Nonlinear ensemble prediction of chaotic daily rainfall

Advances in Water Resources

Volumn 33, Issue 3, 2010, Pages 327-347

  Dhanya, C T ^a   Nagesh Kumar, D ^a  

^a INDIAN INSTITUTE OF SCIENCE   (India)

Author keywords

Chaotic nature of rainfall; Ensembles; Nonlinear prediction; Uncertainty

Indexed keywords

CHAOTIC SYSTEMS; FORECASTING; LYAPUNOV METHODS; PHASE SPACE METHODS; STOCHASTIC SYSTEMS;

CHAOTIC NATURE; CORRELATION DIMENSIONS; ENSEMBLES; MUTUAL INFORMATION METHOD; NON-LINEAR PREDICTIONS; NONLINEAR PREDICTION METHODS; PHASE SPACE RECONSTRUCTION; UNCERTAINTY;

RAIN;

ALGORITHM; ENSEMBLE FORECASTING; PREDICTION; RAINFALL; UNCERTAINTY ANALYSIS;

INDIA;

EID: 77955980441     PISSN: 03091708     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.advwatres.2010.01.001     Document Type: Article

References (49)

1. Casdagli M. Nonlinear prediction of chaotic time series. Physica D 1989;35:335-56.
2. Casdagli M. Chaos and deterministic versus stochastic nonlinear modeling. J Roy Stat Soc B 1991;54:303-24.
3. Elshorbagy A, Simonovic SP, Panu US. Noise reduction in chaotic hydrologic time series: facts and doubts. J Hydrol 2002;256(3/4):845-8.
4. Farmer JD, Sidorowich JJ. Predicting chaotic time series. Phys Rev Lett 1987;59:845-8.
5. Frazer AM, Swinney HL. Independent coordinates for strange attractors from mutual information. Phys Rev A 1986;33(2):1134-40.
6. Grassberger P, Procaccia I. Measuring the strangeness of strange attractors. Physica D 1983;9:189-208.
7. Grassberger P, Procaccia I. Estimation of the Kolmogorov entropy from a chaotic signal. Phys Rev A 1983;28:2591-3.
8. Hegger R, Kantz H. Improved false nearest neighbor method to detect determinism in time series data. Phys Rev E 1999;60:4970-3.
9. Holzfuss J, Mayer-Kress G. An approach to error-estimation in the application of dimension algorithms. In: Mayer-Kress G, editor. Dimensions and entropies in chaotic systems. New York: Springer; 1986. p. 114-22.
10. Islam MN, Sivakumar B. Characterization and prediction of runoff dynamics: a nonlinear dynamical view. Adv Water Resour 2002;25:179-90.
11. Jayawardena AW, Gurung AB. Noise reduction and prediction of hydrometeorological time series: dynamical systems approach vs. stochastic approach. J Hydrol 2000;228:242-64.
12. Jayawardena AW, Lai F. Analysis and prediction of chaos in rainfall and stream flow time series. J Hydrol 1994;153:23-52.
13. Kantz H. A robust method to estimate the maximal Lyapunov exponent of a time series. Phys Lett A 1994;185:77-87.
14. Kantz H, Schreiber T. Nonlinear time series analysis. 2nd ed. Cambridge, UK: Cambridge University Press; 2004.
15. Kennel MB, Brown R, Abarbanel HDI. Determining embedding dimension for phase space reconstruction using a geometric method. Phys Rev A 1992;45:3403-11.
16. Krasovskaia I, Gottschalk L, Kundzewicz ZW. Dimensionality of Scandinavian river flow regimes. Hydrol Sci J 1999;44(5):705-23.
17. Liu Q, Islam S, Rodriguez-lturbe I, Le Y. Phase-space analysis of daily streamflow: characterization and prediction. Adv Water Resour 1998;21:463-75.
18. Nerenberg MAH, Essex C. Correlation dimension and systematic geometric effects. Phys Rev A 1990;42(12):7065-74.
19. Osborne AR, Provenzale A. finite correlation dimension for stochastic systems with power law spectra. Physica D 1989;35:357-81.
20. Packard NH, Crutchfield JP, Farmer JD, Shaw RS. Geometry from a time series. Phys Rev Lett 1980;45(9):712-6.
21. Porporato A, Ridolfi L. Clues to the existence of deterministic chaos in river flow. Int J Mod Phys B 1996;10(15):1821-62.
22. Porporato A, Ridolfi L. Nonlinear analysis of river flow time sequences. Water Resour Res 1997;33(6):1353-67.
23. Porporato A, Ridolfi L. Multivariate nonlinear prediction of riverflow. J Hydrol 2001;248:109-22.
24. Provenzale A, Smith LA, Vio R, Murante G. Distinguishing between lowdimensional dynamics and randomness in measured time series. Physica D 1992;58:31-49.
25. Puente CE, Obregon N. A deterministic geometric representation of temporal rainfall: results for a storm in Boston. Water Resour Res 1996;32(9):2825-39.
26. Ramsey JB, Yuan HJ. The statistical properties of dimension calculations using small data sets. Nonlinearity 1990;3:155-76.
27. Rodriguez-Iturbe I, De Power FB, Sharifi MB, Georgakakos KP. Chaos in rainfall. Water Resour Res 1989;25(7):1667-75.
28. Rosenstein MT, Collins JJ, De Luca CJ. A practical method for calculating largest Lyapunov exponents from small data sets. Physica D 1993;65:117-34.
29. Sangoyomi T, Lall U, Abarbanel HDJ. Nonlinear dynamics of the Great Salt Lake: dimension estimation. Water Resour Res 1996;32(1):149-59.
30. Schreiber T, Grassberger P. A simple noise reduction method for real data. Phys Lett A 1991;160:411-8.
31. Schreiber T, Kantz H. Observing and predicting chaotic signals: Is 2% noise too much? In: Kravtsov YuA, Kadtke JB, editors. Predictability of complex dynamical systems. Springer series in synergetics. Berlin, Germany: Springer; 1996. p. 43-65.
32. Schreiber T, Schmitz A. Improved surrogate data for nonlinearity tests. Phys Rev Lett 1996;77:635-8.
33. Schreiber T, Schmitz A. Surrogate time series. Physica D 2000;142:346-82.
34. Sharifi MB, Georgakakos KP, Rodriguez-Iturbe I. Evidence of deterministic chaos in the pulse of storm rainfall. J Atmos Sci 1990;47:888-93.
35. Sivakumar B. Rainfall dynamics at different temporal scales: a chaotic perspective. Hydrol Earth Syst Sci 2001;5(4):645-51.
36. Sivakumar B, Berndtsson R, Olsson J, Jinn K. Evidence of chaos in the rainfall- runoff process. Hydrol Sci J 2001;46(1):131-45.
37. Sivakumar B, Liong SY, Liaw CY. Evidence of chaotic behavior in Singapore rainfall. J Am Water Resour Assoc 1998;34(2):301-10.
38. Sivakumar B, Liong SY, Liaw CY, Phoon KK. Singapore rainfall behavior: chaotic? J Hydrol Eng 1999;4(1):38-48.
39. Sivakumar B, Phoon KK, Liong SY, Liaw CY. A systematic approach to noise reduction in chaotic hydrological time series. J Hydrol 1999;219(3/4):103-35.
40. Sivakumar B, Sorooshian S, Gupta HV, Gao X. A chaotic approach to rainfall disaggregation. Water Resour Res 2001;37(1):61-72.
41. Smith LA. Intrinsic limits on dimension calculations. Phys Lett A 1988;133(6):283-8.
42. Stehlik J. Deterministic chaos in runoff series. J Hydraul Hydromech 1999;47(4):271-87.
43. Strogatz SH. Nonlinear dynamics and chaos: with applications to physics, biology, chemistry and engineering. Cambridge: Westview Press, Perseus Books Group; 1994.
44. Takens F. Detecting strange attractors in turbulence. In: Rand DA, Young LS, editors. Lectures notes in mathematics, vol. 898. Berlin, Germany: Springer-Verlag; 1981. p. 366-81.
45. Theiler J, Eubank S, Longtin A, Galdikian B, Farmer JD. Testing for nonlinearity in time series: the method of surrogate data. Physica D 1992;58:77-94.
46. Tsonis AA, Elsner JB. The weather attractor over very short timescales. Nature 1988;333:545-7.
47. Wang Q, Gan TY. Biases of correlation dimension estimates of streamflow data in the Canadian prairies. Water Resour Res 1998;34(9):2329-39.
48. Wilks DS. Statistical methods in the atmospheric sciences: an introduction. 2nd ed. New York: Elsevier; 2005.
49. Wolf A, Swift JB, Swinney HL, Vastano A. Determining Lyapunov exponents from a time serie. Physica D 1985;16:285-317.