1.1 Statistics

The observational description of how environmental variables change in time is always limited by the fact that the period of observations is limited to some finite period, and does not necessarily represent the full spectrum of variability. Statistics is the method of choice to deal with such issues and determine to the extent possible whether the observations are representative. This mens that for every estimate made of a property such as the mean value of the variable, there has to be an estimate of the possible error in that estimate. Very often this process entails extracting from the observations some measure of the dominant period of variability, , sometimes estimated as the auto-correlation time. If it is then assumed that periods of observation that are separated by longer than represent different realizations of the process, then the degrees of freedom of the observation can be thought of as the ration of the observation time to .