Toward retrieving properties of the tenuous atmosphere using space-based lidar measurements

This paper introduces a method that can incorporate different information into the lidar retrieval problem as an attempt to address the backscatter-to-extinction ambiguity that plagues the usefulness of lidar backscattering measurements. The approach, suited for application to spaceborne lidar data, inverts the lidar equation via an optimal estimation method. This method is illustrated using three examples drawn from LITE data. Retrievals using only lidar backscatter as input were compared to retrievals performed using an iterative solution to the lidar inversion with the same input. The two methods produced essentially identical results. The new method, however, offers a number of advantages compared to other methods, including (1) the ability to incorporate different kinds of information under a common retrieval philosophy. This feature is illustrated with the formal introduction of optical depth into the lidar inversion. In this paper, optical depth information, derived from the Idar transmission estimates, is combined with backscatter measurements making it possible to retrieve the backscatter-to-extinction ratio in addition to extinction profiles given certain caveats noted in the paper. (2) The method provides a number of ways for evaluating the quality of the retrieval. Notably, the retrieval approach predicts full error diagnostics identifying sources of error due to measurement uncertainty (instrument noise and calibration uncertainty), model error (containing all the assumptions built into the lidar equation and its parameters), as well as a priori error due to the influence of compiled databases on lidar backscatter of aerosol and cloud. When no optical depth information is available, the retrieval errors are largely dominated by the (large) uncertainty attached to the backscatter-to-extinction coefficient k. Under these circumstances the retrievals are only meaningful to the extent that k and its related uncertainty is known. When optical depth is introduced as a form of measurement, the error contributions shift to the extent that retrieval errors become dominated by the measurement error attached to the optical depth itself.