Application of Interval Fields for Uncertainty Modeling in a Geohydrological Case
In situ soil remediation requires a good knowledge about the processes that occur in the subsurface. Groundwater transport models are needed to predict the flow of contaminants. Such a model must contain information on the material layers. This information is obtained from in situ point measurements which are costly and thus limited in number. The overall model is thus characterised by uncertainty. This uncertainty has a spatial character, i.e. the value of an uncertain parameter can vary based on the location in the model itself. In other words the uncertain parameter is non-uniform throughout the model. On the other hand the uncertain parameter does have some spatial dependency, i.e. the particular value of the uncertainty in one location is not totally independent of its value in a location adjacent to it. To deal with such uncertainties the authors have developed the concept of interval fields. The main advantage of the interval field is its ability to represent a field uncertainty in two separate entities: one to represent the uncertainty and one to represent the spatial dependency. The main focus of the paper is on the application of interval fields to a geohydrological problem. The uncertainty taken into account is the material layers’ hydraulic conductivity. The results presented are the uncertainties on the contaminant’s concentration near a river. The second objective of the paper is to define an input uncertainty elasticity of the output. In other words, identify the locations in the model, whose uncertainties influence the uncertainty on the output the most. Such a quantity will indicate where to perform additional in situ point measurements to reduce the uncertainty on the output the most.
KeywordsHydraulic Conductivity Fuzzy Number Base Vector Correlation Length Spatial Domain
The support of the Flemish Government through IWT-SBO project no. 060043: Fuzzy Finite Element Method is gratefully acknowledged.
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