Analyzing spatial data: An assessment of assumptions, new methods, and uncertainty using soil hydraulic data

Environmental scientists today enjoy an ever-increasing array of geostatistical methods to analyze spatial data. Our objective was to evaluate several of these recent developments in terms of their applicability to real-world data sets of the soil field-saturated hydraulic conductivity (Ks). The intended synthesis comprises exploratory data analyses to check for Gaussian data distribution and stationarity; evaluation of robust variogram estimation requirements; estimation of the covariance parameters by least-squares procedures and ( restricted) maximum likelihood; use of the Matern correlation function. We furthermore discuss the spatial prediction uncertainty resulting from the different methods. The log-transformed data showed Gaussian uni- and bivariate distributions, and pronounced trends. Robust estimation techniques were not required, and anisotropic variation was not evident. Restricted maximum likelihood estimation versus the method-of-moments variogram of the residuals accounted for considerable differences in covariance parameters, whereas the Matern and standard models gave very similar results. In the framework of spatial prediction, the parameter differences were mainly reflected in the spatial connectivity of the Ks field. Ignoring the trend component and an arbitrary use of robust estimators would have the most severe consequences in this respect. Our results highlight the superior importance of a thorough exploratory data analysis and proper variogram modeling, and prompt us to encourage restricted maximum likelihood estimation, which is accurate in estimating fixed and random effects.