Previous workers have proposed the use of multivariate geostatistics for the problem of estimating temporal changes in soil properties for soil monitoring, but this has yet to be evaluated. We present a case study of this approach from the Humber-Trent region in North East England. We extracted data from two sources on cobalt, nickel and vanadium concentrations in the topsoil on two dates. Auto-variograms were estimated for each metal on each date, and pseudo cross-variograms for each metal on the two dates. It was shown that robust estimators of the auto and pseudo cross-variograms were needed for the analysis of these data. A linear model of coregionalization was then fitted to describe the spatio-temporal variability of each metal.
While the concentration of each metal in the soil showed pronounced spatial dependence that we know is driven by parent material, the charge over time was only spatially structured for cobalt and vanadium. This shows that information on spatial variability from a single date may be a poor guide to the design of a monitoring scheme. We showed how the cokriging variance of the change in concentration of cobalt and vanadium depends on sampling effort and strategy. The change in these particular variables between two dates is best estimated by sampling with equal intensity at the same sites on both dates; and when resampling an existing baseline survey it is best to sample them at rather than between the original sites. The best strategy in any case depends on how the variable is coregionalized over time.
Keywords: Geostatistics; Pseudo cross-variogram; Cokriging; Robust estimation; Soil monitoring; Heavy metals; Pedometrics』
1.1. The soil monitoring problem
1.2. The coregionalization model of spatio-temporal variation
1.3. Alternative geostatistical approaches and their limitations
1.4. What is needed now
2. Materials and methods
2.1. Soil sampling and analysis
2.2. Combining the data
2.3. Spatial analysis
2.3.1. The pseudo cross-variogram
2.3.2. Robust estimators of the pseudo cross-variogram
2.4. Analytical protocol
2.5. Hypothetical examples