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

Abstract

Observations of weather phenomenon by polarimetric pulsed-Doppler weather radars are employed 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 1 or 2 signal correlation time-lags and may not utilize all the available information intrinsic in the received signals. Weather-variable estimates could benefit from the use of all intrinsic characteristics in the received data; accordingly, more complex estimators use multiple lags to extract additional information. However, not all estimates are improved by the use of more lags; in fact, improvement in estimates depends on 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.