Dam Management in the Era of Climate Change

TL;DR

This paper models dam management under climate change using a Hawkes process to simulate rainfall events, revealing that optimal water levels increase with event clustering, emphasizing flood protection over water reserves.

Contribution

It introduces a novel optimal control framework for dams incorporating self-exciting rainfall models, with new existence results and numerical methods.

Findings

Optimal water level rises with self-exciting parameter.

Dams shift focus from water reserves to flood protection.

Numerical examples demonstrate the model's practical implications.

Abstract

Climate change has a dramatic impact, particularly by concentrating rainfall into a few short periods, interspersed by long dry spells. In this context, the role of dams is crucial. We consider the optimal control of a dam, where the water level must not exceed a designated safety threshold, nor fall below a minimum level to ensure functionality and sustainability for for the outgoing river. To model dry spells and intense rainfall events, commonly referred to as water bombs, we introduce a Hawkes process, a well-known example of a self-exciting process characterised by time-correlated intensity, which endogenously reproduces the concentration of events. The problem is formulated as an optimal switching problem with constraints. We establish existence results and propose numerical methods for approximating the solution. Finally, we illustrate the main achievements of this approach through numerical examples. The main and counterintuitive result of our numerical analysis is that the optimal water level inside the dam increases with the self-exciting parameter. This result shows that, when facing the dilemma of managing the opposing risks of dam overtopping and dry spells, the former ultimately dominates the latter. In conclusion, dams will increasingly lose their role as water reserves and take on a greater role in flood protection.