Soil sampling strategies for spatial prediction by correlation with auxiliary maps

Tomislav Hengl, David G. Rossiter and Alfred Stein

Abstract

The paper evaluates spreading of observations in feature and geographical spaces as a key to sampling optimisation for spatial prediction by correlation with auxiliary maps. Although auxiliary data are commonly used for mapping soil variables, problems associated with the design of sampling strategies are rarely examined. When generalised least-squares estimation is used, the overall prediction error depends upon spreading of points in both feature and geographical space. Allocation of points uniformly over the feature space range proportionally to the distribution of predictor (equal range stratification, or ER design) is suggested as a prudent sampling strategy when the regression model between the soil and auxiliary variables is unknown. An existing 100-observation sample from a 50 by 50 km soil survey in central Croatia was used to illustrate these concepts. It was re-sampled to 25-point datasets using different experimental designs: ER and 2 response surface designs. The designs were compared for their performance in predicting soil organic matter from elevation (univariate example) using the overall prediction error as an evaluation criterion. The ER design gave overall prediction error similar to the minmax design, suggesting that it is a good compromise between accurate model estimation and minimisation of spatial autocorrelation of residuals. In addition, the ER design was extended to the multivariate case. Four predictors (elevation, temperature, wetness index, and NDVI) were transformed to standardised principal components. The sampling points were then assigned to the components in proportion to the variance explained by a principal component analysis and following the ER design. Since stratification of the feature space results in a large number of possible points in each cluster, the spreading in geographical space can also be maximised by selecting the best of several realisations.

Keywords: response surface design, soil survey, general least squares, feature space, principal components.

Australian Journal of Soil Research 41(8) 1403 - 1422 (2003) doi:10.1071/SR03005