How strongly is global temperature linked to ln(CO₂)?

AI SLAI HLAA SLAA HL Ambitious Also in: Statistics, Modelling

Research question

How well does a linear model of global temperature anomaly against the natural logarithm of CO₂ concentration fit the data since 1959, and what warming per doubling of CO₂ does the fitted gradient imply?

Adapt it: change the place, the data or the comparison until the question is yours.

Why it makes a good exploration

Physics predicts warming proportional to the logarithm of CO₂, so a regression of temperature on ln(CO₂) has a meaningful gradient. Estimating it from NASA and NOAA data — and discussing why it is not the full climate sensitivity — is a mature, rigorous IA.

The mathematics you'll need

Logarithmic transformation and why it is expected
Linear regression and correlation
Converting a gradient to warming per doubling (× ln 2)
Residuals and the role of natural variability

Course labels show where a technique sits; using maths from outside your course is fine if you explain it clearly and say it is new to you.

Where the data comes from

Annual global temperature anomalies from NASA GISTEMP and annual mean CO₂ from NOAA GML.

NASA GISTEMP v4 — Global and hemispheric temperature anomalies from 1880, monthly and annual, CSV.
NOAA Global Monitoring Laboratory — Mauna Loa CO₂ — Monthly and annual mean atmospheric CO₂ since 1958 (the Keeling curve), CSV.

Cite every source in a footnote where you use it and in your bibliography. Check the licence of any dataset you download.

A possible outline

Explain why ln(CO₂) rather than CO₂.
Merge the two annual series.
Fit and interpret the regression.
Compute the implied warming per doubling.
Reflect: lag, other gases, aerosols, El Niño years, correlation vs causation.

Pitfalls that cost marks

Presenting the gradient as climate sensitivity without qualification.
Using mismatched years.
Ignoring autocorrelation in residuals (explain it simply).

Showing personal engagement

Compare your estimate with published ranges (cite them).
Identify outlier years and explain them.
Discuss how you would communicate the result responsibly.

See Criterion C: personal engagement for what examiners look for.

Taking it further

Add a one-year lag or an El Niño indicator and compare the fit.

Turn this idea into your IA

Plan this IAOpens the planner with this question, the maths and data sources filled in. Desmos workspacePlot your data, fit models and keep your graphs with your plan. AI feedback on a draftCriterion-by-criterion feedback with evidence from your own text. Coaching, not rewriting. Examiner reviewPete, a practising IA examiner, reads your draft and talks it through with you (€100).