بررسی رفتار مقیاسی و چندفرکتالی سری زمانی جریان روزانه رودخانه کشکان

نویسندگان

1 استادیار آب و هواشناسی گروه جغرافیا، دانشکده ادبیات و علوم انسانی، دانشگاه لرستان

2 دانشیار آب و هواشناسی گروه جغرافیا، دانشکده ادبیات و علوم انسانی، دانشگاه لرستان

چکیده

جریان‌های رودخانه حاوی نوسان‌هایی با افت‌وخیزهای بسیار شدیدی هستند که به‌صورت فرایندهای ناایستا و آشوبی رفتار می‌کنند. پیچیدگی رفتار چنین جریان‌هایی از طریق نمایه هرست استاندارد و نمایه هرست تعمیم‌یافته یا نمایه‌های مقیاس، قابل‌کشف و شناسایی هستند. در این مطالعه به‌منظور شناسایی خصوصیات چندفرکتالی رفتارهای مقیاسی و دینامیک پیچیده جریان رودخانه کشکان که از نوسان‌های بسیار شدیدی برخوردار است از تحلیل فرکتالی (DFA) و چندفرکتالی نوسان‌های روندزدایی‌شده (MF-DFA) استفاده شد. نتایج حاصل از تحلیل نوسان‌های روندزدایی‌شده (DFA)، نشان از وجود یک نقطه تلاقی با مقیاس زمانی 348-405 روز در سیگنال جریان روزانه رودخانه کشکان دارد که این فرایند وجود ساختار فرکتالی و رفتار متفاوت سری زمانی جریان این رودخانه را در مقیاس‌های زمانی متفاوت نشان می‌دهد. چنانکه، نمایه هرست (h=2) مقیاس‌های زمانی کمتر از این مقیاس به مقدار 12/1 بدست آمد که بیانگر حافظه کوتاه‌مدت و ساختار ناپایدار این مقیاس‌های زمانی است در صورتی که سری‌های زمانی با مقیاسی بالاتر از این مقیاس، ساختار نسبتاً پایدار و ایستایی را نشان می‌دهند. وابستگی شدید و کاهش تدریجی نمایه هرست تعمیم‌یافته  نسبت به درجه‌های گشتاور نوسان در بازه 5- تا 5، از یک سو ماهیت چندفرکتالی و دینامیک پیچیده و از سوی دیگر، حافظه غیرخطی سیگنال جریان رودخانه کشکان را نشان می‌دهد. افزون براین، ماهیت چندفرکتالی و مقیاس‌های چندگانه جریان این رودخانه برحسب رابطه غیرخطی بین نمایه جرم  با درجه‌های گشتاور، نیز تأیید شد. پهنای زیاد و عدم تقارن طیف تکینگی، ضمن بیان شدت ساختار چندفرکتالی و دینامیک‌های متفاوت در سیگنال جریان رودخانه، نشان از عدم ترازمندی وزن تأثیر نوسان‌های بزرگ و کوچک بر سیگنال جریان رودخانه دارد. بطوریکه کشیدگی دُم راست این طیف، اثر غالب نوسان‌های محلی با مقادیر کوچک را بر ساختار سری زمانی جریان رودخانه کشکان مشخص می‌کند.

کلیدواژه‌ها

عنوان مقاله [English]

Analysis the Scale and Multi-fractal Behavior of Flow Daily Time Series in the Kashkan River

نویسندگان [English]

  • Hamid Mirhashemi 1
  • Dariush Yarahmadi 2
1 Assist. Prof. of Climatology, Geography Sciences Department, Lorestan University
2 Assoc. Prof. of Climatology, Geography Sciences Department, Lorestan University
چکیده [English]

River flow contain fluctuations with very sharp ups and downs that act as unstable and chaos processes. The complexity of the behavior of such flow can be discovered and identified through the standard Hurst exponent and the generalized Hurst exponent or scale exponent. In this study, in order to identify the multi-fractal characteristics of large-scale and complex dynamics of Kashkan river flow, which has very strong fluctuations, multi-fractal detrended fluctuation analysis (MF-DFA) was used. The results of the detrended fluctuation analysis (DFA) show that there is one crossover with a time scale of 348-405 days in the daily signal of Kashkan river flow, which indicates the existence of fractal structure and different behavior of the time series of the river flow in different time scales. The Hurst exponent (h = 2) of small scales was 1.12, which indicates short-term memory and unstable structure of these time scales, while time series with a scale higher than this scale have a relatively stable structure. The strong dependence and gradual decrease of the generalized Hurst exponent on the degrees of fluctuation (q-order RMS) in the range of -5 to 5, on the one hand, shows the complex multi-fractal nature and dynamics, and on the other hand, the nonlinear memory of the Kashkan river flow signal. In addition, the multi-fractal nature and multiple scales of the river flow were confirmed in terms of the nonlinear relationship between mass exponent (tq) and q-order. The large width and asymmetry of the singularity spectrum, while expressing the intensity of the multi-fractal structure and different dynamics in the river flow signal, indicate the weight imbalance of the effect of large and small fluctuations on the river flow signal. The right tail elongation of this spectrum indicates the predominant effect of local fluctuations with small values on the structure of the Kashkan river flow time series.

کلیدواژه‌ها [English]

  • Fluctuation
  • Hurst exponent
  • Kashkan river
  • Multi-fractal
  • Singularity spectrum

مراجع

Adarsh S, Dharan DS, Anuja P and Suman A, 2019. Unravelling the scaling characteristics of daily streamflows of Brahmani river basin, India, using arbitrary-order Hilbert spectral and detrended fluctuation analyses. SN Applied Sciences. 1(1):  58.
Alami MT, Ghorbani MA and Naghipour L, 2015. Multifractal detrended fluctuation analysis of Sofichia river flow. In 10th International Congress on Civil Engineering.  University of Tabriz.Tabriz. Iran.
Barbi M, Chillemi S, Di Garbo A, Balocchi R, Carpeggiani C, Emdin M, Michelassi C and Santarcangelo E, 1998. Predictability and nonlinearity of the heart rhythm. Chaos, Solitons & Fractals. 9(3):  507-515.
Bhattacharya RN, Gupta VK and Waymire E, 1983. The Hurst effect under trends. Journal of Applied Probability 20(3): 649-662.
Cao G and Xu W, 2016. Multifractal features of EUA and CER futures markets by using multifractal detrended fluctuation analysis based on empirical model decomposition. Chaos, Solitons & Fractals. 83:  212-222.
Di Matteo T, Aste T and Dacorogna MM, 2003. Scaling behaviors in differently developed markets. Physica A: Statistical Mechanics and its Applications 324(1-2):  183-188.
Eke A, Herman P, Kocsis L and Kozak L, 2002. Fractal characterization of complexity in temporal physiological signals. Physiological Measurement. 23(1): R1.
Fan Q, Liu S and Wang K, 2019. Multiscale multifractal detrended fluctuation analysis of multivariate time series. Physica A: Statistical Mechanics and its Applications. 532:121864.
Feder J, Fractals. 2013: Springer Science & Business Media.
Hajian S and Movahed MS, 2010. Multifractal detrended cross-correlation analysis of sunspot numbers and river flow fluctuations. Physica A: Statistical Mechanics and its Applications. 389(21):  4942-4957.
Hekmatzadeh AA, Torabi Haghighi A, Hosseini Guyomi K, Amiri SM and Kløve B, 2020. The effects of extremes and temporal scale on multifractal properties of river flow time series. River Research and Applications. 36(1):  171-182.
Hu K, Ivanov PC, Chen Z, Carpena P and Stanley HE, 2001. Effect of trends on detrended fluctuation analysis. Physical Review 64(1), 011114.
Hurst HE, 1951. Long-term storage capacity of reservoirs. Transaction of America  Society of Civil Engneering 116:  770-799.
Ihlen EA, 2014. Multifractal analyses of human response time: potential pitfalls in the interpretation of results. Frontiers in Human Neuroscience. 8:  523.
Ivanov PC, Nunes Amaral LsA, Goldberger AL, Havlin S, Rosenblum MG, Stanley HE and Struzik ZR, 2001. From 1/f noise to multifractal cascades in heartbeat dynamics. Chaos: An Interdisciplinary Journal of Nonlinear Science 11(3):  641-652.
Kalamaras N, Tzanis CG, Deligiorgi D, Philippopoulos K and Koutsogiannis I, 2019. Distribution of air temperature multifractal characteristics over Greece. Atmosphere  45(2):10.
Kantelhardt JW, Koscielny-Bunde E, Rego HH, Havlin S and Bunde A, 2001. Detecting long-range correlations with detrended fluctuation analysis. Physica A: Statistical Mechanics and its Applications. 295(3-4):  441-454.
Kantelhardt JW, Koscielny‐Bunde E, Rybski D, Braun P, Bunde A and Havlin S, 2006. Long‐term persistence and multifractality of precipitation and river runoff records. Journal of Geophysical Research: Atmospheres. 111(D1.)
Kantelhardt JW, Rybski D, Zschiegner SA, Braun P, Koscielny-Bunde E, Livina V, Havlin S and Bunde A, 2003. Multifractality of river runoff and precipitation: comparison of fluctuation analysis and wavelet methods. Physica A: Statistical Mechanics and its Applications. 330(1-2):  240-245.
Kantelhardt JW, Zschiegner SA, Koscielny-Bunde E, Havlin S, Bunde A and Stanley HE, 2002. Multifractal detrended fluctuation analysis of nonstationary time series. Physica A: Statistical Mechanics and its Applications. 316(1-4):  87-114.
Kestener P and Arneodo A, 2008. A multifractal formalism for vector-valued random fields based on wavelet analysis: application to turbulent velocity and vorticity 3D numerical data. Stochastic Environmental Research and Risk Assessment. 22(3):  421-435.
Koscielny-Bunde E, Kantelhardt JW, Braun P, Bunde A and Havlin S, 2006. Long-term persistence and multifractality of river runoff records: Detrended fluctuation studies. Journal of Hydrology. 322(1-4):  120-137.
Labat D, Masbou J, Beaulieu E and Mangin A, 2011. Scaling behavior of the fluctuations in stream flow at the outlet of karstic watersheds, France. Journal of hydrology. 410(3-4):  162-168.
Li E, Mu X, Zhao G and Gao P, 2015. Multifractal detrended fluctuation analysis of streamflow in the Yellow River Basin, China. Water. 7(4):  1670-1686.
Livina VN, Ashkenazy Y, Bunde A and Havlin S, 2011. Seasonality effects on nonlinear properties of hydrometeorological records, Pp. 266-284, In: In Extremis. Springer.
Losada M, Seoane R, de la Barra A and Caram L, 2020. Fractional Brownian Motions and their multifractal analysis applied to Parana river flow. arXiv preprint arXiv:2002.04532.
Matsoukas C, Islam S and Rodriguez‐Iturbe I, 2000. Detrended fluctuation analysis of rainfall and streamflow time series. Journal of Geophysical Research: Atmospheres 105(D23):  29165-29172.
Mesa OJ and Poveda G, 1993. The Hurst effect: The scale of fluctuation approach. Water Resources Research. 29(12):  3995-4002.
Montanari A, 2003. Long-range dependence in hydrology. Theory and Applications of Long-Range Dependence.  461-472.
Movahed MS, Jafari G, Ghasemi F, Rahvar S and Tabar MRR, 2006. Multifractal detrended fluctuation analysis of sunspot time series. Journal of Statistical Mechanics: Theory and Experiment. 2006(02):  P02003.
Noorigheidari M, 2012. Estimation of design storm using multifractal theory in Ghotvan Dam Site. Water and Soil Science. 22(1):  145-154 (In Persian with English abstract).
Nouri Gheidari M, Danko A and Shahraki M, 2015. Application of Power Law in Flood Frequency Analysis of Sarbaz River. Water and Soil Science. 24(4): 45-59 (In Persian with English abstract).
Peng CK, Havlin S, Stanley HE and Goldberger AL, 1995. Quantification of scaling exponents and crossover phenomena in nonstationary heartbeat time series. Chaos: An Interdisciplinary Journal of Nonlinear Science. 5(1):  82-87.
Rodríguez-Iturbe I and Rinaldo A, 2001. Fractal river basins: chance and self-organization. Cambridge University Press.
Rybski D, Bunde A, Havlin S, Kantelhardt JW and Koscielny-Bunde E, 2011. Detrended fluctuation studies of long-term persistence and multifractality of precipitation and river runoff records, Pp.216-248, In: In Extremis. Springer.
Shang P, Lu Y and Kamae S, 2008. Detecting long-range correlations of traffic time series with multifractal detrended fluctuation analysis. Chaos, Solitons & Fractals. 36(1):  82-90.
Taqqu MS, Teverovsky V and Willinger W, 1995. Estimators for long-range dependence: An Empirical Study. Fractals 3(04):  785-798.
Tiwari AK, Aye GC and Gupta R, 2019. Stock market efficiency analysis using long spans of Data: A multifractal detrended fluctuation approach. Finance Research Letters 28:  398-411.
Xu L, Ivanov PC, Hu K, Chen Z, Carbone A and Stanley HE, 2005. Quantifying signals with power-law correlations: A comparative study of detrended fluctuation analysis and detrended moving average techniques. Physical Review 71(5):  051101.
Yan B, Zhou A and Song S, 2019. Multi-fractal characteristics of daily runoff series of Weihe River Watershed. Journal of Water Resource and Protection 11(9):  1146-1160.
Zhang Q, Xu C-Y and Yang T, 2009. Scaling properties of the runoff variations in the arid and semi-arid regions of China: a case study of the Yellow River basin. Stochastic Environmental Research and Risk Assessment. 23(8):  1103-1111.
Zhang Q, Xu C-Y, Yu Z, Liu C-L and Chen YD, 2009. Multifractal analysis of streamflow records of the East River basin (Pearl River), China. Physica A: Statistical Mechanics and its Applications. 388(6):  927-934.
Zhang Q, Xu CY, Chen YD and Yu Z, 2008. Multifractal detrended fluctuation analysis of streamflow series of the Yangtze River basin, China. Hydrological Processes 22(26):  4997-5003.
دانش آب و خاک
دوره 32، شماره 4
دی 1401
صفحه 75-90

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