Machine learning estimation of off-trail pedestrian travel rates using LiDAR-derived slope, vegetation, and surface roughness

Multiple landscape factors, including slope, vegetation density, and surface roughness, work together to affect pedestrian travel rates in off-path environments. Most previous pedestrian travel rate models have only quantified the effects of these factors at relatively coarse spatiotemporal resolutions, ignoring the fine-scaled information contained within LiDAR data and instantaneous travel trajectories. Previous studies have also relied on parametric function fitting to model off-path travel rates. This paper presents the first known examination of instantaneous travel rates using random forests—a machine learning algorithm well-suited to the presence of non-linear relationships and the ability to robustly evaluate variable importance. Principal components of airborne LiDAR-derived slope, vegetation density, and surface roughness were used as predictor variables in a random forest model. The model explained over 77% of the variance in observed travel rates from an independent test dataset (R² = 0.778). An analysis of permutation importance indicated that LiDAR-derived slope was the most important predictor of travel rate, followed by vegetation density, then surface roughness. Examining the importance of slope, vegetation density, and surface roughness together provides new insight beyond their individual effects, revealing how these landscape factors interact to shape pedestrian travel rates. While slope is the most important single predictor, our results show that vegetation density and surface roughness exert distinct and nonlinear influences that become clearer only when evaluated jointly. Notably, vegetation density reduces travel rate more sharply than surface roughness, and high vegetation density remains strongly limiting even when roughness is low, whereas the reverse is not true. These combined effects also exceed the explanatory power of individual median speed, underscoring the importance of environmental conditions over individual-level differences in exertion or fitness. Potential applications of this work include modeling instantaneous travel rates for wildland firefighter safety, search and rescue, and migration applications.