Need for Caution in Interpreting Extreme Weather Statistics

Given the reality of anthropogenic global warming, it is tempting to seek an anthropogenic component in any recent change in the statistics of extreme weather. This paper cautions that such efforts may, however, lead to wrong conclusions if the distinctively skewed and heavy-tailed aspects of the probability distributions of daily weather anomalies are ignored or misrepresented. Departures of several standard deviations from the mean, although rare, are far more common in such a distinctively non-Gaussian world than they are in a Gaussian world. This further complicates the problem of detecting 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 by so-called stochastically generated skewed (SGS) distributions that include Gaussian distributions as special cases. SGS distributions are associated with damped linear Markov processes perturbed by asymmetric stochastic noise and as such represent the simplest physically based prototypes of the observed distributions. The tails of SGS distributions can also be directly linked to generalized extreme value (GEV) and generalized Pareto (GP) distributions. The Markov process model can be used to provide rigorous confidence intervals and to investigate temporal persistence statistics. The procedure is illustrated for assessing changes in the observed distributions of daily wintertime indices of large-scale atmospheric variability in the North Atlantic and North Pacific sectors over the period 1872-2011. No significant changes in these indices are found from the first to the second half of the period.