The Hurst phenomenon and fractional Gaussian noise made easy;Le phénomène de Hurst et le bruit fractionnel gaussien rendus faciles dans leur utilisation

Hydrological Sciences Journal

Volumn 47, Issue 4, 2002, Pages 573-595

  Koutsoyiannis, Demetris ^a  

^a NATIONAL TECHNICAL UNIVERSITY OF ATHENS   (Greece)

Author keywords

Climate change; Fractional Gaussian noise; Hurst phenomenon; Persistence

Indexed keywords

CORRELATION METHODS; HYDROLOGY; RANDOM PROCESSES;

FRACTIONAL GAUSSIAN NOISE; HYDROLOGICAL PROCESSES;

GAUSSIAN NOISE (ELECTRONIC);

GEOPHYSICAL METHOD; HYDROLOGY; STOCHASTICITY; TIME SERIES;

EID: 0036677908     PISSN: 02626667     EISSN: 21503435     Source Type: Journal    
DOI: 10.1080/02626660209492961     Document Type: Article

References (43)

1. Bak, P., 1996. How Nature Works. The Science of Self-Organized Criticality. New York, USA:Copernicus. Springer-Verlag.
2. Beran, J., 1994. Statistics for Long-Memory Processes Vol. 61, of Monographs on Statistics and Applied Probability, Chapman and Hall, New York, USA
3. Bhattacharya, R. N., Gupta, V. K., and Waymire, E., 1983. The Hurst effect under trends. J. Appl. Prob., 20:649–662.
4. Bloomfield, P., 1992. Trends in global temperature. Climatic Change, 21:1–16.
5. Box, G. E. P., Jenkins, G. M., and Reinsel, G. C., 1994. Time Series Analysis, Forecasting and Control. New Jersey, USA:Prentice Hall, Upper Saddle River.
6. Bras, R. L., and Rodriguez-lturbe, I., 1985. Random Functions in Hydrology. Reading, Massachusetts, USA:Addison-Wesley.
7. Ditlevsen, O. D., 1971. Extremes and first passage times. Lyngby, Denmark:Doctoral dissertation, Technical University of Denmark.
8. Eltahir, E. A. B., 1996. El Niño and the natural variability in the flow of the Nile River. Wat. Resour. Res., 32 (1):131–137.
9. Evans, T. E., 1996. “ The effects of changes in the world hydrological cycle on availability of water resources. ”. In Global Climate Change and Agricultural Production:Direct and Indirect Effects of Changing Hydrological Pedological and Plant Physiological Processes Edited by:Bazzaz, F., and Sombroek, W., Chapter 2. FAO and John Wiley, Chichester, West Sussex, UK
10. Graybill, D. A., 1990. IGBP PAGES/World Data Center for Paleoclimatology. Boulder, Colorado, USA:NOAA/NGDC Paleoclimatology Program.
11. Grygier, J. C., and Stedinger, J. R., 1990. SPIGOT, A synthetic streamflow generation software package, Version 2.5—technical description., Ithaca, New York, USA:School of Civil and Environmental Engineering, Cornell University.
12. Haan, C. T., 1977. Statistical Methods in Hydrology. Ames, Iowa, USA:Iowa State University Press.
13. Haslett, J., and Raftery, A. E., 1989. Space-time modelling with long-memory dependence:assessing Ireland's wind power resource. Appl Statist., 38 (1):1–50.
14. Hosking, J. R. M., 1981. Fractional differencing. Biometrica, 68:165–176.
15. Hosking, J. R. M., 1984. Modeling persistence in hydrological time series using fractional differencing. Wat. Resour. Res., 20 (12):1898–1908.
16. Hurst, H. E., 1951. Long term storage capacities of reservoirs. Trans. ASCE, 116:776–808.
17. Klemeš, V., 1974. The Hurst phenomenon:a puzzle?. Wat. Resour. Res., 10 (4):675–688.
18. Kottegoda, N. T., 1980. Stochastic Water Resources Technology. London, UK:Macmillan Press.
19. Koutsoyiannis, D., 2000. A generalized mathematical framework for stochastic simulation and forecast of hydrologic time series. Wat. Resour Res., 36 (6):1519–1534.
20. Koutsoyiannis, D., 2001.) Coupling stochastic models of different time scales. Wat. Resour. Res., 37 (2):379–392.
21. Koutsoyiannis. 2002. Internal report:http://www.itia.ntua.gr/getfile/511/2/2002 HSJIlurstSuppl.pdf
22. Lane, W. L., and Frevert, D. K., 1990. Applied Stochastic Techniques, User's Manual (Personal Computer Version). Denver, Colorado, USA:Bureau of Reclamation, Engineering and Research Center.
23. Mandelbrot, B. B., 1965. Une classe de processus stochastiques homothétiques a soi:application à la loi climatologique de H. E. Hurst. C. R. Acad. Sci. Paris, 260:3284–3277.
24. Mandelbrot, B. B., 1971. A fast fractional Gaussian noise generator. Wat. Resour. Res., 7 (3):543–553.
25. Mandelbrot, B. B., 1977. The Fractal Geometry of Nature, 248. New York, USA:Freeman.
26. Mandelbrot, B. B., and Wallis, J. R., 1969a. Computer experiments with fractional Gaussian noises, Part 1:Averages and variances. Wat. Resour. Res., 5 (1):228–241.
27. Mandelbrot, B. B., and Wallis, J. R., 1969b. Computer experiments with fractional Gaussian noises, Part 2:Rescaled ranges and spectra. Wat Resour. Res., 5 (1):242–259.
28. Mandelbrot, B. B., and Wallis, J. R., 1969c. Computer experiments with fractional Gaussian noises, Part 3:Mathematical appendix. Wat. Resour. Res., 5 (1):260–267.
29. Mejia, J. M., Rodriguez-lturbe, I., and Dawdy, D. R., 1972. Streamflow simulation, 2:The broken line process as a potential model for hydrologic simulation. Wat. Resour. Res., 8 (4):931–941.
30. Mesa, O. J., and Poveda, G., 1993. The Hurst effect:the scale of fluctuation approach. Wat. Resour. Res., 29 (12):3995–4002.
31. Montanari, A., Rosso, R., and Taqqu, M. S., 1997. Fractionally differenced ARIMA models applied to hydrologic time series. Wat. Resour. Res., 33 (5):1035–1044.
32. National Research Council (Committee on Opportunities in the Hydrologic Sciences). 1991. Opportunities in the Hydrologic Sciences, 21. Washington DC, USA:National Academy Press.
33. Papoulis, A., 1991. Probability, Random Variables, and Stochastic Processes (third edn). 57. New York, USA:McGraw-Hill.
34. Radziejewski, M., and Kundzewicz, Z. W., 1997. Fractal analysis of flow of the river Warta. J. Hydrol., 200:280–294.
35. Salas, J. D., 1993. “ Analysis and modeling of hydrologic time series. ”. In Handbook of Hydrology Edited by:Maidment, D., New York, USA:McGraw-Hill. 19.1–19.72
36. Salas, J. D., and Boes, D. C., 1980. Shifting level modelling of hydrologic time series. Adv. Wat. Resour., 3:59–63.
37. Salas, J. D., Delleur, J. W., Yevjevich, V., and Lane, W. L., 1980. Applied Modeling of Hydrologic Time Series. Littleton, Colorado, USA:Water Resources Publications.
38. Saupe, D., 1988. “ Algorithms for random fractals. ”. In The Science of Fractal Images Edited by:Peitgen, H.-O., and Saupe, D., Chapter 2. Springer-Verlag, Berlin, Germany
39. Stephenson, D. B., Pavan, V., and Bojariu, R., 2000. Is the North Atlantic Oscillation a random walk?. Int. J. Clim., 20:1–18.
40. Toussoun, O., 1925. “ Mémoire sur l'histoire du Nil. ”. In Mémoires a l'Institut d'Egypte Vol. 18, 366–404.
41. Vanmarcke, E., 1983. Random Fields, 225. Cambridge, Massachusetts, USA:TheMIT Press.
42. Vogel, R. M., Tsai, Y., and Limbrunner, J. F., 1998. The regional persistence and variability of annual streamflow in the United States. Wat. Resour. Res., 34 (12):3445–3459.
43. Yevjevich, V., 1972. Stochastic Processes in Hydrology. Fort Collins, Colorado, USA:Water Resources Publications.