Using crowdsourced fitness tracker data to model the relationship between slope and travel rates

Abstract One of the critical factors affecting travel rates while hiking, jogging, or running along a trail is the slope of the underlying terrain. Models for predicting this effect have been used in a wide variety of scientific and applied contexts, including recreation planning, search and rescue, wildland firefighter safety, social network analysis, and recreating historical human movement patterns. Despite their wide use, these models are based on datasets with very small sample sizes that were collected without using instantaneous measures of travel rate and assume symmetrical effects about the slope of maximum travel rate. These models also typically resulted in a single mathematical function, ignoring the significant variability that can occur between a fast and a slow individual, or between walking and running travel rates. In this study we modeled travel rates using a database of GPS tracks from 29,928 individuals representing 421,247 individual hikes, jogs, and runs on trails in and around Salt Lake City, Utah for an entire year between July 1, 2016 and June 30, 2017. Three widely-used probability distribution functions (Laplace, Gauss, and Lorentz) were used to predict travel rates based on terrain slope along segments of trails with uniform slopes. To account for the variability in travel rates between fast and slow movement, a series of travel rate models were generated to predict travel rate percentiles, ranging from the 1st to the 99th, thus providing a flexible basis for predicting travel rates as a function of slope. The large number of samples allowed us to introduce a novel term that accounts for asymmetry in travel rates on uphill and downhill slopes. All three functions performed well, with Lorentz percentile models averaging an R2 of 0.958 and a mean absolute error (MAE) of 0.078 m/s, Laplace with R2 of 0.953 and MAE of 0.088 m/s, and Gauss with R2 of 0.949 and MAE of 0.090 m/s. All three functions performed notably better at estimating lower travel rate percentiles (e.g. 5th: R2Lorentz = 0.941; R2Laplace = 0.940; R2Gauss = 0.934) as compared to higher (e.g. 95th: R2Lorentz = 0.914; R2Laplace = 0.913; R2Gauss = 0.908), indicating greater consistency in walking rates than the fastest running rates. Lorentz outperformed the other functions for the widest range of percentiles (5th, 30th-90th), and thus is recommended for use as a flexible travel rate prediction function. However, Laplace tended to produce the best results at moderately-low travel rate percentiles (10th-25th), suggesting a combination of the two models could produce the highest accuracies. The results of this research provide a sound basis for future studies aiming to estimate travel rates while hiking or running along slopes.