Quantifying the predictive skill in long-range forecasting. Part I: Coarse-grained predictions in a simple ocean model

An information-theoretic framework is developed to assess the long-range coarse-grained predictive skill in a perfect-model environment. Central to the scheme is the notion that long-range forecasting involves regimes; specifically, that the appropriate initial data for ensemble prediction is the affiliation of the system to a coarse-grained partition of phase space representing regimes. The corresponding ensemble prediction probabilities, which are computable using ergodic signals from the model, are then used to quantify through relative entropy the information beyond climatology in the partition. As an application, the authors study the predictability of circulation regimes in an equivalent barotropic double-gyre ocean model using a partition algorithm based on K-means clustering and running-average coarse graining. Besides the established rolled up and extensional phases of the eastward jet, optimal partitions for triennial-scale forecasts feature a jet configuration dominated by the second empirical orthogonal function (EOF) of the streamfunction, as well as phases in which the jet interacts with eddies in higher EOFs. Due to mixing dynamics, the skill beyond threestate models is lost for forecast lead times longer than three years, but significant skill remains in the energy and the leading principal component of the streamfunction for septennial forecasts.