A Controlled Experiment with One-Dimensional Interpolation

Abstract

The performances of various one-dimensional interpolation schemes are evaluated using mean square errors of the point-wise estimates of the function values and component-wise estimates of the power spectrum. The schemes of interpolation considered include Gandin's optimum interpolation, cubic spline, and two-point linear interpolations. The test function is a random analytic function defined in a closed domain with a prescribed power spectrum, satisfying the conditions of homogeneity and ergodicity. The experiment is carried out under the circumstance of interpolation which includes a conservative simulation of the large-scale state of the atmosphere and reflects the levels of data acquisition and resolution as practiced currently in meteorology. The results of the experiment suggest that under all practical circumstances the error of interpolation, which is defined to be the ratio of the sample variance of estimation errors to the sample variance of true values, may not be reduced too much below the value of 0.05. The study also shows that the cubic spline interpolation performs very much like Gandin's optimum interpolation.