Estimation of natural historical flows for the Manitowish River near Manitowish Waters, Wisconsin

Abstract

The Wisconsin Department of Natural Resources is charged with oversight of dam operations throughout Wisconsin and is considering modifications to the operating orders for the Rest Lake Dam in Vilas County, Wisconsin. State law requires that the operation orders be tied to natural low flows at the dam. Because the presence of the dam confounds measurement of natural flows, the U.S. Geological Survey, in cooperation with the Wisconsin Department of Natural Resources, installed streamflow-gaging stations and developed two statistical methods to improve estimates of natural flows at the Rest Lake Dam. Two independent methods were used to estimate daily natural flow for the Manitowish River approximately 1 mile downstream of the Rest Lake Dam. The first method was an adjusted drainage-area ratio method, which used a regression analysis that related measured water yield (flow divided by watershed area) from short-term (2009–11) gaging stations upstream of the Manitowish Chain of Lakes to the water yield from two nearby long-term gaging stations in order to extend the flow record (1991–2011). In this approach, the computed flows into the Chain of Lakes at the upstream gaging stations were multiplied by a coefficient to account for the monthly hydrologic contributions (precipitation, evaporation, groundwater, and runoff) associated with the additional watershed area between the upstream gaging stations and the dam at the outlet of the Chain of Lakes (Rest Lake Dam). The second method used to estimate daily natural flow at the Rest Lake Dam was a water-budget approach, which used lake stage and dam outflow data provided by the dam operator. A water-budget model was constructed and then calibrated with an automated parameter-estimation program by matching simulated flow-duration statistics with measured flow-duration statistics at the upstream gaging stations. After calibration of the water-budget model, the model was used to compute natural flow at the dam from 1973 to 2011. Daily natural flows at the dam, as computed by the adjusted drainage-area ratio method and the water-budget method, were used to compute monthly flow-duration values for the period of historical data available for each method. Monthly flow-durations provide a means for evaluating the frequency and range in flows that have been observed for each month over the course of many years. Both methods described the pattern and timing of measured high-flow and low-flow events at the upstream gaging stations. The adjusted drainage-area ratio method generally had smaller residual errors across the full range of observed flows and had smaller monthly biases than the water-budget method. Although it is not possible to evaluate which method may be more "correct" for estimating monthly natural flows at the dam, comparisons between the results of each method indicate that the adjusted drainage-area ratio method may be susceptible to biases at high flows due to isolated storms outside of the Manitowish River watershed. Conversely, it appears that the water-budget method may be susceptible to biases at low flows because of its sensitivity to the accuracy of reported lake stage and outflows, as well as effects of upstream diversions that could not be fully compensated for with this method. Results from both methods are useful for understanding the natural flow patterns at the dam. Flows for both methods have similar patterns, with high median flows in spring and low median flows in late summer. Similarly, the range from monthly high-flow durations to low-flow durations increases during spring, decreases during summer, and increases again during fall. These seasonal patterns illustrate a challenge with interpreting a single value of natural low flow. That is, a natural low flow computed for September is not representative of a natural low flow in April. Moreover, alteration of natural flows caused by storing water in the Chain of Lakes during spring and releasing it in fall causes a change in the timing of high and low flows compared with natural conditions. That is, the lowest reported dam outflows occurred in spring and highest reported outflows occurred in fall, which is opposite the natural patterns.