Analysis of system drought for Manitoba Hydro using stochastic methods
Stochastic time series models are commonly used in the analysis of large-scale water resources systems. In the stochastic approach, synthetic flow scenarios are generated and used for the analysis of complex events such as multi-year droughts. Conclusions drawn from such analyses are only plausible to the extent that the underlying time series model realistically represents the natural variability of flows. Traditionally hydrologists have favoured autoregressive moving average (ARMA) models to describe annual flows. In this research project, a class of model called Markov-Switching (MS) model (also referred to as a Hidden Markov model) is presented as an alternative to conventional ARMA models. The basic assumption underlying this model is that a limited number of flow regimes exists and that each flow year can be classified as belonging to one of these regimes. The persistence of and switching between regimes is described by a Markov chain. Within each regime, it is assumed that annual flows follow a normal distribution with mean and variance that depend on the regime. The simplicity of this model makes it possible to derive a number of model characteristics analytically such as moments, autocorrelation, and crosscorrelation. Model estimation is possible with the maximum likelihood method implemented using the Expectation Maximization (EM) algorithm. The uncertainty in the model parameters can be assessed through Bayesian inference using Markov Chain Monte Carlo (MCMC) methods. A Markov-Switching disaggregation (MSD) model is also proposed in this research project to disaggregate higher-level flows generated using the MS model into lower-level flows. The MSD model preserves the additivity property because for a given year both the higher-level and lower-level variables are generated from normal distributions. The 2-state MS and MSD models are applied to Manitoba Hydro's system along with more conventional first order autoregressive and disaggregation models and parameter and missing data uncertainty are identified in the analysis of system drought.