Data Assimilation and Online Parameter Optimization in Groundwater Modeling Using Nested Particle Filters

Abstract

Over the past decades, advances in data collection and machine learning have paved the way for the development of autonomous simulation frameworks. Among these, many are capable not only of assimilating real‐time data to correct their predictive shortcomings but also of improving their future performance through self‐optimization. In hydrogeology, such techniques harbor great potential for informing sustainable management practices. Simulating the intricacies of groundwater flow requires an adequate representation of unknown, often highly heterogeneous geology. Unfortunately, it is difficult to reconcile the structural complexity demanded by realistic geology with the simplifying assumptions introduced in many calibration methods. The particle filter framework would provide the necessary versatility to retain such complex information but suffers from the curse of dimensionality, a fundamental limitation discouraging its use in systems with many unknowns. Due to the prevalence of such systems in hydrogeology, the particle filter has received little attention in groundwater modeling so far. In this study, we explore the combined use of dimension‐reducing techniques and artificial parameter dynamics to enable a particle filter framework for a groundwater model. Exploiting freedom in the design of the dimension‐reduction approach, we ensure consistency with a predefined geological pattern. The performance of the resulting optimizer is demonstrated in a synthetic test case for three such geological configurations and compared to two Ensemble Kalman Filter setups. Favorable results even for deliberately misspecified settings make us hopeful that nested particle filters may constitute a useful tool for geologically consistent real‐time parameter optimization.

Non‐Gaussian Parameter Inference for Hydrogeological Models Using Stein Variational Gradient Descent

“…While no reference solution was available for the real test case, inference results were promising as well, significantly reducing simulation error and bias, with the residual error likely being based on model structural inadequacy. Throughout, the algorithm retained uncertainty without the need for artificial variance inflation, a challenge for PF (e.g., Ramgraber et al, 2019Ramgraber et al, , 2020 or the EnKF (Anderson, 2007).…”

Quasi‐Online Groundwater Model Optimization Under Constraints of Geological Consistency Based on Iterative Importance Sampling

“…However, it may be an interesting direction for future research to explore the interaction of variance inflation through artificial random parameter dynamics (e.g., Moradkhani et al, 2005; Ramgraber et al, 2019) with the rejuvenation mechanism used in this study. While the indiscriminate addition of random components will corrupt the posterior, we expect that the inclusion of MCMC steps might limit posterior drift.…”

“…As such, the common practice of optimizing log-conductivity fields sampled from such priors with the EnKF (e.g., Jafarpour & McLaughlin, 2009;Tang et al, 2015Tang et al, , 2017Zhou et al, 2011;Zovi et al, 2017) risks leaving the support of the prior. This, in turn, means that the EnKF eventually erases geological features present in the initial ensemble (Ramgraber et al, 2019;Zovi et al, 2017) and yields posterior samples incompatible with the prior. Attempts to enforce conformance by construction (e.g., Hu et al, 2013) circumvent this issue, but instead often suffer from a weakened linear relation between parameter changes and state response, exploited by the EnKF's parameter update (e.g., Crestani et al, 2013).…”

Non-Gaussian parameter inference for hydrogeological models using Stein Variational Gradient Descent

“…Possible remedies are found in Hamiltonian Monte Carlo (e.g., Betancourt, 2018), which exploit Jacobian information, or approaches like the affineinvariant ensemble sampler for MCMC emcee (Foreman-Mackey et al, 2013), which can restrict itself to a limited subspace. The ensembles of PFs, on the other hand, tend to quickly degenerate and collapse in high-dimensional systems (e.g., Arulampalam et al, 2002;Bengtsson et al, 2008), and may require pragmatic solutions which threaten to corrupt the inference (Moradkhani et al, 2005;Ramgraber et al, 2019;Vrugt et al, 2013). As such, these computational limitations render both methods less efficient in systems with limited computational resources than comparable Gaussian-based approaches.…”

“…While no reference solution was available for the real test case, inference results were promising as well, significantly reducing simulation error and bias, with the residual error likely being based on model structural inadequacy. Throughout, the algorithm retained uncertainty without the need for artificial variance inflation, a challenge for particle filters (e.g., Ramgraber et al, 2019Ramgraber et al, , 2020 or the EnKF (Anderson, 2007).…”