colour.phenomenons.rayleigh Module¶

Rayleigh Optical Depth - Scattering in the Atmosphere¶

Implements rayleigh scattering / optical depth in the atmosphere computation:

• scattering_cross_section()
• rayleigh_optical_depth()
• rayleigh_scattering()

References

colour.phenomenons.rayleigh.STANDARD_AIR_TEMPERATURE = 288.15¶

Standard air temperature \(T[K]\) in kelvin degrees (\(15\circ C\)).

STANDARD_AIR_TEMPERATURE : numeric

colour.phenomenons.rayleigh.STANDARD_CO2_CONCENTRATION = 300¶

Standard air \(CO_2\) concentration in parts per million (ppm).

STANDARD_CO2_CONCENTRATION : numeric

colour.phenomenons.rayleigh.AVERAGE_PRESSURE_MEAN_SEA_LEVEL = 101325¶

Standard air average pressure \(Hg\) at mean sea-level in pascal (Pa).

AVERAGE_PRESSURE_MEAN_SEA_LEVEL : numeric

colour.phenomenons.rayleigh.DEFAULT_LATITUDE = 0¶

Default latitude in degrees (equator).

DEFAULT_LATITUDE : numeric

colour.phenomenons.rayleigh.DEFAULT_ALTITUDE = 0¶

Default altitude in meters (sea level).

DEFAULT_ALTITUDE : numeric

colour.phenomenons.rayleigh.air_refraction_index_Penndorf1957(wavelength, *args)[source]¶

Returns the air refraction index \(n_s\) from given wavelength \(\lambda\) in micrometers (\(\mu m\)) using Penndorf (1957) method.

Parameters:	wavelength (numeric or array_like) – Wavelength \(\lambda\) in micrometers (\(\mu m\)). *args (*) – Arguments.
Returns:	Air refraction index \(n_s\).
Return type:	numeric or ndarray

See also

air_refraction_index_Edlen1966(), air_refraction_index_Peck1972(), air_refraction_index_Bodhaine1999()

Examples

>>> air_refraction_index_Penndorf1957(0.555)  
1.0002777...

colour.phenomenons.rayleigh.air_refraction_index_Edlen1966(wavelength, *args)[source]¶

Returns the air refraction index \(n_s\) from given wavelength \(\lambda\) in micrometers (\(\mu m\)) using Edlen (1966) method.

Parameters:	wavelength (numeric or array_like) – Wavelength \(\lambda\) in micrometers (\(\mu m\)). *args (*) – Arguments.
Returns:	Air refraction index \(n_s\).
Return type:	numeric or ndarray

See also

air_refraction_index_Penndorf1957(), air_refraction_index_Peck1972(), air_refraction_index_Bodhaine1999()

Examples

>>> air_refraction_index_Edlen1966(0.555)  
1.0002777...

colour.phenomenons.rayleigh.air_refraction_index_Peck1972(wavelength, *args)[source]¶

Returns the air refraction index \(n_s\) from given wavelength \(\lambda\) in micrometers (\(\mu m\)) using Peck and Reeder (1972) method.

Parameters:	wavelength (numeric or array_like) – Wavelength \(\lambda\) in micrometers (\(\mu m\)). *args (*) – Arguments.
Returns:	Air refraction index \(n_s\).
Return type:	numeric or ndarray

See also

air_refraction_index_Penndorf1957(), air_refraction_index_Edlen1966(), air_refraction_index_Bodhaine1999()

Examples

>>> air_refraction_index_Peck1972(0.555)  
1.0002777...

colour.phenomenons.rayleigh.air_refraction_index_Bodhaine1999(wavelength, CO2_concentration=300)[source]¶

Returns the air refraction index \(n_s\) from given wavelength \(\lambda\) in micrometers (\(\mu m\)) using Bodhaine, Wood, Dutton and Slusser (1999) method.

Parameters:	wavelength (numeric or array_like) – Wavelength \(\lambda\) in micrometers (\(\mu m\)). CO2_concentration (numeric or array_like) – \(CO_2\) concentration in parts per million (ppm).
Returns:	Air refraction index \(n_s\).
Return type:	numeric or ndarray

See also

air_refraction_index_Penndorf1957(), air_refraction_index_Edlen1966(), air_refraction_index_Peck1972()

Examples

>>> air_refraction_index_Bodhaine1999(0.555)  
1.0002777...

colour.phenomenons.rayleigh.N2_depolarisation(wavelength)[source]¶

Returns the depolarisation of nitrogen \(N_2\) as function of wavelength \(\lambda\) in micrometers (\(\mu m\)).

Parameters:	wavelength (numeric or array_like) – Wavelength \(\lambda\) in micrometers (\(\mu m\)).
Returns:	Nitrogen \(N_2\) depolarisation.
Return type:	numeric or ndarray

Examples

>>> N2_depolarisation(0.555)  
1.0350291...

colour.phenomenons.rayleigh.O2_depolarisation(wavelength)[source]¶

Returns the depolarisation of oxygen \(O_2\) as function of wavelength \(\lambda\) in micrometers (\(\mu m\)).

Parameters:	wavelength (numeric or array_like) – Wavelength \(\lambda\) in micrometers (\(\mu m\)).
Returns:	Oxygen \(O_2\) depolarisation.
Return type:	numeric or ndarray

Examples

>>> O2_depolarisation(0.555)  
1.1020225...

colour.phenomenons.rayleigh.F_air_Penndorf1957(wavelength, *args)[source]¶

Returns \((6+3_p)/(6-7_p)\), the depolarisation term \(F(air)\) or King Factor using Penndorf (1957) method.

Parameters:	wavelength (numeric or array_like) – Wavelength \(\lambda\) in micrometers (\(\mu m\)). *args (*) – Arguments.
Returns:	Air depolarisation.
Return type:	numeric or ndarray

See also

F_air_Young1981(), F_air_Bates1984(), F_air_Bodhaine1999()

Notes

• The argument wavelength is only provided for consistency with the other air depolarisation methods but is actually not used as this definition is essentially a constant in its current implementation.

Examples

>>> F_air_Penndorf1957(0.555)
array(1.0608)

colour.phenomenons.rayleigh.F_air_Young1981(wavelength, *args)[source]¶

Returns \((6+3_p)/(6-7_p)\), the depolarisation term \(F(air)\) or King Factor using Young (1981) method.

Parameters:	wavelength (numeric or array_like) – Wavelength \(\lambda\) in micrometers (\(\mu m\)). *args (*) – Arguments.
Returns:	Air depolarisation.
Return type:	numeric or ndarray

See also

F_air_Penndorf1957(), F_air_Bates1984(), F_air_Bodhaine1999()

Notes

• The argument wavelength is only provided for consistency with the other air depolarisation methods but is actually not used as this definition is essentially a constant in its current implementation.

Examples

>>> F_air_Young1981(0.555)
array(1.048)

colour.phenomenons.rayleigh.F_air_Bates1984(wavelength)[source]¶

Returns \((6+3_p)/(6-7_p)\), the depolarisation term \(F(air)\) or King Factor as function of wavelength \(\lambda\) in micrometers (\(\mu m\)) using Bates (1984) method.

Parameters:	wavelength (numeric or array_like) – Wavelength \(\lambda\) in micrometers (\(\mu m\)).
Returns:	Air depolarisation.
Return type:	numeric or ndarray

See also

F_air_Penndorf1957(), F_air_Young1981(), F_air_Bodhaine1999()

Examples

>>> F_air_Bates1984(0.555)  
1.0481535...

colour.phenomenons.rayleigh.F_air_Bodhaine1999(wavelength, CO2_concentration=300)[source]¶

Returns \((6+3_p)/(6-7_p)\), the depolarisation term \(F(air)\) or King Factor as function of wavelength \(\lambda\) in micrometers (\(\mu m\)) and \(CO_2\) concentration in parts per million (ppm) using Bodhaine, Wood, Dutton and Slusser (1999) method.

Parameters:	wavelength (numeric or array_like) – Wavelength \(\lambda\) in micrometers (\(\mu m\)). CO2_concentration (numeric or array_like, optional) – \(CO_2\) concentration in parts per million (ppm).
Returns:	Air depolarisation.
Return type:	numeric or ndarray

See also

F_air_Penndorf1957(), F_air_Young1981(), F_air_Bates1984()

Examples

>>> F_air_Bodhaine1999(0.555)  
1.1246916...

colour.phenomenons.rayleigh.molecular_density(temperature=288.15, avogadro_constant=6.02214179e+23)[source]¶

Returns the molecular density \(N_s\) (molecules \(cm^{-3}\)) as function of air temperature \(T[K]\) in kelvin degrees.

Parameters:	temperature (numeric or array_like, optional) – Air temperature \(T[K]\) in kelvin degrees. avogadro_constant (numeric or array_like, optional) – Avogadro‘s number (molecules \(mol^{-1}\)).
Returns:	Molecular density \(N_s\) (molecules \(cm^{-3}\)).
Return type:	numeric or ndarray

Notes

• The Avogadro‘s number used in this implementation is the one given by by the Committee on Data for Science and Technology (CODATA): \(6.02214179x10^{23}\), which is different from the reference [1] value \(6.0221367x10^{23}\).

Examples

>>> molecular_density(288.15)  
2.5469021...e+19
>>> molecular_density(288.15, 6.0221367e23)  
2.5468999...e+19

colour.phenomenons.rayleigh.mean_molecular_weights(CO2_concentration=300)[source]¶

Returns the mean molecular weights \(m_a\) for dry air as function of \(CO_2\) concentration in parts per million (ppm).

Parameters:	CO2_concentration (numeric or array_like, optional) – \(CO_2\) concentration in parts per million (ppm).
Returns:	Mean molecular weights \(m_a\) for dry air.
Return type:	numeric or ndarray

Examples

>>> mean_molecular_weights()  
28.9640166...

colour.phenomenons.rayleigh.gravity_List1968(latitude=0, altitude=0)[source]¶

Returns the gravity \(g\) in \(cm/s_2\) (gal) representative of the mass-weighted column of air molecules above the site of given latitude and altitude using List (1968) method.

Parameters:	latitude (numeric or array_like, optional) – Latitude of the site in degrees. altitude (numeric or array_like, optional) – Altitude of the site in meters.
Returns:	Gravity \(g\) in \(cm/s_2\) (gal).
Return type:	numeric or ndarray

Examples

>>> gravity_List1968()  
978.0356070...
>>> gravity_List1968(0, 1500)  
977.5726106...

Gravity \(g\) for Paris:

>>> gravity_List1968(48.8567, 35)  
980.9524178...

colour.phenomenons.rayleigh.scattering_cross_section(wavelength, CO2_concentration=300, temperature=288.15, avogadro_constant=6.02214179e+23, n_s=<function air_refraction_index_Bodhaine1999 at 0x2abef9066140>, F_air=<function F_air_Bodhaine1999 at 0x2abef9066410>)[source]¶

Returns the scattering cross section per molecule \(\sigma\) of dry air as function of wavelength \(\lambda\) in centimeters (cm) using given \(CO_2\) concentration in parts per million (ppm) and temperature \(T[K]\) in kelvin degrees following Van de Hulst (1957) method.

Parameters:	wavelength (numeric or array_like) – Wavelength \(\lambda\) in centimeters (cm). CO2_concentration (numeric or array_like, optional) – \(CO_2\) concentration in parts per million (ppm). temperature (numeric or array_like, optional) – Air temperature \(T[K]\) in kelvin degrees. avogadro_constant (numeric or array_like, optional) – Avogadro‘s number (molecules \(mol^{-1}\)). n_s (object) – Air refraction index \(n_s\) computation method. F_air (object) – \((6+3_p)/(6-7_p)\), the depolarisation term \(F(air)\) or King Factor computation method.
Returns:	Scattering cross section per molecule \(\sigma\) of dry air.
Return type:	numeric or ndarray

Warning

Unlike most objects of colour.phenomenons.rayleigh module, colour.phenomenons.rayleigh.scattering_cross_section() expects wavelength \(\lambda\) to be expressed in centimeters (cm).

Examples

>>> scattering_cross_section(555 * 10e-8)  
4.6613309...e-27

colour.phenomenons.rayleigh.rayleigh_optical_depth(wavelength, CO2_concentration=300, temperature=288.15, pressure=101325, latitude=0, altitude=0, avogadro_constant=6.02214179e+23, n_s=<function air_refraction_index_Bodhaine1999 at 0x2abef9066140>, F_air=<function F_air_Bodhaine1999 at 0x2abef9066410>)[source]¶

Returns the rayleigh optical depth \(T_r(\lambda)\) as function of wavelength \(\lambda\) in centimeters (cm).

Parameters:	wavelength (numeric or array_like) – Wavelength \(\lambda\) in centimeters (cm). CO2_concentration (numeric or array_like, optional) – \(CO_2\) concentration in parts per million (ppm). temperature (numeric or array_like, optional) – Air temperature \(T[K]\) in kelvin degrees. pressure (numeric or array_like) – Surface pressure \(P\) of the measurement site. latitude (numeric or array_like, optional) – Latitude of the site in degrees. altitude (numeric or array_like, optional) – Altitude of the site in meters. avogadro_constant (numeric or array_like, optional) – Avogadro‘s number (molecules \(mol^{-1}\)). n_s (object) – Air refraction index \(n_s\) computation method. F_air (object) – \((6+3_p)/(6-7_p)\), the depolarisation term \(F(air)\) or King Factor computation method.
Returns:	Rayleigh optical depth \(T_r(\lambda)\).
Return type:	numeric or ndarray

Warning

Unlike most objects of colour.phenomenons.rayleigh module, colour.phenomenons.rayleigh.rayleigh_optical_depth() expects wavelength \(\lambda\) to be expressed in centimeters (cm).

Examples

>>> rayleigh_optical_depth(555 * 10e-8)  
0.1004070...

colour.phenomenons.rayleigh.rayleigh_scattering(wavelength, CO2_concentration=300, temperature=288.15, pressure=101325, latitude=0, altitude=0, avogadro_constant=6.02214179e+23, n_s=<function air_refraction_index_Bodhaine1999 at 0x2abef9066140>, F_air=<function F_air_Bodhaine1999 at 0x2abef9066410>)¶

Returns the rayleigh optical depth \(T_r(\lambda)\) as function of wavelength \(\lambda\) in centimeters (cm).

Parameters:	wavelength (numeric or array_like) – Wavelength \(\lambda\) in centimeters (cm). CO2_concentration (numeric or array_like, optional) – \(CO_2\) concentration in parts per million (ppm). temperature (numeric or array_like, optional) – Air temperature \(T[K]\) in kelvin degrees. pressure (numeric or array_like) – Surface pressure \(P\) of the measurement site. latitude (numeric or array_like, optional) – Latitude of the site in degrees. altitude (numeric or array_like, optional) – Altitude of the site in meters. avogadro_constant (numeric or array_like, optional) – Avogadro‘s number (molecules \(mol^{-1}\)). n_s (object) – Air refraction index \(n_s\) computation method. F_air (object) – \((6+3_p)/(6-7_p)\), the depolarisation term \(F(air)\) or King Factor computation method.
Returns:	Rayleigh optical depth \(T_r(\lambda)\).
Return type:	numeric or ndarray

Warning

Unlike most objects of colour.phenomenons.rayleigh module, colour.phenomenons.rayleigh.rayleigh_optical_depth() expects wavelength \(\lambda\) to be expressed in centimeters (cm).

Examples

>>> rayleigh_optical_depth(555 * 10e-8)  
0.1004070...