This paper models large pumped hydro energy storage in a future power system where variable generation, primarily in the form of wind generation, is the dominant source of power generation. The research question posed is how to formulate day-ahead and week-ahead reservoir targets for pumped hydro energy storage in the context of wind forecast uncertainty. The innovation in the work is the use of historical wind data series and wind forecasts to derive a management strategy for the operation of large PHES using stochastic optimization that outperforms current methods in power systems with significant wind generation. This approach derives intertemporal targets for large pumped hydro energy storage that reduce overall system costs when compared to targets derived using a conventional method.