""" 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 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 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 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 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 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 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) 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) 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 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 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 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: """ 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 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 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 ) 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 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 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 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 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...], [ 434. , 0.2569952...], [ 435. , 0.2545605...], [ 436. , 0.2521548...], [ 437. , 0.2497776...], [ 438. , 0.2474285...], [ 439. , 0.2451072...], [ 440. , 0.2428133...], [ 441. , 0.2405463...], [ 442. , 0.2383059...], [ 443. , 0.2360916...], [ 444. , 0.2339033...], [ 445. , 0.2317404...], [ 446. , 0.2296026...], [ 447. , 0.2274895...], [ 448. , 0.2254009...], [ 449. , 0.2233364...], [ 450. , 0.2212956...], [ 451. , 0.2192782...], [ 452. , 0.2172839...], [ 453. , 0.2153124...], [ 454. , 0.2133633...], [ 455. , 0.2114364...], [ 456. , 0.2095313...], [ 457. , 0.2076478...], [ 458. , 0.2057855...], [ 459. , 0.2039442...], [ 460. , 0.2021235...], [ 461. , 0.2003233...], [ 462. , 0.1985432...], [ 463. , 0.1967829...], [ 464. , 0.1950423...], [ 465. , 0.1933209...], [ 466. , 0.1916186...], [ 467. , 0.1899351...], [ 468. , 0.1882702...], [ 469. , 0.1866236...], [ 470. , 0.1849951...], [ 471. , 0.1833844...], [ 472. , 0.1817913...], [ 473. , 0.1802156...], [ 474. , 0.1786570...], [ 475. , 0.1771153...], [ 476. , 0.1755903...], [ 477. , 0.1740818...], [ 478. , 0.1725895...], [ 479. , 0.1711133...], [ 480. , 0.1696529...], [ 481. , 0.1682082...], [ 482. , 0.1667789...], [ 483. , 0.1653648...], [ 484. , 0.1639658...], [ 485. , 0.1625816...], [ 486. , 0.1612121...], [ 487. , 0.1598570...], [ 488. , 0.1585163...], [ 489. , 0.1571896...], [ 490. , 0.1558769...], [ 491. , 0.1545779...], [ 492. , 0.1532925...], [ 493. , 0.1520205...], [ 494. , 0.1507617...], [ 495. , 0.1495160...], [ 496. , 0.1482832...], [ 497. , 0.1470632...], [ 498. , 0.1458558...], [ 499. , 0.1446607...], [ 500. , 0.1434780...], [ 501. , 0.1423074...], [ 502. , 0.1411488...], [ 503. , 0.140002 ...], [ 504. , 0.1388668...], [ 505. , 0.1377433...], [ 506. , 0.1366311...], [ 507. , 0.1355301...], [ 508. , 0.1344403...], [ 509. , 0.1333615...], [ 510. , 0.1322936...], [ 511. , 0.1312363...], [ 512. , 0.1301897...], [ 513. , 0.1291535...], [ 514. , 0.1281277...], [ 515. , 0.1271121...], [ 516. , 0.1261065...], [ 517. , 0.1251110...], [ 518. , 0.1241253...], [ 519. , 0.1231493...], [ 520. , 0.1221829...], [ 521. , 0.1212261...], [ 522. , 0.1202786...], [ 523. , 0.1193405...], [ 524. , 0.1184115...], [ 525. , 0.1174915...], [ 526. , 0.1165806...], [ 527. , 0.1156784...], [ 528. , 0.1147851...], [ 529. , 0.1139004...], [ 530. , 0.1130242...], [ 531. , 0.1121564...], [ 532. , 0.1112971...], [ 533. , 0.1104459...], [ 534. , 0.1096030...], [ 535. , 0.1087681...], [ 536. , 0.1079411...], [ 537. , 0.1071221...], [ 538. , 0.1063108...], [ 539. , 0.1055072...], [ 540. , 0.1047113...], [ 541. , 0.1039229...], [ 542. , 0.1031419...], [ 543. , 0.1023682...], [ 544. , 0.1016019...], [ 545. , 0.1008427...], [ 546. , 0.1000906...], [ 547. , 0.0993456...], [ 548. , 0.0986075...], [ 549. , 0.0978763...], [ 550. , 0.0971519...], [ 551. , 0.0964342...], [ 552. , 0.0957231...], [ 553. , 0.0950186...], [ 554. , 0.0943206...], [ 555. , 0.0936290...], [ 556. , 0.0929438...], [ 557. , 0.0922649...], [ 558. , 0.0915922...], [ 559. , 0.0909256...], [ 560. , 0.0902651...], [ 561. , 0.0896106...], [ 562. , 0.0889620...], [ 563. , 0.0883194...], [ 564. , 0.0876825...], [ 565. , 0.0870514...], [ 566. , 0.0864260...], [ 567. , 0.0858063...], [ 568. , 0.0851921...], [ 569. , 0.0845834...], [ 570. , 0.0839801...], [ 571. , 0.0833822...], [ 572. , 0.0827897...], [ 573. , 0.0822025...], [ 574. , 0.0816204...], [ 575. , 0.0810436...], [ 576. , 0.0804718...], [ 577. , 0.0799051...], [ 578. , 0.0793434...], [ 579. , 0.0787866...], [ 580. , 0.0782347...], [ 581. , 0.0776877...], [ 582. , 0.0771454...], [ 583. , 0.0766079...], [ 584. , 0.0760751...], [ 585. , 0.0755469...], [ 586. , 0.0750234...], [ 587. , 0.0745043...], [ 588. , 0.0739898...], [ 589. , 0.0734797...], [ 590. , 0.0729740...], [ 591. , 0.0724727...], [ 592. , 0.0719757...], [ 593. , 0.0714830...], [ 594. , 0.0709944...], [ 595. , 0.0705101...], [ 596. , 0.0700299...], [ 597. , 0.0695538...], [ 598. , 0.0690818...], [ 599. , 0.0686137...], [ 600. , 0.0681497...], [ 601. , 0.0676895...], [ 602. , 0.0672333...], [ 603. , 0.0667809...], [ 604. , 0.0663323...], [ 605. , 0.0658875...], [ 606. , 0.0654464...], [ 607. , 0.0650091...], [ 608. , 0.0645753...], [ 609. , 0.0641453...], [ 610. , 0.0637187...], [ 611. , 0.0632958...], [ 612. , 0.0628764...], [ 613. , 0.0624604...], [ 614. , 0.0620479...], [ 615. , 0.0616388...], [ 616. , 0.0612331...], [ 617. , 0.0608307...], [ 618. , 0.0604316...], [ 619. , 0.0600358...], [ 620. , 0.0596433...], [ 621. , 0.0592539...], [ 622. , 0.0588678...], [ 623. , 0.0584848...], [ 624. , 0.0581049...], [ 625. , 0.0577281...], [ 626. , 0.0573544...], [ 627. , 0.0569837...], [ 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...], [ 665. , 0.0448782...], [ 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...], [ 689. , 0.0388710...], [ 690. , 0.0386433...], [ 691. , 0.0384173...], [ 692. , 0.0381929...], [ 693. , 0.0379701...], [ 694. , 0.0377490...], [ 695. , 0.0375295...], [ 696. , 0.0373115...], [ 697. , 0.0370952...], [ 698. , 0.0368804...], [ 699. , 0.0366672...], [ 700. , 0.0364556...], [ 701. , 0.0362454...], [ 702. , 0.0360368...], [ 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" ), )