A Bayesian method for multi-site stochastic data generation: Dealing with non-concurrent and missing data, variable transformation and parameter uncertainty

Stochastically generated stream flow and climatic data may be used as input to water resources simulation models for planning purposes. Dealing with non-concurrent and missing data, variable transformation and parameter uncertainty presents a significant challenge in the development of methods for stochastic data generation. In this paper, a Bayesian method is introduced for multi-site stochastic generation of annual stream flow and climatic data. A contemporaneous autoregressive lag-one model CAR(1) with the Box–Cox transformation is used to capture key statistical structure of multiple annual stream flow and climatic time series while keeping the number of model parameters to a minimum. The posterior joint distribution of the model parameters is formulated, allowing for inputs of historical data series that are not continuous or concurrent, thus avoiding the need to infill or truncate data records and maximising the value of available data. Parameter and uncertainty inference are solved numerically by using Markov Chain Monte Carlo simulations. Subsequent stochastic generation of data fully accounts for parameter uncertainty. In addition, a re-parameterization scheme is used to handle the problem of strong inter-parameter dependence from the Box–Cox transformation. The method was applied to the Melbourne Water supply system to demonstrate its computational feasibility.