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Simulation of Stage and Hydrologic Budget for Shell Lake, Washburn County, Wisconsin

Abstract

A model that simulates lake stage was developed to test the current understanding of the hydrology of Shell Lake, Wisconsin and to provide a tool for predicting the effects of withdrawing lake water on future lake stages. The model code is written in Fortran and simulates daily lake stage by summing estimates of hydrologic-budget components—precipitation falling on the lake surface, water evaporating from the lake surface, runoff (consisting of overland flow to the lake and intermittent streams flowing into the lake), and ground-water flow out of the lake. The model was calibrated to intermittent lake stage measurements for the period 1948–98. The hydrologic budget model was coupled to UCODE, a parameter estimation model, to aid in estimating runoff coefficients. Trends in stage simulated by the calibrated model compare reasonably well with historical stage trends. The root mean square of the differences of simulated and measured daily lake stage for the period 1948–98 is 0.54 foot. Predictive simulations indicate that withdrawing lake water is an effective way of reducing lake stage. Several years of pumping for at least 200 days per year at rates of 1,000 to 2,000 gallons per minute would have been required to reduce 1990’s high stages by about one foot.