Interpolation algorithm ranking using cross - validation 1 and the role of smoothing effect . A coal zone example 2

10 For a property measured at several locations, interpolation algorithms provide a 11 unique and smooth function yielding a locally realistic estimation at any point within 12 the sampled region. Previous studies searching for optimal interpolation strategies by 13 measuring cross-validation error have not found consistent rankings; this fact was 14 traditionally explained by differences in the distribution, spatial variability and sampling 15 patterns of the datasets. This article demonstrates that ranking differences are also 16 related to interpolation smoothing, an important factor controlling cross-validation 17 errors that was not considered previously. Indeed, smoothing in average-based 18 interpolation algorithms depends on the number of neighbouring data points used to 19 obtain each interpolated value, among other algorithm parameters. A 3D dataset of 20 calorific value measurements from a coal zone is used to demonstrate that different 21 algorithm rankings can be obtained solely by varying the number of neighbouring points 22 considered (i.e. whilst maintaining the distribution, spatial variability and sampling 23 pattern of the dataset). These results suggest that cross-validation error cannot be used 24 as a unique criterion to compare the performance of interpolation algorithms, as has 25 *Manuscript Click here to download Manuscript: ArticleCV_28_09.pdf