Modeling the Seasonality of Extreme Coastal Water Levels with Mixtures of Circular Probability Density Functions

Managing the risk of concurrent events, such as coastal surges occurring simultaneously with riverine floods, requires understanding when each class of events is most likely to occur within the year. However, analyses of flood seasons rarely address the issues of multiple seasons or the periodicity of seasonal data, yielding results that may be simplified, confusing, or awkward to use. We analyze the timing of extreme coastal water levels at 47 presently operational tide gages located along United States coastlines with periods of record ranging from 29 to 118 years. Because the dates of floods are naturally multimodal, periodic data, we model them with weighted mixtures of circular von Mises distributions. Projecting data onto the circumference of a circle rather than a number line allows periodicity to be handled implicitly, while mixture models provide insight into the timing and importance of the various modes in the overall distribution. To our knowledge, this is the first application of circular statistical models to coastal water levels.

We find clear spatial patterns in the seasons of floods along U.S. coasts. Gages located on the West Coast typically experience their main flood season in the winter and a secondary season in the summer, while those on the East and Gulf coasts have more uniform distributions, fewer seasons, and their greatest flood likelihood in late summer. Analysis of water levels after removal of tides and sea level change (i.e. "storm surge") reduces the importance of secondary and higher seasons and yields greater uniformity of arrival time compared to raw water levels. Finally, peaks-over-threshold datasets reveal secondary flood seasons that are obscured in annual maxima analyses, which may become increasingly impactful as sea levels rise. These findings are pertinent in analysis of coastal floods alone or as components of concurrent floods, and can inform the design of coastal infrastructure, risk sharing via financial instruments, and emergency preparedness and response.