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Geophysical Monograph Series



  • precipitation
  • river runoff
  • scaling
  • memory
  • predictability
  • universality

Index Terms

  • 1817 Hydrology: Extreme events
  • 1821 Hydrology: Floods
  • 1854 Hydrology: Precipitation
  • 1839 Hydrology: Hydrologic scaling



Precipitation and River Flow: Long-Term Memory and Predictability of Extreme Events

A. Bunde, M. I. Bogachev, and S. Lennartz

In this review, we discuss linear and nonlinear long-term correlations in precipitation and river flows and their influence on risk estimation. We outline the standard method for measuring linear and nonlinear correlations that can distinguish between natural fluctuations and external trends, and we use this method to show that, in general, precipitation does not show linear long-term correlation, in contrast to river flows. Both precipitation and river runoff records exhibit nonlinear long-term memory that can be detected by a multifractal detrended fluctuation analysis. Long-term memory has important consequences for the occurrence of extremes. Contrary to the intuition that extremes are uncorrelated and thus occur randomly in time, they tend to cluster in the presence of long-term memory. Here we analyze this clustering feature for the daily precipitation and river flow data. To describe the occurrence of extremes quantitatively, we determine the probability density function of the return intervals between extremes above some threshold value Q and show how it can be used to obtain the hazard function, which is crucial for a risk estimation. Using the hazard function and a Bayesian approach (receiver operator characteristic analysis), we evaluate the contributions of the linear and nonlinear memory to the predictability of precipitation and river flows.

Citation: Bunde, A., M. I. Bogachev, and S. Lennartz (2012), Precipitation and river flow: Long-term memory and predictability of extreme events, in Extreme Events and Natural Hazards: The Complexity Perspective, Geophys. Monogr. Ser., vol. 196, edited by A. S. Sharma et al. 139–152, AGU, Washington, D. C., doi:10.1029/2011GM001112.

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