Radiative Forcing Calculator

Radiative forcing measures the change in net downward energy flux at the tropopause, in watts per square metre, caused by a perturbation such as a change in greenhouse gas concentration, after stratospheric temperatures have adjusted but before the surface and troposphere respond. It is the standard way to place climate influences of different origin on a common scale. The functional forms differ by gas because of how their absorption bands saturate. The main carbon dioxide band near 15 micrometres is already strongly saturated at its centre, so additional CO2 absorbs mainly in the band wings and forcing grows logarithmically, giving RF = 5.35 ln(C/C0). Methane and nitrous oxide occupy weaker, less saturated bands where absorption grows roughly with the square root of concentration, which is why their expressions use square-root differences. With CO2 near 420 ppm against a 278 ppm pre-industrial reference these expressions give about 2.1 W/m2 from CO2 alone, and a doubling of CO2 yields close to 3.7 W/m2. Total anthropogenic effective radiative forcing in IPCC AR6 is roughly 2.7 W/m2 for 2019 relative to 1750, lower than the well-mixed greenhouse gas sum because aerosols exert a substantial negative forcing. Two caveats apply. The simplified formulas neglect overlap between the methane and nitrous oxide bands, which the revised expressions published by Maryam Etminan and colleagues in 2016 correct, raising methane forcing by roughly a quarter. The temperature conversion also uses a fixed climate sensitivity parameter of 0.8 K per W/m2, an equilibrium approximation that ignores ocean heat uptake and so overstates warming realised at any given moment.

The physical basis was laid in the nineteenth century. Joseph Fourier described in the 1820s how the atmosphere retains heat that would otherwise escape to space, John Tyndall measured the infrared absorption of water vapour, carbon dioxide and other gases in laboratory work published in 1859, and Svante Arrhenius calculated in 1896 that halving or doubling atmospheric carbon dioxide would change surface temperature by several degrees C. Guy Callendar assembled temperature and CO2 records in 1938 to argue that warming was already underway. The quantitative modern treatment arrived with the one-dimensional radiative-convective model of Syukuro Manabe and Richard Wetherald in 1967, which produced the first physically defensible estimate of about 2.3 degrees C for doubled CO2 and earned Manabe a share of the 2021 Nobel Prize in Physics. Radiative forcing became the organising concept for climate assessment through the 1979 Charney report and was formalised in the IPCC First Assessment Report of 1990. The specific simplified expressions used here come from a 1998 Geophysical Research Letters paper by Gunnar Myhre, Eleanor Highwood, Keith Shine and Frode Stordal, which fitted compact analytic formulas to line-by-line radiative transfer calculations and revised the CO2 coefficient down from the previously used 6.3 to 5.35, a reduction of roughly 15 percent. NOAA has published the Annual Greenhouse Gas Index since 2004, tracking the combined forcing of the long-lived gases against a 1990 baseline using directly measured concentrations.