Using sequential indicator simulation to assess the uncertainty of delineating heavy-metal contaminated soils

Abstract

Mapping the spatial distribution of soil pollutants is essential for delineating contaminated areas. Currently, geostatistical interpolation, kriging, is increasingly used to estimate pollutant concentrations in soils. The kriging-based approach, indicator kriging (IK), may be used to model the uncertainty of mapping. However, a smoothing effect is usually produced when using kriging in pollutant mapping. The detailed spatial patterns of pollutants could, therefore, be lost. The local uncertainty of mapping pollutants derived by the IK technique is referred to as the conditional cumulative distribution function (ccdf) for one specific location (i.e. single-location uncertainty). The local uncertainty information obtained by IK is not sufficient as the uncertainty of mapping at several locations simultaneously (i.e. multi-location uncertainty or spatial uncertainty) is required to assess the reliability of the delineation of contaminated areas. The simulation approach, sequential indicator simulation (SIS), which has the ability to model not only single, but also multi-location uncertainties, was used, in this study, to assess the uncertainty of the delineation of heavy metal contaminated soils. To illustrate this, a data set of Cu concentrations in soil from Taiwan was used. The results show that contour maps of Cu concentrations generated by the SIS realizations exhausted all the spatial patterns of Cu concentrations without the smoothing effect found when using the kriging method. Based on the SIS realizations, the local uncertainty of Cu concentrations at a specific location of x′, refers to the probability of the Cu concentration z( x′) being higher than the defined threshold level of contamination ( z c). This can be written as Prob SIS[ z( x′)> z c], representing the probability of contamination. The probability map of Prob SIS[ z( x′)> z c] can then be used for delineating contaminated areas. In addition, the multi-location uncertainty of an area A,delineated as contaminated based on the probability map of Prob SIS[ z( x′)> z c], can be calculated to assess the reliability of delineation. Multi-location uncertainty refers to the probability of Cu concentrations in several locations, x′ 1, x′ 2, …, x′ m, in the area A, being higher than the threshold ( z c) as denoted by Prob SIS[ z( x′ 1)> z c, z( x′ 2)> z c, …, and z( x′ m )> z c] or Prob SIS[ z( A)> z c]. The multi-location uncertainty Prob SIS[ z( A)> z c], obtained from the SIS, can be used to assess the reliability of delineation for regions suspected of contamination, ( A), which has been delineated as contaminated. Reliance on this information facilitates the decision making process in determining which areas are contaminated and require cleanup action.