Tuning the Barnes Objective Analysis Parameters by Statistical Interpolation Theory

Abstract

The parameters of the Barnes objective analysis scheme are often chosen on the basis of a desired frequency response, but they can also be chosen using the criterion of the theoretical root-mean-square interpolation error (E). Using the latter criterion, it is shown how the parameters of a common two-parameter Barnes implementation can be optimized for any specified irregular observational distribution. The problem is then generalized by means of design curves that enable the parameters to be chosen according to (i) average data spacing relative to the correlation coefficient function length scale of the field being analyzed, and (ii) the observational error variance relative to the variance of the true field (noise-to-signal ratio). A large set of real data was analyzed using parameters chosen on the basis of interpolation theory. The analyses were assessed by comparison against a set of withheld data. The result suggests that minimum E is a satisfactory criterion for objectively choosing the Barnes parameters when the statistical properties of the true field and of the observational error are known in advance. It is also shown that the chosen two-parameter Barnes implementation is robust, in the sense that a large region of parameter space corresponds to values of E only slightly above the minimum.