A Spatial Analysis of Multivariate Output from Regional ... - IMAGe

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models are typically constructed to reproduce certain features in the current climate, andanalyzing differences as we did should minimize the impact of any biases in the climatemodels (although this approach might be viewed with some healthy skepticism as it is notclear that the biases in current runs are going to be the same as biases in future runs).Observations may be included to help constrain the statistical model, at least with respectto current climate. However, it is still an open question how to include observational datasets for spatial analyses of RCMs of the sort done here. Station-level data does not havethe same spatial and temporal coverage, and there are also numerous additional issueswith using interpolated data products, including reanalysis data that represent a dataassimilation using both station-level data and climate-model output.In addition to the longitude, latitude, and elevation used in this analysis, predictorsbased on climatology (long-run means of temperature and precipitation) were considered(e.g., Furrer et al., 2007a,b), but these were ultimately ruled out as not being effective atpredicting the changes in temperature and precipitation. However, work done by Tebaldiet al. (2005) offers an approach for combining model output and observations. We arecurrently considering how their approach may be useful for spatial analyses of RCM output.Finally, there is also much interest, for example from people examining the impactsof climate change, in combining model output in order to obtain improved projections ofclimate change or to span the variation across a climate-model experiment. Of course,with the more complex climate-model experiments, there is the issue of model-to-modelcorrelations. We believe that the inherent multivariate nature of this model provides anexcellent starting place to consider such correlations.AcknowledgmentsWe would like to express our appreciation to the referees and the editor for their helpfulcomments. The National Center for Atmospheric Research is sponsored by the NationalScience Foundation (NSF). The research of the first author was also supported, in part,by NSF grants DMS-0707069 and ATM-0534173. The research of the second author was30
partially supported by NSF grant DMS-0621118. In addition, much of the research in thispaper was done while the second author was an assistant professor in the Department ofMathematical and Computer Sciences at the Colorado School of Mines in Golden, CO. Theresearch of the third author was supported by the Office of Naval Research under awardN00014-08-1-0464.ReferencesApanasovich, T. V. and Genton, M. G. (2010). Cross-covariance functions for multivariaterandom fields based on latent dimensions. Biometrika, 97, 15–30.Banerjee, S., Carlin, B. P., and Gelfand, A. E. (2004). Hierarchical Modeling and Analysisfor Spatial Data. Chapman & Hall / CRC Press, Bacon Raton, FL.Berliner, L. M. and Kim, Y. (2008). Bayesian design and analysis for superensemble basedclimate forecasting. Journal of Climate, 21, 1891–1910.Besag, J. E. (1974). Spatial interaction and the statistical analysis of lattice systems (withdiscussion). Journal of the Royal Statistical Society, Series B, 35, 192–236.Billheimer, D., Cardoso, T., Freeman, E., Guttorp, P., Ko, H., and Silkey, M. (1997).Natural variability of benthic species composition in the Delaware Bay. Environmentaland Ecological Statistics, 4, 95–115.Carlin, B. P. and Banerjee, S. (2003). Hierarchical multivariate CAR models for spatiotemporallycorrelated data. In Bayesian Statistics 7, 45–63. Oxford University Press, Oxford,UK.Cooley, D. and Sain, S. R. (2010). Spatial hierarchical modeling of precipitation extremesfrom a regional climate model. Journal of Agricultural, Biological, and EnvironmentalStatistics, doi: 10.1007/s13253-010-0023-9.31
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