"""
Rayleigh Optical Depth - Scattering in the Atmosphere
=====================================================
Implement *Rayleigh* scattering / optical depth in the atmosphere computation:
- :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:
"""
Return the air refraction index :math:`n_s` from given wavelength
:math:`\\lambda` in micrometers (:math:`\\mu m`) using *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
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:
"""
Return the air refraction index :math:`n_s` from given wavelength
:math:`\\lambda` in micrometers (:math:`\\mu m`) using *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
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:
"""
Return the air refraction index :math:`n_s` from given wavelength
:math:`\\lambda` in micrometers (:math:`\\mu m`) using
*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
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:
"""
Return the air refraction index :math:`n_s` from given wavelength
:math:`\\lambda` in micrometers (:math:`\\mu m`) using
*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
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:
"""
Return the depolarisation of nitrogen :math:`N_2` as 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
1.0350291...
"""
wl = as_float_array(wavelength)
return 1.034 + 3.17 * 1.0e-4 * (1 / wl**2)
def O2_depolarisation(wavelength: ArrayLike) -> NDArrayFloat:
"""
Return the depolarisation of oxygen :math:`O_2` as 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
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:
"""
Return :math:`(6+3_p)/(6-7_p)`, the depolarisation term :math:`F(air)` or
*King Factor* using *Penndorf (1957)* method.
Parameters
----------
wavelength
Wavelength :math:`\\lambda` in micrometers (:math:`\\mu m`).
Returns
-------
:class:`numpy.ndarray`
Air depolarisation.
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)
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:
"""
Return :math:`(6+3_p)/(6-7_p)`, the depolarisation term :math:`F(air)` or
*King Factor* using *Young (1981)* method.
Parameters
----------
wavelength
Wavelength :math:`\\lambda` in micrometers (:math:`\\mu m`).
Returns
-------
:class:`numpy.ndarray`
Air depolarisation.
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)
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:
"""
Return :math:`(6+3_p)/(6-7_p)`, the depolarisation term :math:`F(air)` or
*King Factor* as function of wavelength :math:`\\lambda` in micrometers
(:math:`\\mu m`) using *Bates (1984)* method.
Parameters
----------
wavelength
Wavelength :math:`\\lambda` in micrometers (:math:`\\mu m`).
Returns
-------
:class:`numpy.ndarray`
Air depolarisation.
Examples
--------
>>> F_air_Bates1984(0.555) # doctest: +ELLIPSIS
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:
"""
Return :math:`(6+3_p)/(6-7_p)`, the depolarisation term :math:`F(air)` or
*King Factor* as function of wavelength :math:`\\lambda` in micrometers
(:math:`\\mu m`) and :math:`CO_2` concentration in parts per million (ppm)
using *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.
Examples
--------
>>> F_air_Bodhaine1999(0.555) # doctest: +ELLIPSIS
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:
"""
Return 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 given by
by the Committee on Data for Science and Technology (CODATA):
:math:`6.02214179x10^{23}`, which is different from the reference
:cite:`Bodhaine1999a` value :math:`6.0221367x10^{23}`.
Examples
--------
>>> molecular_density(288.15) # doctest: +ELLIPSIS
2.5469021...e+19
>>> molecular_density(288.15, 6.0221367e23) # doctest: +ELLIPSIS
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:
"""
Return the mean molecular weights :math:`m_a` for dry air as 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
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:
"""
Return the gravity :math:`g` in :math:`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
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
978.0356070...
>>> gravity_List1968(0.0, 1500.0) # doctest: +ELLIPSIS
977.5726106...
Gravity :math:`g` for Paris:
>>> gravity_List1968(48.8567, 35.0) # doctest: +ELLIPSIS
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:
"""
Return the scattering cross-section per molecule :math:`\\sigma` of dry
air as function of wavelength :math:`\\lambda` in centimeters (cm) using
given :math:`CO_2` concentration in parts per million (ppm) and temperature
:math:`T[K]` in kelvin degrees following *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
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:
"""
Return the *Rayleigh* optical depth :math:`T_r(\\lambda)` as 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
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:
"""
Return the *Rayleigh* spectral distribution for given 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...],
[ 434. , 0.2569952...],
[ 435. , 0.2545605...],
[ 436. , 0.2521548...],
[ 437. , 0.2497776...],
[ 438. , 0.2474285...],
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[ 564. , 0.0876825...],
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[ 636. , 0.0537789...],
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[ 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...],
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[ 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...],
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[ 678. , 0.0414905...],
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[ 680. , 0.0409981...],
[ 681. , 0.0407547...],
[ 682. , 0.0405131...],
[ 683. , 0.0402732...],
[ 684. , 0.0400352...],
[ 685. , 0.0397989...],
[ 686. , 0.0395643...],
[ 687. , 0.0393315...],
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[ 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"
),
)
