def satN2(s, t):
"""Solubility (saturation) of Nitrogen (N2) in sea water.
Parameters
----------
s : array_like
salinity [psu (PSS-78)]
t : array_like
temperature [:math:`^\circ` C (ITS-90)]
Returns
-------
satN2 : array_like
solubility of N2 [ml l :sup:`-1`]
Examples
--------
Data from Weiss 1970.
>>> import seawater as sw
>>> t = sw.T90conv([[ -1, -1], [ 10, 10], [ 20, 20], [ 40, 40]])
>>> s = [[ 20, 40], [ 20, 40], [ 20, 40], [ 20, 40]]
>>> sw.satN2(s, t)
array([[ 16.27952432, 14.00784526],
[ 12.64036196, 11.01277257],
[ 10.46892822, 9.21126859],
[ 7.78163876, 6.95395099]])
References
----------
.. [1] Weiss, R. F. 1970. The Solubility of Nitrogen, Oxygen and Argon in
Water and Seawater Deep-Sea Research Vol. 17, p. 721-735.
doi:10.1016/0011-7471(70)90037-9
Modifications: 97-11-05. Phil Morgan.
99-06-25. Lindsay Pender, Fixed transpose of row vectors.
03-12-12. Lindsay Pender, Converted to ITS-90.
"""
s, t = map(np.asanyarray, (s, t))
# Convert T to Kelvin.
t = Kelvin + T68conv(t)
# Constants for Eqn (4) of Weiss 1970.
a = (-172.4965, 248.4262, 143.0738, -21.7120)
b = (-0.049781, 0.025018, -0.0034861)
# Eqn (4) of Weiss 1970.
lnC = (a[0] + a[1] * (100 / t) + a[2] * np.log(t / 100) + a[3] *
(t / 100) + s * (b[0] + b[1] * (t / 100) + b[2] * ((t / 100)**2)))
return np.exp(lnC)
def satO2(s, t):
"""Solubility (saturation) of Oxygen (O2) in sea water.
Parameters
----------
s : array_like
salinity [psu (PSS-78)]
t : array_like
temperature [:math:`^\circ` C (ITS-68)]
Returns
-------
satO2 : array_like
solubility of O2 [ml l :sup:`-1` ]
Examples
--------
Data from Weiss 1970
>>> import seawater as sw
>>> t = sw.T90conv([[ -1, -1], [ 10, 10], [ 20, 20], [ 40, 40]])
>>> s = [[ 20, 40], [ 20, 40], [ 20, 40], [ 20, 40]]
>>> sw.satO2(s, t)
array([[ 9.162056 , 7.98404249],
[ 6.95007741, 6.12101928],
[ 5.64401453, 5.01531004],
[ 4.0495115 , 3.65575811]])
References
----------
.. [1] Weiss, R. F. 1970. The Solubility of Nitrogen, Oxygen and Argon in
Water and Seawater Deep-Sea Research Vol. 17, p. 721-735.
doi:10.1016/0011-7471(70)90037-9
Modifications: 97-11-05. Phil Morgan.
99-06-25. Lindsay Pender, Fixed transpose of row vectors.
03-12-12. Lindsay Pender, Converted to ITS-90.
"""
s, t = map(np.asanyarray, (s, t))
# Convert T to Kelvin.
t = Kelvin + T68conv(t)
# Constants for Eqn (4) of Weiss 1970.
a = (-173.4292, 249.6339, 143.3483, -21.8492)
b = (-0.033096, 0.014259, -0.0017000)
# Eqn (4) of Weiss 1970.
lnC = (a[0] + a[1] * (100 / t) + a[2] * np.log(t / 100) + a[3] *
(t / 100) + s * (b[0] + b[1] * (t / 100) + b[2] * ((t / 100)**2)))
return np.exp(lnC)
def satAr(s, t):
"""Solubility (saturation) of Argon (Ar) in sea water.
Parameters
----------
s : array_like
salinity [psu (PSS-78)]
t : array_like
temperature [:math:`^\circ` C (ITS-90)]
Returns
-------
satAr : array_like
solubility of Ar [ml l :sup:`-1`]
Examples
--------
Data from Weiss 1970.
>>> import seawater as sw
>>> t = sw.T90conv([[ -1, -1], [ 10, 10], [ 20, 20], [ 40, 40]])
>>> s = [[ 20, 40], [ 20, 40], [ 20, 40], [ 20, 40]]
>>> sw.satAr(s, t)
array([[ 0.4455784 , 0.38766011],
[ 0.33970659, 0.29887756],
[ 0.27660227, 0.24566428],
[ 0.19861429, 0.17937698]])
References
----------
.. [1] Weiss, R. F. 1970. The Solubility of Nitrogen, Oxygen and Argon in
Water and Seawater Deep-Sea Research Vol. 17, p. 721-735.
doi:10.1016/0011-7471(70)90037-9
Modifications: 97-11-05. Phil Morgan.
99-06-25. Lindsay Pender, Fixed transpose of row vectors.
03-12-12. Lindsay Pender, Converted to ITS-90.
"""
s, t = map(np.asanyarray, (s, t))
# Convert T to Kelvin.
t = Kelvin + T68conv(t)
# Constants for Eqn (4) of Weiss 1970.
a = [-173.5146, 245.4510, 141.8222, -21.8020]
b = [-0.034474, 0.014934, -0.0017729]
# Eqn (4) of Weiss 1970.
lnC = (a[0] + a[1] * (100 / t) + a[2] * np.log(t / 100) + a[3] *
(t / 100) + s * (b[0] + b[1] * (t / 100) + b[2] * ((t / 100)**2)))
return np.exp(lnC)
def dens0(s, t):
"""Density of Sea Water at atmospheric pressure.
Parameters
----------
s(p=0) : array_like
salinity [psu (PSS-78)]
t(p=0) : array_like
temperature [:math:`^\circ` C (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
>>> 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
Modifications: 92-11-05. Phil Morgan.
03-12-12. Lindsay Pender, Converted to ITS-90.
"""
s, t = 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 svel(s, t, p):
"""Sound Velocity in sea water using UNESCO 1983 polynomial.
Parameters
----------
s(p) : array_like
salinity [psu (PSS-78)]
t(p) : array_like
temperature [:math:`^\circ` C (ITS-90)]
p : array_like
pressure [db].
Returns
-------
svel : array_like
sound velocity [m/s]
Examples
--------
Data from Pond and Pickard Intro. Dynamical Oceanography 2nd ed. 1986
>>> import seawater as sw
>>> t = T90conv([[ 0, 0, 0, 0, 0, 0],
... [ 10, 10, 10, 10, 10, 10],
... [ 20, 20, 20, 20, 20, 20],
... [ 30, 30, 30, 30, 30, 30],
... [ 40, 40, 40, 40, 40, 40]])
>>> s = [[ 25, 25, 25, 35, 35, 35],
... [ 25, 25, 25, 35, 35, 35],
... [ 25, 25, 25, 35, 35, 35],
... [ 25, 25, 25, 35, 35, 35],
... [ 25, 25, 25, 35, 35, 35]]
>>> p = [ 0, 5000, 10000, 0, 5000, 10000]
>>> sw.svel(s, t, p)
array([[ 1435.789875 , 1520.358725 , 1610.4074 , 1449.13882813,
1533.96863705, 1623.15007097],
[ 1477.68316464, 1561.30635914, 1647.39267114, 1489.82233602,
1573.40946928, 1658.99115504],
[ 1510.31388348, 1593.59671798, 1676.80967748, 1521.4619731 ,
1604.4762822 , 1687.18305631],
[ 1535.21434752, 1618.95631952, 1700.60547902, 1545.59485539,
1628.97322783, 1710.06294277],
[ 1553.44506636, 1638.02522336, 1719.15088536, 1563.20925247,
1647.29949576, 1727.83176404]])
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
Modifications: 93-04-20. Phil Morgan.
99-06-25. Lindsay Pender, Fixed transpose of row vectors.
03-12-12. Lindsay Pender, Converted to ITS-90.
"""
s, t, p = map(np.asanyarray, (s, t, p))
# UNESCO 1983. Eqn..33 p.46.
p = p / 10 # Convert db to bars as used in UNESCO routines.
T68 = T68conv(t)
# Eqn 34 p.46.
c00, c01, c02, c03, c04, c05 = (1402.388, 5.03711, -5.80852e-2, 3.3420e-4,
-1.47800e-6, 3.1464e-9)
c10, c11, c12, c13, c14 = (0.153563, 6.8982e-4, -8.1788e-6, 1.3621e-7,
-6.1185e-10)
c20, c21, c22, c23, c24 = (3.1260e-5, -1.7107e-6, 2.5974e-8, -2.5335e-10,
1.0405e-12)
c30, c31, c32 = (-9.7729e-9, 3.8504e-10, -2.3643e-12)
Cw = (((((c32 * T68 + c31) * T68 + c30) * p +
((((c24 * T68 + c23) * T68 + c22) * T68 + c21) * T68 + c20)) * p +
((((c14 * T68 + c13) * T68 + c12) * T68 + c11) * T68 + c10)) *
p + ((((c05 * T68 + c04) * T68 + c03) * T68 + c02) * T68 + c01) *
T68 + c00)
# Eqn. 35. p.47
a00, a01, a02, a03, a04 = (1.389, -1.262e-2, 7.164e-5, 2.006e-6, -3.21e-8)
a10, a11, a12, a13, a14 = (9.4742e-5, -1.2580e-5, -6.4885e-8, 1.0507e-8,
-2.0122e-10)
a20, a21, a22, a23 = (-3.9064e-7, 9.1041e-9, -1.6002e-10, 7.988e-12)
a30, a31, a32 = (1.100e-10, 6.649e-12, -3.389e-13)
A = (((((a32 * T68 + a31) * T68 + a30) * p +
(((a23 * T68 + a22) * T68 + a21) * T68 + a20)) * p +
((((a14 * T68 + a13) * T68 + a12) * T68 + a11) * T68 + a10)) * p +
(((a04 * T68 + a03) * T68 + a02) * T68 + a01) * T68 + a00)
# Eqn 36 p.47.
b00, b01, b10, b11 = -1.922e-2, -4.42e-5, 7.3637e-5, 1.7945e-7
B = b00 + b01 * T68 + (b10 + b11 * T68) * p
# Eqn 37 p.47.
d00, d10 = 1.727e-3, -7.9836e-6
D = d00 + d10 * p
# Eqn 33 p.46.
return Cw + A * s + B * s * s ** 0.5 + D * s ** 2
def ptmp(s, t, p, pr=0):
"""Calculates potential temperature as per UNESCO 1983 report.
Parameters
----------
s(p) : array_like
salinity [psu (PSS-78)]
t(p) : array_like
temperature [:math:`^\circ` C (ITS-90)]
p : array_like
pressure [db].
pr : array_like
reference pressure [db], default = 0
Returns
-------
pt : array_like
potential temperature relative to PR [:math:`^\circ` C (ITS-90)]
Examples
--------
>>> import seawater as sw
>>> t = T90conv([[0, 0, 0, 0, 0, 0],
... [10, 10, 10, 10, 10, 10],
... [20, 20, 20, 20, 20, 20],
... [30, 30, 30, 30, 30, 30],
... [40, 40, 40, 40, 40, 40]])
>>> s = [[25, 25, 25, 35, 35, 35],
... [25, 25, 25, 35, 35, 35],
... [25, 25, 25, 35, 35, 35],
... [25, 25, 25, 35, 35, 35],
... [25, 25, 25, 35, 35, 35]]
>>> p = [0, 5000, 10000, 0, 5000, 10000]
>>> sw.T68conv(sw.ptmp(s, t, p, pr=0))
array([[ 0. , -0.30614418, -0.96669485, 0. ,
-0.3855565 , -1.09741136],
[ 10. , 9.35306331, 8.46840949, 10. ,
9.29063461, 8.36425752],
[ 20. , 19.04376281, 17.94265 , 20. ,
18.99845171, 17.86536441],
[ 30. , 28.75124632, 27.43529911, 30. ,
28.72313484, 27.38506197],
[ 40. , 38.46068173, 36.92544552, 40. ,
38.44979906, 36.90231661]])
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] Bryden, H. 1973. New Polynomials for thermal expansion, adiabatic
temperature gradient and potential temperature of sea water.
Deep-Sea Res. Vol20,401-408. doi:10.1016/0011-7471(73)90063-6
Modifications: 92-04-06. Phil Morgan.
99-06-25. Lindsay Pender, Fixed transpose of row vectors.
03-12-12. Lindsay Pender, Converted to ITS-90.
"""
s, t, p, pr = map(np.asanyarray, (s, t, p, pr))
# Theta1.
del_P = pr - p
del_th = del_P * adtg(s, t, p)
th = T68conv(t) + 0.5 * del_th
q = del_th
# Theta2.
del_th = del_P * adtg(s, T90conv(th), p + 0.5 * del_P)
th = th + (1 - 1 / 2 ** 0.5) * (del_th - q)
q = (2 - 2 ** 0.5) * del_th + (-2 + 3 / 2 ** 0.5) * q
# Theta3.
del_th = del_P * adtg(s, T90conv(th), p + 0.5 * del_P)
th = th + (1 + 1 / 2 ** 0.5) * (del_th - q)
q = (2 + 2 ** 0.5) * del_th + (-2 - 3 / 2 ** 0.5) * q
# Theta4.
del_th = del_P * adtg(s, T90conv(th), p + del_P)
return T90conv(th + (del_th - 2 * q) / 6)
def adtg(s, t, p):
"""Calculates adiabatic temperature gradient as per UNESCO 1983 routines.
Parameters
----------
s(p) : array_like
salinity [psu (PSS-78)]
t(p) : array_like
temperature [:math:`^\circ` C (ITS-90)]
p : array_like
pressure [db]
Returns
-------
adtg : array_like
adiabatic temperature gradient [:math:`^\circ` C db :sup:`-1`]
Examples
--------
Data from UNESCO 1983 p45.
>>> import seawater as sw
>>> t = sw.T90conv([[ 0, 0, 0, 0, 0, 0],
... [10, 10, 10, 10, 10, 10],
... [20, 20, 20, 20, 20, 20],
... [30, 30, 30, 30, 30, 30],
... [40, 40, 40, 40, 40, 40]])
>>> s = [[25, 25, 25, 35, 35, 35],
... [25, 25, 25, 35, 35, 35],
... [25, 25, 25, 35, 35, 35],
... [25, 25, 25, 35, 35, 35],
... [25, 25, 25, 35, 35, 35]]
>>> p = [0, 5000, 10000, 0, 5000, 10000]
>>> sw.adtg(s, t, p)
array([[ 1.68710000e-05, 1.04700000e-04, 1.69426000e-04,
3.58030000e-05, 1.17956500e-04, 1.77007000e-04],
[ 1.00194580e-04, 1.60959050e-04, 2.06874170e-04,
1.14887280e-04, 1.71364200e-04, 2.12991770e-04],
[ 1.73819840e-04, 2.13534000e-04, 2.44483760e-04,
1.84273240e-04, 2.21087800e-04, 2.49137960e-04],
[ 2.41720460e-04, 2.64764100e-04, 2.82959590e-04,
2.47934560e-04, 2.69466550e-04, 2.86150390e-04],
[ 3.07870120e-04, 3.16988600e-04, 3.23006480e-04,
3.09844920e-04, 3.18839700e-04, 3.24733880e-04]])
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.
http://unesdoc.unesco.org/images/0005/000598/059832eb.pdf
.. [2] Bryden, H. 1973. New Polynomials for thermal expansion, adiabatic
temperature gradient and potential temperature of sea water. Deep-Sea Res.
Vol20,401-408. doi:10.1016/0011-7471(73)90063-6
Modifications: 93-04-22. Phil Morgan.
99-06-25. Lindsay Pender, Fixed transpose of row vectors.
03-12-12. Lindsay Pender, Converted to ITS-90.
"""
s, t, p = map(np.asanyarray, (s, t, p))
T68 = T68conv(t)
a = [3.5803e-5, 8.5258e-6, -6.836e-8, 6.6228e-10]
b = [1.8932e-6, -4.2393e-8]
c = [1.8741e-8, -6.7795e-10, 8.733e-12, -5.4481e-14]
d = [-1.1351e-10, 2.7759e-12]
e = [-4.6206e-13, 1.8676e-14, -2.1687e-16]
return (a[0] + (a[1] + (a[2] + a[3] * T68) * T68) * T68 +
(b[0] + b[1] * T68) * (s - 35) +
((c[0] + (c[1] + (c[2] + c[3] * T68) * T68) * T68) +
(d[0] + d[1] * T68) * (s - 35)) * p +
(e[0] + (e[1] + e[2] * T68) * T68) * p * p)
def cp(s, t, p):
"""Heat Capacity of Sea Water using UNESCO 1983 polynomial.
Parameters
----------
s(p) : array_like
salinity [psu (PSS-78)]
t(p) : array_like
temperature [:math:`^\circ` C (ITS-90)]
p : array_like
pressure [db].
Returns
-------
cp : array_like
specific heat capacity [J kg :sup:`-1` C :sup:`-1`]
Examples
--------
Data from Pond and Pickard Intro. Dynamical Oceanography 2nd ed. 1986.
>>> import seawater as sw
>>> t = T90conv([[0, 0, 0, 0, 0, 0],
... [10, 10, 10, 10, 10, 10],
... [20, 20, 20, 20, 20, 20],
... [30, 30, 30, 30, 30, 30],
... [40, 40, 40, 40, 40, 40]])
>>> s = [[25, 25, 25, 35, 35, 35],
... [25, 25, 25, 35, 35, 35],
... [25, 25, 25, 35, 35, 35],
... [25, 25, 25, 35, 35, 35],
... [25, 25, 25, 35, 35, 35]]
>>> p = [0, 5000, 10000, 0, 5000, 10000]
>>> sw.cp(s, t, p)
array([[ 4048.4405375 , 3896.25585 , 3807.7330375 , 3986.53309476,
3849.26094605, 3769.11791286],
[ 4041.8276691 , 3919.5550066 , 3842.3111366 , 3986.34061786,
3874.72665865, 3804.415624 ],
[ 4044.8438591 , 3938.5978466 , 3866.7400391 , 3993.85441786,
3894.99294519, 3828.29059113],
[ 4049.0984351 , 3952.0375476 , 3882.9855526 , 4000.68382238,
3909.24271128, 3844.32151784],
[ 4051.2244911 , 3966.1132036 , 3905.9162711 , 4003.46192541,
3923.89463092, 3868.28959814]])
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
Modifications: Phil Morgan.
99-06-25. Lindsay Pender, Fixed transpose of row vectors.
03-12-12. Lindsay Pender, Converted to ITS-90.
"""
s, t, p = map(np.asanyarray, (s, t, p))
p = p / 10. # To convert [db] to [bar] as used in UNESCO routines.
T68 = T68conv(t)
# Eqn. 26 p.32.
a = (-7.64357, 0.1072763, -1.38385e-3)
b = (0.1770383, -4.07718e-3, 5.148e-5)
c = (4217.4, -3.720283, 0.1412855, -2.654387e-3, 2.093236e-5)
Cpst0 = ((((c[4] * T68 + c[3]) * T68 + c[2]) * T68 + c[1]) * T68 + c[0] +
(a[0] + a[1] * T68 + a[2] * T68 ** 2) * s +
(b[0] + b[1] * T68 + b[2] * T68 ** 2) * s * s ** 0.5)
# Eqn. 28 p.33.
a = (-4.9592e-1, 1.45747e-2, -3.13885e-4, 2.0357e-6, 1.7168e-8)
b = (2.4931e-4, -1.08645e-5, 2.87533e-7, -4.0027e-9, 2.2956e-11)
c = (-5.422e-8, 2.6380e-9, -6.5637e-11, 6.136e-13)
del_Cp0t0 = ((((((c[3] * T68 + c[2]) * T68 + c[1]) * T68 + c[0]) * p +
((((b[4] * T68 + b[3]) * T68 + b[2]) * T68 + b[1]) *
T68 + b[0])) * p + ((((a[4] * T68 + a[3]) * T68 + a[2]) *
T68 + a[1]) * T68 + a[0])) * p)
# Eqn 29 p.34.
d = (4.9247e-3, -1.28315e-4, 9.802e-7, 2.5941e-8, -2.9179e-10)
e = (-1.2331e-4, -1.517e-6, 3.122e-8)
f = (-2.9558e-6, 1.17054e-7, -2.3905e-9, 1.8448e-11)
g0 = 9.971e-8
h = (5.540e-10, -1.7682e-11, 3.513e-13)
j1 = -1.4300e-12
S3_2 = s * s ** 0.5
del_Cpstp = ((((((d[4] * T68 + d[3]) * T68 + d[2]) * T68 + d[1]) *
T68 + d[0]) * s + ((e[2] * T68 + e[1]) * T68 + e[0]) *
S3_2) * p +
((((f[3] * T68 + f[2]) * T68 + f[1]) * T68 + f[0]) * s +
g0 * S3_2) * p ** 2 + (((h[2] * T68 + h[1]) * T68 + h[0]) *
s + j1 * T68 * S3_2) * p ** 3)
return Cpst0 + del_Cp0t0 + del_Cpstp
def beta(s, t, p, pt=False):
"""Calculate the saline contraction coefficient :math:`\beta` as defined
by T.J. McDougall.
Parameters
----------
s(p) : array_like
salinity [psu (PSS-78)]
t(p) : array_like
temperature or potential temperature [:math:`^\circ` C (ITS-90)]
p : array_like
pressure [db].
pt : bool
True if temperature is potential, default is False
Returns
-------
beta : array_like
saline Contraction Coefficient [psu :sup:`-1`]
Examples
--------
Data from McDouogall 1987
>>> import seawater as sw
>>> s, t, p = 40, 10, 4000
>>> sw.beta(s, t, p, pt=True)
0.00072087661741618932
References
----------
.. [1] McDougall, Trevor J., 1987: Neutral Surfaces. J. Phys.
Oceanogr., 17, 1950-1964. doi: 10.1175/1520-0485(1987)017<1950:NS>2.0.CO;2
Modifications: 93-xx-xx. N.L. Bindoff.
93-04-22. Phil Morgan, Help display modified library.
93-04-23. Phil Morgan, Input argument checking.
94-10-15. Phil Morgan, Pass S,T,P and keyword for 'ptmp'.
99-06-25. Lindsay Pender, Fixed transpose of row vectors.
03-12-12. Lindsay Pender, Converted to ITS-90.
"""
s, t, p, pt = map(np.asanyarray, (s, t, p, pt))
# Ensure we use ptmp in calculations
if not pt:
t = ptmp(s, t, p, 0) # Now we have ptmp.
t = T68conv(t)
c1 = np.array([-0.415613e-9, 0.555579e-7, -0.301985e-5, 0.785567e-3])
c2 = np.array([0.788212e-8, -0.356603e-6])
c3 = np.array([-0.602281e-15, 0.408195e-10, 0.0])
c4 = 0.515032e-8
c5 = np.array([-0.213127e-11, 0.192867e-9, -0.121555e-7])
c6 = np.array([-0.175379e-14, 0.176621e-12])
c7 = 0.121551e-17
# Now calculate the thermal expansion saline contraction ratio adb
sm35 = s - 35
return (np.polyval(c1, t) + sm35 *
(np.polyval(c2, t) + np.polyval(c3, p)) +
c4 * (sm35 ** 2) + p * np.polyval(c5, t) +
(p ** 2) * np.polyval(c6, t) + c7 * (p ** 3))
def aonb(s, t, p, pt=False):
"""Calculate :math:`\alpha/\beta`.
Parameters
----------
s(p) : array_like
salinity [psu (PSS-78)]
t(p) : array_like
temperature or potential temperature [:math:`^\circ` C (ITS-90)]
p : array_like
pressure [db].
pt : bool
True if temperature is potential, default is False
Returns
-------
aonb : array_like
:math:`\alpha/\beta` [psu :math:`^\circ` C :sup:`-1`]
Examples
--------
Data from McDouogall 1987.
>>> import seawater as sw
>>> s, t, p = 40, 10, 4000
>>> sw.aonb(s, t, p, pt=True)
0.347650567047807
References
----------
.. [1] McDougall, Trevor J., 1987: Neutral Surfaces. J. Phys.
Oceanogr., 17, 1950-1964. doi: 10.1175/1520-0485(1987)017<1950:NS>2.0.CO;2
Modifications: 93-xx-xx. N.L. Bindoff.
93-04-22. Phil Morgan, Help display modified library.
93-04-23. Phil Morgan, Input argument checking.
94-10-15. Phil Morgan, Pass S,T,P and keyword for 'ptmp'.
99-06-25. Lindsay Pender, Fixed transpose of row vectors.
03-12-12. Lindsay Pender, Converted to ITS-90.
"""
# Ensure we use ptmp in calculations.
s, t, p, pt = map(np.asanyarray, (s, t, p, pt))
if not pt:
t = ptmp(s, t, p, 0) # Now we have ptmp.
p = np.float_(p)
t = T68conv(t)
c1 = np.array([-0.255019e-7, 0.298357e-5, -0.203814e-3,
0.170907e-1, 0.665157e-1])
c2 = np.array([-0.846960e-4, 0.378110e-2])
c2a = np.array([-0.251520e-11, -0.164759e-6, 0.0])
c3 = -0.678662e-5
c4 = np.array([0.791325e-8, -0.933746e-6, 0.380374e-4])
c5 = 0.512857e-12
c6 = -0.302285e-13
# Now calculate the thermal expansion saline contraction ratio aonb.
sm35 = s - 35.0
return (np.polyval(c1, t) + sm35 *
(np.polyval(c2, t) + np.polyval(c2a, p)) +
sm35 ** 2 * c3 + p * np.polyval(c4, t) +
c5 * (p ** 2) * (t ** 2) + c6 * p ** 3)