Interpolation of Precipitation Extremes on a Large Domain Toward IDF Curve Construction at Unmonitored Locations

Abstract

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.

Convection‐Permitting Climate Models Can Support Observations to Generate Rainfall Return Levels

“…In addition, climate models calculate area averages for grid cells, while in contrast rain gauges only represent measurements at one point leading to higher variability (Schroeer et al., 2018). Fixing the shape parameter for the pointwise GEV and assuming a single shape parameter across space for the spatial GEV models restricts the GEV to a 2‐parameter distribution, which also implies less flexibility, where the shape parameter mainly accounts for the high return periods in the tail of the GEV (Jalbert et al., 2022). Though, the evaluation of the spatial GEV model based on the pointwise GEV has to be carefully interpreted.…”

“…There is no widely used framework to combine information from observations and climate models with respect to extreme precipitation. Jalbert et al (2022) newly propose a Bayesian hierarchical framework to interpolate GEV parameters based on precipitation observations and the Canadian Regional Climate Model version 5 (CRCM5) driven by ERA-INTERIM reanalysis data at 12 × 12 km 2 resolution. In the Bayesian hierarchical framework, they assume the pointwise rainfall maxima to follow a GEV distribution.…”

“…In contrast to Jalbert et al. (2022), we apply smooth spatial GEV models (Blanchet & Lehning, 2010), which estimate smooth trend surfaces for the GEV parameters from the observational data and covariates. We apply them in a smaller domain with a very dense monitoring network at a 1.5 km resolution.…”

“…We generate spatial GEV models for observed daily extreme rainfall Water Resources Research 10.1029/2023WR035159 in southern Germany using information from the high-resolution convection-permitting Weather Research and Forecasting (WRF) model driven by ERA5 reanalysis (Hersbach et al, 2020) as covariates. In contrast to Jalbert et al (2022), we apply smooth spatial GEV models (Blanchet & Lehning, 2010), which estimate smooth trend surfaces for the GEV parameters from the observational data and covariates. We apply them in a smaller domain with a very dense monitoring network at a 1.5 km resolution.…”

Smooth copula‐based generalized extreme value model and spatial interpolation for extreme rainfall in Central Eastern Canada

“…Even given the scarce aspect of the dataset, the obtained results show a robust performance with the considered smooth Generalized Extreme Value (GEV) distribution fitting methods. The same dataset has been analyzed in Perreault et al (2022) where a Bayesian hierarchical interpolation model is proposed with the spatial effect modeled via Gaussian Markov random fields (see, e.g., Rue & Held, 2005). Results of Section 4 can be compared with those of Perreault et al (2019).…”