Reconstructing contaminant plume dynamics from sparse well data using Dynamic Mode Decomposition: Effects of sampling density and support scale

Multiscale heterogeneity in hydraulic conductivity and the sparse, finite-support nature of well measurements complicate the reconstruction of contaminant plume dynamics in natural aquifers. While data-driven reduced-order methods provide a computationally efficient alternative to fully resolved simulations, their sensitivity to observational design remains insufficiently examined. This study evaluates the ability of Dynamic Mode Decomposition (DMD) to recover and extrapolate concentration fields in heterogeneous porous formations using spatially sparse, volume-averaged observations. High-fidelity simulations serve as reference solutions across varying heterogeneity levels and Péclet numbers, enabling systematic assessment of how reconstruction accuracy depends on transport regime, sampling density, and measurement support scale. DMD captures dominant plume structures when observational density is sufficient to resolve the underlying heterogeneity. Performance is strongly governed by the interaction between advective–dispersive dynamics and observational scale: increased sampling density and larger measurement support enhance stability by attenuating small-scale variability, whereas sparse observations in strongly advective, highly heterogeneous settings reduce extrapolation reliability. These results quantify how observational density and sampling support influence data-driven plume reconstruction, offering preliminary guidance for monitoring strategy design under similar idealized transport conditions.