Abstract
AbstractUncertainty estimation plays an important part in practical hydrogeology. With most of the subsurface unobservable, attempts at system characterization will invariably be incomplete. Uncertainty estimation, then, must quantify the influence of unknown parameters, forcings, and structural deficiencies. In this endeavor, numerical modeling frameworks can resolve a high degree of subsurface complexity and its associated uncertainty. Where boundary uncertainty is concerned, however, numerical frameworks can be restrictive. The interdependence of grid discretization and its enclosing boundaries render exploration of uncertainties in their extent or nature challenging. The analytic element method (AEM) may be an interesting complement, as it is computationally efficient, economic with its parameter count, and does not require enclosure through finite boundaries. These properties make AEM well suited for uncertainty estimation, particularly in data‐scarce settings or exploratory studies. In this study, we explore the use of AEM for flow field uncertainty estimation, with a particular focus on boundary uncertainty. To induce diverse, uncertain regional flow more easily, we propose a new element based on a Möbius transformation. We include this element in a simple Python‐based AEM toolbox and benchmark it against MODFLOW. Coupling AEM with a Markov Chain Monte Carlo routine using adaptive proposals, we explore its use in a synthetic case study. We find that AEM permits efficient uncertainty estimation for groundwater flow fields, which may form a basis for stochastic Lagrangian transport modeling or can support advanced model design by informing the placement of numerical model boundaries.
Highlights
Groundwater modeling plays an important role in practical hydrogeology
We explore the use of analytic element method (AEM) for flow field uncertainty estimation, with a particular focus on boundary uncertainty
We find that AEM permits efficient uncertainty estimation for groundwater flow fields, which may form a basis for stochastic Lagrangian transport modeling or can support advanced model design by informing the placement of numerical model boundaries
Summary
Groundwater modeling plays an important role in practical hydrogeology. In a discipline in which neither the system nor its properties can be observed in its entirety, it is the task of models to establish spatial and temporal continuity between point-wise information. Prescribed in- or outflow boundary conditions would be a more versatile choice to represent the uncertain influence of regional flow in a finite domain, but are very difficult to obtain and are rarely used Recognizing this limitation, simulation frameworks such as MODFLOW 6 (Langevin et al, 2017) have since implemented multi-level setups which allow the use of simpler, large-scale models to define the flow boundaries of the main area of interest. Its natural approach to complexity (start simple, add more complexity as required) can make it more suitable for exploratory analyses than numerical models, which are often explored the other way around (start complex, simplify by aggregating grid parameters) Toward this end, we (b) propose a new element based on a Möbius transformation, which can directly induce curving, diverging, or converging regional base flow within a circular model domain of arbitrary size. We provide a modular Python code coupling a simple AEM implementation to a Markov Chain Monte Carlo (MCMC) routine, intended for preliminary explorations of plausible flow fields during model conceptualization, or simple Bayesian flow field inference in data-scarce environments
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