Application
of Geostatistics for Spatial Analysis of Heavy Metals in Soil
Ulrich Leopold
Soil Science Department, Faculty of Geography and Geo Sciences, University of Trier
Correspondence address: Engelstr. 104, 54292 Trier, Germany, e-mail:
[email protected]
Abstract
For inference of the spatial structures and evaluation of the results,
expert-knowledge of the origin, spread and reaction of heavy metals in
soil is necessary. The assessment of soil contamination requires analysis
of exceeding given thresholds.
The survey region of Dortmund lies in the east of the industrial Ruhr-Area
in the federal county Northrhine-Westfalia in the west of Germany. A high
density of settlement as well as a high grade of industrialization have
increased the soil heavy metal contents. In many cases natural contents
are covered by higher concentrations caused by man. The spread of heavy
metals has been accelerated by man. In spite of complex influencing factors,
the performed geostatistical analysis reveals clear spatial structures
of the total soil heavy metal contents. To ensure that the spatial structures
in
the semivariogram are no artefacts several robust variogram estimators
were calculated. Apart from 'traditional' semivariogram, correlogram and
pairwise relative semivariogram revealed clear spatial structures. A short-range
and a long-range structure exist in addition to a nugget. Further splitting
of the Zn contents into percentiles for indicator transform, led to improved
estimation of the two ranges. With increasing indicator thresholds the
nugget and both ranges decreased. Due to additional analysis of the spatial
continuity of soil types and land use by indicator semivariograms, the
revealed spatial structures of the heavy metal contents could be identified
by some soil types and land uses.
Ordinary kriging was performed for prediction of all 5 heavy metals.
The lack of sample locations for Ni in the center of the study area led
to unreliable low concentrations there. This could be improved by accounting
for Cu as secondary information in the cokriging system.
Since only some of the factors controlling the spatial process in the
study area could be analyzed, kriging analysis and factorial kriging could
give further details on possible influences on the spatial distribution
of heavy metals. To assess spatial uncertainty and to reproduce the real
spatial variability, simulation would be an improving alternative, e.g.
simulated annealing based on sequential indicator simulation.
Geostatistics is based on the theory of regionalized variable and the concept
of random function. The assumption of second-order stationarity or at least
intrinsic hypothesis allows to run uni- and multivariate analysis by using
distance intervals instead of absolute location. The spatial analysis is
mainly carried out by calculating the 'traditional' experimental semivariogram
function, which is related to the covariance function. In absence of spatial
continuity in the 'traditional' semivariogram (erratic semivariogram) caused
by skewness and/or extreme values, more robust measures can be considered.
Another possibility to reduce the influence of extreme values and skewness
is to transform the data. The ensuing modeling of the spatial process is
achieved by the best fit of different basic semivariogram models, not only
in a statistical but also an expert sense. For predicting spatial realizations
in the study area different methods are available. Exact local predictions
can be performed by different kriging estimators. To account for the real
variability and to evaluate the spatial uncertainty in the study area,
simulations can be carried out.
Taking the example of Zn, the expected value (e-type estimate) of the
local cumulative distribution function was predicted by indicator kriging.
The e-type estimate corresponds to the ordinary kriging estimate. Furthermore,
the indicator approach enables to assess the local Zn distribution and
its parameters, mean, variance and quantiles, as well as to assess the
local probability of exceeding a defined threshold.
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