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[1] Although being one of the most popular and extensively studied approaches to design water reservoir operations, Stochastic Dynamic Programming is plagued by a dual curse that makes it unsuitable to cope with large water systems: the computational requirement grows exponentially with the number of state variables considered (curse of dimensionality) and an explicit model must be available to describe every system transition and the associated rewards/costs (curse of modeling). A variety of simplifications and approximations have been devised in the past, which, in many cases, make the resulting operating policies inefficient and of scarce relevance in practical contexts. In this paper, a reinforcement-learning approach, called fitted Q-iteration, is presented: it combines the principle of continuous approximation of the value functions with a process of learning off-line from experience to design daily, cyclostationary operating policies. The continuous approximation, performed via tree-based regression, makes it possible to mitigate the curse of dimensionality by adopting a very coarse discretization grid with respect to the dense grid required to design an equally performing policy via Stochastic Dynamic Programming. The learning experience, in the form of a data set generated combining historical observations and model simulations, allows us to overcome the curse of modeling. Lake Como water system (Italy) is used as study site to infer general guidelines on the appropriate setting for the algorithm parameters and to demonstrate the advantages of the approach in terms of accuracy and computational effectiveness compared to traditional Stochastic Dynamic Programming.Citation: Castelletti, A., S. Galelli, M. Restelli, and R. Soncini-Sessa (2010), Tree-based reinforcement learning for optimal water reservoir operation, Water Resour. Res., 46, W09507,

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In a changing climate and society, large storage systems can play a key role for securing water, energy, and food, and rebalancing their cross-dependencies. In this letter, we study the role of large storage operations as flexible means of adaptation to climate change. In particular, we explore the impacts of different climate projections for different future time horizons on the multi-purpose operations of the existing system of large dams in the Red River basin (China-Laos-Vietnam). We identify the main vulnerabilities of current system operations, understand the risk of failure across sectors by exploring the evolution of the system tradeoffs, quantify how the uncertainty associated to climate scenarios is expanded by the storage operations, and assess the expected costs if no adaptation is implemented. Results show that, depending on the climate scenario and the time horizon considered, the existing operations are predicted to change on average from -7 to +5% in hydropower production, +35 to +520% in flood damages, and +15 to +160% in water supply deficit. These negative impacts can be partially mitigated by adapting the existing operations to future climate, reducing the loss of hydropower to 5%, potentially saving around 34.4 million US$ year -1 at the national scale. Since the Red River is paradigmatic of many river basins across south east Asia, where new large dams are under construction or are planned to support fast growing economies, our results can support policy makers in prioritizing responses and adaptation strategies to the changing climate.