Projecting Ocean Acidification using Ordinary Differential Equations

Abstract

As Earth’s atmospheric carbon dioxide (CO₂) levels continue to rise due to industrialization, fossil fuel combustion, and deforestation, the consequences extend far beyond polluted air. A significant portion of this excess CO₂ is absorbed by the world’s oceans, triggering a series of chemical reactions that increase the acidity of seawater. This growing acidity disrupts marine ecosystems, threatening organisms such as coral reefs, shellfish, and plankton that rely on stable carbonate chemistry to survive. This project presents a dynamic mathematical model that uses a a coupled system of ordinary differential equations (ODEs) to track the concentrations of key chemical species involved in ocean acidification, including aqueous CO₂, carbonic acid (H₂CO₃), bicarbonate (HCO₃⁻), carbonate (CO₃²⁻), and hydrogen ions (H⁺). The model captures the reversible reactions that govern the carbonate system in seawater and incorporates temperature-dependent rate constants informed by collision theory and empirical Arrhenius relationships. The model further accounts for how increasing ocean temperatures may also accelerate the rate of acidification, and the ocean’s natural buffering capacity that has been thought to maintain pH stability. By simulating varying levels of atmospheric CO₂ and ocean temperatures, the model explores the limits of this buffering mechanism under future climate scenarios. Our results demonstrate that as atmospheric CO₂ concentrations rise, the buffering capacity of seawater decreases, resulting in a rapid and sustained drop in ocean pH. This decline in pH not only reduces the availability of carbonate ions required for calcifying organisms but also suggests that the ocean’s ability to self-regulate its acidity is weaker than previously assumed. The findings underscore the urgency of reducing anthropogenic CO₂ emissions to protect marine life and preserve the chemical balance of the ocean. This project relates to United Nations SDG goal 14, target 14.3: “minimizing and addressing the impacts of ocean acidification.”