Stochastic modeling of daily temperature fluctuations

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.