Predictability and Chaotic Nature of Daily Streamflow

References

• Apipattanavis, S., Rajagopalan, B. & Lall, U. 2010, “Local Polynomial-Based Flood Frequency Estimator for Mixed Population”, J. Hydrol. Eng., Vol. 15, No. 9, pp. 680-691, doi: 10.1061/(ASCE)HE.1943-5584.0000242.
   Google Scholar
• Dhanya, C. T. & Kumar, D. N. 2010, “Nonlinear ensemble prediction of chaotic daily rainfall”, Advances in water resources, Vol. 33, pp. 327–347.
   Google Scholar
• Dhanya, C. T. & Kumar, D. N. 2011a, “Multivariate Nonlinear Ensemble Prediction of Daily Chaotic Rainfall with Climate Inputs”, Journal of Hydrology, Vol. 403, No. 3-4, pp. 292–306.
   Google Scholar
• Dhanya, C. T. & Kumar, D. N. 2011b, “Predictive Uncertainty of Chaotic Daily Streamflow using Ensemble Wavelet Networks Approach”, Water Resources Research, Vol. 47, No. 6, pp. 327-347, doi: 10.1029/2010WR01017333.
   Google Scholar
• Elshorbagy, A., Simonovic, S. P. & Panu, U. S. 2002, “Noise reduction in chaotic hydrologic time series: facts and doubts”, J. Hydrol., Vol. 256, No. 3/4, pp. 845–848.
   Google Scholar
• Farmer, J. D. & Sidorowich, J. J. 1987, “Predicting chaotic time series”, Phys. Rev. Lett., Vol. 59, pp. 845–848.
   Google Scholar
• Frazer, A. M. & Swinney, H. L. 1986, “Independent coordinates for strange attractors from mutual information” , Phys. Rev. A, Vol. 33, No. 2, pp. 1134–1140.
   Google Scholar
• Grassberger, P. & Procaccia, I. 1983a, “Measuring the strangeness of strange attractors”, Physica D, Vol. 9, pp. 189–208.
   Google Scholar
• Grassberger, P. & Procaccia, I. 1983b, “Estimation of the Kolmogorov entropy from a chaotic signal”, Phys. Rev. A, Vol. 28, pp. 2591–2593.
   Google Scholar
• Hegger, R. & Kantz, H. 1999, “Improved false nearest neighbor method to detect determinism in time series data”, Phys. Rev. E, Vol. 60, pp. 4970–4973.
   Google Scholar
• Holzfuss, J. & Mayer-Kress, G. 1986, “An approach to error-estimation in the application of dimension algorithms”, Dimensions and Entropies in Chaotic Systems, Mayer-Kress, G. (editor), Springer, New York, pp. 114–122.
   Google Scholar
• Islam, M. N. & Sivakumar, B. 2002, “Characterization and prediction of runoff dynamics: a nonlinear dynamical view”, Adv. Wat. Resour., Vol. 25, pp. 179–190.
   Google Scholar
• Jayawardena, A. W. & Gurung, A. B. 2000, “Noise reduction and prediction of hydrometeorological time series: dynamical systems approach vs. stochastic approach”, J. Hydrol., Vol. 228, pp. 242–264.
   Google Scholar
• Jayawardena, A. W. & Lai, F. 1994, “Analysis and prediction of chaos in rainfall and streamflow time series”, J. Hydrol., Vol. 153, pp. 23–52.
   Google Scholar
• Kantz, H. 1994, “A robust method to estimate the maximal Lyapunov exponent of a time series”, Phys. Lett. A, Vol. 185, pp. 77–87.
   Google Scholar
• Kantz, H. & Schreiber, T. 2004, Nonlinear Time Series Analysis, 2nd edition, Cambridge University Press, Cambridge, UK.
   Google Scholar
• Kennel, M. B., Brown, R. & Abarbanel, H. D. I. 1992, “Determining embedding dimension for phase space reconstruction using a geometric method”, Phys. Rev. A, Vol. 45, pp. 3403–3411.
   Google Scholar
• Lee, T. & Ouarda, T. B. M. J. 2010, “Long-term prediction of precipitation and hydrologic extremes with nonstationary oscillation processes”, Journal of Geophysical Research, Vol. 115, No. D13107, doi:10.1029/2009JD012801.
   Google Scholar
• Liu, Q., Islam, S., Rodriguez-Iturbe, I. & Le, Y. 1998, “Phase-space analysis of daily streamflow: characterization and prediction”, Adv. Wat. Resour., Vol. 21, pp. 463–475.
   Google Scholar
• Loader, C. 1999, Local regression and likelihood, Springer, New York.
   Google Scholar
• Lorenz, E.N. 1972, “Predictability: Does the flap of a Butterfly’s wings in Brazil set off a Tornado in Texas?”, AAAS section on environmental Sciences New Approached to Global weather: GARP (The Global Atmospheric research Program), 139th meeting, American Association for the Advancement of Science.
   Google Scholar
• Lucent Technologies, 2001, “LOCFIT: Local Regression and Likelihood”, http://cm.bell-labs. com/cm/ms/departments/sia/project/locfit.
   Google Scholar
• Osborne, A. R. & Provenzale, A. 1989, “Finite correlation dimension for stochastic systems with power law spectra”, Physica D, Vol. 35, pp. 357–381.
   Google Scholar
• Porporato, A. & Ridolfi, L. 1996, “Clues to the existence of deterministic chaos in river flow”, Int. J. Mod. Phys. B, Vol. 10, No. 15, pp. 1821–1862.
   Google Scholar
• Porporato, A. & Ridolfi, L. 1997, “Nonlinear analysis of river flow time sequences”, Water Resour. Res., Vol. 33, No. 6, pp. 1353–1367.
   Google Scholar
• Provenzale, A., Smith, L. A., Vio, R. & Murante, G. 1992, “Distinguishing between low-dimensional dynamics and randomness in measured time series”, Physica D, Vol. 58, pp. 31–49.
   Google Scholar
• Puente, C. E. & Obregon, N. 1996, “A deterministic geometric representation of temporal rainfall: results for a storm in Boston”, Water Resour. Res., Vol. 32, No. 9, pp. 2825–2839.
   Google Scholar
• Regonda, S. K., Rajagopalan, B., Lall, U., Clark, M. & Moon, Y.-I. 2005, “Local polynomial method for ensemble forecast of time series”, Nonlinear Processes in Geophysics, Vol. 12, pp. 397–406.
   Google Scholar
• Rodriguez-Iturbe, I., de Power, F. B., Sharifi, M. B. & Georgakakos, K. P. 1989, “Chaos in rainfall”, Water Resour. Res., Vol. 25, No. 7, pp. 1667–1675.
   Google Scholar
• Rosenstein, M. T., Collins, J. J. & De Luca, C. J. 1993, “A practical method for calculating largest Lyapunov exponents from small data sets”, Physica D, Vol. 65, pp. 117–134.
   Google Scholar
• Sangoyomi, T., Lall, U. & Abarbanel, H. D. J. 1996, “Nonlinear dynamics of the Great Salt Lake: dimension estimation”, Water Resour. Res., Vol. 32, No. 1, pp. 149–159.
   Google Scholar
• Shang, P., Xu, N. & Kamae, S. 2009, “Chaotic analysis of time series in the sediment transport phenomenon”, Chaos, Solitons & Fractals, Vol. 41, No. 1, pp. 368–379.
   Google Scholar
• Sivakumar, B. 2001, “Rainfall dynamics at different temporal scales: A chaotic perspective”, Hydrol. Earth System Sci., Vol. 5, No. 4, pp. 645–651.
   Google Scholar
• Sivakumar, B., Liong, S. Y., Liaw, C. Y. & Phoon, K. K. 1999, “Singapore rainfall behavior: chaotic?”, J. Hydrol. Eng., Vol. 4, No. 1, pp. 38–48.
   Google Scholar
• Sivakumar, B., Berndtsson, R., Olsson, J. & Jinn, K. 2001, “Evidence of chaos in the rainfall-runoff process”, Hydrol. Sci. J., Vol. 46, No. 1, pp. 131–145.
   Google Scholar
• Smith, L. A., Ziehmann, C. & Fraedrich, K. 1998, “Uncertainty dynamics and predictability in chaotic systems”, Q.J.R. Meteorol. Soc., Vol. 125, pp. 2855–2886.
   Google Scholar
• Takens, F. 1981, “Detecting strange attractors in turbulence”, Lectures Notes in Mathematics, Rand, D. A. & Young, L. S. (editors), Springer-Verlag, Berlin, Germany.
   Google Scholar
• Theiler, J., Eubank, S., Longtin, A., Galdikian, B. & Farmer, J. D. 1992, “Testing for nonlinearity in time series: The method of surrogate data”, Physica D, Vol. 58, pp. 77–94.
   Google Scholar
• Tsonis, A. A. & Elsner, J. B. 1988, “The weather attractor over very short timescales”, Nature, Vol. 333, pp. 545–547.
   Google Scholar
• Wang, Q. & Gan, T. Y. 1998, “Biases of correlation dimension estimates of streamflow data in the Canadian prairies”, Water Resour. Res., Vol. 34, No. 9, pp. 2329–2339.
   Google Scholar
• Wilks, D. S. 2005, Statistical Methods in the Atmospheric Sciences - An Introduction, Academic Press, Inc.
   Google Scholar
• Wolf, A., Swift, J. B., Swinney, H. L. & Vastano, A. 1985, “Determining Lyapunov exponents from a time series”, Physica D, Vol. 16, pp. 285–317.
   Google Scholar