Generalization of multivariate optimum interpolation method and the roles of linear constraint and covariance matrix in the method. Part 2 In continuous form.

Abstract

A method of statistical objective analysis in discrete form (Ikawa, 1984b) is extended to a method in continuous form. Analysis equations are integro-differential equations, where their integral kernels are inverse covariance matrices. Comparison between the method and conventional variational objective analysis is made. Analysis equations of variational objective analysis are differential equations, while those of the method in this paper are integro-differential equations. If the method uses diagonal covariance matrices with no correlation with data on other locations, analysis equations of the method reduce to those of variational objective analysis. The spectral representation of analysis equations is presented. The response function of the analysis scheme as a linear filter is expressed in terms of spectral representations of linear constraint and covariance matrices. Some examples of application of spectral representation of analysis equations are shown. The roles of linear constraint and covariance matrix is made clear in the wave number domain.