Decadal predictability and forecast skill

The “potential predictability” of the climate system is the upper limit of available forecast skill and can be characterized by the ratio p of the predictable variance to the total variance. While the potential predictability of the actual climate system is unknown its analog q may be obtained for a model of the climate system. The usual correlation skill score r and the mean square skill score M are functions of p in the case of actual forecasts and potential correlation ρ and potential mean square skill score $\mathcal{M}$ are the same functions of q in the idealized model context. In the large ensemble limit the connection between model-based potential predictability and skill scores is particularly straightforward with $q=\rho^{2}=\mathcal{M}.$ Decadal predictions of annual mean temperature produced with the Canadian Centre for Climate Modelling and Analysis coupled climate model are analyzed for information on decadal climate predictability and actual forecast skill. Initialized forecast results are compared with the results of uninitialized climate simulations. Model-based values of potential predictability q and potential correlation skill ρ are obtained and ρ is compared with the actual forecast correlation skill r. The skill of externally forced and internally generated components of the variability are separately estimated. As expected, ρ > r and both decline with forecast range τ, at least for the first five years. The decline of skill is associated mainly with the decline of the skill of the internally generated component. The potential and actual skill of a forecast of time-averaged temperature depends on the averaging period. The skill of uninitialized simulations is low for short averaging times and increases as averaging time increases. By contrast, skill is high at short averaging times for forecasts initialized from observations and declines as averaging times increase to about three years, then increases somewhat at longer averaging times. The skills of the initialized forecasts and uninitialized simulations begin to converge for longer averaging times. The potential correlation skill ρ of the externally forced component of temperature is largest at tropical latitudes and the skill of the internally generated component is largest over the North Atlantic, parts of the Southern Ocean and to some extent the North Pacific. Potential skill over extratropical land is somewhat weaker than over oceans. The distribution of actual correlation skill r is broadly similar to that of potential skill for the externally forced component but less so for the internally generated component. Differences in potential and actual skill suggest where improvements in the forecast system might be found.