Climate Change 101 - Part 3 (Earth's radiative temperature)

Global temperatures are determined by a balance between the incoming and outgoing radation at the top of the atmosphere. On average, 30% of the incoming solar radiation is reflected back to space. The remaining 70% provides heat for the earth’s surface. In turn, the surface heats up and emits longwave radiation in order to keep its temperature at equilibrium. You can calculate the radiative equilibrium temperature by solving for T in this equation:


The left-hand side of the equation is the amount of solar radiation (in watts) that reaches the earth’s surface. S is the solar constant (the amount of radiation emitted by the sun in watts per square meter). α is the albedo of the earth/atmosphere system. The albedo is the percentage of solar radiation reflected. R is the radius of the earth. At any given time, the sun’s radiation hits an approximately disc-shaped portion of the earth. This disc’s area is πR^2.

On the right-hand side of the equation is the amount of radiation emitted by the earth. σ is the Stefan-Boltzmann constant. This constant is used to calculate the rate of energy emission from a blackbody. A blackbody absorbs 100% of the radiation that hits it and it emits radiation at the maximum rate for its given temperature. Despite the name, a blackbody does not have to black. To the first order, we can approximate the earth as a blackbody. At any given time, the entire surface area (4πR^2) of the earth is emitting radiation.


If you want to solve for T yourself: S = 1,367 Wm^-2, α = 0.3, R = 6,378 km, and σ = 5.67*10-8 Wm^-2K^-4. (The unit for temperature is Kelvin. To convert to celcius, subtract 273.)

The radiative equilibrium temperature of the earth is -18°C (0°F). Think about that for a second. According to this equation, the average temperature of the earth is below freezing. However, the observed global mean surface temperature is 15°C (59°F). Obviously, the equation is not representing some essential properties of the earth’s climate.