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JOURNAL OF THE ATMOSPHERIC SCIENCES, 65, 3636-3651, 2008.
Fast lidar and radar multiple-scattering models: Part II: Wide-angle scattering using the time-dependent two-stream approximation.
Robin J. Hogan and Alessandro Battaglia
Abstract
Spaceborne lidar returns from liquid water clouds contain significant contributions from photons that have experienced
many wide-angle multiple-scattering events, resulting in returns appearing to originate from far beyond the end of the cloud.
A similar effect occurs for spaceborne millimeter-wave radar observations of deep convective clouds. An efficient method is
described for calculating the time-dependent returns from such a medium by splitting the photons into those that have taken
a near-direct path out to and back from a single backscattering event (in the case of lidar, accounting for small-angle forward
scatterings on the way, as described in Part 1 of this paper), and those that have experienced wide-angle multiple-scattering
events. This paper describes the modeling of the latter using the time-dependent two-stream approximation, which reduces the
problem to solving a pair of coupled partial differential equations for the energy of the photons traveling towards and away from
the instrument. To determine what fraction of this energy is detected by the receiver, the lateral variance of photon position is
modeled by the Ornstein-Furth formula, in which both the ballistic and diffusive limits of photon behavior are treated; this is
considerably more accurate than simple diffusion theory. By assuming the lateral distribution to be described by a Gaussian,
the fraction of photons within the receiver field-of-view may be calculated. The method performs well in comparison to Monte
Carlo calculations (for both radar and lidar), but is much more efficient. This opens the way for multiple scattering to be
accounted for in radar and lidar retrieval schemes.
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