A Statistical Method Similar to the Hershfield Method for Estimating Probable Maximum Floods in Ontario

The statistical Hershfield (1961) method has been widely used, as one of the standard methods, for the estimation of probable maximum precipitation (PMP). The PMP can then be used by a rainfall-runoff model to obtain the probable maximum flood (PMF). The PMF is one of the critical design factors for dam safety assessment and design of spillways.

An interesting question is: can this method be applied directly to streamflow statistics for the derivation of PMF? If the answer is yes, the next question is: what is the frequency factor that can be applied?

Based on an analysis using database of 391 streamflow stations in Ontario, it was found that the peak of the probable maximum floods can be estimated by the annual maximum flow’s mean and standard deviation with a suitable frequency factor. An equation of frequency factor as a function of the mean annual floods was developed. The derived PMF was compared to the database of 92 Ontario PMF estimations (Zhou, 2023). Using the drainage area size as the base variable, the two sets of PMF estimates provide comparable results when plotted on Creager Curve. This method allows a simplified way for estimation of the approximate magnitudes of PMF peak flows without going through the full PMP-PMF processes. The frequency factors are applicable for Ontario streams.

It is noted that although the extreme precipitation can be best represented by Gumbel distribution which is a light tailed frequency curve, the resulting extreme floods are best represented by Log Normal Distribution which is a heavy tailed distribution. For this reason, the frequency factors for PMF are higher than the frequency factors for PMP. The paper discusses the possible reasons.

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