Alexander Marshak — NASA - Goddard Space Flight Center
Yuri Knyazikhin — Boston University
J.-Y. Christine Chiu — Colorado State University
Warren J. Wiscombe — Brookhaven National Laboratory
Category
Cloud Properties
Description
The ratio of ω0λ(r)/ω0λ(r0) plotted against ω0λ(r) for four wavelengths λ=0.86, 1.65, 2.13, and 3.75 μm. Single scattering albedos ω0λ(r) are calculated using Mie theory. Droplet effective radius r=10, 20, 30, and 40 μm; r0=5 μm. Droplet sizes are assumed to follow a gamma distribution with effective variance v=0.1.
The single scattering albedo ω0λ in atmospheric radiative transfer is the ratio of the scattering coefficient to the total extinction coefficient. For cloud water droplets both the scattering and absorption coefficients, and thus the single scattering albedo, are functions of wavelength λ and droplet size r. We show that for water droplets at weakly absorbing wavelengths, the ratio ω0λ(r)/ω0λ(r0) of two single scattering albedo spectra for two different droplet sizes is a linear function of ω0λ(r). The slope and intercept of the linear function are wavelength-independent and sum to unity. This relationship allows for a representation of the spectral variation of single scattering albedo ω0λ(r) for any droplet size using the spectral variation for just one size. We provide a simple physical explanation of the discovered relationship. Similar linear relationships characterize the single scattering albedo of non-spherical ice crystals.
