Covariance functions for statistical interpolation
Franke, Richard H.
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The properties of correlation functions (which are special cases of positive definite functions) are developed. The multivariate application of statistical interpolation in the context of objective analysis of meteorological fields is discussed. Conditions for a one dimensional correlation function to be an isotropic two dimensional correlation function are derived, and a sufficient condition applied to some examples of practical interest. Some experiments comparing the accuracy of statistical interpolation are reported. The model correlation was a six term Bessel function fit to published data. Functions for several other classes of functions were fit to the same data and their performance compared with the optimum. One appendix gives a compendium of proposed covariance functions, and another reports some experiments concerning estimation of correlation functions from (simulated) raw data.
NPS Report NumberNPS-53-86-007
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