Climate inference on daily rainfall across the Australian continent, 1876–2015.

*(English)*Zbl 1423.62157Summary: 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.

##### MSC:

62P12 | Applications of statistics to environmental and related topics |

62H12 | Estimation in multivariate analysis |

60G15 | Gaussian processes |

62H30 | Classification and discrimination; cluster analysis (statistical aspects) |

62M10 | Time series, auto-correlation, regression, etc. in statistics (GARCH) |

##### Keywords:

climate; rainfall; Australia; mixture-of-experts; Gaussian processes; parallel and distributed computing##### References:

[1] | Amdahl, G. M. (1967). Validity of the single processor approach to achieving large scale computing capabilities. In Proceedings of the April 18-20, 1967, Spring Joint Computer Conference. AFIPS ’67 (Spring) 483-485. ACM, New York. |

[2] | Andrich, M. A. and Imberger, J. (2013). The effect of land clearing on rainfall and fresh water resources in western Australia: A multi-functional sustainability analysis. J. Appl. Econometrics20 549-563. |

[3] | Bertolacci, M., Cripps, E., Rosen, O., Lau, J. and Cripps, S. (2019a). Conditional distributions for the sampling scheme in “Climate inference on daily rainfall across the Australian continent, 1876-2015.” DOI:10.1214/18-AOAS1218SUPPA. |

[4] | Bertolacci, M., Cripps, E., Rosen, O., Lau, J. and Cripps, S. (2019b). Model comparison supplement for “Climate inference on daily rainfall across the Australian continent, 1876-2015.” DOI:10.1214/18-AOAS1218SUPPB. |

[5] | Bertolacci, M., Cripps, E., Rosen, O., Lau, J. and Cripps, S. (2019c). Model diagnostics for “Climate inference on daily rainfall across the Australian continent, 1876-2015.” DOI:10.1214/18-AOAS1218SUPPC. |

[6] | Cai, W., van Rensch, P., Cowan, T. and Hendon, H. (2012). An asymmetry in the IOD and ENSO teleconnection pathway and its impact on Australian climate. J. Climate25 6318-6329. |

[7] | Charles, S. P., Bates, B. C. and Hughes, J. P. (1999). A spatiotemporal model for downscaling precipitation occurrence and amounts. J. Geophys. Res., Atmos.104 31657-31669. |

[8] | Chib, S. (1996). Calculating posterior distributions and modal estimates in Markov mixture models. J. Econometrics75 79-97. · Zbl 0864.62010 |

[9] | Compo, G. P., Whitaker, J. S., Sardeshmukh, P. D., Matsui, N., Allan, R. J., Yin, X., Gleason, B. E., Vose, R. S., Rutledge, G., Bessemoulin, P. et al. (2011). The twentieth century reanalysis project. Q. J. R. Meteorol. Soc.137 1-28. |

[10] | Damsleth, E. (1975). Conjugate classes for gamma distributions. Scand. J. Stat.2 80-84. · Zbl 0308.62023 |

[11] | Eddelbuettel, D. and Sanderson, C. (2014). RcppArmadillo: Accelerating R with high-performance C\(++\) linear algebra. Comput. Statist. Data Anal.71 1054-1063. · Zbl 06975444 |

[12] | Feng, J., Li, J. and Li, Y. (2010). Is there a relationship between SAM and southwest western Australia winter rainfall. J. Climate23 6082-6089. |

[13] | Furrer, E. M. and Katz, R. W. (2007). Generalized linear modeling approach to stochastic weather generators. Climate Research34 129-144. |

[14] | Gong, D. and Wang, S. (1999). Definition of Antarctic oscillation index. Geophysical Research Letters26 459-462. |

[15] | Hendon, H., Thompson, D. and Wheeler, M. (2007). Australian rainfall and surface temperature variations associated with the southern hemisphere annular mode. J. Climate20 2452-2467. |

[16] | Holsclaw, T., Greene, A. M., Robertson, A. W. and Smyth, P. (2016). A Bayesian hidden Markov model of daily precipitation over South and East Asia. Journal of Hydrometeorology17 3-25. |

[17] | Holsclaw, T., Greene, A. M., Robertson, A. W. and Smyth, P. (2017). Bayesian nonhomogeneous Markov models via Pólya-gamma data augmentation with applications to rainfall modeling. Ann. Appl. Stat.11 393-426. · Zbl 1366.62255 |

[18] | Jacobs, R. A., Jordan, M. I., Nowlan, S. J. and Hinton, G. E. (1991). Adaptive mixtures of local experts. Neural Comput.3 79-87. |

[19] | Kala, J., Lyons, T. J. and Nair, U. S. (2011). Numerical simulations of the impacts of land-cover change on cold fronts in South-West western Australia. Boundary-Layer Meteorology138 121-138. |

[20] | King, A., Alexander, L. and Donat, M. (2013). Asymmetry in the response of eastern Australia extreme rainfall to low-frequency Pacific variability. Geophysical Research Letters40 1-7. |

[21] | Kleiber, W., Katz, R. W. and Rajagopalan, B. (2012). Daily spatiotemporal precipitation simulation using latent and transformed Gaussian processes. Water Resour. Res.48. |

[22] | Lynch, N. A. (1996). Distributed Algorithms. The Morgan Kaufmann Series in Data Management Systems. Morgan Kaufmann, San Francisco, CA. |

[23] | Naveau, P., Huser, R., Ribereau, P. and Hannart, A. (2016). Modeling jointly low, moderate, and heavy rainfall intensities without a threshold selection. Water Resour. Res.52 2753-2769. |

[24] | Pepler, A., Timbal, B., Rakich, C. and Coutts-Smith, A. (2014). Indian Ocean dipole overrides ENSO’s influence on cool season rainfall across the eastern seaboard of Australia. J. Climate27 3816-3826. |

[25] | Pitman, A. J., Narisma, G. G., Pielke, R. A. and Holbrook, N. J. (2004). The impact of land cover change on the climate of southwest western Australia. J. Geophys. Res.109 1-12. |

[26] | Polson, N. G., Scott, J. G. and Windle, J. (2013). Bayesian inference for logistic models using Pólya-Gamma latent variables. J. Amer. Statist. Assoc.108 1339-1349. · Zbl 1283.62055 |

[27] | Rayner, N. A., Parker, D. E., Horton, E. B., Folland, C. K., Alexander, L. V., Rowell, D. P., Kent, E. C. and Kaplan, A. (2003). Global analyses of sea surface temperature, sea ice, and night marine air temperature since the late nineteenth century. J. Geophys. Res., Atmos.108. |

[28] | Richardson, C. W. (1981). Stochastic simulation of daily precipitation, temperature, and solar radiation. Water Resour. Res.17 182-190. |

[29] | Risbey, J., Pook, M., McIntosh, P., Wheeler, M. and Hendon, H. (2009). On the remote drivers of rainfall variability in Australia. Mon. Weather Rev.137 3233-3253. |

[30] | Rosen, O., Stoffer, D. S. and Wood, S. (2009). Local spectral analysis via a Bayesian mixture of smoothing splines. J. Amer. Statist. Assoc.104 249-262. · Zbl 1388.62268 |

[31] | Saji, N. H., Goswami, B. N., Vinayachandran, P. N. and Yamagata, T. (1999). A dipole mode in the tropical Indian Ocean. Nature401 360-363. |

[32] | Stern, R. D. and Coe, R. (1984). A model fitting analysis of daily rainfall data. J. R. Stat. Soc., A147 1-34. |

[33] | Stone, R. (2014). Constructing a framework for national drought policy: The way forward—The way Australia developed and implemented the national drought policy. Weather and Climate Extremes3 117-125. |

[34] | Troup, A. J. (1965). The “southern oscillation”. Q. J. R. Meteorol. Soc.91 490-506. |

[35] | Ummenhofer, C. C., England, M. H., McIntosh, P. C., Meyers, G. A., Pook, M. J., Risbey, J. S., Gupta, A. S. and Taschetto, A. S. (2009). What causes southeast Australia’s worst droughts?. Geophysical Research Letters36 L04707. |

[36] | Ummenhofer, C. C., Gupta, A. S., Briggs, P. R., England, M. H., McIntosh, P. C., Meyers, G. A., Pook, M. J., Raupach, M. R. and Risbey, J. S. (2011). Indian and Pacific Ocean influences on southeast Australian drought and soil moisture. J. Climate24 1313-1336. |

[37] | Ummenhofer, C. C., Gupta, A. S., England, M. H., Taschetto, A. S., Briggs, P. R. and Raupach, M. R. (2015). How did ocean warming affect Australian rainfall extremes during the 2010/2011 La Niña event. Geophysical Letters42 9942-9951. |

[38] | van Dijk, A., Beck, H., Crosbie, R., de Jeu, R., Liu, G., Podger, Y., Timbal, B. and Viney, N. (2013). The Millennium Drought in southeast Australia (2001-2009): Natural and human causes and implications for water resources, ecosystems, economy, and society. Water Resour. Res.49. |

[39] | Vrac, M. and Naveau, P. (2007). Stochastic downscaling of precipitation: From dry events to heavy rainfalls. Water Resour. Res.43. |

[40] | Wahba, G. (1990). Spline Models for Observational Data. CBMS-NSF Regional Conference Series in Applied Mathematics59. SIAM, Philadelphia, PA. · Zbl 0813.62001 |

[41] | Wilks, D. S. (1999). Interannual variability and extreme-value characteristics of several stochastic daily precipitation models. Agricultural and Forest Meteorology93 153-169. |

[42] | Wood, S. (2013). Applications of Bayesian smoothing splines. In Bayesian Theory and Applications (P. Damien, P. Dellaportas, N. G. Polson and D. A. Stephens, eds.) 309-335. Oxford Univ. Press, Oxford. |

[43] | Wood, S., Rosen, O. and Kohn, R. (2011). Bayesian mixtures of autoregressive models. J. Comput. Graph. Statist.20 174-195. |

[44] | Yu, H. (2002). Rmpi: Parallel statistical computing in R. R News2 10-14. |

This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.