Global sensitivity analysis and adaptive stochastic sampling of a subsurface-flow model using active subspaces

Abstract

Abstract. Integrated hydrological modeling of domains with complex subsurface features requires many highly uncertain parameters. Performing a global uncertainty analysis using an ensemble of model runs can help bring clarity as to which of these parameters really influence system behavior and for which high parameter uncertainty does not result in similarly high uncertainty of model predictions. However, already creating a sufficiently large ensemble of model simulation for the global sensitivity analysis can be challenging, as many combinations of model parameters can lead to unrealistic model behavior. In this work we use the method of active subspaces to perform a global sensitivity analysis. While building up the ensemble, we use the already-existing ensemble members to construct low-order meta-models based on the first two active-subspace dimensions. The meta-models are used to pre-determine whether a random parameter combination in the stochastic sampling is likely to result in unrealistic behavior so that such a parameter combination is excluded without running the computationally expensive full model. An important reason for choosing the active-subspace method is that both the activity score of the global sensitivity analysis and the meta-models can easily be understood and visualized. We test the approach on a subsurface-flow model including uncertain hydraulic parameters, uncertain boundary conditions and uncertain geological structure. We show that sufficiently detailed active subspaces exist for most observations of interest. The pre-selection by the meta-model significantly reduces the number of full-model runs that must be rejected due to unrealistic behavior. An essential but difficult part in active-subspace sampling using complex models is approximating the gradient of the simulated observation with respect to all parameters. We show that this can effectively and meaningfully be done with second-order polynomials.

Technical Note: Improved Sampling of Behavioral Subsurface Flow Model Parameters Using Active Subspaces

“…In the following subsections we briefly describe the active-subspace method and the base flow model. More details are given by Erdal and Cirpka (2019).…”

“…The model has 32 unknown parameters, including material properties, boundary-condition values, and geometrical parameters of subsurface zones. Originally, Erdal and Cirpka (2019) In a related study, we constructed a surrogate model using Gaussian Process Emulation (GPE) from roughly 4,000 parameter sets. In the GPE model, the model response f (x i ) at the scaled parameter location x i is constructed by interpolation from the existing set of parameter realizations using kriging in parameter space with optimized statistical parameters.…”

“…Like in our prior work (Erdal and Cirpka, 2019), the model considers 6 observations defining a behavioral performance (for locations see Figure 1):…”

“…For each observation considered, we need to perform an active-subspace decomposition. In our our previous work (Erdal and Cirpka, 2019), a decision on whether to accept or reject a parameter set is made in the following way:…”

“…A common sampling approach is to use a two-stage acceptance sampling scheme, in which a candidate parameter set is first tested with the surrogate model, and only if the surrogate model predicts the parameter set to be behavioral, it is applied in the full model. This idea has been applied to groundwater modelling by Cui et al (2011), Laloy et al (2013), and the authors of the current study (Erdal and Cirpka, 2019).…”