# Uncertainty analysis of index-velocity meters and discharge computations at the Chicago Sanitary and Ship Canal near Lemont, Illinois, water years 2006–16

March 28, 2022

Monitoring discharge in the Chicago Sanitary and Ship Canal is critical for the accounting done by the U.S. Army Corps of Engineers of the diversion of water from Lake Michigan to the Mississippi River Basin by the State of Illinois. The primary streamgage used for this discharge monitoring, the Chicago Sanitary and Ship Canal near Lemont, Illinois (U.S. Geological Survey station 05536890), is operated by the U.S. Geological Survey as an index-velocity station and at the time of this study (water years 2006–16) had two continuous velocity meters (an acoustic Doppler velocity meter and an acoustic velocity meter) and a water-level sensor, among other instruments. Discharge is computed at the streamgage using an index-velocity rating developed by linear regression of the velocity meter values fitted to discharges intermittently measured with an acoustic Doppler current profiler. In this study, the uncertainties of the velocity meters and stage sensors were estimated using a type B (judgment-based) approach, and measured discharge uncertainties were taken from those provided by a common acoustic Doppler current profiler data processing software tool, QRev. The velocity meter uncertainties, expressed as standard deviations, were estimated to be about 2.5 percent of velocity except near zero, where they exceeded that fraction, whereas for the acoustic Doppler current profiler uncertainties, when converted to mean channel velocity, 2.5 percent of velocity was determined to be a lower bound. The estimated velocity meter and measured discharge uncertainties were compared to index-velocity ratings developed from regression analyses of two types: (1) those that allow specification of measurement uncertainties and (2) ordinary least squares (OLS) regression, which does not. Based on the linearity of the index-velocity rating and the approximate agreement of the distributions of the fitting and prediction velocities, the assumptions required for unbiased prediction by OLS regression were determined to be approximately satisfied. From the regression residuals, it was determined that the estimated measurement uncertainties are too small, too similar between acoustic velocity meter and acoustic Doppler velocity meter velocities, and possibly too strongly dependent on velocity. Large, non-Gaussian OLS regression residuals also were observed. The uncertainty of annual mean discharge computed using the different regressions also was considered and was determined to be strongly dependent on the assumed measurement uncertainty. Because the assumptions required for OLS regression to give unbiased and variance-maintaining predictions were determined to be approximately satisfied, the results of discharge computation using the index-velocity rating based on OLS regression were deemed to be reliable. These results indicate about 0.8-percent uncertainty in the computed discharge as measured by the coefficient of variation at the annual time scale when using the acoustic Doppler velocity meter and 1.2-percent uncertainty with the acoustic velocity meter. It may be possible to improve the accuracy of the computed discharge and its uncertainty by further examining the measurement uncertainties and addressing differences in the distributions of the velocities used in fitting the index-velocity ratings and those used in prediction. Although the index-velocity ratings and computed discharges presented in this study are similar to those used in computing the published discharge at the study streamgage, the values presented in this report are not intended to replace the published discharge.

## Citation Information

Publication Year 2022 Uncertainty analysis of index-velocity meters and discharge computations at the Chicago Sanitary and Ship Canal near Lemont, Illinois, water years 2006–16 10.3133/ofr20221007 Thomas M. Over, Marian Muste, James J. Duncker, Heng-Wei Tsai, P. Ryan Jackson, Kevin K. Johnson, Frank L. Engel, Crystal D. Prater Report USGS Numbered Series Open-File Report 2022-1007 ofr20221007 USGS Publications Warehouse Illinois Water Science Center