An intensity–duration–frequency (IDF) curve describes the relationship between rainfall intensity and duration for a given return period and location. Such curves are obtained through frequency analysis of rainfall data and commonly used in infrastructure design, flood protection, water management, and urban drainage systems. However, they are typically available only in sparse locations. Data for other sites must be interpolated as the need arises. This paper describes how extreme precipitation of several durations can be interpolated to compute IDF curves on a large, sparse domain. In the absence of local data, a reconstruction of the historical meteorology is used as a covariate for interpolating extreme precipitation characteristics. This covariate is included in a hierarchical Bayesian spatial model for extreme precipitations. This model is especially well suited for a covariate gridded structure, thereby enabling fast and precise computations. As an illustration, the methodology is used to construct IDF curves over Eastern Canada. An extensive cross-validation study shows that at locations where data are available, the proposed method generally improves on the current practice of Environment and Climate Change Canada which relies on a moment-based fit of the Gumbel extreme-value distribution.

强度 - 持续时间 - 频率 (IDF) 曲线描述了给定重现期和位置的降雨强度和持续时间之间的关系。这些曲线是通过对降雨数据的频率分析获得的，通常用于基础设施设计、防洪、水管理和城市排水系统。但是，它们通常仅在稀疏的位置可用。其他站点的数据必须根据需要进行插值。本文描述了如何对几个持续时间的极端降水进行插值，以计算大型稀疏域上的 IDF 曲线。在没有当地数据的情况下，历史气象学的重建被用作插值极端降水特征的协变量。该协变量包含在极端降水的分层贝叶斯空间模型中。该模型特别适合协变量网格结构，从而实现快速和精确的计算。例如，该方法用于构建加拿大东部的 IDF 曲线。一项广泛的交叉验证研究表明，在数据可用的地方，所提出的方法通常改进了加拿大环境和气候变化部的当前实践，该实践依赖于 Gumbel 极值分布的基于矩的拟合。