Abstract
By randomizing the inputs to the deterministic Nash-Dooge linear reservoir cascade, linear stochastic conceptual response models suitable for small catchments are formulated as simple linear stochastic dynamical systems within the formalism of stochastic differential equations [SDE’s]. The system driving process, rainfall and evapotranspiration losses (negative input) are modelled respectively as a compound Poisson process and a mean zero white Gaussian noise superposed on a deterministic mean. Moments and autocovariance functions for the steady-state system outputs are obtained via application of the Itô differential rule. Results for cascades of one to five reservoirs reveal the additional reservoirs progressively attenuate system response. Generalizations to an n reservoir cascade are given for the variance and autocovariance function.
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© 1987 D. Reidel Publishing Company, Dordrecht, Holland
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Bodo, B.A., Unny, T.E. (1987). On the Outputs of the Stochasticized Nash-Dooge Linear Reservoir Cascade. In: MacNeill, I.B., Umphrey, G.J., McLeod, A.I. (eds) Advances in the Statistical Sciences: Stochastic Hydrology. The University of Western Ontario Series in Philosophy of Science, vol 37. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-4792-4_8
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DOI: https://doi.org/10.1007/978-94-009-4792-4_8
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