Power-Law and Long-Memory Characteristics of the Atmospheric General Circulation

The question of which statistical model best describes internal climate variability on interannual and longer time scales is essential to the ability to predict such variables and detect periodicities and trends in them. For over 30 yr the dominant model for background climate variability has been the autoregressive model of the first order (AR1). However, recent research has shown that some aspects of climate variability are best described by a “long memory” or “power-law” model. Such a model fits a temporal spectrum to a single power-law function, which thereby accumulates more power at lower frequencies than an AR1 fit. In this study, several power-law model estimators are applied to global temperature data from reanalysis products. The methods employed (the detrended fluctuation analysis, Geweke–Porter-Hudak estimator, Gaussian semiparametric estimator, and multitapered versions of the last two) agree well for pure power-law stochastic processes. However, for the observed temperature record, the power-law fits are sensitive to the choice of frequency range and the intrinsic filtering properties of the methods. The observational results converge once frequency ranges are made consistent and the lowest frequencies are included, and once several climate signals have been filtered. Two robust results emerge from the analysis: first, that the tropical circulation features relatively large power-law exponents that connect to the zonal-mean extratropical circulation; and second, that the subtropical lower stratosphere exhibits power-law behavior that is volcanically forced.