Physically motivated empirical models for the spread and intensity of grass fires

We develop empirical models for the rate of spread and intensity of fires in grass fuels. The models are based on a well-known physical analogy for the rate of spread of a fire through a continuous fuelbed. Unlike other models based on this analogy, we do not attempt to directly estimate the model parameters. Rather, we use data on the rate of spread to indirectly estimate parameters that describe aggregate properties of the fire behaviour. The resulting models require information on the moisture content of the fuel and wind speed to predict the rate of spread of fires. To predict fire intensity, the models additionally use information on the heat yield of the fuel and the amount of fuel consumed. We evaluate the models by using them to predict the intensity of independent fires and by comparing them with linear and additive regression models. The additive model provides the best description of the training data but predicts independent data poorly and with high bias. Overall, the empirical models describe the data better than the linear model, and predict independent data with lower bias. Hence our physically motivated empirical models perform better than statistical models and are easier to parameterise than parameter-rich physical models. We conclude that our physically motivated empirical models provide an alternative to statistical models and parameter-rich physical models of fire behaviour.