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 pt0_from_t(SA, t, p):
r"""Calculates potential temperature with reference pressure, pr = 0 dbar.
The present routine is computationally faster than the more general
function "pt_from_t(SA, t, p, pr)" which can be used for any reference
pressure value.
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]
Returns
-------
pt0 : array_like
potential temperature relative to 0 dbar [:math:`^\circ` C (ITS-90)]
See Also
--------
entropy_part, gibbs_pt0_pt0, entropy_part_zerop
Notes
-----
pt_from_t has the same result (only slower)
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.pt0_from_t(SA, t, p)
array([ 28.78319682, 28.42098334, 22.7849304 , 10.23052366,
6.82923022, 4.32451057])
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., 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.
"""
s1 = SA * (35. / SSO)
pt0 = t + p * (8.65483913395442e-6 -
s1 * 1.41636299744881e-6 -
p * 7.38286467135737e-9 +
t * (-8.38241357039698e-6 +
s1 * 2.83933368585534e-8 +
t * 1.77803965218656e-8 +
p * 1.71155619208233e-10))
dentropy_dt = cp0 / ((Kelvin + pt0) * (1 - 0.05 *
(1 - SA / SSO)))
true_entropy_part = entropy_part(SA, t, p)
for Number_of_iterations in range(0, 2, 1):
pt0_old = pt0
dentropy = entropy_part_zerop(SA, pt0_old) - true_entropy_part
pt0 = pt0_old - dentropy / dentropy_dt # Half way through mod. method.
pt0m = 0.5 * (pt0 + pt0_old)
dentropy_dt = -gibbs_pt0_pt0(SA, pt0m)
pt0 = pt0_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 pt0
def pt0_from_t(SA, t, p):
r"""Calculates potential temperature with reference pressure, pr = 0 dbar.
The present routine is computationally faster than the more general
function "pt_from_t(SA, t, p, pr)" which can be used for any reference
pressure value.
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]
Returns
-------
pt0 : array_like
potential temperature relative to 0 dbar [:math:`^\circ` C (ITS-90)]
See Also
--------
entropy_part, gibbs_pt0_pt0, entropy_part_zerop
Notes
-----
pt_from_t has the same result (only slower)
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.pt0_from_t(SA, t, p)
array([ 28.78319682, 28.42098334, 22.7849304 , 10.23052366,
6.82923022, 4.32451057])
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., 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 = np.maximum(SA, 0)
s1 = SA * (35. / SSO)
pt0 = t + p * (8.65483913395442e-6 -
s1 * 1.41636299744881e-6 -
p * 7.38286467135737e-9 +
t * (-8.38241357039698e-6 +
s1 * 2.83933368585534e-8 +
t * 1.77803965218656e-8 +
p * 1.71155619208233e-10))
dentropy_dt = cp0 / ((Kelvin + pt0) * (1 - 0.05 * (1 - SA / SSO)))
true_entropy_part = entropy_part(SA, t, p)
for Number_of_iterations in range(0, 2, 1):
pt0_old = pt0
dentropy = entropy_part_zerop(SA, pt0_old) - true_entropy_part
# Half way the mod. method (McDougall and Wotherspoon, 2012).
pt0 = pt0_old - dentropy / dentropy_dt
pt0m = 0.5 * (pt0 + pt0_old)
dentropy_dt = -gibbs_pt0_pt0(SA, pt0m)
pt0 = pt0_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 pt0
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
