The roles of observational uncertainty and model inadequacy are contrasted in the case of physical simulation models when our best forecast models are chaotic (deterministic models with exponential-on-average sensitivity to initial condition). In the perfect model scenario, the framework of indistinguishable states provides an (?effectively Bayesian?) algorithm for constructing accountable (ideal) probabilistic forecasts. Within the perfect model scenario, the model-class in-hand will admit a model trajectory which shadows the observations: specifically, a trajectory which is consistent with the observations given the observational noise model. Outside the perfect model scenario, it can be proven that the set of indistinguishable states is empty, suggesting that no algorithm exists which can provide accountable probability forecasts. Practical implications differ for weather-like forecast applications and climate modelling. Adaptive observations are considered in this context, and it is noted that state-estimation might be profitably distinguished from
forecast initialisation. Open questions of data assimilation in climate modelling are also touched upon.
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