Assessing Non-Normality of Atmospheric Temperature Variability Across Different Time Scales.

Abstract:

The occurrence of atmospheric temperature extremes is encoded in the tails of the probability distribution and is thus highly dependent on the degree and type of non-normality of that distribution. We use cumulants and higher order spectra to assess non-normality in radiosonde temperature data. For seasonal temperature anomalies, the convergence pattern is consistent with the Hasselmann paradigm of an autoregressive order one process (AR1) forced with non-normal innovations. An AR1 process forced with normal innovations can be rejected as inconsistent with radiosonde temperature observations. Previously observed features such as a variability that is normally distributed on particular time-scales or a parabolic relation between skewness and kurtosis can be explained as artifacts of filtering or sampling procedures. A ubiquitous technique for isolating physical processes is the use of linear band-pass filters or moving averages that remove variability outside of a prescribed frequency band. However, in the spectral domain non-normality is encoded in phase relations between frequencies across the full spectrum, and we show how linear filtering imposes a predictable tendency towards normality by preferentially decaying the higher order cumulants. Our results suggest that non-normality is introduced at the shortest time-scales resolved in daily temperature records, and normality on any particular narrow time scales is an artifact of filtering. As a consequence, it is important to have a sufficiently large spectral band, as controlled by the record’s resolution and duration, in order to properly constrain non-normality in atmospheric temperature variability.