Concurrent functional regression to reconstruct river stage data during flood events

Abstract

On October 4, 2015, the Cedar Creek gage at Congaree National Park stopped reporting stages, and the readings did not resume until approximately 2 weeks later because of record-breaking rainfall that led to some of the worst floodings in South Carolina history. Our goal is to reconstruct the Cedar Creek stage during this missing 2-week window. Our analysis uses a sample of ten historical flood events from the last 25 years. The Congaree River gage in Congaree National Park remained functioning throughout the October 2015 flood, when the stage reached its maximum recorded crest. The stages from the two gages are directly related during floods. We introduce a new method to objectively determine the start and end points of each flood event in the sample and then use these events to predict the missing Cedar Creek stage. We treat the stage as functional data and use a concurrent model to establish the relationship between the two locations during each timepoint of prior flood events. Once this relationship is found, the known Congaree stage is used to predict the missing Cedar Creek stage during the 2015 flood. The results show that there is a strong functional relationship between the two locations, and that the crest of Cedar Creek is a historic high, reaching stages above 17 feet, with a previous high of just over 16 feet.