Sensitivity in Hydrogeology

The project examines groundwater flow and mass transport under uncertainty in the hydro-dispersive parameters of a multi-layered hydrogeological model. Sensitivity analysis is conducted in order to identify input random variables and combinations thereof with significant contributions to the variance of the model response. In the context of this problem, novel methods for conducting sensitivity analysis with correlated input are investigated.

The employed approach for sensitivity analysis is evaluation of Sobol' indices. By not assuming any kind of linearity or monotonicity of the model, Sobol' indices have proven to be particularly good descriptors of the global sensitivity of a model response to the input parameters. The most efficient method to calculate these indices is by post-processing the coefficients of the Polynomial Chaos Expansion (PCE) of the quantity of interest. The key concept of PCE is to expand the model response onto a basis made of orthogonal polynomials in the input variables. PCE models are herein developed with non-intrusive approaches, where the corresponding deterministic model is considered a "black-box". To this end, UQLab, the in-house software of the Chair of Risk, Safety and Uncertainty Quantification at ETH Zürich, is used. The required deterministic analyses of groundwater flow and mass transport are performed at the Centre for Hydrogeology and Geothermics (CHYN) of the University of Neuchâtel.

The figure on the right shows the results of a preliminary study for the water volume outflowing from the top boundary. For the various layers listed in the horizontal axis, the figure shows the total Sobol' indices, representing the sum of individual effects and interactions with other layers. The figure shows that the response variance is essentially controlled by only a few layers.

References

[1]  Sudret, B. Global sensitivity analysis using polynomial chaos expansions, Reliab. Eng. Sys. Safety, 2008, 93, 964-979