Defining Spatial Heterogeneity of Hillslope Infiltration Characteristics Using Geostatistics, Error Modeling, and Autocorrelation Analysis

Abstract

Procedures that can characterize spatial correlation and interpolate values at unknown locations can be valuable in capturing spatial trends, may increase sampling accuracy, and reduce error. This study sought to compare three common methods of measuring infiltration, the double ring (DR), sprinkler (SPR), and frame (FRM) methods, on a hillslope to characterize the spatial structure of the infiltration measurements. All infiltration method measurements were log normally distributed; therefore, universal kriging estimators were developed in conjunction with semivariogram analysis and an error model to interpolate infiltration rates under wet and dry antecedent soil conditions. Variability in measured infiltration rates were greatest from the DR and SPR methods, coefficients of variation (CV) ranged from 42–53%, whereas the CV of the FRM method was 27%. This, however, is not unexpected, as the DR and SPR methods had highly significant directional trends and captured a much larger range in infiltration rates on the hillslope. After removing the directional trend in the data, the semivariograms were able to characterize the spatial correlation reassuringly well. Nugget variance was low for most methods/antecedent conditions, indicating that there was little unexplained variation in the semivariogram model. The range of autocorrelation between measurements varied from 17 m for the SPR method to 33 m for the FRM method. Using the modeled correlation, infiltration rates were interpolated at 284 unsampled locations with an average error of 7.8%. These results indicate that methods of measuring the infiltration rate of a soil differ in first order statistical measures (mean and variance), but not substantially in second order statistical measures (spatial structure). This information can be used to characterize physical or environmental phenomenon not easily modeled with deterministic equations.