Analytical and Stochastic Numerical Methods for the Simulation of Subsurface Flow in Floodplains

Abstract

Floodplain aquifers are important hydraulic connectors between hillslopes and surface-water bodies. The flow field in floodplain aquifers comprises different flow components governed by various geometric and hydrogeologic parameters. In this work, (semi-)analytical and numerical stochastic simulations are used to address three classical problems associated with investigations of floodplain aquifers. To this end, the Ammer floodplain west of Tübingen serves as an exemplary study site.

The first aspect of this dissertation focuses on valley-scale lateral hyporheic exchange in floodplain aquifers driven by widening and subsequent narrowing of the aquifer geometry. By means of a new semi-analytical solution, simple analytical proxy-models can be derived that allow a trivial and quick assessment, whether this type of exchange is relevant in a given setting. The application of these tools to the Ammer floodplain shows that the site has the geometric potential for notable valley-scale hyporheic exchange, but small hydraulic conductivities and lateral influxes from the hillslopes restrict the exchange zone to a negligible extent.

The second topic is concerned with identifying promising points in space, where hydraulic-head information would help to locate groundwater divides separating the catchment area of floodplain aquifers from other catchments. A respective uncertainty-reduction optimization problem is formulated and solved by the application of a stochastic framework based on pre-filtered steady-state flow models. In the context of the Ammer floodplain, this analysis confirms that a presumed shift between groundwater and surface water divide is likely to exist. Three observation points identified by the procedure are predicted to help in reducing the related uncertainty by more than fifty percent.

The third and final subject deals with calibrating steady-state floodplain models to hydraulic-head data. A modified, proxy-model-based, global calibration routine is able to find well-performing parameter sets that bring a steady-state Ammer floodplain model in agreement with measured field data. Neural Posterior Estimation, a technique from the field of Simulation-Based Inference, confirms these parameter sets and sheds light on the related uncertainties and correlations. A key result of this analysis is the confirmed inter-basin flow from the Ammer hillslopes to the Neckar valley, which takes place in the Erfurt formation beneath the Spitzberg ridge and the Wurmlingen saddle.