The Annals of Applied Statistics
- Ann. Appl. Stat.
- Volume 13, Number 2 (2019), 683-712.
Climate inference on daily rainfall across the Australian continent, 1876–2015
Daily precipitation has an enormous impact on human activity, and the study of how it varies over time and space, and what global indicators influence it, is of paramount importance to Australian agriculture. We analyze over 294 million daily rainfall measurements since 1876, spanning 17,606 sites across continental Australia. The data are not only large but also complex, and the topic would benefit from a common and publicly available statistical framework. We propose a Bayesian hierarchical mixture model that accommodates mixed discrete-continuous data. The observational level describes site-specific temporal and climatic variation via a mixture-of-experts model. At the next level of the hierarchy, spatial variability of the mixture weights’ parameters is modeled by a spatial Gaussian process prior. A parallel and distributed Markov chain Monte Carlo sampler is developed which scales the model to large data sets. We present examples of posterior inference on the mixture weights, monthly intensity levels, daily temporal dependence, offsite prediction of the effects of climate drivers and long-term rainfall trends across the entire continent. Computer code implementing the methods proposed in this paper is available as an R package.
Ann. Appl. Stat., Volume 13, Number 2 (2019), 683-712.
Received: April 2018
Revised: October 2018
First available in Project Euclid: 17 June 2019
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Bertolacci, Michael; Cripps, Edward; Rosen, Ori; Lau, John W.; Cripps, Sally. Climate inference on daily rainfall across the Australian continent, 1876–2015. Ann. Appl. Stat. 13 (2019), no. 2, 683--712. doi:10.1214/18-AOAS1218. https://projecteuclid.org/euclid.aoas/1560758424
- Supplement A: Model comparison supplement for “Climate inference on daily rainfall across the Australian continent, 1876–2015”. We fit the model with $K=3$ gamma components and compare the results to those corresponding to $K=2$ gamma components.
- Supplement B: Conditional distributions for the sampling scheme in “Climate inference on daily rainfall across the Australian continent, 1876–2015”. We derive the conditional distributions used by the sampling scheme described in Section 4.1 of this paper.
- Supplement C: Temporal and spatial diagnostics for “Climate inference on daily rainfall across the Australian continent, 1876–2015”. We present log-odds and Spearman correlation diagnostics for the application to Australian daily rainfall, 1876–2015, along with a simulation study to assess the model’s ability to perform spatially varying inference in the presence of spatially correlated observations.