تأثیر کاهش نوفه در تحلیل پویایی غیرخطی سری‌ زمانی دمای حداکثر روزانه در ایستگاه کرمان

نوع مقاله : یادداشت فنی (5 صفحه)

نویسندگان

1 عضو هیأت علمی بخش تحقیقات فنی و مهندسی کشاورزی، مرکز تحقیقات کشاورزی و منابع طبیعی فارس

2 استاد/ گروه مهندسی آب، دانشکده کشاورزی دانشگاه فردوسی مشهد، مشهد، ایران.

3 استادیار/گروه مهندسی آب، دانشکده کشاورزی دانشگاه فردوسی مشهد، مشهد، ایران

4 فوق دکترا/ گروه ریاضی، دانشگاه تور ورگاتای رم ایتالیا، رم، ایتالیا

چکیده

آب و هوا را می‌توان بصورت مجموعه شرایط اتمسفری یک سیستم پویا و آشوب‌ناک دانست. در هر صورت یکی از مسائل اساسی در برآورد بُعد سری‌های زمانی آشوب‌ناک روبرو شدن با این واقعیت است که سیگنال‌ زمانی هر پدیده طبیعی، با نوفه همراه می‌باشد. اهداف تحقیق حاضر شامل (الف) بررسی تاثیر کاهش نوفه در سری زمانی دمای حداکثر روزانه بر بازسازی فضای فاز، زمان تأخیر و بُعد نشاننده؛ (ب) به کمیت در آوردن آشوب برای هر دو سری زمانی قبل و بعد از کاهش نوفه، به کمک روش‌هایی مانند حداکثر نمای لیاپانف و بُعد همبستگی؛ و (پ) مقایسه دقت پیش‌بینی در هر دو سری زمانی می‌باشند. برای این تحقیق از سری زمانی داده‌های دمای حداکثر روزانه ایستگاه کرمان به مدت 25 سال (2008-1984 میلادی) استفاده شد. نتایج نشان داد که بُعد نشاننده و زمان تأخیر در سری زمانی بعد از کاهش نوفه (به ترتیب 5 و 76 روز) نسبت به قبل از آن (به ترتیب 7 و 82 روز) کاهش یافت. در هر دو سری زمانی، حداکثر نمای لیاپانف مثبت (به ترتیب 011/0 و 019/0) و مقادیر پایین بُعد همبستگی (به ترتیب 78/2 و 85/2) نشان از آشوب‌ناکی آن‌ها داشت. با این حال، کاهش نوفه می‌تواند از طریق کاهش مولفه‌ی تصادفی، در به کمیت درآوردن آشوب و دقت پیش‌بینی تأثیرگذار باشد. بنابراین، برای تجزیه و تحلیل پوپایی غیرخطی سری زمانی، کاهش نوفه ضروری می‌باشد ولی این کاهش نباید باعث از بین رفتن مولفه قطعی درونی سیستم شود.

کلیدواژه‌ها

موضوعات


عنوان مقاله [English]

Effect of Noise Reduction in Nonlinear Dynamic Analysis of Maximum Daily Temperature Series in Kerman Station

نویسندگان [English]

  • A. Eslami 1
  • B. Ghahraman 2
  • A. N. Ziaee 3
  • P. Eslami 4
2 Professor, Water Engineering Department, Faculty of Agriculture, Ferdowsi University of Mashhad, Mashhad, Iran
3 Assistant Professor, Water Engineering Department, Faculty of Agriculture, Ferdowsi University of Mashhad, Mashhad, Iran
4 Postdoctoral Fellow, Roma Tor Vergata University, Rome, Italy
چکیده [English]

Climate could be known as a set of atmospheric conditions of a dynamic and chaotic system. However, a fundamental problem in estimating the chaotic time series dimension is dealing with the fact that a temporal signal of any natural phenomenon is always contaminated by noise. The objectives of this study are: a) investigating the effect of noise reduction in daily maximum temperature time series on the reconstructed phase space, time delay and embedding dimension; b) quantifying chaos for both time series before and after noise reduction, by using methods such as maximal Lyapunov exponent and correlation dimension; and c) comparing the prediction accuracy in both time series. For this study, we used daily maximum temperature time series of Kerman station for 25 years (1984-2008 AD). The results showed that the embedding dimension and delay time in time series after the noise was reduced (respectively, 5 and 76 days) from those of before (respectively 7 and 82 days). In both time series, the positive maximal Lyapunov exponent (respectively, 0.011 and 0.019) and low correlation dimension (respectively, 2.78 and 2.85) resemble the chaotic system. However, noise reduction can have some effects on quantifying chaos and the accuracy of prediction by reducing the random component, so, for the analysis of nonlinear dynamics of time series, noise reduction is essential, but this reduction should not destroy the determinism component of the system.

کلیدواژه‌ها [English]

  • "Chaos
  • nonlinear dynamics
  • prediction
  • daily maximum temperature
  • noise reduction"
Anis Hosseini M, Zaker Moshfegh M (2013) Kashkan river flow analysis and forecasting using chaos theory. Hydraulic Journal 8(3): 45-61 (In Persian).
Box GEP, Jenkins GM, Reinsel GC (1994) Time Series Analysis: Forecasting and Control. Prentice-Hall, Third Edition, NJ, USA, 200p.
Chaudhuri S (2006) Predictability of chaos inherent in the occurrence of severe thunderstorms. Advances in complex systems 9:77–85.
Elshorbagy A, Simonovic SP, Panu US (2002) Estimation of missing stream flow data using principles of chaos theory. Journal of Hydrology 255:123-133.
Eslami A, Ghahraman B (2013) Sensitivity analysis and uncertainty parameters affecting in the estimation of reference evapotranspiration in models with different mathematical structure. Iranian J. of Irri. and Drain. 1(7):68-79 (In Persian).
Fraser AM, Swinney HL (1986) Independent coordinates for strange attractors from mutual information. Phys. Rev. A 33:1134–1140.
Ghaheri A, Ghorbani MA, Delafrooz H, Malekini L (2012) Assessment of river flow using chaos theory. Iranian Water J., 6(10): 117-126 (In Persian).
Gottwald G, Melbourne I (2005) Testing for chaos in deterministic systems with noise. Physica D 212:100-110.
Grassberger P, Procaccia I (1983) Measuring the strangeness of strange attractors. Physica D 9:189-208.
Gutiérrez RM (2004) Optimal nonlinear models from empirical time series: an application to climate. International Journal of Bifurcation and Chaos 14(6):2041–2052.
Hegger R, Kantz H, Schreiber T (1999) Practical implementation of nonlinear time series methods: the TISEAN package. Chaos 9:413–440.
Islam MN, Sivakumar B (2002) Characterization and prediction of runoff dynamics: A nonlinear dynamics view. Advances in Water Resources 25:179-190.
Kantz H (1994) A robust method to estimate the maximal Lyaponov exponent of a time series. Physics Letters A 185:77-87.
Kantz H, Schreiber T (2004) Nonlinear time series analysis. Second edition, Cambridge University Press, Cambridge 388p.
Kellert, S., H. (1993). In the wake of chaos. The University of Chicago Press books, 190p.
Kennel MB, Brown R, Abarbanel HDI (1992) Determining embedding dimension for phase space reconstruction using a geometrical construction. Phys. Rev. A 45(6):3403–3411.
Kugiumtzis D (1996) State space reconstruction parameters in the analysis of chaotic time series - the role of the time window length. Physica D 95:13-28.
Larsen ML, Kostinski AB, Tokay A (2005) Observations and analysis on uncorrelated rain. J. Atmos. Sci. 62:4071–4083.
Li BB, Yuan ZF (2008) Non-linear and chaos characteristics of heart sound time series. Proc. IMechE Part H: J. Engineering in Medicine 222:265–272.
Lorenz EN (1963) Deterministic nonperiodic flow. J. Atmos. Sci. 20:130–141.
Lotfollahi Yaghin, M. A., Lashte Neshai, M. A., Ghorbani, M. A. and Baik Lorian, M. (2013) Modeling and prediction of significant wave height of the Caspian Sea with the theory of chaos. AJSR-CEE, 45 (1): 97-105 (In Persian).
Millán,H. Ghanbarian-Alavijeh, B., García-Fornaris, I. (2010) Nonlinear dynamics of mean daily temperature and dewpoint time series at Babolsar, Iran, 1961–2005. Atmospheric Research 98: 89–101.
Millán H. Rodríguez J., Ghanbarian-Alavijeh B., Biondi R., and Llerena G. (2011) Temporal complexity of daily precipitation records from different atmospheric environments: Chaotic and Lévy stable parameters. Journal of Atmospheric Research 101:879–892.
Moradizadeh Kermani F, Ghorbani MA, Dinpashoh Y, Farsadizadeh D (2012) Predicting model of river stream flow based on chaotic phase space reconstruction. Journal of Knowledge of Soil and Water 4 (22):1-16. (In Persian)
Parmesan C, Yohe G (2003) A globally coherent fingerprint of climate change impacts across natural systems. Nature 421:37-42.
Porporato A, Ridolfi L (1996) Clues to the existence of deterministic chaos in river flow. Int. J. Mod. Phys. B. 10 (15):1821-1862.
Regonda SK, Sivakumar B, Jain A (2004) Temporal scaling in river flow: can it be chaotic? Hydrological Sciences Journal 49(3):373-385.
Rosenstein MT, Collins JJ, De Luca, CJ (1993) A practical method for calculating largest Lyapunov exponents from small data sets. Physica D 65:117–134.
Saltzman B (1959) On the maintenance of the large-scale quasi-permanent disturbances in the atmosphere. Tellus 11:425–431.
Schouten JC, Takens F, van den Bleek CM (1994) Estimation of the dimension of a noisy attractor. Physical review E, 50 (3):1851-1861.
Schreiber T, Grassberger P (1991) A simple noise-reduction method for real data. Physics Letters A 160: 411-418.
Sharifi MB, Georgakakos KP, Rodriguez-Iturbe I (1990) Evidence of deterministic chaos in the pulse of storm rainfall. J. Atmos. Sci. 47: 888–893.
Singh VP (2013) Entropy theory and its application in environmental and water engineering. John Wiley & Sons, Ltd., Publication.
Sivakumar B, Liong SY, Liaw CY (1998) Evidence of chaotic behavior in Singapore rainfall. J. Am. Water Resour. Assoc. 34(2):301–310.
Strozzi FEG, Tenrreiro C, Noè T, Rossi M Serati JM, Zaldívar C (2007) Application of non-linear time series analysis techniques to the Nordic spot electricity market data. Liuc Papers n. 200, Serie Tecnologia 11.
Takens F (1981) Detecting strange attractors in turbulence, Lecture Notes in Mathematics, Vol. 898. Springer, New York.
Tsonis AA, Elsner JB, Georgakakos KP (1993) Estimating the dimension of weather and climate attractors: important issues about the procedure and interpretation. J. Atmos. Sci. 50:2549–2555.
Valipour M, Zaker-Moshfegh M (2013) Application of genetic programming in simulation of rainfall-runoff process. Seventh National Congress of Civil Engineering, Zahedan University, Iran.
Zang X, Howell J (2004) Dynamics and control of process systems. A proceeding volume from the 7th IFAC symposium, Cambridge, Massachusetts, USA, V. 1, ELSEVIER IFAC publications.
Zhou Y, Ma Z, Wang L (2002) Chaotic dynamics of the flood series in the Huaihe River basin for the last 500 years. Journal of Hydrology 258:100-110.