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June 2022 Approximate Bayesian inference for analysis of spatiotemporal flood frequency data
Árni V. Jóhannesson, Stefan Siegert, Raphaël Huser, Haakon Bakka, Birgir Hrafnkelsson
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Ann. Appl. Stat. 16(2): 905-935 (June 2022). DOI: 10.1214/21-AOAS1525


Extreme floods cause casualties and widespread damage to property and vital civil infrastructure. Predictions of extreme floods, within gauged and ungauged catchments, is crucial to mitigate these disasters. In this paper a Bayesian framework is proposed for predicting extreme floods, using the generalized extreme-value (GEV) distribution. A major methodological challenge is to find a suitable parametrization for the GEV distribution when multiple covariates and/or latent spatial effects are involved and a time trend is present. Other challenges involve balancing model complexity and parsimony, using an appropriate model selection procedure and making inference based on a reliable and computationally efficient approach. We here propose a latent Gaussian modeling framework with a novel multivariate link function designed to separate the interpretation of the parameters at the latent level and to avoid unreasonable estimates of the shape and time trend parameters. Structured additive regression models, which include catchment descriptors as covariates and spatially correlated model components, are proposed for the four parameters at the latent level. To achieve computational efficiency with large datasets and richly parametrized models, we exploit a highly accurate and fast approximate Bayesian inference approach which can also be used to efficiently select models separately for each of the four regression models at the latent level. We applied our proposed methodology to annual peak river flow data from 554 catchments across the United Kingdom. The framework performed well in terms of flood predictions for both ungauged catchments and future observations at gauged catchments. The results show that the spatial model components for the transformed location and scale parameters as well as the time trend are all important, and none of these should be ignored. Posterior estimates of the time trend parameters correspond to an average increase of about 1.5% per decade with range 0.1% to 2.8% and reveal a spatial structure across the United Kingdom. When the interest lies in estimating return levels for spatial aggregates, we further develop a novel copula-based postprocessing approach of posterior predictive samples in order to mitigate the effect of the conditional independence assumption at the data level, and we demonstrate that our approach indeed provides accurate results.

Funding Statement

The research of one of the authors was partially supported by the University of Iceland Research Fund.


We would like to thank the National River Flow Archive (NRFA, for making the peak flow data series and the catchment descriptors available. We thank Ilaria Prosdocimi and Thomas Kjeldsen for fruitful conversations about these data. We thank Håvard Rue for constructive conversations about ideas on the asymptotic variance. Finally, we thank the Editor, the Associate Editor, and two anonymous reviewers for their careful reading and helpful comments.


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Árni V. Jóhannesson. Stefan Siegert. Raphaël Huser. Haakon Bakka. Birgir Hrafnkelsson. "Approximate Bayesian inference for analysis of spatiotemporal flood frequency data." Ann. Appl. Stat. 16 (2) 905 - 935, June 2022.


Received: 1 July 2020; Revised: 1 August 2021; Published: June 2022
First available in Project Euclid: 13 June 2022

Digital Object Identifier: 10.1214/21-AOAS1525

Keywords: Approximate Bayesian inference , flood frequency analysis , latent Gaussian model , Max-and-Smooth , multivariate link function , spatiotemporal extremes

Rights: Copyright © 2022 Institute of Mathematical Statistics


Vol.16 • No. 2 • June 2022
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