Harnessing Riemannian Geometry to Predict Spotting
A Novel Model for Wildfire Embers

Abstract: Operational wildfire spread models are crucial to informing the decisions made by wildfire responders. However, current models for wildfire spread through spotting (the transport of embers by wind) have limited accuracy, particularly in conditions of irregular terrain and wind. This study introduces a novel spotting prediction model that incorporates wind speed, relative humidity, and topography by employing differential geometry. The model uses a spacetime metric to account for meteorology and terrain and computes geodesic arc lengths between ignition and target points. A cutoff geodesic arc length threshold is set to be the median value based on training data from four California wildfires, occurring between 2000 and 2024, that included significant spotting activity. The model is then tested against the deterministic Albini spotting model, employed in operational tools such as FARSITE, and a control model based on Euclidean distance. Models are tested using data from the Sherpa and Thomas fire perimeters. The geodesic-based model equals or outperforms (within a 0.05 margin) the predictive accuracy of both the Albini model and control. A chi-squared test confirms that geodesic arc length is a better predictor of spotting events than Euclidean distance, specifically at further distances from the fire front. The results suggest that non-Euclidean effects on ember transport are nonnegligible, and geodesic methods can bolster spotting prediction.