On spectral invariance of single scattering albedo for water droplets and ice crystals at weakly absorbing wavelengths

Abstract The single scattering albedo ω 0 λ in atmospheric radiative transfer is the ratio of the scattering coefficient to the extinction coefficient. For cloud water droplets both the scattering and absorption coefficients, thus the single scattering albedo, are functions of wavelength λ and droplet size r . This note shows that for water droplets at weakly absorbing wavelengths, the ratio ω 0 λ ( r )/ ω 0 λ ( r 0 ) of two single scattering albedo spectra is a linear function of ω 0 λ ( r ). The slope and intercept of the linear function are wavelength independent and sum to unity. This relationship allows for a representation of any single scattering albedo spectrum ω 0 λ ( r ) via one known spectrum ω 0 λ ( r 0 ). We provide a simple physical explanation of the discovered relationship. Similar linear relationships were found for the single scattering albedo spectra of non-spherical ice crystals.

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