Stochastic modeling of daily temperature fluctuations

Abstract

Classical spectral, Hurst, and detrended fluctuation analysis have been revealed asymptotic power-law correlations for daily average temperature data. For short-time intervals, however, strong correlations characterize the dynamics that permits a satisfactory description of temperature changes as a low order linear autoregressive process (dominating the texts on climate research). Here we propose a unifying stochastic model reproducing correlations for all time scales. The concept is an extension of a first-order autoregressive model with power-law correlated noise. The inclusion of a nonlinear "atmospheric response function" conveys the observed skew for the amplitude distribution of temperature fluctuations. While stochastic models cannot help to understand the physics behind atmospheric processes, they are capable to extract useful features promoting to benchmark physical models, an example is shown. Possible applications for other systems of strong short-range and asymptotic power-law correlations are discussed.

Comparative Spectral Analysis and Correlation Properties of Observed and Simulated Total Column Ozone Records

“…Long range correlations are present in the signal when the fluctuation function follows a power law F (n) ∼ n α (straight line in a log-log plot) with exponent values α > 1/2. Clean power law behavior is rarely obtained for empirical data, especially for such complex systems as the atmosphere [22,23,28,30]. The reason is that many different processes of different characteristic time scales affect the instantaneous value of any atmospheric parameter, therefore nonstationarities, various trends, cycles etc.…”

“…Apparent periodic components in a signal spoil the results [27,28], therefore the first step is to obtain an anomaly time series a(t) (t = 1...N ) by computing the difference between an instantaneous TO value and the climatic mean for the given calendar day (obtained from as many years as available). Note that this procedure effectively removes stationary semiannual and annual oscillations from a signal, however it cannot wipe out a global trend or quasi-periodic components such as QBO.…”

Effect of nonlinear filters on detrended fluctuation analysis

“…Recent comparative studies have demonstrated that the DFA method outperforms conventional techniques in accurately quantifying correlation properties over a wide range of scales [6,7,8,9,10]. The DFA method has been widely applied to DNA [4,6,7,11,12,13], cardiac dynamics [14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30], human electroencephalographic (EEG) fluctuations [31], human motor activity [32] and gait [33,34,35,36,37], meteorology [38,39], climate temperature fluctuations [40,41,42,43,44,45], river flow and discharge [46,47], electric signals [48,49,50], stellar x-ray binary systems...…”

Is the Atlantic Multidecadal Oscillation (AMO) a statistical phantom?

“…4a. For increasing time window sizes w (in units of month), the statistical inaccuracies result in a widening band for the model sequences, nevertheless their behaviour follows the expectations (Király and Jánosi, 2002) times an AR(1) process has strong "memory" indicated by a large slope of DFA curves, but this slope gradually decreases to the asymptotic value of 1/2. The empirical monthly SST sequence does not really fit into this band: the AR(1) model systematically overestimates observed correlations for the intermediate times [40−135] months, and definitely underestimates them over 690 months (note the log 10 scales in Fig.…”