Environmental statistics

Brown-coloured water flows from a discharge pipe into a river or stream.
A discharge pipe as a potential source of pollution that can be investigated using environmental statistics.

Environmental statistics is a branch of statistics that uses statistical methods to study environmental issues, including those concerning natural ecosystems, interactions between humans and the environment, and environmental conditions in places where people live.

An area of grassland is marked off for sampling.
Determining the size and location of grassland to be surveyed when collecting samples for an ecological study.

Its applications are numerous and varied, ranging from identifying sources of environmental pollution to planning where and how to collect samples for ecosystems studies. Environmental statistics supports many users, including organizations responsible for public health and safety, environmental protection, and water resources, as well as research institutions involved in environmental studies.

When studying complex environmental issues, it can be difficult to collect data that is reliable and consistent, and then be able to confidently interpret the results. For this reason, environmental statistics plays an essential role in understanding and overcoming these challenges.

Terminology

 "Environmental statistics" can refer to both a branch of statistics, which is the subject of this article, and to environmental data that describes the biophysical environment and the socioeconomic factors influencing it. Examples of the latter definition include monthly average temperatures, the area of forest affected by fire, waste generation per unit of GDP, and the proportion of the population using safely managed drinking water services. Although the two terms have different meanings, they both provide useful information for decision-making and supporting sustainable development.

Researcher is recording air quality measurement in a notebook.
Air quality measurements are being recorded, which can then be analyzed using statistical methods.

"Environmental statistics" has also been used interchangeably with the term, "environmetrics," however the latter places greater emphasis on developing and improving statistical models. Both fields of study use statistical principles and methods to address environmental issues, and interest in them has grown in the past few decades in response to increasing concerns over environmental issues. Currently, McGill University in Montreal, Canada offers an Environmetrics Concentration within its Environment major, and North Carolina State University in the United States offers courses in environmental statistics. These programs help prepare the next generation of statisticians and environmental professionals to address emerging environmental challenges.

Evolution

Chimney stacks releasing clouds of smoke into the atmosphere.
Steel plant chimneys releasing pollutants into the atmosphere in the 1970s.

Environmental statistics emerged as an important field of study in the 1970s, following the establishment of the United States Environmental Protection Agency (EPA) in 1970, the passage of the United States Clean Water Act (1972), and the signing of the Great Lakes Water Quality Agreement (1972). Growing concerns over acid rain and pollution during this period further increased the demand for statistical methods to support the development of environmental quality standards, improve air and water quality monitoring, and analyze environmental data.

A road is under water due to intense rainfall.
Flooding following an extreme rainfall event.

Between 2010 and 2020, advances in climate modelling and statistical analysis helped scientists to better understand how human activities affect climate change and more accurately assess changes in the frequency and intensity of extreme weather events.

Environmental statistics is becoming increasingly computational, with advances in computer technology and software, allowing for more sophisticated analyses of climate related hazards, such as extreme precipitation, heat domes, and wildfires.

Environmental studies and statistical methods

Environmental statistics involves two main approaches: descriptive and inferential statistics.

Bar graph illustrating the effect of declining salmon size on egg production, nutrient transport, commercial fishing value, and food insecurity (number of meals provided).
Using descriptive statistics and quantitative estimates, the environmental and economic consequences of declining salmon size can be predicted.

Descriptive statistics use numerical measures such as averages and percentages to describe data, while inferential statistics uses sample data to test hypotheses or make predictions about the environmental conditions.

These approaches can be used in different types of studies, including baseline studies, targeted studies, and regular environmental monitoring. Baseline studies establish existing environmental conditions so that future changes can be measured. Targeted studies assess the potential environmental impacts of a planned change or accident. Environmental monitoring helps detect changes in the environment over time.

A wide range of statistical methods is used in environmental science, reflecting the many different ways they can be applied. While many of these techniques are used in other fields, they often need to be modified to account for the challenges of interpreting environmental data, particularly the difficulty of controlling environmental variables.

Key examples of statistical methods and their applications include:

In some cases, a combination of methods may be required. For example, when examining how ozone concentration varies across locations and changes over time, regression analysis can be combined with spatial and time-series modelling.

Environmental statistics in practice

Environmental statistics are widely used by government agencies, such as the United States Environmental Protection Agency, to inform decisions about environment protection and policy development. Although the following two case studies are historical examples, they illustrate how environmental statistics can influence change at the national level by informing the development of environmental standards and supporting the implementation of regulations.

Line graph showing the effects of increased levels of lead in the blood on IQ scores. The shape is hyperbolic.
An example of log-linear regression modelling: one of the statistical methods used to examine the relationship between levels of lead in the blood and IQ scores in children.

National Ambient Air Quality Standard (NAAQS) for Lead: In 2008, the United States Environmental Protection Agency (EPA) lowered the national air quality standard for lead by 90%, from 1.5 to 0.15 μg/m³. Statistical results showing a relationship between lead exposure and harmful health effects in young children. Several statistical methods helped inform this decision. Regression analysis was used to examine the relationship between lead exposure and children's IQ scores. Log-linear regression helped estimate health effects at lower levels of exposure. Concentration-response modelling was used to estimate how risks change with different levels of lead exposure. This case study demonstrates how environmental statistics can inform government policies and support science-based decision making.

A groundwater monitoring well is being installed to collect groundwater sample for contamination assessment.

United States Environmental Protection Agency (EPA) Unified Guidance: In 2009, the U.S. EPA published the reported titled Statistical Analysis of Groundwater Monitoring Data at RCRA Facilities, Unified Guidance. This report provided guidance to regulators and waste-management facilities on how to evaluate groundwater quality and meet the requirements of the Resource Conservation and Recovery Act (RCRA). 

The guidance included statistical methods for distinguishing natural variations in groundwater quality from significant changes in contamination concentrations. These methods helped determine whether changes in groundwater quality could be due to contamination from waste-management facilities. The statistical methods discussed included Student's t-tests, analysis of variance (ANOVA), confidence intervals, and regression analysis. The report also addressed the risk of false positive and false negative results. This case study demonstrates how environmental statistics can help regulators and waste-management facilities implement environmental policies and meet regulatory requirements.

Future challenges and opportunities

Over the past 50 years, environmental statistics has evolved from a field focused on environmental monitoring to one that uses statistical models and computational methods to examine environmental problems. Looking ahead, emerging environmental challenges will continue to create new opportunities for statistical research and innovation.   

NASA provides an image of earth illustrating the projected increase in temperature by 2099.
Climate models are used to predict global warming trends but different models may result in different predictions.

One challenge is quantifying the uncertainty associated with future climate change projections. Different climate models may produce different predictions, making it necessary to develop statistical methods that can better measure and interpret this uncertainty.

A second challenge is assessing the effects of climate change mitigation efforts at smaller geographic scales. For example, the effects of reducing greenhouse gas emissions may be difficult to distinguish from natural climate variability. Statistical methods are therefore needed to determine whether the observed changes are statistically significant.

A third challenge is accounting for the multiple factors that influence environmental events. For example, the likelihood and severity of flooding following extreme rainfall can depend on several factors, including soil moisture and drainage conditions. Statistical methods must account for these factors to better understand and predict environmental risk.  

Through collaboration with practitioners, researchers, government agencies, and the public, new discoveries in environmental statistics emerge. Supporting the next generation of environmental statisticians will also be essential for advancing research, informing policies, and contributing to a more sustainable future.

Sources

Sources of data for environmental statistics are varied and include surveys related to human populations and the environment, records from agencies managing environmental resources, maps and images, equipment used to examine the environment, and research studies around the world. A primary component of the data is direct observation, although most environmental statistics use a variety of sources.

See also

References

  1. 1 2 3 4 5 6 Barnett, Vic (2004). Environmental statistics: methods and applications. Wiley series in probability and statistics. Chichester, West Sussex, England: J. Wiley. ISBN 978-0-471-48971-9.
  2. 1 2 3 4 United Nations Statistical Division. "Environment Statistics". unstats.un.org. Retrieved 2026-10-29.
  3. 1 2 3 Rong, Yue (2011-09-01). "Environmental Statistics". Environmental Forensics. 12 (3). Taylor & Francis: 189–190. Bibcode:2011EnvFo..12..189R. doi:10.1080/15275922.2011.599263. ISSN 1527-5922.
  4. ↑ El-Shaarawi, A. H. (2012). Piegorsch, W. W. (ed.). Encyclopedia of Environmetrics. Chichester: Wiley. ISBN 978-0-470-05733-9.
  5. 1 2 3 4 5 6 Dean, Charmaine B.; El-Shaarawi, Abdel H.; Esterby, Sylvia R.; Mills Flemming, Joanna; Routledge, Richard D.; Taylor, Stephen W.; Woolford, Douglas G.; Zidek, James V.; Zwiers, Francis W. (2022). "Canadian contributions to environmetrics". Canadian Journal of Statistics. 50 (4): 1355–1386. doi:10.1002/cjs.11743. ISSN 1708-945X.
  6. ↑ Manly, Bryan F. J. (2001). Statistics for environmental science and management. Boca Raton, FL: Chapman & Hall/CRC. ISBN 978-1-58488-029-5.
  7. ↑ Chari, Ramya; Burke, Thomas A.; White, Ronald H.; Fox, Mary A. (2012-03-27). "Integrating Susceptibility into Environmental Policy: An Analysis of the National Ambient Air Quality Standard for Lead". International Journal of Environmental Research and Public Health. 9 (4): 1077–1096. Bibcode:2012IJERP...9.1077C. doi:10.3390/ijerph9041077. ISSN 1660-4601. PMC 3366601. PMID 22690184.
  8. ↑ United States Environmental Protection Agency (2009). "Statistical analysis of groundwater monitoring data at RCRA facilities, Unified Guidance". www.regulations.gov. Retrieved 2026-10-29.
  9. ↑ Manly B.F.J. (2001) Statistics for Environmental Science and Management, Chapman & Hall/CRC. ISBN 1-58488-029-5