2. Statistical Methods for Nonstationary Extremes

There is a long tradition of the use of methods based on the statistical theory of extreme values in hydrology, particular for engineering design (e.g., for the proverbial “100-yr flood”). For the most part, these methods are based on the assumption of stationarity (i.e., an unchanging climate in a statistical sense). The focus of this chapter is on how the familiar distributions that arise in extreme value theory, namely the generalized extreme value (GEV) and generalized Pareto (GP) distributions, can be retained under nonstationarity. But now the extremal distribution is allowed to gradually shift by introducing time as a covariate; that is, expressing one or more of the parameters of the distribution as a function of time. At least for the parameter estimation technique of maximum likelihood, it is straightforward to fit such statistical models. Some detailed examples are provided of how the proposed methods can be applied to the detection and statistical modeling of trends in hydrologic extremes, such as for stream flow and precipitation.