Statistical Properties of Polarimetric Weather Radar Returns for Nonuniformly Filled Beams

An explicit expression for stochastic processes describing the dual-polarization weather radar echoes is presented. The probability distributions of the proposed model are defined in terms of the point values assumed by polarimetric and Doppler variables in the relevant radar sampling volume. The statistical properties of the model are discussed in order to verify its faithfulness as representative of real radar signals. The discussion considers the most general situation, i.e., it is not related to specific hydrometeor distributions or beam filling conditions.