The Annals of Applied Statistics

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

Michael Bertolacci, Edward Cripps, Ori Rosen, John W. Lau, and Sally Cripps

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

Abstract

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.

Article information

Source
Ann. Appl. Stat., Volume 13, Number 2 (2019), 683-712.

Dates
Received: April 2018
Revised: October 2018
First available in Project Euclid: 17 June 2019

Permanent link to this document
https://projecteuclid.org/euclid.aoas/1560758424

Digital Object Identifier
doi:10.1214/18-AOAS1218

Mathematical Reviews number (MathSciNet)
MR3963549

Zentralblatt MATH identifier
07094832

Keywords
Climate rainfall Australia mixture-of-experts Gaussian processes parallel and distributed computing

Citation

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


Export citation

References

  • Amdahl, G. M. (1967). Validity of the single processor approach to achieving large scale computing capabilities. In Proceedings of the April 1820, 1967, Spring Joint Computer Conference. AFIPS ’67 (Spring) 483–485. ACM, New York.
  • 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. Econometrics 20 549–563.
  • 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.
  • 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.
  • 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.
  • 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. Climate 25 6318–6329.
  • 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.
  • Chib, S. (1996). Calculating posterior distributions and modal estimates in Markov mixture models. J. Econometrics 75 79–97.
  • 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.
  • Damsleth, E. (1975). Conjugate classes for gamma distributions. Scand. J. Stat. 2 80–84.
  • Eddelbuettel, D. and Sanderson, C. (2014). RcppArmadillo: Accelerating R with high-performance C$++$ linear algebra. Comput. Statist. Data Anal. 71 1054–1063.
  • Feng, J., Li, J. and Li, Y. (2010). Is there a relationship between SAM and southwest western Australia winter rainfall. J. Climate 23 6082–6089.
  • Furrer, E. M. and Katz, R. W. (2007). Generalized linear modeling approach to stochastic weather generators. Climate Research 34 129–144.
  • Gong, D. and Wang, S. (1999). Definition of Antarctic oscillation index. Geophysical Research Letters 26 459–462.
  • Hendon, H., Thompson, D. and Wheeler, M. (2007). Australian rainfall and surface temperature variations associated with the southern hemisphere annular mode. J. Climate 20 2452–2467.
  • 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 Hydrometeorology 17 3–25.
  • 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.
  • Jacobs, R. A., Jordan, M. I., Nowlan, S. J. and Hinton, G. E. (1991). Adaptive mixtures of local experts. Neural Comput. 3 79–87.
  • 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 Meteorology 138 121–138.
  • King, A., Alexander, L. and Donat, M. (2013). Asymmetry in the response of eastern Australia extreme rainfall to low-frequency Pacific variability. Geophysical Research Letters 40 1–7.
  • Kleiber, W., Katz, R. W. and Rajagopalan, B. (2012). Daily spatiotemporal precipitation simulation using latent and transformed Gaussian processes. Water Resour. Res. 48.
  • Lynch, N. A. (1996). Distributed Algorithms. The Morgan Kaufmann Series in Data Management Systems. Morgan Kaufmann, San Francisco, CA.
  • 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.
  • 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. Climate 27 3816–3826.
  • 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.
  • 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.
  • R Core Team (2016). R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing, Vienna, Austria.
  • 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.
  • Richardson, C. W. (1981). Stochastic simulation of daily precipitation, temperature, and solar radiation. Water Resour. Res. 17 182–190.
  • 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.
  • 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.
  • Saji, N. H., Goswami, B. N., Vinayachandran, P. N. and Yamagata, T. (1999). A dipole mode in the tropical Indian Ocean. Nature 401 360–363.
  • Stern, R. D. and Coe, R. (1984). A model fitting analysis of daily rainfall data. J. R. Stat. Soc., A 147 1–34.
  • 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 Extremes 3 117–125.
  • Troup, A. J. (1965). The “southern oscillation”. Q. J. R. Meteorol. Soc. 91 490–506.
  • 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 Letters 36 L04707.
  • 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. Climate 24 1313–1336.
  • 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 Letters 42 9942–9951.
  • 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.
  • Vrac, M. and Naveau, P. (2007). Stochastic downscaling of precipitation: From dry events to heavy rainfalls. Water Resour. Res. 43.
  • Wahba, G. (1990). Spline Models for Observational Data. CBMS-NSF Regional Conference Series in Applied Mathematics 59. SIAM, Philadelphia, PA.
  • Wilks, D. S. (1999). Interannual variability and extreme-value characteristics of several stochastic daily precipitation models. Agricultural and Forest Meteorology 93 153–169.
  • 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.
  • Wood, S., Rosen, O. and Kohn, R. (2011). Bayesian mixtures of autoregressive models. J. Comput. Graph. Statist. 20 174–195.
  • Yu, H. (2002). Rmpi: Parallel statistical computing in R. R News 2 10–14.

Supplemental materials

  • 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.