Earth’s energy budget and the greenhouse effect

How sunlight in balances infrared out in Earth's energy budget, why gases such as carbon dioxide, methane and water vapour absorb infrared, the natural and enhanced greenhouse effects, Earth's current energy imbalance, climate feedbacks and climate sensitivity, and the limits of the classic jar experiment.

In 1856 an American scientist named Eunice Foote put thermometers in glass cylinders filled with different gases and stood them in the sun. The one filled with carbon dioxide got the hottest, and stayed hot longest. She wrote: "An atmosphere of that gas would give to our earth a high temperature." Her paper was read out at a scientific meeting by a male colleague and then largely forgotten. Three years later the Irish physicist John Tyndall showed exactly why: carbon dioxide and water vapour absorb infrared radiation. The basic physics of climate change is older than the light bulb.

Earth's energy budget

Earth's temperature depends on a balance. Energy arrives as sunlight (mostly visible light) and leaves as infrared radiation (heat) given off by the warm surface and atmosphere. If more comes in than goes out, the planet warms until it radiates enough to balance; if less comes in, it cools.

Earth's average energy flows, in watts per square metre (after IPCC AR6). Notice how much infrared the atmosphere sends back down.

On average, 340 W of sunlight arrives on each square metre at the top of the atmosphere.
About 30% of it (100 W) is reflected straight back to space by clouds, ice, snow and bright ground. This fraction is Earth's albedo (0.3).
The rest is absorbed, mostly by the surface, and the warm surface radiates infrared.
Most of that infrared is absorbed by gases and clouds in the atmosphere, which radiate it in all directions, including back down to the surface. Eventually about 239 W leaves to space.

Without this "back radiation", Earth's average surface temperature would be about −18 °C. With it, the average is about 15 °C. That 33-degree difference is the natural greenhouse effect, and life depends on it.

Why some gases trap heat

Greenhouse gas molecules can vibrate in ways that absorb infrared. Nitrogen and oxygen can't.

Nitrogen (N₂) and oxygen (O₂), which make up 99% of dry air, are made of two identical atoms. When they vibrate, their electric charge stays evenly spread, so they can't absorb infrared. Molecules with three or more atoms, or with two different atoms, can bend and stretch in ways that shift their charge. When infrared of the right wavelength hits them, they absorb it, vibrate, and then re-emit it in a random direction or pass the energy to neighbouring molecules as heat. Sunlight, mostly visible light, passes through almost untouched.

Gas	Main human sources	Before 1750	About 2024	Warming per kg vs CO₂ (100 years)
Carbon dioxide (CO₂)	burning fossil fuels, clearing forests, cement	280 ppm	about 425 ppm	1
Methane (CH₄)	livestock, gas and coal leaks, landfill, rice	0.7 ppm	about 1.9 ppm	about 30
Nitrous oxide (N₂O)	nitrogen fertilisers, manure	0.27 ppm	about 0.34 ppm	about 270
Water vapour (H₂O)	controlled by temperature, not directly by people	varies from almost 0 to about 4%		acts as a feedback

Carbon dioxide is the most important gas people add, because we add so much of it and it lasts for centuries. Methane traps far more heat per kilogram but breaks down within about 12 years, so cutting methane is one of the quickest ways to slow warming.

The enhanced greenhouse effect

Adding greenhouse gases thickens the infrared "blanket". Less heat escapes, so the planet takes in more energy than it gives off until it warms enough to restore the balance. This is the enhanced greenhouse effect. Satellites measure that Earth is now gaining about 1 watt per square metre more than it loses, roughly double the imbalance in the mid-2000s. About 90% of that extra energy goes into the oceans, where it raises sea level as the water expands (7H).

It helps to keep four terms separate:

Greenhouse effect: the natural warming of Earth by gases that absorb infrared.
Enhanced greenhouse effect: the extra warming caused by greenhouse gases that people add.
Global warming: the rise in Earth's average surface temperature that results.
Climate change: the wider, long-term changes that follow: rainfall, ice, sea level, extremes and ecosystems.

Feedbacks and climate sensitivity

Two positive feedbacks that amplify warming.

On its own, doubling CO₂ would warm Earth by only a little over 1 °C, because a warmer planet radiates more heat (a strong negative feedback). But the warming triggers positive feedbacks:

Water vapour: warmer air holds about 7% more water vapour for every degree, and water vapour is itself a greenhouse gas.
Ice–albedo: melting snow and sea ice expose darker land and ocean, which absorb more sunlight.
Clouds: the most uncertain feedback, but the evidence now points to clouds amplifying warming slightly overall.
Carbon cycle: thawing permafrost releases methane and CO₂, and warmer oceans absorb less CO₂.

The total warming after CO₂ doubles and the climate settles is called the climate sensitivity. The IPCC's 2021 report gives a best estimate of 3 °C, very likely between 2 and 5 °C.

InteractiveRun Earth's energy budget

Try this

Press Double with all feedbacks on. How much warmer does Earth become? Now turn off all three feedbacks. What is the difference?
Which single feedback adds the most warming?
Set CO₂ to 180 ppm and add the ice-age ice sheets. How much colder is the planet? Does that match what you know about the last ice age?
Press Today. Why is the warming shown bigger than the 1.3 °C measured so far?

Investigation: testing the jar model

Aim: to test a common classroom model of the greenhouse effect and judge its limitations.

Method: Set up two identical clear plastic bottles, each with a thermometer or temperature probe sealed through the lid. Fill one with air and the other with carbon dioxide made by reacting bicarbonate of soda with vinegar in a separate container and pouring the gas in. Place both the same distance from a lamp, and record the temperature every minute for 15 minutes, then for 10 minutes after the lamp is switched off.

Expected result: the CO₂ bottle usually warms a little faster and cools more slowly.

Evaluate: the effect is real but this model is weak evidence. Plastic and glass walls block much of the infrared anyway (that is how a real glasshouse works: mainly by stopping warm air escaping). CO₂ is also denser and has a different heat capacity from air, and the bottles hold almost 100% CO₂ instead of 0.04%. The real greenhouse effect happens through kilometres of open atmosphere, which is why scientists rely on satellite and laboratory measurements of infrared absorption instead.

Test yourself

Nitrogen and oxygen are not greenhouse gases because
About 30% of incoming sunlight is reflected to space. This fraction is called Earth's
Melting sea ice causing more warming is an example of
Most of the extra heat trapped by greenhouse gases has gone into

Label Earth's energy flows.

Sort the gases.

Earth gives off energy as radiation. Without the natural greenhouse effect, the average temperature would be about −18 °C instead of °C. A change that amplifies itself is a positive . The warming expected when CO₂ doubles is called the climate . The gas with about 30 times the warming effect of CO₂ per kilogram is .

5 marks

Distinguish between the greenhouse effect, the enhanced greenhouse effect and global warming, and explain how the water vapour feedback affects the amount of warming.

Your answer