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This paper summarizes the development of a convergent weighted-averaging interpolation scheme which can be used to obtain any desired amount of detail in the analysis of a set of randomly spaced data. The scheme is based on the supposition that the two-dimensional distribution of an atmospheric variable can be represented by the summation of an infinite number of independent waves, i.e., a Fourier integral representation. The practical limitations of the scheme are that the data distribution be reasonably uniform and that the data be accurate. However, the effect of inaccuracies can be controlled by stopping the convergence scheme before the data errors are greatly amplified. The scheme has been tested in the analysis of 500-mb height data over the United States producing a result with details comparable to those obtainable by careful manual analysis. A test analysis of sea level pressure based on the data obtained at only the upper air network stations produced results with essentially the same features as the analysis produced at the National Meteorological Center. Further tests based on a regional sampling of stations reporting airways data demonstrate the applicability of the scheme to mesoscale wavelengths.
Stanley L. Barnes (Sat,) studied this question.