Repository: colour-science/colour

Issue:
Investigate discrepancies in "Scattering Cross Section" computations compared to ground truth.
I noticed some discrepancies between the output of "colour.scattering_cross_section" definition and Bodhaine, Wood, Dutton and Slusser (1999) ground truth data that need to be investigated.

Discussion:
coveralls: 
[![Coverage Status](https://coveralls.io/builds/60578686/badge)](https://coveralls.io/builds/60578686)

coverage: 99.781%. remained the same when pulling **5f8e6dbedfd87b044fb0f53908fe5010e0a9391b on feature/rayleigh** into **284f5864c1763525238b1cb1566cf42983d1590a on develop**.


Patch:
diff --git a/colour/phenomena/rayleigh.py b/colour/phenomena/rayleigh.py
index 181b6d37d..020b37451 100644
--- a/colour/phenomena/rayleigh.py
+++ b/colour/phenomena/rayleigh.py
@@ -61,6 +61,7 @@ __all__ = [
     "scattering_cross_section",
     "rayleigh_optical_depth",
     "rayleigh_scattering",
+    "sd_rayleigh_scattering",
 ]
 
 CONSTANT_STANDARD_AIR_TEMPERATURE: float = 288.15
@@ -212,7 +213,10 @@ def air_refraction_index_Bodhaine1999(
     wl = as_float_array(wavelength)
     CO2_c = as_float_array(CO2_concentration)
 
-    n = (1 + 0.54 * ((CO2_c * 1e-6) - 300e-6)) * (
+    # 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
 
@@ -400,13 +404,16 @@ def F_air_Bodhaine1999(
     Examples
     --------
     >>> F_air_Bodhaine1999(0.555)  # doctest: +ELLIPSIS
-    1.1246916...
+    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
+
     F_air = (78.084 * N2 + 20.946 * O2 + 0.934 * 1 + CO2_c * 1.15) / (
         78.084 + 20.946 + 0.934 + CO2_c
     )
@@ -589,7 +596,7 @@ def scattering_cross_section(
     Examples
     --------
     >>> scattering_cross_section(555 * 10e-8)  # doctest: +ELLIPSIS
-    4.6613309...e-27
+    4.3466692...e-27
     """
 
     wl = as_float_array(wavelength)
@@ -674,7 +681,7 @@ def rayleigh_optical_depth(
     Examples
     --------
     >>> rayleigh_optical_depth(555 * 10e-8)  # doctest: +ELLIPSIS
-    0.1004070...
+    0.0936290...
     """
 
     wavelength = as_float_array(wavelength)
@@ -758,427 +765,427 @@ def sd_rayleigh_scattering(
     >>> 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...],
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-                          [ 415.        ,    0.3312609...],
-                          [ 416.        ,    0.3279747...],
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-                          [ 426.        ,    0.2972668...],
-                          [ 427.        ,    0.2943989...],
-                          [ 428.        ,    0.2915657...],
-                          [ 429.        ,    0.2887668...],
-                          [ 430.        ,    0.2860017...],
-                          [ 431.        ,    0.2832697...],
-                          [ 432.        ,    0.2805706...],
-                          [ 433.        ,    0.2779037...],
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-                          [ 440.        ,    0.2601016...],
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-                          [ 455.        ,    0.2265373...],
-                          [ 456.        ,    0.2244990...],
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-                          [ 459.        ,    0.2185211...],
-                          [ 460.        ,    0.2165730...],
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-                          [ 469.        ,    0.1999865...],
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-                          [ 585.        ,    0.0810298...],
-                          [ 586.        ,    0.0804687...],
-                          [ 587.        ,    0.0799124...],
-                          [ 588.        ,    0.0793609...],
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-                          [ 590.        ,    0.0782722...],
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-                          [ 599.        ,    0.0735986...],
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+                          [ 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,


Test patch:
diff --git a/colour/phenomena/tests/test_rayleigh.py b/colour/phenomena/tests/test_rayleigh.py
index fc2a4aed1..c759e7e8e 100644
--- a/colour/phenomena/tests/test_rayleigh.py
+++ b/colour/phenomena/tests/test_rayleigh.py
@@ -56,427 +56,427 @@ __all__ = [
 ]
 
 DATA_SD_RAYLEIGH_SCATTERING: tuple = (
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+    0.03774902,
+    0.03752951,
+    0.03731159,
+    0.03709525,
+    0.03688049,
+    0.03666728,
+    0.03645561,
+    0.03624547,
+    0.03603685,
+    0.03582973,
+    0.03562410,
+    0.03541995,
+    0.03521726,
+    0.03501602,
+    0.03481622,
+    0.03461785,
+    0.03442089,
+    0.03422534,
+    0.03403117,
+    0.03383838,
+    0.03364696,
+    0.03345690,
+    0.03326817,
+    0.03308078,
+    0.03289471,
+    0.03270995,
+    0.03252649,
+    0.03234432,
+    0.03216342,
+    0.03198379,
+    0.03180541,
+    0.03162828,
+    0.03145238,
+    0.03127771,
+    0.03110425,
+    0.03093199,
+    0.03076093,
+    0.03059105,
+    0.03042234,
+    0.03025480,
+    0.03008842,
+    0.02992318,
+    0.02975907,
+    0.02959609,
+    0.02943422,
+    0.02927347,
+    0.02911381,
+    0.02895524,
+    0.02879776,
+    0.02864134,
+    0.02848599,
+    0.02833169,
+    0.02817843,
+    0.02802622,
+    0.02787503,
+    0.02772486,
+    0.02757571,
+    0.02742756,
+    0.02728040,
+    0.02713423,
+    0.02698905,
+    0.02684483,
+    0.02670158,
+    0.02655928,
+    0.02641794,
+    0.02627753,
+    0.02613806,
+    0.02599951,
+    0.02586188,
+    0.02572517,
+    0.02558936,
+    0.02545444,
+    0.02532041,
+    0.02518727,
+    0.02505501,
+    0.02492361,
+    0.02479307,
+    0.02466339,
+    0.02453456,
+    0.02440657,
+    0.02427941,
+    0.02415309,
+    0.02402758,
+    0.02390290,
+    0.02377902,
+    0.02365594,
+    0.02353366,
 )
 
 
@@ -1035,15 +1035,15 @@ class TestF_airBodhaine1999(unittest.TestCase):
         """
 
         self.assertAlmostEqual(
-            F_air_Bodhaine1999(0.360), 1.125664021159081, places=7
+            F_air_Bodhaine1999(0.360), 1.052659005129014, places=7
         )
 
         self.assertAlmostEqual(
-            F_air_Bodhaine1999(0.555), 1.124691670240156, places=7
+            F_air_Bodhaine1999(0.555), 1.048769718142427, places=7
         )
 
         self.assertAlmostEqual(
-            F_air_Bodhaine1999(0.830), 1.124386455783539, places=7
+            F_air_Bodhaine1999(0.830), 1.047548896943893, places=7
         )
 
         self.assertAlmostEqual(
@@ -1051,11 +1051,11 @@ class TestF_airBodhaine1999(unittest.TestCase):
         )
 
         self.assertAlmostEqual(
-            F_air_Bodhaine1999(0.555, 360), 1.127993015096689, places=7
+            F_air_Bodhaine1999(0.555, 360), 1.048775791959338, places=7
         )
 
         self.assertAlmostEqual(
-            F_air_Bodhaine1999(0.830, 620), 1.13577082, places=7
+            F_air_Bodhaine1999(0.830, 620), 1.047581672775155, places=7
         )
 
     def test_n_dimensional_F_air_Bodhaine1999(self):
@@ -1279,19 +1279,19 @@ class TestScatteringCrossSection(unittest.TestCase):
 
         self.assertAlmostEqual(
             scattering_cross_section(360 * 10e-8),
-            2.781289234802031e-26,
+            2.600908533851937e-26,
             places=32,
         )
 
         self.assertAlmostEqual(
             scattering_cross_section(555 * 10e-8),
-            4.661330902337604e-27,
+            4.346669248087624e-27,
             places=32,
         )
 
         self.assertAlmostEqual(
             scattering_cross_section(830 * 10e-8),
-            9.125100352218880e-28,
+            8.501515434751428e-28,
             places=32,
         )
 
@@ -1303,31 +1303,31 @@ class TestScatteringCrossSection(unittest.TestCase):
 
         self.assertAlmostEqual(
             scattering_cross_section(555 * 10e-8, 360),
-            4.675013461928133e-27,
+            4.346694421271718e-27,
             places=32,
         )
 
         self.assertAlmostEqual(
             scattering_cross_section(555 * 10e-8, 620),
-            4.707951639592975e-27,
+            4.346803470171720e-27,
             places=32,
         )
 
         self.assertAlmostEqual(
             scattering_cross_section(555 * 10e-8, temperature=200),
-            2.245601437154005e-27,
+            2.094012829135068e-27,
             places=32,
         )
 
         self.assertAlmostEqual(
             scattering_cross_section(555 * 10e-8, temperature=300),
-            5.052603233596510e-27,
+            4.711528865553901e-27,
             places=32,
         )
 
         self.assertAlmostEqual(
             scattering_cross_section(555 * 10e-8, temperature=400),
-            8.982405748616020e-27,
+            8.376051316540270e-27,
             places=32,
         )
 
@@ -1379,15 +1379,15 @@ class TestRayleighOpticalDepth(unittest.TestCase):
         """
 
         self.assertAlmostEqual(
-            rayleigh_optical_depth(360 * 10e-8), 0.599101336848028, places=7
+            rayleigh_optical_depth(360 * 10e-8), 0.560246579231107, places=7
         )
 
         self.assertAlmostEqual(
-            rayleigh_optical_depth(555 * 10e-8), 0.100407017728965, places=7
+            rayleigh_optical_depth(555 * 10e-8), 0.093629074056042, places=7
         )
 
         self.assertAlmostEqual(
-            rayleigh_optical_depth(830 * 10e-8), 0.019655847912114, places=7
+            rayleigh_optical_depth(830 * 10e-8), 0.018312619911882, places=7
         )
 
         self.assertAlmostEqual(
@@ -1396,67 +1396,67 @@ class TestRayleighOpticalDepth(unittest.TestCase):
 
         self.assertAlmostEqual(
             rayleigh_optical_depth(555 * 10e-8, 360),
-            0.100698605176897,
+            0.093626696247360,
             places=7,
         )
 
         self.assertAlmostEqual(
             rayleigh_optical_depth(555 * 10e-8, 620),
-            0.101394382260863,
+            0.093616393371777,
             places=7,
         )
 
         self.assertAlmostEqual(
             rayleigh_optical_depth(555 * 10e-8, temperature=200),
-            0.048371194415621,
+            0.045105912380991,
             places=7,
         )
 
         self.assertAlmostEqual(
             rayleigh_optical_depth(555 * 10e-8, temperature=300),
-            0.108835187435146,
+            0.101488302857230,
             places=7,
         )
 
         self.assertAlmostEqual(
             rayleigh_optical_depth(555 * 10e-8, temperature=400),
-            0.193484777662482,
+            0.180423649523964,
             places=7,
         )
 
         self.assertAlmostEqual(
             rayleigh_optical_depth(555 * 10e-8, pressure=101325),
-            0.100407017728965,
+            0.093629074056042,
             places=7,
         )
 
         self.assertAlmostEqual(
             rayleigh_optical_depth(555 * 10e-8, pressure=100325),
-            0.099416077509583,
+            0.092705026939772,
             places=7,
         )
 
         self.assertAlmostEqual(
             rayleigh_optical_depth(555 * 10e-8, pressure=99325),
-            0.098425137290200,
+            0.091780979823502,
             places=7,
         )
 
         self.assertAlmostEqual(
             rayleigh_optical_depth(555 * 10e-8, latitude=0, altitude=0),
-            0.100407017728965,
+            0.093629074056041,
             places=10,
         )
 
         self.assertAlmostEqual(
             rayleigh_optical_depth(555 * 10e-8, latitude=45, altitude=1500),
-            0.100190076534634,
+            0.093426777407767,
             places=10,
         )
 
         self.assertAlmostEqual(
             rayleigh_optical_depth(555 * 10e-8, latitude=48.8567, altitude=35),
-            0.100108462705423,
+            0.093350672894038,
             places=10,
         )