mom_density_integrals subroutine, public subroutine, public mom_density_integrals::int_density_dz (T, S, z_t, z_b, rho_ref, rho_0, G_e, HI, EOS, US, dpa, intz_dpa, intx_dpa, inty_dpa, bathyT, dz_neglect, useMassWghtInterp) int_density_dz T T S S z_t z_t z_b z_b rho_ref rho_ref rho_0 rho_0 G_e G_e HI HI EOS EOS US US dpa dpa intz_dpa intz_dpa intx_dpa intx_dpa inty_dpa inty_dpa bathyT bathyT dz_neglect dz_neglect useMassWghtInterp useMassWghtInterp Calls the appropriate subroutine to calculate analytical and nearly-analytical integrals in z across layers of pressure anomalies, which are required for calculating the finite-volume form pressure accelerations in a Boussinesq model. hi Ocean horizontal index structures for the arrays t Potential temperature referenced to the surface [degC] s Salinity [ppt] z_t Height at the top of the layer in depth units [Z ~> m] z_b Height at the bottom of the layer [Z ~> m] rho_ref A mean density [R ~> kg m-3] or [kg m-3], that is subtracted out to reduce the magnitude of each of the integrals. rho_0 A density [R ~> kg m-3] or [kg m-3], that is used to calculate the pressure (as p~=-z*rho_0*G_e) used in the equation of state. g_e The Earth's gravitational acceleration [L2 Z-1 T-2 ~> m s-2] or [m2 Z-1 s-2 ~> m s-2] eos Equation of state structure us A dimensional unit scaling type dpa The change in the pressure anomaly intz_dpa The integral through the thickness of the intx_dpa The integral in x of the difference between inty_dpa The integral in y of the difference between bathyt The depth of the bathymetry [Z ~> m] dz_neglect A minuscule thickness change [Z ~> m] usemasswghtinterp If true, uses mass weighting to interpolate T/S for top and bottom integrals. int_density_dz_generic_pcm mom_diagnostics::calculate_vertical_integrals subroutine, public subroutine, public mom_density_integrals::int_density_dz_generic_pcm (T, S, z_t, z_b, rho_ref, rho_0, G_e, HI, EOS, US, dpa, intz_dpa, intx_dpa, inty_dpa, bathyT, dz_neglect, useMassWghtInterp) int_density_dz_generic_pcm T T S S z_t z_t z_b z_b rho_ref rho_ref rho_0 rho_0 G_e G_e HI HI EOS EOS US US dpa dpa intz_dpa intz_dpa intx_dpa intx_dpa inty_dpa inty_dpa bathyT bathyT dz_neglect dz_neglect useMassWghtInterp useMassWghtInterp Calculates (by numerical quadrature) integrals of pressure anomalies across layers, which are required for calculating the finite-volume form pressure accelerations in a Boussinesq model. hi Horizontal index type for input variables. t Potential temperature of the layer [degC] s Salinity of the layer [ppt] z_t Height at the top of the layer in depth units [Z ~> m] z_b Height at the bottom of the layer [Z ~> m] rho_ref A mean density [R ~> kg m-3] or [kg m-3], that is subtracted out to reduce the magnitude of each of the integrals. rho_0 A density [R ~> kg m-3] or [kg m-3], that is used to calculate the pressure (as p~=-z*rho_0*G_e) used in the equation of state. g_e The Earth's gravitational acceleration [L2 Z-1 T-2 ~> m s-2] or [m2 Z-1 s-2 ~> m s-2] eos Equation of state structure us A dimensional unit scaling type dpa The change in the pressure anomaly intz_dpa The integral through the thickness of the intx_dpa The integral in x of the difference between inty_dpa The integral in y of the difference between bathyt The depth of the bathymetry [Z ~> m] dz_neglect A minuscule thickness change [Z ~> m] usemasswghtinterp If true, uses mass weighting to interpolate T/S for top and bottom integrals. mom_error_handler::mom_error int_density_dz subroutine, public subroutine, public mom_density_integrals::int_density_dz_generic_plm (k, tv, T_t, T_b, S_t, S_b, e, rho_ref, rho_0, G_e, dz_subroundoff, bathyT, HI, GV, EOS, US, dpa, intz_dpa, intx_dpa, inty_dpa, useMassWghtInterp) int_density_dz_generic_plm k k tv tv T_t T_t T_b T_b S_t S_t S_b S_b e e rho_ref rho_ref rho_0 rho_0 G_e G_e dz_subroundoff dz_subroundoff bathyT bathyT HI HI GV GV EOS EOS US US dpa dpa intz_dpa intz_dpa intx_dpa intx_dpa inty_dpa inty_dpa useMassWghtInterp useMassWghtInterp Compute pressure gradient force integrals by quadrature for the case where T and S are linear profiles. k Layer index to calculate integrals for hi Ocean horizontal index structures for the input arrays gv Vertical grid structure tv Thermodynamic variables t_t Potential temperature at the cell top [degC] t_b Potential temperature at the cell bottom [degC] s_t Salinity at the cell top [ppt] s_b Salinity at the cell bottom [ppt] e Height of interfaces [Z ~> m] rho_ref A mean density [R ~> kg m-3] or [kg m-3], that is subtracted out to reduce the magnitude of each of the integrals. rho_0 A density [R ~> kg m-3] or [kg m-3], that is used to calculate the pressure (as p~=-z*rho_0*G_e) used in the equation of state. g_e The Earth's gravitational acceleration [L2 Z-1 T-2 ~> m s-2] dz_subroundoff A minuscule thickness change [Z ~> m] bathyt The depth of the bathymetry [Z ~> m] eos Equation of state structure us A dimensional unit scaling type dpa The change in the pressure anomaly across the layer [R L2 T-2 ~> Pa] intz_dpa The integral through the thickness of the layer of intx_dpa The integral in x of the difference between the inty_dpa The integral in y of the difference between the usemasswghtinterp If true, uses mass weighting to interpolate T/S for top and bottom integrals. subroutine, public subroutine, public mom_density_integrals::int_density_dz_generic_ppm (k, tv, T_t, T_b, S_t, S_b, e, rho_ref, rho_0, G_e, dz_subroundoff, bathyT, HI, GV, EOS, US, dpa, intz_dpa, intx_dpa, inty_dpa, useMassWghtInterp) int_density_dz_generic_ppm k k tv tv T_t T_t T_b T_b S_t S_t S_b S_b e e rho_ref rho_ref rho_0 rho_0 G_e G_e dz_subroundoff dz_subroundoff bathyT bathyT HI HI GV GV EOS EOS US US dpa dpa intz_dpa intz_dpa intx_dpa intx_dpa inty_dpa inty_dpa useMassWghtInterp useMassWghtInterp Compute pressure gradient force integrals for layer "k" and the case where T and S are parabolic profiles. k Layer index to calculate integrals for hi Ocean horizontal index structures for the input arrays gv Vertical grid structure tv Thermodynamic variables t_t Potential temperature at the cell top [degC] t_b Potential temperature at the cell bottom [degC] s_t Salinity at the cell top [ppt] s_b Salinity at the cell bottom [ppt] e Height of interfaces [Z ~> m] rho_ref A mean density [R ~> kg m-3] or [kg m-3], that is subtracted out to reduce the magnitude of each of the integrals. rho_0 A density [R ~> kg m-3] or [kg m-3], that is used to calculate the pressure (as p~=-z*rho_0*G_e) used in the equation of state. g_e The Earth's gravitational acceleration [m s-2] dz_subroundoff A minuscule thickness change [Z ~> m] bathyt The depth of the bathymetry [Z ~> m] eos Equation of state structure us A dimensional unit scaling type dpa The change in the pressure anomaly across the layer [R L2 T-2 ~> Pa] intz_dpa The integral through the thickness of the layer of intx_dpa The integral in x of the difference between the inty_dpa The integral in y of the difference between the usemasswghtinterp If true, uses mass weighting to interpolate T/S for top and bottom integrals. subroutine, public subroutine, public mom_density_integrals::int_specific_vol_dp (T, S, p_t, p_b, alpha_ref, HI, EOS, US, dza, intp_dza, intx_dza, inty_dza, halo_size, bathyP, dP_tiny, useMassWghtInterp) int_specific_vol_dp T T S S p_t p_t p_b p_b alpha_ref alpha_ref HI HI EOS EOS US US dza dza intp_dza intp_dza intx_dza intx_dza inty_dza inty_dza halo_size halo_size bathyP bathyP dP_tiny dP_tiny useMassWghtInterp useMassWghtInterp Calls the appropriate subroutine to calculate analytical and nearly-analytical integrals in pressure across layers of geopotential anomalies, which are required for calculating the finite-volume form pressure accelerations in a non-Boussinesq model. There are essentially no free assumptions, apart from the use of Boole's rule to do the horizontal integrals, and from a truncation in the series for log(1-eps/1+eps) that assumes that |eps| < 0.34. hi The horizontal index structure t Potential temperature referenced to the surface [degC] s Salinity [ppt] p_t Pressure at the top of the layer [R L2 T-2 ~> Pa] or [Pa] p_b Pressure at the bottom of the layer [R L2 T-2 ~> Pa] or [Pa] alpha_ref A mean specific volume that is subtracted out to reduce the magnitude of each of the integrals [R-1 ~> m3 kg-1] The calculation is mathematically identical with different values of alpha_ref, but this reduces the effects of roundoff. eos Equation of state structure us A dimensional unit scaling type dza The change in the geopotential anomaly across intp_dza The integral in pressure through the layer of the intx_dza The integral in x of the difference between the inty_dza The integral in y of the difference between the halo_size The width of halo points on which to calculate dza. bathyp The pressure at the bathymetry [R L2 T-2 ~> Pa] or [Pa] dp_tiny A minuscule pressure change with the same units as p_t [R L2 T-2 ~> Pa] or [Pa] usemasswghtinterp If true, uses mass weighting to interpolate T/S for top and bottom integrals. int_spec_vol_dp_generic_pcm mom_interface_heights::find_eta_2d mom_interface_heights::find_eta_3d mom_pressureforce_mont::pressureforce_mont_nonbouss subroutine, public subroutine, public mom_density_integrals::int_spec_vol_dp_generic_pcm (T, S, p_t, p_b, alpha_ref, HI, EOS, US, dza, intp_dza, intx_dza, inty_dza, halo_size, bathyP, dP_neglect, useMassWghtInterp) int_spec_vol_dp_generic_pcm T T S S p_t p_t p_b p_b alpha_ref alpha_ref HI HI EOS EOS US US dza dza intp_dza intp_dza intx_dza intx_dza inty_dza inty_dza halo_size halo_size bathyP bathyP dP_neglect dP_neglect useMassWghtInterp useMassWghtInterp This subroutine calculates integrals of specific volume anomalies in pressure across layers, which are required for calculating the finite-volume form pressure accelerations in a non-Boussinesq model. There are essentially no free assumptions, apart from the use of Boole's rule quadrature to do the integrals. hi A horizontal index type structure. t Potential temperature of the layer [degC] s Salinity of the layer [ppt] p_t Pressure atop the layer [R L2 T-2 ~> Pa] or [Pa] p_b Pressure below the layer [R L2 T-2 ~> Pa] or [Pa] alpha_ref A mean specific volume that is subtracted out to reduce the magnitude of each of the integrals [R-1 ~> m3 kg-1] The calculation is mathematically identical with different values of alpha_ref, but alpha_ref alters the effects of roundoff, and answers do change. eos Equation of state structure us A dimensional unit scaling type dza The change in the geopotential anomaly intp_dza The integral in pressure through the layer of intx_dza The integral in x of the difference between inty_dza The integral in y of the difference between halo_size The width of halo points on which to calculate dza. bathyp The pressure at the bathymetry [R L2 T-2 ~> Pa] or [Pa] dp_neglect A minuscule pressure change with the same units as p_t [R L2 T-2 ~> Pa] or [Pa] usemasswghtinterp If true, uses mass weighting to interpolate T/S for top and bottom integrals. mom_error_handler::mom_error int_specific_vol_dp subroutine, public subroutine, public mom_density_integrals::int_spec_vol_dp_generic_plm (T_t, T_b, S_t, S_b, p_t, p_b, alpha_ref, dP_neglect, bathyP, HI, EOS, US, dza, intp_dza, intx_dza, inty_dza, useMassWghtInterp) int_spec_vol_dp_generic_plm T_t T_t T_b T_b S_t S_t S_b S_b p_t p_t p_b p_b alpha_ref alpha_ref dP_neglect dP_neglect bathyP bathyP HI HI EOS EOS US US dza dza intp_dza intp_dza intx_dza intx_dza inty_dza inty_dza useMassWghtInterp useMassWghtInterp This subroutine calculates integrals of specific volume anomalies in pressure across layers, which are required for calculating the finite-volume form pressure accelerations in a non-Boussinesq model. There are essentially no free assumptions, apart from the use of Boole's rule quadrature to do the integrals. hi A horizontal index type structure. t_t Potential temperature at the top of the layer [degC] t_b Potential temperature at the bottom of the layer [degC] s_t Salinity at the top the layer [ppt] s_b Salinity at the bottom the layer [ppt] p_t Pressure atop the layer [R L2 T-2 ~> Pa] or [Pa] p_b Pressure below the layer [R L2 T-2 ~> Pa] or [Pa] alpha_ref A mean specific volume that is subtracted out to reduce the magnitude of each of the integrals [R-1 ~> m3 kg-1] The calculation is mathematically identical with different values of alpha_ref, but alpha_ref alters the effects of roundoff, and answers do change. dp_neglect !< A miniscule pressure change with the same units as p_t [R L2 T-2 ~> Pa] or [Pa] bathyp The pressure at the bathymetry [R L2 T-2 ~> Pa] or [Pa] eos Equation of state structure us A dimensional unit scaling type dza The change in the geopotential anomaly intp_dza The integral in pressure through the layer of intx_dza The integral in x of the difference between inty_dza The integral in y of the difference between usemasswghtinterp If true, uses mass weighting to interpolate T/S for top and bottom integrals. subroutine, public subroutine, public mom_density_integrals::find_depth_of_pressure_in_cell (T_t, T_b, S_t, S_b, z_t, z_b, P_t, P_tgt, rho_ref, G_e, EOS, US, P_b, z_out, z_tol) find_depth_of_pressure_in_cell T_t T_t T_b T_b S_t S_t S_b S_b z_t z_t z_b z_b P_t P_t P_tgt P_tgt rho_ref rho_ref G_e G_e EOS EOS US US P_b P_b z_out z_out z_tol z_tol Find the depth at which the reconstructed pressure matches P_tgt. t_t Potential temperature at the cell top [degC] t_b Potential temperature at the cell bottom [degC] s_t Salinity at the cell top [ppt] s_b Salinity at the cell bottom [ppt] z_t Absolute height of top of cell [Z ~> m] (Boussinesq ????) z_b Absolute height of bottom of cell [Z ~> m] p_t Anomalous pressure of top of cell, relative to g*rho_ref*z_t [R L2 T-2 ~> Pa] p_tgt Target pressure at height z_out, relative to g*rho_ref*z_out [R L2 T-2 ~> Pa] rho_ref Reference density with which calculation are anomalous to [R ~> kg m-3] g_e Gravitational acceleration [L2 Z-1 T-2 ~> m s-2] eos Equation of state structure us A dimensional unit scaling type p_b Pressure at the bottom of the cell [R L2 T-2 ~> Pa] z_out Absolute depth at which anomalous pressure = p_tgt [Z ~> m] z_tol The tolerance in finding z_out [Z ~> m] frac_dp_at_pos mom_error_handler::mom_error mom_state_initialization::cut_off_column_top mom_state_initialization::mom_state_init_tests real function real function mom_density_integrals::frac_dp_at_pos (T_t, T_b, S_t, S_b, z_t, z_b, rho_ref, G_e, pos, EOS) frac_dp_at_pos T_t T_t T_b T_b S_t S_t S_b S_b z_t z_t z_b z_b rho_ref rho_ref G_e G_e pos pos EOS EOS Returns change in anomalous pressure change from top to non-dimensional position pos between z_t and z_b. t_t Potential temperature at the cell top [degC] t_b Potential temperature at the cell bottom [degC] s_t Salinity at the cell top [ppt] s_b Salinity at the cell bottom [ppt] z_t The geometric height at the top of the layer [Z ~> m] z_b The geometric height at the bottom of the layer [Z ~> m] rho_ref A mean density [R ~> kg m-3], that is subtracted out to reduce the magnitude of each of the integrals. g_e The Earth's gravitational acceleration [L2 Z-1 T-2 ~> m s-2] pos The fractional vertical position, 0 to 1 [nondim] eos Equation of state structure find_depth_of_pressure_in_cell Provides integrals of density.