Extreme events, particularly flooding events, have devastating economic and social effects on the United States. These effects have led meteorologists, hydrologists, as well as statisticians, to study flooding and other extreme events using frequency analysis to estimate their likelihood of occurring. This information can be used as input to protect people and property. The concepts of return level and return period, derived from frequency analysis, were devised long ago to convey the risk of rare events for a stationary climate. It was shown that the traditional concepts of return level and return period are very volatile to a changing climate from the use of frequency analysis and by means of examples from two annual peak stream flow data sets. In order to effectively consider climate change, two possible extensions were developed, one based on the expected frequency of events and the other based on the expected waiting time until the next event.

It was also shown that these two ways of extending the concept of return level are far from equivalent through an example set of annual peak stream flow data used as an analog for climate change. More research is needed to learn which definition would be preferable to convey uncertainty about extreme events under climate change