mom_eos_linear module reference

A simple linear equation of state for sea water with constant coefficients.

Data Types

linear_eos

The EOS_base implementation of a linear equation of state.

Functions/Subroutines

`density_elem_linear()`	Density computed as a linear function of T and S [kg m-3].
`density_anomaly_elem_linear()`	Density anomaly computed as a linear function of T and S [kg m-3].
`spec_vol_elem_linear()`	Specific volume using a linear equation of state for density [m3 kg-1].
`spec_vol_anomaly_elem_linear()`	Specific volume anomaly using a linear equation of state for density [m3 kg-1].
`calculate_density_derivs_elem_linear()`	This subroutine calculates the partial derivatives of density with potential temperature and salinity.
`calculate_density_second_derivs_elem_linear()`	This subroutine calculates the five, partial second derivatives of density w.r.t.
`calculate_specvol_derivs_elem_linear()`	Calculate the derivatives of specific volume with temperature and salinity.
`calculate_compress_elem_linear()`	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.
`avg_spec_vol_linear()`	Calculates the layer average specific volumes.
`eos_fit_range_linear()`	Return the range of temperatures, salinities and pressures permitted for linear equation of state.
`set_params_linear()`	Set coefficients for the linear equation of state.
`int_density_dz_linear()`	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.
`int_spec_vol_dp_linear()`	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.
`calculate_density_array_linear()`	Calculate the in-situ density for 1D arraya inputs and outputs.
`calculate_spec_vol_array_linear()`	Calculate the in-situ specific volume for 1D array inputs and outputs.

Detailed Description

A simple linear equation of state for sea water with constant coefficients.

Type Documentation

type mom_eos_linear/linear_eos

The EOS_base implementation of a linear equation of state.

Type fields:

% rho_t0_s0 :: real, private The density at T=0, S=0 and p=0 [kg m-3].
% drho_dt :: real, private The derivative of density with temperature [kg m-3 degC-1].
% drho_ds :: real, private The derivative of density with salinity [kg m-3 ppt-1].
% drho_dp :: real, private The derivative of density with pressure [s2 m-2].
% density_elem :: procedure, private Implementation of the in-situ density as an elemental function [kg m-3].
% density_anomaly_elem :: procedure, private Implementation of the in-situ density anomaly as an elemental function [kg m-3].
% spec_vol_elem :: procedure, private Implementation of the in-situ specific volume as an elemental function [m3 kg-1].
% spec_vol_anomaly_elem :: procedure, private Implementation of the in-situ specific volume anomaly as an elemental function [m3 kg-1].
% calculate_density_derivs_elem :: procedure, private Implementation of the calculation of derivatives of density.
% calculate_density_second_derivs_elem :: procedure, private Implementation of the calculation of second derivatives of density.
% calculate_specvol_derivs_elem :: procedure, private Implementation of the calculation of derivatives of specific volume.
% calculate_compress_elem :: procedure, private Implementation of the calculation of compressibility.
% eos_fit_range :: procedure, private Implementation of the range query function.
% set_params_linear :: procedure, private Instance specific function to set internal parameters.
% calculate_density_array :: procedure, private Local implementation of generic calculate_density_array for efficiency.
% calculate_spec_vol_array :: procedure, private Local implementation of generic calculate_spec_vol_array for efficiency.

[source]

Function/Subroutine Documentation

function mom_eos_linear/density_elem_linear(this, T, S, pressure)

Density computed as a linear function of T and S [kg m-3].

This is an elemental function that can be applied to any combination of scalar and array inputs.

Parameters:

this :: this [in] This EOS
t :: [in] Potential temperature relative to the surface [degC]
s :: [in] Salinity [ppt]
pressure :: pressure [in] Pressure [Pa]

Called from:

calculate_density_array_linear

[source]

function mom_eos_linear/density_anomaly_elem_linear(this, T, S, pressure, rho_ref)

Density anomaly computed as a linear function of T and S [kg m-3].

This is an elemental function that can be applied to any combination of scalar and array inputs.

Parameters:

this :: this [in] This EOS
t :: [in] Potential temperature relative to the surface [degC]
s :: [in] Salinity [ppt]
pressure :: pressure [in] Pressure [Pa]
rho_ref :: rho_ref [in] A reference density [kg m-3]

Called from:

calculate_density_array_linear

[source]

function mom_eos_linear/spec_vol_elem_linear(this, T, S, pressure)

Specific volume using a linear equation of state for density [m3 kg-1].

This is an elemental function that can be applied to any combination of scalar and array inputs.

Parameters:

this :: this [in] This EOS
t :: [in] Potential temperature relative to the surface [degC].
s :: [in] Salinity [ppt].
pressure :: pressure [in] Pressure [Pa].

Called from:

calculate_spec_vol_array_linear

[source]

function mom_eos_linear/spec_vol_anomaly_elem_linear(this, T, S, pressure, spv_ref)

Specific volume anomaly using a linear equation of state for density [m3 kg-1].

This is an elemental function that can be applied to any combination of scalar and array inputs.

Parameters:

this :: this [in] This EOS
t :: [in] Potential temperature relative to the surface [degC].
s :: [in] Salinity [ppt].
pressure :: pressure [in] Pressure [Pa].
spv_ref :: spv_ref [in] A reference specific volume [m3 kg-1].

Called from:

calculate_spec_vol_array_linear

[source]

subroutine mom_eos_linear/calculate_density_derivs_elem_linear(this, T, S, pressure, dRho_dT, dRho_dS)

This subroutine calculates the partial derivatives of density with potential temperature and salinity.

Parameters:

this :: this [in] This EOS
t :: [in] Potential temperature relative to the surface [degC].
s :: [in] Salinity [ppt].
pressure :: pressure [in] 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].

[source]

subroutine mom_eos_linear/calculate_density_second_derivs_elem_linear(this, T, S, pressure, drho_dS_dS, drho_dS_dT, drho_dT_dT, drho_dS_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.

Parameters:

this :: this [in] This EOS
t :: [in] Potential temperature relative to the surface [degC].
s :: [in] Salinity [ppt].
pressure :: pressure [in] pressure [Pa].
drho_ds_ds :: [inout] The second derivative of density with salinity [kg m-3 ppt-2].
drho_ds_dt :: [inout] The second derivative of density with temperature and salinity [kg m-3 ppt-1 degC-1].
drho_dt_dt :: [inout] The second derivative of density with temperature [kg m-3 degC-2].
drho_ds_dp :: [inout] The second derivative of density with salinity and pressure [kg m-3 ppt-1 Pa-1].
drho_dt_dp :: [inout] The second derivative of density with temperature and pressure [kg m-3 degC-1 Pa-1].

[source]

subroutine mom_eos_linear/calculate_specvol_derivs_elem_linear(this, T, S, pressure, dSV_dT, dSV_dS)

Calculate the derivatives of specific volume with temperature and salinity.

Parameters:

this :: this [in] This EOS
t :: [in] Potential temperature [degC]
s :: [in] Salinity [ppt]
pressure :: pressure [in] pressure [Pa]
dsv_ds :: [inout] The partial derivative of specific volume with salinity [m3 kg-1 ppt-1]
dsv_dt :: [inout] The partial derivative of specific volume with potential temperature [m3 kg-1 degC-1]

[source]

subroutine mom_eos_linear/calculate_compress_elem_linear(this, T, S, pressure, rho, drho_dp)

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.

Parameters:

this :: this [in] This EOS
t :: [in] Potential temperature relative to the surface [degC].
s :: [in] Salinity [ppt].
pressure :: pressure [in] pressure [Pa].
rho :: rho [out] In situ density [kg m-3].
drho_dp :: drho_dp [out] The partial derivative of density with pressure (also the inverse of the square of sound speed) [s2 m-2].

[source]

subroutine mom_eos_linear/avg_spec_vol_linear(T, S, p_t, dp, SpV_avg, start, npts, Rho_T0_S0, dRho_dT, dRho_dS, dRho_dp)

Calculates the layer average specific volumes. The analytical solution is SpV_avg = 1 / (drho_dp*dp) * ln[(1+eps)/(1-eps)] and the expression here is the first five terms of its Taylor series with a trunction error of O(eps**10). |eps|<0.02 for real ocean parameters.

Parameters:

t :: [in] Potential temperature [degC]
s :: [in] Salinity [ppt]
p_t :: p_t [in] Pressure at the top of the layer [Pa]
dp :: dp [in] Pressure change in the layer [Pa]
spv_avg :: [inout] The vertical average specific volume in the layer [m3 kg-1]
start :: start [in] the starting point in the arrays.
npts :: npts [in] the number of values to calculate.
rho_t0_s0 :: [in] The density at T=0, S=0 [kg m-3]
drho_dt :: [in] The derivative of density with temperature [kg m-3 degC-1]
drho_ds :: [in] The derivative of density with salinity [kg m-3 ppt-1]
drho_dp :: [in] The derivative of density with pressure [s2 m-2]

[source]

subroutine mom_eos_linear/eos_fit_range_linear(this, T_min, T_max, S_min, S_max, p_min, p_max)

Return the range of temperatures, salinities and pressures permitted for linear equation of state. Care should be taken when applying this equation of state outside of its fit range.

Parameters:

this :: this [in] This EOS
t_min :: [out] The minimum potential temperature over which this EoS is fitted [degC]
t_max :: [out] The maximum potential temperature over which this EoS is fitted [degC]
s_min :: [out] The minimum salinity over which this EoS is fitted [ppt]
s_max :: [out] The maximum salinity over which this EoS is fitted [ppt]
p_min :: p_min [out] The minimum pressure over which this EoS is fitted [Pa]
p_max :: p_max [out] The maximum pressure over which this EoS is fitted [Pa]

[source]

subroutine mom_eos_linear/set_params_linear(this, Rho_T0_S0, dRho_dT, dRho_dS, dRho_dp)

Set coefficients for the linear equation of state.

Parameters:

this :: this [inout] This EOS
rho_t0_s0 :: [in] The density at T=0, S=0 [kg m-3]
drho_dt :: [in] The derivative of density with temperature, [kg m-3 degC-1]
drho_ds :: [in] The derivative of density with salinity, in [kg m-3 ppt-1]
drho_dp :: [in] The derivative of density with pressure, in [s2 m-2]

[source]

subroutine mom_eos_linear/int_density_dz_linear(T, S, z_t, z_b, rho_ref, rho_0, G_e, HI, Rho_T0_S0, dRho_dT, dRho_dS, dRho_dp, dpa, intz_dpa, intx_dpa, inty_dpa, bathyT, SSH, dz_neglect, MassWghtInterp, Z_0p)

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.

Parameters:

hi :: [in] The horizontal index type for the arrays.
t :: [in] Potential temperature relative to the surface
s :: [in] Salinity [S ~> ppt].
z_t :: z_t [in] Height at the top of the layer in depth units [Z ~> m].
z_b :: z_b [in] Height at the top of the layer [Z ~> m].
rho_ref :: rho_ref [in] A mean density [R ~> kg m-3], that is subtracted out to reduce the magnitude of each of the integrals.
rho_0 :: rho_0 [in] A density [R ~> kg m-3], used to calculate the pressure (as p~=-z*rho_0*G_e) used in the equation of state.
g_e :: [in] The Earth’s gravitational acceleration [L2 Z-1 T-2 ~> m s-2]
rho_t0_s0 :: [in] The density at T=0, S=0 [R ~> kg m-3]
drho_dt :: [in] The derivative of density with temperature, [R C-1 ~> kg m-3 degC-1]
drho_ds :: [in] The derivative of density with salinity, in [R S-1 ~> kg m-3 ppt-1]
drho_dp :: [in] The derivative of density with pressure, in [L-2 T2 ~> m-2 s2]
dpa :: dpa [out] The change in the pressure anomaly across the
intz_dpa :: intz_dpa [out] The integral through the thickness of the layer
intx_dpa :: intx_dpa [out] The integral in x of the difference between the
inty_dpa :: inty_dpa [out] The integral in y of the difference between the
bathyt :: [in] The depth of the bathymetry [Z ~> m].
ssh :: [in] The sea surface height [Z ~> m]
dz_neglect :: dz_neglect [in] A miniscule thickness change [Z ~> m].
masswghtinterp :: [in] A flag indicating whether and how to use mass weighting to interpolate T/S in integrals
z_0p :: [in] The height at which the pressure is 0 [Z ~> m]

[source]

subroutine mom_eos_linear/int_spec_vol_dp_linear(T, S, p_t, p_b, alpha_ref, HI, Rho_T0_S0, dRho_dT, dRho_dS, dRho_dp, dza, intp_dza, intx_dza, inty_dza, halo_size, bathyP, P_surf, dP_neglect, MassWghtInterp)

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.

Parameters:

hi :: [in] The ocean’s horizontal index type.
t :: [in] Potential temperature relative to the surface
s :: [in] Salinity [S ~> ppt].
p_t :: p_t [in] Pressure at the top of the layer [R L2 T-2 ~> Pa]
p_b :: p_b [in] Pressure at the top of the layer [R L2 T-2 ~> Pa]
alpha_ref :: alpha_ref [in] 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 :: [in] The density at T=0, S=0 [R ~> kg m-3]
drho_dt :: [in] The derivative of density with temperature [R C-1 ~> kg m-3 degC-1]
drho_ds :: [in] The derivative of density with salinity, in [R S-1 ~> kg m-3 ppt-1]
drho_dp :: [in] The derivative of density with pressure, in [L-2 T2 ~> m-2 s2]
dza :: dza [out] The change in the geopotential anomaly across
intp_dza :: intp_dza [out] The integral in pressure through the layer of the
intx_dza :: intx_dza [out] The integral in x of the difference between the
inty_dza :: inty_dza [out] The integral in y of the difference between the
halo_size :: halo_size [in] The width of halo points on which to calculate dza.
bathyp :: [in] The pressure at the bathymetry [R L2 T-2 ~> Pa]
p_surf :: [in] The pressure at the ocean surface [R L2 T-2 ~> Pa]
dp_neglect :: [in] A miniscule pressure change with the same units as p_t [R L2 T-2 ~> Pa]
masswghtinterp :: [in] A flag indicating whether and how to use mass weighting to interpolate T/S in integrals