Modeling riverine flood seasonality with mixtures of circular probability density functions

Preparing for and minimizing the negative impacts of flooding requires knowing when floods are likely to occur. However, exploratory analysis of seasons may yield spurious conclusions, and models of flood seasonality can be misleading if they fail to account for the cyclical nature of flood data or the possibility of multiple flood seasons in a year. We modeled the arrival times of floods at 4,505 sites along rivers in the United States using statistical models comprised of weighted combinations of circular von Mises distributions. Circular distributions address the periodicity of arrival time data, while mixture models provide the flexibility to fit multiple seasons and a validation framework to test their significance. Nearly half of all sites we modeled optimized with at least a secondary flood season, a fact hidden by analyses that neglect or conflate multiple seasons. We found spatiotemporal patterns in the modeled dates of elevated flood hazard, which point to common flood-generating mechanisms. Partitioning sites by their modeled flood seasonalities yielded 6–7 clusters of sites along United States rivers with similar flood season numbers, dates, and durations. Results varied depending on whether floods were defined by annual maxima or peaks-over-threshold, and on the threshold chosen. Models of river flood seasonality and the spatial patterns they reveal are potentially useful in informing the timing of infrastructure maintenance, in risk-sharing via financial instruments, and in estimating the likelihood of compound events.