Generalized Multi-Lag Estimators (GMLE) for Polarimetric Weather Radar Observations

Observations of weather phenomenon by polarimetric pulsed-Doppler weather radars are used worldwide to monitor impending severe storms, flash floods, and other weather-related public hazards. The basis for processing received meteorological signals from pulsed-radar waveforms relies on stochastic processes where the accurate estimation of radar variables from received signals in additive white noise is essential for meaningful interpretation of weather phenomena and algorithm-derived products. For polarimetric weather radars, these estimates are calculated from signal correlations in time and across the horizontal and vertical polarization channels. Conventional estimators only use one or two signal correlation time lags and may not use all the available information intrinsic in the received signals. Weather-variable estimates could benefit from the use of all the intrinsic characteristics in the received data; accordingly, more complex estimators use multiple lags to extract additional information. However, not all the estimates are improved by the use of more lags; in fact, improvement in estimates depends on the signal characteristics and requires that the additional correlation lags provide new information. In this article, we derive and examine general multi-lag estimators for reflectivity, differential reflectivity, polarimetric cross correlation coefficient, and Doppler spectrum width. We compare the performance of these proposed estimators against conventional estimators using Monte Carlo simulations on different meteorological signal characteristics to find estimators that can improve the quality of certain radar-variable estimates.