A relative-flux-correction scheme for analyzing three dimensional data of a tile-drained agricultural plot

The use of simple geostatistical tools is often constrained by data trend (nonstationarity) to characterize the spatial variability of soil properties in the subsurface environment influenced by any site-specific feature(s). Adaptive approaches, such as site-specific robust-resistant schemes, median polishing, trend analysis, etc., are thus used to preprocess the spatial data before analyzing for their spatial structures. Soil water nitrate–nitrogen (NO3–N) concentration (mg l−1) and soil moisture content (cm) data collected jointly from 175 sites arranged on a 5×7×5 three-dimensional (3-D) grid network of 7.6 m×7.6 m×0.3 m spacings in a tile-drained agricultural plot were analyzed for their three-dimensional spatial distribution and for possible coregionalization. We propose a physical process-based correction scheme to preprocess the nonstationary spatial data of soil NO3–N concentration and soil moisture content. Using the subsurface-drain flow phenomenon, we developed a relative-Darcy-flux-based correction scheme to remove any tile drainage-induced nonstationarity in the spatial data of soil NO3–N concentration and soil moisture content prior to conducting the spatial analysis in the 3-D soil volume. 3-D composite semivariograms of relative-flux-corrected NO3–N concentration and relative-flux-corrected moisture content showed anisotropic linear structures in three principal directions. Linear models characterized by steep slopes were found in the directions perpendicular to tile line as opposed to nugget models found in the direction parallel to the tile line. Good spatial correlation between the relative-flux-corrected NO3–N concentration and relative-flux-corrected soil moisture content and their anisotropic linear semivariograms produced anisotropic linear cross semivariograms in 3-D. The 3-D composite cross semivariogram will be useful in predicting the more expensive variable, (relative-flux-corrected) soil water NO3–N concentration, at unsampled locations in the soil profile with a cheaper surrogate, the measured (relative-flux-corrected) soil moisture content