INTERPOLATION AND FILTERING OF SPATIAL OBSERVATIONS USING SUCCESSIVE CORRECTIONS AND GAUSSIAN FILTERS

This paper describes a simple empirical analysis system based on Brats eth's method of successive corrections applied to detrended field data , which approximates an optimal interpolation of fields with a spatial ly variable mean sampled within a limited domain by scattered observat ions. As in other empirical interpolation schemes, the influence funct ion that determines the weights applied to increment variables is chos en such that unresolvable scales tend to be strongly damped, even if t he contribution from observation error is not represented in a formall y equivalent correlation model for observed increment variables. Unlik e most empirical successive correction schemes, the number of iteratio ns is not necessarily considered as a prescribed analysis parameter. I nstead, the number of iterations can be chosen on a judgemental, poste rior basis such that the analysis approximates the observed field to w ithin some acceptable limit. The analysis generated by this form of su ccessive corrections can be represented by a continuous function of lo cation variables. Consequently, it is possible to express the result o f posterior filtering of the analysis field as a weighted sum of ''fil tered'' influence functions, each of which is defined by the convoluti on of an increment autocorrelation function with a continuous linear f ilter. If both the autocorrelation model and filter are based on a sim ple Gaussian function of spatial lag, then these convolution integrals can be solved analytically. This leads to a numerically inexpensive m ethod of scale selection analysis that is in some ways less ambiguous than methods based on applying filters directly to the observed data. The performance of the analysis system is demonstrated by applying it to simulated observations sampling two-dimensional fields.