`eos80`¶

seawater.eos80.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 [℃ (ITS-90)]

p : array_like

pressure [db]

Returns:

adtg : array_like

adiabatic temperature gradient [℃ db ^-1]

References

[R1]	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

[R2]	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

Examples

>>> # Data from UNESCO 1983 p45.
>>> import seawater as sw
>>> from seawater.library import T90conv
>>> 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.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]])

seawater.eos80.alpha(s, t, p, pt=False)¶

Calculate the thermal expansion coefficient.

Parameters:

s(p) : array_like

salinity [psu (PSS-78)]

t(p) : array_like

temperature or potential temperature [℃ (ITS-90)]

p : array_like

pressure [db].

pt : bool

True if temperature is potential, default is False

Returns:

alpha : array_like

thermal expansion coeff $\alpha$ [℃ ^-1]

References

[R3]	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

Examples

>>> # Data from McDougall 1987
>>> import seawater as sw
>>> s, t, p = 40, 10, 4000
>>> sw.alpha(s, t, p, pt=True)
0.00025061316481624323

seawater.eos80.aonb(s, t, p, pt=False)¶

Calculate $\alpha/\beta$ .

Parameters:

s(p) : array_like

salinity [psu (PSS-78)]

t(p) : array_like

temperature or potential temperature [℃ (ITS-90)]

p : array_like

pressure [db].

pt : bool

True if temperature is potential, default is False

Returns:

aonb : array_like

$\alpha/\beta$ [psu ℃ ^-1]

References

[R4]	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

Examples

>>> # Data from McDougall 1987.
>>> import seawater as sw
>>> s, t, p = 40, 10, 4000
>>> sw.aonb(s, t, p, pt=True)
0.347650567047807

seawater.eos80.beta(s, t, p, pt=False)¶

Calculate the saline contraction coefficient $\beta$ as defined by T.J. McDougall.

Parameters:

s(p) : array_like

salinity [psu (PSS-78)]

t(p) : array_like

temperature or potential temperature [℃ (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 ^-1]

References

[R5]	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

Examples

>>> # Data from McDougall 1987
>>> import seawater as sw
>>> s, t, p = 40, 10, 4000
>>> sw.beta(s, t, p, pt=True)
0.00072087661741618932

seawater.eos80.dpth(p, lat)¶

Calculates depth in meters from pressure in dbars.

Parameters:

p : array_like

pressure [db].

lat : number or array_like

latitude in decimal degrees north [-90..+90].

Returns:

z : array_like

depth [meters]

References

[R6]	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

Examples

>>> # UNESCO 1983 data p30.
>>> import seawater as sw
>>> lat = [0, 30, 45, 90]
>>> p = [[  500,   500,   500,  500],
...      [ 5000,  5000,  5000, 5000],
...      [10000, 10000, 10000, 10000]]
>>> sw.dpth(p, lat)
array([[  496.65299239,   495.99772917,   495.3427354 ,   494.03357499],
       [ 4915.04099112,  4908.55954332,  4902.08075214,  4889.13132561],
       [ 9725.47087508,  9712.6530721 ,  9699.84050403,  9674.23144056]])

seawater.eos80.g(lat, z=0)¶

Calculates acceleration due to gravity as function of latitude.

Parameters:

lat : array_like

latitude in decimal degrees north [-90..+90].

z : number or array_like. Default z = 0

height in meters (+ve above sea surface, -ve below).

Returns:

g : array_like

gravity [m s ^-2]

References

[R7]	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

[R8]	A.E. Gill 1982. p.54 Eqn. 3.7.15 “Atmosphere-Ocean Dynamics” Academic Press: New York. ISBN: 0-12-283522-0

Examples

>>> import seawater as sw
>>> sw.g(45, z=0)
9.8061898752053995

seawater.eos80.salt(r, t, p)¶

Calculates Salinity from conductivity ratio. UNESCO 1983 polynomial.

Parameters:

r : array_like

conductivity ratio $R = \frac{C(S,T,P)}{C(35,15(IPTS-68),0)}$

t : array_like

temperature [℃ (ITS-90)]

p : array_like

pressure [db]

Returns:

s : array_like

salinity [psu (PSS-78)]

References

[R9]	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

Examples

Data from UNESCO 1983 p9. >>> import seawater as sw >>> from seawater.library import T90conv >>> r = [1, 1.2, 0.65] >>> t = T90conv([15, 20, 5]) >>> p = [0, 2000, 1500] >>> sw.salt(r, t, p) array([ 34.99999992, 37.24562765, 27.99534693])

seawater.eos80.fp(s, p)¶

Freezing point of Sea Water using UNESCO 1983 polynomial.

Parameters:

s : array_like

salinity [psu (PSS-78)]

p : array_like

pressure [db]

Returns:

fp : array_like

freezing point temperature [℃ (ITS-90)]

References

[R10]

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

Examples

>>> # UNESCO DATA p.30.
>>> import seawater as sw
>>> s = [[5, 10, 15, 20, 25, 30, 35, 40],
...      [5, 10, 15, 20, 25, 30, 35, 40]]
>>> p = [[ 0, 0, 0, 0, 0, 0, 0, 0],
...      [500, 500, 500, 500, 500, 500, 500, 500]]
>>> sw.fp(s, p)
array([[-0.27369757, -0.54232831, -0.81142026, -1.0829461 , -1.35804594,
        -1.63748903, -1.9218401 , -2.2115367 ],
       [-0.65010724, -0.91873798, -1.18782992, -1.45935577, -1.73445561,
        -2.01389869, -2.29824976, -2.58794636]])

seawater.eos80.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 [℃ (ITS-90)]

p : array_like

pressure [db].

Returns:

svel : array_like

sound velocity [m/s]

References

[R11]

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

Examples

Data from Pond and Pickard Intro. Dynamical Oceanography 2nd ed. 1986

>>> import seawater as sw
>>> from seawater.library import T90conv
>>> 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]])

seawater.eos80.pres(depth, lat)¶

Calculates pressure in dbars from depth in meters.

Parameters:

depth : array_like

depth [meters]

lat : array_like

latitude in decimal degrees north [-90..+90]

Returns:

p : array_like

pressure [db]

References

[R12]

Saunders, Peter M., 1981: Practical Conversion of Pressure to Depth. J. Phys. Oceanogr., 11, 573-574. doi: 10.1175/1520-0485(1981)011<0573:PCOPTD>2.0.CO;2

Examples

>>> import seawater as sw
>>> depth, lat = 7321.45, 30
>>> sw.pres(depth,lat)
7500.0065130118019

seawater.eos80.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 [℃ (ITS-90)]

Returns:

dens0(s, t) : array_like

density [kg m ³] of salt water with properties (s, t, p=0) 0 db gauge pressure

References

[R13]

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

[R14]

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

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])

seawater.eos80.dens(s, t, p)¶

Density of Sea Water using UNESCO 1983 (EOS 80) polynomial.

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 ³]

References

[R15]

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

[R16]

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

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])

seawater.eos80.pden(s, t, p, pr=0)¶

Calculates potential density of water mass relative to the specified reference pressure by pden = dens(S, ptmp, PR).

Parameters:

s(p) : array_like

salinity [psu (PSS-78)]

t(p) : array_like

temperature [℃ (ITS-90)]

p : array_like

pressure [db].

pr : number

reference pressure [db], default = 0

Returns:

pden : array_like

potential density relative to the ref. pressure [kg m :sup:3]

References

[R17]

A.E. Gill 1982. p.54 Eqn. 3.7.15 “Atmosphere-Ocean Dynamics” Academic Press: New York. ISBN: 0-12-283522-0

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.pden(s, t, p)
array([  999.842594  ,   999.79523994,   995.65113374,   996.36115932,
        1028.10633141,  1028.15738545,  1021.72863949,  1022.59634627])

$\sigma_{4}$ (at 4000 db)

>>> sw.pden(s, t, p, 4000) - 1000
array([ 19.2895493 ,  19.33422519,  12.43271053,  13.27563816,
        46.30976432,  46.48818851,  37.76150878,  38.74500757])

seawater.eos80.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 [℃ (ITS-90)]

p : array_like

pressure [db].

Returns:

cp : array_like

specific heat capacity [J kg ^-1 C ^-1]

References

[R18]

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

Examples

>>> # Data from Pond and Pickard Intro. Dyn. Oceanography 2nd ed. 1986.
>>> import seawater as sw
>>> from seawater.library import T90conv
>>> 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]])

seawater.eos80.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 [℃ (ITS-90)]

p : array_like

pressure [db].

pr : array_like

reference pressure [db], default = 0

Returns:

pt : array_like

potential temperature relative to PR [℃ (ITS-90)]

References

[R19]

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

[R20]

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

Examples

>>> import seawater as sw
>>> from seawater.library import T90conv, T68conv
>>> 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]
>>> 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]])

seawater.eos80.temp(s, pt, p, pr=0)¶

Calculates temperature from potential temperature at the reference pressure PR and in situ pressure P.

Parameters:

s(p) : array_like

salinity [psu (PSS-78)]

pt(p) : array_like

potential temperature [℃ (ITS-90)]

p : array_like

pressure [db].

pr : array_like

reference pressure [db]

Returns:

temp : array_like

temperature [℃ (ITS-90)]

References

[R21]

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

[R22]

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

Examples

>>> import seawater as sw
>>> s, t, p = 35, 15, 100
>>> sw.temp(s, sw.ptmp(s, t, p), p)
15.0

Previous topic

Next topic

This Page

`eos80`¶

eos80¶

`eos80`¶