Parameterizing Single Scattering Properties Across the Electromagnetic Spectrum for Water Cloud Retrieval

Water clouds are composed of spherical water droplets, to which the Mie solution applies for their electromagnetic scattering. The essential variable of Mie solutions is
ξ ≡ 𝑚𝑘𝐷 (or equivalently 𝑚𝑘𝑟), where 𝑚 is the complex index of refraction of water, 𝑘 = 2π/λ the angular wavenumber, λ the wavelength, and 𝐷 (𝑟) the diameter (radius) of the water droplet. Consequently, all water-droplet single-scattering properties, such as extinction and scattering efficiencies, i.e., 𝑄 and , are functions of , 𝑒 𝑄𝑠 ξ which provides a convenient pathway to parameterize water-droplet single-scattering properties across the electromagnetic spectrum or spectrum segments. In this paper, we first demonstrate that the numerical Mie solution indeed depends only on ξ. We then present our first attempt to parameterize extinction efficiency across the visible-infrared spectrum.