Atmospheric Co Radiative Forcing Calculator

Radiative forcing measures how far a change in atmospheric composition pushes the Earth energy budget out of balance, in watts per square metre at the tropopause after stratospheric adjustment. For carbon dioxide the response is logarithmic, because the core of the 15 micrometre absorption band is already opaque at pre-industrial amounts and only the wings keep absorbing as concentration rises. The expression delta_F = 5.35 ln(C/C0) captures that behaviour, so a doubling from 280 to 560 ppm gives 5.35 ln 2, about 3.71 W/m2, and the rise from 280 to 420 ppm gives roughly 2.17 W/m2. Methane and nitrous oxide are handled with square-root rather than logarithmic forms, 0.036 (sqrt CH4 - sqrt CH4_ref) and 0.12 (sqrt N2O - sqrt N2O_ref) in ppb, because their bands are far from saturated at present abundances of about 1900 and 332 ppb against pre-industrial 722 and 270 ppb. Temperature is then scaled from forcing by equilibrium climate sensitivity, the warming per doubling, which the IPCC Sixth Assessment Report assessed as likely 2.5 to 4.0 degrees C with a best estimate of 3.0. Equilibrium sensitivity describes the state reached after the deep ocean has fully adjusted over centuries, so nearer-term warming follows the smaller transient climate response of about 1.4 to 2.2 degrees C. The simplified expressions omit the overlap between the methane and nitrous oxide absorption bands that fuller formulations correct for, and they exclude aerosols, halocarbons, ozone, land-use albedo and other forcings whose net effect on total anthropogenic forcing is substantial. The CO2 coefficient itself also drifts slightly far above 560 ppm.

The chain of reasoning starts with Joseph Fourier, who argued in the 1820s that the atmosphere retains heat that would otherwise escape to space. Eunice Newton Foote reported in 1856 that a vessel of carbon dioxide warmed more in sunlight than one of ordinary air, and John Tyndall demonstrated in 1859 at the Royal Institution that carbon dioxide and water vapour absorb infrared radiation while nitrogen and oxygen do not. In 1896 Svante Arrhenius published the first quantitative estimate, calculating by hand from lunar infrared measurements that halving or doubling carbonic acid would change surface temperature by several degrees, and he already noted that the effect grows roughly with the logarithm of concentration. Guy Stewart Callendar assembled temperature and CO2 records in 1938 to argue that warming was already underway, and Gilbert Plass applied band-by-band radiative transfer in 1956 to obtain a doubling response near 3.6 degrees C. Charles David Keeling began continuous measurements at Mauna Loa in 1958, producing the curve that fixed the modern baseline. Syukuro Manabe and Richard Wetherald published the first radiative-convective and general-circulation estimates in 1967 and 1975, and the 1979 Charney report set the doubling range at 1.5 to 4.5 degrees C. The specific coefficient used here comes from Gunnar Myhre, Eleanor Highwood, Keith Shine and Frode Stordal, whose 1998 paper fitted line-by-line radiative transfer results to give 5.35 ln(C/C0) and the associated methane and nitrous oxide expressions adopted by the IPCC.