Comparison of Three Methodologies for Removal of Random-Noise-Induced Biases From Second-Order Statistical Parameters of Lidar and Radar Measurements.

Random-noise-induced biases are inherent issues to the accurate derivation of second-order statistical parameters (e.g., variances, fluxes, energy densities, and power spectra) from lidar and radar measurements. We demonstrate here for the first time an altitude-interleaved method for eliminating such biases, following the original proposals by Gardner and Chu (2020, https://doi.org/10.1364/ao.400375) who demonstrated a time-interleaved method. Interleaving in altitude bins provides two statistically independent samples over the same time period and nearly the same altitude range, thus enabling the replacement of variances that include the noise-induced biases with covariances that are intrinsically free of such biases. Comparing the interleaved method with previous variance subtraction (VS) and spectral proportion (SP) methods using gravity wave potential energy density calculated from Antarctic lidar data and from a forward model, this study finds the accuracy and precision of each method differing in various conditions, each with its own strengths and weakness. VS performs well in high-SNR, yet its accuracy fails at lower-SNR as it often yields negative values. SP is accurate and precise under high-SNR, remaining accurate in worse conditions than VS would, yet develops a positive bias under low-SNR. The interleaved method is accurate in all SNRs but requires a large number of samples to drive random-noise terms in covariances toward zero and to compensate for the reduced precision due to the splitting of return signals. Therefore, selecting the proper bias removal/elimination method for actual signal and sample conditions is crucial in utilizing lidar/radar data, as neglecting this can conceal trends or overstate atmospheric variability.