A simple climate model

We are now in a position to make what is probably the simplest useful climate model of Earth, a radiationbalance or energy-balance model (EBM), in which the net solar radiation coming in to Earth is balanced by the infrared radiation emitted by Earth. A fraction, a, known as the albedo, of the solar radiation is reflected back to space by clouds, ice, and so forth, so that

Net incoming solar radiation = S0(1 — a) = 239 Wm2, (1.6)

with a = 0.3 (we discuss the factors influencing the albedo more below).

This radiation is balanced by the outgoing infrared radiation. Now, of course, Earth is not a blackbody at a uniform temperature, but we can get some idea of what the average temperature on Earth should be by supposing that it is, and so

Outgoing infrared radiation = vT 4. (1.7)

Equating equations 1.6 and 1.7, we have vT 4 = S0(1 — a), (1.8)

and solving for T, we obtain T = 255 K or — 18°C. For obvious reasons, this temperature is known as the average emitting temperature of Earth, and it would be a decent approximation to the average temperature of Earth's surface if there were no atmosphere. However, it is in fact substantially lower than the average temperature of Earth's surface, which is about 288 K, because of the greenhouse effect of Earth's atmosphere, as we now discuss.

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