Which Interpolation Method is the Best?

Which interpolation method is the most robust?  Dennis Weber and Evan Englund posed this question in two articles in Mathematical Geology in the 1990s in which they tested 15 interpolation methods.  In a study published in 1992, the researchers created a data set for analysis, which consisted of the variance on digital elevation data.  The data set contained 19,800 data points, and was subdivided into 198 blocks each containing 100 data points.  The researchers created 54 data subsets against which they tested the 15 interpolation methods.  The results of each interpolation method for each block and each data set were compared against the true values.  In this particular study, inverse distance squared and inverse distance performed better than kriging and log kriging.  In their next article the authors called these results “somewhat provocative,” as kriging is generally understood to be more robust than inverse distance methods.  They postulated that the results were an artifact of the data set that they had chosen for their experiment.  The data set may simply have randomly favored inverse distance.  It also did not contain strong anisotropy, which kriging is better at handling.

In order to test this idea further the authors conducted a follow-up study, published in 1994, in which they examined several variations of kriging and inverse distance squared interpolation methods.  They selected five databases: three digital elevation data sets and two data sets composed of the variance of elevation data.  60 samples sets of varying population sizes were randomly drawn from each of these data sets, and used to evaluate the interpolation methods: four kriging, four inverse-distance, and one spline.  The results show that inverse distance methods were very sensitive to parameters, the type of data set, and the number of sample points.  Overall, kriging proved more robust, but significant differences were observed based on the method used to estimate the variogram.  The authors suggest that the performance of an interpolation method is somewhat dependent on the data set and data sample on which it is applied.

Weber, D., and Englund, E. 1992. Evaluation and Comparison of Spatial Interpolators. Mathematical Geology. 24(4): 381-391.

Weber, D., and Englund, E. 1994. Evaluation and Comparison of Spatial Interpolators II. Mathematical Geology. 26(5): 589-603.