The sustainable management of groundwater demands a faithful characterization of the subsurface. This, in turn, requires information which is generally not readily available. To bridge the gap between data need and availability, numerical models are often used to synthesize plausible scenarios not only from direct information but also from additional, indirect data. Unfortunately, the resulting system characterizations will rarely be unique. This poses a challenge for practical parameter inference: computational limitations often force modelers to resort to methods based on questionable assumptions of Gaussianity, which do not reproduce important facets of ambiguity such as Pareto fronts or multimodality. In search of a remedy, an alternative could be found in Stein Variational Gradient Descent (SVGD), a recent development in the field of statistics. This ensemble-based method iteratively transforms a set of arbitrary particles into samples of a potentially non-Gaussian posterior, provided the latter is sufficiently smooth. A prerequisite for this method is knowledge of the Jacobian, which is usually exceptionally expensive to evaluate. To address this issue, we propose an ensemble-based, localized approximation of the Jacobian. We demonstrate the performance of the resulting algorithm in two cases: a simple, bimodal synthetic scenario, and a complex numerical model based on a real world, prealpine catchment. Promising results in both cases—even when the ensemble size is smaller than the number of parameters—suggest that SVGD can be a valuable addition to hydrogeological parameter inference.

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Once data have been recorded, data validation procedures have to be conducted to assess the quality of the data, i.e. give a confidence grade. Furthermore, gaps may occur in time series and, depending on the purposes, these can be given values by application of e.g. interpolation. Since both aspects are strongly correlated, this chapter gives an overview on the main data validation and data curation/imputation methods. Instead of offering exhaustive details on existing methods, this chapter aims at providing concepts for most popular techniques, a discussion of their advantages and disadvantages in the light of different cases of application, and some thoughts on potential impacts of the choices that must be made. Despite involving mathematical methods, data validation remains a largely subjective process: every data user must be aware of those subjectivities.@en

Data collection in urban drainage systems comes with many challenges. However, many examples already exist, containing numerous useful lessons learned. This chapter therefore contains several urban drainage and stormwater management metrology case studies, selected to cover a wide range of scopes, scales, objectives, climates, data validation methods, and data storage approaches. The case studies are initiated by academics as well as by institutions from the water industry.@en