Nonuniversal atmospheric persistence: different scaling of daily minimum and maximum temperatures.

An extensive investigation of 61 daily temperature records by means of detrended fluctuation analysis has revealed that the value of correlation exponent is not universal, contrary to earlier claims. Furthermore, statistically significant differences are found for daily minimum and maximum temperatures measured at the same station, suggesting different degrees of long-range correlations for the two extremes. Numerical tests on synthetic time series demonstrate that a correlated signal interrupted by uncorrelated segments exhibits an apparently lower exponent value over the usual time window of empirical data analysis. In order to find statistical differences between the two daily extreme temperatures, high frequency (10 min) records were evaluated for two distant locations. The results show that daily maxima characterize better the dynamic equilibrium state of the atmosphere than daily minima, for both stations. This provides a conceptual explanation why scaling analysis can yield different exponent values for minima and maxima.

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.