About this Journal Submit a Manuscript Table of Contents
Mathematical Problems in Engineering
Volume 2012 (2012), Article ID 843676, 10 pages
http://dx.doi.org/10.1155/2012/843676
Research Article

Cauchy-Matern Model of Sea Surface Wind Speed at the Lake Worth, Florida

1School of Information Science & Technology, East China Normal University, Shanghai 200241, China
2Faculty of Engineering, Multimedia University, 63100 Cyberjaya, Selangor, Malaysia
3Department of Computer and Information Science, University of Macau, Avenida Padre Tomas Pereira, Taipa, Macau, China

Received 4 November 2012; Accepted 5 December 2012

Academic Editor: Sheng-yong Chen

Copyright © 2012 Ming Li et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. B. B. Mandelbrot, Gaussian Self-Affinity and Fractals, Springer, 2001. View at Zentralblatt MATH
  2. J. Beran, Statistics for Long-Memory Processes, Chapman & Hall, 1994. View at Zentralblatt MATH
  3. B. B. Mandelbrot and J. W. van Ness, “Fractional Brownian motions, fractional noises and applications,” SIAM Review, vol. 10, no. 4, pp. 422–437, 1968. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  4. A. J. Lawrance and N. T. Kottegoda, “Stochastic modelling of riverflow time series,” Journal of the Royal Statistical Society A, vol. 140, no. 1, pp. 1–47, 1977. View at Scopus
  5. L. M. Kaplan and C.-C. J. Kuo, “Extending self-similarity for fractional Brownian motion,” IEEE Transactions on Signal Processing, vol. 42, no. 12, pp. 3526–3530, 1994. View at Publisher · View at Google Scholar · View at Scopus
  6. R. J. Martin and A. M. Walker, “A power-law model and other models for long-range dependence,” Journal of Applied Probability, vol. 34, no. 3, pp. 657–670, 1997. View at Scopus
  7. C. W. J. Granger and Z. Ding, “Varieties of long memory models,” Journal of Econometrics, vol. 73, no. 1, pp. 61–77, 1996. View at Publisher · View at Google Scholar · View at Scopus
  8. J. Beran, “Fitting long-memory models by generalized linear regression,” Biometrika, vol. 80, no. 4, pp. 817–822, 1993. View at Publisher · View at Google Scholar · View at Scopus
  9. B. Yazici and R. L. Kashyap, “A class of second-order stationary self-similar processes for 1/f phenomena,” IEEE Transactions on Signal Processing, vol. 45, no. 2, pp. 396–410, 1997. View at Scopus
  10. M. Li, W. Jia, and W. Zhao, “Correlation form of timestamp increment sequences of self-similar traffic on Ethernet,” Electronics Letters, vol. 36, no. 19, pp. 1668–1669, 2000. View at Scopus
  11. J.-P. Chilès and P. Delfiner, Geostatistics, Modeling Spatial Uncertainty, John Wiley & Sons, 1999. View at Publisher · View at Google Scholar
  12. B. Matérn, Spatial Variation, vol. 36 of Lecture Notes in Statistics, Springer, 2nd edition, 1980.
  13. A. M. Yaglom, Correlation Theory of Stationary and Related Random Functions, vol. 1 of Basic Results, Springer, New York, NY, USA, 1987.
  14. G. A. Korn and T. M. Korn, Mathematical Handbook For Scientists and Engineers, McGraw-Hill, 1961.
  15. M. Li and W. Zhao, “On 1/f noise,” Mathematical Problems in Engineering, vol. 2012, Article ID 673648, 23 pages, 2012.
  16. J. Bertoin, “The convex minorant of the cauchy process,” Electronic Communications in Probability, vol. 5, pp. 51–55, 2000. View at Scopus
  17. P. A. Zanzotto, “On stochastic differential equations driven by a cauchy process and other stable Lévy motions,” The Annals of Probability, vol. 30, no. 2, pp. 802–825, 2002. View at Publisher · View at Google Scholar · View at Scopus
  18. P. Garbaczewski and R. Olkiewicz, “Ornstein-Uhlenbeck-Cauchy process,” Journal of Mathematical Physics, vol. 41, no. 10, pp. 6843–6860, 2000. View at Scopus
  19. I. M. Gelfand and K. Vilenkin, Generalized Functions, vol. 1, Academic Press, New York, NY, USA, 1964.
  20. I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series, and Products, Elsevier, Singapore, 7th edition, 2007, Edited by: A. Jeffrey and D. Zwillinger.
  21. P. Todorovic, An Introduction to Stochastic Processes and Their Applications, Springer, New York, NY, USA, 1992. View at Publisher · View at Google Scholar
  22. S. C. Lim and S. V. Muniandy, “Generalized Ornstein-Uhlenbeck processes and associated self-similar processes,” Journal of Physics A, vol. 36, no. 14, pp. 3961–3982, 2003. View at Publisher · View at Google Scholar · View at Scopus
  23. R. L. Wolpert and M. S. Taqqu, “Fractional Ornstein-Uhlenbeck Lévy processes and the Telecom process: upstairs and downstairs,” Signal Processing, vol. 85, no. 8, pp. 1523–1545, 2005. View at Publisher · View at Google Scholar · View at Scopus
  24. J. W. Lamperti, “Semi-stable stochastic processes,” Transactions of the American Mathematical Society, vol. 104, no. 1, pp. 62–78, 1962. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  25. P. Flandrin, P. Borgnat, and P.-O. Amblard, From Stationarity to Self-Similarity, and Back: Variations on the Lamperti Transformation, vol. 621, Springer, 2003, Edited by: G. Ra-ganjaran and M. Ding.
  26. S. R. Massel, Ocean Surface Waves: Their Physics and Prediction, World Scientific, 1997.
  27. M. Li, “A method for requiring block size for spectrum measurement of ocean surface waves,” IEEE Transactions on Instrumentation and Measurement, vol. 55, no. 6, pp. 2207–2215, 2006. View at Publisher · View at Google Scholar · View at Scopus
  28. http://www.ndbc.noaa.gov/station_page.php?station=lkwf1.
  29. http://www.ndbc.noaa.gov/historical_data.shtml.
  30. D. B. Gilhousen, “A field evaluation of NDBC moored buoy winds,” Journal of Atmospheric and Oceanic Technology, vol. 4, no. 1, pp. 94–104, 1987.
  31. http://www.ndbc.noaa.gov/wndav.shtml.
  32. Schlumberger Electronics Ltd, 1200 Real Time Signal Processor Operating Manual, London, UK, 1983.
  33. S. K. Mitra and J. F. Kaiser, Handbook For Digital Signal Processing, John Wiley & Sons, 1993.
  34. M. Li, “Modeling autocorrelation functions of long-range dependent teletraffic series based on optimal approximation in Hilbert space—a further study,” Applied Mathematical Modelling, vol. 31, no. 3, pp. 625–631, 2007. View at Publisher · View at Google Scholar · View at Scopus
  35. J. W. Kantelhardt, E. Koscielny-Bunde, H. H. A. Rego, S. Havlin, and A. Bunde, “Detecting long-range correlations with detrended fluctuation analysis,” Physica A, vol. 295, no. 3-4, pp. 441–454, 2001. View at Publisher · View at Google Scholar · View at Scopus
  36. M. S. Taqqu, V. Teverovsky, and W. Willinger, “Estimators for long-range dependence: an empirical study,” Fractals, vol. 3, no. 4, pp. 785–798, 1995.
  37. A. G. Davenport, “The spectrum of horizontal gustiness near the ground in high winds,” Quarterly Journal of the Royal Meteorological Society, vol. 87, no. 372, pp. 194–211, 1961.
  38. J. C. Kaimal, J. C. Wyngaard, Y. Izumi, and O. R. Coté, “Spectral characteristics of surface-layer turbulence,” Quarterly Journal of the Royal Meteorological Society, vol. 98, no. 417, pp. 563–589, 1972.
  39. I. Antoniou, D. Asimakopoulos, A. Fragoulis, A. Kotronaros, D. P. Lalas, and I. Panourgias, “Turbulence measurements on top of a steep hill,” Journal of Wind Engineering and Industrial Aerodynamics, vol. 39, no. 1–3, pp. 343–355, 1992. View at Scopus
  40. D. Hiriart, J. L. Ochoa, and B. García, “Wind power spectrum measured at the San Pedro Mártir Sierra,” Revista Mexicana de Astronomia y Astrofisica, vol. 37, no. 2, pp. 213–220, 2001. View at Scopus
  41. J. Hojstrup, S. E. Larsen, and P. H. Madsen, “Power spectra of horizontal wind components in the neutral atmospheric boundary layer,” in Proceedings of the 9th Symposium of Turbulence and Diffusion, N. O. Jensen, L. Kristiansen, and S. E. Larsen, Eds., pp. 305–308, American Meteorology Society, 1990.
  42. M. de O. Santos, T. Stosic, and B. D. Stosic, “Long-term correlations in hourly wind speed records in Pernambuco, Brazil,” Physica A, vol. 391, no. 4, pp. 1546–1552, 2012.
  43. A. C. Brett and S. E. Tuller, “The autocorrelation of hourly wind speed observations,” Journal of Applied Meteorology, vol. 30, no. 6, pp. 823–833, 1991. View at Scopus
  44. R. G. Kavasseri and R. Nagarajan, “A multifractal description of wind speed records,” Chaos, Solitons & Fractals, vol. 24, no. 1, pp. 165–173, 2005. View at Publisher · View at Google Scholar · View at Scopus
  45. R. G. Kavasseri and R. Nagarajan, “A qualitative description of boundary layer wind speed records,” Fluctuation & Noise Letters, vol. 6, no. 2, pp. L201–L213, 2006. View at Publisher · View at Google Scholar · View at Scopus
  46. M. S. Santhanam and H. Kantz, “Long-range correlations and rare events in boundary layer wind fields,” Physica A, vol. 345, no. 3-4, pp. 713–721, 2005. View at Publisher · View at Google Scholar · View at Scopus
  47. M. Li, Y.-Q. Chen, J.-Y. Li, and W. Zhao, “Hölder scales of sea level,” Mathematical Problems in Engineering, vol. 2012, Article ID 863707, 22 pages, 2012.
  48. C. Cattani, E. Laserra, and I. Bochicchio, “Simplicial approach to fractal structures,” Mathematical Problems in Engineering, vol. 2012, Article ID 958101, 21 pages, 2012. View at Publisher · View at Google Scholar
  49. C. Cattani, “Fractals and hidden symmetries in DNA,” Mathematical Problems in Engineering, vol. 2010, Article ID 507056, 31 pages, 2010. View at Publisher · View at Google Scholar · View at Scopus
  50. X. A. Yin, X. H. Yang, and Z. F. Yang, “Using the R/S method to determine the periodicity of time series,” Chaos, Solitons & Fractals, vol. 39, no. 2, pp. 731–745, 2009. View at Publisher · View at Google Scholar · View at Scopus
  51. X.-H. Yang and Y.-Q. Li, “DNA optimization threshold autoregressive prediction model and its application in ice condition time series,” Mathematical Problems in Engineering, vol. 2012, Article ID 191902, 10 pages, 2012. View at Publisher · View at Google Scholar
  52. C. Toma, “Advanced signal processing and command synthesis for memory-limited complex systems,” Mathematical Problems in Engineering, vol. 2012, Article ID 927821, 13 pages, 2012. View at Publisher · View at Google Scholar
  53. E. G. Bakhoum and C. Toma, “Specific mathematical aspects of dynamics generated by coherence functions,” Mathematical Problems in Engineering, vol. 2011, Article ID 436198, 10 pages, 2011. View at Publisher · View at Google Scholar · View at Scopus
  54. E. G. Bakhoum and C. Toma, “Mathematical transform of traveling-wave equations and phase aspects of quantum interaction,” Mathematical Problems in Engineering, vol. 2010, Article ID 695208, 15 pages, 2010. View at Publisher · View at Google Scholar · View at Scopus
  55. R. S. A. R. Abdullah, M. F. A. Rasid, and M. K. Mohamed, “Improvement in detection with forward scattering radar,” Science China Information Sciences, vol. 54, no. 12, pp. 2660–2672, 2011.
  56. T. J. Koo, R. Q. Li, M. M. Quottrup, C. A. Clifton, R. Izadi-Zamanabadi, and T. Bak, “A framework for multi-robot motion planning from temporal logic specifications,” Science China Information Sciences, vol. 55, no. 7, pp. 1675–1692, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  57. C. Z. Fan, Y. H. Liu, B. Q. Song, and D. X. Zhou, “Dynamic visual servoing of a small scale autonomous helicopter in uncalibrated environments,” Science China Information Sciences, vol. 54, no. 9, pp. 1855–1867, 2011. View at Publisher · View at Google Scholar · View at Scopus
  58. J. Gavaldà, J. Massons, J. Camps, and F. Díaz, “Statistical and spectral analysis of the wind regime in the area of Catalonia,” Theoretical and Applied Climatology, vol. 46, no. 2-3, pp. 143–152, 1992. View at Publisher · View at Google Scholar · View at Scopus
  59. E. G. Pavia and J. J. O'Brien, “Weibull statistics of wind speed over the ocean,” Journal of Climate and Applied Meteorology, vol. 25, no. 10, pp. 1324–1332, 1986. View at Scopus
  60. P. Sorensen, A. D. Hansen, and P. A. C. Rosas, “Wind models for simulation of power fluctuations from wind farms,” Journal of Wind Engineering and Industrial Aerodynamics, vol. 90, no. 12–15, pp. 1381–1402, 2002. View at Publisher · View at Google Scholar · View at Scopus