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...