The city of Sioux Falls, in southeastern South Dakota, is the largest city in South Dakota. The U.S. Geological Survey (USGS), in cooperation with the city of Sioux Falls, completed a groundwater-flow model to use for improving the understanding of groundwater-flow processes, estimating hydrogeologic properties, and analyzing groundwater and surface-water interactions for the Big Sioux aquifer in the model area.

The model area includes the Big Sioux aquifer and the underlying hydrogeologic units from Dell Rapids, South Dakota, to the confluence of the Big Sioux River and the outlet of the Sioux Falls Diversion Channel in eastern Sioux Falls, S. Dak. The Big Sioux aquifer is the primary aquifer in the model area and the focus of the groundwater-flow model. The Big Sioux River is the largest stream in the model area and is in hydraulic connection with the Big Sioux aquifer.

A conceptual model for the area was constructed and includes a characterization of the hydrogeologic framework, analysis and construction of potentiometric surfaces, and summary of estimated water budget components in the model area. The primary hydrogeologic units in the model area consist of (1) the Big Sioux aquifer, (2) a glacial till confining unit, and (3) bedrock aquifers (Split Rock Creek and Sioux Quartzite aquifers). Sources of groundwater recharge included infiltration of precipitation, stream seepage, and groundwater exchanges among the hydraulically connected Big Sioux aquifer, glacial till confining unit, and bedrock aquifers. Groundwater losses included evapotranspiration, groundwater discharge to streams, and groundwater withdrawal to supply water-use needs.

A numerical groundwater-flow model (numerical model) was constructed and was used to simulate all aspects of the conceptual model for predevelopment (steady-state) and time-varying (transient) monthly conditions for 1950–2017. The numerical model was constructed using the USGS modular hydrologic simulation program, MODFLOW–6, and was calibrated using the Parameter ESTimation software, PEST++.

The transient numerical model was calibrated for steady-state and transient monthly conditions for 1950–2017. Calibration targets were observations of hydraulic head, changes in hydraulic head, monthly mean streamflow (as a rate), and cumulative monthly stream discharge (as a volume). Parameters adjusted during model calibration were horizontal and vertical hydraulic conductivity, specific storage, specific yield, recharge and evapotranspiration multipliers, and streambed hydraulic conductivity. Horizontal and vertical hydraulic conductivity were estimated at pilot points distributed within the model area; specific storage and specific yield were assigned to uniform values in each layer in the model area; recharge and evapotranspiration multipliers were assigned uniformly for every stress period in the numerical model; and streambed hydraulic conductivity values were assigned uniformly between stream confluences.

The final calibrated parameter values of horizontal and vertical hydraulic conductivity, specific yield, specific storage, streambed hydraulic conductivity, recharge, and evapotranspiration were considered reasonable for the hydrogeologic materials and conditions in the model area for 1950–2017.

Overall, simulated hydraulic head altitudes had a linear regression coefficient of determination (R²) of 0.48. Hydraulic head altitude residuals for the glacial till confining unit and bedrock aquifers were typically greater in magnitude when compared to residuals in the Big Sioux aquifer, but simulated hydraulic head altitudes in the Big Sioux aquifer compared favorably with mean observed hydraulic head altitudes and had a linear regression R² of 0.93.

Simulated streamflow hydrographs matched the general trends of observed increases and decreases in streamflow for USGS streamgages 06482000 (Big Sioux River at Sioux Falls, S. Dak.) and 06482020 (Big Sioux River at North Cliff Avenue at Sioux Falls, S. Dak.), but larger streamflows were overestimated at the first streamgage and underestimated at the second streamgage. The numerical model reasonably estimated cumulative monthly stream discharge for the first 10–15 years of available streamflow records at both USGS streamgages. After the first 10–15 years of available streamflow record, cumulative monthly stream discharge was closely estimated for USGS streamgage 06482000 and underestimated at USGS streamgage 06482020.

Composite sensitivities without regularization were calculated by PEST++ for the calibrated numerical model parameters and were averaged by parameter group. The parameter group with the highest mean composite sensitivity was the recharge multiplier parameter group.

Model simplifications, assumptions, and limitations were necessary for construction of the conceptual and numerical models and for calibration efficiency. Spatial simplification of hydraulic properties could cause the numerical model to misrepresent reactions to changes in localized stresses, such as additional demands for groundwater withdrawal. The numerical model was temporally discretized into monthly periods and required scaling daily rates into representative monthly rates for model input and calibration targets. Based on the comparison between the observed and simulated groundwater levels, monthly mean streamflow and cumulative monthly stream discharge, and general groundwater distribution and flow, the numerical model favorably simulated the flow in the Big Sioux aquifer.

Eventual capture was calculated in the model area using a steady-state numerical groundwater-flow model. The eventual capture map shows areas of higher streamflow capture adjacent to the Big Sioux River north of the city of Sioux Falls and along the lower part of the Sioux Falls Diversion Channel, and areas of lower streamflow capture along aquifer boundaries and near the southern Sioux Quartzite barrier.

The timing of capture was determined using a transient numerical groundwater-flow model to determine the likely captured water sources for 30 years of groundwater withdrawal at three hypothetical wells using three continuous withdrawal rates (112.5, 450.0, and 900.0 gallons per minute). Supply for all three hypothetical wells became capture-dominated after only a short period of continuous withdrawal. Capture stabilized after about 10–15 years for well A, and after 20–25 years for well B, and after about 10–15 years for well C.

The groundwater-flow model is a suitable tool to use for improving the understanding of groundwater-flow processes, estimating hydrogeologic properties, and analyzing groundwater and surface-water interactions for the Big Sioux aquifer near Sioux Falls, S. Dak. The numerical model can be used to simulate hydrologic scenarios, advance understanding of groundwater budgets, compute system response to stress, and determine likely sources of water supplied to wells.