A flexible parameterization for shortwave optical properties of ice crystals

We present a simple, yet accurate parameterization that provides the single-scattering albedo (ω) and asymmetry parameter (g) of ice crystals for any combination of volume, projected area, aspect ratio and crystal distortion at any wavelength in the shortwave. Unlike existing parameterizations, this scheme is flexible enough to obtain ice crystal optical properties that are consistent with any assumptions about ice crystal mass (equivalent to bulk volume), projected area and aspect ratio used in modern cloud and climate model ice microphysics schemes to parameterize the fall-speed and capacitance of particles. Similar to previous parameterizations, our scheme makes use of geometric optics approximations and the observation that optical properties of complex, aggregated ice crystals can be well approximated by those of single hexagonal crystals with varying size, aspect ratio and crystal distortion level. We show that ω is largely determined by the particle aspect ratio and the newly defined absorption size parameter, which is proportional to the ratio of the imaginary part of the refractive index to the wavelength and the ratio of particle volume to projected area. The dependence of ω on absorption size parameter and aspect ratio is parameterized using a combination of exponential, log- normal and polynomial functions. The variation of g with aspect ratio and crystal distortion level is parameterized for one reference wavelength using a combination of several polynomials. Subsequently, a newly determined semi-empirical relation is used to scale the parameterized g to provide values appropriate for other wavelengths. Also, a correction for the dependence of the ray-tracing asymmetry parameter on single-scattering albedo is proposed. In total, the parameterization scheme consists of only 88 coefficients. The scheme is tested for a large variety of hexagonal crystals with varying crystal distortions in several wavelength bands from 0.2 to 4 micron, revealing absolute errors in both ω and g generally below 0.015. We will show that, in general, the resulting errors in cloud reflectance and transmittance are below 1%. Finally, some practical applications of the parameterization scheme are highlighted. A simple computer code for this parameterization is freely available.