Climate Sensitivity Calculator

Climate sensitivity converts a change in CO2 into a change in temperature by way of radiative forcing. The forcing from CO2 is logarithmic, well approximated by F = 5.35 * ln(C/C0) watts per square meter, so each doubling adds about 3.7 W/m2 regardless of the starting concentration. The logarithm arises because the strong absorption bands of CO2 are already saturated near their centers, leaving only the band wings available to absorb additional outgoing radiation. Equilibrium climate sensitivity, ECS, is the eventual warming once the ocean has fully adjusted to doubled CO2; the IPCC Sixth Assessment gives a best estimate of 3.0 degrees C with a likely range of 2.5 to 4.0. Transient climate response, TCR, is the warming at the moment of doubling under a 1 percent per year increase, best estimate 1.8 degrees C. The gap between TCR and ECS is committed or in-the-pipeline warming, currently a few tenths of a degree to somewhat under one degree, because the ocean absorbs roughly 90 percent of the excess energy and mixes it downward over centuries. The feedback parameter lambda equals 3.7 divided by ECS, about 1.23 W/m2 per degree C at an ECS of 3.0; a smaller lambda means weaker restoring feedbacks and higher sensitivity. Water vapor and lapse rate together form the largest positive feedback, surface albedo a smaller one, and clouds remain the dominant uncertainty. Scaling warming linearly with forcing, as done here, ignores that effective sensitivity varies with the spatial pattern of ocean warming and with ice-sheet and vegetation feedbacks that act over millennia.

Svante Arrhenius made the first quantitative estimate in 1896, calculating by hand from Samuel Langley's lunar infrared measurements that halving or doubling atmospheric carbon dioxide would change surface temperature by roughly 5 to 6 degrees C. Guy Callendar revisited the question in 1938 using station temperature records and early absorption data. Syukuro Manabe and Richard Wetherald produced the first physically consistent modern estimate in 1967 with a one-dimensional radiative-convective model that held relative humidity fixed, obtaining about 2.3 degrees C for doubled CO2; Manabe shared the 2021 Nobel Prize in Physics for this line of work. The canonical range came from a 1979 US National Academy of Sciences study chaired by Jule Charney, which examined two early general circulation models and reported 3 degrees C plus or minus 1.5. That 1.5 to 4.5 degree window then survived essentially unchanged through successive IPCC assessments for more than three decades. Progress eventually came from combining independent lines of evidence rather than from models alone: Steven Sherwood and a large group of coauthors published an assessment in 2020 that merged process understanding, the historical instrumental record, and paleoclimate constraints into a single probabilistic framework, and the IPCC drew on it in 2021 to narrow the likely range to 2.5 to 4.0 degrees C around a 3.0 degree best estimate.