The use of observed data for the initial-value problem in numerical weather prediction
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The problem of combining observed and predicted values of meteorological variables, all with error, to obtain current weather conditions is considered. Statistical interpolation is in common use for this problem. Properties of isotropic spatial covariance functions are developed. The performance of several families of covariance functions in fitting published data is investigated. The second-order autoregressive covariance function is identified as having suitable theoretical and excellent approximation properties. Sensitivity of the errors in statistical interpolation to misspecification of the statistical parameters is explored, showing that the process is quite stable under such perturbations.
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