Probability Density Functions as Botanical-Climatological Transfer Functions for Climate Reconstruction

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Abstract
We present a new procedure, the pdf method (pdf=probability density function), for reconstructing Quaternary climate utilizing botanical data. The procedure includes the advantages of the indicator species method by considering the fossil and modern presence and absence of taxa rather than their frequencies, thus avoiding the need for modern analog plant communities. Overcoming the problematic use of absolute limits to describe climate response ranges is the main progress of the pdf method in comparison to the indicator species method. This advantage results from estimating probability density functions (pdfs) for monthly mean January and July temperature conditional on the present day occurrence of single taxa. Gaussian distributions sufficiently approximate pdfs of many, although not all, studied taxa. On the assumption of statistical independence, the procedure calculates a joint pdf as the product of the pdfs of the individual taxa. This algorithm weights each taxon according to the extent of its climate response range expressed by its covariance structure. We interpret the maximum of the resulting pdf as the most likely climate and its confidence interval as the uncertainty range. To avoid an artificial reduction of uncertainty arising from the use of numerous similar pdfs, a preselection method is proposed based on the Mahalanobis distance between pdfs. The pdf method was applied to the Carpinus phase of a profile from Gröbern, Germany, that spans the last interglaciation (Eemian). The reconstructed most probable January and July temperatures of about 0.0°C and 18.4°C barely differ from the modern values of −0.5°C and 18.3°C.