def entropy_derivative_SA_SA(SA, CT):
CT_SA = (gibbs(n1, n0, n0, SA, pt, 0) -
(abs_pt * gibbs(n1, n1, n0, SA, pt, 0))) / cp0
eta_SA_CT = entropy_derivative_SA_CT(SA, CT)
return -gibbs(n2, n0, n0, SA, pt, 0) / abs_pt - CT_SA * eta_SA_CT
def enthalpy_derivative_SA_SA(SA, CT, p):
SA[SA < 1e-100] = 1e-100 # NOTE: Here is the changes from 2.0 to 3.0.
h_CT_CT = enthalpy_derivative_CT_CT(SA, CT, p)
return (gibbs(n2, n0, n0, SA, t, p) -
temp_ratio * gibbs(n2, n0, n0, SA, pt0, 0) +
temp_ratio * gST_pt0 ** 2 * rec_gTT_pt0 -
gST_t ** 2 * rec_gTT_t - 2.0 * gS_pt0 * part +
factor ** 2 * h_CT_CT)
def entropy_first_derivatives(SA, CT):
r"""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
----------
SA : array_like
Absolute salinity [g kg :sup:`-1`]
CT : array_like
Conservative Temperature [:math:`^\circ` C (TEOS-10)]
Returns
-------
eta_SA : array_like
The derivative of specific entropy with respect to SA at constant
CT [J g :sup:`-1` K :sup:`-1`]
eta_CT : array_like
The derivative of specific entropy with respect to CT at constant
SA [ J (kg K :sup:`-2`) :sup:`-1` ]
See Also
--------
TODO
Notes
-----
TODO
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.entropy_first_derivatives(SA, CT)
array([[ -0.2632868 , -0.26397728, -0.2553675 , -0.23806659,
-0.23443826, -0.23282068],
[ 13.22103121, 13.23691119, 13.48900463, 14.08659902,
14.25772958, 14.38642995]])
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. (A.12.8) and (P.14a,c).
Modifications:
2011-03-29. Trevor McDougall.
"""
n0, n1 = 0, 1
pt = pt_from_CT(SA, CT)
eta_SA = -(gibbs(n1, n0, n0, SA, pt, 0)) / (Kelvin + pt)
eta_CT = cp0 / (Kelvin + pt)
return eta_SA, eta_CT
def entropy_from_CT(SA, CT):
r"""Calculates specific entropy of seawater.
Parameters
----------
SA : array_like
Absolute salinity [g kg :sup:`-1`]
CT : array_like
Conservative Temperature [:math:`^\circ` C (ITS-90)]
Returns
-------
entropy : array_like
specific entropy [J kg :sup:`-1` K :sup:`-1`]
See Also
--------
TODO
Notes
-----
TODO
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.entropy_from_CT(SA, CT)
array([ 400.38916315, 395.43781023, 319.86680989, 146.79103279,
98.64714648, 62.79185763])
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 appendix A.10.
Modifications:
2011-04-04. Trevor McDougall & Paul Barker
"""
SA = np.maximum(SA, 0)
n0, n1 = 0, 1
pt0 = pt_from_CT(SA, CT)
return -gibbs(n0, n1, n0, SA, pt0, 0)
def entropy_from_pt(SA, pt):
r"""Calculates specific entropy of seawater.
Parameters
----------
SA : array_like
Absolute salinity [g kg :sup:`-1`]
pt : array_like
potential temperature [:math:`^\circ` C (ITS-90)]
Returns
-------
entropy : array_like
specific entropy [J kg :sup:`-1` K :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, 28.4210, 22.7850, 10.2305, 6.8292, 4.3245]
>>> gsw.entropy_from_pt(SA, pt)
array([ 400.38946744, 395.43839949, 319.86743859, 146.79054828,
98.64691006, 62.79135672])
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 appendix A.10.
Modifications:
2011-04-03. Trevor McDougall & Paul Barker
"""
SA = np.maximum(SA, 0)
n0, n1 = 0, 1
return -gibbs(n0, n1, n0, SA, pt, 0)
def entropy_from_CT(SA, CT):
r"""Calculates specific entropy of seawater.
Parameters
----------
SA : array_like
Absolute salinity [g kg :sup:`-1`]
CT : array_like
Conservative Temperature [:math:`^\circ` C (ITS-90)]
Returns
-------
entropy : array_like
specific entropy [J kg :sup:`-1` K :sup:`-1`]
See Also
--------
TODO
Notes
-----
TODO
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.entropy_from_CT(SA, CT)
array([ 400.38916315, 395.43781023, 319.86680989, 146.79103279,
98.64714648, 62.79185763])
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 appendix A.10.
Modifications:
2011-04-04. Trevor McDougall & Paul Barker
"""
SA = np.maximum(SA, 0)
pt0 = pt_from_CT(SA, CT)
return -gibbs(n0, n1, n0, SA, pt0, 0)
def entropy_from_pt(SA, pt):
r"""Calculates specific entropy of seawater.
Parameters
----------
SA : array_like
Absolute salinity [g kg :sup:`-1`]
pt : array_like
potential temperature [:math:`^\circ` C (ITS-90)]
Returns
-------
entropy : array_like
specific entropy [J kg :sup:`-1` K :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, 28.4210, 22.7850, 10.2305, 6.8292, 4.3245]
>>> gsw.entropy_from_pt(SA, pt)
array([ 400.38946744, 395.43839949, 319.86743859, 146.79054828,
98.64691006, 62.79135672])
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 appendix A.10.
Modifications:
2011-04-03. Trevor McDougall & Paul Barker
"""
SA = np.maximum(SA, 0)
return -gibbs(n0, n1, n0, SA, pt, 0)
def entropy_from_t(SA, t, p):
"""
gsw_entropy_from_t specific entropy of seawater
==========================================================================
USAGE:
entropy = gsw_entropy_from_t(SA,t,p)
DESCRIPTION:
Calculates specific entropy of seawater.
INPUT:
SA = Absolute Salinity [ g/kg ]
t = in-situ temperature (ITS-90) [ deg C ]
p = sea pressure [ dbar ]
( i.e. absolute pressure - 10.1325 dbar )
SA & t need to have the same dimensions.
p may have dimensions 1x1 or Mx1 or 1xN or MxN, where SA & t are MxN.
OUTPUT:
entropy = specific entropy [ J/(kg*K) ]
AUTHOR:
David Jackett, Trevor McDougall and Paul Barker [ [email protected] ]
VERSION NUMBER: 3.03 (29th April, 2013)
REFERENCES:
IOC, SCOR and IAPSO, 2010: The international thermodynamic equation of
seawater - 2010: Calculation and use of thermodynamic properties.
Intergovernmental Oceanographic Commission, Manuals and Guides No. 56,
UNESCO (English), 196 pp. Available from http://www.TEOS-10.org
"""
return -gibbs(n0, n1, n0, SA, t, p)
def CT_first_derivatives(SA, pt):
r"""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
----------
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_SA : array_like
The derivative of CT with respect to SA at constant potential
temperature reference sea pressure of 0 dbar.
[K (g kg :sup:`-1`) :sup:`-1`]
CT_pt : array_like
The derivative of CT with respect to pt at constant SA.
[ unitless ]
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_first_derivatives(SA, pt)
array([[-0.04198109, -0.04155814, -0.03473921, -0.0187111 , -0.01407594,
-0.01057172],
[ 1.00281494, 1.00255482, 1.00164514, 1.00000377, 0.99971636,
0.99947433]])
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. (A.12.3) and (A.12.9a,b).
.. [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:
2010-08-05. Trevor McDougall and Paul Barker.
"""
# FIXME: Matlab version 3.0 has a copy-and-paste of the gibbs function here
# instead of a call. Why?
abs_pt = Kelvin + pt
CT_pt = -(abs_pt * gibbs(n0, n2, n0, SA, pt, 0)) / cp0
x2 = sfac * SA
x = np.sqrt(x2)
y_pt = 0.025 * pt
g_SA_T_mod = (1187.3715515697959 + x * (-1480.222530425046 + x *
(2175.341332000392 + x * (-980.14153344888 +
220.542973797483 * x) + y_pt * (-548.4580073635929 + y_pt *
(592.4012338275047 + y_pt * (-274.2361238716608 +
49.9394019139016 * y_pt)))) + y_pt * (-258.3988055868252 +
y_pt * (-90.2046337756875 + y_pt * 10.50720794170734))) +
y_pt * (3520.125411988816 + y_pt * (-1351.605895580406 +
y_pt * (731.4083582010072 + y_pt * (-216.60324087531103 +
25.56203650166196 * y_pt)))))
g_SA_T_mod *= 0.5 * sfac * 0.025
g_SA_mod = (8645.36753595126 + x * (-7296.43987145382 + x *
(8103.20462414788 + y_pt * (2175.341332000392 + y_pt *
(-274.2290036817964 + y_pt * (197.4670779425016 + y_pt *
(-68.5590309679152 + 9.98788038278032 * y_pt)))) + x *
(-5458.34205214835 - 980.14153344888 * y_pt + x *
(2247.60742726704 - 340.1237483177863 * x + 220.542973797483 *
y_pt))) + y_pt * (-1480.222530425046 + y_pt *
(-129.1994027934126 + y_pt * (-30.0682112585625 + y_pt *
(2.626801985426835))))) + y_pt * (1187.3715515697959 + y_pt *
(1760.062705994408 + y_pt * (-450.535298526802 + y_pt *
(182.8520895502518 + y_pt * (-43.3206481750622 +
4.26033941694366 * y_pt))))))
g_SA_mod *= 0.5 * sfac
CT_SA = (g_SA_mod - abs_pt * g_SA_T_mod) / cp0
return CT_SA, CT_pt
def entropy_derivative_CT_CT(SA, CT):
CT_pt = -(abs_pt * gibbs(n0, n2, n0, SA, pt, 0)) / cp0
return - cp0 / (CT_pt * abs_pt ** 2)
def pt_from_t(SA, t, p, p_ref=0):
r"""Calculates potential temperature with the general reference pressure,
pr, from in situ temperature.
Parameters
----------
SA : array_like
Absolute salinity [g kg :sup:`-1`]
t : array_like
in situ temperature [:math:`^\circ` C (ITS-90)]
p : array_like
pressure [dbar]
p_ref : int, float, optional
reference pressure, default = 0
Returns
-------
pt : array_like
potential temperature [:math:`^\circ` C (ITS-90)]
See Also
--------
TODO
Notes
-----
This function calls `entropy_part` which evaluates entropy except for the
parts which are a function of Absolute Salinity alone. A faster routine
exists pt0_from_t(SA,t,p) if p_ref is indeed zero dbar.
Examples
--------
>>> import gsw
>>> SA = [34.7118, 34.8915, 35.0256, 34.8472, 34.7366, 34.7324]
>>> t = [28.7856, 28.4329, 22.8103, 10.2600, 6.8863, 4.4036]
>>> p = [10, 50, 125, 250, 600, 1000]
>>> gsw.pt_from_t(SA, t, p)
array([ 28.78319682, 28.42098334, 22.7849304 , 10.23052366,
6.82923022, 4.32451057])
>>> gsw.pt_from_t(SA, t, p, pr = 1000)
array([ 29.02665528, 28.662375 , 22.99149634, 10.35341725,
6.92732954, 4.4036 ])
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 3.1.
.. [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:
2011-03-29. Trevor McDougall, David Jackett, Claire Roberts-Thomson and
Paul Barker.
"""
p_ref = np.asanyarray(p_ref)
SA = np.maximum(SA, 0)
s1 = SA * 35. / SSO
pt = (t + (p - p_ref) * (8.65483913395442e-6 -
s1 * 1.41636299744881e-6 -
(p + p_ref) * 7.38286467135737e-9 +
t * (-8.38241357039698e-6 +
s1 * 2.83933368585534e-8 +
t * 1.77803965218656e-8 +
(p + p_ref) * 1.71155619208233e-10)))
dentropy_dt = cp0 / ((Kelvin + pt) *
(1 - 0.05 * (1 - SA / SSO)))
true_entropy_part = entropy_part(SA, t, p)
for Number_of_iterations in range(0, 2, 1):
pt_old = pt
dentropy = entropy_part(SA, pt_old, p_ref) - true_entropy_part
pt = pt_old - dentropy / dentropy_dt # half way through the method
ptm = 0.5 * (pt + pt_old)
dentropy_dt = -gibbs(n0, n2, n0, SA, ptm, p_ref)
pt = pt_old - dentropy / dentropy_dt
"""maximum error of 6.3x10^-9 degrees C for one iteration. maximum error
is 1.8x10^-14 degrees C for two iterations (two iterations is the default,
"for Number_of_iterations = 1:2). These errors are over the full
"oceanographic funnel" of McDougall et al. (2010), which reaches down to
p = 8000 dbar."""
return pt
def enthalpy_derivative_p(SA, CT, p):
return gibbs(n0, n0, n1, SA, t, p)
def enthalpy_second_derivatives(SA, CT, p):
r"""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
----------
SA : array_like
Absolute salinity [g kg :sup:`-1`]
CT : array_like
Conservative Temperature [:math:`^\circ` C (TEOS-10)]
p : array_like
pressure [dbar]
Returns
-------
h_SA_SA : array_like
The second derivative of specific enthalpy with respect to
Absolute Salinity at constant CT & p. [J/(kg (g/kg)^2)]
h_SA_CT : array_like
The second derivative of specific enthalpy with respect to SA and
CT at constant p. [J/(kg K(g/kg))]
h_CT_CT : array_like
The second derivative of specific enthalpy with respect to CT at
constant SA and p. [J/(kg K^2)]
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. (A.11.18), (A.11.15) and (A.11.12.)
.. [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. To
be submitted to Ocean Science Discussions.
Modifications:
2011-03-29. Trevor McDougall.
"""
# NOTE: The Matlab version 3.0 mentions that this function is unchanged,
# but that's not true!
pt0 = pt_from_CT(SA, CT)
abs_pt0 = Kelvin + pt0
t = pt_from_t(SA, pt0, 0, p)
temp_ratio = (Kelvin + t) / abs_pt0
rec_gTT_pt0 = 1 / gibbs(n0, n2, n0, SA, pt0, 0)
rec_gTT_t = 1 / gibbs(n0, n2, n0, SA, t, p)
gST_pt0 = gibbs(n1, n1, n0, SA, pt0, 0)
gST_t = gibbs(n1, n1, n0, SA, t, p)
gS_pt0 = gibbs(n1, n0, n0, SA, pt0, 0)
part = ((temp_ratio * gST_pt0 * rec_gTT_pt0 - gST_t * rec_gTT_t) /
(abs_pt0))
factor = gS_pt0 / cp0
# h_CT_CT is naturally well-behaved as SA approaches zero.
def enthalpy_derivative_CT_CT(SA, CT, p):
return (cp0 ** 2 * ((temp_ratio * rec_gTT_pt0 - rec_gTT_t) /
(abs_pt0 * abs_pt0)))
# h_SA_SA has a singularity at SA = 0, and blows up as SA approaches zero.
def enthalpy_derivative_SA_SA(SA, CT, p):
SA[SA < 1e-100] = 1e-100 # NOTE: Here is the changes from 2.0 to 3.0.
h_CT_CT = enthalpy_derivative_CT_CT(SA, CT, p)
return (gibbs(n2, n0, n0, SA, t, p) -
temp_ratio * gibbs(n2, n0, n0, SA, pt0, 0) +
temp_ratio * gST_pt0 ** 2 * rec_gTT_pt0 -
gST_t ** 2 * rec_gTT_t - 2.0 * gS_pt0 * part +
factor ** 2 * h_CT_CT)
"""h_SA_CT should not blow up as SA approaches zero. The following lines of
code ensure that the h_SA_CT output of this function does not blow up in
this limit. That is, when SA < 1e-100 g/kg, we force the h_SA_CT output to
be the same as if SA = 1e-100 g/kg."""
def enthalpy_derivative_SA_CT(SA, CT, p):
h_CT_CT = enthalpy_derivative_CT_CT(SA, CT, p)
return cp0 * part - factor * h_CT_CT
return (enthalpy_derivative_SA_SA(SA, CT, p),
enthalpy_derivative_SA_CT(SA, CT, p),
enthalpy_derivative_CT_CT(SA, CT, p))
def enthalpy_derivative_SA(SA, CT, p):
return (gibbs(n1, n0, n0, SA, t, p) -
temp_ratio * gibbs(n1, n0, n0, SA, pt0, 0))
def entropy_second_derivatives(SA, CT):
r"""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
----------
SA : array_like
Absolute salinity [g kg :sup:`-1`]
CT : array_like
Conservative Temperature [:math:`^\circ` C (TEOS-10)]
Returns
-------
eta_SA_SA : array_like
The second derivative of specific entropy with respect to SA at
constant CT [J (kg K (g kg :sup:`-1` ) :sup:`2`) :sup:`-1`]
eta_SA_CT : array_like
The second derivative of specific entropy with respect to
SA and CT [J (kg (g kg :sup:`-1` ) K :sup:`2`) :sup:`-1` ]
eta_CT_CT : array_like
The second derivative of specific entropy with respect to CT at
constant SA [J (kg K :sup:`3`) :sup:`-1` ]
See Also
--------
TODO
Notes
-----
TODO
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.entropy_second_derivatives(SA, CT)
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. (P.14b) and (P.15a,b).
Modifications:
2011-03-29. Trevor McDougall and Paul Barker.
"""
pt = pt_from_CT(SA, CT)
abs_pt = Kelvin + pt
CT_SA = ((gibbs(n1, n0, n0, SA, pt, 0) -
(abs_pt * gibbs(n1, n1, n0, SA, pt, 0))) / cp0)
CT_pt = -(abs_pt * gibbs(n0, n2, n0, SA, pt, 0)) / cp0
eta_CT_CT = - cp0 / (CT_pt * abs_pt ** 2)
eta_SA_CT = CT_SA * eta_CT_CT
eta_SA_SA = -gibbs(n2, n0, n0, SA, pt, 0) / abs_pt - CT_SA * eta_SA_CT
return eta_SA_SA, eta_SA_CT, eta_CT_CT
def entropy_derivative_SA_CT(SA, CT):
CT_SA = (gibbs(n1, n0, n0, SA, pt, 0) -
(abs_pt * gibbs(n1, n1, n0, SA, pt, 0))) / cp0
return -CT_SA * entropy_derivative_CT_CT(SA, CT)
def pt_derivative_SA(SA, CT):
CT_SA = (gibbs(n1, n0, n0, SA, pt, 0) - abs_pt *
gibbs(n1, n1, n0, SA, pt, 0)) / cp0
return - CT_SA / CT_pt
def pt_from_t(SA, t, p, p_ref=0):
r"""Calculates potential temperature with the general reference pressure,
pr, from in situ temperature.
Parameters
----------
SA : array_like
Absolute salinity [g kg :sup:`-1`]
t : array_like
in situ temperature [:math:`^\circ` C (ITS-90)]
p : array_like
pressure [dbar]
p_ref : int, float, optional
reference pressure, default = 0
Returns
-------
pt : array_like
potential temperature [:math:`^\circ` C (ITS-90)]
See Also
--------
TODO
Notes
-----
This function calls `entropy_part` which evaluates entropy except for the
parts which are a function of Absolute Salinity alone. A faster routine
exists pt0_from_t(SA,t,p) if p_ref is indeed zero dbar.
Examples
--------
>>> import gsw
>>> SA = [34.7118, 34.8915, 35.0256, 34.8472, 34.7366, 34.7324]
>>> t = [28.7856, 28.4329, 22.8103, 10.2600, 6.8863, 4.4036]
>>> p = [10, 50, 125, 250, 600, 1000]
>>> gsw.pt_from_t(SA, t, p)
array([ 28.78319682, 28.42098334, 22.7849304 , 10.23052366,
6.82923022, 4.32451057])
>>> gsw.pt_from_t(SA, t, p, pr = 1000)
array([ 29.02665528, 28.662375 , 22.99149634, 10.35341725,
6.92732954, 4.4036 ])
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 3.1.
.. [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:
2011-03-29. Trevor McDougall, David Jackett, Claire Roberts-Thomson and
Paul Barker.
"""
p_ref = np.asanyarray(p_ref)
n0, n2 = 0, 2
SA[SA < 0] = 0
s1 = SA * 35. / SSO
pt = (t + (p - p_ref) * (8.65483913395442e-6 -
s1 * 1.41636299744881e-6 -
(p + p_ref) * 7.38286467135737e-9 +
t * (-8.38241357039698e-6 +
s1 * 2.83933368585534e-8 +
t * 1.77803965218656e-8 +
(p + p_ref) * 1.71155619208233e-10)))
dentropy_dt = cp0 / ((Kelvin + pt) * (1 - 0.05 *
(1 - SA / SSO)))
true_entropy_part = entropy_part(SA, t, p)
for Number_of_iterations in range(0, 2, 1):
pt_old = pt
dentropy = entropy_part(SA, pt_old, p_ref) - true_entropy_part
pt = pt_old - dentropy / dentropy_dt # half way through the method
ptm = 0.5 * (pt + pt_old)
dentropy_dt = -gibbs(n0, n2, n0, SA, ptm, p_ref)
pt = pt_old - dentropy / dentropy_dt
"""maximum error of 6.3x10^-9 degrees C for one iteration. maximum error
is 1.8x10^-14 degrees C for two iterations (two iterations is the default,
"for Number_of_iterations = 1:2). These errors are over the full
"oceanographic funnel" of McDougall et al. (2010), which reaches down to
p = 8000 dbar."""
return pt
def pt_first_derivatives(SA, CT):
r"""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
----------
SA : array_like
Absolute salinity [g kg :sup:`-1`]
CT : array_like
Conservative Temperature [:math:`^\circ` C (TEOS-10)]
Returns
-------
pt_SA : array_like
The derivative of potential temperature with respect to Absolute
Salinity at constant Conservative Temperature. [K/(g/kg)]
pt_CT : array_like
The derivative of potential temperature with respect to
Conservative Temperature at constant Absolute Salinity. [unitless]
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 Eqns. (A.12.6), (A.12.3), (P.6) and (P.8).
.. [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. To
be submitted to Ocean Science Discussions.
Modifications:
2011-03-29. Trevor McDougall and Paul Barker.
"""
pt = pt_from_CT(SA, CT)
abs_pt = Kelvin + pt
CT_SA = ((gibbs(n1, n0, n0, SA, pt, 0) - abs_pt *
gibbs(n1, n1, n0, SA, pt, 0)) / cp0)
CT_pt = - (abs_pt * gibbs(n0, n2, n0, SA, pt, 0)) / cp0
pt_SA = - CT_SA / CT_pt
pt_CT = 1.0 / CT_pt
return pt_SA, pt_CT
def CT_first_derivatives(SA, pt):
r"""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
----------
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_SA : array_like
The derivative of CT with respect to SA at constant potential
temperature reference sea pressure of 0 dbar.
[K (g kg :sup:`-1`) :sup:`-1`]
CT_pt : array_like
The derivative of CT with respect to pt at constant SA.
[ unitless ]
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_first_derivatives(SA, pt)
array([[-0.04198109, -0.04155814, -0.03473921, -0.0187111 , -0.01407594,
-0.01057172],
[ 1.00281494, 1.00255482, 1.00164514, 1.00000377, 0.99971636,
0.99947433]])
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. (A.12.3) and (A.12.9a,b).
.. [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:
2010-08-05. Trevor McDougall and Paul Barker.
"""
# FIXME: Matlab version 3.0 has a copy-and-paste of the gibbs function here
# instead of a call. Why?
n0, n1, n2 = 0, 1, 2
abs_pt = Kelvin + pt
g100 = gibbs(n1, n0, n0, SA, pt, 0)
g110 = gibbs(n1, n1, n0, SA, pt, 0)
g020 = gibbs(n0, n2, n0, SA, pt, 0)
def CT_derivative_SA(SA, pt):
return (g100 - abs_pt * g110) / cp0
def CT_derivative_pt(SA, pt):
return - (abs_pt * g020) / cp0
return CT_derivative_SA(SA, pt), CT_derivative_pt(SA, pt)