Coverage for phenomena/rayleigh.py: 64%
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1"""
2Rayleigh Optical Depth - Scattering in the Atmosphere
3=====================================================
5Implement *Rayleigh* scattering and optical depth computation in the
6atmosphere.
8- :func:`colour.scattering_cross_section`
9- :func:`colour.phenomena.rayleigh_optical_depth`
10- :func:`colour.rayleigh_scattering`
12References
13----------
14- :cite:`Bodhaine1999a` : Bodhaine, B. A., Wood, N. B., Dutton, E. G., &
15 Slusser, J. R. (1999). On Rayleigh Optical Depth Calculations. Journal of
16 Atmospheric and Oceanic Technology, 16(11), 1854-1861.
17 doi:10.1175/1520-0426(1999)016<1854:ORODC>2.0.CO;2
18- :cite:`Wikipedia2001c` : Wikipedia. (2001). Rayleigh scattering. Retrieved
19 September 23, 2014, from http://en.wikipedia.org/wiki/Rayleigh_scattering
20"""
22from __future__ import annotations
24import typing
26import numpy as np
28from colour.algebra import sdiv, sdiv_mode
29from colour.colorimetry import (
30 SPECTRAL_SHAPE_DEFAULT,
31 SpectralDistribution,
32 SpectralShape,
33)
34from colour.constants import CONSTANT_AVOGADRO
36if typing.TYPE_CHECKING:
37 from colour.hints import ArrayLike, Callable, NDArrayFloat
39from colour.utilities import as_float, as_float_array, filter_kwargs
41__author__ = "Colour Developers"
42__copyright__ = "Copyright 2013 Colour Developers"
43__license__ = "BSD-3-Clause - https://opensource.org/licenses/BSD-3-Clause"
44__maintainer__ = "Colour Developers"
45__email__ = "colour-developers@colour-science.org"
46__status__ = "Production"
48__all__ = [
49 "CONSTANT_STANDARD_AIR_TEMPERATURE",
50 "CONSTANT_STANDARD_CO2_CONCENTRATION",
51 "CONSTANT_AVERAGE_PRESSURE_MEAN_SEA_LEVEL",
52 "CONSTANT_DEFAULT_LATITUDE",
53 "CONSTANT_DEFAULT_ALTITUDE",
54 "air_refraction_index_Penndorf1957",
55 "air_refraction_index_Edlen1966",
56 "air_refraction_index_Peck1972",
57 "air_refraction_index_Bodhaine1999",
58 "N2_depolarisation",
59 "O2_depolarisation",
60 "F_air_Penndorf1957",
61 "F_air_Young1981",
62 "F_air_Bates1984",
63 "F_air_Bodhaine1999",
64 "molecular_density",
65 "mean_molecular_weights",
66 "gravity_List1968",
67 "scattering_cross_section",
68 "rayleigh_optical_depth",
69 "rayleigh_scattering",
70 "sd_rayleigh_scattering",
71]
73CONSTANT_STANDARD_AIR_TEMPERATURE: float = 288.15
74"""*Standard air* temperature :math:`T[K]` in kelvin degrees (:math:`15\\circ C`)."""
76CONSTANT_STANDARD_CO2_CONCENTRATION: float = 300
77"""*Standard air* :math:`CO_2` concentration in parts per million (ppm)."""
79CONSTANT_AVERAGE_PRESSURE_MEAN_SEA_LEVEL: float = 101325
80"""*Standard air* average pressure :math:`Hg` at mean sea-level in pascal (Pa)."""
82CONSTANT_DEFAULT_LATITUDE: float = 0
83"""Default latitude in degrees (equator)."""
85CONSTANT_DEFAULT_ALTITUDE: float = 0
86"""Default altitude in meters (sea level)."""
89def air_refraction_index_Penndorf1957(
90 wavelength: ArrayLike,
91) -> NDArrayFloat:
92 """
93 Compute the air refraction index :math:`n_s` from the specified wavelength
94 :math:`\\lambda` in micrometers (:math:`\\mu m`) using the
95 *Penndorf (1957)* method.
97 Parameters
98 ----------
99 wavelength
100 Wavelength :math:`\\lambda` in micrometers (:math:`\\mu m`).
102 Returns
103 -------
104 :class:`numpy.ndarray`
105 Air refraction index :math:`n_s`.
107 Examples
108 --------
109 >>> air_refraction_index_Penndorf1957(0.555) # doctest: +ELLIPSIS
110 1.0002777...
111 """
113 wl = as_float_array(wavelength)
115 n = 6432.8 + 2949810 / (146 - wl ** (-2)) + 25540 / (41 - wl ** (-2))
116 n /= 1.0e8
117 n += +1
119 return n
122def air_refraction_index_Edlen1966(
123 wavelength: ArrayLike,
124) -> NDArrayFloat:
125 """
126 Compute the air refraction index :math:`n_s` from the specified wavelength
127 :math:`\\lambda` in micrometers (:math:`\\mu m`) using the
128 *Edlen (1966)* method.
130 Parameters
131 ----------
132 wavelength
133 Wavelength :math:`\\lambda` in micrometers (:math:`\\mu m`).
135 Returns
136 -------
137 :class:`numpy.ndarray`
138 Air refraction index :math:`n_s`.
140 Examples
141 --------
142 >>> air_refraction_index_Edlen1966(0.555) # doctest: +ELLIPSIS
143 1.0002777...
144 """
146 wl = as_float_array(wavelength)
148 n = 8342.13 + 2406030 / (130 - wl ** (-2)) + 15997 / (38.9 - wl ** (-2))
149 n /= 1.0e8
150 n += +1
152 return n
155def air_refraction_index_Peck1972(
156 wavelength: ArrayLike,
157) -> NDArrayFloat:
158 """
159 Compute the air refraction index :math:`n_s` from the specified wavelength
160 :math:`\\lambda` in micrometers (:math:`\\mu m`) using the
161 *Peck and Reeder (1972)* method.
163 Parameters
164 ----------
165 wavelength
166 Wavelength :math:`\\lambda` in micrometers (:math:`\\mu m`).
168 Returns
169 -------
170 :class:`numpy.ndarray`
171 Air refraction index :math:`n_s`.
173 Examples
174 --------
175 >>> air_refraction_index_Peck1972(0.555) # doctest: +ELLIPSIS
176 1.0002777...
177 """
179 wl = as_float_array(wavelength)
181 n = 8060.51 + 2480990 / (132.274 - wl ** (-2)) + 17455.7 / (39.32957 - wl ** (-2))
182 n /= 1.0e8
183 n += +1
185 return n
188def air_refraction_index_Bodhaine1999(
189 wavelength: ArrayLike,
190 CO2_concentration: ArrayLike = CONSTANT_STANDARD_CO2_CONCENTRATION,
191) -> NDArrayFloat:
192 """
193 Compute the air refraction index :math:`n_s` from the specified wavelength
194 :math:`\\lambda` in micrometers (:math:`\\mu m`) using the
195 *Bodhaine, Wood, Dutton and Slusser (1999)* method.
197 Parameters
198 ----------
199 wavelength
200 Wavelength :math:`\\lambda` in micrometers (:math:`\\mu m`).
201 CO2_concentration
202 :math:`CO_2` concentration in parts per million (ppm).
204 Returns
205 -------
206 :class:`numpy.ndarray`
207 Air refraction index :math:`n_s`.
209 Examples
210 --------
211 >>> air_refraction_index_Bodhaine1999(0.555) # doctest: +ELLIPSIS
212 1.0002777...
213 """
215 wl = as_float_array(wavelength)
216 CO2_c = as_float_array(CO2_concentration)
218 # Converting from parts per million (ppm) to parts per volume (ppv).
219 CO2_c = CO2_c * 1e-6
221 n = (1 + 0.54 * (CO2_c - 300e-6)) * (air_refraction_index_Peck1972(wl) - 1) + 1
223 return as_float(n)
226def N2_depolarisation(wavelength: ArrayLike) -> NDArrayFloat:
227 """
228 Compute the depolarisation of nitrogen :math:`N_2` as a function of
229 wavelength :math:`\\lambda` in micrometers (:math:`\\mu m`).
231 Parameters
232 ----------
233 wavelength
234 Wavelength :math:`\\lambda` in micrometers (:math:`\\mu m`).
236 Returns
237 -------
238 :class:`numpy.ndarray`
239 Nitrogen :math:`N_2` depolarisation.
241 Examples
242 --------
243 >>> N2_depolarisation(0.555) # doctest: +ELLIPSIS
244 1.0350291...
245 """
247 wl = as_float_array(wavelength)
249 return 1.034 + 3.17 * 1.0e-4 * (1 / wl**2)
252def O2_depolarisation(wavelength: ArrayLike) -> NDArrayFloat:
253 """
254 Compute the depolarisation of oxygen :math:`O_2` as a function of
255 wavelength :math:`\\lambda` in micrometers (:math:`\\mu m`).
257 Parameters
258 ----------
259 wavelength
260 Wavelength :math:`\\lambda` in micrometers (:math:`\\mu m`).
262 Returns
263 -------
264 :class:`numpy.ndarray`
265 Oxygen :math:`O_2` depolarisation.
267 Examples
268 --------
269 >>> O2_depolarisation(0.555) # doctest: +ELLIPSIS
270 1.1020225...
271 """
273 wl = as_float_array(wavelength)
275 return 1.096 + 1.385 * 1.0e-3 * (1 / wl**2) + 1.448 * 1.0e-4 * (1 / wl**4)
278def F_air_Penndorf1957(wavelength: ArrayLike) -> NDArrayFloat:
279 """
280 Compute the depolarisation term :math:`F(air)` or *King Factor* using
281 the *Penndorf (1957)* method.
283 Parameters
284 ----------
285 wavelength
286 Wavelength :math:`\\lambda` in micrometers (:math:`\\mu m`).
288 Returns
289 -------
290 :class:`numpy.ndarray`
291 Air depolarisation term.
293 Notes
294 -----
295 - The *wavelength* parameter is provided for consistency with other
296 air depolarisation methods but is not used in this implementation,
297 which returns a constant value.
299 Examples
300 --------
301 >>> F_air_Penndorf1957(0.555)
302 1.0608
303 """
305 wl = as_float_array(wavelength)
307 return as_float(np.resize(np.array([1.0608]), wl.shape))
310def F_air_Young1981(wavelength: ArrayLike) -> NDArrayFloat:
311 """
312 Compute the depolarisation term :math:`F(air)` or *King Factor* using
313 the *Young (1981)* method.
315 Parameters
316 ----------
317 wavelength
318 Wavelength :math:`\\lambda` in micrometers (:math:`\\mu m`).
320 Returns
321 -------
322 :class:`numpy.ndarray`
323 Air depolarisation term.
325 Notes
326 -----
327 - The *wavelength* parameter is provided for consistency with other
328 air depolarisation methods but is not used in this implementation,
329 which returns a constant value.
331 Examples
332 --------
333 >>> F_air_Young1981(0.555)
334 1.048
335 """
337 wl = as_float_array(wavelength)
339 return as_float(np.resize(np.array([1.0480]), wl.shape))
342def F_air_Bates1984(wavelength: ArrayLike) -> NDArrayFloat:
343 """
344 Compute the depolarisation term :math:`F(air)` or *King Factor* using
345 the *Bates (1984)* method.
346 (:math:`\\mu m`) using *Bates (1984)* method.
348 Parameters
349 ----------
350 wavelength
351 Wavelength :math:`\\lambda` in micrometers (:math:`\\mu m`).
353 Returns
354 -------
355 :class:`numpy.ndarray`
356 Air depolarisation term.
358 Examples
359 --------
360 >>> F_air_Bates1984(0.555) # doctest: +ELLIPSIS
361 1.0481535...
362 """
364 O2 = O2_depolarisation(wavelength)
365 N2 = N2_depolarisation(wavelength)
366 Ar = 1.00
367 CO2 = 1.15
369 return (78.084 * N2 + 20.946 * O2 + CO2 + Ar) / (78.084 + 20.946 + Ar + CO2)
372def F_air_Bodhaine1999(
373 wavelength: ArrayLike,
374 CO2_concentration: ArrayLike = CONSTANT_STANDARD_CO2_CONCENTRATION,
375) -> NDArrayFloat:
376 """
377 Compute the depolarisation term :math:`F(air)` or *King Factor* as a
378 function of wavelength :math:`\\lambda` in micrometers (:math:`\\mu m`)
379 and :math:`CO_2` concentration in parts per million (ppm) using the
380 *Bodhaine, Wood, Dutton and Slusser (1999)* method.
382 Parameters
383 ----------
384 wavelength
385 Wavelength :math:`\\lambda` in micrometers (:math:`\\mu m`).
386 CO2_concentration
387 :math:`CO_2` concentration in parts per million (ppm).
389 Returns
390 -------
391 :class:`numpy.ndarray`
392 Air depolarisation term.
394 Examples
395 --------
396 >>> F_air_Bodhaine1999(0.555) # doctest: +ELLIPSIS
397 1.0487697...
398 """
400 O2 = O2_depolarisation(wavelength)
401 N2 = N2_depolarisation(wavelength)
402 CO2_c = as_float_array(CO2_concentration)
404 # Converting from parts per million (ppm) to parts per volume per percent.
405 CO2_c = CO2_c * 1e-4
407 return (78.084 * N2 + 20.946 * O2 + 0.934 * 1 + CO2_c * 1.15) / (
408 78.084 + 20.946 + 0.934 + CO2_c
409 )
412def molecular_density(
413 temperature: ArrayLike = CONSTANT_STANDARD_AIR_TEMPERATURE,
414 avogadro_constant: ArrayLike = CONSTANT_AVOGADRO,
415) -> NDArrayFloat:
416 """
417 Compute the molecular density :math:`N_s` (molecules :math:`cm^{-3}`)
418 as function of air temperature :math:`T[K]` in kelvin degrees.
420 Parameters
421 ----------
422 temperature
423 Air temperature :math:`T[K]` in kelvin degrees.
424 avogadro_constant
425 *Avogadro*'s number (molecules :math:`mol^{-1}`).
427 Returns
428 -------
429 :class:`numpy.ndarray`
430 Molecular density :math:`N_s` (molecules :math:`cm^{-3}`).
432 Notes
433 -----
434 - The *Avogadro*'s number used in this implementation is the one
435 specified by the Committee on Data for Science and Technology
436 (CODATA): :math:`6.02214179 \\times 10^{23}`, which differs from
437 the reference :cite:`Bodhaine1999a` value
438 :math:`6.0221367 \\times 10^{23}`.
440 Examples
441 --------
442 >>> molecular_density(288.15) # doctest: +ELLIPSIS
443 2.5469021...e+19
444 >>> molecular_density(288.15, 6.0221367e23) # doctest: +ELLIPSIS
445 2.5468999...e+19
446 """
448 T = as_float_array(temperature)
449 avogadro_constant = as_float_array(avogadro_constant)
451 with sdiv_mode():
452 return (avogadro_constant / 22.4141) * sdiv(273.15, T) * (1 / 1000)
455def mean_molecular_weights(
456 CO2_concentration: ArrayLike = CONSTANT_STANDARD_CO2_CONCENTRATION,
457) -> NDArrayFloat:
458 """
459 Compute the mean molecular weights :math:`m_a` for dry air as a function
460 of :math:`CO_2` concentration in parts per million (ppm).
462 Parameters
463 ----------
464 CO2_concentration
465 :math:`CO_2` concentration in parts per million (ppm).
467 Returns
468 -------
469 :class:`numpy.ndarray`
470 Mean molecular weights :math:`m_a` for dry air.
472 Examples
473 --------
474 >>> mean_molecular_weights() # doctest: +ELLIPSIS
475 28.9640166...
476 """
478 CO2_concentration = as_float_array(CO2_concentration)
480 CO2_c = CO2_concentration * 1.0e-6
482 return 15.0556 * CO2_c + 28.9595
485def gravity_List1968(
486 latitude: ArrayLike = CONSTANT_DEFAULT_LATITUDE,
487 altitude: ArrayLike = CONSTANT_DEFAULT_ALTITUDE,
488) -> NDArrayFloat:
489 """
490 Compute the gravity :math:`g` in :math:`cm/s^2` (gal) representative of
491 the mass-weighted column of air molecules above the site at the specified
492 latitude and altitude using the *List (1968)* method.
494 Parameters
495 ----------
496 latitude
497 Latitude of the site in degrees.
498 altitude
499 Altitude of the site in meters.
501 Returns
502 -------
503 :class:`numpy.ndarray`
504 Gravity :math:`g` in :math:`cm/s^2` (gal).
506 Examples
507 --------
508 >>> gravity_List1968() # doctest: +ELLIPSIS
509 978.0356070...
510 >>> gravity_List1968(0.0, 1500.0) # doctest: +ELLIPSIS
511 977.5726106...
513 Gravity :math:`g` for Paris:
515 >>> gravity_List1968(48.8567, 35.0) # doctest: +ELLIPSIS
516 980.9524178...
517 """
519 latitude = as_float_array(latitude)
520 altitude = as_float_array(altitude)
522 cos2phi = np.cos(2 * np.radians(latitude))
524 # Sea level acceleration of gravity.
525 g0 = 980.6160 * (1 - 0.0026373 * cos2phi + 0.0000059 * cos2phi**2)
527 return (
528 g0
529 - (3.085462e-4 + 2.27e-7 * cos2phi) * altitude
530 + (7.254e-11 + 1.0e-13 * cos2phi) * altitude**2
531 - (1.517e-17 + 6e-20 * cos2phi) * altitude**3
532 )
535def scattering_cross_section(
536 wavelength: ArrayLike,
537 CO2_concentration: ArrayLike = CONSTANT_STANDARD_CO2_CONCENTRATION,
538 temperature: ArrayLike = CONSTANT_STANDARD_AIR_TEMPERATURE,
539 avogadro_constant: ArrayLike = CONSTANT_AVOGADRO,
540 n_s_function: Callable = air_refraction_index_Bodhaine1999,
541 F_air_function: Callable = F_air_Bodhaine1999,
542) -> NDArrayFloat:
543 """
544 Compute the scattering cross-section per molecule :math:`\\sigma` of dry
545 air as a function of wavelength :math:`\\lambda` in centimeters (cm)
546 using the specified :math:`CO_2` concentration in parts per million
547 (ppm) and temperature :math:`T[K]` in kelvin degrees following the
548 *Van de Hulst (1957)* method.
550 Parameters
551 ----------
552 wavelength
553 Wavelength :math:`\\lambda` in centimeters (cm).
554 CO2_concentration
555 :math:`CO_2` concentration in parts per million (ppm).
556 temperature
557 Air temperature :math:`T[K]` in kelvin degrees.
558 avogadro_constant
559 *Avogadro*'s number (molecules :math:`mol^{-1}`).
560 n_s_function
561 Air refraction index :math:`n_s` computation method.
562 F_air_function
563 :math:`(6+3_p)/(6-7_p)`, the depolarisation term :math:`F(air)` or
564 *King Factor* computation method.
566 Returns
567 -------
568 :class:`numpy.ndarray`
569 Scattering cross-section per molecule :math:`\\sigma` of dry air.
571 Warnings
572 --------
573 Unlike most objects of :mod:`colour.phenomena.rayleigh` module,
574 :func:`colour.scattering_cross_section` expects wavelength
575 :math:`\\lambda` to be expressed in centimeters (cm).
577 References
578 ----------
579 :cite:`Bodhaine1999a`, :cite:`Wikipedia2001c`
581 Examples
582 --------
583 >>> scattering_cross_section(555 * 10e-8) # doctest: +ELLIPSIS
584 4.3466692...e-27
585 """
587 wl = as_float_array(wavelength)
588 CO2_c = as_float_array(CO2_concentration)
589 temperature = as_float_array(temperature)
591 wl_micrometers = wl * 10e3
593 N_s = molecular_density(temperature, avogadro_constant)
594 n_s = n_s_function(wl_micrometers)
595 # n_s = n_s_function(**filter_kwargs(
596 # n_s_function, wavelength=wl_micrometers, CO2_concentration=CO2_c))
597 F_air = F_air_function(
598 **filter_kwargs(
599 F_air_function, wavelength=wl_micrometers, CO2_concentration=CO2_c
600 )
601 )
603 sigma = 24 * np.pi**3 * (n_s**2 - 1) ** 2 / (wl**4 * N_s**2 * (n_s**2 + 2) ** 2)
604 sigma *= F_air
606 return sigma
609def rayleigh_optical_depth(
610 wavelength: ArrayLike,
611 CO2_concentration: ArrayLike = CONSTANT_STANDARD_CO2_CONCENTRATION,
612 temperature: ArrayLike = CONSTANT_STANDARD_AIR_TEMPERATURE,
613 pressure: ArrayLike = CONSTANT_AVERAGE_PRESSURE_MEAN_SEA_LEVEL,
614 latitude: ArrayLike = CONSTANT_DEFAULT_LATITUDE,
615 altitude: ArrayLike = CONSTANT_DEFAULT_ALTITUDE,
616 avogadro_constant: ArrayLike = CONSTANT_AVOGADRO,
617 n_s_function: Callable = air_refraction_index_Bodhaine1999,
618 F_air_function: Callable = F_air_Bodhaine1999,
619) -> NDArrayFloat:
620 """
621 Compute the *Rayleigh* optical depth :math:`T_r(\\lambda)` as a function
622 of wavelength :math:`\\lambda` in centimeters (cm).
624 Parameters
625 ----------
626 wavelength
627 Wavelength :math:`\\lambda` in centimeters (cm).
628 CO2_concentration
629 :math:`CO_2` concentration in parts per million (ppm).
630 temperature
631 Air temperature :math:`T[K]` in kelvin degrees.
632 pressure
633 Surface pressure :math:`P` of the measurement site.
634 latitude
635 Latitude of the site in degrees.
636 altitude
637 Altitude of the site in meters.
638 avogadro_constant
639 *Avogadro*'s number (molecules :math:`mol^{-1}`).
640 n_s_function
641 Air refraction index :math:`n_s` computation method.
642 F_air_function
643 :math:`(6+3_p)/(6-7_p)`, the depolarisation term :math:`F(air)`
644 or *King Factor* computation method.
646 Returns
647 -------
648 :class:`numpy.ndarray`
649 *Rayleigh* optical depth :math:`T_r(\\lambda)`.
651 Warnings
652 --------
653 Unlike most objects of :mod:`colour.phenomena.rayleigh` module,
654 :func:`colour.phenomena.rayleigh_optical_depth` expects wavelength
655 :math:`\\lambda` to be expressed in centimeters (cm).
657 References
658 ----------
659 :cite:`Bodhaine1999a`, :cite:`Wikipedia2001c`
661 Examples
662 --------
663 >>> rayleigh_optical_depth(555 * 10e-8) # doctest: +ELLIPSIS
664 0.0936290...
665 """
667 wavelength = as_float_array(wavelength)
668 CO2_c = as_float_array(CO2_concentration)
669 pressure = as_float_array(pressure)
670 latitude = as_float_array(latitude)
671 altitude = as_float_array(altitude)
672 avogadro_constant = as_float_array(avogadro_constant)
673 # Conversion from pascal to dyne/cm2.
674 P = as_float_array(pressure * 10)
676 sigma = scattering_cross_section(
677 wavelength,
678 CO2_c,
679 temperature,
680 avogadro_constant,
681 n_s_function,
682 F_air_function,
683 )
685 m_a = mean_molecular_weights(CO2_c)
686 g = gravity_List1968(latitude, altitude)
688 T_R = sigma * (P * avogadro_constant) / (m_a * g)
690 return as_float(T_R)
693rayleigh_scattering = rayleigh_optical_depth
696def sd_rayleigh_scattering(
697 shape: SpectralShape = SPECTRAL_SHAPE_DEFAULT,
698 CO2_concentration: ArrayLike = CONSTANT_STANDARD_CO2_CONCENTRATION,
699 temperature: ArrayLike = CONSTANT_STANDARD_AIR_TEMPERATURE,
700 pressure: ArrayLike = CONSTANT_AVERAGE_PRESSURE_MEAN_SEA_LEVEL,
701 latitude: ArrayLike = CONSTANT_DEFAULT_LATITUDE,
702 altitude: ArrayLike = CONSTANT_DEFAULT_ALTITUDE,
703 avogadro_constant: ArrayLike = CONSTANT_AVOGADRO,
704 n_s_function: Callable = air_refraction_index_Bodhaine1999,
705 F_air_function: Callable = F_air_Bodhaine1999,
706) -> SpectralDistribution:
707 """
708 Generate *Rayleigh* scattering spectral distribution for the specified
709 spectral shape.
711 Parameters
712 ----------
713 shape
714 Spectral shape used to create the *Rayleigh* scattering spectral
715 distribution.
716 CO2_concentration
717 :math:`CO_2` concentration in parts per million (ppm).
718 temperature
719 Air temperature :math:`T[K]` in kelvin degrees.
720 pressure
721 Surface pressure :math:`P` of the measurement site.
722 latitude
723 Latitude of the site in degrees.
724 altitude
725 Altitude of the site in meters.
726 avogadro_constant
727 *Avogadro*'s number (molecules :math:`mol^{-1}`).
728 n_s_function
729 Air refraction index :math:`n_s` computation method.
730 F_air_function
731 :math:`(6+3_p)/(6-7_p)`, the depolarisation term :math:`F(air)` or
732 *King Factor* computation method.
734 Returns
735 -------
736 :class:`colour.SpectralDistribution`
737 *Rayleigh* optical depth spectral distribution.
739 References
740 ----------
741 :cite:`Bodhaine1999a`, :cite:`Wikipedia2001c`
743 Examples
744 --------
745 >>> from colour.utilities import numpy_print_options
746 >>> with numpy_print_options(suppress=True):
747 ... sd_rayleigh_scattering() # doctest: +ELLIPSIS
748 SpectralDistribution([[ 360. , 0.5602465...],
749 [ 361. , 0.5537481...],
750 [ 362. , 0.5473446...],
751 [ 363. , 0.5410345...],
752 [ 364. , 0.5348161...],
753 [ 365. , 0.5286877...],
754 [ 366. , 0.5226477...],
755 [ 367. , 0.5166948...],
756 [ 368. , 0.5108272...],
757 [ 369. , 0.5050436...],
758 [ 370. , 0.4993425...],
759 [ 371. , 0.4937224...],
760 [ 372. , 0.4881820...],
761 [ 373. , 0.4827199...],
762 [ 374. , 0.4773348...],
763 [ 375. , 0.4720253...],
764 [ 376. , 0.4667902...],
765 [ 377. , 0.4616282...],
766 [ 378. , 0.4565380...],
767 [ 379. , 0.4515186...],
768 [ 380. , 0.4465686...],
769 [ 381. , 0.4416869...],
770 [ 382. , 0.4368724...],
771 [ 383. , 0.4321240...],
772 [ 384. , 0.4274405...],
773 [ 385. , 0.4228209...],
774 [ 386. , 0.4182641...],
775 [ 387. , 0.4137692...],
776 [ 388. , 0.4093350...],
777 [ 389. , 0.4049607...],
778 [ 390. , 0.4006451...],
779 [ 391. , 0.3963874...],
780 [ 392. , 0.3921867...],
781 [ 393. , 0.3880419...],
782 [ 394. , 0.3839523...],
783 [ 395. , 0.3799169...],
784 [ 396. , 0.3759348...],
785 [ 397. , 0.3720053...],
786 [ 398. , 0.3681274...],
787 [ 399. , 0.3643003...],
788 [ 400. , 0.3605233...],
789 [ 401. , 0.3567956...],
790 [ 402. , 0.3531163...],
791 [ 403. , 0.3494847...],
792 [ 404. , 0.3459001...],
793 [ 405. , 0.3423617...],
794 [ 406. , 0.3388689...],
795 [ 407. , 0.3354208...],
796 [ 408. , 0.3320169...],
797 [ 409. , 0.3286563...],
798 [ 410. , 0.3253386...],
799 [ 411. , 0.3220629...],
800 [ 412. , 0.3188287...],
801 [ 413. , 0.3156354...],
802 [ 414. , 0.3124822...],
803 [ 415. , 0.3093687...],
804 [ 416. , 0.3062941...],
805 [ 417. , 0.3032579...],
806 [ 418. , 0.3002596...],
807 [ 419. , 0.2972985...],
808 [ 420. , 0.2943741...],
809 [ 421. , 0.2914858...],
810 [ 422. , 0.2886332...],
811 [ 423. , 0.2858157...],
812 [ 424. , 0.2830327...],
813 [ 425. , 0.2802837...],
814 [ 426. , 0.2775683...],
815 [ 427. , 0.2748860...],
816 [ 428. , 0.2722362...],
817 [ 429. , 0.2696185...],
818 [ 430. , 0.2670324...],
819 [ 431. , 0.2644775...],
820 [ 432. , 0.2619533...],
821 [ 433. , 0.2594594...],
822 [ 434. , 0.2569952...],
823 [ 435. , 0.2545605...],
824 [ 436. , 0.2521548...],
825 [ 437. , 0.2497776...],
826 [ 438. , 0.2474285...],
827 [ 439. , 0.2451072...],
828 [ 440. , 0.2428133...],
829 [ 441. , 0.2405463...],
830 [ 442. , 0.2383059...],
831 [ 443. , 0.2360916...],
832 [ 444. , 0.2339033...],
833 [ 445. , 0.2317404...],
834 [ 446. , 0.2296026...],
835 [ 447. , 0.2274895...],
836 [ 448. , 0.2254009...],
837 [ 449. , 0.2233364...],
838 [ 450. , 0.2212956...],
839 [ 451. , 0.2192782...],
840 [ 452. , 0.2172839...],
841 [ 453. , 0.2153124...],
842 [ 454. , 0.2133633...],
843 [ 455. , 0.2114364...],
844 [ 456. , 0.2095313...],
845 [ 457. , 0.2076478...],
846 [ 458. , 0.2057855...],
847 [ 459. , 0.2039442...],
848 [ 460. , 0.2021235...],
849 [ 461. , 0.2003233...],
850 [ 462. , 0.1985432...],
851 [ 463. , 0.1967829...],
852 [ 464. , 0.1950423...],
853 [ 465. , 0.1933209...],
854 [ 466. , 0.1916186...],
855 [ 467. , 0.1899351...],
856 [ 468. , 0.1882702...],
857 [ 469. , 0.1866236...],
858 [ 470. , 0.1849951...],
859 [ 471. , 0.1833844...],
860 [ 472. , 0.1817913...],
861 [ 473. , 0.1802156...],
862 [ 474. , 0.1786570...],
863 [ 475. , 0.1771153...],
864 [ 476. , 0.1755903...],
865 [ 477. , 0.1740818...],
866 [ 478. , 0.1725895...],
867 [ 479. , 0.1711133...],
868 [ 480. , 0.1696529...],
869 [ 481. , 0.1682082...],
870 [ 482. , 0.1667789...],
871 [ 483. , 0.1653648...],
872 [ 484. , 0.1639658...],
873 [ 485. , 0.1625816...],
874 [ 486. , 0.1612121...],
875 [ 487. , 0.1598570...],
876 [ 488. , 0.1585163...],
877 [ 489. , 0.1571896...],
878 [ 490. , 0.1558769...],
879 [ 491. , 0.1545779...],
880 [ 492. , 0.1532925...],
881 [ 493. , 0.1520205...],
882 [ 494. , 0.1507617...],
883 [ 495. , 0.1495160...],
884 [ 496. , 0.1482832...],
885 [ 497. , 0.1470632...],
886 [ 498. , 0.1458558...],
887 [ 499. , 0.1446607...],
888 [ 500. , 0.1434780...],
889 [ 501. , 0.1423074...],
890 [ 502. , 0.1411488...],
891 [ 503. , 0.140002 ...],
892 [ 504. , 0.1388668...],
893 [ 505. , 0.1377433...],
894 [ 506. , 0.1366311...],
895 [ 507. , 0.1355301...],
896 [ 508. , 0.1344403...],
897 [ 509. , 0.1333615...],
898 [ 510. , 0.1322936...],
899 [ 511. , 0.1312363...],
900 [ 512. , 0.1301897...],
901 [ 513. , 0.1291535...],
902 [ 514. , 0.1281277...],
903 [ 515. , 0.1271121...],
904 [ 516. , 0.1261065...],
905 [ 517. , 0.1251110...],
906 [ 518. , 0.1241253...],
907 [ 519. , 0.1231493...],
908 [ 520. , 0.1221829...],
909 [ 521. , 0.1212261...],
910 [ 522. , 0.1202786...],
911 [ 523. , 0.1193405...],
912 [ 524. , 0.1184115...],
913 [ 525. , 0.1174915...],
914 [ 526. , 0.1165806...],
915 [ 527. , 0.1156784...],
916 [ 528. , 0.1147851...],
917 [ 529. , 0.1139004...],
918 [ 530. , 0.1130242...],
919 [ 531. , 0.1121564...],
920 [ 532. , 0.1112971...],
921 [ 533. , 0.1104459...],
922 [ 534. , 0.1096030...],
923 [ 535. , 0.1087681...],
924 [ 536. , 0.1079411...],
925 [ 537. , 0.1071221...],
926 [ 538. , 0.1063108...],
927 [ 539. , 0.1055072...],
928 [ 540. , 0.1047113...],
929 [ 541. , 0.1039229...],
930 [ 542. , 0.1031419...],
931 [ 543. , 0.1023682...],
932 [ 544. , 0.1016019...],
933 [ 545. , 0.1008427...],
934 [ 546. , 0.1000906...],
935 [ 547. , 0.0993456...],
936 [ 548. , 0.0986075...],
937 [ 549. , 0.0978763...],
938 [ 550. , 0.0971519...],
939 [ 551. , 0.0964342...],
940 [ 552. , 0.0957231...],
941 [ 553. , 0.0950186...],
942 [ 554. , 0.0943206...],
943 [ 555. , 0.0936290...],
944 [ 556. , 0.0929438...],
945 [ 557. , 0.0922649...],
946 [ 558. , 0.0915922...],
947 [ 559. , 0.0909256...],
948 [ 560. , 0.0902651...],
949 [ 561. , 0.0896106...],
950 [ 562. , 0.0889620...],
951 [ 563. , 0.0883194...],
952 [ 564. , 0.0876825...],
953 [ 565. , 0.0870514...],
954 [ 566. , 0.0864260...],
955 [ 567. , 0.0858063...],
956 [ 568. , 0.0851921...],
957 [ 569. , 0.0845834...],
958 [ 570. , 0.0839801...],
959 [ 571. , 0.0833822...],
960 [ 572. , 0.0827897...],
961 [ 573. , 0.0822025...],
962 [ 574. , 0.0816204...],
963 [ 575. , 0.0810436...],
964 [ 576. , 0.0804718...],
965 [ 577. , 0.0799051...],
966 [ 578. , 0.0793434...],
967 [ 579. , 0.0787866...],
968 [ 580. , 0.0782347...],
969 [ 581. , 0.0776877...],
970 [ 582. , 0.0771454...],
971 [ 583. , 0.0766079...],
972 [ 584. , 0.0760751...],
973 [ 585. , 0.0755469...],
974 [ 586. , 0.0750234...],
975 [ 587. , 0.0745043...],
976 [ 588. , 0.0739898...],
977 [ 589. , 0.0734797...],
978 [ 590. , 0.0729740...],
979 [ 591. , 0.0724727...],
980 [ 592. , 0.0719757...],
981 [ 593. , 0.0714830...],
982 [ 594. , 0.0709944...],
983 [ 595. , 0.0705101...],
984 [ 596. , 0.0700299...],
985 [ 597. , 0.0695538...],
986 [ 598. , 0.0690818...],
987 [ 599. , 0.0686137...],
988 [ 600. , 0.0681497...],
989 [ 601. , 0.0676895...],
990 [ 602. , 0.0672333...],
991 [ 603. , 0.0667809...],
992 [ 604. , 0.0663323...],
993 [ 605. , 0.0658875...],
994 [ 606. , 0.0654464...],
995 [ 607. , 0.0650091...],
996 [ 608. , 0.0645753...],
997 [ 609. , 0.0641453...],
998 [ 610. , 0.0637187...],
999 [ 611. , 0.0632958...],
1000 [ 612. , 0.0628764...],
1001 [ 613. , 0.0624604...],
1002 [ 614. , 0.0620479...],
1003 [ 615. , 0.0616388...],
1004 [ 616. , 0.0612331...],
1005 [ 617. , 0.0608307...],
1006 [ 618. , 0.0604316...],
1007 [ 619. , 0.0600358...],
1008 [ 620. , 0.0596433...],
1009 [ 621. , 0.0592539...],
1010 [ 622. , 0.0588678...],
1011 [ 623. , 0.0584848...],
1012 [ 624. , 0.0581049...],
1013 [ 625. , 0.0577281...],
1014 [ 626. , 0.0573544...],
1015 [ 627. , 0.0569837...],
1016 [ 628. , 0.0566160...],
1017 [ 629. , 0.0562513...],
1018 [ 630. , 0.0558895...],
1019 [ 631. , 0.0555306...],
1020 [ 632. , 0.0551746...],
1021 [ 633. , 0.0548215...],
1022 [ 634. , 0.0544712...],
1023 [ 635. , 0.0541237...],
1024 [ 636. , 0.0537789...],
1025 [ 637. , 0.0534369...],
1026 [ 638. , 0.0530977...],
1027 [ 639. , 0.0527611...],
1028 [ 640. , 0.0524272...],
1029 [ 641. , 0.0520960...],
1030 [ 642. , 0.0517674...],
1031 [ 643. , 0.0514413...],
1032 [ 644. , 0.0511179...],
1033 [ 645. , 0.0507970...],
1034 [ 646. , 0.0504786...],
1035 [ 647. , 0.0501627...],
1036 [ 648. , 0.0498493...],
1037 [ 649. , 0.0495383...],
1038 [ 650. , 0.0492298...],
1039 [ 651. , 0.0489236...],
1040 [ 652. , 0.0486199...],
1041 [ 653. , 0.0483185...],
1042 [ 654. , 0.0480194...],
1043 [ 655. , 0.0477227...],
1044 [ 656. , 0.0474283...],
1045 [ 657. , 0.0471361...],
1046 [ 658. , 0.0468462...],
1047 [ 659. , 0.0465585...],
1048 [ 660. , 0.0462730...],
1049 [ 661. , 0.0459898...],
1050 [ 662. , 0.0457087...],
1051 [ 663. , 0.0454297...],
1052 [ 664. , 0.0451529...],
1053 [ 665. , 0.0448782...],
1054 [ 666. , 0.0446055...],
1055 [ 667. , 0.0443350...],
1056 [ 668. , 0.0440665...],
1057 [ 669. , 0.0438000...],
1058 [ 670. , 0.0435356...],
1059 [ 671. , 0.0432731...],
1060 [ 672. , 0.0430127...],
1061 [ 673. , 0.0427542...],
1062 [ 674. , 0.0424976...],
1063 [ 675. , 0.0422430...],
1064 [ 676. , 0.0419902...],
1065 [ 677. , 0.0417394...],
1066 [ 678. , 0.0414905...],
1067 [ 679. , 0.0412434...],
1068 [ 680. , 0.0409981...],
1069 [ 681. , 0.0407547...],
1070 [ 682. , 0.0405131...],
1071 [ 683. , 0.0402732...],
1072 [ 684. , 0.0400352...],
1073 [ 685. , 0.0397989...],
1074 [ 686. , 0.0395643...],
1075 [ 687. , 0.0393315...],
1076 [ 688. , 0.0391004...],
1077 [ 689. , 0.0388710...],
1078 [ 690. , 0.0386433...],
1079 [ 691. , 0.0384173...],
1080 [ 692. , 0.0381929...],
1081 [ 693. , 0.0379701...],
1082 [ 694. , 0.0377490...],
1083 [ 695. , 0.0375295...],
1084 [ 696. , 0.0373115...],
1085 [ 697. , 0.0370952...],
1086 [ 698. , 0.0368804...],
1087 [ 699. , 0.0366672...],
1088 [ 700. , 0.0364556...],
1089 [ 701. , 0.0362454...],
1090 [ 702. , 0.0360368...],
1091 [ 703. , 0.0358297...],
1092 [ 704. , 0.0356241...],
1093 [ 705. , 0.0354199...],
1094 [ 706. , 0.0352172...],
1095 [ 707. , 0.0350160...],
1096 [ 708. , 0.0348162...],
1097 [ 709. , 0.0346178...],
1098 [ 710. , 0.0344208...],
1099 [ 711. , 0.0342253...],
1100 [ 712. , 0.0340311...],
1101 [ 713. , 0.0338383...],
1102 [ 714. , 0.0336469...],
1103 [ 715. , 0.0334569...],
1104 [ 716. , 0.0332681...],
1105 [ 717. , 0.0330807...],
1106 [ 718. , 0.0328947...],
1107 [ 719. , 0.0327099...],
1108 [ 720. , 0.0325264...],
1109 [ 721. , 0.0323443...],
1110 [ 722. , 0.0321634...],
1111 [ 723. , 0.0319837...],
1112 [ 724. , 0.0318054...],
1113 [ 725. , 0.0316282...],
1114 [ 726. , 0.0314523...],
1115 [ 727. , 0.0312777...],
1116 [ 728. , 0.0311042...],
1117 [ 729. , 0.0309319...],
1118 [ 730. , 0.0307609...],
1119 [ 731. , 0.0305910...],
1120 [ 732. , 0.0304223...],
1121 [ 733. , 0.0302548...],
1122 [ 734. , 0.0300884...],
1123 [ 735. , 0.0299231...],
1124 [ 736. , 0.0297590...],
1125 [ 737. , 0.0295960...],
1126 [ 738. , 0.0294342...],
1127 [ 739. , 0.0292734...],
1128 [ 740. , 0.0291138...],
1129 [ 741. , 0.0289552...],
1130 [ 742. , 0.0287977...],
1131 [ 743. , 0.0286413...],
1132 [ 744. , 0.0284859...],
1133 [ 745. , 0.0283316...],
1134 [ 746. , 0.0281784...],
1135 [ 747. , 0.0280262...],
1136 [ 748. , 0.0278750...],
1137 [ 749. , 0.0277248...],
1138 [ 750. , 0.0275757...],
1139 [ 751. , 0.0274275...],
1140 [ 752. , 0.0272804...],
1141 [ 753. , 0.0271342...],
1142 [ 754. , 0.0269890...],
1143 [ 755. , 0.0268448...],
1144 [ 756. , 0.0267015...],
1145 [ 757. , 0.0265592...],
1146 [ 758. , 0.0264179...],
1147 [ 759. , 0.0262775...],
1148 [ 760. , 0.0261380...],
1149 [ 761. , 0.0259995...],
1150 [ 762. , 0.0258618...],
1151 [ 763. , 0.0257251...],
1152 [ 764. , 0.0255893...],
1153 [ 765. , 0.0254544...],
1154 [ 766. , 0.0253204...],
1155 [ 767. , 0.0251872...],
1156 [ 768. , 0.0250550...],
1157 [ 769. , 0.0249236...],
1158 [ 770. , 0.0247930...],
1159 [ 771. , 0.0246633...],
1160 [ 772. , 0.0245345...],
1161 [ 773. , 0.0244065...],
1162 [ 774. , 0.0242794...],
1163 [ 775. , 0.0241530...],
1164 [ 776. , 0.0240275...],
1165 [ 777. , 0.0239029...],
1166 [ 778. , 0.0237790...],
1167 [ 779. , 0.0236559...],
1168 [ 780. , 0.0235336...]],
1169 SpragueInterpolator,
1170 {},
1171 Extrapolator,
1172 {'method': 'Constant', 'left': None, 'right': None})
1173 """
1175 return SpectralDistribution(
1176 rayleigh_optical_depth(
1177 shape.wavelengths * 10e-8,
1178 CO2_concentration,
1179 temperature,
1180 pressure,
1181 latitude,
1182 altitude,
1183 avogadro_constant,
1184 n_s_function,
1185 F_air_function,
1186 ),
1187 shape.wavelengths,
1188 name=(
1189 "Rayleigh Scattering - "
1190 f"{CO2_concentration!r} ppm, "
1191 f"{temperature!r} K, "
1192 f"{pressure!r} Pa, "
1193 f"{latitude!r} Degrees, "
1194 f"{altitude!r} m"
1195 ),
1196 )