In hydrological research, data assimilation (DA) is a powerful tool for integrating observational data with numerical models, significantly enhancing predictive accuracy. However, non-linear 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 (ES(K)). To address these challenges, we previously introduced ES(DL), which replaces the linear Kalman update with a non-linear deep learning (DL)-based update, enabling improved handling of non-Gaussian issues. Despite its advantages, ES(DL) is constrained by the high computational cost of DL model training and limited utilization of ensemble statistics. In this study, we propose ES(K-DL), a hybrid DA approach that integrates Kalman with DL-based updates to overcome these limitations. Tailored for non-linear and non-Gaussian groundwater systems, ES(K-DL) combines the computational efficiency of ES(K) with the adaptability of ES(DL). To evaluate ES(K-DL), we apply it to a challenging case study involving the joint inversion of eight contaminant source parameters and a 3,321-dimensional non-Gaussian 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 ES(K-DL) variant achieves superior performance compared to ES(K) and ES(DL) individually, highlighting the benefits of this complementary approach.  

To reduce simulation uncertainty and improve process understanding of hydrological systems, integrating models with observations through data assimilation techniques is paramount. Among these, the ensemble smoother (ES) stands out for its ease of implementation and high computational efficiency. When tackling problems involving non-linear processes and non-Gaussian distributions, leveraging deep learning (DL) within ES, termed the ES(DL) method, proves superior to the Kalman-based counterpart. However, the original ES(DL) method is constrained by the traditional paradigm that builds a mapping from the innovation vector (i.e., the difference between observations and model predictions) to the update vector (i.e., the difference between posterior and prior state/parameters). In this study, we introduce a generalized form of ES(DL), where the traditional ES(DL) approach becomes its special case. We explore the optimal implementation of ES(DL) through surface and subsurface scenarios, spanning various dimensions (low to high) and parameter distributions (Gaussian to non-Gaussian). Notably, certain implementations of ES(DL), which diverge significantly from the traditional approach, can yield similar or even better outcomes, especially under the non-Gaussian condition. While this study’s focus lies on the smoothing approach for parameter estimation, the proposed formulation can be extended to filtering problems, facilitating model state updates.

Hydrology has a long history due to its early origin, but it is still considered young due to lack of a solid scientific foundation as a natural science. To lay a solid foundation of hydrology, field experimentation is crucial for investigating hydrological processes and revealing hydrological mechanisms. Professor Wei-Zu Gu (1932–2022) was an internationally renowned scientist in the field of hydrology and is recognized as the greatest pioneer of experimental hydrology and isotope hydrology in China. He created the Hydrohill experimental catchment, which serves as both a great public works for experimental hydrology and a valuable legacy for future researchers to conduct hydrological experiments. This legacy represents an innovative infrastructure that bridges the gap between natural watershed experiments and artificial physical models. The Hydrohill is an intensively-instrumented experimental catchment, allowing for comprehensive measurement of elements of the hydrologic cycle and their tracing indicators in a sophisticated manner. To provide an in-depth understanding of the Hydrohill, this paper presents its short history, experimental objectives, site description (including location, construction, and instrumentation), site conditions (such as soil, hydrological and meteorological properties), and contributions to hydrologic science. We pay our respects to Professor Gu for his hard work in creating the Hydrohill for experimental hydrology and enhancing our understanding of hydrological processes and mechanisms. Finally, we hope that with healthy operation at Chuzhou Scientific Hydrology Laboratory (CSHL) along with support from Professor Gu’s friends, CSHL will enable the continued growth of the Hydrohill so that it can address some unsolved problems in hydrology.

Knowledge of soil properties is essential for risk assessment of vapor intrusion (VI). Data assimilation (DA) provides a valuable means to characterize contaminated sites by fusing the information contained in the measurement data (such as concentrations of volatile organic chemicals). Nevertheless, the application of DA in risk assessment of VI is quite limited. Moreover, soil heterogeneity is often overlooked in VI-related research. To fill these knowledge gaps, we apply a state-of-the-art DA method based on deep learning (DL), that is, ES(DL), to better characterize the contaminated sites in VI risk assessment. The effectiveness of ES(DL) is well demonstrated by three representative scenarios with increasing soil heterogeneity. The results clearly show that ignoring soil heterogeneity will significantly undermine one’s ability to make reasonable decisions in VI risk assessment. As a preliminary attempt of applying an advanced DA method in VI research, this work provides implications for the potential of using DL and DA in complex problems that couple hydrological and environmental processes.