Behaviors of Variational and Nudging Assimilation Techniques with a Chaotic Low-Order Model

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Abstract
Variational and nudging data-assimilation schemes are examined within the framework of a model initialization problem using the Lorenz three-component model of Rayleigh–Benard convection. Since the intent of this study is to explore what factors influence the abilities of the two assimilation techniques to produce accurate initial conditions, identical twin experiments are conducted for various lengths of the data-assimilation window when the flow is both study state and chaotic. These experiments illustrate that the location of the model solution in phase space is an important consideration when applying either data-assimilation scheme. Decision points, when the model “chooses” which stationary point to orbit, are found to affect the ability of the assimilation techniques to find an accurate initial condition. For chaotic flow, variational assimilation produces a better initial condition when the assimilation window is short, while nudging produces a better initial condition when the assimilation window is long. This is due to both the increasing complexity of the cost-function shape as the assimilation window is lengthened and the longer time period over which nudging can operate. When using a variational technique, extending the assimilation window past a certain length may be detrimental. Admittedly, it is uncertain to what extent these results can be generalized to more complicated models of the atmosphere, since we have examined only one particular model and variants of the assimilation methods used may lead to different results with the same model. Studies using mesoscale and small-scale models, however, show similar behaviors. These behaviors suggest that decision points are present in these more complicated models. Thus, chaotic low-order models that include decision points may be useful in exploring the characteristics of data-assimilation techniques.

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