Can a sum of sine waves predict the tides?

AA SLAA HLAI SLAI HL Solid Also in: Modelling

Research question

How accurately can tide heights at [a harbour] be predicted by one sinusoid with a period of about 12.42 hours, and how much does adding a second component with a period of about 12 hours improve the model?

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

Why it makes a good exploration

Tides are caused by the Moon and Sun, whose periods differ slightly, producing spring and neap tides. Building a model from sine waves and testing it against six-minute measurements is modelling at its most satisfying.

The mathematics you'll need

Sinusoidal functions and parameters
Sum of sinusoids and beats
Fitting with technology; residuals
Predicting future tides and measuring error

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 water levels from NOAA Tides & Currents for a station (or your national tide authority).

NOAA Tides & Currents — Water levels every 6 minutes at hundreds of stations, CSV download.

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 lunar (M2) and solar (S2) tides.
Fit one sinusoid to a week of data.
Add the second component and compare.
Predict the next week.
Reflect on weather surges and local geography.

Pitfalls that cost marks

Choosing the period by eye without justification.
Fitting too short a window.
Ignoring datum definitions.

Showing personal engagement

Choose a harbour you have visited.
Predict a spring tide and check.
Explain the beat period of about 14.8 days.

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

Taking it further

Add the diurnal components and compare with the official tide prediction.

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).