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Hong Li, Eugenia Kalnay, Takemasa Miyoshi, and Christopher M. Danforth

nature run in the perfect-model experiments by the NNR fields. Since the NNR assimilated real observations, we assume that the NNR fields are an approximate estimate of the unknown true atmosphere (a quantitative validation of this assumption is beyond the scope of this research). Random noise with the same standard deviation used in the perfect-model experiments is added to simulate “NNR observations.” The density of observations remains the same as that in the perfect-model experiments. a. Effects

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Seung-Jong Baek, Istvan Szunyogh, Brian R. Hunt, and Edward Ott

the attractor of the true dynamics. In such a situation, making a correction to the background state, which moves the background state estimate from the model attractor to the true system attractor, as done in bias model I, may trigger an adjustment process during the next model integration step. The effects of such an adjustment on the accuracy of the state estimate are unpredictable and often negative. To avoid triggering a strong adjustment process, in bias model II we search for a state

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Chris Snyder, Thomas Bengtsson, Peter Bickel, and Jeff Anderson

than 0.8 and max w i > 0.5 with probability 0.9. Collapse of the weights occurs frequently for N x = 100 despite the ensemble size N e = 10 3 . Two comparisons illustrate the detrimental effects of collapse. The correct posterior mean in this Gaussian example is given by x a = ( x f + y )/2, where the superscript a (for “analysis”) indicates a posterior quantity and the prior mean x f = 0 in this example. The expected squared error of x a is E (| x a − x | 2 ) = [ E (| x f − x

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