Towards Assessing the Information Content of Radar Polarimetry Measurements

Improving utilization of dual polarization radar measurements, including for the retrieval of larger-scale rainfall accumulation, detailed phase partitioning and drop size distributions (DSDs), is one potential path toward developing or improving process-level cloud models and parameterizations for climate prediction. There are known and immediate demands for high-quality rainfall-accumulation maps to act as a key component for continuous climate-model-forcing datasets. Similarly, the monitoring of particle size and phase evolution may serve as key constraint for modeled deep convective processes. Whereas there is no shortage of dual-polarization retrieval methodologies for the key geophysical quantities of interest (e.g., precipitation estimates, DSD), less emphasis has been on the use of dual-polarization quantities as constraints for such retrievals. Here we explore the application of principles of maximum entropy for approximating the droplet size distribution. By integrating over the retrieved constrained maximum entropy distribution with respect to the rainfall kernel, we are able to estimate rainfall rates with high accuracy and quantify the information content of each radar measurement. We have combined this approach with linear programming to quantify uncertainty in the retrievals by finding the upper and lower bound consistent with a set of radar measurements. This new approach is an accurate alternative to the empirical relationships and, unlike existing techniques, can be applied to radar measurements under a range of atmospheric conditions.