This is a note to the decision tree.

(after Wikipedia, 2005a) A residual is an observable estimate of the unobservable error. The simplest case involves a random sample of n men whose heights are measured. The sample average is used as an estimate of the population average. Then we have:

• The difference between the height of each man in the sample and the unobservable population average is an error, and

• The difference between the height of each man in the sample and the observable sample average is a residual.

Residuals are observable; errors are not. http://en.wikipedia.org/wiki/Residuals

The model residuals can be explained by for example simple distributions such as the normal distribution. Most residual structures are more complicated and cannot be easily approximated.

In general we would argue that most environmental models have a complicated residual structure which can rarely be approximated in advance or indeed after the analysis.