Earth Energy Balance Calculator

Planetary energy balance is a single accounting identity: over the long run a planet must radiate to space as much energy as it absorbs from its star. Total solar irradiance at 1 AU is about 1361 W per square meter, but a sphere intercepts sunlight across pi R squared while radiating from 4 pi R squared, so the globally averaged input is one quarter of that, near 340 W per square meter. Removing the roughly 30 percent reflected by clouds, ice, bright land, and air molecules leaves about 240 W per square meter absorbed. Setting that equal to sigma T to the fourth gives an effective radiating temperature near 255 K. The observed surface mean is about 288 K, and in this single-slab model the 33 K difference is carried by an effective emissivity near 0.61, the fraction of surface emission that escapes directly to space. Two derived outputs deserve care. The imbalance is absorbed shortwave plus any imposed forcing minus outgoing longwave radiation; the real planet currently runs a surplus estimated at roughly 0.5 to 1.0 W per square meter, more than 90 percent of which enters the ocean. The sensitivity term, 1 divided by 4 eps sigma T cubed, comes to only about 0.3 K per W per square meter and represents the bare Planck response, so applying it to the 3.7 W per square meter of a carbon dioxide doubling yields about 1.1 K rather than the 2.5 to 4.0 K equilibrium range that includes water vapour, cloud, and ice-albedo feedbacks. The grey slab also omits latent and sensible heat fluxes, which move roughly 80 and 20 W per square meter from surface to atmosphere, and it has no latitudes, no seasons, and no ocean lag.

The framing is nearly two centuries old. Joseph Fourier posed the problem in 1824 and 1827, arguing that Earth temperature results from a balance between solar heating and emission to space and that the atmosphere retains part of the outgoing heat. Claude Pouillet built the first pyrheliometer in 1838 and produced an early solar constant near 1228 W per square meter. John Tyndall measured the infrared absorption of water vapour and carbon dioxide in 1859, and Svante Arrhenius published the first numerical estimate of the temperature effect of changing carbon dioxide in 1896. Charles Greeley Abbot and the Smithsonian Astrophysical Observatory then spent decades refining ground-based solar constant measurements. Closing the budget required leaving the atmosphere. The flat-plate radiometer built by Verner Suomi and flown on Explorer 7 in 1959 returned the first satellite measurements of the Earth radiation budget, followed by the Nimbus series, the Earth Radiation Budget Experiment launched in 1984, and the CERES instruments flying on Terra since 1999 and Aqua since 2002. Satellite radiometers pin down the shape and variability of the budget far better than its absolute offset, so the imbalance itself is anchored instead by ocean heat content from the Argo float array deployed from 2000 onward. The widely reproduced global energy budget diagram, with its arrows for incoming, reflected, and surface-emitted flux, comes from Kevin Trenberth, John Fasullo, and Jeffrey Kiehl in 2009 and its later updates.