Abstract
We consider the problem of retrieving the aerosol extinction coefficient from Raman lidar measurements. This is an ill-posed inverse problem that needs regularization, and we propose to use the Expectation-Maximization (EM) algorithm to provide stable solutions. Indeed, EM is an iterative algorithm that imposes a positivity constraint on the solution, and provides regularization if iterations are stopped early enough. We describe the algorithm and propose a stopping criterion inspired by a statistical principle. We then discuss its properties concerning the spatial resolution. Finally, we validate the proposed approach by using both synthetic data and experimental measurements; we compare the reconstructions obtained by EM with those obtained by the Tikhonov method, by the Levenberg-Marquardt method, as well as those obtained by combining data smoothing and numerical derivation.
Highlights
Lidar systems are increasingly used to characterize the temporal and spatial distribution of the aerosol optical characteristics in the atmosphere [1, 2]
In this paper we have described the application of the Expectation Maximization (EM) iterative algorithm, stopped with a cumulative residuals criterion, for reconstruction of the extinction coefficient from Raman lidar data
Our choice of EM was mostly due to the presence of some desirable properties, namely: the natural and seemless incorporation of a positivity constraint; the fact that, despite being an iterative algorithm, the solution does not depend on the order of magnitude of the first guess; its simplicity and computational efficiency
Summary
Lidar systems are increasingly used to characterize the temporal and spatial distribution of the aerosol optical characteristics in the atmosphere [1, 2]. Lidar signals provide a very indirect measure of the relative concentration and distribution of the aerosols: the energy observed by a lidar is a function of the extinction and backscattering coefficients which in turn are functions of the microphysical properties of the aerosols Deriving such properties is possible, but only via the numerical solution of two inverse problems: the first one allows the estimation of the extinction coefficients from the experimental data [4,5,6,7] and the second one allows the reconstruction of the size distribution, shape and refractive index of the aerosols [8,9,10,11], starting from the knowledge of the extinction and backscatter coefficient at multiple wavelengths.
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