Investigating the spectral analysis of groundwater level fluctuations in a numerical model of the upper Danube catchment in Germany

Common in-situ methods like pumping tests, slug tests and laboratory analysis reveal aquifer parameters (that is the transmissivity and storativity) that are localized and specific to the measurement location. A need for regionally valid aquifer parameters arises when setting up regional scale physically based groundwater models. The models would help water resource managers to plan and predict the quality and quantity of groundwater resources, thus supports decision making as well as sustainable fresh water supply. A study from Houben et al. 2022 indicate that regional aquifer parameters can be obtained by analysing the frequency content of groundwater level time-series. Their work builds upon a semi-analytical solution for the groundwater head spectrum stochastically derived from the Boussinesq equation evoking the Dupuit assumptions. They found that the solution can be used to infer the transmissivity and storativity from groundwater level fluctuations and validated their hypothesis in simplified numerical environments of different complexity.

In this work, we extended the numerical experiments and applied the semi-analytical solution in homogeneous and heterogeneous 2D (x-y-plane) aquifers as well as in a complex numerical 2D (x-y-plane) model of the upper Danube catchment. We tested the hypothesis that certain locations can reveal regional aquifer parameters. In a homogeneous simulated model, the semi-analytical solution reveals effectively the model input parameters which serves as a proof-of-concept. In a heterogeneous numerical model, the obtained parameters show the complex interplay between zones of different permeability. The effects of high permeable zones can be observed on the low permeable zones which are further apart and vice versa. The obtained parameters were in the range of the model input parameters and followed the trend of the input parameters along the direction of flow. In the model of the upper Danube the obtained parameters were systematically larger than the input parameters. The shift in the obtained parameters was attributed to a violation of the assumptions of the semi-analytical solution. Thus, the complexity of model leads to a breakdown of the semi-analytical solution in some areas. Analyses on a sub-catchment scale revealed that when the assumptions of the analytical solution are met, the obtained parameters reflect the effective parameters.