In the previous sections we have seen that most of the survey techniques that can be used underwater rely on being able to measure distances and depths. All distance and depth measurements have errors. This section explains these errors, why some survey techniques are more accurate than others and why we take check measurements. The ideas in this section are based on statistics so if it gets a bit complicated then skip to the next section and come back here later.

There are three types of errors; mistakes, systematic errors and random errors.

The procedures we use for making measurements and then processing them to form a site plan should aim to remove mistakes and systematic errors. We cannot remove the effects of random error but we can ensure that they are kept within acceptable limits.

There are two ways of getting rid of mistakes, avoid making them or find them during processing. It is usually better to avoid making mistakes at all, finding mistakes in processing means a repeat measurement must be made and having to repeat work is expensive.

If there is no independent check on the position of a point then there may well be a mistake in one of the measurements and the position will be wrong. Finding mistakes that have been made is done using check measurements. To find the position of a point in three dimensions needs three measurements, any extra measurements can be used as a check on the other three. Extra measurements are called redundant measurements. Making extra redundant measurements takes time so a balance is needed between making the check measurements and minimising on work. The simple rule is that each point should have at least one check measurement for detail work, for positioning the control points at least two should be used.

Systematic errors in tape and depth measurements can be found by calibrating the tape measures and depth sensors against a known standard.

We have said that all measurements have random errors and the size of the random error can vary, but how does that affect our underwater survey?

Calculating the position of a point is in fact only half of the problem, in surveying it is also important to work out how well you know the position. Giving a value for the quality of the position is similar to saying 'the point is here, plus or minus X metres'. What we need to work out is the size of the plus or minus X value. If we do not do this then the plus or minus number could be small or very large and you would not know, this makes the position of the point meaningless if we are trying to do accurate work.

If the measurements used to position a point have small random errors, or are precise, then the position error for a point will also be small. This is the reason why techniques using angles to record positions underwater are used for assessment surveys or for small areas. The precision of a tape measure is much smaller than that of an angle measurement made with a divers compass.

A problem also arises if you make extra, redundant measurements as a check on position. Because of the random errors the measurements will never fit together to give a position at a single point, lots of positions can be calculated using different selections of the measurements in the set. It is not possible to calculate the true position for the point so we must find the most likely or most probable position using some maths.

If we go back to our set of tape measurements it happens that the most probable value for the true measurement is the average or mean value. If we take each measurement in turn and compare it with the average value, the difference between them is called the residual.

Now if we want to compute the position of a point using lots of measurements, not just the minimum three required, we can use a technique called Least Squares to tell us the most probable position. In short, the most probable position is the one where the sum of the squares of the residuals is the smallest. In that position, you add together the residual for each measurement ignoring the sign and the total will be smaller than that for any other position.

Least Squares is also used in setting up control and in Direct Survey Measurement (DSM) to deal with the direct tape measurements between points that are so difficult to plot by hand. All you have to do is to type in the measurements into a computer program and the least squares turns them into positions for points. Least squares produces a single solution no matter how many measurements are used, the type of measurements or how they were collected. The technique also tells you how well the measurements fit together so least squares can be used to help find mistakes.

We may also need to find an answer using measurements with different precision, fortunately least squares can do this as well.