Ensemble Kalman filtering for parameter estimation in groundwater flow modeling : implementation and robust comparison of filter variants within the SHEMAT-Suite stochastic mode

  • Ensemble Kalman Filter zur Parameterschätzung bei der Grundwasserflussmodellierung : Implementierung und Vergleich von Filtervarianten im SHEMAT-Suite Stochastic Mode

Keller, Johannes Joachim; Hendricks Franssen, Harrie-Jan (Thesis advisor); Clauser, Christoph (Thesis advisor); Kowalski, Julia (Thesis advisor); Nowak, Wolfgang (Thesis advisor)

Aachen : RWTH Aachen University (2020, 2022)
Dissertation / PhD Thesis

Dissertation, Rheinisch-Westfälische Technische Hochschule Aachen, 2020


Modeling groundwater flow is important for many scientific and commercial applications related to the geosciences. Two such applications are the simulation of geothermal systems where a combination of flow and heat is simulated, and monitoring contaminant transport where a combination of flow and species transport is simulated. All such applications have in common that uncertainty quantification is essential, in particular the correct modeling of permeabilities of the porous medium through which the fluid, often water, flows. This thesis presents a framework for applying the ensemble Kalman filter (EnKF) for permeability estimation. The EnKF is a method for data assimilation and parameter estimation adapted to large-scale, non-linear models. In the first part of the thesis, the focus is on the numerical code SHEMAT-Suite. SHEMAT-Suite is described, in particular the workflow for ensuring error-free and reproducible implementation that was implemented during this thesis. This concerns two parts of the software: the groundwater flow simulation and the EnKF update. A special focus is laid on the stochastic mode of SHEMAT-Suite. During this thesis, the existing software that allowed the usage of a potentially damped EnKF was completely refactored. This included among other tasks: a module implementation of the methods, a remodeling of the input file of the stochastic mode to match the main input file of the software, and, finally, including numerous error messages. Additionally, the suite of EnKF methods that is used in the remainder of this thesis was implemented in the same modular way. In the future, the modular implementation facilitates adding EnKF methods and robustly comparing the existing EnKF methods. In the remainder of this thesis, I use this framework for investigating possible inaccuracies related to the EnKF and groundwater flow simulation. First, the influence of the sampling error stemming from random seed initialization is analyzed in a comparison of EnKF variants. Secondly, the pilot point EnKF is introduced. The pilot point EnKF is a novel EnKF method that is good at suppressing unwanted spurious correlations that may occur when using EnKF methods for parameter estimation. The results of this thesis provide insights for the robust and efficient usage of growing computer resources for permeability estimation and groundwater flow estimation. In the majority of scientific disciplines, quantifying uncertainties is of high importance and, due to improving computer performance, uncertainty quantification becomes feasible for previously too computationally intensive simulations. For permeability estimation and groundwater flow simulation, quantifying uncertainty is particularly essential for a number of reasons. (1) There are usually many uncertain influences in subsurface models used for groundwater flow, (2) subsurface models are typically large-scale, and, (3) as a consequence, small ensemble sizes have to suffice for ensemble-based uncertainty quantification methods. In this work, a framework for using ensemble Kalman filters (EnKF) for parameter estimation is presented. In this framework, the EnKF methods are implemented as part of the scientific software SHEMAT-Suite in such a way that the implementation supports scientific principles, such as reproducibility and falsifiability. By comparing performances of EnKF methods, it is shown that the random seed has a non-negligible influence on these performance comparisons. Finally, the PP-EnKF is introduced, an EnKF variant tailored towards suppressing spurious correlations that result from undersampling in the EnKF.


  • E.ON Energy Research Center [080052]
  • Division of Earth Sciences and Geography [530000]
  • Scientific Computing in Terrestrial Systems Teaching and Research Area [532820]