Misusing Langbein’s Equation when Predicting Low-Return-Period Extreme Events: A CONUS-Scale Investigation of Consequences on Frequent Flood Prediction

Abstract Submission: Annual maxima (AM) and partial duration series (PDS) frequency analyses (FAs) predict different frequency estimates of extreme events, expressed as return periods (T’s) and average recurrence intervals (ARIs), respectively. For large-return-period events, both methods yield similar results. However, for more frequent events (return periods of about ten years or less), AM-FA tends to predict larger T values compared to ARIs from PDS-FA, for the same event magnitude. Langbein’s theoretical equation allows converting AM-based T values into PDS-based ARIs and vice versa. PDS-FA is generally considered more appropriate for small, regular events, and many guidelines (e.g., Bulletin 17C, Atlas 14) recommend using PDS-FA, or at least adopting correction methodologies based on Langbein’s formula, to indirectly convert AM-based values into PDS-based estimates. Nonetheless, many U.S. estimates use uncorrected AM-FA for small-return-period events, especially in flood predictions. There is limited awareness of Langbein’s formula validity, despite empirical studies showing remarkable departures from the expected theoretical behavior, depending on geographic location. We analyze a large hydrologic dataset from several hundred basins across CONUS to investigate deviations between PDS- and uncorrected AM-based flood estimates, focusing on the influences of regional characteristics and Langbein’s formula validity. Our results indicate that climate is the main driver of variability in prediction deviations. Greater departures from Langbein’s theoretical behavior are observed in locations with mixed populations, where distinct major flood drivers coexist, violating the theoretical assumptions behind the formula.

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