The effect of clustering of flood peaks on a flood risk analysis for the Red River

Abstract

The nearly 100 year record of spring flood peaks on the Red River at Winnipeg, Manitoba, shows a clustering of high annual peak flows that is possibly, but not likely, due to chance. A similar degree of clustering has been observed in other long-term geophysical records. It can be measured by means of the Hurst statistic. Clustering increases the uncertainty in the parameters of the probability distribution of peak flows estimated from the record. As such it profoundly affects the weight that must be given to the unusually high historical floods that preceded the period of record, in particular the 1826 and the 1852 floods. Incorporating this historical information in the probability analysis requires a time series model that tends to produce the appropriate degree of clustering. A fractional noise model was adopted for this purpose. Bayes' theorem was then used to update the distribution parameters, obtained from the record, with the additional information about the historical floods. The result shows the flood risk to the City of Winnipeg and the Red River Valley to be substantially higher than was estimated by conventional methods that assume serial independence of the peak flows. Key words: Red River floods, flood risk, historical floods, Hurst phenomenon, fractional noise, Bayesian probability distribution, Bayesian updating, time series.