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11 IMSC Session Program Mann, M. E., S. Rutherford, E. Wahl, and C. Ammann (2007), Robustness of proxybased climate field reconstruction methods, Journal of Geophysical Research (Atmospheres), 112(D11), 12,109–+, doi:10. 1029/2006JD008272. Mann, M. E., Z. Zhang, M. K. Hughes, R. S. Bradley, S. K. Miller, S. Rutherford, and F. Ni (2008), Proxy-based reconstructions of hemispheric and global surface temperature variations over the past two millennia, Proceedings of the National Academy of Sciences, 105(36), 13,252–13,257, doi:10.1073/pnas. 0805721105. Mann, M. E., Z. Zhang, S. D. Rutherford, R. S. Bradley, M. K. Hughes, D. T. Shindell, C. M. Ammann, G. Faluvegi, and F. Ni (2009), Global Signatures of the “Little Ice Age” and “Medieval Climate Anomaly” and Plausible Dynamical Origins, Science, 326(5957):1256–1260. Smerdon, J. E., and A. Kaplan (2007), Comments on "Testing the Fidelity of Methods Used in Proxy-Based Reconstructions of Past Climate": The Role of the Standardization Interval, J. Clim., pp. 5666–5670. Abstracts 131
11 IMSC Session Program A Bayesian hierarchical modelling approach to reconstructing past climates Tuesday - Parallel Session 3 David Hirst Norwegian Computing Center, Norway Using proxy data to estimate past temperature has a number of inherent problems: Individual proxies have different time spans and resolutions, they have a complex relationship to temperature, and in some cases may have no relationship at all, they rarely have good instrumental data for calibration, and usually can only reflect local conditions. I will attempt to address some of these problems by developing a Bayesian hierarchical model to relate proxy data to an underlying true temperature. The model assumes a temperature field T which has a spatio-temporal structure. The data (both proxy and instrumental) are then regarded as observations, with error, of this field. A simple example could be that T is autoregressive order 1 with no spatial 2 variability, ie Tt ~ N( βTT t− 1, σ T ) . This could represent a regional or global mean temperature. Each observation series O y, t is then a function g y of this series, plus temporally (and possibly spatially) correlated error (t) , plus iid measurement error ε : O y, t = g y ( Ty, t ) + hy ( t) + ε y, t hy y, t The model can be fitted using a Bayesian approach, which in principle allows almost any proxy series to be included in the analysis, since g can take whatever form is necessary. For example if the proxy is considered to represent an average temperature over some (known) period, this can easily be incorporated. Also missing data cause no problems, and multiple proxies of different lengths can be included. The uncertainty in the reconstruction is automatically calculated as the posterior distribution of T. The talk will be illustrated with and example using multiple proxies and instrumental records. Abstracts 132
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