Hazard function analysis for flood planning under nonstationarity

The field of hazard function analysis (HFA) involves a probabilistic assessment of the “time to failure” or “return period,” T , of an event of interest. HFA is used in epidemiology, manufacturing, medicine, actuarial statistics, reliability engineering, economics, and elsewhere. For a stationary process, the probability distribution function (pdf) of the return period always follows an exponential distribution, the same is not true for nonstationary processes. When the process of interest, X , exhibits nonstationary behavior, HFA can provide a complementary approach to risk analysis with analytical tools particularly useful for hydrological applications. After a general introduction to HFA, we describe a new mathematical linkage between the magnitude of the flood event, X , and its return period, T , for nonstationary processes. We derive the probabilistic properties of T for a nonstationary one‐parameter exponential model of X , and then use both Monte‐Carlo simulation and HFA to generalize the behavior of T when X arises from a nonstationary two‐parameter lognormal distribution. For this case, our findings suggest that a two‐parameter Weibull distribution provides a reasonable approximation for the pdf of T . We document how HFA can provide an alternative approach to characterize the probabilistic properties of both nonstationary flood series and the resulting pdf of T .