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Optimizing Sampling Schemes for Mapping
and Dredging Polluted Sediment Layers
L. Hazelhoffl and F. Hoefslootl
Abstract.-An optimal sample scheme of measurements of
sediment depth was constructed for mapping and dredging a
polluted sediment layer, taking into account economic constraints.
The layer in question was deposited in a lake near Kampen in the
Netherlands and consists of sediment discharged by the Rhine
during the period 1932 - 1980. A stochastic approach was chosen to
estimate the depth of dredging that would result in a given amount
of polluted sediment remaining in the lake after dredging has been
carried out. The dredging result, i.e. the amount of sediment that is
not removed, depends on the probability distribution of the
estimated depth and the difference between the mean of this
distribution and a chosen dredging depth. Two independent sources
of error determine this probability distribution: i) the interpolation
error and ii) the precision of the determination of the depth of
dredging. The two sources of error are independent. Spatial
interpolation was done using ordinary point kriging. The kriging
error depends on the sampling scheme and the spatial variability of
the depth of the bottom of the polluted sediment layer. Spatial
correlation at three different scales was modelled with a nested
variogram. The sampling distance of the sediment depth
measurements was evaluated as a function of dredging result and
dredging depth precision. This information can be used to derive a
relation between sampling costs and dredging result. The amount
of unnecessarily dredged clean sediment was estimated and
incorporated in the procedure for designing an optimal sample
scheme.
INTRODUCTION
In the period 1932 - 1980 polluted Rhine sediments were deposited in lake
Ketelmeer, located near Kampen in the Netherlands. This pol luted sediment now
has to be removed from an area of about 30 km2. A pilot study was carried out in
two small areas to get an impression of the spatial variability of the depth of the
under side of this layer. The sampling was proceeded in stages, with information
from the first area being used for sampling the second. Within the pilot areas
different sample stages were also applied.
'Physical (3wgrnpkers, IJnivcrsity of IJfrecl~r,771~.Ne1hcdcrnr1.s.
Dredging companies have recently used triangulation (TIN) to construct a digital
model of the level of dredging, and in some cases the spatial variability was
estimated using spectral waves or ARIMA models. The results of these studies
were used to increase the depth of dredging below the TIN surface to ensure that
downward fluctuations in the level of the polluted sediment will be removed. The
sampling distance was arbitrarily determined. The main objective of this study is
to estimate the extra dredging depth with reference to an interpolated DEM using
Kriging and the Kriging variance. Using the Kriging variances, a relation can
established between extra dredging depth, sample distance and the amount of
polluted sediment that is not removed by dredging. A second objective is to
extrapolate the spatial variability of the polluted layer in two pilot areas to the
whole lake so that economic assessments can be made of the sample scheme
needed for the lake for a given fraction of polluted sediment that is not removed.
A problem in this area is non-stationary spatial variation caused by human activity
in the past and today. Digging of clay and sand has resulted in pits have mostly
been filled with polluted sediment, and along the shipping channels vessels cause
resuspension and redeposition of the sediment along the channels. Both
disturbances must be identified as outliers in the data, so careful exploratory
analysis of the spatial data is necessary. First the spatial variability of the two
samples areas is explored, then the method of determining the economically
optimal dredging in re1ation with environmental constraints is explained and
applied on the results of the second sample area.
The study was funded by the Ministry of Public Works (RWS).
Area one
sample scheme
This area is 800x800 m and was chosen by RWS as a test location for
redevelopment using new methods of dredging. Based on information from a
survey on a slightly different sediment layer in the same area the following sample
scheme was designed. Four subareas of 100x100 m were randomly chosen
containing sample grids of 20 meter (figure 1). This approach can be justified by
the knowledge of the sedimentation process; it is assumed that the spatial
variability at this scale in the four selected blocks will be representative for the
whole lake. To investigate whether the subareas are influenced by variation at a
larger scale, a 100 rneter grid was sampled in the whole area. A third level of scale
was investigated at sample distances ranging from 0.5 to 5 m, realized by three
groups of two short transects designed with the shape of a cross. The main
objective of this short distance sampling was to test measurement accuracy; at
these distances spatial variation was assumed lower than expected measurement
error, RWS planned this lowest level of sampling. The information was also used
to make a better estimate of the nugget.
-500 -475 -450 -425 -400 -375 -350 -325 -300
Depth (cm)
Figure 1. Sample design and interpolated surface of area one.
Gamma (h) : 4 + 124*Gauss 63 (h) + 1.2*Pow 1 (h)
Omnidirectional
360?
Ihl
figuur 2. Semivariogram of the under side of the polluted layer in area one.
results
In this area variation over distances of 100-500 m is clearly present with two of
the subareas being located in zones with a trend. Performing an analysis on
residuals reveals the variability at the 20-100 m scale, but spatial outliers were
found in these subareas, using exploratory data analysis (EDA) software. The
EDA software visualizes spatial variability by connecting measurement locations
to lines which can be selected from a graph displaying the variogram cloud
(Hazelhoff & Gunnink, 1992). These spatial outliers were identified as being
caused by human interferences, and so they could not be used for investigating
spatial variation at the 20-100 m scale. The variogram in figure 2 is based on 2 x
25 samples in this range. A nested variogram has been constructed; the
experimental variograms for three spatial scales were calculated separately and
then combined for fitting. It shows a low nugget caused by the limited spatial
variation at the level of the crosses (0.5 to 5 m). A steep slope between 0 and 60m
is clearly present.
Area two
sample scheme
In this area measuring 400x500 meter (figure 3) a dredging test was planned, so a
DEM had to be constructed. A grid mesh of 50m was planned, based on the
variogram of area one with the steep increase in the range of 0 - 60 m, so much
lower kriging variances will occur when a 50 m grid mesh is used instead of 100
m. Due to practical constraints the realized sample scheme is somewhat different.
In this area one subarea of l00x 100 m was sampled at distances of 20 m located
on a grid to compare the results with area one. Furthermore two crosses (with the
same configuration as in area one) were added with sampling distances ranging
from 0.5 to 5 m. A second sampling has been carried out for validation of the
DEM. These samples also are plotted in figure 3, many of them are located close
to the samples taken in the first stage.
I
I
-360
-350
-340
Depth (cm)
-330
Figure 3. Sample scheme and interpolated surface of area two.
Gamma (h) : 9 + 10'Sph 30 (h) + 0.013*Pow 1.53 (h)
Omnidirectional
70
&
e,
A
120
150
1
Ihl
Figure 4. Semivariogram of the under side of the polluted layer in area two.
results
After using EDA to identify human induced spatial outliers, the spatial variability
appeared to be much lower than in areas one. The second stage of sampling for
validation confirms the originally variogram, except the nugget variance appears
now too low. Pairs of samples close together ( 4 0 meter) and are not in the
crosses show much higher semivariances then samples within the crosses. Two
possible reasons can be given: 1) the crosses are located in areas with low spatial
variability at short distances, and 2) measurement errors are lower within the
crosses then outside the crosses. The variogram based on all samples is showed in
figure 4. The steepest part ranges from 10 to 30 m, which is the important interval
for kriging the 50 meter grid. The right part of the variogram fitted with a power
model represents some linear trend in this area. For coarser grids this trend will be
important.
Dredging depth & residual sediment
The DEM of the lower side of the polluted layer in area two was made using
ordinary point kriging (OPK). During the dredging tests the dredging depth was
set at the level of the interpolated DEM which means that polluted sediment is
still present (residual sediment) in half of the area, assuming a normal distribution
of the deviations. The volume of the residual sediment can be calculated if the
distribution of the deviations is known. In this study the kriging variance (normal
distributed) and the error of estimating the dredging depth are used to describe the
deviations from the DEM. These two sources of error are supposed to be
independent, simply adding the variances gives the total error. Increasing the
dredging depth relative to the DEM results in smaller volumes of residual
sediment. The amount of residual sediment is calculated using the tail of the
normal probability function. For example, if o = 1 cm then increasing the
dredging depth by 1 cm results in a coverage of 16% of the area with polluted
sediment. The residual volume V per unit of area can be calculated using (1).
Zd
z is the depth relative to the DEM where the center of the distribution lies and p(z)
is the probability density of the normal distribution. Integration starts at dredging
depth z d . This integral is discretised to calculate V. The quantity V depends on 0,
the kriging standard deviation (KSD) and z d . KSD depends on the variogram and
the sample scheme. The dredging result is defined as the result of dividing the
residual volume by the total area.
For area two the extra dredging depth (EDD) was calculated for a range of
dredging results, and is repeated for different values of the dredging depth error.
During the calculation each grid cell gets a different value for V because KSD
varies over the area. A special computer program was written to work out this
iterative procedure. Another interesting quantity is the volume of clean sediment
dredged as function of EDD. Dredging at DEM depth means that dredged clean
sediment (DCS) is equal to V. The volume of dredged polluted sediment is equal
- V(zd). The volume of clean sediment is calculated from formula 2.
to V(zd=zDEM)
EDD is here expressed as a volume with an area of 1.
It is obvious from (2) that increasing EDD at low values of V(zd) yields small
improvement in the dredging result relative to the increase of DCS.
DREDGING RESULT & SAMPLE SCHEME
For economic reasons the most interesting question is how does the EDD depend
on the sample distance (regular grid) given a certain dredging result and a given
the spatial variability described with a variogram? For the variogram of area two
this relationship was calculated and plotted in figure 5. For three sample distances
(100, 50 and 25 m) the relation between dredging standard deviation DSTD and
EDD is plotted. The dredging result is set at 1 cm, which is a practical value.
DSTD is an important error source because the values are comparable with the
KSTD based on the three sample distances. Improvement of estimating dredging
depth results in a significantly lower EDD. At the moment some dredging
companies claim values for DSTD near 2 cm. It is up to RWS to balance
increasing cost due to extra dredging depth against the increasing cost of denser
sampling.
DREDGING STANDARD DEVIATION (MM)
Figure 5.
Relation between dredging standard deviation and extra dredging depth
with a given dredging result of 1 cm.
Extrapolation from pilot areas to the whole lake
The relations between sample density and EDD were derived from the variogram
of area two. The variogram in area one differs considerable from this variogram;
in area one kriging variances are larger for any given sample distance. But the
spatial variability in area two is most likely to be the most representative. Area
one is located near the border of the lake with a lot of human disturbance. If it is
true that area two is representative for the lake, a 50 m grid uses information from
the spherical part of the variogram. The recommendation to RWS is to start with a
100 m grid to explore the spatial variability at a larger scale than 50 m, as is
clearly present in the two areas. In areas with such a large spatial variability that a
large EDD is needed to match the desired dredging result, the 50 m grid is
advisable. Another important fact is the presence of human disturbances which
need dense sampling to be tracked. There is a risk that disturbances of at most 1
ha will be missed using a 100 m grid, which can be important because the
thickness of the polluted sediment in the areas may be more than doubled.
CONCLUSIONS
Spatial correlation at two distinctive scales separated at about 40 meter is present
in the lower boundary of the polluted sediment.
Ordinary point kriging can be used together with an error specified for estimating
dredging depth, to optimize sample schemes given a dredging result. This
information cannot be derived from TIN models and associated approximators of
variability like ARIMA and spectral waves.
For the spatial variability in the second pilot area, dredge depth accuracy is an
important source of error.
REFERENCES
Hazelhoff, L. & Gunnink, J.L. 1992. Linking Tools for Exploratory Analysis for
Spatial Data. In Harts. J., Ottens, F.L.; Conference Proceedings EGIS 1992.
BIOGRAPHICAL SKETCH
Lodewijk Hazelhoff is a Physical Geographer specialized in environmental
assessment and GIs. He graduated from the University of Amsterdam in 1980.
Frans Hoefsloot is a Physical Geographer specialized in environmental
assessment. He graduated from the University of Utrecht in 1992.