Measurement-Based Spatial Dependence of Aquifer Parameters: Modelling and Impact Assessment

• Applicant: Dr.-Ing. Claus Haslauer
• Subject Area: Hydrogeology, Hydrology, Limnology, Urban Water Management, Water Chemistry, Integrated Water Resources Management
• Term: from 2015 to 2021
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 275319324

Geostatistical models and techniques such as Kriging exploit spatial dependence as expressed by correlations to evaluate natural resources, help optimize their development, and address environmental issues related for example to air and water quality, soil pollution, and forestry.Spatial heterogeneity of natural occurring variables leads to problems when numerically modelling environmental systems. Observations can be made only at selected locations or are available only indirectly on a larger scale. Hence, assumptions about the not measured values are necessary, both for the modelling and the estimation of system states. Geostatistical tools offer reasonable solutions for this problem. Spatial copulae are one of very few existing approaches that are based on real field measurements and go beyond pairwise dependence. By employing spatial copulae, it is possible to fit a multidimensional model of spatial dependence to the structure observed in the data. Usually, the fit is drastically improved compared to models using pairwise symmetric dependence.The goal of the proposed work is to improve and expand existing copula models, demonstrate their necessity when dealing with heterogeneous variables, and take non-Gaussian dependence for inversion into account. The improved models will take censored measurements into account. Censored measurements, such as measurements below some detection limit, will be fully considered for simulating spatially distributed fields. Indirect measurements (of hydraulic head) are often more comprehensively available than the variable of interest (hydraulic conductivity). The proposed work will use the improved geostatistical model, to honour the spatial structure of observations during the inversion process, even if it may be non-Gaussian.The relevance of this work will be demonstrated with a numerical groundwater flow and solute transport model of a very heterogeneous field site where the spreading of a solute plume has been observed in great detail; at the same time, hydraulic conductivity at the site has been measured comprehensively. For a justification of the advancement in geostatistical approaches, it needs to be shown these advances in the geostatistical model of a spatially distributed variable (hydraulic conductivity) lead to improvement of the prediction of some dependent variable (solute concentration). An improved prediction of solute transport behaviour based on an improved model of spatial dependence could have far-reaching consequences for source water protection and management of polluted sites. The models could be applied outside the realm of hydrogeology (e.g., air pollution, atmospheric sciences, or mining) to any spatially distributed variable.

• DFG Programme: Research Grants