CAMBIO: A Carbon Mass Balance Model for Undergraduates

Année de publication

2026

The mathematical complexity of climate modeling presents significant challenges to teaching climate change at the undergraduate level. Here, we address this challenge with the CAMBIO climate model, a set of ordinary time-dependent differential equations that simulate carbon exchanges between Earth's atmosphere, ocean, and land reservoirs. Students obtain solutions to versions of these equations that embed a series of feedbacks, progressively adding (i) temperature-dependent Henry's law equilibration of carbon dioxide (CO2) between oceans and atmosphere, (ii) reductions in global albedo as parameterized by anticipated reductions in Earth's cryosphere, and (iii) reductions in the efficiency of terrestrial CO2 fertilization parameterized by observed changes in net atmosphere-land CO2 fluxes. As validation, we find that the range of anthropogenic warming produced by this progression plausibly replicates the range of published warming values, even for a fixed Charney equilibrium climate sensitivity. We have found that students taking an undergraduate general education course on modeling Earth's climate with minimal prerequisites and no programming experience can learn the necessary programming skills to write the code to create CAMBIO from the ground up. Creating and implementing CAMBIO themselves helps students develop skills needed to understand the nonlinear processes inherent in climate dynamics, including feedbacks, time delays, reservoir stocks, and flows between reservoirs. We also describe an analytical solution to the CAMBIO equations that reproduces observed log-linear increases in atmospheric and oceanic carbon reservoirs. We conclude with pedagogical insights regarding the use of scaffolded Python/Jupyter Notebooks, as a way to reach a wide range of students. Significance Statement The computational model presented here, CAMBIO, provides a pedagogical resource that bridges the gap between qualitative instruments (e.g., feedback diagrams) and quantitative tools such as global climate models (GCMs). By filling this gap, CAMBIO provides students (and instructors) a means of efficiently obtaining quantitative answers to "what-if" questions, such as questions exploring the consequences of an earlier or later timeline for reductions in global anthropogenic carbon emissions, variations in temperature thresholds for the onset of ice/albedo feedback, and the vulnerability of key natural ecosystem services (such as the planetary "CO2 fertilization effect") to higher global temperatures. Insights derived from such investigations, in turn, can provide a starting point for generating hypotheses to explain the variability of projections of more complex climate models, even when subject to identical carbon emission scenarios.</div>

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