Noah, Joseph, and Operational Hydrology

@article{Mandelbrot1968NoahJA,
  title={Noah, Joseph, and Operational Hydrology},
  author={Benoit B. Mandelbrot and James R. Wallis},
  journal={Water Resources Research},
  year={1968},
  volume={4},
  pages={909-918}
}
By ‘Noah Effect’ we designate the observation that extreme precipitation can be very extreme indeed, and by ‘Joseph Effect’ the finding that a long period of unusual (high or low) precipitation can be extremely long. Current models of statistical hydrology cannot account for either effect and must be superseded. As a replacement, ‘self-similar’ models appear very promising. They account particularly well for the remarkable empirical observations of Harold Edwin Hurst. The present paper… 
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References

SHOWING 1-10 OF 18 REFERENCES
Misconceptions in hydrology and their consequences
Several misconceptions have been introduced into hydrology that have had adverse consequences on the science and on water-resources development. Persistent use of the concept of maximum precipitation…
Some long‐run properties of geophysical records
By preparing this book Chris Barton and Paul La Pointe have earned the gratitude of all geologists and students of fractals. I continue to belong to this second group, and Chris and Paul clearly have…
How Long Is the Coast of Britain? Statistical Self-Similarity and Fractional Dimension
Geographical curves are so involved in their detail that their lengths are often infinite or, rather, undefinable. However, many are statistically "selfsimilar," meaning that each portion can be…
Robustness of the rescaled range R/S in the measurement of noncyclic long run statistical dependence
The rescaled range R(t, s) / S(t, s) is shown by extensive computer simulation to be a very robust statistic for testing the presence of noncyclic long run statistical dependence in records and, in…
The Variation of Certain Speculative Prices
The classic model of the temporal variation of speculative prices (Bachelier 1900) assumes that successive changes of a price Z(t) are independent Gaussian random variables. But, even if Z(t) is…
ON THE RANGE OF PARTIAL SUMS OF A FINITE NUMBER OF INDEPENDENT NORMAL VARIATES
The present investigation was suggested by the problem of planning the storage capacity of a reservoir, where one would like to know the distribution of the water level over a given number n of…
Some noises with I/f spectrum, a bridge between direct current and white noise
  • B. Mandelbrot
  • Mathematics, Computer Science
    IEEE Trans. Inf. Theory
  • 1967
TLDR
The present paper reinterprets spectral measurements without paradox, by introducing a concept to be called "conditional spectrum," and examples are given of functions ruled by chance, that have the observed "erratic" behavior and conditional spectral density.
The variation of certain •ecularive prices
  • J. Business Univ. Chicago,
  • 1963
Fractional Brownian Motions, Fractional Noises and Applications
Some noises with 1/f spectrum, a bridge between direct current and white noise, Inst. Electrical Electronic Eng., Tra.•s
  • Information Theory,
  • 1967
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