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Climate Science 1896

On the Influence of Carbonic Acid in the Air upon the Temperature of the Ground

Svante Arrhenius

The first calculation that more carbon dioxide in the air warms the whole planet.

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In depth · the introduction

In 1896, with nothing but pencil, paper, and a few beams of moonlight, a Swedish chemist became the first person to calculate that burning coal could warm the entire planet.

The big idea

The Earth is kept warm by a thin blanket of gases. Sunlight passes through the clear air and heats the ground; the ground radiates that warmth back as invisible heat rays, and certain gases — above all carbon dioxide and water vapour — soak up those rays and send some back down. Arrhenius worked out, with arithmetic alone, how much warmer the planet would get if there were more carbon dioxide in the air.

His answer was a simple rule: the more you add, the warmer it gets — and steadily enough that each doubling of the carbon dioxide adds about the same jump in temperature. Doubling it, he found, would warm the world by five or six degrees.

How it came about

He wasn't worried about coal smoke; he was puzzling over the ice ages. Geologists had shown that vast sheets of ice once buried northern Europe and then melted away. What could turn the Earth's thermostat up and down by so much? Arrhenius wondered whether the amount of carbon dioxide in the air might be the dial.

To test it he needed to know how strongly the gas absorbs heat — so he borrowed Samuel Langley's measurements of moonlight, the faint warmth of the Moon dimmed as it passed down through the atmosphere. Then came the labour: tens of thousands of calculations by hand, band of latitude by band of latitude, season by season. It took him about a year. He found that halving the carbon dioxide could bring on an ice age, and doubling it would warm the world by five or six degrees.

Why it mattered

No one had ever put a number on it. Arrhenius turned a vague idea — that the air can trap heat — into a measurable physical law linking one gas to the temperature of a whole planet. Everything we now know about climate change rests on the very question he was the first to answer: how much does the Earth warm when we add carbon dioxide?

A way to picture it

Think of a parked car on a sunny day. Light pours in through the glass and warms the seats; the seats give off heat, but the glass won't let that heat back out so easily — so the car ends up hotter than the air outside. Carbon dioxide is the glass for the whole planet. Add more of it and you thicken the glass, and the Earth settles at a warmer temperature. And like piling on blankets, each layer you add warms a little less than the last — but it always warms you more.

Interactive greenhouse model: slide the amount of carbon dioxide in the air from half to four times a starting value and watch the predicted temperature rise along a line; each doubling of the gas adds about the same step of warming. Buttons compare the estimate Arrhenius made in 1896 with the value scientists use today.

Where it sits

Arrhenius built on Joseph Fourier, who in the 1820s first asked why the Earth is warmer than empty space, and on John Tyndall, who in the 1860s measured in the laboratory that carbon dioxide and water vapour really do trap heat. Arrhenius supplied the missing number. For decades the idea was brushed aside, then revived in the 1930s and confirmed once Charles Keeling began measuring the steady rise of CO₂ in 1958 — the same rise we live with today.

The original document
Original source text
Svante Arrhenius · Philosophical Magazine (5th series) 41 (1896): 237–276 · developed from a paper read to the Royal Swedish Academy of Sciences, 11 December 1895
The paper opens from a geological puzzle. Vast ice sheets had once buried northern Europe and then withdrawn; what could turn the Earth's thermostat up and down by so much? Arrhenius asks whether a change in the amount of "carbonic acid" (carbon dioxide) and water vapour in the air could be the cause.
The absorbing power of the atmosphere
He needed to know how strongly carbon dioxide and water vapour soak up heat radiation. For this he borrowed Samuel Langley's measurements of the Moon's infrared rays reaching the ground through different thicknesses and dampnesses of air — reasoning that the Moon's heat, descending through the atmosphere, is absorbed much as the Earth's heat ascending through it.
The calculation
He then balanced incoming sunlight against outgoing heat for ten-degree bands of latitude across the seasons, including the water-vapour feedback, and solved by hand for the surface temperature with carbonic acid set to 0.67, 1, 1.5, 2, 2.5 and 3 times its present amount — many thousands of arithmetical operations.
The rule
If the quantity of carbonic acid increases in geometric progression, the augmentation of the temperature will increase nearly in arithmetic progression.
He found that lowering the carbonic acid to roughly 0.55–0.62 of its value would cool the middle and high latitudes by some 4–5 °C — enough, he argued, to bring on an ice age — while doubling it would warm the globe by about 5–6 °C, the change being greatest toward the poles.
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Stockholm · 1896