Use of Generalized Extreme Value Covariates to Improve Estimation of Trends and Return Frequencies for Lake Levels

One of the most important tools in water management is the accurate forecast of both long-term and short- term extreme values for both flood and drought conditions. Traditional methods of trend detection, such as ordinary least squares (OLS) or the Mann-Kendall test, are not aptly suited for hydrologic systems while traditional methods of predicting extreme flood and drought frequencies, such as distribution fitting without parameter covariates, may be highly inaccurate in lake-type systems, especially in the short-term. In the case of lakes, traditional frequency return estimates assume extremes are independent of trend or starting lake stages. However, due to the significant autocorrelation of lake levels, the initial stage can have a significant influence on the severity of a given event. The aim of this research was to accurately identify the direction and magnitude of trends in flood and drought stages and provide more accurate predictions of both long-term and short-term flood and drought stage return frequencies utilizing the generalized extreme value distribution with time and starting stage covariates. All of the lakes researched evidenced either no trend or very small trends unlikely to significantly alter prediction of future flood or drought return levels. However, for all of the lakes significant improvement in the prediction of extremes was obtained with the inclusion of starting lake stage as a covariate. Traditional methods of predicting flood or drought stages significantly overpredict stages when starting lake stages are low and underpredict stages when starting stages are high. The difference between these predictions can be nearly two meters, a significant amount in urbanized watersheds in areas of the world with flat topography. Differences of near two meters can mean significant alterations in evacuation or other water management decisions. In addition to improving prediction of extreme events, utilizing GEV with time or starting stage covariates can provide guidance in lake management decisions in regards to how much water to release from a lake in preparation for an approaching hurricane, appropriate lake levels to maintain throughout the year or determining minimum structure floor elevations in the watershed and allow more accurate forecasting of future water supply or impacts to tourism. The methods utilized in this research to determine lake level return period of flood and drought can be applied to nearly any region globally.