Environmental
Pollution,
Vol. 94,
No. 2, pp. 205215, 1996 Cc 1997 Elsevier Science Ltd Great Britain. All rights reserved 02697491/96 $15.00+0.00
Copyright
Printed in PII:
SO2697491(96)000607
tLSEVlER
MAPPING HEAVY METALS IN POLLUTED DISJUNCTIVE KRIGING
B. von Steiger,” R. Webster,b
SOIL BY
R. Schulin” & R. Lehmannc
UETH Ztirich, Institut fir terrestrische dkologie, Grabenstrasse 3, 8952 Schlieren, Switzerland ‘Rothamsted Experimental Station, Harpenden, Hertfordshire AL5 2JQ, UK “Amt ftir Umweltschutz und Wasserwirtschaft, Bahnhofstrasse 55, 8500 Frauenfeld, Switzerland (Received
4 January
1996; accepted
Abstract The soil of some 50 km2 around the town of Weinfelden in northeast Switzerland has been sampled and analysed to estimate and map the concentrations of heavy metals before an incinerator for the canton’s waste is built. Given that the estimates are subject to error, the probabilities thut true values exceed the maximum tolerable concentrations of the Swiss,federal guide have also been estimuted by disjunctive kriging. These may now be used by the local planners ,for making decisions. Of the metals examined, lead exceeded the guide value at several sampling points, and a moderate probability of excess of lead is fuir1.y widespread. Copper exceeded the guide value in vineyards and orchards, but ulso in a few places elsewhere, and the estimated probabilities of excess were not negligible. The other two metals of concern, cadmium (with one exception) and zinc, had concentrations much less than the guide values. The patterns of distribution of the four metals were similar, the productmoment correlations umong them are substantial, except in the vineyards and orchurds, and it seems likely that they hud common sources. 0 1997 Elsevier Science Ltd. All rights reserved. Keywords: probability
Heavy metals, mapping.
soil,
disjunctive
26 April 1996)
guide values are exceeded then they must measure the concentrations, map the areas concerned accurately and decide how to deal with those places where the guide values are exceeded. In recent years, environmental scientists have come to appreciate the merits of geostatistics, and specifically kriging, for investigating and mapping soil pollution by heavy metals in particular: there are several examples in the literature (Leenaers et al., 1990; Atteia et al., 1994; Stein, 1994). The Swiss government has published recommendations on the proper application of geostatistics for mapping concentrations of toxic metals (Schulin et al., 1994). Almost all applications of kriging for mapping have used ordinary kriging for the interpolation, and Stein (1994) elaborated the technique by stratifying the data using prior information. Working from more or less sparse data, investigators have estimated values at the nodes of fine grids, which they have then displayed either as they are or ‘contoured’ to produce the final maps. The results are best in the sense that the estimates are unbiased linear combinations of the data and have minimum variance. Nevertheless, they are only estimates and therefore subject to error. So, before an agency attempts to reclaim land that appears to be contaminated or invokes legislation to distrain a polluter, it may wish to know the likelihood that the true concentrations in the soil exceed the threshold. It will not want to spend money unnecessarily on reclamation or law enforcement. Equally, where estimates fall somewhat short of a threshold the true values might exceed it, and again the agency will want to know the probabilities of this and of the risk it runs by doing nothing. Yates and Yates (1988) described such a situation where soil was contaminated by a virus in sewage, and Wood et al. (1990) followed the same line of thinking for controlling salinity of soil. If the underlying distribution functions were known, these probabilities could themselves be estimated from ordinary kriging. In practice, however, the functions are not known, and the actual distributions of data seldom conform closely to any theoretical one, such as Normal. Matheron (1976) developed disjunctive kriging to cope with this situation, and Webster and Oliver (1989),
kriging,
INTRODUCTION The soil of Switzerland, like that in other longsettled industrial countries, is locally contaminated with heavy metals. The metals derive from manufacturing and metallurgical industry, waste incineration and waste disposal, including sewage, crop protection, and motor traffic. In places they are toxic to plants and grazing animals, and they threaten the proper functioning of the soil and ultimately the health of people. The Swiss federal government recognizes the threat, and it has set guide values for the more common contaminants. It has published them in its ordinance relating to pollutants in soil, the VSBo of 1986 (FOEFL, 1987), and it charges the cantons with controlling contamination within these limits. Therefore, the cantons must know the concentrations. Where there is any serious likelihood that the 20.5
206
B. von Steiger et al.
Webster (1991) and Webster and Rivoirard (1991) explored its potential for mapping deficiency of trace metals in soil, which may be seen as the complement of toxicity. The Canton of Thurgau faces a similar situation in the region around Weinfelden, where it plans to build an incinerator for domestic waste. Contamination was suspected in the vicinity at the outset, and the canton did not wish to add substantially to the soil’s burden of pollutant metals if concentrations were already close to the federal guide values. It sampled the soil and determined the concentrations of cadmium, copper, lead, zinc and mercury. Of these, the last two had only small concentrations everywhere, and the likely additions of them in the fallout from the incinerator were considered to pose no threat. The largest concentrations of copper were found in orchards and in vineyards, in which copper salts were and still are used as fungicides. This is a wellknown situation specific to fruit production, and the problem that it poses remains to be solved. However, large concentrations of copper occur elsewhere, and on investigation these were usually found to be in former vineyards and orchards. Sample concentrations of cadmium and lead exceeded the federal guide values locally and were close to the guide values more widely. The authors decided to map their distributions, therefore, and to estimate the probabilities of their exceeding the thresholds throughout the region. The data from the surveys have been analysed with these aims using disjunctive kriging to estimate concentrations and probabilities of excess. This paper summarizes the steps involved in disjunctive kriging and reports the results of using the procedure for the four metals (cadmium, copper, lead and zinc) around Weinfelden.
DISJUNCTIVE KRIGING
The theory underlying disjunctive kriging is somewhat complex. Rivoirard (1994) provides a modern account with full derivation of the equations, and readers should consult it for details. Here, only an outline of the procedure, is given. The concentration of a heavy metal in the soil in a region R is a continuous variable on a scale taking values everywhere from zero to some unspecified maximum. It is assumed that it is a realization of a random variable Z(x), where x denotes the spatial coordinates in two dimensions. If a threshold concentration, say z,, is defined, marking the limit of what is acceptable, then the scale is dissected into two classes: one has concentrations less than z, and the other more. At any one place the soil must belong to one class or the otherit cannot belong to both: a disjoint classification has been made. The values 0 and 1, respectively, can be assigned to the two classes, thereby creating a new binary variable, or indicator, which is denoted by sZ[Z(x)>z,]. Thus, the guide values published in the VSBo of 1986 create indicators, one for each metal in the list. These, too, are random variables.
At the sampling points the values of Z are known, and so the values 0 and 1 can be assigned with certainty. Elsewhere, one can at best estimate (predict) sZ[Z(x)> z,]. In fact, it is necessary to do this in such a way that the estimate at any place x0 approximates the conditional probability, given the data, that Z(x) equals or exceeds z,: fi [z(xo) >
4 25Wxo) 2 z&(x1),dx2), ..4Fv)1~ (1)
where the z(xJ, i= 1,2,...N are the known values of Z at the sampling points. Disjunctive kriging aims to do this. In the form used, which is the commonest, the variable is assumed to be secondorder stationary, with constant mean and variance. It is also assumed to be the outcome of a diffusion process, by which is meant that variation in space passes from zones of small concentration to ones of large concentration through zones of intermediate values; the variation is gradual. Disjunctive kriging of a measured environmental variable begins with a transformation of the data, z(xi), z(x2),...z(xN) from the random variable Z(x) to standard normal deviates, y(x,), y(xz),...~(xN) representing Y(x). This is accomplished by expressing Z(x) as a linear combination of Hermite polynomials, Hk{ Y(x)}, i.e. Z(x) =Q>[WI
[email protected]~oIY(x)}+ 41 HI + 42ff2{
WJ
+
1 Y(x))
(2)
17
which is invertible. Hermite polynomials are orthogonal with respect to the weighting function exp(y2/2) on the interval cc to +oo and are related to the Normal distribution. They are defined by Rodrigues’s formula, which Matheron expresses as H/&J) =
! dkgW dyk ’
d!gcy)
where gb) is the probability density of the standard l/&l is a standardizing normal distribution and factor. The polynomial H&) is of degree k, k 20 and, specifically,
[email protected]) = 1, HlCV)
=
YT
and thereafter the higher order polynomials recurrence relation for k > 1:
obey the
So the Hermite polynomials can be calculated readily up to any order for a standard normal distribution. The coefficients, &, can be found by first arranging the data
207
Mapping heavy metals in polluted soil in ascending order, matching them with their equivalents on the standard normal scale, and fitting an nthorder polynomial to the pairs of data (see Yates et al., 1986). The values of Y(x) are obtained using this polynomial function. Their experimental variogram is computed from the usual formula:

(5)
y(Xi + h))*,
and the variance
a&(z, Xo)= Since and y, sZ[Z(x) can be nomials a[Y(x)
and equivalently
Y(x)  Y(x + IQ}*]
(6)
C(h) = C(O) y(h),
i=l
The weights, system:
hik, are found
by solving
the kriging
(12)
Y(x) is a monotonic transformation of Z(x), z, are equivalent, and their indicator functions > zc] and sZ[Y(x) 2 y,] are the same. They too expressed in terms of the same Hermite polyby > Y,I = 1  WY,) (13) Y(x)},
where G(y,) is the cumulative distribution of Y(x) from cc to y,, and g(y,) is its derivative, the probability density at yc. The indicator is then estimated by > Ycl =
1 
Wc)
(14)
(7)
where C(0) is the a priori variance and equals 1, since the variogram is bounded and Y(x) is standard normal. An authorized model is fitted to the ordered set of experimental values obtained by incrementing h. This variogram is then used to estimate by simple kriging the Hermite polynomials, as follows:
2 4;a2Wk,Xo).
 ~~Hal{Y&‘(J’&rk(
[email protected])
the covariance
of Z is
k=l
where y(h) estimates the semivariance at lag h, y(Xi) and y(xi + h) are the transformed data at positions xi and xi+ h respectively, and m(h) is the number of comparisons at that lag. These estimate y(h) = ;E[{
of the estimate
 ~~Hkl{Y~}gOl,)lj*{Y~Xo)}, where L is some fairly small number. To make a map the Hermite polynomials are kriged on a fine grid. The disjunctive kriging estimates of Z(x) and Q[Z(x)>z,] are calculated from them, and isarithms (‘contours’) are threaded through the grid and displayed. Yates et al. (1986) published their Fortran coding for the whole procedure, and the present authors incorporated substantial sections of it into their own program to produce the results shown below.
THE REGION 2
hxcOV[~k{Y(Xi)}~
ffk{.Y(Xj)}]
i=l
=
(9)
COV[Hk {Y(Xo)} ffk {Y
)] 7
for all j,
in which the COV[Hk{y(Xi)}, Hk(y(xj)}] are the covariances between the sampling points, and Cov[Hk{y(xo)}, Hk{y(xj)}] are the covariances between the sampling points and the point x0 for which an estimate is wanted. The covariances are obtained from the covariance function, eqn (7), raised to the power of the polynomial (see Rivoirard, 1994). The Hk{y(xo)} are inserted into eqn (2) to give sDK(XO)
=
40 + hfil
{+O)]
+ 42fi2{Y(xO)}
at each point of interest. The kriging kth Hermite polynomial is
C’*(Hkt XO) = 1 
+
variance
...
(10)
for the
2 ~ik(Cov[Hk{y(Xo)},Hk(J'(Xj)}])k, i=l
(11)
Weinfelden is a small town (population 9000) in Canton Thurgau in northeast Switzerland (see inset in Fig. 1). Samples of soil from its vicinity have been found to contain lead and cadmium in excess of the federal guide values. These were originally thought to have come predominantly from motor traffic and sewage sludge, respectively. The copper content of some samples has exceeded the federal guide value, too. However, this has usually been in orchards or vineyards, where copper salts are used as fungicides (see above). The canton needs to build a new incinerator for town waste, and it has chosen a site outside the town (Fig. 1). Some heavy metals would inevitably be emitted from the plant and further contaminate the soil in its neighbourhood. Therefore, the canton had to evaluate the potential impact of the incinerator. It surveyed a region of some 50 km2 around the site, elongated from east to west in the directions of the prevailing winds, to identify those parts of the soil which appear already to contain large concentrations of heavy metals and those where any additions to the load would not be hazardous.
208
B. von Steiger et al.
_
_ 730 .9
Legend town outlines ‘*_.,
river Thur
T .
incinerator expected
fallout
region outline
Fig. 1. Location and perimeter of the region surveyed.
 arable
land
I
/
272
E 270 s F? r E 2 266
266 722
724
726
720
Eating
Fig. 2. Sampling
730
732
/km
locations.
Figure 1 shows the bounds of the region and the present limits qf the town and manufacturing. Most of the region is agricultural, divided approximately equally between arable and grass. About 20% is forest, and there are a few vineyards. It is underlain by moraine,
but the river Thur, passing to the south of Weinfelden, deposited gravel over much of it during the Holocene. The soil on both substrates is loamy. On the moraine it is naturally acid (pH 4 under forest, and between 6 and 7 on agricultural land), whereas on the gravel its pH is around 7. The soil was surveyed in three separate campaigns from 1990 to 1993. In the first campaign, initially a region of 8 km2 near to the site of the incinerator was stratified into rectangles, and one sampling point was chosen in each rectangle to give even coverage. The same operation was repeated covering 40 km2. Additional samples of soil were taken during the two other campaigns downwind to the east and to the west. In all, 204 sites were visited. Of these, 98 were meadow, 73 arable land and 30 under forest, and three were vineyards. Their positions are shown in Fig. 2. The protocol for sampling was almost the same throughout. At most sites, 10 cylindrical cores of soil, each of 5 cm diameter, were taken from the surface down to 20 cm within an area of 10 mx 10 m, which was therefore the support of the sample. At the points of the initial sampling near the site, the area sampled was reduced to 5 mx5 m, and five cylindrical cores of 8 cm diameter were taken. The cores were bulked, thoroughly mixed and ground to pass 2 mm. Subsamples of the mixture were extracted with 2 M HN03 at 105°C for 2 h, and the metals were determined in the extracts by plasma emission spectroscopy. The results of the three campaigns were compared in an interlaboratory test. A fourth campaign covering a part of the region shown in Fig. 1 could not be included. No interlaboratory comparison had been done, and so differences in the statistical distribution were suspected to originate from laboratory differences.
SUMMARY
STATISTICS
Table 1 summarizes the data for lead, cadmium, copper and zinc, and Fig. 3 displays their histograms (a) on the
Table 1. Summary statistics of heavy metal concentrations in topsoil (from measurements
Number of observations Minimum Maximum Mean Median Standard deviation Variance Skewness Swiss guide value Number exceeding guide value Mean Median Standard deviation Skewness Kurtosis “With three outliers
Lead
Cadmium
Copper
204 6.7
204 0.05 1.05
204 5.1
110.4 23.3 20.3 12.9 166.17 3.62 50 8
1.33 1.31 0.170 1.16 2.88 removed.
0.238 0.23 0.110 0.1217 3.79 0.8 2 Transformed 0.656 0.636 0.172 0.43 4.17
Copper” 201 5.1 142.9 20.4 18.2 12.7 162.29 5.43 50 3
528.3 25.6 18.3 46.5 2166.1 8.39 50 6 to common 1.28 1.26 0.246 2.20 10.28
in mg kg~‘)
Zinc 204 18.0 142.4 53.8 50.7 18.6 3448.2 1.43 200 0
logarithms 1.26 1.26 0.191 0.48 2.74
1.70 1.70 0.140 0.15 0.54
Mapping
3
heavy metals in polluted soil
huanbalj
209
210
B. von Steiger
Table 2. Means of loglo concentration of metal under forest (30 sites) and other forms of land use (174 sites), standard errors (SE) and backtransformed means
Mean lo810 Lead Cadmium Copper Zinc
Forest Other Forest Other Forest Other Forest Other
1.28 1.33 0.834 0.604 1.03 1.32 1.56 1.73
SE
Backtransformed
0.031 0.013 0.026 0.011 0.041 0.017 0.023 0.010
20.8 23.3 0.144 0.252 12.2 24.0 38.7 56.2
original scales and (b) as common logarithms (log,,). Initially tables were prepared separately for the three campaigns. However, there was no evidence to suggest that different standards applied on the different occasions, and so the data have been pooled. The data have two notable features. The first is that the concentrations of the first three metals exceed the federal guide values in some places and are close to them elsewhere. Thus, there is a task for the canton. The second is that the data are skewed (Table 1): the distributions of cadmium, copper and lead have long upper tails, and there are several data that might be considered as outliers. Some transformation was desirable for further analysis. Taking logarithms achieved approx
et al. imate symmetry (Fig. 3(b)) and allowed a confident comparison of mean values for different forms of land use (see below). It also brought the apparent outliers of lead within the distributions and showed that they should not be treated as exceptional. However, the transformation does not achieve normality. All three distributions remained more strongly peaked than normal (leptokurtic), with kurtoses exceeding 2.7. The long tails in the histogram of logiecadmium are especially marked, and the kurtosis is 4.17 (Table 1). The two largest values, the only two that exceed the federal guide value, might be regarded as outliers. Transformation of copper concentration left out three sites appearing very evidently as outliers. Their sample concentrations were 289, 307 and 528 mg kg‘. These values exceed greatly the federal guide of 50 mg kg‘. Two are in vineyards and one is in an orchard, and they have been omitted from the analysis that follows. Of course, this means that the results apply to a target population that excludes vineyards and orchards. Another three values exceed the guide value. Figure 3(b) suggests that they belong to the same population as the bulk of the data, and they share no common feature of use. Therefore they have been retained. The mean concentration of zinc is 54 mg kg‘, and the maximum is 142 mg kg‘. Judged against a guide value of 200 mg kg‘, they present no problem to the cantonal authority. Nevertheless, the element has been included in the analyses Cadmium
Lead 32lO1 2. I 0.0
0.2
0.4
0.6
Zinc
Concentration Fig. 4.
mg/kg
Transform functions.
0.8
1.0
Mapping
heavy metals in polluted
because it is so closely associated with the others (see below). The distribution of zinc is only moderately skewed: its skewness coefficient is only 1.43, and there are no outliers. Taking logarithms brings the skewness to only 0.15 and the kurtosis is 0.54. Clearly, its distribution is close to lognormal. The measured concentrations were somewhat smaller in the soil under forest than under other forms of land use (see Table 2). For lead the difference is insignificant, and for copper the difference results largely from the copper in the vineyards. The forest soil might contain less cadmium and zinc because it has not received these as impurities in fertilizer, but it is generally on the poorer soil, which might have contained less to start with. The effects of land use and geology are confounded. In any event, the differences across the forest boundaries seem gradual and do not upset the assumptions for kriging.
soil
211
are displayed in Fig. 4. Those for cadmium, copper and lead are strongly convex upwards, a shape that results from their strong positive skewness. The graph for zinc is much less convex, because its distribution is more nearly normal. Experimental variograms of the transforms were computed using eqn (5) and plausible models were fitted to the experimental values by weighted least squares approximation. Weights, w(h) for each lag h, were chosen as w(h)
= m(h)
y*[email protected])’
in which m(h) is the number of paired contributing to the estimate of y(h), and value expected under the model. The best fitting models were retained for cadmium and zinc, these were the isotropic variograms with nugget:
(15)
comparisons y*(h) is the kriging. For exponential
KRIGING The measured concentrations of each of the metals were transformed to standard normal deviates by Hermite polynomials, as described above. For cadmium, lead and zinc all the data were included; for copper, the three largest values were excluded. The transform functions
Y(h)=co+c(lexp(:)]forh>O
(16)
Y(0)= 0, in which h, the lag, is now a scalar in distance only (h= /hi). The parameters are co, the nugget variance, c Cadmium
Lead
Copper
Zinc t I
*t
*
Lag distance/km Fig. 5. Variograms
of transformed
data with experimental values plotted as points and the fitted models shown as solid lines.
212
B. von Steiger et al.
the ‘sill’, i.e. the a priori variance, of the autocorrelated process, or equivalently the total sill minus the nugget, For lead and copper co, and r a distance parameter. the best fitting model was the isotropic pentaspherical variogram (Webster & Oliver, 1990):
forh
the assumption of secondorder stationarity seemed reasonable. Using these models and the data, concentrations were estimated by disjunctive kriging at the nodes of a grid with intervals of 0.1 km over the region. Simultaneously, the indicators of excess, defined by the thresholds in Table 1, were kriged. The resulting maps for lead are shown in Fig. b(a) shows the estimated concentration and (b) the estimated indicator or probability of excess. Also shown as an example is a map of the kriging variance of lead (Fig. 7). The resulting maps for copper (estimates and probabilites) are given in Fig. 8. Maps of estimates are also shown for cadmium and zinc (Figs 9 and 10). The probabilities of these metals exceeding the federal guide values are so small that we have thought it not worth mapping them.
(u
y(h) = CO+ c for h > a y(0) = 0.
(17)
where the parameters co and c have the same meaning as before, and a is also a distance parameter equal to the correlation range of the process. Figure 5 shows these models as solid lines, with the experimental values plotted as points. The types of model and their coefficients are listed in Table 3. In all instances the variograms were bounded, and
(a)
DISCUSSION
AND
CONCLUSIONS
As above, if the concentration of a heavy metal in the soil in a canton exceeds that of the federal guide value, the canton should know and take appropriate action.
272
I
ABOVE
80
70
80
60
70
50
60
40
50
30
40
20
30
BELOW
20
720
722
724
726
728
730
732 
(b)
270ABOVE
0.7
0.6 
0.7
0.5 
0.6
:
0.3 0.4
0.4 0.5
I
0.2 .

‘.’ BELOW

268
0.3 ;::
266720
722
724
Fig. 6. (a) Map of kriged lead concentration,
726
728
730
and (b) map of estimates of Q[Pb>SO].
732
Mapping heavy metals in polluted soil Clearly, it should not add to the soil’s burden where a metal is in excess. Lead exceeded the guide concentration (50 mg kg‘) at eight sampling points. Around the points at which the concentrations are largest, the estimates exceed 50 mg kg‘, and surrounding them are
213
patches of land where the estimates are almost in excess (Fig. 6(a)). The map of the probabilities of excess (Fig. 6(b)) has a similar pattern. Bearing in mind that the estimates are subject to error (Fig. 7) one might take a conservative attitude and treat places where the
272
27 ABOVE 180 
200 200
180
180
140
160
120 
140
ioo
120
80 
100
BELOW
80
268
26 :
720
722
724
726
Fig. 7. Map of kriging variance
728
730
732
728
730
732
of lead.
80 50 
60
40 
50
30 
40
20 
30
lo
20
BELOW
10
720
(b)
722
724
726
272
270
m II
L___ / :
ABOVE 0.4 0.5
0.6 0.6 0.5
0.3 
0.4
0.2 
0.3
0.1 BELOW
o.2 0.1
268
266
720
I
I
I
I
I
I
722
724
726
728
730
732
Fig. 8. (a) Map of kriged copper
concentration
and (b) map of estimates
of fi[Cu>SO].
B.von Steiger et al.
214
estimated probability exceeded 0.3 as either already carrying too large a load or as being threatened. Three patches, one to the north of the town of Weinfelden and two to the east, fall into this class. Incidentally, Fig. 7 of the kriging variance essentially reflects the sampling configuration: kriging variances are smallest where the sampling was most dense and largest where it was sparse, especially near the borders of the region, beyond which there were no data. The concentration of copper has a similar spatial pattern to that of lead (Fig. 8(a)). However, the two patches where the concentrations are large do not coincide completely with those where lead is the most
ABOVE 0.6 
0.7 0.7
0.5 
0.6
0.4 
0.5
0.3 
0.4
0.2 
0.3
BELOW
concentrated (see Figure 8(a) and (b)). Only in the patch to the north of and inside the town do the conditional probabilities of excess (sZ[Cu 2501) appear to be of consequence, and there they might result from the application of copperbased fungicide in former vineyards or orchards. If this were to be verified by further survey, an inventory of former vineyards and orchards might be included in the analysis as prior information following Stein’s (1994) procedure. The patterns of both cadmium (Fig. 9) and zinc (Fig. 10) are similar, with the belt of country to the north of the town and the smaller patch to the east having the largest concentrations. Even where the
0.2
720
722
724
726
728
730
732
730
732
Fig. 9. Map of kriged cadmium concentration.
ABOVE
90
80 
90
70 
80
60 
70
50 
60
40 BELOW
50 40
720
722
724
726
728
Fig. 10. Map of kriged zinc concentration. Table 3. Models fitted to experimental variograms of transformed data Lead Model Nugget, Sill, c Distance r
CO
(km), a
Pentaspherical 0.160 0.840 1.291
Cadmium
Copper
Exponential 0.288 0.712
Pentaspherical 0.332 0.668 2.316
0.543
Zinc Exponential 0.240 0.760 0.524
Mapping heavy metals in polluted soil Table 4. Productmoment correlation coefficients on transformed data Cd CU Zn
215
REFERENCES Atteia, O., Dubois, J. P. & Webster, R. (1994). Geostatistical analysis of soil contamination in the Swiss Jura. Environ.
0.54 0.63 0.76
0.64 0.70
0.80
Pb
Cd
Cu
concentration of cadmium exceeded 0.8 mg kg’ (the guide value), the estimated probabilities of excess in the neighbourhood are less than 0.01. The similarities in the spatial distributions of the four metals have been noted, both in terms of their variograms and their maps. To add to the evidence, the productmoment correlation coefficients on transformed data were computed and these are tabulated in Table 4. The coefficients are all positive and substantial, and with so many data they are highly significant in the usual sense. It seems likely that the metals have a common origin, whether it is manmade or geochemical. Alternatively, they might have more than one source, but one dominates. There are local dissimilarities in pattern, and these may have arisen as a result of contributions from different sources not mentioned in text. In any event, of course, the authorities must recognize the existence of the large measured concentrations and where the true concentrations are likely to exceed the guide values. Around Weinfelden, except in the vineyards, lead seems to be the only heavy metal of concern. The maps of lead made by disjunctive kriging show where this is so, and clearly the authorities should not add to the soil’s burden where the concentration already exceeds the guide value or where the probability of its exceeding that value is substantial. In the zone of expected fallout from the incinerator (see Fig. 1) the probability of exceeding the guide value is generally less than 0.1. However, to the northwest and to the south of the zone where fallout is expected the probabilities of excess are larger, and some kind of control will be needed to prevent further pollution. The maps of lead concentration and conditional probability provide the information for the purpose.
Pollut., 86, 3 1S327. FOEFL (1987). Commentary on the Ordinance relating to Pollutants in Soil ( VSBo of 9 June 1986). Swiss Federal Office of Environment, Forests and Landscape (FOEFL), Bern, Switzerland. Leenaers, H., Okx, J. P. & Burrough, P. A. (1990). Employing elevation data for efficient mapping of soil pollution on flood plains. Soil Use Manage., 6, 105114. Matheron, G. (1976). A simple substitute for conditional expectation: the disjunctive kriging. In Advanced Geostatistics in the Mining Industry, ed. M. Guarascio, M. David 8z
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