Estimating Soil Hydraulic Conductivity at the Field Scale with a State-Space Approach

A precise description of saturated (K_s) and near-saturated hydraulic conductivity (K_-10) and their spatial variability is important for understanding water/solute transport in the vadose zone. However, it is laborious to measure K directly. Alternatively, K could be predicted from easily measurable soil properties using pedotransfer functions (PTFs). Because PTFs ignore the spatial relationships and covariance between soil variables, they often perform unsatisfactorily when field-scale estimations of K are needed. Therefore, the objective of this study was to improve the estimation of K at field scale through consideration of spatial dependences between soil variables. K was measured at 48 locations in a 71 × 71-m grid within a farmland under no-till. An autoregressive state-space approach was used to quantify the spatial relations between K and soil properties and to analyze the spatial variability of K in the field. In comparison, multiple linear regression (MLR) was used to derive PTFs for K estimation. Using various combinations of variables, state-space analysis outperformed PTFs in estimating spatial K distribution across the field. While state-space approach explained 69%, MLR method explained only 6% of the total variation in K_s. For K_-10, the best state-space model included silt, clay, and macroporosity and performed almost perfectly (R² >95%) in characterizing the spatial variability of K_-10. In that case, the best MLR-type PTF explained only 60% of the variation. The results indicate that, by considering the spatial relations between soil variables, state-space approach is an effective tool for analyzing the spatial variability of K at field scale.