A hierarchical Bayesian model of storm surge and total water levels across the Great Lakes shoreline – Lake Ontario

Abstract

This study presents a novel approach to determine the distribution of compound flood events composed of storm surge and static water levels along the Great Lakes shoreline. A mixture distribution of the bulk (Student-t) and tail (GPD-negative binomial) components of storm surge is estimated in a hierarchical Bayesian modeling framework. Parameters are modeled across the entire shoreline using Gaussian processes and hourly gauged data, with priors for spatial autocorrelation informed by numerical output from a lake hydrodynamic model. The distribution of total water levels is obtained through Monte Carlo sampling that combines the estimated distribution of surge with stochastic traces of static lake levels that account for water level management, seasonality, and plausible variability in water supplies. The approach can therefore support coastal flood risk assessments in cases when the distribution of static water levels changes are due to altered water level management or climate change. The model is applied in a case study on Lake Ontario. Results suggest that spatial variability in parameter estimates varies significantly by month and mixture distribution component. Evaluations of performance indicate the model is able to capture adequately storm surge behavior at gauges across the lakeshore, even under cross-validation. A frequency analysis of total water levels at two ungauged sites is presented, with specific attention given to the implications of model assumptions on uncertainty in design events. The paper concludes with a discussion of model limitations and avenues for future work.