D. Earth and Space Science: Climate Change · Climate Change

Testing a Climate Hypothesis: Fossil Fuels, CO₂ and Temperature

D2.4 A1.1 A1.8 A1.10 A1.12 A1.13About 75 minutes

Learning goals

I can turn a popular claim about climate change into a testable hypothesis and predictions.
I can graph and analyse time-trend data, including a scatter plot, a line of best fit and a rate of change.
I can explain the difference between correlation and causation, and what evidence supports a cause-and-effect conclusion.
I can use a climate simulation to test predictions.
I can draw and justify a conclusion, and describe its limitations.

Words to know

hypothesis
A testable explanation, often written as "If ..., then ..., because ...".

prediction
What should be observed if the hypothesis is correct.

time-trend data
Measurements of a variable taken over time, showing how it changes.

temperature anomaly
The difference between a temperature and a long-term average (baseline).

correlation
A relationship in which two variables change together.

causation
When a change in one variable actually produces a change in another.

line of best fit
A straight line that best represents the trend in a scatter plot.

simulation
A computer model that uses mathematical rules to imitate a real system, used to test "what if" questions.

Let's start with a claim

You've heard it many times: "Burning fossil fuels is causing global warming." It's a popular statement, but in science, popularity isn't evidence. How would you test it?

In this lesson you'll act like a climate scientist: turn the claim into a hypothesis, make predictions, analyse real data, consider other explanations, and test your ideas with a simulation. The same steps work for any cause-and-effect claim.

Step 1: A testable hypothesis and predictions

Hypothesis: If humans burn more fossil fuels, then the concentration of CO₂ in the atmosphere will rise, and global average temperature will rise, because CO₂ absorbs infrared radiation and strengthens the greenhouse effect.

Predictions (what we should see if the hypothesis is right):

CO₂ concentration should rise as fossil fuel use rises.
Global temperature should rise as CO₂ rises (allowing for natural ups and downs).
The extra CO₂ should carry the chemical fingerprint of fossil fuels.
Other possible causes (the Sun, volcanoes) should not explain the warming.
The pattern of warming should match what greenhouse gases produce.

Testing a cause-and-effect hypothesis takes more than one graph. Scientists look for a correlation, a physical mechanism, a match in timing, and evidence that other explanations don't fit, then test it all with simulations.

Step 2: Look at the time-trend data

Charles David Keeling began measuring CO₂ on Mauna Loa, Hawaii, in 1958, far from local pollution. His record, continued today, is called the Keeling Curve. Global temperatures come from thousands of weather stations, ships and buoys, combined by agencies such as NASA, NOAA, the UK Met Office and others. All the major datasets agree closely.

Here are rounded values every ten years (CO₂: annual mean at Mauna Loa; temperature: anomaly compared with the 1951–1980 average, from NASA's record):

Year	CO₂ (ppm)	Temperature anomaly (°C)
1960	317	−0.03
1970	326	+0.03
1980	339	+0.26
1990	354	+0.45
2000	370	+0.39
2010	390	+0.72
2020	414	+1.01

Values are rounded and approximate. For comparison: CO₂ averaged about 425 ppm in 2024, and 2024 was the warmest year on record, about 1.5 °C above the late-1800s average.

Rounded values every ten years: CO₂ measured at Mauna Loa, Hawaii (top) and the global average temperature anomaly compared with the 1951–1980 average (bottom). Both rise, though temperature bounces around more from year to year.

Worked example

Example 1: Rates of change

Use the table to find the average rate of increase of CO₂ in ppm per year (a) from 1960 to 1990 and (b) from 1990 to 2020. Then find the rate of temperature change from 1960 to 2020 in °C per decade.

(a) (354 − 317) ÷ (1990 − 1960) = 37 ÷ 30 ≈ 1.2 ppm per year.
(b) (414 − 354) ÷ 30 = 60 ÷ 30 = 2.0 ppm per year.
CO₂ is not just rising; it is rising faster (the curve bends upward), matching the growth in fossil fuel use.
Temperature: (1.01 − (−0.03)) ÷ 6 decades = 1.04 ÷ 6 ≈ 0.17 °C per decade.

CO₂ rose about 1.2 ppm/yr (1960–1990) and 2.0 ppm/yr (1990–2020); temperature rose about 0.17 °C per decade.

Step 3: Scatter plot, line of best fit and correlation

To check prediction 2 directly, plot temperature (dependent variable, y) against CO₂ (independent variable, x). If the points fall close to a line, the variables are correlated.

The correlation coefficient (r) measures how closely points fit a straight line: r = 1 is a perfect positive fit, r = 0 is no linear relationship. You may have calculated r with technology in Grade 9 math.

A scatter plot of the same seven points, with temperature against CO₂. The points lie close to a straight line (strong positive correlation). The point for 2000 sits below the line because of natural year-to-year variability.

Worked example

Example 2: Using the line of best fit

For the scatter plot, a spreadsheet gives the line of best fit T ≈ 0.0103 × CO₂ − 3.30, with r ≈ 0.98. (a) Interpret the slope. (b) Use the line to estimate the anomaly at 425 ppm. (c) Is it reasonable to use this line to predict the temperature at 800 ppm?

(a) The slope means that, over this period, each extra 1 ppm of CO₂ went with about 0.01 °C of warming, or about 1 °C per 100 ppm.
(b) T ≈ 0.0103 × 425 − 3.30 = 4.378 − 3.30 ≈ 1.08 °C. (The actual 2024 anomaly was a bit higher, about 1.3 °C, partly because of El Niño, a reminder that one year can differ from the trend.)
(c) No. 800 ppm is far outside the range of the data (this would be extrapolation). The real relationship isn't exactly linear, the ocean takes decades to warm up fully, and feedbacks may change. Predictions that far out need physics-based climate models, not a straight line.

Slope ≈ 0.01 °C per ppm; estimate ≈ 1.1 °C at 425 ppm; don't extrapolate to 800 ppm with this line.

Step 4: Correlation is not causation

A strong correlation alone doesn't prove one thing causes another. Ice cream sales and drownings both rise in summer, but ice cream doesn't cause drowning: hot weather causes both. To claim causation, scientists look for several kinds of evidence together:

A mechanism: a physical explanation of how one causes the other. Laboratory physics, known since the 1800s, shows that CO₂ absorbs infrared (Lesson 7).
The right timing: the cause comes first. Fossil fuel use rose, then CO₂ rose, then temperature.
Fingerprints: the extra CO₂ has the isotope signature of fossil carbon; oxygen in the air is decreasing slightly, as expected from burning; the stratosphere is cooling while the lower atmosphere warms.
Alternatives ruled out: solar output has been flat or slightly declining since the 1950s, volcanic eruptions cause only short cooling, and orbital cycles are far too slow (Lesson 9).
Consistency: the same result appears in many independent datasets and studies.

When all of these line up, scientists can conclude causation with high confidence. That's why the IPCC concluded that it is unequivocal that human influence has warmed the atmosphere, ocean and land.

Step 5: Simulations

Scientists can't run a controlled experiment on a second Earth. Instead, they build climate models: computer simulations based on physics (energy balance, fluid flow, radiation) that divide the atmosphere and ocean into millions of boxes. They run the model twice:

With natural factors only (the Sun and volcanoes): the simulated temperature stays roughly flat since the mid-1900s.
With natural and human factors: the simulated temperature rises in line with observations.

Only the second matches what really happened. Early climate models from the 1970s and 1980s projected the warming of the following decades reasonably well, which is evidence that the physics in them is sound.

You can try simplified, free online simulations, such as En-ROADS (from Climate Interactive and the MIT Sloan School of Management), which lets you change emissions policies and see projected warming, or the PhET "Greenhouse Effect" simulation (University of Colorado).

Just for fun

The Keeling Curve wiggles up and down every single year, as if the planet were breathing. Each northern spring and summer, forests and fields soak up CO₂ and the level dips; each fall and winter, decay wins and it rises again. The Northern Hemisphere has much more land (and many more plants) than the Southern, so its seasons set the rhythm. Earth breathes in time with the northern seasons.

Hands-on activity

Run your own hypothesis test with data and a simulation (A1.1, A1.8, A1.10, A1.12, A1.13)

You need: graph paper or a spreadsheet (or Desmos), the data table in this lesson, internet access with a grown-up's OK.

Part 1: Analyse the data

Make two time-series graphs (CO₂ vs year; temperature anomaly vs year) with titles, labelled axes and units.
Make a scatter plot of temperature anomaly (y) against CO₂ (x). Draw a line of best fit by eye, or use technology to find it and r.
Calculate the slope of your line in °C per ppm. Express it with an appropriate number of significant digits (2 is plenty).
Find one point that sits far from the line. Suggest a natural reason (El Niño, La Niña, a volcanic eruption).

Part 2: Test with a simulation

Open a climate policy simulator such as En-ROADS.
Record the projected warming in 2100 for the starting (baseline) scenario.
Write a hypothesis of your own about one policy (for example, "If coal use is greatly reduced, then projected 2100 warming will decrease, because less CO₂ will be emitted").
Change only that one setting and record the new projected warming. Then test a second policy separately.
Conclude: do the results support your hypotheses? Which policies had the biggest effect? What are the limitations of a simulation?

What to look for: correct graphs, a sensible slope (about 0.01 °C per ppm), a clear distinction between correlation and causation, and a conclusion that is justified by evidence and names limitations (simplified model, uncertain future choices, assumptions built into the model).

Your turn

Write the claim "burning fossil fuels causes warming" as a hypothesis in "If ..., then ..., because ..." form.

What is a temperature anomaly?

Calculate the average rate of CO₂ increase from 1980 to 2010 using the table.

The temperature anomaly in 2000 (0.39 °C) was lower than in 1990 (0.45 °C). Does this disprove the hypothesis? Explain.

Give an example of two things that are correlated but where one doesn't cause the other.

Name three kinds of evidence, besides correlation, that support the conclusion that fossil fuels cause warming.

Why do scientists use simulations to test climate hypotheses?

More practice: warm-up

Who started the Mauna Loa CO₂ record, and when?

What does r = 0.98 tell you about a scatter plot?

In a temperature vs CO₂ scatter plot, which variable goes on the x-axis?

What is it called when you predict far outside the range of your data?

Name one free online climate simulation.

More practice: on your own

Using the slope 0.0103 °C per ppm, how much warming is associated with the rise from 280 ppm (pre-industrial) to 420 ppm? Compare with the observed warming of roughly 1.3 °C, and suggest a reason for any difference.

Explain why the CO₂ rate of increase from 1990 to 2020 (2.0 ppm/yr) being larger than from 1960 to 1990 (1.2 ppm/yr) supports the hypothesis.

A student plots number of cars in Canada against global temperature and finds r = 0.95. Does this prove cars cause global warming? Explain.

Describe how a climate model test can distinguish natural from human causes.

Give two limitations of the data table used in this lesson.

Challenge

CO₂'s warming effect grows roughly with the logarithm of its concentration: each doubling adds about the same warming. Explain why this means the linear fit in this lesson may over- or under-estimate future warming, and why scientists rely on physics-based models instead.

A popular claim is that "the warming is caused by the Sun". Turn it into a testable hypothesis, give two predictions, and use evidence from this unit to evaluate it.

Design an investigation to test the hypothesis "Cities are warmer than the surrounding countryside" (the urban heat island). Include variables, data collection and how you would analyse the data.

Check your understanding

Quiz

Which statement is a testable hypothesis?

CO₂ was 354 ppm in 1990 and 414 ppm in 2020. What was the average rate of increase?

A correlation coefficient of r = 0.98 means...

Which evidence shows a mechanism for CO₂ causing warming?

Why can't we simply extend the line of best fit to predict temperature at 800 ppm?

In climate model tests, which runs match the observed warming since the mid-1900s?

For parents and teachers

Big idea: A popular cause-and-effect claim (burning fossil fuels causes warming) can be tested like any hypothesis: make predictions, analyse time-trend data, look for a mechanism and fingerprints, rule out alternatives, and test with simulations. This covers D2.4 and many investigation skills (A1.1, A1.8, A1.10, A1.12, A1.13).

How to help: A spreadsheet or Desmos makes the scatter plot and line of best fit easy. Try En-ROADS together and talk about which policies make the biggest difference and why. Ask your teen to explain the difference between correlation and causation with an everyday example.

Common difficulties:

Thinking one cool year disproves a trend.
Treating correlation as proof of causation, or dismissing a cause because "correlation isn't causation" without looking at the other evidence.
Extrapolating a straight line far beyond the data.

The data table uses rounded values; exact values differ slightly between datasets and updates.