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Current rural propagation models only consider paths (direct, ground reflected, terrain diffracted, troposphere scattered) that lie in the vertical plane containing the transmitter and receiver. This paper shows that nonspecular scattering from terrain can give significant additional contributions to the received signal in hilly/mountainous environments. To show this, we have carried out Monte Carlo simulations of scattering in many different types of rural regions. These simulations model scattering using the bi-static radar equation with a Lambert's law coefficient. In order to permit simulations for many radio links and many terrain databases, we have developed a novel algorithm to rapidly search for terrain scattering elements that are visible to both the transmit and receive antennas. Results show that in sufficiently rugged terrain, the scattered paths can give a greater contribution to received power than vertical plane paths in more than 80% of links. Conclusions are drawn for radio channel characteristics, such as angle spread and short-term spatial fading. Statistical models dependent on terrain variation for path loss, and temporal response are also developed.