Modelling the Keeling curve: trend plus seasons

AA SLAA HLAI SLAI HL Solid Also in: Modelling

Research question

Can monthly Mauna Loa CO₂ be modelled as a smooth trend (quadratic or exponential) plus a sine wave with a one-year period, and how well does a model fitted to 1960–2010 predict the last decade?

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

Why it makes a good exploration

The Keeling curve rises and wiggles: the wiggle is the Northern Hemisphere's plants breathing. Separating the two parts is a proper modelling problem with world-class data, and testing predictions on recent years keeps it honest.

The mathematics you'll need

Polynomial and exponential trend models
Sinusoidal functions: amplitude, period, phase
Fitting a combined model (subtract the trend, then fit the residuals)
Out-of-sample testing and residual analysis

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

Download monthly mean CO₂ at Mauna Loa from NOAA GML.

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 the two processes behind the curve.
Fit trend models to 1960–2010 and compare.
Fit a sinusoid to the detrended data.
Predict 2011–present and measure the error.
Reflect on why the trend model may not hold into the future.

Pitfalls that cost marks

Fitting everything at once with no explanation.
Using a period other than 12 months without justification.
Treating a good fit as proof of a mechanism.

Showing personal engagement

Explain why the seasonal amplitude is larger in the north.
Compare with a Southern Hemisphere station.
Predict when 450 ppm will be passed and state your uncertainty.

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

Taking it further

Test whether the seasonal amplitude itself has changed over time.

Turn this idea into your IA

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