namespace mom_eos¶
Overview¶
Provides subroutines for quantities specific to the equation of state. More…
namespace mom_eos { // interfaces interface calculate_density; interface calculate_density_derivs; interface calculate_density_second_derivs; interface calculate_spec_vol; interface calculate_tfreeze; // global variables integer, parameter, public eos_linear = 1; integer, parameter, public eos_unesco = 2; integer, parameter, public eos_wright = 3; integer, parameter, public eos_teos10 = 4; integer, parameter, public eos_nemo = 5; // global functions subroutine, public calculate_specific_vol_derivs( T T, S S, pressure pressure, dSV_dT dSV_dT, dSV_dS dSV_dS, start start, npts npts, EOS EOS ); subroutine, public calculate_compress( T T, S S, pressure pressure, rho rho, drho_dp drho_dp, start start, npts npts, EOS EOS ); subroutine, public int_specific_vol_dp( T T, S S, p_t p_t, p_b p_b, alpha_ref alpha_ref, HI HI, EOS EOS, 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 ); subroutine, public 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, HII HII, HIO HIO, EOS EOS, dpa dpa, intz_dpa intz_dpa, intx_dpa intx_dpa, inty_dpa inty_dpa, bathyT bathyT, dz_neglect dz_neglect, useMassWghtInterp useMassWghtInterp ); logical function, public query_compressible(EOS EOS); subroutine, public eos_init(param_file param_file, EOS EOS); subroutine, public eos_manual_init( EOS EOS, form_of_EOS form_of_EOS, form_of_TFreeze form_of_TFreeze, EOS_quadrature EOS_quadrature, Compressible Compressible, Rho_T0_S0 Rho_T0_S0, drho_dT drho_dT, dRho_dS dRho_dS, TFr_S0_P0 TFr_S0_P0, dTFr_dS dTFr_dS, dTFr_dp dTFr_dp ); subroutine, public eos_allocate(EOS EOS); subroutine, public eos_end(EOS EOS); subroutine, public eos_use_linear( Rho_T0_S0 Rho_T0_S0, dRho_dT dRho_dT, dRho_dS dRho_dS, EOS EOS, use_quadrature use_quadrature ); subroutine, public int_density_dz_generic( T T, S S, z_t z_t, z_b z_b, rho_ref rho_ref, rho_0 rho_0, G_e G_e, HII HII, HIO HIO, EOS EOS, dpa dpa, intz_dpa intz_dpa, intx_dpa intx_dpa, inty_dpa inty_dpa, bathyT bathyT, dz_neglect dz_neglect, useMassWghtInterp useMassWghtInterp ); subroutine, public int_density_dz_generic_plm( 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, rho_0 rho_0, G_e G_e, dz_subroundoff dz_subroundoff, bathyT bathyT, HII HII, HIO HIO, EOS EOS, dpa dpa, intz_dpa intz_dpa, intx_dpa intx_dpa, inty_dpa inty_dpa, useMassWghtInterp useMassWghtInterp ); subroutine, public 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, P_b P_b, z_out z_out, z_tol z_tol ); subroutine, public int_density_dz_generic_ppm( T T, T_t T_t, T_b T_b, S S, S_t S_t, S_b S_b, z_t z_t, z_b z_b, rho_ref rho_ref, rho_0 rho_0, G_e G_e, HII HII, HIO HIO, EOS EOS, dpa dpa, intz_dpa intz_dpa, intx_dpa intx_dpa, inty_dpa inty_dpa ); subroutine, public int_spec_vol_dp_generic( T T, S S, p_t p_t, p_b p_b, alpha_ref alpha_ref, HI HI, EOS EOS, 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 ); subroutine, public 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, dza dza, intp_dza intp_dza, intx_dza intx_dza, inty_dza inty_dza, useMassWghtInterp useMassWghtInterp ); subroutine, public convert_temp_salt_for_teos10(T T, S S, press press, G G, kd kd, mask_z mask_z, EOS EOS); subroutine, public extract_member_eos( EOS EOS, form_of_EOS form_of_EOS, form_of_TFreeze form_of_TFreeze, EOS_quadrature EOS_quadrature, Compressible Compressible, Rho_T0_S0 Rho_T0_S0, drho_dT drho_dT, dRho_dS dRho_dS, TFr_S0_P0 TFr_S0_P0, dTFr_dS dTFr_dS, dTFr_dp dTFr_dp ); } // namespace mom_eos
Detailed Documentation¶
Provides subroutines for quantities specific to the equation of state.
The MOM_EOS module is a wrapper for various equations of state (e.g. Linear, Wright, UNESCO) and provides a uniform interface to the rest of the model independent of which equation of state is being used.
Global Variables¶
integer, parameter, public eos_linear = 1
A named integer specifying an equation of state.
integer, parameter, public eos_unesco = 2
A named integer specifying an equation of state.
integer, parameter, public eos_wright = 3
A named integer specifying an equation of state.
integer, parameter, public eos_teos10 = 4
A named integer specifying an equation of state.
integer, parameter, public eos_nemo = 5
A named integer specifying an equation of state.
Global Functions¶
subroutine, public calculate_specific_vol_derivs( T T, S S, pressure pressure, dSV_dT dSV_dT, dSV_dS dSV_dS, start start, npts npts, EOS EOS )
Calls the appropriate subroutine to calculate specific volume derivatives for an array.
Parameters:
t |
Potential temperature referenced to the surface [degC] |
s |
Salinity [ppt] |
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 ppt-1]. |
start |
Starting index within the array |
npts |
The number of values to calculate |
eos |
Equation of state structure |
subroutine, public calculate_compress( T T, S S, pressure pressure, rho rho, drho_dp drho_dp, start start, npts npts, EOS EOS )
Calls the appropriate subroutine to calculate the density and compressibility for 1-D array inputs.
Parameters:
t |
Potential temperature referenced to the surface [degC] |
s |
Salinity [ppt] |
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) in s2 m-2. |
start |
Starting index within the array |
npts |
The number of values to calculate |
eos |
Equation of state structure |
subroutine, public int_specific_vol_dp( T T, S S, p_t p_t, p_b p_b, alpha_ref alpha_ref, HI HI, EOS EOS, 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 alculate 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 Bode’s rule to do the horizontal integrals, and from a truncation in the series for log(1-eps/1+eps) that assumes that |eps| < .
Parameters:
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 [Pa]. |
p_b |
Pressure at the bottom of the layer [Pa]. |
alpha_ref |
A mean specific volume that is subtracted out to reduce the magnitude of each of the integrals, 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 |
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 [Pa] |
dp_tiny |
A miniscule pressure change with the same units as p_t (Pa?) |
usemasswghtinterp |
If true, uses mass weighting to interpolate T/S for top and bottom integrals. |
subroutine, public 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, HII HII, HIO HIO, EOS EOS, 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.
Parameters:
hii |
Ocean horizontal index structures for the input arrays |
hio |
Ocean horizontal index structures for the output 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 [kg m-3], that is subtracted out to reduce the magnitude of each of the integrals. |
rho_0 |
A density [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 [m2 Z-1 s-2 ~> m s-2]. |
eos |
Equation of state structure |
dpa |
The change in the pressure anomaly across the layer [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 |
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. |
logical function, public query_compressible(EOS EOS)
Returns true if the equation of state is compressible (i.e. has pressure dependence)
Parameters:
eos |
Equation of state structure |
subroutine, public eos_init(param_file param_file, EOS EOS)
Initializes EOS_type by allocating and reading parameters.
Parameters:
param_file |
Parameter file structure |
eos |
Equation of state structure |
subroutine, public eos_manual_init( EOS EOS, form_of_EOS form_of_EOS, form_of_TFreeze form_of_TFreeze, EOS_quadrature EOS_quadrature, Compressible Compressible, Rho_T0_S0 Rho_T0_S0, drho_dT drho_dT, dRho_dS dRho_dS, TFr_S0_P0 TFr_S0_P0, dTFr_dS dTFr_dS, dTFr_dp dTFr_dp )
Manually initialized an EOS type (intended for unit testing of routines which need a specific EOS)
Parameters:
eos |
Equation of state structure |
form_of_eos |
A coded integer indicating the equation of state to use. |
form_of_tfreeze |
A coded integer indicating the expression for the potential temperature of the freezing point. |
eos_quadrature |
If true, always use the generic (quadrature) code for the integrals of density. |
compressible |
If true, in situ density is a function of pressure. |
rho_t0_s0 |
Density at T=0 degC and S=0 ppt [kg m-3] |
drho_dt |
Partial derivative of density with temperature in [kg m-3 degC-1] |
drho_ds |
Partial derivative of density with salinity in [kg m-3 ppt-1] |
tfr_s0_p0 |
The freezing potential temperature at S=0, P=0 [degC]. |
dtfr_ds |
The derivative of freezing point with salinity in [degC ppt-1]. |
dtfr_dp |
The derivative of freezing point with pressure in [degC Pa-1]. |
subroutine, public eos_allocate(EOS EOS)
Allocates EOS_type.
Parameters:
eos |
Equation of state structure |
subroutine, public eos_end(EOS EOS)
Deallocates EOS_type.
Parameters:
eos |
Equation of state structure |
subroutine, public eos_use_linear( Rho_T0_S0 Rho_T0_S0, dRho_dT dRho_dT, dRho_dS dRho_dS, EOS EOS, use_quadrature use_quadrature )
Set equation of state structure (EOS) to linear with given coefficients.
This routine is primarily for testing and allows a local copy of the EOS_type (EOS argument) to be set to use the linear equation of state independent from the rest of the model.
Parameters:
rho_t0_s0 |
Density at T=0 degC and S=0 ppt [kg m-3] |
drho_dt |
Partial derivative of density with temperature [kg m-3 degC-1] |
drho_ds |
Partial derivative of density with salinity [kg m-3 ppt-1] |
use_quadrature |
If true, always use the generic (quadrature) code for the integrals of density. |
eos |
Equation of state structure |
subroutine, public int_density_dz_generic( T T, S S, z_t z_t, z_b z_b, rho_ref rho_ref, rho_0 rho_0, G_e G_e, HII HII, HIO HIO, EOS EOS, 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 (by numerical quadrature) integrals of pressure anomalies across layers, which are required for calculating the finite-volume form pressure accelerations in a Boussinesq model.
Parameters:
hii |
Horizontal index type for input variables. |
hio |
Horizontal index type for output 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 [kg m-3], that is subtracted out to reduce the magnitude of each of the integrals. |
rho_0 |
A density [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 [m2 Z-1 s-2 ~> m s-2]. |
eos |
Equation of state structure |
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 miniscule thickness change [Z ~> m]. |
usemasswghtinterp |
If true, uses mass weighting to interpolate T/S for top and bottom integrals. |
subroutine, public int_density_dz_generic_plm( 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, rho_0 rho_0, G_e G_e, dz_subroundoff dz_subroundoff, bathyT bathyT, HII HII, HIO HIO, EOS EOS, 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.
Parameters:
hii |
Ocean horizontal index structures for the input arrays |
hio |
Ocean horizontal index structures for the output arrays |
t_t |
Potential temperatue at the cell top [degC] |
t_b |
Potential temperatue 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_b |
The geometric height at the bottom of the layer [Z ~> m]. |
rho_ref |
A mean density [kg m-3], that is subtracted out to reduce the magnitude of each of the integrals. |
rho_0 |
A density [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 [m2 Z-1 s-2 ~> m s-2]. |
dz_subroundoff |
A miniscule thickness change [Z ~> m]. |
bathyt |
The depth of the bathymetry [Z ~> m]. |
eos |
Equation of state structure |
dpa |
The change in the pressure anomaly across the layer [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 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, P_b P_b, z_out z_out, z_tol z_tol )
Find the depth at which the reconstructed pressure matches P_tgt.
Parameters:
t_t |
Potential temperatue at the cell top [degC] |
t_b |
Potential temperatue 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 [Pa] |
p_tgt |
Target pressure at height z_out, relative to g*rho_ref*z_out [Pa] |
rho_ref |
Reference density with which calculation are anomalous to |
g_e |
Gravitational acceleration [m2 Z-1 s-2 ~> m s-2] |
eos |
Equation of state structure |
p_b |
Pressure at the bottom of the cell [Pa] |
z_out |
Absolute depth at which anomalous pressure = p_tgt [Z ~> m]. |
z_tol |
The tolerance in finding z_out [Z ~> m]. |
subroutine, public int_density_dz_generic_ppm( T T, T_t T_t, T_b T_b, S S, S_t S_t, S_b S_b, z_t z_t, z_b z_b, rho_ref rho_ref, rho_0 rho_0, G_e G_e, HII HII, HIO HIO, EOS EOS, dpa dpa, intz_dpa intz_dpa, intx_dpa intx_dpa, inty_dpa inty_dpa )
Compute pressure gradient force integrals for the case where T and S are parabolic profiles.
Parameters:
hii |
Ocean horizontal index structures for the input arrays |
hio |
Ocean horizontal index structures for the output arrays |
t |
Potential temperature referenced to the surface [degC] |
t_t |
Potential temperatue at the cell top [degC] |
t_b |
Potential temperatue at the cell bottom [degC] |
s |
Salinity [ppt] |
s_t |
Salinity at the cell top [ppt] |
s_b |
Salinity at the cell bottom [ppt] |
z_t |
Height at the top of the layer [Z ~> m]. |
z_b |
Height at the bottom of the layer [Z ~> m]. |
rho_ref |
A mean density [kg m-3], that is subtracted out to reduce the magnitude of each of the integrals. |
rho_0 |
A density [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] |
eos |
Equation of state structure |
dpa |
The change in the pressure anomaly across the layer [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 |
subroutine, public int_spec_vol_dp_generic( T T, S S, p_t p_t, p_b p_b, alpha_ref alpha_ref, HI HI, EOS EOS, 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 Bode’s rule quadrature to do the integrals.
Parameters:
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 [Pa]. |
p_b |
Pressure below the layer [Pa]. |
alpha_ref |
A mean specific volume that is subtracted out to reduce the magnitude of each of the integrals [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 |
dza |
The change in the geopotential anomaly |
intp_dza |
The integral in pressure through the |
intx_dza |
The integral in x of the difference |
inty_dza |
The integral in y of the difference |
halo_size |
The width of halo points on which to calculate dza. |
bathyp |
The pressure at the bathymetry [Pa] |
dp_neglect |
A miniscule pressure change with the same units as p_t (Pa?) |
usemasswghtinterp |
If true, uses mass weighting to interpolate T/S for top and bottom integrals. |
subroutine, public 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, 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 Bode’s rule quadrature to do the integrals.
Parameters:
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 [Pa]. |
p_b |
Pressure below the layer [Pa]. |
alpha_ref |
A mean specific volume that is subtracted out to reduce the magnitude of each of the integrals [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 (Pa?) |
bathyp |
The pressure at the bathymetry [Pa] |
eos |
Equation of state structure |
dza |
The change in the geopotential anomaly |
intp_dza |
The integral in pressure through the |
intx_dza |
The integral in x of the difference |
inty_dza |
The integral in y of the difference |
usemasswghtinterp |
If true, uses mass weighting to interpolate T/S for top and bottom integrals. |
subroutine, public convert_temp_salt_for_teos10( T T, S S, press press, G G, kd kd, mask_z mask_z, EOS EOS )
Convert T&S to Absolute Salinity and Conservative Temperature if using TEOS10.
Parameters:
g |
The ocean’s grid structure |
t |
Potential temperature referenced to the surface [degC] |
s |
Salinity [ppt] |
press |
Pressure at the top of the layer [Pa]. |
eos |
Equation of state structure |
mask_z |
3d mask regulating which points to convert. |
kd |
The number of layers to work on |
subroutine, public extract_member_eos( EOS EOS, form_of_EOS form_of_EOS, form_of_TFreeze form_of_TFreeze, EOS_quadrature EOS_quadrature, Compressible Compressible, Rho_T0_S0 Rho_T0_S0, drho_dT drho_dT, dRho_dS dRho_dS, TFr_S0_P0 TFr_S0_P0, dTFr_dS dTFr_dS, dTFr_dp dTFr_dp )
Extractor routine for the EOS type if the members need to be accessed outside this module.
Parameters:
eos |
Equation of state structure |
form_of_eos |
A coded integer indicating the equation of state to use. |
form_of_tfreeze |
A coded integer indicating the expression for the potential temperature of the freezing point. |
eos_quadrature |
If true, always use the generic (quadrature) code for the integrals of density. |
compressible |
If true, in situ density is a function of pressure. |
rho_t0_s0 |
Density at T=0 degC and S=0 ppt [kg m-3] |
drho_dt |
Partial derivative of density with temperature in [kg m-3 degC-1] |
drho_ds |
Partial derivative of density with salinity in [kg m-3 ppt-1] |
tfr_s0_p0 |
The freezing potential temperature at S=0, P=0 [degC]. |
dtfr_ds |
The derivative of freezing point with salinity [degC PSU-1]. |
dtfr_dp |
The derivative of freezing point with pressure [degC Pa-1]. |