Measuring the skill of variance-scaled climate reconstructions and a test for the capture of extremes

Abstract

Climate reconstructions produced using regression, with a proxy as the independent variable, are inevitably biased towards the mean, exhibit reduced variance and underestimate extremes. Scaling the mean and variance to fit those of the target climate data produces a more realistic range of reconstructed values but the cost, in terms of inflated error, is seldom assessed. We provide a simple metric that allows the loss of skill because of scaling to be quantified. It can be calculated retrospectively for published studies, some of which exhibit little or no reconstructive skill. Although scaled reconstructions must have a range that is close to that of the target climate data, there is no guarantee that the correct years are pushed to the extremes. We propose a simple non-parametric test for ‘Extreme Value Capture’ that gives the statistical significance of a given number of the correct years being ‘captured’ beyond the thresholds defined by the upper and lower 10% of the measured climate data. The methods are tested using three annually resolved case studies. A tree-growth-based summer temperature reconstruction for northern Fennoscandia captures cold summers very well, but the capture rate of the warmest summers is no better than might be expected purely because of chance. Such failure to correctly capture the warmest years has important implications for interpretation of the frequency and magnitude of very warm summers in the past.