Greenhouse Effect Strength Calculator

The strength of the greenhouse effect can be quantified three ways, and this calculator reports all of them. The temperature measure is simply Ts minus Te, about 33 K for Earth. The energy measure is surface emission minus outgoing longwave radiation, roughly 390 minus 240, so on the order of 150 W per square meter of infrared that leaves the surface but never leaves the planet. The dimensionless normalized greenhouse parameter is 1 minus the fourth power of Te over Ts, close to 0.39 for present-day Earth. Attribution studies place water vapour and clouds at roughly three quarters of total longwave absorption and carbon dioxide near one fifth, so removing carbon dioxide alone would not remove the full 33 K directly, though it would cool the planet enough to condense out much of the water vapour that supplies the rest. The forcing side uses the Myhre expression dF = 5.35 times ln(C divided by C0), which returns 3.71 W per square meter for a doubling and about 2.2 W per square meter for the rise from 280 to 420 ppm. The logarithm reflects saturation at the core of the 15 micrometer band, so incremental absorption comes from the band wings rather than the center. Dividing the doubling forcing by the equilibrium climate sensitivity gives the net feedback parameter, about 1.24 W per square meter per K at an ECS of 3.0 K. Note the limits of that coefficient: 5.35 is a fit valid roughly between 200 and 1000 ppm and carries no overlap corrections, and more recent formulations such as Etminan and coauthors in 2016 add explicit nitrous oxide overlap terms and are what current assessments use.

Joseph Fourier raised the question in the 1820s, and Claude Pouillet argued in 1838 that the atmosphere is more transparent to sunlight than to terrestrial heat. The decisive laboratory work was done by John Tyndall at the Royal Institution in 1859, whose ratio spectrophotometer showed that the bulk gases nitrogen and oxygen are nearly transparent in the infrared while water vapour, carbon dioxide, ozone, and hydrocarbons absorb strongly. Svante Arrhenius put numbers to it in 1896, calculating roughly 5 to 6 degrees C of warming for a doubling of what he called carbonic acid, and Knut Angstrom raised the band-saturation objection in 1900 that would delay acceptance for half a century. The modern quantitative treatment arrived with spectroscopic databases and computers. Gilbert Plass recomputed the carbon dioxide effect on early digital machines in 1956, and Syukuro Manabe and Richard Wetherald published the first credible radiative-convective calculation in 1967, obtaining about 2.3 degrees C for a doubling under fixed relative humidity; Manabe shared the 2021 Nobel Prize in Physics for that line of work. The 1979 Charney report for the US National Academy of Sciences set the 1.5 to 4.5 degrees C sensitivity range that stood for roughly four decades before observational and paleoclimate constraints narrowed it. The logarithmic forcing coefficient used in this calculator comes from Gunnar Myhre and coauthors, published in Geophysical Research Letters in 1998.