Incorporating Parameter and Data Uncertainties in the Analysis of Energy Drought

The stochastic approach is commonly employed in the probabilistic analysis of water resources systems. In this approach, a selected stochastic time series model is used to generate synthetic series that mimic the important statistical properties of observed hydrological variables. Due to the use of limited amount of data for model estimation, the estimated parameters have sampling errors. This is usually referred to as parameter uncertainty. In multi-site applications, the length of the observed records at different sites must be the same. In order to use all available data, the shorter series are extended using record extension methods. However, since extended data are not observed values, some data uncertainty is introduced. Although parameter and data uncertainties may have significant impact on the conclusions drawn from a study, they are neglected in most practical applications. In this study, an attempt is made to integrate and quantify uncertainty associated with parameters and extended data in the frequency analysis of energy drought for Manitoba Hydro, Manitoba, Canada. In the frequency analysis, a multivariate Markov-Switching model is employed in the modelling of annual streamflow data. Parameter uncertainty is then incorporated in the Markov-Switching model through Bayesian inference. In the Bayesian approach, the unknown parameters of the stochastic model are treated as random variables instead of fixed quantities. Parameter uncertainty is quantified by determining the posterior distribution of model parameters. Since the posterior distribution of the parameters cannot be derived analytically for the Markov-Switching model, a Markov chain Monte Carlo (MCMC) method is used to numerically approximate the distribution. In the MCMC method, the extended data are also treated as parameters and simulated along with the model parameters in order to quantify the combined effect of data and parameter uncertainties in the frequency analysis of energy drought.