Validation of Bayesian kriging of arsenic, chromium, lead, and mercury surface soil concentrations based on internode sampling

Abstract

Bayesian kriging is a useful tool for estimating spatial distributions of metals; however, estimates are generally only verified statistically. In this study surface soil samples were collected on a uniform grid and analyzed for As, Cr, Pb, and Hg. The data were interpolated at individual locations by Bayesian kriging. Estimates were validated using a leave-one-out cross validation (LOOCV) statistical method which compared the measured and LOOCV predicted values. Validation also was carried out using additional field sampling of soil metal concentrations at points between original sampling locations, which were compared to kriging prediction distributions. LOOCV results suggest that Bayesian kriging was a good predictor of metal concentrations. When measured internode metal concentrations and estimated kriged values were compared, the measured values were located within the 5th-95th percentile prediction distributions in over half of the internode locations. Estimated and measured internode concentrations were most similar for As and Pb. Kriged estimates did not compare as well to measured values for concentrations below the analytical minimum detection limit, or for internode samples that were very close to the original sampling node. Despite inherent variability in, metal concentrations in soils, the kriged estimates were validated statistically and by in situ measurement.

Figure 1

Original (•) and internode (+) L1-L15 locations of soil collected for As, Cr, Pb and Hg measurements.

Figure 2

Frequency distributions of concentrations of A) As, B) Cr, C) Pb, and D) Hg from original sampling locations and skewness coefficients.

Figure 3

Predicted versus true values of transformed concentrations of A) As, B) Cr, C) Pb, and D) Hg from the leave-one-out cross validation (LOOCV) method with regression and reference lines.

Figure 4

Measured concentrations (Δ) and box plots of prediction distributions for internode sampling locations L1 through L15 for transformed A) As and B) Cr concentrations. Transformation of As concentrations was based on equation 3 with λ=−0.4; and for ln (Cr) (λ=0). Measured values at L2, L5, L8, L11 and L14 are the median of six closely-spaced samples.

Figure 5

Measured concentrations (Δ) and box plots of prediction distributions for internode sampling locations L1 through L15 for transformed A) Pb and B) Hg concentrations. Measured values at L2, L5, L8, L1 1 and L14 are the median of six closely-spaced samples.