Peaks-Over-Threshold Flood Analysis

Annual-maximum analysis keeps one peak — the largest — per year and fits a GEV (or log-Pearson III) distribution. Peaks-over-threshold keeps every independent peak above a high threshold, however many fall in a given year, and models occurrences as a Poisson process and magnitudes as a Generalized Pareto distribution. The two are equivalent in the asymptotic limit and should give similar high-return-period floods, but POT uses more of the data and typically has lower estimation variance at short return periods. The cost is that POT requires a continuous record and the additional steps of threshold selection and declustering.

Threshold selection is a bias-variance trade-off: too low and the asymptotic Generalized Pareto approximation fails (bias); too high and too few peaks remain (variance). The standard tools are the mean residual life (mean excess) plot, which should become approximately linear above a valid threshold, and threshold-stability plots, where the shape parameter and the modified scale should be roughly constant above the right level. A common practical starting point is to choose a threshold yielding on the order of one to three independent peaks per year, then confirm with the diagnostics.

The Generalized Pareto and Poisson models assume the over-threshold peaks are independent events. A single flood, however, can cross the threshold, recede slightly, and cross again, producing several correlated exceedances that belong to one event. Declustering keeps only one representative peak per genuine flood, typically by requiring a minimum time gap between retained peaks and a sufficient drop in flow between them. Without declustering the occurrence rate is overstated and the fitted distribution is distorted, so independence criteria are as important to get right as the threshold itself.