Seventy-Five Years Underestimating Frequent Events and Other Frequently Underestimated Implications of Langbein's Equation

It is seldom realized that whether one uses annual maxima (AM) or partial duration (PD) series for frequency analysis has major implications when predicting the magnitudes and probabilities of smaller, frequently recurring geophysical events. Langbein's seminal 1949 article on "Annual Floods and the Partial-Duration Series" elucidated the differences between the two approaches, providing a theoretical relationship between AM-based return periods and PD-based average recurrence intervals that applies not only to floods but also to other processes modeled using either AM or PD series, such as wind gusts, rain depths, and wave heights. He observed that "& mldr; for equivalent floods (i.e., of the same magnitude), the recurrence intervals in the partial-duration series are smaller than in the annual-flood (AM) series," and that they "& mldr; differ markedly for the smaller or more frequent floods, but are nearly equal for the higher floods," concluding that PD is more appropriate for capturing the actual frequency of occurrence of smaller events. Yet 75 years (and more than 400 citations) later, many still predict frequent events based solely on AM series, while others invoke Langbein's equation to somehow convert AM-based estimates into PD-based estimates. However, when both AM and PD frequency analyses are concurrently performed on geophysical data sets, departures from Langbein's relationship are often observed, suggesting limitations in the underlying assumptions of the formula. These considerations affect various engineering and scientific fields where accurate estimation of frequent, low-recurrence-interval events is needed, underscoring potential biases and misconceptions in many current estimates of such occurrences.