HOME /

Temperature Extremes

Spectral Structure of Non-Normal variability

Understanding the structure of the non-normal component of temperature variability is important for interpreting changes in temperature extremes [Huybers et al. 2014], and may provide insight into the underlying dynamics of a system. However, traditional methods of variance decomposition through band-pass filtering may not be appropriate when analyzing higher order moments. This has resulted in uncertainty as whether non-normality can be localized as arising on a particular time scale.

We find that apparent normal variations on synoptic time scales are an artifact of filtering. Daily radiosonde temperature is consistent with models of temperature variability requiring non-normal variations at the highest resolved frequency, while also allowing for additional sources of non-normality to be introduced through longer time-scale non-stationarity [Proistosescu et al., submitted].
Tendency towards normality of a temperature record filtered to progressively narrower pass-bands (indicated top plot by colored lines). Dashed black line denotes the pdf of a standard normal. From Proistosescu et al [2015].
  
  
 
This is proven to be a consequence of the effect of filtering on higher order moments/cumulants (e.g. skewness and kurtosis) and their associated spectra (e.g. bispectrum and trispectrum). While the tendency towards normality of certain types of filtered data has been known in the applied mathematics literature since at least the 1950s, the formalism developed here allows for a comparison of theoretical decay rates towards normality with those of real data. 

Skewness of filtered data relative to unfiltered data,
as a function of the relative width of the pass-band
 
References:
  • Huybers, McKinnon, Rhines, and Tingley (2014): U.S. daily temperatures: the meaning of extremes in the context of non-normality, Journal of Climate.
  • Proistosescu, Rhines, Huybers, 2015: Identification and interpretation of non-normality in atmospheric time series. Submitted to GRL (pdf)(supp)