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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 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...

Significant Figures in Calculations

Significant Figures in Calculations

Uncertainty in measurements can be avoided by reporting the results of a calculation with the correct number of significant figures. This can be determined by the following rules for rounding numbers:

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...

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 particular...

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...

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Related Experiment Video

Updated: May 23, 2026

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

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

Published on: September 7, 2019

Quantification of emission factor uncertainty.

George Pouliot¹, Emily Wisner, David Mobley

¹Atmospheric Modeling and Analysis Division, National Exposure Research Laboratory Environmental Protection Agency, Research Triangle Park, NC, USA. pouliot.george@epa.gov

Journal of the Air & Waste Management Association (1995)

|April 10, 2012

Summary

This summary is machine-generated.

This study quantifies uncertainty for emission factors used in air pollution estimation. Results show current factors for Electric Generating Unit NOx need updates, with uncertainty ranges varying by data quality rating.

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

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Area of Science:

Environmental Science
Atmospheric Chemistry
Air Pollution Analysis

Background:

Emission factors are crucial for air pollution assessment but lack quantitative uncertainty measures.
Existing emission factor datasets are often insufficient for uncertainty computation.
Locating data for uncertainty analysis of emission factors is challenging.

Purpose of the Study:

To compare Electric Generating Unit (EGU) NOx emission factors with continuous emission monitoring data.
To develop quantitative uncertainty indicators for U.S. Environmental Protection Agency (EPA) data quality rated emission factors.
To determine uncertainty ranges associated with EPA's emission factor data quality ratings.

Main Methods:

Compared current EGU NOx emission factors with continuous emission monitoring data.
Developed quantitative uncertainty indicators based on EPA's qualitative data quality ratings (A-E).
Assumed similar quantifiable uncertainty for emission factors with the same data quality rating and robustness.

Main Results:

EPA's current emission factor values for NOx from combustion sources are reasonably representative for some, but over half require updates based on current data (AP-42).
Quantified uncertainty ranges: A (25-62%), B (45-75%), C (60-82%), D (69-86%), E (82-92%).
Significant variability in uncertainty exists across different data quality ratings.

Conclusions:

Quantitative uncertainty indicators for emission factors are feasible and necessary for accurate air pollution estimation.
Updating emission factors, particularly AP-42 values, is essential to reflect current data for NOx sources.
The developed uncertainty ranges provide a crucial tool for risk assessment and regulatory compliance in air quality management.