mom_eos_linear mom_eos_linear::calculate_density_derivs_linear mom_eos_linear::calculate_density_linear mom_eos_linear::calculate_density_second_derivs_linear mom_eos_linear::calculate_spec_vol_linear subroutine, public subroutine, public mom_eos_linear::calculate_density_scalar_linear (T, S, pressure, rho, Rho_T0_S0, dRho_dT, dRho_dS, rho_ref) calculate_density_scalar_linear T T S S pressure pressure rho rho Rho_T0_S0 Rho_T0_S0 dRho_dT dRho_dT dRho_dS dRho_dS rho_ref rho_ref This subroutine computes the density of sea water with a trivial linear equation of state (in [kg m-3]) from salinity (sal [PSU]), potential temperature (T [degC]), and pressure [Pa]. t Potential temperature relative to the surface [degC]. s Salinity [PSU]. pressure pressure [Pa]. rho In situ density [kg m-3]. rho_t0_s0 The density at T=0, S=0 [kg m-3]. drho_dt The derivatives of density with temperature [kg m-3 degC-1]. drho_ds The derivatives of density with salinity in [kg m-3 ppt-1]. rho_ref A reference density [kg m-3]. subroutine, public subroutine, public mom_eos_linear::calculate_density_array_linear (T, S, pressure, rho, start, npts, Rho_T0_S0, dRho_dT, dRho_dS, rho_ref) calculate_density_array_linear T T S S pressure pressure rho rho start start npts npts Rho_T0_S0 Rho_T0_S0 dRho_dT dRho_dT dRho_dS dRho_dS rho_ref rho_ref This subroutine computes the density of sea water with a trivial linear equation of state (in kg/m^3) from salinity (sal in psu), potential temperature (T [degC]), and pressure [Pa]. t potential temperature relative to the surface [degC]. s salinity [PSU]. pressure pressure [Pa]. rho in situ density [kg m-3]. start the starting point in the arrays. npts the number of values to calculate. rho_t0_s0 The density at T=0, S=0 [kg m-3]. drho_dt The derivatives of density with temperature [kg m-3 degC-1]. drho_ds The derivatives of density with salinity in [kg m-3 ppt-1]. rho_ref A reference density [kg m-3]. subroutine subroutine mom_eos_linear::calculate_spec_vol_scalar_linear (T, S, pressure, specvol, Rho_T0_S0, dRho_dT, dRho_dS, spv_ref) calculate_spec_vol_scalar_linear T T S S pressure pressure specvol specvol Rho_T0_S0 Rho_T0_S0 dRho_dT dRho_dT dRho_dS dRho_dS spv_ref spv_ref This subroutine computes the in situ specific volume of sea water (specvol in [m3 kg-1]) from salinity (S [PSU]), potential temperature (T [degC]) and pressure [Pa], using a trivial linear equation of state for density. If spv_ref is present, specvol is an anomaly from spv_ref. t potential temperature relative to the surface [degC]. s Salinity [PSU]. pressure Pressure [Pa]. specvol In situ specific volume [m3 kg-1]. rho_t0_s0 The density at T=0, S=0 [kg m-3]. drho_dt The derivatives of density with temperature [kg m-3 degC-1]. drho_ds The derivatives of density with salinity [kg m-3 ppt-1]. spv_ref A reference specific volume [m3 kg-1]. subroutine subroutine mom_eos_linear::calculate_spec_vol_array_linear (T, S, pressure, specvol, start, npts, Rho_T0_S0, dRho_dT, dRho_dS, spv_ref) calculate_spec_vol_array_linear T T S S pressure pressure specvol specvol start start npts npts Rho_T0_S0 Rho_T0_S0 dRho_dT dRho_dT dRho_dS dRho_dS spv_ref spv_ref This subroutine computes the in situ specific volume of sea water (specvol in [m3 kg-1]) from salinity (S [PSU]), potential temperature (T [degC]) and pressure [Pa], using a trivial linear equation of state for density. If spv_ref is present, specvol is an anomaly from spv_ref. t potential temperature relative to the surface [degC]. s Salinity [PSU]. pressure Pressure [Pa]. specvol in situ specific volume [m3 kg-1]. start the starting point in the arrays. npts the number of values to calculate. rho_t0_s0 The density at T=0, S=0 [kg m-3]. drho_dt The derivatives of density with temperature [kg m-3 degC-1]. drho_ds The derivatives of density with salinity [kg m-3 ppt-1]. spv_ref A reference specific volume [m3 kg-1]. subroutine subroutine mom_eos_linear::calculate_density_derivs_array_linear (T, S, pressure, drho_dT_out, drho_dS_out, Rho_T0_S0, dRho_dT, dRho_dS, start, npts) calculate_density_derivs_array_linear T T S S pressure pressure drho_dT_out drho_dT_out drho_dS_out drho_dS_out Rho_T0_S0 Rho_T0_S0 dRho_dT dRho_dT dRho_dS dRho_dS start start npts npts This subroutine calculates the partial derivatives of density * with potential temperature and salinity. t Potential temperature relative to the surface [degC]. s Salinity [PSU]. pressure Pressure [Pa]. drho_dt_out The partial derivative of density with potential temperature [kg m-3 degC-1]. drho_ds_out The partial derivative of density with salinity [kg m-3 ppt-1]. rho_t0_s0 The density at T=0, S=0 [kg m-3]. drho_dt The derivative of density with temperature [kg m-3 degC-1]. drho_ds The derivative of density with salinity [kg m-3 ppt-1]. start The starting point in the arrays. npts The number of values to calculate. subroutine, public subroutine, public mom_eos_linear::calculate_density_derivs_scalar_linear (T, S, pressure, drho_dT_out, drho_dS_out, Rho_T0_S0, dRho_dT, dRho_dS) calculate_density_derivs_scalar_linear T T S S pressure pressure drho_dT_out drho_dT_out drho_dS_out drho_dS_out Rho_T0_S0 Rho_T0_S0 dRho_dT dRho_dT dRho_dS dRho_dS This subroutine calculates the partial derivatives of density * with potential temperature and salinity for a single point. t Potential temperature relative to the surface [degC]. s Salinity [PSU]. pressure pressure [Pa]. drho_dt_out The partial derivative of density with potential temperature [kg m-3 degC-1]. drho_ds_out The partial derivative of density with salinity [kg m-3 ppt-1]. rho_t0_s0 The density at T=0, S=0 [kg m-3]. drho_dt The derivatives of density with temperature [kg m-3 degC-1]. drho_ds The derivatives of density with salinity [kg m-3 ppt-1]. subroutine subroutine mom_eos_linear::calculate_density_second_derivs_scalar_linear (T, S, pressure, drho_dS_dS, drho_dS_dT, drho_dT_dT, drho_dS_dP, drho_dT_dP) calculate_density_second_derivs_scalar_linear T T S S pressure pressure drho_dS_dS drho_dS_dS drho_dS_dT drho_dS_dT drho_dT_dT drho_dT_dT drho_dS_dP drho_dS_dP drho_dT_dP drho_dT_dP This subroutine calculates the five, partial second derivatives of density w.r.t. potential temperature and salinity and pressure which for a linear equation of state should all be 0. t Potential temperature relative to the surface [degC]. s Salinity [PSU]. pressure pressure [Pa]. drho_ds_ds The second derivative of density with salinity [kg m-3 PSU-2]. drho_ds_dt The second derivative of density with temperature and salinity [kg m-3 ppt-1 degC-1]. drho_dt_dt The second derivative of density with temperature [kg m-3 degC-2]. drho_ds_dp The second derivative of density with salinity and pressure [kg m-3 PSU-1 Pa-1]. drho_dt_dp The second derivative of density with temperature and pressure [kg m-3 degC-1 Pa-1]. subroutine subroutine mom_eos_linear::calculate_density_second_derivs_array_linear (T, S, pressure, drho_dS_dS, drho_dS_dT, drho_dT_dT, drho_dS_dP, drho_dT_dP, start, npts) calculate_density_second_derivs_array_linear T T S S pressure pressure drho_dS_dS drho_dS_dS drho_dS_dT drho_dS_dT drho_dT_dT drho_dT_dT drho_dS_dP drho_dS_dP drho_dT_dP drho_dT_dP start start npts npts This subroutine calculates the five, partial second derivatives of density w.r.t. potential temperature and salinity and pressure which for a linear equation of state should all be 0. t Potential temperature relative to the surface [degC]. s Salinity [PSU]. pressure pressure [Pa]. drho_ds_ds The second derivative of density with salinity [kg m-3 PSU-2]. drho_ds_dt The second derivative of density with temperature and salinity [kg m-3 ppt-1 degC-1]. drho_dt_dt The second derivative of density with temperature [kg m-3 degC-2]. drho_ds_dp The second derivative of density with salinity and pressure [kg m-3 PSU-1 Pa-1]. drho_dt_dp The second derivative of density with temperature and pressure [kg m-3 degC-1 Pa-1]. start The starting point in the arrays. npts The number of values to calculate. subroutine, public subroutine, public mom_eos_linear::calculate_specvol_derivs_linear (T, S, pressure, dSV_dT, dSV_dS, start, npts, Rho_T0_S0, dRho_dT, dRho_dS) calculate_specvol_derivs_linear T T S S pressure pressure dSV_dT dSV_dT dSV_dS dSV_dS start start npts npts Rho_T0_S0 Rho_T0_S0 dRho_dT dRho_dT dRho_dS dRho_dS Calculate the derivatives of specific volume with temperature and salinity. t Potential temperature relative to the surface [degC]. s Salinity [PSU]. pressure pressure [Pa]. dsv_ds The partial derivative of specific volume with salinity [m3 kg-1 PSU-1]. dsv_dt The partial derivative of specific volume with potential temperature [m3 kg-1 degC-1]. start The starting point in the arrays. npts The number of values to calculate. rho_t0_s0 The density at T=0, S=0 [kg m-3]. drho_dt The derivative of density with temperature, [kg m-3 degC-1]. drho_ds The derivative of density with salinity [kg m-3 ppt-1]. subroutine, public subroutine, public mom_eos_linear::calculate_compress_linear (T, S, pressure, rho, drho_dp, start, npts, Rho_T0_S0, dRho_dT, dRho_dS) calculate_compress_linear T T S S pressure pressure rho rho drho_dp drho_dp start start npts npts Rho_T0_S0 Rho_T0_S0 dRho_dT dRho_dT dRho_dS dRho_dS This subroutine computes the in situ density of sea water (rho) and the compressibility (drho/dp == C_sound^-2) at the given salinity, potential temperature, and pressure. t Potential temperature relative to the surface [degC]. s Salinity [PSU]. pressure pressure [Pa]. rho In situ density [kg m-3]. drho_dp The partial derivative of density with pressure (also the inverse of the square of sound speed) [s2 m-2]. start The starting point in the arrays. npts The number of values to calculate. rho_t0_s0 The density at T=0, S=0 [kg m-3]. drho_dt The derivative of density with temperature [kg m-3 degC-1]. drho_ds The derivative of density with salinity [kg m-3 ppt-1]. mom_eos::calculate_compress_array subroutine, public subroutine, public mom_eos_linear::int_density_dz_linear (T, S, z_t, z_b, rho_ref, rho_0_pres, G_e, HI, Rho_T0_S0, dRho_dT, dRho_dS, dpa, intz_dpa, intx_dpa, inty_dpa, bathyT, dz_neglect, useMassWghtInterp) int_density_dz_linear T T S S z_t z_t z_b z_b rho_ref rho_ref rho_0_pres rho_0_pres G_e G_e HI HI Rho_T0_S0 Rho_T0_S0 dRho_dT dRho_dT dRho_dS dRho_dS dpa dpa intz_dpa intz_dpa intx_dpa intx_dpa inty_dpa inty_dpa bathyT bathyT dz_neglect dz_neglect useMassWghtInterp useMassWghtInterp This subroutine calculates analytical and nearly-analytical integrals of pressure anomalies across layers, which are required for calculating the finite-volume form pressure accelerations in a Boussinesq model. hi The horizontal index type for the arrays. t Potential temperature relative to the surface s Salinity [PSU]. z_t Height at the top of the layer in depth units [Z ~> m]. z_b Height at the top 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_pres A density [R ~> kg m-3], used to calculate the pressure (as p~=-z*rho_0_pres*G_e) used in the equation of state. rho_0_pres is not used. g_e The Earth's gravitational acceleration [L2 Z-1 T-2 ~> m s-2] or [m2 Z-1 s-2 ~> m s-2]. rho_t0_s0 The density at T=0, S=0 [R ~> kg m-3] or [kg m-3]. drho_dt The derivative of density with temperature, [R degC-1 ~> kg m-3 degC-1] or [kg m-3 degC-1]. drho_ds The derivative of density with salinity, in [R ppt-1 ~> kg m-3 ppt-1] or [kg m-3 ppt-1]. dpa The change in the pressure anomaly across the intz_dpa The integral through the thickness of the layer intx_dpa The integral in x of the difference between the inty_dpa The integral in y of the difference between the bathyt The depth of the bathymetry [Z ~> m]. dz_neglect A miniscule thickness change [Z ~> m]. usemasswghtinterp If true, uses mass weighting to interpolate T/S for top and bottom integrals. subroutine, public subroutine, public mom_eos_linear::int_spec_vol_dp_linear (T, S, p_t, p_b, alpha_ref, HI, Rho_T0_S0, dRho_dT, dRho_dS, dza, intp_dza, intx_dza, inty_dza, halo_size, bathyP, dP_neglect, useMassWghtInterp) int_spec_vol_dp_linear T T S S p_t p_t p_b p_b alpha_ref alpha_ref HI HI Rho_T0_S0 Rho_T0_S0 dRho_dT dRho_dT dRho_dS dRho_dS 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 Calculates 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. Specific volume is assumed to vary linearly between adjacent points. hi The ocean's horizontal index type. t Potential temperature relative to the surface s Salinity [PSU]. p_t Pressure at the top of the layer [R L2 T-2 ~> Pa] or [Pa]. p_b Pressure at the top 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. rho_t0_s0 The density at T=0, S=0 [R ~> kg m-3] or [kg m-3]. drho_dt The derivative of density with temperature [R degC-1 ~> kg m-3 degC-1] or [kg m-3 degC-1]. drho_ds The derivative of density with salinity, in [R ppt-1 ~> kg m-3 ppt-1] or [kg m-3 ppt-1]. 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_neglect A miniscule 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_eos::analytic_int_specific_vol_dp A simple linear equation of state for sea water with constant coefficients.