Potential Scenario Ideas : climate change: temperature, CO2, and some other factor in a feedback loop?

By Andrew M Ross

Mathematics, Eastern Michigan University, Ypsilanti MI USA

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Looking at graphs of atmospheric CO2 and global average temperature, such as this famous one from "An Inconvenient Truth" https://smallpond.ca/jim/ref/inconvenientTruth/full/00_22_49.jpg

or the 2nd graph on this page: https://19january2017snapshot.epa.gov/climate-change-science/causes-climate-change_.html

it occurs to me that there is probably some negative feedback going on to bring temperature back down after an upward excursion--otherwise CO2 and temperature would just spiral upwards, which the graph doesn't show. That is, an obviously naive model of the system that only said:

dTemp/dt = (positive constant)*CO2(t)

dCO2/dt = (other positive constant)*Temp(t) [because of release of CO2 from permafrost, for example]

seems to be contradicted by this data, since that simple system would run away. Yet that seems to be the model that is sort-of implied in some pop-sci treatments of climate change.

I know there are very complicated feedback things going on ( https://en.wikipedia.org/wiki/Climate_change_feedback ), and that actual climate models are huge systems of differential equations that we can't expect to bring into the introductory differential equations classroom. But is there a moderately or slightly realistic way to have perhaps just 1 or 2 more variables besides CO2 and temperature that would allow for some sort of negative feedback and moderate stability, at least in a region of phase space? Or would introducing a delay term be realistic and result in a graph like what we see?

To be clear, I am not looking to say "we don't need to worry about climate change because there's negative feedback that will save us." I'm just looking to have a way to talk about how negative feedback can keep a system from running away, at least within a certain region.

I do see https://www.simiode.org/resources/6799/download/1-010-Text-S-AtmosphericCO2Bifurcation-StudentVersion.pdf but it doesn't motivate the various terms in the differential equation it gives.

Sorry I don't have any actual ways to do this, it's just the seed of an idea.

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Researchers should cite this work as follows:

  • Andrew M Ross (2022), "Potential Scenario Ideas : climate change: temperature, CO2, and some other factor in a feedback loop?," https://simiode.org/resources/8969.

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