Planning and Communicating Risk for Nonstationary Natural Hazards

This work investigates the probabilistic behavior of the time to occurrence of natural hazards that exhibit nonstationarity through time with special attention to floods. Chapter one combines existing theoretical and empirical results from the literature to provide the first general, comprehensive description of the probabilistic behavior of the return period and reliability under nonstationarity for the case of floods. Findings indicate that under nonstationarity, the underlying distribution of the return period exhibits a more complex shape than the exponential distribution under stationary conditions. Chapter two provides an introduction to the field of hazard function analysis (HFA) for flood events under nonstationary conditions, and demonstrates how HFA can be used to characterize the probability distribution of the return period and the reliability -- two primary metrics in hydrologic design. This is the first paper to explicitly link the probabilistic properties of a flood series (X) with failure times (T) associated with a particular infrastructure design. This work shows that HFA is a relevant and useful approach for characterizing nonstationary flood series, and can provide engineers with tools to support hydrologic design decisions under nonstationary conditions. Chapter three investigates the suitability of HFA to characterize a wide class of nonstationary natural hazards whose peaks over threshold (POT) magnitudes are assumed to follow the widely applied Generalized Pareto (GP) model. Such natural hazards might include: wind speeds, landslides, wildfires, precipitation, streamflow, sea levels, and earthquakes. The hazard function equations are derived for a natural hazard event series (X) whose POT follows the 2-parameter GP distribution. The derived model and HFA are used to compute reliabilities and average return periods associated with nonstationary behavior of the original hazard series. These generalized results for a wide class of natural hazards are consistent with the results in Chapters 1 and 2 for floods: nonstationarity adds complexity to computation of traditional design metrics and changes the shape of the probability distribution of the return period. General implications for planning and design of nonstationary natural hazards are discussed.