Browsing by Author "Erdal, Daniel"

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Open Access
Sampling behavioral model parameters for ensemble-based sensitivity analysis using Gaussian process emulation and active subspaces
(2020) Erdal, Daniel; Xiao, Sinan; Nowak, Wolfgang; Cirpka, Olaf A.
Ensemble-based uncertainty quantification and global sensitivity analysis of environmental models requires generating large ensembles of parameter-sets. This can already be difficult when analyzing moderately complex models based on partial differential equations because many parameter combinations cause an implausible model behavior even though the individual parameters are within plausible ranges. In this work, we apply Gaussian Process Emulators (GPE) as surrogate models in a sampling scheme. In an active-training phase of the surrogate model, we target the behavioral boundary of the parameter space before sampling this behavioral part of the parameter space more evenly by passive sampling. Active learning increases the subsequent sampling efficiency, but its additional costs pay off only for a sufficiently large sample size. We exemplify our idea with a catchment-scale subsurface flow model with uncertain material properties, boundary conditions, and geometric descriptors of the geological structure. We then perform a global-sensitivity analysis of the resulting behavioral dataset using the active-subspace method, which requires approximating the local sensitivities of the target quantity with respect to all parameters at all sampled locations in parameter space. The Gaussian Process Emulator implicitly provides an analytical expression for this gradient, thus improving the accuracy of the active-subspace construction. When applying the GPE-based preselection, 70-90% of the samples were confirmed to be behavioral by running the full model, whereas only 0.5% of the samples were behavioral in standard Monte-Carlo sampling without preselection. The GPE method also provided local sensitivities at minimal additional costs.
Open Access
A stochastic framework to optimize monitoring strategies for delineating groundwater divides
(2020) Allgeier, Jonas; González-Nicolás, Ana; Erdal, Daniel; Nowak, Wolfgang; Cirpka, Olaf A.
Surface-water divides can be delineated by analyzing digital elevation models. They might, however, significantly differ from groundwater divides because the groundwater surface does not necessarily follow the surface topography. Thus, in order to delineate a groundwater divide, hydraulic-head measurements are needed. Because installing piezometers is cost- and labor-intensive, it is vital to optimize their placement. In this work, we introduce an optimal design analysis that can identify the best spatial configuration of piezometers. The method is based on formal minimization of the expected posterior uncertainty in localizing the groundwater divide. It is based on the preposterior data impact assessor, a Bayesian framework that uses a random sample of models (here: steady-state groundwater flow models) in a fully non-linear analysis. For each realization, we compute virtual hydraulic-head measurements at all potential well installation points and delineate the groundwater divide by particle tracking. Then, for each set of virtual measurements and their possible measurement values, we assess the uncertainty of the groundwater-divide location after Bayesian updating, and finally marginalize over all possible measurement values. We test the method mimicking an aquifer in South-West Germany. Previous works in this aquifer indicated a groundwater divide that substantially differs from the surface-water divide. Our analysis shows that the uncertainty in the localization of the groundwater divide can be reduced with each additional monitoring well. In our case study, the optimal configuration of three monitoring points involves the first well being close to the topographic surface water divide, the second one on the hillslope toward the valley, and the third one in between.