Biases in lidar-based retrievals of cirrus properties due to uncertain ice particle size distributions

We investigate potential biases in cirrus cloud properties retrieved from lidar extinction measurements when the information on particle size distribution (PSD) is conveyed using a parametrization approach. By reducing parameters to their most likely values determined from in situ measurements and neglecting their natural variability, a bias can occur in mean property estimates. This happens because the average value of a property determined from a series of model evaluations sampling the parameter variability is generally not equivalent to that of a single evaluation using the most likely parameters, a result otherwise known as Jensen's inequality. A bias correction strategy is proposed when the uncertain parameters are normally distributed and their variance-covariance matrix can be provided. We estimate the bias of current parametrizations by modeling cirrus ice water content and sedimentation flux as functions of optical extinction and a finite set of parameters informing on ice PSD. We show that the bias correction formula applied to those models compares favorably with direct estimations from a Monte Carlo approach. We also show that the average ice water content and sedimentation flux estimated from current approaches can be biased (low or high) if the PSD parameters exhibit even a small amount of variance while the sign and magnitude of that bias is determined by the correlations between extinction and the PSD parameters.