# All functions¶

The following section documents all functions alphabetically.

This is a Python implementation of the Gibbs SeaWater (GSW) Oceanographic Toolbox of TEOS-10. Extensive documentation is available from http://www.teos-10.org/; users of this Python package are strongly encouraged to study the documents posted there.

This implementation is based on GSW-C for core functions, with additional functions written in Python. GSW-C is the work of Frank Delahoyde and Glenn Hyland (author of GSW-Fortran, on which GSW-C is based), who translated and re-implemented the algorithms originally written in Matlab by David Jackett, Trevor McDougall, and Paul Barker.

The present Python library has an interface that is similar to the original Matlab code, but with a few important differences:

• Many functions in the GSW-Matlab toolbox are not yet available here.

• Taking advantage of Python namespaces, we omit the “gsw” prefix from the function names.

• Missing values may be handled using numpy.ma masked arrays, or using nan values.

• All functions follow numpy broadcasting rules; function arguments must be broadcastable to the dimensions of the highest-dimensioned argument. Recall that with numpy broadcasting, extra dimensions are automatically added as needed on the left, but must be added explicitly as needed on the right.

• Functions such as Nsquared that operate on profiles rather than scalars have an axis keyword argument to specify the index that is incremented along the pressure (depth) axis.

`gsw.``CT_first_derivatives`(SA, pt)[source]

Calculates the following two derivatives of Conservative Temperature (1) CT_SA, the derivative with respect to Absolute Salinity at constant potential temperature (with pr = 0 dbar), and 2) CT_pt, the derivative with respect to potential temperature (the regular potential temperature which is referenced to 0 dbar) at constant Absolute Salinity.

Parameters
SAarray-like

Absolute Salinity, g/kg

ptarray-like

Potential temperature referenced to a sea pressure, degrees C

Returns
CT_SAarray-like, K/(g/kg)

The derivative of Conservative Temperature with respect to Absolute Salinity at constant potential temperature (the regular potential temperature which has reference sea pressure of 0 dbar).

CT_ptarray-like, unitless

The derivative of Conservative Temperature with respect to potential temperature (the regular one with pr = 0 dbar) at constant SA. CT_pt is dimensionless.

`gsw.``CT_first_derivatives_wrt_t_exact`(SA, t, p)[source]

Calculates the following three derivatives of Conservative Temperature. These derivatives are done with respect to in-situ temperature t (in the case of CT_T_wrt_t) or at constant in-situ tempertature (in the cases of CT_SA_wrt_t and CT_P_wrt_t). (1) CT_SA_wrt_t, the derivative of CT with respect to Absolute Salinity at constant t and p, and (2) CT_T_wrt_t, derivative of CT with respect to in-situ temperature t at constant SA and p. (3) CT_P_wrt_t, derivative of CT with respect to pressure P (in Pa) at constant SA and t.

Parameters
SAarray-like

Absolute Salinity, g/kg

tarray-like

In-situ temperature (ITS-90), degrees C

parray-like

Sea pressure (absolute pressure minus 10.1325 dbar), dbar

Returns
CT_SA_wrt_tarray-like, K kg/g

The first derivative of Conservative Temperature with respect to Absolute Salinity at constant t and p. [ K/(g/kg)] i.e.

CT_T_wrt_tarray-like, unitless

The first derivative of Conservative Temperature with respect to in-situ temperature, t, at constant SA and p.

CT_P_wrt_tarray-like, K/Pa

The first derivative of Conservative Temperature with respect to pressure P (in Pa) at constant SA and t.

`gsw.``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.``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.``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.``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.``CT_from_enthalpy`(SA, h, p)[source]

Calculates the Conservative Temperature of seawater, given the Absolute Salinity, specific enthalpy, h, and pressure p. The specific enthalpy input is the one calculated from the computationally-efficient expression for specific volume in terms of SA, CT and p (Roquet et al., 2015).

Parameters
SAarray-like

Absolute Salinity, g/kg

harray-like

Specific enthalpy, J/kg

parray-like

Sea pressure (absolute pressure minus 10.1325 dbar), dbar

Returns
CTarray-like, deg C

Conservative Temperature ( ITS-90)

`gsw.``CT_from_enthalpy_exact`(SA, h, p)[source]

Calculates the Conservative Temperature of seawater, given the Absolute Salinity, SA, specific enthalpy, h, and pressure p. The specific enthalpy input is calculated from the full Gibbs function of seawater, gsw_enthalpy_t_exact.

Parameters
SAarray-like

Absolute Salinity, g/kg

harray-like

Specific enthalpy, J/kg

parray-like

Sea pressure (absolute pressure minus 10.1325 dbar), dbar

Returns
CTarray-like, deg C

Conservative Temperature ( ITS-90)

`gsw.``CT_from_entropy`(SA, entropy)[source]

Calculates Conservative Temperature with entropy as an input variable.

Parameters
SAarray-like

Absolute Salinity, g/kg

entropyarray-like

Specific entropy, J/(kg*K)

Returns
CTarray-like, deg C

Conservative Temperature (ITS-90)

`gsw.``CT_from_pt`(SA, pt)[source]

Calculates Conservative Temperature of seawater from potential temperature (whose reference sea pressure is zero dbar).

Parameters
SAarray-like

Absolute Salinity, g/kg

ptarray-like

Potential temperature referenced to a sea pressure, degrees C

Returns
CTarray-like, deg C

Conservative Temperature (ITS-90)

`gsw.``CT_from_rho`(rho, SA, p)[source]

Calculates the Conservative Temperature of a seawater sample, for given values of its density, Absolute Salinity and sea pressure (in dbar), using the computationally-efficient expression for specific volume in terms of SA, CT and p (Roquet et al., 2015).

Parameters
rhoarray-like

Seawater density (not anomaly) in-situ, e.g., 1026 kg/m^3.

SAarray-like

Absolute Salinity, g/kg

parray-like

Sea pressure (absolute pressure minus 10.1325 dbar), dbar

Returns
CTarray-like, deg C

Conservative Temperature (ITS-90)

CT_multiplearray-like, deg C

Conservative Temperature (ITS-90)

`gsw.``CT_from_t`(SA, t, p)[source]

Calculates Conservative Temperature of seawater from in-situ temperature.

Parameters
SAarray-like

Absolute Salinity, g/kg

tarray-like

In-situ temperature (ITS-90), degrees C

parray-like

Sea pressure (absolute pressure minus 10.1325 dbar), dbar

Returns
CTarray-like, deg C

Conservative Temperature (ITS-90)

`gsw.``CT_maxdensity`(SA, p)[source]

Calculates the Conservative Temperature of maximum density of seawater. This function returns the Conservative temperature at which the density of seawater is a maximum, at given Absolute Salinity, SA, and sea pressure, p (in dbar). This function uses the computationally-efficient expression for specific volume in terms of SA, CT and p (Roquet et al., 2015).

Parameters
SAarray-like

Absolute Salinity, g/kg

parray-like

Sea pressure (absolute pressure minus 10.1325 dbar), dbar

Returns
CT_maxdensityarray-like, deg C

Conservative Temperature at which the density of seawater is a maximum for given Absolute Salinity and pressure.

`gsw.``CT_second_derivatives`(SA, pt)[source]

Calculates the following three, second-order derivatives of Conservative Temperature (1) CT_SA_SA, the second derivative with respect to Absolute Salinity at constant potential temperature (with p_ref = 0 dbar), (2) CT_SA_pt, the derivative with respect to potential temperature (the regular potential temperature which is referenced to 0 dbar) and Absolute Salinity, and (3) CT_pt_pt, the second derivative with respect to potential temperature (the regular potential temperature which is referenced to 0 dbar) at constant Absolute Salinity.

Parameters
SAarray-like

Absolute Salinity, g/kg

ptarray-like

Potential temperature referenced to a sea pressure, degrees C

Returns
CT_SA_SAarray-like, K/((g/kg)^2)

The second derivative of Conservative Temperature with respect to Absolute Salinity at constant potential temperature (the regular potential temperature which has reference sea pressure of 0 dbar).

CT_SA_ptarray-like,

The derivative of Conservative Temperature with respect to potential temperature (the regular one with

p_refarray-like, 1/(g/kg)

0 dbar) and Absolute Salinity.

CT_pt_ptarray-like,

The second derivative of Conservative Temperature with respect to potential temperature (the regular one with

p_refarray-like, 1/K

0 dbar) at constant SA.

`gsw.``C_from_SP`(SP, t, p)[source]

Calculates conductivity, C, from (SP,t,p) using PSS-78 in the range 2 < SP < 42. If the input Practical Salinity is less than 2 then a modified form of the Hill et al. (1986) fomula is used for Practical Salinity. The modification of the Hill et al. (1986) expression is to ensure that it is exactly consistent with PSS-78 at SP = 2.

Parameters
SParray-like

Practical Salinity (PSS-78), unitless

tarray-like

In-situ temperature (ITS-90), degrees C

parray-like

Sea pressure (absolute pressure minus 10.1325 dbar), dbar

Returns
Carray-like, mS/cm

conductivity

`gsw.``Fdelta`(p, lon, lat)[source]

Calculates Fdelta from the Absolute Salinity Anomaly Ratio (SAAR). It finds SAAR by calling the function “gsw_SAAR(p,long,lat)” and then simply calculates Fdelta from

Parameters
parray-like

Sea pressure (absolute pressure minus 10.1325 dbar), dbar

lonarray-like

Longitude, -360 to 360 degrees

latarray-like

Latitude, -90 to 90 degrees

Returns
Fdeltaarray-like, unitless

ratio of SA to Sstar, minus 1

`gsw.``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

`gsw.``Hill_ratio_at_SP2`(t)[source]

Calculates the Hill ratio, which is the adjustment needed to apply for Practical Salinities smaller than 2. This ratio is defined at a Practical Salinity = 2 and in-situ temperature, t using PSS-78. The Hill ratio is the ratio of 2 to the output of the Hill et al. (1986) formula for Practical Salinity at the conductivity ratio, Rt, at which Practical Salinity on the PSS-78 scale is exactly 2.

Parameters
tarray-like

In-situ temperature (ITS-90), degrees C

Returns
Hill_ratioarray-like, unitless

Hill ratio at SP of 2

`gsw.``IPV_vs_fNsquared_ratio`(SA, CT, p, p_ref=0, axis=0)[source]

Calculates the ratio of the vertical gradient of potential density to the vertical gradient of locally-referenced potential density. This is also the ratio of the planetary Isopycnal Potential Vorticity (IPV) to f times N^2, hence the name for this variable, IPV_vs_fNsquared_ratio (see Eqn. (3.20.17) of IOC et al. (2010)).

Parameters
SAarray-like

Absolute Salinity, g/kg

tarray-like

In-situ temperature (ITS-90), degrees C

parray-like

Sea pressure (absolute pressure minus 10.1325 dbar), dbar

p_reffloat

Reference pressure, dbar

Returns
IPV_vs_fNsquared_ratioarray

The ratio of the vertical gradient of potential density referenced to p_ref, to the vertical gradient of locally-referenced potential density, dimensionless.

p_midarray

Pressure at midpoints of p, dbar. The array shape matches IPV_vs_fNsquared_ratio.

`gsw.``Nsquared`(SA, CT, p, lat=None, axis=0)[source]

Calculate the square of the buoyancy frequency.

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

latarray-like, 1-D, optional

Latitude, degrees.

axisint, optional

The dimension along which pressure increases.

Returns
N2array

Buoyancy frequency-squared at pressure midpoints, 1/s. The shape along the pressure axis dimension is one less than that of the inputs.

p_midarray

Pressure at midpoints of p, dbar. The array shape matches N2.

`gsw.``O2sol`(SA, CT, p, lon, lat)[source]

Calculates the oxygen concentration expected at equilibrium with air at an Absolute Pressure of 101325 Pa (sea pressure of 0 dbar) including saturated water vapor. This function uses the solubility coefficients derived from the data of Benson and Krause (1984), as fitted by Garcia and Gordon (1992, 1993).

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

lonarray-like

Longitude, -360 to 360 degrees

latarray-like

Latitude, -90 to 90 degrees

Returns
O2solarray-like, umol/kg

solubility of oxygen in micro-moles per kg

`gsw.``O2sol_SP_pt`(SP, pt)[source]

Calculates the oxygen concentration expected at equilibrium with air at an Absolute Pressure of 101325 Pa (sea pressure of 0 dbar) including saturated water vapor. This function uses the solubility coefficients derived from the data of Benson and Krause (1984), as fitted by Garcia and Gordon (1992, 1993).

Parameters
SParray-like

Practical Salinity (PSS-78), unitless

ptarray-like

Potential temperature referenced to a sea pressure, degrees C

Returns
O2solarray-like, umol/kg

solubility of oxygen in micro-moles per kg

`gsw.``SAAR`(p, lon, lat)[source]

Calculates the Absolute Salinity Anomaly Ratio, SAAR, in the open ocean by spatially interpolating the global reference data set of SAAR to the location of the seawater sample.

Parameters
parray-like

Sea pressure (absolute pressure minus 10.1325 dbar), dbar

lonarray-like

Longitude, -360 to 360 degrees

latarray-like

Latitude, -90 to 90 degrees

Returns
SAARarray-like, unitless

Absolute Salinity Anomaly Ratio

`gsw.``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.``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.``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.``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.``SA_from_SP`(SP, p, lon, lat)[source]

Calculates Absolute Salinity from Practical Salinity. Since SP is non-negative by definition, this function changes any negative input values of SP to be zero.

Parameters
SParray-like

Practical Salinity (PSS-78), unitless

parray-like

Sea pressure (absolute pressure minus 10.1325 dbar), dbar

lonarray-like

Longitude, -360 to 360 degrees

latarray-like

Latitude, -90 to 90 degrees

Returns
SAarray-like, g/kg

Absolute Salinity

`gsw.``SA_from_SP_Baltic`(SP, lon, lat)[source]

Calculates Absolute Salinity in the Baltic Sea, from Practical Salinity. Since SP is non-negative by definition, this function changes any negative input values of SP to be zero. Note. This programme will only produce Absolute Salinity values for the Baltic Sea.

Parameters
SParray-like

Practical Salinity (PSS-78), unitless

lonarray-like

Longitude, -360 to 360 degrees

latarray-like

Latitude, -90 to 90 degrees

Returns
SA_balticarray-like, g kg^-1

Absolute Salinity in the Baltic Sea

`gsw.``SA_from_Sstar`(Sstar, p, lon, lat)[source]

Calculates Absolute Salinity from Preformed Salinity.

Parameters
Sstararray-like

Preformed Salinity, g/kg

parray-like

Sea pressure (absolute pressure minus 10.1325 dbar), dbar

lonarray-like

Longitude, -360 to 360 degrees

latarray-like

Latitude, -90 to 90 degrees

Returns
SAarray-like, g/kg

Absolute Salinity

`gsw.``SA_from_rho`(rho, CT, p)[source]

Calculates the Absolute Salinity of a seawater sample, for given values of its density, Conservative Temperature and sea pressure (in dbar). This function uses the computationally-efficient 75-term expression for specific volume in terms of SA, CT and p (Roquet et al., 2015).

Parameters
rhoarray-like

Seawater density (not anomaly) in-situ, e.g., 1026 kg/m^3.

CTarray-like

Conservative Temperature (ITS-90), degrees C

parray-like

Sea pressure (absolute pressure minus 10.1325 dbar), dbar

Returns
SAarray-like, g/kg

Absolute Salinity.

`gsw.``SP_from_C`(C, t, p)[source]

Calculates Practical Salinity, SP, from conductivity, C, primarily using the PSS-78 algorithm. Note that the PSS-78 algorithm for Practical Salinity is only valid in the range 2 < SP < 42. If the PSS-78 algorithm produces a Practical Salinity that is less than 2 then the Practical Salinity is recalculated with a modified form of the Hill et al. (1986) formula. The modification of the Hill et al. (1986) expression is to ensure that it is exactly consistent with PSS-78 at SP = 2. Note that the input values of conductivity need to be in units of mS/cm (not S/m).

Parameters
Carray-like

Conductivity, mS/cm

tarray-like

In-situ temperature (ITS-90), degrees C

parray-like

Sea pressure (absolute pressure minus 10.1325 dbar), dbar

Returns
SParray-like, unitless

Practical Salinity on the PSS-78 scale

`gsw.``SP_from_SA`(SA, p, lon, lat)[source]

Calculates Practical Salinity from Absolute Salinity.

Parameters
SAarray-like

Absolute Salinity, g/kg

parray-like

Sea pressure (absolute pressure minus 10.1325 dbar), dbar

lonarray-like

Longitude, -360 to 360 degrees

latarray-like

Latitude, -90 to 90 degrees

Returns
SParray-like, unitless

Practical Salinity (PSS-78)

`gsw.``SP_from_SA_Baltic`(SA, lon, lat)[source]

Calculates Practical Salinity for the Baltic Sea, from a value computed analytically from Absolute Salinity. Note. This programme will only produce Practical Salinty values for the Baltic Sea.

Parameters
SAarray-like

Absolute Salinity, g/kg

lonarray-like

Longitude, -360 to 360 degrees

latarray-like

Latitude, -90 to 90 degrees

Returns
SP_balticarray-like, unitless

Practical Salinity

`gsw.``SP_from_SK`(SK)[source]

Calculates Practical Salinity from Knudsen Salinity.

Parameters
SKarray-like

Knudsen Salinity, ppt

Returns
SParray-like, unitless

Practical Salinity (PSS-78)

`gsw.``SP_from_SR`(SR)[source]

Calculates Practical Salinity from Reference Salinity.

Parameters
SRarray-like

Reference Salinity, g/kg

Returns
SParray-like, unitless

Practical Salinity (PSS-78)

`gsw.``SP_from_Sstar`(Sstar, p, lon, lat)[source]

Calculates Practical Salinity from Preformed Salinity.

Parameters
Sstararray-like

Preformed Salinity, g/kg

parray-like

Sea pressure (absolute pressure minus 10.1325 dbar), dbar

lonarray-like

Longitude, -360 to 360 degrees

latarray-like

Latitude, -90 to 90 degrees

Returns
SParray-like, unitless

Practical Salinity (PSS-78)

`gsw.``SP_salinometer`(Rt, t)[source]

Calculates Practical Salinity SP from a salinometer, primarily using the PSS-78 algorithm. Note that the PSS-78 algorithm for Practical Salinity is only valid in the range 2 < SP < 42. If the PSS-78 algorithm produces a Practical Salinity that is less than 2 then the Practical Salinity is recalculated with a modified form of the Hill et al. (1986) formula. The modification of the Hill et al. (1986) expression is to ensure that it is exactly consistent with PSS-78 at SP = 2.

Parameters
Rtarray-like

C(SP,t_68,0)/C(SP=35,t_68,0), unitless

tarray-like

In-situ temperature (ITS-90), degrees C

Returns
SParray-like, unitless

Practical Salinity on the PSS-78 scale t may have dimensions 1x1 or Mx1 or 1xN or MxN, where Rt is MxN.

`gsw.``SR_from_SP`(SP)[source]

Calculates Reference Salinity from Practical Salinity.

Parameters
SParray-like

Practical Salinity (PSS-78), unitless

Returns
SRarray-like, g/kg

Reference Salinity

`gsw.``Sstar_from_SA`(SA, p, lon, lat)[source]

Converts Preformed Salinity from Absolute Salinity.

Parameters
SAarray-like

Absolute Salinity, g/kg

parray-like

Sea pressure (absolute pressure minus 10.1325 dbar), dbar

lonarray-like

Longitude, -360 to 360 degrees

latarray-like

Latitude, -90 to 90 degrees

Returns
Sstararray-like, g/kg

Preformed Salinity

`gsw.``Sstar_from_SP`(SP, p, lon, lat)[source]

Calculates Preformed Salinity from Absolute Salinity. Since SP is non-negative by definition, this function changes any negative input values of SP to be zero.

Parameters
SParray-like

Practical Salinity (PSS-78), unitless

parray-like

Sea pressure (absolute pressure minus 10.1325 dbar), dbar

lonarray-like

Longitude, -360 to 360 degrees

latarray-like

Latitude, -90 to 90 degrees

Returns
Sstararray-like, g/kg

Preformed Salinity

`gsw.``Turner_Rsubrho`(SA, CT, p, axis=0)[source]

Calculate the Turner Angle and the Stability Ratio.

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

axisint, optional

The dimension along which pressure increases.

Returns
Tuarray

Turner Angle at pressure midpoints, degrees. The shape along the pressure axis dimension is one less than that of the inputs.

Rsubrhoarray

Stability Ratio, dimensionless. The shape matches Tu.

p_midarray

Pressure at midpoints of p, dbar. The array shape matches Tu.

`gsw.``adiabatic_lapse_rate_from_CT`(SA, CT, p)[source]

Calculates the adiabatic lapse rate of sea water from Conservative Temperature.

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

Returns

`gsw.``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

`gsw.``alpha`(SA, CT, p)[source]

Calculates the thermal expansion coefficient of seawater with respect to Conservative Temperature using the computationally-efficient expression for specific volume in terms of SA, CT and p (Roquet et al., 2015).

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

Returns
alphaarray-like, 1/K

thermal expansion coefficient with respect to Conservative Temperature

`gsw.``alpha_on_beta`(SA, CT, p)[source]

Calculates alpha divided by beta, where alpha is the thermal expansion coefficient and beta is the saline contraction coefficient of seawater from Absolute Salinity and Conservative Temperature. This function uses the computationally-efficient expression for specific volume in terms of SA, CT and p (Roquet et al., 2015).

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

Returns
alpha_on_betaarray-like, kg g^-1 K^-1

thermal expansion coefficient with respect to Conservative Temperature divided by the saline contraction coefficient at constant Conservative Temperature

`gsw.``alpha_wrt_t_exact`(SA, t, p)[source]

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

Parameters
SAarray-like

Absolute Salinity, g/kg

tarray-like

In-situ temperature (ITS-90), degrees C

parray-like

Sea pressure (absolute pressure minus 10.1325 dbar), dbar

Returns
alpha_wrt_t_exactarray-like, 1/K

thermal expansion coefficient with respect to in-situ temperature

`gsw.``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

`gsw.``beta`(SA, CT, p)[source]

Calculates the saline (i.e. haline) contraction coefficient of seawater at constant Conservative Temperature using the computationally-efficient 75-term expression for specific volume in terms of SA, CT and p (Roquet et al., 2015).

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

Returns
betaarray-like, kg/g

saline contraction coefficient at constant Conservative Temperature

`gsw.``beta_const_t_exact`(SA, t, p)[source]

Calculates the saline (i.e. haline) contraction coefficient of seawater at constant in-situ temperature.

Parameters
SAarray-like

Absolute Salinity, g/kg

tarray-like

In-situ temperature (ITS-90), degrees C

parray-like

Sea pressure (absolute pressure minus 10.1325 dbar), dbar

Returns
beta_const_t_exactarray-like, kg/g

saline contraction coefficient at constant in-situ temperature

`gsw.``cabbeling`(SA, CT, p)[source]

Calculates the cabbeling coefficient of seawater with respect to Conservative Temperature. This function uses the computationally- efficient expression for specific volume in terms of SA, CT and p (Roquet et al., 2015).

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

Returns
cabbelingarray-like, 1/K^2

cabbeling coefficient with respect to Conservative Temperature.

`gsw.``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

`gsw.``chem_potential_water_t_exact`(SA, t, p)[source]

Calculates the chemical potential of water in seawater.

Parameters
SAarray-like

Absolute Salinity, g/kg

tarray-like

In-situ temperature (ITS-90), degrees C

parray-like

Sea pressure (absolute pressure minus 10.1325 dbar), dbar

Returns
chem_potential_water_t_exactarray-like, J/g

chemical potential of water in seawater

`gsw.``cp_ice`(t, p)[source]

Calculates the isobaric heat capacity of seawater.

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

`gsw.``cp_t_exact`(SA, t, p)[source]

Calculates the isobaric heat capacity of seawater.

Parameters
SAarray-like

Absolute Salinity, g/kg

tarray-like

In-situ temperature (ITS-90), degrees C

parray-like

Sea pressure (absolute pressure minus 10.1325 dbar), dbar

Returns
cp_t_exactarray-like, J/(kg*K)

heat capacity of seawater

`gsw.``deltaSA_atlas`(p, lon, lat)[source]

Calculates the Absolute Salinity Anomaly atlas value, SA - SR, in the open ocean by spatially interpolating the global reference data set of deltaSA_atlas to the location of the seawater sample.

Parameters
parray-like

Sea pressure (absolute pressure minus 10.1325 dbar), dbar

lonarray-like

Longitude, -360 to 360 degrees

latarray-like

Latitude, -90 to 90 degrees

Returns
deltaSA_atlasarray-like, g/kg

Absolute Salinity Anomaly atlas value

`gsw.``deltaSA_from_SP`(SP, p, lon, lat)[source]

Calculates Absolute Salinity Anomaly from Practical Salinity. Since SP is non-negative by definition, this function changes any negative input values of SP to be zero.

Parameters
SParray-like

Practical Salinity (PSS-78), unitless

parray-like

Sea pressure (absolute pressure minus 10.1325 dbar), dbar

lonarray-like

Longitude, -360 to 360 degrees

latarray-like

Latitude, -90 to 90 degrees

Returns
deltaSAarray-like, g/kg

Absolute Salinity Anomaly

`gsw.``dilution_coefficient_t_exact`(SA, t, p)[source]

Calculates the dilution coefficient of seawater. The dilution coefficient of seawater is defined as the Absolute Salinity times the second derivative of the Gibbs function with respect to Absolute Salinity, that is, SA.*g_SA_SA.

Parameters
SAarray-like

Absolute Salinity, g/kg

tarray-like

In-situ temperature (ITS-90), degrees C

parray-like

Sea pressure (absolute pressure minus 10.1325 dbar), dbar

Returns
dilution_coefficient_t_exactarray-like, (J/kg)(kg/g)

dilution coefficient

`gsw.``distance`(lon, lat, p=0, axis=-1)[source]

Great-circle distance in m between lon, lat points.

Parameters
lon, latarray-like, 1-D or 2-D (shapes must match)

Longitude, latitude, in degrees.

parray-like, scalar, 1-D or 2-D, optional, default is 0

Sea pressure (absolute pressure minus 10.1325 dbar), dbar

axisint, -1, 0, 1, optional

The axis or dimension along which lat and lon vary. This differs from most functions, for which axis is the dimension along which p increases.

Returns
distance1-D or 2-D array

distance in meters between adjacent points.

`gsw.``dynamic_enthalpy`(SA, CT, p)[source]

Calculates dynamic enthalpy of seawater using the computationally- efficient expression for specific volume in terms of SA, CT and p (Roquet et al., 2015). Dynamic enthalpy is defined as enthalpy minus potential enthalpy (Young, 2010).

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

Returns
dynamic_enthalpyarray-like, J/kg

dynamic enthalpy

`gsw.``enthalpy`(SA, CT, p)[source]

Calculates specific enthalpy of seawater using the computationally- efficient expression for specific volume in terms of SA, CT and p (Roquet et al., 2015).

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

Returns
enthalpyarray-like, J/kg

specific enthalpy

`gsw.``enthalpy_CT_exact`(SA, CT, p)[source]

Calculates specific enthalpy of seawater from Absolute Salinity and Conservative Temperature and pressure.

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

Returns
enthalpy_CT_exactarray-like, J/kg

specific enthalpy

`gsw.``enthalpy_diff`(SA, CT, p_shallow, p_deep)[source]

Calculates the difference of the specific enthalpy of seawater between two different pressures, p_deep (the deeper pressure) and p_shallow (the shallower pressure), at the same values of SA and CT. This function uses the computationally-efficient expression for specific volume in terms of SA, CT and p (Roquet et al., 2015). The output (enthalpy_diff) is the specific enthalpy evaluated at (SA,CT,p_deep) minus the specific enthalpy at (SA,CT,p_shallow).

Parameters
SAarray-like

Absolute Salinity, g/kg

CTarray-like

Conservative Temperature (ITS-90), degrees C

p_shallowarray-like

Upper sea pressure (absolute pressure minus 10.1325 dbar), dbar

p_deeparray-like

Lower sea pressure (absolute pressure minus 10.1325 dbar), dbar

Returns
enthalpy_diffarray-like, J/kg

difference of specific enthalpy (deep minus shallow)

`gsw.``enthalpy_first_derivatives`(SA, CT, p)[source]

Calculates the following two derivatives of specific enthalpy (h) of seawater using the computationally-efficient expression for specific volume in terms of SA, CT and p (Roquet et al., 2015). (1) h_SA, the derivative with respect to Absolute Salinity at constant CT and p, and (2) h_CT, derivative with respect to CT at constant SA and p. Note that h_P is specific volume (1/rho) it can be caclulated by calling gsw_specvol(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

Returns
h_SAarray-like, J/g

The first derivative of specific enthalpy with respect to Absolute Salinity at constant CT and p. [ J/(kg (g/kg))] i.e.

h_CTarray-like, J/(kg K)

The first derivative of specific enthalpy with respect to CT at constant SA and p.

`gsw.``enthalpy_first_derivatives_CT_exact`(SA, CT, p)[source]

Calculates the following two derivatives of specific enthalpy, h, (1) h_SA, the derivative with respect to Absolute Salinity at constant CT and p, and (2) h_CT, derivative with respect to CT at constant SA and p. Note that h_P is specific volume, v, it can be calulated by calling gsw_specvol_CT_exact(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

Returns
h_SAarray-like, J/g

The first derivative of specific enthalpy with respect to Absolute Salinity at constant CT and p. [ J/(kg (g/kg))] i.e.

h_CTarray-like, J/(kg K)

The first derivative of specific enthalpy with respect to CT at constant SA and p.

`gsw.``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

`gsw.``enthalpy_second_derivatives`(SA, CT, p)[source]

Calculates the following three second-order derivatives of specific enthalpy (h),using the computationally-efficient expression for specific volume in terms of SA, CT and p (Roquet et al., 2015). (1) h_SA_SA, second-order derivative with respect to Absolute Salinity at constant CT & p. (2) h_SA_CT, second-order derivative with respect to SA & CT at constant p. (3) h_CT_CT, second-order derivative with respect to CT at constant SA and 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

Returns
h_SA_SAarray-like, J/(kg (g/kg)^2)

The second derivative of specific enthalpy with respect to Absolute Salinity at constant CT & p.

h_SA_CTarray-like, J/(kg K(g/kg))

The second derivative of specific enthalpy with respect to SA and CT at constant p.

h_CT_CTarray-like, J/(kg K^2)

The second derivative of specific enthalpy with respect to CT at constant SA and p.

`gsw.``enthalpy_second_derivatives_CT_exact`(SA, CT, p)[source]

Calculates the following three second-order derivatives of specific enthalpy (h), (1) h_SA_SA, second-order derivative with respect to Absolute Salinity at constant CT & p. (2) h_SA_CT, second-order derivative with respect to SA & CT at constant p. (3) h_CT_CT, second-order derivative with respect to CT at constant SA and 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

Returns
h_SA_SAarray-like, J/(kg (g/kg)^2)

The second derivative of specific enthalpy with respect to Absolute Salinity at constant CT & p.

h_SA_CTarray-like, J/(kg K(g/kg))

The second derivative of specific enthalpy with respect to SA and CT at constant p.

h_CT_CTarray-like, J/(kg K^2)

The second derivative of specific enthalpy with respect to CT at constant SA and p.

`gsw.``enthalpy_t_exact`(SA, t, p)[source]

Calculates the specific enthalpy of seawater.

Parameters
SAarray-like

Absolute Salinity, g/kg

tarray-like

In-situ temperature (ITS-90), degrees C

parray-like

Sea pressure (absolute pressure minus 10.1325 dbar), dbar

Returns
enthalpy_t_exactarray-like, J/kg

specific enthalpy

`gsw.``entropy_first_derivatives`(SA, CT)[source]

Calculates the following two partial derivatives of specific entropy (eta) (1) eta_SA, the derivative with respect to Absolute Salinity at constant Conservative Temperature, and (2) eta_CT, the derivative with respect to Conservative Temperature at constant Absolute Salinity.

Parameters
SAarray-like

Absolute Salinity, g/kg

CTarray-like

Conservative Temperature (ITS-90), degrees C

Returns
eta_SAarray-like, J/(g K)

The derivative of specific entropy with respect to Absolute Salinity (in units of g kg^-1) at constant Conservative Temperature.

eta_CTarray-like, J/(kg K^2)

The derivative of specific entropy with respect to Conservative Temperature at constant Absolute Salinity.

`gsw.``entropy_from_CT`(SA, CT)[source]

Calculates specific entropy of seawater from Conservative Temperature.

Parameters
SAarray-like

Absolute Salinity, g/kg

CTarray-like

Conservative Temperature (ITS-90), degrees C

Returns
entropyarray-like, J/(kg*K)

specific entropy

`gsw.``entropy_from_pt`(SA, pt)[source]

Calculates specific entropy of seawater as a function of potential temperature.

Parameters
SAarray-like

Absolute Salinity, g/kg

ptarray-like

Potential temperature referenced to a sea pressure, degrees C

Returns
entropyarray-like, J/(kg*K)

specific entropy

`gsw.``entropy_from_t`(SA, t, p)[source]

Calculates specific entropy of seawater from in-situ temperature.

Parameters
SAarray-like

Absolute Salinity, g/kg

tarray-like

In-situ temperature (ITS-90), degrees C

parray-like

Sea pressure (absolute pressure minus 10.1325 dbar), dbar

Returns
entropyarray-like, J/(kg*K)

specific entropy

`gsw.``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

`gsw.``entropy_second_derivatives`(SA, CT)[source]

Calculates the following three second-order partial derivatives of specific entropy (eta) (1) eta_SA_SA, the second derivative with respect to Absolute Salinity at constant Conservative Temperature, and (2) eta_SA_CT, the derivative with respect to Absolute Salinity and Conservative Temperature. (3) eta_CT_CT, the second derivative with respect to Conservative Temperature at constant Absolute Salinity.

Parameters
SAarray-like

Absolute Salinity, g/kg

CTarray-like

Conservative Temperature (ITS-90), degrees C

Returns
eta_SA_SAarray-like, J/(kg K(g/kg)^2)

The second derivative of specific entropy with respect to Absolute Salinity (in units of g kg^-1) at constant Conservative Temperature.

eta_SA_CTarray-like, J/(kg (g/kg) K^2)

The second derivative of specific entropy with respect to Conservative Temperature at constant Absolute

eta_CT_CTarray-like, J/(kg K^3)

The second derivative of specific entropy with respect to Conservative Temperature at constant Absolute

`gsw.``f`(lat)[source]

Coriolis parameter in 1/s for latitude in degrees.

`gsw.``frazil_properties`(SA_bulk, h_bulk, p)[source]

Calculates the mass fraction of ice (mass of ice divided by mass of ice plus seawater), w_Ih_final, which results from given values of the bulk Absolute Salinity, SA_bulk, bulk enthalpy, h_bulk, occuring at pressure p. The final values of Absolute Salinity, SA_final, and Conservative Temperature, CT_final, of the interstitial seawater phase are also returned. This code assumes that there is no dissolved air in the seawater (that is, saturation_fraction is assumed to be zero throughout the code).

Parameters
SA_bulkarray-like

bulk Absolute Salinity of the seawater and ice mixture, g/kg

h_bulkarray-like

bulk enthalpy of the seawater and ice mixture, J/kg

parray-like

Sea pressure (absolute pressure minus 10.1325 dbar), dbar

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 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.

`gsw.``frazil_properties_potential`(SA_bulk, h_pot_bulk, p)[source]

Calculates the mass fraction of ice (mass of ice divided by mass of ice plus seawater), w_Ih_eq, which results from given values of the bulk Absolute Salinity, SA_bulk, bulk potential enthalpy, h_pot_bulk, occuring at pressure p. The final equilibrium values of Absolute Salinity, SA_eq, and Conservative Temperature, CT_eq, of the interstitial seawater phase are also returned. This code assumes that there is no dissolved air in the seawater (that is, saturation_fraction is assumed to be zero thoughout the code).

Parameters
SA_bulkarray-like

bulk Absolute Salinity of the seawater and ice mixture, g/kg

h_pot_bulkarray-like

bulk enthalpy of the seawater and ice mixture, J/kg

parray-like

Sea pressure (absolute pressure minus 10.1325 dbar), dbar

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 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.

`gsw.``frazil_properties_potential_poly`(SA_bulk, h_pot_bulk, p)[source]

Calculates the mass fraction of ice (mass of ice divided by mass of ice plus seawater), w_Ih_eq, which results from given values of the bulk Absolute Salinity, SA_bulk, bulk potential enthalpy, h_pot_bulk, occuring at pressure p. The final equilibrium values of Absolute Salinity, SA_eq, and Conservative Temperature, CT_eq, of the interstitial seawater phase are also returned. This code assumes that there is no dissolved air in the seawater (that is, saturation_fraction is assumed to be zero thoughout the code).

Parameters
SA_bulkarray-like

bulk Absolute Salinity of the seawater and ice mixture, g/kg

h_pot_bulkarray-like

bulk enthalpy of the seawater and ice mixture, J/kg

parray-like

Sea pressure (absolute pressure minus 10.1325 dbar), dbar

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 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.

`gsw.``frazil_ratios_adiabatic`(SA, p, w_Ih)[source]

Calculates the ratios of SA, CT and P changes when frazil ice forms or melts in response to an adiabatic change in pressure of a mixture of seawater and frazil ice crystals.

Parameters
SAarray-like

Absolute Salinity, g/kg

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.

Returns
dSA_dCT_frazilarray-like, g/(kg K)

the ratio of the changes in Absolute Salinity to that of Conservative Temperature

dSA_dP_frazilarray-like, g/(kg Pa)

the ratio of the changes in Absolute Salinity to that of pressure (in Pa)

dCT_dP_frazilarray-like, K/Pa

the ratio of the changes in Conservative Temperature to that of pressure (in Pa)

`gsw.``frazil_ratios_adiabatic_poly`(SA, p, w_Ih)[source]

Calculates the ratios of SA, CT and P changes when frazil ice forms or melts in response to an adiabatic change in pressure of a mixture of seawater and frazil ice crystals.

Parameters
SAarray-like

Absolute Salinity, g/kg

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.

Returns
dSA_dCT_frazilarray-like, g/(kg K)

the ratio of the changes in Absolute Salinity to that of Conservative Temperature

dSA_dP_frazilarray-like, g/(kg Pa)

the ratio of the changes in Absolute Salinity to that of pressure (in Pa)

dCT_dP_frazilarray-like, K/Pa

the ratio of the changes in Conservative Temperature to that of pressure (in Pa)

`gsw.``geo_strf_dyn_height`(SA, CT, p, p_ref=0, axis=0, max_dp=1.0, interp_method='pchip')[source]

Dynamic height anomaly as a function of pressure.

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

p_reffloat or array-like, optional

Reference pressure, dbar

axisint, optional, default is 0

The index of the pressure dimension in SA and CT.

max_dpfloat

If any pressure interval in the input p exceeds max_dp, the dynamic height will be calculated after interpolating to a grid with this spacing.

interp_methodstring {‘pchip’, ‘linear’}

Interpolation algorithm.

Returns
dynamic_heightarray

This is the integral of specific volume anomaly with respect to pressure, from each pressure in p to the specified reference pressure. It is the geostrophic streamfunction in an isobaric surface, relative to the reference surface.

`gsw.``geostrophic_velocity`(geo_strf, lon, lat, p=0, axis=0)[source]

Calculate geostrophic velocity from a streamfunction.

Calculates geostrophic velocity relative to a reference pressure, given a geostrophic streamfunction and the position of each station in sequence along an ocean section. The data can be from a single isobaric or “density” surface, or from a series of such surfaces.

Parameters
geo_strfarray-like, 1-D or 2-D

geostrophic streamfunction; see Notes below.

lonarray-like, 1-D

Longitude, -360 to 360 degrees

latarray-like, 1-D

Latitude, degrees

pfloat or array-like, optional

Sea pressure (absolute pressure minus 10.1325 dbar), dbar. This used only for a tiny correction in the distance calculation; it is safe to omit it.

axisint, 0 or 1, optional

The axis or dimension along which pressure increases in geo_strf. If geo_strf is 1-D, it is ignored.

Returns
velocityarray, 2-D or 1-D

Geostrophic velocity in m/s relative to the sea surface, averaged between each successive pair of positions.

mid_lon, mid_latarray, 1-D

Midpoints of input lon and lat.

Notes

The geostrophic streamfunction can be:

• geo_strf_dyn_height (in an isobaric surface)

• geo_strf_Montgomery (in a specific volume anomaly surface)

• geo_strf_Cunninhgam (in an approximately neutral surface such as a potential density surface).

• geo_strf_isopycnal (in an approximately neutral surface such as a potential density surface, a Neutral Density surface, or an omega surface (Klocker et al., 2009)).

Only `geo_strf_dyn_height()` is presently implemented in GSW-Python.

`gsw.``gibbs_ice_part_t`(t, p)[source]

part of the the first temperature derivative of Gibbs energy of ice that is the outout is gibbs_ice(1,0,t,p) + S0

Parameters
tarray-like

In-situ temperature (ITS-90), degrees C

parray-like

Sea pressure (absolute pressure minus 10.1325 dbar), dbar

Returns
gibbs_ice_part_tarray-like, J kg^-1 K^-1

part of temperature derivative

`gsw.``gibbs_ice_pt0`(pt0)[source]

part of the the first temperature derivative of Gibbs energy of ice that is the outout is “gibbs_ice(1,0,pt0,0) + s0”

Parameters
pt0array-like

Potential temperature with reference pressure of 0 dbar, degrees C

Returns
gibbs_ice_part_pt0array-like, J kg^-1 K^-1

part of temperature derivative

`gsw.``gibbs_ice_pt0_pt0`(pt0)[source]

The second temperature derivative of Gibbs energy of ice at the potential temperature with reference sea pressure of zero dbar. That is the output is gibbs_ice(2,0,pt0,0).

Parameters
pt0array-like

Potential temperature with reference pressure of 0 dbar, degrees C

Returns
gibbs_ice_pt0_pt0array-like, J kg^-1 K^-2

temperature second derivative at pt0

`gsw.``grav`(lat, p)[source]

Calculates acceleration due to gravity as a function of latitude and as a function of pressure in the ocean.

Parameters
latarray-like

Latitude, -90 to 90 degrees

parray-like

Sea pressure (absolute pressure minus 10.1325 dbar), dbar

Returns
gravarray-like, m s^-2

gravitational acceleration

`gsw.``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.

`gsw.``indexer`(shape, axis, order='C')[source]

Generator of indexing tuples for “apply_along_axis” usage.

The generator cycles through all axes other than axis. The numpy np.apply_along_axis function only works with functions of a single array; this generator allows us work with a function of more than one array.

`gsw.``internal_energy`(SA, CT, p)[source]

Calculates specific internal energy of seawater using the computationally-efficient expression for specific volume in terms of SA, CT and p (Roquet et al., 2015).

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

Returns
internal_energyarray-like, J/kg

specific internal energy

`gsw.``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)

`gsw.``kappa`(SA, CT, p)[source]

Calculates the isentropic compressibility of seawater. This function has inputs of Absolute Salinity and Conservative Temperature. This function uses the computationally-efficient expression for specific volume in terms of SA, CT and p (Roquet et al., 2015).

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

Returns
kappaarray-like, 1/Pa

isentropic compressibility of seawater

`gsw.``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

`gsw.``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

`gsw.``kappa_t_exact`(SA, t, p)[source]

Calculates the isentropic compressibility of seawater.

Parameters
SAarray-like

Absolute Salinity, g/kg

tarray-like

In-situ temperature (ITS-90), degrees C

parray-like

Sea pressure (absolute pressure minus 10.1325 dbar), dbar

Returns
kappa_t_exactarray-like, 1/Pa

isentropic compressibility

`gsw.``latentheat_evap_CT`(SA, CT)[source]

Calculates latent heat, or enthalpy, of evaporation at p = 0 (the surface). It is defined as a function of Absolute Salinity, SA, and Conservative Temperature, CT, and is valid in the ranges 0 < SA < 42 g/kg and 0 < CT < 40 deg C. The errors range between -0.4 and 0.6 J/kg.

Parameters
SAarray-like

Absolute Salinity, g/kg

CTarray-like

Conservative Temperature (ITS-90), degrees C

Returns
latentheat_evaparray-like, J/kg

latent heat of evaporation

`gsw.``latentheat_evap_t`(SA, t)[source]

Calculates latent heat, or enthalpy, of evaporation at p = 0 (the surface). It is defined as a function of Absolute Salinity, SA, and in-situ temperature, t, and is valid in the ranges 0 < SA < 40 g/kg and 0 < CT < 42 deg C. The errors range between -0.4 and 0.6 J/kg.

Parameters
SAarray-like

Absolute Salinity, g/kg

tarray-like

In-situ temperature (ITS-90), degrees C

Returns
latentheat_evaparray-like, J/kg

latent heat of evaporation

`gsw.``latentheat_melting`(SA, p)[source]

Calculates latent heat, or enthalpy, of melting. It is defined in terms of Absolute Salinity, SA, and sea pressure, p, and is valid in the ranges 0 < SA < 42 g kg^-1 and 0 < p < 10,000 dbar. This is based on the IAPWS Releases IAPWS-09 (for pure water), IAPWS-08 (for the saline compoonent of seawater and IAPWS-06 for ice Ih.

Parameters
SAarray-like

Absolute Salinity, g/kg

parray-like

Sea pressure (absolute pressure minus 10.1325 dbar), dbar

Returns
latentheat_meltingarray-like, J/kg

latent heat of melting

`gsw.``match_args_return`(f)[source]

Decorator for most functions that operate on profile data.

`gsw.``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

`gsw.``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

`gsw.``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.

`gsw.``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.

`gsw.``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 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.

`gsw.``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

`gsw.``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

`gsw.``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.

`gsw.``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.

`gsw.``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 orignal seawater

CT_finalarray-like, deg C

Conservative Temperature of the mixture of the melted sea ice (or ice) and the orignal seawater

`gsw.``p_from_z`(z, lat, geo_strf_dyn_height=0, sea_surface_geopotential=0)[source]

Calculates sea pressure from height using computationally-efficient 75-term expression for density, in terms of SA, CT and p (Roquet et al., 2015). Dynamic height anomaly, geo_strf_dyn_height, if provided, must be computed with its p_ref = 0 (the surface). Also if provided, sea_surface_geopotental is the geopotential at zero sea pressure. This function solves Eqn.(3.32.3) of IOC et al. (2010) iteratively for p.

Parameters
zarray-like

Depth, positive up, m

latarray-like

Latitude, -90 to 90 degrees

geo_strf_dyn_heightarray-like
dynamic height anomaly, m^2/s^2

Note that the reference pressure, p_ref, of geo_strf_dyn_height must be zero (0) dbar.

sea_surface_geopotentialarray-like

geopotential at zero sea pressure, m^2/s^2

Returns
parray-like, dbar

sea pressure ( i.e. absolute pressure - 10.1325 dbar )

`gsw.``pchip_interp`(x, y, xi, axis=0)[source]

Interpolate using Piecewise Cubic Hermite Interpolating Polynomial

This is a shape-preserving algorithm; it does not introduce new local extrema. The implementation in C that is wrapped here is largely taken from the scipy implementation, https://docs.scipy.org/doc/scipy/reference/generated/scipy.interpolate.PchipInterpolator.html.

Points outside the range of the interpolation table are filled using the end values in the table. (In contrast, scipy.interpolate.pchip_interpolate() extrapolates using the end polynomials.)

Parameters
x, yarray-like

Interpolation table x and y; n-dimensional, must be broadcastable to the same dimensions.

xiarray-like

One-dimensional array of new x values.

axisint, optional, default is 0

Axis along which xi is taken.

Returns
yiarray

Values of y interpolated to xi along the specified axis.

`gsw.``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

`gsw.``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

`gsw.``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.``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.``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.``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.``pot_rho_t_exact`(SA, t, p, p_ref)[source]

Calculates potential density of seawater. Note. This function outputs potential density, not potential density anomaly; that is, 1000 kg/m^3 is not subtracted.

Parameters
SAarray-like

Absolute Salinity, g/kg

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
pot_rho_t_exactarray-like, kg/m^3

potential density (not potential density anomaly)

`gsw.``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

`gsw.``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.``pt0_from_t`(SA, t, p)[source]

Calculates potential temperature with reference pressure, p_ref = 0 dbar. The present routine is computationally faster than the more general function “gsw_pt_from_t(SA,t,p,p_ref)” which can be used for any reference pressure value. This subroutine calls “gsw_entropy_part(SA,t,p)”, “gsw_entropy_part_zerop(SA,pt0)” and “gsw_gibbs_pt0_pt0(SA,pt0)”.

Parameters
SAarray-like

Absolute Salinity, g/kg

tarray-like

In-situ temperature (ITS-90), degrees C

parray-like

Sea pressure (absolute pressure minus 10.1325 dbar), dbar

Returns
pt0array-like, deg C

potential temperature with reference sea pressure (p_ref) = 0 dbar.

`gsw.``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)

`gsw.``pt_first_derivatives`(SA, CT)[source]

Calculates the following two partial derivatives of potential temperature (the regular potential temperature whose reference sea pressure is 0 dbar) (1) pt_SA, the derivative with respect to Absolute Salinity at constant Conservative Temperature, and (2) pt_CT, the derivative with respect to Conservative Temperature at constant Absolute Salinity.

Parameters
SAarray-like

Absolute Salinity, g/kg

CTarray-like

Conservative Temperature (ITS-90), degrees C

Returns
pt_SAarray-like, K/(g/kg)

The derivative of potential temperature with respect to Absolute Salinity at constant Conservative Temperature.

pt_CTarray-like, unitless

The derivative of potential temperature with respect to Conservative Temperature at constant Absolute Salinity. pt_CT is dimensionless.

`gsw.``pt_from_CT`(SA, CT)[source]

Calculates potential temperature (with a reference sea pressure of zero dbar) from Conservative Temperature. This function uses 1.5 iterations through a modified Newton-Raphson (N-R) iterative solution proceedure, starting from a rational-function-based initial condition for both pt and dCT_dpt.

Parameters
SAarray-like

Absolute Salinity, g/kg

CTarray-like

Conservative Temperature (ITS-90), degrees C

Returns
ptarray-like, deg C

potential temperature referenced to a sea pressure of zero dbar (ITS-90)

`gsw.``pt_from_entropy`(SA, entropy)[source]

Calculates potential temperature with reference pressure p_ref = 0 dbar and with entropy as an input variable.

Parameters
SAarray-like

Absolute Salinity, g/kg

entropyarray-like

Specific entropy, J/(kg*K)

Returns
ptarray-like, deg C

potential temperature with reference sea pressure (p_ref) = 0 dbar.

`gsw.``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)

`gsw.``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)

`gsw.``pt_from_t`(SA, t, p, p_ref)[source]

Calculates potential temperature with the general reference pressure, p_ref, from in-situ temperature, t. This function calls “gsw_entropy_part” which evaluates entropy except for the parts which are a function of Absolute Salinity alone. A faster gsw routine exists if p_ref is indeed zero dbar. This routine is “gsw_pt0_from_t(SA,t,p)”.

Parameters
SAarray-like

Absolute Salinity, g/kg

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
ptarray-like, deg C

potential temperature with reference pressure, p_ref, on the ITS-90 temperature scale

`gsw.``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

`gsw.``pt_second_derivatives`(SA, CT)[source]

Calculates the following three second-order derivatives of potential temperature (the regular potential temperature which has a reference sea pressure of 0 dbar), (1) pt_SA_SA, the second derivative with respect to Absolute Salinity at constant Conservative Temperature, (2) pt_SA_CT, the derivative with respect to Conservative Temperature and Absolute Salinity, and (3) pt_CT_CT, the second derivative with respect to Conservative Temperature at constant Absolute Salinity.

Parameters
SAarray-like

Absolute Salinity, g/kg

CTarray-like

Conservative Temperature (ITS-90), degrees C

Returns
pt_SA_SAarray-like, K/((g/kg)^2)

The second derivative of potential temperature (the regular potential temperature which has reference sea pressure of 0 dbar) with respect to Absolute Salinity at constant Conservative Temperature.

pt_SA_CTarray-like, 1/(g/kg)

The derivative of potential temperature with respect to Absolute Salinity and Conservative Temperature.

pt_CT_CTarray-like, 1/K

The second derivative of potential temperature (the regular one with p_ref = 0 dbar) with respect to Conservative Temperature at constant SA.

`gsw.``rho`(SA, CT, p)[source]

Calculates in-situ density from Absolute Salinity and Conservative Temperature, using the computationally-efficient expression for specific volume in terms of SA, CT and p (Roquet et al., 2015).

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

Returns
rhoarray-like, kg/m

in-situ density

`gsw.``rho_alpha_beta`(SA, CT, p)[source]

Calculates in-situ density, the appropiate thermal expansion coefficient and the appropriate saline contraction coefficient of seawater from Absolute Salinity and Conservative Temperature. This function uses the computationally-efficient expression for specific volume in terms of SA, CT and p (Roquet et al., 2015).

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

Returns
rhoarray-like, kg/m

in-situ density

alphaarray-like, 1/K

thermal expansion coefficient with respect to Conservative Temperature

betaarray-like, kg/g

saline (i.e. haline) contraction coefficient at constant Conservative Temperature

`gsw.``rho_first_derivatives`(SA, CT, p)[source]

Calculates the three (3) partial derivatives of in-situ density with respect to Absolute Salinity, Conservative Temperature and pressure. Note that the pressure derivative is done with respect to pressure in Pa, not dbar. This function uses the computationally-efficient expression for specific volume in terms of SA, CT and p (Roquet et al., 2015).

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

Returns
rho_SAarray-like, (kg/m^3)(g/kg)^-1

partial derivative of density with respect to Absolute Salinity

rho_CTarray-like, kg/(m^3 K)

partial derivative of density with respect to Conservative Temperature

rho_Parray-like, kg/(m^3 Pa)

partial derivative of density with respect to pressure in Pa

`gsw.``rho_first_derivatives_wrt_enthalpy`(SA, CT, p)[source]

Calculates the following two first-order derivatives of specific volume (v), (1) rho_SA, first-order derivative with respect to Absolute Salinity at constant CT & p. (2) rho_h, first-order derivative with respect to SA & CT at constant 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

Returns
rho_SAarray-like, J/(kg (g/kg)^2)

The first derivative of rho with respect to Absolute Salinity at constant CT & p.

rho_harray-like, J/(kg K(g/kg))

The first derivative of rho with respect to SA and CT at constant p.

`gsw.``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 subracted 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)

`gsw.``rho_second_derivatives`(SA, CT, p)[source]

Calculates the following five second-order derivatives of rho, (1) rho_SA_SA, second-order derivative with respect to Absolute Salinity at constant CT & p. (2) rho_SA_CT, second-order derivative with respect to SA & CT at constant p. (3) rho_CT_CT, second-order derivative with respect to CT at constant SA & p. (4) rho_SA_P, second-order derivative with respect to SA & P at constant CT. (5) rho_CT_P, second-order derivative with respect to CT & P at constant SA.

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

Returns
rho_SA_SAarray-like, (kg/m^3)(g/kg)^-2

The second-order derivative of rho with respect to Absolute Salinity at constant CT & p.

rho_SA_CTarray-like, (kg/m^3)(g/kg)^-1 K^-1

The second-order derivative of rho with respect to SA and CT at constant p.

rho_CT_CTarray-like, (kg/m^3) K^-2

The second-order derivative of rho with respect to CT at constant SA & p

rho_SA_Parray-like, (kg/m^3)(g/kg)^-1 Pa^-1

The second-order derivative with respect to SA & P at constant CT.

rho_CT_Parray-like, (kg/m^3) K^-1 Pa^-1

The second-order derivative with respect to CT & P at constant SA.

`gsw.``rho_second_derivatives_wrt_enthalpy`(SA, CT, p)[source]

Calculates the following three second-order derivatives of rho with respect to enthalpy, (1) rho_SA_SA, second-order derivative with respect to Absolute Salinity at constant h & p. (2) rho_SA_h, second-order derivative with respect to SA & h at constant p. (3) rho_h_h, second-order derivative with respect to h at constant SA & 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

Returns
rho_SA_SAarray-like, J/(kg (g/kg)^2)

The second-order derivative of rho with respect to Absolute Salinity at constant h & p.

rho_SA_harray-like, J/(kg K(g/kg))

The second-order derivative of rho with respect to SA and h at constant p.

rho_h_harray-like,

The second-order derivative of rho with respect to h at constant SA & p

`gsw.``rho_t_exact`(SA, t, p)[source]

Calculates in-situ density of seawater from Absolute Salinity and in-situ temperature. Note that the output, rho, is density, not density anomaly; that is, 1000 kg/m^3 is not subracted from it.

Parameters
SAarray-like

Absolute Salinity, g/kg

tarray-like

In-situ temperature (ITS-90), degrees C

parray-like

Sea pressure (absolute pressure minus 10.1325 dbar), dbar

Returns
rho_t_exactarray-like, kg/m^3

in-situ density (not density anomaly)

`gsw.``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.

`gsw.``sigma0`(SA, CT)[source]

Calculates potential density anomaly with reference pressure of 0 dbar, this being this particular potential density minus 1000 kg/m^3. This function has inputs of Absolute Salinity and Conservative Temperature. This function uses the computationally-efficient expression for specific volume in terms of SA, CT and p (Roquet et al., 2015).

Parameters
SAarray-like

Absolute Salinity, g/kg

CTarray-like

Conservative Temperature (ITS-90), degrees C

Returns
sigma0array-like, kg/m^3

potential density anomaly with respect to a reference pressure of 0 dbar, that is, this potential density - 1000 kg/m^3.

`gsw.``sigma1`(SA, CT)[source]

Calculates potential density anomaly with reference pressure of 1000 dbar, this being this particular potential density minus 1000 kg/m^3. This function has inputs of Absolute Salinity and Conservative Temperature. This function uses the computationally-efficient expression for specific volume in terms of SA, CT and p (Roquet et al., 2015).

Parameters
SAarray-like

Absolute Salinity, g/kg

CTarray-like

Conservative Temperature (ITS-90), degrees C

Returns
sigma1array-like, kg/m^3

potential density anomaly with respect to a reference pressure of 1000 dbar, that is, this potential density - 1000 kg/m^3.

`gsw.``sigma2`(SA, CT)[source]

Calculates potential density anomaly with reference pressure of 2000 dbar, this being this particular potential density minus 1000 kg/m^3. Temperature. This function uses the computationally-efficient expression for specific volume in terms of SA, CT and p (Roquet et al., 2015).

Parameters
SAarray-like

Absolute Salinity, g/kg

CTarray-like

Conservative Temperature (ITS-90), degrees C

Returns
sigma2array-like, kg/m^3

potential density anomaly with respect to a reference pressure of 2000 dbar, that is, this potential density - 1000 kg/m^3.

`gsw.``sigma3`(SA, CT)[source]

Calculates potential density anomaly with reference pressure of 3000 dbar, this being this particular potential density minus 1000 kg/m^3. Temperature. This function uses the computationally-efficient expression for specific volume in terms of SA, CT and p (Roquet et al., 2015).

Parameters
SAarray-like

Absolute Salinity, g/kg

CTarray-like

Conservative Temperature (ITS-90), degrees C

Returns
sigma3array-like, kg/m^3

potential density anomaly with respect to a reference pressure of 3000 dbar, that is, this potential density - 1000 kg/m^3.

`gsw.``sigma4`(SA, CT)[source]

Calculates potential density anomaly with reference pressure of 4000 dbar, this being this particular potential density minus 1000 kg/m^3. Temperature. This function uses the computationally-efficient expression for specific volume in terms of SA, CT and p (Roquet et al., 2015).

Parameters
SAarray-like

Absolute Salinity, g/kg

CTarray-like

Conservative Temperature (ITS-90), degrees C

Returns
sigma4array-like, kg/m^3

potential density anomaly with respect to a reference pressure of 4000 dbar, that is, this potential density - 1000 kg/m^3.

`gsw.``sound_speed`(SA, CT, p)[source]

Calculates the speed of sound in seawater. This function has inputs of Absolute Salinity and Conservative Temperature. This function uses the computationally-efficient expression for specific volume in terms of SA, CT and p (Roquet et al., 2015).

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

Returns
sound_speedarray-like, m/s

speed of sound in seawater

`gsw.``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

`gsw.``sound_speed_t_exact`(SA, t, p)[source]

Calculates the speed of sound in seawater.

Parameters
SAarray-like

Absolute Salinity, g/kg

tarray-like

In-situ temperature (ITS-90), degrees C

parray-like

Sea pressure (absolute pressure minus 10.1325 dbar), dbar

Returns
sound_speed_t_exactarray-like, m/s

speed of sound in seawater

`gsw.``specvol`(SA, CT, p)[source]

Calculates specific volume from Absolute Salinity, Conservative Temperature and pressure, using the computationally-efficient 75-term polynomial expression for specific volume (Roquet et al., 2015).

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

Returns
specvolarray-like, m^3/kg

specific volume

`gsw.``specvol_alpha_beta`(SA, CT, p)[source]

Calculates specific volume, the appropiate thermal expansion coefficient and the appropriate saline contraction coefficient of seawater from Absolute Salinity and Conservative Temperature. This function uses the computationally-efficient expression for specific volume in terms of SA, CT and p (Roquet et al., 2015).

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

Returns
specvolarray-like, m/kg

specific volume

alphaarray-like, 1/K

thermal expansion coefficient with respect to Conservative Temperature

betaarray-like, kg/g

saline (i.e. haline) contraction coefficient at constant Conservative Temperature

`gsw.``specvol_anom_standard`(SA, CT, p)[source]

Calculates specific volume anomaly from Absolute Salinity, Conservative Temperature and pressure. It uses the computationally-efficient expression for specific volume as a function of SA, CT and p (Roquet et al., 2015). The reference value to which the anomally is calculated has an Absolute Salinity of SSO and Conservative Temperature equal to 0 degress C.

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

Returns
specvol_anomarray-like, m^3/kg

specific volume anomaly

`gsw.``specvol_first_derivatives`(SA, CT, p)[source]

Calculates the following three first-order derivatives of specific volume (v), (1) v_SA, first-order derivative with respect to Absolute Salinity at constant CT & p. (2) v_CT, first-order derivative with respect to CT at constant SA & p. (3) v_P, first-order derivative with respect to P at constant SA and CT.

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

Returns
v_SAarray-like, (m^3/kg)(g/kg)^-1

The first derivative of specific volume with respect to Absolute Salinity at constant CT & p.

v_CTarray-like, m^3/(K kg)

The first derivative of specific volume with respect to CT at constant SA and p.

v_Parray-like, m^3/(Pa kg)

The first derivative of specific volume with respect to P at constant SA and CT.

`gsw.``specvol_first_derivatives_wrt_enthalpy`(SA, CT, p)[source]

Calculates the following two first-order derivatives of specific volume (v), (1) v_SA_wrt_h, first-order derivative with respect to Absolute Salinity at constant h & p. (2) v_h, first-order derivative with respect to h at constant SA & 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

Returns
v_SA_wrt_harray-like, (m^3/kg)(g/kg)^-1 (J/kg)^-1

The first derivative of specific volume with respect to Absolute Salinity at constant CT & p.

v_harray-like, (m^3/kg)(J/kg)^-1

The first derivative of specific volume with respect to SA and CT at constant p.

`gsw.``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

`gsw.``specvol_second_derivatives`(SA, CT, p)[source]

Calculates the following five second-order derivatives of specific volume (v), (1) v_SA_SA, second-order derivative with respect to Absolute Salinity at constant CT & p. (2) v_SA_CT, second-order derivative with respect to SA & CT at constant p. (3) v_CT_CT, second-order derivative with respect to CT at constant SA and p. (4) v_SA_P, second-order derivative with respect to SA & P at constant CT. (5) v_CT_P, second-order derivative with respect to CT & P at constant SA.

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

Returns
v_SA_SAarray-like, (m^3/kg)(g/kg)^-2

The second derivative of specific volume with respect to Absolute Salinity at constant CT & p.

v_SA_CTarray-like, (m^3/kg)(g/kg)^-1 K^-1

The second derivative of specific volume with respect to SA and CT at constant p.

v_CT_CTarray-like, (m^3/kg) K^-2)

The second derivative of specific volume with respect to CT at constant SA and p.

v_SA_Parray-like, (m^3/kg) Pa^-1

The second derivative of specific volume with respect to SA and P at constant CT.

v_CT_Parray-like, (m^3/kg) K^-1 Pa^-1

The second derivative of specific volume with respect to CT and P at constant SA.

`gsw.``specvol_second_derivatives_wrt_enthalpy`(SA, CT, p)[source]

Calculates the following three first-order derivatives of specific volume (v) with respect to enthalpy, (1) v_SA_SA_wrt_h, second-order derivative with respect to Absolute Salinity at constant h & p. (2) v_SA_h, second-order derivative with respect to SA & h at constant p. (3) v_h_h, second-order derivative with respect to h at constant SA & 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

Returns
v_SA_SA_wrt_harray-like, (m^3/kg)(g/kg)^-2 (J/kg)^-1

The second-order derivative of specific volume with respect to Absolute Salinity at constant h & p.

v_SA_harray-like, (m^3/kg)(g/kg)^-1 (J/kg)^-1

The second-order derivative of specific volume with respect to SA and h at constant p.

v_h_harray-like, (m^3/kg)(J/kg)^-2

The second-order derivative with respect to h at constant SA & p.

`gsw.``specvol_t_exact`(SA, t, p)[source]

Calculates the specific volume of seawater.

Parameters
SAarray-like

Absolute Salinity, g/kg

tarray-like

In-situ temperature (ITS-90), degrees C

parray-like

Sea pressure (absolute pressure minus 10.1325 dbar), dbar

Returns
specvol_t_exactarray-like, m^3/kg

specific volume

`gsw.``spiciness0`(SA, CT)[source]

Calculates spiciness from Absolute Salinity and Conservative Temperature at a pressure of 0 dbar, as described by McDougall and Krzysik (2015). This routine is based on the computationally-efficient expression for specific volume in terms of SA, CT and p (Roquet et al., 2015).

Parameters
SAarray-like

Absolute Salinity, g/kg

CTarray-like

Conservative Temperature (ITS-90), degrees C

Returns
spiciness0array-like, kg/m^3

spiciness referenced to a pressure of 0 dbar, i.e. the surface

`gsw.``spiciness1`(SA, CT)[source]

Calculates spiciness from Absolute Salinity and Conservative Temperature at a pressure of 1000 dbar, as described by McDougall and Krzysik (2015). This routine is based on the computationally-efficient expression for specific volume in terms of SA, CT and p (Roquet et al., 2015).

Parameters
SAarray-like

Absolute Salinity, g/kg

CTarray-like

Conservative Temperature (ITS-90), degrees C

Returns
spiciness1array-like, kg/m^3

spiciness referenced to a pressure of 1000 dbar

`gsw.``spiciness2`(SA, CT)[source]

Calculates spiciness from Absolute Salinity and Conservative Temperature at a pressure of 2000 dbar, as described by McDougall and Krzysik (2015). This routine is based on the computationally-efficient expression for specific volume in terms of SA, CT and p (Roquet et al., 2015).

Parameters
SAarray-like

Absolute Salinity, g/kg

CTarray-like

Conservative Temperature (ITS-90), degrees C

Returns
spiciness2array-like, kg/m^3

spiciness referenced to a pressure of 2000 dbar

`gsw.``t90_from_t68`(t68)[source]

ITS-90 temperature from IPTS-68 temperature

This conversion should be applied to all in-situ data collected between 1/1/1968 and 31/12/1989.

`gsw.``t_deriv_chem_potential_water_t_exact`(SA, t, p)[source]

Calculates the temperature derivative of the chemical potential of water in seawater so that it is valid at exactly SA = 0.

Parameters
SAarray-like

Absolute Salinity, g/kg

tarray-like

In-situ temperature (ITS-90), degrees C

parray-like

Sea pressure (absolute pressure minus 10.1325 dbar), dbar

Returns
chem_potential_water_dtarray-like, J g^-1 K^-1

temperature derivative of the chemical potential of water in seawater

`gsw.``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.``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.``t_freezing_first_derivatives_poly`(SA, p, saturation_fraction)[source]

Calculates the frist 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.``t_freezing_poly`(SA, p, saturation_fraction)[source]

Calculates the in-situ temperature at which seawater freezes from a comptationally efficient polynomial.

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.``t_from_CT`(SA, CT, p)[source]

Calculates in-situ temperature from the Conservative Temperature of 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

Returns
tarray-like, deg C

in-situ temperature (ITS-90)

`gsw.``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)

`gsw.``thermobaric`(SA, CT, p)[source]

Calculates the thermobaric coefficient of seawater with respect to Conservative Temperature. This routine is based on the computationally-efficient expression for specific volume in terms of SA, CT and p (Roquet et al., 2015).

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

Returns
thermobaricarray-like, 1/(K Pa)

thermobaric coefficient with respect to Conservative Temperature.

`gsw.``z_from_p`(p, lat, geo_strf_dyn_height=0, sea_surface_geopotential=0)[source]

Calculates height from sea pressure using the computationally-efficient 75-term expression for specific volume in terms of SA, CT and p (Roquet et al., 2015). Dynamic height anomaly, geo_strf_dyn_height, if provided, must be computed with its p_ref = 0 (the surface). Also if provided, sea_surface_geopotental is the geopotential at zero sea pressure. This function solves Eqn.(3.32.3) of IOC et al. (2010).

Parameters
parray-like

Sea pressure (absolute pressure minus 10.1325 dbar), dbar

latarray-like

Latitude, -90 to 90 degrees

geo_strf_dyn_heightarray-like
dynamic height anomaly, m^2/s^2

Note that the reference pressure, p_ref, of geo_strf_dyn_height must be zero (0) dbar.

sea_surface_geopotentialarray-like

geopotential at zero sea pressure, m^2/s^2

Returns
zarray-like, m

height