Statistics of the slope-method estimator

Abstract

The slope method has customarily been used and is still used for inversion of atmospheric optical parameters, extinction, and backscatter in homogeneous atmospheres from lidar returns. Our aim is to study the underlying statistics of the old slope method and ultimately to compare its inversion performance with that of the present-day nonlinear least-squares solution (the so-called exponential-curve fitting). The contents are twofold: First, an analytical study is conducted to characterize the bias and the mean-square-estimation error of the regression operator, which permits estimation of the optical parameters from the logarithm of the range-compensated lidar return. Second, universal plots for most short- and far-range tropospheric backscatter lidars are presented as a rule of thumb for obtaining the optimum regression interval length that yields unbiased estimates. As a result, the simple graphic basis of the slope method is still maintained, and its inversion performance improves up to that of the present-day computer-oriented exponential-curve fitting, which ends the controversy between these two algorithms.