Theory of Time-Dependent Multiple Backscattering from Clouds

Qiming Cai Department of Meteorology. University of Utah, Salt Lake City 84112

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Kuo-Nan Liou Department of Meteorology. University of Utah, Salt Lake City 84112

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Abstract

Time-dependent transfer models for double, triple and general multiple backscattering problems involving the integration of a pulsed laser beam and clouds have been developed using a spherical polar coordinate system. The general solution of the time-dependent multiple-backscattering problem is expressed in terms of a series of integral equations based on specific geometrical considerations under the time constraint of the return pulses. The theory developed includes a general four-by-four scattering phase matrix and requires no specific physical approximations. Numerical computations have been carried out for doubly and triply backscattered powers employing the phase matrix for a typical cumulus cloud composed exclusively of water droplets illuminated by laser wavelengths of 0.7 and 10.6 μm. We investigate effects of the transmitter beam width and receiver field-of-view on the multiply backscattered return, and depolarization and polarization characteristics. We also examine comprehensively and discuss physically the relative contributions due to primary, double and triple backscattering as functions of the laser penetration depth. Highlights and new finds derived from this theoretical analysis are presented and finally summarized in the conclusion.

Abstract

Time-dependent transfer models for double, triple and general multiple backscattering problems involving the integration of a pulsed laser beam and clouds have been developed using a spherical polar coordinate system. The general solution of the time-dependent multiple-backscattering problem is expressed in terms of a series of integral equations based on specific geometrical considerations under the time constraint of the return pulses. The theory developed includes a general four-by-four scattering phase matrix and requires no specific physical approximations. Numerical computations have been carried out for doubly and triply backscattered powers employing the phase matrix for a typical cumulus cloud composed exclusively of water droplets illuminated by laser wavelengths of 0.7 and 10.6 μm. We investigate effects of the transmitter beam width and receiver field-of-view on the multiply backscattered return, and depolarization and polarization characteristics. We also examine comprehensively and discuss physically the relative contributions due to primary, double and triple backscattering as functions of the laser penetration depth. Highlights and new finds derived from this theoretical analysis are presented and finally summarized in the conclusion.

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