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land to come to thermal equilibrium with those increases result in a net gain of ener gy, hence warming, on Earth. Most of this excess energy (about 90%) warms the ocean, with the remainder heating the land, melting snow and ice, and warming the at mosphere. Here we compare satellite observations of the net radiant energy absorbed by Earth with a global array of measurements used to determine heating within the ocean, land, and atmosphere, and melting of snow and ice. We show that these two independent approaches yield a decadal increase in the rate of energy uptake by Earth from mid 2005 through mid - 2019, which we attribute to decreased reflection of energy back into space by clouds and sea - ice and increases in well - mixed greenhouse gases and water va por. (p.1) Anderson, T.R., Hawkins, E. & Jones, P.D. (2016). CO₂, the greenhouse effect and global warming: From the pioneering work of Arrhenius and Callendar to to day's Earth System Models. Endeavor, 40 (3), 178 - 187. Choate, E. (2020). Covid - 19 and the chain rule are linked: Understanding R0 through calculus, Virginia Mathematics Teacher, 47 (1), 15 - 20. Flath, D., Kaper, H.G., Wattenberg, F. & Widiasih, E. (2018). Energy Balance Models. (http:archive.dimacs.rutgers.edu) Harte, J. (1985). Consider a Spherical Cow. A Course in Environmental Problem Solving. William Kaufmann, Inc. Cook, John (https://skepticalscience.com/)

Digital (http:// www.katharinehayhoe.com/wp2016) Series.

Heinlein, R. (1973). Time Enough for Love . G.P. Putnam & Sons.

Loeb, N. G., Johnson, G.C., Thorsen, T.J., Lyman, J.M., Rose, F.G. & Kato, S. (2021). Satellite and Ocean Data Reveal Marked Increase in Earth ’ s Heating Rate. Geophysical Research Letters, 48 (13). doi.org/10.1029/2021GL093047 Randall, D. (2012). Atmosphere, Clouds and Climate. Princeton University Press. Weinstein, L. & Adam, J. A. (2008). Guesstimation, Solving the World ’ s Problems on the Back of a Cocktail Napkin. Princeton University Press.

References

John Adam Professor of Mathematics Old Dominion University jadam@odu.edu

Hayhoe, K. (2016). Global Weirding , PBS

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