Bayes Design of a Reservoir Under Random Sediment Yield

The design of a reservoir subject to long-range sediment accumulation stemming from the sum of a random number of random sedimentation events is investigated. The event-based simulation method, which is applied to a case study in southern Arizona, involves generating synthetic sequences of Poisson inputs into the modified universal soil loss equation. The stochastic inputs result from a fitted bivariate distribution of runoff-producing precipitation events (representing the amount and duration of such precipitation) and an independent fitted exponential distribution of interarrival time between events. The simulated sequences of sediment yield events thus obtained are used to calculate accumulated sediment yield and cost of a given design for each sequence. The optimum design and corresponding Bayes risk are evaluated in four cases: (1) under natural uncertainty, (2) under natural uncertainty and uncertainty in the bivariate rainfall distribution parameters, (3) under natural uncertainty and uncertainty in the Poisson counting distribution parameter, and (4) under all three types of uncertainty. The effect of rainfall record length is ascertained by further computer experiments, but only a partial Bayesian analysis is provided because of the complexity created by a three-dimensional parameter uncertainty. The optimum reservoir capacity and corresponding Bayes risk are shown to increase substantially (up to 20 and 90%, respectively) as more uncertainties are incorporated into the model.

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