Journal of the
Korean Mathematical Society JKMS

To predict the fate of groundwater contaminants, accurate spatially continuous information is needed. Because most field sampling of groundwater contaminants are not conducted spatially continuous manner, a special estimation technique is required to interpolate/extrapolate concentration distributions at unmeasured locations. A practical three-dimensional estimation method for {\it in situ} groundwater contaminant concentrations is introduced. It consists of two general steps: estimation of macroscopic transport process and kriging. Using field data and nonlinear optimization techniques, the macroscopic behavior of the contaminant plume is estimated. A spatial distribution of residuals is obtained by subtracting the macroscopic transport portion from field data, then kriging is applied to estimate residuals at unsampled locations. To reduce outlier effects on obtaining correlations between residual data which are needed for determining variogram models, the ${\mathcal R}_{p}$-estimator is introduced. The proposed estimation method is applied to a field data set.

Keywords: groundwater contaminants, geostatistics, ${\mathcal R}_{p}$-estimator, kriging

MSC numbers: 86A32, 65U05