Parameter estimation for numerical models can synthesize different types of information into a physically plausible narrative. This is of particular relevance for the discipline of hydrogeology, where informed management demands detailed knowledge of the system, but direct measurements of the relevant subsurface properties are scarce and often of limited spatial representativeness (e.g., Rubin, 2003). The process of inferring subsurface properties from dependent information such as hydraulic head, chemical concentrations, or flow is known as inverse modeling (e.g., Carrera et al., 2005).Unfortunately, as a consequence of the exceptional complexity of many hydrogeological systems (Figure 1), there usually exists more than a single plausible explanation for the observed data (Linde et al, 2015(Linde et al, , 2017Moeck et al., 2020). Variations in aquifer depth, sediment properties, atmospheric and hydrogeological forcing, anthropogenic influences, and complex geological features interact with each other and can create similar hydraulic responses in different arrangements. The consequence of this has been summarized succinctly by Poeter and Townsend (1994): "A true evaluation of the possible subsurface configurations and their impact on the decision at hand is the only honest approach to groundwater analyses." and hence surmised that "The era of drawing conclusions on the basis of deterministic flow and transport models has come to a close."Where deterministic models only seek a single promising model configuration, stochastic approaches based on Bayesian statistics explore multiple alternative configurations at once. This process hopes to identify ambiguities in order to endow model predictions with reliable uncertainty estimates. Unfortunately, 25 years later, Poeter and Townsend (1994)'s prediction has yet to fully come to pass. While the need for probabilistic groundwater models has been widely acknowledged (e.g.
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.
The increasing use of wireless sensor networks and remote sensing permits real-time access to environmental observations. Data assimilation frameworks tap into such data streams to autonomously update and gradually improve numerical models. In hydrogeology, such methods are relevant in areas of long-term interest in water quality and quantity, for example, in drinking water production. Unfortunately, accurate hydrogeological predictions often demand a degree of geological realism, which is difficult to reconcile with the operational limitations of many data assimilation frameworks. Alluvial aquifers, for example, are sometimes characterized by paleo-channels of unknown extent and properties, which may act as preferential flow paths. Gradually optimizing such fields in real-time or quasi-real-time settings is a formidable task. Besides subsurface properties, ill-specified model forcings are a further source of predictive bias, which an optimizer could learn to compensate. In this study, we explore the use of a quasi-online optimizer based on the iterative batch importance sampling framework for a groundwater model of a field site near Valdobbiadene, Italy. This site is characterized by the presence of paleo-channels and heavily exploited for drinking water production and irrigation. We use Markov chain Monte Carlo steps to explore new parameterizations while maintaining consistency between states and parameters as well as conformance to a multipoint statistics training image. We also optimize a preprocessor designed to compensate for potential bias in the model forcing. We achieve promising and geologically consistent quasi-real-time optimization, albeit at the loss of parameter uncertainty. Numerical modeling plays a crucial role in informing such hydrogeological practices (Reilly & Harbaugh, 2004). The parameterization of groundwater models demands a full characterization of subsurface properties, information which can only partially be obtained from direct measurements. Consequently, modelers often find themselves tasked with the synthesis of plausible parameter fields from different sources of information (
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