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To sustain perpetual operation, systems that harvest environmental energy must carefully regulate their usage to satisfy their demand. Regulating energy usage is challenging if a system's demands are not elastic and its hardware components are not energy-proportional, since it cannot precisely scale its usage to match its supply. Instead, the system must choose when to satisfy its energy demands based on its current energy reserves and predictions of its future energy supply. In this paper, we explore the use of weather forecasts to improve a system's ability to satisfy demand by improving its predictions. We analyze weather forecast, observational, and energy harvesting data to formulate a model that translates a weather forecast to a wind or solar energy harvesting prediction, and quantify its accuracy. We evaluate our model for both energy sources in the context of two different energy harvesting sensor systems with inelastic demands: a sensor testbed that leases sensors to external users and a lexicographically fair sensor network that maintains steady node sensing rates. We show that using weather forecasts in both wind- and solar-powered sensor systems increases each system's ability to satisfy its demands compared with existing prediction strategies.