A systematic and comprehensive procedure for extracting the predictability of climate variables from a set of observations and forecasts is proposed. This procedure, which is based on information theory, clarifies the fundamental definition of predictability and the role of imperfect forecast models in assessing predictability. Limitations due to imperfect forecast models are addressed by a statistical procedure which, in principle, accounts for all of the information contained in the ensemble forecasts and observations. In addition, the procedure identifies the optimally predictable components of an imperfect forecast model, and identifies components in the initial condition and boundary conditions which can be attributed to the model's predictability. If all variables are Gaussian, then the optimal procedure becomes equivalent to an ordered sequence of standard methods associated with linear regression, canonical correlation analysis, and discriminant analysis. While parts of the full methodology have been proposed in the literature, information theory provides a guiding framework for unifying the parts into a sensible whole. For instance, the theory clarifies such things as how to account for multiple forecasts in the context of linear regression and canonical correlation analysis.

A fundamental limitation of the above procedure, which is common among many regression procedures, is that it is sensitive to sampling errors. We propose a solution to this long outstanding problem which is mathematically rigorous and computationally feasible. This solution is based on a set of assumptions regarding the predictability of the system which appear to be satisfied in the problem of predicting monthly or seasonal means. Results of applying this method to predicting land surface temperature will be discussed.