Detection and predictive modeling of chaos in finite hydrological time series

Nonlinear Processes in Geophysics

Volumn 12, Issue 1, 2005, Pages 41-53

  Khan, S ^a   Ganguly, A R ^b   Saigal, S ^a  

^a UNIVERSITY OF SOUTH FLORIDA   (United States)

^b OAK RIDGE NATIONAL LABORATORY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

CHAOS THEORY; HYDROLOGICAL MODELING; RUNOFF; SIGNAL-TO-NOISE RATIO; TIME SERIES ANALYSIS;

EID: 14944374458     PISSN: 10235809     EISSN: None     Source Type: Journal    
DOI: 10.5194/npg-12-41-2005     Document Type: Article

References (58)

1. Abarbanel, H. D.: Nonlinear Systems, VCH Publishers, New York, 1994.
2. Almog, Y., Oz, O., and Akselrod, S.: Correlation dimension estimation: can this nonlinear description contribute to the characterization of blood pressure control in rats?, IEEE Transactions on Biomedical Engineering, 46, 5, 535-537, 1990.
3. ASCE: Task Committee on Applications of Artificial Neural Networks in Hydrology, II, Hydrologic applications, J. Hydrol. Eng., 5, 2, 124-137, 2000.
4. Basu, S. and Foufoula-Georgiou, E.: Detection of nonlinearity and chaocity in time series using the transportation distance function, Phy. Lett. A, 301, 413-423, 2002.
5. Bishop, C. M.: Neural Networks for pattern recognitions, Oxford University Press, 1995.
6. BoR: Bureau of Reclamation, private communication, 2004.
7. Bras, R. L. and Rodriguez-Iturbe, I.: Rainfall generation: A non-stationary time varying multidimensional model, Water Resour. Res., 12, 450-456, 1976.
8. Cornelis, A. L.: Visualization of Chaos for Finance Majors, in 2000 Finance Educators Conference: Finance Education in the New Millennium, Proceedings of the 2000 Annual Conference, Deakin University, Burwood, Victoria, Australia, 187-226, 2000.
9. Douglas, E. and Barros, A. P.: Probable Maximum Precipitation Estimation Using Multifractals: Application in the Eastern United States, J. Hydrometeorology, 4, 6, 1012-1024, 2003.
10. Elshorbagy, A.: Noise reduction approach in chaotic hydrologic time series revisited, Canadian Water Resources Journal, 26, 4, 537-550, 2001.
11. Elshorbagy, A., Panu, U., and Simonovic, S.: Analysis of cross-correlated chaotic streamflows, Hydrological Sciences Journal, 46, 5, 781-794, 2001.
12. Elshorbagy, A., Simonovic, S. P., and Panu, U. S.: Estimation of missing streamflow data using principles of chaos theory, Journal of Hydrology, 255, 1-4, 123-133, 2002a.
13. Elshorbagy, A., Simonovic, S. P., and Panu, U. S.: Noise reduction in chaotic hydrologic time series: Facts and doubts, Journal of Hydrology, 256, 3-4, 147-165, 2002b.
14. Essex, C., Lookman, T., and Nerenberg, M. A. H.: The climate attractor on short time scales, Nature, 326, 64-66, 1987.
15. Farmer, J. D. and Sidorowich, J. J.: Predicting Chaotic Time Series, Phys. Rev. Lett., 59, 845-848, 1987.
16. Fraedrich, K.: Estimating the dimensions of weather and climate attractors, J. Atmos. Sci., 43, 419-432, 1986.
17. Fraedrich, K.: Estimating weather and climate predictability on attractors, J. Atmos. Sci., 44, 722-728, 1987.
18. Ganguly, A. R. and Bras, R. L.: Distributed quantitative precipitation forecasting combining information from radar and numerical weather prediction model outputs, J. of Hydrometeorology, American Meteorological Society, 4, 6, 1168-1180, 2003.
19. Grassberger, P. and Procaccia, I.: Measuring the strangeness of strange attractors, Physica D, 9, 189-208, 1983.
20. Hense, A.: On the possible existence of a strange attractor for the southern oscillation, Beitr Phy. Atmos., 60, 1, 34-47, 1987.
21. Hilborn, R. C.: Chaos and Nonlinear Dynamics, Oxford University Press, 2000.
22. Hsieh, D.: Chaos and nonlinear dynamics: Applications to financial markets, Journal of Finance, 46, 1839-1878, 1991.
23. Islam, M. N. and Sivakumar, B.: Characterization and prediction of runoff dynamics: a nonlinear dynamical view, Adv. Water Resour., 25, 179-190, 2002.
24. Islam, S., Bras, R. L., and Rodriguez-Iturbe, I.: A possible explanation for low correlation dimension estimates for the atmosphere, J. Appl. Meteorol., 32, 203-208, 1993.
25. Jayawardena, A. W. and Lai, F.: Analysis and prediction of chaos in rainfall and streamflow time series, J. Hydrol., 153, 23-52, 1994.
26. Kim, G. and Barros, A. P.: Quantitative Flood Forecasting Using Multisensor Data and Neural Networks, J. Hydrology, 246, 45-62, 2001.
27. Koutsoyiannis, D. and Pachakis, D.: Deterministic chaos versus stochasticity in analysis and modeling of point rainfall series, J. Geophys. Res., 101, 26 441-26 451, 1996.
28. Kuligowski, R. J. and Barros, A. P.: Localized Precipitation Forecasts from a Numerical Weather Prediction Model Using Artificial Neural Networks, Weather and Forecasting, 13, 4, 1194-1204, 1998a.
29. Kuligowski, R. J. and Barros, A. P.: Using Artificial Neural Networks to Estimate Missing Rainfall Data, J. of American Water Resources Association, 34, 6, 1-11, 1998b.
30. Lorenz, E. N.: Atmospheric predictability as revealed by naturally occurring analogues, J. Atmos. Sci., 26, 636-646, 1969.
31. Lorenz, E. N.: The Essence of Chaos (The Jessie and John Danz Lecture Series), University of Washington Press, 1996.
32. Nerenberg, M. A. H. and Essex, C.: Correlation dimension and systematic geometric effects, Phys. Rev. Lett. A, 42, 12, 7065-7074, 1990.
33. Osborne, A. R. and Provenzale, A.: Finite correlation dimension for stochastic systems with power-law spectra, Physica D, 35, 357-381, 1989.
34. Porporato, A. and Ridolfi, L.: Clues to the existence of deterministic chaos in river flow, Int. J. Mod. Phys. B, 10, 1821-1862, 1996.
35. Rodriguez-Iturbe, I., De Power, F. B., Sharifi, M. B., and Georgakakos, K. P.: Chaos in rainfall, Water Resour. Res., 25, 7, 1667-1675, 1989.
36. Schertzer, D., Tchiginskaya, Y., Lovejoy, S., Hubert, P., Bendjoudi, H., and Larchevque, M.: Which chaos in the rainfall-runoff process?, Hydrological Sciences Journal, 47, 1, 139-149, 2002.
37. Sivakumar, B.: Chaos theory in hydrology: important issues and interpretations, J. Hydrol., 227, 1-4, 1-20, 2000.
38. Sivakumar, B.: Discussion on "Analysis of cross-correlated chaotic streamflows" by Elshorbagy et al., Hydrological Sciences Journal, 47, 3, 523-527, 2002.
39. Sivakumar, B.: Forecasting monthly streamflow dynamics in the western United States: A nonlinear dynamical approach, Environmental Modeling and Software, 18, 8/9, 721-728, 2003.
40. Sivakumar, B.: Chaos theory in geophysics: Past, present and future, Chaos, Solitons and Fractals, 19, 2, 441-462, 2004.
41. Sivakumar, B., Liong, S. Y., Liaw, C. Y., and Phoon, K. K.: Evidence of chaotic behavior in singapore rainfall, J. Am. Water Resour. Assoc., 34, 301-310, 1998.
42. Sivakumar, B., Berndtsson, R., Olsson, J., Jinno, K., and Kawamura, A.: Dynamics of monthly rainfall-runoff process at the Gota basin: A search for chaos, Hydrology and Earth System Sciences, 4, 3, 407-417, 2000, SRef-ID: 1607-7938/hess/2000-4-407.
43. Sivakumar, B., Berndtsson, R., Olsson, J., and Jinno, K.: Evidence of chaos in rainfall-runoff process, Hydrological Sciences Journal, 46, 1, 131-146, 2001a.
44. Sivakumar, B., Berndtsson, R., and Persson, M.: Monthly runoff prediction using phase-space reconstruction, Hydrological Sciences Journal, 46, 3, 377-387, 2001b.
45. Sivakumar, B., Berndtsson, R., Olsson, J., and Jinno, K.: Reply to Which chaos in the rainfall-runoff process? by Schertzer et al, Hydrological Sciences Journal, 47, 1, 149-158, 2002a.
46. Sivakumar, B., Persson, M., Berndtsson, R., and Uvo, C. B.: Is correlation dimension a reliable indicator of low-dimensional chaos in short hydrological time series?, Water Resources Research, 38, 2, doi:10.1029/2001WR000333, 31-38, 2002b.
47. Stehlik, J.: Deterministic chaos in runoff series, J. Hydrol. Hydromech, 47, 271-287, 1999.
48. Sugihara, G. and May, R. M.: Nonlinear forecasting as a way of distinguishing chaos from measurement error in time series, Nature, 344, 734-741, 1990.
49. Takens, F.: Detecting strange attractors in turbulence, in Dynamical Systems and Turbulence, Lecture notes in Mathematics, 898, Springer Verlag, New York, 366-381, 1980.
50. Tessier, Y., Lovejoy, S., Hubert, P., Schertzer, D., and Pecknold, S.: Multifractal analysis and modeling of rainfall and river flows and scaling, causal transfer functions, J. geophysical Res., 101, D21, 26 427-26 440, 1996.
51. Theiler, J., Eubank, S., Longtin, A., Galdrikian, B., and Farmer, J. D.: Testing for Nonlinearity in Time Series: The Method of Surrogate Data, Physica D, 58, 77-94, 1992.
52. Trippi, R. R.: Chaos & Nonlinear Dynamics in the Financial Markets: Theory, Evidence and Applications, Irwin Professional Publishing, 1995.
53. USGS: private communication, 2004.
54. Wang, G.: A conceptual modeling study on biosphere-atmosphere interactions and its implications for physically based climate models, Journal of Climate, 17, 13, 2572-2583, 2004.
55. Weigend, A. S. and Gershenfeld, N. A.: Time Series Prediction: Forecasting the Future and Understanding the Past, Addison-Wesley, Reading, MA, 1994.
56. Wilcox, B. P., Seyfried, M. S., and Matison, T. H.: Searching for chaotic dynamics in snowmelt runoff, Water Resour. Res., 27, 6, 1005-1010, 1991.
57. Yim, G. S., Ryu, J. W., Park, Y. J., Rim, S., Lee, S. Y., Kye, W. H., and Kim, C. M.: Chaotic behaviors of operational amplifiers, Physical Review E, 69, 2004.
58. Zhang, G., Patuwo, B. E., and Hu, M. Y.: Forecasting with artificial neural networks: The state of the art, Int. J. Forecasting, 14, 35-62, 1998.