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Declustering groups dependent threshold exceedances into extreme-event clusters and retains a representative, commonly the cluster maximum. It aims to make the events used in a peaks-over-threshold method approximately independent. The event rate must be estimated consistently with the retained clusters when computing return levels.

A 100-year return level is a flow threshold whose probability of being exceeded in a given year is one percent, under a stationary model for annual extremes. Equivalently, its long-run average waiting time between years with an exceedance is one hundred years. It does not imply that exceedances occur regularly one hundred years apart, or that one is guaranteed in any particular hundred-year interval. This definition uses yearly exceedance events even when the underlying observations are daily maxima.

In the original PDF's probability plot, most points lie close to the diagonal. The quantile plot likewise agrees well over most of the range, but the largest empirical flow, around $68.5$, is well above its fitted quantile, around $66$. The density plot captures the strongly decreasing right-skewed bulk of the excesses. The return level plot shows a broadly reasonable fit to most observations, with one conspicuously high extreme and increasingly wide uncertainty at long return periods. Consequently the generalized Pareto distribution is a reasonable first approximation, but its most extreme tail is less convincingly represented.

Reading the return-level curve at the 100-year tick givesThese are approximate graphical readings, not parameter-based calculations; rounding to whole units would give about $67$ with an interval roughly $65$ to $69$. The two blue curves are uncertainty bounds for the fitted return level, not prediction bounds for individual observations. The daily-data independence assumption and the stability of the fit as the threshold changes should be checked, for example by examining clusters of high flows and using declustering of extremes where necessary. A 100-year level also extrapolates beyond the 25-year record.

For the geometric distribution supported on positive integers, set $q=1-p$. The geometric series and its derivative giveEquivalently, the sum of the tail probabilities is ${\sum }_{k\ge 0}P(T>k)={\sum }_{k\ge 0}{q}^k=1/p$. For $p=0.02$, the expected wait is 50 years, so this is the 50-year return level. The exceedance probability determines the return period, but does not by itself determine a numerical flow rate.

The peaks-over-threshold method fits a generalized Pareto distribution to exceedances of a high threshold and also estimates their frequency. Together these determine tail probabilities and return levels. For dependent observations, threshold exceedances may occur in clusters; declustering of extremes can separate extreme events before fitting a model for independent events.

A return level plot shows estimated return levels against their return periods, often on a logarithmic horizontal axis. Confidence curves describe uncertainty in estimated return levels. They are not prediction bands for individual extreme observations, and uncertainty typically increases when extrapolating far beyond the observation window.