mom_eos_wright mom_eos_wright::calculate_density_derivs_wright mom_eos_wright::calculate_density_second_derivs_wright mom_eos_wright::calculate_density_wright mom_eos_wright::calculate_spec_vol_wright real, parameter real, parameter mom_eos_wright::a0 a0 = 7.057924e-4 Parameters in the Wright equation of state. calculate_compress_wright calculate_density_array_wright calculate_density_derivs_array_wright calculate_density_second_derivs_array_wright calculate_spec_vol_array_wright int_density_dz_wright int_spec_vol_dp_wright real, parameter real, parameter mom_eos_wright::a1 a1 = 3.480336e-7 Parameters in the Wright equation of state. calculate_compress_wright calculate_density_array_wright calculate_density_derivs_array_wright calculate_density_second_derivs_array_wright calculate_spec_vol_array_wright calculate_specvol_derivs_wright int_density_dz_wright int_spec_vol_dp_wright real, parameter real, parameter mom_eos_wright::a2 a2 = -1.112733e-7 Parameters in the Wright equation of state. calculate_compress_wright calculate_density_array_wright calculate_density_derivs_array_wright calculate_density_second_derivs_array_wright calculate_spec_vol_array_wright calculate_specvol_derivs_wright int_density_dz_wright int_spec_vol_dp_wright real, parameter real, parameter mom_eos_wright::b0 b0 = 5.790749e8 Parameters in the Wright equation of state. calculate_compress_wright calculate_density_array_wright calculate_density_derivs_array_wright calculate_density_second_derivs_array_wright calculate_spec_vol_array_wright calculate_specvol_derivs_wright int_density_dz_wright int_spec_vol_dp_wright real, parameter real, parameter mom_eos_wright::b1 b1 = 3.516535e6 Parameters in the Wright equation of state. calculate_compress_wright calculate_density_array_wright calculate_density_derivs_array_wright calculate_density_second_derivs_array_wright calculate_spec_vol_array_wright calculate_specvol_derivs_wright int_density_dz_wright int_spec_vol_dp_wright real, parameter real, parameter mom_eos_wright::b2 b2 = -4.002714e4 Parameters in the Wright equation of state. calculate_compress_wright calculate_density_array_wright calculate_density_derivs_array_wright calculate_density_second_derivs_array_wright calculate_spec_vol_array_wright calculate_specvol_derivs_wright int_density_dz_wright int_spec_vol_dp_wright real, parameter real, parameter mom_eos_wright::b3 b3 = 2.084372e2 Parameters in the Wright equation of state. calculate_compress_wright calculate_density_array_wright calculate_density_derivs_array_wright calculate_density_second_derivs_array_wright calculate_spec_vol_array_wright calculate_specvol_derivs_wright int_density_dz_wright int_spec_vol_dp_wright real, parameter real, parameter mom_eos_wright::b4 b4 = 5.944068e5 Parameters in the Wright equation of state. calculate_compress_wright calculate_density_array_wright calculate_density_derivs_array_wright calculate_density_second_derivs_array_wright calculate_spec_vol_array_wright calculate_specvol_derivs_wright int_density_dz_wright int_spec_vol_dp_wright real, parameter real, parameter mom_eos_wright::b5 b5 = -9.643486e3 Parameters in the Wright equation of state. calculate_compress_wright calculate_density_array_wright calculate_density_derivs_array_wright calculate_density_second_derivs_array_wright calculate_spec_vol_array_wright calculate_specvol_derivs_wright int_density_dz_wright int_spec_vol_dp_wright real, parameter real, parameter mom_eos_wright::c0 c0 = 1.704853e5 Parameters in the Wright equation of state. calculate_compress_wright calculate_density_array_wright calculate_density_derivs_array_wright calculate_density_second_derivs_array_wright calculate_spec_vol_array_wright calculate_specvol_derivs_wright int_density_dz_wright int_spec_vol_dp_wright real, parameter real, parameter mom_eos_wright::c1 c1 = 7.904722e2 Parameters in the Wright equation of state. calculate_compress_wright calculate_density_array_wright calculate_density_derivs_array_wright calculate_density_second_derivs_array_wright calculate_spec_vol_array_wright calculate_specvol_derivs_wright int_density_dz_wright int_spec_vol_dp_wright real, parameter real, parameter mom_eos_wright::c2 c2 = -7.984422 Parameters in the Wright equation of state. calculate_compress_wright calculate_density_array_wright calculate_density_derivs_array_wright calculate_density_second_derivs_array_wright calculate_spec_vol_array_wright calculate_specvol_derivs_wright int_density_dz_wright int_spec_vol_dp_wright real, parameter real, parameter mom_eos_wright::c3 c3 = 5.140652e-2 Parameters in the Wright equation of state. calculate_compress_wright calculate_density_array_wright calculate_density_derivs_array_wright calculate_density_second_derivs_array_wright calculate_spec_vol_array_wright calculate_specvol_derivs_wright int_density_dz_wright int_spec_vol_dp_wright real, parameter real, parameter mom_eos_wright::c4 c4 = -2.302158e2 Parameters in the Wright equation of state. calculate_compress_wright calculate_density_array_wright calculate_density_derivs_array_wright calculate_density_second_derivs_array_wright calculate_spec_vol_array_wright calculate_specvol_derivs_wright int_density_dz_wright int_spec_vol_dp_wright real, parameter real, parameter mom_eos_wright::c5 c5 = -3.079464 Parameters in the Wright equation of state. calculate_compress_wright calculate_density_array_wright calculate_density_derivs_array_wright calculate_density_second_derivs_array_wright calculate_spec_vol_array_wright calculate_specvol_derivs_wright int_density_dz_wright int_spec_vol_dp_wright subroutine subroutine mom_eos_wright::calculate_density_scalar_wright (T, S, pressure, rho, rho_ref) calculate_density_scalar_wright T T S S pressure pressure rho rho rho_ref rho_ref This subroutine computes the in situ density of sea water (rho in [kg m-3]) from salinity (S [PSU]), potential temperature (T [degC]), and pressure [Pa]. It uses the expression from Wright, 1997, J. Atmos. Ocean. Tech., 14, 735-740. t Potential temperature relative to the surface [degC]. s Salinity [PSU]. pressure pressure [Pa]. rho In situ density [kg m-3]. rho_ref A reference density [kg m-3]. calculate_density_array_wright subroutine subroutine mom_eos_wright::calculate_density_array_wright (T, S, pressure, rho, start, npts, rho_ref) calculate_density_array_wright T T S S pressure pressure rho rho start start npts npts rho_ref rho_ref This subroutine computes the in situ density of sea water (rho in [kg m-3]) from salinity (S [PSU]), potential temperature (T [degC]), and pressure [Pa]. It uses the expression from Wright, 1997, J. Atmos. Ocean. Tech., 14, 735-740. 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_ref A reference density [kg m-3]. a0 a1 a2 b0 b1 b2 b3 b4 b5 c0 c1 c2 c3 c4 c5 calculate_density_scalar_wright subroutine subroutine mom_eos_wright::calculate_spec_vol_scalar_wright (T, S, pressure, specvol, spv_ref) calculate_spec_vol_scalar_wright T T S S pressure pressure specvol specvol 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]. It uses the expression from Wright, 1997, J. Atmos. Ocean. Tech., 14, 735-740. 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]. spv_ref A reference specific volume [m3 kg-1]. calculate_spec_vol_array_wright subroutine subroutine mom_eos_wright::calculate_spec_vol_array_wright (T, S, pressure, specvol, start, npts, spv_ref) calculate_spec_vol_array_wright T T S S pressure pressure specvol specvol start start npts npts 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]. It uses the expression from Wright, 1997, J. Atmos. Ocean. Tech., 14, 735-740. 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. spv_ref A reference specific volume [m3 kg-1]. a0 a1 a2 b0 b1 b2 b3 b4 b5 c0 c1 c2 c3 c4 c5 calculate_spec_vol_scalar_wright subroutine subroutine mom_eos_wright::calculate_density_derivs_array_wright (T, S, pressure, drho_dT, drho_dS, start, npts) calculate_density_derivs_array_wright T T S S pressure pressure drho_dT drho_dT drho_dS drho_dS start start npts npts For a given thermodynamic state, return the thermal/haline expansion coefficients. t Potential temperature relative to the surface [degC]. s Salinity [PSU]. pressure pressure [Pa]. drho_dt The partial derivative of density with potential temperature [kg m-3 degC-1]. drho_ds The partial derivative of density with salinity, in [kg m-3 PSU-1]. start The starting point in the arrays. npts The number of values to calculate. a0 a1 a2 b0 b1 b2 b3 b4 b5 c0 c1 c2 c3 c4 c5 calculate_density_derivs_scalar_wright subroutine subroutine mom_eos_wright::calculate_density_derivs_scalar_wright (T, S, pressure, drho_dT, drho_dS) calculate_density_derivs_scalar_wright T T S S pressure pressure drho_dT drho_dT drho_dS drho_dS The scalar version of calculate_density_derivs which promotes scalar inputs to a 1-element array and then demotes the output back to a scalar. t Potential temperature relative to the surface [degC]. s Salinity [PSU]. pressure pressure [Pa]. drho_dt The partial derivative of density with potential temperature [kg m-3 degC-1]. drho_ds The partial derivative of density with salinity, in [kg m-3 PSU-1]. calculate_density_derivs_array_wright subroutine subroutine mom_eos_wright::calculate_density_second_derivs_array_wright (T, S, P, drho_ds_ds, drho_ds_dt, drho_dt_dt, drho_ds_dp, drho_dt_dp, start, npts) calculate_density_second_derivs_array_wright T T S S P P 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 Second derivatives of density with respect to temperature, salinity, and pressure. t Potential temperature referenced to 0 dbar [degC] s Salinity [PSU] p Pressure [Pa] drho_ds_ds Partial derivative of beta with respect to S [kg m-3 PSU-2] drho_ds_dt Partial derivative of beta with respcct to T [kg m-3 PSU-1 degC-1] drho_dt_dt Partial derivative of alpha with respect to T [kg m-3 degC-2] drho_ds_dp Partial derivative of beta with respect to pressure [kg m-3 PSU-1 Pa-1] drho_dt_dp Partial derivative of alpha with respect to pressure [kg m-3 degC-1 Pa-1] start Starting index in T,S,P npts Number of points to loop over a0 a1 a2 b0 b1 b2 b3 b4 b5 c0 c1 c2 c3 c4 c5 calculate_density_second_derivs_scalar_wright subroutine subroutine mom_eos_wright::calculate_density_second_derivs_scalar_wright (T, S, P, drho_ds_ds, drho_ds_dt, drho_dt_dt, drho_ds_dp, drho_dt_dp) calculate_density_second_derivs_scalar_wright T T S S P P 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 Second derivatives of density with respect to temperature, salinity, and pressure for scalar inputs. Inputs promoted to 1-element array and output demoted to scalar. t Potential temperature referenced to 0 dbar s Salinity [PSU] p pressure [Pa] drho_ds_ds Partial derivative of beta with respect to S [kg m-3 PSU-2] drho_ds_dt Partial derivative of beta with respcct to T [kg m-3 PSU-1 degC-1] drho_dt_dt Partial derivative of alpha with respect to T [kg m-3 degC-2] drho_ds_dp Partial derivative of beta with respect to pressure [kg m-3 PSU-1 Pa-1] drho_dt_dp Partial derivative of alpha with respect to pressure [kg m-3 degC-1 Pa-1] calculate_density_second_derivs_array_wright subroutine, public subroutine, public mom_eos_wright::calculate_specvol_derivs_wright (T, S, pressure, dSV_dT, dSV_dS, start, npts) calculate_specvol_derivs_wright T T S S pressure pressure dSV_dT dSV_dT dSV_dS dSV_dS start start npts npts For a given thermodynamic state, return the partial derivatives of specific volume with temperature and salinity. t Potential temperature relative to the surface [degC]. s Salinity [PSU]. pressure pressure [Pa]. dsv_dt The partial derivative of specific volume with potential temperature [m3 kg-1 degC-1]. dsv_ds The partial derivative of specific volume with salinity [m3 kg-1 / Pa]. start The starting point in the arrays. npts The number of values to calculate. a1 a2 b0 b1 b2 b3 b4 b5 c0 c1 c2 c3 c4 c5 subroutine, public subroutine, public mom_eos_wright::calculate_compress_wright (T, S, pressure, rho, drho_dp, start, npts) calculate_compress_wright T T S S pressure pressure rho rho drho_dp drho_dp start start npts npts This subroutine computes the in situ density of sea water (rho in [kg m-3]) and the compressibility (drho/dp = C_sound^-2) (drho_dp [s2 m-2]) from salinity (sal in psu), potential temperature (T [degC]), and pressure [Pa]. It uses the expressions from Wright, 1997, J. Atmos. Ocean. Tech., 14, 735-740. Coded by R. Hallberg, 1/01. 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. a0 a1 a2 b0 b1 b2 b3 b4 b5 c0 c1 c2 c3 c4 c5 subroutine, public subroutine, public mom_eos_wright::int_density_dz_wright (T, S, z_t, z_b, rho_ref, rho_0, G_e, HI, dpa, intz_dpa, intx_dpa, inty_dpa, bathyT, dz_neglect, useMassWghtInterp, rho_scale, pres_scale) int_density_dz_wright 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 dpa dpa intz_dpa intz_dpa intx_dpa intx_dpa inty_dpa inty_dpa bathyT bathyT dz_neglect dz_neglect useMassWghtInterp useMassWghtInterp rho_scale rho_scale pres_scale pres_scale 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. (The pressure is calucated as p~=-z*rho_0*G_e.) rho_0 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]. 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. rho_scale A multiplicative factor by which to scale density from kg m-3 to the desired units [R m3 kg-1 ~> 1] pres_scale A multiplicative factor to convert pressure into Pa [Pa T2 R-1 L-2 ~> 1]. a0 a1 a2 b0 b1 b2 b3 b4 b5 c0 c1 c2 c3 c4 c5 subroutine, public subroutine, public mom_eos_wright::int_spec_vol_dp_wright (T, S, p_t, p_b, spv_ref, HI, dza, intp_dza, intx_dza, inty_dza, halo_size, bathyP, dP_neglect, useMassWghtInterp, SV_scale, pres_scale) int_spec_vol_dp_wright T T S S p_t p_t p_b p_b spv_ref spv_ref HI HI 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 SV_scale SV_scale pres_scale pres_scale This subroutine 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. 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 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]. spv_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 spv_ref, but this reduces the effects of roundoff. dza The change in the geopotential anomaly across intp_dza The integral in pressure through the layer of 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. sv_scale A multiplicative factor by which to scale specific volume from m3 kg-1 to the desired units [kg m-3 R-1 ~> 1] pres_scale A multiplicative factor to convert pressure into Pa [Pa T2 R-1 L-2 ~> 1]. a0 a1 a2 b0 b1 b2 b3 b4 b5 c0 c1 c2 c3 c4 c5 The equation of state using the Wright 1997 expressions.