Different scaling behaviors in daily temperature records over China

Long-range correlations of five kinds of daily temperature records (i.e. daily average temperature records, daily maximum temperature records, daily minimum temperature records, diurnal temperature range and the sum of daily maximum and minimum temperature records) from 164 weather stations over China during 1951-2004 are analyzed by means of detrended fluctuation analysis (DFA). These five kinds of fluctuation series are found to be power-law correlated with scaling exponents larger than 0.5. Local changes of scaling exponents are examined and the spatial distributions of these different kinds of temperature records are similar except the diurnal temperature range (DTR for short) records. Furthermore, the differences of the scaling behavior among diurnal temperature records and other kinds of temperature records are discussed.     

Levels of complexity in turbulent time series for weakly and high Reynolds number

We use the detrended fluctuation analysis (DFA), the detrended cross correlation analysis (DCCA) and the magnitude and sign decomposition analysis to study the fluctuations in the turbulent time series and to probe long-term nonlinear levels of complexity in weakly and high turbulent flow. The DFA analysis indicate that there is a time scaling region in the fluctuation function, segregating regimes with different scaling exponents. We discuss that this time scaling region is related to inertial range in turbulent flows. The DCCA exponent implies the presence of power-law cross correlations. In addition, we conclude its multifractality for high Reynold’s number in inertial range. Further, we find that turbulent time series exhibit complex features by magnitude and sign scaling exponents.     

脑电信号的标度分析及其在睡眠状态区分中的应用

脑电信号具有长程幂律相关性及多重分形的标度特性,并随生理病理状态改变.本文首次针对睡眠脑电信号应用单重分形去趋势波动分析(detrended fluctuation analysis,简记为DFA)方法与多重分形奇异谱对睡眠脑电信号的标度特征进行系统的对比研究.发现DFA标度指数α对于不同导联和样本组间的差异较为敏感,随睡眠状态的变化不规律;而多重分形奇异强度区间Δα随睡眠状态的变化更为规律,睡眠Ⅰ期至Ⅳ期不断增大,并且导联间差异和样本组间差异均较小.多重分形Δα参数更适合作为判定睡眠状态的定量参数.     

Universal scaling behaviors of meteorological variables’ volatility and relations with original records

Volatility series (defined as the magnitude of the increments between successive elements) of five different meteorological variables over China are analyzed by means of detrended fluctuation analysis (DFA for short). Universal scaling behaviors are found in all volatility records, whose scaling exponents take similar distributions with similar mean values and standard deviations. To reconfirm the relation between long-range correlations in volatility and nonlinearity in original series, DFA is also applied to the magnitude records (defined as the absolute values of the original records). The results clearly indicate that the nonlinearity of the original series is more pronounced in the magnitude series.     

Scaling analysis of phase fluctuations in experimental three-phase flows

The characterization of complex patterns arising from three-phase (e.g., oil-gas-water) flows is an important problem with significant engineering and industrial applications. Based solely on measured conductance fluctuation signals from experimental three-phase flows, we propose a method to characterize and distinguish three commonly observed flow patterns. Using the phase characterization method, we first calculate the instantaneous phase from the signals. Then, through performing a scaling analysis, detrended fluctuation analysis (DFA), we extract scaling behaviors associated with the phase fluctuations and find that the DFA scaling exponent is sensitive to the transition among different flow patterns, which can be used to characterize nonlinear dynamics of the three-phase flow. From a novel perspective, we investigate the three-phase flow in terms of phase characterization and scaling analysis. The results indicate that our method can provide new insights into the exploration of complex mechanism in flow pattern transition. The effectiveness of the method is demonstrated and its broader applicability is articulated.     

Scaling instability in self-potential earthquake-related signals

Scaling behavior of the temporal variability in self-potential data recorded in the frequency range during 1995 at Acapulco station (Mexico) was identified and analyzed. In this period, a strong earthquake (Ms=7.4) struck the monitored area on September 14, 1995. Using the detrended fluctuation analysis (DFA), which is a powerful method to detect scaling in nonstationary time series, deviations from stable power-law scaling were quantified. Our findings point to an evident unstable scaling behavior in self-potential data before the occurrence of the seismic event. These first results could be useful in the framework of earthquake prediction studies.     

Detrended Fluctuation Analysis on Correlations of Complex Networks Under Attack and Repair Strategy

We analyze the correlation properties of the Erdos-Rényi random graph (RG) and the Barabási-Albert scale-free network (SF) under the attack and repair strategy with detrended fluctuation analysis (DFA). The maximum degree k representing the local property of the system, shows similar scaling behaviors for random graphs and scale-free networks. The fluctuations are quite random at short time scales but display strong anticorrelation at longer time scales under the same system size N and different repair probability pre. The average degree , revealing the statistical property of the system, exhibits completely different scaling behaviors for random graphs and scale-free networks. Random graphs display long-range power-law correlations. Scale-free networks are uncorrelated at short time scales; while anticorrelated at longer time scales and the anticorrelation becoming stronger with the increase of pre.     

Preservation of long range temporal correlations under extreme random dilution

Many natural time series exhibit long range temporal correlations that may be characterized by power-law scaling exponents. However, in many cases, the time series have uneven time intervals due to, for example, missing data points, noisy data, and outliers. Here we study the effect of randomly missing data points on the power-law scaling exponents of time series that are long range temporally correlated. The Fourier transform and detrended fluctuation analysis (DFA) techniques are used for scaling exponent estimation. We find that even under extreme dilution of more than 50%, the value of the scaling exponent remains almost unaffected. Random dilution is also applied on heart interbeat interval time series. It is found that dilution of 70%-80% of the data points leads to a reduction of only 8% in the scaling exponent; it is also found that it is possible to discriminate between healthy and heart failure subjects even under extreme dilution of more than 90%.     

Detrending fluctuation analysis based on high-pass filtering

Detrended fluctuation analysis (DFA) is a scaling method commonly used for detecting long-range correlations in non-stationary time series. The DFA method uses a trend based on polynomial fitting to extract and quantify fluctuations at different time scales. Basically, such procedure acts as a (non-dynamical) high-pass filter that removes time series components below a given time scale. As an alternative to the polynomial fitting approach, this paper proposes a DFA method based on well-known high-pass filters (e.g., Butterworth, elliptic, etc.). Numerical results show that the proposed DFA approach yields results similar to traditional DFA method. Maybe, the main advantage of the proposed DFA method is that efficient implementations of high-pass filters are available commercially.     

Cycles,scaling and crossover phenomenon in length of the day (LOD) time series

The dynamics of the temporal fluctuations of the length of the day (LOD) time series from January 1, 1962 to November 2, 2006 were investigated. The power spectrum of the whole time series has revealed annual, semi-annual, decadal and daily oscillatory behaviors, correlated with oceanic–atmospheric processes and interactions. The scaling behavior was analyzed by using the detrended fluctuation analysis (DFA), which has revealed two different scaling regimes, separated by a crossover timescale at approximately 23 days. Flicker-noise process can describe the dynamics of the LOD time regime involving intermediate and long timescales, while Brownian dynamics characterizes the LOD time series for small timescales.     

Interpretation of heart rate variability via detrended fluctuation analysis and alphabeta filter

Detrended fluctuation analysis (DFA), suitable for the analysis of nonstationary time series, has confirmed the existence of persistent long-range correlations in healthy heart rate variability data. In this paper, we present the incorporation of the alphabeta filter to DFA to determine patterns in the power-law behavior that can be found in these correlations. Well-known simulated scenarios and real data involving normal and pathological circumstances were used to evaluate this process. The results presented here suggest the existence of evolving patterns, not always following a uniform power-law behavior, that cannot be described by scaling exponents estimated using a linear procedure over two predefined ranges. Instead, the power law is observed to have a continuous variation with segment length. We also show that the study of these patterns, avoiding initial assumptions about the nature of the data, may confer advantages to DFA by revealing more clearly abnormal physiological conditions detected in congestive heart failure patients related to the existence of dominant characteristic scales.     

Scaling characteristics of ocean wave height time series

Fluctuations in the significant wave height can be quantified by using scaling statistics. In this paper, the scaling properties of the significant wave height were explored by using a large data set of hourly series from 25 monitoring stations located off the west coast of the US. Detrended fluctuation analysis (DFA) was used to investigate the scaling properties of the series. DFA is a robust technique that can be used to detect long-range correlations in nonstationary time series. The significant wave height data was analyzed by using scales from hourly to monthly. It was found that a common scaling behavior can be observed for all stations. A breakpoint in the scaling region around 4-5 days was apparent. Spectral analysis confirms this result. This breakpoint divided the scaling region into two distinct parts. The first part was for finer scales (up to 4 days) which exhibited Brown noise characteristics, while the second one showed 1/f noise behavior at coarser scales (5 days to 1 month). The first order and the second order DFA (DFA1 and DFA2) were used to check the effect of seasonality. It was found that there were no differences between DFA1 and DFA2 results, indicating that there is no effect of trends in the wave height time series. The resulting scaling coefficients range from 0.696 to 0.890 indicating that the wave height exhibits long-term persistence. There were no coherent spatial variations in the scaling coefficients.     

Non-uniform scaling behavior in ultra-low-frequency (ULF) earthquake-related geomagnetic signals

Investigating highly non-stationary time series, which typically exhibit long-range correlations, is a classic problem in physics. Here, we analyze the scaling properties of the dynamics of ultra-low-frequency (ULF) geomagnetic data (in the frequency range between 1 mHz and 10 Hz) observed at Izu Peninsula in Japan. On the basis of the detrended fluctuation analysis (DFA), deviations from uniform power-law scaling were quantified. Our findings point out to a significant non-uniform scaling behavior in ULF geomagnetic data in relationship with the occurrence of intense seismic clusters.     

基于长程相关性特征的北京气候中心气候系统模式对中国气温的模拟性能评估

传统对数值模式模拟效果的评估主要是基于均值、趋势、概率密度分布、极值等方面的特征比较模拟要素与观测值的差异或是通过分析模拟值与观测值之间的相关性来定量判断.这类评估方法主要考虑了模式模拟结果与观测资料在统计上的差异,缺乏对两者在动力学特征上的比较.鉴于此,本文基于气象观测资料演变过程中所展现的长程相关性特征,利用去趋势波动分析方法对观测资料和模式模拟数据进行标度分析,研究模式模拟结果是否具有类似于观测资料中的长程相关性特征,进而通过比较观测资料和模式模拟结果的标度指数,从大气演变的内在动力学特征上对模式模拟性能进行评估.本文对北京气候中心气候系统模式对中国地表气温的模拟性能进行了评估,结果表明,该模式能够较好地反映出中国区域气温要素的长程相关性特征,对东北、西北中东部、江淮、江南东部等地模拟效果较好,但对于青藏高原地区及西北大部、华北、黄淮等地的模拟效果相对较差,其中对青藏高原地区和西北西部的模拟效果最差.     

Effects of quantization on detrended fluctuation analysis

Detrended fluctuation analysis(DFA) is a method foro estimating the long-range power-law correlation exponent in noisy signals.It has been used successfully in many different fields,especially in the research of physiological signals.As an inherent part of these studies,quantization of continuous signals is inevitable.In addition,coarse-graining,to transfer original signals into symbol series in symbolic dynamic analysis,can also be considered as a quantization-like operation.Therefore,it is worth considering whether the quantization of signal has any effect on the result of DFA and if so,how large the effect will be.In this paper we study how the quantized degrees for three types of noise series(anti-correlated,uncorrelated and long-range power-law correlated signals) affect the results of DFA and find that their effects are completely different.The conclusion has an essential value in choosing the resolution of data acquisition instrument and in the processing of coarse-graining of signals.     

Analysis of temporal fluctuations in Bach’s sinfonias

The correlation structures in 15 Bach’s sinfonias were analyzed. Each sinfonia is characterized by the superposition of three voices. Each voice is a sequence of pitches. Each voice was transformed in a time series, in which the sampling time was given by the smallest pitch duration in that voice. The scaling properties of the three voices of each sinfonia was quantified by means of the estimate of the scaling exponent, performed using the power spectral density (PSD) and the detrended fluctuation analysis (DFA). The results show that the voice time series are persistent. The DFA was applied not only to any single voice time series, but also to couples (2-DFA) of voices and to the triple (3-DFA) of voices. It was found that the first voice of each sinfonia modulates the scaling behavior of the whole sinfonia.     

Temporal variations of long-term correlations in seismic activity fluctuations

The scaling behavior of the 1998-2009 seismicity in Guerrero, southern Mexico, was studied by means of the detrended fluctuation analysis (DFA). We found that inter-seismic periods are correlated with a transition in the scaling behavior at about 200 seismic events. Correlations are relatively weak for small time scales. However, for large time scales, correlations are associated with a 1/f fractional process, indicating that the seismicity pattern emerges from a self-organized critical state. Temporal variations of the scaling exponent along years computed from the DFA indicate the presence of a quasi-biennial cycle in the seismicity correlations. This cyclic behavior was apparently triggered by the large 2001-2002 slow slip event in the Guerrero seismic gap. Besides, the significant seismic events (M_w>5) originate, on the average, at deeper regions in each cycle.     

Fluctuations and pseudo long range dependence in network flows: A non-stationary Poisson process model

In the study of complex networks (systems), the scaling phenomenon of flow fluctuations refers to a certain power-law between the mean flux (activity) < F_i> of the i-th node and its variance σ_i as F_{i ∝ <Fi^α. Such scaling laws are found to be prevalent both in natural and man-made network systems, but the understanding of their origins still remains limited. This paper proposes a non-stationary Poisson process model to give an analytical explanation of the non-universal scaling phenomenon: the exponent α varies between 1/2 and 1 depending on the size of sampling time window and the relative strength of the external/internal driven forces of the systems. The crossover behaviour and the relation of fluctuation scaling with pseudo long range dependence are also accounted for by the model. Numerical experiments show that the proposed model can recover the multi-scaling phenomenon.}     

Detecting long-range correlations in fire sequences with Detrended fluctuation analysis

The spatial-temporal power-law distributions are found in many natural systems, which have self-similarity and fractal behavior. By analyzing the time series of such systems, we could expect to explore and understand the underlying mechanisms. In this paper, the Detrended fluctuation analysis (DFA) is used to analyze the long-range correlations of forest and urban fires in Japan and China. It is found that the interevent time series of both forest and urban fires have the persistent long-range power-law correlations, and they all have two scaling exponents, α₁ and α₂, which are both bigger than 0.5 and smaller than 1.0, despite the different regions and countries. For forest fires, 0.61<α₁<0.73,0.87<α₂<0.98 and for urban fires, 0.52<α₁<0.61,0.59<α₂<0.88. The result suggests that fires have self-similarity characteristics. The occurrence of forest fires may have connection with the weather fluctuations, which have significant effects on the ignition and have the similar temporal correlations. It is shown that the interval sequences of urban fires closely resemble that of white noise in small timescale, and the correlations are weaker than that of forest fires. Human behavior and human density may affect the long-range correlation in some way. This seems to be helpful to understand the complexity of fire system in temporal aspect.     

北京气候中心气候系统模式对中国四季日平均气温的模拟性能评估

利用去趋势波动分析方法对中国四季日平均气温观测资料进行了研究, 发现四季日平均气温均具有很好的长程相关性特征, 中国西部地区尤其是新疆和西藏的长程相关性较强. 基于观测资料中的这种长程相关性特征, 评估了北京气候中心气候系统模式对中国四季日平均气温的模拟性能, 发现该模式能够较好地反映中国四季日平均气温的长程相关性特征. 总体而言, 模式对春季的日平均气温的长程相关性模拟效果最好, 仅对江南地区的长程相关性的模拟较差; 夏季, 模式模拟误差较大的地区包括中国中东部地区及西藏大部, 其中华北南部、黄淮西部、江南大部、华南等地模拟效果最差; 秋季, 模式对东部沿海及东北大部、华北西南部等地模拟的长程相关性偏强, 而在西北大部模拟的长程相关性明显偏弱; 冬季, 除东部沿海地区模拟的长程相关性偏强外, 全国其余大部分地区接近观测或偏弱, 其中西北、西南、华南北部、江南南部、东北北部偏弱明显, 青藏高原西部偏弱最为显著.