Simulation of Discharge, Water-Surface Elevations, and Water Temperatures for the St. Louis River Estuary, Minnesota-Wisconsin, 2016–17

Scientific Investigations Report 2020-5028
Prepared in cooperation with the U.S. Environmental Protection Agency
By: , and 



The St. Louis River estuary is a large freshwater estuary, next to Duluth, Minnesota, that encompasses the headwaters of Lake Superior. The St. Louis River estuary is one of the most complex and compromised near-shore systems in the upper Great Lakes with a long history of environmental contamination caused by logging, mining, paper mills, and other heavy industrial activities. Presently (2020), a widely available, science-based assessment tool capable of evaluating ecosystem-level responses to remediation and restoration projects has not existed for the estuary. To address this need, the U.S. Geological Survey (USGS) built a predictive, mechanistic, three-dimensional hydrodynamic model for the estuary using the Environmental Fluid Dynamics Code framework. In the current version, the model can simulate continuous discharge, water-surface elevations, water temperature, and flow velocity, although the modular framework allows for future additions of water-quality modeling.

The model was calibrated using data collected from April 2016 through November 2016 and validated with data collected from April 2017 through November 2017. The four types of data used to evaluate model performance were water-surface elevations, discharge, water temperature, and flow velocities. Streamflow and temperature boundary condition data included a mixture of USGS streamgage data, Minnesota Department of Natural Resources gage data, and estimates derived from the gage data.

The model was able to simulate the water-surface elevations with generally good agreement between the simulated and measured values for both years at the daily time step. Specifically, the model was able to demonstrate excellent
agreement with the measured data with Nash-Sutcliffe efficiency coefficients greater than 0.8 for all three locations; however, the model was unable to produce hourly water-surface elevations with such accuracy for 2016–17.

Discharge was more dynamic than the water-surface elevations, both for the measured and simulated data. Generally, most of the discharge ranged from −650 to 1,200 cubic meters per second, but the constantly changing flux exiting the estuary into Lake Superior (positive flows) and entering the estuary from Lake Superior (negative flows) occurred throughout the year. Even upstream at the St. Louis River at Oliver, Wisconsin, gage (USGS station 0402403250), the effect of flows into the estuary from Lake Superior did occur, demonstrating the strong effect of the Lake Superior seiche on flows for the estuary.

From a performance standpoint, the model was able to simulate discharge with generally good agreement in both years, although the 2017 validation was better than the 2016 calibration period. For the daily Nash-Sutcliffe efficiency coefficients, the simulated values were 0.98, 0.62, 0.49, and 0.71 for the Oliver gage; the Superior Bay entry channel at Superior, Wisc., (USGS station 464226092005600); the Superior Bay Duluth Ship Canal at Duluth, Minn., (USGS station 464646092052900); and total entries (combination of the Superior entry and Duluth entry), respectively. For the hourly evaluation criteria, the model performed poorly, with Nash-Sutcliffe efficiency coefficients less than 0 for the two entries into Lake Superior; therefore, as a predictor of discharge at the hourly scale, the model performed worse than using the measured data average. Similar to discharge, the model was a good predictor of flow velocity at the daily time scale but had difficulty matching the measured data at the hourly scale. For discharge and flow velocity, matching at subdaily time steps for a system as complicated as the St. Louis River estuary is considered difficult because the match is highly sensitive to coordinating the exact measurement location to the simulated value.

The final calibration target was water temperature, calibrated for the Oliver gage and the Duluth entry. For calibration purposes, the Duluth entry was the more important water temperature target because the Oliver gage was more of an internal check on the model. The Nash-Sutcliffe efficiency coefficients for the Duluth entry were high; hourly Nash-Sutcliffe efficiency coefficients at the Duluth entry were either at or greater than 0.7 for both years, and daily values were 0.84 and 0.82 for 2016 and 2017, respectively.

Suggested Citation

Smith, E.A., Kiesling, R.L., and Hayter, E.J., 2020, Simulation of discharge, water-surface elevations, and water temperatures for the St. Louis River estuary, Minnesota-Wisconsin, 2016–17: U.S. Geological Survey Scientific Investigations Report 2020–5028, 31 p.,

ISSN: 2328-0328 (online)

Study Area

Table of Contents

  • Acknowledgments
  • Abstract
  • Introduction
  • Methods
  • Model Calibration and Results
  • Model Limitations
  • Summary
  • References Cited
Publication type Report
Publication Subtype USGS Numbered Series
Title Simulation of discharge, water-surface elevations, and water temperatures for the St. Louis River estuary, Minnesota-Wisconsin, 2016–17
Series title Scientific Investigations Report
Series number 2020-5028
DOI 10.3133/sir20205028
Year Published 2020
Language English
Publisher U.S. Geological Survey
Publisher location Reston, VA
Contributing office(s) Upper Midwest Water Science Center
Description Report: viii, 31 p.; Data Release; Dataset
Country United States
State Minnesota, Wisconsin
Other Geospatial St. Louis River estuary
Online Only (Y/N) Y
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