This article examines mathematical models for the rate of spread of bushfires across inclined terrains. We analyze a specific postulate that has been adopted in the literature asserting that the rate of spread across an undulating landscape is well approximated by that of fire spreading across flat ground. We prove that the downslope equations proposed in the bushfire literature are equivalent to this postulate holding for symmetric hills. In contrast, we further prove that, if the postulate holds for all hills, then the rate-of-spread function must take a specific form not seen in established empirical models. Our findings demonstrate that the assumption such a postulate holds in full generality may be too restrictive for applications, and calls for further empirical and theoretical investigation to determine when it can be assumed to hold.
Thomas et al. (Mon,) studied this question.