Deterministic nature of the underlying dynamics of surface wind fluctuations

Abstract. Modelling the fluctuations of the Earth's surface wind has a significant role in understanding the dynamics of atmosphere besides its impact on various fields ranging from agriculture to structural engineering. Most of the studies on the modelling and prediction of wind speed and power reported in the literature are based on statistical methods or the probabilistic distribution of the wind speed data. In this paper we investigate the suitability of a deterministic model to represent the wind speed fluctuations by employing tools of nonlinear dynamics. We have carried out a detailed nonlinear time series analysis of the daily mean wind speed data measured at Thiruvananthapuram (8.483° N,76.950° E) from 2000 to 2010. The results of the analysis strongly suggest that the underlying dynamics is deterministic, low-dimensional and chaotic suggesting the possibility of accurate short-term prediction. As most of the chaotic systems are confined to laboratories, this is another example of a naturally occurring time series showing chaotic behaviour.

[1]  Mohammad Monfared,et al.  A new strategy for wind speed forecasting using artificial intelligent methods , 2009 .

[2]  J. Yorke,et al.  Chaos: An Introduction to Dynamical Systems , 1997 .

[3]  C. W. Fairall,et al.  Signatures of deterministic chaos in radar sea clutter and ocean surface winds. , 1995, Chaos.

[4]  Leonard A. Smith,et al.  Distinguishing between low-dimensional dynamics and randomness in measured time series , 1992 .

[5]  Theiler,et al.  Spurious dimension from correlation algorithms applied to limited time-series data. , 1986, Physical review. A, General physics.

[6]  T. O. Halawani,et al.  A neural networks approach for wind speed prediction , 1998 .

[7]  W. Rivera,et al.  Wind speed forecasting in the South Coast of Oaxaca, México , 2007 .

[8]  Holger Kantz,et al.  Practical implementation of nonlinear time series methods: The TISEAN package. , 1998, Chaos.

[9]  A. Brett,et al.  The Autocorrelation of Hourly Wind Speed Observations , 1991 .

[10]  F. Takens.  Detecting strange attractors in turbulence , 1981 .

[11]  A. Elliott,et al.  A PROBABILISTIC DESCRIPTION OF THE WIND OVER LIVERPOOL BAY WITH APPLICATION TO OIL SPILL SIMULATIONS , 2004 .

[12]  M. Bilgili,et al.  Application of artificial neural networks for the wind speed prediction of target station using reference stations data , 2007 .

[13]  Kazuyuki Aihara,et al.  Wind Modelling and its Possible Application to Control of Wind Farms , 2008 .

[14]  P. Grassberger,et al.  Measuring the Strangeness of Strange Attractors , 1983 .

[15]  Athanasios Sfetsos,et al.  A novel approach for the forecasting of mean hourly wind speed time series , 2002 .

[16]  L. V. Cremades,et al.  Analysis and modelling of time series of surface wind speed and direction , 1999 .

[17]  Mario Ragwitz,et al.  Detecting non-linear structure and predicting turbulent gusts in surface wind velocities , 2000 .

[18]  J. Torres,et al.  Forecast of hourly average wind speed with ARMA models in Navarre (Spain) , 2005 .

[19]  James P. Crutchfield,et al.  Geometry from a Time Series , 1980 .

[20]  E. Fernandez,et al.  Estimation of Energy Yield From Wind Farms Using Artificial Neural Networks , 2009, IEEE Transactions on Energy Conversion.

[21]  J. Yorke,et al.  HOW MANY DELAY COORDINATES DO YOU NEED , 1993 .

[22]  S. Basu,et al.  Prediction of Mean Winds at an Indian Coastal Station Using a Data–Driven Technique Applied on Weibull Parameters , 2011 .

[23]  E. Ott.  Chaos in Dynamical Systems: Contents , 1993 .

[24]  Lueder von Bremen.  Combination of Deterministic and Probabilistic Meteorological Models to enhance Wind Farm Power Forecasts , 2007 .

[25]  Fraser,et al.  Independent coordinates for strange attractors from mutual information. , 1986, Physical review. A, General physics.

[26]  Schreiber,et al.  Extremely simple nonlinear noise-reduction method. , 1993, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[27]  D. Kugiumtzis,et al.  Nonlinear analysis of magnetospheric data Part I. Geometric characteristics of the AE index time series and comparison with nonlinear surrogate data , 1999 .

[28]  K. S. Kumar,et al.  Analysis of the fluctuations of the total electron content (TEC) measured at Goose Bay using tools of nonlinear methods , 2004 .

[29]  A. Celik.  A statistical analysis of wind power density based on the Weibull and Rayleigh models at the southern region of Turkey , 2004 .

[30]  H. Kantz.  A robust method to estimate the maximal Lyapunov exponent of a time series , 1994 .

[31]  H. Kantz,et al.  Nonlinear time series analysis , 1997 .

[32]  K. S. Kumar,et al.  Nonlinear time series analysis of the fluctuations of the geomagnetic horizontal field , 2002 .

[33]  James Theiler,et al.  Testing for nonlinearity in time series: the method of surrogate data , 1992 .

[34]  L. Kamal,et al.  Time series models to simulate and forecast hourly averaged wind speed in Quetta, Pakistan , 1997 .

[35]  Schreiber,et al.  Improved Surrogate Data for Nonlinearity Tests. , 1996, Physical review letters.

[36]  Joseph P. Hennessey.  Some Aspects of Wind Power Statistics , 1977 .

[37]  R. Kavasseri,et al.  Day-ahead wind speed forecasting using f-ARIMA models , 2009 .

[38]  H. Abarbanel,et al.  Determining embedding dimension for phase-space reconstruction using a geometrical construction. , 1992, Physical review. A, Atomic, molecular, and optical physics.

[39]  J. Gavaldà,et al.  Statistical and spectral analysis of the wind regime in the area of Catalonia , 1992 .

[40]  Fedor Mitschke,et al.  CHAOS VERSUS NOISE IN EXPERIMENTAL DATA , 1993 .

[41]  A. Rigas,et al.  Evidence for strange attractor structures in space plasmas. , 1992 .

[42]  E. Lorenz.  Deterministic nonperiodic flow , 1963 .

[43]  T. Schreiber,et al.  Discrimination power of measures for nonlinearity in a time series , 1997, chao-dyn/9909043.

[44]  James A. Yorke,et al.  Coping with chaos , 2013 .

[45]  Hung Man Tong,et al.  Threshold models in non-linear time series analysis. Lecture notes in statistics, No.21 , 1983 .

[46]  Raul J. Alvarez,et al.  Dependence of daily peak O3 concentrations near Houston, Texas on environmental factors: Wind speed, temperature, and boundary-layer depth , 2011 .

[47]  T. Palmer.  Extended-range atmospheric prediction and the Lorenz model , 1993 .