Single and multiple scattering contributions to circumsolar radiation

M. A. Box; A. Deepak

doi:10.1364/AO.17.003794

Applied Optics
Vol. 17,
Issue 23,
pp. 3794-3797
(1978)
•https://doi.org/10.1364/AO.17.003794

Single and multiple scattering contributions to circumsolar radiation

M. A. Box and A. Deepak

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M. A. Box and A. Deepak, "Single and multiple scattering contributions to circumsolar radiation," Appl. Opt. 17, 3794-3797 (1978)

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Abstract

Single and multiple scattering contributions to the circumsolar radiation along the almucantar and sun vertical have been computed by a Gauss-Seidel solution to the radiative transfer equation. In the near forward direction, the multiple scattering contributions are significant for optical depths of the order of 0.4. However, the shape of the angular distribution of almucantar radiance up to 10° appears less sensitive to multiple scattering. The results have been compared against an existing radiative transfer code.

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Wavelength	λ	= 0.55 μm
Rayleigh optical depth	τ_R	= 0.1
Particulate scattering optical depth	τ_PS	= 0.01026
Particulate absorption optical depth	τ_PA	= 0.00236
Ozone absorption optical depth	$τ_{O_{3}}$	= 0.0
Total optical depth	τ	= 0.11262
Solar zenith angle	θ_SUN	= 60°
Unattenuated solar flux	F	= 100π
Aerosol Characteristics
Refractive index	m	= 1.50 – i0.03
Size distribution	n(r)	= C, 0.03 μm ≤ r ≤ 0.1 μm
		= C(r/0.1)⁻⁴, 0.1 μm ≤ r ≤ 2.0 μm
		= 0, otherwise
The value of C is determined by τ_PS.
Volume scattering coefficient β_scat = 4.85 × 10⁻¹⁰ cm⁻¹ per particle
Volume absorption coefficient β_abs = 1.12 × 10⁻¹⁰ cm⁻¹ per particle
Volume extinction coefficient β_ext = 5.97 × 10⁻¹⁰ cm⁻¹ per particle

Azimuth angle (deg)	I_RT (Dave)		I_SS (A = 0.0)	I_RT (Our)
Azimuth angle (deg)	A = 0.0	A = 0.25	I_SS (A = 0.0)	A = 0.0	A = 0.25
0	15.556	16.627	17.015	18.003	19.056
30	7.864	8.935	7.209	8.142	9.195
60	5.450	6.522	4.655	5.452	6.506
90	4.086	5.158	3.352	4.039	5.092
120	3.843	4.915	3.123	3.780	4.833
150	4.293	5.365	3.530	4.214	5.268
180	4.588	5.660	3.796	4.501	5.550

Zenith angle (deg)	I_RT (Dave)		I_SS (A = 0.0)	I_RT (Our)
Zenith angle (deg)	A = 0.0	A = 0.25	I_SS (A = 0.0)	A = 0.0	A = 0.25
0	2.486	3.044	2.157	2.471	3.017
10	2.903	3.470	2.553	2.905	3.459
20	3.514	4.107	3.141	3.553	4.132
30	4.407	5.048	4.030	4.526	5.152
40	5.812	6.532	5.500	6.112	6.816
50	8.574	9.423	8.613	9.388	10.220
60	15.556	16.627	17.015	18.003	19.056
70	15.225	16.730	15.283	16.624	18.110
80	20.889	23.495	19.720	21.892	24.482

Azimuth angle (deg)	Scattering angle (deg)	$I_{SS}^{N}$	$I_{RT}^{N}$		$\frac{(I_{RT}^{N} - I_{SS}^{N})}{I_{SS}^{N}}$
Azimuth angle (deg)	Scattering angle (deg)	$I_{SS}^{N}$	A = 0	A = 0.25	A = 0	A = 0.25
Solar zenith angle = 30°
τ_R = 0.1,τ_PS = 0.2
Normalization constant =		1.0920	1.1406	1.1574	4.5	6.0

0	0.0	1.0000	1.0000	1.0000	0.0	0.0
4	2.0	0.9779	0.9787	0.9790	0.1	0.1
8	4.0	0.9161	0.9191	0.9202	0.3	0.4
12	6.0	0.8257	0.8318	0.8342	0.7	1.0
16	8.0	0.7211	0.7306	0.7344	1.3	1.8
Solar zenith angle = 30°
τ_R = 0.2, τ_PS = 0.2
Normalization constant =		1.0003	1.0652	1.0904	6.5	9.0

0	0.0	1.0000	1.0000	1.0000	0.0	0.0
4	2.0	0.9785	0.9797	0.9802	0.1	0.2
8	4.0	0.9183	0.9227	0.9245	0.5	0.7
12	6.0	0.8303	0.8393	0.8430	1.1	1.5
16	8.0	0.7284	0.7426	0.7485	1.9	2.8
Solar zenith angle = 60°
τ_R = 0.1, τ_PS = 0.2
Normalization constant =		1.4679	1.5860	1.6026	8.0	9.2

0	0.0	1.0000	1.0000	1.0000	0.0	0.0
4	3.5	0.9360	0.9399	0.9405	0.4	0.5
8	6.9	0.7774	0.7908	0.7930	1.7	2.0
12	10.4	0.5932	0.6167	0.6207	4.0	4.6
16	13.9	0.4347	0.4658	0.4714	7.2	8.4
Solar zenith angle = 60°
τ_R = 0.2, τ_PS = 0.2
Normalization constant =		1.2357	1.3683	1.3905	10.7	12.5

0	0.0	1.0000	1.0000	1.0000	0.0	0.0
4	3.5	0.9377	0.9429	0.9438	0.6	0.7
8	6.9	0.7833	0.8012	0.8043	2.3	2.7
12	10.4	0.6039	0.6343	0.6414	5.0	6.2
16	13.9	0.4494	0.4920	0.5001	9.5	11.3

Wavelength	λ	= 0.55 μm
Rayleigh optical depth	τ_R	= 0.1
Particulate scattering optical depth	τ_PS	= 0.01026
Particulate absorption optical depth	τ_PA	= 0.00236
Ozone absorption optical depth	$τ_{O_{3}}$	= 0.0
Total optical depth	τ	= 0.11262
Solar zenith angle	θ_SUN	= 60°
Unattenuated solar flux	F	= 100π
Aerosol Characteristics
Refractive index	m	= 1.50 – i0.03
Size distribution	n(r)	= C, 0.03 μm ≤ r ≤ 0.1 μm
		= C(r/0.1)⁻⁴, 0.1 μm ≤ r ≤ 2.0 μm
		= 0, otherwise
The value of C is determined by τ_PS.
Volume scattering coefficient β_scat = 4.85 × 10⁻¹⁰ cm⁻¹ per particle
Volume absorption coefficient β_abs = 1.12 × 10⁻¹⁰ cm⁻¹ per particle
Volume extinction coefficient β_ext = 5.97 × 10⁻¹⁰ cm⁻¹ per particle

Abstract

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Figures (2)

Tables (4)

Equations (4)

Applied Optics