Title: Generalizations of Langbein's Formula under Non-Stationarity, Mixed Populations, and Over- or Under-Dispersion in the Number of Exceedances Show Chinese title

Title: 非平稳性、混合种群以及超出次数的过度或不足离散情况下的Langbein公式推广

Abstract: Since its publication in 1949, Langbein's formula has been applied ubiquitously in both research documents and national guidelines concerning frequency analyses (FAs) of hydrologic extremes. Given a time series of independent peak-over-threshold (POT) events and the corresponding annual maxima (AM) series-defined as the subset of extremes representing the largest event in each year-the formula provides a theoretical relationship between the return period T derived from the AM series and the average recurrence interval ARI from the POT series, for any fixed event magnitude. Despite the minimal assumptions required-specifically, that exceedance counts follow a homogeneous Poisson process-there are real-world situations where the validity of the formula may be compromised. Typical cases include non-stationary processes, mixed-event populations, and over- or under-dispersion in exceedance counts. In this work, we extend Langbein's formula to account for these three cases. We demonstrate that, with appropriate adaptations to the definitions of T and ARI, the traditional functional form of Langbein's relationship remains valid for non-stationary processes and mixed populations. However, accounting for dispersion effects in exceedance counts requires a generalization of Langbein's relationship, of which the traditional version represents a limiting case. Show Chinese abstract

Abstract: 自1949年发表以来，Langbein公式已被广泛应用于研究文献和关于水文极端事件频率分析（FAs）的国家指南中。 给定一个独立的超过阈值（POT）事件的时间序列以及相应的年最大值（AM）序列——定义为代表每年最大事件的极端值子集——该公式提供了从AM序列得出的重现期T与从POT序列得出的平均重现间隔ARI之间的理论关系，对于任何固定的事件强度。 尽管所需的假设最少——即超过次数遵循同质泊松过程——但在某些现实情况中，公式的有效性可能会受到损害。 典型的例子包括非平稳过程、混合事件群体以及超过次数的过度或不足分散。 在本研究中，我们将Langbein公式扩展以考虑这三种情况。 我们证明，通过适当调整T和ARI的定义，Langbein关系的传统函数形式对于非平稳过程和混合群体仍然有效。 然而，考虑超过次数中的分散效应需要对Langbein关系进行推广，传统版本是其中的一个极限情况。