Towards Robust Tail Risk Estimation for Freezing Rain Hazard: A Bayesian Extreme Value Approach

Freezing rain is among the most damaging winter weather hazards, yet robust statistical characterization of its extremes remains challenging due to data sparsity, strong spatial variability, and low signal-to-noise ratio in distribution tails. The traditional Maximum Likelihood Estimation (MLE) approach for estimating Generalized Pareto Distribution (GPD) parameters frequently demonstrates instability when applied to sparse datasets. This often necessitates ad hoc parameter clipping to prevent physically implausible tail behavior. Furthermore, the MLE approach provides limited uncertainty quantification and systematically underestimates risk at higher return periods. This study develops a Bayesian framework for GPD fitting for robust tail risk estimation of freezing rain hazard over North America.

We reconstruct ice accretion for historical event footprints from 43 years of ERA5 reanalysis data (1980–2022) using the Crawford et al. (2021) cyclone tracking algorithm. Freezing rain is identified using ERA5 precipitation type, and ice accretion is computed using the Jones (1998) formulation. Freezing rain occurrences within 1,500 km of tracked extratropical cyclone centers are aggregated into event-level accumulations. After systematic footprint cleaning to remove duplicates and truncated events, several hundred independent freezing rain events are obtained across the domain.

Bayesian GPD fitting is implemented using Markov Chain Monte Carlo (MCMC) sampling with weakly informative priors for the shape and scale parameters. Exceedance thresholds are defined as the 2-year return period level where statistically estimable; in data-sparse regions where the 2-year return period cannot be reliably determined, a minimum accumulation threshold is applied instead. We systematically compare Bayesian and MLE approaches through Event Exceedance Frequency (EEF) curves at multiple locations and return period maps across key economic exposure regions including the Northeast, Southern Plains, and Pacific Northwest, where freezing rain causes significant infrastructure damage.

Analysis indicates that the Bayesian approach yields smoother and more stable tail estimates. Return period maps from the Bayesian framework demonstrate substantially improved agreement with historical observations, with spatial clustering patterns that better capture known climatological gradients and topographic influences. The Bayesian fits demonstrate superior goodness-of-fit, particularly in the extreme tail, where divergence from MLE estimates is most pronounced. In data-sparse regions, particularly the southern United States, the Bayesian framework shows enhanced signal clarity and spatial consistency compared to MLE, which tends to suppress topographic and climatological signals. The Bayesian framework additionally provides full posterior distributions, enabling credible interval estimation that transparently communicates parameter uncertainty.

This methodology provides defensible tail risk estimates for stochastic winter storm models and demonstrates applicability to other sparse extreme event problems.