Search

Sinds 22 december 2000 is de Kaderrichtlijn Water van kracht, die ertoe moet leiden dat in 2015 het oppervlaktewater van goede kwaliteit is. Ook van boeren in het veenweidegebied wordt verwacht dat zij bijdragen aan schoon oppervlaktewater. Maar hoe bepaal je of het slootwater van de vereiste kwaliteit is? Hoe beoordeel je of de maatregelen om de kwaliteit te verbeteren werken? Wat moet je bemonsteren, op hoeveel en welke locaties en hoe vaak? Het antwoord op deze vragen is een monitoringstrategie onder het motto 'begin aan het eind en redeneer dan terug'

In het kader van de actualisatie van de grondwatertrappen voor het beheergebied van Waterschap Regge en Dinkel is besloten om gebruik te maken van recent gekarteerde detailkarteringen. Om combinatie van Gd-informatie in de vorm van gridinformatie met een resolutie van 25 meter en informatie van grondwatertrappen uit detailkarteringen in de vorm van bodemGt-vlakken mogelijk te maken is een nieuwe interpolatietechniek ontwikkeld. Hiermee moet zo min mogelijk detailinformatie verloren gaan. De techniek maakt het mogelijk om verschillende variabelen die een verwantschap hebben, op een lokale wijze mee te nemen. Op deze manier is getracht de interpolatietechniek zo veel mogelijk aan te laten sluiten bij hetgeen een karteerder in het veld vastlegt

De afgelopen jaren zijn allerlei methoden ontwikkeld om onvolledige datasets om te zetten naar dekkende verspreidingsbeelden. Een gehanteerde techniek bestaat uit het genereren van de zogeheten 'kans op voorkomen', ofwel abundatiekaart, ook wel kansenkaart. Aan de hand van twee voorbeelden (Heivlinder en Gestreepte waterroofkever) wordt de verspreiding van soorten inzichtelijk gemaakt. Een analyse van gegevens verricht door Universiteit Amsterdam, Alterra en SOVON

In this study, two techniques for spatio-temporal (ST) kriging of soil water content are compared. The first technique, spatio-temporal ordinary kriging, is the simplest of the two, and uses only information about soil water content. The second technique, spatio-temporal kriging with external drift, uses also the relationship between soil water content and net-precipitation to aid the interpolation. It is shown that the behaviour of the soil water content predictions is physically more realistic when using spatio-temporal kriging with external drift. Also, the prediction uncertainties are slightly smaller. The data used in this study consist of Time Domain Reflectometry (TDR) measurements from a 30-day irrigation experiment on a 60 x 60-m grassland in the Netherlands. (C) 2002 Elsevier Science B.V. All rights reserved.

Rice paddies are an important source of the greenhouse gas methane (CH4). Global methane emission estimates are highly uncertain and do not account for effects of interpolation or data resolution errors. This paper determines such scaling effects for the influence of soil properties on calculated CH4 emissions for the island of Java, Indonesia. The effects of different interpolation techniques, variograms and neighbor optimization were tested for soil properties by cross-validation. Interpolated organic carbon values were not significantly different from the original soil samples, in contrast to interpolated soil iron contents. Interpolation of soil properties coupled to a process-based model on CH4 emissions led to a significant change in distribution of calculated CH4 emissions, i.e., the variance decreased. Effects of data resolution were examined by interpolating soil properties to derive data at different data resolutions and then calculating CH4 emissions by applying the process-based model at these resolutions. The soil properties did not differ significantly for different data resolutions, in contrast to calculated CH4 emissions. These scaling effects were caused by the combination of interpolation and a non-linear model. Real scaling effects may even be larger because small-scale variability was not accounted for. Scaling effects, including those caused by small-scale variability, have to be considered to achieve unbiased and less uncertain global CH4 emissions estimates from rice paddies.

This paper reviews design-based estimators for two-stage and three-stage sampling designs to estimate the mean of finite populations. This theory is then extended to spatial populations with continuous, infinite populations of sampling units at the latter stages. We then assume that the spatial pattern is the result of a spatial stochastic process, so the sampling variance of the estimators can be predicted from the variogram. A realistic cost function is then developed, based on several factors including laboratory analysis, time of fieldwork, and numbers of samples. Simulated annealing is used to find designs with minimum sampling variance for a fixed budget. The theory is illustrated with a real-world problem dealing with the volume of contaminated bed sediments in a network of watercourses. Primary sampling units are watercourses, secondary units are transects perpendicular to the axis of the watercourse, and tertiary units are points. Optimal designs had one point per transect, from one to three transects per watercourse, and the number of watercourses varied depending on the budget. However, if laboratory costs are reduced by grouping all samples within a watercourse into one composite sample, it appeared to be efficient to sample more transects within a watercourse.

Groundwater table (GWT) class maps have been mapped for the whole of The Netherlands at a scale of 1:50,000, and provide useful information for a variety of purposes. Due to strong human impact on the Dutch landscape, water tables have changed and the maps now need updating. Six updating methods have been defined, varying in data requirements and in the smallest spatial unit that can be updated. The performance and cost of each of the methods were measured in a 9228-ha test area. The costs were also extrapolated to larger areas of 46,994 and 75,684 ha using measures of sampling error as criteria. The major cost factor is largely determined by the sample size, which is method dependent. A method that updates GWT maps by evaluating an objective function in locations obtained through stratified random sampling showed the best performance in the test area and a reasonable cost development at larger areas. Validation in the 75,684 ha area supported this conclusion. A kriging-based method performed well, but was expensive. In the near future, elevation data will be available at the national scale. Using these data as ancillary information will decrease cost and increase the accuracy of GWT map updates. This will allow for drawing new map polygons instead of re-labeling existing ones.

The precision of design-based sampling strategies can be increased by using regression models at the estimation stage. A general regression estimator is given that can be used for a wide variety of models and any well-defined sampling design. It equals the estimator plus an adjustment term that accounts for the differences between the estimators for the spatial means of the auxiliary variables and the true spatial means of these variables. The regression estimator and ratio estimator follow from certain assumptions on the model and the sampling design. These are compared with the estimator in two case studies. In one study a bivariate field of linearly related variables was simulated and repeatedly sampled by Simple Random Sampling without replacement and sample sizes 10, 25, 50, 100 and 200. For all sample sizes the ratio of the standard error of the simple regression estimator to that of the estimator was approximately 55ÐThe bias of the simple regression estimator was negligibly small. The confidence interval estimators were valid for all sample sizes except for n = 10. Also the ratio estimator was approximately unbiased, and the confidence interval estimators were valid for all sample sizes, even for n = 10. This is remarkable because the ratio estimator assumes that the intercept of the regression line is 0 which was incorrect for the simulated field. On the other hand, only approximately 55␘f the potential gain was achieved because the model was inappropriate. In a second study the spatial means of the Mean Highest Watertable of map units were estimated by Stratified Simple Random Sampling and the combined (multiple) regression estimator. The NAP elevation, the local elevation, the Easting and the Northing were used as auxiliary variables. For all map units except one the combined (multiple) regression estimator was more precise than the estimator. The ratio of the standard errors varied from 0.36 to 1.04. The domain for which the regression estimator was less precise than the estimator showed strong variation between strata. For this domain it was more efficient to group the strata into two groups and to fit simple models for these groups separately.

Effectiveness of regular sampling grids to collect multivariate contamination data in urban areas is often strongly reduced by buildings and boundary effects. In addition, earlier observations and knowledge on the history of the area may provide valuable information. This paper extends a simulated annealing-based procedure to optimize the sampling scheme, taking sampling constraints and preliminary information into account. A new optimization criterion is formulated that is able to handle multivariate problems. The sampling scheme is optimized using a spatial weight function that allows to distinguish between areas with different priorities. A case study in Rotterdam harbour with five contaminants at two depths showed two sequential sampling stages, in which two weight functions were applied. The first stage combined earlier observations and historical knowledge, with emphasis on areas with high priority. The resulting scheme showed a contamination at 17.4␘f the samples, with 1.5␑eavily contaminated. The second stage used probability maps of exceeding intermediate threshold values to guide additional sampling to possible hot-spots. This yielded 26.7␌ontaminated samples, with 16.7␋eing heavily contaminated. This included new locations that were not detected during the first stage. The proposed method allows to incorporate important preliminary information, and can be used as a valuable tool in environmental decision-making.

The potential of using National Oceanic and Atmospheric Administration (NOAA) Advanced Very High Resolution Radiometer (AVHRR) images for large areas is often limited by cloud cover. It could be increased when small clouds are replaced by estimated reflection and emission values. In this study seven replacement methods are compared, ranging from simple replacement to stratified co-kriging. Images of subsequent days serve as co-variable, enabling the use of spatial and temporal information. For validation, cloud-free pixels were replaced with four patterns of artificially clouded pixels. Co-kriging as a combination of both temporal and spatial information resulted in the best estimates, reducing the mean squared errors by 20-70%. Stratification of the image did not result in better cloud replacement. Once kriging options have been implemented in existing image processing packages, co-kriging will be an easy-to-use solution to missing values, provided that images of subsequent days of low cloud coverage are available. | The potential of using National Oceanic and Atmospheric Administration (NOAA) Advanced Very High Resolution Radiometer (AVHRR) images for large areas is often limited by cloud cover. It could be increased when small clouds are replaced by estimated reflection and emission values. In this study seven replacement methods are compared, ranging from simple replacement to stratified co-kriging. Images of subsequent days serve as co-variable, enabling the use of spatial and temporal information. For validation, cloud-free pixels were replaced with four patterns of artificially clouded pixels. Co-kriging as a combination of both temporal and spatial information resulted in the best estimates, reducing the mean squared errors by 20-70%. Stratification of the image did not result in better cloud replacement. Once kriging options have been implemented in existing image processing packages, co-kriging will be an easy-to-use solution to missing values, provided that images of subsequent days of low cloud coverage are available.

Different soil acidification models have been developed for use on different scales, i.e., NUCSAM for the local scale, RESAM for the regional (national) scale and SMART for the continental scale. This paper focuses on the uncertainties associated with scale transfer by a simpler model description by (i) temporal aggregation of process descriptions, (ii) neglection of processes associated with vertical aggregation of soil layers and (iii) the use of less detailed formulations of processes (process aggregation) and by spatial aggregation of input data. Results obtained for simulations in acid (sandy) soils indicate that (i) temporal aggregation and process aggregation have a limited impact on the long-term (decades) annual response of soil solution chemistry to atmospheric deposition, (ii) vertical aggregation mainly affects predictions of solutes which show a strong concentration gradient with depth and (iii) spatial aggregation hardly affects the average output for a given forest/soil combination. However, ignoring the variability in input parameters, largely affects the frequency distribution of model outputs in a region. Results imply that model simplification is an adequate step in the upscaling of modelling results from a local to a regional scale.

Geostatistics provides an efficient tool for mapping environmental variables from observations and layers of explanatory variables. The number and configuration of the observations importantly determine the accuracy of geostatistical inference and prediction. Data collection is costly, and coarse sampling may lead to large uncertainties in interpolated maps. In such case, additional information may be gathered from experts who are knowledgeable about the spatial variability of environmental variables. Statistical expert elicitation has gradually become a mature research field and has proved to be able to extract from experts reliable information to form a sound scientific database. In this thesis, expert knowledge has been elicited and incorporated in geostatistical models for inference and prediction. Various extensions to the expert elicitation literature were required to make it suitable for elicitation of spatial data. The use of expert knowledge in geostatistical research is promising, yet challenging.

Classical sampling theory has been repeatedly identified with classical statistics which assumes that data are identically and independently distributed. This explains the switch of many soil scientists from design-based sampling strategies, based on classical sampling theory, to the model-based approach, which is based on geostatistics. However, in design-based sampling, independence has a different meaning and is determined by the sampling design, whereas in the model-based approach it is determined by the postulated model for the process studied. Design-based strategies are therefore also valid in areas with autocorrelation. Design-based and model-based estimates of spatial means are compared in a simulation study on the basis of the design-based quality criteria. The simulated field consists of four homogeneous units that are realizations of models with different means, variances and variograms. Performance is compared for two sample sizes (140 and 1520) and two block sizes (8 × 6.4 km 2 , 1.6 × 1.6 km 2 ). The two strategies are Stratified Simple Random Sampling combined with the Horvitz-Thompson estimator ( STSI , t HT ), and Systematic Sampling combined with the block kriging predictor ( SY , t OK ). Point estimates of spatial means by ( SY , t OK ) were more accurate in all cases except the global mean (8 × 6.4 km 2 block) estimated from the small sample. In interval estimates on the other hand, p -coverages were in general better with the design-based strategy, except when the number of sample points in the block was small. Factors that determine the effectiveness and efficiency of the two approaches are the type of request, the interest in objective estimates, the need for separate unique estimates of the estimation variance for all points or subregions, the interest in valid and accurate estimates of the estimation or prediction variance, the quality of the model, the autocorrelation between observation and prediction points, and the sample size. These factors will be assembled in a decision-tree that can be helpful in choosing between the two approaches. Models can also be used in the design-based approach. They describe the population itself, whereas in the model-based approach they describe the data generating processes. Errors in such models result in less accurate estimates, but the estimated accuracy is still valid.

This paper investigates methods to compare spatial patterns of pearl millet [Pennisetum glaucum (L.) R. Br.] yield with spatial patterns of soil variables in a farmer's 1-ha field on an undulating sand plain in Niger near ICRISAT-SC. Spatial pattern comparisons are important for precision farming applications. Methods included the correlation coefficient, linear regression, a distance measure to compare separate maps and the cross-correlation function. Millet grain yield varied from 0 to 2885 kg ha -1 on 5 by 5 m sub-plots. Pearl millet yield was correlated with measured soil variables at three different depths, elevation, and crust formation for two successive years. Only 30% of the total variation in millet dry yield was explained by regressing yield against soil variables. Detrended elevation showed a significant negative relation with yield (r = -0.421). The cation-exchange capacity (CEC) at all the depths showed a significant negative relation with yield (r of -0.238 to -0.290) because crusting and erosion increase with CEC extending to distances up to 30 to 40 m. Pattern comparison using the cross-correlogram related local hillocks in the area with high yields and local dips with low yields at a distance of 15 to 20 m. From this study, we concluded that the cross-correlogram was beneficial to compare data at various distances. Yield patterns are best explained by soil variables related to erosion as the major determining factor in the area.

Costa Rican land use and cover (in 1973 and 1984) were investigated using a nested scale analysis. Spatial distributions of potential biophysical and human land use/cover drivers were statistically related to the distribution of pastures, arable lands, permanent crops, natural and secondary vegetation, for 0.1° grid units and five artificially aggregated spatial scales. Multiple regression models describing land use/cover variability have changing model fits and varying contributions of biophysical and human factors, indicating a considerable scale dependence of the land use/cover patterns. The observation that for both years each land use/cover type has its own specific scale dependencies suggests a rather stable scale-dependent system. In Costa Rica two land use/cover trends between 1973 and 1984 can be discerned: (a) intensification in the urbanized Central Valley and its surroundings, where agriculture is extended to steeper and less favourable soils due to a high population density; and (b) land use expansion in remoter areas, where the extension of arable land and pastures increased at the cost of natural vegetation. This deforestation was not driven by land shortage. The scale analysis of the Costa Rica land use/cover confirms that land use/cover heterogeneity is, like ecosystem and landscape heterogeneity, a multiscale characteristic which can best be described as a nested hierarchical system.

The impact of soil heterogeneity on the spatially average water budget of the unsaturated zone is investigated using a framework of analytical solutions. This framework was previously shown to adequately represent the long-term average water budget as well as its transient evolution. Nine combinations of three climate and three soil types are considered, covering a wide range of different conditions. In highly conductive soils, where evapotranspiration is limited by percolation through the lower boundary, heterogeneity increases the spatially average evapotranspiration relative to the uniform (scaled average) soil. In contrast, for less conductive soils the decreasing infiltration rates due to soil heterogeneity cause evapotranspiration to become smaller. Formally derived “equivalent” parameters, which are intended to capture the effect of soil heterogeneity by means of one set of soil hydraulic parameters, are shown to depend not only on the spatially heterogeneous parameters, but on climate as well. Moreover, the “equivalent” parameters derived for the long-term average water budgets are not valid for transient behavior.

Uncertainties in major input variables in water and solute models were quantified and their effects on simulated functional aspects of soil behaviour were studied using basic soil properties from an important soil map unit in the Netherlands. Two sources of uncertainty were studied: spatial variability of basic soil properties, and the use of pedotransfer functions to predict soil hydraulic functions. Depending on the type of process studied, variability of basic soil properties explained between 40 and 99.9% of the total variance. Uncertainty of pedotransfer functions is of importance mainly when physical soil behaviour (e.g. workable days and aeration status) is studied.

Soil maps are used to characterize spatial patterns of soil behaviour. A first approach is to characterize each soil map unit (SMU) by the behaviour of a pedogenetically representative profile; a second is to subsample each SMU and select from the sample a characteristic profile by its behaviour. The first approach was tested against the second. Using pedogenetically representative profiles resulted in biased estimations of functional properties related to water and solute transport. Soil profiles fitting to the definition of the SMU (impurities) corresponded to extreme values for four properties, which implies that impurities must be sampled when risk assessments must be made.

Fluxes of nitrous oxide (N2O) were measured in mown and intensively-grazed plots on a slightly-sloping, poorly-drained clay soil, using 144 flux chambers on four consecutive days. We tested the hypotheses that (i) spatial variability of N2O fluxes is larger in grazed than in mown grassland and (ii) spatial dependency is larger in mown than in grazed grassland. Distributions were approximately log-normal. Fluxes from grazed grassland were larger than those from mown grassland. Multiple linear regression analyses showed weak relationships between N2O flux and moisture, NH4 , NO3− and C contents, with less than 15% of the variance in N2O flux accounted for. Spatial variability was large both on a relatively small scale (less than 6 m) and on a larger scale (10–100 m) and was larger on mown grassland than on grazed grassland. Geostatistics showed that N2O fluxes were spatially dependent for a lag distance of less than 6 m on mown grassland. On grazed grassland fluxes were spatially independent on a scale of < 6 m. The large spatial variability of N2O fluxes suggests that even measurement techniques that integrate N2O fluxes over a large area may be hampered by the large spatial variability of N2O fluxes.

Simulated estimates of crop yield were made for rainfed rice in a 50 ha dryland rice area. The aim was to investigate how soil units and management units of different sizes with different yields could be used to obtain values for areas of land. Two procedures were applied. First, yields were simulated at six sites, that were representative of six soil mapping units. Second, yields were simulated using soil information from 133 auger sites, and were interpolated over management units using block kriging. Differences between the two procedures for the total area and for a test set of 22 additionally sampled locations were small. A 60% increase in precision was achieved when relatively large management units were defined. A Geographical Information System was used to identify areas with greatest yield potential for rainfed dryland rice. Statistical analysis showed that the six soil units could be grouped into three yield classes. The largest yields were obtained for a sub-area comprising 11% of the survey area which was associated with a slowly permeable Bg horizon in the soil profile. It was concluded that the best procedure for the spatial interpolation of simulated rice yield should be based on preliminary simulation of crop yields. A sensitivity analysis of the impact of weather variability and soil heterogeneity on the variation of yield was useful to detect the importance of their contributions. The procedures developed in this study are of value in obtaining a reliable estimate of average yield, and can consequently be used for associated cost-benefit calculations.

SUMMARY Variograms are used to describe the spatial variability of environmental variables. In this study, the parameters that characterize the variogram are obtained from a variogram in a different but comparably polluted area. A procedure is presented for improving the variogram modelling when data become available from the area of interest. Interpolation is carried out by means of a Bayesian form of kriging, where prior distributions of the variogram parameters are used. This procedure differs from current procedures, since commonly applied least squares estimation for the variogram is avoided. The study is illustrated with data from a cadmium pollution in the Netherlands, where this form of extrapolation was compared with ordinary kriging. When sufficient data are available (more than 140), ordinary kriging gave the most precise predictions. When the number of data was small (i.e. less than 60), predictions obtained with Bayesian kriging were more precise as compared to those obtained with ordinary kriging. This leads to a considerable reduction of costs, without loss of information.

niet beschikbaar

Van een 25-tal grondwaterkwaliteitsvariabelen werden landsdekkende statistische kaartbeelden gegenereerd, waarin schattingen van ruitmediane waarden van 4 km x 4 km-ruiten werden weergegeven. De schattingen werden weergegeven in de vorm van 95% betrouwbaarheidsintervallen, die in de hoofdkaarten (de zwart/wit-kaarten 1 t/m 25) telkens in 4 afzonderlijke kaartbeelden werden gerelateerd aan 4 verschillende, veelal aan normstelling ontleende niveaus. De kaartbeelden zijn gebaseerd op waarnemingen uit een 400-tal voor dit doel representatief geachte meetpunten: 252 van het Landelijk Meetnet Grondwaterkwaliteit en 173 van de Provinciale Meetnetten. Aan de basis van de schattingsprocedure vond een categorieindeling naar landgebruik en bodemtype plaats, gebruik makend van geautomatiseerde landsdekkende beelden dienaangaande. De meetnetinformatie werd uiteindelijk per categorie landgebruik/bodemtype ruimtelijk geinterpoleerd, waarbij (per categorie) rekening werd gehouden met ruimtelijke samenhang in variatie en regionale verschillen in niveau. De op basis van bodemkundige kennis ingegeven stratificatie naar landgebruik en bodemtype is essentieel gebleken: het niet of slechts partieel uitvoeren van de betreffende stratificatie leidt tot wezenlijk afwijkende kaartbeelden. De effecten van meetnetdichtheid zijn onderzocht door eveneens kaartbeelden te genereren op basis van de meetpuntenverzameling van het Landelijk Meetnet Grondwaterkwaliteit alleen. Daarbij blijkt dat de toevoeging van de informatie uit de Provinciale Meetnetten in wezenlijke aanpassingen van het landelijke beeld heeft geresulteerd. De aanpassingen zijn in belangrijke mate toe te schrijven aan de toegenomen informatie aangaande korte-afstand-variatie en de toegenomen hoeveelheid locatiespecifieke informatie. Beleidsmatig kunnen de kaarten (a) rechtstreeks worden benut enerzijds in relatie tot de meer diffuse vormen van grondwaterverontreiniging, anderzijds voor het verkrijgen van een ruimtelijk gedifferentieerd beeld van achtergrondwaarden waartegen strikt locatiespecifieke verontreinigingssituaties kunnen worden beoordeeld ; (b) meer indirect worden benut als invoer- en toetsingsmateriaal voor de de beleidsonderbouwing ten dienste staande regionale en landelijke modellen voor grondwaterkwaliteitsontwikkeling. De kaarten kunnen worden gezien als een vertaling van de uit de meetnetten afkomstige puntinformatie naar een ruimtelijk schaalniveau waarop bijvoorbeeld gangbare regionale modellering aansluit. Meetnetoptimalisatie kan efficient en locatiespecifiek worden gericht op aspecten van het gegenereerde landelijke beeld. In het algemeen kan worden gesteld, dat de gepresenteerde kaarten weinig aanleiding geven tot meetnetreductie (brede betrouwbaarheidsintervallen). Wiskundige aspecten werden tot elementaire eenvoud beperkt.

niet beschikbaar

Van een 25-tal grondwaterkwaliteitsvariabelen werden landsdekkende statistische kaartbeelden gegenereerd, waarin schattingen van ruitmediane waarden van 4 km x 4 km-ruiten werden weergegeven. De schattingen werden weergegeven in de vorm van 95% betrouwbaarheidsintervallen, die in de hoofdkaarten (de zwart/wit-kaarten 1 t/m 25) telkens in 4 afzonderlijke kaartbeelden werden gerelateerd aan 4 verschillende, veelal aan normstelling ontleende niveaus. De kaartbeelden zijn gebaseerd op waarnemingen uit een 400-tal voor dit doel representatief geachte meetpunten: 252 van het Landelijk Meetnet Grondwaterkwaliteit en 173 van de Provinciale Meetnetten. Aan de basis van de schattingsprocedure vond een categorieindeling naar landgebruik en bodemtype plaats, gebruik makend van geautomatiseerde landsdekkende beelden dienaangaande. De meetnetinformatie werd uiteindelijk per categorie landgebruik/bodemtype ruimtelijk geinterpoleerd, waarbij (per categorie) rekening werd gehouden met ruimtelijke samenhang in variatie en regionale verschillen in niveau. De op basis van bodemkundige kennis ingegeven stratificatie naar landgebruik en bodemtype is essentieel gebleken: het niet of slechts partieel uitvoeren van de betreffende stratificatie leidt tot wezenlijk afwijkende kaartbeelden. De effecten van meetnetdichtheid zijn onderzocht door eveneens kaartbeelden te genereren op basis van de meetpuntenverzameling van het Landelijk Meetnet Grondwaterkwaliteit alleen. Daarbij blijkt dat de toevoeging van de informatie uit de Provinciale Meetnetten in wezenlijke aanpassingen van het landelijke beeld heeft geresulteerd. De aanpassingen zijn in belangrijke mate toe te schrijven aan de toegenomen informatie aangaande korte-afstand-variatie en de toegenomen hoeveelheid locatiespecifieke informatie. Beleidsmatig kunnen de kaarten (a) rechtstreeks worden benut enerzijds in relatie tot de meer diffuse vormen van grondwaterverontreiniging, anderzijds voor het verkrijgen van een ruimtelijk gedifferentieerd beeld van achtergrondwaarden waartegen strikt locatiespecifieke verontreinigingssituaties kunnen worden beoordeeld ; (b) meer indirect worden benut als invoer- en toetsingsmateriaal voor de de beleidsonderbouwing ten dienste staande regionale en landelijke modellen voor grondwaterkwaliteitsontwikkeling. De kaarten kunnen worden gezien als een vertaling van de uit de meetnetten afkomstige puntinformatie naar een ruimtelijk schaalniveau waarop bijvoorbeeld gangbare regionale modellering aansluit. Meetnetoptimalisatie kan efficient en locatiespecifiek worden gericht op aspecten van het gegenereerde landelijke beeld. In het algemeen kan worden gesteld, dat de gepresenteerde kaarten weinig aanleiding geven tot meetnetreductie (brede betrouwbaarheidsintervallen). Wiskundige aspecten werden tot elementaire eenvoud beperkt.

Areas, models and variability are relevant sources of prior information for spatial statistics. These sources can be exploited when spatial data are to be used for interpolation and sampling. Both stochastic and deterministic covariables can be used in regression equations for spatial interpolation. The ideas are illustrated with a study on cadmium pollution in the Netherlands. Prior information is shown to be crucial when deciding where to sample. Interpolation benefits from prior stratification, reducing the MSE value with 50% in homogeneous strata. Further research is needed to deal with other forms of prior information.

To evaluate the effect of various levels of fertilizer applications, six fertilizing scenarios were analyzed by computer simulations using a process-based simulation model. By using simulation results of one of the fertilizer scenarios as a covariable in disjunctive cokriging (DCK), the number of simulations in the remaining scenarios could be reduced to 20% of the original number, while the prediction quality in fifty test points still satisfied two criteria based on the sample variance. When the conditional probability of exceeding a threshold value is to be mapped, an expanded data set is of limited use because some variance is lost in the expansion process.

Op grond van twee maatschappelijke ontwikkelingen, het streven naar een landsdekkend beeld van de bodemkwaliteit en de ontwikkeling van normen voor bodemverontreiniging die gerelateerd zijn aan het bodemgebruik (bodemgebruikswaarden), heeft Alterra kaarten geproduceerd van de zware-metaalgehalten in de bovengrond, de kritieke gehalten voor het huidige landgebruik, en de overschrijdingskans van het kritieke gehalte in de bodem. De kritieke bodemgehalten voor zware metalen zijn berekend aan de hand van de gewasnorm (kritieke gehalte in het gewas i.v.m. de voedselveiligheid) en de bodemvariabelen kleigehalte, organische-stofgehalte en zuurgraad. Als illustratie de resulterende kaartbeelden voor cadmium

Metingen van concentraties van gewasbeschermingsmiddelen in het Nederlandse oppervlaktewater worden met een geostatistische methode opgeschaald naar landelijke waarden. De methode maakt gebruik van ruimte-tijd regressie-kriging, waarbij zowel informatie in de metingen zelf als in landsdekkende kaarten van gecorreleerde omgevingsvariabelen wordt benut. De methode berekent eveneens de onzekerheid in de opgeschaalde waarde zodat ook de statistische significantie van temporele trends in landelijke waarden kan worden bepaald. Toepassing van de methode op metribuzin en carbendazim voor de periode 1997-2006 geeft plausibele resultaten die voor metribuzin in alle jaren rond 12 ng/liter liggen en voor carbendazim een dalende trend van 170 ng/liter in 1997 naar 100 ng/liter in 2006 laat zien. De methode is bewerkelijk en stelt hoge eisen aan de beschikbaarheid van data. Belangrijke aandachtspunten voor toekomstig onderzoek zijn statistische validatie van modeluitkomsten, analyse van de gevoeligheid van het model voor gemaakte aannames en de verbeterde verwerking van metingen beneden de kwantificeringslimiet. Trefwoorden: gewasbeschermingsmiddelen, kriging, milieu, regressie, statistische modellering, trend, waterkwaliteit

Metingen van concentraties van gewasbeschermingsmiddelen in het Nederlandse oppervlaktewater worden met een geostatistische methode opgeschaald naar landelijke waarden. De methode maakt gebruik van ruimte-tijd regressie-kriging, waarbij zowel informatie in de metingen zelf als in landsdekkende kaarten van gecorreleerde omgevingsvariabelen wordt benut. De methode berekent eveneens de onzekerheid in de opgeschaalde waarde zodat ook de statistische significantie van temporele trends in landelijke waarden kan worden bepaald. Toepassing van de methode op metribuzin en carbendazim voor de periode 1997-2006 geeft plausibele resultaten die voor metribuzin in alle jaren rond 12 ng/liter liggen en voor carbendazim een dalende trend van 170 ng/liter in 1997 naar 100 ng/liter in 2006 laat zien. De methode is bewerkelijk en stelt hoge eisen aan de beschikbaarheid van data. Belangrijke aandachtspunten voor toekomstig onderzoek zijn statistische validatie van modeluitkomsten, analyse van de gevoeligheid van het model voor gemaakte aannames en de verbeterde verwerking van metingen beneden de kwantificeringslimiet. Trefwoorden: gewasbeschermingsmiddelen, kriging, milieu, regressie, statistische modellering, trend, waterkwaliteit

A method to calculate the statistical distribution of a scaling factor from soil-water retention curves consists of measuring the particle-size distribution by laser scattering, computing soil water retention curves using the Arya and Paris model, and calculating a scale factor for each function. The method was tested by comparing measured and predicted soil-water retention curves. The advantage of this method is in its simplicity and ease of use. The applicability of the method to a given soil texture depends on the verification of the calculated soil-water retention functions.

Underwater sediments of two Dutch moorland pools, Gerritsfles and Kliplo, have been compared statistically with respect to total S and S-related sediment contents. Horizontal and vertical distribution of S in the two pools are significantly different from each other. Statistical analyses indicate that spatial variation of S in Gerritsfles is probably due to variation in inorganic S contents and in Kliplo due to variations in organically bound S. As evidenced by this study, a choice for a measurement unit like mass fraction (g g −1 ) or volumetric mass (mg cm −3 ) is crucial for the interpretation of spatial variability. In spatial studies of sediment constituents, it is essential to express contents of these constituents in volumetric mass fractions, since spatial sediment patterns are often obscured by spatial variations in bulk density. Taking spatial variability into account may highly affect the quantification of S-budgets of pools or lakes.

Als je vaste grond onder de voeten hebt, dan hoef je niet meer te twijfelen. Maar hoe zeker kun je zijn over de grond onder je voeten? Hoe betrouwbaar is de bodemkaart, schaal 1:50.000?

A large collection of interpolation techniques is available for application in environmental research. To help environmental scientists in choosing an appropriate technique a disposition is made, based on 1) applicability in space, time and space-time, 2) quantification of accuracy of interpolated values, 3) incorporation of ancillary information, and 4) incorporation of process knowledge. The described methods include inverse distance weighting, nearest neighbour methods, geostatistical interpolation methods, Kalman filter methods, Bayesian Maximum Entropy methods, etc. The applicability of methods in aggregation (upscaling) and disaggregation (downscaling) is discussed. Software for interpolation is described. The application of interpolation techniques is illustrated in two case studies: temporal interpolation of indicators for ecological water quality, and spatio-temporal interpolation and aggregation of pesticide concentrations in Dutch surface waters. A valuable next step will be to construct a decision tree or decision support system, that guides the environmental scientist to easy-to-use software implementations that are appropriate to solve their interpolation problem. Validation studies are needed to assess the quality of interpolated values, and the quality of information on uncertainty provided by the interpolation method.

Daily precipitation amounts show spatial variation over sub-continential regions. Point measurements, represntative for regions of land, have to be interpolated towards unobserved locations. In this study four days in 1984 were selected to investigate the spatial variability of daily precipitation amount in north-western Europe in relation to the meteorological conditions. Data were interpolated using kriging. Crossvalidation was used to compare interpolated values with measured values. Large differences in the spatial structure of daily precipitation amount are observed as a result of different meteorological conditions. Stratification of the study area into a coast, a mountain and an interior stratum proved to be successful, reducing the Mean Squared Error of Prediction with up to 55%.

Salinity and sodicity of soils are two common problems encountered in the Hola Irrigation Scheme in east Kenya. Both result in poor crop performance and reduced yields. Based upon a detailed survey in a 405 ha area consisting of 45 irrigation blocks, the spatial variability of pH, EC e and ESP was studied. Data obtained were analyzed using geostatistical procedures in a geographical information system. As it turned out, sodicity in the area has a clear spatial structure. Also differences in homogeneity per block were observed. Reclamation will be necessary, mainly because of the sodicity in the area, while salinity is still at an acceptable level for all crops grown and only small amounts of water are needed to maintain these EC levels. This results in varying gypsum requirements for reclamation for different blocks. A Geographical Information System (GIS) was used to handle large amounts of data and to compare the effects of different land use scenarios.

Former galvanic factory premises are often heavily contaminated with cyanide, requiring redevelopment of the soil. In this study attention is focused on one particular site in the Netherlands. In an area of 0.8 ha 344 observations were taken at different depths in the upper 3 m of soil. Three different procedures based on spatial variability studies are compared to calculate the extent of polluted soil as well as the uncertainties associated with it on the basis of this number of observations. As it turns out, a more evenly distributed data configuration results in a reduction of the extent of soil to be redeveloped when the decision procedure involved is based on the probability of exceeding a critical concentration level. Hence a small but structural reduction of the associated costs was achieved.

Voor het bepalen van de kwaliteit van de bodem als hulpbron is er behoefte aan een regelmatige bepaling van de chemische en fysische eigenschappen, zowel in ruimte als tijd. Kwantitatieve schatting van de exacte hoeveelheid, ruimtelijke verdeling en temporele verandering van bodemeigenschappen is nog steeds een uitdaging. Het onderwerp van dit proefschrift is hoe spectrale reflectie informatie gelinkt kan worden aan bodemeigenschappen