Calculate volo in scaled units

  Calculate the volo diagnostic in scaled units using the tmp_scale argument to
global_area_integral and undo this scaling with a conversion argument on its
register_scalar_field call.  Also corrected the units in the comments describing
the mass_celland masso variables in calculate_diagnostic_fields.  All answers
are bitwise identical.

Author: Hallberg-NOAA

src/diagnostics/MOM_diagnostics.F90

@@ -204,7 +204,7 @@ subroutine calculate_diagnostic_fields(u, v, h, uh, vh, tv, ADp, CDp, p_surf, &
                                             ! including [nondim] and [H ~> m or kg m-2].
   real :: uh_tmp(SZIB_(G),SZJ_(G),SZK_(GV)) ! A temporary zonal transport [H L2 T-1 ~> m3 s-1 or kg s-1]
   real :: vh_tmp(SZI_(G),SZJB_(G),SZK_(GV)) ! A temporary meridional transport [H L2 T-1 ~> m3 s-1 or kg s-1]
-  real :: mass_cell(SZI_(G),SZJ_(G))       ! The vertically integrated mass in a grid cell [kg]
+  real :: mass_cell(SZI_(G),SZJ_(G))       ! The vertically integrated mass in a grid cell [R Z L2 ~> kg]
   real :: rho_in_situ(SZI_(G))             ! In situ density [R ~> kg m-3]
   real :: cg1(SZI_(G),SZJ_(G))             ! First baroclinic gravity wave speed [L T-1 ~> m s-1]
   real :: Rd1(SZI_(G),SZJ_(G))             ! First baroclinic deformation radius [L ~> m]
@@ -226,7 +226,7 @@ subroutine calculate_diagnostic_fields(u, v, h, uh, vh, tv, ADp, CDp, p_surf, &
   real, dimension(SZK_(GV)) :: salt_layer_ave ! The average salinity in a layer [S ~> ppt]
   real :: thetaoga  ! The volume mean potential temperature [C ~> degC]
   real :: soga      ! The volume mean ocean salinity [S ~> ppt]
-  real :: masso     ! The total mass of the ocean [kg]
+  real :: masso     ! The total mass of the ocean [R Z L2 ~> kg]
   real :: tosga     ! The area mean sea surface temperature [C ~> degC]
   real :: sosga     ! The area mean sea surface salinity [S ~> ppt]
 
@@ -1341,7 +1341,7 @@ subroutine post_surface_thermo_diags(IDs, G, GV, US, diag, dt_int, sfc_state, tv
     zos  ! dynamic sea lev (zero area mean) from inverse-barometer adjusted ssh [Z ~> m]
   real :: I_time_int    ! The inverse of the time interval [T-1 ~> s-1].
   real :: zos_area_mean ! Global area mean sea surface height [Z ~> m]
-  real :: volo          ! Total volume of the ocean [m3]
+  real :: volo          ! Total volume of the ocean [Z L2 ~> m3]
   real :: ssh_ga        ! Global ocean area weighted mean sea seaface height [Z ~> m]
   integer, dimension(2) :: EOSdom ! The i-computational domain for the equation of state
   integer :: i, j, is, ie, js, je
@@ -1375,7 +1375,7 @@ subroutine post_surface_thermo_diags(IDs, G, GV, US, diag, dt_int, sfc_state, tv
     do j=js,je ; do i=is,ie
       work_2d(i,j) = G%mask2dT(i,j) * (ssh(i,j) + G%bathyT(i,j))
     enddo ; enddo
-    volo = global_area_integral(work_2d, G, unscale=US%Z_to_m)
+    volo = global_area_integral(work_2d, G, tmp_scale=US%Z_to_m)
     call post_data(IDs%id_volo, volo, diag)
   endif
 
@@ -1914,7 +1914,7 @@ subroutine register_surface_diags(Time, G, US, IDs, diag, tv)
 
   ! Vertically integrated, budget, and surface state diagnostics
   IDs%id_volo = register_scalar_field('ocean_model', 'volo', Time, diag, &
-      long_name='Total volume of liquid ocean', units='m3', &
+      long_name='Total volume of liquid ocean', units='m3', conversion=US%Z_to_m*US%L_to_m**2, &
       standard_name='sea_water_volume')
   IDs%id_zos = register_diag_field('ocean_model', 'zos', diag%axesT1, Time, &
       standard_name = 'sea_surface_height_above_geoid', &