Analyzing rear-end collision risks in foggy weather through a generalized extreme value model

OBJECTIVES: Fog substantially impairs visibility and driver perception, leading to increased risk of crashes, especially rear-end collisions. Traditional crash-based safety studies are constrained by underreporting, low event frequency, and the inability to assess proactive risk under rare weather conditions. This study introduces a data-driven, proactive framework that integrates naturalistic vehicle trajectory data, anticipated collision time (ACT) as a surrogate safety measure, and extreme value theory (EVT) for estimating fog-related crash risks on multilane Indian highways. METHODS: Vehicle trajectory and fog data were collected from 8 highway sites in India, comprising both 4- and 6-lane divided segments. Visibility in fog was estimated using contrast-based image processing algorithms. Vehicle trajectories were extracted from traffic videos through advanced object detection and tracking algorithm, followed by smoothing using locally weighted polynomial regression. From over 165,000 trajectory points, 21,461 valid vehicle conflicts were identified and classified based on ACT profiles into rear-end, sideswipe, and angled interactions. Crash probabilities were estimated using extreme value theory (EVT) models under the block maxima framework, enabling risk. Stationary and nonstationary models were developed to examine how crash risk varies across visibility levels and road types using generalized extreme value distribution (GEV). RESULTS: The findings suggest rear-end conflicts pose a greater safety risk than sideswipe conflicts due to the car-following behavior of drivers during foggy weather. Results show that safety margin shrinks significantly during dense fog, especially for cars and 2-wheelers and on 4-lane highways, indicating elevated crash potential in mixed traffic. In 6-lane highways, crash risk of 2-wheelers increases sevenfold in dense fog compared to clear weather. Heavy commercial vehicles are observed to be safer during fog on 6-lane highways compared to other vehicle types. CONCLUSIONS: This research demonstrates the feasibility of ACT-based EVT modeling using field trajectory data for proactive safety evaluation in low-visibility environments where crash data are limited. The developed framework supports real-time risk estimation and can inform adaptive countermeasures such as variable speed limits, fog-responsive warning systems, and improved lane delineation for enhanced roadway safety.