Modeling River Flood Seasonality with Mixtures of Circular Probability Density Functions

Abstract:

Managing flood risk, whether via infrastructure design, financial instruments, or early warning, requires knowledge of when floods are most likely to occur. Yet statistical models of the arrival times of floods rarely address the natural periodicity of these data or the possibility of multiple flood seasons. As a result, estimates of flood season may be biased, incomplete, or difficult to communicate to the public. We analyze the timing of flood arrivals at 4505 streamgages in the United States with at least 90% hourly completeness in 25 of the most recent 30 years. Because the dates of floods are naturally multimodal, periodic data, we model them as weighted linear combinations of circular von Mises distributions. Modeling these data on the circumference of the circle rather than the number line allows periodicity to be handled implicitly, without the need for defining local water years a priori, while mixture models allow fitting of distributions with multiple flood seasons. For locations with multimodal distributions of flood season, we developed a framework to rank seasons by significance based on their apex flood arrival probability and length of season. This is, to our knowledge, the first application of mixture models of circular distributions to the characterization of river flood seasons.

Our results show clear spatial patterns in the seasonality of floods in the United States. Primary flood seasons exhibit spatial clustering, as do secondary and tertiary seasons, when they exist, and locations exhibiting circular uniformity rather than any statistically significant season. The spatial patterns of flood seasons vary for floods defined on the basis of annual streamflow maxima compared to those defined using peaks over threshold. Furthermore, spatial patterns of flood season depend on flood magnitude, as evidenced by variations in pattern when comparing flood events which exceed the thresholds necessary to yield one, two, or four events per year on average. These findings are valuable to decision-makers who require information on when floods are likeliest, and provide a method for summarizing and communicating this information to the public in a concise and understandable way.