Modeling the seasonality of extreme coastal water levels with mixtures of circular probability density functions

Understanding when floods occur is fundamental to reducing flood risk, yet depictions of flood seasonality rarely address two key issues: multiple seasons and the periodicity of seasonal data. We analyze the timing of extreme water levels at 47 presently operational tide gages located along the US coastlines with periods of record ranging from 29 to 118 years. Because the dates of extreme water levels are naturally multimodal periodic data, we model them with weighted mixtures of circular von Mises distributions. Fitting probability density functions on the circumference of a circle allow 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 modeling to coastal water levels. We find clear spatial patterns in extreme water level seasonality along the US coasts. Gages located on the West Coast 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 maximum flood likelihood in the late summer. Analysis of water level after removing tides and sea level change reduces the importance of secondary and higher seasons and yields greater uniformity compared with raw water levels. Finally, peaks-over-threshold datasets reveal secondary flood seasons that are obscured in annual maxima series, which may become increasingly impactful as sea levels rise. These findings are pertinent to coastal infrastructure design, risk sharing via financial instruments, and emergency preparedness and response.