Simplifying the Carbon Cycle with Mathematics

By Lina Sorg

Climate change, fossil fuels, and the rising amount of carbon dioxide in the atmosphere are topics that continue to permeate global discussion. Daniel Rothman, a professor of geophysics at the Massachusetts Institute of Technology, works to advance public understanding of the natural environment, and studies topics including carbon cycle dynamics and the co-evolution of life and the environment.

Photosynthesis and respiration comprise the biological loop of the carbon cycle, which circulates approximately one hundred gigatons of carbon every year. Fundamentally, the carbon cycle helps govern climate, CO₂ levels in the atmosphere, and organisms’ interactions with their physical environment. It allows for a better understanding of the connectivity between the natural world’s many facets.

Although the cycle is undoubtedly complicated, Rothman believes that mathematical concepts can help simplify it.

Observational data demonstrates that the cycle displays a fundamental mathematical structure. Examination of this structure reveals the existence of global dynamical coupling amongst life and the environment, and offers a means of visualizing how smaller processes govern the strength of coupling. For example, Rothman uses the generality of the lognormal rate’s distribution – a continuous probability distribution – to propose a new means of comprehending plant-matter decay. He also connects kinetics (the measurement and study of reaction rates) occurring at small space and time scales to long-standing global changes.

Additionally, Rothman focuses on two types of problems: decomposition, during which organic matter becomes CO₂, and dynamics, the study of the cycle’s motion and rates of change. He presents scaling laws seemingly resulting from decomposition’s heterogeneity, and refers to historical records to demonstrate the seriousness of the cycle’s dynamics.

Due to the cycle’s complexity, Rothman invites mathematicians to continue with this research, as this problem of social significance presents many opportunities for quantitative work. He equates the carbon cycle with “metabolism at a global scale,” and writes that mathematics will undoubtedly be significant in future studies.

Last month, Rothman received the American Mathematical Society’s 2016 Levi L. Conant Prize for a paper entitled “Earth’s Carbon Cycle: A Mathematical Perspective,” which relates traditional concepts of applied mathematics to existing data about Earth’s carbon cycle.

Learn more about Rothman and the prize here.

Lina Sorg is the associate editor of SIAM News.