The Interpretation of Short Climate Records, with Comments on the North Atlantic and Southern Oscillations

The intense interest in possible climate change has led to increasing scrutiny of relatively long time series for indications of secular trends in climate indicators. Changes in mean levels of simple fields such as temperature, or shifts in the apparent return times (or oscillation periods) of various phenomena such as the El Niño–Southern Oscillation (ENSO) or the North Atlantic oscillation (NAO), have all been discussed. But purely random processes, particularly those that have even mildly “red” spectra, have a behavior that comes as a surprise to many, and there is great risk of misinterpretation. That is, the purely random behavior of a rigorously stationary process often appears visually interesting, particularly over brief time intervals, and creates the temptation to interpret it as arising from specific and exciting deterministic causes. The issue is related to the often unintuitive behavior of systems undergoing random walk (e.g., Feller 1957; Hasselmann 1977; Frankignoul and Hasselmann 1977; Wunsch 1992). There is nothing here that will be regarded as new by practitioners of time series analysis in a wide geophysical context (this paper started out as a classroom note). My intention is to simply introduce a bit of caution into an important discussion of the behavior of climate signals. In what follows, I explore some of the behavior of the simplest of all time series, those that have a normal probability density and are stationary (i.e., having statistics that do not change in time). Here “wide-sense stationarity,” requiring only that the first and second moments be time independent, is adequate. Climate surely exhibits nonstationary, nonlinear/ nonnormal behavior, but one should be very careful The Interpretation of Short Climate Records, with Comments on the North Atlantic and Southern Oscillations