Abstract
The goal of this work is to characterize the extreme precipitation simulated by a regional climate model (RCM) over its spatial domain. For this purpose, we develop a Bayesian hierarchical model. Since extreme value analyses typically only use data considered to be extreme, the hierarchical approach is particularly useful as it sensibly pools the limited data from neighboring locations. We simultaneously model the data from both a control and future run of the RCM which allows for easy inference about projected change. Additionally, this hierarchical model is the first to spatially model the shape parameter which characterizes the nature of the distribution’s tail. Our hierarchical model shows that for the winter season, the RCM indicates a general increase in 100-year precipitation return levels for most of the study region. For the summer season, the RCM surprisingly indicates a significant decrease in the 100-year precipitation return level.
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References
Banerjee, S., Carlin, B., and Gelfand, A. (2004), Hierarchical Modeling and Analysis for Spatial Data. Monographs on Statistics and Applied Probability, Boca Raton: Chapman and Hall/CRC.
Banerjee, S., Gelfand, A., and Polasek, W. (2000), “Geostatistical Modelling of Spatial Interaction Data with Application to Postal Service Performance,” Journal of Statistical Planning and Inference, 90, 87–105.
Beirlant, J., Goegebeur, Y., Segers, J., Teugels, J., Waal, D. D., and Ferro, C. (2004), Statistics of Extremes: Theory and Applications, New York: Wiley.
Berliner, M. (1996), “Hierarchical Bayesian Time Series Models,” in Maximum Entropy and Bayesian Methods, eds. K. Hanson and R. Silver, Dordrecht: Kluwer Academic, pp. 15–22.
Besag, J. (1974), “Spatial Interaction and the Statistical Analysis of Lattice Systems” (with discussion), Journal of the Royal Statistical Society, Series B, 35, 192–236.
Besag, J., Green, P. J., Higdon, D., and Mengersen, K. (1995), “Bayesian Computation and Stochastic Systems” (with discussion), Statistical Science, 10, 3–66.
Casson, E., and Coles, S. (1999), “Spatial Regression Models for Extremes,” Extremes, 1, 449–468.
Cooley, D., Nychka, D., and Naveau, P. (2007), “Bayesian Spatial Modeling of Extreme Precipitation Return Levels,” Journal of the American Statistical Association, 102, 824–840.
Dalrymple, T. (1960), “Flood Frequency Analyses,” Water supply paper 1543-a, U.S. Geological Survey, Reston, VA.
de Haan, L., and Ferreira, A. (2006), Extreme Value Theory. Springer Series in Operations Research and Financial Engineering, New York: Springer.
Diggle, P., Tawn, J., and Moyeed, R. (1998), “Model-Based Geostatistics,” Applied Statistics, 47, 299–350.
Fisher, R. A., and Tippett, L. H. C. (1928), “Limiting Forms of the Frequency Distribution of the Larges or Smallest Members of a Sample,” Proceedings of the Cambridge Philosophical Society, 24, 180–190.
Frei, C., Scholl, R., Fukutome, S., Schmidli, J., and Vidale, P. L. (2006), “Future Change of Precipitation Extremes in Europe: Intercomparison of Scenarios from Regional Climate Models,” Journal of Geophysical Research, 111, D06105.
Furrer, R. (2008), “spam: SPArse Matrix,” R package version 0.14-1.
Gelman, A. (1996), “Inference and Monitoring Convergence,” in Markov Chain Monte Carlo in Practice, eds. W. R. Gilks, S. Richarson, and D. J. Spiegelhalter, London: Chapman and Hall.
Hosking, J., Wallis, J., and Wood, E. (1985), “Estimation of the Generalized Extreme-Value Distribution by the Method of Probability-Weighted-Moments,” Technometrics, 27, 251–261.
Hosking, J. R. M., and Wallis, J. R. (1997), Regional Frequency Analysis: An Approach Based on L-Moments, Cambridge: Cambridge University Press.
Kharin, V. V., Zwiers, F. W., Zhang, X. B., and Hegerl, G. C. (2007), “Changes in Temperature and Precipitation Extremes in the IPCC Ensemble of Global Coupled Model Simulations,” Journal of Climate, 20, 1419–1444.
Leung, L., Qian, Y., Bian, X., Washington, W. M., Han, J., and Roads, J. O. (2004), “Mid-Century Ensemble Regional Climate Change Scenarios for the Western United States,” Climatic Change, 62, 75–113.
Martins, E., and Stedinger, J. (2000), “Generalized Maximum-Likelihood Generalized Extreme-Value Quantile Estimators for Hydrologic Data,” Water Resources Research, 36, 737–744.
Pickands, J. (1975), “Statistical Inference Using Extreme Order Statistics,” Annals of Statistics, 3, 119–131.
Rue, H., and Held, L. (2005), Gaussian Markov Random Fields: Theory and Applications. Monographs on Statistics and Applied Probability, Boca Raton: Chapman and Hall.
Sain, S., Furrer, R., and Cressie, N. (2008), “Combining Ensembles of Regional Climate Model Output via a Multivariate Markov Random Field Model,” Annals of Applied Statistics.
Sang, H., and Gelfand, A. E. (2009), “Hierarchical Modeling for Extreme Values Observed Over Space and Time,” Environmental and Ecological Statistics, 16, 407–426.
Schlather, M. (2002), “Models for Stationary Max-Stable Random Fields,” Extremes, 5 (1), 33–44.
Smith, R. (1990), “Max-Stable Processes and Spatial Extremes,” unpublished Manuscript.
Spiegelhalter, D., Best, N., Carlin, B., and van der Linde, A. (2002), “Bayesian Measures of Model Complexity and Fit,” Journal of the Royal Statistical Society, Series B, 64, 583–639.
Trenberth, K. (1999), “Conceptual Framework for Changes of Extremes of the Hydrological Cycle with Climate Change,” Climatic Change, 42, 327–339.
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Cooley, D., Sain, S.R. Spatial Hierarchical Modeling of Precipitation Extremes From a Regional Climate Model. JABES 15, 381–402 (2010). https://doi.org/10.1007/s13253-010-0023-9
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DOI: https://doi.org/10.1007/s13253-010-0023-9