Noise reduction and prediction of hydrometeorological time series: Dynamical systems approach vs. stochastic approach

Journal of Hydrology

Volumn 228, Issue 3-4, 2000, Pages 242-264

  Jayawardena, A W ^a   Gurung, A B ^a  

^a UNIVERSITY OF HONG KONG   (Hong Kong)

Author keywords

Correlation dimension; Dynamical systems; Noise reduction; Phase space; Prediction

Indexed keywords

ALGORITHMS; CORRELATION METHODS; MATHEMATICAL MODELS; METEOROLOGY; PHASE SPACE METHODS; RANDOM PROCESSES; TIME SERIES ANALYSIS;

GRASSBERGER ALGORITHM; HYDROMETEOROLOGY; PROCACCIA ALGORITHM;

HYDROLOGY;

DATA QUALITY; HYDROMETEOROLOGY; PREDICTION; TIME SERIES;

EID: 0034642947     PISSN: 00221694     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0022-1694(00)00142-6     Document Type: Article

References (62)

1. Abarbanel H.D.I. Analysis of Observed Chaotic Data. 2nd ed. 1995;Springer, New York.
2. Abarbanel H.D.I., Brown R., Kadtke J.B. Prediction in chaotic nonlinear systems: methods for time series with broad band Fourier spectra. Phys. Rev. A. 41:(4):1990;1782-1807.
3. Akaike H. A new look at the statistical model identification. IEEE Trans. Auto. Control. AC-19:1974;716-723.
4. Bentley J.L., Friedman J.H. Data structures for range searching. ACM Comput. Surv. 11:(4):1979;397-409.
5. Box G.E.P., Jenkins G.M., Reinsel G.C. Time Series Analysis: Forecasting and Control. 3rd ed. 1994;Prentice Hall, Englewood Cliffs, NJ.
6. Broomhead D.S., King G.P. Extracting qualitative dynamics from experimental data. Physica D. 20:1986;217-236. (Reprinted in Ott et al. (1994)).
7. Casdagli M. Nonlinear prediction of chaotic time series. Physica D. 35:1989;335-356. (Reprinted in Ott et al. (1994)).
8. Casdagli M., Eubank S. Nonlinear modeling and forecasting. Proceeding of the Workshop on Nonlinear Modeling and Forecasting held September 1990 in Santa Fe, New Mexico. vol. 12:1992;Addison-Wesley, Reading, MA.
9. Cawley R., Hsu G.H. Local-geometric projection method for noise reduction in chaotic maps and flows. Phys. Rev. A. 46:(6):1992;3057-3082.
10. Farmer J.D., Sidorowich J.J. Predicting chaotic time series. Phys. Rev. Lett. 59:(8):1987;845-848. (Reprinted in Ott et al. (1994)).
11. Farmer J.D., Sidorowich J.J. Optimal shadowing and noise reduction. Physica D. 47:1991;373-392.
12. Fraedrich K. Estimating the dimension of weather and climate attractors. J. Atm. Sc. 43:(5):1986;419-432.
13. Frazer A.M., Swinney H.L. Independent coordinates for strange attractors from mutual information. Phys. Rev. A. 33:1986;1134-1140.
14. Gershenfeld, N.A., Weigend, A.S., 1993. The Future of Time Series: Learning and Understanding, pp. 1-70. In Weigend and Gershenfeld (1993).
15. Grassberger P. Generalized dimensions of strange attractors. Phys. Lett. A. 97:(6):1983;227-230.
16. Grassberger P. An optimized box-assisted algorithm for fractal dimensions. Phys. Lett. A. 148:(1/2):1990;63-68.
17. Grassberger P., Procaccia I. Characterization of strange attractors. Phys. Rev. Lett. 50:(5):1983a;346-349.
18. Grassberger P., Procaccia I. Measuring the strangeness of strange attractors. Physica D. 9:1983b;189-208.
19. Grassberger P., Schreiber T., Schaffrath C. Nonlinear time sequence analysis. Int. J. Bifurcation Chaos. 1:(3):1991;521-547.
20. Grassberger P., Hegger R., Kantz H., Schaffrath C., Schreiber T. On noise reduction methods for chaotic data. Chaos. 3:1993;127-141. (Reprinted in Ott et al. (1994)).
21. Grebogi C., Hammel S.M., Yorke J.A., Sauer T. Shadowing of physical trajectories in chaotic dynamics: containment and refinement. Phys. Rev. Lett. 65:(13):1990;1527-1530.
22. Hammel S.M. A noise reduction method for chaotic systems. Phys. Lett. A. 148:1990;421-428. (Reprinted in Ott et al. (1994)).
23. Hénon M. A two-dimensional mapping with a strange attractor. Commun. Math. Phys. 50:1976;69-77.
24. Holzfuss J., Kadtke J. Global nonlinear noise reduction using radial basis functions. Int. J. Bifurcation Chaos. 3:(3):1993;589-596.
25. Jayawardena A.W., Lai F. Time series analysis of water quality data in Pearl River, China. J. Env. Engng, ASCE. 115:(3):1989;590-607.
26. Jayawardena A.W., Lai F. Analysis and prediction of chaos in rainfall and stream flow time series. J. Hydrol. 153:1994;23-52.
27. Kantz, H., 1993. Noise Reduction by Local Reconstruction of the Dynamics, pp. 475-490. In Weigend and Gershenfeld (1993).
28. Kantz H., Schreiber T. Nonlinear Time Series Analysis. 1997;Cambridge University Press, Cambridge, MA.
29. Kawamura A., McKerchar A.I., Spigel R.H., Jinno K. Chaotic characteristics of the Southern Oscillation index time series. J. Hydrol. 204:1998;168-181.
30. Kennel M.B., Brown R., Abarbanel H.D.I. Determining minimum embedding dimension for phase space reconstruction using a geometrical construction. Phys. Rev. A. 45:1992;3403-3411. (Reprinted in Ott et al. (1994)).
31. Kostelich E.J., Schreiber T. Noise reduction in chaotic time-series data: a survey of common methods. Phys. Rev. E. 48:(3):1993;1752-1763.
32. Ljung G.M., Box G.E.P. On a measure of lack of fit in time series models. Biometrika. 65:(2):1978;297-303.
33. Lorenz E. Deterministic nonperiodic flow. J. Atm. Sc. 20:(2):1963;130-141.
34. May R.M. Simple mathematical models with very complicated dynamics. Nature. 261:1976;459-467.
35. Osborne A.R., Provenzale A. Finite correlation dimension for stochastic systems with power law spectra. Physica D. 35:1989;357-381.
36. 2 entropy for random noises with power law spectra. Physica D. 47:1991;361-372.
37. Ott E. Chaos in Dynamical Systems. 1st ed. 1993;Cambridge University Press, Cambridge, MA.
38. Ott E., Sauer T., Yorke J.A. Coping with Chaos: Analysis of Chaotic Data and the Exploitation of Chaotic Systems. 1994;Wiley, New York.
39. Packard N.H., Crutchfield J.P., Farmer J.D., Shaw R.S. Geometry from a time series. Phys. Rev. Lett. 45:(9):1980;712-716. (Reprinted in Ott et al. (1994)).
40. Porporato A., Ridolfi L. Nonlinear analysis of river flow time sequences. Wat. Resour. Res. 33:(6):1997;1353-1367.
41. Press W.H., Vetterling W.T., Teukolsky S.A., Flannery B.P. Numerical Recipe in Fortran, The art of Scientific computation. 1992;Cambridge University Press, Cambridge, MA.
42. Provenzale A., Smith L.A., Vio R., Murante G. Distinguishing between low-dimensional dynamics and randomness in measured time series. Physica D. 58:1992;31-49.
43. Rosentein M.T., Collins J.J., Luca C.J.D. A practical method for calculating largest Lyapunov exponents from small data sets. Physica D. 65:1993;117-134.
44. Sauer T. A noise reduction method for signals from nonlinear systems. Physica D. 58:1992;193-201.
45. Schouten, J.C., van den Bleek, C.M., 1994. RRCHAOS: a menu-driven software package for chaotic time series analysis. Reactor Research Foundation, Delft, The Netherlands.
46. Schouten J.C., Takens F., van den Bleek C.M. Estimation of the dimension of a noisy attractor. Phys. Rev. E. 50:(3):1994;1851-1861.
47. Schreiber T. Determination of the noise level of chaotic time series. Phys. Rev. E. 48:(1):1993a;R13-R16.
48. Schreiber T. Extremely simple noise reduction method. Phys. Rev. E. 47:(4):1993b;2401-2404.
49. Schreiber T. Efficient neighbor searching in nonlinear time series analysis. Int. J. Bifurcation Chaos. 5:(2):1995;349-358.
50. Schreiber T., Grassberger P. A simple noise-reduction method for real data. Phys. Lett. A. 160:1991;411-418.
51. Sharifi M.B., Georgakakos K.P., Rodriguez-Iturbe I. Evidence of deterministic chaos in the pulse of storm rainfall. J. Atm. Sc. 47:(7):1989;888-893.
52. Sivakumar B., Phoon K.K., Liong S.Y., Liaw C.Y. A systematic approach to noise reduction in chaotic hydrological time series. J. Hydrol. 219:1999;103-135.
53. Sproull R.F. Refinements to nearest-neighbor searching in k-dimensional tree. Algorithmica. 6:1991;579-589.
54. Takens F. Detecting strange attractors in turbulence. Rand D.A., Young L.S. Dynamical Systems and Turbulence, Lecture Notes in Mathematics. Proceeding of a Symposium Held at the University of Warwick 1979/1980. vol. 898:1981;366-381 Springer, New York.
55. Theiler J. Efficient algorithm for estimating the correlation dimension from a set of discrete points. Phys. Rev. A. 36:(9):1987;4456-4462.
56. Theiler, J., Galdrikian, B., Longtin, A., Eubank, S., Farmer, J.D., 1992. Using Surrogate Data to Detect Nonlinearity in Time Series, pp. 163-188. In Casdagli and Eubank, 1992.
57. Tong H., Lim K.S. Threshold autogression, limit cycles and cyclical data. J. R. Statist. Soc. B. 42:1980;245-292.
58. Tsonis A.A. Chaos from Theory to Application. 1992;Plenum Press, New York.
59. Tsonis A.A., Elsner J.B. Nonlinear prediction as a way of distinguishing chaos from random fractal sequences. Nature. 358:1992;217-220.
60. Weigend A.S., Gershenfeld N.A. Time series prediction: forecasting the future and understanding the past. Proceedings of the NATO advanced research workshop on comparative time series analysis, Santa Fe, New Mexico, May 14-17, 1992. vol. xv:1993;Addison-Wesley, Reading, MA.
61. Wright P.B. Relationship between the indices of the southern oscillation. Mon. Weath. Rev. 112:1984;1913-1919.
62. Wright P.B. Homogenized long-period southern oscillation indices. Int. J. Climatol. 9:1989;33-54.