An application of power-law distributions to the tail of flood frequency data: a search for a physical connection in flood frequency statistics

Floods are natural phenomena that occur when river flow exceeds the capacity of the channel and spills over the banks, often posing danger to human life and causing significant damage. Over the past decades, many floods have occurred on the rivers of Iowa. Though these devastating events are rare, it is important to determine how often they occur. Because flood frequency is approximated based on exceedingly short streamflow records at gauging stations, calculating the chances of a certain magnitude flood is subject to large uncertainty. While standard engineering methods for estimating flood frequency exist and are used in infrastructure design and flood mitigation planning, efforts continue to determine more appropriate and potentially more accurate approaches. This thesis explored one such advance of applying a simple mathematical relation, known as power law, to describe the behavior of very large, infrequent floods. This study explored hydrological and statistical aspects of this approach applied to historical streamflow records observed at 62 gauging stations in Iowa. The results suggest that these large, rare floods are more likely to occur than what current standards predict.