Reliability, return periods, and risk under nonstationarity

Water resources design has widely used the average return period as a concept to inform management and communication of the risk of experiencing an exceedance event within a planning horizon. Even though nonstationarity is often apparent, in practice hydrologic design often mistakenly assumes that the probability of exceedance, p, is constant from year to year which leads to an average return period To equal to 1/p; this expression is far more complex under nonstationarity. Even for stationary processes, the common application of an average return period is problematic: it does not account for planning horizon, is an average value that may not be representative of the time to the next flood, and is generally not applied in other areas of water planning. We combine 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. We show that under nonstationarity, the underlying distribution of the return period exhibits a more complex shape than the exponential distribution under stationary conditions. Using a nonstationary lognormal model, we document the increased complexity and challenges associated with planning for future flood events over a planning horizon. We compare application of the average return period with the more common concept of reliability and recommend replacing the average return period with reliability as a more practical way to communicate event likelihood in both stationary and nonstationary contexts.