add diags for tracer budget terms and forcing FEISTY

src/tracer/MARBL_tracers.F90

@@ -199,6 +199,12 @@ module MARBL_tracers
   !! so currently using temp_MARBL_diag for that.
   integer, allocatable :: id_surface_flux_out(:)  !< register_diag indices for surface_flux output
   integer, allocatable :: id_surface_flux_from_salt_flux(:)  !< register_diag indices for surface_flux from salt_flux
+  integer, allocatable :: id_boundary_forcing_content_tend(:)  !< register_diag indices for tracer content tendency
+                                                               !! from boundary forcing
+  integer, allocatable :: id_diabatic_content_tend(:)  !< register_diag indices for tracer content tendency
+                                                       !! from diabatic diffusion
+  integer, allocatable :: id_interior_content_tend(:)  !< register_diag indices for tracer content tendency
+                                                       !! from MARBL interior tendencies
   type(temp_MARBL_diag), allocatable :: interior_tendency_out(:)  !< collect interior tendencies for diagnostic output
   type(temp_MARBL_diag), allocatable :: interior_tendency_out_zint(:)  !< vertical integral of interior tendencies
                                                                        !! (full column)
@@ -958,6 +964,9 @@ subroutine initialize_MARBL_tracers(restart, day, G, GV, US, h, param_file, diag
   ! Register per-tracer diagnostics computed from MARBL surface flux / interior tendency values
   allocate(CS%id_surface_flux_out(CS%ntr))
   allocate(CS%id_surface_flux_from_salt_flux(CS%ntr))
+  allocate(CS%id_boundary_forcing_content_tend(CS%ntr))
+  allocate(CS%id_diabatic_content_tend(CS%ntr))
+  allocate(CS%id_interior_content_tend(CS%ntr))
   allocate(CS%interior_tendency_out(CS%ntr))
   allocate(CS%interior_tendency_out_zint(CS%ntr))
   allocate(CS%interior_tendency_out_zint_100m(CS%ntr))
@@ -970,11 +979,39 @@ subroutine initialize_MARBL_tracers(restart, day, G, GV, US, h, param_file, diag
         day, trim(longname), trim(units), conversion=US%Z_to_m*US%s_to_T)
 
     write(name, "(2A)") "STF_SALT_", trim(MARBL_instances%tracer_metadata(m)%short_name)
-    write(longname, "(2A)") trim(MARBL_instances%tracer_metadata(m)%long_name), " Surface Flux from Salt Flux"
+    write(longname, "(2A)") trim(MARBL_instances%tracer_metadata(m)%long_name), &
+        " Surface Flux from Salt Flux"
     CS%id_surface_flux_from_salt_flux(m) = register_diag_field("ocean_model", trim(name), &
         diag%axesT1, & ! T => tracer grid? 1 => no vertical grid
         day, trim(longname), trim(units), conversion=US%Z_to_m*US%s_to_T)
 
+    write(name, "(3A)") "boundary_forcing_", trim(MARBL_instances%tracer_metadata(m)%short_name), &
+        "_cont_tendency"
+    write(longname, "(3A)") "Boundary forcing ", &
+        trim(MARBL_instances%tracer_metadata(m)%short_name), " Layer Content Tendency"
+    write(units, "(2A)") trim(MARBL_instances%tracer_metadata(m)%units), " m/s"
+    CS%id_boundary_forcing_content_tend(m) = register_diag_field("ocean_model", trim(name), &
+        diag%axesTL, day, trim(longname), trim(units), v_extensive=.true., &
+        conversion=GV%H_to_m*US%s_to_T)
+
+    write(name, "(3A)") "diabatic_", trim(MARBL_instances%tracer_metadata(m)%short_name), &
+        "_cont_tendency"
+    write(longname, "(3A)") "Diabatic ", &
+        trim(MARBL_instances%tracer_metadata(m)%short_name), " Layer Content Tendency"
+    write(units, "(2A)") trim(MARBL_instances%tracer_metadata(m)%units), " m/s"
+    CS%id_diabatic_content_tend(m) = register_diag_field("ocean_model", trim(name), &
+        diag%axesTL, day, trim(longname), trim(units), v_extensive=.true., &
+        conversion=GV%H_to_m*US%s_to_T)
+
+    write(name, "(3A)") "interior_", trim(MARBL_instances%tracer_metadata(m)%short_name), &
+        "_cont_tendency"
+    write(longname, "(2A)") trim(MARBL_instances%tracer_metadata(m)%short_name), &
+        " Layer Content Tendency from Interior Source-Sink"
+    write(units, "(2A)") trim(MARBL_instances%tracer_metadata(m)%units), " m/s"
+    CS%id_interior_content_tend(m) = register_diag_field("ocean_model", trim(name), &
+        diag%axesTL, day, trim(longname), trim(units), v_extensive=.true., &
+        conversion=GV%H_to_m*US%s_to_T)
+
     write(name, "(2A)") "J_", trim(MARBL_instances%tracer_metadata(m)%short_name)
     write(longname, "(2A)") trim(MARBL_instances%tracer_metadata(m)%long_name), " Source Sink Term"
     write(units, "(2A)") trim(MARBL_instances%tracer_metadata(m)%units), "/s"
@@ -1511,15 +1548,19 @@ subroutine MARBL_tracers_column_physics(h_old, ea, eb, fluxes, dt, G, GV, US, CS
   real, dimension(SZI_(G),SZJ_(G)) :: ref_mask ! Mask for 2D MARBL diags using ref_depth [1]
   real, dimension(SZI_(G),SZJ_(G)) :: riv_flux_loc ! Local copy of CS%RIV_FLUXES*dt [conc H ~> mmol m-2]
   real, dimension(SZI_(G),SZJ_(G),SZK_(G)) :: h_work ! Used so that h can be modified [H ~> m or kg m-2]
+  real, dimension(SZI_(G),SZJ_(G),SZK_(G)) :: tr_work ! tracer value before process is applied [conc]
+  real, dimension(SZI_(G),SZJ_(G),SZK_(G)) :: cont_tend ! tracer content tend [conc m s-1 or conc kg m-2 s-1]
   real, dimension(SZI_(G),SZJ_(G),SZK_(G)) :: bot_flux_to_tend  ! Conversion factor for bottom tlux -> tend
                                                                 ! [Z-1 ~> m-1]
   real :: cum_bftt_dz     ! sum of bot_flux_to_tend * dz from the bottom layer to current layer [1]
   real, dimension(0:GV%ke) :: zi  ! z-coordinate interface depth [Z ~> m]
   real, dimension(GV%ke) :: zc  ! z-coordinate layer center depth [Z ~> m]
   real, dimension(GV%ke) :: dz  ! z-coordinate cell thickness [H ~> m]
+  real :: Idt  ! The inverse of the timestep [T-1 ~> s-1]
   integer :: i, j, k, is, ie, js, je, nz, m
 
   is = G%isc ; ie = G%iec ; js = G%jsc ; je = G%jec ; nz = GV%ke
+  Idt = 0.0 ; if (dt > 0.0) Idt = 1. / dt
 
   if (.not.associated(CS)) return
 
@@ -1953,14 +1994,37 @@ subroutine MARBL_tracers_column_physics(h_old, ea, eb, fluxes, dt, G, GV, US, CS
         if (CS%debug) &
           call hchksum(riv_flux_loc(:,:), &
               trim(MARBL_instances%tracer_metadata(m)%short_name)//' riv flux', G%HI, unscale=GV%H_to_m)
+        if (CS%id_boundary_forcing_content_tend(m) > 0) then
+          do k=1,nz ;do j=js,je ; do i=is,ie
+            tr_work(i,j,k) = CS%tracer_data(m)%tr(i,j,k)
+          enddo ; enddo ; enddo
+        endif
         call applyTracerBoundaryFluxesInOut(G, GV, CS%tracer_data(m)%tr(:,:,:) , dt, fluxes, h_work, &
             evap_CFL_limit, minimum_forcing_depth, in_flux_optional=riv_flux_loc)
+        if (CS%id_boundary_forcing_content_tend(m) > 0) then
+          do k=1,nz ;do j=js,je ; do i=is,ie
+            cont_tend(i,j,k) = Idt * &
+                (h_work(i,j,k) * CS%tracer_data(m)%tr(i,j,k) - h_old(i,j,k) * tr_work(i,j,k))
+          enddo ; enddo ; enddo
+          call post_data(CS%id_boundary_forcing_content_tend(m), cont_tend, CS%diag, alt_h=h_old)
+        endif
+        if (CS%id_diabatic_content_tend(m) > 0) then
+          do k=1,nz ;do j=js,je ; do i=is,ie
+            tr_work(i,j,k) = CS%tracer_data(m)%tr(i,j,k)
+          enddo ; enddo ; enddo
+        endif
       else
         call applyTracerBoundaryFluxesInOut(G, GV, CS%tracer_data(m)%tr(:,:,:) , dt, fluxes, h_work, &
             evap_CFL_limit, minimum_forcing_depth)
       endif
       call tracer_vertdiff(h_work, ea, eb, dt, CS%tracer_data(m)%tr(:,:,:), G, GV, &
           sfc_flux=GV%Rho0 * CS%STF(:,:,m))
+      if (CS%id_diabatic_content_tend(m) > 0) then
+        do k=1,nz ;do j=js,je ; do i=is,ie
+          cont_tend(i,j,k) = Idt * (h_work(i,j,k) * (CS%tracer_data(m)%tr(i,j,k) - tr_work(i,j,k)))
+        enddo ; enddo ; enddo
+        call post_data(CS%id_diabatic_content_tend(m), cont_tend, CS%diag, alt_h=h_work)
+      endif
     enddo
   else
     ! TODO: do we want to support these options? does not apply river fluxes!
@@ -2028,6 +2092,12 @@ subroutine MARBL_tracers_column_physics(h_old, ea, eb, fluxes, dt, G, GV, US, CS
     if (allocated(CS%interior_tendency_out(m)%field_3d)) &
       call post_data(CS%interior_tendency_out(m)%id, &
           CS%interior_tendency_out(m)%field_3d(:,:,:), CS%diag)
+      if (CS%id_interior_content_tend(m) > 0) then
+        do k=1,nz ;do j=js,je ; do i=is,ie
+          cont_tend(i,j,k) = h_old(i,j,k) * CS%interior_tendency_out(m)%field_3d(i,j,k)
+        enddo ; enddo ; enddo
+        call post_data(CS%id_interior_content_tend(m), cont_tend, CS%diag, alt_h=h_old)
+      endif
     if (allocated(CS%interior_tendency_out_zint(m)%field_2d)) &
       call post_data(CS%interior_tendency_out_zint(m)%id, &
           CS%interior_tendency_out_zint(m)%field_2d(:,:), CS%diag)
@@ -2364,6 +2434,12 @@ subroutine MARBL_tracers_end(CS)
     endif
     if (allocated(CS%ind_tr)) deallocate(CS%ind_tr)
     if (allocated(CS%id_surface_flux_out)) deallocate(CS%id_surface_flux_out)
+    if (allocated(CS%id_surface_flux_from_salt_flux)) &
+        deallocate(CS%id_surface_flux_from_salt_flux)
+    if (allocated(CS%id_boundary_forcing_content_tend)) &
+        deallocate(CS%id_boundary_forcing_content_tend)
+    if (allocated(CS%id_diabatic_content_tend)) deallocate(CS%id_diabatic_content_tend)
+    if (allocated(CS%id_interior_content_tend)) deallocate(CS%id_interior_content_tend)
     if (allocated(CS%interior_tendency_out)) deallocate(CS%interior_tendency_out)
     if (allocated(CS%interior_tendency_out_zint)) deallocate(CS%interior_tendency_out_zint)
     if (allocated(CS%interior_tendency_out_zint_100m)) &

src/tracer/MOM_tracer_registry.F90

@@ -309,6 +309,8 @@ subroutine register_tracer_diagnostics(Reg, h, Time, diag, G, GV, US, use_ALE, u
                                  ! [units] m3 s-1 or [units] kg s-1.
   character(len=48)  :: conv_units ! The units for flux convergences, either
                                  ! [units] m s-1 or [units] kg m-2 s-1.
+  character(len=48)  :: content_units ! The units of layer content, either
+                                 ! [units] m or [units] kg m-2.
   character(len=48)  :: unit2    ! The dimensions of the tracer squared
   character(len=72)  :: cmorname ! The CMOR name of this tracer.
   character(len=120) :: cmor_longname ! The CMOR long name of that variable.
@@ -346,6 +348,25 @@ subroutine register_tracer_diagnostics(Reg, h, Time, diag, G, GV, US, use_ALE, u
     elseif (GV%Boussinesq) then ; conv_units = trim(units)//" m s-1"
     else ; conv_units = trim(units)//" kg m-2 s-1" ; endif
 
+    ! content_units = conv_units + " s"
+    ! Basing content_units on conv_units instead of units yields content values
+    ! more easily relatable to convergence values when conv_units is specified,
+    ! e.g. with "salt" where conv_units = "kg m-2 s-1".
+    ! If conv_units ends with " s-1", remove that substring to construct content_units.
+    ! Otherwise, just append " s", not attempting other simplifications.
+    i = index(conv_units, " s-1")
+    if ((i > 0) .and. (i + len(" s-1") == len_trim(conv_units) + 1)) then
+      ! If there are only spaces before "s-1", the result is dimensionless, i.e. units= "1".
+      ! Otherwise, take substring before " s-1".
+      if (len_trim(conv_units(1:i)) == 0) then
+        content_units = "1"
+      else
+        content_units = conv_units(1:i-1)
+      endif
+    else
+      content_units = trim(conv_units) // " s"
+    endif
+
     if (len_trim(cmorname) == 0) then
       Tr%id_tr = register_diag_field("ocean_model", trim(name), diag%axesTL, &
           Time, trim(longname), trim(units), conversion=Tr%conc_scale)
@@ -359,6 +380,12 @@ subroutine register_tracer_diagnostics(Reg, h, Time, diag, G, GV, US, use_ALE, u
         trim(name)//"_post_horzn", diag%axesTL, Time, &
         trim(longname)//" after horizontal transport (advection/diffusion) has occurred", &
         trim(units), conversion=Tr%conc_scale)
+    Tr%id_trxh = register_diag_field('ocean_model', trim(shortnm)//'_content', &
+        diag%axesTL, Time, "Layer integrated "//lowercase(longname), &
+        content_units, conversion=Tr%conv_scale, v_extensive=.true.)
+    Tr%id_trxh_2d = register_diag_field('ocean_model', trim(shortnm)//'_content_2d', &
+        diag%axesT1, Time, "Vertical sum of layer integrated "//lowercase(longname), &
+        content_units, conversion=Tr%conv_scale)
     if (Tr%diag_form == 1) then
       Tr%id_adx = register_diag_field("ocean_model", trim(shortnm)//"_adx", &
           diag%axesCuL, Time, trim(flux_longname)//" advective zonal flux" , &
@@ -443,6 +470,14 @@ subroutine register_tracer_diagnostics(Reg, h, Time, diag, G, GV, US, use_ALE, u
         diag%axesT1, Time, &
         "Thickness-weighted integral of " // trim(longname), &
         trim(units) // " m", conversion=Tr%conc_scale*US%Z_to_m)
+    Tr%id_mean_150m = register_diag_field("ocean_model", trim(shortnm)//"_mean_150m", &
+        diag%axesT1, Time, &
+        "Thickness-weighted average of "// trim(longname) // " over top 150m", &
+        trim(units), conversion=Tr%conc_scale)
+    Tr%id_zint_150m = register_diag_field("ocean_model", trim(shortnm)//"_zint_150m", &
+        diag%axesT1, Time, &
+        "Thickness-weighted integral of "// trim(longname) // " over top 150m", &
+        trim(units) // " m", conversion=Tr%conc_scale*US%Z_to_m)
     Tr%id_zint_100m = register_diag_field("ocean_model", trim(shortnm)//"_zint_100m", &
         diag%axesT1, Time, &
         "Thickness-weighted integral of "// trim(longname) // " over top 100m", &
@@ -752,6 +787,19 @@ subroutine post_tracer_diagnostics_at_sync(Reg, h, diag_prev, diag, G, GV, dt)
   do m=1,Reg%ntr ; if (Reg%Tr(m)%registry_diags) then
     Tr => Reg%Tr(m)
     if (Tr%id_tr > 0) call post_data(Tr%id_tr, Tr%t, diag)
+    if ((Tr%id_trxh > 0) .or. (Tr%id_trxh_2d > 0)) then
+      do k=1,nz ; do j=js,je ; do i=is,ie
+        work3d(i,j,k) = Tr%t(i,j,k)*h(i,j,k)
+      enddo ; enddo ; enddo
+      if (Tr%id_trxh > 0) call post_data(Tr%id_trxh, work3d, diag)
+      if (Tr%id_trxh_2d > 0) then
+        work2d(:,:) = 0.0
+        do k=1,nz ; do j=js,je ; do i=is,ie
+          work2d(i,j) = work2d(i,j) + work3d(i,j,k)
+        enddo ; enddo ; enddo
+        call post_data(Tr%id_trxh_2d, work2d, diag)
+      endif
+    endif
     if (Tr%id_tendency > 0) then
       work3d(:,:,:) = 0.0
       do k=1,nz ; do j=js,je ; do i=is,ie
@@ -835,39 +883,89 @@ subroutine post_tracer_integral_diagnostics(G, GV, US, Reg, h_diag, tv, diag)
                                                  !! thermodynamic variables.
   type(diag_ctrl),            intent(in) :: diag !< structure to regulate diagnostic output
 
-  integer :: i, j, k, is, ie, js, je, nz, m, khi
-  real    :: work2d(SZI_(G),SZJ_(G))  ! The vertically integrated tracer amounts [CU Z T-1 ~> conc m]
+  integer :: i, j, k, is, ie, js, je, nz, m, khi_150, khi_100
+  real    :: I_denom_mean_150m(SZI_(G),SZJ_(G))  ! Inverse of denominator for computing mean over top 150m [Z ~> m]
+  real    :: work2d(SZI_(G),SZJ_(G))  ! The vertically integrated tracer amounts [CU Z ~> conc m]
   real    :: dz(SZI_(G),SZJ_(G),SZK_(GV)) !< Geometric layer thicknesses in height units [Z ~> m]
+  real    :: frac_under_150m(SZI_(G),SZJ_(G),SZK_(GV)) ! weights used to compute 150m vertical integrals [nondim]
   real    :: frac_under_100m(SZI_(G),SZJ_(G),SZK_(GV)) ! weights used to compute 100m vertical integrals [nondim]
   real    :: ztop(SZI_(G),SZJ_(G))    ! position of the top interface [Z ~> m]
   real    :: zbot(SZI_(G),SZJ_(G))    ! position of the bottom interface [Z ~> m]
+  real    :: Z_150  ! 150 m in depth units [Z ~> m]
   real    :: Z_100  ! 100 m in depth units [Z ~> m]
-  logical :: dz_needed, dz100_used
+  logical :: dz_needed, comp_mean_150m_denom, dz150_used, dz100_used
   type(tracer_type), pointer :: Tr=>NULL()
 
   is = G%isc ; ie = G%iec ; js = G%jsc ; je = G%jec ; nz = GV%ke
 
   dz_needed = .false.
+  comp_mean_150m_denom = .false.
+  dz150_used = .false.
   dz100_used = .false.
   do m=1,Reg%ntr ; if (Reg%Tr(m)%registry_diags) then
-    if (Reg%Tr(m)%id_zint_100m > 0) dz100_used = .true.
     if (Reg%Tr(m)%id_zint > 0) dz_needed = .true.
+    if (Reg%Tr(m)%id_mean_150m > 0) then
+      comp_mean_150m_denom = .true.
+      dz150_used = .true.
+    endif
+    if (Reg%Tr(m)%id_zint_150m > 0) dz150_used = .true.
+    if (Reg%Tr(m)%id_zint_100m > 0) dz100_used = .true.
   endif ; enddo
-  if (dz100_used) dz_needed = .true.
+  if (dz150_used .or. dz100_used) dz_needed = .true.
 
   if (dz_needed) then
     ! Convert the layer thicknesses into geometric depths, using the pre-stored layer-mean specific
     ! volumes when in non-Boussinesq mode.
     call thickness_to_dz(h_diag, tv, dz, G, GV, US)
   endif
 
+  if (dz150_used) then
+    ! If any tracers are posting 150m vertical integrals, compute weights
+    frac_under_150m(:,:,:) = 0.0
+    ! khi_150 will be the largest layer index corresponding where ztop < 150m and ztop >= 150m
+    ! in any column (we can reduce computation of 150m integrals by only looping through khi_150
+    ! rather than GV%ke)
+    khi_150 = 0
+
+    Z_150 = 150.0*US%m_to_Z
+    I_denom_mean_150m(:,:) = 0.0
+    zbot(:,:) = 0.0
+    do k=1,nz
+      do j=js,je ; do i=is,ie
+        ztop(i,j) = zbot(i,j)
+        zbot(i,j) = ztop(i,j) + dz(i,j,k)
+        if (zbot(i,j) <= Z_150) then
+          frac_under_150m(i,j,k) = 1.0
+        elseif (ztop(i,j) < Z_150) then
+          frac_under_150m(i,j,k) = (Z_150 - ztop(i,j)) / (zbot(i,j) - ztop(i,j))
+        else
+          frac_under_150m(i,j,k) = 0.0
+        endif
+        ! frac_under_150m(i,j,k) = max(0, min(1.0, (Z_150 - ztop(i,j)) / (zbot(i,j) - ztop(i,j))))
+      enddo ; enddo
+      if (any(frac_under_150m(:,:,k) > 0)) then
+        khi_150 = k
+        if (comp_mean_150m_denom) then
+          do j=js,je ; do i=is,ie
+            I_denom_mean_150m(i,j) = I_denom_mean_150m(i,j) + frac_under_150m(i,j,k) * dz(i,j,k)
+          enddo ; enddo
+        endif
+      endif
+    enddo
+    if (comp_mean_150m_denom) then
+      do j=js,je ; do i=is,ie
+        if (I_denom_mean_150m(i,j) > 0.0) I_denom_mean_150m(i,j) = 1.0 / I_denom_mean_150m(i,j)
+      enddo ; enddo
+    endif
+  endif
+
   if (dz100_used) then
     ! If any tracers are posting 100m vertical integrals, compute weights
     frac_under_100m(:,:,:) = 0.0
-    ! khi will be the largest layer index corresponding where ztop < 100m and ztop >= 100m
-    ! in any column (we can reduce computation of 100m integrals by only looping through khi
+    ! khi_100 will be the largest layer index corresponding where ztop < 100m and ztop >= 100m
+    ! in any column (we can reduce computation of 100m integrals by only looping through khi_100
     ! rather than GV%ke)
-    khi = 0
+    khi_100 = 0
 
     Z_100 = 100.0*US%m_to_Z
     zbot(:,:) = 0.0
@@ -884,7 +982,7 @@ subroutine post_tracer_integral_diagnostics(G, GV, US, Reg, h_diag, tv, diag)
         endif
         ! frac_under_100m(i,j,k) = max(0, min(1.0, (Z_100 - ztop(i,j)) / (zbot(i,j) - ztop(i,j))))
       enddo ; enddo
-      if (any(frac_under_100m(:,:,k) > 0)) khi = k
+      if (any(frac_under_100m(:,:,k) > 0)) khi_100 = k
     enddo
   endif
 
@@ -900,10 +998,25 @@ subroutine post_tracer_integral_diagnostics(G, GV, US, Reg, h_diag, tv, diag)
       call post_data(Tr%id_zint, work2d, diag)
     endif
 
+    ! Compute 150m vertical mean and integral
+    if ((Tr%id_mean_150m > 0) .or. (Tr%id_zint_150m > 0)) then
+      work2d(:,:) = 0.0
+      do k=1,khi_150 ; do j=js,je ; do i=is,ie
+        work2d(i,j) = work2d(i,j) + frac_under_150m(i,j,k) * dz(i,j,k)*Tr%t(i,j,k)
+      enddo ; enddo ; enddo
+      if (Tr%id_zint_150m > 0) call post_data(Tr%id_zint_150m, work2d, diag)
+      if (Tr%id_mean_150m > 0) then
+        do j=js,je ; do i=is,ie
+          work2d(i,j) = I_denom_mean_150m(i,j) * work2d(i,j)
+        enddo ; enddo
+        call post_data(Tr%id_mean_150m, work2d, diag)
+      endif
+    endif
+
     ! Compute 100m vertical integral
     if (Tr%id_zint_100m > 0) then
       work2d(:,:) = 0.0
-      do k=1,khi ; do j=js,je ; do i=is,ie
+      do k=1,khi_100 ; do j=js,je ; do i=is,ie
         work2d(i,j) = work2d(i,j) + frac_under_100m(i,j,k) * dz(i,j,k)*Tr%t(i,j,k)
       enddo ; enddo ; enddo
       call post_data(Tr%id_zint_100m, work2d, diag)