Marian Muste
IIHR Hydroscience and Engineering, University of Iowa
marian-muste@uiowa.edu
HydroLearn
Uncertainty Analysis for Hydrometric Measurements
Quantifying, combining, and reporting the uncertainty of streamflow measurements with the GUM framework.
Problem Statement
Every streamflow measurement is reported as a single discharge Q, yet the value always carries an uncertainty U(Q) from the instrument, the cross-section, the sampling, and the measurement equation. Reporting Q without U(Q) hides a noise floor that every downstream product inherits: rating curves, model calibration, and Flood Inundation Maps.
Module Overview
This module gives practicing hydrologists a compact, hands-on workflow for putting a defensible uncertainty on a streamflow measurement using the international GUM framework: terminology, the six-step workflow, two Python notebooks (a Pitot warm-up and a full mid-section current-meter discharge with a Monte Carlo cross-check), and a capstone task where you write a defensible measurement record.
The hands-on activities run on the published HydroShare resource (Open with: CUAHSI JupyterHub) or on Google Colab.
Topics Covered
Error vs. uncertainty; Type A and Type B evaluation and their divisors; the GUM six-step workflow; sensitivity coefficients; the law of propagation of uncertainty; coverage factor and expanded uncertainty; Monte Carlo validation (JCGM 101); uncertainty budgets; reporting conventions (ISO 748, WMO); propagation into model calibration and Flood Inundation Mapping.
Prerequisites
- Exposure to at least one streamflow measurement method (current meter, ADCP, or stage-discharge rating).
- Basic statistics: mean, standard deviation, normal distribution.
- Enough Python to run a Jupyter notebook end-to-end (numpy, pandas, matplotlib).
Learning Objectives
At the end of this module, learners will be able to:
- Distinguish error from uncertainty and classify contributions as Type A or Type B with the right divisor.
- Write a Data Reduction Equation and compute sensitivity coefficients.
- Combine elemental uncertainties into u_c(Q) and expand with a stated coverage factor.
- Build an uncertainty budget, identify the dominant contributors, and validate the result with Monte Carlo.
- Write a defensible ten-element measurement record and explain how U(Q) propagates into calibration and flood mapping.
Suggested Implementation
Four sections, self paced, about 2 hours total.
| Section | Estimated time |
|---|---|
| Section 1, Introduction | 5 min |
| Section 2, Foundations of measurement uncertainty | 30 min |
| Section 3, Hands-on labs (includes Learning Activities 1 and 2) | 70 min |
| Section 4, Authentic task | 15 min |
Course Authors
Mohamed Abdelkader
IIHR Hydroscience and Engineering, University of Iowa
mohamed-abdelkader@uiowa.edu
Humberto Vergara
IIHR Hydroscience and Engineering, University of Iowa
Target Audience
Practicing hydrologists, agency field staff, and CIROH developers who collect or use streamflow data and need to put a defensible uncertainty on it.
Tools Needed
A computer with internet access and a modern browser. For the hands-on activities, the published HydroShare resource (Open with: CUAHSI JupyterHub) or Google Colab; the notebooks need only numpy, pandas, and matplotlib.
Expected Effort
About 2 hours total. Self paced.
Course Sharing and Adaptation
This course is available for export by clicking the "Export Link" at the top right of this page. You will need a HydroLearn instructor studio account to do this. You will first need to sign up for a hydrolearn.org account, then register as an instructor by clicking 'studio.hydrolearn' and requesting course creation permissions.
Recommended Citation
Muste, M., Abdelkader, M., & Vergara, H. (2026). Uncertainty Analysis for Hydrometric Measurements. University of Iowa.
Companion notebooks: Abdelkader, M. (2026). Theory and Applications of Uncertainty Analysis for Extreme Event Hydrometry, CIROH DevCon 2026 Workshop, HydroShare, https://www.hydroshare.org/resource/78f5144c38de461eb4d951ec2ed2a23f/.
Acknowledgments
This research was supported partially by the Cooperative Institute for Research to Operations in Hydrology (CIROH) with joint funding under award NA22NWS4320003 from the NOAA Cooperative Institute Program and the University of Iowa Public-Private Partnership (P3) program.