def dynamic_enthalpy_CT_exact(SA, CT, p):
r"""Calculates the dynamic enthalpy of seawater from Absolute Salinity and
Conservative Temperature and pressure. Dynamic enthalpy is defined as
enthalpy minus potential enthalpy (Young, 2010).
Parameters
----------
SA : array_like
Absolute Salinity [g/kg]
CT : array_like
Conservative Temperature [:math:`^\circ` C (ITS-90)]
p : array_like
sea pressure [dbar]
Returns
-------
dynamic_enthalpy_CT_exact : array_like
dynamic enthalpy [J/kg]
See Also
--------
TODO
Notes
-----
This function uses the full Gibbs function. There is an alternative to
calling this function, namely dynamic_enthalpy(SA, CT, p), which uses the
computationally efficient 48-term expression for density in terms of SA, CT
and p (McDougall et al., 2011).
Examples
--------
TODO
References
----------
.. [1] IOC, SCOR and IAPSO, 2010: The international thermodynamic equation
of seawater - 2010: Calculation and use of thermodynamic properties.
Intergovernmental Oceanographic Commission, Manuals and Guides No. 56,
UNESCO (English), 196 pp. See apendix A.30.
.. [2] McDougall T.J., P.M. Barker, R. Feistel and D.R. Jackett, 2011: A
computationally efficient 48-term expression for the density of
seawater in terms of Conservative Temperature, and related properties
of seawater.
.. [3] Young, W.R., 2010: Dynamic enthalpy, Conservative Temperature, and
the seawater Boussinesq approximation. Journal of Physical Oceanography,
40, 394-400.
Modifications:
2011-04-05. Trevor McDougall and Paul Barker.
"""
t = t_from_CT(SA, CT, p)
return enthalpy_t_exact(SA, t, p) - cp0 * CT
def rho_CT_exact(SA, CT, p):
r"""Calculates in-situ density from Absolute Salinity and Conservative
Temperature.
Parameters
----------
SA : array_like
Absolute Salinity [g/kg]
CT : array_like
Conservative Temperature [:math:`^\circ` C (ITS-90)]
p : array_like
sea pressure [dbar]
Returns
-------
rho_CT_exact : array_like
in-situ density [kg/m**3]
See Also
--------
TODO
Notes
-----
The potential density with respect to reference pressure, p_ref, is
obtained by calling this function with the pressure argument being p_ref
(i.e. "rho_CT_exact(SA, CT, p_ref)"). This function uses the full Gibbs
function. There is an alternative to calling this function, namely
rho_CT(SA, CT, p), which uses the computationally efficient 48-term
expression for density in terms of SA, CT and p (McDougall et al., 2011).
Examples
--------
TODO
References
----------
.. [1] IOC, SCOR and IAPSO, 2010: The international thermodynamic equation
of seawater - 2010: Calculation and use of thermodynamic properties.
Intergovernmental Oceanographic Commission, Manuals and Guides No. 56,
UNESCO (English), 196 pp. See Eqn. (2.8.2).
.. [2] McDougall T.J., P.M. Barker, R. Feistel and D.R. Jackett, 2011: A
computationally efficient 48-term expression for the density of
seawater in terms of Conservative Temperature, and related properties
of seawater.
Modifications:
2011-04-03. Trevor McDougall and Paul Barker.
"""
t = t_from_CT(SA, CT, p)
return rho_t_exact(SA, t, p)
def alpha_CT_exact(SA, CT, p):
r"""Calculates the thermal expansion coefficient of seawater with respect
to Conservative Temperature from Absolute Salinity and Conservative
Temperature.
Parameters
----------
SA : array_like
Absolute salinity [g kg :sup:`-1`]
CT : array_like
Conservative Temperature [:math:`^\circ` C (ITS-90)]
p : array_like
pressure [dbar]
Returns
-------
alpha_CT_exact : array_like
thermal expansion coefficient [K :sup:`-1`]
with respect to Conservative Temperature
See Also
--------
TODO
Notes
-----
This function uses the full Gibbs function. There is an alternative to
calling this function, namely alpha_wrt_CT(SA, CT, p) which uses the
computationally efficient 48-term expression for density in terms of SA,
CT and p (McDougall et al., (2011)).
Examples
--------
TODO
References
----------
.. [1] IOC, SCOR and IAPSO, 2010: The international thermodynamic equation
of seawater - 2010: Calculation and use of thermodynamic properties.
Intergovernmental Oceanographic Commission, Manuals and Guides No. 56,
UNESCO (English), 196 pp. See Eqn. (2.18.3).
.. [2] McDougall T.J., P.M. Barker, R. Feistel and D.R. Jackett, 2011: A
computationally efficient 48-term expression for the density of
seawater in terms of Conservative Temperature, and related properties
of seawater.
Modifications:
2011-03-23. David Jackett, Trevor McDougall and Paul Barker.
"""
t = t_from_CT(SA, CT, p)
return alpha_wrt_CT_t_exact(SA, t, p)
def specvol_anom_CT_exact(SA, CT, p):
r"""Calculates specific volume anomaly from Absolute Salinity, Conservative
Temperature and pressure. The reference value of Absolute Salinity is SSO
and the reference value of Conservative Temperature is equal to 0 deg C.
Parameters
----------
SA : array_like
Absolute Salinity [g/kg]
CT : array_like
Conservative Temperature [:math:`^\circ` C (ITS-90)]
p : array_like
sea pressure [dbar]
Returns
-------
specvol_anom_CT_exact : array_like
specific volume anomaly [m**3/kg]
See Also
--------
TODO
Notes
-----
This function uses the full Gibbs function. There is an alternative to
calling this function, namely specvol_anom_CT(SA, CT, p), which uses the
computationally efficient 48-term expression for density in terms of SA, CT
and p (McDougall et al., 2011).
Examples
--------
TODO
References
----------
.. [1] IOC, SCOR and IAPSO, 2010: The international thermodynamic equation
of seawater - 2010: Calculation and use of thermodynamic properties.
Intergovernmental Oceanographic Commission, Manuals and Guides No. 56,
UNESCO (English), 196 pp. See Eqn. (3.7.3).
.. [2] McDougall T.J., P.M. Barker, R. Feistel and D.R. Jackett, 2011: A
computationally efficient 48-term expression for the density of
seawater in terms of Conservative Temperature, and related properties
of seawater.
Modifications:
2011-04-06. Trevor McDougall and Paul Barker.
"""
t = t_from_CT(SA, CT, p)
return specvol_anom_t_exact(SA, t, p)
def rho_alpha_beta_CT_exact(SA, CT, p):
r"""Calculates in-situ density, the appropriate thermal expansion
coefficient and the appropriate saline contraction coefficient of seawater
from Absolute Salinity and Conservative Temperature.
See the individual functions rho_CT_exact, alpha_CT_exact, and
beta_CT_exact. Retained for compatibility with the Matlab GSW toolbox.
"""
t = t_from_CT(SA, CT, p)
rho_CT_exact = rho_t_exact(SA, t, p)
alpha_CT_exact = alpha_wrt_CT_t_exact(SA, t, p)
beta_CT_exact = beta_const_CT_t_exact(SA, t, p)
return rho_CT_exact, alpha_CT_exact, beta_CT_exact
def sound_speed_CT_exact(SA, CT, p):
r"""Calculates the speed of sound in seawater from Absolute Salinity and
Conservative Temperature and pressure.
Parameters
----------
SA : array_like
Absolute salinity [g kg :sup:`-1`]
CT : array_like
Conservative Temperature [:math:`^\circ` C (ITS-90)]
p : array_like
pressure [dbar]
Returns
-------
sound_speed_CT_exact : array_like
Speed of sound in seawater [m s :sup:`-1`]
See Also
--------
TODO
Notes
-----
TODO
Examples
--------
TODO
References
----------
.. [1] IOC, SCOR and IAPSO, 2010: The international thermodynamic equation
of seawater - 2010: Calculation and use of thermodynamic properties.
Intergovernmental Oceanographic Commission, Manuals and Guides No. 56,
UNESCO (English), 196 pp. See Eqn. (2.17.1).
Modifications:
2011-04-05. David Jackett, Paul Barker and Trevor McDougall.
"""
t = t_from_CT(SA, CT, p)
return sound_speed_t_exact(SA, t, p)
def internal_energy_CT_exact(SA, CT, p):
r"""Calculates the specific internal energy of seawater from Absolute
Salinity, Conservative Temperature and pressure.
Parameters
----------
SA : array_like
Absolute Salinity [g/kg]
CT : array_like
Conservative Temperature [:math:`^\circ` C (ITS-90)]
p : array_like
sea pressure [dbar]
Returns
-------
internal_energy_CT_exact: array_like
specific internal energy (u) [J/kg]
See Also
--------
TODO
Notes
-----
TODO
Examples
--------
TODO
References
----------
.. [1] IOC, SCOR and IAPSO, 2010: The international thermodynamic equation
of seawater - 2010: Calculation and use of thermodynamic properties.
Intergovernmental Oceanographic Commission, Manuals and Guides No. 56,
UNESCO (English), 196 pp. See Eqn. (2.11.1).
Modifications:
2011-04-05. Trevor McDougall.
"""
t = t_from_CT(SA, CT, p)
return internal_energy_t_exact(SA, t, p)
def t_freezing(SA, p, saturation_fraction=1):
r"""Calculates the in-situ temperature at which seawater freezes.
Parameters
----------
SA : array_like
Absolute Salinity [g/kg]
p : array_like
sea pressure [dbar]
saturation_fraction : fraction between 0, 1. The saturation fraction of
dissolved air in seawater. Default is 0 or
completely saturated.
Returns
-------
t_freezing : array_like
in-situ temperature at which seawater freezes
[:math:`^\circ` C (ITS-90)]
See Also
--------
TODO
Notes
-----
TODO
Examples
--------
TODO
References
----------
.. [1] IOC, SCOR and IAPSO, 2010: The international thermodynamic equation
of seawater - 2010: Calculation and use of thermodynamic properties.
Intergovernmental Oceanographic Commission, Manuals and Guides No. 56,
UNESCO (English), 196 pp. See sections 3.33 and 3.34.
Modifications:
2011-11-03. Trevor McDougall, Paul Barker and Rainer Feistal.
"""
"""This function, t_freezing, calculates the in-situ freezing temperature,
t_freezing, of seawater by first evaluating a polynomial of the
Conservative Temperature at which seawater freezes, CT_freezing, using
the GSW function CT_freezing. The in-situ freezing temperature is then
calculated using the GSW function t_from_CT. However, if one wanted to
compute the in-situ freezing temperature directly from a single polynomial
expression without first calculating the Conservative Temperature at the
freezing point, the following lines of code achieve this. The error of the
following fit is similar to that of the present function, t_freezing, and
ranges between -8e-4 K and 3e-4 K when compared with the in-situ freezing
temperature evaluated by Newton-Raphson iteration of the equality of the
chemical potentials of water in seawater and in ice. (Note that the
in-situ freezing temperature can be found by this exact method using the
function sea_ice_freezingtemperature_si in the SIA library).
SA_r = SA * 1e-2
x = np.sqrt(SA_r)
p_r = p * 1e-4
t_freeze = T[0] + SA_r * (T[1] + x * (T[2] + x * (T[3] + x * (T[4] + x *
(T[5] + T[6] * x))))) + p_r * (T[7] + p_r * (T[8] + T[9] *
p_r)) + SA_r * p_r * (T[10] + p_r * (T[12] + p_r * (T[15] +
T[21] * SA_r)) + SA_r * (T[13] + T[17] * p_r + T[19] * SA_r) +
x * (T[11] + p_r * (T[14] + T[18] * p_r) + SA_r * (T[16] +
T[20] * p_r + T[22] * SA_r)))
Adjust for the effects of dissolved air
t_freezing -= saturation_fraction * (1e-3) * (2.4 - SA / 70.33008)
"""
SA, p, saturation_fraction = np.broadcast_arrays(SA, p,
saturation_fraction)
if (SA < 0).any():
raise ValueError('SA must be non-negative!')
if np.logical_or(saturation_fraction < 0, saturation_fraction > 1).any():
raise ValueError('Saturation_fraction MUST be between zero and one.')
CT_freeze = CT_freezing(SA, p, saturation_fraction)
t_freeze = t_from_CT(SA, CT_freeze, p)
tmp = np.logical_or(p > 10000, SA > 120)
out = np.logical_or(tmp, p + SA * 71.428571428571402 > 13571.42857142857)
t_freeze[out] = np.ma.masked
return t_freeze
def enthalpy_diff_CT_exact(SA, CT, p_shallow, p_deep):
r"""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. The output
(enthalpy_diff_CT_exact) is the specific enthalpy evaluated at
(SA, CT, p_deep) minus the specific enthalpy at (SA,CT,p_shallow).
parameters
----------
Parameters
----------
SA : array_like
Absolute Salinity [g/kg]
CT : array_like
Conservative Temperature [:math:`^\circ` C (ITS-90)]
p_shallow : array_like
lower sea pressure [dbar]
p_deep : array-like
upper sea pressure [dbar]
returns
-------
enthalpy_diff_CT_exact : array_like
difference of specific enthalpy [J/kg]
(deep minus shallow)
See Also
--------
TODO
Notes
-----
This function uses the full Gibbs function. There is an alternative to
calling this function, namely enthalpy_diff_CT(SA, CT, p), which uses the
computationally efficient 48-term expression for density in terms of SA, CT
and p (McDougall et al., 2011).
Examples
--------
TODO
References
----------
.. [1] IOC, SCOR and IAPSO, 2010: The international thermodynamic equation
of seawater - 2010: Calculation and use of thermodynamic properties.
Intergovernmental Oceanographic Commission, Manuals and Guides No. 56,
UNESCO (English), 196 pp. See Eqns (3.32.2).
.. [2] McDougall T.J., P.M. Barker, R. Feistel and D.R. Jackett, 2011: A
computationally efficient 48-term expression for the density of
seawater in terms of Conservative Temperature, and related properties
of seawater.
Modifications:
2011-04-06. Trevor McDougall and Paul Barker.
"""
t_shallow = t_from_CT(SA, CT, p_shallow)
t_deep = t_from_CT(SA, CT, p_deep)
return (enthalpy_t_exact(SA, t_deep, p_deep) -
enthalpy_t_exact(SA, t_shallow, p_shallow))
def sigma4_CT_exact(SA, CT):
r"""Calculates potential density anomaly with reference pressure of
4000 dbar."""
t = t_from_CT(SA, CT, 4000.)
return rho_t_exact(SA, t, 4000.) - 1000
def t_freezing(SA, p, saturation_fraction=1):
r"""Calculates the in-situ temperature at which seawater freezes.
Parameters
----------
SA : array_like
Absolute Salinity [g/kg]
p : array_like
sea pressure [dbar]
saturation_fraction : fraction between 0, 1. The saturation fraction of
dissolved air in seawater. Default is 0 or
completely saturated.
Returns
-------
t_freezing : array_like
in-situ temperature at which seawater freezes
[:math:`^\circ` C (ITS-90)]
See Also
--------
TODO
Notes
-----
TODO
Examples
--------
TODO
References
----------
.. [1] IOC, SCOR and IAPSO, 2010: The international thermodynamic equation
of seawater - 2010: Calculation and use of thermodynamic properties.
Intergovernmental Oceanographic Commission, Manuals and Guides No. 56,
UNESCO (English), 196 pp. See sections 3.33 and 3.34.
Modifications:
2011-11-03. Trevor McDougall, Paul Barker and Rainer Feistal.
"""
"""This function, t_freezing, calculates the in-situ freezing temperature,
t_freezing, of seawater by first evaluating a polynomial of the
Conservative Temperature at which seawater freezes, CT_freezing, using
the GSW function CT_freezing. The in-situ freezing temperature is then
calculated using the GSW function t_from_CT. However, if one wanted to
compute the in-situ freezing temperature directly from a single polynomial
expression without first calculating the Conservative Temperature at the
freezing point, the following lines of code achieve this. The error of the
following fit is similar to that of the present function, t_freezing, and
ranges between -8e-4 K and 3e-4 K when compared with the in-situ freezing
temperature evaluated by Newton-Raphson iteration of the equality of the
chemical potentials of water in seawater and in ice. (Note that the
in-situ freezing temperature can be found by this exact method using the
function sea_ice_freezingtemperature_si in the SIA library).
SA_r = SA * 1e-2
x = np.sqrt(SA_r)
p_r = p * 1e-4
t_freeze = T[0] + SA_r * (T[1] + x * (T[2] + x * (T[3] + x * (T[4] + x *
(T[5] + T[6] * x))))) + p_r * (T[7] + p_r * (T[8] + T[9] *
p_r)) + SA_r * p_r * (T[10] + p_r * (T[12] + p_r * (T[15] +
T[21] * SA_r)) + SA_r * (T[13] + T[17] * p_r + T[19] * SA_r) +
x * (T[11] + p_r * (T[14] + T[18] * p_r) + SA_r * (T[16] +
T[20] * p_r + T[22] * SA_r)))
Adjust for the effects of dissolved air
t_freezing -= saturation_fraction * (1e-3) * (2.4 - SA / 70.33008)
"""
SA, p, saturation_fraction = np.broadcast_arrays(SA, p,
saturation_fraction)
if (SA < 0).any():
raise ValueError('SA must be non-negative!')
if np.logical_or(saturation_fraction < 0, saturation_fraction > 1).any():
raise ValueError('Saturation_fraction MUST be between zero and one.')
CT_freeze = CT_freezing(SA, p, saturation_fraction)
t_freeze = t_from_CT(SA, CT_freeze, p)
tmp = np.logical_or(p > 10000, SA > 120)
out = np.logical_or(tmp, p + SA * 71.428571428571402 > 13571.42857142857)
t_freeze[out] = np.ma.masked
return t_freeze
