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

A disposition of interpolation techniques

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

On the uncertainty of stream networks derived from elevation data: the error propagation approach

DEM error propagation methodology is extended to the derivation of vector-based objects (stream networks) using geostatistical simulations. First, point sampled elevations are used to fit a variogram model. Next 100 DEM realizations are generated using conditional sequential Gaussian simulation; the stream network map is extracted for each of these realizations, and the collection of stream networks is analyzed to quantify the error propagation. At each grid cell, the probability of the occurrence of a stream and the propagated error are estimated. The method is illustrated using two small data sets: Baranja hill (30 m grid cell size; 16 512 pixels; 6367 sampled elevations), and Zlatibor (30 m grid cell size; 15 000 pixels; 2051 sampled elevations). All computations are run in the open source software for statistical computing R: package geoR is used to fit variogram; package gstat is used to run sequential Gaussian simulation; streams are extracted using the open source GIS SAGA via the RSAGA library. The resulting stream error map (Information entropy of a Bernoulli trial) clearly depicts areas where the extracted stream network is least precise – usually areas of low local relief and slightly convex (0–10 difference from the mean value). In both cases, significant parts of the study area (17.3% for Baranja Hill; 6.2% for Zlatibor) show high error (H>0.5) of locating streams. By correlating the propagated uncertainty of the derived stream network with various land surface parameters sampling of height measurements can be optimized so that delineated streams satisfy the required accuracy level. Such error propagation tool should become a standard functionality in any modern GIS. Remaining issue to be tackled is the computational burden of geostatistical simulations: this framework is at the moment limited to small data sets with several hundreds of points. Scripts and data sets used in this article are available on-line via the www.geomorphometry.org website and can be easily adopted/adjusted to any similar case study

Automatic real-time interpolation of radiation hazards: prototype and system architecture considerations

Detecting and monitoring the development of radioactive releases in the atmosphere is important. In many European countries monitoring networks have been established to perform this task. In the Netherlands the National Radioactivity Monitoring network (NRM) was installed. Currently, point maps are used to interpret the data from the NRM. Automatically generating maps in realtime would improve the interpretation of the data by giving the user a clear overview of the present radiological situation and provide an estimate of the radioactivity level at unmeasured locations. In this paper we present a prototype system that automatically generates real-time maps of radioactivity levels and presents results in an interoperable way through a Web Map Service. The system defines a first step towards a emergency management system and is suited primarily for data without large outliers. The automatic interpolation is done using universal kriging in combination with an automatic variogram fitting procedure. The focus is on mathematical and operational issues and on architectural considerations on how to improve the interoperability and portability of the prototype system

Transfer function-noise modeling and spatial interpolation to evaluate the risk of extreme (shallow) water-table levels in the Brazilian Cerrados

Water regimes in the Brazilian Cerrados are sensitive to climatological disturbances and human intervention. The risk that critical water-table levels are exceeded over long periods of time can be estimated by applying stochastic methods in modeling the dynamic relationship between water levels and driving forces such as precipitation and evapotranspiration. In this study, a transfer function-noise model, the so called PIRFICT-model, is applied to estimate the dynamic relationship between water-table depth and precipitation surplus/deficit in a watershed with a groundwater monitoring scheme in the Brazilian Cerrados. Critical limits were defined for a period in the Cerrados agricultural calendar, the end of the rainy season, when extremely shallow levels

Geostatistische opschaling van concentraties van gewasbeschermingsmiddelen in het Nederlandse oppervlaktewater

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, waterkwalitei