Here’s another excerpt from the draft manuscript of my forthcoming book, Computing the Climate.

The idea that the temperature of the planet could be analyzed as a mathematical problem was first suggested by the French mathematician, Joseph Fourier, in the 1820s. Fourier had studied the up-and-down cycles of temperature between day and night, and between summer and winter, and had measured how deep into the ground these heating and cooling cycles reach. It turns out they don’t go very deep. At about 30 meters below the surface, temperatures remain constant all year round, showing no sign of daily or annual change. Today, Fourier is perhaps best remembered for his work on the mathematics of such cycles, and the Fourier transform, a technique for discovering cyclic waveforms in complex data series, was named in his honour.

The temperature of any object is due to the balance of heat entering and leaving it. If more heat is entering, the object warms up, and if more heat is leaving, it cools down. For the planet as a whole, Fourier pointed out there are only three possible sources of heat: the sun, the earth’s core, and background heat from space. His measurements showed that the heat at the earth’s core no longer warms the surface, because the diffusion of heat through layers of rock is too slow to make a noticeable difference. He thought that the temperature of space itself was probably about the same as the coldest temperatures on earth, as that would explain the temperature reached at the poles in the long polar winters. On this point, he was wrong—we now know space is close to absolute zero, a couple of hundred degrees colder than anywhere on earth. But he was correct about the sun being the main source of heat at the earth’s surface.

Fourier also realized there must be more to the story than that, otherwise the heat from the sun would escape to space just as fast as it arrived, causing night-time temperatures to drop back down to the temperature of space—and yet they don’t. We now know this is what happens on the moon, where temperatures drop by hundreds of degrees after the lunar sunset. So why doesn’t this happen on Earth?

The solution lay in the behaviour of ‘dark heat’, an idea that was new and mysterious to the scientists of the early nineteenth century. Today we call it infra-red radiation. Fourier referred to it as ‘radiant heat’ or ‘dark rays’ to distinguish it from ‘light heat’, or visible light. But really, they’re just different parts of the electromagnetic spectrum. Any object that’s warmer than its surroundings continually radiates some of its heat to those surroundings. If the object is hot enough, say a stove, you can feel this ‘dark heat’ if you put your hand near it, although it has to get pretty hot before we can feel the infra-red it gives off. As you heat up an object, the heat it radiates spreads up the spectrum from infra-red to visible light—it starts to glow red, and then, eventually white hot.

Fourier’s theory was elegantly simple. Because the sun is so hot, much of its energy arrives in the form of visible light, which passes through the atmosphere relatively easily, and warms the earth’s surface. As the earth’s surface is warm, it also radiates energy. The earth is cooler than the sun, so the energy the earth radiates is in the form of dark heat. Dark heat doesn’t pass though the atmosphere anywhere near as easily as light heat, so this slows the loss of energy back to space.

The surface temperature of the earth is determined by the balance between the incoming heat from the sun (shortwave rays, mainly in the visible light and ultra-violet) and the outgoing infra-red, radiated in all directions from the earth. The incoming short-wave rays passes through the atmosphere much more easily than the long-wave outgoing infra-red.

To explain the idea, Fourier used an analogy with the hotbox, a kind of solar oven, invented by the explorer Horace Bénédicte de Saussure. The hotbox was a very well-insulated wooden box, painted black inside, with three layers of glass in the lid. De Saussure had demonstrated that the sun would heat the inside of the box to over 100°C, and that this temperature remains remarkably consistent, even at the top of Mont Blanc, where the outside air is much colder. The glass lets the sun’s rays through, but slows the rate at which the heat can escape. Fourier argued that layers of air in the atmosphere play a similar role to the panes of glass in the hotbox, by trapping the outgoing heat; like the air in the hotbox, the planet would stay warmer than its surroundings. A century later, Fourier’s theory came to be called the ‘greenhouse effect’, perhaps because a greenhouse is more familiar to most people than a hotbox.

While Fourier had observed that air does indeed trap some of the dark heat from the ground, it wasn’t clear why, until the English scientist John Tyndall conducted a series of experiments in the 1850s to measure how well this ‘dark heat’ passes through different gases. Tyndall’s experiments used a four foot brass tube, sealed at both ends with transparent disks of salt crystal—glass was no good as it also blocks the dark heat. The tube could be filled with different kinds of gas. A tub of boiling water at one end provided a source of heat, and a galvanometer at the other compared the heat received through the tube with the heat from a second tub of boiling water.

Tyndall’s experimental equipment for testing the absorption properties of different gases. The brass tube was first evacuated, and the equipment calibrated by moving the screens until the temperature readings from the two heat sources were equal. Then the gas to be tested was pumped into the brass tube, and change in deflection of the galvanometer noted. (Figure adapted from Tyndall, 1861)

When Tyndall filled the tube with dry air, or oxygen, or nitrogen, there was very little change. But when he filled it with the hydrocarbon gas ethene, the temperature at the end of the tube dropped dramatically. This was so surprising that he first suspected something had gone wrong with the equipment—perhaps the gas had reacted with the salt, making the ends opaque? After re-testing every aspect of the equipment, he finally concluded that it was the ethene gas itself that was blocking the heat. He went on to test dozens of other gases and vapours, and found that more complex chemicals such as vapours of alcohols and oils were the strongest heat absorbers, while pure elements such as oxygen and nitrogen had the least effect.

Why do some gases allow visible light through, but block infra-red? It turns out that the molecules of each gas react to different wavelengths of light, depending on the molecule’s shape, similar to the way sound waves of just the right wavelength can cause a wine glass to resonate. Each type of molecule will vibrate when certain wavelengths of light hit it, making it stretch, contract, or rotate. So the molecule gains a little energy, and the light rays lose some. Scientists use this to determine which gases are in distant stars, because each gas makes a distinct pattern of dark lines across the spectrum from white light that has passed though it.

Tyndall noticed that gases made of more than one element, such as water vapour (H2O) or carbon dioxide (CO2), tend to absorb more energy from the infra-red rays than gases made of a single type of element, such as hydrogen or oxygen. He argued this provides evidence of atomic bonding: it wouldn’t happen if water was just a mixture of oxygen and hydrogen atoms. On this, he was partially right. We now know that what matters isn’t just the existence of molecular bonds, but whether the molecules are asymmetric—after all, oxygen gas molecules (O2) are also pairs of atoms bonded together. The more complex the molecular structure, the more asymmetries it has, and the more modes of vibration and spin the bonds have, allowing them to absorb energy at more different wavelengths. Today, we call any gas that absorbs parts of the infra-red spectrum a greenhouse gas. Compounds such as methane (CH4) and ethene (C2H4) absorb energy at more wavelengths than carbon dioxide, making them stronger greenhouse gases.

Tyndall’s experiments showed that greenhouse gases absorb infra-red even when the gases are only present in very small amounts. Increasing the concentration of the gas increases the amount of energy absorbed, but only up to a point. Once the concentration is high enough, adding more gas molecules has no further effect—all of the rays in that gas’s absorption bands have been blocked, while rays of other wavelengths pass through unaffected. Today, we call this saturation.

Tyndall concluded that, because of its abundance in the atmosphere, water vapour is responsible for most of the heat trapping effect, with carbon dioxide second. Some of the other vapours he tested have a much stronger absorption effect, but are so rare in the atmosphere they contribute little to the overall effect. Tyndall clearly understood the implications of his experiments for the earth’s climate, arguing that it explains why, for example, temperatures in dry regions such as deserts drop overnight far more than in more humid regions. In the 1861 paper describing his experimental results, Tyndall argued that any change in the levels of water vapour and carbon dioxide, “must produce a change of climate”. He speculated that “Such changes in fact may have produced all the mutations of climate which the researches of geologists reveal”.


  1. When is the Australian book tour happening?

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