DO i=Istr,Iend+1 !^ tl_VFx(i,j)=0.25_r8* & !^ & ((tl_vbar(i ,j,krhs)+ & # ifdef WEC_MELLOR !^ & tl_vbar_stokes(i ,j)+ & !^ & tl_vbar_stokes(i-1,j)+ & # endif !^ & tl_vbar(i-1,j,krhs)- & !^ & cff*(tl_grad (i,j)+tl_grad (i-1,j)))* & !^ & (DUon(i,j)+DUon(i,j-1)- & !^ & cff*(Dgrad(i,j)+Dgrad(i,j-1)))+ & !^ & (vbar(i ,j,krhs)+ & # ifdef WEC_MELLOR !^ & vbar_stokes(i ,j)+ & !^ & vbar_stokes(i-1,j)+ & # endif !^ & vbar(i-1,j,krhs)- & !^ & cff*(grad (i,j)+grad (i-1,j)))* & !^ & (tl_DUon(i,j)+tl_DUon(i,j-1)- & !^ & cff*(tl_Dgrad(i,j)+tl_Dgrad(i,j-1)))) !^ adfac=0.25_r8*ad_VFx(i,j) adfac1=adfac*(DUon(i,j)+DUon(i,j-1)- & & cff*(Dgrad(i,j)+Dgrad(i,j-1))) adfac2=adfac1*cff adfac3=adfac*(vbar(i ,j,krhs)+ & # ifdef WEC_MELLOR & vbar_stokes(i ,j)+ & & vbar_stokes(i-1,j)+ & # endif & vbar(i-1,j,krhs)- & & cff*(grad (i,j)+grad (i-1,j))) adfac4=adfac3*cff ad_vbar(i-1,j,krhs)=ad_vbar(i-1,j,krhs)+adfac1 ad_vbar(i ,j,krhs)=ad_vbar(i ,j,krhs)+adfac1 # ifdef WEC_MELLOR ad_vbar_stokes(i-1,j)=ad_vbar_stokes(i-1,j)+adfac1 ad_vbar_stokes(i ,j)=ad_vbar_stokes(i ,j)+adfac1 # endif ad_grad (i-1,j)=ad_grad (i-1,j)-adfac2 ad_grad (i ,j)=ad_grad (i ,j)-adfac2 ad_DUon(i,j-1)=ad_DUon(i,j-1)+adfac3 ad_DUon(i,j )=ad_DUon(i,j )+adfac3 ad_Dgrad(i,j-1)=ad_Dgrad(i,j-1)-adfac4 ad_Dgrad(i,j )=ad_Dgrad(i,j )-adfac4 ad_VFx(i,j)=0.0_r8 END DO END DO ! DO j=JstrV-1,Jend DO i=Istr,Iend+1 !^ tl_Dgrad(i,j)=tl_DUon(i,j-1)-2.0_r8*tl_DUon(i,j)+ & !^ & tl_DUon(i,j+1) !^ ad_DUon(i,j-1)=ad_DUon(i,j-1)+ad_Dgrad(i,j) ad_DUon(i,j )=ad_DUon(i,j )-2.0_r8*ad_Dgrad(i,j) ad_DUon(i,j+1)=ad_DUon(i,j+1)+ad_Dgrad(i,j) ad_Dgrad(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_grad(Iend+1,j)=tl_grad(Iend,j) !^ ad_grad(Iend,j)=ad_grad(Iend,j)+ad_grad(Iend+1,j) ad_grad(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_grad(Istr-1,j)=tl_grad(Istr,j) !^ ad_grad(Istr,j)=ad_grad(Istr,j)+ad_grad(Istr-1,j) ad_grad(Istr-1,j)=0.0_r8 END DO END IF END IF DO j=JstrV,Jend DO i=Istrm1,Iendp1 !^ tl_grad(i,j)=tl_vbar(i-1,j,krhs)-2.0_r8*tl_vbar(i,j,krhs)+ & # ifdef WEC_MELLOR !^ & tl_vbar_stokes(i-1,j)-2.0_r8*tl_vbar_stokes(i,j)+& !^ & tl_vbar_stokes(i+1,j)+ & # endif !^ & tl_vbar(i+1,j,krhs) !^ ad_vbar(i-1,j,krhs)=ad_vbar(i-1,j,krhs)+ad_grad(i,j) ad_vbar(i ,j,krhs)=ad_vbar(i ,j,krhs)- & & 2.0_r8*ad_grad(i,j) ad_vbar(i+1,j,krhs)=ad_vbar(i+1,j,krhs)+ad_grad(i,j) # ifdef WEC_MELLOR ad_vbar_stokes(i-1,j)=ad_vbar_stokes(i-1,j)+ad_grad(i,j) ad_vbar_stokes(i ,j)=ad_vbar_stokes(i ,j)- & & 2.0_r8*ad_grad(i,j) ad_vbar_stokes(i+1,j)=ad_vbar_stokes(i+1,j)+ad_grad(i,j) # endif ad_grad(i,j)=0.0_r8 END DO END DO ! ! Fourth-order, centered differences u-momentum advection fluxes. ! DO j=Jstrm1,Jendp1 ! BASIC STATE DO i=IstrU,Iend grad(i,j)=ubar(i,j-1,krhs)-2.0_r8*ubar(i,j,krhs)+ & # ifdef WEC_MELLOR & ubar_stokes(i,j-1)-2.0_r8*ubar_stokes(i,j)+ & & ubar_stokes(i,j+1)+ & # endif & ubar(i,j+1,krhs) END DO END DO IF (.not.(CompositeGrid(isouth,ng).or.NSperiodic(ng))) THEN IF (DOMAIN(ng)%Southern_Edge(tile)) THEN DO i=IstrU,Iend grad(i,Jstr-1)=grad(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 grad(i,Jend+1)=grad(i,Jend) END DO END IF END IF DO j=Jstr,Jend+1 DO i=IstrU-1,Iend Dgrad(i,j)=DVom(i-1,j)-2.0_r8*DVom(i,j)+DVom(i+1,j) END DO END DO ! d/dy(Duv/m) cff=1.0_r8/6.0_r8 DO j=Jstr,Jend+1 DO i=IstrU,Iend !^ tl_UFe(i,j)=0.25_r8* & !^ & ((tl_ubar(i,j ,krhs)+ & # ifdef WEC_MELLOR !^ & tl_ubar_stokes(i,j )+ & !^ & tl_ubar_stokes(i,j-1)+ & # endif !^ & tl_ubar(i,j-1,krhs)- & !^ & cff*(tl_grad (i,j)+tl_grad (i,j-1)))* & !^ & (DVom(i,j)+DVom(i-1,j)- & !^ & cff*(Dgrad(i,j)+Dgrad(i-1,j)))+ & !^ & (ubar(i,j ,krhs)+ & # ifdef WEC_MELLOR !^ & ubar_stokes(i,j )+ & !^ & ubar_stokes(i,j-1)+ & # endif !^ & ubar(i,j-1,krhs)- & !^ & cff*(grad (i,j)+grad (i,j-1)))* & !^ & (tl_DVom(i,j)+tl_DVom(i-1,j)- & !^ & cff*(tl_Dgrad(i,j)+tl_Dgrad(i-1,j)))) !^ adfac=0.25_r8*ad_UFe(i,j) adfac1=adfac*(DVom(i,j)+DVom(i-1,j)- & & cff*(Dgrad(i,j)+Dgrad(i-1,j))) adfac2=adfac1*cff adfac3=adfac*(ubar(i,j ,krhs)+ & # ifdef WEC_MELLOR & ubar_stokes(i,j )+ & & ubar_stokes(i,j-1)+ & # endif & ubar(i,j-1,krhs)- & & cff*(grad (i,j)+grad (i,j-1))) adfac4=adfac3*cff ad_ubar(i,j-1,krhs)=ad_ubar(i,j-1,krhs)+adfac1 ad_ubar(i,j ,krhs)=ad_ubar(i,j ,krhs)+adfac1 # ifdef WEC_MELLOR ad_ubar_stokes(i,j-1)=ad_ubar_stokes(i,j-1)+adfac1 ad_ubar_stokes(i,j )=ad_ubar_stokes(i,j )+adfac1 # endif ad_grad (i,j-1)=ad_grad (i,j-1)-adfac2 ad_grad (i,j )=ad_grad (i,j )-adfac2 ad_DVom(i-1,j)=ad_DVom(i-1,j)+adfac3 ad_DVom(i ,j)=ad_DVom(i ,j)+adfac3 ad_Dgrad(i-1,j)=ad_Dgrad(i-1,j)-adfac4 ad_Dgrad(i ,j)=ad_Dgrad(i ,j)-adfac4 ad_UFe(i,j)=0.0_r8 END DO END DO ! DO j=Jstr,Jend+1 DO i=IstrU-1,Iend !^ tl_Dgrad(i,j)=tl_DVom(i-1,j)-2.0_r8*tl_DVom(i,j)+ & !^ & tl_DVom(i+1,j) !^ ad_DVom(i-1,j)=ad_DVom(i-1,j)+ad_Dgrad(i,j) ad_DVom(i ,j)=ad_DVom(i ,j)-2.0_r8*ad_Dgrad(i,j) ad_DVom(i+1,j)=ad_DVom(i+1,j)+ad_Dgrad(i,j) ad_Dgrad(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_grad(i,Jend+1)=tl_grad(i,Jend) !^ ad_grad(i,Jend)=ad_grad(i,Jend)+ad_grad(i,Jend+1) ad_grad(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_grad(i,Jstr-1)=tl_grad(i,Jstr) !^ ad_grad(i,Jstr)=ad_grad(i,Jstr)+ad_grad(i,Jstr-1) ad_grad(i,Jstr-1)=0.0_r8 END DO END IF END IF DO j=Jstrm1,Jendp1 DO i=IstrU,Iend !^ tl_grad(i,j)=tl_ubar(i,j-1,krhs)-2.0_r8*tl_ubar(i,j,krhs)+ & # ifdef WEC_MELLOR !^ & tl_ubar_stokes(i,j-1)-2.0_r8*tl_ubar_stokes(i,j)+& !^ & tl_ubar_stokes(i,j+1)+ & # endif !^ & tl_ubar(i,j+1,krhs) !^ ad_ubar(i,j-1,krhs)=ad_ubar(i,j-1,krhs)+ad_grad(i,j) ad_ubar(i,j ,krhs)=ad_ubar(i,j ,krhs)- & & 2.0_r8*ad_grad(i,j) ad_ubar(i,j+1,krhs)=ad_ubar(i,j+1,krhs)+ad_grad(i,j) # ifdef WEC_MELLOR ad_ubar_stokes(i,j-1)=ad_ubar_stokes(i,j-1)+ad_grad(i,j) ad_ubar_stokes(i,j )=ad_ubar_stokes(i,j)- & & 2.0_r8*ad_grad(i,j) ad_ubar_stokes(i,j+1)=ad_ubar_stokes(i,j+1)+ad_grad(i,j) # endif ad_grad(i,j)=0.0_r8 END DO END DO ! DO j=Jstr,Jend ! BASIC STATE DO i=IstrUm1,Iendp1 grad (i,j)=ubar(i-1,j,krhs)-2.0_r8*ubar(i,j,krhs)+ & # ifdef WEC_MELLOR & ubar_stokes(i-1,j)-2.0_r8*ubar_stokes(i,j)+ & & ubar_stokes(i+1,j)+ & # endif & ubar(i+1,j,krhs) Dgrad(i,j)=DUon(i-1,j)-2.0_r8*DUon(i,j)+DUon(i+1,j) END DO END DO IF (.not.(CompositeGrid(iwest,ng).or.EWperiodic(ng))) THEN IF (DOMAIN(ng)%Western_Edge(tile)) THEN DO j=Jstr,Jend grad (Istr,j)=grad (Istr+1,j) Dgrad(Istr,j)=Dgrad(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 grad (Iend+1,j)=grad (Iend,j) Dgrad(Iend+1,j)=Dgrad(Iend,j) END DO END IF END IF ! d/dx(Duu/n) cff=1.0_r8/6.0_r8 DO j=Jstr,Jend DO i=IstrU-1,Iend !^ tl_UFx(i,j)=0.25_r8* & !^ & ((ubar(i ,j,krhs)+ & # ifdef WEC_MELLOR !^ & ubar_stokes(i ,j)+ & !^ & ubar_stokes(i+1,j)+ & # endif !^ & ubar(i+1,j,krhs)- & !^ & cff*(grad (i,j)+grad (i+1,j)))* & !^ & (tl_DUon(i,j)+tl_DUon(i+1,j)- & !^ & cff*(tl_Dgrad(i,j)+tl_Dgrad(i+1,j)))+ & !^ & (tl_ubar(i ,j,krhs)+ & # ifdef WEC_MELLOR !^ & tl_ubar_stokes(i ,j)+ & !^ & tl_ubar_stokes(i+1,j)+ & # endif !^ & tl_ubar(i+1,j,krhs)- & !^ & cff*(tl_grad (i,j)+tl_grad (i+1,j)))* & !^ & (DUon(i,j)+DUon(i+1,j)- & !^ & cff*(Dgrad(i,j)+Dgrad(i+1,j)))) !^ adfac=0.25_r8*ad_UFx(i,j) adfac1=adfac*(DUon(i,j)+DUon(i+1,j)- & & cff*(Dgrad(i,j)+Dgrad(i+1,j))) adfac2=adfac1*cff adfac3=adfac*(ubar(i ,j,krhs)+ & # ifdef WEC_MELLOR & ubar_stokes(i ,j)+ & & ubar_stokes(i+1,j)+ & # endif & ubar(i+1,j,krhs)- & & cff*(grad (i,j)+grad (i+1,j))) adfac4=adfac3*cff ad_ubar(i ,j,krhs)=ad_ubar(i ,j,krhs)+adfac1 ad_ubar(i+1,j,krhs)=ad_ubar(i+1,j,krhs)+adfac1 # ifdef WEC_MELLOR ad_ubar_stokes(i ,j)=ad_ubar_stokes(i ,j)+adfac1 ad_ubar_stokes(i+1,j)=ad_ubar_stokes(i+1,j)+adfac1 # endif ad_grad (i ,j)=ad_grad (i ,j)-adfac2 ad_grad (i+1,j)=ad_grad (i+1,j)-adfac2 ad_DUon(i ,j)=ad_DUon(i ,j)+adfac3 ad_DUon(i+1,j)=ad_DUon(i+1,j)+adfac3 ad_Dgrad(i ,j)=ad_Dgrad(i ,j)-adfac4 ad_Dgrad(i+1,j)=ad_Dgrad(i+1,j)-adfac4 ad_UFx(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=Jstr,Jend !^ tl_Dgrad(Iend+1,j)=tl_Dgrad(Iend,j) !^ ad_Dgrad(Iend,j)=ad_Dgrad(Iend,j)+ad_Dgrad(Iend+1,j) ad_Dgrad(Iend+1,j)=0.0_r8 !^ tl_grad (Iend+1,j)=tl_grad (Iend,j) !^ ad_grad (Iend,j)=ad_grad (Iend,j)+ad_grad (Iend+1,j) ad_grad (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_Dgrad(Istr,j)=tl_Dgrad(Istr+1,j) !^ ad_Dgrad(Istr+1,j)=ad_Dgrad(Istr+1,j)+ad_Dgrad(Istr,j) ad_Dgrad(Istr,j)=0.0_r8 !^ tl_grad (Istr,j)=tl_grad (Istr+1,j) !^ ad_grad (Istr+1,j)=ad_grad (Istr+1,j)+ad_grad (Istr,j) ad_grad (Istr,j)=0.0_r8 END DO END IF END IF DO j=Jstr,Jend DO i=IstrUm1,Iendp1 !^ tl_Dgrad(i,j)=tl_DUon(i-1,j)-2.0_r8*tl_DUon(i,j)+ & !^ & tl_DUon(i+1,j) !^ ad_DUon(i-1,j)=ad_DUon(i-1,j)+ad_Dgrad(i,j) ad_DUon(i ,j)=ad_DUon(i ,j)-2.0_r8*ad_Dgrad(i,j) ad_DUon(i+1,j)=ad_DUon(i+1,j)+ad_Dgrad(i,j) ad_Dgrad(i,j)=0.0_r8 !^ tl_grad(i,j)=tl_ubar(i-1,j,krhs)-2.0_r8*tl_ubar(i,j,krhs)+ & # ifdef WEC_MELLOR !^ & tl_ubar_stokes(i-1,j)-2.0_r8*tl_ubar_stokes(i,j)+& !^ & tl_ubar_stokes(i+1,j)+ & # endif !^ & tl_ubar(i+1,j,krhs) !^ ad_ubar(i-1,j,krhs)=ad_ubar(i-1,j,krhs)+ad_grad (i,j) ad_ubar(i ,j,krhs)=ad_ubar(i ,j,krhs)- & & 2.0_r8*ad_grad (i,j) ad_ubar(i+1,j,krhs)=ad_ubar(i+1,j,krhs)+ad_grad (i,j) # ifdef NEARHSORE_MELLOR ad_ubar_stokes(i-1,j)=ad_ubar_stokes(i-1,j)+ad_grad (i,j) ad_ubar_stokes(i ,j)=ad_ubar_stokes(i ,j)- & & 2.0_r8*ad_grad (i,j) ad_ubar_stokes(i+1,j)=ad_ubar_stokes(i+1,j)+ad_grad (i,j) # endif ad_grad(i,j)=0.0_r8 END DO END DO # endif #endif ! !----------------------------------------------------------------------- ! Adjoint of compute pressure-gradient terms. !----------------------------------------------------------------------- ! ! Notice that "rubar" and "rvbar" are computed within the same to allow ! shared references to array elements (i,j), which increases the ! computational density by almost a factor of 1.5 resulting in overall ! more efficient code. ! cff1=0.5*g cff2=0.333333333333_r8 #if !defined SOLVE3D && defined ATM_PRESS fac=0.5_r8*100.0_r8/rho0 #endif DO j=Jstr,Jend DO i=Istr,Iend IF (j.ge.JstrV) THEN #ifdef DIAGNOSTICS_UV !! DiaV2rhs(i,j,M2pgrd)=rvbar(i,j) #endif #if defined TIDE_GENERATING_FORCES && !defined SOLVE3D !^ tl_rvbar(i,j)=tl_rvbar(i,j)- & !^ & cff1*om_v(i,j)* & !^ & ((tl_h(i,j-1)+tl_h(i,j)+ & !^ & tl_rzeta(i,j-1)+tl_rzeta(i,j))* & !^ & (eq_tide(i,j)-eq_tide(i,j-1))+ & !^ & (h(i,j-1)+h(i,j)+ & !^ & rzeta(i,j-1)+rzeta(i,j))* & !^ & (tl_eq_tide(i,j)-tl_eq_tide(i,j-1))) !^ adfac=cff1*om_v(i,j)*ad_rvbar(i,j) adfac1=adfac*(eq_tide(i,j)-eq_tide(i,j-1)) adfac2=adfac*(h(i,j-1)+h(i,j)+ & & rzeta(i,j-1)+rzeta(i,j)) ad_h(i,j-1)=ad_h(i,j-1)-adfac1 ad_h(i,j )=ad_h(i,j )-adfac1 ad_rzeta(i,j-1)=ad_rzeta(i,j-1)-adfac1 ad_rzeta(i,j )=ad_rzeta(i,j )-adfac1 ad_eq_tide(i,j-1)=ad_eq_tide(i,j-1)+adfac2 ad_eq_tide(i,j )=ad_eq_tide(i,j )-adfac2 #endif #if defined ATM_PRESS && !defined SOLVE3D !^ tl_rvbar(i,j)=tl_rvbar(i,j)- & !^ & fac*om_v(i,j)* & !^ & (tl_h(i,j-1)+tl_h(i,j)+ & !^ & tl_rzeta(i,j-1)+tl_rzeta(i,j))* & !^ & (Pair(i,j)-Pair(i,j-1)) !^ adfac=-fac*om_v(i,j)*(Pair(i,j)-Pair(i,j-1)*ad_rvbar(i,j) ad_h(i,j-1)=ad_h(i,j-1)+adfac ad_h(i,j )=ad_h(i,j )+adfac ad_rzeta(i,j-1)=ad_rzeta(i,j-1)+adfac ad_rzeta(i,j )=ad_rzeta(i,j )+adfac #endif !^ tl_rvbar(i,j)=cff1*om_v(i,j)* & !^ & ((tl_h(i,j-1)+ & !^ & tl_h(i,j ))* & !^ & (rzeta(i,j-1)- & !^ & rzeta(i,j ))+ & !^ & (h(i,j-1)+ & !^ & h(i,j ))* & !^ & (tl_rzeta(i,j-1)- & !^ & tl_rzeta(i,j ))+ & #if defined VAR_RHO_2D && defined SOLVE3D !^ & (tl_h(i,j-1)- & !^ & tl_h(i,j ))* & !^ & (rzetaSA(i,j-1)+ & !^ & rzetaSA(i,j )+ & !^ & cff2*(rhoA(i,j-1)- & !^ & rhoA(i,j ))* & !^ & (zwrk(i,j-1)- & !^ & zwrk(i,j )))+ & !^ & (h(i,j-1)- & !^ & h(i,j ))* & !^ & (tl_rzetaSA(i,j-1)+ & !^ & tl_rzetaSA(i,j )+ & !^ & cff2*((tl_rhoA(i,j-1)- & !^ & tl_rhoA(i,j ))* & !^ & (zwrk(i,j-1)- & !^ & zwrk(i,j ))+ & !^ & (rhoA(i,j-1)- & !^ & rhoA(i,j ))* & !^ & (tl_zwrk(i,j-1)- & !^ & tl_zwrk(i,j ))))+ & #endif !^ & (tl_rzeta2(i,j-1)- & !^ & tl_rzeta2(i,j ))) !^ adfac=cff1*om_v(i,j)*ad_rvbar(i,j) adfac1=adfac*(rzeta(i,j-1)-rzeta(i,j )) adfac2=adfac*(h(i,j-1)+h(i,j )) ad_h(i,j-1)=ad_h(i,j-1)+adfac1 ad_h(i,j )=ad_h(i,j )+adfac1 ad_rzeta(i,j-1)=ad_rzeta(i,j-1)+adfac2 ad_rzeta(i,j )=ad_rzeta(i,j )-adfac2 ad_rzeta2(i,j-1)=ad_rzeta2(i,j-1)+adfac ad_rzeta2(i,j )=ad_rzeta2(i,j )-adfac #if defined VAR_RHO_2D && defined SOLVE3D adfac3=adfac*(rzetaSA(i,j-1)+ & & rzetaSA(i,j )+ & & cff2*(rhoA(i,j-1)- & & rhoA(i,j ))* & & (zwrk(i,j-1)- & & zwrk(i,j ))) adfac4=adfac2*cff2*(zwrk(i,j-1)-zwrk(i,j)) adfac5=adfac2*cff2*(rhoA(i,j-1)-rhoA(i,j)) ad_h(i,j-1)=ad_h(i,j-1)+adfac3 ad_h(i,j )=ad_h(i,j )-adfac3 ad_rzetaSA(i,j-1)=ad_rzetaSA(i,j-1)+adfac2 ad_rzetaSA(i,j )=ad_rzetaSA(i,j )+adfac2 ad_rhoA(i,j-1)=ad_rhoA(i,j-1)+adfac4 ad_rhoA(i,j )=ad_rhoA(i,j )-adfac4 ad_zwrk(i,j-1)=ad_zwrk(i,j-1)+adfac5 ad_zwrk(i,j )=ad_zwrk(i,j )-adfac5 #endif ad_rvbar(i,j)=0.0_r8 END IF ! IF (i.ge.IstrU) THEN #ifdef DIAGNOSTICS_UV !! DiaU2rhs(i,j,M2pgrd)=rubar(i,j) #endif #if defined TIDE_GENERATING_FORCES && !defined SOLVE3D !^ tl_rubar(i,j)=tl_rubar(i,j)- & !^ & cff1*on_u(i,j)* & !^ & ((tl_h(i-1,j)+tl_h(i,j)+ & !^ & tl_rzeta(i-1,j)+tl_rzeta(i,j))* & !^ & (eq_tide(i,j)-eq_tide(i-1,j))+ & !^ & (h(i-1,j)+h(i,j)+ & !^ & rzeta(i-1,j)+rzeta(i,j))* & !^ & (tl_eq_tide(i,j)-tl_eq_tide(i-1,j))) !^ adfac=cff1*on_u(i,j)*ad_rubar(i,j) adfac1=adfac*(eq_tide(i,j)-eq_tide(i-1,j)) adfac2=adfac*(h(i-1,j)+h(i,j)+ & & rzeta(i-1,j)+rzeta(i,j)) ad_h(i-1,j)=ad_h(i-1,j)-adfac1 ad_h(i ,j)=ad_h(i ,j)-adfac1 ad_rzeta(i-1,j)=ad_rzeta(i-1,j)-adfac1 ad_rzeta(i ,j)=ad_rzeta(i ,j)-adfac1 ad_eq_tide(i-1,j)=ad_eq_tide(i-1,j)+adfac2 ad_eq_tide(i ,j)=ad_eq_tide(i ,j)-adfac2 #endif #if defined ATM_PRESS && !defined SOLVE3D !^ tl_rubar(i,j)=tl_rubar(i,j)- & !^ & fac*on_u(i,j)* & !^ & (tl_h(i-1,j)+tl_h(i,j)+ & !^ & tl_rzeta(i-1,j)+tl_rzeta(i,j))* & !^ & (Pair(i,j)-Pair(i-1,j)) !^ adfac=-fac*on_u(i,j)*(Pair(i,j)-Pair(i-1,j))*ad_rubar(i,j) ad_h(i-1,j)=ad_h(i-1,j)+adfac ad_h(i ,j)=ad_h(i ,j)+adfac ad_rzeta(i-1,j)=ad_rzeta(i-1,j)+adfac ad_rzeta(i ,j)=ad_rzeta(i ,j)+adfac #endif !^ tl_rubar(i,j)=cff1*on_u(i,j)* & !^ & ((tl_h(i-1,j)+ & !^ & tl_h(i ,j))* & !^ & (rzeta(i-1,j)- & !^ & rzeta(i ,j))+ & !^ & (h(i-1,j)+ & !^ & h(i ,j))* & !^ & (tl_rzeta(i-1,j)- & !^ & tl_rzeta(i ,j))+ & #if defined VAR_RHO_2D && defined SOLVE3D !^ & (tl_h(i-1,j)- & !^ & tl_h(i ,j))* & !^ & (rzetaSA(i-1,j)+ & !^ & rzetaSA(i ,j)+ & !^ & cff2*(rhoA(i-1,j)- & !^ & rhoA(i ,j))* & !^ & (zwrk(i-1,j)- & !^ & zwrk(i ,j)))+ & !^ & (h(i-1,j)- & !^ & h(i ,j))* & !^ & (tl_rzetaSA(i-1,j)+ & !^ & tl_rzetaSA(i ,j)+ & !^ & cff2*((tl_rhoA(i-1,j)- & !^ & tl_rhoA(i ,j))* & !^ & (zwrk(i-1,j)- & !^ & zwrk(i ,j))+ & !^ & (rhoA(i-1,j)- & !^ & rhoA(i ,j))* & !^ & (tl_zwrk(i-1,j)- & !^ & tl_zwrk(i ,j))))+ & #endif !^ & (tl_rzeta2(i-1,j)- & !^ & tl_rzeta2(i ,j))) !^ adfac=cff1*on_u(i,j)*ad_rubar(i,j) adfac1=adfac*(rzeta(i-1,j)-rzeta(i ,j)) adfac2=adfac*(h(i-1,j)+h(i ,j)) ad_h(i-1,j)=ad_h(i-1,j)+adfac1 ad_h(i ,j)=ad_h(i ,j)+adfac1 ad_rzeta(i-1,j)=ad_rzeta(i-1,j)+adfac2 ad_rzeta(i ,j)=ad_rzeta(i ,j)-adfac2 ad_rzeta2(i-1,j)=ad_rzeta2(i-1,j)+adfac ad_rzeta2(i ,j)=ad_rzeta2(i ,j)-adfac #if defined VAR_RHO_2D && defined SOLVE3D adfac3=adfac*(rzetaSA(i-1,j)+ & & rzetaSA(i ,j)+ & & cff2*(rhoA(i-1,j)- & & rhoA(i ,j))* & & (zwrk(i-1,j)- & & zwrk(i ,j))) adfac4=adfac2*cff2*(zwrk(i-1,j)-zwrk(i,j)) adfac5=adfac2*cff2*(rhoA(i-1,j)-rhoA(i,j)) ad_h(i-1,j)=ad_h(i-1,j)+adfac3 ad_h(i ,j)=ad_h(i ,j)-adfac3 ad_rzetaSA(i-1,j)=ad_rzetaSA(i-1,j)+adfac2 ad_rzetaSA(i ,j)=ad_rzetaSA(i ,j)+adfac2 ad_rhoA(i-1,j)=ad_rhoA(i-1,j)+adfac4 ad_rhoA(i ,j)=ad_rhoA(i ,j)-adfac4 ad_zwrk(i-1,j)=ad_zwrk(i-1,j)+adfac5 ad_zwrk(i ,j)=ad_zwrk(i ,j)-adfac5 #endif ad_rubar(i,j)=0.0_r8 END IF END DO END DO ! !----------------------------------------------------------------------- ! Adjoint of advance free-surface. !----------------------------------------------------------------------- ! ! Apply boundary conditions to newly computed free-surface "zeta_new" ! and load into global state array. Notice that "zeta_new" is always ! centered at time step "m+1", while zeta(:,:,knew) should be centered ! either at "m+1/2" after predictor step and at "m+1" after corrector. ! Chosing it to be this way makes it possible avoid storing RHS for ! zeta, ubar, and vbar between predictor and corrector sub-steps. ! IF (PREDICTOR_2D_STEP) THEN IF (FIRST_2D_STEP) THEN cff1=0.5_r8 cff2=0.5_r8 cff3=0.0_r8 ELSE cff1=0.5_r8-gamma cff2=0.5_r8+2.0_r8*gamma cff3=-gamma END IF DO j=JstrR,JendR DO i=IstrR,IendR !^ tl_zeta(i,j,knew)=cff1*tl_zeta_new(i,j)+ & !^ & cff2*tl_zeta(i,j,kstp)+ & !^ & cff3*tl_zeta(i,j,kbak) !^ ad_zeta_new(i,j)=ad_zeta_new(i,j)+cff1*ad_zeta(i,j,knew) ad_zeta(i,j,kstp)=ad_zeta(i,j,kstp)+cff2*ad_zeta(i,j,knew) ad_zeta(i,j,kbak)=ad_zeta(i,j,kbak)+cff3*ad_zeta(i,j,knew) ad_zeta(i,j,knew)=0.0_r8 END DO END DO ELSE DO j=JstrR,JendR DO i=IstrR,IendR !^ tl_zeta(i,j,knew)=tl_zeta_new(i,j) !^ ad_zeta_new(i,j)=ad_zeta_new(i,j)+ad_zeta(i,j,knew) ad_zeta(i,j,knew)=0.0_r8 END DO END DO END IF ! ! Here, we use the local "zetabc" since the private array "zeta_new" ! is passed as an argument to allow computing the lateral boundary ! conditions on the range IstrU-1:Iend and JstrV-1:Jend, so parallel ! tile exchanges are avoided. ! !^ CALL tl_zetabc_local (ng, tile, & !^ & LBi, UBi, LBj, UBj, & !^ & IminS, ImaxS, JminS, JmaxS, & !^ & kstp, & !^ & zeta, tl_zeta, & !^ & zeta_new, tl_zeta_new) !^ CALL ad_zetabc_local (ng, tile, & & LBi, UBi, LBj, UBj, & & IminS, ImaxS, JminS, JmaxS, & & kstp, & & zeta, ad_zeta, & & zeta_new, ad_zeta_new) ! ! Apply mass point sources (volume vertical influx), if any. ! ! Dsrc(is) = 2, flow across grid cell w-face (positive or negative) ! IF (LwSrc(ng)) THEN DO is=1,Nsrc(ng) IF (INT(SOURCES(ng)%Dsrc(is)).eq.2) THEN i=SOURCES(ng)%Isrc(is) j=SOURCES(ng)%Jsrc(is) IF (((IstrR.le.i).and.(i.le.IendR)).and. & & ((JstrR.le.j).and.(j.le.JendR))) THEN !^ tl_zeta_new(i,j)=tl_zeta_new(i,j)+0.0_r8 END IF END IF END DO END IF ! ! Compute "zeta_new" at the new time step andinterpolate backward for ! the subsequent computation of barotropic pressure-gradient terms. ! Notice that during the predictor of the first 2D step in 3D mode, ! the pressure gradient terms are computed using just zeta(:,:,kstp), ! i.e., like in the Forward Euler step, rather than the more accurate ! predictor of generalized RK2. This is to keep it consistent with the ! computation of pressure gradient in 3D mode, which uses precisely ! the initial value of "zeta" rather than the value changed by the ! first barotropic predictor step. Later in this code, just after ! "rufrc, rvfrc" are finalized, a correction term based on the ! difference zeta_new(:,:)-zeta(:,:,kstp) to "rubar, rvbar" to make ! them consistent with generalized RK2 stepping for pressure gradient ! terms. ! IF (PREDICTOR_2D_STEP) THEN IF (FIRST_2D_STEP) THEN ! Modified RK2 time step (with cff=dtfast(ng) ! Forward-Backward feedback with #ifdef SOLVE3D cff1=0.0_r8 !==> Forward Euler cff2=1.0_r8 #else cff1=0.333333333333_r8 ! optimally chosen beta=1/3 and cff2=0.666666666667_r8 ! epsilon=2/3, see below) is used #endif cff3=0.0_r8 ! here for the start up. ELSE cff=2.0_r8*dtfast(ng) ! In the code below "zwrk" is cff1=beta ! time-centered at time step "n" cff2=1.0_r8-2.0_r8*beta ! in the case of LF (for all but cff3=beta ! the first time step) END IF ! DO j=JstrV-1,Jend DO i=IstrU-1,Iend fac=cff*pm(i,j)*pn(i,j) #if defined VAR_RHO_2D && defined SOLVE3D !^ tl_rzetaSA(i,j)=tl_zwrk(i,j)*(rhoS(i,j)-rhoA(i,j))+ & !^ & zwrk(i,j)*(tl_rhoS(i,j)-tl_rhoA(i,j)) !^ adfac=zwrk(i,j)*ad_rzetaSA(i,j) ad_zwrk(i,j)=ad_zwrk(i,j)+ & & (rhoS(i,j)-rhoA(i,j))*ad_rzetaSA(i,j) ad_rhoS(i,j)=ad_rhoS(i,j)+adfac ad_rhoA(i,j)=ad_rhoA(i,j)-adfac ad_rzetaSA(i,j)=0.0_r8 !^ tl_rzeta2(i,j)=tl_rzeta(i,j)*zwrk(i,j)+ & !^ & rzeta(i,j)*tl_zwrk(i,j) !^ ad_rzeta(i,j)=ad_rzeta(i,j)+zwrk(i,j)*ad_rzeta2(i,j) ad_zwrk(i,j)=ad_zwrk(i,j)+rzeta(i,j)*ad_rzeta2(i,j) ad_rzeta2(i,j)=0.0_r8 !^ tl_rzeta(i,j)=(1.0_r8+rhoS(i,j))*tl_zwrk(i,j)+ & !^ & tl_rhoS(i,j)*zwrk(i,j) !^ ad_rhoS(i,j)=ad_rhoS(i,j)+zwrk(i,j)*ad_rzeta(i,j) ad_zwrk(i,j)=ad_zwrk(i,j)+(1.0_r8+rhoS(i,j))*ad_rzeta(i,j) ad_rzeta(i,j)=0.0_r8 #else !^ tl_rzeta2(i,j)=2.0_r8*tl_zwrk(i,j)*zwrk(i,j) !^ tl_rzeta(i,j)=tl_zwrk(i,j) !^ ad_zwrk(i,j)=ad_zwrk(i,j)+ & & 2.0_r8*zwrk(i,j)*ad_rzeta2(i,j)+ & & ad_rzeta(i,j) #endif !^ tl_zwrk(i,j)=cff1*tl_zeta_new(i,j)+ & !^ & cff2*tl_zeta(i,j,kstp)+ & !^ & cff3*tl_zeta(i,j,kbak) !^ ad_zeta_new(i,j)=ad_zeta_new(i,j)+cff1*ad_zwrk(i,j) ad_zeta(i,j,kstp)=ad_zeta(i,j,kstp)+cff2*ad_zwrk(i,j) ad_zeta(i,j,kbak)=ad_zeta(i,j,kbak)+cff3*ad_zwrk(i,j) ad_zwrk(i,j)=0.0_r8 !^ tl_Dnew(i,j)=tl_zeta_new(i,j)+tl_h(i,j) !^ ad_h(i,j)=ad_h(i,j)+ad_Dnew(i,j) ad_Dnew(i,j)=0.0_r8 #ifdef MASKING # ifdef WET_DRY_NOT_YET !! zeta_new(i,j)=zeta_new(i,j)+ & !! & (Dcrit(ng)-h(i,j))*(1.0_r8-rmask(i,j)) # endif !^ tl_zeta_new(i,j)=tl_zeta_new(i,j)*rmask(i,j) !^ ad_zeta_new(i,j)=ad_zeta_new(i,j)*rmask(i,j) #endif !^ tl_zeta_new(i,j)=tl_zeta(i,j,kbak)+ & !^ & fac*(DUon(i,j)-DUon(i+1,j)+ & !^ & DVom(i,j)-DVom(i,j+1)) !^ adfac=fac*ad_zeta_new(i,j) ad_zeta(i,j,kbak)=ad_zeta(i,j,kbak)+ad_zeta_new(i,j) ad_DUon(i ,j)=ad_DUon(i ,j)+adfac ad_DUon(i+1,j)=ad_DUon(i+1,j)-adfac ad_DVom(i,j )=ad_DVom(i,j )+adfac ad_DVom(i,j+1)=ad_DVom(i,j+1)-adfac ad_zeta_new(i,j)=0.0_r8 END DO END DO ELSE !--> CORRECTOR STEP IF (FIRST_2D_STEP) THEN cff =0.333333333333_r8 ! Modified RK2 weighting: cff1=0.333333333333_r8 ! here "zwrk" is time- cff2=0.333333333333_r8 ! centered at "n+1/2". cff3=0.0_r8 ELSE cff =1.0_r8-epsil ! zwrk is always time- cff1=(0.5_r8-gamma)*epsil ! centered at n+1/2 cff2=(0.5_r8+2.0_r8*gamma)*epsil ! during corrector sub- cff3=-gamma *epsil ! step. END IF ! DO j=JstrV-1,Jend DO i=IstrU-1,Iend fac=dtfast(ng)*pm(i,j)*pn(i,j) #if defined VAR_RHO_2D && defined SOLVE3D !^ tl_rzetaSA(i,j)=tl_zwrk(i,j)*(rhoS(i,j)-rhoA(i,j))+ & !^ & zwrk(i,j)*(tl_rhoS(i,j)-tl_rhoA(i,j)) !^ adfac=zwrk(i,j)*ad_rzetaSA(i,j) ad_zwrk(i,j)=ad_zwrk(i,j)+ & & (rhoS(i,j)-rhoA(i,j))*ad_rzetaSA(i,j) ad_rhoS(i,j)=ad_rhoS(i,j)+adfac ad_rhoA(i,j)=ad_rhoA(i,j)-adfac ad_rzetaSA(i,j)=0.0_r8 !^ tl_rzeta2(i,j)=tl_rzeta(i,j)*zwrk(i,j)+ & !^ & rzeta(i,j)*tl_zwrk(i,j) !^ ad_rzeta(i,j)=ad_rzeta(i,j)+zwrk(i,j)*ad_rzeta2(i,j) ad_zwrk(i,j)=ad_zwrk(i,j)+rzeta(i,j)*ad_rzeta2(i,j) ad_rzeta2(i,j)=0.0_r8 !^ tl_rzeta(i,j)=(1.0_r8+rhoS(i,j))*tl_zwrk(i,j)+ & !^ & tl_rhoS(i,j)*zwrk(i,j) !^ ad_rhoS(i,j)=ad_rhoS(i,j)+zwrk(i,j)*ad_rzeta(i,j) ad_zwrk(i,j)=ad_zwrk(i,j)+(1.0_r8+rhoS(i,j))*ad_rzeta(i,j) ad_rzeta(i,j)=0.0_r8 #else !^ tl_rzeta2(i,j)=2.0_r8*tl_zwrk(i,j)*zwrk(i,j) !^ tl_rzeta(i,j)=tl_zwrk(i,j) !^ ad_zwrk(i,j)=ad_zwrk(i,j)+ & & 2.0_r8*zwrk(i,j)*ad_rzeta2(i,j)+ & & ad_rzeta(i,j) #endif !^ tl_zwrk(i,j)=cff *tl_zeta(i,j,krhs)+ & !^ & cff1*tl_zeta_new(i,j)+ & !^ & cff2*tl_zeta(i,j,kstp)+ & !^ & cff3*tl_zeta(i,j,kbak) !^ ad_zeta_new(i,j)=ad_zeta_new(i,j)+cff1*ad_zwrk(i,j) ad_zeta(i,j,krhs)=ad_zeta(i,j,krhs)+cff *ad_zwrk(i,j) ad_zeta(i,j,kstp)=ad_zeta(i,j,kstp)+cff2*ad_zwrk(i,j) ad_zeta(i,j,kbak)=ad_zeta(i,j,kbak)+cff3*ad_zwrk(i,j) ad_zwrk(i,j)=0.0_r8 !^ tl_Dnew(i,j)=tl_zeta_new(i,j)+tl_h(i,j) !^ ad_h(i,j)=ad_h(i,j)+ad_Dnew(i,j) ad_zeta_new(i,j)=ad_zeta_new(i,j)+ad_Dnew(i,j) ad_Dnew(i,j)=0.0_r8 #ifdef MASKING # ifdef WET_DRY_NOT_YET !! zeta_new(i,j)=zeta_new(i,j)+ & !! & (Dcrit(ng)-h(i,j))*(1.0_r8-rmask(i,j)) # endif !^ tl_zeta_new(i,j)=tl_zeta_new(i,j)*rmask(i,j) !^ ad_zeta_new(i,j)=ad_zeta_new(i,j)*rmask(i,j) #endif !^ tl_zeta_new(i,j)=tl_zeta(i,j,kstp)+ & !^ & fac*(tl_DUon(i,j)-tl_DUon(i+1,j)+ & !^ & tl_DVom(i,j)-tl_DVom(i,j+1)) !^ adfac=fac*ad_zeta_new(i,j) ad_zeta(i,j,kstp)=ad_zeta(i,j,kstp)+ad_zeta_new(i,j) ad_DUon(i ,j)=ad_DUon(i ,j)+adfac ad_DUon(i+1,j)=ad_DUon(i+1,j)-adfac ad_DVom(i,j )=ad_DVom(i,j )+adfac ad_DVom(i,j+1)=ad_DVom(i,j+1)-adfac ad_zeta_new(i,j)=0.0_r8 END DO END DO END IF #ifdef SOLVE3D ! !----------------------------------------------------------------------- ! Adjoint of fields averaged over all barotropic time steps. !----------------------------------------------------------------------- ! ! Notice that the index ranges here are designed to include physical ! boundaries only. Periodic ghost points and internal mpi computational ! margins are NOT included. ! ! Reset all barotropic mode time-averaged arrays during the first ! predictor step. At all subsequent time steps, accumulate averages ! of the first kind using the DELAYED way. For example, "Zt_avg1" is ! not summed immediately after the corrector step when computed but ! during the subsequent predictor substep. It allows saving operations ! because "DUon" and "DVom" are calculated anyway. The last time step ! has a special code to add all three barotropic variables after the ! last corrector substep. ! IF (PREDICTOR_2D_STEP) THEN ! PREDICTOR STEP IF (FIRST_2D_STEP) THEN DO j=JstrR,JendR DO i=IstrR,IendR !^ tl_DV_avg2(i,j)=0.0_r8 !^ ad_DV_avg2(i,j)=0.0_r8 !^ tl_DU_avg2(i,j)=0.0_r8 !^ ad_DU_avg2(i,j)=0.0_r8 !^ tl_DV_avg1(i,j)=0.0_r8 !^ ad_DV_avg1(i,j)=0.0_r8 !^ tl_DU_avg1(i,j)=0.0_r8 !^ ad_DU_avg1(i,j)=0.0_r8 !^ tl_Zt_avg1(i,j)=0.0_r8 !^ ad_Zt_avg1(i,j)=0.0_r8 END DO END DO ELSE cff=weight(1,iif(ng)-1,ng) DO j=JstrR,JendR DO i=IstrR,IendR IF (j.ge.Jstr) THEN !^ tl_DV_avg1(i,j)=tl_DV_avg1(i,j)+cff*tl_DVom(i,j) !^ ad_DVom(i,j)=ad_DVom(i,j)+cff*ad_DV_avg1(i,j) END IF IF (i.ge.Istr) THEN !^ tl_DU_avg1(i,j)=tl_DU_avg1(i,j)+cff*tl_DUon(i,j) !^ ad_DUon(i,j)=ad_DUon(i,j)+cff*ad_DU_avg1(i,j) END IF !^ tl_Zt_avg1(i,j)=tl_Zt_avg1(i,j)+cff*tl_zeta(i,j,krhs) !^ ad_zeta(i,j,krhs)=ad_zeta(i,j,krhs)+cff*ad_Zt_avg1(i,j) END DO END DO END IF ELSE ! CORRECTOR STEP cff=weight(2,iif(ng),ng) DO j=JstrR,JendR DO i=IstrR,IendR IF (j.ge.Jstr) THEN !^ tl_DV_avg2(i,j)=tl_DV_avg2(i,j)+cff*tl_DVom(i,j) !^ ad_DVom(i,j)=ad_DVom(i,j)+cff*ad_DV_avg2(i,j) END IF IF (i.ge.Istr) THEN !^ tl_DU_avg2(i,j)=tl_DU_avg2(i,j)+cff*tl_DUon(i,j) !^ ad_DUon(i,j)=ad_DUon(i,j)+cff*ad_DU_avg2(i,j) END IF END DO END DO END IF #endif ! !----------------------------------------------------------------------- ! Adjoint of preliminary steps. !----------------------------------------------------------------------- ! ! Set vertically integrated mass fluxes DUon and DVom along the open ! boundaries in such a way that the integral volume is conserved. ! IF (ANY(VolCons(:,ng))) THEN !^ CALL tl_set_DUV_bc_tile (ng, tile, & !^ & LBi, UBi, LBj, UBj, & !^ & IminS, ImaxS, JminS, JmaxS, & !^ & krhs, & #ifdef MASKING !^ & umask, vmask, & #endif !^ & om_v, on_u, & !^ & ubar, vbar, & !^ & tl_ubar, tl_vbar, & !^ & Drhs, DUon, DVom, & !^ & tl_Drhs, tl_DUon, tl_DVom) !^ CALL ad_set_DUV_bc_tile (ng, tile, & & LBi, UBi, LBj, UBj, & & IminS, ImaxS, JminS, JmaxS, & & krhs, & #ifdef MASKING & umask, vmask, & #endif & om_v, on_u, & & ubar, vbar, & & ad_ubar, ad_vbar, & & Drhs, DUon, DVom, & & ad_Drhs, ad_DUon, ad_DVom) END IF #if defined DISTRIBUTE && \ defined UV_ADV && defined UV_C4ADVECTION && !defined SOLVE3D ! ! In distributed-memory, the I- and J-ranges are different and a ! special exchange is done here to avoid having three ghost points ! for high-order numerical stencils. Notice that a private array is ! passed below to the exchange routine. It also applies periodic ! boundary conditions, if appropriate and no partitions in I- or ! J-directions. ! !^ CALL mp_exchange2d (ng, tile, iTLM, 2, & !^ & IminS, ImaxS, JminS, JmaxS, & !^ & NghostPoints, & !^ & EWperiodic(ng), NSperiodic(ng), & !^ & DUon, DVom, & !^ & tl_DUon, tl_DVom) !^ CALL ad_mp_exchange2d (ng, tile, iTLM, 2, & & IminS, ImaxS, JminS, JmaxS, & & NghostPoints, & & EWperiodic(ng), NSperiodic(ng), & & ad_DUon, ad_DVom) ! IF (EWperiodic(ng).or.NSperiodic(ng)) THEN !^ CALL exchange_v2d_tile (ng, tile, & !^ & IminS, ImaxS, JminS, JmaxS, & !^ & tl_DVom) !^ CALL ad_exchange_v2d_tile (ng, tile, & & IminS, ImaxS, JminS, JmaxS, & & ad_DVom) !^ CALL exchange_u2d_tile (ng, tile, & !^ & IminS, ImaxS, JminS, JmaxS, & !^ & tl_DUon) !^ CALL ad_exchange_u2d_tile (ng, tile, & & IminS, ImaxS, JminS, JmaxS, & & ad_DUon) END IF #endif ! ! Compute total depth of the water column and vertically integrated ! mass fluxes, which are used in computation of free-surface elevation ! time tendency and advection terms for the barotropic momentum ! equations. ! #if defined DISTRIBUTE && !defined NESTING # define IR_RANGE IstrUm2-1,Iendp2 # define JR_RANGE JstrVm2-1,Jendp2 # define IU_RANGE IstrUm1-1,Iendp2 # define JU_RANGE Jstrm1-1,Jendp2 # define IV_RANGE Istrm1-1,Iendp2 # define JV_RANGE JstrVm1-1,Jendp2 #else # define IR_RANGE IstrUm2-1,Iendp2 # define JR_RANGE JstrVm2-1,Jendp2 # define IU_RANGE IstrUm2,Iendp2 # define JU_RANGE JstrVm2-1,Jendp2 # define IV_RANGE IstrUm2-1,Iendp2 # define JV_RANGE JstrVm2,Jendp2 #endif DO j=JV_RANGE DO i=IV_RANGE cff=0.5_r8*om_v(i,j) cff1=cff*(Drhs(i,j)+Drhs(i,j-1)) !^ tl_DVom(i,j)=tl_vbar(i,j,krhs)*cff1+ & !^ & vbar(i,j,krhs)*tl_cff1 !^ ad_vbar(i,j,krhs)=ad_vbar(i,j,krhs)+cff1*ad_DVom(i,j) ad_cff1=ad_cff1+vbar(i,j,krhs)*ad_DVom(i,j) ad_DVom(i,j)=0.0_r8 !^ tl_cff1=cff*(tl_Drhs(i,j)+tl_Drhs(i,j-1)) !^ adfac=cff*ad_cff1 ad_Drhs(i,j-1)=ad_Drhs(i,j-1)+adfac ad_Drhs(i,j )=ad_Drhs(i,j )+adfac ad_cff1=0.0_r8 END DO END DO DO j=JU_RANGE DO i=IU_RANGE cff=0.5_r8*on_u(i,j) cff1=cff*(Drhs(i,j)+Drhs(i-1,j)) !^ tl_DUon(i,j)=tl_ubar(i,j,krhs)*cff1+ & !^ & ubar(i,j,krhs)*tl_cff1 !^ ad_ubar(i,j,krhs)=ad_ubar(i,j,krhs)+cff1*ad_DUon(i,j) ad_cff1=ad_cff1+ubar(i,j,krhs)*ad_DUon(i,j) ad_DUon(i,j)=0.0_r8 !^ tl_cff1=cff*(tl_Drhs(i,j)+tl_Drhs(i-1,j)) !^ adfac=cff*ad_cff1 ad_Drhs(i-1,j)=ad_Drhs(i-1,j)+adfac ad_Drhs(i ,j)=ad_Drhs(i ,j)+adfac ad_cff1=0.0_r8 END DO END DO DO j=JR_RANGE DO i=IR_RANGE !^ tl_Drhs(i,j)=tl_zeta(i,j,krhs)+tl_h(i,j) !^ ad_h(i,j)=ad_h(i,j)+ad_Drhs(i,j) ad_zeta(i,j,krhs)=ad_zeta(i,j,krhs)+ad_Drhs(i,j) ad_Drhs(i,j)=0.0_r8 END DO END DO #undef IR_RANGE #undef IU_RANGE #undef IV_RANGE #undef JR_RANGE #undef JU_RANGE #undef JV_RANGE ! ! Deallocate local new free-surface. ! deallocate ( ad_zeta_new ) ! RETURN END SUBROUTINE ad_step2d_tile ! END MODULE ad_step2d_mod