In his biography of the great twentieth-century theoretical physicist Richard Feynman, Gleick (1993) writes: ‘He (Feynman) believed in the primacy of doubt, not as a blemish on our ability to know, but as the essence of knowing’. Feynman's philosophy applies as much to weather and climate forecasting as to fundamental physics, as made explicit by Tennekes et al. (1987) when they wrote: ‘no forecast is complete without a forecast of forecast skill’.

The estimation of uncertainty in weather and climate prediction is encapsulated in the word ‘predictability’. If something is said to be predictable, then presumably it can be predicted! However, initial conditions are never perfect and neither are the models used to make these predictions. Hence, the predictability of the forecast is a measure of how these inevitable imperfections leave their imprint on the forecast. By virtue of the non-linearity of the climate, this imprint varies from day to day, just as the weather itself varies; predictability is as much a climatic variable as rainfall, temperature or wind.

Of course, it is one thing to talk about predictability as if it were just another climatic variable; it is another thing to estimate it quantitatively. The predictability of a system is determined by its instabilities and non-linearities, and by the structure of the imperfections. Estimating these instabilities, non-linearities and structures provides a set of tough problems, and real progress requires sophisticated mathematical analysis on both idealised and realistic models.