Copula-based modeling of earthen levee breach due to overtopping

The level of protection offered by an earthen levee is typically described in terms of flood water level that the levee is capable of containing. If a larger flood occurs, floodwaters exceed the height of the levee and flow over its crest. As the water passes over the top, it may erode the levee, worsening the flooding and potentially causing a breach. In order to determine the annual probability that an earthen levee breaches due to overtopping, multiple flood characteristics such as peak flood water level, or related peak flow discharge, and flood duration need to be characterized statistically by using multivariate statistics. In this study, critical conditions for levee failure are described by using a Clayton copula relating peak flow discharge to flood duration. The obtained model is tested over a real river site located along the Panaro River, in northern Italy, where a 52-year time series of hourly flow discharge and a normal flow rating curve are available. The developed model makes it possible to delimitate the levee failure region within the population of flood events and to statistically describe earthen levee breach due to overtopping. Breach probability is found to be underestimated when the statistical association between peak flow discharge and flood duration is neglected. The proposed copula-based model is therefore important to support the design and construction of earthen levees, and to identify the actions needed to save lives and property when a flood exceeding the levee design limit occurs.