Climate change poses several issues for the statistical modeling of extremes. One issue concerns how to introduce non-stationarity into extreme value distributions for extreme weather and climate variables. The most common approach entails using time as a covariate through one or more of the parameters of extreme value distributions. For precipitation (with an apparent heavy tail and high variation on small spatial and temporal scales), this approach is usually unable to detect trends when applied to single sites. Rather, borrowing strength across space (termed regional analysis in hydrology) will be necessary, but would require accounting for the spatial dependence of extremes.
Another issue concerns what is an appropriate measure of the risk of non-stationary extreme events (e.g., for use in engineering design). Under a stationary climate, the risk of extreme events is usually measured in terms of a return level with a specified return period (i.e., a high quantile such as the so-called "100-year flood"). Under nonstationarity, I advocate abandoning the concept of return level and, instead, using the Design Life Level, a measure based on a desired "risk of failure" over a specified design period. The Design Life Level corresponds to a high quantile of the distribution of the maximum of the variable over the design period. For illustrative purposes, two real-world examples are used, one involving peak streamflow and another precipitation extremes.