This file was created by scanning the printed publication. Errors identified by the software have been corrected; however, some errors may remain. 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 re1 ation 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) 360? Omnidirectional 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 -340-330 Depth (cm) 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 (40 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 zd. This integral is discretised to calculate V. The quantity V depends on 0, the kriging standard deviation (KSD) and zd. 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 to V(zd=zDEM) - V(zd). The volume of clean sediment is calculated from formula 2. 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.