Multivariate Bayesian Regression Approach to Forecast Releases from a System of Multiple Reservoirs

This research presents a model that simultaneously forecasts required water releases 1 and 2 days ahead from two reservoirs that are in series. In practice, multiple reservoir system operation is a difficult process that involves many decisions for real-time water resources management. The operator of the reservoirs has to release water from more than one reservoir taking into consideration different water requirements (irrigation, environmental issues, hydropower, recreation, etc.) in a timely manner. A model that forecasts the required real-time releases in advance from a multiple reservoir system could be an important tool to allow the operator of the reservoir system to make better-informed decisions for releases needed downstream. The model is developed in the form of a multivariate relevance vector machine (MVRVM) that is based on a sparse Bayesian regression model approach. With this Bayesian approach, a predictive confidence interval is obtained from the model that captures the uncertainty of both the model and the data. The model is applied to the multiple reservoir system located in the Lower Sevier River Basin near Delta, Utah. The results show that the model learns the input–output patterns with high accuracy. Computing multiple-time-ahead predictions in real-time would require a model which guarantees not only good prediction accuracy but also robustness with respect to future changes in the nature of the inputs data. A bootstrap analysis is used to guarantee good generalization ability and robustness of the MVRVM. Test results demonstrate good performance of predictions and statistics that indicate robust model generalization abilities. The MVRVM is compared in terms of performance and robustness with another multiple output model such as Artificial Neural Network (ANN). Copyright Springer Science+Business Media B.V. 2011