Abstract
Numerical experiments based on atmosphere–ocean general circulation models (AOGCMs) are one of the primary tools in deriving projections for future climate change. Although each AOGCM has the same underlying partial differential equations modeling large scale effects, they have different small scale parameterizations and different discretizations to solve the equations, resulting in different climate projections. This motivates climate projections synthesized from results of several AOGCMs’ output. We combine present day observations, present day and future climate projections in a single highdimensional hierarchical Bayes model. The challenging aspect is the modeling of the spatial processes on the sphere, the number of parameters and the amount of data involved. We pursue a Bayesian hierarchical model that separates the spatial response into a large scale climate change signal and an isotropic process representing small scale variability among AOGCMs. Samples from the posterior distributions are obtained with computer-intensive MCMC simulations. The novelty of our approach is that we use gridded, high resolution data covering the entire sphere within a spatial hierarchical framework. The primary data source is provided by the Coupled Model Intercomparison Project (CMIP) and consists of 9 AOGCMs on a 2.8 by 2.8 degree grid under several different emission scenarios. In this article we consider mean seasonal surface temperature and precipitation as climate variables. Extensions to our model are also discussed.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Allen MR, Stott PA, Mitchell JFB, Schnur R and Delworth TL (2000). Quantifying the uncertainty in forecasts of anthropogenic climate change. Nature 407: 617–620
Banerjee S, Gelfrand AE, Carlin BP (2004) Hierarchical modeling and analysis for spatial data. Chapman & Hall/CRC
Berliner LM, Wikle L and Cressie N (2000). Long-lead prediction of Pacific SST via Bayesian dynamic modelling. J Clim 13: 3953–3968
Bernardo JM and Smith AFM (1994). Bayesian theory. John Wiley & Sons Inc., Chichester
Covey C, AchutaRao KM, Lambert SJ, Taylor KE (2000) Intercomparison of present and future climates simulated by coupled ocean-atmosphere GCMs. PCMDI Report No. 66, UCRL-ID-140325, Lawrence Livermore National Laboratory, Livermore, CA
Cressie NAC (1993). Statistics for spatial data. John Wiley & Sons Inc., New York (revised reprint)
Forest CE, Stone PH, Sokolov AP, Allen MR and Webster M (2002). Quantifying uncertainties in climate system properties with the use of recent climate observations. Science 295: 113–117
Frame DJ, Booth BBB, Kettleborough JA, Stainforth DA, Gregory JM, Collins M and Allen MR (2005). Constraining climate forecasts: the role of prior assumptions. J Geophys Res 32: L09702
Fuentes M and Raftery AE (2005). Model evaluation and spatial interpolation by bayesian combination of observations with outputs from numerical models. Biometrics 66: 36–45
Gaspari G and Cohn SE (1999). Construction of correlation functions in two and three dimensions. Quart J Roy Meteorol Soc 125: 723–757
Gelfand A and Smith A (1990). Sampling based approaches to calculating marginal densities. J Am Stat Assoc 85: 398–409
Geman S and Geman D (1984). Stochastic relaxation, gibbs distributions and the Bayesian restoration of images. IEEE Trans Pattern Anal Machine Intell 6: 721–741
Gilks WR, Richardson S, Spiegelhalter DJ (1996) Markov Chain Monte Carlo in practice. Chapman & Hall
Gneiting T (1999). Correlation functions for atmospheric data analysis. Quart J Roy Meteorol Soc 125: 2449–2464
Gregory JM, Stouffer RJ, Raper SCB, Stott PA and Rayner NA (2002). An observationally based estimate of the climate sensitivity. J Clim 15: 3117–3121
Handcock MS and Wallis JR (1994). An approach to statistical spatial-temporal modeling of meteorological fields. J Am Stat Assoc 89: 368–390
Houghton JT, Ding Y, Griggs DJ, Noguer M, Xiaosu D, Maskell K, Johnson CA and Linden PJ (2001). Climate Change 2001: the scientific basis. Cambridge University Press, Cambridge
Ihaka R and Gentleman R (1996). R: A language for data analysis and graphics. J Comput Graph Stat 5: 299–314
Jones RH (1963). Stochastic processes on a sphere. Ann Math Stat 34: 213–218
Kalnay E, Kanamitsu M, Kistler R, Collins W, Deaven D, Gandin L, Iredell M, Saha S, White G, Woolen J, Zhu Y, Chelliah M, Ebisuzaki W, Higgins W, Janowiak J, Mo KC, Ropelewski C, Wang J, Leetma A, Reynolds R, Jenne R and Joseph D (1996). The NCEP/NCAR 40-year reanalysis project. Am Meteorol Soc Bull 77: 437–471
Knutti R, Stocker TF, Joos F and Plattner G-K (2002). Constraints on radiative forcing and future climate change from observations and climate model ensembles. Nature 416: 719–723
Knutti R, Stocker TF, Joos F and Plattner G-K (2003). Probabilistic climate change projections using neural networks. Clim Dyn 21: 257–272
Matérn B (1986). Spatial variation, 2nd edn. Springer-Verlag, Berlin
Meehl GA, Boer GJ, Covey C, Latif M and Stouffer RJ (2000). The coupled model intercomparison project (CMIP). Am Meteorol Soc Bull 81: 313–318
R Development Core Team (2004) R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria. http://www.R-project.org
Robert CP, Casella G (1999) Monte carlo statistical methods. Springer
Schneider SH (2001). What is dangerous climate change?. Nature 411: 17–19
Schoenberg IJ (1942). Positive definite functions on spheres. Duke Math J 9: 96–108
Tebaldi C, Smith RL, Nychka D and Mearns LO (2005). Quantifying uncertainty in projections of regional climate change: a Bayesian approach to the analysis of multimodel ensembles. J Clim 18: 1524–1540
Weber RO and Talkner P (1993). Some remarks on spatial correlation function models. Monthly Weather Rev 121: 2611–2137; Corrigendum: (1999) 127:576.
Wigley TML and Raper SCB (2001). Interpretation of high projections for global-mean warming. Science 293: 451–454
Wikle C, Berliner L and Cressie N (1998). Hierarchical Bayesian space-time models. Environ Ecol Stat 5: 117–154
Wikle CK and Cressie N (1999). A dimension-reduced approach to space-time Kalman filtering. Biometrika 86: 815–829
Wikle CK, Milliff RF, Nychka D and Berliner LM (2001). Spatio-temporal hierarchical Bayesian modeling: Tropical ocean surface winds. J Am Stat Assoc 96: 382–397
Yaglom AM (1987). Correlation theory of stationary and related random functions, vol. I. Springer Series in Statistics. Springer-Verlag, New York
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Furrer, R., Sain, S.R., Nychka, D. et al. Multivariate Bayesian analysis of atmosphere–ocean general circulation models. Environ Ecol Stat 14, 249–266 (2007). https://doi.org/10.1007/s10651-007-0018-z
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10651-007-0018-z