Information Theory for Risk-based Water System Operation

Abstract

Operational management of water resources needs predictions of future behavior of water systems, to anticipate shortage or excess of water in a timely manner. Because the natural systems that are part of the hydrological cycle are complex, the predictions inevitably are subject to considerable uncertainty. Still, definitive decisions about e.g. hydropower reservoir releases or polder pump flows have to be made looking ahead into the uncertain future. This demands risk-based approach, in which, ideally, all possible future events should be considered, along with their probabilities that represent the information and uncertainty available at the time of decision. The thesis deals with water, but the flows studied are mostly those of information. Like the flow of water, also information flows obey certain fundamental laws. These are the laws of Information Theory, which also provide guidelines for developing models, handling data, and designing statistical procedures to make predictions and decisions. The information-theoretical perspective used in the thesis leads to the conclusion that predictions should necessarily be probabilistic and should be evaluated using a relative entropy measure, of which an intuitive decomposition into three components is presented. Other chapters in the thesis deal with the use of model predictive control and stochastic dynamic programming for operational water management, the time-dynamics of information, generation of weighted ensemble forecasts that balance uncertainty and information, and a perspective on data compression as philosophy of science. Recommendations for practice and further research indicate that entropy has a bright future, not only as an ever-increasing thermodynamic measure, but also as an information-theoretical measure of uncertainty that is useful in any field where predictions and decisions have to be made in a context of complex and largely unobservable systems.