Need for Caution in Interpreting Daily Temperature Extremes

Given the substantial anthropogenic contribution to global warming, it is tempting to seek an anthropogenic component in any unusual recent weather event, or more generally in any recent change in extreme weather statistics. We caution that such detection and attribution efforts may, however, lead to wrong conclusions if the distinctively skewed and heavy-tailed features of the probability distributions of daily weather variations are not properly accounted for. Large deviations from the mean are far more common in such a non-Gaussian world than they are in a Gaussian world. In such a world, a mean climate shift is also generally accompanied by changes in the width and shape of the probability distribution. Consequently, even the sign of the changes in tail probabilities cannot be inferred unequivocally from the mean shift. These realities further complicate the establishment of significant changes in tail probabilities from historical records of limited length and accuracy. A possible solution is to exploit the fact that the salient non-Gaussian features of the observed distributions are captured in a general class of probability distributions introduced in the meteorological literature by Sardeshmukh and Sura (2009). These distributions, called Stochastically Generated Skewed (SGS) distributions (of which Gaussian distributions are special cases), are associated with modified forms of stochastically perturbed damped linear processes, and as such represent perhaps the simplest physically based non-Gaussian prototypes of the observed distributions. Importantly, the distribution of an SGS variable remains an SGS distribution under a mean climate shift. We show further that fitting SGS distributions to all daily values in limited climate records yields extreme value distributions of block maxima with smaller sampling uncertainties than GEV distributions fitted to only the block maxima. Extreme value analysis based on SGS distributions thus provides an attractive alternative to that based on GEV or Generalized Pareto distributions, and can be used to assess changes not only in tail probabilities but the entire distribution. The procedure will be illustrated to assess changes in the observed distributions of daily temperature anomalies in several regions of the globe over the 1874 to 2010 period.