Statistical considerations on the extinction error variance for the Raman lidar inversion algorithm

At the basis of the Raman lidar extinction inversion algorithm is the derivative of the logarithm of the ratio between the atmospheric nitrogen number density and the range-corrected Raman power return. While its computation is straightforward under ideal (noiseless) conditions, this is not the case under low signal-to-noise ratios, for which the observation noise may lead the logarithm to singular values. This work presents an analytical-statistical overview of the inversion problem and related errorbars, tentative noise limiting criteria, and justifies the approximations at play to estimate the inversion error by means of error-propagation techniques for high signal-to-noise ratios. Simulation examples consider a 532/607-nm elastic-Raman system.