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The return of a spaceborne lidar system contains essential contributions form multiple scattering. Hence, methods for the retrieval of cloud parameters from such returns must be based on equations which take into account such multiple scattering. The more precisely this is done the more complicated these equations will be and the less changes are to be able to retrieve the parameters. At least this is true for retrieval procedures which are based on solving integro- differential equations. Hence, in such a case it is necessary to use simplified equations to describe such returns. Such simplified equations may be equations which introduce a correction term into the classical (single scattering) lidar equation or which take into account one or two orders of multiple scattering only or which have the for of some sophisticated exponential series including knowledge of depolarization. Of course, it is necessary to check the validity of such approximative multiple scattering lidar equations. We show simulations of lidar returns from different clouds. These simulations are obtained by variance reduction Monte Carlo methods which are based on an exact multiple scattering lidar equation obtained within the framework of a stochastic model from the transport of polarized light through the atmosphere. These simulations demonstrate the great importance of the contributions from multiple scattering to the return signal, the diffusion of the laser beam in the cloud seen from the receiver, the difficulty of determining the type and the location of the particles contributing to the return, and the need of careful analysis of returns of spaceborne lidar systems. We show simulations of such returns from clouds of aerosols (randomly oriented oblate and prolate spheroids) and a sensitivity analysis for such returns from water clouds with varying extinction coefficient and droplet size distribution. The simulations and the sensitivity analysis clearly show that the validity of retrieval procedures based on approximative multiple scattering lidar equations has to be examined with care.
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