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Research Collection
Doctoral Thesis
Spatial data management and decision making for soilimprovement measures
Author(s): Schnabel, Ute
Publication Date: 2003
Permanent Link: https://doi.org/10.3929/ethz-a-004625319
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ETH Library
Diss. ETHNr. 15125
Spatial Data Management and Decision Making
for Soil Improvement Measures
A dissertation submitted to
Swiss Federal Institute of Technology Zurich
for the degree of
Doctor of Natural Sciences
presented by
Ute Schnabel
Dipl. Geogr., Technical University of Hannover
born 12 July 1966 in Lehrte
citizen of Germany
accepted on the recommendation of
Prof. Dr. Roland W. Scholz, examiner
Dr. Olaf Tietje, co-examiner
Dr. Martin Fritsch, co-examiner
Prof. Dr. Willy A. Schmid, co-examiner
2003
Summary
The demand to manage the natural environment in a way that takes into
account the ecological, economic, and social aspects of development challenges
environmental planners, policymakers and other decision-makers. Decisions that
are indispensable to support such a development often rely on uncertain and
incomplete but complex information. As a result, sparse information are analyzed
and translated from micro spatial scales to macro spatial scales (and wee versa).
Consequently data generation and scale translation create a high degree of
uncertainty in results and decisions. To cope with these uncertainties the purpose
of this thesis is to improve spatial data analysis, spatial prediction and evaluation
of heavy metals in soil for the purpose of decision-making on the application of soil
remediation methods.
For a combined spatial, statistical data analysis a non-parametric Kernel
density regression was used. The results were presented as blankets drawn from
three-dimensional regression, which clearly showed spatial tendencies, hot spots,
and outliers. Herewith the method bridges the gap between explanatory data
analysis and three-dimensional visualization of spatial interrelated parameters.
Moreover, the spatial interpolation with a Gaussian Kernel density function is a
convenient alternative to ordinary kriging when the spatial, stochastic structure of
underlying data shows a trend.
With a second data set, the spatial distribution of cadmium was predicted with
lognormal ordinary kriging and conditional simulation. The results showed a
geometric mean distribution of 1.08 mg cadmium per kg soil and a standard
deviation of 2.27 mg/kg. Since cadmium was emitted from a metal smelter, the
data exploration focused on trend models and anisotropy. However the
consideration of contamination patterns reveals no significant improvement for
spatial prediction of cadmium. Regardless of high mean uncertainty for the total
area, the use of likelihoods to exceed a certain threshold at single points was
presented. Although the prediction of cadmium revealed no reliable, deterministic
estimation the handling of uncertainties with probability knowledge led to useable
and trustworthy results for the decision maker.
The uncertainty from prediction was used in multi-criteria utility analysis in
order to evaluate decisions on application of remediation alternatives like soil
washing, phytoremediation and no remediation. An overall utility was calculated
from linear and non-linear utility functions for the criteria i) human health ii) long-
term productivity of soil iii) cost of techniques and iv) change of market value.
Without weighting single criteria with a decision maker's preference 'human health'
and 'long-term productivity of soil' were decisive arguments for all remediation
alternatives.
The uncertainty of decision was quantified by the lognormal probability
distribution from predicted cadmium content. The expected utility for any true value
(or hypothesis) beyond the prediction assesses the quality of decision. Further the
goodness of decision (hit, false alarm, miss and correct rejection) describes the
deviation from hypothesized to predicted contamination. The evaluation revealed
that soil washing was preferred within a distance of 300 m to the source of
contamination, whereas no remediation is recommended beyond this distance.
Phytoremediation was only superior for concentrations around 3 mg cadmium per
kg soil.
The investigated methods improve scaling and transmission of information
and data. They are suitable for a spatial delineation of varying demands in the
context of soil improvement measures and advanced decision-making.
Zusammenfassung
Entscheidungsträger in der Umweltplanung und der Politik sehen sich in der
Förderung einer nachhaltigen Entwicklung der natürlichen Umwelt mit zahlreichen
Entscheidungen konfrontiert, die Eingriffe auf Ökosysteme, Landschaften und
andere natürlichen Ressourcen zur Folge haben. Die notwendigen
Entscheidungen müssen sich jedoch oft auf unsichere und unvollständige aber
komplexe Informationen stützen. Lückenhafte Datensätze werden für räumliche
Fragestellungen analysiert und über mehre räumliche Skalen transformiert. Die
Datenanalyse und die Datentransformation erzeugen dann einen hohen Grad an
Unsicherheit in den Ergebnissen und Entscheidungen. Diese Arbeit leistet einen
Beitrag zu der Verbesserung räumlicher Datenanalyse, räumlicher Interpolation
und der Bewertung von Schwermetallen im Boden mit dem Ziel einer verlässlichen
Entscheidungsfindung für die Anwendung von Bodenverbesserungsmassnahmen.
Für die räumlich-statistische Datenanalyse von Schwermetall¬
konzentrationen im Oberboden einer Schweizerischen Agglomerationslandschaft
(Furttal, Kanton Zurich) wird eine Kernel Density Regression eingesetzt. Mit dieser
Methode kann eine dreidimensionale Visualisierung von räumlichen Trends,
Verdichtungen und Ausreissern berechnet und gezeigt werden. Die Methode
schliesst damit eine Lücke zwischen Datenanalyse einerseits und der
Visualisierung von räumlich voneinander abhängigen Parametern andererseits.
Darüber hinaus ist die räumliche Interpolation mit einer Gauß'schen Kernel
Density Funktion eine geeignete Alternative zu Ordinary Kriging, wenn die
räumliche, stochastische Struktur der zugrunde liegenden Daten einen Trend
aufweist.
Mit einem zweiten Datensatz (Dornach, Kanton Solothurn) wird die räumliche
Verteilung von Cadmium mit einem lognormalen Ordinary Kriging Verfahren und
einer Conditional Simulation interpoliert. Die Ergebnisse ergeben eine mittlere
geometrische Verteilung von 1,08 mg Cadmium per kg Boden mit einer
Standardabweichung von 2,27 mg/kg. In der geostatistischen Datenanalyse
werden räumliche Trends und Anisotropie untersucht, da Cadmium von einem
Buntmetallwerk emittiert und mit dem Wind in den Oberboden transportiert wurde.
Die Berücksichtigung des Kontaminationsmusters erzielt jedoch keine signifikante
Verbesserung für die räumliche Vorhersage. Trotz der hohen mittleren
Unsicherheit für das gesamte Untersuchungsgebiet, können die
Eintrittswahrscheinlichkeiten für Grenzwerte an jedem einzelnen Punkt des
Untersuchungsgebietes vorhergesagt werden. Obgleich die Interpolation von
Cadmium keine verlässlichen deterministischen Ergebnisse erzielt, führt der
Umgang mit den Unsicherheiten in Form von Wahrscheinlichkeitsvorhersagen zu
einem verwendbaren und zuverlässigem Ergebnis für den Entscheidungsträger.
Die Unsicherheiten aus der Datenanalyse werden in einem weiteren Schritt
in den Prozess der Entscheidungsfindung integriert. Zunächst bestimmt eine multi-
kriteriellen Nutzenanalyse für die Sanierungsalternativen Phytoremediation,
Bodenwäsche und .keine Sanierung' den Gesamtnutzen durch die Berechung von
linearen und nicht-linearen Nutzenfunktionen. Die Abschätzung des funktionellen
Nutzens einer Cadmiumreduktion im Boden erfolgte für i) die Gesundheit des
Menschen, ii) die Langzeitproduktivität des Bodens, iii) die Verfahrenskosten und
iv) die Veränderung des Bodenmarktpreises. Ohne eine Gewichtung der einzelnen
Kriterien durch die Entscheidungsträger ist die menschliche Gesundheit und die
Langzeitproduktivität des Bodens ein entscheidungskräftiges Argument für oder
gegen die Anwendung der drei Sanierungsalternativen. Die Unsicherheit der
Entscheidung, die sich über eine lognormale Wahrscheinlichkeitsverteilung der
vorhergesagten Kontamination quantifizieren lässt, wird durch den
Erwartungsnutzen für jeden möglichen wahren Wert der Kontamination jenseits
der Vorhersage modelliert. Die Güte der getroffenen Entscheidung lässt sich
schliesslich mit der Abweichung einer hypothetischen möglichen Kontamination
zur berechneten Vorhersage validieren.
Die untersuchten Methoden zeigen einen transparenten und konsistenten
Ansatz zum Umgang mit Unsicherheiten in der Datenanalyse und Datenver¬
wendung. Somit können die dargelegten Ergebnisse zu einer verbesserten
räumlichen Interpretation und Darstellung verschiedenster Ansprüche im Kontext
von Bodenverbesserungsmassnahmen und Entscheidungsfindung beitragen.
Table of Contents
List of Figures VIII
List of Tables IX
1 Introduction 1
1.1 Motivation 1
1.1.1 Soil improvement measures 2
1.1.2. Spatial management of sparse data 3
1.1.3. Geostatistical interpolation techniques 5
1.1.4. Decision making under uncertainty 6
1.2 Aim of this study 7
1.3 References 8
2 Explorative data analysis of heavy metal contaminated soil usingmultidimensional spatial regression 11
2.1 Introduction 12
2.2 Data 13
2.3 Interpolation methods 15
2.3.1 Mollifier approach 15
2.3.2 Geostatistical approach 18
2.4 Results 19
2.4.1 Comparing Mollifier with kriging interpolation 20
2.4.2 Explorative Data Analysis with the Mollifier approach 25
2.4.3 Including co-variables for spatial prediction 31
2.5 Discussion and Conclusion 32
2.6 References 34
V
3 Uncertainty assessment for management of soil contaminants with sparse
data 30
3.1 Introduction 40
3.2 Data 42
3.3 Methods 44
3.3.1 Analysis of spatial dependency 45
3.3.2 Ordinary kriging 46
3.3.3 Geostatistical conditional simulation 48
3.3.4 Uncertainty assessment 50
3.4 Results 51
3.4.1 Spatial estimation 51
3.4.2 Uncertainty assessment 56
3.4.2 Relevance for decisions on soil remediation 57
3.5 Conclusion 59
3.6 Literature Cited 61
3.6 Annotations 65
4 Decision making under uncertainty in case of soil remediation 67
4.1 Introduction 68
4.2 The case of contaminated land 69
4.3 Probability knowledge on the contamination 71
4.4 Decision alternatives on soil remediation 74
4.5 Utilities of soil remediation 75
4.6 Utility functions for decision alternatives 77
4.6.1 Construction of utility functions 77
4.6.2 The alternative ex situ remediation (soil washing) A^ 80
4.6.3 The alternative in situ remediation (phytoremediation) Ain 82
4.6.4 The alternative no remediation Am 84
4.7 Results 86
4.7.1 The utility functions 86
4.7.2 The overall utility of remediation alternatives 87
4.7.3 The expected utility at coordinate x 89
4.7.4 Deviation from predicted to hypothesized contamination 91
VI
4.8 Discussion 92
4.9 Conclusion 94
4.10 References 95
5 Conclusion 101
5.1 Multiple spatial regression improves data management 101
5.2 Predictability versus uncertainty 102
5.3 'Correct' decisions for soil improvement measures 103
5.4 Outlook 104
Danksagung 102
Curriculum Vitae 104
VII
List of Figures
Figure 1.1.1 Scaling processes in spatial data assessment 4
Figure 2.2.1 Area of the investigation and spatial distribution of measurements 14
Figure 2.3.1 One-dimensional Gaussian density for window size 0=1 16
Figure 2.3.2 Probability weight for an arbitrarily selected grid point 17
Figure 2.4.1 Comparison of Mollifier interpolation and lognormal kriging 22
Figure 2.4.2 Spherical variogram of logarithmic transformed cadmium 23
Figure 2.4.3 Cadmium depending on lead/zinc, lead/copper and chromium/nickel 24
Figure 2.4.4 Cadmium dependency on copper (x-axis) and zinc (y-axis) 26
Figure 2.4.5 Interpolated cadmium concentration and its uncertainty 28
Figure 2.4.6 Cadmium concentration depending on soil pH 30
Figure 2.4.7 Cadmium concentration depending on altitude and land use 30
Figure 3.2.1 Spatial distribution of sampling points in Dornach 42
Figure 3.3.1 Variogram map of the logarithmically transformed cadmium data 45
Figure 3.4.1 Anisotropic variograms in the directions D1-D4 53
Figure 3.4.2 Isotropic variogram 53
Figure 3.4.3 Spatial distribution ofcadmium after conditional simulation 55
Figure 3.4.4 A south-north transection of one singular realization 56
Figure 3.4.5 Map of the likelihood ofexceeding the threshold value C=2 mg/kg 57
Figure 4.2.1 Map of a cadmium contaminated land 70
Figure 4.3.1 Model for the true value of contamination 72
Figure 4.6.1 Two examples how to derive the ecological benefit from remediation 78
Figure 4.7.1 Utility functions derived for remediation options 86
Figure 4.7.2 Contribution of each utility dimension to the overall utility 87
Figure 4.7.3 Sum functions of utilities from four dimensions 88
Figure 4.7.4 Expected utility and feasible decisions 89
Figure 4.7.5 The evaluation of decision 91
VIII
List of Tables
Table 2.1 Statistical description of the heavy metal concentration 15
Table 2.2 Different types of kernel density functions 21
Table 2.3 Comparative descriptive statistics for predicted cadmium 25
Table 2.4 Multiple R2 from multiple regression analysis 27
Table 2.5 Root mean square difference (RMSD) for Mollifier 31
Table 3.1 Statistic properties of the data 43
Table 3.2 Test of normality with a One-Sample Kolmogorov-Smirnov Test 43
Table 3.3 Legal threshold values for remediation of cadmium in soil 44
Table 3.4 Mean square error from cross validation for five different trends 52
Table 3.5 Geostatistical properties of the variograms 52
Table 3.6 Statistical properties of the interpolations (isotropic and anisotropic) 54
Table 3.7 Statistic properties of the interpolation for the core area ofpollution 55
Table 4.1 Different types of decisions depending on the estimation z(x) 73
Table 4.2 Three principles for the construction of utility functions 77
Table 4.3 Mean probabilities of occurrence for decisions 90
IX
1 Introduction
1.1 Motivation
Today the growing population and increasing consumption of natural
resources create a shortage in usable land, land quality, and biodiversity of
ecosystems. In Switzerland the settlement area raised about 13% from 1985 to
1997 while at the same time the area for agricultural use decreased. Soil
resources are contaminated with heavy metals and other pollutants and in more
than 9 % of these resources soil fertility is constrained. With ongoing pollution,
degradation, and destruction of soil resources only 40 % of the natural grown
surface will have sustained its ecological functionality in 2050 (Desaules 1998;
Häberli et al. 2002). Clearly, these and other impacts on resources ecosystems
and landscapes challenge environmental planners, policymakers and other
decision-makers. They are confronted with the demand to manage the natural
environment in a way that takes into account the ecological, economic, and social
aspects of development.
However, decisions that are indispensable to support such development
often have to rely on uncertain, incomplete and complex information. As a result,
sparse information have to be assessed, analyzed and translated from micro
spatial scales to macro spatial scales (and wee versa). Both, data generation and
scale translation create a high degree of uncertainty that increases throughout the
investigation. Since the process of decision-making is the final step after
assessment of impacts on agents, uncertainties may lead to decisions that cause
legal, medical and economic unintended consequences e.g. when a pollutant is
cumulated in higher concentrations than predicted.
Chapter 1
Reducing uncertainty with supplementary information, e.g. through additional
data sampling is a widely discussed issue (Scholz et al. 1994; Van Groenigen
2000; Wagner et al. 2001). A benefit from information gain is not guaranteed, while
auxiliary sampling induces additional costs, which often expense the financial
budget of the project.
In order to cope with the uncertainties from data analysis and data
interpretation within the context of soil improvement measures this thesis focus on
a) the usefulness of an data analysis method for land management purpose
(Chapter 2)
b) the reliability of an interpolation method (Chapter 3) and
c) the trustworthiness of decisions under uncertainty (Chapter 4)
1.1.1 Soil improvement measures
Several research activities addressed different types of remediation
techniques for the spatial management of heavy metal polluted soil and land
(Hammer 2002; Genske 2003; Sasek 2003). 'Harsh' remediation methods like soil
washing, thermal treatment, electro kinetic removal, and others irreversibly change
soil structure and properties while removing the pollutant. Since these methods
cause high costs, they are mostly applied for small areas with high
contaminations. For large and low contaminated areas 'harsh' remediation
techniques are inefficient and economically not viable. Alternatively, the potential
and feasibility of 'gentle' removal techniques was intensively studied over the last
years (Krebs 1996; Wu et al. 1999; Kayser et al. 2001). 'Gentle' soil remediation is
defined as a remediation technique that does not constrain soil properties. The
technique is distinguished in
a) methods that aim for the immobilization of heavy metals in soil through the
addition of binding agents (Wenger 2000) and
b) phytoremediation that uses the ability of heavy metal tolerant plants to
extract and to translocate heavy metals from the soil to the aboveground
parts of the plant (Kayser 2000).
Comprehensive studies concluded that phytoremediation is suitable for large
areas of small and widely spread amounts of heavy metal contamination (McGrath
et al. 2002). Moreover, the method is appropriate where a decrease of
2
Introduction
contamination induce an improvement of soil fertility. Hepperle (2002) points out
that phytoremediation has a precautionary character. Soil remediation that
reduces the heavy metal content to an amount of concentrations, where all soil
functions are maintained, saves costs for monitoring and guarantees a
multifunctional use of soil and land. Hence, the cultivation of plants that
accumulate heavy metals from the soil is suitable to improve the quality of soil and
land, as also defined by Mc Grath and Zhao et al. (McGrath, et al. 2002) and
discussed by Gupta and Wenger (Gupta et al. 2002).
1.1.2. Spatial management of sparse data
Before the implementation of soil improvement measures the prior scaling of
information about the impact on soil is a main issue. Land use and soil
management studies scale data from sampling at single points (pedon in Figure
1.1) to an area-wide distribution of data. Hereafter, the information is translated to
the scale of decision and consequences. Management models focus on decisions
and functionality instead of detailed modeling of single processes. They try to give
a reasonable answers with the help of an empirical relation and a low degree of
complexity (Hoosbeck et al. 1992). The transmission of knowledge from a detailed
micro scale to a broad macro scale of policy requirements and decision-making,
therefore requires indicators, spatial inter- and extrapolations, and evaluations
(Dumanski et al. 1998; Hoosbeck et al. 1998). Figure 1.1.1 shows three different
levels of scaling for e.g. a land management study that aims for a decision on the
application of soil improvement measures. Soil data sampling is conducted here
on an area of 10 square meters (composite sampling). Heavy metals in soil can
have a direct environmental impact on the scale1 of a three dimensional natural
body that represents the natural variability (a pedon).
An interpolation assesses the spatial distribution of heavy metals at the field
scale. The "scale of decision" that evaluates economic and social aspects besides
Here, the term scale is not determined from the cartographical point of view, which defines
a large scale as a very small area. The term does embrace larger and smaller spatial areas, but
also indicates a hierarchy and aggregation of variables within a landscape and is similarly used to
the term level (Addiscott, T.M. 1998).
3
Chapter 1
environmental impact on soil, is understood as the macro scale or community
scale.
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Figure 1.1.1 Scaling processes in spatial data assessment and context of soil improvementmeasures. Pedon is understood as a three dimensional natural body large enough to present the
nature and of its variability as defined by Hoosbeck and Bryant (1993). The degree of complexity
explains the relation between variables on this level. Arrows indicate the research chain and the
transfer of knowledge.
In most European countries data are stored in land register, soil databases
and in analog or digital maps. They differ in quality, collection standards and
spatial geometry (Burrough et al. 1998). Therefore, they rarely provide consistent,
comprehensive and area-wide data on soil and land use. International and national
land use and soil databases, for example provided by the Dutch National Institute
of Public Health and the Environment (RIVM 1998), or CORINNE land cover data
(European Environmental Agency 2000) and others, also store data on common
classification and geometry. However, for local and regional studies these data are
too sparse. They do not present the necessary degree of detail and spatial
reference in order to evaluate objectives for sustainable development of land and
soil.
4
Introduction
Hence, a great challenge in the management of land quality and other
environmental issues is the lack in consistent, homogenously and densely
sampled data for inter- or extrapolation, evaluation and finally decision-making. As
a consequence, up scaling from one level to another causes both, a loss of
information and an increase in uncertainty that accumulates from different data
sources and methods. Then, the final decision based on data scaling and
interpretation is likely to bare high risks of errors, negative consequences and
other drawbacks.
A crucial first step in data assessment is the range of uncertainty obtained
from sampling techniques and chemical soil analysis. If soil data are gathered,
sampling and sample investigation, such as chemical analysis, are the main
sources of uncertainty (Lischer 2001; Wagner, Desaules et al. 2001). Particularly,
soil parameter show natural heterogeneity as well as spatial autocorrelation. The
latter is taken into account when scaling is conducted with geostatistical
interpolation methods.
1.1.3. Geostatistical interpolation techniques
Geostatistical methods were originally proposed to predict the metal
concentration in block of rocks in South African goldmines by Krige and in the
French mining school by Matheron (Matheron 1963; Krige 1966). Within the 1980s
soil scientists discovered that the geostatistical interpolation, the so-called kriging,
suitably analyzes and predicts the spatial heterogeneity of soil and soil properties
(Burgess et al. 1980; McBratney et al. 1981; Yost et al. 1982). The implicit theory
of regionalized variable assumes a spatial model with a structural component
(Journel et al. 1978). This component consists of a) a constant mean or a trend, b)
a random component, that is spatially correlated, and c) a spatially uncorrelated
random noise. However, in environmental case studies the spatial distribution of a
soil pollutant is often induced by point sources (like industrial plants or dumps) and
transportation through a medium like air or water. As a result, concentrations of
contaminants differ with distance to the source and do not fulfill the assumption of
a random component. As a consequence several studies uses non-linear
methods, like disjunctive kriging (von Steiger et al. 1996), indicator kriging
(Barabas et al. 2001; Goovaerts 2001), and lognormal kriging (Saito et al. 2000) to
5
Chapter 1
correctly predict the spatial distribution of contaminants in soil. Additionally, the
consideration of trend models in geostatistical prediction is widely discussed
(Crawford et al. 1997; Oliver et al. 2001 ; Saito et al. 2001).
1.1.4. Decision making under uncertainty
At the end of an environmental case study the information gathered
throughout the investigation are considered to support a rational choice among
different remediation alternatives. Moreover, decision-makers have to deal with the
uncertainties about the state of the real world and are faced with probabilistic
information, e.g. about the concentration of contaminants. To achieve a 'good'
decision, decision makers trade uncertainties against the consequences of the
decision. Keeney and Raiffa (Keeney et al. 1976) defined the paradigm of
decision-making with five steps:
a) the pre-analysis shapes the problem to decide about and identifies various
alternatives
b) the structural analysis asks for the information that is needed for decision
and formalizes the structure of the decision and its choices within a decision
tree
c) the uncertainty analysis assigns probability knowledge about the empirical
data analysis and the subjective judgments of the decision maker to the
branches of the decision tree
d) the utility analysis associates consequences (utilities) to the implications of
a decision and finally
e) the optimization analysis that calculates and maximizes the expected
utility.
The construction of utilities for decision alternatives provides an information
gain and hence increases the ability to make a correct or "good" decision
(Papazoglou et al. 2000; Schmoldt et al. 2001). Although utilities are subjective
measures, they can be seen as a compromise between accurate scientific
knowledge and concise information (von Winterfeldt et al. 1986; Beinat 1997).
However, the set of attributes assigned for different utility functions has to be
sufficient and relevant with respect to the objectives of the study (Scholz et al.
2002).
6
Introduction
1.2 Aim of this study
The overall aim of this thesis is the improvement of spatial data analysis,
prediction and evaluation of sparse data for the purpose of land and soil use
management. In particular the following questions were addressed within three
publications:
• Does the use of additional co-variables like pH, soil use or land quality
indicators improve analysis and interpolation based on kernel density
regression? (Chapter 2)
• What are the differences between the spatial prediction of cadmium
concentrations with a kernel density regression and kriging? (Chapter 2)
• How can distant, irregularly distributed data be efficiently interpolated for
environmental management purposes? (Chapter 3)
• What kind of uncertainty assessment is appropriate in practical applications
and how can the uncertainty in an interpolation be assessed accordingly?
(Chapter 3)
• What are the chances and limits of the interpolation method and its resulting
uncertainty for practical purpose? (Chapter 3)
• How to use uncertain spatial data of soil contamination in a decision-making
process on soil remediation methods? (Chapter 4)
• How to derive multi-criteria utility for the evaluation of remediation
alternatives including the cost of remediation, impacts on human health,
agricultural productivity, and economic gain? (Chapter 4)
7
Chapter 1
1.3 References
Barabas, N., Goovaerts, P. and Adriaens, P. (2001) Geostatistical assessment and validation of
uncertainty for three-dimensional dioxin data from sediments in an estuarine river.
Environmental Science and Technology 35: 3294-3301.
Beinat, E. (1997) Value functions for environmental management, Environment & Management, 7.
Dordrecht Boston London, Kluwer. 241 pp.
Burgess, T.M. and Webster, R. (1980) Optimal interpolation and isarithmic mapping of soil
properties. Journal of Soil Science 31: 315-331.
Burrough, P.A. and McDonnell, R.A. (1998) Principles of geographical information systems. In:
Burrough, P. A., Goodchild, M. F., McDonnell, R. A.et al, Spatial information systems and
geostatistics. New York, Oxford University Press. 333 pp.
Crawford, C.A.G. and Hergert, G.W. (1997) Incorporating spatial trends and anisotropy in
geostatistical mapping of soil properties. Journal of Soil Science Society of America 61,1:
298-309.
Desaules, A. (1998) Nationale Bodenbeobachtung (NABO). Informationshefte Raumplanung 4: 8-
10.
Dumanski, J., Pettapiece, W.W. and McGregor, R.J. (1998) Relevance of scale dependent
approaches for integrating biophysical and socio-economic information and development of
agroecological indicators. Nurtient Cyclling in Agroecosytems 50:13-22.
European Environmental Agency (2000) CORINNE Land Cover. European Topic Centre on
Terrestrial Environment, available at:
Http://dataservice.eea.eu.int/dataservice/othersources.asp.
Genske, D. (2003) Urban land: Degradation, investigation, remediation. Berlin, Springer. 331 pp.
Goovaerts, P. (2001) Geostatistical modelling of uncertainty in soil science. Geoderma 103: 3-26.
Gupta, S.-K., Wenger, K., Tietje, O. and Schulin, R. (2002) Von der Idee der sanften Sanierung
zum nachhaltigen Umgang mit schwermetallbelasteten Böden. Terra Tech 2: 53-54.
Häberli, R., Gessler, R., Grossenbach-Mansuy, W. and Lehmann Pollheimer, D. (2002) Vision
Lebensqualität. Zürich, vdf Hochschulverlag. 345 pp.
Hammer, D. (2002) Application of phytoextraction to contaminated soils: Factors, which influence
heavy metal phytoavailability. Ph D Thesis, Ecole Polytechnique Fédérale de Lausanne.
169 pp.
Hepperle, E. (2002) Nachhaltiger Umgang mit Böden in der Schweiz: Rechtliche Instrumente.
Terra Tech 2: 49-52.
Hoosbeck, M.R. and Bouma, J. (1998) Obtaining soil and land quality indicators using research
chains and geostatisitical methods. Nutrient Cycling in Agroecosystems 50: 35-50.
Hoosbeck, M.R. and Bryant, R.B. (1992) Towards the quantitative modeling of pedogenesis - a
review. Geoderma, 55:183-210.
Journel, A.G. and Huijbregts, C.J. (1978) Mining Geostatistics. London, Academic Press. 599 pp.
8
Introduction
Kayser, A. (2000) Evaluation and enhancement of phytoextraction of heavy metals from
contaminated soils. Ph D Thesis, Swiss Federal Institute of Technology Zurich. 149 pp.
Kayser, A., Schröder, T.J., Grünwald, A. and Schulin, R. (2001) Solubilization and plant uptake of
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McBratney, A.B., Webster, R. and Burgess, T.M. (1981) The design of optimal sampling schemes
for local estimation and mapping of regionalized variables. Computers & Geoscience 7,4:
331-334.
McGrath, S.P., Zhao, F.J. and Lombi, E. (2002) Phytoremediation of metals, metalloids, and
radionuclides. Advances in Agronomy 75:1-56.
Oliver, M.A., Frogbrook, Z.L., et al. (2001) Exploring the spatial variation in wheat quality using
geostatistics. Aspects of Applied Biology 64: 207-208.
Papazoglou, I.A., Bonanos, G. and Briassoulis, H. (2000) Risk informed decision making in land
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Chapter 1
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10
2 Explorative data analysis of heavy metal contaminated soil
using multidimensional spatial regression
Ute Schnabel and Olaf Tietje (2003) Environmental Geology 44 (8) 893-904
ABSTRACT/To obtain data on heavy metal contaminated soil requires
laborious and time-consuming data sampling and analysis. Not only has the
contamination to be measured, but also additional data characterizing the soil and
the boundary conditions of the site, such as pH, land use, and soil fertility. For an
integrative approach, combining the analysis of spatial distribution, and of factors
influencing the contamination, and its treatment, the Mollifier interpolation was
used, which is a non-parametric kernel density regression. The Mollifier was
capable of including additional independent variables (beyond the spatial
dimensions x and y) in the spatial interpolation and hence explored the combined
influence of spatial and other variables, such as land use, on the heavy metal
distribution. The Mollifier could also represent the interdependence between
different heavy metal concentrations and additional site characteristics. Although
the uncertainty measure supplied by the Mollifier first seems somewhat unusual, it
is a valuable feature and supplements the geostatistical uncertainty assessment.
Chapter 2
2.1 Introduction
Heavy metal soil pollution, for example with cadmium, copper, and zinc, has
lead to an enormous number of investigations studying the spatial distribution of
heavy metal concentrations, statistical relationships between soil properties and
soil use or deriving models for heavy metal behavior in soil, subsoil, and plant
compartments. The spatial distribution of the contaminants is mostly analyzed by
geostatistical methods (Goovaerts et al., 1997; Papritz and Moyeed, 1999;
Schloeder et al., 2001; von Steiger et al., 1996). Other Statistical analyze often
apply ANOVA (Brandvold and McLemore, 1998; Yun et al., 2000; Hoosbeek et al,
1998) and factor analysis (Davies, 1997; Korre, 1999). Models for heavy metals in
soil often rely on empirical relationships between different variables (Diels et al.,
1996; Filius et al., 1998; Krebs et al., 1998). Data analysis for heavy metal
contaminated soil management includes modeling and estimation techniques
(Batjes et al., 1997), and soil evaluation procedures (soil quality assessment)
(Fraters and van Beurden, 1993; Stein and Staritsky, 1995; Tiktak et al., 1998). In
this context Keyzer and Sonneveld (1997) and Albersen and Keyzer (1998)
proposed the Mollifier method for a combined spatial and statistical soil data
analysis including management related issues like e.g. the integration of
biophysical and socio-economic data. The approach applies a Nadaraya-Watson
Kernel density function (Hardie, 1990), as a statistical data smoothing in multiple
dimensions. The kernel density function determines the weights for the
interpolation. It uses the window size (or bandwidth) as smoothing parameter to fit
the function to the data. The Mollifier is a non-parametric method and - applied for
spatial interpolation - an alternative to ordinary kriging or - in case of combining
the spatial dimensions with additional co-variables - to co-kriging. Albersen and
Keyzer (1998) implemented the Mollifier interpolation and its visualization within
the SAS environment and demonstrated its usefulness when estimating soil
erosion (Keyzer and Sonneveld, 1997) by using a dataset for the universal soil
loss equation (Keyzer and Sonneveld, 2001). The method is capable of
investigating smooth functional relations between the independent and dependent
variables. However, Keyzer and Sonneveld (2001) emphasize that the derived
regression model for interpolation is strongly data driven. Moreover, Voortman and
12
Explorative data analysis of heavy metal contaminated soil
Brouwer (2001) used the Mollifier method in combination with a parametric model
estimation based on autocorrelation and emphasize, that the spatial variability of
millet yield is better explained with a spatial autocorrelation function, rather than
with a regression of variables only. Nevertheless they considered the Mollifier
regression as an essential method for the identification of the functional form,
which fits the data best.
In this investigation the proposed Mollifier method is applied to spatially
distributed heavy metal soil data and compared with a standard kriging
interpolation. The Mollifier method is implemented in a Delphi® software
environment (Borland, 2001) and is extended to cope with different window sizes
for different co-variables. Additionally this implementation is able to visualize the
differences between the interpolation and the individual measurements and
calculates the root mean squared difference for the set of measurements as a
whole (Tietje, 2003). The study shows the potentials and limits of the Mollifier
interpolation discussing the following issues
• Does smoothing and mollifying help to analyze the dependence of cadmium
on other heavy metals and on variables known to influence the
contamination, such as soil pH?
• Does the use of co-variables like pH, soil use or a land quality indicator
improve the Mollifier interpolation of cadmium concentrations in soil?
• What are the differences between predicting cadmium concentrations with
the Mollifier and with Kriging?
2.2 Data
The study is based on a data set of heavy metal measurements in topsoil.
The site is located in the agglomeration area in the north west of Zurich
(Switzerland). Different types of land use like agriculture, pasture, forest, dwelling
and a few industrial sites characterize it. The main sources of the heavy metal
content in soil were the application of fertilizer in intensive market gardening,
winegrowing (former use) and private gardening. Local points of high pollution
were found at old industrial places like foundries or dumps (Gsponer, 1996). The
data set was gathered in 1992 and 1993 (Meuli, 1997). It is based on the nested
13
Chapter 2
sampling design proposed by Youden and Mehlich (1937) (compare Figure 2.2.1).
At every point, soil was taken at 25cm of depth from five different locations and
combined into a composite sample later in the laboratory. Most of the
measurements were located at a height around 400 m above sea level; the
highest point reached 619 m altitude.
672200
253508
••• ••• • ••
• • • • •
• • • * • & • w m
m ••• ••• • •• ••
• • • ••
• • • • • •
• ••
•#
•m •• * • 9 •
m • m
•••• • ••• ••
• • •
• •••• ••••
• • •* • •# • «fc •
• • • • • .
• • • • • •
• ••• •••
• • • ^ • • f . K • *
•• • • •
•• •••• • •
• ••• ••• ••••
»• •
• • •
• • • • •
• • ••
258464
675807
N
AFigure 2.2.1 Area of the investigation and spatial distribution of measurements in
Furttal, Canton Zurich, Switzerland
14
Explorative data analysis of heavy metal contaminated soil
Statistical parameter Cadmium Copper Zinc Lead Chromium Nickel PH
n=299 [mg/kg] [mfl/kfll [mg/kg] [mg/kg] [mg/kgl [mg/kg]
Mean 0.36 37.5 66 24 23.3 27.3 6.56
Geometric mean 0.31 25 59.4 22.6 22 25.8 6.44
Variance 59.2 3152 4126 219.8 68.5 71.4 1.18
Minimum 0.06 4.4 18.4 9.8 8.2 6.2 3.33
Maximum 2.7 587.7 1025 215.7 50.8 53.9 7.60
Kurtosis 35.6 43.9 174.2 117.8 0.78 -0.08 1.77
Skewness 4.6 5.9 12.3 10 0.99 0.15 -1.7
Guide value 0.8 40 150 50 50 50 -
(VBBo, 1998)
Table 2.1 Statistical description of the heavy metal concentration. The guide value indicates the
concentration in top soil beyond which negative impacts on soil fertility are assumed (Gysi et al.,
1991; VBBo, 1998)
For the interpolation with co-variables soil and land use data from the local
office for regional planning and surveying provided the spatially distributed data for
pH, land use and the soil quality indicator (Amt für Raumordnung und
Vermessung, 1996; Jäggli et al., 1998)
2.3 Interpolation methods
2.3.1 Mollifier approach
The Mollifier interpolation approach (Albersen and Keyzer, 1998) uses a
kernel density regression (Nadaraya, 1964; Watson, 1964) for smoothing spatially
distributed data. The regression is
y = R(x) + e (1)
where e is an error term with mean zero, bounded variance, and unknown density.
The regression R(x) is calculated as a weighted mean of the S measurements
y' y5
Ä(jo-/tf(*)=iyws=l
(2)
For a given value of x the weighting function P°(x) determines the weight of
the measurement y5 with which it contributes to the overall estimation of the
dependent variable y at the point x. For spatial interpolation x is the (in our case
two-dimensional) vector of coordinates. But due to the general approach x might
be any multidimensional vector of independent variables. This general approach to
15
Chapter 2
calculate the weights uses a kernel density function (Nadaraya, 1964; Watson,
1964) such as a one dimensional Gaussian kernel density (XploRe, 1999).
4Va)=;srxp —u (3)
with t/Bfx-x'J/land 9 a scaling factor (window size)
The kernel density (see Figure 2.3.1) has its maximum at u=0 (i.e. when the
weight is calculated at a value of x, for which a measurement Xs is available),
decreases with increasing distance to a measurement, and depends on the
window size 9. Further characteristics of kernel regression methods and additional
kernel density functions can be found in Albersen and Keyzer (1998) and Hardie
(1990) as well as on the world wide web (XploRe, 1999). The resulting weight of
measurement y5 is
WH
Ve{{x-x*)l9)if^(jc)>0
yl(x)0
(4)
otherwise
The denominator ensures, that all the weights sum up to 1
5
*=1
*Z(*)=£%«*-*)/?) (5)
1-dimensional Gaussian kernel density
0.45
0.4
0.3S
0.3 -
0.25
0,2 -
0.15
0.1
0.05
0
-5 -3 -1 0 1
distance to a measurement
Figure 2.3.1 One-dimensional Gaussian density for window size 0=1
The Mollifier interpolation determines a soft blanket between the minimal and
maximal measurements. The kind of density function and the window size
determines the degree of smoothing or "mollifying" the interpolation. The optimal
window size depends on the density of sample points (see Equation 4,5). The
16
Explorative data analysis of heavy metal contaminated soil
Mollifier approach also provides an uncertainty measure for the interpolation at
every estimation point. The likelihood ratio (Albersen and Keyzer, 1998)
8
S*¥(0)m
estimates the probability of y(x) coinciding with any of the measurements y3,. The
Mollifier interpolation requires for each point y(x), to be interpolated, and each
measurement / the calculation of the weight according to Equation (4). For an
arbitrarily selected grid point (xt= 673,985 m, x2=255,900 m, interpolated cadmium
concentration c= 862.98 u.g/kg) the weights Pg(x) are shown in Figure 2.3.2
3000
2500
2000
a.
I 1500
<3
1000
500
04-
* measured
interpolated
lower
- - - - upper
0.05 0.1 0.15
Probability Weight P(x,theta)
0.2
Figure 2.3.2 Probability weight for an arbitrarily selected grid point (Xi= 673,985 m, x2=255,900 m,
interpolated cadmium concentration c= 862.98 jug I kg ). The weights p£(x) are shown, which are
used for the interpolation according to Equation (2). The uncertainty Q(x,a) (see Equation 7) of the
interpolation is measured as the sum of the probability weights of those measurements, whose
difference to the interpolated value (yse) is larger than \a\ (with a defined as 200 fig I'kg, in this
case Q(x,a)=0.263)
17
Chapter 2
The sum of the weights of measurements outside a given range (see Figure 2.3.2
where a equals 200 ßglkg) estimates the uncertainty of the interpolation
(Albersen and Keyzer, 1998)
Q0(x,a) = £ P;(x) withS(x,a) = {s\ \\ys ->£(x)|>a] (7)S(x,a)
2.3.2 Geostatistical approach
The geostatistical model of spatial variability assumes that the sampling S is
one realization of a stochastic process (Cressie, 1993; Webster and Oliver, 2001).
The measurements y(xs) indicate the heavy metal concentration at data
coordinates xi,...,xs and differ in dependence on the distance vector h (Matheron,
1963). The spatial dependency is shown in the variance model (semivariogram) by
calculating half the variances y{h)of concentration differences y(x)-y(x+h) of all
measurement pairs with the same distance
2ntf
where h is the (e.g. Euclidean) distance, n the number of pairs and h > 0
The derived empirical model of spatial dependency is fitted to a variogram
model, which in our case of cadmium data (see Table 2.1) is a spherical function
(Armstrong, 1998; Geovariances, 1997; Webster and Oliver, 2001).
y(h) =c0 + q
v2ûf \a)j
for h <; a(9)
c0 + c1 otherwise
where h is the distance between two points in two dimensions and a is the range,
the distance of spatial dependency. Other functions (like gaussian, exponential)
are discussed, for instance in (Cressie, 1993; Journel and Huijbregts, 1978;
Matheron, 1963, 1973; Tietje and Richter, 1992). At small distances any
discontinuity for y{h) is shown by the nugget effect (co), that is where the
variogram function (see Figure 2.4.2) intercepts the ordinate. This might be
caused by a lack of data (sparse data sampling) or high local heterogeneity of the
18
Explorative data analysis ofheavy metal contaminated soil
variable (Webster and Oliver, 2001). The interpolation method of ordinary kriging
is a weighted average for every estimation point.
where y*(xQ) is the estimated value at the coordinate x0, and /(xjis the
measured value at xs, and the A, are the weights determinded by minimization of
the variance of the interpolation (Cressie, 1993; Goovaerts, 1997; Journel, 1989).
The uncertainty of the interpolation is expressed by the kriging variance a^(Xs),
n
which is a] = £Xsy{x, ,x0 )+i//{x0 ) (11)
where Xs are the weights distributed in terms of the data model and y/ is the
Lagrangean multiplier (Armstrong, 1998; Goovaerts, 2001). The kriging variance is
a weighted sum of the semivariances y{xs,x0) between the estimation pointxq and
the measured point x$. All weights sum up to one and are determined by
minimizing the estimation variance with the help of Lagrangean multipliers.
Assuming that estimation points near by a measurement are more correlated to
the measurement than those more distant, they carry a higher weight. The nugget
effect influences the distribution of weights in such a way that more distant
estimation points carry a slightly larger weight than they would do without a nugget
effect (Webster and Oliver, 2001).
2.4 Results
The results are divided into three sections. In the first section the
interpolation of cadmium with the Mollifier density regression is compared with
geostatistical interpolation. In the second section results of the Mollifier
interpolation are shown, where the cadmium concentration was analyzed for any
interdependency on copper, lead, nickel, and chromium. In the third section co-
variables like a soil quality indicator, land use and altitude have been included for
spatial prediction of cadmium.
19
Chapter 2
2.4.1 Comparing Mollifier with kriging interpolation
The Mollifier approach as spatial interpolation in two dimensions is
comparable to other interpolation methods like inverse distance interpolation
(Gotway et al., 1996), spline interpolation (Hutchinson and Gessler, 1994; Press et
al., 1989) or kriging (Webster and Oliver, 2001). Heavy metal concentrations in soil
are known to exhibit spatial heterogeneity and geostatistical dependence (Meuli,
1997; Van Groenigen, 2000). Several investigations have shown how ordinary
kriging (Kravchenkto and Bullock, 1999; Saito and Goovaerts, 2000;
Schloeder.Zimmermann, Jacobs, 2001), lognormal kriging (Papritz and Moyeed,
1999), indicator kriging (Goovaerts.Webster, Dubois, 1997; Stein et al., 2001), and
co-kriging (Castrignanô et al., 2000; Einax and Soldt, 1998; Yu-Pin, 2002) can
lead to a reasonable spatial assessment. For this reason, a comparison of the
Mollifier interpolation with kriging is a kind of benchmarking for the Mollifier
approach.
The Mollifier depends on the number of independent variables (see below),
the type of kernel density function and, its main parameter, the window size. In
principle any measurable decreasing function with its maximum at the origin can
be used for mollifying. For practical purpose there are three types of kernel density
functions:
1. piecewise continuous functions on a finite window, which are best
applicable to non-continuous (ordinal or even categorical) data, such as
land use type or classes of soil fertility.
2. Continuously differentiable functions within a finite window, which yield a
more 'soft' interpolation and hence are best applicable to continuous
(metric) data, such as soil characteristics like the pH or contaminant
concentrations
3. Continuously differentiable functions within a principally infinite window,
which is mainly the Gaussian density, leading to the softest interpolation
'blankets'.
20
Explorative data analysis of heavy metal contaminated soil
Table 2.2 gives an overview of tested kernel density functions.
Mollifier Kernel Tested Comment
density dimension
function
Uniform square 2 and 3 piecewise continuous within a finite window
Uniform circle 2 piecewise continuous within a finite window
Cone 2 piecewise continuous within a finite window
Epanechnikov 2 Continuously differentiable within a finite window
Quartic 2 Continuously differentiable within a finite window
Triweight 2 Continuously differentiable within a finite window
Fourweight 2 and 3 Continuously differentiable within a finite window
Gaussian 2 and 3 Continuously differentiable within a principally
infinite window
Cosine 2 Continuously differentiable within a finite window
Table 2.2 Different types of kernel density functions implemented and tested in MolliD (Tietje,
2003). A more detailed description of the kernel functions can be found in Parzen (1961) and
Cressie (1993)
The window size is the parameter determining the spatial range in between
measurements that is taken into account for interpolation. For a small window size
the interpolation results are heterogeneous and tend to map the sampling points
only. For a window size lower than half of the distance between the measurements
an interpolation is not possible. Then, the Mollifier interpolation shows 'wholes' in
the interpolated blanket (like kriging interpolation would do, if there were grid
points outside the geostatistical range of any measurements). For large window
sizes the interpolation is smoothed. If the window size is larger than the
interpolated area, then the result is an almost constant value throughout the area.
Figure 2.4.1 shows a on the right hand side a Mollifier interpolation with a
Gaussian density and a window size of 200 m. The 'blanket' is largely 'mollified'
with a reduced heterogeneity, leaving some large differences between the
measurements and the interpolation. Please note that this is a non-parametric
regression with the value of the window size determining the degree of data
smoothing. This parameter has to be defined according to the purpose of
interpolation.
21
ALognormalkr
igin
g
RMSD=
163.68(n=299)
RRMSD-
112
*2-Y
y1-Cd
[OlÉUUU.HZJ3UUUWI
BMollifier
RMSD=
14100[n-299]
RRMSD=
D.10
(672
0000
2590
00.0
1(6
7600
0.0
2590
00.0
)
(6733000
2530000)
(S7600O0253000HJ
Figure2.4.1A:ComparisonofMollifierinte
rpol
atio
nandlognormalkr
igin
goftotalcadmiumconcentration(between100and2700yg/kg)
onasp
atia
lgndfrom672,000
mto676,000m
(easting)and253,000m
to259,000m
(northing).The
verticalbarsrepresentthecadmiummeasurementsabove
(fightgrayba
r),below(darkgrayba
r),
orequal(black
dots
)tothein
terp
olat
ion.
B:LognormalKr
igin
gin
terp
olat
ionwithsp
heri
calvariogram,range=2177,
sill=0.2,nugget=0.08
Explorative data analysis of heavy metal contaminated soil
For the geostatistical analysis the data were logarithmically transformed and
fitted to a spherical variogram (Equation 7, Figure 2.4.2). The data show a spatial
dependency within a distance of 2,177 m. The model behaves discontinuous near
the origin and reveals a nugget effect of 0.08(ng/kg)2 and a sill of 0.22 (jag/kg)2
(both on the log-scale). Lognormal ordinary kriging was performed with the
parameters of the variogram discussed above.
0.3
0.2
rih)
0.1
°'°0. 1000. 2000. 3000. 4000. "5000.
distance [meter]
Figure 2.4.2 Spherical variogram of logarithmic transformed cadmium with a sill of 0.22 (ng/kg)2, a
nugget effect of 0.08 (|J.g/kg)2 and a spatial range of 2,177 m
The comparison of both methods, kriging and the Mollifier interpolation,
reveals a similar smoothing of the data. Both blankets are presented in Figure
2.4.1. Table 2.3 shows the descriptive statistics of both interpolations. If a
variogram model (such as the spherical model in Figure 2.4.2) can be well fitted to
the empirical variogram (Equation 10), then kriging is superior, because it
consistently explains the stochastic spatial structure of the data. Otherwise the
Mollifier interpolation is preferred, because it does neither rely on nor indicate a
questionable geostatistical characteristic of the data. If the Mollifier software
23
y-^
\y
Cadmium
Interpolation
Uncertainty
Q0
(>-,
200
)ofCadmium
inte
rpol
atio
n
A2
Copper
Zinc
-JSOO,6GOt
io
Nickel
Figure2.4.3Cadmiumdependingon
lead/zinc,
lead/copperandchromium/nickel.Forcopperandzincthewindowsizeis
10mg/kg,
foraitothervariables5
mg/kg.
Note
the
different
scales
of
the
independent
vari
able
s,the
cadmium
inte
rpol
atio
n,and
the
sum
of
weights
Q(x,a)
Explorative data analysis of heavy metal contaminated soil
became more widespread, it could be easily applied for the screening of spatial
data. The three-dimensional representations of the interpolated grid together with the
resulting data deviations (gray and black bars) largely support the interpretation of
both interpolation techniques. Especially because a good fit of the variogram (Figure
2.4.2) could be falsely interpretated as indicating a good fit of the kriging interpolation
(RMSD=163, Equation 12 and Figure 2.4.1A), which might not be better than the
Mollifier interpolation (RMSD=141, Equation 12 and Figure 2.4.1B).
Mollifier interpolation
cadmium [u.g/kg]Lognormal ordinary kriging
cadmium [u.g/kg]
Fitting parameter gaussian density function,window size 200
spherical model, sill 0.22,
nugget 0.08, range 2,177 m
Mean 308 275
Variance 41,997 21,819
Standard Deviation 205 148
Maximum 1,898 1,458
Minimum 95 72
Geomean 268 249
Table 2.3 Comparative descriptive statistics for predicted cadmium concentrations with both
interpolation methods
2.4.2 Explorative Data Analysis with the Mollifier approach
For the explorative data analysis the dependency of cadmium on other heavy
metals (like copper, lead, nickel and chromium) in soil is analyzed with the Mollifier
interpolation. In Figure 2.6 the results of the regression analysis for the relevant
heavy metals copper, zinc and lead are shown.
Comparing the blankets for the independent variables lead/zinc, lead/copper
and chromium/nickel it is obvious that the latter reveals the smallest deviations from
measurements (indicated as gray and black bars below and above the blanket). The
cadmium content seems to increase with increasing chromium and nickel content.
For lead and copper only a few measurements determine the increase of cadmium.
25
15IB
CO
1001
00
500.
00
250000
200000
1500.00
1000.00
500.00
0.00
POO
0.0]
Figure2.4.4Cadmiumdependencyoncopper
(x-axis)
andzinc
(y-axis).Thewindowsizeonthe
righ
thandside
is10timessmallerthanonthe
lefthand
side.Theregression
iscalculatedwithaGaussiandensityfunction.Thecadmiumaxis
isdenoted
inpg/kg
Explorative data analysis of heavy metal contaminated soil
Although calculated with the same parameters of fit (density function, window size)
the influence of copper as independent variable is different to that of zinc for the
prediction of cadmium. Compared with a multiple regression analysis the squared
sum of the multiple correlations (multiple R squared between cadmium, copper, zinc
and lead reveals only a weak dependency between the variables. However it reveals
a similar portion of variance for the dependent variable (see Table 2.4). As opposed
to that the prediction of cadmium with the Mollifier results in different blankets for the
independent variables copper/lead and zinc/lead.
Cu/Pb Zn/Pb Cr/Ni Cu/Zn
Multiple R squared 0.569 0.576 0.230 0.477
Table 2,4 Multiple R2 from multiple regression analysis for the explorative variable cadmium. As a
measure of fit for the regression model it indicates the explainable proportion of variation in the
dependent variable cadmium
A detailed view of the distribution of probability weights in Figure 2.4.3 shows
that the highest interpolations of the dependent variable are calculated from widely
scattered measurement points. The higher the weights, the more the interpolated
value differs form the accounting associated point. In this case the probability that the
difference between interpolated point and any measurement point is larger than 200
pg/kg is summed up for the uncertainty measure Q0(x,à) (compare Equation 7). The
highest cadmium contents reveal the highest probabilities of being outside a range of
200 pg/kg around the interpolated value. This is due to sparse data sampling
(compare Figure 2.4.3). Although the results are uncertain for high cadmium contents
the distribution of the uncertainty and the contributing measurements are clearly
visible. Therefore an explorative data analysis with the Mollifier gives a
comprehensible view on the data point.
However, in order to analyze any interdependency a cautionary fit of
interpolation parameters is necessary. On the left side in Figure 2.4.4 the
interpolation turned into an extrapolation, because two single measurements
determine a large area without any further data whereas most of the data
concentrate in the lower left corner with marginal influence on the interpolated area.
In this case the window size and the scale (size) of the interpolated area have to be
27
[3.0.110.0)10
1100)
Cd[u
g/kg
]
(3.0.1100)10.0)
Zn[mg/kg]
[3.0
1001(110.10.01
pH
ß,(*,200)
Zn[m
g/kg
]
(30.(110.100]
pH
Figure2.4.5In
terp
olat
edcadmiumconcentrationand
itsuncertaintyQ(
x,a)
asdependentonpHandzinc
Explorative data analysis of heavy metal contaminated soil
reduced. The result is visible on the right hand side of Figure 2.4.4. The
correlation of cadmium (with copper and zinc) is visible with the increase of the
blanket in the upper right corner. All regressions were computed with a Gaussian
kernel density function.
In a next step soil and land use data are tested for any interdependency with
cadmium. Total cadmium and zinc contents in soil behave similar in same pH-
milieu. Both heavy metals are soluble at a pH-value lower 7 (Filius.Streck, Richter,
1998; Geiger, Schulin, 1995). Therefore cadmium dependency is tested for pH-
value and zinc in Figure 2.4.5. From the interpolation it is visible that the cadmium
content in soil tends to rise with increasing pH-value and zinc content. High
cadmium concentrations are correlated with high zinc contents above a pH-value
of 6. For further information on the spatial and stochastic distribution of cadmium
additional land and land use properties are taken into account. In Figure 2.4.6 it is
visible that pH-values below 5 occur mainly above 500 m altitudes (above see
level), whereas high cadmium concentrations occur at the lowest altitude with high
pH-values. This is mainly due to agricultural use in the bottom of the valley and to
forest and winegrowing plots in higher altitudes.
A blanket (Figure 2.4.7) of the independent variables 'altitude' and 'land use'
against cadmium concentrations confirms the results from Figure 2.4.6 High
cadmium contents are interpolated for land uses in low altitude, like agriculture,
dwelling and industry, while the cadmium concentration decreases with increasing
altitude and mainly under forest. This also explains low cadmium contents in soil
with pH-values below 5 (see Figure 2.4.6), which are common for soils under
forestry use. Note that this blanket is calculated with a Uniform square kernel
density function and a small window size for the dimension of land use (20 m) so
that the interpolations of different land uses do not influence each other. This
piecewise continuous kernel function (see Table 2.2), applied within a small finite
window size, results in a more reasonable interpolation of ordinal scaled data than
the Gaussian kernel functions for the same data does (blanket not shown).
However the blanket shows general tendencies of spatial distribution of the
dependent variable. In all land use categories the interpolated cadmium
concentration is slightly above the measured value, except for a few locations with
large underestimations. This reflects the lognormal distribution of cadmium, which
was not accounted for in the non-parametric Mollifier interpolation.
29
Chapter 2
(30, 70) (80, 70)
2500 00
2000 ro
Cadmium [ug/kg ]
1500 00 '
1000 00
500 00
(30 40)
pH
(80 40)
2500.00
3300 00
1500.00
1000 00
500 00
0.00
Altitude
Figure 2.4.6 Cadmium concentration depending on soil pH (window size 0.5) and altitude (elevation
above sea level, window size 20 m)
(400,6 0m)
i
(700m, 6 0)
1 250000
I 1 BOO 00
Cadmium [|jg/kg ]
.000
6: Unused Area
(400m, 0 0) (0 0,700m)
Altitude
Figure 2.4.7 Cadmium concentration depending on altitude (400 - 700 m, window size 20 m) and
against land use (window size 0.1). The kernel density function is Uniform square
30
Explorative data analysis of heavy metal contaminated soil
2.4.3 Including co-variables for spatial prediction
In order to improve the interpolation of cadmium, soil agricultural suitability is
included as a third independent variable. However the results show only marginal
change of the interpolated value compared to mollifying without co-variables
(presumed same grid, function and window size). As a general measure of the
goodness of the interpolation serves a root mean squared difference criterion:
RMSD =
y/2
-!,(?,-y'J\n~i
(12)
where the differences between the predicted (interpolated) yp' and measured
cadmium concentrations ym' of the n=299 measurements is assessed.
Although the interpolation reveals similar results the use of the co-variable
allows a more precise prediction in the vicinity of the measurements if the window
size is varified according to the third independent variable. The use of a third
window size for the co-variable reveals also a less smoothed blanket as a
consequence of the higher preciseness (see Table 2.5). The uncertainty of
prediction can even be improved by the use of a density function with finite window
size (compare Table 2.2). But the choice of density function has to be made with
respect to the data (compare Figure 2.4.6).
Co-Mollifier Mollifier
Xr=laltitude , x2= lonqitude, Xa= soil suitability Xi=laltitude, x2= lonqitude,
Kernel Density Function Window size RMSD RMSD
Uniform square 200 m, 200 m, 5 106.10 109.61
200 m, 200 m, 1 96.16 -
Fourweight 200 m, 200 m, 1 47.47 55.24
Gaussian 200 m, 200 m, 1 128.82 141.00
100 m, 100 m, 0.1 51.55 63.50
50 m, 50 m, 0.1 42.91 47.95
Table 2.5 Root mean square difference (RMSD) for Mollifier with and without co-variable according
to change of density function and window size. Soil suitability is classified from 1 to 11
(nondimensional) according to the soil map (Jäggi et al. 1996)
31
Chapter 2
2.5 Discussion and Conclusion
The results from different interpolations with kernel density regression show
the explorative data analysis as a main use of the Mollifier approach. Especially for
multivariate explorative analysis of spatial distributed data the three-dimensional
blanket of dependency between variables is able to show general tendencies,
outliers, hot spots, and punctual dependencies. Herewith it is a useful tool
between a Geographical Information System (GIS, like Arc/Info) (Burrough and
McDonnell, 1998; Hendriks et al., 1998) and descriptive statistics, using e.g.
scatter plot matrices or regression analysis. A GIS often is able to spatially
interpolate single variables (with e.g. Spline interpolation, Inverse Distance
Weighting or Kriging), to create overlay maps, and to query first-order statistics of
different variables. The results are mostly shown in two dimensions only (Fedra,
1998; Kooistra et al., 2001). In contrast any correlation between variables is simply
to analyze with descriptive analysis, but gets more difficult when more than two
variables and the spatial extension are of interest. Within this gap, the Mollifier
reveals convenient results as it is seen for example in Figure 2.4.1 and Figure
2.4.3. Moreover the method is easy to apply and results are quickly visible and
useable. The comparison with a multiple regression analysis (Table 2.4) showed
that the variance in the predicted variable is visible with the Mollifier regression at
single points and yields a more detailed analysis therefore. As opposed to the
Mollifier version used by Albersen and Keyzer (1998), the Mollifier program used
in this study (see Tietje, 2003), shows the deviation of the data from the
interpolated blanket as black and gray bars at the sampling points. This allows a
valid interpretation of the blanket with respect to the measured values. The
interpretation is additionally supported by the uncertainty measure (Equation 7).
Moreover the preciseness of interpolation (in terms of the root mean squared
difference between the measurements and the interpolation) can be improved with
an additional independent variable, especially around the measurements. The
improvement is even enlarged, when the choice of the density function and the
window size is adapted to the data.
Compared with the widely used geostatistics and kriging (Andronikov et al.,
2000; Goovaerts, 2000; Juang and Lee 1998) the Mollifier approach is
conveniently usable for spatial prediction. The method strongly depends on the
32
Explorative data analysis of heavy metal contaminated soil
density of the data and therefore the kind of density function and the window size
are an important choice to be made. The type of the kernel density function
determines the degree of smoothing, but even more the window size does.
Therefore both parameters have to be chosen carefully and appropriate to data
structure and the purpose of interpolation. From the analysis of interdependency of
cadmium to land use it is shown that a continuous differentiable density function,
like the gaussian, is recommended for quantitative continuous data. In most of the
cases the interpolation of qualitative ordinal data can be better calculated with any
continuous differentiable kernel density function with finite window size. In the
case of sparse sampling the flexibility of the non-parametric approach turns in a
disadvantage because the measures of fit, Q and A (Equation 6 und 7), are not
reliable for low data density (Stahel, 2000). In environmental case studies the
spatial distribution of a contaminant is often caused by point sources (like plants or
dumps) and transportation through a medium like wind or water. As a result
concentrations of pollutants differ with distance to the source and therefore do not
fulfill the assumption of a gaussian random distribution with a stationary mean.
However this presumption is needed for (geo)statistical predictions (Limpert et al.,
2001). Then, non-linear methods have to be used instead which are reported to
interpolate with a loss of preciseness (Papritz and Moyeed, 1999). The Mollifier
approach may serve as an appropriate alternative to geostatistical methods if the
required assumptions of stationarity cannot be validated.
Acknowledgments
We are grateful to Günter Fischer and Silvia Prieler at the International Institute of Applied
System Analysis, Austria for the first contact and help with the Mollifier, M. Keyzer and B.
Sonneveld at the Centre for World Food Studies, The Netherlands for helpful comments on a first
manuscript of this paper and also P.J. Albersen at the same institute for the help with the Mollifier
programme. Last but not least we would like to thank Martin Fritsch, R.W. Scholz and the
colleagues at UNS for discussions and support of our work. The project was funded by the Swiss
National Science of Foundation (Project Number 50011-44758) and the Swiss Federal Institute of
Technology (Project Number 0048-41-2609-5)
33
Chapter 2
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Seite Leer /
Blank leaf
3 Uncertainty assessment for management of soil contaminants
with sparse data
Ute Schnabel, Olaf Tietje, Roland W. Scholz (In press), Environmental Management
ABSTRACT/ln order for soil resources to be sustainably managed, it is
necessary to have reliable, valid data on the spatial distribution of their
environmental impact. However, in practice, one often has to cope with spatial
interpolation achieved from few data that show a skewed distribution and uncertain
information about soil contamination. We present a case study with 76 soil
samples taken from a site of 15 square km in order to assess the usability of
information gleaned from sparse data. The soil was contaminated with cadmium
as a result of airborne emissions from a metal smelter. The spatial interpolation
applies lognormal anisotropic kriging and conditional simulation for logtransformed
data. The uncertainty of cadmium concentration acquired through data sampling,
sample preparation, analytical measurement, and interpolation is factor 2 within
68.3 % confidence. Uncertainty predominantly results from the spatial interpolation
necessitated by low sampling density and spatial heterogeneity. The interpolation
data are shown in maps presenting likelihood's of exceeding threshold values as a
result of a lognormal probability distribution. Although the results are imprecise,
this procedure yields a quantified and transparent estimation of the contamination,
which can be used to delineate areas for soil improvement, remediation, or
restricted area use, based on the decision makers' probability safety requirement.
Chapter 3
3.1 Introduction
Land-use management is challenging for the planning departments of both
local and regional governments, especially where land use is extensive and
contaminants are widespread (Roe and van Eeten, 2001). Low concentrations of
pollutants have long-term impacts, e.g., on soil fertility in the case of soil
contaminants (Grunewald, 1997; Gysi and others, 1991). The impact of
contaminants contributes to a shortage of usable land and consequently to
competition of interest among different land uses. As a result, the market value of
usable land may change and thus affect sustainable land-use management as
Prato (2000) demonstrated.
We present a case study involving a location with cadmium-contaminated
soil. For a large part of the area considered, soil measurements show
contamination levels above the guide value, but below the remediation value as
outlined in the Swiss Ordinance Relating to Pollutants in Soil (VBBo, 1998) (Table
3.3 and Table 3.1). If the guide value is exceeded, remediation of the soil may be
considered appropriate where contamination of groundwater, crops, or soil fertility
could be endangered. However, in this case, there are no standards mandating a
cleanup. According to Swiss Ordinance Relating to Pollutants in Soil (VBBo, 1998)
soil contamination levels between the guide value and remediation value indicate
the necessity of a change in land use, for example, from food production to
residential use. Such changes often provide a less expensive alternative to
remediation. Remediation is only legally obligatory when the remediation value is
exceeded. This legal situation shows that assessment of soil contamination is
relevant for sustainable land management, even when the pollutants pose no risk
to human health. Assessment of soil contamination for precautionary soil
improvement is difficult, because of the lack of data and high degree of uncertainty
from sparse data. Decisions on soil use change are difficult to substantiate. In
order to evaluate the affected areas in a valid, reliable, and cost-effective way, a
spatial interpolation that includes appropriate uncertainty information is required.
The common sources of uncertainty in spatial prediction are data sampling
(sparseness and inaccuracy), the preparation and measurement of samples in the
laboratory (Dubois and Schulin, 1993; Muntau and others, 2001), the spatial
40
Uncertainty assessment for management ofsoil contaminants
interpolation of the data (Goovaerts, 2001; Meuli, 1997), and subsequent modeling
(Hendriks and others, 2000; Keller and others, 2001; 2002). Several geostatistical
models address the amount of uncertainty from interpolation techniques (Barabas
and others, 2001; Bouma and others, 1996; von Steiger and others, 1996).
Modeling uncertainty by means of stochastic simulation is also widely used
(Gotway and Rutherford, 1993; Pan, 1997; Van Meirvenne, 2001). For example,
Goovaerts (2001) compared kriging-based estimation to simulation-based spatial
estimation and concluded that simulation offers several advantages, the most
important one being that it provides a model of spatially local uncertainty. In cases
of lognormally distributed data, ordinary lognormal kriging is easy to implement
and yields better results than other kriging methods (Papritz and Moyeed, 1999;
Saito and Goovaerts, 2000). Other investigations applied indicator kriging (Van
Meirvenne, 2001; Webster and Oliver, 2001) or disjunctive kriging (Papritz and
Moyeed, 1999; von Steiger and others, 1996), because of the complications to
estimating local probability density function when applying a traditional
backtransformation (Geovariances, 1997; Webster and Oliver, 2001, p. 19).
Therefore, we follow the approach of Limpert and others (2001), who presented
the uncertainty on the raw scale by means of the geometric mean, the
multiplicative standard deviation, and consequently, the multiplicative confidence
intervals for a multitude of lognormal distributed data.
Thompson and Fearn (1990, p.271) discuss the relation between sampling
and cost of analysis as well as the quality of data appropriate for data assessment.
They define fitness for purpose as "the property of data, produced by a
measurement process, that enables a user of the data to make technically correct
decisions for a stated purpose." The decision whether or not the information
supplied by the available data and its degree of uncertainty are useful depends on
the purpose for which the data will be used. Decision-makers have to judge the
appropriateness of using uncertainties as a substantive base for their decision
(Ramsey and others, 1998; Thompson, 1995). It is the decision and its
consequences that matter, rather than the accuracy of the prediction (Goovaerts
and Meirvenne, 2001). Thus, the main objective of this study is to analyze the
usability of the information given by spatial interpolation of few measurements,
41
Chapter 3
combined with probabilistic reasoning based on sparse data for the case of
Dornach (Canton Solothum, Switzerland).
The following questions will be addressed:
• What kind of spatial prediction is suitable when distant, irregularly
distributed measurements are analyzed for environmental management
purposes?
• How can the uncertainty in an interpolation be best assessed and
presented?
• What possibilities and limitations are posed by applying the
interpolation method and its resulting uncertainty for practical planning
purpose?
3.2 Data
We present a case study from Switzerland where 76 soil samples were taken
in an area of 15 square kilometers. Each was a composite sample from topsoil (20
cm depth) within a range of 10 square meters (Wirz and Winistörfer, 1987). Soil
samples were taken without a specific sample design, and the sites were more or
less randomly distributed. An attempt was made to cover the supposed area of
contamination (Figure 3.2.1) and take local circumstances into account.
42
Uncertainty assessment for management of soil contaminants
The total heavy metal content of the soil was determined in a 2 M HNO3
extract following the Swiss Ordinance Relating to Pollutants in Soil (VBBo, 1998)
and measured with a atom adsorption spectrometer (AAS) using the flame-AAS
method.
Value Cd (mg/kg) In Cd (mg/kg)
Count 76 76
Geometric Mean 0.93
Average 1.43 -0.08
Standard deviation 2.69 0.80
Variance 7.26 0.64
exp(average(ln(Cd))) 0.93
exp(stddev(ln(Cd))) 2.22
Median 0.86 -0.16
exp(median(ln(Cd))) 0.86
Skewness 7.36 0.78
Kurtosis 59.67 2.89
Min 0.12 -2.12
Max 23;3 3/I5
Table 3.1 Statistic properties of the data
The data analysis in Table 3.1 reveals that the distribution of heavy metal
measurements is highly skewed (Skewness 7.36). This also shows the difference
between the median (0.86 mg/kg) and the geometric mean (0.93 mg/kg) of the raw
data. For such data, logarithmic transformation may be appropriate before
interpolation. The statistics from a Kolmogorov-Smirnov-Test show that the
logarithmically transformed data follow a normal distribution (p > 0.35, Table 3.2).
Because the test presumes independency of the observations, a random set from
the data, chosen with the most possible distance from every other measurement
point, was also tested and accepted (p=0.74, Table 3.2).
Cd (mg/kg) Ln(Cd) (mg/kg) Ln(Cd) (mg/kg)
N 76 76 29
Normal Parameters Mean 1.43 -0.08 -0.06
Std. Deviation 2.69 0.80 0.98
Most Extreme Differences Absolute 0.31 0.11 0.13
Positive 0.30 0.11 0.13
Negative 0.31 -0.06 0.13
Kolmogorov-Smirnov Z 2.74 0.94 0.68
Asymp. Sig. (2-tailed) 0.00 0.35 0.74
Table 3.2 Test of normality with a One-Sample Kolmogorov-Smirnov Test for the logtransformeddata. A subsample of spatial independent data fulfill the assumption of independency (test
distribution is normal, mean and standard deviation are calculated from data)
43
Chapter 3
Cadmium was emitted from a metal smelter (Figure 3.2.1, Dornach, Canton
Solothum, Switzerland) during the past century. Today the pollutant can be found
on the west side of Dornach (Figure 3.1), a result of the west to east dominant
wind direction (Schweizerische Meteorologische Anstalt, 1982-91) and the
northwest facing slope on which the community of Dornach was built (Hesske and
others, 1998). In addition to the airborne contamination, the intrinsic cadmium
content in parent material is above the Swiss average of 0.3 mg per kilogram of
soil (Tuchschmid, 1995, Keller, 2001).
Swiss Ordinance Relating to Pollutants in Soil Cadmium, total,
Verordnung über Belastungen im Boden (VBBo) HN03 soluble
vom 1. Juli 1998 fmg/kg]
Guide value / Richtwert 0.8
Trigger value / Prüfwert
- use with probable oral intake / Nutzung mit möglicher direkter 10
Bodenaufnahme 2
- use for food planting / Futterpflanzenanbau 2
- use for feed planting / Nahrungspflanzenanbau
Remediation value / Sanierungswert-agriculture and horticulture / Landwirtschaft und Gartenbau 30
- gardening / Haus- und Familiengärten 20
- playgrounds / Kinderspielplätze 20
Table 3.3 Legal threshold values for remediation ofcadmium in soil in Switzerland (VBBo, 1998)
Geiger and Schulin (1995) found high variability (n=50, average^ 4.38 mg/kg,
variance= 0.72 (mg/kg)2, min=2.37 mg/kg, max=5.92 mg/kg) on a 40 m transection
in the same area. Soil parameters and contaminants tend to behave randomly on
the small scale (Webster, 2000). Thus, for this case study, it was necessary to
take the variability of the data on a scale of a few tens of meters into account when
we analyzed it.
3.3 Methods
Within the framework of geostatistical analysis, the measured cadmium
concentrations (see above) are assumed to be one realization a stochastic
process {Z(x):xeD} (Cressie, 1993; Goovaerts, 1997), where D denotes the
sample space for the investigated case study area of Dornach (see Figure 3.1).
Let xv...,xn denote the data coordinates and Z(Xj),...,Z(^) the logarithms of the
44
Uncertainty assessment for management of soil contaminants
measured cadmium concentrations of the 76 measurements. Then, the
differenceZ(x)-Z(x + h) with x,x + h<=D depends on the distance vector h
(Matheron, 1963). This dependency is expressed by means of the semivariance
y(h), which is defined as half the variance of concentration differences of all data
pairs with the same distance h (Journel, 1989). The range r - the "spatial
dependency" - indicates the maximum distance between sites. Beyond this,
concentrations are considered to be uncorrelated. Properties and characteristics of
this function are discussed in geostatistical textbooks (e.g., Cressie, 1993, pp.
58ff).
3.3.1 Analysis of spatial dependency
The spatial dependency of the cadmium concentrations is empirically
investigated using standard geostatistical software (Geovariances, 1997). This
investigation includes the (supposed) total area of contamination.
1000°
D4 70° 1000^
7(h)
x meter
Figure 3.3.1 Variogram map of the logarithmically transformed cadmium data. Each grid cell shows
the semivarince ofthe lag vector (x,y). D1-D4 indicate the direction ofthe anisotropic variograms
A variogram map (see Figure 3.3.1) of the logarithmically transformed
cadmium data shows an empirical semivariance function, which depends on the
length and direction of distance vector h. It shows that in the southeast direction
the range is larger than in other directions. This indicates that an anisotropic
45
Chapter 3
semivariance should be considered. For the variogram model we used a spherical
function (see Figure 3.4.1), which is expressed as
fth,9) = c0+Cl<3/i 1
20(9) 2 Q(9)forO</*<ß(0) (1)
y(h, 0) = c0 + cx for h > 0.(9), y(0) = 0
where y{h,9) is the semivariance dependent on h (the lag, which is defined as the
Euclidian distance between 2 points in 2 dimensions), and on 6, the angle
representing the direction of the lag. c0 is the nugget effect; d, the sill; and
0(9) = (a2 cos2 (9- a)+#2sin2 (9 - a)f, which defines the geometric anisotropy by
means of an ellipsoid with angle a, the direction in which the continuity is
greatest; A, the maximum diameter; and B, the minimum diameter, which is
perpendicular to A (Webster and Oliver, 2001). This expresses the so-called
geometric anisotropy, for which the range (but not the sill) depends on the
direction. Referring to the variogram map, the direction a of the largest diameter
is set to -65° (155° in geographical notation, see Figure 3.3.1). Other kinds of
semivariance functions (like Gaussian or exponential) and zonal anisotropy are
discussed by authors such as Journel and Huijbregts (1978) and Matheron (1973).
Further, for the analysis of spatial contamination pattern, trend models for the
components of distance to the metal smelter (of) and deviation from the dominant
wind direction (A9) are used as suggested by Saito and Goovaerts (2001). Trend
factors are fitted with five different regressions and residues are used to predict
the spatial dependency. Hereafter the mean square error (MSE) from cross
validation (Goovaerts, 2001; Armstrong, 1998) indicates the goodness of
prediction with a trend.
3.3.2 Ordinary kriging
The interpolation applies an ordinary kriging method, where the data are
logarithmically transformed before kriging, and then transformed back afterwards.
Lognormal ordinary kriging interpolates by means of a weighted average
r(x0) = £4z(x,) (2)
46
Uncertainty assessment for management of soil contaminants
where Z*(x0) is the estimated value at point x0> Z(x;) is the measured value at xn
and Xt are the weights (adding up to 1). Nearby measurements are considered to
be more correlated to the estimation point and, therefore, carry a higher weight
than more distant measurements. A moving (ellipsoidal) neighborhood is defined
by the parameters of anisotropy, i.e., a rotation of «=-65° and a range of A=900 m
(direction D1, D2) and B=500 m (direction D3, D4). This distributes the weight of
the sampling points along the preferred direction, thus emphasizing the local
spatial structure of contamination.
The kriging variance o-J(jc0) is computed as the weighted sum of the
estimation point (jc0)and the measured points (Equation 3). The kriging variance is
then
<4(*o) = ZW;,*o)+îK*o) (3)
where y(x,.x0) is the semivariance between the data point jc, and the estimation
point x0. The weights Ât are distributed in terms of the data model (see above) and
under the requirement of unbiasedness. y/(x0) is the Lagrange multiplier used for
minimization of the kriging variance (Cressie, 1993; Journel, 1989). The kriging
system is given in detail in the annotations.
After kriging, the lognormal estimates are transformed back to the original
scale. Several backtransformations methods have been proposed (Cressie, 1993,
p. 136; Saito and Goovaerts, 2000; Webster and Oliver, 2001 p. 180). We
transformed the values back according to equation (4)
z; = exp z +-Z- (4)
where Z* is the estimated value in the raw scale, Z* is the estimated value, and
o-2z, is the kriging variance, all on the logarithmic scale. For the kriging variance the
transformation (Limpertand others, 2001; Stahel, 2000, p.136) is
47
Chapter 3
<7*.=wre''afl-c"^*J (5)
where mr is the mean, s2r is the dispersion variance of the raw variable, and o\, is
the kriging variance (on the log scale) (Geovariances, 1997). For the statistical
characterization of the interpolated data, we calculated the median of the raw
variable given the mean Z* on the log scale as Z^(x) = exp(z*(x)) (median of the
raw variable) and the multiplicative standard deviation from the untransformed
kriging variance o\. on the log scale as g (x) - exp(<rz. {x)) (Limpert and others,
2001; Stahel, 2000, p.136). Please note that Zf is the median (and not the mean)
of the raw variable and that the multiplicative standard deviation (sometimes called
the geometric standard deviation) is calculated as the exponential of the standard
deviation cz. on the log scale (and not as the exponential of the variance on the
log scale).
3.3.3 Geostatistical conditional simulation
To characterize the small-scale variability without a smoothing effect, a
random realization of a stochastic process is generated. The idea is to compute a
multitude of such random realizations and characterize the distribution at each
estimation point through the average and standard deviation. All calculations are
conducted using the logarithmically transformed data.
The stochastic simulation was performed using the turning bands method
(Matheron, 1973; Tietje, 1993), which is one of the two available methods (as
sequential Gaussian simulantion (Deutsch and Journel, 1998). The turning bands
method simulates realizations of a one-dimensional Gaussian process
{Y(tu):teR} along the L lines LX,...,LL through the origin defined by the unit
vectors^,...,uL. The lines all have the same arbitrary origin (Gotway, 1994) and
are uniformly distributed within the (in this case) 2-dimensional space. If uu...,uL
are unit vectors in the direction L\,...,LL, the simulated value Zs(x),xeD, is an
average of those values, which are generated at the orthogonal projection tui(x) of
the terminal point x onto the line of direction u\{Y(tui(x)ui):i = l,...,L}- Finally, the
generated value at point x is
48
Uncertainty assessment for management of soil contaminants
A detailed discussion of the method can be found in Gotway (1994) and
Journel (1974). Conditioning the simulation means to force the simulated surface
to pass through the measurements. Hence, the simulated value is obtained
through the formula (Journel and Huijbregts, 1978)
z;m=z*(x)+|z,m-z;m] m
where Z*{x) is the kriged value obtained from the data Z(x,), (measurements
i = lt...,n), Zs(x) is the simulated value from Equation (6), and z]{x) is a kriged
value obtained from z,(x,) using the realizations at the coordinates of the
measurements. The conditional simulation was conducted with 100 turning bands
for each of 100 realizations at each gridpoint x D. A simulation post-processing
averages the results of simulations according to Equation 7 for each grid node
1 100
At each gridpoint x e D the mean is used to interpolate the cadmium
concentration, and the standard deviation
^w=^Sfcw-^w)2 (9)
is used for uncertainty assessment. Similar to the lognormal kriging method, the
following equations are used for calculation of the median and the multiplicative
standard deviation:
Zr(x) = exp(z;(x)) (10)
which is the median of conditional simulation of the raw variable and
<7c,(x) = exp(<7;(x)) (11)
which is the standard deviation of conditional simulation of the raw variable.
49
Chapter 3
3.3.4 Uncertainty assessment
To assess the overall uncertainty of the interpolated concentrations, we
consider the following sources of error: soil sampling, sample preparation for
analytical measurement, analytical measurement itself, and interpolation. One
model for these sources of error is the sum of variances induced throughout the
assessment. Following the approach of the Analytical Methods Committee (1995)
and Ramsey and Argyraki (1997), we assume the uncertainty U(x) (Equation 10)
as random field
U(X) = ^Lunt + V(X) for all X<= D (12)
which includes a constant part <r^n8tant and a spatially variable part V(x).
V(x) indicates the error due to interpolation. cr2on8taW indicates the uncertainty
induced by soil sampling and measuring. The latter is considered to be the sum of
the uncertainties of soil sampling (sampling pattern, density, composite or spot
sample), preparation of the soil sample (fragment removal, drying, grinding,
sieving, splitting), and measurement of the cadmium content (flame-atom-
spectrometer (AAS)) itself (Muntau and others, 2001; Theocharopoulos and
others, 2001).
2 _2 ,_2 , _2 (I'i)
^constant sampling' ^ sampUngpreparathn ^measurement ' '
The project "European methods in soil sampling" (CEEM) (Desaules and
others, 2001; Wagner and others, 2001a) has evaluated the sources of uncertainty
in soil pollutants assessment. It demonstrated that sampling and/or sampling
preparation are the main sources of uncertainty, to what degree depends on the
element analyzed and its concentration level (Wagner and others, 2001b).
Moreover, the investigation emphasized the deviation from sampling being higher
than the analytical deviations. This is especially true for cadmium. From the results
of the CEEM project, we derived an uncertainty of 0.3 mg/kg for sampling and
sampling posttreatment for the constant part of the overall uncertainty (<72onstam)
(Wagner and others 2001b, p. 87). This uncertainty might also be caused by the
use of different sampling techniques (with variations in sampling depth, sieving,
etc.), the presence of small-scale heterogeneity (about 40% (see Wagner and
others, 2001b, p.92)), and diversity of conditions associated with type of land use
50
Uncertainty assessment for management ofsoil contaminants
(variation coefficients of 8.1 %, 7.2 %, and 2.7 % for forest, agriculture, and
grassland use (Desaules and others, 2001)). Von Hoist (1997) claims that
sampling itself causes the highest degree of error followed by sampling
preparation. Wächter (1997) even infers that the error of the measurement
instruments is negligible relative to the high error influence of sampling.
Concerning the spatially variable part of the uncertainty {V(x), Equation 10),
the geostatistical theory (Armstrong, 1998; Webster and Oliver, 2001) states that
the kriging variance is zero at measurement points and minimized (Equations 2,3)
between the sampling points. The magnitude of the kriging variance, therefore,
depends on the distribution of the sampling points (note that the kriging
characteristics - neighborhoods, anisotropy, the support, etc. - have to be set
carefully). Because the sampling in the investigated area is sparse, large parts of
the investigated area are expected to show a high kriging variance. The maximum
of the kriging variance is related to the sill of the variogram and hence depends on
the overall variance of the data (see above).
Finally, the overall uncertainty is calculated as £/(x) = exp(lnöyw-i-lnl.35),
which is used to estimate the spatially distributed uncertainty. Due to the
geometric distribution (and hence the multiplicative confidence intervals) of the
results, it is called the uncertainty factor throughout the text. In conclusion, the
probability of exceeding a threshold of concentration C is estimated by solving
P(Z' > C) = l-4(lnC-Z1*og)/a„(x)] (14)
for the probability px of the standard normal distribution 0.
3.4 Results
3.4.1 Spatial estimation
The estimation of the spatial distribution of the cadmium concentration relies
on the geostatistical analysis of the data. The trend analysis reveals no significant
spatial trend. Besides a linear trend (Webster and Oliver, 2001), the distance to
the metal smelter and/or the main wind direction is additionally computed as
regression parameters (Saito and Goovaerts, 2001). Residues from regression are
used for kriging and cross validation. Table 3.4 shows the mean square error of
51
Chapter 3
prediction with these trends compared to ordinary kriging without a trend. The
results of Table 3.4 justify a spatial prediction without a trend in the investigated
area.
Trend models Mean square Model Parameter
errorRange [m] Nugget [(mg/kg)2]
t0 — ct0 + tfjX + a2y0.48 666 0.10
tx = a0 + ax ln(d) 0.55 631 0.14
h = ao+ a\ Wd) + d2A9 0.50 737 0.10
?3 = ao+al(\n.(d)*A0) 0.53 597 0.12
t^=a0+ a,A0 + a2(\a.(d)* A9) 0.46 696 0.23
Ordinary kriging 0.50 813 0.30
Table 3.4 Mean square error from cross validation for five different trend models and ordinary
kriging (isotropic variogram) for 76 data, (d) denotes the distance to the metal smelter and (AÖ) is
the deviation of wind direction from west to east, x,yare data coordinates. All models are
calculated in accordance to Saito and Goovaerts (2001). Models of spatial dependency are derived
from the residues of regression
Spherical models are suitable for both empirical variograms (see Table 3.5,
Equation 1, and the isotropic spherical funtion is given in the annotations).
Isotropic variogram Anisotropic variogram
Model Spherical spherical
Direction Omnidirectional four directions, D1-D4
Range
Nugget effect
813 m
0.297 (mg/kg)2
-65°= 900m, -20°,+20°, +70°=
500m
0.125 (mg/kg)2
Sill 0.332 (mg/kg)2 0.528 (mg/kg)2
7ab/e 3.5 Geostatistical properties of the variograms, all data shown on log- scale
In both cases, the sill approximately equals the data variance. The
anisotropic and isotropic variograms on the log scale are shown in Figures 3.4.1
and 3.4.2. For the interpolation of cadmium, we use the anisotropic model
displayed in Figure 3.4.1, because the variability of the cadmium contents depend
on direction, as shown in the variogram map in Figure 3.3.1. The range is from
500 to 900 meters, encompassing the range of the isotropic model. The
anisotropic model is computed for lag classes of 230 m and is discontinuous near
the origin showing a nugget effect of 0.125 (mg/kg)2 (log scale).
52
Uncertainty assessment for management of soil contaminants
2.0 _
1.5_
y(h)1.0
_
0.5
Figure 3.4.1 Anisotropic variograms in the directions D1-D4; their ranges are 900 m to 500 m, the
nugget effect is 0.13 (mg/kg)2, and the sill is 0.53 (mg/kg)2. Number of pairs and lag value for each
lag are shown in the annotations
7(h)
1000. 2000. 3000.
Figure 3.4.2 Isotropic variogram with a range of 813 m, a nugget effect of 0.297 (mg/kg), and a sill
of 0.332 (mg/kg)2
53
Chapter 3
The interpolated cadmium concentrations are displayed in Figure 3.4.3,
which is a cutout of the interpolated area. The statistical properties of the
interpolations (isotropic and anisotropic) and the conditional simulation
(anisotropic) are shown in Table 3.6.
Data Isotropic Anisotropic Conditional
estimation estimation simulation
Counts 76
Geometric mean [eM mg/kg]°-93
Standard deviation [ eß mg/kg]2-22
Minimum [mg/kg] 0.12
Maximum [mg/kg] 23.3
Table 3.6 Statistical properties of the interpolations (isotropic and anisotropic) and the conditional
simulation
Differences between kriging of cadmium with isotropic and anisotropic
variograms mainly results from their different nugget effects. The larger nugget
effect leads to a smoother isotropic kriging interpolation (Webster and Oliver,
2001) with less variance and an underestimation of cadmium concentrations.
The statistical properties of the anisotropic interpolation (Table 3.7) have
been calculated for the area indicated to be the core area in Figure 3.2.1.
11878
1.05
2.33
0.12
4.36
10802
1.08
2.27
0.12
8.81
10802
1.09
2.33
0.14
9.03
54
Uncertainty assessment for management of soil contaminants
Cadmium [mg/kg]
~H 0-0.8
M 0.8-1.3
1.3-2
2 - 7.3
0 measurement
[ Cd mg/kg]
Figure 3.4.3 Spatial distribution of cadmium concentrations in topsoil after conditional simulation.
The median of 100 realizations on the raw scale [Z^] is displayed, taken only from the core area
indicated in figure 1
Anisotropic modeling Core area Total area
Cadmium
estimated
Cadmiumsimulated
Cadmium
estimated
Cadmium
simulated
Counts 3Ô70 3870 10802 10802
Geometric mean [eM mg/kg]103 1.03 1.08 1.09
Standard deviation [eß mg/kg]1.95 1.97 2.27 2.33
Minimum [mg/kg] 0.28 0.28 0.12 0.14
Maximum [mg/kg] S.81 9,03 8.81 9.03
Table 3.7 Statistic properties of the interpolation for the core area ofpollution ( indicated in Figure 1)
and the total area of pollution
55
Chapter 3
3.4.2 Uncertainty assessment
The uncertainty of factor 2 (two times the estimate by multiplicative standard
deviation) - postulated by the Analytical Methods Committee (1995); Ramsey and
Argyraki (1997); as well as Fresenius and others (1995) - can only be estimated at
a probability of 68.3 %, whereas the demand of px =97.5 % accuracy leads to an
uncertainty factor of about 4.2. The uncertainty only decreases in the vicinity of the
measurements.
The rationale of the spatially variable part V(x) of the overall uncertainty is
illustrated by Figure 3.4.4, which shows a north/south transection of Dornach. A
single realization of the conditional simulation demonstrates considerable
variability and randomly high cadmium concentrations.
257800 258000 258200 258400 258600 258800 259000
northing coordinate [m]
--conditional simulation 50th percentile -•— conditional simulation 84th percentile
-*— conditional simulation 16th percentile -^-lognormal kriging 50th percentile
-+-lognormal kriging 84th percentile -X- tognormal kriging 16th percentile
-+- singular realization
Figure 3.4.4 A south-north transection with the results of one singular realization and some
percentiles of the conditional simulation and lognormal kriging. The 50th percentiles are estimated
by taking the exponential of the mean values on the logarithmic scale. The other percentiles are
calculated as the exponential of the percentiles on the logarithmic scale
exp(Z*og(x)±0(p)alog(x)), with the léh and 84th percentile of the normal distribution
0(16*)--1 and 0(84(A) = 1
56
Uncertainty assessment for management of soil contaminants
As can be seen from Figure 3.4.4, in reality some cadmium concentrations
beyond the 68.3% confidence interval of the interpolation and simulation could
occur. The results for the spatially variable part are indicated in Table 3.6 as is the
geometric standard deviation eM mg/kg.
3.4.2 Relevance for decisions on soil remediation
To come to any decision, the results of the kriging interpolation and the
uncertainty assessment have to be correlated with the standards set out in the
Swiss Ordinance Relating to Pollutants in Soil (VBBo, 1998) (Table 3.3). This
document contains the three threshold values associated with a long-term fertility
goal (guide value), the concentration beyond which a more detailed investigation is
required (trigger value), and the concentration beyond which a remediation is
prescribed (remediation value).
Figure 3.4.5 Map of the likelihood of exceeding the threshold value C-2 mg/kg
Figure 3.4.5 presents the probability of exceeding 2 mg cadmium per kg soil
(trigger value for food and feed planting). Clearly, the probability of any other
threshold value can be presented. In practice, decision makers have to agree on a
probability statement that they consider reliable and safe enough for the specific
57
Chapter 3
case. Figure 3.4.4 shows one randomly chosen realization out of a total of 100
realizations that determine the simulated value. As can be seen, some local
cadmium concentrations at this point exceed the 84th percentile of the prediction.
Presentations, as the one demonstrated in Figure 3.4.5, facilitate understanding of
the meaning and consequences of the results, which are stated as "there is a 16
% likelihood that a specific cadmium concentration will be exceeded". In addition, it
is possible to delineate corresponding areas, which may be subjected to further
investigations (e.g., additional measurements). A combination of the spatially
distributed probability of occurrence with other data of a geographic information
system (GIS), such as land use classifications, might lead to a valuable decision.
However, if a high degree of reliability and confidence is required (e.g., 95 %) and
the costs of soil treatment are very high Figure 3.4.5 suggests that further
measurements should be collected. In general, knowledge about the probability of
exceeding legal threshold values helps to become aware of necessary actions to
be taken in sustainable soil improvement - depending on the decision-makers risk
level. For the case considered in this study the following conclusion became
evident from the interpolation and the uncertainty assessment:
• Cadmium contamination above legal remediation value (for all kind of
uses) is not likely (even with a probability below 50 % ) on any side
• A small area is contaminated above trigger value with a probability of more
than 90%
• Cadmium contamination above guide value is widespread with more than
50% probability
• High probabilities for cadmium contamination above 0.8 mg/kg are
delineated mainly around the emission source and
• Only a small domain of the case area is not contaminated above the Guide
value of Swiss Ordinance related to Soil (VBBo, 1998)
Since the contamination from different sources like sewage sludge or
fertilizer is ongoing (Keller and others 2001 ) decision makers should also bear in
mind that the cadmium concentration might still be accumulating and any kind of
soil improvement might help to sustain the multi-functional use of soil (Bouma,
2002).
58
Uncertainty assessment for management of soil contaminants
3.5 Conclusion
The case study shows that even sparse data are suitable for an assessment
of contaminated land. In our case we state an uncertainty factor of 2 with 68.3 %
accuracy and we acknowledge statements such as "The probability that the soil
contamination at this point exceeds 2 mg cadmium per kg soil is less than 40 %".
We infer from the preceding analysis that statements of this kind can be given in a
reliable way.
For the spatial interpolation of the cadmium concentrations, a lognormal
ordinary kriging (Papritz and Moyeed, 1999; Matheron, 1963) and a conditional
simulation (Goovaerts, 2000; Journel, 1974) were applied. The ordinary kriging
was improved by the application of an anisotropic variogram. The anisotropic
variogram shows varying distances of autocorrelation in different directions.
Several two dimensional stochastic realizations were produced and a conditional
simulation was applied to analyze the local variability. The conditional simulation
(as the stochastic realizations are forced to hit the measured data) yielded also an
estimation of the local uncertainty. A logarithmic transformation of the data and a
backtransformation after interpolation according to Limpert and others (2001) was
used to obtain the geometric mean and the multiplicative standard deviation. The
geometric mean of all realizations approximated the geometric mean of the
(lognormal) ordinary kriging estimation. Moreover, the standard deviation of all the
realizations approximated the standard deviation of the (lognormal) ordinary
kriging, i.e. the square root of the kriging variance (see Table 3.5). The geometric
distribution was also used to obtain the percentiles of the probability density
function and to predict the conditional cumulative density function including the
uncertainty. With this approach, the uncertainties involved in the interpolation are
conveniently estimated. Hence, this procedure can be applied for uncertainty
assessment of lognormally and spatially distributed data.
The uncertainty assessment exemplifies, that the main part of the overall
uncertainty is due to the sparseness of the data that underlies the spatial
interpolation. The second important uncertainty is due to the sampling and sample
preparation. Because corresponding data are hardly to obtain (see e.g. CEEM-
Project, Wagner and others, 2001b) we roughly estimated this as 35% of the
estimated cadmium concentration using quantitative (von Hoist, 1997; Wächter,
59
Chapter 3
1997; Wagner and others, 2001b) and qualitative results (Ramsey, 1998; Tiktak
and others, 1999) as a reference. For the purpose of this investigation, other
sources of uncertainty, such as the analytical measurement have been determined
to be negligible. In conclusion, the resulting overall uncertainty is suitable to
identify regions with a high risk of contamination. The interpolation combined with
the uncertainty assessment is sufficiently reliable to delineate potentially
contaminated sites pictured in "maps of probability of occurrence".
Acknowledgements
The work reported in this paper was conducted in the context of the Integrated Project Soil of
the Swiss Priority Program Environment. We are grateful to Martin Fritsch, who initiated the project
and guided it until 2000, and to the colleagues at UNS and within the IP Soil for the helpful
discussions. We also appreciate the comment of three anonymous reviewers. The project was
funded by the Swiss National Science of Foundation (Project Number 5001-44758) and the Swiss
Federal Institute of Technology (Project Number 0048-41-2609-5).
60
Uncertainty assessment for management of soil contaminants
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64
Uncertainty assessment for management of soil contaminants
3.6 Annotations
I. Number of pairs and semivariances for single lags of the variogram,
calculated in Equation (1) and shown in Figure 3.3
Number of pairs Value (mg/kg)D1 D2 D3 D4 D1 D2 D3 D4
Lag1 28 35 31 31 0.38 0.34 0.28 0.43
Lag 2 50 72 60 53 0.5 0.51 0.8 0.51
Lag 3 74 77 75 72 0.34 0.67 0.89 0.82
Lag 4 74 84 80 72 0.73 0.7 0.74 0.83
Lag 5 82 86 87 74 0.55 0.67 0.58 0.61
Lag 6 49 95 75 54 0.53 0.66 0.48 0.59
Lag 7 53 84 77 42 0.44 0.6 0.61 0.4
Lag 8 28 97 56 25 0.39 0.66 0.54 0.62
Lag 9 18 90 46 10 0.29 0.61 0.81 0.58
Lag 10 11 92 39 2 0.38 0.76 0.62 1.84
Lag 11 3 70 39 2 0.3 0.84 0.52 0.19
II. The formal kriging system is
Z'(x0)Â = b
Z\x0) =Y(x2 > X\) Y\Xi? ^2/
7\Xf{»Xj) j\XNix2)
1 1
/\Xi>Xjf)
/\X2 j xN )
¥\xn>xn)
1
1 ^
1
X =
(K }r
K*
,and b =
K
,?K*o), V
y\X\ > ^o /
/yx2,x0)
Y\xn,Xq)
1
65
Chapter 3
III. Spherical function calculated for Figure 3.5 and Table 3.4 and 3.5
^»MIHOl'for h<-a
y(h) = cQ+cx for h > a
where c0 is the nugget effect, c1 is the sill, h is the lag and a a the range.
IV. Accuracy plot for the variogram model calculated in Equation (1). Dots
indicate outliers being outside the 99 % confidence limit of a normal
distribution
In Z*(x) rag/kg
3. -
£à *
0. -
2. -
-2. -1. 0. 1. 2. 3.
i i i
•
1 1 i
-
•
+ JJT y
-
4+
•• -
-
/ +
+-
'
+
1 1 i i i
-2. -1. 0. 1. 2.
In Z*(x) mg/kg
- 3.
- 2.
- 1.
- 0,
- -1.
- -2
CSJ
if
66
4 Decision making under uncertainty in case of soil remediation
Ute Schnabel and Roland W. Scholz
Submitted to Journal of Environmental Management
ABSTRACT/Decisions on soil remediation are one of the most difficult
management issues of municipal and state agencies. The assessment of
contamination is uncertain, the costs of the remediation are high, and the impacts
on the environment are multiple. The paper presents a general, transparent, and
consistent method for decision-making among the remediation alternatives. Soil
washing, phytoremediation and no remediation are exemplarily considered. Multi
criteria utility functions including a) the cost of remediation b) the impact on human
health and agricultural productivity, and c) the economic gain after remediation are
constructed along a case in which the contamination at each site coordinate are
represented by a probability distribution. Herewith different types of i) correct
decisions such as a hit or a correct rejection and ii) erroneous decisions such as a
false alarm or a miss lead to a evaluation of each state of contamination and its'
expected utility. The case study reveals the nonlinear structure of multi criteria-
decision making. If one alternative scores best for high and low concentration the
second alternative can fit for medium concentration. Typically doing nothing was
best for very low concentrations.
Chapter 4
4.1 Introduction
In most European countries, brown fields and contaminated sites are
currently recorded in registers of contaminated land. Municipal and state agencies
are facing the challenge to manage soil contamination resulting from the industrial
age (Bell, F.G., Genske, Bell, A.W. 2000; U.S. Environmental Protection Agency
2000). The problem to allocate sites of interest leads into the question on how to
cope with the uncertainty of data stored in these land registers, and, in particular,
how to evaluate different types of errors and - complementary - different correct
decisions that can result (Gsponer, 1996). For instance overseeing or ignoring a
highly contaminated site may cause severe effects. Contrary, acting based on a
false alarm might result in unwarranted high investments in remediation
procedures. Thus, a decision maker has to balance the consequences from
correct or false decisions and the probabilities of occurrence of these correct and
false decisions. This leads the practitioner into the core of decision theory
(Kleindorfer, Kunreuther Schoemaker, 1993).
However, the handling of different types of errors is relevant not only for the
case of soil remediation. For instance, when visiting a developing country with
cholera incidence, one has to deliberate whether to apply a vaccination or not.
There is always a chance of 40-50% of becoming infected in spite of vaccination
(Levine and Kaper, 1996). On the other hand in case of not being inoculated, there
is a higher chance of becoming infected during the travel with even worse
consequences as medical care is supposed to be poorer during the travel. Also in
this case, as in many other situations of life, the costs of negative consequences
resulting from missed action (becoming infected given no vaccination) and false
alarms (being inoculated and not getting infected) have to be negotiated. The
procedure presented in this paper thus will also be of relevance for other decision
situation.
In case of soil contamination the decision-making on the application of
remediation alternatives is a crucial step after a comprehensive analysis and
assessment of contaminants and their impacts on safeguards. The ability to make
a correct or "good" decision develops with increasing experience and knowledge
about the consequences of the decision and with the capability to comprehend
68
Decision making under uncertainty in case of soil remediation
and to structure the decision problem (Scholz, 1981; Papazoglou, Bonanos,
Briassoulis, 2000). Clearly, gathering of supplementary knowledge about the
contaminated area by additional soil samples is one possibility to improve decision
making issue (Scholz, Nothbaum, May, 1994; Van Groenigen 2000; Wagner,
Desaules, Muntau, Theocharopoulos, Quevauviller, 2001). However, soil sampling
induces additional costs, which often exceed the financial budget of the project or
at least of the planned costs for data sampling. In the following a method is
introduced that explicitly allows to deliberate about different types of correct and
false decisions on soil remediation when referring to signal detection theory
(Green and Swets, 1988; Tuzlukov, 2001). For the sake of simplicity, only one
criterion, e.g. one contaminant, is considered significant for causing negative
impacts. However a multitude of consequences and their impacts are considered
with multi-criteria utility theory. Utility functions provide evaluations on the
consequences of action and can be seen as a compromise between accurate
scientific knowledge and concise information (Beinat, 1997). Utilities ask for a rigor
scaling, as utility functions are supposed to have a zero point and consequently
differences can be relatively compared (von Winterfeldt and Edwards, 1986;
Parson and Wooldridge, 2002). In the following case study, a procedure that
combines utilities for decisions options with the related probabilities of errors is
proposed.
4.2 The case of contaminated land
The study was applied to an area of heavy metal soil contamination in
Dornach, Canton Solothurn, Switzerland. The soil was polluted from a metal
smelter for several decades (Hesske, Schärli, Tietje, Scholz, 1998). Several
studies assessed the spatial extension of the contamination and the potential for a
sustainable remediation. An overview of research studies and results can be found
in various studies (Wirz and Winistörfer, 1987; Geiger, Federer, Sticher, 1993; von
Steiger, Webster, Schulin, Lehmann, 1996; Schulin and Borer 1997; Fritsch,
Tietje, Hepperle, Schnabel, 1999; Keller, Jauslin, Schulin, 1999; Gupta, Wenger,
Tietje, Schulin, 2002; Schulin and Gupta 2002). The cadmium contamination was
spatially interpolated with lognormal ordinary kriging (Schnabel, Tietje, Scholz,
2002). Results were presented in terms of a probability that certain cadmium
69
Chapter 4
contents in topsoil occur (Figure 4.2.1). The estimation reveals an uncertainty of a
factor 2. This means that the 68,3 % confidence interval was between the double
and the 50% concentration of the estimated value. A confidence interval of 97,5%
is only achievable with a factor of 4.2 times of the estimated mean contaminant
level.
Cadmium
estimated [mg/kg]
0-0.5
0.5 - 0.8
0.8-1.5
1.5-2
2-2.5
2.5-3
3-4
4-6
6-10
No Data
probability [%] to exceed a
/V threshold value of 2 mg/kg in soil
^H metal smelter
Figure 4.2.1 Map of a cadmium contaminated land and the probability that a threshold value of 2
mg/kg soil is exceeded
Our study evaluates cadmium contamination in soil and its consequences
according to the threshold values of Swiss Ordinance Relating to Pollutants in Soil
(VBBo, 1998), which is the following
• The Guide value of 0.8 mg/kg cadmium in soil indicates a loss in soil
fertility, especially damages in microbial activity of soil organism (Laczko,
Rudaz, Aragno, 1996). Local authorities are advised to find the cause of
impact and to prevent an additional increase of contamination. The guide
value denotes the threshold value for a sustainable loss of soil function and
hence of resources.
• The Trigger value is a threshold value for different kind of land uses. In
case of contamination, soil use for food and feed planting is judged to be
without any consequences for human, animals and plants up to a cadmium
content of 2 mg/kg soil. For uncovered soil, where the possibility of oral
intake (especially by children and animals) is given (Ruck, 1990), the
threshold value is 10 mg/kg. In the case that a trigger values is exceeded,
local authorities have to prove the actual endangerment of human, animals,
70
Decision making under uncertainty in case of soil remediation
and plants. If a health risk is evident, land use must be restricted. Current
research and experience showed that above trigger values a health risk for
humans, animals and plants is likely (Harris, Karlen, Mulla, 1996; VBBo,
1998).
• Remediation values are also different for different types of land uses. The
threshold value for gardening and playgrounds is set to 20 mg/kg, while the
use of agro- and horticulture is forbidden when more than 30 mg/kg
cadmium in soil has been measured. If the remediation value is exceeded
the land use is prohibited and a remediation is obligatory in cases where
spatial planning intended a use for gardening, playgrounds, agriculture, or
horticulture.
The regional governmental planning organizations have to decide upon the
treatment of contaminated soil. It is a spatial choice referring to the different
probabilities to exceed the threshold value occurring throughout the whole area.
Since the community of Dornach has an increasing figure of new inhabitants
(Hesske et al., 1998) the area is of interest for dwelling and house gardening.
4.3 Probability knowledge on the contamination
Consider the data coordinates xe X of a certain area. Let z(x) denote the
predicted cadmium value at each point x in the considered area. The predicted
value z(x) is derived from measurements x„ by means of geostatistical
procedures based on the available data (Schnabel et al, 2002) and is the mean of
a lognormal distributed random variable at each point x (Limpert, Stahel, Abt,
2001). Each predicted value z(x) has a probability (density value) f(z(x))dz(x)
that can be considered as the best prediction for the "true value"
p(z(x))=\f(t(x))dt(x) = E(t(x)). Hence the probability of occurrence for every
possible state of contamination at each x is known for the decision maker, if we
interpret "known" as best available information or best model on the occurrence of
true value t(x) of contamination.
A threshold value c separates contaminated from uncontaminated areas and
has to be considered as a prior decision threshold (see Figure 4.3.1). If the
71
Chapter 4
predicted value z(x) is below the threshold value c, the decision maker usually will
consider the coordinate x to be not contaminated. Consequently the probability of
contamination, p(C) -.= p(z(x) > c), or non-contamination p(->c) := p(z(x) < c) is
calculable by the following formulas for the lognormal distribution at each x.
p(Q:=P(z(x)^c) = l-0[\nc-zln(x)/(Jbi(x)] , zln(x)~N({i,<r2) (V
and p(-iC).p(z(x)<c) = 0[\nc-z]n(x)/(Tln(x)],zln(x)~N(ß,o'2) (2)
m*»
t(x)<c t(x)>c t(x)<c t(x)Z c
/W*)U #x) /<«*» JM
c t(x) c t(x)0 c
piporrrejec ) = \f(t(x))dt{x) pQmss) = Jf(t(x))dt(x)
c t(x) ce
t(x)
pifalse alarm) = )f(t{x))dt(x) p(hü) = \f(t{x))dt{x)
CORRECTREJECTION MISS FALSE ALARM HIT
Figure 4.3.1 Model for the true value of contamination. The probability density functions are derived
form the geostatistical estimation of the contaminant. The probability of falling below or above the
threshold value c serves as a prediction of the true value t(x) [x-axis] and leads to four types of
decisions (see text)
A decision on an treatment at coordinate x is based on the estimation z(x)
and the corresponding probability distribution, i.e. model for the true value (Green
and Swets, 1988). The decision maker does not know with certainty about the true
value, neither if t(x)>c nor if t(x)<c. Two situations can appear (see Figure
4.3.1). The true value /(x)can be (a) smaller than c or (b) greater or equal than c.
72
Decision making under uncertainty in case of soil remediation
Case (a) is displayed in the lower left density function of Figure 4.3.1 (correct
rejection). Analogously is the case (b) in the lower right part of Figure 4.3.1 (hit).
The probabilities of t(x) exceeding c (Equation 3), respectively not exceeding c
(Equation 4) given z(x) > c is
p(hit) := p(t(x) > c | z(x) >c) = J" f(z(x))dz(x) (3)
/?(false alarm) := p(t(x) < c | z(x) _ c) = I f(z(x))dz(x) (4)
Analogously the conditional probabilities of *(x) being above c (Equation 5)
and being below c (Equation 6), given z(x) < c is
p(miss) := p(t(x) > c \ z(x) < c) = f f(z(x))dz(x) (5)
/?(correct rejection) := p(t(x) < c | z(x) < c) = f(z(x))dz(x) (6)
As described in signal detection theory (Tuzlukov, 2001) and shown in Table
4.1, the decision maker is either facing a hit or false alarm (if z(x) > c ) or a miss or
correct rejection (ifz(x) < c).
z(x) > C z(x) < C_____ _
_
t(x) < C False alarm Correct rejection
Table 4.1 Different types of decisions depending on the estimation z(x) and the hypothesis (the true
value t(x))
Deliberating between different remediation alternatives, the decision maker
has to consider each possible t(x) and has to trade off the utilities and
probabilities of hits and misses in case of z(x)>cand analogously the utilities and
probabilities between false alarms and correct rejections in case of z(x)<c. Thus,
given z(x), the decision maker gets a utility score for each (possible) true value
and for each alternative. When looking for the better alternative, these utility
scores have to be integrated along the density function f(z(x))dz(x). This is
shown below after introducing the multi-criteria utility framework.
73
Chapter 4
4.4 Decision alternatives on soil remediation
In practice, decision makers are supposed to be confronted with different
decision alternatives Ar In general there will be a finite set of alternatives A{,
i = X„„n, a countable set of alternatives / = 1,...,°° or a continuous set of
alternatives, for instance if the time of a treatment is considered. For the sake of
simplicity the subsequent analysis is restricted on three alternatives, 4», 4* and
An-
• No remediation Am: The contaminated land will not be remediated. The
pollutants remain in soil and safeguarding is the main action that will follow the
decision for this alternative. Agricultural yield and human health remains
endangered depending on the level of contamination. The market value of the site
presumably decreases due to the unknown risk from pollutants.
• Ex situ remediation Am: We assume a soil washing treatment as an example
for ex situ remediation. The contaminated soil is removed and treated off site and
exchanged with unpolluted soil, which is taken from another site. Environmental
and human health is no longer endangered. A decrease of agricultural production
depends on the land reclamation method (i.e. the way how the soil is substituted)
and goodness of reclamation practice. Once, an appropriate topsoil is replaced,
physical properties of soil develops towards the original state within a few years
(Geiger et al, 1993; Haering, Daniels, Roberts, 1993).
• In situ remediation Ain: We assume an in situ remediation method like
phytoremediation (Kumar, Dushenkov, Motto, Raskin, 1995; Cunningham and Ow,
1996; McGrath, Zhao, Lombi, 2002). The soil is not excavated, instead cleaned up
on the spot. However, phytoremediation methods are not able to remove a huge
amount of pollutants and the degree of removal depends on the level of
contamination (McGrath et al, 2002). Agricultural yield is influenced or even
improved by phytoremediation, the cost for the application of remediation method
is usually low (Eiermann, 1999; Ebiox, 2003) compared to other remediation
methods, but the market value of the area changes considerably due to a long
remediation time.
74
Decision making under uncertainty in case of soil remediation
4.5 Utilities of soil remediation
We propose four dimensions of utilities (partial utilities) that are relevant for a
decision on soil remediation for each alternative. The choice of dimensions reflects
the impact on human living from soil contamination, the economic impact from
polluted soil and technology that is applied for remediation, and the ecological
impact on soil.
The utility for human health impact uh(A,): An impact on human health is
particular relevant in case of high contamination for the most contaminants like
cadmium, copper, zinc, etc (Oliver, 1997). Human health is mainly affected
through the ingestion of contaminated food or through hand-to-mouth contact with
contaminated soil. Cadmium is a contaminant that accumulates in the human body
due to his half-life period of at least 20 years (Kazemi, 1983). Therefore, even low
concentrations are relevant for human health impact. In decision makers' practice,
it will be impossible to assess a precise and crisp utility function of human health
impact as the conditions and data of exposure and kinetics of intake are not
completely known (Beinat, 1997; Paustenbach, 2002, pp207 et seqq). The utility
uh(A,) is derived from the enhancement for human health after the application of
remediation method Ai.
It is assumed that cadmium is a natural resource up to a certain range of
concentrations (Bachmann, Schmidt, Bannick, 1996; McGrath et al. 2002).
Consequently, there is small or even zero utility after a remediation in case of low
concentration (e.g. below the guide value of Swiss Ordinance Relating to
Pollutants in Soil (VBBo, 1998)). The slope of the utility function for health impacts
is a result of the toxicity of contaminant (i.e. cadmium, in this case).
The costs of remediation technology u^): The costs of remediation are
significant in the decision-makers choice and particularly become relevant when
different alternatives A, are deliberated for the decision (Rivett, Petts, Butler,
Martin, 2002). Costs of remediation arise from the specific site conditions (e.g.
type of soil), the size of remediation area, and the remediation technology. Finally
the costs are a function of demand and supply. In case of soil washing, the costs
rise with the level of contamination and the size of contaminated area, but also
depends on the disposal of remaining residuals after remediation (Eberhard,
75
Chapter 4
1996). Analogous considerations can be assumed in case of phytoremediation for
the deposition and breeding of plants. For the alternative 'no remediation' costs of
safeguarding arise for a specific time span. For the sake of simplicity a simple
rating of costs for different remediation alternatives is used in the construction of
utility functions: uv(AJ <uv(Ano) <uv(AJ. The maximum utility for each alternative
is then uv(Ain) = lt uv(Ano) = 0.B, u^(Aex) = 0.5. Given all other properties of an
alternative remain unchanged, it is assumed that the lower the costs the higher is
the utility of the application (Janikowski, Kucharski, Sas-Nowosielska, 2000). The
utility of costs for each spatial unit are calculated with 1/10 000 of the assumed
costs.
77io long-term productivity of soil up(A) valuates soil quality for agricultural
production after remediation. The chosen remediation technologies, A,, have
different effects on the improvement of agricultural long-term productivity. Soil
fertility is a sensible indicator for agricultural productivity that is difficult to measure
or to assess (Johnson et al., 1997; Herrick, 2000). Soil scientists assume a
noticeable decrease of soil fertility at a certain level of concentrations for heavy
metals (Schmitt and Sticher, 1986; Hämmann and Gupta, 1997). However, a
change in agricultural productivity, is a multi-factorial process in soil (Hess et al.,
2000). Hence, for the construction of a utility after remediation it is assumed that
the productivity decreases non-linearly with increasing cadmium content.
The market value of land after action um(At): For the assessment of an
economic impact of remediation, financial experts calculate the costs caused by a)
remediation, b) the loss of land quality during and after remediation, and c) the
loss of market value due to missing liquidity of the landowner. The latter is taken
into account, if the landowner is forced to sell the land property, as he or she
cannot afford the remediation costs. The construction of an economic utility is
based on loans that will be given to landowners by banks for the contaminated
land. According to a survey run by Sell, Weber and Scholz (2000), the credit
officers of small and medium banks show reservation about the success of
phytoremediation. Based on the quoted surveys it is reasonable to assume that
the application of phytoremediation reveals 50% higher reduction of market value
than the application of soil washing does (Sell et. al, 2000, p. 25). The derivation of
76
Decision making under uncertainty in case of soil remediation
utility functions is based on the assumption that the market value is reduced
proportionally to the contamination and increases again after remediation. A high
reduction of market value results not necessarily in a low utility, the economic
utility depends on the success of remediation method. For example after the
application of phytoremediation only half of the market value before remediation is
achievable. Consequently the method gains less economic utility than more
successful methods.
4.6 Utility functions for decision alternatives
4.6.1 Construction of utility functions
Referring to utility theory as proposed by Keeney and Raiffa (1976) and
discussed and applied by von Winterfeldt and Edwards (1986), there are various
principles to construct a utility function. As shown in Table 4.2 and described
below utilities are displayed in one dimensional versus multidimensional, discrete
versus continuous, and deterministic versus stochastic utility functions. In general
utility functions have an absolute scale (von Winterfeldt and Edwards, 1986). This
means that they have a zero point and different values can be proportionally
compared (e.g. a utility 5 is five times bigger than a utility 1 as 50 is compared to
10).
77
Chapter 4
a) Dimensionality of utility: The simplest case is a one-dimensional utility
function. For the variable that is affected by the decision, a utility wlW(4) of anv
alternative 4 is determined for each value z(x). The utility evaluates
consequences and outcomes applying A, and has to be derived from experts'
knowledge. For a multi-dimensional utility type, the decision maker differentiates
between different types of consequences (i.e. costs, environmental benefits or
agriculture yield). This leads to partial utilities u{{x)(A,) for each value z(x). The
overall utility for an alternative 4 is then attained by the sum of these partial
utilities: c/z(;[)(4)-X<Je)(4)-j
b) Continuity of utility: Figure 4.6.1a shows an example for a discrete utility
function. We present a simple function for the remediation case assigning
uz(x)(A,)=0.9 for all contaminations between Guide and Trigger value and
wlW(4)=0.5 for contaminations between the Trigger and the Remediation value
(explanation of threshold values see above or Harris et al. (1996)). In this case the
values of the utility function are degrees of goal attainment in legal compliance and
standards given in the Swiss Ordinance Relating to Pollutants in Soil (VBBo,
1998).
a) b)
H
î 0.5-_
0.8 2 20
cadmium mg/kg cadmium mg/kg
Figure 4.6.1 Two examples how to derive the ecological benefit from remediation. The utility
between one and zero is the degree of goal attainment in legal compliance. Threshold values for
cadmium are described in Swiss Ordinance Relating to Pollutants in Soil (Guide value= 0.8 mg/kg;
Trigger value=2 mg/kg; Remediation value- 20 mg/kg)
78
Decision making under uncertainty in case of soil remediation
Schärli, Scholz, Tietje, Heitzer and Hesske (1997) and Sell et al. (2000)
provide an example of a continuous utility function (see Figure 4.6.1b). They
assess the ecological benefit (utility) of a remediation option for different types of
land use, when referring to the above-cited legal compliance. Exceeding the
Remediation value provides a utility of 0 and rises continuously up to 1 until the
soil contamination falls below the Guide value. The utility of the Trigger value is
supposed to be 0.5 and linear functions are proposed between the remediation
respectively the Guide and the Trigger value.
However, the assumption of a linear continuous utility function is not
reasonable for the behavior of most environmental variables. For example, the
remediation of heavy metals by plants (i.e. phytoremediation) is influenced by
several interacting variables in a complex ecosystem (Kumar et al., 1995; Filius,
Streck, Richter, 1998; Ensley, 2000). Therefore, instead assuming a linear uptake,
Kayser (2000) suggest a first-order-kinetic for the decontamination of lead by
plants (i.e. B.juneca), taking into account the depletion of phytoavailable lead that
is faster than the re-supply of strongly bounded lead in the soil matrix.
Although the interrelation between variables under consideration is often not
known, the assumption of a linear relationship is often not appropriate for variables
related to environmental issues (Limpert et al., 2001). Therefore, we construct
non-linear utility functions, if the rationale of interrelation of the variable under
consideration is known, as e.g. in the kinetics of heavy metal intake by plants.
c) Assessment of utility: A deterministic utility function is constructed, if for
the application of each alternative A, a single utility «,w(4) or partial utilities
m/w(4) will result with certainty. If there is uncertainty about the utility, e.g. on the
success of an alternative, a stochastic utility function can be appropriate (Tietje
and Scholz, 1996). In this case, the decision maker has to discuss reasonable
arguments about the distribution of the utilities (Quiggin 1989). However, the
assumption of a probabilistic utility function usually exceeds the degree of
complexity and available knowledge that is manageable in practice.
In this paper, multidimensional, continuous and deterministic utility functions
(see below) are proposed for decisions on soil remediation. The utility function is
normalized to a range between zero and one, when referring to the maximum and
minimum possible valuation. Each utility function is an evaluation of the
79
Chapter 4
consequences from a treatment 4. for all possible true values of contaminations
t(x). For each alternative and each coordinate x we construct the overall utility
C/(4) by the sum of partial utilities:
_r(4) = „*(4)+_v(4)+«'(4)+ttm(4) (7)
In practical decision-making, stakeholders or experts distribute different
weights to the utility functions. Besides the criteria selection, the weighting of the
different utility dimensions is the most critical aspect in stakeholder analysis
(Saaty, 1990; Scholz and Tietje, 2002). We do not discuss the methods of
weighting in this paper and assume that all weights are equal, instead.
The decision support is given with the overall utility f/(4)of a remediation
alternative and a density value f(z(x))dz(x) that describes the uncertainty of
cadmium estimation. Based on the probability knowledge of estimation, the
decision maker decides for each remediation alternative at each coordinate x
with the help of the density function from estimation and the overall utility. The
overall utility C/(4) for a true value t(x) and the density function derived from the
estimated point describes the expected utility:
E[U(-)] = _T,t/(4)] = \U(Ai)f(z(x))dz(x) (8)0
4.6.2 The alternative ex situ remediation (soil washing) Aa
The utility for human health u^iA^): Soil washing results in a complete
removal of contaminant at one time and for the total amount of contamination.
Consequently, the utility is derived from either having cleaned up and having no
health impacts or not having cleaned up and having health impacts. There is no
impact on human health below the natural background level N of cadmium content
in soil. Consequently soil washing results in zero utility, when it is applied in the
presence of contaminations below N. As a result the value 1 or 0 respectively is
assumed and displayed with a discrete function for the utility from health impacts:
80
Decision making under uncertainty in case ofsoil remediation
h , JO forz(x)<iVUxMex)
|j f0Tz(x)>N (9)
where N denotes a value of natural background level of contaminant. In the case
study, the natural background level Wis set to 0.3 mg/kg total cadmium content
(Tuchschmid, 1995; Bachmann et al., 1996).
The utility of cost tt*(J0(4_)- The calculation of cost is based on the
assumption of 100 Swiss Franks/t (72 US $) for excavation (Heitzer, Scholz,
Stäubli, Stünzi, 1997; Ebiox, 2003). The estimation for a spatial unit used in our
case study (=1600m2) is 120,000 Swiss Franks (86,880 US $). The costs of
remediation rise with increasing contamination, but reach a maximum score of 0.5,
due to a simple rating of costs of remediation alternatives, that is:
uv(Ain)<uv(Ano)<uv(Aex) (see also above). This results in a linear utility function up
to a cadmium contamination of 6 mg/kg.
<mUJ = -
— *z(x) forz(x)<6mg/kg
0.5 forz(x)_6mg/kg
The utility gained for long-term productivity «£„(4-) : The utility is derived
from the improvement achieved by an exchange of soil. Assuming that an
appropriate unpolluted soil is exchanged, the comprehensive functionality of the
soil system will have been fully developed within an unspecified period after
remediation (Haering et al., 1993). Comprehensive functionality is difficult to
assess and therefore a most simple utility function is derived. The utility from soil
washing procedure is zero when agricultural productivity was not negatively
affected before remediation. Consequently the utility function discriminates
between no improvement (ttf(x)(4_)~°) and improvement («^ (4J = 1).
p[0 forz(x)<S
"iw(4h)"[1 forz(x)>S (11)
where S denotes a threshold value of impact on soil functionality. The
threshold value S is 0.8 mg/kg total cadmium in soil, which is the Swiss legislation
Guide value (see above).
81
Chapter 4
The utility gained for the change of market value _?(x)(4_): The derivation of
an economic utility is based on the assumption that the market value of land after
soil washing equals the market value before contamination. The correction of
market value increases linear to the increasing contamination. The utility for the
maximum concentration under consideration is assumed to be 1, presuming the
market value of land increases after soil washing. For the calculation a maximum
contamination of 30 mg/kg is assumed.
to^-M'nk; forz(x)*°
4.6.3 The alternative in situ remediation (phytoremediation) 4,
The utility for human health uh(AiR) : The application of phytoremediation
continuously reduces the contaminantion in soil. However, the reduction is not a
linear process due to several interacting factors in soil like for example the mobility
of heavy metals, species selection of plants, and the influence of cropping
systems. The process of heavy metal extraction from soil to plant is investigated
by Wenger, Gupta, Furrer, Schulin (2002), Kayser (2000) and others. Kayser
(2000, p.130) emphasizes that the heavy metal removal rate decreases with
decreasing phytoavaiiable concentrations of heavy metals. Hence, from a
conservative, risk-averse point of view (as also taken in k*w(4_)). there is a
remaining impact on human health after applying phytoremediation. Therefore, we
propose a utility function that increases non-linear with increasing contamination:
„ Üz(x)/c forz(x)_#
Mz(*MJ~jl forz(x)>* (13)
where R denotes the value of toxicity for human health (20 mg/kg, Remediation
value of Swiss legislation (VBBo, 1998)).
The utility of cost uvz(x)(Ain) : The calculation of cost is based on an estimate of
2 Swiss Franks /m2/a (-1.50 US $) for phytoremediation (Scholz, et al. 1999). The
82
Decision making under uncertainty in case of soil remediation
estimation for a spatial unit (=1600m2) during 10 years1 is 32 000 Swiss Franks
(-23 168 US $). The costs of remediation rise with increasing contamination, but
reach a maximum score of 0.5, due to a simple rating of costs of remediation
alternatives, that is: uv(Ain)<uv(Ano)<uv(Aex) (see also above). This results in a
linear utility function up to a cadmium contamination of 3 mg/kg.
"2vw(4)"'
i— *z(x) forz(x)< 3.2 mg/kg3-2
(14)1 forz(x)> 3.2 mg/kg
The utility gained for long-term productivity upx{x)(Ain): The utility is derived
from the improvement achieved by the application of phytoremediation {Ain). The
remediation method is an in situ remediation method that sustains the structure
and functionality of the polluted soil (Krebs, 1996). For the constructing of a utility
function, we distinguish three different levels of improvement after applying
phytoremediation: i) the range of contamination where the method is not able to
reduce the contamination below a critical impact value for the agricultural
productivity, ii) the range of contamination where the method reduces cadmium
concentration below a critical impact value and iii) the range of concentration
where phytoremediation gains no improvement for agricultural productivity due to
low cadmiums loads. In the study area plants with biomass production of 10 t/ha
and an uptake of 45 mg/kg cadmium are able to reduce the contamination for 50%
of total contamination (Kayser et al, 2000). However, environmental scientist
dispute whether there are plants with such a performance. Some studies reported
about plants with high uptakes of heavy metals (Kumar et al., 1995; Ebbs and
Kochian, 1998; Lombi, Zhao, Dunham, McGrath, 2001), which could attain the
necessary level of performance. The cadmium uptake is dependent on soil,
climate, plant species and other properties (McGrath et al., 2002). Therefore it is
not reasonable to assume a removal of pollutants in a reasonable time span and
no maximal utility can be expected for case i). In this case the residual
1The reader has to acknowledge that residents and landowners are not prone to accept the
application of in situ soil remediation, if the procedure last longer than five years (Weber, Scholz,
Bühlmann, Grasmück, 2001). Thus, we assume a time span of maximal 10 years for the
assessment of the utility function.
83
Chapter 4
contaminants will cause a remaining effect to long-term productivity after
remediation. For case ii) a certain removal rate yields maximum utility, because
the amount of removed cadmium provides a cadmium load below a critical impact
value. For case iii) one has to acknowledge that low cadmium concentrations have
no effects on plant growth and phytoremediation gains no improvement for
agricultural production, therefore. Based on these arguments the utility function for
long term soil productivity after phytoremediation is
«fw (4„ ) = e-(lnz(x)-°-9f, z(x) 6 R+ \ {0} (15)
The utility gained for change of market value u^x)(Ain)\ The derivation of
utility function is based on the assumption that only half of the reduced market
value can be corrected after phytoremediation (Sell et al., 2000). Therefore the
maximum achievable utility is set to 0.5. Simplifying, the correction of market value
increases linear with increasing contamination. In accordance to a utility gained for
soil washing the following function is suggested:
«„«I (4« ) = *(*) *—-— for z(x) * °
<wV in)2*z(x)max (16)
4.6.4 The alternative no remediation Ano
The utility for human health w*w(40): The proposed utility function of a
human health impact is derived from a conservative, risk-averse point of view.
Based on the fact that cadmium accumulates in the human body for a long time
period contaminations below the legal threshold values are are taken into account
for an impact on human health (see also above). May, Scholz and Nothbaum
(1991) calculate the human health impact with dose-response curves that consider
environmental harm from cadmium exposure and intake by linear-logistic
functions. In this study the utility for a human health impact is constructed as a
nonlinear, polynomial function of the predicted cadmium contamination. Utilities
decrease nonlinearly with increasing contamination, because this remediation
alternative gains no improvement for human health.
84
Decision making under uncertainty in case of soil remediation
« (Â ._fl-V^ÖÖÄ-T forz(x)</?
U^KA°}-o forz(x)>* M
where R denotes the value of toxicity for human health (20 mg/kg, Remediation
value of Swiss legislation (VBBo, 1998)). The Remediation value of agro-and
horticulture is not considered, because the study area is mainly located within the
municipal zone (Hesske et al., 1998)
The utility of cost «^ (Am) : The calculation of cost is based on an estimate of
3 Swiss Franks /m2/a (~ 2 US $) for safeguarding of the contaminated area. The
estimation of costs for a spatial unit that is used in our case study (= 1600m2) are
48 000 Swiss Franks (-34 750 US $), assuming the duration of 10 years
safeguarding. Further the maximum utility is determined to 0.8, due to a simple
rating of costs of remediation alternatives: uv(Aln)<uv(Ano)<uv(Aex)(see also
above). The utility function is presented as a linear, deterministic function, simply
assuming that increasing contaminations causes increasing costs.
'
1
«.vw(4_) = '
*z(x) for z(x)< 3.84 mg/kg4.8 (1°)
0.8 forz(x)_ 3.84 mg/kg
The utility gained for long-term productivity up(x)(A„0) ; Plant growth is getting
more and more incomplete and soil fertility decreases with increasing
contamination (Geiger et al., 1993). But, the impact of increasing cadmium in soil
and plants is not linear and therefore the proposed utility function decreases
nonlinearly with increasing content of contaminants. The utility is equal to one for
concentrations without any effect on soil fertility (low concentrations), but
decreases continuously and is zero for high states of contaminations.
u^(AJ =e^^ z(x)eR+ (19)
The utility gained from change of market value w)(40): In case of no
remediation, the lenders show reservations about profitableness of this decision
alternative due to the remaining risk from contamination and the unforeseeable
time span for a reduction of contamination (Sell et al, 2000). Consequently, this
85
Chapter 4
alternative results in no economic benefit and a utility of zero for all concentrations
under consideration: um (4o) = 0*(»>
4.7 Results
4.7.1 The utility functions
We construct nine different utility functions for three different remediation
alternatives as displayed in Figure 4.7.1. The utility functions were constructed
from the available knowledge about cadmium in soil and their impact on human
health, the influence of long-term productivity of soil, the cost of remediation and
the change of market value after remediation. This leads to continuous, non-linear
functions for four utility functions (impact on human health and long-term
productivity for in situ and no remediation alternatives). Three utility functions had
to be derived in a discrete way, like the impact for human health or long-term
productivity of soil after soil washing. For all other utility functions a linear or partial
linear function appropriately describes the impacts from cadmium in soil.
OJtility
Alternative \Human health Costs Long-term productivity Change of market value
1-
os-
1-
05-
0 5-
Soil washing0 5- 05-
/"
3 6 OS 30
Phytoremediation 05- // 03- os
20 i 3
1
30
No
remediation
0 5- / 05-
»_A_W>
20 3
t
3
Figure 4.7.1 Utility functions derived for remediation options and four dimensions of evaluation. The
x-axis denotes cadmium in topsoil from 0-30 mg/kg. The y-axis denotes the utility score from zero
to one
86
Decision making under uncertainty in case of soil remediation
4.7.2 The overall utility of remediation alternatives
The calculated overall utility t/(4) at each coordinate (10799 spatial units à
1600 m2 in total) and for each remediation alternative shows for the Dornach area
that only at 69 spatial units the alternative phytoremediation reveals the highest
score of overall utility. The utilities for soil washing (5422 spatial units) and no
remediation (5308 spatial units) reveal similar numeric results, but they are
specific for their spatial distribution. According to the fact that the maximum
contamination is located around the metal smelter, the cases with highest overall
utility scores for soil washing concentrate around the source of contamination. The
alternative no remediation yields best results in at least 300 m distance to the
metal smelter due to the fact that the cadmium concentration in soil is low.
Considering the contribution of single utility dimensions to the overall utility, it
is obvious that the utility of the change of market value is not relevant for none of
the remediation alternatives (Figure 4.7.2). For all remediation options the utility
gained from improvement for long-term productivity of soil is a decisive argument.
However, the main cause for the highest scores in soil washing is the
improvement for human health impact.
No remediation Soil washing Phytoremediation
H Human health nCost «Long term productivity Change of market value
Figure 4.7.2 Contribution of each utility dimension to the overall utility for each remediation option.
Displayed is the mean utility ui^A,) [y-axis] of all considered areas (10799 spatial units à
1600m2) for each utility dimension and remediation option [x-axis]
87
Chapter 4
The overall utility for phytoremediation is mainly influenced by the argument
from (low) cost and long-term productivity, while the impact for human health is
less important. Each single utility dimension for phytoremediation reveals in
average the lowest scores of utilities of all remediation options. Note that this is
true for the mean partial utilities, but maybe different for single spatial units.
The sum function of U(A,) for each remediation alternative, as displayed in
Figure 6, explains the result of only 69 spatial units of highest utility for
phytoremediation. There is a small range of highest overall utility scores for
phytoremediation around the concentration of 3 mg/kg cadmium in soil. This is
mainly influenced by the utility function that describes the improvement for long-
term productivity of soil (compare Figure 4.7.3). According to the utility function
used the long-term productivity is attained only within a small range of
contamination, due to the limited removal of pollutants when phytoremediation is
applied.
1 4 5 6
Cadmium [mg/kg]
- - No Remediation — Soil washing — Phytoremediation
Figure 4.7.3 Sum functions of utilities from four dimensions and for each remediation alternative
88
Decision making under uncertainty in case of soil remediation
4.7.3 The expected utility at coordinate x
The expected utility is calculable for any cadmium concentration that could
occur at point x with estimation z(x). Therefore, the expected utility is a tool to
picture the uncertainty from estimation and its' consequences for the decision.
Figure 4.7.4 exemplarily shows three estimated values of z(x) and the expected
utility for two values of t(x) for each remediation alternative. The decision
preference is indicated and derived from the expected utility for the predicted
cadmium content z(x).
Cadmium, predicted [z(x) in mg/kg]
2.55
a3.1
Expected Utility
E[U(Am|| washing)]E[U(Aperem«Nation)]
C[U(Ano remsdlationJJ
Decision for.
t(x)=1.5 z(x)=2.55 t(x)=4.5 t(x)=1.5 z(x)=3.1 t(x)=4.5
0.987
0.1
0.948
0.998
SM8 0.991
0.915 0.826
c=2 mg/kg
z(x)"
p(false alanm)=0.33 p(fa|Se a|arm)=0.2
z(x)
p(hit)=0.8
0.78
t(x)=0.3 z(x)=0.78 t(x)=1.5
0.981 1.000
0.997
0.999
p(correct rejection)=0.93
z(x)
$
.c=2„mg/kg
p(miss)=0.07
Figure 4.7.4 Expected utility and feasible decisions for three examples of cadmium contamination
and different remediation alternatives Ar The true value [t(x)J denotes a possible state of
contamination beyond the prediction [z(x)]. The density distribution at the predicted value picturesthe probability of occurrence for different types of decisions (defined in Table 1) referring to a
threshold value of 2 mg/kg cadmium in soil.
89
Chapter 4
In accordance with Figure 4.7.3 the difference between the expected utility
for soil washing and phytoremediation is small and even negligible in some cases.
Nonetheless the variation in expected utility for different states of contamination is
obvious and provides transparency for the decision between remediation
alternatives. Another transparent approach of judging the decision is given by the
density distribution shown in Figure 4.7.4 The probability of any true value falling
below or above the threshold value of 2 mg/kg cadmium in soil serves as quality
criteria for the decision. For the exemplarily taken values of z(x) the probabilities
for a correct decision are [p(t(x)>2\z(x) = 2.55)=] 0.67 (hit),
[p(/(x)_2|z(x) = 3.1)=] 0.8 (hit) and [/?(*(x)<2|z(x) = 0.78)=] 0.93 (correct
rejection). In other words the true value is likely to occur in accordance with the
prediction above or below the threshold value. More general Table 4.3 records the
goodness of decisions for all predicted and analyzed spatial units. The results are
valid for a threshold value of 2 mg/kg cadmium in soil and present mean
probabilities of occurrence for the correspondence of prediction and hypothesis.
Beside the fact that only 69 spatial units show preferences for phytoremediation,
the high mean probability for correct decision in case of the alternative no
remediation is obvious.
Spatial units Mean probability for Mean probability for
(à 1600 m2) erroneous decision correct decision
[p(false alarm); p(miss)] [p(hit); p(corr.rejection)]
Soil washing 5422 0.29 0.70
Phytoremediation 69 0.27 0.73
No remediation 5308 0.05 0.94
Table 4.3 Mean probabilities of occurrence for decisions above or below a threshold value of 2
mg/kg cadmium in soil. The mean probability of occurrence indicates the goodness of decision for
all cases in which the remediation alternative reveals the highest utility score
90
Decision making under uncertainty in case of soil remediation
4.7.4 Deviation from predicted to hypothesized contamination
Alternatively the goodness of decision can be determined by a confidence
interval around the predicted value (within or without the true value is likely to
occur) or simply a certain distance above or below the predicted value as shown in
Figure 4.7.5.
False alarm
Correct
rejection
/15 20 25 30
Cadmium mg/kg
Acceptable true value
13 20
Phytoremediation Cadmium mg/kg
3 10 15 30 23 30
Soil washingCadmium mg/kg
i id IS 30 23 30
NoremedationCadmium mg/kg
Figure 4.7.5 The evaluation of decision as function of deviation from prediction to hypothesis of
contamination
Then the distance or deviation from predicted value to the accepted true
value determines the goodness of decision (hit, a false alarm, a miss or a correct
rejection). The defined distance to the accepted true value may differ with
remediation alternative due to the defined utilities and its effectiveness. For a
correct decision on phytoremediation the distance may be smaller than the
distance to the accepted true value for soil washing or no remediation (see Figure
4.7.5). Clearly the acceptable difference between prediction and hypothesis is
subject of negotiation between decision makers and case agents. It also
determines the magnitude of failure cost resulting from erroneous decisions.
Erroneous decisions (miss and false alarm) and their consequences and failure
91
Chapter 4
costs are multiple, different for each remediation alternative, and mainly case
dependent.
4.8 Discussion
The presented decision procedure integrates uncertainty about the
estimation of cadmium in soil with multi-criteria utility for a proper decision on soil
remediation alternatives. The method uses a geostatistical prediction of cadmium
content in soil that is based on sparse data measurement and reveals high
uncertainty of estimation. The uncertainty is a result of sparse sampling and the
overall variance of sampled data. The reason for a high variance in the data can
be found in the air-borne distribution of cadmium. Although there is no trend in the
data, the variability of data is a function of the distance. Therefore, certainty for
single points is likely to increase after an additional sampling, but the overall
variance of all sample data will still be high. Further, the data will still contain an
uncertainty from sampling procedure (sampling pattern, sampling density,
composite or spot sample), which is estimated about 35% of the predicted
cadmium concentration (Wagner et al., 2001, Schnabel et al., 2002).
The probability density function from geostatistically predicted mean values
for cadmium serves as a model for the true value that is likely to occur beside the
predicted value. The model is considered as a quality criterion in four kinds of
decisions (hit, false alarm, correct rejection, miss). In our case study the decision
is evaluated with a legal compulsory threshold value that refers to Swiss
legislation. This may not be useful in any practical application.
Utility functions are mathematical representations of the decision-makers
mental model and a subjective view of the world, therefore. However, the concept
of multidimensional utilities, as used in this paper, supports a rational and
transparent decision process. Considering different aspects of impacts follows the
demand of complete and decomposable, but non-redundant and comparable
criteria for the decision (Werner and Scholz, 2002). The constructed utilities ask
for simple criteria when discrete and continuous functions are used. The
assessment of deterministic instead of stochastic functions guarantees
manageability and is adequate for the investigated case. Introducing stochastic
utility functions (from empirical surveys) will increase the degree of uncertainty and
Decision making under uncertainty in case of soil remediation
complexity and finally may lead to nontransparent decisions. In such a case the
utility that is most likely to occur (for example with 95% certainty) for the predicted
value or another expected value might be defined as minimal acceptable (and
most certain) utility. The intersection of uncertainty from utility value and
uncertainty for the true value is then defined as expected utility.
In decision makers' practice the success of the introduced method depends
on the available data and knowledge about the contamination and its' impact.
Especially for the case of sparse measurements the method is able to generate
transparent decision that include high uncertainty. However for a final decision on
soil remediation the relative importance of each utility for different stakeholders
has to be determined. The algorithm of weighting was not a subject of this paper,
but is an important step forward to the selection of the best alternative. Examples
of weighting methods and ranking algorithms for case studies can be found in
Prato (2003) and Scholz and Tietje (2002).
Finally the introduced method supports the management of contaminated
land for example within the context of regional planning. Since potentially
contaminated plots are stored in register due to a certain suspicious land use
history, the uncertainty of the real state of contamination is high. All plots within
these registers are contaminated or not and they are suspicious (of contamination)
or not. Then four different cases are likely to occur for one single plot. This is an
unsuspicious and uncontaminated state, which resembles a correct rejection (of
suspicion) in the decision heuristic presented. Consequently a suspicious and
contaminated plot is a hit. Erroneous decisions on the registered plot are
characterized through a suspicious but uncontaminated case (false alarm) or a
contaminated but suspicious case (miss). In this situation the additional application
of the Bayes' Theorem is able to estimate the rate of real contaminated plots from
all contaminated plots (hit rate) and from all suspicious plots (diagnosis). This
resembles the decision heuristic introduced in this paper. It allows for transparency
and prevents erroneous decisions on contaminated land.
93
Chapter 4
4.9 Conclusion
We introduced a simple approach of generating utility functions for the
situations of soil contamination, which resembles many other decision situations.
Although, the proposed methodology implies some strong assumptions, it opens a
practical and reasonable approach to support decisions on soil remediation.
Further, we presented four different types of goodness in order to validate the
decision for a remediation alternative. The density value for overall utility at each
true value around a crucial threshold under decision sheds light into fuzzy results
of prediction and evaluation. Herewith, the decision-maker is able to deliberate
between remediation alternatives at each possible state of contamination and
therefore is likely to prevent erroneous decisions.
The applied technique increases decision-makers knowledge, provides
insight into the comparison of different remediation options, and presents a formal
and consistent approach for decisions on contaminated land management.
Acknowledgments
We would like to thank Olaf Tietje and the colleagues at UNS for discussions and support of
our work. The project was funded by the Swiss National Science of Foundation (Project Number
50011-44758) and the Swiss Federal Institute of Technology (Project Number 0048-41-2609-5).
94
Decision making under uncertainty in case of soil remediation
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5 Conclusion
The major goal of this thesis was to improve spatial data analysis, the
prediction and the evaluation of heavy metals in soil for the purpose of decision¬
making on the application of soil remediation methods. To accomplish this
objective, the spatial distribution of cadmium concentrations in soil was analyzed
from two different areas in Switzerland. The study started with the evaluation of a
method for multidimensional explorative data analysis and further focused on the
application of geostatistical measures to forecast cadmium contamination of
unsampled areas. The prediction revealed uncertain, but nonetheless suitable
results. The suitability has been demonstrated by the evaluation of different soil
remediation methods. At the end a spatial choice of remediation methods is
delineated based on the benefits gained after removal of pollutants. In the
following the main results are described in more details.
5.1 Multiple spatial regression improves data management
Data smoothing or - mollifying - with a Kernel density regression is used for
a combined spatial and statistical analysis. The Mollifier method was applied with
a data set of cadmium, copper, zinc, nickel, and chromium samples attained from
the Furttal, north west of Zurich (Switzerland). The evaluation of the method
produced two main results that are suitable to improve data analysis and
prediction of cadmium content in soil and other variables:
a) Blankets drawn from three-dimensional regression clearly visualize spatial
interrelation between different heavy metals. Further, spatial relevant boundary
variables like land use, pH value, and altitude support an identification of spatial
tendencies, hot spots, and outliers. Herewith, the Mollifier method bridges a gap
Chapter 5
between explanatory data analysis and three-dimensional visualization of spatial
interrelated parameters.
b) The spatial interpolation with a Gaussian Kernel density function attained
results equally good to those of ordinary kriging (the prediction for cadmium
reveals a mean of 275 ug per kg soil from ordinary kriging and a mean of 308 pg
per kg soil from the Mollifier interpolation). Moreover, the Mollifier method is a
convenient alternative to kriging, when the stochastic, spatial structure of
underlying data shows a spatial trend.
However, the practicability of the Mollifier method strongly depends on the
density of data. Therefore, a precautionary fit of regression parameters, like
window size and regression function was essential.
5.2 Predictability versus uncertainty
The second data set consists of 76 samples, spread over an area of 15
square kilometers in Dornach (Canton Solothurn, Switzerland). The area-wide
distribution of cadmium was assessed with geostatistical methods. Since cadmium
was emitted from a metal smelter, the data exploration focused on trend models
and anisotropy. However, the consideration of contamination patterns reveals no
significant improvement for spatial prediction. Lognormal ordinary kriging and
conditional simulation was applied for interpolation. The outcome was a geometric
mean distribution of 1.08 mg cadmium per kg soil and a standard deviation of 2.27
mg/kg. After an assessment of the overall uncertainty, it was ascertained that the
high uncertainty predominantly results from the spatial interpolation and was
induced by low sampling density and spatial heterogeneity of contaminants.
Regardless of high mean uncertainty for the total area of 15 square kilometers the
use of probability knowledge at single small areas provided practicable and
useable results. Conclusively, a small part of the investigated area is contaminated
with more than 2 mg cadmium per kg soil with a probability of more than 90 %,
however a contamination above the legal remediation value (20 resp. 30 mg/kg) is
not likely at any side. Cadmium concentrations above 0.8 mg/kg soil are
widespread with more than 50 % probability of occurrence. The exact spatial
allocation of these results were presented in maps showing likelihood's to exceed
threshold values in accordance to legal compliance. The probability information
102
Conclusion
can be dedicated to any other threshold value, taking into account the decision
makers safety requirements. Herewith, the estimation can be used to delineate
areas for soil improvement, remediation, or restricted area use.
5.3 'Correct' decisions for soil improvement measures
The application of soil improvement measures was evaluated with a multi-
criteria utility analysis for soil washing, phytoremediation and the alternative of no
remediation. Considering different aspects of impacts, the constructed utility
functions asked for simple criteria when discrete and continuous functions were
used. Presuming some strong assumptions, a linear utility function was modeled
to express the benefit from 'cost of remediation techniques' and 'change of market
value'. Non-linear utility functions were developed for the impact on 'human health'
and 'long-term productivity of soil' after the application of remediation methods.
Without weighting single criteria with a decision maker's preference, 'human
health' and 'long-term productivity' of soil were decisive arguments for all
remediation alternatives.
The evaluation with an additive overall utility revealed a spatial structure of
highest scores for soil washing and no remediation. Soil-washing methods were
preferred within a distance of 300 m to the source of contamination, whereas no
remediation were recommended beyond this distance. Phytoremediation was
superior only in few cases with a cadmium concentration around 3 mg/kg soil. This
is a consequence of the limited capacity of phytoremediation to extract cadmium
from soil to plants, which have been accounted for in the utility function on long-
term productivity of soil.
The uncertainty of decisions was validated with the concept of expected
utility. The probability density function from geostatistically predicted mean values
for cadmium served as a model for any true value that is likely to occur beside the
prediction. The model was considered as a quality criterion in four kinds of
decisions (hit, false alarm, correct rejection, miss). The results are calculated for
the Trigger value of Swiss Ordinance Relating to Pollutants in Soil, which is 2 mg
cadmium per kg soil. Then the probability of any true value falling below or above
the Trigger value is able to determine the magnitude of failure cost.
103
Chapter 5__
Concluding, the investigated methods improve scaling and transmission of
sparse information in the context of soil improvement measures. Although the
prediction of cadmium revealed no reliable deterministic estimation the handling of
uncertainties with probability information led to useable and trustworthy results for
the decision maker. Therefore the choice of best suitable soil improvement
measures is transparent and avoids ambiguous decisions.
5.4 Outlook
This thesis showed that despite of a sparse data set, data exploration and
prediction is not only feasible, but also results in convenient and reliable decisions.
The experiences gathered throughout the study concerning data, prediction and
remediation methods, lead to a couple of desirable foci for future research studies.
In Switzerland national soil observation services (NABO and others) collect
data about pollutants in soil. Since these data are sampled at single random
points, a method for area-wide prediction of pollutants in soil is so far missing.
With the methods and results demonstrated in this study, the collected data can be
reliably analyzed and spatially predicted. Thus, it becomes possible to delineate
areas of a priority treatment for soil improvement measures or soil remediation.
This is of particular interest for a nationally consistent processing of measures to
sustain soil resources. The compilation of a national standardized soil database
may benefit from the methods of data analysis and interpolation demonstrated in
this thesis. Future work that aims for an interpretation of sparse data should
include boundary land use variables and the use of a Geographical Information
System (GIS). From a technical point of view the Mollifier method should be
integrated into a GIS in order to not only confirm an efficient and user-friendly
explorative data analysis, but also to bridge the gap between three dimensional
data analysis and visualization of spatial interdependency of variables.
Future work should focus on the application of phytoremediation as a soil
improvement measure. Since phytoremediation is only feasible to reduce a certain
but limited amount of heavy metals from soil, it is rather suitable to be used as a
tool to improve soil quality, e.g. in regional planning, than to be used as a sufficient
remediation method. In the context of regional planning, phytoremedation can be
used e.g. as an ecological buffer area or for a periodical decontamination of lowly
104
Conclusion
contaminated agricultural areas. Herewith, the aim to sustain soil fertility, claimed
in Swiss legislation, could be realized in practice.
Finally the results presented in this thesis may help for a break through in the
accomplishment of sustainable soil protection and further sustainable development
of the natural environment.
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Danksagung
Zahlreiche Personen haben mich in den letzten Jahren bei der
Bearbeitung dieser Dissertation auf unterschiedlichste Weise begleitet und
unterstützt. Die ersten zwei Jahre am Institut für Kulturtechnik waren durch
eine in jeder Hinsicht sehr offene und wissenschaftliche Atmosphäre geprägt,
die mich mit dem institutionellen, strategischen und politischen Alltag an der
ETH vertraut machte. Die letzten drei Jahre an der Professur für Umweltnatur-
und Umweltsozialwissenschaften stellte eine grosse thematische Bereiche¬
rung dar, in der ich mich auf die wesentlichen Fragen meiner Arbeit
konzentrieren konnte. Allen Kollegen und Freunden sei an dieser Stelle für
Rat, Tat und Freundschaft herzlich gedankt. Mein ganz besonderer Dank gilt
folgenden Personen:
Prof. Dr. Roland W. Scholz für die Übernahme des Referats und die
Möglichkeit die Arbeit an seiner Professur zu Ende zu führen. Ich habe die
durch Vertrauen und Grosszügigkeit geprägte Arbeitsatmosphäre sowie den
zu jeder Zeit möglichen Dialog sehr geschätzt.
Dr. Olaf Tietje für die umfassende, weitreichende und beständige Zusammen¬
arbeit in den letzten fünf Jahren. Olaf Tietje ist es gelungen einem Fisch das
Fahrrad fahren beizubringen, indem er mit viel Geduld meine Gedanken
immer wieder in die richtigen mathematischen Bahnen lenkte. Für die
zahlreichen, mathematischen Diskussionen möchte ich mich ganz besonders
bedanken.
Dr. Martin Fritsch für visionäre Idee zu dem vorliegenden Projekt, durch das
ich wertvolle Erfahrungen während eines Forschungsaufenthaltes am
International Institute for Applied System Analysis (IIASA) sammeln konnte.
Prof. Dr. Willy Schmid für die freundliche Übernahme des Korreferats und die
finanzielle Unterstützung.
Hélène Renard-Demougeot gab mir wertvollen geostatistischen Tipps und
Tricks. Merci beaucoup!
Ich danke den Mitgliedern der Bewertungsgruppe des Integrierten Projektes
Boden (IP Boden, Schwerpunktprogramm Umwelt)), insbesondere Armin
Keller und Achim Kayser, für die anregenden Diskussionen über
Bodenbewertungen und Phytoremediation.
Von Herzen möchte ich mich bei meinen Freunden bedanken, die mir immer
wieder die Perspektive gaben, dass die Dissertation nur die eine Hälfte
meines Lebens ist:
Christoph Jung für die niemals endende Zuversicht, die Geduld und den
Ansporn, der mir nicht nur das Ende dieser Arbeit erleichtert hat.
Dani Güttinger für die Wärme, die Herzlichkeit, das offene Ohr zu jeder Zeit
und den besten Wein der Welt in guten und in schlechten Zeiten.
Marcus Fenchel für die unendliche Fröhlichkeit, die (gewonnenen!)
Sektwetten und die Austreibung des Morgenmuffels in mir.
Anita Jost, Sonja Wipf und Verena Schatanek für das Gefühl in einem frem¬
den Land zu Hause zu sein. Danke für die tiefe Freundschaft und den
Glauben an die Richtigkeit meines Tuns!
Julia Bolzek für die Inspiration, die konstruktive Kritik und die immerwährende
Freundschaft, trotz so mancher Leere, die ich hinterlassen musste.
Markus Gallus - für die vorbehaltlose, tiefe Freundschaft und den rettenden
Anker in jeder Situation.
Ein ganz besonderer Dank gebührt meinen Eltern Klaus und Ruth Schnabel,
die mich zu jeder Zeit ermutigt haben, den Weg zu gehen, den ich für richtig
halte. Ohne ihre Unterstützung hätte ich diese Arbeit nicht schreiben können.
108
Curriculum Vitae
1966 Born in Lehrte, Germany
1972-1976 Primary School, Lehrte
1977-1983 Secondary School, Lehrte
1983-1988 Bookseller, Schmorl und von Seefeld, Hannover
1987-1988 Advanced technical college certificate in economics,
Economy Secondary School, Hannover
1988-1990 University entrance diploma by second-chance education,
Hannover-Kolleg, Hannover
1990-1997 Studies of Geography, Soil Science and Geology
Georg-August Universität Göttingen and Technical
University of Hannover
Diploma Thesis: Bewertung von Landschaftseingriffen in
Skigebieten der französischen Alpen (Tarentaise)/Tignes
- La Plagne - Méribel unter besonderer Berücksichtung
des Sommertourismus
2000 Participant of the Young Scientist Summer Programm
Land Use and Land Cover Change Project,
International Institute of Applied System Analysis,
Laxenburg
1998-2002 PhD Student
Institute for Land Improvement and Water Management
and Natural and Social Science Interface
Swiss Federal Institute of Technology, Zurich
Publications
Ute Schnabel and Olaf Tietje (2003): Explorative data analysis of heavy metal
contaminated soil using multidimensional spatial regression, Environmental
Geology 44 (8), 893-904
Ute Schnabel, Olaf Tietje and Roland W. Scholz (in press): Uncertainty
assessment for management of soil contaminants with sparse data,
Environmental Management
Ute Schnabel, Olaf Tietje and Roland W. Scholz (2002): Using the power of
information of sparse data for soil improvement management, Working Paper
33, Natural and Social Science Interface, Swiss Federal Institute of
Technology Zurich, pp. 27
Martin Fritsch, Olaf Tietje, Erwin Hepperle und Ute Schnabel (1999):
Landnutzungsmodelle als Planungsinstrumente für den Einsatz von sanften
Bodensanierungen, Terra Tech 6, 24-27
Manuscripts
Ute Schnabel and Roland W. Scholz (submitted): Decision making under
uncertainty in case of soil remediation, Journal of Environmental Management
Ute Schnabel (2000): Mollifier or B.L.U.E. A comparison of two interpolation
methods, Final report for the Young Scientist Summer Program, International
Institute for Applied System Analysis, Laxenburg, pp 28, unpublished
Ute Schnabel (1998): Methodische Grundlagen zur Ausscheidung von
Sanierungseinheiten kontaminierter Böden im städtischen Umfeld, interner
Bericht, Institut für Kulturtechnik, Eidgenössische Technische Hochschule,
Zürich, 16 S., unveröffentlicht
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