Annual Extreme Lake Elevations by Total Probability Theorem
HYDROLOGIC ENGINEERING CENTER DAVIS CA
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Annual extreme water levels on the Great Lakes, whether maximums or minimums, have a high serial dependence. Therefore, application of traditional frequency analysis techniques must be interpreted in a different manner and more sophisticated statistical techniques must be applied to account for this dependence. The terms Percent Chance Exceedence and Return Period are applied to the expectation values of annual extreme events that are random in nature and have an equal liklihood of occurring in any given year. Annual extreme lake elevations on the Great Lakes are not random from one year to the next therefore, the usual terms to define the expectation should not be used to describe events. An acceptable term is Percent of Years Exceeded. This is comparable to the label Percent to Time Exceeded that is applied to flow- or elevation-duration curves. Decomposition of the annual extremes into two parts, one containing the highly dependent part and the other containing the random part, is one method of dealing with the dependence in the lake elevations. Appropriate statistical analyses can be applied to the separate parts and then the individual results combined to obtain the final frequency relation. This study develops mean monthly lake elevation duration curves to represent the dependent part and wind setup frequency curves for random part. These parts are then combined by application of the total probability theorem.
- Hydrology, Limnology and Potamology