Freezing
Freezing-point functions.
- gsw.freezing.CT_freezing(SA, p, saturation_fraction)[source]
Calculates the Conservative Temperature at which seawater freezes. The Conservative Temperature freezing point is calculated from the exact in-situ freezing temperature which is found by a modified Newton-Raphson iteration (McDougall and Wotherspoon, 2014) of the equality of the chemical potentials of water in seawater and in ice.
- Parameters
- SAarray-like
Absolute Salinity, g/kg
- parray-like
Sea pressure (absolute pressure minus 10.1325 dbar), dbar
- saturation_fractionarray-like
Saturation fraction of dissolved air in seawater. (0..1)
- Returns
- CT_freezingarray-like, deg C
Conservative Temperature at freezing of seawater That is, the freezing temperature expressed in terms of Conservative Temperature (ITS-90).
- gsw.freezing.CT_freezing_first_derivatives(SA, p, saturation_fraction)[source]
Calculates the first derivatives of the Conservative Temperature at which seawater freezes, with respect to Absolute Salinity SA and pressure P (in Pa).
- Parameters
- SAarray-like
Absolute Salinity, g/kg
- parray-like
Sea pressure (absolute pressure minus 10.1325 dbar), dbar
- saturation_fractionarray-like
Saturation fraction of dissolved air in seawater. (0..1)
- Returns
- CTfreezing_SAarray-like, K kg/g
the derivative of the Conservative Temperature at freezing (ITS-90) with respect to Absolute Salinity at fixed pressure [ K/(g/kg) ] i.e.
- CTfreezing_Parray-like, K/Pa
the derivative of the Conservative Temperature at freezing (ITS-90) with respect to pressure (in Pa) at fixed Absolute Salinity
- gsw.freezing.CT_freezing_first_derivatives_poly(SA, p, saturation_fraction)[source]
Calculates the first derivatives of the Conservative Temperature at which seawater freezes, with respect to Absolute Salinity SA and pressure P (in Pa) of the comptationally efficient polynomial fit of the freezing temperature (McDougall et al., 2014).
- Parameters
- SAarray-like
Absolute Salinity, g/kg
- parray-like
Sea pressure (absolute pressure minus 10.1325 dbar), dbar
- saturation_fractionarray-like
Saturation fraction of dissolved air in seawater. (0..1)
- Returns
- CTfreezing_SAarray-like, K kg/g
the derivative of the Conservative Temperature at freezing (ITS-90) with respect to Absolute Salinity at fixed pressure [ K/(g/kg) ] i.e.
- CTfreezing_Parray-like, K/Pa
the derivative of the Conservative Temperature at freezing (ITS-90) with respect to pressure (in Pa) at fixed Absolute Salinity
- gsw.freezing.CT_freezing_poly(SA, p, saturation_fraction)[source]
Calculates the Conservative Temperature at which seawater freezes. The error of this fit ranges between -5e-4 K and 6e-4 K when compared with the Conservative Temperature calculated from the exact in-situ freezing temperature which is found by a Newton-Raphson iteration of the equality of the chemical potentials of water in seawater and in ice. Note that the Conservative Temperature freezing temperature can be found by this exact method using the function gsw_CT_freezing.
- Parameters
- SAarray-like
Absolute Salinity, g/kg
- parray-like
Sea pressure (absolute pressure minus 10.1325 dbar), dbar
- saturation_fractionarray-like
Saturation fraction of dissolved air in seawater. (0..1)
- Returns
- CT_freezingarray-like, deg C
Conservative Temperature at freezing of seawater That is, the freezing temperature expressed in terms of Conservative Temperature (ITS-90).
- gsw.freezing.SA_freezing_from_CT(CT, p, saturation_fraction)[source]
Calculates the Absolute Salinity of seawater at the freezing temperature. That is, the output is the Absolute Salinity of seawater, with Conservative Temperature CT, pressure p and the fraction saturation_fraction of dissolved air, that is in equilibrium with ice at the same in situ temperature and pressure. If the input values are such that there is no positive value of Absolute Salinity for which seawater is frozen, the output, SA_freezing, is made a NaN.
- Parameters
- CTarray-like
Conservative Temperature (ITS-90), degrees C
- parray-like
Sea pressure (absolute pressure minus 10.1325 dbar), dbar
- saturation_fractionarray-like
Saturation fraction of dissolved air in seawater. (0..1)
- Returns
- SA_freezingarray-like, g/kg
Absolute Salinity of seawater when it freezes, for given input values of its Conservative Temperature, pressure and air saturation fraction.
- gsw.freezing.SA_freezing_from_CT_poly(CT, p, saturation_fraction)[source]
Calculates the Absolute Salinity of seawater at the freezing temperature. That is, the output is the Absolute Salinity of seawater, with the fraction saturation_fraction of dissolved air, that is in equilibrium with ice at Conservative Temperature CT and pressure p. If the input values are such that there is no positive value of Absolute Salinity for which seawater is frozen, the output, SA_freezing, is put equal to NaN.
- Parameters
- CTarray-like
Conservative Temperature (ITS-90), degrees C
- parray-like
Sea pressure (absolute pressure minus 10.1325 dbar), dbar
- saturation_fractionarray-like
Saturation fraction of dissolved air in seawater. (0..1)
- Returns
- SA_freezingarray-like, g/kg
Absolute Salinity of seawater when it freezes, for given input values of Conservative Temperature pressure and air saturation fraction.
- gsw.freezing.SA_freezing_from_t(t, p, saturation_fraction)[source]
Calculates the Absolute Salinity of seawater at the freezing temperature. That is, the output is the Absolute Salinity of seawater, with the fraction saturation_fraction of dissolved air, that is in equilibrium with ice at in-situ temperature t and pressure p. If the input values are such that there is no positive value of Absolute Salinity for which seawater is frozen, the output, SA_freezing, is set to NaN.
- Parameters
- tarray-like
In-situ temperature (ITS-90), degrees C
- parray-like
Sea pressure (absolute pressure minus 10.1325 dbar), dbar
- saturation_fractionarray-like
Saturation fraction of dissolved air in seawater. (0..1)
- Returns
- SA_freezingarray-like, g/kg
Absolute Salinity of seawater when it freezes, for given input values of in situ temperature, pressure and air saturation fraction.
- gsw.freezing.SA_freezing_from_t_poly(t, p, saturation_fraction)[source]
Calculates the Absolute Salinity of seawater at the freezing temperature. That is, the output is the Absolute Salinity of seawater, with the fraction saturation_fraction of dissolved air, that is in equilibrium with ice at in-situ temperature t and pressure p. If the input values are such that there is no positive value of Absolute Salinity for which seawater is frozen, the output, SA_freezing, is put equal to NaN.
- Parameters
- tarray-like
In-situ temperature (ITS-90), degrees C
- parray-like
Sea pressure (absolute pressure minus 10.1325 dbar), dbar
- saturation_fractionarray-like
Saturation fraction of dissolved air in seawater. (0..1)
- Returns
- SA_freezingarray-like, g/kg
Absolute Salinity of seawater when it freezes, for given input values of in situ temperature, pressure and air saturation fraction.
- gsw.freezing.pot_enthalpy_ice_freezing(SA, p)[source]
Calculates the potential enthalpy of ice at which seawater freezes.
- Parameters
- SAarray-like
Absolute Salinity, g/kg
- parray-like
Sea pressure (absolute pressure minus 10.1325 dbar), dbar
- Returns
- pot_enthalpy_ice_freezingarray-like, J/kg
potential enthalpy of ice at freezing of seawater
- gsw.freezing.pot_enthalpy_ice_freezing_first_derivatives(SA, p)[source]
Calculates the first derivatives of the potential enthalpy of ice at which seawater freezes, with respect to Absolute Salinity SA and pressure P (in Pa).
- Parameters
- SAarray-like
Absolute Salinity, g/kg
- parray-like
Sea pressure (absolute pressure minus 10.1325 dbar), dbar
- Returns
- pot_enthalpy_ice_freezing_SAarray-like, K kg/g
the derivative of the potential enthalpy of ice at freezing (ITS-90) with respect to Absolute salinity at fixed pressure [ K/(g/kg) ] i.e.
- pot_enthalpy_ice_freezing_Parray-like, K/Pa
the derivative of the potential enthalpy of ice at freezing (ITS-90) with respect to pressure (in Pa) at fixed Absolute Salinity
- gsw.freezing.pot_enthalpy_ice_freezing_first_derivatives_poly(SA, p)[source]
Calculates the first derivatives of the potential enthalpy of ice Ih at which ice melts into seawater with Absolute Salinity SA and at pressure p. This code uses the comptationally efficient polynomial fit of the freezing potential enthalpy of ice Ih (McDougall et al., 2015).
- Parameters
- SAarray-like
Absolute Salinity, g/kg
- parray-like
Sea pressure (absolute pressure minus 10.1325 dbar), dbar
- Returns
- pot_enthalpy_ice_freezing_SAarray-like, J/g
the derivative of the potential enthalpy of ice at freezing (ITS-90) with respect to Absolute salinity at fixed pressure [ (J/kg)/(g/kg) ] i.e.
- pot_enthalpy_ice_freezing_Parray-like, (J/kg)/Pa
the derivative of the potential enthalpy of ice at freezing (ITS-90) with respect to pressure (in Pa) at fixed Absolute Salinity
- gsw.freezing.pot_enthalpy_ice_freezing_poly(SA, p)[source]
Calculates the potential enthalpy of ice at which seawater freezes. The error of this fit ranges between -2.5 and 1 J/kg with an rms of 1.07, between SA of 0 and 120 g/kg and p between 0 and 10,000 dbar (the error in the fit is between -0.7 and 0.7 with an rms of 0.3, between SA of 0 and 120 g/kg and p between 0 and 5,000 dbar) when compared with the potential enthalpy calculated from the exact in-situ freezing temperature which is found by a Newton-Raphson iteration of the equality of the chemical potentials of water in seawater and in ice. Note that the potential enthalpy at freezing can be found by this exact method using the function gsw_pot_enthalpy_ice_freezing.
- Parameters
- SAarray-like
Absolute Salinity, g/kg
- parray-like
Sea pressure (absolute pressure minus 10.1325 dbar), dbar
- Returns
- pot_enthalpy_ice_freezingarray-like, J/kg
potential enthalpy of ice at freezing of seawater
- gsw.freezing.pressure_freezing_CT(SA, CT, saturation_fraction)[source]
Calculates the pressure (in dbar) of seawater at the freezing temperature. That is, the output is the pressure at which seawater, with Absolute Salinity SA, Conservative Temperature CT, and with saturation_fraction of dissolved air, freezes. If the input values are such that there is no value of pressure in the range between 0 dbar and 10,000 dbar for which seawater is at the freezing temperature, the output, pressure_freezing, is put equal to NaN.
- Parameters
- SAarray-like
Absolute Salinity, g/kg
- CTarray-like
Conservative Temperature (ITS-90), degrees C
- saturation_fractionarray-like
Saturation fraction of dissolved air in seawater. (0..1)
- Returns
- pressure_freezingarray-like, dbar
sea pressure at which the seawater freezes ( i.e. absolute pressure - 10.1325 dbar )
- gsw.freezing.t_freezing(SA, p, saturation_fraction)[source]
Calculates the in-situ temperature at which seawater freezes. The in-situ temperature freezing point is calculated from the exact in-situ freezing temperature which is found by a modified Newton-Raphson iteration (McDougall and Wotherspoon, 2013) of the equality of the chemical potentials of water in seawater and in ice.
- Parameters
- SAarray-like
Absolute Salinity, g/kg
- parray-like
Sea pressure (absolute pressure minus 10.1325 dbar), dbar
- saturation_fractionarray-like
Saturation fraction of dissolved air in seawater. (0..1)
- Returns
- t_freezingarray-like, deg C
in-situ temperature at which seawater freezes. (ITS-90)
- gsw.freezing.t_freezing_first_derivatives(SA, p, saturation_fraction)[source]
Calculates the first derivatives of the in-situ temperature at which seawater freezes with respect to Absolute Salinity SA and pressure P (in Pa). These expressions come from differentiating the expression that defines the freezing temperature, namely the equality between the chemical potentials of water in seawater and in ice.
- Parameters
- SAarray-like
Absolute Salinity, g/kg
- parray-like
Sea pressure (absolute pressure minus 10.1325 dbar), dbar
- saturation_fractionarray-like
Saturation fraction of dissolved air in seawater. (0..1)
- Returns
- tfreezing_SAarray-like, K kg/g
the derivative of the in-situ freezing temperature (ITS-90) with respect to Absolute Salinity at fixed pressure [ K/(g/kg) ] i.e.
- tfreezing_Parray-like, K/Pa
the derivative of the in-situ freezing temperature (ITS-90) with respect to pressure (in Pa) at fixed Absolute Salinity
- gsw.freezing.t_freezing_first_derivatives_poly(SA, p, saturation_fraction)[source]
Calculates the first derivatives of the in-situ temperature at which seawater freezes with respect to Absolute Salinity SA and pressure P (in Pa). These expressions come from differentiating the expression that defines the freezing temperature, namely the equality between the chemical potentials of water in seawater and in ice.
- Parameters
- SAarray-like
Absolute Salinity, g/kg
- parray-like
Sea pressure (absolute pressure minus 10.1325 dbar), dbar
- saturation_fractionarray-like
Saturation fraction of dissolved air in seawater. (0..1)
- Returns
- tfreezing_SAarray-like, K kg/g
the derivative of the in-situ freezing temperature (ITS-90) with respect to Absolute Salinity at fixed pressure [ K/(g/kg) ] i.e.
- tfreezing_Parray-like, K/Pa
the derivative of the in-situ freezing temperature (ITS-90) with respect to pressure (in Pa) at fixed Absolute Salinity