STOCHASTIC RENEWAL MODEL OF LOW-FLOW STREAMFLOW SEQUENCES

It is shown that runs of low-flow annual streamflow in a coastal semia rid 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 the n derived from first principles, ultimately leading to the distributio n of the number of low-flow runs in a specified time period, the expec ted number of low-flow runs, the risk of drought, and other important probabilistic indicators of low-how. The authors argue that if one ide ntifies drought threat with the occurrence of multiyear low-flow runs, as it is done by water supply managers in the study area, then our re newal model provides a number of interesting results concerning drough t threat in areas historically subject to inclement, dry, climate. A 4 30-year long annual streamflow time series reconstructed by tree-ring analysis serves as the basis for testing our renewal model of low-flow sequences.