Journal of Water Resource and Protection, 2011, 3, 563-583
doi:10.4236/jwarp.2011.38066 Published Online August 2011 (http://www.SciRP.org/journal/jwarp)
Copyright © 2011 SciRes. JWARP
Geostatistical Modeling of Uncertainty for the Risk
Analysis of a Contaminated Site
Enrico Guastaldi
CGT Center for GeoTechnologies, University of Siena, Arezzo, Italy
E-mail: guastaldi@unisi.it
Received June 12, 2011; revised July 12, 2011; accepted August 14, 2011
Abstract
This work is a study of multivariate simulations of pollutants to assess the sampling uncertainty for the risk
analysis of a contaminated site. The study started from data collected for a remediation project of a steel-
works in northern Italy. The soil samples were taken from boreholes excavated a few years ago and analyzed
by a chemical laboratory. The data set comprises concentrations of several pollutants, from which a subset of
ten organic and inorganic compounds were selected. The first part of study is a univariate and bivariate sta-
tistical analysis of the data. All data were spatially analyzed and transformed to the Gaussian space so as to
reduce the effects of extreme high values due to contaminant hot spots and the requirements of Gaussian
simulation procedures. The variography analysis quantified spatial correlation and cross-correlations, which
led to a hypothesized linear model of coregionalization for all variables. Geostatistical simulation methods
were applied to assess the uncertainty. Two types of simulations were performed: correlation correction of
univariate sequential Gaussian simulations (SGS), and sequential Gaussian co-simulations (SGCOS). The
outputs from the correlation correction simulations and SGCOS were analyzed and grade-tonnage curves
were produced to assess basic environmental risk.
Keywords: Uncertainty Modeling, Multivariate Geostatistical Simulations, Risk Analysis, Environmental
Pollution, Remediation Project
1. Introduction
The assessment of the risks associated with contamina-
tion by elevated levels of pollutants is a major issue in
most parts of the world. Risk is generally taken to mean
the probability of the occurrence of an adverse event, in
this case contamination above legally and/or socially
acceptable levels. Risk arises from the presence of a pol-
lutant and from the uncertainty associated with estimate-
ing its concentration, extent and trajectory. The uncer-
tainty arises from the difficulty of measuring the pollut-
ant concentration accurately at any given location and
the impossibility of measuring it at all study. Estimations
tend to give smoothed versions of reality (i.e. estimates
are less variable than real values) with the smoothing
effect being inversely proportional to the amount of data
(i.e. directly proportional to the uncertainty). If risk is a
measure of the probability of pollutant concentrations
exceeding specified thresholds then variability, or vari-
ance, is the key characteristic in risk assessment and risk
analysis. For this reason, geostatistical simulation pro-
vides an appropriate way of quantifying risk by simulate-
ing possible “realities” and determining how many of
these realities exceed the contamination thresholds [1].
Since the publication of the first applications of geo-
statistics to soil data in the early 1980s ([2-6]), geostatis-
tical methods have become popular in soil science, as
illustrated by the increasing number of studies reported
in the literature.
Geostatistics involves the analysis and prediction of
spatial or temporal phenomena, such as metal grades,
porosities, pollutant concentrations, price of oil in time,
and so forth. Nowadays, geostatistics is simply a name
associated with a class of techniques utilized to analyze
and predict values of a variable distributed in space or
time. Such values are implicitly assumed to be spatially
or/and temporally correlated with each other, and the
study of such a correlation is usually called a “structural
analysis” or “variogram modeling”. Following structural
analysis, predictions at unsampled locations are made
using any of the various forms of “kriging” or they can
be simulated using “conditional simulations”.