Seasonal patterns of water storage as signatures of the climatological equilibrium between resource and demand

Water is accumulated in reservoirs to adapt in time the availability of the resource to various demands like hydropower production, irrigation, water supply or ecological constraints. Deterministic dynamic programming retrospectively optimizes the use of the resource during a given time period. One of its by-products is the estimation of the marginal storage water value (MSWV), defined by the marginal value of the future goods and benefits obtained from an additional unit of storage water volume. Knowledge of the MSWV makes it possible to determine a posteriori the storage requirement scheme that would have led to the best equilibrium between the resource and the demand. The MSWV depends on the water level in the reservoir and shows seasonal as well as inter-annual variations. This study uses the inter-annual average of both the storage requirement scheme and the MSWV cycle as signatures of the best temporal equilibrium that is achievable in a given resource/demand context (the climatological equilibrium). For a simplified water resource system in a French mountainous region, we characterize how and why these signatures change should the climate and/or the demand change, mainly if changes are projected in the mean regional temperature (increase) and/or precipitation (decrease) as well as in the water demand for energy production and/or maintenance of a minimum reservoir level. Results show that the temporal equilibrium between water resource and demand either improves or degrades depending on the considered future scenario. In all scenarios, the seasonality of MSWV changes when, for example, earlier water storage is required to efficiently satisfy increasing summer water demand. Finally, understanding how MSWV signatures change helps to understand changes in the storage requirement scheme.

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