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978-1-4673-0024-7/10/$26.00 ©2012 IEEE 2700
2012 9th International Conference on Fuzzy Systems and Knowledge Discovery (FSKD 2012)
1
Heavy Metals Contamination in Urban Topsoil
Na WANG, Qingzheng XU, Li Peng
Xi’an Communication Institute
Xi’an, China
xuqingzheng@hotmail.com
Abstract—As important component part of urban ecological
system, urban soil is of great significance to human health and
urban development. Based on the concentration of primary
heavy metals at the sampling sites, we analyze the stochastic and
constitutive property of concentration distribution by the
geostatistics. Considering the semivariance function structure,
the concentration at the unsamped sites is computed using
Kriging interpolation, and then the contour line of primary
heavy metals is drafted so as to show directional distribution in
visual form. The distribution feature of primary heavy metals
and the cause of pollution are determined combined with social
function at the sampling sites in this paper. Finally, an object
function is established to determine the exact location of
pollution resources in a wide area, and then solved by
intelligence computation method. Results show that, the
approach is feasible to determine the accurate coordinates of
pollution sources.
Keywords-heavy metals contamination; semivariance function;
Kriging interpolation; pollution source; intelligence computation
I. INTRODUCTION
Some scholars have proposed different definition and
classification of urban soil, which has no precise or uniform
definition at the present time. It is generally agreed that, an
urban soil is a soil material having a nonagricultural, usually
manmade surface layer more than 50 centimeters thick, which
has been produced by mixing, filling, or by contamination of
land surface in urban and suburban areas [1]. They are widely
distributed in park, road, stadium, urban river, refuse landfill,
displaced factory, mine, or are covered by building and
industrial facilities. As an important component part of urban
ecological system, urban soil is the growing medium and the
nourishment provider for green plant, the natural habitats and
the energy source for edaphon, the integrating pool and
cleaning cartridge for contamination. So it has a great
significance to urban sustainable development.
Due to the rapid urbanization and industrialization
occurring in China over the last few decades, a large collection
of contamination produced in the course of industrial
production, transportation and social activities significantly
alters the original native soils. Heavy metals do not decay with
time because of their nonbiodegradable nature and long
biological half-life in bodies. Therefore, excessive inputs of
heavy metals into urban soils can impose a long-term burden
on the biogeochemical cycle in the urban ecosystem by
causing effects such as soil function deterioration, changes in
soil properties and other environmental problems.
Furthermore, past studies have revealed that heavy metals in
urban soils can accumulate in the human body, where they
cause damage to the nervous system and internal organs.
Therefore, heavy metals contamination in urban soil has
become research hotspot in recent years [2-6].
CUMCM (The Contemporary Undergraduate
Mathematical Contest in Modeling) is an annual contest for
undergraduates all over the world, organized by CSIAM
(China Society for Industrial and Applied Mathematics). The
contest problem A of CUMCM-2011 is set as the heavy metals
contamination problem in urban topsoil [7]. In [8], the
directional distribution of primary heavy metals is determined
by Griddata interpolation to the initial data, the spatial
variability property in soils is described with the tools of mean,
variance, standard deviation and coefficient of variation, and
then the evolution model of urban geological environment is
This work is partially supported by the Natural Science Foundation of
China (No. 61100009).
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established with many influence factors. In [9], the similar
model is also established with the help of factor analysis and
potential ecological risk assessment, and then some
rationalization proposals are proposed to pollution control and
management. In [10], the dynamic weighted comprehensive
evaluation model is set up, and then heavy metals
contamination in a particular area is discussed and evaluated in
details with the benefit of multiple nonlinear regression
analysis.
II. ANALYSIS AND SOLVING THE PROBLEM
A. Analysis and Solving the Problem 1
Until recently, regression analysis and auto-regression
trend model were used to study the cause, analysis and
modeling of urban development to soil quality. However, the
precondition of these methods based on classical statistical
theory, is the large sampling and typical probability
distribution, which are very difficult to achieve in practice. In
addition, these tools can only summarize the whole features of
variables, and yet not show the variability, stochastic property,
constitutive property, independence, relativity. The same
sampling can not be repeated, and then the concentration of
heavy metals is regionalized variable with stochastic and
constitutive property. Therefore, it is essential to study the
spatial variability property of heavy metals in urban soil,
which is benefit to discuss the influence factor, to deepen some
geochemical process, and to put forward some pointed
treatment measure.
The approach of studying directional distribution, such as
the geostatistics, will describe quantitatively the constitutive
property of the directional distribution, such as relativity,
directivity, and complexity [11]. Especially, the semivariance
function is used to analyze space structure, and the Kriging
interpolation to draw concentration distribution by
geochemists.
Let p(x, y, t) is a point in three dimensions space, and
regionalized variable Z(x, y, t) = Z(p) describing the
concentration of heavy metal in point p. Unlike usual variable,
regionalized variable is a function of variable and location
information, and is a specific occurrence of variable at an exact
location in specific area.
The semivariance function )(* h
γ
is used to describe
the stochastic and constitutive property of regionalized
variable, as shown in (1). This equation shows the relationship
between the variation of soil sample and the distance of
different samples in this paper.
() () () ( )
[]
()
∑
≈
=
+−Ζ=
hhji
i
ii
ij
hxZxE
hN
h
,
1
2
*
2
1
γ
(1)
There are three important parameters of semivariance
function: range a, nugget C0 and sill C0+C. They are quantified
measures of spatial variability and degree of correlation of
regionalized variable on a scale. The range indicates the
distance which values are spatially correlated, and a distance
which may also be interpreted as average patch size. Positive
values of the nugget represent a combination of experimental
error and of unresolved spatial variability occurring at scales
smaller than inter-sampling lag distance. The smaller nugget
makes clear that the process is not neglected at smaller scales.
The sill, the maximal semivariance among different sampling
interval, is composed of stochastic variation and constitutive
variation, and represents the spatial variability caused together
by the natural factor, such as soil parent material and
topography, and socioeconomic factor, such as fertilizing and
plant.
The sampling data under such actual geographical
conditions often demonstrate nonnormal distribution.
However, the distribution like this may lead to scale effect and
aberration of semivariance function, which will drive up the
nugget and the sill and enlarge the measurement error. The
violent fluctuation of semivariance function even conceals its
inherent architecture. Therefore, the concentration of heavy
metals is the logarithm (base e) of the original data, and then
the semivariance function is fitting.
So far, the most popular semivariance model is spherical
model, exponential model, and Gaussian model. To optimum
fitted model, we firstly compute the )(* h
γ
-h scattergraph of
semivariance function of heavy metals (As and Cd) in soils, as
shown in Fig. 1. It is well known that the scattergraph, the
effective tool in geostatistics, can present the spatial variability
of regionalized variable in two dimension surface vividly, and
reveal the directional distribution and the variation law of
regionalized variable.
Next, the functions of 8 kinds of heavy metals are fitted
considering their shape feature. The results are listed in Table
1.
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1
As
Cd
Figure 1. Scattergraph of semivariance function of heavy metals: As and Cd
TABLE I. THE MODEL TYPE AND ITS PARAMETERS OF FITTED SEMIVARIANCE FUNCTION
As Cd Cr Cu Hg Ni Pb Zn
Fitted model type Spherical Spherical Exponential Gaussian Gaussian Spherical Spherical Spherical
Nugget C0 0.091 0.008 0.001 0.001 0.121 0.001 0.191 0.086
Range a 2500 2000 3000 2500 2200 2100 1800 3000
Sill C0+C 0.17 0.36 0.22 0.41 1.07 0.14 0.20 0.48
Within limits of geographical situation, economic cost and
human resources, it is impossible to select the sampling sites
densely. However, it is difficult to present the directional
distribution of heavy metals in the given area by the sparse
sampling sites. It is essential for this reason that, we should
compute the concentration of more geographical location and
try to keep the spatial relationship and the semivariance
function structure between estimation point and sampling site,
and among sampling sites. Kriging interpolation, a linear
optimization unbiased estimation to the regionalized variable
of unsampled sites, is very much the approach by the use of the
initial data of regionalized variable and the semivariance
function structure, such as range a, nugget C0 and sill C0+C.
Therein the so-called “linear” means that the estimation value
is a linear combination of sampling values, “unbiased” means
the semi-mean of estimation value is equal to the semi-mean of
sampling value, and “optimization” means the error variance
of estimation value is minimization.
In this paper, we estimate the directional distribution of
concentration of primary heavy metals with the tool of Kriging
interpolation to fitted semivariance function, and then draw the
contour line of concentration. The results, for example, As and
Cd, are shown in Fig. 2.
As
Cd
Figure 2. Directional distribution of concentration of heavy metals: As and
Cd
Semivariance function
Semivariance function
Intervals
Intervals
Concentration
Resid ential ar ea
Indu strial ar ea
Mountain area
Main roads area
Park green space
Concentration
Resid ential ar ea
Indu strial ar ea
Mountain area
Main roads area
Park green space
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B. Analysis and Solving the Problem 2
Generally speaking, heavy metal contamination show
different propagate features in different environment, and then
it is quite distinct from the harm range and influence way of
population. We presents the distribution rule of As and Cd, for
example.
The pollution area of heavy metal As is wide and relative
centralized. By the order of concentration, the main area of this
heavy metal is main roads area, industrial area, residential area,
and urban park green space. Therein, main roads area and
industrial area, in which the contamination is more than 10, are
the most serious areas. And then, the contamination in
residential area and urban park green space fluctuates between
4 and 10. Finally, the contamination in mountain area is less
than 4 and it is relatively better.
The pollution area of heavy metal Cd is relative dispersive.
The main area of this heavy metal is main roads area,
residential area, and industrial area, which are less than an
elevation of 50 meters. The contamination in these areas is
more than 700. Comparatively speaking, the contamination in
mountain area and urban park green space is less than 300 and
it is relatively better.
After an incomplete analysis of directional distribution of
heavy metals in urban soils, we can conclude that, the order of
concentration of primary heavy metals is Hg, Zn, Cu, Cd, Cr,
Pb and Ni, and the order of main pollution area is main roads
area, residential area, and industrial area. Further, another
remarkable feature of heavy metals contamination is that the
pollution in urban topsoil doesn’t have evident spatial
continuity.
C. Analysis and Solving the Problem 3
The object of problem 3 is to determine the exact location
of pollution resource in a wide area. To handle this, we choose
the heavy metal’s approximate location based on the
directional distribution of heavy metals. And then, an objective
function with the important parameters in pollution propagate
model and geographical location of pollution sources is
established. The classical approach can not quickly solve the
complicated function with multi-variables, and then we try to
solve the optimization problem by an intelligence computation
method.
The flow or progress of determining the exact location of
pollution resource is as follows. (1) Observe carefully and
choose a larger approximate area, in which the pollution
resource is included; (2) Determine a smaller severe area based
on the coordinates of sampling site with highest concentration
in that approximate area; (3) Record the coordinates and its
concentration of the all sampling sites in that severe area; (4)
Let pollution propagate model with distance changing is C = a
+ me-nd, where a is the background value, a+m is the
background value plus the highest pollution value; (5) Then
the objective function is ∑
=
−−+=
N
i
i
nd cmeaF i
1
2
)( , where
222 )()()( optzzoptyyoptxxd iiii −+−+−= , N is
the number of sampling sites in that severe area. The physical
meaning of this optimization problem is to determine the
parameters so as to the pollution propagate model is close to
the sampling results in practice. The variables to be defined are
the parameters m and n of pollution propagate model and the
coordinate (optx, opty, optz) of pollution resource. (6) Solving
the minimization problem by some intelligence computation
method.
Differential Evolution (DE) is a branch of evolutionary
population-based algorithms proposed by Storn and Price [12,
13], which is an effective, robust, reliable, and simple global
optimization algorithm. According to frequently reported
comprehensive studies, DE has been preferred to many other
optimization techniques such as genetic algorithm,
evolutionary programming, and particle swarm optimization in
terms of accuracy, convergence speed, computation
complexity, and robustness over both well-known benchmark
functions and hard real-world problems. Generally speaking,
each of these population-based optimization algorithms has its
own characteristics, strengths, and weaknesses, and long
computational time is a common and crucial drawback for
both of them because of its evolutionary/stochastic nature
during optimization processes. In recent years, many efforts
have been done to improve the performance of DE. A novel
Opposition-based Differential Evolution using the Current
Optimum (COODE) is proposed for function optimization by
Xu [14]. This approach overcomes the drawbacks of previous
Opposition-based Differential Evolution (ODE) [15], in which
opposite points may lapse from the global optimum and the
utilization rate of opposite points is decreasing during the later
stage of evolution.
In the following section, we try to show that the COODE is
feasibility and efficiency on heavy metal Cd. The directional
distribution of concentration of heavy metals Cd is shown as
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Fig. 3. The area (7500 < x < 9500, 6000 < y < 8000) marked in
red in Fig. 3 is fixed with a pollution resource by observing,
and then is enlarged as shown in Fig. 4. As you can see in Fig.
4, there are four sampling sites in that severe area, and then the
number, coordinates and concentration of these locations are
listed in Table 2.
Figure 3. Directional distribution of concentration of heavy metals Cd
Figure 4. Partial en larged view of the area marked in red in Figure 3
TABLE II. SAMPLING SITES IN THE SEVERE AREA
No. x(m) y(m) z(m) C
39 8077 6401 29 449.10
40 8017 7210 39 852.70
46 9062 7639 45 600.70
47 9319 6799 49 567.60
Considering the pollution propagate model, the objective
function ∑
=
−−+=
4
1
2
0)(
i
i
nd cmecF i is established, where
c0 is the background value,
222 )()()( optzzoptyyoptxxd iiii −+−+−= is the
Euclidean distance between the pollution resource and the
sampling site, ci is the concentration of sampling site.
Finally, we try to solve the complicated optimization
problem with multi-variables by COODE. In our experiment,
the population size Np = 100, differential amplification factor F
= 0.5, crossover probability constant Cr = 0.9, jumping rate
constant Jr = 0.3, mutation strategy DE/rand/1/bin (classic
version of DE), maximum NFC (number of function calls)
MAXNFC = 106. Experiment results are shown in Fig. 5, in
which the blue line represents the best population fitness and
the green line represents the average population fitness.
Experiment results show that, COODE algorithm can find out
the global optimum quickly by searching the problem spaces
in relatively small generation, and then it can meet the
engineering requirements very well. At the same time, the
location of pollution resource is definite at (8380, 7352, 48),
and two parameters in the pollution propagate model m =
700.8307, n = 0.0003. The locations of all pollution resources
as shown in Table 3 are computed using the same method.
050 100 150 200 250 300 350 400 450 500
0
2
4
6
8
10
12
x 105
050 100 150 200 250 300 350 400 450 500
0
2
4
6
8
10
12
x 10
5
••••
Figure 5. Performance of our approach
Figure 6. CONCLUSION
For the spatial variability at small scales in the area with
abundant heavy metals, it is not effective to reflect the soil
quality in particular area with the overall evaluation results
based on the sampling data. In this paper, the geostatistics is
fist applied to the soil quality research with more precision
results representing the directional distribution of heavy metals
in urban topsoil. Kriging interpolation is a linear optimization
unbiased estimation, so the conclusion is more believable. At
last, to determine the exact location of pollution resource
quickly, a complicated objective function is established and
then solved by an intelligence computation approach.
Unfortunately, the sampling sites are limited, and their
natural attribute and social attribute is not clear so far. For
Concentration
Resid ential ar ea
Indu strial ar ea
Mountain area
Main roads area
Park green space
Concentration
Resid ential ar ea
Indu strial ar ea
Mountain area
Main roads area
Park green space
Best population fitness
Average population fitness
Generation
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4
these reasons, it is difficult to obtain some more instructive
conclusions in reality. So we should collect more information
to overcome the forementioned shortcomings of the current
model and to study evolution mode of urban environment in
the near future. The helpful information may involve season,
era of original data, river, lake in urban and suburban areas,
minerals distribution, type of business, et al.
TABLE III. LOCATION OF POLLUTION RESOURCES
No. Heavy metal x(m) y(m) t(m)
As-1 As 18137 10040 41
As-2 As 12606 3002 27
Cd-1 Cd 8380 7352 48
Cd-2 Cd 201 3983 1
Cd-3 Cd 3291 5995 4
Cd-4 Cd 5117 11538 0.
Cr-1 Cr 3300 6015 5
Cr-2 Cr 4572 4607 6
Cu-1 Cu 3610 2388 30
Cu-2 Cu 3275 5983 4
Hg-1 Hg 2671 2229 22
Hg-2 Hg 13808 2344 79
Ni-1 Ni 3300 5912 4
Pb-1 Pb 473 3974 1
Pb-2 Pb 4800 5001 8
Zn-1 Zn 13855 9637 0
ACKNOWLEDGMENT
The authors are deeply grateful to the anonymous
reviewers for their helpful comments which have significantly
improved the quality of this work.
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