Irrigation in agriculture mitigates the adverse effects of drought and improves crop production and yield. Still, water scarcity remains a persistent issue and water resources need to be used responsibly. To improve water use efficiency, precision irrigation is emerging as an approach where farmers can vary the application of irrigation according to within field variation in soil and topographic conditions. As a precursor, methods to characterize spatial variation of soil hydraulic properties is needed. One such property is soil water holding capacity (WHC). This analysis develops a Bayesian multivariate spatial model for predicting WHC across a field at various soil depths using sparse WHC observations and covariates such as soil electrical conductivity. To capture spatially-varying cross correlations in an efficient manner, we propose a novel conditional specification of a multivariate Gaussian process with spatially-varying coefficients. Because data is already sparse, our analysis fully utilizes incomplete observations by imputing missing values that we treat as not missing at random. Additionally, due to the high cost of measuring WHC, we use a multivariate integrated mean square error criterion to choose a new observation location that, after sampling, will result in the least predictive uncertainty across the entire field.
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