Rapid, reproducible, and wrong? Exploring sequential data assimilation as a coping mechanism for model structural error in groundwater decision support modeling

Model structural error, arising from the inevitable simplification and abstraction modelers must make of complex real-world system and processes, has been shown to produce biased predictions as a direct result of parameter compensation during data assimilation. The specter of structural error especially plagues groundwater decision support modeling, since the inverse methods underpinning calibration and uncertainty analysis favor a computationally efficient and numerically stable model, or in other words, a simpler model. This work explores sequential data assimilation (DA) as a potential coping mechanism for the structural error encountered by simpler models. Unlike traditional batch methods, sequential methods assimilate data in discrete time intervals or ‘cycles’, and simultaneously estimate model state along with model parameters in order to advance the model forward in time. We hypothesize that the estimable model states in sequential DA afford more flexible and appropriate receptacles for the noise introduced into observations from model structural error. Using a paired complex-simple model approach, we empirically evaluate the predictive outcomes of batch and sequential DA in two model error scenarios: first where error arises from coarser resolution in the simple model, and second where error arises from both coarser resolution and fixed pumping rates in the simple model. Overall, we find that both formulations perform well in both history matching and forecasting when employing a high-dimensional parameterization stance, that is, treating all properties and stresses as uncertain and adjustable during the inversion process. When uncertain parameters are removed from the inversion process, however, the data assimilation process is degraded in different ways for batch and sequential formulations. These results have implications for groundwater decision support modeling as they underscore the pitfalls of fixing parameters a priori, such as with pumping, and present a proof of concept for using adjustable model states to cope with model error in decision support modeling contexts.