23 - Tides

Summary

Aims of the project

You are given data consisting of a series of tidal measurements taken over some period of time and are required to analyse these, draw some conclusions and make some predictions. Specifically, the data are the measured heights (in metres) of the sea level taken at the given equally spaced times (in hours) at a fixed place. You are asked to find such things as the mean sea level, mean tidal range, mean period between high tides, estimated sea level at particular time on a particular day etc. The times given, are with respect to 0 : 00 hours on 1 January 1992.

Mathematical ideas used

Since tidal effects are clearly periodic in nature, you are given some assistance in learning about Fourier series and their application.

MATLAB techniques used

There are a number of built-in MATLAB routines which can be used to help with Fourier analysis and manipulating vectors of data:

fourier – demo of Fourier series for square wave;

fftdemo – demo of FFT for signal analysis;

fft – Fourier transform;

ifft – inverse Fourier transform;

spline – interpolation of data points;

mean – mean of data;

max – maximum of data.

In addition to these standard procedures, the following M-files are provided for this project. You may have to modify some of these in the course of your study. In each case typing help gives some information on the purpose and usage.