Long term persistence and the Hurst phenomenon

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Presentation transcript:

Long term persistence and the Hurst phenomenon Loucks, D. P., J. R. Stedinger and D. A. Haith, (1981), Water Resource Systems Planning and Analysis, Prentice-Hall, Englewood Cliffs, NJ, 559 p. Chapter 6 sections 6.6 on Hurst and Fractional Brownian Noise Feder, J., (1988), Fractals, Plenum Press. Chapter 8 on Fractal Records in Time and Chapter 9 on Random Walks and Fractals. Tarboton, D. G., (1994), "The Source Hydrology of Severe Sustained Drought in the Southwestern United States," Journal of Hydrology, 161: 31-69. Barnett, T. P. and D. W. Pierce, (2008), "When will Lake Mead go dry?," Water Resour. Res., 44: W03201, http://dx.doi.org/10.1029/2007WR006704 Bras, R. L. and I. Rodriguez-Iturbe, (1985), Random Functions and Hydrology, Addison-Wesley, Reading, MA, Chapter 5, p 210-225.

Given fluctuating inflow to a reservoir qt, what storage would have been required to release a volume each year equal to the mean influx From Loucks et al, 1981

Some Hurst exponents for natural data From Feder, 1988

Simulating Fractional Gaussian Noise with ARMA (1,1) From Bras and Rodriguez-Iturbe, 1985