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WATER LEVEL EXTREMES AND DISTRIBUTIONAL ANALYSIS Measured Water Levels (i.e. storm surge, lake level, river stage, etc.) are often utilized for estimation of Return Periods of extreme events. As a related example, often the Log Pearson Type III distribution is utilized in fitting extreme values of river "flood flows" and corresponding return periods of the "flows". Various distributions exist (i.e. Gumbel, Frechet, Weibull, Log-Normal, Poisson-Pareto, etc.) with which to assess corresponding water levels although there is no recommended approach apriori. It is left to the judgement of "reviewers" as to the proper choice of frequency distribution to utilize in assessing the Return Periods for the extreme water levels at a given site. As benefit-cost ratios for various projects are highly dependent on assessment of the "Return Period" of higher events (which is functionally related to the distribution chosen) , a thorough analysis of various distribution fits may be beneficial to proper project design and economic analysis. Two cumulative frequency distribution fits are provided below for one long term record of water level at a coastal site. In the approach shown, the distribution fits have been made in "observation" space where the measured surge (in meters) is shown on the plot ordinate scale and the inverse of the Cumulative Frequency Distribution (in meters) is shown on the plot abscissa scale. This type of data fitting procedure allows for a much better judgement of "adequacy of fit" for the higher observations in the "upper tail" of the frequency distribution. The solid line is the "theoretical distribution" using the "estimated" parameters of the distribution. The circles are the "observed" maximas of the (surge) water level in a given time period (typically yearly). Note that although the plots seem similar, there are considerable differences in the "Return Periods" of the higher events depending on the distribution chosen.
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