Abstract
This paper describes a method for reconstructing a synoptic state by fitting dynamics to asynoptic data. The best fit is defined by the minimum of a quadratic cost function and dynamics are enforced through the use of a penalty term. When the coefficient of the penalty term is identified as the inverse of the variance of model error, the method yields the same results as Kalman filtering, and in the limit of infinitely large coefficient, the same as strong-constraint formalisms. The self-adjoint nature of the equations for the best fit motivated the use of a relaxation method for their solution. The method is illustrated within the context of one-dimensional, linear, shallow-water wave dynamics, where computational examples indicate that a synoptic state is properly determined only if the asynoptic data are equivalent to complete initial conditions.
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Thacker, W.C. A cost-function approach to the assimilation of asynoptic data. J Sci Comput 2, 137–158 (1987). https://doi.org/10.1007/BF01061483
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DOI: https://doi.org/10.1007/BF01061483