Spatial prediction of soil particle-size fractions as compositional data

Particle-size fractions (psf) of mineral soils and, hence, soil texture, are the most important attributes affecting physical and chemical processes in the soil. More often, psf data are available only at a few locations for a given area and, therefore, require some form of interpolation or spatial prediction. However, psf data are compositional and, therefore, require special treatment before spatial prediction. This includes ensuring positive definiteness and a constant sum of interpolated values at a given location, error minimization, and lack of bias. In order to meet these requirements, this study applied two methods of data transformation prior to kriging of the psf of soils in two regions of eastern Australia. The two methods are additive log-ratio transformation of the psf (ALR(OK)) and modified log-ratio transformation (mALR(OK)). The performance of the transformed values by ordinary kriging was compared with the spatial prediction of the untransformed psf data using ordinary kriging, compositional kriging (CK) (UTOK), and cokriging, based on the criteria-prediction bias or mean error (ME) and precision (root mean square error (RMSE)), and validity of textural classification. ALR(OK) and mALR(OK) outperformed UTOK and CK in terms of prediction ME and RMSE. Because of the closure effect on the psf data, UTOK and, to a lesser extent, CK, did not meet all of the requirements for spatially predicting compositional data and, therefore, performed poorly. mALR(OK) outperformed all of the interpolation methods in terms of misclassification of soils into textural classes. The results show that without considering the special requirements of compositional data, spatial interpolation of psf data win necessarily produce uncertain and unreliable interpolated psf values.