Abstract Safe and cost-effective design of infrastructures, such as dams, bridges, highways, often requires knowing the magnitude and frequency of peak floods. The Generalized Extreme Value distribution ( G E V ) prevailed in flood frequency analysis along with distributions comprising location, scale, and shape parameters. Here we explore alternative models and propose power-type models, having one scale and two shape parameters. The Burr type III (ƁrIII) and XII (ƁrXII) distributions are compared against the G E V in 1088 streamflow records of annual peaks across Canada. A generic L-moment algorithm is devised to fit the distributions, also applicable to distributions without analytical L-moment expressions. The analysis shows: (1) the models perform equally well when describing the observed annual peaks; (2) the right tail appears heavier in the ƁrIII and ƁrXII models leading to larger streamflow predictions when compared to those of G E V ; (3) the G E V predicts upper streamflow limits in 39.1% of the records—these limits have realistic exceedance probabilities based on the other two models; (4) the tail heaviness estimation seems not robust in the G E V case when compared to the ƁrIII and ƁrXII models and this could challenge G E V ’s reliability in predicting streamflow at large return periods; and, (5) regional variation is observed in the behaviour of flood peaks across different climatic regions of Canada. The findings of this study reveal potential limitations in using the G E V for flood frequency analysis and suggest the ƁrIII and ƁrXII as consistent alternatives worth exploring.

中文翻译：

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重新审视洪水峰值分布：一项泛加拿大调查

摘要 水坝、桥梁、高速公路等基础设施的安全且具有成本效益的设计通常需要了解洪水高峰的大小和频率。广义极值分布 (GEV) 以及包括位置、规模和形状参数的分布在洪水频率分析中占主导地位。在这里，我们探索替代模型并提出具有一个尺度和两个形状参数的功率型模型。将 Burr 类型 III (ƁrIII) 和 XII (ƁrXII) 分布与加拿大 1088 年年度峰值流量记录中的 GEV 进行比较。设计了通用 L 矩算法来拟合分布，也适用于没有分析 L 矩表达式的分布。分析表明：（1）模型在描述观测到的年度峰值时表现同样出色；(2) 与 GEV 相比，ƁrIII 和ƁrXII 模型中的右尾看起来更重，导致更大的流量预测；(3) GEV 预测了 39.1% 的记录中的上游流量限制——这些限制具有基于其他两个模型的实际超出概率；(4) 与 ƁrIII 和 ƁrXII 模型相比，GEV 情况下的尾部重量估计似乎不可靠，这可能会挑战 GEV 在预测大重现期流量的可靠性；(5) 在加拿大不同气候区域的洪水高峰行为中观察到区域差异。这项研究的结果揭示了使用 GEV 进行洪水频率分析的潜在局限性，并建议 ƁrIII 和 ƁrXII 作为值得探索的一致替代方案。