Scientists have been studying the Earth's climate for nearly 200 years. Over that time, and especially over the past 30 years, a sophisticated and well-validated theory of our climate has emerged. In this chapter, we take the fundamental physics we learned in Chapter 3 and use it to explain how greenhouse gases warm the planet and why the temperature of the Earth is what it is. By the end of the chapter, we will understand why scientists have such high confidence that adding greenhouse gases to the atmosphere will warm the planet.

The source of energy for our climate system

The first step to understanding the climate is to do an energy budget calculation: What is the energy in and energy out for the Earth? The ultimate source of energy for our planet is the Sun, which puts out an amazing 3.8×1026 W (380 trillion trillion W) of power. The Sun emits photons in all directions, so only a small fraction of the photons emitted end up falling on the Earth. To determine the exact amount of solar energy hitting the Earth, imagine a sphere surrounding the Sun, with a radius equal to the Sun–Earth distance, or 150 million km (Figure 4.1). Because the sphere completely encloses the Sun, all of the sunlight emitted by the Sun must fall on the interior of the sphere. The surface area of the sphere is 4πr2 = 4π(150 million km)2 = 2.8×1017 km2 = 2.8×1023 m2. This means that the energy emitted by the Sun falling on a 1-m2 surface of the sphere is 3.8×1026 W ÷ 2.8×1023 m2 = 1,360 W/m2. This value, 1,360 W/m2, is known as the solar constant for the Earth; it is represented in certain equations by the symbol S.

An example: What is the solar constant for Venus?

Our next-door neighbor Venus is located 108 million km from the Sun. Thus, the solar constant for Venus is 3.8×1026 W divided by the surface area of a sphere with a radius of 108 million km, 1.47×1023 m2 – which yields a value of 2,600 W/m2.

Another way to calculate this is to take the Earth's solar constant and multiply by the squared ratio of the radius of the Earth's orbit to Venus’ orbit, (150/108)2. In general, the solar constant scales as 1/r2, so that a planet with half the orbital radius has a solar constant that is four times larger whereas a planet with twice the orbital radius has a solar constant one fourth as large.