The operation of water reservoirs involves a spectrum of timescales based on the distribution of stream flow travel times between reservoirs, as well as the technical, environmental, and social constraints imposed on the operation. In this research, a hydrodynamically based description of the flow between hydropower stations was implemented to study the relative importance of wave diffusion on the spectrum of hydrograph variance in a regulated watershed. Using spectral decomposition of the effluence hydrograph of a watershed, an exact expression of the variance in the outflow response was derived, as a function of the trends of hydraulic and geomorphologic dispersion and management of production and reservoirs. We show that the power spectra of involved time-series follow nearly fractal patterns, which facilitates examination of the relative importance of wave diffusion and possible changes in production demand on the outflow spectrum. The exact spectral solution can also identify statistical bounds of future demand patterns due to limitations in storage capacity. The impact of the hydraulic description of the stream flow on the reservoir discharge was examined for a given power demand in River Dal€ alven, Sweden, as function of a stream flow Peclet number. The regulation of hydropower production on the River Dal€ alven generally increased the short-term variance in the effluence hydrograph, whereas wave diffusion decreased the short-term variance over periods of <1 week, depending on the Peclet number (Pe) of the stream reach. This implies that flow variance becomes more erratic (closer to white noise) as a result of current production objectives.
Climate‐driven fluctuations in the runoff and potential energy of surface water are generally large in comparison to the capacity of hydropower regulation, particularly when hydropower is used to balance the electricity production from covarying renewable energy sources such as wind power. To define the bounds of reservoir storage capacity, we introduce a dedicated reservoir volume that aggregates the storage capacity of several reservoirs to handle runoff from specific watersheds. We show how the storage bounds can be related to a spectrum of the climate‐driven modes of variability in water availability and to the covariation between water and wind availability. A regional case study of the entire hydropower system in Sweden indicates that the longest regulation period possible to consider spans from a few days of individual subwatersheds up to several years, with an average limit of a couple of months. Watershed damping of the runoff substantially increases the longest considered regulation period and capacity. The high covariance found between the potential energy of the surface water and wind energy significantly reduces the longest considered regulation period when hydropower is used to balance the fluctuating wind power.
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