Climate.

Step 1 of 6

The balance

The Earth is warmed by one thing, sunlight, and cooled by one thing, its own glow. Everything warm gives off invisible infrared light, and the ground and oceans shine it out to space day and night. When the energy going out matches the energy coming in, the temperature holds steady. A warm body radiates a power of $\sigma T^4$⁠ from each square metre, by the Stefan–Boltzmann law: twice the temperature, sixteen times the radiation.

In the Scene, short yellow waves are sunlight, and long red waves are infrared. Greenhouse gas is at None, and Sunlight is locked at 100%.

Step 2 of 6

The trap

Most of the air, nitrogen and oxygen, is transparent to both sunlight and infrared. But a few gases, water vapour, carbon dioxide and methane, are transparent to sunlight and not to infrared. Greenhouse gas is now at Pre-industrial. Watch the red packets rising from the ground and the molecules flashing.

Step 3 of 6

Radiative forcing

Two centuries of burning coal, oil and gas have raised the carbon dioxide in the air from about 280 to about 420 parts per million, ppm: less than a twentieth of a per cent of the air, yet a rise of half. The extra gas holds back a little more of the escaping heat. That difference is measured in watts per square metre.

Step 4 of 6

Each doubling

The forcing depends on the amount of gas through a logarithm: $\Delta F = 5.35 \ln\dfrac{C}{C_0}$$\Delta F =$$5.35 \ln\dfrac{C}{C_0}$⁠. And since $\ln(ab) = \ln a + \ln b$$\ln(ab) =$$\ln a + \ln b$⁠, each doubling of $C$⁠ adds the same $5.35 \ln 2$⁠ to the forcing. Greenhouse gas is at Doubled, 560 ppm.

Step 5 of 6

How much warmer

A forcing is an imbalance: more comes in than goes out. The Earth warms until it glows strongly enough to restore the balance. That takes decades, because the oceans store heat.

Step 6 of 6

Feedbacks

Warming sets off changes that in turn change it, feedbacks. Some amplify it, and some steady it. Greenhouse gas is at 840 ppm.