Ryan Pittman

Date of Award

Fall 2021

Document Type

Open Access Dissertation

Department

Statistics

First Advisor

David B. Hitchcock

Second Advisor

John M. Grego

Abstract

On October 4, 2015, the Cedar Creek gage at Congaree National Park stopped reporting stages, and the readings did not resume until approximately two weeks later because of record-breaking rainfall that led to some of the worst flooding in South Carolina history. Our goal is to reconstruct the Cedar Creek stage during this missing two-week window. 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 as water travels through the local spillways and flood planes to connect the two locations. We introduce a new method called Landmark Aligned L1 (L AL1) distance to objectively determine the start and end points of each of the 10 flood events in the sample and then use these events to reconstruct the missing Cedar Creek stage. This alignment substantially improves the accuracy of the reconstruction and reduces the related prediction interval for the target event. We treat the stage as functional data and use a concurrent functional 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 from October 2015 is used to reconstruct the missing Cedar Creek stage during the 2015 flood. The results show that the novel L AL1 distance data selection method is effective, and that there is a strong functional relationship between the two locations. Based on our reconstruction, we estimate that the crest of Cedar Creek reached a historic high in October 2015, with stages exceeding 17 feet, compared to a previous high of just over 16 feet. Furthermore, the next aim of this project is to determine which of the functional observations are most influential to the fitted concurrent model and reconstruction/prediction. We modify preexisting linear regression measures of influence (DF F I T S, DF BET AS, Cook’s Distance) and create two additional metrics (∆ and AI P) to measure the sensitivity of the reconstruction and the impact of the known prior flood events. These functional measures can be used independently or in conjunction to identify the functional observations with the largest influence. Lastly, we introduce a weighted bootstrapping (with perturbations) method to approximate a null distribution for each influence measure to assess the significance level of the influence for each observation.

Rights

© 2021, Ryan Pittman

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