Introduction

The Chain of Lakes is a reservoir system on the Fox River in northeastern Illinois with a total surface area of about 6,900 acres (Kothandaramon and others, 1977; fig. 1). As the Fox River flows south near the Illinois-Wisconsin border, it transforms from a river channel environment into a series of interconnected lakes known as the Chain of Lakes. At the Pistakee Lake outlet near Johnsburg, Illinois, the Chain of Lakes naturally constricts back to the Fox River channel and flows south about 7 miles (mi) to the Stratton Dam at McHenry, Ill. (fig. 1). The Stratton Dam controls the outflow from the Chain of Lakes to maintain pool levels in the reservoir system. The Chain of Lakes is primarily used for recreation with some downstream flood control benefits. There are about 1,250 square miles (mi²) of drainage area upstream from the Stratton Dam with contributions from the Fox River, Nippersink Creek, and local drainage areas (fig. 1).

The Stratton Dam has been operated by the Illinois Department of Natural Resources–Office of Water Resources (IDNR–OWR) since 1939. The IDNR–OWR has a target pool level of 736.8–737.2 feet (ft) and winter drawdown of 735.5 ft above the National Geodetic Vertical Datum of 1929, and the Chain of Lakes provides about 14,400 acre-feet of storage between those stages (Illinois Department of Natural Resources, 2012). The National Geodetic Vertical Datum of 1929 was used for the “Operation of the Stratton & Algonquin Dams” report (Illinois Department of Natural Resources, 2012) and was the datum used for the USGS streamgages in the study area pre-2022. These USGS streamgages were surveyed to the North American Vertical Datum of 1988 in 2022, which is the referenced datum hereinafter used in the report. The target pool level converts to about 736.6–737.0 ft and the winter drawdown to 735.3 ft (North American Vertical Datum of 1988). Hydrologic forecasts entering and leaving the Chain of Lakes are critical to the optimal operation of the Stratton Dam. The National Weather Service–North Central River Forecasting Center (NWS–NCRFC) provides the IDNR–OWR with 0–7-day hydrologic forecasts for inflows entering the Chain of Lakes which is used to develop gate operations to manage Chain of Lakes pool levels and to help mitigate flooding in the Chain of Lakes system.

In 2020, the U.S. Geological Survey (USGS) and IDNR–OWR began a cooperative study to update modeling techniques developed from a previous USGS study (Domanski, 2017). In this study, a hydraulic model was constructed and used to develop a system that enables engineers and planners to simulate and communicate predicted water-surface elevations and flows and to proactively prepare for runoff events forecasted for the Chain of Lakes. The Hydrologic Engineering Center–River Analysis System (HEC–RAS) program (version 6.5; U.S. Army Corps of Engineers, 2022) was used to simulate water-surface elevations and flows through the Chain of Lakes to 1.7 mi downstream from the Stratton Dam (fig. 1). Extending the downstream distance allowed the normal-depth slope to stabilize and not propagate upstream to the Stratton Dam tailwater where it could affect the hydraulic model performance of the Stratton Dam control structures.

The NWS–NCRFC provided simulated flow hydrographs to account for the inflows entering the Chain of Lakes. These simulated flow hydrographs for selected events were used to calibrate the hydraulic model. Five USGS streamgages within the model extent were used to calibrate the hydraulic model (fig. 1; table 1). Because the Chain of Lakes consists of several largely connected lakes, they can be modeled as a single reservoir from the inlet for the Fox River at Grass Lake to the Pistakee Lake outlet (fig. 1). The USGS streamgage Nippersink Lake at Fox Lake, Ill., (USGS station 05548000; U.S. Geological Survey, 2023f) provided Chain of Lakes pool level elevations for the hydraulic model. A low gradient in channel elevation exists for the 7-mi reach of the Fox River from Johnsburg to the Stratton Dam so the USGS streamgage Fox River at Johnsburg, Ill. (USGS station 05548500; U.S. Geological Survey, 2023b), was used for water-level stages at Johnsburg, and the USGS streamgage Fox River near McHenry, Ill. (USGS station 05549500; U.S. Geological Survey, 2023d), provided headwater stages at the Stratton Dam. The Stratton Dam tailwater stages are recorded at the USGS streamgage Fox River (tailwater) near McHenry, Ill. (USGS station 05549501; U.S. Geological Survey, 2023e). The USGS streamgage Fox River at Miller Bridge near McHenry, Ill. (USGS station 05549400; U.S. Geological Survey, 2023c), is an index-velocity gage (Levesque and Oberg, 2012) that also records flows and was used for model calibration.

Model Development

The hydraulic model was constructed using the U.S. Army Corps of Engineers modeling system HEC–RAS (version 6.5; U.S. Army Corps of Engineers, 2022). The HEC–RAS modeling system allows one- or two-dimensional models with steady-state or unsteady-state computation options; the two-dimensional and unsteady-state options were used for the Chain of Lakes hydraulic model. The HEC–RAS model was used to simulate water-surface elevations and flows through the Chain of Lakes using gate specifications and gate operations at the Stratton Dam and is available at Cigrand (2024).

Model Calibration and Validation

Model calibration was completed by adjusting n-values, normal depth, two-dimensional mesh cell size and alignment, and initial conditions with model warmup until the results of the hydraulic computations closely agreed with the observed water-surface elevations and flows at the streamgage locations. The HEC–RAS model was calibrated to three observed events that were detected after the torque-tube crest gates became operational in 2020. These calibration events include April–May 2022 (April 23–May 3), September 2022 (September 9–26), and March 2023 (February 28–March 15) (figs. 3, 4, and 5, respectively). The differences between observed and simulated peak water-surface elevations of the three calibration events at the USGS streamgage locations ranged from −0.32 to 0.15 ft (table 2). The differences between observed and simulated peak flow at the Miller Bridge near McHenry streamgage ranged from −236 to 50 cubic feet per second (ft³/s; table 3).

The RMSE and percentage bias (PBIAS) were used for model evaluation statistics (Gupta and others, 1999; table 3). The RMSE describes the difference between model simulations and observations in the units of the variable, and values close to zero indicate a perfect fit (Singh and others, 2005). The calibrated model had RMSE values ranging from 0.09 to 0.49 ft in water-surface elevation and 150 to 185 ft³/s for flow (tables 2 and 3). The USGS station 05549501 at the Stratton Dam tailwater had the three highest RMSE values ranging from 0.49 to 0.36 ft. The remaining USGS stations had low RMSE values of 0.31 ft or less. The PBIAS is a measure of the simulated data’s average tendency to be larger or smaller than observed values. Values of PBIAS can vary from −∞ to ∞ (where ∞ represents infinity) with an optimum value of 0. The calibrated model yielded PBIAS values of –5.41 to 4.27 percent for flow at USGS station 05549400, indicating a good model fit. The results demonstrate that the model can simulate accurate water levels throughout the Chain of Lakes and Stratton Dam headwater and tailwater areas.

After calibration, the model was used to simulate conditions for a validation event in January–February 2024 (January 28–February 22, specifically) to confirm model performance (fig. 6). The differences between observed and simulated peak water-surface elevations for this validation event at USGS streamgages ranged from −0.24 to −0.04 ft (table 2). The difference between observed and simulated peak flow at the Miller Bridge near McHenry (USGS station 05549400) was −219 ft³/s. The validation event yielded a PBIAS value of 2.15 percent for flow and an RMSE value of 242 ft³/s at USGS station 05549400 (table 3). The validation event had RMSE values of 0.09–0.49 ft of water-surface elevation (table 2). In the beginning of the event simulation, the Stratton Dam tailwater (USGS station 05549501) was 1.21 ft lower than observed measurements. The tailwater area improved during the simulation with a depth that was 0.21 ft lower than observed measurements at the end of the simulation. The estimated flow values resulting from effects of ice debris and missing time series data created a larger margin of error when comparing simulated and observed flows. This is a conservative validation in a sense that the model performance statistics are exaggerated high because of the added fluctuations at Stratton Dam tailwater and uncertainty in observed data as a result of the ice conditions.

A second validation event was simulated for the July 2017 historical flooding event which produced one of the top three record peaks at USGS stations 05548000, 05548500, and 05549501, all of which have a record of more than 80 years (table 1). This event predates the construction of the torque-tube crest gates but was an important flooding event to simulate because no substantial flooding has been detected since the torque-tube crest gates became operational. Because the five sluice gates were of similar size in gate height and cumulative widths (Illinois Department of Natural Resources, 2022), the percentage the sluice gates were opened in 2017 can be applied to the torque-tube crest gates openings and operation. The differences between observed and simulated peak water-surface elevations for this validation event at the USGS streamgage locations ranged from −0.36 to 0.05 ft (fig. 7; table 2). The historical flooding event had RMSE values of 0.19–0.49 ft of water-surface elevation; however, no flow hydrographs could be compared because this event predates USGS station 05549400.

Model Sensitivity, Uncertainties, and Limitations

The sensitivity of the hydraulic model was assessed using changes in n-values and normal depth. The n-values and normal depth were modified by +10 and −10 percent, and the March 2023 calibration event was used for the base simulation in the sensitivity analysis. The difference in peak water-surface elevations from the base simulation ranged from −0.34 to 0.29 ft (table 4; fig. 8). The percentage difference in peak flow from the base simulation varied from −4.2 to 4.6 percent. The USGS station 05549501 at the Stratton Dam tailwater was the most sensitive to change; the tailwater decreased by 0.34 and 0.16 ft for the lower n-value and higher normal depth, respectively, and increased by 0.29 and 0.18 ft from the higher n-value and lower normal depth, respectively. The USGS station 05549500 at the Stratton Dam headwater was sensitive to n-values with an increase and decrease of 0.12 ft for higher and lower n-values, respectively. The USGS stations 05548500 and 05548000, farthest upstream in the Chain of Lakes, were also sensitive to n-values with about a 0.20-ft increase with the higher n-value and a similar decrease with the lower n-value. The USGS station 05549400 had changes in peak flow with a 4.6-percent increase from the lower n-value and 4.2-percent decrease from the higher n-value. Normal depth had no significant effect at the USGS stations upstream from the Stratton Dam.

The Chain of Lakes can pose challenging conditions for model simulations. Because of the basin’s low-gradient slope, the upstream observed streamgages (USGS stations 05548000 and 05548500) on the Chain of Lakes are at times lower than the Stratton Dam headwater (USGS station 05549500; fig. 9). This phenomenon was often detected immediately after heavy precipitation and produced negative slope values near the Stratton Dam headwater. The most likely cause is local inflows that take place near McHenry, Ill., such as Boone Creek (fig. 2).

Several peaks from the calibration and validation events are underestimated (figs. 3–7; tables 2–3), which may be the result of additional drainage areas not covered by the three NWS–NCRFC hydrologic basins used in the model. The hydrologic basins from the NWS–NCRFC used for the model boundary conditions do not include any areas downstream from the natural outlet of Nippersink Lake near Johnsburg, Ill. This area is instead included in the AFBI2 hydrologic basin which covers the Fox River basin downstream to the Algonquin Dam (fig. 2). A ratio of this hydrologic basin could not be used for the accounted drainage area on the Chain of Lakes because the inflows and runoff are routed to the basin outlet at the Algonquin Dam and would likely produce attenuated flows from the smaller drainage areas such as Boone Creek. Secondly, the hydrologic basin JHNI2 does not account for rain that falls directly on the reservoir system and instead only simulates runoff and baseflow. Finally, the NWS hydrologic forecasts have their own uncertainties, and the operational hydrologists rely on experience and intuition to adjust hydrologic model inputs and parameters. These model adjustments are called “modifiers” by National Weather Service hydrologists. The most common modifiers are precipitation, antecedent soil moisture, and shape of the unit hydrograph for a basin (Zhu and others, 2021). These modifiers can affect peak flows, timing, and total volume of the hydrograph inputs to the Chain of Lakes model.

The Stratton Dam tailwater also is affected by the Algonquin Dam (fig. 2). The low-gradient water-surface slope of the 17-mi reach from the Stratton Dam tailwater to the Algonquin Dam headwater affects the normal-depth values computed for the model. On September 11, 2022, the recorded water levels were higher at the Algonquin Dam headwater than at the Stratton Dam tailwater (fig. 9) and produced negative slope values. The simulation for the September 2022 calibration event started on September 12 when the Stratton Dam tailwater began to have higher water levels than the Algonquin Dam headwater. At the end of the September 2022 calibration event, the observed headwater at the Algonquin Dam water-surface elevation was only 0.36 ft lower than the Stratton Dam tailwater, and similar water level elevations were observed from the Stratton Dam upstream to the Chain of Lakes. Because the model simulation uses a constant normal-depth slope value (fig. 4), the model could not replicate the observed values at USGS station 05549501 that resulted from variable normal-depth slopes during an event. The model could diverge from the observed tailwater conditions without accounting for variable normal-depth slopes as a downstream boundary condition during a simulation.

The Chain of Lakes can also produce negative flows from strong southwestern winds that push the water upstream (Schrader and Holmes, 2000). Streamgage data have unsteady fluctuations during windy days; the fluctuations have the potential to affect the hydraulic model performance when using the observed data for model output comparisons or model inputs.

Additions to the hydraulic model might help account for some of these limitations. A model extension to the Algonquin Dam would help simulate the interactions of water-surface elevations in the river reach between the Stratton and Algonquin Dams and allow the Stratton Dam tailwater to not be constrained to a single normal-depth slope. The model extension would include the hydrologic basin AFBI2 to account for additional runoff to the Algonquin Dam (fig. 2); furthermore, the NWS–NCRFC has the hydrologic basin JHNI2ROR to account for rain that has fallen on the reservoir system. The datasets for this basin are in a precipitation time series, and a rain-on-grid feature could be added to the two-dimensional mesh in the hydraulic model to account for this input. Wind forces on moving water is another function that could be implemented in the hydraulic model to account for the wind and streamflow interaction.

Workflow Development

A workflow was developed in Python to facilitate efficient model scenario testing for the Chain of Lakes HEC–RAS model. This model was developed to assess how gate operations at the Stratton Dam affect water levels within the Chain of Lakes and flow rates downstream from the dam. The workflow uses a combination of input data and customized functions to do the following:

The workflow also contains batch processing capabilities that allow multiple model scenarios to be run sequentially. Automating pre- and postprocessing tasks in this workflow can significantly expedite model scenario testing, which is critical to the practical management of Stratton Dam gate operations.

The primary inputs to the workflow are Standard Hydrologic Exchange Format (SHEF) files obtained from the NWS–NCRFC and Excel files supplied by the end user. The SHEF files contain observed and predicted flow rates from NWS–NCRFC hydrologic basins that flow into the Chain of Lakes (WMTW3, NIPI2, and JHNI2), and the Excel files contain hourly time series of gate openings for three torque-tube crest gates and one hinged-crest gate at the Stratton Dam. The workflow incorporates these new time series into the model files and uses their start and end dates to modify the model simulation period and to obtain initial water-surface elevations at five reference locations within the model domain (at USGS stations 05548000, 05548500, 05549500, and 05549501 and at the downstream extent of the model). As mentioned in the “Model Inputs and Initial Conditions” section, the initial conditions at USGS station 05549500 were used for the initial conditions at the Stratton Dam tailwater (USGS station 05549501) and downstream extent to a maximum value of 736 ft. Using these initial conditions allowed the model to stabilize and draw down during the model warmup period. The primary outputs of the workflow are hourly time series and graphical representations of hydrographs for the Stratton Dam tailwater and water-surface elevations at the five reference locations.

The key Python libraries used in this workflow include pyhecdss, dataretrieval, rascontrol, and h5py. Pyhecdss is used to edit and update Hydrologic Engineering Center–Digital Storage System (HEC–DSS) files with the new flow time series provided by the NWS–NCRFC (Sandhu and others, 2019). Dataretrieval is used to obtain initial water-surface elevations at the four USGS streamgage reference points (Hodson and others, 2023). Rascontrol is used to run HEC–RAS simulations through Python (Bannister, 2019), and h5py (version 2.7.1) is used to extract model results from the Hierarchical Data Format output files (Collette and others, 2018). These libraries were used to complete the core series of tasks involved in HEC–RAS modeling; however, common Python libraries like Pandas (The Pandas Development Team, 2024) and Numpy (Harris and others, 2020) were used to resolve workflow complexities, such as time zone conflicts and unit conversions. The workflow converts all time series to coordinated universal time for simulations but converts back to central daylight time before generating results. The workflow was designed so that end users only operate in central daylight time.

End users will interact with the workflow by first providing pathways to a variety of files, including the SHEF files, the model files (that is, u-, p-, prj-, and Hierarchical Data Format-files), and gate operation files. Next, the user will select a HEC–DSS file to use for scenario testing. The user will then run predefined lines of code to generate an Excel template for entering the gate operations data. Once the user has populated these Excel files, they will simply run the remaining code in the workflow, which will run the model and output the results. The workflow also has the capacity to supply unique date ranges for model simulation periods and to supply multiple gate operation files in advance for batch processing.

The product of this workflow is four Python scripts. The first script contains all the backend functions needed to perform the data formatting tasks described previously, and the second script contains the workflow that executes these functions. The two remaining Python scripts are identical to the first two scripts but are used for simulations involving the 3-, 5-, and 7-day scenarios provided by the NWS–NCRFC. These latter scripts prompt users to select a forecast scenario they wish to simulate from the HEC–DSS file, but they otherwise function the same as the first two scripts. These scripts were separated to avoid end-user confusion. The output Python files document the hydraulic model outputs tailored to IDNR–OWS Stratton Dam operations and interpretations of the simulated water-surface elevations and flows. The workflow streamlines implementation of hydraulic model inputs and provides an efficient way to simulate and assess a range of hydrologic forecasts and gate operations.

Summary

Hydrologic forecasts entering and leaving the Chain of Lakes are critical to the optimal operation of the Stratton Dam at McHenry, Illinois. The National Weather Service–North Central River Forecasting Center provides the Illinois Department of Natural Resources–Office of Water Resources (IDNR–OWR) with 0–7-day hydrologic forecasts of inflows entering the Chain of Lakes. The IDNR–OWR uses the hydrologic forecasts to develop gate operations to manage Chain of Lakes pool levels and to help mitigate flooding in the Chain of Lakes system. In 2020, the U.S. Geological Survey (USGS) and IDNR–OWR began a cooperative study to develop a system that enables engineers and planners to simulate and communicate predicted water-surface elevations and flows and to proactively prepare for runoff events forecasted for the Chain of Lakes. This hydraulic model and forecast workflow may be helpful to the IDNR–OWR for optimizing the operation of the Stratton Dam and includes the implementation of three newly installed torque-tube crest gates that became operational in 2020.

The Hydrologic Engineering Center–River Analysis System program (version 6.5) was used to simulate water-surface elevations and flows through the 18.5-mile Chain of Lakes system to 1.7 miles downstream from the Stratton Dam. Five USGS streamgages within the study area were used as reference points for model calibration and initial water-surface elevations for the beginning of the simulation. The hydraulic model was calibrated to runoff events in April–May 2022, September 2022, and March 2023 and incorporated the design specifications and observed gate operations of the Stratton Dam. The hydraulic model was validated by simulating a January–February 2024 event and a significant flooding event during July 2017. The July 2017 event predated the torque-tube crest gate installation but nevertheless tested the performance of the model for such a significant event. The model simulation results were a good fit to observed records at USGS streamgages with peak water-surface elevations within −0.36–0.15 foot of observed events. The hydraulic model was implemented into a forecast workflow that streamlines implementation of model inputs and documents the model outputs in a manner that is tailored to the IDNR–OWR Stratton Dam operations and interpretations of the simulated water-surface elevations and flows.