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A latent Gaussian Markov random‐field model for spatiotemporal rainfall disaggregation

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  • David J. Allcroft
  • Chris A. Glasbey

Abstract

Summary. Rainfall data are often collected at coarser spatial scales than required for input into hydrology and agricultural models. We therefore describe a spatiotemporal model which allows multiple imputation of rainfall at fine spatial resolutions, with a realistic dependence structure in both space and time and with the total rainfall at the coarse scale consistent with that observed. The method involves the transformation of the fine scale rainfall to a thresholded Gaussian process which we model as a Gaussian Markov random field. Gibbs sampling is then used to generate realizations of rainfall efficiently at the fine scale. Results compare favourably with previous, less elegant methods.

Suggested Citation

  • David J. Allcroft & Chris A. Glasbey, 2003. "A latent Gaussian Markov random‐field model for spatiotemporal rainfall disaggregation," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 52(4), pages 487-498, October.
    • Handle: RePEc:bla:jorssc:v:52:y:2003:i:4:p:487-498
    DOI: 10.1111/1467-9876.00419
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    References listed on IDEAS

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    1. Durbán, María & Glasbey, C.A., 2001. "Weather modelling using a multivariate latent Gaussian model," DES - Working Papers. Statistics and Econometrics. WS ws011610, Universidad Carlos III de Madrid. Departamento de Estadística.
    2. Håvard Rue, 2001. "Fast sampling of Gaussian Markov random fields," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 63(2), pages 325-338.
    3. Leonhard Knorr‐Held & Håvard Rue, 2002. "On Block Updating in Markov Random Field Models for Disease Mapping," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 29(4), pages 597-614, December.
    4. J. P. Hughes & P Guttorp & S. P. Charles, 1999. "A non‐homogeneous hidden Markov model for precipitation occurrence," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 48(1), pages 15-30.
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    Cited by:

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    3. Moreno Bevilacqua & Christian Caamaño‐Carrillo & Reinaldo B. Arellano‐Valle & Víctor Morales‐Oñate, 2021. "Non‐Gaussian geostatistical modeling using (skew) t processes," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 48(1), pages 212-245, March.
    4. Pierre Ailliot & Craig Thompson & Peter Thomson, 2009. "Space–time modelling of precipitation by using a hidden Markov model and censored Gaussian distributions," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 58(3), pages 405-426, July.
    5. Thordis L. Thorarinsdottir & Tilmann Gneiting, 2010. "Probabilistic forecasts of wind speed: ensemble model output statistics by using heteroscedastic censored regression," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 173(2), pages 371-388, April.
    6. Moreno Bevilacqua & Christian Caamaño‐Carrillo & Carlo Gaetan, 2020. "On modeling positive continuous data with spatiotemporal dependence," Environmetrics, John Wiley & Sons, Ltd., vol. 31(7), November.
    7. Yilan Luo & Deniz Sezer & David Wood & Mingkuan Wu & Hamid Zareipour, 2019. "Estimation of the Daily Variability of Aggregate Wind Power Generation in Alberta, Canada," Energies, MDPI, vol. 12(10), pages 1-29, May.
    8. S. R. Johnson & S. E. Heaps & K. J. Wilson & D. J. Wilkinson, 2023. "A Bayesian spatio‐temporal model for short‐term forecasting of precipitation fields," Environmetrics, John Wiley & Sons, Ltd., vol. 34(8), December.
    9. Sabyasachi Mukhopadhyay & Joseph O. Ogutu & Gundula Bartzke & Holly T. Dublin & Hans-Peter Piepho, 2019. "Modelling Spatio-Temporal Variation in Sparse Rainfall Data Using a Hierarchical Bayesian Regression Model," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 24(2), pages 369-393, June.
    10. De Oliveira, Victor & Wang, Binbin & Slud, Eric V., 2018. "Spatial modeling of rainfall accumulated over short periods of time," Journal of Multivariate Analysis, Elsevier, vol. 166(C), pages 129-149.
    11. Launay, Marie & Zurfluh, Olivier & Huard, Frederic & Buis, Samuel & Bourgeois, Gaétan & Caubel, Julie & Huber, Laurent & Bancal, Marie-Odile, 2020. "Robustness of crop disease response to climate change signal under modeling uncertainties," Agricultural Systems, Elsevier, vol. 178(C).
    12. Ganggang Xu & Marc G. Genton, 2017. "Tukey -and- Random Fields," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(519), pages 1236-1249, July.
    13. Adam Butler & Chris Glasbey, 2008. "A latent Gaussian model for compositional data with zeros," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 57(5), pages 505-520, December.

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