A mathematical framework is presented for the study of the predictability of small changes in the climatic system. From a statistical definition of climate in terms of ensemble averages, a limit to predictability is found arising from random weather fluctuations. This limit, typically referred to as climate noise, is often able to obscure a possible climate signal produced by external forcing. A separation of timescales of climatic response is also presented as a convenient means to distinguish between the fast internal (for example, the atmosphere) and the slow external (for example, the oceans) systems. In this way, it is possible to estimate the climate signal in the internal system that arises from small changes in the slow external system. Finally, a theoretical approach is presented for the inclusion of possible feedback effects in the estimation of a climate signal. Such feedback effects could result from the external climatic system being influenced by a change in the mean properties of the fast internal climatic system.
