A Computer-Aided Approach for Adapting Stage-Discharge Ratings and Characterizing Uncertainties of Streamflow Data with Discrete Measurements

Scientific Investigations Report 2022-5083



Relations between stage (water level) and discharge of streamflow through a natural channel are the result of time-varying processes, which are commonly described by time-varying stage-discharge ratings. Hydrographers with the U.S. Geological Survey successfully maintain the accuracy of streamflow data by manually applying time-tested approaches to adapt ratings to temporal changes in hydraulic conditions. The difficulty with the manual approach is that it is a subjective, time-consuming process that requires considerable skill and experience to implement. In addition, manual adjustments of ratings make quantification of resulting streamflow data uncertainties problematic. A computer-aided adaptive stage-discharge estimation approach is proposed to track sequential changes in the relation between stage and discharge at continuous-record streamgages. In this report, adaptations are based strictly on discrete measurement data that are then used to compute the magnitudes and uncertainties of streamflow. The approach entails the parameterization of a cubic regression spline (CRS) for the stage-discharge relation based on an existing rating or on a set of discrete measurements. A state-space model is then parameterized to track temporal changes in stage-discharge relations beginning with the initial CRS parameterization using discrete measurements. Finally, Kalman estimation is used with the state-space model to estimate the magnitude and uncertainty of flows. In a case study using data from streamgage U.S. Geological Survey 04122500 Marquette River at Scottville, Michigan, a five-parameter CRS model was estimated from data in an existing stage-discharge rating to provide an initial CRS parameter set for a state-space model. The initial CRS parameters were updated sequentially in a state-space model based on periodic discrete measurements of stage and discharge that spanned a 30-year period for this analysis. Additional analysis is needed to determine the timing of rapidly varying shifts more precisely in stage-discharge relations than the relatively infrequent discrete measurements currently enabled. Unit streamflow estimates based on flow in a local streamgaging network may provide a basis for adapting a stage-discharge rating at unit time intervals by augmenting discrete measurement data within the state-space model.

Suggested Citation

Holtschlag, D.J., 2022, A computer-aided approach for adapting stage-discharge ratings and characterizing uncertainties of streamflow data with discrete measurements: U.S. Geological Survey Scientific Investigations Report 2022–5083, 36 p., https://doi.org/10.3133/sir20225083.

ISSN: 2328-0328 (online)

Study Area

Table of Contents

  • Acknowledgments
  • Abstract
  • Introduction
  • Discrete and Continuous Measurements at Streamgages
  • Methods for Computer-Aided Adaptation of Stage-Discharge Ratings
  • Methods for Computing Magnitudes and Uncertainties of Unit Discharges
  • Results and Discussion
  • Limitations
  • Summary and Conclusions
  • References Cited
Publication type Report
Publication Subtype USGS Numbered Series
Title A computer-aided approach for adapting stage-discharge ratings and characterizing uncertainties of streamflow data with discrete measurements
Series title Scientific Investigations Report
Series number 2022-5083
DOI 10.3133/sir20225083
Year Published 2022
Language English
Publisher U.S. Geological Survey
Publisher location Reston, VA
Contributing office(s) Upper Midwest Water Science Center
Description viii, 36 p.
Country United States
State Michigan
Other Geospatial Pere Marquette River
Online Only (Y/N) Y
Google Analytic Metrics Metrics page
Additional publication details