To date, there exists no complete, computationally efficient, physics-based model to compute the radar backscatter from forest canopies. Several models attempt to predict the backscatter coefficient for random forest canopies by using the Vector Radiative Transfer (VRT) Theory with success, however, these models often rely on purely time-harmonic formulations and approximations to integrals. Forms of VRT models have recently been developed which account for a Gaussian pulse incident waveform, however, these models often rely heavily on very specific and obfuscated approximations to solve the associated integrals. This thesis attempts to resolve this problem by outlining a method by which existing, proven, time harmonic solutions to the VRT equation can be modified to account for arbitrary pulse waveforms through simple path delay method. These techniques lend physical insight into the actual scattering mechanisms behind the returned waveform, as well as offer explanations for why approximations of previous authors' break down in certain regions. Furthermore, these radiative transfer solutions can be reformulated into a convolutional model which is capable of quickly and accurately predicting the radar return of random volumes. A brief overview of radiative transfer theory as it applies to remote sensing is also given. / Master of Science