Calibrating pollen data in climatic terms: Improving the methods

When properly calibrated, Holocene pollen data provide an important source of quantitative information about Holocene climates. Multiple linear regression of modern climate and pollen data allows the development of statistical calibration functions that transform percentages of certain pollen types into quantitative estimates of climatic variables, and these functions, when applied to Holocene pollen data, yield estimates of climatic variables for past times. Confidence intervals for the climatic variables provide estimates of the statistical errors. These interval estimates are based upon the following statistical assumptions: (1) the regression model is appropriate; (2) the errors in measuring the climate variables are independent, normally distributed and have constant variance; and (3) no outliers are present. We outline the steps to be followed in calculating calibration functions, including (1) selecting the calibration region; (2) selecting a pollen sum; (3) analyzing scatter diagrams of a given climate variable against each pollen type; (4) deleting outliers and transforming pollen data; (5) performing the regression; and (6) testing the appropriateness of the statistical assumptions. We used available computer programs for most of this study. In addition, we developed new software to compute the Moran statistic to test for spatial autocorrelation among the regression residuals, using the dual of the Voronoi diagram to describe the spatial relationships among the sites. In order to illustrate the sequence of procedures, we used data from the lower peninsula of Michigan to develop a calibration function for July mean temperature and then used Holocene pollen data from central lower Michigan to estimate past temperatures.