Relationship between asymmetry parameter and hemispheric backscatter ratio: implications for climate forcing by aerosols

Stephen F. Marshall; David S. Covert; Robert J. Charlson

doi:10.1364/AO.34.006306

Applied Optics
Vol. 34,
Issue 27,
pp. 6306-6311
(1995)
•https://doi.org/10.1364/AO.34.006306

Relationship between asymmetry parameter and hemispheric backscatter ratio: implications for climate forcing by aerosols

Stephen F. Marshall, David S. Covert, and Robert J. Charlson

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Stephen F. Marshall, David S. Covert, and Robert J. Charlson, "Relationship between asymmetry parameter and hemispheric backscatter ratio: implications for climate forcing by aerosols," Appl. Opt. 34, 6306-6311 (1995)

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Abstract

Calculations of direct climate forcing by anthropogenic aerosols commonly use radiative transfer parameters, including asymmetry parameter g. One method of obtaining the asymmetry parameter of a particle population is to convert measured values of the hemispheric-to-total-scatter ratio (backscatter ratio b) into their corresponding g values. We compare a conversion derived from Mie calculations with one derived from the Henyey–Greenstein (HG) phase function to show that the HG method systematically overestimates g for typical size distributions of accumulation-mode aerosols. A delta-Eddington radiative transfer calculation is used to show that a 10% overestimation of g can systematically reduce climate forcing as a result of aerosols by 12% or more. Mie computations are used to derive an empirical relationship between backscatter ratio and asymmetry parameter for log-normal accumulation-mode aerosols. This relationship can be used to convert the backscatter ratio to the asymmetry parameter, independent of geometric mean diameter D_gv or complex refractive index m, but the conversion requires knowledge of the breadth σ_g of the size distribution.

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ω	Δ(ΔF) (%)
0.999999	−12.4
0.9	−12.7
0.75	−14.7
0.586	−20.1

Valid for	l	C_1,0	C_1,1	C_1,2	C_1,3	A_l (σ_g = 1.4)	A_l (σ_g = 2.0)
0 < k < 0.16	0	4.284 × 10⁻¹	5.989 × 10⁻¹	−2.590 × 10⁻¹	4.167 × 10⁻²	0.8735	0.9234
	1	−4.675	3.250	−2.063	3.611 × 10⁻¹	−3.178	−3.539
	2	2.759 × 10¹	−4.003 × 10¹	2.352 × 10¹	−4.194	6.133	8.044
	3	−5.405 × 10¹	8.953 × 10¹	−5.369 × 10¹	9.833	−6.966	−11.10
k = 0	0	2.476 × 10⁻¹	8.840 × 10⁻¹	−3.836 × 10⁻¹	5.556 × 10⁻²	0.8872	0.9277
	1	−3.171	1.677	−2.140	6.111 × 10⁻¹	−3.342	−3.491
	2	3.365 × 10¹	−6.044 × 10¹	4.307 × 10¹	−9.750	6.717	7.080
	3	−1.078 × 10²	2.097 × 10²	−1.424 × 10²	3.122	−7.620	−8.145
k = 0.16	0	4.284 × 10¹	5.990 × 10⁻¹	−2.604 × 10⁻¹	4.167 × 10⁻²	0.8669	0.9238
	1	−6.031	4.977	−2.516	3.112 × 10⁻¹	−3.142	−3.654
	2	2.878 × 10¹	−3.667 × 10¹	1.742 × 10¹	−1.974	6.179	9.343
	3	−7.727	−6.755	1.315 × 10¹	−5.744	−7.215	−14.546

ω	Δ(ΔF) (%)
0.999999	−12.4
0.9	−12.7
0.75	−14.7
0.586	−20.1

Valid for	l	C_1,0	C_1,1	C_1,2	C_1,3	A_l (σ_g = 1.4)	A_l (σ_g = 2.0)
0 < k < 0.16	0	4.284 × 10⁻¹	5.989 × 10⁻¹	−2.590 × 10⁻¹	4.167 × 10⁻²	0.8735	0.9234
	1	−4.675	3.250	−2.063	3.611 × 10⁻¹	−3.178	−3.539
	2	2.759 × 10¹	−4.003 × 10¹	2.352 × 10¹	−4.194	6.133	8.044
	3	−5.405 × 10¹	8.953 × 10¹	−5.369 × 10¹	9.833	−6.966	−11.10
k = 0	0	2.476 × 10⁻¹	8.840 × 10⁻¹	−3.836 × 10⁻¹	5.556 × 10⁻²	0.8872	0.9277
	1	−3.171	1.677	−2.140	6.111 × 10⁻¹	−3.342	−3.491
	2	3.365 × 10¹	−6.044 × 10¹	4.307 × 10¹	−9.750	6.717	7.080
	3	−1.078 × 10²	2.097 × 10²	−1.424 × 10²	3.122	−7.620	−8.145
k = 0.16	0	4.284 × 10¹	5.990 × 10⁻¹	−2.604 × 10⁻¹	4.167 × 10⁻²	0.8669	0.9238
	1	−6.031	4.977	−2.516	3.112 × 10⁻¹	−3.142	−3.654
	2	2.878 × 10¹	−3.667 × 10¹	1.742 × 10¹	−1.974	6.179	9.343
	3	−7.727	−6.755	1.315 × 10¹	−5.744	−7.215	−14.546

Abstract

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Equations (7)

Applied Optics