Stationarity, variability and change in hydrologic extremes

In one sense climate may be considered as the entire set of descriptive statistics of the atmosphere over some interval of interest. The tails of the frequency distributions have great influence on human structures and systems and on the function of natural systems. Hydrologic extremes at both the wet and dry tails, floods and droughts, likewise produce disproportionate physical and economic consequences. Much design attention is focused on survivability of extreme conditions. As climate fluctuates through time, the probability distributions from which the climate system "selects" events also fluctuate. We cannot generate these distributions from first principles, and thus do not know their true theoretical shapes. Therefore our knowledge of their shapes is based on empirical evidence, in the form of observations from the past. In practical terms these statistics are often represented as IDF (intensity-duration-frequency) curves. It is still not clear how well one might expect distributions from climate models to replicate distributions from observations. These distributions are typically highly non-normal, and indeed in hydrology are heavy-tailed. It is not known for certain whether atmospheric models are intrinsically capable of generating heavy tails, but evidence suggests they cannot. However, it may be possible to post-treat model output to create heavy tails. From various types of evidence we know that the likelihood of extremes does vary through time, sometimes considerably. There are also indications that climate change induced by human activity will lead to changes in extreme behavior and in the shape and location of IDF curves. Although stationarity has been a common assumption in engineering design, this presumption does not appear to have a firm theoretical basis, and has been much discussed through time. Guidelines for the engineering profession (e.g. Bulletin 17B) do contain "escape clauses" for addressing the possibility of nonstationarity. Difficulties in communicating these ideas to public and professional audiences may stem from differing definitions and from differing concepts about time scales. These time scales refer to both the expected lifetime of a structure, and to the time scales on which climate and its driving mechanisms and feedbacks fluctuate. A general expectation, widely expressed, is that hydrologic extremes will become "more extreme" or that extremes of a given magnitude will become more frequent. However, there have been few studies of how well models reproduce current IDF curves, and therefore we have unknown confidence in the accuracy of projections of how these might evolve over the next century.