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Visualizing predictability with chaotic ensembles

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The self-consistent prediction of nonlinear, potentially chaotic, systems must account for observational noise both when constructing the model and when determining the current state of the system to be used as `the' initial condition. In fact, there exists an ensemble of initial states of the system, whose members are each consistent with a given observation. Determining the reliability of a forecast, even under a perfect model, requires an understanding of the evolution of this ensemble, and implies that traditional prediction of a single trajectory is rarely consistent with the assumptions upon which the underlying model is based. The implications of ensemble forecasts for chaotic systems are considered, drawing heavily from research in forecast verification of numerical weather prediction models. Applications in `simpler' laboratory scale systems are made, where nonlinear dynamical systems theory can be put to the test. In brief, it is argued that self consistency requires the estimation of probability density functions through ensemble prediction even in the case of deterministic systems: if observational noise is considered in the construction of the model, it must also be accepted in the determination of the initial condition

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