Ice

Functions about ice and melting, but not the freezing point.

gsw.ice.Helmholtz_energy_ice(t, p)[source]

Calculates the Helmholtz energy of ice.

Parameters:

tarray-like: In-situ temperature (ITS-90), degrees C
parray-like: Sea pressure (absolute pressure minus 10.1325 dbar), dbar

Returns:

Helmholtz_energy_icearray-like, J/kg: Helmholtz energy of ice

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.ice.adiabatic_lapse_rate_ice(t, p)[source]

Calculates the adiabatic lapse rate of ice.

Parameters:

tarray-like: In-situ temperature (ITS-90), degrees C
parray-like: Sea pressure (absolute pressure minus 10.1325 dbar), dbar

Returns:

adiabatic_lapse_rate_icearray-like, K/Pa: adiabatic lapse rate

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.ice.alpha_wrt_t_ice(t, p)[source]

Calculates the thermal expansion coefficient of ice with respect to in-situ temperature.

Parameters:

tarray-like: In-situ temperature (ITS-90), degrees C
parray-like: Sea pressure (absolute pressure minus 10.1325 dbar), dbar

Returns:

alpha_wrt_t_icearray-like, 1/K: thermal expansion coefficient of ice with respect to in-situ temperature

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 Eqn. (2.18.1) of this TEOS-10 manual.

gsw.ice.chem_potential_water_ice(t, p)[source]

Calculates the chemical potential of water in ice from in-situ temperature and pressure.

Parameters:

tarray-like: In-situ temperature (ITS-90), degrees C
parray-like: Sea pressure (absolute pressure minus 10.1325 dbar), dbar

Returns:

chem_potential_water_icearray-like, J/kg: chemical potential of ice

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.ice.cp_ice(t, p)[source]

Calculates the isobaric heat capacity of ice.

Parameters:

tarray-like: In-situ temperature (ITS-90), degrees C
parray-like: Sea pressure (absolute pressure minus 10.1325 dbar), dbar

Returns:

cp_icearray-like, J kg^-1 K^-1: heat capacity of ice

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.ice.enthalpy_ice(t, p)[source]

Calculates the specific enthalpy of ice (h_Ih).

Parameters:

tarray-like: In-situ temperature (ITS-90), degrees C
parray-like: Sea pressure (absolute pressure minus 10.1325 dbar), dbar

Returns:

enthalpy_icearray-like, J/kg: specific enthalpy of ice

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.ice.entropy_ice(t, p)[source]

Calculates specific entropy of ice.

Parameters:

tarray-like: In-situ temperature (ITS-90), degrees C
parray-like: Sea pressure (absolute pressure minus 10.1325 dbar), dbar

Returns:

ice_entropyarray-like, J kg^-1 K^-1: specific entropy of ice

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.ice.ice_fraction_to_freeze_seawater(SA, CT, p, t_Ih)[source]

Calculates the mass fraction of ice (mass of ice divided by mass of ice plus seawater), which, when melted into seawater having (SA,CT,p) causes the final dilute seawater to be at the freezing temperature. The other outputs are the Absolute Salinity and Conservative Temperature of the final diluted seawater.

Parameters:

SAarray-like: Absolute Salinity, g/kg
CTarray-like: Conservative Temperature (ITS-90), degrees C
parray-like: Sea pressure (absolute pressure minus 10.1325 dbar), dbar
t_Iharray-like: In-situ temperature of ice (ITS-90), degrees C

Returns:

SA_freezearray-like, g/kg: Absolute Salinity of seawater after the mass fraction of ice, ice_fraction, at temperature t_Ih has melted into the original seawater, and the final mixture is at the freezing temperature of seawater.
CT_freezearray-like, deg C: Conservative Temperature of seawater after the mass fraction, w_Ih, of ice at temperature t_Ih has melted into the original seawater, and the final mixture is at the freezing temperature of seawater.
w_Iharray-like, unitless: mass fraction of ice, having in-situ temperature t_Ih, which, when melted into seawater at (SA,CT,p) leads to the final diluted seawater being at the freezing temperature. This output must be between 0 and 1.

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.

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. See Eqn. (9) of this manuscript.

gsw.ice.internal_energy_ice(t, p)[source]

Calculates the specific internal energy of ice.

Parameters:

tarray-like: In-situ temperature (ITS-90), degrees C
parray-like: Sea pressure (absolute pressure minus 10.1325 dbar), dbar

Returns:

internal_energy_icearray-like, J/kg: specific internal energy (u)

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.ice.kappa_const_t_ice(t, p)[source]

Calculates isothermal compressibility of ice. Note. This is the compressibility of ice AT CONSTANT IN-SITU TEMPERATURE

Parameters:

tarray-like: In-situ temperature (ITS-90), degrees C
parray-like: Sea pressure (absolute pressure minus 10.1325 dbar), dbar

Returns:

kappa_const_t_icearray-like, 1/Pa: isothermal compressibility

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.ice.kappa_ice(t, p)[source]

Calculates the isentropic compressibility of ice.

Parameters:

tarray-like: In-situ temperature (ITS-90), degrees C
parray-like: Sea pressure (absolute pressure minus 10.1325 dbar), dbar

Returns:

kappa_icearray-like, 1/Pa: isentropic compressibility

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.ice.melting_ice_SA_CT_ratio(SA, CT, p, t_Ih)[source]

Calculates the ratio of SA to CT changes when ice melts into seawater. It is assumed that a small mass of ice melts into an infinite mass of seawater. Because of the infinite mass of seawater, the ice will always melt.

Parameters:

SAarray-like: Absolute Salinity, g/kg
CTarray-like: Conservative Temperature (ITS-90), degrees C
parray-like: Sea pressure (absolute pressure minus 10.1325 dbar), dbar
t_Iharray-like: In-situ temperature of ice (ITS-90), degrees C

Returns:

melting_ice_SA_CT_ratioarray-like, g kg^-1 K^-1: the ratio of SA to CT changes when ice melts into a large mass of seawater

Notes

The output, melting_seaice_SA_CT_ratio, is dSA/dCT rather than dCT/dSA. This is done so that when SA = 0, the output, dSA/dCT is zero whereas dCT/dSA would be infinite.

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. See Eqn. (13) of this manuscript.

gsw.ice.melting_ice_SA_CT_ratio_poly(SA, CT, p, t_Ih)[source]

Calculates the ratio of SA to CT changes when ice melts into seawater. It is assumed that a small mass of ice melts into an infinite mass of seawater. Because of the infinite mass of seawater, the ice will always melt.

Parameters:

SAarray-like: Absolute Salinity, g/kg
CTarray-like: Conservative Temperature (ITS-90), degrees C
parray-like: Sea pressure (absolute pressure minus 10.1325 dbar), dbar
t_Iharray-like: In-situ temperature of ice (ITS-90), degrees C

Returns:

melting_ice_SA_CT_ratioarray-like, g kg^-1 K^-1: the ratio of SA to CT changes when ice melts into a large mass of seawater

Notes

The output, melting_seaice_SA_CT_ratio, is dSA/dCT rather than dCT/dSA. This is done so that when SA = 0, the output, dSA/dCT is zero whereas dCT/dSA would be infinite.

Note that the 75-term equation has been fitted in a restricted range of parameter space, and is most accurate inside the “oceanographic funnel” described in McDougall et al. (2003). The GSW library function “gsw_infunnel(SA,CT,p)” is available to be used if one wants to test if some of one’s data lies outside this “funnel”.

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. See Eqn. (13) of this manuscript.

Roquet, F., G. Madec, T.J. McDougall, P.M. Barker, 2015: Accurate polynomial expressions for the density and specific volume of seawater using the TEOS-10 standard. Ocean Modelling., 90, pp. 29-43.

gsw.ice.melting_ice_equilibrium_SA_CT_ratio(SA, p)[source]

Calculates the ratio of SA to CT changes when ice melts into seawater with both the seawater and the seaice temperatures being almost equal to the equilibrium freezing temperature. It is assumed that a small mass of ice melts into an infinite mass of seawater. If indeed the temperature of the seawater and the ice were both equal to the freezing temperature, then no melting or freezing would occur; an imbalance between these three temperatures is needed for freezing or melting to occur (the three temperatures being (1) the seawater temperature, (2) the ice temperature, and (3) the freezing temperature.

Parameters:

SAarray-like: Absolute Salinity, g/kg
parray-like: Sea pressure (absolute pressure minus 10.1325 dbar), dbar

Returns:

melting_ice_equilibrium_SA_CT_ratioarray-like, g/(kg K): the ratio dSA/dCT of SA to CT changes when ice melts into seawater, with the seawater and seaice being close to the freezing temperature.

Notes

The output, melting_ice_equilibrium_SA_CT_ratio, is dSA/dCT rather than dCT/dSA. This is done so that when SA = 0, the output, dSA/dCT is zero whereas dCT/dSA would be infinite.

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. See Eqn. (16) of this manuscript.

gsw.ice.melting_ice_equilibrium_SA_CT_ratio_poly(SA, p)[source]

Calculates the ratio of SA to CT changes when ice melts into seawater with both the seawater and the seaice temperatures being almost equal to the equilibrium freezing temperature. It is assumed that a small mass of ice melts into an infinite mass of seawater. If indeed the temperature of the seawater and the ice were both equal to the freezing temperature, then no melting or freezing would occur; an imbalance between these three temperatures is needed for freezing or melting to occur (the three temperatures being (1) the seawater temperature, (2) the ice temperature, and (3) the freezing temperature.

Parameters:

SAarray-like: Absolute Salinity, g/kg
parray-like: Sea pressure (absolute pressure minus 10.1325 dbar), dbar

Returns:

melting_ice_equilibrium_SA_CT_ratioarray-like, g/(kg K): the ratio dSA/dCT of SA to CT changes when ice melts into seawater, with the seawater and seaice being close to the freezing temperature.

Notes

The output, melting_ice_equilibrium_SA_CT_ratio, is dSA/dCT rather than dCT/dSA. This is done so that when SA = 0, the output, dSA/dCT is zero whereas dCT/dSA would be infinite.

Note that the 75-term equation has been fitted in a restricted range of parameter space, and is most accurate inside the “oceanographic funnel” described in McDougall et al. (2003). The GSW library function “gsw_infunnel(SA,CT,p)” is available to be used if one wants to test if some of one’s data lies outside this “funnel”.

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. See Eqn. (16) of this manuscript.

Roquet, F., G. Madec, T.J. McDougall, P.M. Barker, 2015: Accurate polynomial expressions for the density and specific volume of seawater using the TEOS-10 standard. Ocean Modelling., 90, pp. 29-43.

gsw.ice.melting_ice_into_seawater(SA, CT, p, w_Ih, t_Ih)[source]

Calculates the final Absolute Salinity, final Conservative Temperature and final ice mass fraction that results when a given mass fraction of ice melts and is mixed into seawater whose properties are (SA,CT,p). This code takes the seawater to contain no dissolved air.

Parameters:

SAarray-like: Absolute Salinity, g/kg
CTarray-like: Conservative Temperature (ITS-90), degrees C
parray-like: Sea pressure (absolute pressure minus 10.1325 dbar), dbar
w_Iharray-like: mass fraction of ice: the mass of ice divided by the sum of the masses of ice and seawater. 0 <= wIh <= 1. unitless.
t_Iharray-like: In-situ temperature of ice (ITS-90), degrees C

Returns:

SA_finalarray-like, g/kg: Absolute Salinity of the seawater in the final state, whether or not any ice is present.
CT_finalarray-like, deg C: Conservative Temperature of the seawater in the final state, whether or not any ice is present.
w_Ih_finalarray-like, unitless: mass fraction of ice in the final seawater-ice mixture. If this ice mass fraction is positive, the system is at thermodynamic equilibrium. If this ice mass fraction is zero there is no ice in the final state which consists only of seawater which is warmer than the freezing temperature.

Notes

When the mass fraction w_Ih_final is calculated as being a positive value, the seawater-ice mixture is at thermodynamic equilibrium.

This code returns w_Ih_final = 0 when the input bulk enthalpy, h_bulk, is sufficiently large (i.e. sufficiently “warm”) so that there is no ice present in the final state. In this case the final state consists of only seawater rather than being an equilibrium mixture of seawater and ice which occurs when w_Ih_final is positive. Note that when w_Ih_final = 0, the final seawater is not at the freezing temperature.

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.

gsw.ice.melting_seaice_SA_CT_ratio(SA, CT, p, SA_seaice, t_seaice)[source]

Calculates the ratio of SA to CT changes when sea ice melts into seawater. It is assumed that a small mass of sea ice melts into an infinite mass of seawater. Because of the infinite mass of seawater, the sea ice will always melt.

Parameters:

SAarray-like: Absolute Salinity, g/kg
CTarray-like: Conservative Temperature (ITS-90), degrees C
parray-like: Sea pressure (absolute pressure minus 10.1325 dbar), dbar
SA_seaicearray-like: Absolute Salinity of sea ice: the mass fraction of salt in sea ice, expressed in g of salt per kg of sea ice.
t_seaicearray-like: In-situ temperature of the sea ice at pressure p (ITS-90), degrees C

Returns:

melting_seaice_SA_CT_ratioarray-like, g/(kg K): the ratio dSA/dCT of SA to CT changes when sea ice melts into a large mass of seawater

Notes

Ice formed at the sea surface (sea ice) typically contains between 2 g/kg and 12 g/kg of salt (defined as the mass of salt divided by the mass of ice Ih plus brine) and this programme returns NaN’s if the input SA_seaice is greater than 15 g/kg. If the SA_seaice input is not zero, usually this would imply that the pressure p should be zero, as sea ice only occurs near the sea surface. The code does not impose that p = 0 if SA_seaice is non-zero. Rather, this is left to the user.

The Absolute Salinity, SA_brine, of the brine trapped in little pockets in the sea ice, is in thermodynamic equilibrium with the ice Ih that surrounds these pockets. As the seaice temperature, t_seaice, may be less than the freezing temperature, SA_brine is usually greater than the Absolute Salinity of the seawater at the time and place when and where the sea ice was formed. So usually SA_brine will be larger than SA.

The output, melting_seaice_SA_CT_ratio, is dSA/dCT rather than dCT/dSA. This is done so that when (SA - seaice_SA) = 0, the output, dSA/dCT is zero whereas dCT/dSA would be infinite.

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. See Eqn. (28) of this manuscript.

gsw.ice.melting_seaice_SA_CT_ratio_poly(SA, CT, p, SA_seaice, t_seaice)[source]

Calculates the ratio of SA to CT changes when sea ice melts into seawater. It is assumed that a small mass of sea ice melts into an infinite mass of seawater. Because of the infinite mass of seawater, the sea ice will always melt.

Parameters:

SAarray-like: Absolute Salinity, g/kg
CTarray-like: Conservative Temperature (ITS-90), degrees C
parray-like: Sea pressure (absolute pressure minus 10.1325 dbar), dbar
SA_seaicearray-like: Absolute Salinity of sea ice: the mass fraction of salt in sea ice, expressed in g of salt per kg of sea ice.
t_seaicearray-like: In-situ temperature of the sea ice at pressure p (ITS-90), degrees C

Returns:

melting_seaice_SA_CT_ratioarray-like, g/(kg K): the ratio dSA/dCT of SA to CT changes when sea ice melts into a large mass of seawater

Notes

Ice formed at the sea surface (sea ice) typically contains between 2 g/kg and 12 g/kg of salt (defined as the mass of salt divided by the mass of ice Ih plus brine) and this programme returns NaN’s if the input SA_seaice is greater than 15 g/kg. If the SA_seaice input is not zero, usually this would imply that the pressure p should be zero, as sea ice only occurs near the sea surface. The code does not impose that p = 0 if SA_seaice is non-zero. Rather, this is left to the user.

The Absolute Salinity, SA_brine, of the brine trapped in little pockets in the sea ice, is in thermodynamic equilibrium with the ice Ih that surrounds these pockets. As the seaice temperature, t_seaice, may be less than the freezing temperature, SA_brine is usually greater than the Absolute Salinity of the seawater at the time and place when and where the sea ice was formed. So usually SA_brine will be larger than SA.

The output, melting_seaice_SA_CT_ratio, is dSA/dCT rather than dCT/dSA. This is done so that when (SA - seaice_SA) = 0, the output, dSA/dCT is zero whereas dCT/dSA would be infinite.

Note that the 75-term equation has been fitted in a restricted range of parameter space, and is most accurate inside the “oceanographic funnel” described in McDougall et al. (2003). The GSW library function “gsw_infunnel(SA,CT,p)” is available to be used if one wants to test if some of one’s data lies outside this “funnel”.

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. See Eqn. (31) of this manuscript.

Roquet, F., G. Madec, T.J. McDougall, P.M. Barker, 2015: Accurate polynomial expressions for the density and specific volume of seawater using the TEOS-10 standard. Ocean Modelling., 90, pp. 29-43.

gsw.ice.melting_seaice_equilibrium_SA_CT_ratio(SA, p)[source]

Calculates the ratio of SA to CT changes when sea ice melts into seawater with both the seawater and the sea ice temperatures being almost equal to the equilibrium freezing temperature. It is assumed that a small mass of seaice melts into an infinite mass of seawater. If indeed the temperature of the seawater and the sea ice were both equal to the freezing temperature, then no melting or freezing would occur; an imbalance between these three temperatures is needed for freezing or melting to occur (the three temperatures being (1) the seawater temperature, (2) the sea ice temperature, and (3) the freezing temperature.

Parameters:

SAarray-like: Absolute Salinity, g/kg
parray-like: Sea pressure (absolute pressure minus 10.1325 dbar), dbar

Returns:

melting_seaice_equilibrium_SA_CT_ratioarray-like, g/(kg K): the ratio dSA/dCT of SA to CT changes when sea ice melts into seawater, with the seawater and sea ice being close to the freezing temperature.

Notes

Note that the output of this function, dSA/dCT is independent of the sea ice salinity, SA_seaice. That is, the output applies equally to pure ice Ih and to sea ice with seaice salinity, SA_seaice. This result is proven in McDougall et al. (2014).

The output, melting_seaice_equilibrium_SA_CT_ratio, is dSA/dCT rather than dCT/dSA. This is done so that when SA = 0, the output, dSA/dCT is zero whereas dCT/dSA would be infinite.

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. See Eqn. (29) of this manuscript.

gsw.ice.melting_seaice_equilibrium_SA_CT_ratio_poly(SA, p)[source]

Calculates the ratio of SA to CT changes when sea ice melts into seawater with both the seawater and the sea ice temperatures being almost equal to the equilibrium freezing temperature. It is assumed that a small mass of seaice melts into an infinite mass of seawater. If indeed the temperature of the seawater and the sea ice were both equal to the freezing temperature, then no melting or freezing would occur; an imbalance between these three temperatures is needed for freezing or melting to occur (the three temperatures being (1) the seawater temperature, (2) the sea ice temperature, and (3) the freezing temperature.

Parameters:

SAarray-like: Absolute Salinity, g/kg
parray-like: Sea pressure (absolute pressure minus 10.1325 dbar), dbar

Returns:

melting_seaice_equilibrium_SA_CT_ratioarray-like, g/(kg K): the ratio dSA/dCT of SA to CT changes when sea ice melts into seawater, with the seawater and sea ice being close to the freezing temperature.

Notes

Note that the output of this function, dSA/dCT is independent of the sea ice salinity, SA_seaice. That is, the output applies equally to pure ice Ih and to sea ice with seaice salinity, SA_seaice. This result is proven in McDougall et al. (2014).

The output, melting_seaice_equilibrium_SA_CT_ratio, is dSA/dCT rather than dCT/dSA. This is done so that when SA = 0, the output, dSA/dCT is zero whereas dCT/dSA would be infinite.

Note that the 75-term equation has been fitted in a restricted range of parameter space, and is most accurate inside the “oceanographic funnel” described in McDougall et al. (2003). The GSW library function “gsw_infunnel(SA,CT,p)” is available to be used if one wants to test if some of one’s data lies outside this “funnel”.

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. See Eqn. (29) of this manuscript.

Roquet, F., G. Madec, T.J. McDougall, P.M. Barker, 2015: Accurate polynomial expressions for the density and specific volume of seawater using the TEOS-10 standard. Ocean Modelling., 90, pp. 29-43.

gsw.ice.melting_seaice_into_seawater(SA, CT, p, w_seaice, SA_seaice, t_seaice)[source]

Calculates the Absolute Salinity and Conservative Temperature that results when a given mass of sea ice (or ice) melts and is mixed into a known mass of seawater (whose properties are (SA,CT,p)).

Parameters:

SAarray-like: Absolute Salinity, g/kg
CTarray-like: Conservative Temperature (ITS-90), degrees C
parray-like: Sea pressure (absolute pressure minus 10.1325 dbar), dbar
w_seaicearray-like: mass fraction of ice: the mass of sea-ice divided by the sum of the masses of sea-ice and seawater. 0 <= wIh <= 1. unitless.
SA_seaicearray-like: Absolute Salinity of sea ice: the mass fraction of salt in sea ice, expressed in g of salt per kg of sea ice.
t_seaicearray-like: In-situ temperature of the sea ice at pressure p (ITS-90), degrees C

Returns:

SA_finalarray-like, g/kg: Absolute Salinity of the mixture of the melted sea ice (or ice) and the original seawater
CT_finalarray-like, deg C: Conservative Temperature of the mixture of the melted sea ice (or ice) and the original seawater

Notes

If the ice contains no salt (e.g. if it is of glacial origin), then the input ‘SA_seaice’ should be set to zero.

Ice formed at the sea surface (sea ice) typically contains between 2 g/kg and 12 g/kg of salt (defined as the mass of salt divided by the mass of ice Ih plus brine) and this programme returns NaN’s if the input SA_seaice is greater than 15 g/kg. If the SA_seaice input is not zero, usually this would imply that the pressure p should be zero, as sea ice only occurs near the sea surface. The code does not impose that p = 0 if SA_seaice is non-zero. Rather, this is left to the user.

The Absolute Salinity, SA_brine, of the brine trapped in little pockets in the sea ice, is in thermodynamic equilibrium with the ice Ih that surrounds these pockets. As the sea ice temperature, t_seaice, may be less than the freezing temperature, SA_brine is usually greater than the Absolute Salinity of the seawater at the time and place when and where the sea ice was formed. So usually SA_brine will be larger than SA.

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. Eqns. (8) and (9) are the simplifications when SA_seaice = 0.

gsw.ice.pot_enthalpy_from_pt_ice(pt0_ice)[source]

Calculates the potential enthalpy of ice from potential temperature of ice (whose reference sea pressure is zero dbar).

Parameters:

pt0_icearray-like: Potential temperature of ice (ITS-90), degrees C

Returns:

pot_enthalpy_icearray-like, J/kg: potential enthalpy of ice

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.ice.pot_enthalpy_from_pt_ice_poly(pt0_ice)[source]

Calculates the potential enthalpy of ice from potential temperature of ice (whose reference sea pressure is zero dbar). This is a compuationally efficient polynomial fit to the potential enthalpy of ice.

Parameters:

pt0_icearray-like: Potential temperature of ice (ITS-90), degrees C

Returns:

pot_enthalpy_icearray-like, J/kg: potential enthalpy of ice

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.ice.pressure_coefficient_ice(t, p)[source]

Calculates pressure coefficient of ice.

Parameters:

tarray-like: In-situ temperature (ITS-90), degrees C
parray-like: Sea pressure (absolute pressure minus 10.1325 dbar), dbar

Returns:

pressure_coefficient_icearray-like, Pa/K: pressure coefficient of ice

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 Eqn. (2.15.1) of this TEOS-10 Manual.

gsw.ice.pt0_from_t_ice(t, p)[source]

Calculates potential temperature of ice Ih with a reference pressure of 0 dbar, from in-situ temperature, t.

Parameters:

tarray-like: In-situ temperature (ITS-90), degrees C
parray-like: Sea pressure (absolute pressure minus 10.1325 dbar), dbar

Returns:

pt0_icearray-like, deg C: potential temperature of ice Ih with reference pressure of zero dbar (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 appendix I 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.ice.pt_from_pot_enthalpy_ice(pot_enthalpy_ice)[source]

Calculates the potential temperature of ice from the potential enthalpy of ice. The reference sea pressure of both the potential temperature and the potential enthalpy is zero dbar.

Parameters:

pot_enthalpy_icearray-like: Potential enthalpy of ice, J/kg

Returns:

pt0_icearray-like, deg C: potential temperature of ice (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/

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.ice.pt_from_pot_enthalpy_ice_poly(pot_enthalpy_ice)[source]

Calculates the potential temperature of ice (whose reference sea pressure is zero dbar) from the potential enthalpy of ice. This is a compuationally efficient polynomial fit to the potential enthalpy of ice.

Parameters:

pot_enthalpy_icearray-like: Potential enthalpy of ice, J/kg

Returns:

pt0_icearray-like, deg C: potential temperature of ice (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/

gsw.ice.pt_from_t_ice(t, p, p_ref)[source]

Calculates potential temperature of ice Ih with the general reference pressure, p_ref, from in-situ temperature, t.

Parameters:

tarray-like: In-situ temperature (ITS-90), degrees C
parray-like: Sea pressure (absolute pressure minus 10.1325 dbar), dbar
p_refarray-like: Reference pressure, dbar

Returns:

pt_icearray-like, deg C: potential temperature of ice Ih with reference pressure, p_ref, on the ITS-90 temperature scale

Notes

A faster gsw routine exists if p_ref is indeed zero dbar. This routine is “gsw_pt0_from_t_ice(t,p)”.

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 appendix I 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.ice.rho_ice(t, p)[source]

Calculates in-situ density of ice from in-situ temperature and pressure. Note that the output, rho_ice, is density, not density anomaly; that is, 1000 kg/m^3 is not subtracted from it.

Parameters:

tarray-like: In-situ temperature (ITS-90), degrees C
parray-like: Sea pressure (absolute pressure minus 10.1325 dbar), dbar

Returns:

rho_icearray-like, kg/m^3: in-situ density of ice (not density anomaly)

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.ice.seaice_fraction_to_freeze_seawater(SA, CT, p, SA_seaice, t_seaice)[source]

Calculates the mass fraction of sea ice (mass of sea ice divided by mass of sea ice plus seawater), which, when melted into seawater having the properties (SA,CT,p) causes the final seawater to be at the freezing temperature. The other outputs are the Absolute Salinity and Conservative Temperature of the final seawater.

Parameters:

SAarray-like: Absolute Salinity, g/kg
CTarray-like: Conservative Temperature (ITS-90), degrees C
parray-like: Sea pressure (absolute pressure minus 10.1325 dbar), dbar
SA_seaicearray-like: Absolute Salinity of sea ice: the mass fraction of salt in sea ice, expressed in g of salt per kg of sea ice.
t_seaicearray-like: In-situ temperature of the sea ice at pressure p (ITS-90), degrees C

Returns:

SA_freezearray-like, g/kg: Absolute Salinity of seawater after the mass fraction of sea ice, w_seaice, at temperature t_seaice has melted into the original seawater, and the final mixture is at the freezing temperature of seawater.
CT_freezearray-like, deg C: Conservative Temperature of seawater after the mass fraction, w_seaice, of sea ice at temperature t_seaice has melted into the original seawater, and the final mixture is at the freezing temperature of seawater.
w_seaicearray-like, unitless: mass fraction of sea ice, at SA_seaice and t_seaice, which, when melted into seawater at (SA,CT,p) leads to the final mixed seawater being at the freezing temperature. This output is between 0 and 1.

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.

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. See Eqn. (23) of this manuscript.

gsw.ice.sound_speed_ice(t, p)[source]

Calculates the compression speed of sound in ice.

Parameters:

tarray-like: In-situ temperature (ITS-90), degrees C
parray-like: Sea pressure (absolute pressure minus 10.1325 dbar), dbar

Returns:

sound_speed_icearray-like, m/s: compression speed of sound in ice

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.ice.specvol_ice(t, p)[source]

Calculates the specific volume of ice.

Parameters:

tarray-like: In-situ temperature (ITS-90), degrees C
parray-like: Sea pressure (absolute pressure minus 10.1325 dbar), dbar

Returns:

specvol_icearray-like, m^3/kg: specific volume

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.ice.t_from_pt0_ice(pt0_ice, p)[source]

Calculates in-situ temperature from the potential temperature of ice Ih with reference pressure, p_ref, of 0 dbar (the surface), and the in-situ pressure.

Parameters:

pt0_icearray-like: Potential temperature of ice (ITS-90), degrees C
parray-like: Sea pressure (absolute pressure minus 10.1325 dbar), dbar

Returns:

tarray-like, deg C: in-situ 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 appendix I of this TEOS-10 Manual.