On stochastic stability of regional ocean models with uncertainty in wind forcing

A shallow-water model was used to understand model error induced by non-Gaussian wind uncertainty. Although the model was simple, it described a generic system with many degrees of freedom randomized by external noise. The study focused on the nontrivial collective behavior of finite-amplitude perturbations on different scales and their influence on model predictability. The error growth strongly depended on the intensity and degree of spatial inhomogeneity of wind perturbations. For moderate but highly inhomogeneous winds, the error grew as a power law. This behavior was a consequence of varying local characteristic exponents and nonlinear interactions between different scales. Coherent growth of perturbations was obtained for different scales at various stages of error evolution. For the nonlinear stage, statistics of prediction error could be approximated by a Weibull distribution. An approach based on the Kullback-Leibler distance (the relative entropy) and probability-weighted moments was developed for identification of Weibull statistics. Bifurcations of the variance, skewness and kurtosis of the irreversible predictability time (a measure of model prediction skill) were detected when the accepted prediction accuracy (tolerance) exceeded some threshold.