# Simple Question, Simple Answer… Not

It was not until the 1950s that scientists had both good data on the absorption of infrared radiation, and digital computers that could speed through the multitudinous calculations. Gilbert N. Plass used the data and computers to demonstrate that adding carbon dioxide to a column of air would raise the surface temperature. But nobody believed the precise number he calculated (2.5ºC of warming if the level of CO_{2} doubled). Critics pointed out that he had ignored a number of crucial effects. First of all, if global temperature started to rise, the atmosphere would contain more water vapor. Its own greenhouse effect would make for more warming. On the other hand, with more water vapor wouldn’t there be more clouds? And wouldn’t those shade the planet and make for less warming? Neither Plass nor anyone before him had tried to calculate changes in cloudiness. (For details and references see this history site.)

Fritz Möller followed up with a pioneering computation that took into account the increase of absolute humidity with temperature. Oops… his results showed a monstrous feedback. As the humidity rose, the water vapor would add its greenhouse effect, and the temperature might soar. The model could give an almost arbitrarily high temperature! This weird result stimulated Syukuro Manabe to develop a more realistic one-dimensional model. He included in his column of air the way convective updrafts carry heat up from the surface, a basic process that nearly every earlier calculation had failed to take into account. It was no wonder Möller’s surface had heated up without limit: his model had not used the fact that hot air would rise. Manabe also worked up a rough calculation for the effects of clouds. By 1967, in collaboration with Richard Wetherald, he was ready to see what might result from raising the level of CO_{2}. Their model predicted that if the amount of CO_{2} doubled, global temperature would rise roughly two degrees C. This was probably the first paper to convince many scientists that they needed to think seriously about greenhouse warming. The computation was, so to speak, a “proof of principle.”

But it would do little good to present a copy of the Manabe-Wetherald paper to a senior engineer who demands a proof that global warming is a problem. The paper gives only a sketch of complex and lengthy computations that take place, so to speak, offstage. And nobody at the time or since would trust the paper’s numbers as a precise prediction. There were still too many important factors that the model did not include. For example, it was only in the 1970s that scientists realized they had to take into account how smoke, dust and other aerosols from human activity interact with radiation, and how the aerosols affect cloudiness as well. And so on and so forth.

The greenhouse problem was not the first time climatologists hit this wall. Consider, for example, attempts to calculate the trade winds, a simple and important feature of the atmosphere. For generations, theorists wrote down the basic equations for fluid flow and heat transfer on the surface of a rotating sphere, aiming to produce a precise description of our planet’s structure of convective cells and winds in a few lines of equations… or a few pages… or a few dozen pages. They always failed. It was only with the advent of powerful digital computers in the 1960s that people were able to solve the problem through millions of numerical computations. If someone asks for an “explanation” of the trade winds, we can wave our hands and talk about tropical heating, the rotation of the earth and baroclinic instability. But if we are pressed for details with actual numbers, we can do no more than dump a truckload of printouts showing all the arithmetic computations.

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