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Uncertainty: Overview

Uncertainty: Overview

In analytical chemistry, we often perform repetitive measurements to detect and minimize inaccuracies caused by both determinate and indeterminate errors. Despite the cares we take, the presence of random errors means that repeated measurements almost never have exactly the same magnitude. The collective difference between these measurements - observed values - and the estimated or expected value is called uncertainty. Uncertainty is conventionally written after the estimated or expected value.

Propagation of Uncertainty from Systematic Error

Propagation of Uncertainty from Systematic Error

The atomic mass of an element varies due to the relative ratio of its isotopes. A sample's relative proportion of oxygen isotopes influences its average atomic mass. For instance, if we were to measure the atomic mass of oxygen from a sample, the mass would be a weighted average of the isotopic masses of oxygen in that sample. Since a single sample is not likely to perfectly reflect the true atomic mass of oxygen for all the molecules of oxygen on Earth, the mass we obtain from this...

Propagation of Uncertainty from Random Error

Propagation of Uncertainty from Random Error

An experiment often consists of more than a single step. In this case, measurements at each step give rise to uncertainty. Because the measurements occur in successive steps, the uncertainty in one step necessarily contributes to that in the subsequent step. As we perform statistical analysis on these types of experiments, we must learn to account for the propagation of uncertainty from one step to the next. The propagation of uncertainty depends on the type of arithmetic operation performed on...

Estimation of the Physical Quantities

Estimation of the Physical Quantities

On many occasions, physicists, other scientists, and engineers need to make estimates of a particular quantity. These are sometimes referred to as guesstimates, order-of-magnitude approximations, back-of-the-envelope calculations, or Fermi calculations. The physicist Enrico Fermi was famous for his ability to estimate various kinds of data with surprising precision. Estimating does not mean guessing a number or a formula at random. Instead, estimation means using prior experience and sound...

Uncertainty in Measurement: Accuracy and Precision

Uncertainty in Measurement: Accuracy and Precision

Scientists typically make repeated measurements of a quantity to ensure the quality of their findings and to evaluate both the precision and the accuracy of their results. Measurements are said to be precise if they yield very similar results when repeated in the same manner. A measurement is considered accurate if it yields a result that is very close to the true or the accepted value. Precise values agree with each other; accurate values agree with a true value.

Uncertainty in Measurement: Reading Instruments

Uncertainty in Measurement: Reading Instruments

Counting is the type of measurement that is free from uncertainty, provided the number of objects being counted does not change during the process. Such measurements result in exact numbers. By counting the eggs in a carton, for instance, one can determine exactly how many eggs are there in the carton. Similarly, the numbers of defined quantities are also exact. For example, 1 foot is exactly 12 inches, 1 inch is exactly 2.54 centimeters, and 1 gram is exactly 0.001 kilograms. Quantities...

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Related Experiment Video

Updated: Jun 12, 2025

Design and Use of a Full Flow Sampling System FFS for the Quantification of Methane Emissions

Design and Use of a Full Flow Sampling System FFS for the Quantification of Methane Emissions

Published on: June 12, 2016

Estimation and Applications of Uncertainty in Methane Emissions Quantification Technologies: A Bayesian Approach.

Augustine Wigle¹, Audrey Béliveau¹, Daniel Blackmore²

¹Department of Statistics and Actuarial Science, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada.

ACS ES&T Air

|September 19, 2024

Summary

Understanding measurement uncertainty is crucial for accurate methane emission estimates from oil and gas operations. New methods using controlled release data improve uncertainty quantification for various measurement technologies.

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Last Updated: Jun 12, 2025

Design and Use of a Full Flow Sampling System FFS for the Quantification of Methane Emissions

Design and Use of a Full Flow Sampling System FFS for the Quantification of Methane Emissions

Published on: June 12, 2016

Split Point Analysis and Uncertainty Quantification of Thermal-Optical Organic/Elemental Carbon Measurements

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Published on: September 7, 2019

The Use of an Automated System GreenFeed to Monitor Enteric Methane and Carbon Dioxide Emissions from Ruminant Animals

The Use of an Automated System GreenFeed to Monitor Enteric Methane and Carbon Dioxide Emissions from Ruminant Animals

Published on: September 7, 2015

Area of Science:

Environmental Science
Atmospheric Chemistry
Oil and Gas Industry

Background:

Accurate methane emission estimates are vital for upstream oil and gas operations.
Interpreting these estimates requires a robust understanding of measurement uncertainty.
Existing methods may not fully capture the complexities of measurement error.

Purpose of the Study:

To characterize measurement uncertainty for methane emission estimation technologies.
To develop novel methods for quantifying uncertainty using controlled release data.
To provide a framework for synthesizing measurements with external information.

Main Methods:

Examined controlled release (CR) data from five technology providers (e.g., quantitative gas imaging, TDLAS, NIR HS imaging).
Developed an empirical method to create probability distributions of measurements given true emission rates.
Created an algorithm to determine the distribution of true emission rates based on measurements and CR data.

Main Results:

Flexible models accommodating nonlinear behavior are necessary for accurate error modeling.
Measurement error can vary significantly under different conditions.
Repeated measurements can effectively reduce measurement uncertainty.

Conclusions:

The developed methodology provides improved uncertainty quantification for methane emission estimates.
The models highlight the need for flexible approaches to account for complex measurement errors.
Future work can extend the methodology to diverse industrial settings and conditions.