Different Multifractal Scaling of the 0？cm Average Ground Surface Temperature of Four Representative Weather Stations over China

The temporal scaling properties of the daily 0？cm average ground surface temperature (AGST) records obtained from four selected sites over China are investigated using multifractal detrended fluctuation analysis (MF-DFA) method. Results show that the AGST records at all four locations exhibit strong persistence features and different scaling behaviors. The differences of the generalized Hurst exponents are very different for the AGST series of each site reflecting the different scaling behaviors of the fluctuation. Furthermore, the strengths of multifractal spectrum are different for different weather stations and indicate that the multifractal behaviors vary from station to station over China. 1. Introduction In recent years, a variety of methods such as power spectrum analysis, autocorrelation functions, and detrended fluctuation analysis (DFA), among others, have been widely used to study the correlations and fluctuations of different time series [1–6]. The DFA method as an important technique established by Peng et al. [1] and extended by Bunde et al. [2] and Kantelhardt et al. [7], has been used to detect long-range correlations and determine monofractal scaling properties [7–9]. Moreover, it has been successfully applied to a variety of systems ranging from DNA [1], atmospheric temperature [3–6, 10–13], relative humidity [14], wind speed [15], column ozone [16], and air pollution [17]. However, in DFA analysis to reliably infer the scaling effect, it is necessary to establish power law scaling, investigating both constancy of local slopes in a sufficient range and rejection of an exponential decay of the autocorrelation function [18, 19]. Many studies have shown that a monofractal behavior cannot fully describe uneven multifractal properties [7, 8]. Multifractal theory is an effective method to describe quantitatively the nonlinear evolution of complex climate system and the multiscale characteristics of the physical quantity. Thus, studying the multifractal characteristics of climatic system makes us further understand intrinsic regularity and restriction mechanism of climate change. The theoretical results of multifractal study in the practical application are limited to some extent because the classical estimation method of multifractal spectrum is complicated and difficult [20, 21]. Recently, an extension approach based on the DFA method, namely, MF-DFA, has been applied to analyze the multifractal behaviors of nonstationary time series [22]. It has also been successfully utilized in diverse fields [23–26]. The temperature records as an