On the use of Cox regression to examine the temporal clustering of flooding and heavy precipitation across the central United States

The central United States is plagued by frequent catastrophic flooding, such as the flood events of 1993, 2008, 2011, 2013, 2014 and 2016. The goal of this study is to examine whether it is possible to describe the occurrence of flood and heavy precipitation events at the sub-seasonal scale in terms of variations in the climate system. Daily streamflow and precipitation time series over the central United States (defined here to include North Dakota, South Dakota, Nebraska, Kansas, Missouri, Iowa, Minnesota, Wisconsin, Illinois, West Virginia, Kentucky, Ohio, Indiana, and Michigan) are used in this study. We model the occurrence/non-occurrence of a flood and heavy precipitation event over time using regression models based on Cox processes, which can be viewed as a generalization of Poisson processes. Rather than assuming that an event (i.e., flooding or precipitation) occurs independently of the occurrence of the previous one (as in Poisson processes), Cox processes allow us to account for the potential presence of temporal clustering, which manifests itself in an alternation of quiet and active periods. Here we model the occurrence/non-occurrence of flood and heavy precipitation events using two climate indices as time-varying covariates: the Arctic Oscillation (AO) and the Pacific-North American pattern (PNA). We find that AO and/or PNA are important predictors in explaining the temporal clustering in flood occurrences in over 78% of the stream gages we considered. Similar results are obtained when working with heavy precipitation events. Analyses of the sensitivity of the results to different thresholds used to identify events lead to the same conclusions. The findings of this work highlight that variations in the climate system play a critical role in explaining the occurrence of flood and heavy precipitation events at the sub-seasonal scale over the central United States.