Analytically tractable climate–carbon cycle feedbacks under 21st century anthropogenic forcing
Summary
Changes to climate–carbon cycle feedbacks may significantly affect the Earth system’s response to
greenhouse gas emissions. These feedbacks are usually analysed from numerical output of complex and arguably
opaque Earth system models. Here, we construct a stylised global climate–carbon cycle model, test its output
against comprehensive Earth system models, and investigate the strengths of its climate–carbon cycle feedbacks
analytically. The analytical expressions we obtain aid understanding of carbon cycle feedbacks and the operation
of the carbon cycle. Specific results include that different feedback formalisms measure fundamentally the same
climate–carbon cycle processes; temperature dependence of the solubility pump, biological pump, and CO2
solubility all contribute approximately equally to the ocean climate–carbon feedback; and concentration–carbon
feedbacks may be more sensitive to future climate change than climate–carbon feedbacks. Simple models such
as that developed here also provide “workbenches” for simple but mechanistically based explorations of Earth
system processes, such as interactions and feedbacks between the planetary boundaries, that are currently too
uncertain to be included in comprehensive Earth system models.
