Freezing

Freezing-point functions.

gsw.freezing.CT_freezing(SA, p, saturation_fraction)

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).

Notes

An alternative GSW function, gsw_CT_freezing_poly, it is based on a computationally-efficient polynomial, and is accurate to within -5e-4 K and 6e-4 K, when compared with this function.

References

IOC, SCOR and IAPSO, 2010: The international thermodynamic equation of seawater - 2010: Calculation and use of thermodynamic properties. Intergovernmental Oceanographic Commission, Manuals and Guides No. 56, UNESCO (English), 196 pp. Available from https://www.teos-10.org/. See sections 3.33 and 3.34 of this TEOS-10 Manual.

McDougall, T.J., and S.J. Wotherspoon, 2014: A simple modification of Newton’s method to achieve convergence of order 1 + sqrt(2). Applied Mathematics Letters, 29, 20-25.

gsw.freezing.CT_freezing_first_derivatives(SA, p, saturation_fraction)

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

References

IOC, SCOR and IAPSO, 2010: The international thermodynamic equation of seawater - 2010: Calculation and use of thermodynamic properties. Intergovernmental Oceanographic Commission, Manuals and Guides No. 56, UNESCO (English), 196 pp. Available from https://www.teos-10.org/.

gsw.freezing.CT_freezing_first_derivatives_poly(SA, p, saturation_fraction)

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

References

IOC, SCOR and IAPSO, 2010: The international thermodynamic equation of seawater - 2010: Calculation and use of thermodynamic properties. Intergovernmental Oceanographic Commission, Manuals and Guides No. 56, UNESCO (English), 196 pp. Available from https://www.teos-10.org/. See sections 3.33 and 3.34 of this TEOS-10 Manual.

McDougall, T.J., P.M. Barker, R. Feistel and B.K. Galton-Fenzi, 2014: Melting of Ice and Sea Ice into Seawater and Frazil Ice Formation. Journal of Physical Oceanography, 44, 1751-1775.

gsw.freezing.CT_freezing_poly(SA, p, saturation_fraction)

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).

References

IOC, SCOR and IAPSO, 2010: The international thermodynamic equation of seawater - 2010: Calculation and use of thermodynamic properties. Intergovernmental Oceanographic Commission, Manuals and Guides No. 56, UNESCO (English), 196 pp. Available from https://www.teos-10.org/. See sections 3.33 and 3.34 of this TEOS-10 Manual.

McDougall, T.J., P.M. Barker, R. Feistel and B.K. Galton-Fenzi, 2014: Melting of Ice and Sea Ice into Seawater and Frazil Ice Formation. Journal of Physical Oceanography, 44, 1751-1775.

gsw.freezing.SA_freezing_from_CT(CT, p, saturation_fraction)

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.

References

IOC, SCOR and IAPSO, 2010: The international thermodynamic equation of seawater - 2010: Calculation and use of thermodynamic properties. Intergovernmental Oceanographic Commission, Manuals and Guides No. 56, UNESCO (English), 196 pp. Available from https://www.teos-10.org/. See section 3.33 of this TEOS-10 Manual.

McDougall, T.J., P.M. Barker, R. Feistel and B.K. Galton-Fenzi, 2014: Melting of Ice and Sea Ice into Seawater and Frazil Ice Formation. Journal of Physical Oceanography, 44, 1751-1775.

McDougall, T.J., and S.J. Wotherspoon, 2014: A simple modification of Newton’s method to achieve convergence of order 1 + sqrt(2). Applied Mathematics Letters, 29, 20-25.

gsw.freezing.SA_freezing_from_CT_poly(CT, p, saturation_fraction)

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.

References

IOC, SCOR and IAPSO, 2010: The international thermodynamic equation of seawater - 2010: Calculation and use of thermodynamic properties. Intergovernmental Oceanographic Commission, Manuals and Guides No. 56, UNESCO (English), 196 pp. Available from https://www.teos-10.org/. See section 3.33 of this TEOS-10 Manual.

McDougall, T.J., P.M. Barker, R. Feistel and B.K. Galton-Fenzi, 2014: Melting of Ice and Sea Ice into Seawater and Frazil Ice Formation. Journal of Physical Oceanography, 44, 1751-1775.

McDougall T. J. and S. J. Wotherspoon, 2014: A simple modification of Newton’s method to achieve convergence of order 1 + sqrt(2). Applied Mathematics Letters, 29, 20-25.

gsw.freezing.SA_freezing_from_t(t, p, saturation_fraction)

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.

References

IOC, SCOR and IAPSO, 2010: The international thermodynamic equation of seawater - 2010: Calculation and use of thermodynamic properties. Intergovernmental Oceanographic Commission, Manuals and Guides No. 56, UNESCO (English), 196 pp. Available from https://www.teos-10.org/. See section 3.33 of this TEOS-10 Manual.

McDougall, T.J., P.M. Barker, R. Feistel and B.K. Galton-Fenzi, 2014: Melting of Ice and Sea Ice into Seawater and Frazil Ice Formation. Journal of Physical Oceanography, 44, 1751-1775.

McDougall, T.J., and S.J. Wotherspoon, 2013: A simple modification of Newton’s method to achieve convergence of order 1 + sqrt(2). Applied Mathematics Letters, 29, 20-25.

gsw.freezing.SA_freezing_from_t_poly(t, p, saturation_fraction)

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.

References

IOC, SCOR and IAPSO, 2010: The international thermodynamic equation of seawater - 2010: Calculation and use of thermodynamic properties. Intergovernmental Oceanographic Commission, Manuals and Guides No. 56, UNESCO (English), 196 pp. Available from https://www.teos-10.org/. See section 3.33 of this TEOS-10 Manual.

McDougall, T.J., P.M. Barker, R. Feistel and B.K. Galton-Fenzi, 2014: Melting of Ice and Sea Ice into Seawater and Frazil Ice Formation. Journal of Physical Oceanography, 44, 1751-1775.

McDougall T. J. and S. J. Wotherspoon, 2014: A simple modification of Newton’s method to achieve convergence of order 1 + sqrt(2). Applied Mathematics Letters, 29, 20-25.

gsw.freezing.pot_enthalpy_ice_freezing(SA, p)

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

References

IOC, SCOR and IAPSO, 2010: The international thermodynamic equation of seawater - 2010: Calculation and use of thermodynamic properties. Intergovernmental Oceanographic Commission, Manuals and Guides No. 56, UNESCO (English), 196 pp. Available from https://www.teos-10.org/. See sections 3.33 and 3.34 of this TEOS-10 Manual.

McDougall, T.J., P.M. Barker, R. Feistel and B.K. Galton-Fenzi, 2014: Melting of Ice and Sea Ice into Seawater and Frazil Ice Formation. Journal of Physical Oceanography, 44, 1751-1775.

gsw.freezing.pot_enthalpy_ice_freezing_first_derivatives(SA, p)

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

References

IOC, SCOR and IAPSO, 2010: The international thermodynamic equation of seawater - 2010: Calculation and use of thermodynamic properties. Intergovernmental Oceanographic Commission, Manuals and Guides No. 56, UNESCO (English), 196 pp. Available from https://www.teos-10.org/. See sections 3.33 and 3.34 of this TEOS-10 Manual.

McDougall, T.J., P.M. Barker, R. Feistel and B.K. Galton-Fenzi, 2014: Melting of Ice and Sea Ice into Seawater and Frazil Ice Formation. Journal of Physical Oceanography, 44, 1751-1775.

gsw.freezing.pot_enthalpy_ice_freezing_first_derivatives_poly(SA, p)

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 computationally 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

References

IOC, SCOR and IAPSO, 2010: The international thermodynamic equation of seawater - 2010: Calculation and use of thermodynamic properties. Intergovernmental Oceanographic Commission, Manuals and Guides No. 56, UNESCO (English), 196 pp. Available from https://www.teos-10.org/. See sections 3.33 and 3.34 of this TEOS-10 Manual.

McDougall, T.J., P.M. Barker, R. Feistel and B.K. Galton-Fenzi, 2014: Melting of Ice and Sea Ice into Seawater and Frazil Ice Formation. Journal of Physical Oceanography, 44, 1751-1775.

McDougall et al. 2015: A reference for this polynomial.

gsw.freezing.pot_enthalpy_ice_freezing_poly(SA, p)

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

References

IOC, SCOR and IAPSO, 2010: The international thermodynamic equation of seawater - 2010: Calculation and use of thermodynamic properties. Intergovernmental Oceanographic Commission, Manuals and Guides No. 56, UNESCO (English), 196 pp. Available from https://www.teos-10.org/. See sections 3.33 and 3.34 of this TEOS-10 Manual.

McDougall, T.J., P.M. Barker, R. Feistel and B.K. Galton-Fenzi, 2014: Melting of Ice and Sea Ice into Seawater and Frazil Ice Formation. Journal of Physical Oceanography, 44, 1751-1775.

gsw.freezing.pressure_freezing_CT(SA, CT, saturation_fraction)

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 )

References

IOC, SCOR and IAPSO, 2010: The international thermodynamic equation of seawater - 2010: Calculation and use of thermodynamic properties. Intergovernmental Oceanographic Commission, Manuals and Guides No. 56, UNESCO (English), 196 pp. Available from https://www.teos-10.org/. See section 3.33 of this TEOS-10 Manual.

McDougall T. J. and S. J. Wotherspoon, 2013: A simple modification of Newton’s method to achieve convergence of order 1 + sqrt(2). Applied Mathematics Letters, 29, 20-25.

gsw.freezing.t_freezing(SA, p, saturation_fraction)

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)

Notes

An alternative GSW function, gsw_t_freezing_poly, it is based on a computationally-efficient polynomial, and is accurate to within -5e-4 K and 6e-4 K, when compared with this function.

References

IOC, SCOR and IAPSO, 2010: The international thermodynamic equation of seawater - 2010: Calculation and use of thermodynamic properties. Intergovernmental Oceanographic Commission, Manuals and Guides No. 56, UNESCO (English), 196 pp. Available from https://www.teos-10.org/. See sections 3.33 and 3.34 of this TEOS-10 Manual.

McDougall T.J., and S.J. Wotherspoon, 2013: A simple modification of Newton’s method to achieve convergence of order 1 + sqrt(2). Applied Mathematics Letters, 29, 20-25.

gsw.freezing.t_freezing_first_derivatives(SA, p, saturation_fraction)

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

References

IOC, SCOR and IAPSO, 2010: The international thermodynamic equation of seawater - 2010: Calculation and use of thermodynamic properties. Intergovernmental Oceanographic Commission, Manuals and Guides No. 56, UNESCO (English), 196 pp. Available from https://www.teos-10.org/.

gsw.freezing.t_freezing_first_derivatives_poly(SA, p, saturation_fraction)

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

References

IOC, SCOR and IAPSO, 2010: The international thermodynamic equation of seawater - 2010: Calculation and use of thermodynamic properties. Intergovernmental Oceanographic Commission, Manuals and Guides No. 56, UNESCO (English), 196 pp. Available from https://www.teos-10.org/.

McDougall, T.J., P.M. Barker, R. Feistel and B.K. Galton-Fenzi, 2014: Melting of Ice and Sea Ice into Seawater and Frazil Ice Formation. Journal of Physical Oceanography, 44, 1751-1775.