Gaussian process regression for three-dimensional soil mapping over multiple spatial supports

This study investigates the complexity of spatial soil modelling, particularly focusing on the challenge of variable vertical support in traditional soil data collection. Traditional soil sampling, described in terms of horizons, often fails to accurately pinpoint the specific depths for specific soil properties. This gap is significant, as depth-specific data is crucial for a thorough understanding of soil formation processes and for assessing potential environmental impacts. In digital soil mapping (DSM), the prevalent reliance on standardised depth intervals and mass-preserving spline functions for data resampling results in a modelling approach that tends to disregard depth-related details, thereby introducing potential uncertainties. To address these limitations, this work explores how effectively Gaussian process regression (GPR) can model soil in 3D. This technique comprises two key components: a mean function and a semivariogram-like kernel. Unlike conventional methods that make a single prediction, GPR provides detailed probability distributions. This capability allows for the quantification of prediction uncertainty at various points, offering insights for decision-making and risk assessment purposes. Moreover, GPR has the capability to make volume or block estimates and assess associated uncertainties. Enabling volume-based predictions enriches the range of strategies available for land management. In this research, we employ GPR as a novel 3D soil modelling technique and compare its performance with traditional spline-based methods. The comparison is conducted through a case study on a farm in northern New South Wales, Australia, focusing on the 3D mapping of soil pH and electrical conductivity (EC). Our results demonstrate the ability of GPR to estimate soil properties across various volumes, utilising data from multiple vertical supports, thereby offering a more versatile approach for soil modelling in diverse spatial contexts.