Corrected many unit descriptions in comments

  Corrected the descriptions of the units of about 113 variables spread across
30 files.  These were either inconsistent unit descriptions or descriptions
using a non-standard syntax.  Only comments are changed, and all answers are
bitwise identical.

src/ALE/MOM_ALE.F90

@@ -756,7 +756,7 @@ subroutine ALE_remap_tracers(CS, G, GV, h_old, h_new, Reg, debug, dt, PCM_cell)
   real, dimension(SZI_(G),SZJ_(G),SZK_(GV)) :: work_conc ! The rate of change of concentrations [Conc T-1 ~> Conc s-1]
   real, dimension(SZI_(G),SZJ_(G),SZK_(GV)) :: work_cont ! The rate of change of cell-integrated tracer
                                                        ! content [Conc H T-1 ~> Conc m s-1 or Conc kg m-2 s-1] or
-                                                       ! cell thickness [H T-1 ~> m s-1 or Conc kg m-2 s-1]
+                                                       ! cell thickness [H T-1 ~> m s-1 or kg m-2 s-1]
   real, dimension(SZI_(G),SZJ_(G))          :: work_2d ! The rate of change of column-integrated tracer
                                                        ! content [Conc H T-1 ~> Conc m s-1 or Conc kg m-2 s-1]
   logical :: PCM(GV%ke) ! If true, do PCM remapping from a cell.

src/ALE/MOM_regridding.F90

@@ -2051,7 +2051,7 @@ subroutine setCoordinateResolution( dz, CS, scale )
   type(regridding_CS), intent(inout) :: CS !< Regridding control structure
   real,      optional, intent(in)    :: scale !< A scaling factor converting dz to the internal represetation
                                            !! of coordRes, in various units that depend on the coordinate,
-                                           !! such as [Z m-1 ~> 1 for a z-coordinate or [R m3 kg-1 ~> 1] for
+                                           !! such as [Z m-1 ~> 1] for a z-coordinate or [R m3 kg-1 ~> 1] for
                                            !! a density coordinate.
 
   if (size(dz)/=CS%nk) call MOM_error( FATAL, &

src/core/MOM_barotropic.F90

@@ -609,7 +609,7 @@ subroutine btstep(U_in, V_in, eta_in, dt, bc_accel_u, bc_accel_v, forces, pbce,
     Datv          ! Basin depth at v-velocity grid points times the x-grid
                   ! spacing [H L ~> m2 or kg m-1].
   real, dimension(:,:), pointer :: um2, uk1, vm2, vk1
-                  ! M2 and K1 velocities from the output of streaming filters [m s-1]
+                  ! M2 and K1 velocities from the output of streaming filters [L T-1 ~> m s-1]
   real, target, dimension(SZIW_(CS),SZJW_(CS)) :: &
     eta, &        ! The barotropic free surface height anomaly or column mass
                   ! anomaly [H ~> m or kg m-2]

src/core/MOM_checksum_packages.F90

@@ -61,9 +61,9 @@ subroutine MOM_state_chksum_5arg(mesg, u, v, h, uh, vh, G, GV, US, haloshift, sy
   logical,       optional, intent(in) :: symmetric !< If true, do checksums on the fully symmetric
                                                    !! computational domain.
   logical,       optional, intent(in) :: omit_corners !< If true, avoid checking diagonal shifts
-  real,          optional, intent(in) :: vel_scale !< The scaling factor to convert velocities to [m s-1]
+  real,          optional, intent(in) :: vel_scale !< The scaling factor to convert velocities to [T m L-1 s-1 ~> 1]
 
-  real :: scale_vel ! The scaling factor to convert velocities to [m s-1]
+  real :: scale_vel ! The scaling factor to convert velocities to mks units [T m L-1 s-1 ~> 1]
   logical :: sym
   integer :: hs
 

src/core/MOM_density_integrals.F90

@@ -1360,7 +1360,7 @@ subroutine int_spec_vol_dp_generic_pcm(T, S, p_t, p_b, alpha_ref, HI, EOS, US, d
   real :: S5((5*HI%isd+1):(5*(HI%ied+2)))  ! Salinities along a line of subgrid locations [S ~> ppt]
   real :: p5((5*HI%isd+1):(5*(HI%ied+2)))  ! Pressures along a line of subgrid locations [R L2 T-2 ~> Pa]
   real :: a5((5*HI%isd+1):(5*(HI%ied+2)))  ! Specific volumes anomalies along a line of subgrid
-                                           ! locations [R-1 ~> m3 kg-3]
+                                           ! locations [R-1 ~> m3 kg-1]
   real :: T15((15*HI%isd+1):(15*(HI%ied+1))) ! Temperatures at an array of subgrid locations [C ~> degC]
   real :: S15((15*HI%isd+1):(15*(HI%ied+1))) ! Salinities at an array of subgrid locations [S ~> ppt]
   real :: p15((15*HI%isd+1):(15*(HI%ied+1))) ! Pressures at an array of subgrid locations [R L2 T-2 ~> Pa]
@@ -1621,7 +1621,7 @@ subroutine int_spec_vol_dp_generic_plm(T_t, T_b, S_t, S_b, p_t, p_b, alpha_ref,
   real :: S5((5*HI%iscB+1):(5*(HI%iecB+2)))  ! Salinities along a line of subgrid locations [S ~> ppt]
   real :: p5((5*HI%iscB+1):(5*(HI%iecB+2)))  ! Pressures along a line of subgrid locations [R L2 T-2 ~> Pa]
   real :: a5((5*HI%iscB+1):(5*(HI%iecB+2)))  ! Specific volumes anomalies along a line of subgrid
-                                             ! locations [R-1 ~> m3 kg-3]
+                                             ! locations [R-1 ~> m3 kg-1]
   real :: T15((15*HI%iscB+1):(15*(HI%iecB+1))) ! Temperatures at an array of subgrid locations [C ~> degC]
   real :: S15((15*HI%iscB+1):(15*(HI%iecB+1))) ! Salinities at an array of subgrid locations [S ~> ppt]
   real :: p15((15*HI%iscB+1):(15*(HI%iecB+1))) ! Pressures at an array of subgrid locations [R L2 T-2 ~> Pa]

src/core/MOM_interface_heights.F90

@@ -339,7 +339,7 @@ subroutine find_col_avg_SpV(h, SpV_avg, tv, G, GV, US, halo_size)
   integer,        optional, intent(in)    :: halo_size !< width of halo points on which to work
 
   ! Local variables
-  real :: h_tot(SZI_(G))        ! Sum of the layer thicknesses [H ~> m or kg m-3]
+  real :: h_tot(SZI_(G))        ! Sum of the layer thicknesses [H ~> m or kg m-2]
   real :: SpV_x_h_tot(SZI_(G))  ! Vertical sum of the layer average specific volume times
                                 ! the layer thicknesses [H R-1 ~> m4 kg-1 or m]
   real :: I_rho                 ! The inverse of the Boussiensq reference density [R-1 ~> m3 kg-1]

src/diagnostics/MOM_diagnostics.F90

@@ -1574,7 +1574,7 @@ subroutine MOM_diagnostics_init(MIS, ADp, CDp, Time, G, GV, US, param_file, diag
   real :: wave_speed_tol      ! The fractional tolerance for finding the wave speeds [nondim]
   real :: convert_H           ! A conversion factor from internal thickness units to the appropriate
                               ! MKS units (m or kg m-2) for thicknesses depending on whether the
-                              ! Boussinesq approximation is being made [m H-1 or kg m-2 H-1 ~> 1]
+                              ! Boussinesq approximation is being made [m H-1 ~> 1] or [kg m-2 H-1 ~> 1]
   logical :: better_speed_est ! If true, use a more robust estimate of the first
                               ! mode wave speed as the starting point for iterations.
   logical :: split            ! True if using the barotropic-baroclinic split algorithm

src/diagnostics/MOM_wave_speed.F90

@@ -99,7 +99,7 @@ subroutine wave_speed(h, tv, G, GV, US, cg1, CS, halo_size, use_ebt_mode, mono_N
     S_int, &      ! Salinity interpolated to interfaces [S ~> ppt]
     H_top, &      ! The distance of each filtered interface from the ocean surface [H ~> m or kg m-2]
     H_bot, &      ! The distance of each filtered interface from the bottom [H ~> m or kg m-2]
-    gprime        ! The reduced gravity across each interface [L2 H-1 T-2 ~> m s-2 or m4 s-1 kg-1].
+    gprime        ! The reduced gravity across each interface [L2 H-1 T-2 ~> m s-2 or m4 s-2 kg-1].
   real, dimension(SZK_(GV)) :: &
     Igl, Igu      ! The inverse of the reduced gravity across an interface times
                   ! the thickness of the layer below (Igl) or above (Igu) it, in [T2 L-2 ~> s2 m-2].
@@ -163,7 +163,7 @@ subroutine wave_speed(h, tv, G, GV, US, cg1, CS, halo_size, use_ebt_mode, mono_N
   integer :: i, j, k, k2, itt, is, ie, js, je, nz, halo
   real :: hw      ! The mean of the adjacent layer thicknesses [H ~> m or kg m-2]
   real :: sum_hc  ! The sum of the layer thicknesses [H ~> m or kg m-2]
-  real :: gp      ! A limited local copy of gprime [L2 H-1 T-2 ~> m s-2 or m4 s-1 kg-1]
+  real :: gp      ! A limited local copy of gprime [L2 H-1 T-2 ~> m s-2 or m4 s-2 kg-1]
   real :: N2min   ! A minimum buoyancy frequency, including a slope rescaling factor [L2 H-2 T-2 ~> s-2 or m6 kg-2 s-2]
   logical :: below_mono_N2_frac  ! True if an interface is below the fractional depth where N2 should not increase.
   logical :: below_mono_N2_depth ! True if an interface is below the absolute depth where N2 should not increase.
@@ -853,7 +853,7 @@ subroutine wave_speeds(h, tv, G, GV, US, nmodes, cn, CS, w_struct, u_struct, u_s
   real :: drxh_sum   ! The sum of density differences across interfaces times thicknesses [R H ~> kg m-2 or kg2 m-5]
   real :: dSpVxh_sum ! The sum of specific volume differences across interfaces times
                      ! thicknesses [R-1 H ~> m4 kg-1 or m], negative for stable stratification.
-  real :: g_Rho0     ! G_Earth/Rho0 [L2 T-2 H-1 R-1 ~> m4 s-2 kg-1 pr m7 s-2 kg-1].
+  real :: g_Rho0     ! G_Earth/Rho0 [L2 T-2 H-1 R-1 ~> m4 s-2 kg-1 or m7 s-2 kg-2].
   real :: tol_Hfrac  ! Layers that together are smaller than this fraction of
                      ! the total water column can be merged for efficiency [nondim].
   real :: min_h_frac ! tol_Hfrac divided by the total number of layers [nondim].

src/ocean_data_assim/MOM_oda_driver.F90

@@ -675,9 +675,9 @@ subroutine apply_oda_tracer_increments(dt, Time_end, G, GV, tv, h, CS)
   integer :: i, j
   integer :: isc, iec, jsc, jec
   real, dimension(SZI_(G),SZJ_(G),SZK_(G)) :: T_tend_inc !< an adjustment to the temperature
-                                                    !! tendency [C T-1 -> degC s-1]
+                                                    !! tendency [C T-1 ~> degC s-1]
   real, dimension(SZI_(G),SZJ_(G),SZK_(G)) :: S_tend_inc !< an adjustment to the salinity
-                                                    !! tendency [S T-1 -> ppt s-1]
+                                                    !! tendency [S T-1 ~> ppt s-1]
   real, dimension(SZI_(G),SZJ_(G),SZK_(CS%Grid)) :: T_tend !< The temperature tendency adjustment from
                                                            !! DA [C T-1 ~> degC s-1]
   real, dimension(SZI_(G),SZJ_(G),SZK_(CS%Grid)) :: S_tend !< The salinity tendency adjustment from DA

src/parameterizations/lateral/MOM_MEKE_types.F90

@@ -24,7 +24,7 @@ module MOM_MEKE_types
                                     !! backscatter from unresolved eddies (see Jansen and Held, 2014).
   real, allocatable :: Au(:,:)      !< The MEKE-derived lateral biharmonic viscosity
                                     !! coefficient [L4 T-1 ~> m4 s-1].
-  real, allocatable :: Le(:,:)      !< Eddy length scale [L m]
+  real, allocatable :: Le(:,:)      !< Eddy length scale [L ~> m]
 
   ! Parameters
   real :: KhTh_fac = 1.0 !< Multiplier to map Kh(MEKE) to KhTh [nondim]

src/parameterizations/lateral/MOM_hor_visc.F90

@@ -325,8 +325,8 @@ subroutine horizontal_viscosity(u, v, h, uh, vh, diffu, diffv, MEKE, VarMix, G,
                   ! at some points in the code it is not yet layer integrated, so is in [L2 T-2 ~> m2 s-2].
     str_xx_GME,&  ! smoothed diagonal term in the stress tensor from GME [L2 T-2 ~> m2 s-2]
     bhstr_xx, &   ! A copy of str_xx that only contains the biharmonic contribution [H L2 T-2 ~> m3 s-2 or kg s-2]
-    FrictWorkIntz, & ! depth integrated energy dissipated by lateral friction [R L2 T-3 ~> W m-2]
-    FrictWorkIntz_bh, & ! depth integrated energy dissipated by biharmonic lateral friction [R L2 T-3 ~> W m-2]
+    FrictWorkIntz, & ! depth integrated energy dissipated by lateral friction [R Z L2 T-3 ~> W m-2]
+    FrictWorkIntz_bh, & ! depth integrated energy dissipated by biharmonic lateral friction [R Z L2 T-3 ~> W m-2]
     grad_vort_mag_h, & ! Magnitude of vorticity gradient at h-points [L-1 T-1 ~> m-1 s-1]
     grad_vort_mag_h_2d, & ! Magnitude of 2d vorticity gradient at h-points [L-1 T-1 ~> m-1 s-1]
     grad_div_mag_h, &     ! Magnitude of divergence gradient at h-points [L-1 T-1 ~> m-1 s-1]
@@ -387,9 +387,9 @@ subroutine horizontal_viscosity(u, v, h, uh, vh, diffu, diffv, MEKE, VarMix, G,
     Ah_h, &          ! biharmonic viscosity at thickness points [L4 T-1 ~> m4 s-1]
     Kh_h, &          ! Laplacian viscosity at thickness points [L2 T-1 ~> m2 s-1]
     dz, &            ! Height change across layers [Z ~> m]
-    FrictWork, &     ! work done by MKE dissipation mechanisms [R L2 T-3 ~> W m-2]
-    FrictWork_bh, &  ! work done by the biharmonic MKE dissipation mechanisms [R L2 T-3 ~> W m-2]
-    FrictWork_GME, & ! work done by GME [R L2 T-3 ~> W m-2]
+    FrictWork, &     ! work done by MKE dissipation mechanisms [R Z L2 T-3 ~> W m-2]
+    FrictWork_bh, &  ! work done by the biharmonic MKE dissipation mechanisms [R Z L2 T-3 ~> W m-2]
+    FrictWork_GME, & ! work done by GME [R Z L2 T-3 ~> W m-2]
     div_xx_h,      & ! horizontal divergence [T-1 ~> s-1]
     sh_xx_h,       & ! horizontal tension (du/dx - dv/dy) including metric terms [T-1 ~> s-1]
     NoSt, &          ! A diagnostic array of normal stress [T-1 ~> s-1].