Stochastic renewal model of low-flow streamflow sequences |
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| Authors: | H A Loaiciga R B Leipnik |
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| Institution: | (1) Dept. of Geography and Environmental Studies, University of California, 93106 Santa Barbara, CA, USA;(2) Department of Mathematics, University of California, 93106 Santa Barbara, CA, USA |
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| 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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| Keywords: | Streamflow drought tree-ring data renewal model geometric variables |
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