Despite its importance, accurate representation of the spatial distribution of water table depth remains one of the greatest deficiencies in many hydrological investigations. Historically, both inverse distance weighting (IDW) and ordinary kriging (OK) have been used to interpolate depths. These methods, however, have major limitations: namely they require large numbers of measurements to represent the spatial variability of water table depth and they do not represent the variation between measurement points. We address this issue by assessing the benefits of using stepwise multiple linear regression (MLR) with three different ancillary data sets to predict the water table depth at 100-m intervals. The ancillary data sets used are Electromagnetic (EM34 and EM38), gamma radiometric: potassium (K), uranium (eU), thorium (eTh), total count (TC), and morphometric data. Results show that MLR offers significant precision and accuracy benefits over OK and IDW. Inclusion of the morphometric data set yielded the greatest (16%) improvement in prediction accuracy compared with IDW, followed by the electromagnetic data set (5%). Use of the gamma radiometric data set showed no improvement. The greatest improvement, however, resulted when all data sets were combined (37% increase in prediction accuracy over IDW). Significantly, however, the use of MLR also allows for prediction in variations in water table depth between measurement points, which is crucial for land management.

At the field level the demand for spatial information of soil properties is rapidly increasing owing to its requirements in precision agriculture and soil management. One of the most important properties is the cation exchange capacity (CEC, cmol(+)/kg) because it is an index of the shrink–swell potential and hence is a measure of soil structural resilience to tillage. However, CEC is time-consuming and expensive to measure. Various ancillary datasets and statistical methods can be used to predict CEC, but there is little scientific literature which implements this approach to map CEC or addresses the issue of the amount of ancillary data required to maximise precision and minimise bias of spatial prediction at the field level. We compare a standard least-squares multiple linear regression (MLR) model which includes 2 proximally sensed (EM38 and EM31), 3 remotely sensed (Red, Green and Blue spectral brightness), and 2 trend surface (Easting and Northing) variables as ancillary data or independent variables, and a stepwise MLR model which only includes the statistically valid EM38 signal data and the Easting trend surface vector. The latter is used as the basis for developing a hierarchical spatial regression model to predict CEC. The reliability of the model is analysed by comparing prediction precision (root mean square error) and bias (mean error) using degraded EM38 transect spacing (i.e. 96, 144, 192, 240, and 288 m) and comparing these with predictions achieved with the 48-m spacing. We conclude that the EM38 data available on the 96- and 144-m spacing are suitable at a reconnaissance level (i.e. broad-scale farming) and 24- or 48-m spacing are suitable at smaller levels where detailed information is necessary for siting the location of water reservoirs. In terms of soil management, CEC predictions determine where suitable subsoil exists for the purpose of soil profile inversion to improve the structural resilience of a topsoil that is susceptible to dispersion and surface crusting.

The soil particle-size fractions (PSFs) are one of the most important attributes to influence soil physical (e.g., soil hydraulic properties) and chemical (e.g., cation exchange) processes. There is an increasing need, therefore, for high-resolution digital prediction of PSFs to improve our ability to manage agricultural land. Consequently, use of ancillary data to make cheaper high-resolution predictions of soil properties is becoming popular. This approach is known as “digital soil mapping.” However, most commonly employed techniques (e.g., multiple linear regression or MLR) do not consider the special requirements of a regionalized composition, namely PSF; (1) should be nonnegative (2) should sum to a constant at each location, and (3) estimation should be constrained to produce an unbiased estimation, to avoid false interpretation. Previous studies have shown that the use of the additive log-ratio transformation (ALR) is an appropriate technique to meet the requirements of a composition. In this study, we investigated the use of ancillary data (i.e., electromagnetic (EM), gamma-ray spectrometry, Landsat TM, and a digital elevation model to predict soil PSF using MLR and generalized additive models (GAM) in a standard form and with an ALR transformation applied to the optimal method (GAM-ALR). The results show that the use of ancillary data improved prediction precision by around 30% for clay, 30% for sand, and 7% for silt for all techniques (MLR, GAM, and GAM-ALR) when compared to ordinary kriging. However, the ALR technique had the advantage of adhering to the special requirements of a composition, with all predicted values nonnegative and PSFs summing to unity at each prediction point and giving more accurate textural prediction.