Estimation of snow in extratropical cyclones from multiple frequency airborne radar observations. An Expectation-Maximization approach

A major challenge in deriving accurate estimates of physical properties of falling snow particles from single frequency space- or airborne radar observations is that snow particles exhibit a large variety of shapes and their electromagnetic scattering characteristics are highly dependent on these shapes. Triple frequency (Ku-Ka-W) radar observations are expected to facilitate the derivation of more accurate snow estimates because specific snow particle shapes tend to have specific signatures in the associated two-dimensional dual-reflectivity-ratio (DFR) space. However, the derivation of accurate snow estimates from triple frequency radar observations is by no means a trivial task. This is because the radar observations can be subject to non-negligible attenuation (especially at W-band when super-cooled water is present), which may significantly impact the interpretation of the information in the DFR space. Moreover, the electromagnetic scattering properties of snow particles are computationally expensive to derive, which makes the derivation of reliable parameterizations usable in estimation methodologies challenging. In this study, we formulate an two-step Expectation Maximization (EM) methodology to derive accurate snow estimates in Extratropical Cyclones (ECTs) from triple frequency airborne radar observations. The Expectation (E) step consists of a least-squares triple frequency estimation procedure applied with given assumptions regarding the relationships between the density of snow particles and their sizes, while the Maximization (M) step consists of the optimization of the assumptions used in step E. The electromagnetic scattering properties of snow particles are derived using the Rayleigh-Gans approximation. The methodology is applied to triple frequency radar observations collected during the Olympic Mountains Experiment (OLYMPEX). Results show that snowfall estimates above the freezing level in ETCs consistent with the triple frequency radar observations as well as with independent rainfall estimates below the freezing level may be derived using the EM methodology formulated in the study.