def CT_from_pt(SA, pt):
r"""Calculates Conservative Temperature of seawater from potential
temperature (whose reference sea pressure is zero dbar).
Parameters
----------
SA : array_like
Absolute salinity [g kg :sup:`-1`]
pt : array_like
potential temperature referenced to a sea pressure of zero dbar
[:math:`^\circ` C (ITS-90)]
Returns
-------
CT : array_like
Conservative Temperature [:math:`^\circ` C (ITS-90)]
See Also
--------
TODO
Notes
-----
TODO
Examples
--------
>>> import gsw
>>> SA = [34.7118, 34.8915, 35.0256, 34.8472, 34.7366, 34.7324]
>>> pt = [28.7832, 28.4209, 22.7850, 10.2305, 6.8292, 4.3245]
>>> gsw.CT_from_pt(SA, pt)
array([ 28.80992302, 28.43914426, 22.78624661, 10.22616561,
6.82718342, 4.32356518])
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 section 3.3.
Modifications:
2011-03-29. David Jackett, Trevor McDougall and Paul Barker.
"""
SA, pt, mask = strip_mask(SA, pt)
pot_enthalpy = pot_enthalpy_from_pt(SA, pt)
CT = pot_enthalpy / cp0
return np.ma.array(CT, mask=mask, copy=False)
def CT_from_pt(SA, pt):
r"""Calculates Conservative Temperature of seawater from potential
temperature (whose reference sea pressure is zero dbar).
Parameters
----------
SA : array_like
Absolute salinity [g kg :sup:`-1`]
pt : array_like
potential temperature referenced to a sea pressure of zero dbar
[:math:`^\circ` C (ITS-90)]
Returns
-------
CT : array_like
Conservative Temperature [:math:`^\circ` C (ITS-90)]
See Also
--------
TODO
Notes
-----
TODO
Examples
--------
>>> import gsw
>>> SA = [34.7118, 34.8915, 35.0256, 34.8472, 34.7366, 34.7324]
>>> pt = [28.7832, 28.4209, 22.7850, 10.2305, 6.8292, 4.3245]
>>> gsw.CT_from_pt(SA, pt)
array([ 28.80992302, 28.43914426, 22.78624661, 10.22616561,
6.82718342, 4.32356518])
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 section 3.3.
Modifications:
2011-03-29. David Jackett, Trevor McDougall and Paul Barker.
"""
SA, pt, mask = strip_mask(SA, pt)
pot_enthalpy = pot_enthalpy_from_pt(SA, pt)
CT = pot_enthalpy / cp0
return np.ma.array(CT, mask=mask, copy=False)
def pt_from_CT(SA, CT):
r"""Calculates potential temperature (with a reference sea pressure of zero
dbar) from Conservative Temperature.
Parameters
----------
SA : array_like
Absolute salinity [g kg :sup:`-1`]
CT : array_like
Conservative Temperature [:math:`^\circ` C (ITS-90)]
Returns
-------
pt : array_like
potential temperature referenced to a sea pressure of zero dbar
[:math:`^\circ` C (ITS-90)]
See Also
--------
specvol_anom
Notes
-----
This function uses 1.5 iterations through a modified Newton-Raphson (N-R)
iterative solution procedure, starting from a rational-function-based
initial condition for both pt and dCT_dpt.
Examples
--------
>>> import gsw
>>> SA = [34.7118, 34.8915, 35.0256, 34.8472, 34.7366, 34.7324]
>>> CT = [28.8099, 28.4392, 22.7862, 10.2262, 6.8272, 4.3236]
>>> gsw.pt_from_CT(SA, CT)
array([ 28.78317705, 28.4209556 , 22.78495347, 10.23053439,
6.82921659, 4.32453484])
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 3.1 and 3.3.
.. [2] McDougall T. J., D. R. Jackett, P. M. Barker, C. Roberts-Thomson,
R. Feistel and R. W. Hallberg, 2010: A computationally efficient 25-term
expression for the density of seawater in terms of Conservative
Temperature, and related properties of seawater.
Modifications:
2011-03-29. Trevor McDougall, David Jackett, Claire Roberts-Thomson and
Paul Barker.
"""
SA, CT, mask = strip_mask(SA, CT)
s1 = SA * 35. / SSO
a0 = -1.446013646344788e-2
a1 = -3.305308995852924e-3
a2 = 1.062415929128982e-4
a3 = 9.477566673794488e-1
a4 = 2.166591947736613e-3
a5 = 3.828842955039902e-3
b0 = 1.000000000000000e+0
b1 = 6.506097115635800e-4
b2 = 3.830289486850898e-3
b3 = 1.247811760368034e-6
a5CT = a5 * CT
b3CT = b3 * CT
CT_factor = (a3 + a4 * s1 + a5CT)
pt_num = a0 + s1 * (a1 + a2 * s1) + CT * CT_factor
pt_den = b0 + b1 * s1 + CT * (b2 + b3CT)
pt = pt_num / pt_den
dCT_dpt = pt_den / (CT_factor + a5CT - (b2 + b3CT + b3CT) * pt)
# 1.5 iterations through the modified Newton-Rapshon iterative method
CT_diff = CT_from_pt(SA, pt) - CT
pt_old = pt
pt = pt_old - CT_diff / dCT_dpt # 1/2-way through the 1st modified N-R.
ptm = 0.5 * (pt + pt_old)
# This routine calls gibbs_pt0_pt0(SA,pt0) to get the second derivative of
# the Gibbs function with respect to temperature at zero sea pressure.
dCT_dpt = -(ptm + Kelvin) * gibbs_pt0_pt0(SA, ptm) / cp0
pt = pt_old - CT_diff / dCT_dpt # End of 1st full modified N-R iteration.
CT_diff = CT_from_pt(SA, pt) - CT
pt_old = pt
pt = pt_old - CT_diff / dCT_dpt # 1.5 iterations of the modified N-R.
return np.ma.array(pt, mask=mask, copy=False)
def pot_enthalpy_from_pt(SA, pt):
r"""Calculates the potential enthalpy of seawater from potential
temperature (whose reference sea pressure is zero dbar).
Parameters
----------
SA : array_like
Absolute salinity [g kg :sup:`-1`]
pt : array_like
potential temperature referenced to a sea pressure of zero dbar
[:math:`^\circ` C (ITS-90)]
Returns
-------
pot_enthalpy : array_like
potential enthalpy [J kg :sup:`-1`]
See Also
--------
TODO
Notes
-----
TODO
Examples
--------
>>> import gsw
>>> SA = [34.7118, 34.8915, 35.0256, 34.8472, 34.7366, 34.7324]
>>> pt = [28.7832, 28.4209, 22.7850, 10.2305, 6.8292, 4.3245]
>>> gsw.pot_enthalpy_from_pt(SA, pt)
array([ 115005.40853458, 113525.30870246, 90959.68769935,
40821.50280454, 27253.21472227, 17259.10131183])
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 section 3.2.
Modifications:
2011-03-29. David Jackett, Trevor McDougall and Paul Barker
"""
SA, pt, mask = strip_mask(SA, pt)
x2 = sfac * SA
x = np.sqrt(x2)
y = pt * 0.025 # Normalize for F03 and F08
pot_enthalpy = (61.01362420681071 + y * (168776.46138048015 +
y * (-2735.2785605119625 + y * (2574.2164453821433 +
y * (-1536.6644434977543 + y * (545.7340497931629 +
(-50.91091728474331 - 18.30489878927802 * y) * y))))) +
x2 * (268.5520265845071 + y * (-12019.028203559312 +
y * (3734.858026725145 + y * (-2046.7671145057618 +
y * (465.28655623826234 + (-0.6370820302376359 -
10.650848542359153 * y) * y)))) +
x * (937.2099110620707 + y * (588.1802812170108 +
y * (248.39476522971285 + (-3.871557904936333 -
2.6268019854268356 * y) * y)) +
x * (-1687.914374187449 + x * (246.9598888781377 +
x * (123.59576582457964 - 48.5891069025409 * x)) +
y * (936.3206544460336 +
y * (-942.7827304544439 + y * (369.4389437509002 +
(-33.83664947895248 - 9.987880382780322 * y) * y)))))))
"""The above polynomial for pot_enthalpy is the full expression for
potential enthalpy in terms of SA and pt, obtained from the Gibbs function
as below. It has simply collected like powers of x and y so that it is
computationally faster than calling the Gibbs function twice as is done in
the commented code below. When this code below is run, the results are
identical to calculating pot_enthalpy as above, to machine precision.
n0, n1 = 0, 1
g000 = gibbs(n0, n0, n0, SA, pt, 0)
g010 = gibbs(n0, n1, n0, SA, pt, 0)
pot_enthalpy = g000 - (Kelvin + pt) * g010
This is the end of the alternative code
%timeit gsw.CT_from_pt(SA, pt)
1000 loops, best of 3: 1.34 ms per loop <- calling gibbs
1000 loops, best of 3: 254 us per loop <- standard
"""
return np.ma.array(pot_enthalpy, mask=mask, copy=False)
def pt_from_CT(SA, CT):
r"""Calculates potential temperature (with a reference sea pressure of zero
dbar) from Conservative Temperature.
Parameters
----------
SA : array_like
Absolute salinity [g kg :sup:`-1`]
CT : array_like
Conservative Temperature [:math:`^\circ` C (ITS-90)]
Returns
-------
pt : array_like
potential temperature referenced to a sea pressure of zero dbar
[:math:`^\circ` C (ITS-90)]
See Also
--------
specvol_anom
Notes
-----
This function uses 1.5 iterations through a modified Newton-Raphson (N-R)
iterative solution procedure, starting from a rational-function-based
initial condition for both pt and dCT_dpt.
Examples
--------
>>> import gsw
>>> SA = [34.7118, 34.8915, 35.0256, 34.8472, 34.7366, 34.7324]
>>> CT = [28.8099, 28.4392, 22.7862, 10.2262, 6.8272, 4.3236]
>>> gsw.pt_from_CT(SA, CT)
array([ 28.78317705, 28.4209556 , 22.78495347, 10.23053439,
6.82921659, 4.32453484])
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 3.1 and 3.3.
.. [2] McDougall T. J., D. R. Jackett, P. M. Barker, C. Roberts-Thomson,
R. Feistel and R. W. Hallberg, 2010: A computationally efficient 25-term
expression for the density of seawater in terms of Conservative
Temperature, and related properties of seawater.
Modifications:
2011-03-29. Trevor McDougall, David Jackett, Claire Roberts-Thomson and
Paul Barker.
"""
SA, CT, mask = strip_mask(SA, CT)
SA = np.maximum(SA, 0)
s1 = SA * 35. / SSO
a0 = -1.446013646344788e-2
a1 = -3.305308995852924e-3
a2 = 1.062415929128982e-4
a3 = 9.477566673794488e-1
a4 = 2.166591947736613e-3
a5 = 3.828842955039902e-3
b0 = 1.000000000000000e+0
b1 = 6.506097115635800e-4
b2 = 3.830289486850898e-3
b3 = 1.247811760368034e-6
a5CT = a5 * CT
b3CT = b3 * CT
CT_factor = (a3 + a4 * s1 + a5CT)
pt_num = a0 + s1 * (a1 + a2 * s1) + CT * CT_factor
pt_den = b0 + b1 * s1 + CT * (b2 + b3CT)
pt = pt_num / pt_den
dCT_dpt = pt_den / (CT_factor + a5CT - (b2 + b3CT + b3CT) * pt)
# 1.5 iterations through the modified Newton-Rapshon iterative method
CT_diff = CT_from_pt(SA, pt) - CT
pt_old = pt
pt = pt_old - CT_diff / dCT_dpt # 1/2-way through the 1st modified N-R.
ptm = 0.5 * (pt + pt_old)
# This routine calls gibbs_pt0_pt0(SA, pt0) to get the second derivative of
# the Gibbs function with respect to temperature at zero sea pressure.
dCT_dpt = -(ptm + Kelvin) * gibbs_pt0_pt0(SA, ptm) / cp0
pt = pt_old - CT_diff / dCT_dpt # End of 1st full modified N-R iteration.
CT_diff = CT_from_pt(SA, pt) - CT
pt_old = pt
pt = pt_old - CT_diff / dCT_dpt # 1.5 iterations of the modified N-R.
# Abs max error of result is 1.42e-14 deg C.
return np.ma.array(pt, mask=mask, copy=False)
def pot_enthalpy_from_pt(SA, pt):
r"""Calculates the potential enthalpy of seawater from potential
temperature (whose reference sea pressure is zero dbar).
Parameters
----------
SA : array_like
Absolute salinity [g kg :sup:`-1`]
pt : array_like
potential temperature referenced to a sea pressure of zero dbar
[:math:`^\circ` C (ITS-90)]
Returns
-------
pot_enthalpy : array_like
potential enthalpy [J kg :sup:`-1`]
See Also
--------
TODO
Notes
-----
TODO
Examples
--------
>>> import gsw
>>> SA = [34.7118, 34.8915, 35.0256, 34.8472, 34.7366, 34.7324]
>>> pt = [28.7832, 28.4209, 22.7850, 10.2305, 6.8292, 4.3245]
>>> gsw.pot_enthalpy_from_pt(SA, pt)
array([ 115005.40853458, 113525.30870246, 90959.68769935,
40821.50280454, 27253.21472227, 17259.10131183])
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 section 3.2.
Modifications:
2011-03-29. David Jackett, Trevor McDougall and Paul Barker
"""
SA, pt, mask = strip_mask(SA, pt)
SA = np.maximum(SA, 0)
x2 = sfac * SA
x = np.sqrt(x2)
y = pt * 0.025 # Normalize for F03 and F08
pot_enthalpy = (
61.01362420681071 + y *
(168776.46138048015 + y *
(-2735.2785605119625 + y *
(2574.2164453821433 + y *
(-1536.6644434977543 + y *
(545.7340497931629 +
(-50.91091728474331 - 18.30489878927802 * y) * y))))) + x2 *
(268.5520265845071 + y *
(-12019.028203559312 + y *
(3734.858026725145 + y *
(-2046.7671145057618 + y *
(465.28655623826234 +
(-0.6370820302376359 - 10.650848542359153 * y) * y)))) + x *
(937.2099110620707 + y *
(588.1802812170108 + y *
(248.39476522971285 +
(-3.871557904936333 - 2.6268019854268356 * y) * y)) + x *
(-1687.914374187449 + x *
(246.9598888781377 + x *
(123.59576582457964 - 48.5891069025409 * x)) + y *
(936.3206544460336 + y *
(-942.7827304544439 + y *
(369.4389437509002 +
(-33.83664947895248 - 9.987880382780322 * y) * y)))))))
"""The above polynomial for pot_enthalpy is the full expression for
potential enthalpy in terms of SA and pt, obtained from the Gibbs function
as below. It has simply collected like powers of x and y so that it is
computationally faster than calling the Gibbs function twice as is done in
the commented code below. When this code below is run, the results are
identical to calculating pot_enthalpy as above, to machine precision.
g000 = gibbs(n0, n0, n0, SA, pt, 0)
g010 = gibbs(n0, n1, n0, SA, pt, 0)
pot_enthalpy = g000 - (Kelvin + pt) * g010
This is the end of the alternative code
%timeit gsw.CT_from_pt(SA, pt)
1000 loops, best of 3: 1.34 ms per loop <- calling gibbs
1000 loops, best of 3: 254 us per loop <- standard
"""
return np.ma.array(pot_enthalpy, mask=mask, copy=False)
