One-Lag Estimators for Cross-Polarization Measurements

Abstract

Estimators of the linear depolarization ratio (LDR) and cross-polarization correlation coefficients (?xh) free from noise biases are devised. The estimators are based on the 1-lag correlation functions. The 1-lag estimators can be implemented with radar with simultaneous reception of copolar and cross-polar returns. Absence of noise biases makes the 1-lag estimators useful in eliminating variations of the system gain and in observations of heavy precipitation with enhanced thermal radiation. The 1-lag estimators allow for measurements at lower signal-to-noise ratios than the conventional algorithms. The statistical biases and standard deviations of 1-lag estimates are obtained via the perturbation analysis. It is found that both the 1-lag and conventional estimates of ?xh experience strong statistical biases at ?xh less than 0.3 (i.e., at low canting angles of oblate hydrometeors), and a procedure to correct for this bias is proposed.