INDICATOR VARIOGRAMS ESTIMATED FROM SPATIALLY-BIASED FIELD DATA

Spatial statistics (mean, variance, and variogram) of unsaturated hydraulic properties can be accurately estimated when measurement errors are unbiased. Unfortunately, property errors become spatially biased (i.e., their spatial pattern is systematically distorted) when random observation errors are propagated through non-linear inversion models or inversion models incorrectly describe experimental physics. This type of bias causes distortion of the property distribution and variogram. Non-parametric indicator approaches for characterizing spatial variability are subject to fewer restrictions and are considered more robust than continuous spatial statistics. We use a Monte Carlo approach to investigate the impact of measurement error bias on indicator variograms of field-estimated unsaturated hydraulic properties. Hydraulic properties are determined by simulating tension-infiltrometer measurements across a parameter space representative of poorly- to well-sorted, sandy silt to coarse sand. Two types of observation error are considered, along with one inversion-model error resulting from poor contact between the instrument and the medium. Hydraulic property data are transformed to indicator functions based on quantiles, and empirical distribution functions and variograms are determined from the indicator data. For the purpose of comparison, we also determine the mean, variance, and variogram for the non-transformed data. The mean and variance of indicator-based empirical distribution functions show significant bias, which is comparable to that of the non-transformed data. Correlation lengths determined from indicator variograms are more accurate than those determined from the continuous data because indicator errors reflect only misclassification. Our results suggest that indicator functions can reveal the spatial structure of even highly biased hydraulic property fields, even while the empirical distribution remains unknown.