A catalog of infrared intensities Sometimes it is useful to make a list of things in order to make comparisons. In the discussion below, I will use the term intensity to mean power per unit area. Sunlight reaches our orbit at 1366 W/m2; averaged over the surface of the sphere, it amounts to 341.5 W/m2. Presently, 30% is reflected, so the amount of sunlight absorbed is 239 W/m2. At equilibrium all planets radiate the same amount of heat energy to outer space that they receive from the sun. The earth has a seasonal imbalance of about 2.5 W/m2 between the heat received and the heat emitted, but on a yearly average basis, the heat received is about 0.6 W/m2 greater than the heat radiation sent to space. (This number is very hard to measure, as it necessarily involves subtraction of large numbers, each with their own uncertainties.) If the albedo decreases by one percentage point (30% down to 29%), the incoming/outgoing heat radiation increases by 3.5 W/m2. Infrared radiation from the surface is described by the Stefan-Boltzmann radiation law, Isurf = T 4 , with = 5.67 W m–2 K–4. At the present average surface temperature of 289 K, the surface radiates at 398 W/m 2. For temperature changes that are small compared to 289 K, the surface radiation varies about 5.5 W/m2 for every change of 1ºC. The greenhouse effect is the numerical difference between the surface intensity and the IR intensity sent to space, presently 159 W/m2. The change in the greenhouse effect due only to changes in CO2 concentration is called forcing by the IPCC, W C and is given by F = 5.35 2 ln . If the concentration doubles, the increase in the greenhouse effect is 3.7 m C0 W/m2. Note that it is a 2.3% increase. IPCC’s most-probable temperature rise for doubling is 3ºC; a 3ºC rise will increase surface radiation by 16.5 W/m2. From ca. 18,000 years ago until 8,000 years ago, the earth’s surface warmed by about 10ºC, and the CO2 concentration increased from 190 ppmv to 260 ppmv. That is, the surface radiated about 55 W/m 2 more after the warming, and CO2 was responsible for 1.7 W/m2 of “forcing.” Worldwide energy consumption is about 600 EJ/year, or around 19 TW. The surface area of the world is 5.1 × 1014 m2, so the power consumed per unit area is 0.037 W/m2. Here is the summary table, in order of decreasing intensity.
Description Sunlight at orbit IR emitted by surface (averaged over surface) Sunlight averaged over surface of earth IR emitted to space by the earth Absorbed sunlight (albedo = 30%) Greenhouse effect (reduction of IR from surface to IR to space) Increased surface radiation, glacial-to-interglacial Increased surface radiation for 3ºC rise (IPCC; for CO2 doubling) Increased surface radiation from 1ºC warming “Radiative forcing” from doubling CO2 Increase from albedo decrease by 1 percentage point “Radiative forcing” from increasing CO2, glacial-to-interglacial) Worldwide energy consumption Howard “Cork” Hayden, corkhayden@comcast.net, 10/26/2021
W/m2 1366 398 341.5 239 0.6 239 159 55 16.5 5.5 3.7 3.5 1.7 0.037