Box 3 Mirror Lake

The USGS initiated studies of Mirror Lake located in a basin composed of glacial deposits and bedrock in New Hampshire, USA, in the late 1970’s. They used both physical measurements of water budget components, chemical water budget analyses, and regional groundwater modeling to assess the water balance. Their work also attempted to examine uncertainties in budget parameters. Energy budget methods were used to compute evaporation using data collected on a floating raft and at a land station. Precipitation estimates were derived from two gauges located 400 m from the lake. Stage recorders were used with stream gauging to measure surface-water inflows and outflows. Lake stage measurements were used to compute changes in storage, and groundwater inflow and outflow were computed using Darcy’s law with a measured hydraulic conductivity value, hydraulic gradients derived from well networks and lake stage measurements, and estimates of cross-sectional areas based on site geology and well logs.

Annual and monthly chemical and water budgets were computed for the period 1981 to 2000 (Table Box 3-1). The groundwater inflow and outflow components of the annual budget were identified as having the largest uncertainty. The single measured hydraulic conductivity value used in the Darcy’s Law calculations generalized the complex nature of the geologic material adjacent to the lake boundaries. Groundwater inflow was estimated at 47,000 m³/y using the single hydraulic conductivity value to represent the properties of the cross sections. A second method using geochemical modeling and analysis of isotopic ratios of oxygen-18 to oxygen-16 data yielded a groundwater inflow value of 95,000 m³/y. A third approach used a groundwater basin numerical flow model to generate the groundwater inflow to the lake. Modeling estimated groundwater inflow was 133,000 m³/y, about 2.8 times greater than the initial computed value (Tiedeman et al., 1997). The researchers recognized the uncertainty in the groundwater inflow term and settled on 113,000 m³/y as the input estimate.

Applications of multiple methods to estimate groundwater inflow to the lake may shed light on the possible variability of poorly resolved water budget components. The relatively high degree of uncertainty in component measurements supports the need to employ additional dense spatial and temporal instrumentation, and data collection and analyses to reduce uncertainty. Healy and others (2007) estimated uncertainties of 5-10 percent for precipitation measurements, 10 to 15 percent for evaporation values, 5 to 10 percent for streamflow, and 30 to 50 percent for groundwater exchange. They computed an overall budget uncertainty of 13 percent. This study suggests that choosing a representative value for the water budget groundwater inflow and outflow components of a water budget requires an evaluation of uncertainty and professional judgement based on the quality and distribution of parameters used for the computations. Uncertainty analyses suggest additional data collection may be required to obtain a more representative water budget.

Table Box 3-1 – Annual Initial and Final (modeled) Water Budgets for Mirror Lake, New Hampshire, USA. Initial groundwater inflow is estimated using a single hydraulic conductivity value to calculate discharge to the lake. Values are in 100,000 m³/y. Estimated percent uncertainty in parameters is also shown. The imbalance (residual) is the difference between inflow and outflow and represents the uncertainty (error) in the budget (modified from Healy et al., 2007).

Return to where text links to Box 3