Effect of Trends on Detrended Fluctuation Analysis of Precipitation Series

We use detrended fluctuation analysis (DFA) method to detect the long-range correlation and scaling properties of daily precipitation series of Beijing from 1973 to 2004 before and after adding diverse trends to the original series. The correlation and scaling properties of the original series are difficult to analyze due to existing crossovers. The effects of the coefficient and the power of the added trends on the scaling exponents and crossovers of the series are tested. A crossover is found to be independent of the added trends, which arises from the intrinsic periodic trend of the precipitation series. However, another crossover caused by the multifractal vanishes with the increasing power of added trends.

[1]  C. Peng,et al.  Mosaic organization of DNA nucleotides. , 1994, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[2]  Ming Li.  Generation of teletraffic of generalized Cauchy type , 2010 .

[3]  Ming Li,et al.  Modeling network traffic using generalized Cauchy process , 2008 .

[4]  Harvard Medical School,et al.  Effect of nonstationarities on detrended fluctuation analysis. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[5]  Carlo Cattani,et al.  Application of Periodized Harmonic Wavelets towards Solution of Eigenvalue Problems for Integral Equations , 2010 .

[6]  Merab Menabde,et al.  Multifractal characterization of rain fields with a strong orographic influence , 1996 .

[7]  Pengjian Shang,et al.  Detecting long-range correlations of traffic time series with multifractal detrended fluctuation analysis , 2008 .

[8]  I. Rodríguez‐Iturbe,et al.  Detrended fluctuation analysis of rainfall and streamflow time series , 2000 .

[9]  H. Stanley,et al.  Effect of nonlinear filters on detrended fluctuation analysis. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[10]  Jianwei Zhang,et al.  Vision Processing for Realtime 3-D Data Acquisition Based on Coded Structured Light , 2008, IEEE Transactions on Image Processing.

[11]  Ivo Grosse,et al.  Fractionally integrated process with power-law correlations in variables and magnitudes. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[12]  Thadeu Josino Pereira Penna,et al.  Fourier-detrended fluctuation analysis , 2005 .

[13]  Schwartz,et al.  Method for generating long-range correlations for large systems. , 1995, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[14]  Ghiocel Toma.  Specific Differential Equations for Generating Pulse Sequences , 2010 .

[15]  Massimo Scalia,et al.  Analysis of Large-Amplitude Pulses in Short Time Intervals: Application to Neuron Interactions , 2010 .

[16]  H. Stanley,et al.  Effect of trends on detrended fluctuation analysis. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[17]  E. Bakhoum,et al.  Dynamical Aspects of Macroscopic and Quantum Transitions due to Coherence Function and Time Series Events , 2010 .

[18]  Wei-Xing Zhou,et al.  Modified detrended fluctuation analysis based on empirical mode decomposition for the characterization of anti-persistent processes , 2009, 0907.3284.

[19]  H. Stanley,et al.  Multifractal Detrended Fluctuation Analysis of Nonstationary Time Series , 2002, physics/0202070.

[20]  Radhakrishnan Nagarajan,et al.  Minimizing the effect of periodic and quasi-periodic trends in detrended fluctuation analysis , 2005 .

[21]  S. Y. Chena,et al.  Real-time three-dimensional surface measurement by color encoded light projection , 2006 .

[22]  Ming Li.  Fractal Time Series—A Tutorial Review , 2010 .

[23]  Robert K. Crane,et al.  Prediction of Attenuation by Rain , 1980, IEEE Trans. Commun..

[24]  M. Reza Rahimi Tabar,et al.  Fractal analysis of discharge current fluctuations , 2007, 0710.3849.

[25]  Shengyong Chen,et al.  Real-time three-dimensional surface measurement by color encoded light projection , 2006 .

[26]  S. Havlin,et al.  Detecting long-range correlations with detrended fluctuation analysis , 2001, cond-mat/0102214.

[27]  C.-Y. Chu,et al.  Effects of rain fading on the efficiency of the Ka-band LMDS system in the Taiwan area , 2005, IEEE Transactions on Vehicular Technology.

[28]  Ming Li,et al.  Representation of a Stochastic Traffic Bound , 2010, IEEE Transactions on Parallel and Distributed Systems.

[29]  D. Schertzer,et al.  New Uncertainty Concepts in Hydrology and Water Resources: Multifractals and rain , 1995 .

[30]  Jeffrey M. Hausdorff,et al.  Quantifying Fractal Dynamics of Human Respiration: Age and Gender Effects , 2002, Annals of Biomedical Engineering.

[31]  R. Crane.  A local model for the prediction of rain-rate statistics for rain-attenuation models , 2003 .

[32]  Ming Li,et al.  On the Predictability of Long-Range Dependent Series , 2010 .

[33]  Jiann-Shing Shieh,et al.  Human heart beat analysis using a modified algorithm of detrended fluctuation analysis based on empirical mode decomposition. , 2009, Medical engineering & physics.

[34]  I. Jánosi,et al.  Empirical mode decomposition and correlation properties of long daily ozone records. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[35]  Klaus Fraedrich,et al.  Scaling regimes of composite rainfall time series , 1993 .

[36]  Pengjian Shang,et al.  Chaotic SVD method for minimizing the effect of exponential trends in detrended fluctuation analysis , 2009 .