A Simple Model for Interpreting Temperature Variability and Its Higher-Order Changes

Abstract

Atmospheric temperature distributions are often identified with their variance, while the higher-order moments receive less attention. This can be especially misleading for extremes, which are associated with the tails of the probability density functions (PDFs), and thus depend strongly on the higher-order moments. For example, skewness is related to the asymmetry between positive and negative anomalies, while kurtosis is indicative of the “extremity” of the tails. Here we show that for near-surface atmospheric temperature, an approximate linear relationship exists between kurtosis and skewness squared. We present a simple model describing this relationship, where the total PDF is written as the sum of three Gaussians, representing small deviations from the climatological mean together with the larger-amplitude cold and warm temperature anomalies associated with synoptic systems. This model recovers the PDF structure in different regions of the world, as well as its projected response to climate change, giving a simple physical interpretation of the higher-order temperature variability changes. The kurtosis changes are found to be largely predicted by the skewness changes. Building a deeper understanding of what controls the higher-order moments of the temperature variability is crucial for understanding extreme temperature events and how they respond to climate change.