| 07 Nov 2025
Joint characterization of heterogeneous conductivity fields and pumping well attributes through iterative ensemble smoother with a reduced-order modeling strategy for solute transport
Abstract. We develop and test an efficient and accurate theoretical and computational framework to jointly estimate spatially variable hydraulic conductivity and identify unknown pumping well locations and rates in a two-dimensional confined aquifer. The approach (denoted as iES_ROM) integrates an iterative Ensemble Smoother (iES) with a Reduced-Order Model (ROM) for solute transport taking place across an otherwise steady-state groundwater flow field. This offers a computationally efficient alternative to the Full System Model (iES_FSM) upon addressing the high computational demands of ensemble-based data assimilation methods, which typically require large ensemble sizes to characterize uncertainties in (randomly) heterogeneous aquifers. Our iES_ROM is constructed through proper orthogonal decomposition. It is then evaluated across a collection of 28 test cases exploring variations in model dimension, ensemble size, measurement noise, monitoring network, and statistical properties of the (underlying randomly heterogeneous) conductivity field. Our results support the ability of iES_ROM to accurately estimate conductivity and identify pumping well attributes under diverse configurations, attaining a quality of performance similar to iES_FSM. When using moderate ROM dimensions (n = 25–30) and ensemble size (i.e., 500–1000), the accuracy of iES_ROM does not vary significantly while computational time is reduced by nearly an order of magnitude. Our approach thus provides a reliable and cost-effective tool for inverse modeling in groundwater systems with uncertain parameters.
Competing interests: At least one of the (co-)authors is a member of the editorial board of Hydrology and Earth System Sciences.
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The paper presents a solid and carefully executed study on coupling a POD-based reduced order transport model with an iterative ensemble smoother for joint estimation of K and well attributes. Results are convincing, and the work is publishable after some focused improvements.
Improve the novelty statement in the Introduction and Conclusions; what is new relative to existing ROM+DA studies: (i) joint estimation of heterogeneous K and hidden pumping well attributes, (ii) reduction of only the transport equation while keeping flow full-order, and (iii) the systematic multi-factor analysis (ROM size, ensemble size, prior stats, noise, snapshot size).
Provide concrete numbers and protocol: how many realizations and time levels are used, whether snapshots come from prior draws or a single reference field, and whether their statistics match those used in the DA experiments. Add a short discussion of how ROM performance might change if the prior used for snapshot generation differs from that used in assimilation. Add also a short discussion (no need for new runs) on how sensitive the ROM is if the prior used for snapshot generation differs from the prior used for DA.
State whether snapshots are mean-centered, and discuss briefly how omitting a separate mean field affects accuracy. Add a short justification of why a “mean + anomalies” representation is less convenient in your iES implementation, and whether it might reduce ROM error.
Make clear which ensemble sizes are realistic for applied hydrogeological problems (e.g. a few hundred to 1000), and present N_MC = 10000 explicitly as a reference benchmark. Emphasize results and cost accuracy trade offs for the practically relevant range.
Use Tables 1–5 and possibly a small schematic/flowchart to clearly show what each group (A–E) varies and why. In the results, slightly condense repetitive descriptions and highlight cross-group patterns and any non-intuitive behaviors (e.g. non-monotonic trends).
In the Conclusions, clearly delimit the domain of validity: 2D confined aquifer, steady-state flow, single non-reactive solute, single well. Briefly comment on expected challenges and required modifications for transient flow, multiple wells, or reactive/density-dependent transport.
Overall, these changes are mostly clarifications and presentation refinements; the core methodology and results appear sound.