Objective analysis accuracies of statistical interpolation and successive correction schemes

This report considers schemes for the objective analysis of meteorological fields, in which the interpolated increment to a background (first guess) field can be expressed as a weighted sum of observed increments. The expected mean square interpolation error of such schemes can be computed theoretically. Statistical (‘optimum’) interpolation methods (Gandin 1963; Rutherford 1972), and successive correction methods (Cressman 1959), both satisfy the above criterion. The sensitivity of statistical interpolation, to departures of the assumed statistical properties of observational and background field errors from their true values, is discussed. The theoretical interpolation errors of statistical interpolation and successive correction methods are compared. Corresponding differences in the observational weights, and in actual analyses, using the two methods, are discussed and illustrated by examples.