Source code for colour.phenomena.rayleigh

"""
Rayleigh Optical Depth - Scattering in the Atmosphere
=====================================================

Implements *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 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
from colour.hints import Callable, FloatingOrArrayLike, FloatingOrNDArray
from colour.utilities import as_float, as_float_array, filter_kwargs

__author__ = "Colour Developers"
__copyright__ = "Copyright 2013 Colour Developers"
__license__ = "New BSD License - 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",
]

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: FloatingOrArrayLike,
) -> FloatingOrNDArray:
    """
    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.floating` or :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: FloatingOrArrayLike,
) -> FloatingOrNDArray:
    """
    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.floating` or :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: FloatingOrArrayLike,
) -> FloatingOrNDArray:
    """
    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.floating` or :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: FloatingOrArrayLike,
    CO2_concentration: FloatingOrArrayLike = CONSTANT_STANDARD_CO2_CONCENTRATION,
) -> FloatingOrNDArray:
    """
    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.floating` or :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)

    n = (1 + 0.54 * ((CO2_c * 1e-6) - 300e-6)) * (
        air_refraction_index_Peck1972(wl) - 1
    ) + 1

    return as_float(n)


def N2_depolarisation(wavelength: FloatingOrArrayLike) -> FloatingOrNDArray:
    """
    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.floating` or :class:`numpy.ndarray`
        Nitrogen :math:`N_2` depolarisation.

    Examples
    --------
    >>> N2_depolarisation(0.555)  # doctest: +ELLIPSIS
    1.0350291...
    """

    wl = as_float_array(wavelength)

    N2 = 1.034 + 3.17 * 1.0e-4 * (1 / wl**2)

    return N2


def O2_depolarisation(wavelength: FloatingOrArrayLike) -> FloatingOrNDArray:
    """
    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.floating` or :class:`numpy.ndarray`
        Oxygen :math:`O_2` depolarisation.

    Examples
    --------
    >>> O2_depolarisation(0.555)  # doctest: +ELLIPSIS
    1.1020225...
    """

    wl = as_float_array(wavelength)

    O2 = (
        1.096 + 1.385 * 1.0e-3 * (1 / wl**2) + 1.448 * 1.0e-4 * (1 / wl**4)
    )

    return O2


def F_air_Penndorf1957(wavelength: FloatingOrArrayLike) -> FloatingOrNDArray:
    """
    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.floating` or :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: FloatingOrArrayLike) -> FloatingOrNDArray:
    """
    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.floating` or :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: FloatingOrArrayLike) -> FloatingOrNDArray:
    """
    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.floating` or :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

    F_air = (78.084 * N2 + 20.946 * O2 + CO2 + Ar) / (
        78.084 + 20.946 + Ar + CO2
    )

    return F_air


def F_air_Bodhaine1999(
    wavelength: FloatingOrArrayLike,
    CO2_concentration: FloatingOrArrayLike = CONSTANT_STANDARD_CO2_CONCENTRATION,
) -> FloatingOrNDArray:
    """
    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.floating` or :class:`numpy.ndarray`
        Air depolarisation.

    Examples
    --------
    >>> F_air_Bodhaine1999(0.555)  # doctest: +ELLIPSIS
    1.1246916...
    """

    O2 = O2_depolarisation(wavelength)
    N2 = N2_depolarisation(wavelength)
    CO2_c = as_float_array(CO2_concentration)

    F_air = (78.084 * N2 + 20.946 * O2 + 0.934 * 1 + CO2_c * 1.15) / (
        78.084 + 20.946 + 0.934 + CO2_c
    )

    return F_air


def molecular_density(
    temperature: FloatingOrArrayLike = CONSTANT_STANDARD_AIR_TEMPERATURE,
    avogadro_constant: FloatingOrArrayLike = CONSTANT_AVOGADRO,
) -> FloatingOrNDArray:
    """
    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.floating` or :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():
        N_s = (avogadro_constant / 22.4141) * sdiv(273.15, T) * (1 / 1000)

    return N_s


def mean_molecular_weights(
    CO2_concentration: FloatingOrArrayLike = CONSTANT_STANDARD_CO2_CONCENTRATION,
) -> FloatingOrNDArray:
    """
    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.floating` or :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

    m_a = 15.0556 * CO2_c + 28.9595
    return m_a


def gravity_List1968(
    latitude: FloatingOrArrayLike = CONSTANT_DEFAULT_LATITUDE,
    altitude: FloatingOrArrayLike = CONSTANT_DEFAULT_ALTITUDE,
) -> FloatingOrNDArray:
    """
    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.floating` or :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)

    g = (
        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
    )

    return g


[docs]def scattering_cross_section( wavelength: FloatingOrArrayLike, CO2_concentration: FloatingOrArrayLike = CONSTANT_STANDARD_CO2_CONCENTRATION, temperature: FloatingOrArrayLike = CONSTANT_STANDARD_AIR_TEMPERATURE, avogadro_constant: FloatingOrArrayLike = CONSTANT_AVOGADRO, n_s_function: Callable = air_refraction_index_Bodhaine1999, F_air_function: Callable = F_air_Bodhaine1999, ) -> FloatingOrNDArray: """ 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.floating` or :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 4.6613309...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: FloatingOrArrayLike, CO2_concentration: FloatingOrArrayLike = CONSTANT_STANDARD_CO2_CONCENTRATION, temperature: FloatingOrArrayLike = CONSTANT_STANDARD_AIR_TEMPERATURE, pressure: FloatingOrArrayLike = CONSTANT_AVERAGE_PRESSURE_MEAN_SEA_LEVEL, latitude: FloatingOrArrayLike = CONSTANT_DEFAULT_LATITUDE, altitude: FloatingOrArrayLike = CONSTANT_DEFAULT_ALTITUDE, avogadro_constant: FloatingOrArrayLike = CONSTANT_AVOGADRO, n_s_function: Callable = air_refraction_index_Bodhaine1999, F_air_function: Callable = F_air_Bodhaine1999, ) -> FloatingOrNDArray: """ 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.floating` or :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 0.1004070... """ 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) # 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: FloatingOrArrayLike = CONSTANT_STANDARD_CO2_CONCENTRATION, temperature: FloatingOrArrayLike = CONSTANT_STANDARD_AIR_TEMPERATURE, pressure: FloatingOrArrayLike = CONSTANT_AVERAGE_PRESSURE_MEAN_SEA_LEVEL, latitude: FloatingOrArrayLike = CONSTANT_DEFAULT_LATITUDE, altitude: FloatingOrArrayLike = CONSTANT_DEFAULT_ALTITUDE, avogadro_constant: FloatingOrArrayLike = 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. , 0.5991013...], [ 361. , 0.5921706...], [ 362. , 0.5853410...], [ 363. , 0.5786105...], [ 364. , 0.5719774...], [ 365. , 0.5654401...], [ 366. , 0.5589968...], [ 367. , 0.5526460...], [ 368. , 0.5463860...], [ 369. , 0.5402153...], [ 370. , 0.5341322...], [ 371. , 0.5281354...], [ 372. , 0.5222234...], [ 373. , 0.5163946...], [ 374. , 0.5106476...], [ 375. , 0.5049812...], [ 376. , 0.4993939...], [ 377. , 0.4938844...], [ 378. , 0.4884513...], [ 379. , 0.4830934...], [ 380. , 0.4778095...], [ 381. , 0.4725983...], [ 382. , 0.4674585...], [ 383. , 0.4623891...], [ 384. , 0.4573889...], [ 385. , 0.4524566...], [ 386. , 0.4475912...], [ 387. , 0.4427917...], [ 388. , 0.4380568...], [ 389. , 0.4333856...], [ 390. , 0.4287771...], [ 391. , 0.4242302...], [ 392. , 0.4197439...], [ 393. , 0.4153172...], [ 394. , 0.4109493...], [ 395. , 0.4066391...], [ 396. , 0.4023857...], [ 397. , 0.3981882...], [ 398. , 0.3940458...], [ 399. , 0.3899576...], [ 400. , 0.3859227...], [ 401. , 0.3819402...], [ 402. , 0.3780094...], [ 403. , 0.3741295...], [ 404. , 0.3702996...], [ 405. , 0.366519 ...], [ 406. , 0.3627868...], [ 407. , 0.3591025...], [ 408. , 0.3554651...], [ 409. , 0.3518740...], [ 410. , 0.3483286...], [ 411. , 0.344828 ...], [ 412. , 0.3413716...], [ 413. , 0.3379587...], [ 414. , 0.3345887...], [ 415. , 0.3312609...], [ 416. , 0.3279747...], [ 417. , 0.3247294...], [ 418. , 0.3215245...], [ 419. , 0.3183593...], [ 420. , 0.3152332...], [ 421. , 0.3121457...], [ 422. , 0.3090962...], [ 423. , 0.3060841...], [ 424. , 0.3031088...], [ 425. , 0.3001699...], [ 426. , 0.2972668...], [ 427. , 0.2943989...], [ 428. , 0.2915657...], [ 429. , 0.2887668...], [ 430. , 0.2860017...], [ 431. , 0.2832697...], [ 432. , 0.2805706...], [ 433. , 0.2779037...], [ 434. , 0.2752687...], [ 435. , 0.2726650...], [ 436. , 0.2700922...], [ 437. , 0.2675500...], [ 438. , 0.2650377...], [ 439. , 0.2625551...], [ 440. , 0.2601016...], [ 441. , 0.2576770...], [ 442. , 0.2552807...], [ 443. , 0.2529124...], [ 444. , 0.2505716...], [ 445. , 0.2482581...], [ 446. , 0.2459713...], [ 447. , 0.2437110...], [ 448. , 0.2414768...], [ 449. , 0.2392683...], [ 450. , 0.2370851...], [ 451. , 0.2349269...], [ 452. , 0.2327933...], [ 453. , 0.2306841...], [ 454. , 0.2285989...], [ 455. , 0.2265373...], [ 456. , 0.2244990...], [ 457. , 0.2224838...], [ 458. , 0.2204912...], [ 459. , 0.2185211...], [ 460. , 0.2165730...], [ 461. , 0.2146467...], [ 462. , 0.2127419...], [ 463. , 0.2108583...], [ 464. , 0.2089957...], [ 465. , 0.2071536...], [ 466. , 0.2053320...], [ 467. , 0.2035304...], [ 468. , 0.2017487...], [ 469. , 0.1999865...], [ 470. , 0.1982436...], [ 471. , 0.1965198...], [ 472. , 0.1948148...], [ 473. , 0.1931284...], [ 474. , 0.1914602...], [ 475. , 0.1898101...], [ 476. , 0.1881779...], [ 477. , 0.1865633...], [ 478. , 0.1849660...], [ 479. , 0.1833859...], [ 480. , 0.1818227...], [ 481. , 0.1802762...], [ 482. , 0.1787463...], [ 483. , 0.1772326...], [ 484. , 0.1757349...], [ 485. , 0.1742532...], [ 486. , 0.1727871...], [ 487. , 0.1713365...], [ 488. , 0.1699011...], [ 489. , 0.1684809...], [ 490. , 0.1670755...], [ 491. , 0.1656848...], [ 492. , 0.1643086...], [ 493. , 0.1629468...], [ 494. , 0.1615991...], [ 495. , 0.1602654...], [ 496. , 0.1589455...], [ 497. , 0.1576392...], [ 498. , 0.1563464...], [ 499. , 0.1550668...], [ 500. , 0.1538004...], [ 501. , 0.1525470...], [ 502. , 0.1513063...], [ 503. , 0.1500783...], [ 504. , 0.1488628...], [ 505. , 0.1476597...], [ 506. , 0.1464687...], [ 507. , 0.1452898...], [ 508. , 0.1441228...], [ 509. , 0.1429675...], [ 510. , 0.1418238...], [ 511. , 0.1406916...], [ 512. , 0.1395707...], [ 513. , 0.1384610...], [ 514. , 0.1373624...], [ 515. , 0.1362747...], [ 516. , 0.1351978...], [ 517. , 0.1341316...], [ 518. , 0.1330759...], [ 519. , 0.1320306...], [ 520. , 0.1309956...], [ 521. , 0.1299707...], [ 522. , 0.1289559...], [ 523. , 0.1279511...], [ 524. , 0.1269560...], [ 525. , 0.1259707...], [ 526. , 0.1249949...], [ 527. , 0.1240286...], [ 528. , 0.1230717...], [ 529. , 0.1221240...], [ 530. , 0.1211855...], [ 531. , 0.1202560...], [ 532. , 0.1193354...], [ 533. , 0.1184237...], [ 534. , 0.1175207...], [ 535. , 0.1166263...], [ 536. , 0.1157404...], [ 537. , 0.1148630...], [ 538. , 0.1139939...], [ 539. , 0.1131331...], [ 540. , 0.1122804...], [ 541. , 0.1114357...], [ 542. , 0.1105990...], [ 543. , 0.1097702...], [ 544. , 0.1089492...], [ 545. , 0.1081358...], [ 546. , 0.1073301...], [ 547. , 0.1065319...], [ 548. , 0.1057411...], [ 549. , 0.1049577...], [ 550. , 0.1041815...], [ 551. , 0.1034125...], [ 552. , 0.1026507...], [ 553. , 0.1018958...], [ 554. , 0.1011480...], [ 555. , 0.1004070...], [ 556. , 0.0996728...], [ 557. , 0.0989453...], [ 558. , 0.0982245...], [ 559. , 0.0975102...], [ 560. , 0.0968025...], [ 561. , 0.0961012...], [ 562. , 0.0954062...], [ 563. , 0.0947176...], [ 564. , 0.0940352...], [ 565. , 0.0933589...], [ 566. , 0.0926887...], [ 567. , 0.0920246...], [ 568. , 0.0913664...], [ 569. , 0.0907141...], [ 570. , 0.0900677...], [ 571. , 0.0894270...], [ 572. , 0.0887920...], [ 573. , 0.0881627...], [ 574. , 0.0875389...], [ 575. , 0.0869207...], [ 576. , 0.0863079...], [ 577. , 0.0857006...], [ 578. , 0.0850986...], [ 579. , 0.0845019...], [ 580. , 0.0839104...], [ 581. , 0.0833242...], [ 582. , 0.0827430...], [ 583. , 0.082167 ...], [ 584. , 0.0815959...], [ 585. , 0.0810298...], [ 586. , 0.0804687...], [ 587. , 0.0799124...], [ 588. , 0.0793609...], [ 589. , 0.0788142...], [ 590. , 0.0782722...], [ 591. , 0.0777349...], [ 592. , 0.0772022...], [ 593. , 0.0766740...], [ 594. , 0.0761504...], [ 595. , 0.0756313...], [ 596. , 0.0751166...], [ 597. , 0.0746063...], [ 598. , 0.0741003...], [ 599. , 0.0735986...], [ 600. , 0.0731012...], [ 601. , 0.072608 ...], [ 602. , 0.0721189...], [ 603. , 0.0716340...], [ 604. , 0.0711531...], [ 605. , 0.0706763...], [ 606. , 0.0702035...], [ 607. , 0.0697347...], [ 608. , 0.0692697...], [ 609. , 0.0688087...], [ 610. , 0.0683515...], [ 611. , 0.0678981...], [ 612. , 0.0674485...], [ 613. , 0.0670026...], [ 614. , 0.0665603...], [ 615. , 0.0661218...], [ 616. , 0.0656868...], [ 617. , 0.0652555...], [ 618. , 0.0648277...], [ 619. , 0.0644033...], [ 620. , 0.0639825...], [ 621. , 0.0635651...], [ 622. , 0.0631512...], [ 623. , 0.0627406...], [ 624. , 0.0623333...], [ 625. , 0.0619293...], [ 626. , 0.0615287...], [ 627. , 0.0611312...], [ 628. , 0.0607370...], [ 629. , 0.0603460...], [ 630. , 0.0599581...], [ 631. , 0.0595733...], [ 632. , 0.0591917...], [ 633. , 0.0588131...], [ 634. , 0.0584375...], [ 635. , 0.0580649...], [ 636. , 0.0576953...], [ 637. , 0.0573286...], [ 638. , 0.0569649...], [ 639. , 0.0566040...], [ 640. , 0.0562460...], [ 641. , 0.0558909...], [ 642. , 0.0555385...], [ 643. , 0.0551890...], [ 644. , 0.0548421...], [ 645. , 0.0544981...], [ 646. , 0.0541567...], [ 647. , 0.053818 ...], [ 648. , 0.0534819...], [ 649. , 0.0531485...], [ 650. , 0.0528176...], [ 651. , 0.0524894...], [ 652. , 0.0521637...], [ 653. , 0.0518405...], [ 654. , 0.0515198...], [ 655. , 0.0512017...], [ 656. , 0.0508859...], [ 657. , 0.0505726...], [ 658. , 0.0502618...], [ 659. , 0.0499533...], [ 660. , 0.0496472...], [ 661. , 0.0493434...], [ 662. , 0.0490420...], [ 663. , 0.0487428...], [ 664. , 0.0484460...], [ 665. , 0.0481514...], [ 666. , 0.0478591...], [ 667. , 0.0475689...], [ 668. , 0.0472810...], [ 669. , 0.0469953...], [ 670. , 0.0467117...], [ 671. , 0.0464302...], [ 672. , 0.0461509...], [ 673. , 0.0458737...], [ 674. , 0.0455986...], [ 675. , 0.0453255...], [ 676. , 0.0450545...], [ 677. , 0.0447855...], [ 678. , 0.0445185...], [ 679. , 0.0442535...], [ 680. , 0.0439905...], [ 681. , 0.0437294...], [ 682. , 0.0434703...], [ 683. , 0.0432131...], [ 684. , 0.0429578...], [ 685. , 0.0427044...], [ 686. , 0.0424529...], [ 687. , 0.0422032...], [ 688. , 0.0419553...], [ 689. , 0.0417093...], [ 690. , 0.0414651...], [ 691. , 0.0412226...], [ 692. , 0.0409820...], [ 693. , 0.0407431...], [ 694. , 0.0405059...], [ 695. , 0.0402705...], [ 696. , 0.0400368...], [ 697. , 0.0398047...], [ 698. , 0.0395744...], [ 699. , 0.0393457...], [ 700. , 0.0391187...], [ 701. , 0.0388933...], [ 702. , 0.0386696...], [ 703. , 0.0384474...], [ 704. , 0.0382269...], [ 705. , 0.0380079...], [ 706. , 0.0377905...], [ 707. , 0.0375747...], [ 708. , 0.0373604...], [ 709. , 0.0371476...], [ 710. , 0.0369364...], [ 711. , 0.0367266...], [ 712. , 0.0365184...], [ 713. , 0.0363116...], [ 714. , 0.0361063...], [ 715. , 0.0359024...], [ 716. , 0.0357000...], [ 717. , 0.0354990...], [ 718. , 0.0352994...], [ 719. , 0.0351012...], [ 720. , 0.0349044...], [ 721. , 0.0347090...], [ 722. , 0.0345150...], [ 723. , 0.0343223...], [ 724. , 0.0341310...], [ 725. , 0.0339410...], [ 726. , 0.0337523...], [ 727. , 0.033565 ...], [ 728. , 0.0333789...], [ 729. , 0.0331941...], [ 730. , 0.0330106...], [ 731. , 0.0328284...], [ 732. , 0.0326474...], [ 733. , 0.0324677...], [ 734. , 0.0322893...], [ 735. , 0.0321120...], [ 736. , 0.0319360...], [ 737. , 0.0317611...], [ 738. , 0.0315875...], [ 739. , 0.0314151...], [ 740. , 0.0312438...], [ 741. , 0.0310737...], [ 742. , 0.0309048...], [ 743. , 0.0307370...], [ 744. , 0.0305703...], [ 745. , 0.0304048...], [ 746. , 0.0302404...], [ 747. , 0.0300771...], [ 748. , 0.0299149...], [ 749. , 0.0297538...], [ 750. , 0.0295938...], [ 751. , 0.0294349...], [ 752. , 0.0292771...], [ 753. , 0.0291203...], [ 754. , 0.0289645...], [ 755. , 0.0288098...], [ 756. , 0.0286561...], [ 757. , 0.0285035...], [ 758. , 0.0283518...], [ 759. , 0.0282012...], [ 760. , 0.0280516...], [ 761. , 0.0279030...], [ 762. , 0.0277553...], [ 763. , 0.0276086...], [ 764. , 0.027463 ...], [ 765. , 0.0273182...], [ 766. , 0.0271744...], [ 767. , 0.0270316...], [ 768. , 0.0268897...], [ 769. , 0.0267487...], [ 770. , 0.0266087...], [ 771. , 0.0264696...], [ 772. , 0.0263314...], [ 773. , 0.0261941...], [ 774. , 0.0260576...], [ 775. , 0.0259221...], [ 776. , 0.0257875...], [ 777. , 0.0256537...], [ 778. , 0.0255208...], [ 779. , 0.0253888...], [ 780. , 0.0252576...]], SpragueInterpolator, {}, Extrapolator, {'method': 'Constant', 'left': None, 'right': None}) """ wavelengths = shape.range() return SpectralDistribution( rayleigh_optical_depth( wavelengths * 10e-8, CO2_concentration, temperature, pressure, latitude, altitude, avogadro_constant, n_s_function, F_air_function, ), 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" ), )