Small and large particle limits of single scattering alb e do for homogeneous, spherical particles
The aerosol single scattering albedo (SSA) is the dominant intensive particle parameter determining aerosols direct radiative forcing. For homogeneous spherical particles and a complex refractive index in- dependent of wavelength, the SSA is solely dependent on size parameter (ratio of particle circumference and wavelength) and complex refractive index of the particle. Here, we explore this dependency for the small and large particle limits with size parameters much smaller and much larger than one. We show that in the small particle limit of Rayleigh scattering, a novel, generalized size parameter can be introduced that unifies the SSA dependence on particle size parameter independent of complex refractive index. In the large particle limit, SSA decreases with increasing product of imaginary part of the refractive index and size parameter, another generalized parameter, until this product becomes about one, then stays fairly constant until the imaginary part of the refractive index becomes comparable with the real part minus one. Beyond this point, particles start to acquire metallic character and SSA quickly increases with the imaginary part of the refractive index and approaches one.
Authors:
;
Award ID(s):
Publication Date:
NSF-PAR ID:
10056818
Journal Name:
Journal of Quantitative Spectroscopy & Radiative Transfer
Volume:
204
Page Range or eLocation-ID:
250-255
ISSN:
0022-4073
4. The scattered intensity from large spheres with a real part of the refractive index of$n=1.33,1.5,2.0$is investigated as the radius$R$and an imaginary part of the refractive index$κ<#comment/>$are varied. It is shown that the product of$κ<#comment/>$and the size parameter$kR$,$κ<#comment/>kR$, is a universal parameter describing the quenching of the refraction phenomenon of the scattered light: the refraction hump, the generalized rainbows, and the glory. The physical reason for this is that$κ<#comment/>kR$is the inverse of the relative skin depth of light penetration into the sphere, which is demonstrated by calculations of the internal fields that darken universally as$κ<#comment/>kR$increases.
5. We show that for spherical particles greater than ca. 5 µm, the differential scattering cross section is only weakly dependent on the real and imaginary parts of the refractive index ($m=n+iκ<#comment/>$) when integrated over angle ranges near$37±<#comment/>5∘<#comment/>$and$115±<#comment/>5∘<#comment/>$, respectively. With this knowledge, we set up an arrangement that collects scattered light in the ranges$37±<#comment/>5∘<#comment/>$,$115±<#comment/>5∘<#comment/>$, and$80±<#comment/>5∘<#comment/>$. The weak functionality on refractive index for the first two angle ranges simplifies the inversion of scattering to the particle properties of diameter and the real and imaginary refractive indices. Our setup also uses a diamond-shaped incident beam profile that allows us to determine when a particle went through the exact center of the beam. Application of our setup to droplets of an absorbing liquid successfully determined the diameter and complex refractive index to accuracies ranging from a few to ten percent. Comparisons to simulated data derived from the Mie equations yielded similar results.