First Passage Time (FPT) for Determining Large Ocean Model Predictability

First passage time (FPT) is used to evaluate large ocean (or atmosphere) model predictability. FPT is defined as the time period when the prediction error first exceeds a pre-determined criterion (i.e., the tolerance level). It depends not only on the instantaneous error growth, but also on the noise level, the initial error, and tolerance level. The model predictability skill is then represented by a single scalar, FPT. The longer the FPT, the higher the model predictability skill is. A theoretical framework on the base of the backward Fokker-Planck equation is developed to determine FPT. In this paper, we investigate error propagation near an unstable equilibrium state (classified as an unstable focus) for spatially uncorrelated and correlated finite-amplitude initial perturbations using short- (up to several weeks) and intermediate (up to two months) range forecast ensembles produced by a barotropic regional ocean model. An ensemble of initial perturbations is generated by the Latin Hypercube design strategy, and its optimal size is estimated through the Kullback- Liebler distance (the relative entropy). Although the ocean model is simple, the prediction error (PE) demonstrates non-trivial behavior similar to that existing in 3D ocean circulation models. In particular, in the limi