By Ethan Siegel
15 March 2017
(Forbes) – Modeling the Earth's climate is one of the most daunting, complicated tasks out there. If only we were more like the Moon, things would be easy. The Moon has no atmosphere, no oceans, no icecaps, no seasons, and no complicated flora and fauna to get in the way of simple radiative physics. No wonder it's so challenging to model! In fact, if you google “climate models wrong“, eight of the first ten results showcase failure. But headlines are never as reliable as going to the scientific source itself, and the ultimate source, in this case, is the first accurate climate model ever: by Syukuro Manabe and Richard T. Wetherald. 50 years after their groundbreaking 1967 paper, the science can be robustly evaluated, and they got almost everything exactly right.
If there were no atmosphere on Earth, calculating the climate would be easy. The Sun emits radiation, the Earth absorbs some of the incident radiation and reflects the rest, then the Earth re-radiates away that energy. Temperatures would be easily calculable based on albedo (i.e., reflectivity), the angle of the surface to the Sun, the length/duration of the day, and the efficiency of how it re-radiates that energy. If we were to strip the atmosphere away entirely, our planet’s typical temperature would be 255 Kelvin (-18 °C / 0 °F), which is most definitely colder than what we observe. In fact, it's about 33 °C (59 °F) colder than what we see, and what we need to account for that difference is an accurate climate model.
The number one contributor, by far, to this difference? The atmosphere. This “blanket-like” effect of the gases in our atmosphere was first discovered nearly two centuries ago by Joseph Fourier and worked out in detail by Svante Arrhenius in 1896. Each of the gases present has some amount of absorptive effects in the infrared portion of the spectrum, which is the portion where Earth re-radiates most of its energy. Nitrogen and oxygen are terrible absorbers, but good ones include water vapor, methane, nitrous oxide, ozone, and carbon dioxide. When we add (or take away) more of those gases from our planet’s atmosphere, it’s like thickening (or thinning) the blanket that the planet wears. This, too, was worked out by Arrhenius over 100 years ago.
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. [more]
ABSTRACT: Radiative convective equilibrium of the atmosphere with a given distribution of relative humidity is computed as the asymptotic state of an initial value problem.
The results show that it takes almost twice as long to reach the state of radiative convective equilibrium for the atmosphere with a given distribution of relative humidity than for the atmosphere with a given distribution of absolute humidity.
Also, the surface equilibrium temperature of the former is almost twice as sensitive to change of various factors such as solar constant, CO2 content, O3 content, and cloudiness, than that of the latter, due to the adjustment of water vapor content to the temperature variation of the atmosphere.
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 2C. Our model does not have the extreme sensitivity of atmospheric temperature to changes of CO2 content which was adduced by Möller.