Abstract
It is shown that runs of low-flow annual streamflow in a coastal semiarid basin of Central California can be adequately modelled by renewal theory. For example, runs of below-median annual streamflows are shown to follow a geometric distribution. The elapsed time between runs of below-median streamflow are geometrically distributed also. The sum of these two independently distributed geometric time variables defines the renewal time elapsing between the initiation of a low-flow run and the next one. The probability distribution of the renewal time is then derived from first principles, ultimately leading to the distribution of the number of low-flow runs in a specified time period, the expected number of low-flow runs, the risk of drought, and other important probabilistic indicators of low-flow. The authors argue that if one identifies drought threat with the occurrence of multiyear low-flow runs, as it is done by water supply managers in the study area, then our renewal model provides a number of interesting results concerning drought threat in areas historically subject to inclement, dry, climate. A 430-year long annual streamflow time series reconstructed by tree-ring analysis serves as the basis for testing our renewal model of low-flow sequences.
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Loaiciga, H.A., Leipnik, R.B. Stochastic renewal model of low-flow streamflow sequences. Stochastic Hydrol Hydraul 10, 65–85 (1996). https://doi.org/10.1007/BF01581794
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DOI: https://doi.org/10.1007/BF01581794