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The Effect of Thinning and Superobservations in a Simple One-Dimensional Data Analysis with Mischaracterized Error
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    A one-dimensional (1D) analysis problem is defined and analyzed to explore the interaction of observation thinning or superobservation with observation errors that are correlated or systematic. The general formulation might be applied to a 1D analysis of radiance or radio occultation observations in order to develop a strategy for the use of such data in a full data assimilation system, but is applied here to a simple analysis problem with parameterized error covariances. Findings for the simple problem include the following. For a variational analysis method that includes an estimate of the full observation error covariances, the analysis is more sensitive to variations in the estimated background and observation error standard deviations than to variations in the corresponding correlation length scales. Furthermore, if everything else is fixed, the analysis error increases with decreasing true background error correlation length scale and with increasing true observation error correlation length scale. For a weighted least squares analysis method that assumes the observation errors are uncorrelated, best results are obtained for some degree of thinning and/or tuning of the weights. Without tuning, the best strategy is superobservation with a spacing approximately equal to the observation error correlation length scale.
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