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A high frequency theoretical model of propagation and scattering in vegetation is presented which uses scalar radiative transport theory. The specific problem analyzed is that of a periodic sequence of Gaussian pulses incident from free space into a forest region (vegetation). The incident pulse train is taken to be a spherical wave that is restricted to a specified solid angle, which is characteristic of radiation produced by a microwave or mm-wave antenna. The forest is modeled as a half-space of randomly distributed particles that scatter and absorb electromagnetic energy. In the forest, strong forward scattering occurs and the theory allows for a comprehensive characterization of the effect of vegetation on the propagation and scattering of spherical wave pulses: their attenuation, their angular spread, their distortion due to pulse broadening.