Underestimation of Frequent Floods when Using Annual Maxima for Frequency Analysis: Drivers, Spatial Variability, and Possible Solutions

Abstract

Because they are conceptually unable to consider events at the sub-annual scale, probabilistic flood analyses based on annual maxima (AM) underestimate the actual frequency of frequent floods (with return periods under 5 years), so that peaks-over-threshold (POT) approaches should be preferred. While this has been acknowledged for decades, frequent floods are still estimated too often using AM, probably because the procedure is simpler, and AM series are longer and easier to obtain. However, the negative bias incurred when performing flood frequency with AM can be severe. This affects fields such as river restoration, stream ecology, and fluvial geomorphology, which require a correct characterization of frequent floods. Using hundreds of U.S. watersheds with natural flow regimes, across different climatic and geomorphic conditions, we systematically study the variability in how AM frequency analyses underestimate frequent floods, finding clear spatial patterns. Exploiting the duality between the Generalized Extreme Value and the Generalized Pareto distributions (used for modeling AM and POT, respectively), we identify the drivers of frequent-flood underestimation, studying the influence of the distributions’ shapes. In turn, with the support of an optimal feature-selection technique, we determine the physical drivers explaining underestimation, from a wide spectrum of basin descriptors, investigating their linkages with the distributional characteristics that affect underestimation. A theoretical relationship is derived to infer the underestimation rate, allowing for post-hoc correction of AM-predicted frequent floods, without the need to perform POT frequency analyses. However, this approach underperforms at sites with mixed flood populations.