Thermal Equilibrium of the Atmosphere with a Given Distribution of Relative Humidity
Shrink the whole sky to one column held in radiative–convective balance, and doubling CO₂ warms the surface about 2 °C while the stratosphere cools.
How do you forecast the climate of an entire planet? Manabe and Wetherald started by shrinking the whole sky down to a single column of air — and got an answer close to the one we trust today.
The idea, unpacked
Imagine the atmosphere reduced to one tall column. Sunlight warms the ground; the warm air near the surface rises and mixes, carrying heat upward; and from the top, the planet radiates heat back to space. When the incoming and outgoing heat balance at every level, the column has a settled temperature from bottom to top.
Manabe and Wetherald wrote the physics of that balance down as equations and solved them on a computer. Then they did the key experiment: add more carbon dioxide and let the column find its new balance. The surface warmed by about 2 °C for a doubling of CO₂ — and, surprisingly, the high stratosphere got colder. That split — warm below, cool above — is the signature of a greenhouse gas at work, not a brighter Sun.
The most influential climate paper ever written
Syukuro Manabe had come from Japan to a small US weather-research lab; Richard Wetherald was the colleague who built and ran much of the model with him. The greenhouse idea was old — Arrhenius had estimated CO₂ warming back in 1896 — but earlier computer attempts kept misbehaving, sometimes running off to impossible temperatures. The reason was a subtle choice about water vapour. Manabe and Wetherald fixed it by holding the air's RELATIVE humidity steady, so a warmer world automatically holds more water vapour, which adds its own warming in a controlled way. With that single insight the model became stable and believable. Decades later, in a 2015 poll, climate scientists voted this 1967 paper the most influential in their field's history, and in 2021 Manabe shared the Nobel Prize in Physics for the line of work it began.
Why it mattered
Before this, the question “how much will CO₂ warm the Earth?” had only rough, contested answers. Manabe and Wetherald turned it into a calculation grounded in real radiation physics, and got a number — about 2 °C for a doubling — that has barely moved in sixty years of far bigger models. They also handed us a way to tell the cause apart from coincidence: a warming Sun would heat the whole atmosphere, but more CO₂ warms the surface while cooling the stratosphere. Satellites have since watched exactly that happen, which is among the strongest evidence that today's warming is driven by greenhouse gases.
A microphone near its speaker
The water-vapour feedback works like a microphone held near its own loudspeaker. A small sound gets picked up, amplified, played out, picked up again — louder each round. Here, a little CO₂ warming lets the air hold more water vapour, which warms it more, which holds yet more vapour. The difference from a screeching PA system is that this loop settles instead of running away: each round adds less than the last, and the total lands at roughly double the warming CO₂ would manage alone.
Before and after
The thread runs straight through this Library. Svante Arrhenius (1896) first did the CO₂-warming sum by hand; Charles Keeling (1960) proved the CO₂ was actually rising, turning a thought experiment into a forecast about our own future. Manabe and Wetherald, between them, supplied the credible physics. What came next was scale: by 1975 the same team had grown the column into three-dimensional models of the whole circulating atmosphere and ocean, the ancestors of the global climate models the IPCC relies on today.
Radiative convective equilibrium of the atmosphere with a given distribution of relative humidity is computed as the asymptotic state of an initial value problem.