But a true climate model is more complex, because there’s more at play than just the atmosphere. The oceans ensure that the amount of water vapor (and cloud cover, which impacts temperature significantly) change dependent on conditions, and if you tinker with one component of the atmosphere — like carbon dioxide, for instance — it impacts the concentrations of other components. Scientists refer to this general process as feedback, and it’s one of the largest uncertainties in climate modeling.

The big advance of Manabe and Wetherald’s work was to model not just the feedbacks but the interrelationships between the different components that contribute to the Earth’s temperature. As the atmospheric contents change, so do both the absolute and relative humidity, which impacts cloud cover, water vapor content and cycling/convection of the atmosphere. What they found is that if you start with a stable initial state — roughly what Earth experienced for thousands of years prior to the start of the industrial revolution — you can tinker with one component (like CO2) and model how everything else evolves.

The title of their paper, Thermal Equilibrium of the Atmosphere with a Given Distribution of Relative Humidity (full download for free here), describes their big advances: they were able to quantify the interrelationships between various contributing factors to the atmosphere, including temperature/humidity variations, and how that impacts the equilibrium temperature of Earth. Their major result, from 1967?

According to our estimate, a doubling of the CO2 content in the atmosphere has the effect of raising the temperature of the atmosphere (whose relative humidity is fixed) by about 2 °C.

What we’ve seen from the pre-industrial revolution until today matches that extremely well. We haven’t doubled CO2, but we have increased it by about 50%. Temperatures, going back to the first measurements of accurate global temperatures in the 1880s, have increased by nearly (but not quite) 1 °C.