Analysis of the probability distribution of the late Pleistocene climatic record implications for model validation

Some statistical properties of the late Pleistocene climatic changes, as inferred from the analysis of the Probability Density Function (PDF) of the deep-sea ¹⁸O record, are discussed. Estimates of the probability distribution of the SPECMAP record seem to reveal a bimodal character over the last 600 000 years BP, with a transition to a unimodal distribution for a longer time interval. Based on knowledge of the accuracy of the measurements, we try to remove the arbitrariness of such estimates, and by employing a number of different estimators we show that the major features observed are not affected by the particular method used. Possible dynamic interpretations are discussed. The abruptness of many transitions between the two modes and their symmetric occurrence seem to be significant features of the past climatic changes, which should be reproduced by climate models. The distribution of this indicator is then used to compare the performances of two climate models. Various statistical tests are employed and it is shown that, for a proper determination of the physical significance of such tests, information about the accuracy and reliability of the data must be included. For example, the comparison of two generalized isotopic curves, independently developed, shows a correlation coefficient of the order of 70%; therefore any account of the variance of any particular target curve beyond this level cannot be considered significant. These types of analyses suggest how the standard data evaluation and model validation techniques can be improved when discussing the essential features of observed and simulated dynamical systems.