Estimating Terminal Lake Level Frequencies

Abstract

A reliable method of predicting long‐term future lake levels with associate exceedance frequencies is essential to establish planning elevations in the lakeshore environment. A methodology is proposed here to develop level‐frequency relationships for terminal lakes. The methodology is applied to Devils Lake, North Dakota. An autoregressive moving average (ARMA) model with a deterministic trend component for the annual storage changes is used as the basis. The storage changes are derived from the historical annual average level time series, and the level‐storage relationship. Using the validated ARMA model and simulation techniques, many sequences of annual incremental storage time series are generated. The concepts of mass curve and range analysis are applied to each synthetic sequence for deriving maximum and minimum lake volumes in each sequence. The resulting set of maximum and minimum lake volumes are then analyzed for their underlying frequency distributions. Utilizing the elevation‐storage function, the lake volume‐frequency relationship is converted to an annual average lake level‐frequency relationship. A separate treatment of within‐year maximum fluctuations about the average level is also developed. Both the average level and within‐year maximum fluctuation distributions represent the stochastic behavior of the lake and thus are found to be necessary to the development of the level‐frequency relationship.