Climate Science: evidence and models

01

Earth's energy budget: what comes in, what goes out

In simple words

Earth is like a bathtub with the tap on and the drain open. Sunlight pours energy in, and Earth lets heat out to space. If the drain is partly blocked, the water level (the temperature) rises until the outflow matches the inflow again. Greenhouse gases partly block the drain.

Before this course: Weather & Climate Data: analysis (course 15.6.2). You should be able to find official climate data, calculate means and anomalies, name your baseline, draw a trend line and spot cherry-picking. You also know the greenhouse effect idea from course 15.6. Now we look at why the climate changes and how scientists test their explanations.

Key facts

Incoming sunlight: the solar irradiance at Earth is about 1361 W/m² (watts per square metre) (NASA Earth Fact Sheet).
Reflected: Earth's Bond albedo (the share of sunlight reflected back to space) is 0.294 (NASA).
Balance temperature: if Earth had no greenhouse effect, it would settle where outgoing heat equals absorbed sunlight. NASA lists Earth's black-body temperature as 254 K (about -19 °C). Earth's actual average surface temperature is 288 K (15 °C) (NASA). The difference, about 33 to 34 °C, is the warming from the natural greenhouse effect.
Check the maths yourself (Python): absorbed sunlight = 1361 x (1 - 0.294) / 4 = 240 W/m². (Divide by 4 because sunlight hits one disc but Earth's whole sphere radiates.) The Stefan-Boltzmann law, energy = 5.67 x 10⁻⁸ x T⁴, gives T = about 255 K, close to NASA's 254 K.
Greenhouse gases in the atmosphere include carbon dioxide (CO₂, listed as 420 ppm on NASA's fact sheet), methane and water vapour (about 1%, highly variable) (NASA).
Energy imbalance: WMO reported in 2026 that Earth's energy imbalance has increased since its observational record began in 1960 (WMO, State of the Global Climate 2025).

Example (practice, checked with Python)

Albedo	Balance temperature
0.28	256.4 K
0.29	255.5 K
0.30	254.6 K
0.31	253.7 K

A change of 0.01 in albedo moves the balance temperature by about 0.9 K. Small changes in reflection (ice, clouds) matter.

Step by step

Write the numbers: S = 1361 W/m², albedo = 0.294, σ = 5.67 x 10⁻⁸.
Calculate absorbed energy: 1361 x (1 - 0.294) / 4.
Divide your answer by σ.
Take the fourth root (square root twice on a calculator).
Subtract 273.15 to get °C.
Compare with Earth's real average of 15 °C and write the difference.
Check: you get about 255 K (about -18 °C) and a gap of about 33 °C.

Watch on YouTube

Why does the Sun matter for Earth's energy budget?NASA Goddard · YouTube · youtube.com

Videos by other creators on YouTube, for reference. They are not made by or affiliated with The Future Market.

LESSON 01Earth's energy budget: what comes in, what goes out

LESSON 01 / ANIMATED LESSON / AI VOICE00:00 / 01:15

Voice

Read the video script

[Host next to a bathtub with the tap running] "Energy in, energy out. That is the whole climate in one sentence."
[Text on screen: 1361 W/m², 29% reflected] "The Sun delivers about 1361 watts per square metre. About 29 percent bounces straight back."
[Text on screen: no greenhouse effect: about -18 °C] "Without a greenhouse effect, the maths says Earth would sit near minus 18 degrees."
[Text on screen: real average: 15 °C] "The real average is about 15. The natural greenhouse effect makes the difference."
[Host] "Add more greenhouse gas and the drain gets smaller. The level has to rise."

Try it now

Use the formula to calculate the balance temperature for albedo 0.25 and 0.35. Write which one could describe an Earth with much more ice, and why. Then explain in two sentences why Earth's real surface is warmer than the balance temperature.

ClaudeStuck? Copy a ready-made prompt for Claude

Copy this, open Claude, paste it, and Claude will walk you through the lesson step by step.

For a grown-up: Claude is for adults (18+). Copy this, paste it into Claude, and use the answer to explain the lesson to your child.

I'm learning "Climate Science: evidence and models" on The Future Market. Lesson 1: "Earth's energy budget: what comes in, what goes out".

What the lesson teaches:
- Incoming sunlight: the solar irradiance at Earth is about 1361 W/m² (watts per square metre) (NASA Earth Fact Sheet).
- Reflected: Earth's Bond albedo (the share of sunlight reflected back to space) is 0.294 (NASA).
- Balance temperature: if Earth had no greenhouse effect, it would settle where outgoing heat equals absorbed sunlight. NASA lists Earth's black-body temperature as 254 K (about -19 °C). Earth's actual average surface temperature is 288 K (15 °C) (NASA). The difference, about 33 to 34 °C, is the warming from the natural greenhouse effect.
- Check the maths yourself (Python): absorbed sunlight = 1361 x (1 - 0.294) / 4 = 240 W/m². (Divide by 4 because sunlight hits one disc but Earth's whole sphere radiates.) The Stefan-Boltzmann law, energy = 5.67 x 10⁻⁸ x T⁴, gives T = about 255 K, close to NASA's 254 K.
- Greenhouse gases in the atmosphere include carbon dioxide (CO₂, listed as 420 ppm on NASA's fact sheet), methane and water vapour (about 1%, highly variable) (NASA).
- Energy imbalance: WMO reported in 2026 that Earth's energy imbalance has increased since its observational record began in 1960 (WMO, State of the Global Climate 2025).

The exercise I'm working on:
Use the formula to calculate the balance temperature for albedo 0.25 and 0.35. Write which one could describe an Earth with much more ice, and why. Then explain in two sentences why Earth's real surface is warmer than the balance temperature.

I'm stuck. Please:
1. Explain the main idea in plain, simple words with one everyday example.
2. Walk me through the exercise one small step at a time. Ask me what I've done so far before giving the next step.
3. Don't just give me the final answer. Help me do it myself, and check my work when I share it.

I'm a parent helping my child (about 8 years old) with a lesson called "Earth's energy budget: what comes in, what goes out" from the course "Climate Science: evidence and models".

Here's what the lesson says:
Earth is like a bathtub with the tap on and the drain open. Sunlight pours energy in, and Earth lets heat out to space. If the drain is partly blocked, the water level (the temperature) rises until the outflow matches the inflow again. Greenhouse gases partly block the drain.

The activity:
Use the formula to calculate the balance temperature for albedo 0.25 and 0.35. Write which one could describe an Earth with much more ice, and why. Then explain in two sentences why Earth's real surface is warmer than the balance temperature.

Please explain this so an 8-year-old understands: short sentences, a fun everyday example, and no hard words.
Then give me 3 simple questions I can ask my child to check they understood, and a way to do the activity together, one tiny step at a time.

Open Claude

Sources

NASA, Earth Fact Sheet (solar irradiance, albedo, black-body and mean temperature, CO₂ 420 ppm): nssdc.gsfc.nasa.gov/planetary/factsheet/earthfact.html
WMO, Earth's climate swings increasingly out of balance (23 March 2026): wmo.int/news/media-centre/earths-climate-swings-increasingly-out-of-ba

My notes

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02