Document frequency units with square brackets

  Changed comments to use the square bracket notation to document the units of
about 50 frequency, inverse timescale, or potential vorticity variables.  Only
comments have been changed and all answers are bitwise identical.

config_src/mct_driver/ocn_cap_methods.F90

@@ -154,7 +154,7 @@ subroutine ocn_export(ind, ocn_public, grid, o2x, dt_int, ncouple_per_day)
   real, dimension(grid%isd:grid%ied,grid%jsd:grid%jed) :: ssh !< Local copy of sea_lev with updated halo
   integer :: i, j, n, ig, jg  !< Grid indices
   real    :: slp_L, slp_R, slp_C, slope, u_min, u_max
-  real :: I_time_int  !< The inverse of coupling time interval in s-1.
+  real :: I_time_int  !< The inverse of coupling time interval [s-1].
 
   !-----------------------------------------------------------------------
 

src/core/MOM_barotropic.F90

@@ -475,14 +475,14 @@ subroutine btstep(U_in, V_in, eta_in, dt, bc_accel_u, bc_accel_v, forces, pbce,
                   ! of H (m or kg m-2, the same as eta and h).
 
   ! These are always allocated with symmetric memory and wide halos.
-  real :: q(SZIBW_(CS),SZJBW_(CS))  ! A pseudo potential vorticity in s-1 m-1.
+  real :: q(SZIBW_(CS),SZJBW_(CS))  ! A pseudo potential vorticity [s-1 Z-1 ~> s-1 m-1].
   real, dimension(SZIBW_(CS),SZJW_(CS)) :: &
     ubt, &        ! The zonal barotropic velocity [m s-1].
     bt_rem_u, &   ! The fraction of the barotropic zonal velocity that remains
                   ! after a time step, the remainder being lost to bottom drag.
                   ! bt_rem_u is a nondimensional number between 0 and 1.
     BT_force_u, & ! The vertical average of all of the u-accelerations that are
-                  ! not explicitly included in the barotropic equation, m s-2.
+                  ! not explicitly included in the barotropic equation [m s-2].
     u_accel_bt, & ! The difference between the zonal acceleration from the
                   ! barotropic calculation and BT_force_u [m s-2].
     uhbt, &       ! The zonal barotropic thickness fluxes [H m2 s-1 ~> m3 s-1 or kg s-1].
@@ -503,7 +503,7 @@ subroutine btstep(U_in, V_in, eta_in, dt, bc_accel_u, bc_accel_v, forces, pbce,
     Cor_ref_u, &  ! The zonal barotropic Coriolis acceleration due
                   ! to the reference velocities [m s-2].
     PFu, &        ! The zonal pressure force acceleration [m s-2].
-    Rayleigh_u, & ! A Rayleigh drag timescale operating at u-points, in s-1.
+    Rayleigh_u, & ! A Rayleigh drag timescale operating at u-points [s-1].
     PFu_bt_sum, & ! The summed zonal barotropic pressure gradient force [m s-2].
     Coru_bt_sum, & ! The summed zonal barotropic Coriolis acceleration [m s-2].
     DCor_u, &     ! A simply averaged depth at u points [Z ~> m].
@@ -515,7 +515,7 @@ subroutine btstep(U_in, V_in, eta_in, dt, bc_accel_u, bc_accel_v, forces, pbce,
                   ! remains after a time step, the rest being lost to bottom
                   ! drag.  bt_rem_v is a nondimensional number between 0 and 1.
     BT_force_v, & ! The vertical average of all of the v-accelerations that are
-                  ! not explicitly included in the barotropic equation, m s-2.
+                  ! not explicitly included in the barotropic equation [m s-2].
     v_accel_bt, & ! The difference between the meridional acceleration from the
                   ! barotropic calculation and BT_force_v [m s-2].
     vhbt, &       ! The meridional barotropic thickness fluxes [H m2 s-1 ~> m3 s-1 or kg s-1].
@@ -532,7 +532,7 @@ subroutine btstep(U_in, V_in, eta_in, dt, bc_accel_u, bc_accel_v, forces, pbce,
     Cor_ref_v, &  ! The meridional barotropic Coriolis acceleration due
                   ! to the reference velocities [m s-2].
     PFv, &        ! The meridional pressure force acceleration [m s-2].
-    Rayleigh_v, & ! A Rayleigh drag timescale operating at v-points, in s-1.
+    Rayleigh_v, & ! A Rayleigh drag timescale operating at v-points [s-1].
     PFv_bt_sum, & ! The summed meridional barotropic pressure gradient force,
                   ! [m s-2].
     Corv_bt_sum, & ! The summed meridional barotropic Coriolis acceleration,
@@ -587,7 +587,7 @@ subroutine btstep(U_in, V_in, eta_in, dt, bc_accel_u, bc_accel_v, forces, pbce,
   real :: be_proj     ! The fractional amount by which velocities are projected
                       ! when project_velocity is true. For now be_proj is set
                       ! to equal bebt, as they have similar roles and meanings.
-  real :: Idt         ! The inverse of dt, in s-1.
+  real :: Idt         ! The inverse of dt [s-1].
   real :: det_de      ! The partial derivative due to self-attraction and loading
                       ! of the reference geopotential with the sea surface height.
                       ! This is typically ~0.09 or less.
@@ -3654,7 +3654,7 @@ subroutine bt_mass_source(h, eta, set_cor, G, GV, CS)
   real :: d_eta               ! The difference between estimates of the total
                               ! thicknesses [H ~> m or kg m-2].
   real :: limit_dt            ! The fractional mass-source limit divided by the
-                              ! thermodynamic time step, in s-1.
+                              ! thermodynamic time step [s-1].
   integer :: is, ie, js, je, nz, i, j, k
   real, parameter :: frac_cor = 0.25
   real, parameter :: slow_rate = 0.125

src/core/MOM_continuity_PPM.F90

@@ -282,8 +282,8 @@ subroutine zonal_mass_flux(u, h_in, uh, dt, G, GV, CS, LB, uhbt, OBC, &
   real :: FA_u    ! A sum of zonal face areas [H m ~> m2 or kg m-1].
   real :: I_vrm   ! 1.0 / visc_rem_max, nondim.
   real :: CFL_dt  ! The maximum CFL ratio of the adjusted velocities divided by
-                  ! the time step, in s-1.
-  real :: I_dt    ! 1.0 / dt, in s-1.
+                  ! the time step [s-1].
+  real :: I_dt    ! 1.0 / dt [s-1].
   real :: du_lim  ! The velocity change that give a relative CFL of 1 [m s-1].
   real :: dx_E, dx_W ! Effective x-grid spacings to the east and west, in m.
   integer :: i, j, k, ish, ieh, jsh, jeh, n, nz
@@ -946,7 +946,7 @@ subroutine set_zonal_BT_cont(u, h_in, h_L, h_R, BT_cont, uh_tot_0, duhdu_tot_0,
                        ! of visc_rem from leading to large CFL numbers.
   real :: CFL_min ! A minimal increment in the CFL to try to ensure that the
                   ! flow is truly upwind, ND.
-  real :: Idt     ! The inverse of the time step, in s-1.
+  real :: Idt     ! The inverse of the time step [s-1].
   logical :: domore
   integer :: i, k, nz
 
@@ -1100,8 +1100,8 @@ subroutine meridional_mass_flux(v, h_in, vh, dt, G, GV, CS, LB, vhbt, OBC, &
     visc_rem      ! A 2-D copy of visc_rem_v or an array of 1's.
   real :: I_vrm   ! 1.0 / visc_rem_max, nondim.
   real :: CFL_dt  ! The maximum CFL ratio of the adjusted velocities divided by
-                  ! the time step, in s-1.
-  real :: I_dt    ! 1.0 / dt, in s-1.
+                  ! the time step [s-1].
+  real :: I_dt    ! 1.0 / dt [s-1].
   real :: dv_lim  ! The velocity change that give a relative CFL of 1 [m s-1].
   real :: dy_N, dy_S ! Effective y-grid spacings to the north and south [m].
   integer :: i, j, k, ish, ieh, jsh, jeh, n, nz
@@ -1765,7 +1765,7 @@ subroutine set_merid_BT_cont(v, h_in, h_L, h_R, BT_cont, vh_tot_0, dvhdv_tot_0,
                        ! of visc_rem from leading to large CFL numbers.
   real :: CFL_min ! A minimal increment in the CFL to try to ensure that the
                   ! flow is truly upwind, ND.
-  real :: Idt     ! The inverse of the time step, in s-1.
+  real :: Idt     ! The inverse of the time step [s-1].
   logical :: domore
   integer :: i, k, nz
 

src/core/MOM_grid.F90

@@ -148,10 +148,10 @@ module MOM_grid
     Dblock_v, &   !< Topographic depths at v-points at which the flow is blocked, in depth units.
     Dopen_v       !< Topographic depths at v-points at which the flow is open at width dx_Cv, in depth units.
   real ALLOCABLE_, dimension(NIMEMB_PTR_,NJMEMB_PTR_) :: &
-    CoriolisBu    !< The Coriolis parameter at corner points, in s-1.
+    CoriolisBu    !< The Coriolis parameter at corner points [s-1].
   real ALLOCABLE_, dimension(NIMEM_,NJMEM_) :: &
-    df_dx, &      !< Derivative d/dx f (Coriolis parameter) at h-points, in s-1 m-1.
-    df_dy         !< Derivative d/dy f (Coriolis parameter) at h-points, in s-1 m-1.
+    df_dx, &      !< Derivative d/dx f (Coriolis parameter) at h-points [s-1 m-1].
+    df_dy         !< Derivative d/dy f (Coriolis parameter) at h-points [s-1 m-1].
   real :: g_Earth !< The gravitational acceleration [m s-2].
 
   ! These variables are global sums that are useful for 1-d diagnostics

src/core/MOM_open_boundary.F90

@@ -156,9 +156,9 @@ module MOM_open_boundary
                                                             !! the OB segment [m s-1].
   real, pointer, dimension(:,:)   :: eta=>NULL()            !< The sea-surface elevation along the segment (m).
   real, pointer, dimension(:,:,:) :: grad_normal=>NULL()    !< The gradient of the normal flow along the
-                                                            !! segment (s-1)
+                                                            !! segment [s-1]
   real, pointer, dimension(:,:,:) :: grad_tan=>NULL()       !< The gradient of the tangential flow along the
-                                                            !! segment (s-1)
+                                                            !! segment [s-1]
   real, pointer, dimension(:,:,:) :: grad_gradient=>NULL()  !< The gradient of the gradient of tangential flow along the
                                                             !! segment (m-1 s-1)
   real, pointer, dimension(:,:,:) :: rx_normal=>NULL()      !< The rx_old_u value for radiation coeff
@@ -172,7 +172,7 @@ module MOM_open_boundary
   real, pointer, dimension(:,:,:) :: nudged_tangential_vel=>NULL() !< The layer velocity tangential to the OB segment
                                                             !! that values should be nudged towards [m s-1].
   real, pointer, dimension(:,:,:) :: nudged_tangential_grad=>NULL() !< The layer dvdx or dudy towards which nudging
-                                                            !! can occur (s-1).
+                                                            !! can occur [s-1].
   type(segment_tracer_registry_type), pointer  :: tr_Reg=> NULL()!< A pointer to the tracer registry for the segment.
   type(hor_index_type) :: HI !< Horizontal index ranges
   real :: Tr_InvLscale3_out                                     !< An effective inverse length scale cubed (m-3)

src/diagnostics/MOM_diagnostics.F90

@@ -1188,7 +1188,7 @@ subroutine post_surface_thermo_diags(IDs, G, GV, US, diag, dt_int, sfc_state, tv
   real, dimension(SZI_(G),SZJ_(G)) :: work_2d  ! A 2-d work array
   real, dimension(SZI_(G),SZJ_(G)) :: &
     zos  ! dynamic sea lev (zero area mean) from inverse-barometer adjusted ssh (meter)
-  real :: I_time_int    ! The inverse of the time interval in s-1.
+  real :: I_time_int    ! The inverse of the time interval [s-1].
   real :: zos_area_mean, volo, ssh_ga
   integer :: i, j, is, ie, js, je
 

src/framework/MOM_dyn_horgrid.F90

@@ -148,10 +148,10 @@ module MOM_dyn_horgrid
     Dblock_v, &   !< Topographic depths at v-points at which the flow is blocked [Z ~> m].
     Dopen_v       !< Topographic depths at v-points at which the flow is open at width dx_Cv [Z ~> m].
   real, allocatable, dimension(:,:) :: &
-    CoriolisBu    !< The Coriolis parameter at corner points, in s-1.
+    CoriolisBu    !< The Coriolis parameter at corner points [s-1].
   real, allocatable, dimension(:,:) :: &
-    df_dx, &      !< Derivative d/dx f (Coriolis parameter) at h-points, in s-1 m-1.
-    df_dy         !< Derivative d/dy f (Coriolis parameter) at h-points, in s-1 m-1.
+    df_dx, &      !< Derivative d/dx f (Coriolis parameter) at h-points [s-1 m-1].
+    df_dy         !< Derivative d/dy f (Coriolis parameter) at h-points [s-1 m-1].
 
   ! These variables are global sums that are useful for 1-d diagnostics
   real :: areaT_global  !< Global sum of h-cell area in m2

src/initialization/MOM_shared_initialization.F90

@@ -56,7 +56,7 @@ end subroutine MOM_shared_init_init
 !> MOM_initialize_rotation makes the appropriate call to set up the Coriolis parameter.
 subroutine MOM_initialize_rotation(f, G, PF, US)
   type(dyn_horgrid_type),                       intent(in)  :: G  !< The dynamic horizontal grid type
-  real, dimension(G%IsdB:G%IedB,G%JsdB:G%JedB), intent(out) :: f  !< The Coriolis parameter in s-1
+  real, dimension(G%IsdB:G%IedB,G%JsdB:G%JedB), intent(out) :: f  !< The Coriolis parameter [s-1]
   type(param_file_type),                        intent(in)  :: PF !< Parameter file structure
   type(unit_scale_type),              optional, intent(in)  :: US !< A dimensional unit scaling type
 

src/parameterizations/lateral/MOM_MEKE.F90

@@ -33,7 +33,7 @@ module MOM_MEKE
   ! Parameters
   real :: MEKE_FrCoeff  !< Efficiency of conversion of ME into MEKE (non-dim)
   real :: MEKE_GMcoeff  !< Efficiency of conversion of PE into MEKE (non-dim)
-  real :: MEKE_damping  !< Local depth-independent MEKE dissipation rate in s-1.
+  real :: MEKE_damping  !< Local depth-independent MEKE dissipation rate [s-1].
   real :: MEKE_Cd_scale !< The ratio of the bottom eddy velocity to the column mean
                         !! eddy velocity, i.e. sqrt(2*MEKE). This should be less than 1
                         !! to account for the surface intensification of MEKE.

src/parameterizations/lateral/MOM_hor_visc.F90

@@ -213,7 +213,7 @@ subroutine horizontal_viscosity(u, v, h, diffu, diffv, MEKE, VarMix, G, GV, CS,
     FrictWorkIntz ! depth integrated energy dissipated by lateral friction (W/m2)
 
   real, dimension(SZIB_(G),SZJB_(G)) :: &
-    dvdx, dudy, & ! components in the shearing strain (s-1)
+    dvdx, dudy, & ! components in the shearing strain [s-1]
     sh_xy,  &     ! horizontal shearing strain (du/dy + dv/dx) (1/sec) including metric terms
     str_xy, &     ! str_xy is the cross term in the stress tensor (H m2 s-2)
     bhstr_xy, &   ! A copy of str_xy that only contains the biharmonic contribution (H m2 s-2)
@@ -245,8 +245,8 @@ subroutine horizontal_viscosity(u, v, h, diffu, diffv, MEKE, VarMix, G, GV, CS,
   real :: mod_Leith  ! nondimensional coefficient for divergence part of modified Leith
                      ! viscosity. Here set equal to nondimensional Laplacian Leith constant.
                      ! This is set equal to zero if modified Leith is not used.
-  real :: Shear_mag  ! magnitude of the shear (1/s)
-  real :: Vort_mag   ! magnitude of the vorticity (1/s)
+  real :: Shear_mag  ! magnitude of the shear [s-1]
+  real :: Vort_mag   ! magnitude of the vorticity [s-1]
   real :: h2uq, h2vq ! temporary variables [H2 ~> m2 or kg2 m-4].
   real :: hu, hv     ! Thicknesses interpolated by arithmetic means to corner
                      ! points; these are first interpolated to u or v velocity
@@ -263,8 +263,8 @@ subroutine horizontal_viscosity(u, v, h, diffu, diffv, MEKE, VarMix, G, GV, CS,
   real :: Kh_scale  ! A factor between 0 and 1 by which the horizontal
                     ! Laplacian viscosity is rescaled
   real :: RoScl     ! The scaling function for MEKE source term
-  real :: FatH      ! abs(f) at h-point for MEKE source term (s-1)
-  real :: local_strain ! Local variable for interpolating computed strain rates (s-1).
+  real :: FatH      ! abs(f) at h-point for MEKE source term [s-1]
+  real :: local_strain ! Local variable for interpolating computed strain rates [s-1].
 
   logical :: rescale_Kh, legacy_bound
   logical :: find_FrictWork
@@ -969,12 +969,12 @@ subroutine hor_visc_init(Time, G, param_file, diag, CS)
   real :: grid_sp_h3       ! Harmonic mean of the squares of the grid^(3/2)
   real :: grid_sp_q2       ! spacings at h and q points (m2)
   real :: grid_sp_q3       ! spacings at h and q points^(3/2) (m3)
-  real :: Kh_Limit         ! A coefficient (1/s) used, along with the
+  real :: Kh_Limit         ! A coefficient [s-1] used, along with the
                            ! grid spacing, to limit Laplacian viscosity.
   real :: fmax             ! maximum absolute value of f at the four
-                           ! vorticity points around a thickness point (1/s)
+                           ! vorticity points around a thickness point [s-1]
   real :: BoundCorConst    ! constant (s2/m2)
-  real :: Ah_Limit         ! coefficient (1/s) used, along with the
+  real :: Ah_Limit         ! coefficient [s-1] used, along with the
                            ! grid spacing, to limit biharmonic viscosity
   real :: Kh               ! Lapacian horizontal viscosity (m2/s)
   real :: Ah               ! biharmonic horizontal viscosity (m4/s)
@@ -985,7 +985,7 @@ subroutine hor_visc_init(Time, G, param_file, diag, CS)
   real :: Leith_Lap_const  ! nondimensional Laplacian Leith constant
   real :: Leith_bi_const   ! nondimensional biharmonic Leith constant
   real :: dt               ! dynamics time step (sec)
-  real :: Idt              ! inverse of dt (1/s)
+  real :: Idt              ! inverse of dt [s-1]
   real :: denom            ! work variable; the denominator of a fraction
   real :: maxvel           ! largest permitted velocity components [m s-1]
   real :: bound_Cor_vel    ! grid-scale velocity variations at which value

src/parameterizations/lateral/MOM_internal_tides.F90

@@ -432,7 +432,7 @@ subroutine propagate_int_tide(h, tv, cn, TKE_itidal_input, vel_btTide, Nb, dt, &
           ! Dissipate energy if Fr>1; done here with an arbitrary time scale
           if (Fr2_max > 1.0) then
             En_initial = sum(CS%En(i,j,:,fr,m)) ! for debugging
-            ! Calculate effective decay rate (s-1) if breaking occurs over a time step
+            ! Calculate effective decay rate [s-1] if breaking occurs over a time step
             loss_rate = (1/Fr2_max - 1.0)/dt
             do a=1,CS%nAngle
               ! Determine effective dissipation rate (Wm-2)
@@ -759,7 +759,7 @@ subroutine refract(En, cn, freq, dt, G, NAngle, use_PPMang)
   real :: f2              ! The squared Coriolis parameter [s-2].
   real :: favg            ! The average Coriolis parameter at a point [s-1].
   real :: df2_dy, df2_dx  ! The x- and y- gradients of the squared Coriolis parameter, in s-2 m-1.
-  real :: df_dy, df_dx    ! The x- and y- gradients of the Coriolis parameter, in s-1 m-1.
+  real :: df_dy, df_dx    ! The x- and y- gradients of the Coriolis parameter [s-1 m-1].
   real :: dlnCn_dx        ! The x-gradient of the wave speed divided by itself in m-1.
   real :: dlnCn_dy        ! The y-gradient of the wave speed divided by itself in m-1.
   real :: Angle_size, dt_Angle_size, angle

src/parameterizations/lateral/MOM_lateral_mixing_coeffs.F90

@@ -433,7 +433,7 @@ subroutine calc_Visbeck_coeffs(h, slope_x, slope_y, N2_u, N2_v, G, GV, CS)
   ! Local variables
   real :: Khth_Loc      ! Locally calculated thickness mixing coefficient (m2/s)
   real :: S2            ! Interface slope squared (non-dim)
-  real :: N2            ! Brunt-Vaisala frequency (1/s)
+  real :: N2            ! Brunt-Vaisala frequency [s-1]
   real :: Hup, Hdn      ! Thickness from above, below [H ~> m or kg m-2]
   real :: H_geom        ! The geometric mean of Hup*Hdn [H ~> m or kg m-2].
   integer :: is, ie, js, je, nz
@@ -590,7 +590,7 @@ subroutine calc_slope_functions_using_just_e(h, G, GV, US, CS, e, calculate_slop
   real :: h_neglect     ! A thickness that is so small it is usually lost
                         ! in roundoff and can be neglected [H ~> m or kg m-2].
   real :: S2            ! Interface slope squared (non-dim)
-  real :: N2            ! Brunt-Vaisala frequency (1/s)
+  real :: N2            ! Brunt-Vaisala frequency [s-1]
   real :: Hup, Hdn      ! Thickness from above, below [H ~> m or kg m-2]
   real :: H_geom        ! The geometric mean of Hup*Hdn [H ~> m or kg m-2].
   real :: Z_to_L        ! A conversion factor between from units for e to the