Comparison of several spatial prediction methods for soil pH

TLDR

These methods have been classified as global or local, interpolating or non‑interpolating, and smooth or non‑smooth predictors. The study surveyed topsoil pH to compare the performance of several two‑dimensional spatial prediction methods. The authors tested global means and medians, moving averages, inverse squared distance interpolation, Akima's interpolation, natural neighbour interpolation, quadratic trend surface, Laplacian smoothing splines, and ordinary kriging. All methods exhibited deficiencies; interpolating methods performed poorly or had theoretical drawbacks, whereas Laplacian smoothing splines and kriging performed best, and variance estimates revealed short‑range correlations that should be accounted for in predictive modelling.

Abstract

SUMMARY A survey of topsoil pH has been designed specifically to compare the performance of several two‐dimensional spatial prediction methods. These methods have been classified as global or local, and interpolating or non‐interpolating, and smooth or non‐smooth predictors. The techniques tested were global means and medians, moving averages, inverse squared distance interpolation, Akima's interpolation, natural neighbour interpolation, quadratic trend surface, Laplacian smoothing splines and ordinary kriging. All methods showed some deficiencies; for example, prediction sums‐of‐squares were higher than expected for all methods. Interpolating methods either were very poor predictors, or suffered from theoretical drawbacks, or both. Of the non‐interpolating methods, Laplacian smoothing splines and kriging generally performed best. Estimates of variance derived from models which assume independent errors were greater than estimates of variance derived from neighbouring pairs of data sites, suggesting that short range correlations definitely exist, and should be taken into account in any predictive modelling.