We apply the probabilistic approach to analyze model stability to uncertain initial conditions and evolution law. The approach is based on the first passage time as the predictability time. For a stochastic process, the first passage time is defined by the time when the process, starting from a given point of the phase space, reaches a predetermined level (the predictability tolerance) for the first time, and is a random variable. There are several principle advantages using this approach. First, it is convenient to analyze both linear and nonlinear perspectives of model error. Second, it can estimate the high-order moments of the predictability time. Third, it can analyze the second kind of predictability (Lorenz, 1975). We demonstrate the usefulness of our approach through the stability analysis on the Princeton Ocean Model in a semi-closed basin with stochastic forcing.

Reference

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Ivanov, L.M., T.M. Margolina, and O.V.Melnichenko, 1999: Prediction and Management of extreme events based on a simple probabilistic model of the first-passage boundary. Phys. Chem. Earth (A) 24,2, 169-173.