Specification and estimation of the transfer function in dendroclimatological reconstructions
We identify two issues with the reverse regression approach as implemented in several classic reconstructions of past climate fluctuations from dendroclimatologcical data series. First, instead of estimating the causal relationship between the proxy, which is measured with significant error, as function of climate and formally inverting the relationship, most papers estimate the inverted relationship directly. This leads to biased coefficients and reconstructions with artificially low variance. Second, we show that inversion of the relationship is often done incorrectly when the underlying causal relationship is dynamic in nature. We show analytically as well as using Monte Carlo experiments and actual tree ring data, that the reverse regression method results in biased coefficients, reconstructions with artificially low variance and overly smooth reconstructions. We further demonstrate that correct application of the inverse regression method is preferred. However, if the measurement error in the tree ring index is significant, neither method provides reliable reconstructions.
KeywordsClimate change Climate variability Inversion Paleoclimatic data Reconstruction method
Auffhammer thanks the Giannini Foundation for support. Lis research was partially supported by the NSF Grant DMS-1007686. The authors thank the Guest Editor and two anonymous referees for their helpful comments and suggestions.
- Bradley R, Jones P (1992) Climate since AD 1500. Routledge, LondonGoogle Scholar
- Brown PJ (1993) Measurement, regression and calibration. Oxford University Press, New YorkGoogle Scholar
- Fritts H (1991) Reconstructing large-scale climatic patterns from tree-ring data: a diagnostic analysis. University of Arizona Press, TusconGoogle Scholar
- Hamilton J (1994) Time series analysis. Princeton University Press, PrincetonGoogle Scholar
- Hughes M, Brown P (1992) Drought frequency in central California since 101 BC recorded in giant sequoia tree rings. Clim Dyn 6(3):161–167Google Scholar
- Jones P, Hulme M (1997) The changing temperature of Central England. In: Hulme M, Barrow E (eds) Climate of the British Isles: past, present and future. Routledge, London, pp 173–196Google Scholar
- National Research Council (1998) Decade-to-Century-Scale climate variability and change: a science strategy. National Academies Press, WashingtonGoogle Scholar
- National Research Council (2006) Surface Temperature Reconstructions for the last 2000 years. National Academies Press, Washington, DCGoogle Scholar
- Seater J (1993) World temperature-trend uncertainties and their implications for economic policy. J Bus Econ Stat 11(3):265–277Google Scholar
- Yoo SJ, Wright BD (2000) Persistence of growth variation in tree-ring chronologies. For Sci 46(4):507–520Google Scholar