Predictive skill of climate indices compared to mean quantities in seasonal forecasts

Seasonal forecasting models are increasingly being used to forecast application-relevant aspects of upcoming climatic conditions, often summarised by climate indices. Little is known, however, on how the predictive skill of such forecasts of climate indices relates to the predictive skill in forecasting seasonal mean conditions. Here we analyse forecasts of two generalised indices derived from daily minimum and maximum temperature: counts of events such as the number of frost days and accumulated threshold exceedances such as degree days. We find that the predictive skill of forecasts of these two types of indices is generally lower than the skill of seasonal mean daily minimum and maximum temperature. By use of a toy model we demonstrate that this reduction in skill is more pronounced for skilful forecasts and climate indices defined relative to a threshold at the tail of the distribution. Based on the toy model results we conclude that there is no indication of additional predictability in forecasts of these indices in excess of what is expected due to the predictability of the seasonal mean. To further support this hypothesis, we show that the skill in predicting climate indices can be statistically modelled successfully using the toy model and the skill in the seasonal mean.