Dispersion coefficients and the average solute transport velocity are pivotal for groundwater solute transport modeling. Accurately and efficiently determining these parameters is challenging due to difficulties in directly correlating them with pore-space structure. To address this issue, we introduced the Physics-enhanced Convolutional Neural Network-Transformer (PhysenCT-Net), an innovative model designed to concurrently estimate the longitudinal dispersion coefficient and average solute transport velocity in three-dimensional porous media. PhysenCT-Net exhibited excellent predictive performance on unseen testing datasets and significantly reduced computational demands. Comprehensive evaluations confirmed its robust generalization across various flow conditions and pore structures. Notably, the longitudinal dispersion coefficient predictions closely align with established empirical relationships involving flow velocity, affirming the model’s physical interpretability and potential to aid in simulating transport phenomena in porous media.

In various research fields such as hydrogeology, environmental science and energy engineering, geological formations with fractures are frequently encountered. Accurately characterizing these fractured media is of paramount importance when it comes to tasks that demand precise predictions of liquid flow and the transport of solute and energy within them. Since directly measuring fractured media poses inherent challenges, data assimilation (DA) techniques are typically employed to derive inverse estimates of media properties using observed state variables like hydraulic head, concentration, and temperature. Nonetheless, the considerable difficulties arising from the strong heterogeneity and non-Gaussian nature of fractured media have diminished the effectiveness of existing DA methods. In this study, we formulate a novel DA approach known as PEDL (parameter estimator with deep learning) that harnesses the capabilities of DL to capture nonlinear relationships and extract non-Gaussian features. To evaluate PEDL’s performance, we conduct two numerical case studies with increasing complexity. Our results unequivocally demonstrate that PEDL outperforms three popular DA methods: ensemble smoother with multiple DA (ESMDA), iterative local updating ES (ILUES), and ES with DL-based update (ESDL). Sensitivity analyses confirm PEDL’s validity and adaptability across various ensemble sizes and DL model architectures. Moreover, even in scenarios where structural difference exists between the accurate reference model and the simplified forecast model, PEDL adeptly identifies the primary characteristics of fracture networks.

The direct acquisition of the permeability of porous media by digital images helps to enhance our understanding of and facilitate research into the problem of subsurface flow. A complex pore space makes the numerical simulation methods used to calculate the permeability quite time-consuming. Deep learning models represented by three-dimensional convolutional neural networks (3D CNNs), as a promising approach to improving efficiency, have made significant advances concerning predicting the permeability of porous media. However, 3D CNNs only have the ability to represent the local information of 3D images, and they cannot consider the spatial correlation between 2D slices, a significant factor in the reconstruction of porous media. This study combines a 2D CNN and a self-attention mechanism to propose a novel CNN-Transformer hybrid neural network that can make full use of the 2D slice sequences of porous media to accurately predict their permeability. In addition, we added physical information to the slice sequences and built a PhyCNN-Transformer model to reflect the impact of physical properties on permeability prediction. In terms of dataset preparation, we used the publicly available DeePore porous media dataset with the labeled permeability calculated by pore network modelling (PNM). We compared the two transformer-based models with a 3D CNN in terms of parameter number, training efficiency, prediction performance, and generalization, and the results showed significant improvement. Combined with the transfer learning method, we demonstrate the superior generalization ability of the transformer-based models to unfamiliar samples with small sample sizes.

There is an approximately one-year observation gap of terrestrial water storage anomalies (TWSAs) between the Gravity Recovery and Climate Experiment (GRACE) satellite and its successor GRACE Follow-On (GRACE-FO). This poses a challenge for water resources management, as discontinuity in the TWSA observations may introduce significant biases and uncertainties in hydrological model predictions and consequently mislead decision making. To tackle this challenge, a Bayesian convolutional neural network (BCNN) is proposed in this study to bridge this gap using climatic data as inputs. Enhanced by integrating recent advances in deep learning, BCNN can efficiently extract important features for TWSA predictions from multi-source input data. The predicted TWSAs are compared to the hydrological model outputs and three recent TWSA prediction products. Results suggest the superior performance of BCNN in bridging the gap. The extreme dry and wet events during the gap period are also successfully identified by BCNN.

Groundwater discharge to headwater streams and concomitant terrestrial dissolved inorganic carbon (DIC) export play a significant role in headwater stream CO2 evasion. However, previous studies rarely examined diffuse groundwater discharge and its impact on headwater stream CO2 evasion, thereby lacking the understanding of the role of diffuse groundwater discharge in terrestrial DIC export and stream CO2 evasion. This study quantified diffuse groundwater discharge along a 43 km semiarid headwater stream by combining hydraulic, isotopic (radon-222) and chemical (electrical conductivity) approaches, and estimated the reach-level CO2 budgets of the stream. Reach-scale water and mass balance modeling yielded highly variable diffuse groundwater discharge rates (n = 16, range: 1.08-7.80 m2/d, mean ± 1 sd: 4.57 ± 1.81 m2/d). Groundwater was supersaturated with CO2 at all sites, with strongly variable CO2 partial pressure (pCO2) and DIC concentrations at 1,223-27,349 μatm and 30-119 mg/L, respectively. Diffuse groundwater discharge dominated terrestrial DIC export to the stream (12-111 g C m-2 d-1, normalized to water surface area). A portion of groundwater dissolved CO2 transported to the stream was emitted to the atmosphere with evasion rates varying at 0.62-3.18 g C m-2 d-1. However, most dissolved CO2 was transformed into HCO3- through carbonate buffering because of the regulation of carbonate equilibrium. Overall, the stream CO2 evasion was driven by carbon transfer but limited by carbon supply. This study provides a bottom-up perspective to understand terrestrial DIC export and stream CO2 evasion in arid and semiarid areas.

Hot extremes may adversely impact human health and agricultural production. Owing to anthropogenic and climate changes, the close and dynamic interaction between drought and hot extremes in most areas of China need to be revisited from the perspective of nonstationarity. This study therefore proposes a time-varying Copula-based model to describe the nonstationary dependence structure of extreme temperature (ET) and antecedent soil moisture condition to quantify the dynamic risk of hot extremes conditioned on dry/wet condition. This study proposed a new approach to identify the soil moisture driving law over extreme temperature from the point view of tail monotonicity and nonstationary risk assessment. Owing to the LTI-RTD (left tail increasing and right tail decreasing) tail monotonicity for dependence structure of these two extremes derived from most areas, the driving laws of soil moisture over ET follows DDL1-WDL1 laws (DDL1: drier antecedent soil moisture condition would trigger a higher risk of ET; WDL1: wetter antecedent soil moisture condition would alleviate the occurrence risk of ET). Because of the spatiotemporal divergence of sensitivity index derived from tail monotonicity (SITM), we can conclude that the spatial and temporal heterogeneity of response degree of ET over the variations of antecedent dry/wet conditions is evident. Incorporation of nonstationarity and tail monotonicity helps identify the changes of driving mechanism (laws) between soil moisture and hot extremes. From the comparison of different kinds of nonstationary behaviours over the spatial distribution of conditional probability of ET (CP1), the dependence nonstationarity can impose greater variations on the spatial distribution of conditional risk of ET given antecedent dry condition (CP1).

The flow regime is of vital importance for the sustainable development of both human society and aquatic biota. Alterations in natural streamflow will modify the stability and biophysical distribution of river conditions, causing a series of adverse ecological and economic consequences. Climate change has been proven to pose potential threats to ecosystems; however, few studies have been conducted to quantify the variations between the flow regime of a future period and pristine natural flow specifically. This study investigates the future impacts induced by the changing climate in the Jinsha River Basin, which is known as the “Asian Water Tower” due to its rich hydroelectric energy resources. The SWAT model is used and calibrated to predict future streamflow. Seven GCMs from NASA NEX-GDDP with one ensemble average under two RCPs (RCP4.5 and RCP8.5) are used for both the NFP (2040s) and the FFP (2080s). The Indicators of Hydrologic Alteration (IHA) software and the river regime index (RRI) are used to assess the potential flow alterations of the Jinsha River. The results show that Pr, Tmax and Tmin all denote increasing trends, with the temperature trends being more obvious. For interannual alterations in flow regimes, most IHA values show moderate and high changes in all predicted conditions. In regard to the intra-annual changes, the results of the RRI show that river flow tends to be more concentrated in wet seasons than in cold seasons and denote evident seasonality and transience with advanced overall peaks of the river system. These findings together indicate that the flow patterns may have noticeable changes corresponding to the natural river regime.