Sampling design for compliance monitoring of surface water quality: A case study in a Polder area

International agreements such as the EU Water Framework Directive (WFD) ask for efficient sampling methods for monitoring natural resources. In this paper a general methodology for designing efficient, statistically sound monitoring schemes is described. An important decision is the choice between a design-based and a model-based method, implying the choice between probability (random) sampling and purposive sampling. For mapping purposes, model-based methods are more appropriate, whereas to obtain valid results for the universe as a whole, such as in testing water quality standards against legal standards, we generally prefer a design-based method. Four basic sampling patterns in space-time universe are described: static, synchronous, static-synchronous, and rotational. A case study is carried out for monitoring the quality of surface water at two farms in western Netherlands, wherein a synchronous sampling design is applied, with stratified simple random sampling in both space and time. To reduce laboratory costs the aliquots taken at the locations of a given sampling round are bulked to form a composite. To test the spatiotemporal mean N-total concentration during the summer half-year against the MAR standard with a power of 80% at a concentration 15% below the MAR standard and with a confidence of 95%, six to nine sampling rounds are needed with 50 to 75 locations per sampling round. For P-total the required number of sampling rounds differs strongly between the two farms, but is for both farms much larger than for N-total

Monte Carlo and spatial sampling effects in regional uncertainty propagation analyses

Spatial uncertainty propagation analysis (UPA) aims at analysing how uncertainties in model inputs propagate through spatial models. Monte Carlo methods are often used, which estimate the output uncertainty by repeatedly running the model with inputs that are sampled from their probability distribution. Regional application of UPA usually means that the model output must be aggregated to a larger spatial support. For instance, decision makers may want to know the uncertainty about the annual nitrate leaching averaged over an entire region, whereas a model typically predicts the leaching for small plots. For models without spatial interactions there is no need to run the model at all points within the region of interest. A sufficiently large sample of locations may represent the region sufficiently well. The reduction in computational load can then be used to increase the number of Monte Carlo runs. In this paper we explore how a combination of analytical and numerical methods can be used to evaluate the errors introduced by Monte Carlo and spatial sampling. This is important to be able to correct for the bias inflicted by the spatial sampling, to determine how many model runs are needed to reach accurate results and to determine the optimum ratio of the Monte Carlo and spatial sample sizes

Estimating space-time mean concentrations of nutrients in surface waters of variable depth

A monitoring scheme has been designed to test whether the space-time mean concentration total Nitrogen (N-total) in the surface water in the Northern Frisian Woodlands (NFW, The Netherlands) complies with standards of the European Water Framework directive. Since in statistical testing for compliance monitoring valid estimators for the mean and its variance are important, a design-based method is preferred above a model-based method. In the NFW-area the surface water depth varies in both space and time and can periodically equal zero, due to variation in precipitation and evapotranspiration. To account for this, space-time mean concentrations are estimated by the ratio of the estimated total mass of nutrient and the estimated total volume of water. The method is applied in the period from 1 April to 30 September 2008 to four hydrologically different subareas. Besides, the aim was to use the information on the spatial and temporal variance of N-total concentrations to optimize the numbers of sampling rounds and sampling locations per sampling round in future monitoring campaigns, given budgetary constraints. A bootstrap procedure was applied to account for uncertainty about the temporal and spatial variances in estimating the optimal number of sampling rounds and sampling locations. For two subareas the accuracy of the estimated space-time means can be improved by sampling more frequently at less locations (compared to the design applied in 2008), whereas for one subarea sampling less frequently at more locations increases the precision. For one subarea the sample data were rather inconclusive about the optimal sample sizes

Incorporating models of spatial variation in sampling strategies for soil

The efficiency of soil sampling strategies can be increased by incorporating a spatial variation model. The model can be used in the random selection of sample points i.e. in the sampling design, or in spatial estimation (prediction). In the first approach inference is based on a sampling design, in the second on a probabilistic model. The advantages and disadvantages of these two approaches, referred to as the design-based and model-based approach, are dealt with from a theoretical and a practical point of view. Estimation by random sampling stratified by soil map unit, and kriging are taken as examples of the two approaches in several case studies.The commonly accepted belief in geostatistical literature that the design-based approach is not valid in areas with autocorrelation is incorrect. Furthermore, the claimed optimality of the model-based approach is questionable. The two approaches use different criteria for assesment of the quality of estimates, consequently optimum estimation has a different meaning in each approach.In a regional survey with small observation density (1 observation per 25 ha), estimates of values at points were generally not significantly improved by soil map stratification (α=0.10), neither by estimation with variograms as in kriging. Stratified random sample estimates of values at points were as accurate as those provided by kriging.In the model-based approach the quality of the estimates depends on the quality of the model. To avoid this, a new approach for spatial estimation is proposed, the model-assisted approach, making use of non-ergodic variograms. This approach incorporates the sampling error of the non-ergodic variogram in the kriging error, making the estimation variance estimates always valid. A set of new methods is presented for unbiased and robust estimation of the non-ergodic variogram and its sampling error.Many factors determine the efficiency of an approach that incorporates spatial variation models, making the decision process rather complicated. A simple decision-tree is presented with seven questions related to the aim of the survey (local or global estimation, criteria for assessment of the quality of the estimates), the constraints (available budget and sampling costs) and prior information (soil map)

Beslissen over vrij grondverzet op basis van Bayesiaanse toets op oppervlaktefractie ernstig verontreinigde grond

De vrijstellingsregeling grondverzet biedt de mogelijkheid tot vrijstelling van partijkeuringen wanneer aangetoond wordt dat de oppervlaktefractie ernstig verontreinigde grond kleiner is dan 5%. In dit onderzoek wordt de beslissing gebaseerd op een statistische toets omdat dan rekening wordt gehouden met het aantal monsters dat in sterke mate de mate van onzekerheid over de oppervlaktefractie bepaald. Bayesiaans toetsen biedt interessante mogelijkheden in vergelijking met klassiek toetsen omdat, gegeven het aantal monsters en het aantal ernstig verontreinigde monsters in de steekproef, de betrouwbaarheid van de conclusie `oppervlaktefractie <0.05¿ door het gebruik van de a priori verdeling over de oppervlaktefractie toeneemt. Ook het verlies van foute beslissingen (schade tengevolge van als bodem hergebruikte ernstig verontreinigde partij grond, en kosten van keuren van niet ernstig verontreinigde partijen) kan hierdoor gereduceerd worden

Towards a Soil Information System with quantified accuracy : a prototype for mapping continuous soil properties

This report describes the potential and functionality of software for spatial analysis, prediction and stochastic simulation of continuous soil properties using data from the Dutch Soil Information System (BIS). A geostatistical framework and R codes were developed. The geostatistical model of a soil property has a deterministic component representing the mean value within a soil category, and a stochastic component of standardized residuals. The standardized residuals are interpolated or simulated based on the simple kriging system. The software was tested in four case studies: exchangeable soil pH, clay content, organic matter content and Mean Spring Water table depth (MSW). It is concluded that the geostatistical framework and R codes developed in this study enable to predict values of continuous soil properties spatially, and to quantify the inaccuracy of these predictions. The inaccuracy of a spatial prediction at a certain location is quantified by the kriging variance, which can be interpreted as an indication of the uncertainty about the true value

Landelijke en provinciale bodemkwaliteitsmeetnetten : vlees noch vis?

Essay over monitoring. De Technische Commissie Bodembescherming concludeerde onlangs dat het fundament onder de meetnetten voor bodemkwaliteit in Nederland goed is. Dick Brus is het daarmee niet eens. “De huidige meetnetten zijn mijns inziens niet geschikt voor het doen van statistische uitspraken over de toestand en veranderingen in de kwaliteit van bodem en grondwater in Nederland.

Onderzoek naar de baggerkwaliteit in watergangen

Beschrijving van een methode voor het ontwerpen van efficiente inventarisatieplannen voor onderzoek naar de kwaliteit van bagger in watergangen. De nauwkeurigheid en de kosten van de uit te voeren inventarisatie wordt met modellen voorspeld. De methode wordt geillustreerd aan de hand van de vaarten en tochten in oostelijk en zuidelijk Flevoland (Fleverwaard