Overview. In this chapter we review several additional topics that are important in atmospheric, oceanic or other geo-environmental sciences. These topics are as follows.

In Section 17.1 we discuss the ‘decorrelation time’, a concept that is often misunderstood, because of its confusing name. The term suggests that it is a physical time scale that represents the interval between consecutive, uncorrelated observations. In fact, it is a statistical measure that compares the information content of correlated observations with that of uncorrelated observations. If a sample of n′ uncorrelated observations gives a particular amount of information about the population mean then n = n′ × ‘decorrelation time’ is the number of correlated observations required to obtain the same amount of information about the population mean. Similarly, other ‘decorrelation times’ can be derived for other parameters such as the population variance or the lag-1 correlation (cf. Trenberth [368]) by comparing the information contained about the parameters in samples of independent and dependent observations. Not only is the nomenclature confusing, but its meaning is highly dependent upon the parameter of interest.

We describe a concept called potential predictability in Section 17.2. Measures of potential predictability determine whether the variation in seasonal mean climate variables is caused by anything other than daily weather variations. If seasonal means have more variance than can be accounted for by weather noise, then part of the seasonal mean variance may be predictable from slowly varying external sources.