Reply on RC2

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.