"""
Rayleigh Optical Depth - Scattering in the Atmosphere
=====================================================
Implement *Rayleigh* scattering and optical depth computation in the
atmosphere.
- :func:`colour.scattering_cross_section`
- :func:`colour.phenomena.rayleigh_optical_depth`
- :func:`colour.rayleigh_scattering`
References
----------
- :cite:`Bodhaine1999a` : Bodhaine, B. A., Wood, N. B., Dutton, E. G., &
Slusser, J. R. (1999). On Rayleigh Optical Depth Calculations. Journal of
Atmospheric and Oceanic Technology, 16(11), 1854-1861.
doi:10.1175/1520-0426(1999)016<1854:ORODC>2.0.CO;2
- :cite:`Wikipedia2001c` : Wikipedia. (2001). Rayleigh scattering. Retrieved
September 23, 2014, from http://en.wikipedia.org/wiki/Rayleigh_scattering
"""
from __future__ import annotations
import typing
import numpy as np
from colour.algebra import sdiv, sdiv_mode
from colour.colorimetry import (
SPECTRAL_SHAPE_DEFAULT,
SpectralDistribution,
SpectralShape,
)
from colour.constants import CONSTANT_AVOGADRO
if typing.TYPE_CHECKING:
from colour.hints import ArrayLike, Callable, NDArrayFloat
from colour.utilities import as_float, as_float_array, filter_kwargs
__author__ = "Colour Developers"
__copyright__ = "Copyright 2013 Colour Developers"
__license__ = "BSD-3-Clause - https://opensource.org/licenses/BSD-3-Clause"
__maintainer__ = "Colour Developers"
__email__ = "colour-developers@colour-science.org"
__status__ = "Production"
__all__ = [
"CONSTANT_STANDARD_AIR_TEMPERATURE",
"CONSTANT_STANDARD_CO2_CONCENTRATION",
"CONSTANT_AVERAGE_PRESSURE_MEAN_SEA_LEVEL",
"CONSTANT_DEFAULT_LATITUDE",
"CONSTANT_DEFAULT_ALTITUDE",
"air_refraction_index_Penndorf1957",
"air_refraction_index_Edlen1966",
"air_refraction_index_Peck1972",
"air_refraction_index_Bodhaine1999",
"N2_depolarisation",
"O2_depolarisation",
"F_air_Penndorf1957",
"F_air_Young1981",
"F_air_Bates1984",
"F_air_Bodhaine1999",
"molecular_density",
"mean_molecular_weights",
"gravity_List1968",
"scattering_cross_section",
"rayleigh_optical_depth",
"rayleigh_scattering",
"sd_rayleigh_scattering",
]
CONSTANT_STANDARD_AIR_TEMPERATURE: float = 288.15
"""*Standard air* temperature :math:`T[K]` in kelvin degrees (:math:`15\\circ C`)."""
CONSTANT_STANDARD_CO2_CONCENTRATION: float = 300
"""*Standard air* :math:`CO_2` concentration in parts per million (ppm)."""
CONSTANT_AVERAGE_PRESSURE_MEAN_SEA_LEVEL: float = 101325
"""*Standard air* average pressure :math:`Hg` at mean sea-level in pascal (Pa)."""
CONSTANT_DEFAULT_LATITUDE: float = 0
"""Default latitude in degrees (equator)."""
CONSTANT_DEFAULT_ALTITUDE: float = 0
"""Default altitude in meters (sea level)."""
def air_refraction_index_Penndorf1957(
wavelength: ArrayLike,
) -> NDArrayFloat:
"""
Compute the air refraction index :math:`n_s` from the specified wavelength
:math:`\\lambda` in micrometers (:math:`\\mu m`) using the
*Penndorf (1957)* method.
Parameters
----------
wavelength
Wavelength :math:`\\lambda` in micrometers (:math:`\\mu m`).
Returns
-------
:class:`numpy.ndarray`
Air refraction index :math:`n_s`.
Examples
--------
>>> air_refraction_index_Penndorf1957(0.555) # doctest: +ELLIPSIS
np.float64(1.0002777...)
"""
wl = as_float_array(wavelength)
n = 6432.8 + 2949810 / (146 - wl ** (-2)) + 25540 / (41 - wl ** (-2))
n /= 1.0e8
n += +1
return n
def air_refraction_index_Edlen1966(
wavelength: ArrayLike,
) -> NDArrayFloat:
"""
Compute the air refraction index :math:`n_s` from the specified wavelength
:math:`\\lambda` in micrometers (:math:`\\mu m`) using the
*Edlen (1966)* method.
Parameters
----------
wavelength
Wavelength :math:`\\lambda` in micrometers (:math:`\\mu m`).
Returns
-------
:class:`numpy.ndarray`
Air refraction index :math:`n_s`.
Examples
--------
>>> air_refraction_index_Edlen1966(0.555) # doctest: +ELLIPSIS
np.float64(1.0002777...)
"""
wl = as_float_array(wavelength)
n = 8342.13 + 2406030 / (130 - wl ** (-2)) + 15997 / (38.9 - wl ** (-2))
n /= 1.0e8
n += +1
return n
def air_refraction_index_Peck1972(
wavelength: ArrayLike,
) -> NDArrayFloat:
"""
Compute the air refraction index :math:`n_s` from the specified wavelength
:math:`\\lambda` in micrometers (:math:`\\mu m`) using the
*Peck and Reeder (1972)* method.
Parameters
----------
wavelength
Wavelength :math:`\\lambda` in micrometers (:math:`\\mu m`).
Returns
-------
:class:`numpy.ndarray`
Air refraction index :math:`n_s`.
Examples
--------
>>> air_refraction_index_Peck1972(0.555) # doctest: +ELLIPSIS
np.float64(1.0002777...)
"""
wl = as_float_array(wavelength)
n = 8060.51 + 2480990 / (132.274 - wl ** (-2)) + 17455.7 / (39.32957 - wl ** (-2))
n /= 1.0e8
n += +1
return n
def air_refraction_index_Bodhaine1999(
wavelength: ArrayLike,
CO2_concentration: ArrayLike = CONSTANT_STANDARD_CO2_CONCENTRATION,
) -> NDArrayFloat:
"""
Compute the air refraction index :math:`n_s` from the specified wavelength
:math:`\\lambda` in micrometers (:math:`\\mu m`) using the
*Bodhaine, Wood, Dutton and Slusser (1999)* method.
Parameters
----------
wavelength
Wavelength :math:`\\lambda` in micrometers (:math:`\\mu m`).
CO2_concentration
:math:`CO_2` concentration in parts per million (ppm).
Returns
-------
:class:`numpy.ndarray`
Air refraction index :math:`n_s`.
Examples
--------
>>> air_refraction_index_Bodhaine1999(0.555) # doctest: +ELLIPSIS
np.float64(1.0002777...)
"""
wl = as_float_array(wavelength)
CO2_c = as_float_array(CO2_concentration)
# Converting from parts per million (ppm) to parts per volume (ppv).
CO2_c = CO2_c * 1e-6
n = (1 + 0.54 * (CO2_c - 300e-6)) * (air_refraction_index_Peck1972(wl) - 1) + 1
return as_float(n)
def N2_depolarisation(wavelength: ArrayLike) -> NDArrayFloat:
"""
Compute the depolarisation of nitrogen :math:`N_2` as a function of
wavelength :math:`\\lambda` in micrometers (:math:`\\mu m`).
Parameters
----------
wavelength
Wavelength :math:`\\lambda` in micrometers (:math:`\\mu m`).
Returns
-------
:class:`numpy.ndarray`
Nitrogen :math:`N_2` depolarisation.
Examples
--------
>>> N2_depolarisation(0.555) # doctest: +ELLIPSIS
np.float64(1.0350291...)
"""
wl = as_float_array(wavelength)
return 1.034 + 3.17 * 1.0e-4 * (1 / wl**2)
def O2_depolarisation(wavelength: ArrayLike) -> NDArrayFloat:
"""
Compute the depolarisation of oxygen :math:`O_2` as a function of
wavelength :math:`\\lambda` in micrometers (:math:`\\mu m`).
Parameters
----------
wavelength
Wavelength :math:`\\lambda` in micrometers (:math:`\\mu m`).
Returns
-------
:class:`numpy.ndarray`
Oxygen :math:`O_2` depolarisation.
Examples
--------
>>> O2_depolarisation(0.555) # doctest: +ELLIPSIS
np.float64(1.1020225...)
"""
wl = as_float_array(wavelength)
return 1.096 + 1.385 * 1.0e-3 * (1 / wl**2) + 1.448 * 1.0e-4 * (1 / wl**4)
def F_air_Penndorf1957(wavelength: ArrayLike) -> NDArrayFloat:
"""
Compute the depolarisation term :math:`F(air)` or *King Factor* using
the *Penndorf (1957)* method.
Parameters
----------
wavelength
Wavelength :math:`\\lambda` in micrometers (:math:`\\mu m`).
Returns
-------
:class:`numpy.ndarray`
Air depolarisation term.
Notes
-----
- The *wavelength* parameter is provided for consistency with other
air depolarisation methods but is not used in this implementation,
which returns a constant value.
Examples
--------
>>> F_air_Penndorf1957(0.555)
np.float64(1.0608)
"""
wl = as_float_array(wavelength)
return as_float(np.resize(np.array([1.0608]), wl.shape))
def F_air_Young1981(wavelength: ArrayLike) -> NDArrayFloat:
"""
Compute the depolarisation term :math:`F(air)` or *King Factor* using
the *Young (1981)* method.
Parameters
----------
wavelength
Wavelength :math:`\\lambda` in micrometers (:math:`\\mu m`).
Returns
-------
:class:`numpy.ndarray`
Air depolarisation term.
Notes
-----
- The *wavelength* parameter is provided for consistency with other
air depolarisation methods but is not used in this implementation,
which returns a constant value.
Examples
--------
>>> F_air_Young1981(0.555)
np.float64(1.048)
"""
wl = as_float_array(wavelength)
return as_float(np.resize(np.array([1.0480]), wl.shape))
def F_air_Bates1984(wavelength: ArrayLike) -> NDArrayFloat:
"""
Compute the depolarisation term :math:`F(air)` or *King Factor* using
the *Bates (1984)* method.
(:math:`\\mu m`) using *Bates (1984)* method.
Parameters
----------
wavelength
Wavelength :math:`\\lambda` in micrometers (:math:`\\mu m`).
Returns
-------
:class:`numpy.ndarray`
Air depolarisation term.
Examples
--------
>>> F_air_Bates1984(0.555) # doctest: +ELLIPSIS
np.float64(1.0481535...)
"""
O2 = O2_depolarisation(wavelength)
N2 = N2_depolarisation(wavelength)
Ar = 1.00
CO2 = 1.15
return (78.084 * N2 + 20.946 * O2 + CO2 + Ar) / (78.084 + 20.946 + Ar + CO2)
def F_air_Bodhaine1999(
wavelength: ArrayLike,
CO2_concentration: ArrayLike = CONSTANT_STANDARD_CO2_CONCENTRATION,
) -> NDArrayFloat:
"""
Compute the depolarisation term :math:`F(air)` or *King Factor* as a
function of wavelength :math:`\\lambda` in micrometers (:math:`\\mu m`)
and :math:`CO_2` concentration in parts per million (ppm) using the
*Bodhaine, Wood, Dutton and Slusser (1999)* method.
Parameters
----------
wavelength
Wavelength :math:`\\lambda` in micrometers (:math:`\\mu m`).
CO2_concentration
:math:`CO_2` concentration in parts per million (ppm).
Returns
-------
:class:`numpy.ndarray`
Air depolarisation term.
Examples
--------
>>> F_air_Bodhaine1999(0.555) # doctest: +ELLIPSIS
np.float64(1.0487697...)
"""
O2 = O2_depolarisation(wavelength)
N2 = N2_depolarisation(wavelength)
CO2_c = as_float_array(CO2_concentration)
# Converting from parts per million (ppm) to parts per volume per percent.
CO2_c = CO2_c * 1e-4
return (78.084 * N2 + 20.946 * O2 + 0.934 * 1 + CO2_c * 1.15) / (
78.084 + 20.946 + 0.934 + CO2_c
)
def molecular_density(
temperature: ArrayLike = CONSTANT_STANDARD_AIR_TEMPERATURE,
avogadro_constant: ArrayLike = CONSTANT_AVOGADRO,
) -> NDArrayFloat:
"""
Compute the molecular density :math:`N_s` (molecules :math:`cm^{-3}`)
as function of air temperature :math:`T[K]` in kelvin degrees.
Parameters
----------
temperature
Air temperature :math:`T[K]` in kelvin degrees.
avogadro_constant
*Avogadro*'s number (molecules :math:`mol^{-1}`).
Returns
-------
:class:`numpy.ndarray`
Molecular density :math:`N_s` (molecules :math:`cm^{-3}`).
Notes
-----
- The *Avogadro*'s number used in this implementation is the one
specified by the Committee on Data for Science and Technology
(CODATA): :math:`6.02214179 \\times 10^{23}`, which differs from
the reference :cite:`Bodhaine1999a` value
:math:`6.0221367 \\times 10^{23}`.
Examples
--------
>>> molecular_density(288.15) # doctest: +ELLIPSIS
np.float64(2.5469021...e+19)
>>> molecular_density(288.15, 6.0221367e23) # doctest: +ELLIPSIS
np.float64(2.5468999...e+19)
"""
T = as_float_array(temperature)
avogadro_constant = as_float_array(avogadro_constant)
with sdiv_mode():
return (avogadro_constant / 22.4141) * sdiv(273.15, T) * (1 / 1000)
def mean_molecular_weights(
CO2_concentration: ArrayLike = CONSTANT_STANDARD_CO2_CONCENTRATION,
) -> NDArrayFloat:
"""
Compute the mean molecular weights :math:`m_a` for dry air as a function
of :math:`CO_2` concentration in parts per million (ppm).
Parameters
----------
CO2_concentration
:math:`CO_2` concentration in parts per million (ppm).
Returns
-------
:class:`numpy.ndarray`
Mean molecular weights :math:`m_a` for dry air.
Examples
--------
>>> mean_molecular_weights() # doctest: +ELLIPSIS
np.float64(28.9640166...)
"""
CO2_concentration = as_float_array(CO2_concentration)
CO2_c = CO2_concentration * 1.0e-6
return 15.0556 * CO2_c + 28.9595
def gravity_List1968(
latitude: ArrayLike = CONSTANT_DEFAULT_LATITUDE,
altitude: ArrayLike = CONSTANT_DEFAULT_ALTITUDE,
) -> NDArrayFloat:
"""
Compute the gravity :math:`g` in :math:`cm/s^2` (gal) representative of
the mass-weighted column of air molecules above the site at the specified
latitude and altitude using the *List (1968)* method.
Parameters
----------
latitude
Latitude of the site in degrees.
altitude
Altitude of the site in meters.
Returns
-------
:class:`numpy.ndarray`
Gravity :math:`g` in :math:`cm/s^2` (gal).
Examples
--------
>>> gravity_List1968() # doctest: +ELLIPSIS
np.float64(978.0356070...)
>>> gravity_List1968(0.0, 1500.0) # doctest: +ELLIPSIS
np.float64(977.5726106...)
Gravity :math:`g` for Paris:
>>> gravity_List1968(48.8567, 35.0) # doctest: +ELLIPSIS
np.float64(980.9524178...)
"""
latitude = as_float_array(latitude)
altitude = as_float_array(altitude)
cos2phi = np.cos(2 * np.radians(latitude))
# Sea level acceleration of gravity.
g0 = 980.6160 * (1 - 0.0026373 * cos2phi + 0.0000059 * cos2phi**2)
return (
g0
- (3.085462e-4 + 2.27e-7 * cos2phi) * altitude
+ (7.254e-11 + 1.0e-13 * cos2phi) * altitude**2
- (1.517e-17 + 6e-20 * cos2phi) * altitude**3
)
[docs]
def scattering_cross_section(
wavelength: ArrayLike,
CO2_concentration: ArrayLike = CONSTANT_STANDARD_CO2_CONCENTRATION,
temperature: ArrayLike = CONSTANT_STANDARD_AIR_TEMPERATURE,
avogadro_constant: ArrayLike = CONSTANT_AVOGADRO,
n_s_function: Callable = air_refraction_index_Bodhaine1999,
F_air_function: Callable = F_air_Bodhaine1999,
) -> NDArrayFloat:
"""
Compute the scattering cross-section per molecule :math:`\\sigma` of dry
air as a function of wavelength :math:`\\lambda` in centimeters (cm)
using the specified :math:`CO_2` concentration in parts per million
(ppm) and temperature :math:`T[K]` in kelvin degrees following the
*Van de Hulst (1957)* method.
Parameters
----------
wavelength
Wavelength :math:`\\lambda` in centimeters (cm).
CO2_concentration
:math:`CO_2` concentration in parts per million (ppm).
temperature
Air temperature :math:`T[K]` in kelvin degrees.
avogadro_constant
*Avogadro*'s number (molecules :math:`mol^{-1}`).
n_s_function
Air refraction index :math:`n_s` computation method.
F_air_function
:math:`(6+3_p)/(6-7_p)`, the depolarisation term :math:`F(air)` or
*King Factor* computation method.
Returns
-------
:class:`numpy.ndarray`
Scattering cross-section per molecule :math:`\\sigma` of dry air.
Warnings
--------
Unlike most objects of :mod:`colour.phenomena.rayleigh` module,
:func:`colour.scattering_cross_section` expects wavelength
:math:`\\lambda` to be expressed in centimeters (cm).
References
----------
:cite:`Bodhaine1999a`, :cite:`Wikipedia2001c`
Examples
--------
>>> scattering_cross_section(555 * 10e-8) # doctest: +ELLIPSIS
np.float64(4.3466692...e-27)
"""
wl = as_float_array(wavelength)
CO2_c = as_float_array(CO2_concentration)
temperature = as_float_array(temperature)
wl_micrometers = wl * 10e3
N_s = molecular_density(temperature, avogadro_constant)
n_s = n_s_function(wl_micrometers)
# n_s = n_s_function(**filter_kwargs(
# n_s_function, wavelength=wl_micrometers, CO2_concentration=CO2_c))
F_air = F_air_function(
**filter_kwargs(
F_air_function, wavelength=wl_micrometers, CO2_concentration=CO2_c
)
)
sigma = 24 * np.pi**3 * (n_s**2 - 1) ** 2 / (wl**4 * N_s**2 * (n_s**2 + 2) ** 2)
sigma *= F_air
return sigma
[docs]
def rayleigh_optical_depth(
wavelength: ArrayLike,
CO2_concentration: ArrayLike = CONSTANT_STANDARD_CO2_CONCENTRATION,
temperature: ArrayLike = CONSTANT_STANDARD_AIR_TEMPERATURE,
pressure: ArrayLike = CONSTANT_AVERAGE_PRESSURE_MEAN_SEA_LEVEL,
latitude: ArrayLike = CONSTANT_DEFAULT_LATITUDE,
altitude: ArrayLike = CONSTANT_DEFAULT_ALTITUDE,
avogadro_constant: ArrayLike = CONSTANT_AVOGADRO,
n_s_function: Callable = air_refraction_index_Bodhaine1999,
F_air_function: Callable = F_air_Bodhaine1999,
) -> NDArrayFloat:
"""
Compute the *Rayleigh* optical depth :math:`T_r(\\lambda)` as a function
of wavelength :math:`\\lambda` in centimeters (cm).
Parameters
----------
wavelength
Wavelength :math:`\\lambda` in centimeters (cm).
CO2_concentration
:math:`CO_2` concentration in parts per million (ppm).
temperature
Air temperature :math:`T[K]` in kelvin degrees.
pressure
Surface pressure :math:`P` of the measurement site.
latitude
Latitude of the site in degrees.
altitude
Altitude of the site in meters.
avogadro_constant
*Avogadro*'s number (molecules :math:`mol^{-1}`).
n_s_function
Air refraction index :math:`n_s` computation method.
F_air_function
:math:`(6+3_p)/(6-7_p)`, the depolarisation term :math:`F(air)`
or *King Factor* computation method.
Returns
-------
:class:`numpy.ndarray`
*Rayleigh* optical depth :math:`T_r(\\lambda)`.
Warnings
--------
Unlike most objects of :mod:`colour.phenomena.rayleigh` module,
:func:`colour.phenomena.rayleigh_optical_depth` expects wavelength
:math:`\\lambda` to be expressed in centimeters (cm).
References
----------
:cite:`Bodhaine1999a`, :cite:`Wikipedia2001c`
Examples
--------
>>> rayleigh_optical_depth(555 * 10e-8) # doctest: +ELLIPSIS
np.float64(0.0936290...)
"""
wavelength = as_float_array(wavelength)
CO2_c = as_float_array(CO2_concentration)
pressure = as_float_array(pressure)
latitude = as_float_array(latitude)
altitude = as_float_array(altitude)
avogadro_constant = as_float_array(avogadro_constant)
# Conversion from pascal to dyne/cm2.
P = as_float_array(pressure * 10)
sigma = scattering_cross_section(
wavelength,
CO2_c,
temperature,
avogadro_constant,
n_s_function,
F_air_function,
)
m_a = mean_molecular_weights(CO2_c)
g = gravity_List1968(latitude, altitude)
T_R = sigma * (P * avogadro_constant) / (m_a * g)
return as_float(T_R)
rayleigh_scattering = rayleigh_optical_depth
[docs]
def sd_rayleigh_scattering(
shape: SpectralShape = SPECTRAL_SHAPE_DEFAULT,
CO2_concentration: ArrayLike = CONSTANT_STANDARD_CO2_CONCENTRATION,
temperature: ArrayLike = CONSTANT_STANDARD_AIR_TEMPERATURE,
pressure: ArrayLike = CONSTANT_AVERAGE_PRESSURE_MEAN_SEA_LEVEL,
latitude: ArrayLike = CONSTANT_DEFAULT_LATITUDE,
altitude: ArrayLike = CONSTANT_DEFAULT_ALTITUDE,
avogadro_constant: ArrayLike = CONSTANT_AVOGADRO,
n_s_function: Callable = air_refraction_index_Bodhaine1999,
F_air_function: Callable = F_air_Bodhaine1999,
) -> SpectralDistribution:
"""
Generate *Rayleigh* scattering spectral distribution for the specified
spectral shape.
Parameters
----------
shape
Spectral shape used to create the *Rayleigh* scattering spectral
distribution.
CO2_concentration
:math:`CO_2` concentration in parts per million (ppm).
temperature
Air temperature :math:`T[K]` in kelvin degrees.
pressure
Surface pressure :math:`P` of the measurement site.
latitude
Latitude of the site in degrees.
altitude
Altitude of the site in meters.
avogadro_constant
*Avogadro*'s number (molecules :math:`mol^{-1}`).
n_s_function
Air refraction index :math:`n_s` computation method.
F_air_function
:math:`(6+3_p)/(6-7_p)`, the depolarisation term :math:`F(air)` or
*King Factor* computation method.
Returns
-------
:class:`colour.SpectralDistribution`
*Rayleigh* optical depth spectral distribution.
References
----------
:cite:`Bodhaine1999a`, :cite:`Wikipedia2001c`
Examples
--------
>>> from colour.utilities import numpy_print_options
>>> with numpy_print_options(suppress=True):
... sd_rayleigh_scattering() # doctest: +ELLIPSIS
SpectralDistribution([[360. , 0.5602465...],
[361. , 0.5537481...],
[362. , 0.5473446...],
[363. , 0.5410345...],
[364. , 0.5348161...],
[365. , 0.5286877...],
[366. , 0.5226477...],
[367. , 0.5166948...],
[368. , 0.5108272...],
[369. , 0.5050436...],
[370. , 0.4993425...],
[371. , 0.4937224...],
[372. , 0.4881820...],
[373. , 0.4827199...],
[374. , 0.4773348...],
[375. , 0.4720253...],
[376. , 0.4667902...],
[377. , 0.4616282...],
[378. , 0.4565380...],
[379. , 0.4515186...],
[380. , 0.4465686...],
[381. , 0.4416869...],
[382. , 0.4368724...],
[383. , 0.4321240...],
[384. , 0.4274405...],
[385. , 0.4228209...],
[386. , 0.4182641...],
[387. , 0.4137692...],
[388. , 0.4093350...],
[389. , 0.4049607...],
[390. , 0.4006451...],
[391. , 0.3963874...],
[392. , 0.3921867...],
[393. , 0.3880419...],
[394. , 0.3839523...],
[395. , 0.3799169...],
[396. , 0.3759348...],
[397. , 0.3720053...],
[398. , 0.3681274...],
[399. , 0.3643003...],
[400. , 0.3605233...],
[401. , 0.3567956...],
[402. , 0.3531163...],
[403. , 0.3494847...],
[404. , 0.3459001...],
[405. , 0.3423617...],
[406. , 0.3388689...],
[407. , 0.3354208...],
[408. , 0.3320169...],
[409. , 0.3286563...],
[410. , 0.3253386...],
[411. , 0.3220629...],
[412. , 0.3188287...],
[413. , 0.3156354...],
[414. , 0.3124822...],
[415. , 0.3093687...],
[416. , 0.3062941...],
[417. , 0.3032579...],
[418. , 0.3002596...],
[419. , 0.2972985...],
[420. , 0.2943741...],
[421. , 0.2914858...],
[422. , 0.2886332...],
[423. , 0.2858157...],
[424. , 0.2830327...],
[425. , 0.2802837...],
[426. , 0.2775683...],
[427. , 0.2748860...],
[428. , 0.2722362...],
[429. , 0.2696185...],
[430. , 0.2670324...],
[431. , 0.2644775...],
[432. , 0.2619533...],
[433. , 0.2594594...],
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[538. , 0.1063108...],
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[551. , 0.0964342...],
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[555. , 0.0936290...],
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[557. , 0.0922649...],
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[623. , 0.0584848...],
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[626. , 0.0573544...],
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[628. , 0.0566160...],
[629. , 0.0562513...],
[630. , 0.0558895...],
[631. , 0.0555306...],
[632. , 0.0551746...],
[633. , 0.0548215...],
[634. , 0.0544712...],
[635. , 0.0541237...],
[636. , 0.0537789...],
[637. , 0.0534369...],
[638. , 0.0530977...],
[639. , 0.0527611...],
[640. , 0.0524272...],
[641. , 0.0520960...],
[642. , 0.0517674...],
[643. , 0.0514413...],
[644. , 0.0511179...],
[645. , 0.0507970...],
[646. , 0.0504786...],
[647. , 0.0501627...],
[648. , 0.0498493...],
[649. , 0.0495383...],
[650. , 0.0492298...],
[651. , 0.0489236...],
[652. , 0.0486199...],
[653. , 0.0483185...],
[654. , 0.0480194...],
[655. , 0.0477227...],
[656. , 0.0474283...],
[657. , 0.0471361...],
[658. , 0.0468462...],
[659. , 0.0465585...],
[660. , 0.0462730...],
[661. , 0.0459898...],
[662. , 0.0457087...],
[663. , 0.0454297...],
[664. , 0.0451529...],
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[666. , 0.0446055...],
[667. , 0.0443350...],
[668. , 0.0440665...],
[669. , 0.0438000...],
[670. , 0.0435356...],
[671. , 0.0432731...],
[672. , 0.0430127...],
[673. , 0.0427542...],
[674. , 0.0424976...],
[675. , 0.0422430...],
[676. , 0.0419902...],
[677. , 0.0417394...],
[678. , 0.0414905...],
[679. , 0.0412434...],
[680. , 0.0409981...],
[681. , 0.0407547...],
[682. , 0.0405131...],
[683. , 0.0402732...],
[684. , 0.0400352...],
[685. , 0.0397989...],
[686. , 0.0395643...],
[687. , 0.0393315...],
[688. , 0.0391004...],
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[690. , 0.0386433...],
[691. , 0.0384173...],
[692. , 0.0381929...],
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[694. , 0.0377490...],
[695. , 0.0375295...],
[696. , 0.0373115...],
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[701. , 0.0362454...],
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[703. , 0.0358297...],
[704. , 0.0356241...],
[705. , 0.0354199...],
[706. , 0.0352172...],
[707. , 0.0350160...],
[708. , 0.0348162...],
[709. , 0.0346178...],
[710. , 0.0344208...],
[711. , 0.0342253...],
[712. , 0.0340311...],
[713. , 0.0338383...],
[714. , 0.0336469...],
[715. , 0.0334569...],
[716. , 0.0332681...],
[717. , 0.0330807...],
[718. , 0.0328947...],
[719. , 0.0327099...],
[720. , 0.0325264...],
[721. , 0.0323443...],
[722. , 0.0321634...],
[723. , 0.0319837...],
[724. , 0.0318054...],
[725. , 0.0316282...],
[726. , 0.0314523...],
[727. , 0.0312777...],
[728. , 0.0311042...],
[729. , 0.0309319...],
[730. , 0.0307609...],
[731. , 0.0305910...],
[732. , 0.0304223...],
[733. , 0.0302548...],
[734. , 0.0300884...],
[735. , 0.0299231...],
[736. , 0.0297590...],
[737. , 0.0295960...],
[738. , 0.0294342...],
[739. , 0.0292734...],
[740. , 0.0291138...],
[741. , 0.0289552...],
[742. , 0.0287977...],
[743. , 0.0286413...],
[744. , 0.0284859...],
[745. , 0.0283316...],
[746. , 0.0281784...],
[747. , 0.0280262...],
[748. , 0.0278750...],
[749. , 0.0277248...],
[750. , 0.0275757...],
[751. , 0.0274275...],
[752. , 0.0272804...],
[753. , 0.0271342...],
[754. , 0.0269890...],
[755. , 0.0268448...],
[756. , 0.0267015...],
[757. , 0.0265592...],
[758. , 0.0264179...],
[759. , 0.0262775...],
[760. , 0.0261380...],
[761. , 0.0259995...],
[762. , 0.0258618...],
[763. , 0.0257251...],
[764. , 0.0255893...],
[765. , 0.0254544...],
[766. , 0.0253204...],
[767. , 0.0251872...],
[768. , 0.0250550...],
[769. , 0.0249236...],
[770. , 0.0247930...],
[771. , 0.0246633...],
[772. , 0.0245345...],
[773. , 0.0244065...],
[774. , 0.0242794...],
[775. , 0.0241530...],
[776. , 0.0240275...],
[777. , 0.0239029...],
[778. , 0.0237790...],
[779. , 0.0236559...],
[780. , 0.0235336...]],
SpragueInterpolator,
{},
Extrapolator,
{'method': 'Constant', 'left': None, 'right': None})
"""
return SpectralDistribution(
rayleigh_optical_depth(
shape.wavelengths * 10e-8,
CO2_concentration,
temperature,
pressure,
latitude,
altitude,
avogadro_constant,
n_s_function,
F_air_function,
),
shape.wavelengths,
name=(
"Rayleigh Scattering - "
f"{CO2_concentration!r} ppm, "
f"{temperature!r} K, "
f"{pressure!r} Pa, "
f"{latitude!r} Degrees, "
f"{altitude!r} m"
),
)
