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Using Rank-Order Geostatistics for Spatial Interpolation of Highly Skewed Data in a Heavy-Metal Contaminated Site

^a Graduate Institute of Agricultural Chemistry, National Taiwan Univ., Taipei, 106 Taiwan
^b Dep. of Natural Resources and Environmental Sciences, Univ. of Illinois, Urbana–Champaign, IL 61801

View larger version (20K): [in a new window]   Fig. 1. The study site and the sampling points. The coordinate system is 2°UTM for Taiwan.

View larger version (15K): [in a new window]   Fig. 2. A hypothetical empirical distribution function (EDF) for a sample data set with great variation and high skewness used to illustrate a deviation, d, in the standardized-rank space back-transformed into greatly contrasting uncertainty intervals or in the concentration space.

View larger version (34K): [in a new window]   Fig. 3. Sampling location map and soil Cd concentrations.

View larger version (28K): [in a new window]   Fig. 4. Histograms of (a) soil Cd concentrations and (b) logarithmic-transformed values.

View larger version (18K): [in a new window]   Fig. 5. Semivariograms of (a) soil Cd concentration values and (b) normal-scored values.

View larger version (20K): [in a new window]   Fig. 6. Experimental indicator semivariograms for the (a) 5th, (b) 25th, (c) 50th, (d) 75th, and (e) 95th percentiles of the sample distribution. The solid lines depict the indicator semivariograms for the multi-Gaussian distribution.

View larger version (14K): [in a new window]   Fig. 7. Empirical distribution function for the soil Cd concentrations.

View larger version (13K): [in a new window]   Fig. 8. Semivariogram of standardized ranks for Cd concentrations.

View larger version (33K): [in a new window]   Fig. 9. Contour map of estimated Cd concentrations.

View larger version (22K): [in a new window]   Fig. 10. Contour maps of the (a) lower and (b) upper bounds of the concentration interval for soil Cd concentrations.

View larger version (24K): [in a new window]   Fig. 11. Contour maps of (a) the interval range (the deviation between the upper and lower bounds) for soil Cd concentrations and (b) the kriging standard deviation for standardized ranks.

View larger version (48K): [in a new window]   Fig. 12. Contour map of the probability of soil Cd concentration z(x) being higher than 10 mg/kg.