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A general Bayesian framework for calibrating and evaluating stochastic models of annual multi-site hydrological data |
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| Authors: | Andrew J Frost Mark A Thyer R Srikanthan George Kuczera |
| Institution: | aHydrology Unit, Bureau of Meteorology, P.O. Box 1289, Melbourne 3001, Australia bSchool of Engineering, University of Newcastle, University Drive, Callaghan NSW 2308, Australia |
| Abstract: | Multi-site simulation of hydrological data are required for drought risk assessment of large multi-reservoir water supply systems. In this paper, a general Bayesian framework is presented for the calibration and evaluation of multi-site hydrological data at annual timescales. Models included within this framework are the hidden Markov model (HMM) and the widely used lag-1 autoregressive (AR(1)) model. These models are extended by the inclusion of a Box–Cox transformation and a spatial correlation function in a multi-site setting. Parameter uncertainty is evaluated using Markov chain Monte Carlo techniques. Models are evaluated by their ability to reproduce a range of important extreme statistics and compared using Bayesian model selection techniques which evaluate model probabilities. The case study, using multi-site annual rainfall data situated within catchments which contribute to Sydney’s main water supply, provided the following results: Firstly, in terms of model probabilities and diagnostics, the inclusion of the Box–Cox transformation was preferred. Secondly the AR(1) and HMM performed similarly, while some other proposed AR(1)/HMM models with regionally pooled parameters had greater posterior probability than these two models. The practical significance of parameter and model uncertainty was illustrated using a case study involving drought security analysis for urban water supply. It was shown that ignoring parameter uncertainty resulted in a significant overestimate of reservoir yield and an underestimation of system vulnerability to severe drought. |
| Keywords: | Stochastic rainfall Long-term persistence Parameter and model uncertainty Hidden Markov models Lag-one autoregressive models Box–Cox transformation |
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