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seawater_functions.py
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def dens0(s, t):
"""
Density of Sea Water at atmospheric pressure.
Copied from the Seawater Package: https://pypi.org/project/seawater/
Parameters
----------
s(p=0) : array_like
salinity [psu (PSS-78)]
t(p=0) : array_like
temperature [℃ (ITS-90)]
Returns
-------
dens0(s, t) : array_like
density [kg m :sup:`3`] of salt water with properties
(s, t, p=0) 0 db gauge pressure
Examples
--------
>>> # Data from UNESCO Tech. Paper in Marine Sci. No. 44, p22
>>> import seawater as sw
>>> from seawater.library import T90conv
>>> s = [0, 0, 0, 0, 35, 35, 35, 35]
>>> t = T90conv([0, 0, 30, 30, 0, 0, 30, 30])
>>> sw.dens0(s, t)
array([ 999.842594 , 999.842594 , 995.65113374, 995.65113374,
1028.10633141, 1028.10633141, 1021.72863949, 1021.72863949])
References
----------
.. [1] Fofonoff, P. and Millard, R.C. Jr UNESCO 1983. Algorithms for
computation of fundamental properties of seawater. UNESCO Tech. Pap. in
Mar. Sci., No. 44, 53 pp. Eqn.(31) p.39.
http://unesdoc.unesco.org/images/0005/000598/059832eb.pdf
.. [2] Millero, F.J. and Poisson, A. International one-atmosphere
equation of state of seawater. Deep-Sea Res. 1981. Vol28A(6) pp625-629.
doi:10.1016/0198-0149(81)90122-9
"""
import numpy as np
s, t = list(map(np.asanyarray, (s, t)))
T68 = T68conv(t)
# UNESCO 1983 Eqn.(13) p17.
b = (8.24493e-1, -4.0899e-3, 7.6438e-5, -8.2467e-7, 5.3875e-9)
c = (-5.72466e-3, 1.0227e-4, -1.6546e-6)
d = 4.8314e-4
return (smow(t) + (b[0] + (b[1] + (b[2] + (b[3] + b[4] * T68) * T68) *
T68) * T68) * s + (c[0] + (c[1] + c[2] * T68) * T68) * s *
s ** 0.5 + d * s ** 2)
def dens(s, t, p):
"""
Density of Sea Water using UNESCO 1983 (EOS 80) polynomial.
Copied from the Seawater Package: https://pypi.org/project/seawater/
Parameters
----------
s(p) : array_like
salinity [psu (PSS-78)]
t(p) : array_like
temperature [℃ (ITS-90)]
p : array_like
pressure [db].
Returns
-------
dens : array_like
density [kg m :sup:`3`]
Examples
--------
>>> # Data from Unesco Tech. Paper in Marine Sci. No. 44, p22.
>>> import seawater as sw
>>> from seawater.library import T90conv
>>> s = [0, 0, 0, 0, 35, 35, 35, 35]
>>> t = T90conv([0, 0, 30, 30, 0, 0, 30, 30])
>>> p = [0, 10000, 0, 10000, 0, 10000, 0, 10000]
>>> sw.dens(s, t, p)
array([ 999.842594 , 1045.33710972, 995.65113374, 1036.03148891,
1028.10633141, 1070.95838408, 1021.72863949, 1060.55058771])
References
----------
.. [1] Fofonoff, P. and Millard, R.C. Jr UNESCO 1983. Algorithms for
computation of fundamental properties of seawater. UNESCO Tech. Pap. in
Mar. Sci., No. 44, 53 pp. Eqn.(31) p.39.
http://unesdoc.unesco.org/images/0005/000598/059832eb.pdf
.. [2] Millero, F.J., Chen, C.T., Bradshaw, A., and Schleicher, K. A new
high pressure equation of state for seawater. Deap-Sea Research., 1980,
Vol27A, pp255-264. doi:10.1016/0198-0149(80)90016-3
"""
import numpy as np
s, t, p = list(map(np.asanyarray, (s, t, p)))
# UNESCO 1983. Eqn..7 p.15.
densP0 = dens0(s, t)
K = seck(s, t, p)
p = p / 10. # Convert from db to atm pressure units.
return densP0 / (1 - p / K)
def seck(s, t, p=0):
"""
Secant Bulk Modulus (K) of Sea Water using Equation of state 1980.
UNESCO polynomial implementation.
Parameters
----------
s(p) : array_like
salinity [psu (PSS-78)]
t(p) : array_like
temperature [℃ (ITS-90)]
p : array_like
pressure [db].
Returns
-------
k : array_like
secant bulk modulus [bars]
Examples
--------
>>> # Data from Unesco Tech. Paper in Marine Sci. No. 44, p22.
>>> import seawater as sw
>>> s = [0, 0, 0, 0, 35, 35, 35, 35]
>>> t = T90conv([0, 0, 30, 30, 0, 0, 30, 30])
>>> p = [0, 10000, 0, 10000, 0, 10000, 0, 10000]
>>> sw.seck(s, t, p)
array([ 19652.21 , 22977.2115 , 22336.0044572 , 25656.8196222 ,
21582.27006823, 24991.99729129, 23924.21823158, 27318.32472464])
References
----------
.. [1] Fofonoff, P. and Millard, R.C. Jr UNESCO 1983. Algorithms for
computation of fundamental properties of seawater. UNESCO Tech. Pap. in
Mar. Sci., No. 44, 53 pp. Eqn.(31) p.39.
http://unesdoc.unesco.org/images/0005/000598/059832eb.pdf
.. [2] Millero, F.J. and Poisson, A. International one-atmosphere equation
of state of seawater. Deep-Sea Res. 1981. Vol28A(6) pp625-629.
doi:10.1016/0198-0149(81)90122-9
"""
import numpy as np
s, t, p = list(map(np.asanyarray, (s, t, p)))
# Compute compression terms.
p = p / 10.0 # Convert from db to atmospheric pressure units.
T68 = T68conv(t)
# Pure water terms of the secant bulk modulus at atmos pressure.
# UNESCO Eqn 19 p 18.
# h0 = -0.1194975
h = [3.239908, 1.43713e-3, 1.16092e-4, -5.77905e-7]
AW = h[0] + (h[1] + (h[2] + h[3] * T68) * T68) * T68
# k0 = 3.47718e-5
k = [8.50935e-5, -6.12293e-6, 5.2787e-8]
BW = k[0] + (k[1] + k[2] * T68) * T68
# e0 = -1930.06
e = [19652.21, 148.4206, -2.327105, 1.360477e-2, -5.155288e-5]
KW = e[0] + (e[1] + (e[2] + (e[3] + e[4] * T68) * T68) * T68) * T68
# Sea water terms of secant bulk modulus at atmos. pressure.
j0 = 1.91075e-4
i = [2.2838e-3, -1.0981e-5, -1.6078e-6]
A = AW + (i[0] + (i[1] + i[2] * T68) * T68 + j0 * s ** 0.5) * s
m = [-9.9348e-7, 2.0816e-8, 9.1697e-10]
B = BW + (m[0] + (m[1] + m[2] * T68) * T68) * s # Eqn 18.
f = [54.6746, -0.603459, 1.09987e-2, -6.1670e-5]
g = [7.944e-2, 1.6483e-2, -5.3009e-4]
K0 = (KW + (f[0] + (f[1] + (f[2] + f[3] * T68) * T68) * T68 +
(g[0] + (g[1] + g[2] * T68) * T68) * s ** 0.5) * s) # Eqn 16.
return K0 + (A + B * p) * p # Eqn 15.
def T68conv(T90):
"""
Convert ITS-90 temperature to IPTS-68
:math:`T68 = T90 * 1.00024`
Parameters
----------
t : array_like
temperature [℃ (ITS-90)]
Returns
-------
t : array_like
temperature [℃ (IPTS-68)]
Notes
-----
The International Practical Temperature Scale of 1968 (IPTS-68) need to be
correct to the ITS-90. This linear transformation is accurate within
0.5 ℃ for conversion between IPTS-68 and ITS-90 over the
oceanographic temperature range.
Examples
--------
>>> import seawater as sw
>>> T68conv(19.995201151723585)
20.0
References
----------
.. [1] Saunders, P. M., 1991: The International Temperature Scale of 1990,
ITS-90. WOCE Newsletter, No. 10, WOCE International Project Office,
Southampton, United Kingdom, 10.
"""
import numpy as np
T90 = np.asanyarray(T90)
return T90 * 1.00024
def smow(t):
"""
Density of Standard Mean Ocean Water (Pure Water) using EOS 1980.
Parameters
----------
t : array_like
temperature [℃ (ITS-90)]
Returns
-------
dens(t) : array_like
density [kg m :sup:`3`]
Examples
--------
>>> # Data from UNESCO Tech. Paper in Marine Sci. No. 44, p22.
>>> import seawater as sw
>>> t = T90conv([0, 0, 30, 30, 0, 0, 30, 30])
>>> sw.smow(t)
array([ 999.842594 , 999.842594 , 995.65113374, 995.65113374,
999.842594 , 999.842594 , 995.65113374, 995.65113374])
References
----------
.. [1] Fofonoff, P. and Millard, R.C. Jr UNESCO 1983. Algorithms for
computation of fundamental properties of seawater. UNESCO Tech. Pap. in
Mar. Sci., No. 44, 53 pp. Eqn.(31) p.39.
http://unesdoc.unesco.org/images/0005/000598/059832eb.pdf
.. [2] Millero, F.J. and Poisson, A. International one-atmosphere equation
of state of seawater. Deep-Sea Res. 1981. Vol28A(6) pp625-629.
doi:10.1016/0198-0149(81)90122-9
"""
import numpy as np
t = np.asanyarray(t)
a = (999.842594, 6.793952e-2, -9.095290e-3, 1.001685e-4, -1.120083e-6,
6.536332e-9)
T68 = T68conv(t)
return (a[0] + (a[1] + (a[2] + (a[3] + (a[4] + a[5] * T68) * T68) * T68) *
T68) * T68)