Joint Simulation of Spatially Correlated Soil Health Indicators, Using Independent Component Analysis and Minimum/Maximum Autocorrelation Factors

Soil health plays a major role in the ability of any nation to meet the Sustainable Development Goals. Understanding the spatial variability of soil health indicators (SHIs) may help decision makers develop effective policy strategies and make appropriate management decisions. SHIs are often spatially correlated, and if this is the case, a geostatistical model is required to capture the spatial interactions and uncertainty. Geostatistical simulation provides equally probable realizations that can account for uncertainty in the variables. This study used the following SHIs extracted from the Africa Soil Information Service “Legacy Database” for Nigeria: bulk density, organic matter, and total nitrogen. Maximum and minimum autocorrelation factors (MAF) and independent component analysis (ICA) are two techniques that can be used to transform correlated SHIs into uncorrelated factors/components that can be simulated independently. To confirm spatial orthogonality, the relative deviation from orthogonality, τ(h), and spatial diagonalization efficiency, k(h), approach 0 and 1 for both techniques. To validate the performance of each technique, 100 equally probable realizations were simulated by using MAF and ICA. Direct and cross-variograms showed adequate reproduction, using E-type, where E was defined as the “conditional expectation” of realizations (i.e., average estimate of realizations). It should be noted that only direct variograms of MAF and ICA were independently simulated. The average of 100 back-transformed simulated realizations and randomly selected realizations compared well with the original variables, in terms of spatial distribution, correlation, and pattern. Overall, both techniques were able to reproduce important geostatistical features of the original variables, making them important in joint simulations of spatially correlated variables in soil management.