Abstract Data assimilation (DA) plays a critical role in reducing simulation uncertainty in hydrological systems by leveraging available observations to estimate model states and/or parameters. Among DA methods, the ensemble smoother (ES) has emerged as an attractive option for parameter estimation due to its computational efficiency and straightforward implementation. For problems involving nonlinear processes and non‐Gaussian distributions, the deep learning (DL)‐based ES demonstrates superior performance over its Kalman‐based counterpart . However, least‐squares formulation of the innovation vector is optimal only under Gaussian error structure and linear mappings; when the relevant distributions are non‐Gaussian and/or the system is highly nonlinear, the conventional innovation vector may not adequately encode the observation‐model mismatch structure required for effective updates. This study introduces a generalized formulation of , where the conventional innovation vector is replaced with a data‐driven, learned representation that is more flexible and can deviate from normality. We evaluate the proposed method across surface and subsurface hydrological applications, encompassing systems of varying dimensions (from low to high) and parameter distributions (from Gaussian to non‐Gaussian). Our results show that under non‐Gaussian conditions, outperforms both and , highlighting its potential as a robust and flexible DA tool for hydrological systems. Overall, tends to deliver comparable or lower root‐mean‐square errors and continuous ranked probability scores for parameter estimation and/or data matching, while also exhibiting comparable or improved prior‐to‐posterior contraction and coverage diagnostics relative to the other two approaches.
Zhang et al. (Mon,) studied this question.