Mixed Flood Distributions in Wisconsin

Abstract

Traditional flood frequency analysis is predicted on the assumption that the annual flood series can be considered to be a sample from a single population. In Wisconsin this is not a valid assumption. Wisconsin floods are of two types, which are hydrologically and statistically distinct.

An analysis of the time of occurrence of Wisconsin floods indicates two dominant flood seasons: spring and summer. Late May is the boundary between these two seasons.

Using May 20 as the date of separation, we constructed parallel spring and summer flood series for all Wisconsin partial flood series with ten or more years of record (29 series). (A seasonal series is the series of largest spring floods from each year of record.) Based on two-sample Kolmogorov-Smirnov test the hypothesis that spring and summer floods are identically distributed was rejected for 18 of the 29 pairs of flood series at the 5 percent significance level and for 23 pairs of flood series at the 10 percent significance level. We interpret this as convincing evidence that spring and summer floods in Wisconsin generally have distinct statistical distributions.

An analysis of runoff data for eight of the 29 partial series gages demonstrates that the spring and summer floods in Wisconsin are also hydrologically distinct. Spring floods show relatively high runoff precipitation ratios.

Future work is needed, both to better understand the hydrology of spring and summer floods and to determine if and how this understanding can improve quantile estimation.