Water quality and mathematics
Water quality is essential for human health, as only a small portion of the Earth's water is suitable for consumption, with many sources potentially contaminated by chemicals or biological agents. Various methods, such as extracting underground water, collecting precipitation, or desalinizing seawater, are employed to provide safe drinking water. However, contamination can frequently occur through agricultural runoff or aging infrastructure, even in developed regions. Regular monitoring and regulation of water quality are crucial, with agencies like the Environmental Protection Agency (EPA) setting standards for contaminants and providing annual reports to consumers about water safety.
Mathematics plays a vital role in water quality management, utilizing mathematical modeling to analyze the dynamics of contaminants and predict their spread. Techniques such as reactive transport models and statistical analyses support the evaluation of water quality over time and under varying conditions. Additionally, advancements in data collection, including remote monitoring and artificial intelligence, enhance the ability to assess and manage water quality effectively. Overall, the integration of mathematics into water quality research and policy is helping to address global challenges related to access to safe drinking water.
Water quality and mathematics
Summary: Water quality standards and data are mathematically modeled and analyzed to help keep drinking water safe.
Water is fundamental for human life. Approximately 70% of the Earth’s surface is covered by water but only a very small fraction is consumable fresh water, and much of that has chemical or biological contaminants. Drinking water comes from a variety of sources. Underground water, such as aquifers or springs, may be tapped by wells; surface water, such as rivers and streams, are diverted for use; precipitation may be collected or allowed to flow into other sources; and plants may be processed for moisture. Desalinization (the process of removing salt from water) makes seawater drinkable. Waterborne diseases in open water sources like rivers are endemic to many parts of the developing world. Natural disasters may spread contamination via flooding. Some global warming researchers predict that increased rainfall, flooding, and warmer weather will result in more waterborne disease worldwide. In developed countries, water is commonly piped to end users and may be recycled via sewage treatment. The standards for potable water in many countries are set by government agencies, though the regulation of bottled water differs from piped and well water. Even in nations with extensive closed water distribution systems and sewage treatment, contamination occurs in a number of ways, including agricultural runoff, dumping of manufacturing byproducts into streams and rivers, and degradation of systems that may contain outdated materials such as lead. One of the Millennium Development Goals adopted by the United Nations and other international organizations is to cut in half the proportion of people that do not have reliable access to safe drinking water by 2015. Mathematicians and mathematical methods contribute significantly to the discovery, testing, and delivery of potable water.
How Safe is Your Drinking Water?
The Environmental Protection Agency (EPA) sets the standards for drinking water in the United States. For each potentially harmful substance, the EPA identifies the maximum contaminant level (MCL) allowed and the maximum contaminant level goal (MCLG). The MCLG is the level below which there is zero expected risk to human health. While it would be best to have levels of a substance like arsenic at or below the MCLG, the EPA sets MLC requirements at concentrations that can be higher. U.S. citizens who receive water from a community water system should receive a Water Quality Report each year. Those curious about water quality at work may request a copy from the building owner. Each report includes the source of the water (such as a river or lake); a list of all detected regulated contaminants and their levels; potential health effects of contaminants detected that violate the standards; information for people with weakened immune systems; and contact information for the company or agency that supplies the water. The report will alert the public to violations of the EPA safe drinking water standards and, equally important, will list information about potentially harmful substances that are below the legal limit. For example, a report may list arsenic, describe that it is measured in parts per billion (ppb), give the highest level measured, and list the range measured in the water. The report will also provide the MCLG (0.0 ppb for Arsenic) and the MCL (10.0 ppb). If the report states that the water ranges from 0.5 to 2 ppb for arsenic, water consumers will know that it is safe to drink according to EPA standards. However, upon comparing the MCL and MCLG, consumers may consider drinking water from other sources or request additional information from the water company since 0.5 ppb is higher than the 0.0 ppb MCLG.
Mathematical Analysis and Modeling
The management of water resources is increasingly reliant on mathematical modeling and analysis. For example, the dynamics and kinetics of surface water, along with distributions and dispersal over time of contaminants, have been extensively modeled and simulated. Reactive transport (RT) models use coupled equations to examine particle transportation through porous surfaces, which are widely used to model infiltration of contaminants into ground water. They may utilize mathematical and statistical concepts such as stochastic differential equations, which can be traced in part to physicist Paul Langevin’s work on the mathematical theories of dynamic molecular systems. Animal behavioral responses to variables like water quality have been successfully modeled using the Eulerian–Lagrangian–Agent Method (ELAM). The Eulerian framework, named for mathematician Leonhard Euler, mathematically models environment factors affecting the animal agents, while the Lagrangian framework, named for mathematician Joseph Lagrange, governs the perception and movement of individual agents.
Near-continuous water quality monitoring provides a wealth of data and facilitates time series analyses and other statistical models of water quality as functions of variables like land use and precipitation patterns, as well as other measurable human behaviors and natural occurrences. Model calibration, verification, and sensitivity analysis often require comparing mathematical equations and simulation results with observed data. Mathematicians, engineers, and scientists have improved systems for remote water quality monitoring and assessment using data, mathematical methods, and theories from many sciences. Some applications include remote automated stations with the ability to wirelessly network and transmit data, artificial intelligence algorithms that can adaptively sample in response to problems or concerns, and satellite or aircraft observation and analysis of large areas.
These analyses also influence public policy and legislation, such as the U.S. Safe Drinking Water Act and the Clean Water Act. Scientists in many fields continue to seek methods to provide easily accessible clean water for everyone.
Bibliography
Chapra, Steven. Surface Water-Quality Modeling. Long Grove, IL: Waveland Press, 2008
U.S. Environmental Protection Agency (EPA). Drinking Water and Health: What You Need to Know! Washington, DC: EPA, 1999. http://www.epa.gov/safewater/dwh/dw-health.pdf.