Measures of Predictability with Applications to the Southern Oscillation

Abstract

A relative measure of actual, rather than potential, predictability of a meteorological variable on the basis of its past history alone is proposed. This measure is predicated on the existence of a parametric time series model to represent the meteorological variable. Among other things, it provides an explicit representation of forecasting capability in terms of the individual parameters of such time series models. As an application, the extent to which the Southern Oscillation (S0), a major component of climate, can be predicted on a monthly as well as a seasonal time scale on the basis of its past history alone is determined. In particular, on a monthly time scale up to about 44% of the variation in SO can be predicted one month ahead (zero months lead time) and about 35% two months ahead (one month lead time), or on a seasonal time scale about 53% one season ahead (zero seasons lead time) and about 31% two masons ahead (one season lead time). In general, the degree of predictability naturally decays as the lead time increases with essentially no predictability on a monthly time scale beyond ten months (nine months lead time) or on a seasonal time scale beyond seasons (two seasons lead time).