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Computing Discharge Using the Entropy-Based Probability Concept

Techniques and Methods 3-A26
By: , , , and 
https://doi.org/10.3133/tm3A26

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Abstract

This report describes the techniques and methods for computing the mean-channel velocity and discharge using the entropy-based probability concept (probability concept). The method is an alternative to or augments standard streamgaging methods adopted by the U.S. Geological Survey (USGS). Although sensor technology for measuring the mean velocity and discharge has advanced, standard streamgaging and computational methods have remained relatively unchanged since the USGS established its first streamgage at the Rio Grande at Embudo, New Mexico in 1889.

Standard streamgaging methods rely on integrating velocities and depths measured at multiple verticals at a channel cross section (standard cross section) to compute a discharge. The probability concept computes discharge at a single vertical (y-axis) using the ratio of the mean-channel velocity (mean velocity) and maximum velocity, the measured maximum velocity, and the area as a function of stage at the standard cross section. Proper siting and operation and maintenance are required. If siting is conducted appropriately, the probability concept parameters and the y-axis stationing will be similar for different streamflow conditions. The timing of operation and maintenance visits should be based on hydrologic and meteorologic occurrences and seasonality and should capture low, medium, high, and opportunistic streamflow conditions.

Advantages of the probability concept are the capacity to (1) compute discharge time series immediately after streamgage siting, (2) compute discharge for complex streamflow conditions that cannot be quantified by stage-discharge methods, (3) augment time-series data where gaps exist, and (4) integrate with surface velocity sensors such as Doppler velocity radars and cameras, which are not subject to damage caused by ice, debris, and flood flows. Potential sources of bias in discharge derived from the probability concept include (1) rain, (2) wind, and (3) geomorphologic and hydraulic instabilities. Recommendations to address these biases are provided.

This report guides users through the steps to parameterize the probability concept, process field data, and compute the mean velocity and discharge using the probability concept.

Plain Language Summary

This report describes the steps and the theory to compute the speed and flow of water in streams using the probability concept.

Suggested Citation

Fulton, J.W., Engel, F.L., Eggleston, J.R., and Chiu, C.-L., 2025, Computing discharge using the entropy-based probability concept: U.S. Geological Survey Techniques and Methods book 3, chap. A26, 66 p., https://doi.org/10.3133/tm3A26.

ISSN: 2328-7055 (online)

Table of Contents

  • Acknowledgments
  • Abstract
  • Plain Language Summary
  • Introduction
  • Methods
  • Derivation of the Probability Concept
  • Order of Operations When Deploying the Probability Concept
  • Factors to Consider When Using the Probability Concept
  • Summary
  • References Cited
  • Glossary
  • Appendix 1. Velocity Distribution Equations Based on Probability Law
  • Appendix 2. Standard Forms to Assist with Siting
  • Appendix 3. Correction for Wind Bias
  • Appendix 4. Computing Where a Turbulent Boundary Layer Develops
Publication type Report
Publication Subtype USGS Numbered Series
Title Computing discharge using the entropy-based probability concept
Series title Techniques and Methods
Series number 3-A26
DOI 10.3133/tm3A26
Publication Date September 29, 2025
Year Published 2025
Language English
Publisher U.S. Geological Survey
Publisher location Reston VA
Contributing office(s) Colorado Water Science Center, Texas Water Science Center, WMA - Observing Systems Division
Description Report: viii, 66 p.; Appendix
Online Only (Y/N) Y
Additional publication details