On stochastic stability of regional ocean models to finite-amplitude perturbations of initial conditions
Ivanov, Leonid M.
Chu, Peter C.
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We consider 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 2 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 limit of zero horizontal viscosity, the PE at ﬁrst decays with time for all scales due to dissipation caused by non-linear bottom friction, and then grows faster than (quasi)- exponentially. Statistics of a prediction time scale (the irreversible predictability time (IPT)) quickly depart from Gaussian (the linear predictability regime) and becomes Weibullian (the non-linear predictability regime) as amplitude of initial perturbations grows. A transition from linear to non-linear predictability is clearly detected by the speciﬁc behavior of IPT variance. A new analytical formula for the model predictability horizon is introduced and applied to estimate the limit of predictability for the ocean model.
Dynamics of Atmosphere and Oceans, 43, (3-4), 199-225.The article of record as published may be located at http://dx.doi.org/10.1016/j.dynatmoce.2007.03.001
RightsThis publication is a work of the U.S. Government as defined in Title 17, United States Code, Section 101. Copyright protection is not available for this work in the United States.
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