A Hybrid Data Assimilation Approach Integrating Kalman With Deep Learning‐Based Updates for Nonlinear and Non‐Gaussian Groundwater Systems

Abstract In hydrological research, data assimilation (DA) is a powerful tool for integrating observational data with numerical models, significantly enhancing predictive accuracy. However, nonlinear groundwater systems often exhibit high‐dimensional and non‐Gaussian characteristics in observations, parameters, and state variables, posing substantial challenges for traditional DA methods such as Markov chain Monte Carlo and ensemble smoother based on the Kalman update (). To address these challenges, we previously introduced , which replaces the linear Kalman update with a nonlinear deep learning (DL)‐based update, enabling improved handling of the non‐Gaussianity issue. Despite its advantages, is constrained by the computational cost of DL model training and limited utilization of ensemble statistics. In this study, we propose , a hybrid DA approach that integrates Kalman with DL‐based updates to overcome these limitations. Tailored for nonlinear and non‐Gaussian groundwater systems, combines the efficiency and statistical elegance of with the adaptability of . To evaluate , we apply it to a challenging case study involving the joint inversion of eight contaminant source parameters and a 3,321‐dimensional, non‐Gaussian distributed hydraulic conductivity field. Comprehensive numerical experiments are conducted to investigate factors influencing performance, including the number of DL‐based updates, the sequencing of Kalman and DL‐based updates, and the configuration of error inflation factors. The results demonstrate that the hybrid updating strategy reduces computational costs while maintaining stability and reliability in DA outcomes. The optimal variant achieves superior performance compared to and individually, highlighting the benefits of this complementary approach.