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• The groundwater flow equation of mean water table was used in inversions. • The total relative error of temporal heads and mean heads was proposed. • Uncertainties of real mean heads by t Location-scale distribution were more accurate. • Uncertainty of the mean water table depth in the CONUS was analyzed. • The results by our inverse method are more accurate than those by other models. Because of spatiotemporal observation gaps and prohibitive computational cost, estimating uncertainty of mean water table depth in the continental scale is a challenging problem. Based on the groundwater flow of mean water table, we first analyzed uncertainty of the mean water table depth in the contiguous US using a highly parameterized linear inverse method with unknown boundary condition and source/sink terms. To estimate uncertainty of the mean heads, the total relative errors of temporal heads and mean heads for all observed wells with more than one head instead of the relative error of temporal heads and mean head for each observed well was proposed to obtain t Location-scale and Gaussian distributions of the total relative errors in the synthetic cases. The results indicate that uncertainties of the mean heads by t Location-scale distribution are more accurate than those by Gaussian distribution. Then, we applied the inverse method and t Location-scale distribution of the total relative errors in the contiguous US to estimate uncertainty of the mean water table depth during 1900–2016. The results demonstrate that uncertainty in the K values did not result in large uncertainty of the mean water table depth. Uncertainty of the mean water table depth in the contiguous US was first estimated based on variation of hydraulic conductivity and the observed mean water table, where 100 realizations of the mean water table depth were obtained by t Location-scale distribution. The results demonstrate both the feasibility and high precision of the inverse method. [ABSTRACT FROM AUTHOR]

• Hydrological studies carried out in an area having five nuclear power plants (NPPs) in operation. Most of the groundwater samples are situated closer to the river index, which indicates that shallow groundwater is mainly recharged by the surface water sources. On the other hand, mixed recharge is associated to the samples located between the river and rain indices. • Groundwater residence time was investigated by analyzing CFCs-12,11,113 and H-3 in groundwater samples. Tracer LPM model reveals that most of the groundwater samples have fresh recharge and classified as young water (14–59 years old). • Groundwater flow direction assed by using multi-well tracer technique and groundwater table contours. Data indicate that the groundwater generally flows towards river in south-west direction, suggesting that the south-western region of the study area is susceptible to groundwater contamination. • The real and filtration velocity were 22.2 cm/day and 10.94 cm/day, respectively, whereas the estimated in-situ effective porosity of the aquifer is 49.3 %, which is in good agreement with the porosity of fine to medium sand. • The hydraulic conductivity of the aquifer varies from 48 to 278 m/day with increasing trend from North-East to South-West direction in the study area. The average hydraulic conductivity was 139 m/day. The study conducted on "Chashma-Mianwali" area to investigate the impact of canals, lake and rivers flowing through the area on groundwater recharge and dynamics of the area. Isotopic and noble gases data suggested localize impacts of canals, lake and river on groundwater recharge. Groundwater residence time using Tracer Lump Parameter Model (LPM), and Chloroflourocarbons (CFCs) data suggest a very young water in the range of 14–59 years. The real and filtration velocities of groundwater were found to be 22.2 cm/day and 10.94 cm/day, respectively, in south-west direction and in-situ effective porosity of the aquifer was 49.3 %. The hydraulic conductivity of the aquifer was estimated with average value of 143 m/day with Transmissivity (T) of 43,127 m2/day. [ABSTRACT FROM AUTHOR]

• Multiple machine-learning algorithms were used to develop new PTFs for SHP prediction. • 1-km resolution maps of 0–2 m SHPs were generated for China's arid region. • The new PTFs had a higher accuracy than other commonly used PTFs. • Regional terrestrial biosphere modeling by using global SHP datasets should be endorsed with caution. Accurately quantifying the mass (water, nutrients, and carbon) and energy exchange processes between the Earth's atmosphere, biosphere, and lithosphere requires the accurate parameterization of soil hydraulic properties (SHPs) and their spatial heterogeneity. Because direct measurements of SHPs are difficult, time-consuming, and impossible at larger spatial scales, various pedotransfer functions (PTFs) have been developed in the last few decades, providing divergent estimates of SHPs from readily measurable variables. However, existing PTFs are mostly developed for specific regions and may not be suitable for other pedoclimatic conditions. Here, PTFs were developed using multiple machine-learning algorithms to estimate SHPs and examined the weaknesses and strengths of each method in estimating the average and variability of SHPs across China's arid region. The optimal PTFs were applied to a 1 × 1 km2 regional map of texture and bulk density, thus producing maps of the saturated hydraulic conductivity (K s), the parameters of the van Genuchten (VG) formulation, field capacity (θ fc), wilting point (θ wp), plant available water (θ pa), and soil macroporosity (ϕ m) in the 0–2 m soil profile throughout the region. The results indicate that the ensemble model with the averaging method (EMA) is the most robust for estimating all SHPs. The EMA-PTFs for K s yielded the best performance for sand textures, followed by sandy loam, loam, silty loam, silty clay loam, loamy sand, and clay loam textures. There were no significant differences in estimating soil water retention curve parameters among the different soil texture classes. Using the same observed data set, we demonstrated that the new EMA-PTFs outperformed those of existing PTFs, such as Rosetta and HYPRES, with RMSE values decreasing by 25–83 % depending on the SHPs. Furthermore, our SHP datasets exhibited significantly deeper soil profiles and higher accuracy than other available regional and global SHP products. The VG retention parameter α shows the greatest variation vertically throughout the 0–2 m soil profile, followed by ln(K s), θ r , θ pa , θ fc , θ wp , ϕ m , θ s and n. All SHPs exhibit much lower variability in the desert than in other areas, likely due to the homogeneous particle size distribution of desert areas. This study provides more accurate SHP estimates in China's arid region than the existing SHP products by developing advanced PTFs and highlights the inconsistency in SHPs among different global or regional products; the uncertainties induced by PTFs should thus be considered in future terrestrial biosphere modeling. [ABSTRACT FROM AUTHOR]

• The BR function is robust to heterogeneous and noisy data. • The BR function can successfully be applied in ANNs to describe the SHCC. • The second-order derivative functions performed better than the first-order. • The GDM function had poor accuracy and reliability in estimating SHCC. The estimation of the soil hydraulic conductivity curve (SHCC) through machine learning tools for determining pedotransfer functions (PTFs) is essential in various agriculture, hydrological, and environmental management-related studies. The accuracy and reliability of machine learning tools such as backpropagation neural network (BNN) for estimating SHCC mainly depends on the optimization of its architecture, specifically the selection of the network training algorithms. By comparing the performance of network training algorithms, various researchers related to agriculture science, hydrology and environmental can choose the appropriate algorithm that provides the best balance of accuracy, speed, computational efficiency, and robustness for hydrological modeling purposes. Therefore, the present study assessed and compared the performance of 4 training algorithms including, gradient descent with momentum (GDM), Quasi-Newton (QN), Bayesian regularization (BR) and Levenberg-Marquardt (LM) for the estimation of the parametric-based PTFs of the van Genuchten-Mualem hydraulic conductivity equation as novelty of this research, which has not been investigated, so far. In this study four GDM, BR, LM and QN-based PTFs were derived to estimate the SHCC from different combinations of readily available properties of 86 soil samples from UNSODA database. The integral root mean square error (IRMSE) and coefficient of determination (R 2) and were used to assess the estimations. The performance of BR algorithm-based PTFs on testing data varied from 4.634 to 6.690 with average 5.476 cm day−1 in terms of IRMSE , and 0.958 to 0.966 with average 0.963 in terms of R 2, which provided better simulation than other training algorithms. The outcome of the present study on testing data showed that the BR algorithm was stable and robust to heterogeneous and noisy data compared to other training algorithms. Finally, development of accurate and reliable PTFs using efficient algorithms can play a crucial role in soil resource assessments, water resource management, irrigation planning, and designing effective drainage systems, because accurate knowledge of SHCC is vital for optimizing irrigation and fertilization practices and minimizing wastage of water and nutrients. [ABSTRACT FROM AUTHOR]

• Soil moisture fluctuations invert saturated hydraulic conductivity (K s) • Multi-frequency fluctuations contain non-redundant information, benefiting K s inversion. • Inversion algorithm can accommodate nonlinear data based on VG model. Soils are heterogeneous at multiple scales. Estimates of spatially varying saturated hydraulic conductivity (K s) of soils dictate the resolution of modeling water flux based on the Richardson-Richards equation (RRE), but direct measurements of K s everywhere in a field are practically impossible. As a result, this study develops an inverse approach to estimate spatially varying K s utilizing soil moisture observations driven by periodic weather variability at different frequencies. Using a numerical solution to vertical, one-dimensional RRE based on Gardner-Kozeny (GK) model in a heterogeneous soil with periodic flux, we investigate the spatial cross-correlation between K s and observations (the amplitude or phase shift) of soil moisture fluctuation at different frequencies without high computational cost in the conventional time-domain model. These correlation patterns vary with the spatial location and frequency, suggesting that soil moisture fluctuations at different frequencies at one monitoring location carry non-redundant information about the heterogeneous distribution of K s. Guided by cross-correlation maps, several inverse experiments reveal the effectiveness of multi-frequency data of soil moisture fluctuation for mapping the heterogeneous distribution of K s. Monte Carlo simulations suggest that multi-frequency data can provide non-redundant and useful information about the estimation of heterogeneous K s. Synthetic data based on a commonly-applied nonlinear van Genuchten-Mualem (VG) model is then tested in our inversion algorithm. The results indicate that the spatial pattern of the inverted GK K s is very similar to that of the VG K s , although these two parameters are inherently not identical since they are used in two different models. In addition, the inverted GK K s can successfully predict the soil moisture fluctuation of frequencies that were not used in the inversion. Despite having no field experiments to validate this model, we believe this is the first attempt to conduct frequency-domain inverse modeling in vadose zone hydrology using soil moisture fluctuation. [ABSTRACT FROM AUTHOR]

• Development of reference curves to describe temporal variation in soil properties. • Two-step model is proposed to obtain soil hydraulic properties at any time step. • Reduce need for extensive field measurements and numerical computations. • The developed model is validated with numerical and experimental data. Accurate knowledge of temporal variability in soil hydraulic properties (SHPs) can improve the prediction capability of flow and transport models. Lab and field measurements for determining SHPs at multiple timescales are expensive and time-consuming. Further, the existing Fokker-Plank equation (FPE) based numerical and analytical models for describing temporal variation in SHPs require parameterization. In this study, a scaling model is proposed to describe temporal variation in SHPs of four different soils. As field studies related to temporal variation in SHPs are limited, first synthetic temporally varying SHPs, soil water characteristic curves and hydraulic conductivity curves are generated using the analytical solution of FPE. Functional normalization approach is then used to develop reference curves and to obtain scale factors at different time-steps. The time-varying scale factors and the initial SHPs are related by two-step regression equations. The reference curves and the regression equations together can be used to estimate SHPs at any time given the initial SHPs. The developed model is validated using a 5-fold cross validation method and with experimental data at two study sites. The average percentage error in predicted van Genuchten parameters (θ s , n and K sat) except for α are mostly less than 10 %. The performance of the proposed model is comparable to that of FPE analytical model for experimental data. The proposed method holds promise for describing temporal variation in SHPs using only the initial SHPs. [ABSTRACT FROM AUTHOR]

• A physical laboratory model was designed and used for tests with varying conditions. • The increase in the vadose zone thickness will intensify the buffer effect. • Karstification degree impacts infiltration differently with or without epikarst. • Epikarst influences the soil layer's drainage channel and storage capacity. Groundwater in karst systems is a vital resource, which is often highly vulnerable to contaminants that infiltrate through the vadose zone. Understanding the processes of water and contaminant infiltration in the vadose zone is extremely important for protecting and managing karst water resources. A laboratory-scale physical model based on a typical conceptual model of the karst vadose zone was constructed to characterize the influence of the rainfall intensity and internal structure on the infiltration process and solute transport in the karst vadose zone under controlled conditions. Five factors, including the rainfall intensity, the surface slope, the degree of karstification, the thickness of the transfer zone, and the existence of epikarst, were considered in laboratory experiments. A corresponding lumped-parameter model was subsequently developed to further analyze and investigate the water and solute infiltration processes in the laboratory scale physical model. Recession- and breakthrough curves generated from the lab experiments and the water and solute loss from each reservoir generated from the simulation results were analyzed. The downward trend of breakthrough curves' peak value and the variation of solute loss's proportion in three rainfall events demonstrate that both the increase in thickness and karstification degree will intensify the buffer effect of the karst vadose zone, and this buffer effect is mainly affected by the slow flow system which can be inferred from the increasing percentage of cumulative discharge of slow reservoir (q S). With increasing karstification degree, the recession coefficient (α) exhibits opposite trends depending on the existence of epikarst or not, indicating the karstification degree has a more significant effect on hydraulic conductivity (K) when an epikarst is present while affecting effective porosity (φ) more noticeably in the absence of epikarst. The rainfall intensity affects the results of both experimental and numerical simulation most significantly. The percentage of discharge and solutes flowing from the slow reservoir (q S and m soil_S) have negative correlations with rainfall intensity, suggesting a greater influence on fast flow with increasing rainfall intensity. [ABSTRACT FROM AUTHOR]

• A novel approach is developed for groundwater contaminant sources identification. • The approach integrates ensemble Kalman filtering and multi-level factorial analysis. • The individual and interactive effects of sources of uncertainty are revealed. • The performance of the approach is deeply evaluated by two cases. The ensemble Kalman filter (EnKF) is recognized as a widely used approach for groundwater contamination sources (GCSs) parameters identification. The identification accuracy is affected by the quantification of sources of uncertainty (such as random disturbances on model inputs and measurements) in the assimilation process, but few studies have revealed the contributions of different sources of uncertainty on identification accuracy. To this end, this study developed an innovative multi-level factorial data assimilation (MFDA) approach, which integrates ensemble Kalman filtering and multi-level factorial analysis, to comprehensively reveal the impact of sources of uncertainty on the GCSs parameters identification accuracy for the first time. Not only did it explore the direct impact of individual sources of uncertainty on the GCSs parameters identification accuracy, more importantly, it also revealed the composite ones from multi-parameter interactions among these sources of uncertainty. The developed MFDA approach quantified the contributions of multiple sources of uncertainty, including model input data error (i.e. precipitation), model parameter error (i.e. hydraulic conductivity), contaminant concentration measurements error, and ensemble size. And the feasibility of the developed approach was verified by two hypothetical numerical case studies. The results indicated that: i) it was critically important to reduce the contamination concentration measurement errors to improve GCSs parameter identification accuracy. ii) model parameter and model input data were not sensitive to the identification accuracy. iii) the interaction between sources of uncertainty significantly affects the identification accuracy, which illustrated the interaction cannot be ignored in the identification process. Overall, this study highlights that the developed MFDA approach represents a promising solution for improving GCSs parameters identification accuracy. [ABSTRACT FROM AUTHOR]

• Hydrogeological model using Equivalent Porous Media and Conduit Network approaches. • Discrete features tool application to represent karst conduits with turbulent flow. • Using tracer test results to calibrate the flow rate of karst springs. The current study consisted of the development of a hydrogeological numerical model in the Lagoa Santa Karst Environmental Protection region, in order to represent the conduit-flow karst springs in the most well-studied karst system in Brazil. Once carbonate aquifers are characterized by a complex 3D pattern with a combination of a double porosity of matrix and conduits, two different modelling approaches were used: Equivalent Porous Medium (EPM), based on Darcy's law, to represent laminar flow in the fractured massif and Conduit Network (CN), using Manning-Stricker Law and the discrete feature tool, to represent the karst conduits with turbulent flow. Modeling was calibrated in a steady-state and simulations of groundwater flow and an evaluation of water exchanges between the karstic aquifer and the other hydrogeological units, were conducted. The model was developed based on data available for many studies carried out in the area, including tracer-derived route data. The calibration results for spring discharges, water levels and mass balance were satisfactory and aligned with modeling good practices. In turn, the hydraulic conductivities and recharge rates obtained by back-analysis were in agreement with literature references. The regional groundwater flow was well represented and indicated how external water entrances can be relevant to explain the higher discharge rates observed in some karstic springs. In addition, the representation of conduits allowed for the simulation of tracer pathways, enabling the inference of potential flow rates to the karstic springs from the particle simulations. [ABSTRACT FROM AUTHOR]

• Analytical solutions for defining the riparian lens extent and saltwater discharge in stratified aquifers are developed. • The applicability of the proposed analytical solution is validated through numerical simulations and sand-tank experiments. • The impact of aquifer stratification on riparian lenses depends on inland boundary conditions. Analytical solutions for defining stable freshwater lenses within saline riparian aquifers ("riparian lenses") are largely limited to homogenous aquifers. However, real-world riparian aquifers typically consist of a surficial layer of low-permeability soils or deposits, the impact of which on the occurrence of riparian lenses has not been investigated. This study develops steady-state, sharp-interface analytical solutions for riparian lens shape and saltwater discharge in a two-layered riparian aquifer. The developed analytical solutions are verified by sand tank experiments and numerical simulations, showing good agreement. The sensitivity analysis based on the proposed analytical solutions suggests that aquifer stratification (i.e., considering a low-permeability layer overlying a high-permeability layer) leads to larger lenses in head-controlled systems (i.e., with the inland constant-head boundary) but smaller lenses in flux-controlled systems (i.e., with the inland constant-flux boundary), compared to the scenario of a homogenous aquifer. The surficial layer with hydraulic conductivity only an order of magnitude lower than the underlying high-permeability layer would have a pronounced effect on lens extent and volume. Importantly, the results suggest that the presence of the surficial low-permeability layer may lead to the outcropping of the groundwater table, favoring the occurrence of saline groundwater seepage near the edge of the river valley (i.e., a phenomenon reported by the field survey of the Murray River floodplains in South Australia). The analytical solution presented in this study can be used to provide a preliminary assessment of riparian lenses in saline stratified aquifers, expanding the applicability of analytical methods to more realistic riparian settings. [ABSTRACT FROM AUTHOR]

• Hydrogeological parameters are main uncertainty source of physical methods • Lag effect of the thick vadose zone limits WTF and dating-based methods • Ignoring the mixing and dispersion may overestimate recharge by 36–48 % for CFC • Aquifer heterogeneity reduces the potential of 14C for recharge estimation • CMB is recommended as the optimal method for GR estimation in the loess area Groundwater recharge (GR) can be estimated with physical, tracer techniques and numerical modelling; however, the uncertainties in these methods have not been fully interpreted. This study selected six methods for actual GR estimation in the saturated zones with different data requirements and method assumptions, including two physical methods (i.e., water table fluctuation WTF and Darcy's law DL) and four tracer techniques (i.e., chloride mass balance CMB, tritium renewal rate TRR, chlorofluorocarbons CFC and 14C dating method CBD). Taking the loess tablelands of China as an example study area, we first analyzed the uncertainties in these methods and then recommended the appropriate methods for GR estimation in regions with thick vadose zones. Overall, the recharge rates from WTF, CMB and CFC (88 ± 24, 98 ± 33 and 53 ± 9 mm/year) were much greater than those from DL, TRR and CBD (10 ± 3, 14 ± 3 and 7 ± 5 mm/year). The differences in estimated GR are closely related to the method parameters, assumptions and temporal scales. Specifically, the model parameters (e.g., specific yield, hydraulic conductivity) exhibit large ranges due to spatiotemporal heterogeneity, and the physical methods are more sensitive to hydrogeological parameters compared with the tracer techniques. The uncertainties related to model assumptions originate from the simplified water/solute movement processes. The lag effect of the thick vadose zone largely limits WTF and TRR, but contributes to CMB. Ignoring the mixing and dispersion effect may overestimate recharge by 36–48 % for CFC, and the heterogeneity of the aquifer reduces the potential of CBD for recharge estimation. Overall, CMB is considered as the most optimal method for estimating GR in the thick loess deposits. This study deepens the understanding of the uncertainties in GR assessment methods in regions with thick vadose zones. [ABSTRACT FROM AUTHOR]

• The recession curves of all features followed the triple permeability model. • The percentages of water capacity in the three aquifer media were calculated. • The average values of EC in fissure, fracture and conduit water were calculated. • A hydrogeological conceptual model was constructed for each karst feature. Understanding of the hydrological behaviors in different karst features is crucial for evaluating the hydrological storage and transfer functions of a karst system. In this study, the Maocun karst underground river system, characterized by typical karst features, was selected as the research area in the southwest region of China. The main objectives of this research are to analyze the hydrogeological structure characteristics of each karst feature and assess water storage capacity in different aquifer media. Frequency distribution curve (FDC) of electrical conductivity (EC) values revealed that recharge sources in the five karst features differed and varied according to the amount of precipitation. All hydrographs of water levels in five karst features were divided into three periods due to the presence of triple aquifer media in the basin. The spatial structure of each feature was interpreted by analyzing the variation characteristics of recession exponential coefficients (λ). Additionally, the ratios of fissure water, fracture water, and conduit water sources were calculated based on the recession curves of water levels. Results showed that fast water flow had the highest proportion in the relatively open subsystem located upstream, while fracture water flow had the lowest proportion. The slow water flow was the main pattern of water storage in the basin. Values of EC in water decreased with a well-connected spatial structure and high hydraulic conductivity. There were significant differences in the values of EC among conduit water, fracture water, and matrix water. These values were calculated using mathematical relationships between EC and water level hydrographs. The results indicated that the EC values in matrix water exceeded 200 μS/cm, while EC values in conduit water/channel water were below 100 μS/cm. Finally, hydrogeological conceptual models were constructed for five karst features based on the depletion characteristics of the aquifer media during each recession period. These characteristics were interpreted using variation curves of EC and hydrographs of water levels. These findings not only elucidated the characteristics of hydrogeological structures in multiple karst features, but also had significant implications for the assessment of karst water sources. [ABSTRACT FROM AUTHOR]

• Conductivity is employed in flow models upon averaged Monte Carlo fields. • A Monte Carlo volume of 10 % of that required for full numerical stability. • A 10 % volume returns stable outputs, i.e. heads and residuals at wells' locations. The knowledge of aquifer systems, their geological setting, their structure, and subsequent modeling is highly uncertain and is usually faced through Monte Carlo-based methods in hydrogeology. One of the most important uncertainty sources for groundwater models is represented by input hydraulic conductivities, related to the aquifer's structure. There are no specific rules when simulating hydraulic conductivity fields within Monte Carlo frameworks to instruct numerical models, and information about employed conductivity fields and their numerical convergence is often not given. This technical work aims to fill this gap by investigating the impact of employing conductivity information upon different volumes of Monte Carlo simulations applied to a real case study. Thus, this work estimates the minimum volumes of Monte Carlo hydraulic conductivity fields to be employed in groundwater flow models for achieving numerically stable (i) boundary conditions, (ii) global model performances, and (iii) local ones such as simulated hydraulic heads. The present results aim to be indicative of similar hydrogeological settings and will serve as a basis for more complex ones and for investigating transport problems. [ABSTRACT FROM AUTHOR]

• Van Genuchten-Mualem soil's steady flux analyzed; analytical solutions developed. • First solution for flow equation without prior assumptions on pressure head's form. • Solution derived using double Maclaurin series and multinomial theorem. • Analytically identify hydraulic parameters, avoiding numerical inverse procedures. Various analytical solutions for steady-state vertical flux through unsaturated soils exist in the literature. These solutions often assume specific hydraulic conductivity forms such as exponential form, rational power form, or power-law form such as the Brooks-Corey model. The van Genuchten-Mualem model is widely used in practical applications of flow through unsaturated soils. It is among the most complicated hydraulic conductivity forms for which no analytical solutions are available. This paper deals with the development of an analytical solution for steady-state vertical flux using van Genuchten-Mualem model. The analytical solution is obtained using Maclaurin series expansions and the multinomial theorem. The general form expresses the depth as a function of pressure head. The analytical solution can be used to model both infiltration (positive flux rate) and evaporation (negative flux rate). The derived analytical solution is compared with numerical results and shows excellent agreement. It can also be used to identify the hydraulic parameters analytically, eliminating the need of a numerical inverse procedure. As far as the author's knowledge, the proposed solution is the first analytical solution dealing with van Genuchten-Mualem model, which is directly derived from the flow equation without any predefined mathematical form of the pressure head. [ABSTRACT FROM AUTHOR]

• A novel T -form hydraulic conductivity (k w) function of frozen soils (HCFF) is proposed. • The proposed T -form HCFF is extended to consider vapor flow and bimodality. • HCFF prediction is supported by statistical k w models and thermodynamic equilibrium. • HCFF prediction is clarified as 3 routes: single SWCC, single SFCC and combining two. Hydraulic conductivity function for frozen soils (HCFF) is crucial for accurately simulating the water transfer process in cold regions, impacting hydrological states and frost heave diseases. However, the HCFF model capturing the relation between hydraulic conductivity and unfrozen water content (θ) or temperature (T) remains an open question. This study delves into HCFF encompassing both empirical and prediction models. This study begins with introducing θ -form and innovative T -form empirical HCFF models, showcasing their solid performance in fitting measured hydraulic conductivity data. Furthermore, the extension of the T -form empirical model to incorporate vapor flow and bimodal soils, through the introduction of maximum vapor conductivity and weighting factors, demonstrates a closer alignment with physical mechanisms and observed trends. In terms of predicting HCFF, the study provides a theoretical foundation through statistical hydraulic conductivity models and thermodynamic equilibrium in frozen soils. Additionally, it clarifies three routes for HCFF prediction—single Soil Freeze Characteristic Curve (SFCC), single Soil Water Characteristic Curve (SWCC), and a combination of the two—and validates their effectiveness through test results and comparison of HCFF prediction outcomes using SWCC and SFCC data from specific soil samples. In practice, the empirical and prediction models are recommended for available hydraulic conductivity data and available SFCC or SWCC data, respectively. Overall, this study not only lays the theoretical groundwork for most prediction models but also presents a valid empirical equation for modeling hydraulic conductivity function tailored specifically for frozen soils. [ABSTRACT FROM AUTHOR]

• A three-dimensional coupled model is used to quantify seepage from lined canals. • The effects of cracks on the hydraulic conductivity of lining materials are evaluated. • A quantitative relationship between hydraulic conductivity and its factors is formed. • The accuracy of empirical formula and numerical model for canal seepage is improved. The equivalent saturated hydraulic conductivity of concrete lining (K sce) is a key parameter to estimate seepage loss, while few studies have quantified the effect of cracks on K sce , potentially leading to significant errors in canal seepage estimation. A three-dimensional numerical model is employed to simulate seepage loss from canals lined with concrete, and then to obtain the value of K sce by an equivalent method. A total of 58,400 scenarios are simulated for different concrete lining and crack conditions (e.g., crack length, crack width, crack location, hydraulic conductivity of concrete (K sc), and underlying soil (K soil)), and the corresponding K sce values are estimated. Results show that the K sce value determined by the equivalent method is reliable in calculating seepage loss from concrete lined canals. K sce increases linearly with crack length with a slope C k , and C k exhibits a power function relationship with crack width, reaching a maximum value when the crack width surpasses the critical threshold, which ranges from 0.424 to 0.435 mm. When the crack width follows a log-normal distribution, the logarithmic value of C k increases linearly with the mean value of the logarithmic crack width. The influence of crack location and K sc on K sce can be negligible. The maximum increment of K sce of a crack is proportional to K soil. Considering the variation of K sce with crack parameters and K soil , equations to determine the value of K sce are established by adding the increment of K sce caused by cracks to K sc. This study establishes a quantitative relationship between K sce and crack parameters, thereby enhancing the accuracy of seepage loss calculations in lined canal under different damage status. [ABSTRACT FROM AUTHOR]

[Display omitted] • Streambed temperatures monitored for 22 months in an international watercourse. • Six methods for deriving seepage flux from temperature time series are benchmarked. • Hydraulic gradient data are utilized to evaluate the consistency of each method. The importance of the interaction between groundwater and surface water is increasingly being recognized for both understanding and managing water systems. Many efforts have been made to characterize and quantify groundwater–surface water exchange. In particular, temperature–based methods have quickly established themselves given their monetary and practical advantages. In the last 15 years, several methods for interpreting passive temperature time series measured in the streambed have been developed. Still, the benchmarking of these methods has only been carried out in specific and distinct hydrological conditions. This article aims to fill this research gap by benchmarking the performance of six commonly used methods for deriving seepage fluxes using a two-year-long temperature time series covering various meteorological and thermal conditions. This work compares three analytical methods that calculate seepage flux using the amplitude and/or phase of the temperature signals, and three numerical methods that use different schemes to inversely solve the one–dimensional heat transport equation in the streambed. The temperature measurements were made in the context of an international dispute between Chile and Bolivia over the status and use of the waters of the Silala River, Northern Chile. Flux estimations are tested against Darcy's flux derived from measured hydraulic gradient and hydraulic conductivity. Flux estimations from the benchmarked methods ranged from −0.5 to 3.5 m/d (with positive fluxes directed downwards), whereas fluxes estimated using Darcy's law ranged from 0.5 to 6 m/d. Results show that the amplitude method is the best–performing method. This method is best suited for estimating the direction of the fluxes, while the method using both the thermal amplitude and phase is best suited for monthly flux trends, and the combination of a Local Polynomial (LP) method and a Maximum Likelihood Estimator (MLE) method (LPMLEn) is appropriate for estimating flux in transient conditions. The use of heat as a tracer proved to be an effective tool for monitoring groundwater–surface water exchange in a river reach for two years, and yielded exchange flux estimates with lower point-scale variability than Darcy's law. [ABSTRACT FROM AUTHOR]

• Transport model guided conditional generative adversarial networks are proposed. • The new networks improve the characterization of groundwater contaminations. • The networks can also help to accurately identify the contaminant sources. Accurate characterization of sources and spatial distribution of contamination remains crucial in groundwater survey and remediation efforts. Nevertheless, conventional geo-statistical methods, like kriging, usually produce overly smooth concentration fields that violate the transport physics. Furthermore, the identification of contaminant sources based on kriging methods may be misleading. As a deep learning approach, Generative adversarial networks (GANs) is being increasingly employed to extract patterns and insights from intricate geospatial data. The conditional variant of GANs (CGANs), can reconstruct complete spatial data from sparse point observations. In this study, we propose a deep learning framework with CGANs for the purpose of groundwater contamination characterization and source identification. In ensure compliance with the principles of transport physics, we use a numerical transport model as the underlying prior model for training the CGANs. Through the adaptation of network architecture, the generator transforms low-dimensional random variables and observation data into concentration images, while the discriminator is responsible for extracting source information from these images. The developed framework is tested through two numerical cases with channelized random hydraulic conductivity fields, which pose a challenge due to the complexity of the concentration fields. The results demonstrate that the proposed method can give accurate results for both contaminant characterization and source identification in groundwater. CGANs excel in reconstructing concentration fields compared to traditional interpolation methods such as Kriging and inverse distance weighting (IDW). Additionally, CGANs offer the capability to estimate uncertainty and exhibit a certain level of error robustness. [ABSTRACT FROM AUTHOR]

• Hydraulic properties of tuff breccia bedrock cores were measured in the laboratory. • Relationships between hydraulic properties and weathering degree were examined. • Core shape and in situ saturated hydraulic conductivity were also determined. • The contributions of matrix and fractures to total water flow are discussed. Although recent studies have emphasized the importance of water flow through bedrock to hydrological processes in headwater catchments, information on the hydraulic properties of bedrock, required for physically characterizing water flow processes, is lacking. In this study, the saturated hydraulic conductivity, K s , and water retention curve of tuff breccia bedrock core were determined in samples collected from boreholes in a headwater catchment in northern Japan. These core-scale properties, together with core shape and in situ K s values, were used to define two groups of bedrock: C M - and C L -class (weakly to moderately weathered) and D-class (highly weathered). Little change in the volumetric water content θ of C M - and C L -class bedrock was observed in the dry range at a pressure head ψ < –200 cm, but slight changes occurred in the wet range (ψ > –200 cm), resulting in low core-scale K s values of 10–8–10–7 cm s−1. Core shape and in situ K s values much larger than the core-scale values suggested that in situ water flow is restricted to fractures, with little contribution of the matrix to total flow. In D-class bedrock, on the other hand, the change in θ with ψ was somewhat larger than in C M - and C L -class bedrock, especially in the wet range, resulting in moderate core-scale K s values of 10–5 cm s−1. These results indicated that flow in D-class bedrock is better represented by matrix flow than by preferential flow through fractures. The hydraulic properties presented herein provide a basis for analyzing subsurface water flow, including through bedrock layers. Those analyses will provide a better understanding of water flow processes in headwater catchments. [ABSTRACT FROM AUTHOR]

• GALDIT inspired, z-number based modeling applied for GW quality assessment. • Method applied for aquifers around Urmia Lake where is facing environmental problems. • Classic GALDIT, Fuzzy logic (FL) and proposed Z-number based methods were compared. • GALDIT parameters and EC considered as inputs and output for FL and Z-number models. • Z-number outperformed GALDIT, FL methods by 85% and 35%, respectively based on HSS. Groundwater (GW) quality assessment is an essential issue, especially in arid and semi-arid regions, due to its critical role in obtaining requirements for freshwater. The GALDIT method is widely recognized as a practical approach for assessing GW susceptibility, which considers six key factors, including the occurrence of groundwater (G), hydraulic conductivity of the aquifer (A), elevation of groundwater above sea level (L), distance from the shoreline (D), impact of existing seawater intrusion (I), and thickness of the aquifer (T). The GALDIT method, being an unsupervised model, has a drawback in that it depends on expert opinion for parameter ranking, leading to an increase in uncertainty. To address this uncertainty and evaluate the susceptibility of the aquifers of Urmia lake basin to saltwater intrusion, this study employed the Z-number which is a novel adaptation of Fuzzy Logic (FL). In contrast to classic FL that does not account for data reliability, the Z-number approach considers both constraints and data reliability, making it a more effective method to manage data uncertainty compared to classic fuzzy models. To illustrate this methodology, the GALDIT parameters (inputs) and Electrical Conductivity (EC) values (outputs) were employed to determine the vulnerability of aquifers. Additionally, the GALDIT method was utilized as a benchmark model to evaluate the inherent vulnerability of aquifers, and its outcomes were compared with those of the proposed model. Upon analyzing the results, it was found that the Z-number Based Modeling (ZBM) not only outperformed the GALDIT method but also enhanced the quality of outcomes by 85% and 35% based on Heidke Skill Score (HSS) and Total Accuracy (TA) criteria compared to the classic FL. [ABSTRACT FROM AUTHOR]

• Critical rainfall for recharging flat sandy lands is 15 mm in hyper-arid desert. • Lateral gravity water flow and surface flow on sandy slopes were identified. • Water flow on sandy slope improves the recharge rate of deep soil from rainfall. • Local rainfall has the capacity to sustain the development of Badain Jaran Lake. • Extreme rainfall does not play a decisive role in the sustaining of desert lake. To elucidate the slope hydrology and their influence on the regional water balance and desert lake development, water migration and soil water conditions were studied in the megadunes of Badain Jaran Desert. Simulated rainfall of 15–60 mm with infiltration depths of ∼ 0.3–0.5 m, the lateral water migration ratios of ∼ 52.9 %-86.2 % and the differential distribution of tracers with depth in the flat sand lands indicate that 15 mm rainfall is the critical rainfall for effective recharge of deep soil water and that there is a shift from piston flow to preferential flow of water during infiltration. Soil micro-bedding and 4.2 % soil gravity water from locally wet surface soils and 6 mm of natural rainfall resulted in lateral migration of the tracer ∼ 1.2 m and 0.4 m in the slope surface and soil respectively, indicate surface flow and lateral gravity water flow resulting from differences in hydraulic conductivity and water-holding capacity of the soil micro-bedding. Soil water storage at 0–4 m depth showed that the bottom of the slope was ∼ 30 mm higher than the middle of the slope after the rainy season and ∼ 9 mm higher before the rainy season; in general the post-rainy season was ∼ 30–40 mm higher than the pre-rainy season. Surface flow and lateral gravity water flow in unsaturated soils increase the intensity of lateral water movement on the slope and improve the effective conversion rate of rainfall to deep soil water, especially below 15 mm. Annual recharge of deep soil water, assessed using soil water change and critical rainfall, will not be less than 8.5 mm and may even reach an upper limit of ∼ 30–40 mm. The megadune slopes respond strongly to local precipitation, which is sufficient to maintain the lake, but extreme precipitation does not play a decisive role. The methods and results provided in this work can advance our understanding of the desert hydrological cycle and water resources. [ABSTRACT FROM AUTHOR]

• Natural internal redistribution reduces overall soil evaporation following surface wetting. • A new analytical framework quantifies surface evaporation rates with concurrent redistribution. • Experiments reveal nonlinear relations between evaporative losses and initial water content. Under natural conditions, infiltrated rainwater redistributed into the soil profile, becomes partially sheltered from surface evaporative losses relative to undrained wet surfaces. Surface evaporation rates and internal drainage dynamics are both sensitive to soil hydraulic properties and initial soil hydration state. We report a novel analytical framework for quantifying surface evaporation rates with concurrent internal drainage, considering soil properties and dynamic surface evaporation resistance. Interplay among soil hydraulic properties, boundary conditions, and atmospheric demand result in nonlinear relationships between cumulative evaporative losses and initial water content. The new analytical solution shows good agreement with laboratory column experiments and literature data. Results highlight the role of soil texture on evaporative losses and the nonlinear effects of initial wetness on evaporation. The largest evaporative losses per rainfall amount are predicted for small rainfall events over initially dry loamy soils due to the detention of infiltrated rainwater near the surface for soils with large porosity and low hydraulic conductivity. The analytical framework uses readily available parameters hence can be implemented in land surface models to explicitly consider how soil properties and rainfall event size affect surface evaporation dynamics. [ABSTRACT FROM AUTHOR]

• Hydraulic and pneumatic tomography studies in fractured media are reviewed. • Field, laboratory, and synthetic studies concerning fractured media are summarized. • Continuum and discrete fracture network modeling approaches are compared. This work reviews various studies of hydraulic and pneumatic tomography for estimation of flow properties of fractured geologic media with hydraulic and pneumatic tomography. The underlying conceptual inversion models can be broadly classified as continuum and discrete fracture network models and deterministic and stochastic approaches. A heterogeneous continuum method applies porous media parameters, while a DFN approach utilizes structural and hydraulic properties of fractures. An overview of field, laboratory, and synthetic studies with applications of hydraulic, pneumatic, or tracer tomography for the characterization of fractured geologic media shows that most studies rely on a heterogeneous continuum conceptual model and geostatistical methods to achieve a solution to the inverse problem. The application of a heterogeneous continuum model results in hydraulic properties that are representative of both fracture and matrix. Therefore, this approach may be more operationally useful for large scale sites with a non-negligible hydraulic conductivity of the rock matrix and high fracture intensity. The flow properties of single fractures can be estimated by applying a discrete fracture network (DFN) model. However, assumptions concerning fracture patterns and corresponding flow properties can lead to an oversimplified geological model. Possibilities for future research include integrating additional data and results from other inversion methods, the application of neural networks for inversion, the implementation of inversion results for the prediction and optimization of processes according to the planned application at the site, and opportunities for real-time inversion. [ABSTRACT FROM AUTHOR]

• A low dimensional lateral subsurface flow model in hillslopes. • Development of a kinematic wave model describing percolation effect. • The proposed model can reproduce percolation effect calculated by the Richards equation. Kinematic wave (KW) models are commonly used for flood forecasting in large river basins, but have limitations in their ability to simulate percolation effects. Here, we suggest an extended KW model wherein the vertical pressure head is under non-hydrostatic conditions. The proposed model uses the Brooks Corey and Mualem models to estimate the water retention curve and unsaturated hydraulic conductivity and adopts the pressure head gradient as a new variable to calculate runoff based on changing water content distributions over time due to percolation. The increase in the pressure head gradient with rainfall infiltration is determined from the relationship between water storage and pressure head distribution, while the decrease in pressure head gradient due to percolation is modeled as exponential decay with time. A comparison of the proposed KW model and a numerical solution of the Richards equation shows that the proposed KW model can reproduce the storage effect caused by percolation, delaying runoff and reducing peak discharge. The agreement between the proposed KW model and the Richards equation is high for soils with high water retention. Conversely, the agreement becomes lower for soil with low water retention or deep soil layer thickness, where the complexity of water content distribution requires further refinement. The proposed model can easily be incorporated into distributed models while low computational cost with keeping the important percolation effects. [ABSTRACT FROM AUTHOR]

• Roles of recharge rate and flow regime on conduit flow are quantified. • Roles of conduit properties, density and morphology on spring discharge. • The percentage of conduit flow over spring discharge is quantified for Silver Springs. The physical controls on the contribution of conduit to spring discharge, quantified as the ratio of conduit flow to spring discharge (Q c / Q), are evaluated through numerical simulations using MODFLOW-Conduit Flow Process. The controlling factors include the ratio of conduit surface roughness to conduit diameter (ε / D), the hydraulic conductivity ratio between the conduit wall and the porous matrix (K c / K), the ratio of groundwater recharge to the hydraulic conductivity of the porous matrix, and conduit density (C d) defined as the ratio of total conduit length to springshed area. For a single conduit, Q c / Q increases with K c / K when flow in the conduit is laminar. When flow is turbulent, Q c / Q is stable and then decreases with ε / D , increases with K c / K , and decreases with R / K due to the limited exchange capacity between matrix and conduit (i.e., small K c / K). The results of hypothetical conduit networks show that Q c / Q increases with C d but is not sensitive to the two sets of network structure evaluated. The sensitivity analysis for the Silver Springs in Florida shows that the spatial heterogeneity of conduit diameter causes higher Q c / Q , and Q c / Q is most sensitive to the conduit density, followed by R / K , and then K c / K. [ABSTRACT FROM AUTHOR]

• A modelling approach to study the fate of infiltrated stormwater. • Centralized infiltration systems increase stream baseflow. • Distributed infiltration systems bring microclimate benefits to urban landscapes. • Important implications to design and spatial arrangement of infiltration systems. Urbanization inevitably involves the replacement of native soils with impervious areas. Doing so reduces infiltration and thus the contribution of groundwater to stream baseflows. The use of infiltration-based Stormwater Control Measures (SCMs) is increasingly common to restore lost baseflows in urban areas, although there remains considerable uncertainty regarding the optimal arrangement of such measures in the landscape, along with the influence of site conditions on the path and fate of infiltrated stormwater. This study aimed to investigate how site conditions and arrangement of infiltration-based SCMs influence the water cycle and stream baseflows. To undertake this study, we used a modelling approach which combined the outputs from a stormwater model (MUSIC) with a 3D groundwater flow model (MIKE SHE). We simulated a range of plausible site conditions and spatial arrangements of SCMs for a hypothetical hillslope situated in two different locations in Australia—Gold Coast (sub-tropical climate) and Melbourne (temperate climate). The modelling results predicted that placing the SCMs in a centralized way at the bottom of the hillslope (End of the pipe approach) could deliver more stream baseflows compared with a distributed network of systems. Placing the SCMs in a distributed manner throughout the landscape was predicted to deliver local benefits such as enhanced evapotranspiration and augmented soil moisture. In addition, we found that soil hydraulic conductivity played a major role in the fate of infiltrated stormwater for all scenarios. Our results highlight the importance of placing infiltration-based SCMs appropriately in the landscape if the goal is baseflow restoration. They also point to the importance of understanding local site conditions before designing and siting stormwater infiltration systems. A mix of different SCM strategies (e.g. rainwater tanks with a dedicated baseflow outlet) will be required for sites with very low hydraulic conductivities. [ABSTRACT FROM AUTHOR]

Space-temporal distribution of the contaminant plumes and aquifer properties is critical for groundwater management. However, most previous studies have focused on point source identification, barely exploring the identification of non-point sources. Xu et al. (2022) proposed to identify non-point sources but did not consider uncertainties in aquifer properties and release mass loading. In this work, we have implemented an application of the localized ensemble smoother with multiple data assimilation (LES-MDA) for the simultaneous identification of Gaussian hydraulic conductivities and non-point source parameters including Gaussian release mass-loading by assimilating both piezometric head and concentration observations in a synthetic confined aquifer. The results prove that the LES-MDA is not only capable of providing accurate identification of the spatial architecture of non-point contaminant sources and related release parameters (such as initial release time, and release duration) but also spatially heterogeneous release mass-loading and hydraulic conductivities. • Localized ES-MDA jointly identifies non-point source and conductivity field. • Uncertainty in the spatial distribution of field and mass-loading is considered. • Three scenarios with two different techniques test the joint identification. • Combining localization reduces filter inbreeding and spurious correlation. [ABSTRACT FROM AUTHOR]

This study applies two hybrid inversion frameworks, GAN-ILUES and GAN-OANW-ILUES, to accurately estimate the line contaminant source information and hydraulic conductivity in non-Gaussian groundwater fields. These frameworks combine data assimilation and deep learning methods, using WGAN-GP as a generator model for non-Gaussian hydraulic conductivity field and a CNN-based surrogate model, OANW, for surrogating the original forward groundwater model. The effectiveness and feasibility of WGAN-GP and OANW are verified separately. Then, the frameworks are verified on a 64 m by 64 m channelized aquifer with a linear contaminant source using measurement data from 20 observation wells. Results show that both frameworks can estimate model parameters and reproduce the contaminant concentration field. Compared with GAN-ILUES, GAN-OANW-ILUES with OANW surrogate model significantly improves simulation efficiency at a price of slightly larger model deviations. The inversion time for GAN-OANW-ILUES is less than 5% of that for GAN-ILUES. This study demonstrates the potential of combining data assimilation and deep learning methods for improving the performance of traditional inversion methods on tracing line contaminants in non-Gaussian fields. • Two deep-learning methods are integrated with data assimilation for inverse modeling of groundwater pollution. • The proposed modeling framework successfully traces the line contaminant source in non-Gaussian conductivity fields. • Model error slightly increases when the conductivity changes drastically. • The combined inversion framework significantly enhances inversion efficiency. [ABSTRACT FROM AUTHOR]

Current groundwater models face significant challenges in their implementation due to heavy computational burdens. To overcome this, our work proposes a cost-effective emulator that efficiently and accurately forecasts the impact of abstraction in an aquifer. Our approach uses a deep neural operator (DeepONet) framework to learn operators that map between infinite-dimensional function spaces via deep neural networks. The goal is to infer the distribution of hydraulic heads in a confined aquifer in the presence of a pumping well. We successfully tested the DeepONet framework on multiple problems, including forward time-dependent problems, an inverse analysis, and a nonlinear system. Additionally, we propose a novel extension of the DeepONet-based architecture to generate accurate predictions for varied hydraulic conductivity fields and pumping well locations that are unseen during training. Our emulator's predictions match the target data with excellent performance, demonstrating that the proposed model can act as an efficient and fast tool to support a range of tasks that require repetitive forward numerical simulations or inverse simulations of groundwater flow problems. Overall, our work provides a promising avenue for developing cost-effective and accurate groundwater models. • We propose, for the first time, a neural operator (DeepONet) as a surrogate model to efficiently and accurately emulate the impact of abstraction in the distribution of hydraulic heads in confined, heterogeneous aquifers. • The proposed method can efficiently learn solutions of both the forward and inverse operator. • By proposing a modification to the original formulation of DeepONet, we have achieved precise predictions for varied groundwater head distributions, accommodating the random positioning of wells in the heterogeneous aquifer. • Our experiments demonstrate DeepONet's capability in tackling tasks demanding repetitive forward numerical simulations, even in time-dependent and nonlinear setups. [ABSTRACT FROM AUTHOR]

• High-permeability and water-rich zones were identified by the hydraulic tomography. • Strong groundwater runoff paths were inferred for the water source area. • The hydraulic tomography was improved with various prior information. • THT can better reveal larger-scale heterogeneity of aquifers compared to SSHT. • Hydraulic tomography holds valuable applications in groundwater exploitation plans. Determining the spatial hydraulic parameters of aquifers is of paramount importance for the development and utilization of groundwater in water source areas. However, most methods are unable to accurately characterize the heterogeneity of aquifers because of the influences of complex geology, hydrogeology, structure and insufficient information. Hydraulic tomography (HT) is an effective and robust method for hydraulic parameter inversion to characterize heterogeneity. In this study, a two-dimensional HT model was established to simulate hydraulic parameter fields for a fractured karst aquifer in the Zhangji water source area (Xuzhou city, China). Steady-state hydraulic tomography (SSHT) and transient hydraulic tomography (THT) with different prior information conditions were applied to determine the high-permeability area and water-rich zones, and to infer possible locations of karst conduits and strong runoff paths in the water source area. The results indicate that: (1) THT can better reveal larger-scale heterogeneous characteristics of hydraulic properties compared to SSHT. The hydraulic conductivity distribution estimated by THT correlates well with the geological conditions of the area, especially in identifying water-rich zones formed by faults and other formations. (2) When combined with geological conditions, HT possesses the ability to identify strong runoff paths in fractured karst aquifers. (3) Accurate prior information, which is more relevant to the head response information, is conducive to obtaining more acceptable HT results. (4) THT can simultaneously identify high-permeability and high-storage zones, and the analysis of the overlap of these two regions has the potential to predict underground water reservoirs, which is of the utmost importance for the development and utilization of groundwater resources in water source areas. [ABSTRACT FROM AUTHOR]

• Green-Ampt model under muddy water conditions was developed. • A model describing the variation of hydraulic conductivity of infiltration in saturated soil columns under muddy water conditions was developed. • The established Green-Ampt model under muddy water conditions was simplified and validation tests showed it to be very reliable. The Green-Ampt infiltration model has been widely used because of its simple structure and clear physical meaning of the parameters. The model parameters were improved using the equivalent saturated hydraulic conductivity to develop the Green-Ampt infiltration model for muddy water (MWGA). A saturated soil column infiltration test with muddy water was conducted to determine the influence of the soil texture (sandy soil and silt loam) and the sand content (S = 3 %, 6 %, 9 %, and 12 %) on the hydraulic conductivity of saturated soil columns. The equivalent saturated hydraulic conductivity was derived based on several assumptions and under different conditions. Eight one-dimensional vertical infiltration tests were conducted under the same conditions for verification. The MWGA was simplified according to the results, and four tests with different sand contents (S = 4 % and 10 %) were conducted to validate the MWGA for both soils (the simplified infiltration model was used for the sandy soil). The results indicated that the hydraulic conductivity trend of the saturated soil column during the infiltration of muddy water into sandy soil was in accordance with the physical model. The hydraulic conductivity of the silt loam was only influenced by the sand content and showed a significant linear relationship with the sand content. The root mean square error (S RMSE) obtained from the validation test under the same conditions was close to 0, and the absolute value of the relative error (S RE) was less than 15 %, indicating a good fit. The results of the validation tests for different sand contents showed that the simulated and observed values were close to the 1:1 line, demonstrating high model accuracy. Our results provide new insights into the infiltration of muddy water and the mechanism of reducing the infiltration rate due to the dense layer formed on the soil surface. [ABSTRACT FROM AUTHOR]

• We study pumping optimization for both fixed well cases and moving well cases. • For fixed well cases, we derive an analytical solution for the critical pumping rate. • For moving well cases, Bayesian optimization is employed. • The critical pumping rate of a well network is independent of hydraulic conductivity. • In moving well cases, different solutions can achieve the same maximum pumping rate. For residents living on small islands, groundwater serves as their primary source of freshwater, which exists in the form of a freshwater lens floating above denser seawater. Previous research on optimizing pumping strategies in freshwater lenses focused on pumping from fixed wells using numerical models, and optimal well locations have not been explored. In this study, we analyze pumping optimization for both fixed well cases and moving well cases in a rectangular island using an analytical approach. This approach allows for a clear understanding of the relationship between hydrogeological parameters and optimization results. For fixed well cases, we provide an analytical solution for the critical pumping rate of each well. For moving well cases, Bayesian optimization is employed to efficiently search the extensive space of possible well locations and identify the critical pumping rate. Our results reveal that the well location has a substantial impact on the critical pumping rate in the fixed well cases, indicating that investigating the optimization of well placement is essential. In the discussion of the moving well cases, the maximum total pumping rate of a pumping well network is independent of hydraulic conductivity, and the critical pumping percentage relative to total recharge is independent of both hydraulic conductivity and recharge. The distribution of optimized well locations for islands with a fixed aspect ratio but different sizes follows the same pattern. In the moving well cases, different solutions can achieve the same maximum pumping rate, especially when multiple wells are involved. In addition, our approach is applicable to scenarios where new wells are added to an existing well system. Our solutions and findings significantly contribute to a deeper understanding of the hydraulic performance of pumping activities from freshwater lenses and offer valuable insights for developing more sustainable and robust groundwater management strategies in small islands. [ABSTRACT FROM AUTHOR]

• The hyporheic exchange is positively correlated with hydraulic conductivity, with K near the dune trough matters the most. • With limited sampling of K , the high cross-correlation zone is the preference of sampling location of K. • The optimal sampling location of hydraulic conductivity can be estimated by a linear formula on height and stoss length of dunes. The hyporheic exchange is not evenly influenced by heterogeneous hydraulic conductivity (K) values throughout the streambed. Few studies have investigated the impact of K heterogeneity in different regions of the streambed on the hyporheic exchange. This study employed a first-order stochastic analysis and a dislocation superposition method to examine the cross-correlation between hyporheic exchange flux (HEF) and K anywhere in synthetic, heterogeneous, 2-D cross-sectional streambed models. Results show that hyporheic exchange flux positively correlates with K heterogeneity in every part of the streambeds. This relationship provides a mechanistic explanation for the impact of high / low K zones on the HEF in the hyporheic zone. The effect of K impact on the HEF intensifies in streambeds when 1) upwelling groundwater flux increases, 2) the dunes are steep and asymmetric, or 3) the streambed is stratified. This study develops an empirical linear formula based on dune height and stoss length for estimating the high cross-correlation zone (HCZ) locations, potentially guiding the sampling scheme of hydraulic conductivities for evaluating the HEF in practical fieldwork. [ABSTRACT FROM AUTHOR]

• 3D pathways of IGF are identified with an assessment on flow rates. • IGF contributes 36%∼59% to the baseflow and 32%∼52% to the streamflow in the studied river. • Infiltration recharge and aquifer properties affect the development of IGF. Inter-basin groundwater flow (IGF), defined as groundwater flows across the topographic divides, occurs in nature as a common phenomenon, and seriously affect water balance and solute transport in a basin. Although the existence of IGF has been checked in drainage basins with indirect methods, such as using information of hydrogeochemistry, few studies are conducted to directly identify and quantify the IGF in the three-dimensional (3D) space using numerical modeling of groundwater flow. In this study, we identify, partition and quantify IGF based on a regional-scale 3D groundwater flow model covering several traditional surface water basins. The investigation is focused on the Hailiutu River, a groundwater-fed stream in the Ordos Plateau, China. It is the first time that the source zones and 3D paths of IGF as well as its contribution to the streamflow are fully captured for a groundwater-fed stream. Results indicate that the IGF contributes 36%∼59% to the baseflow and 32%∼52% to the streamflow of the Hailiutu River, through different groups of circulation paths with the maximum depth up to ∼ 1000 m. Uncertainty analyses of the model show that the contribution of IGF to the streamflow is positively correlated to the infiltration recharge and hydraulic conductivities of the aquifer media. Several indirect methods are also checked for comparison, but they could only be used to assess the potential contribution of IGF, not the IGF paths. This study will facilitate in deeply understanding the evolution mechanism of the inter-basin groundwater circulation and the interaction between surface water and groundwater. [ABSTRACT FROM AUTHOR]

• Analytical solution for water release of a nonlinear consolidated aquitard is derived. • A new method was developed to estimate the hydraulic parameters of the aquitard. • The proposed method was applied to aquitards in Changzhou and Shanghai. Estimation of hydraulic parameters and groundwater depletion of aquitards is necessary to evaluate the groundwater resources and land subsidence. In this study, an analytical solution for water release from a nonlinear consolidated aquitard was derived by approximating the drawdown history as a continuous piecewise linear drawdown function (PLD) with several stages, while the water level in adjacent aquifers varies arbitrarily over time. According to dimensionless and parameter sensitivity analyses, groundwater depletion of an aquitard increases with an increase in compression index, aquitard thickness, and water drawdown rate in adjacent aquifers, decreases with an increase in initial void ratio and effective stress, and is not affected by the consolidation coefficient. In addition, we proposed a type-curve fitting method to calculate the hydraulic parameters of the aquitard under the condition of PLD in adjacent aquifers. The proposed method was applied to estimate the hydraulic parameters of aquitards at two field sites in the Yangtze River Delta in China, i.e., Changzhou and Shanghai. Results show that the compression index of the aquitards in Changzhou and Shanghai are 0.074 and 0.24, respectively, while the consolidation coefficients are 7.62 × 10-7 m2/s and 2.16 × 10-6 m2/s, respectively. The hydraulic conductivity and specific storage estimated by the proposed method are in good agreement with previous studies and the results of the geological method of Konikow and Neuzil (2007). The proposed analytical method for estimating hydraulic parameters and groundwater depletion of aquitards will contribute to the sustainable management of groundwater resources in multi-layer aquifer systems. [ABSTRACT FROM AUTHOR]

• Impacts of wall porosity on fracture flow were systematically investigated at pore scale. • Mechanisms governing direction and magnitude of fluid exchange at the fracture-matrix interface were elucidated. • Flux contributions of porous walls to fracture outlet and fracture-matrix interface were functionalized by wall porosity. • Influence of porous walls cannot be equivalently represented by applying slip boundary conditions. This study investigates the influence of porous walls on fluid flow behavior in single rough-walled fractures. A series of direct numerical simulations (DNS) were conducted to examine fluid flow through rough-walled fractures surrounded by porous walls under various hydraulic gradients. The simulation results clearly demonstrate the progressively significant impact of porous walls on flow characteristics as porosity increases. Regression analyses indicate that the Forchheimer's law, which characterizes the nonlinear flow of rock fractures, remains valid in the presence of porous walls. Moreover, increased porosity enhances fluid exchange and leads to an increased ability for single fractures to transmit fluid. Two double-parameter equations were established to quantitatively characterize the effects of porous walls on hydraulic conductivity of the fracture and fluid exchange between porous walls and the fracture. Further analysis revealed that the angle between the fracture profile and main flow direction profoundly influences the inflow/outflow exchange between the fracture and its adjacent porous walls. Moreover, the pore-scale results indicate that it is unreasonable to equate the effect of porous walls with slip boundaries as suggested in previous studies. The results and findings of this study deepen our understanding of flow behavior at the interface between the rough-walled fracture and adjacent porous walls, and they serve as a basis for accurately simulating large-scale fracture networks that consider the hydraulic contribution of fracture walls. [ABSTRACT FROM AUTHOR]

• Correction methods were developed to remove wellbore effects from slug test data. • Successful characterization of synthetic aquifer heterogeneity using corrected data. • A field application was performed at a fractured porous media site. Slug tests provide an efficient way to obtain information about the spatial heterogeneity of an investigated site. Combining with the imaging method of hydraulic tomography, they can present broad application prospects in aquifer reconstruction. However, unlike pumping tests, the water level responses of slug tests may be significantly affected by wellbore effects, especially for underdamped cases. This study proposes a new characterization framework for characterization of aquifer heterogeneity based on water level responses recorded during cross well slug tests with a tomographical arrangement. The peak head of each water level response and its corresponding time, i.e. the hydraulic travel time, are utilized in the inversion process, rather than the whole water level time series. To eliminate the influence of wellbore effects, two correction methods with respect to the hydraulic travel time and peak head amplitude are developed. Based on corrected data, the distributions of hydraulic diffusivity (D) and specific storage (S s) are obtained through travel time-based and attenuation-based inversions, respectively. The new framework is verified by a series of simulated tomographic slug tests through a synthetic example based on an aquifer outcrop analog, where the hydraulic parameter distribution is known. The verification results indicate that the distributions of D and S s are well estimated, and their mean values are much improved compared to the old framework. With the same method, a field application is employed at a fractured rock experimental site located in Göttingen, Germany. Three potential transmissive fractures are revealed with hydraulic conductivities varying from 6.9 × 10–5 to 3.4 × 10–4 m/s. The uncertainty of the inversion results is discussed for future studies and related applications. [ABSTRACT FROM AUTHOR]

• Random forest model is trained on hydrogeological dataset for aquitards. • Dominant factors are clay fraction, depth, geology, sedimentology and location. • Detailed grain size fractions and grain size percentiles do not improve the model. Aquitards are common hydrogeological features and their hydraulic conductivity is an important property for various groundwater management issues. Predicting their hydraulic conductivity proves challenging, given its dependence on numerous variables. In this study, the dominant factors for predicting aquitard hydraulic conductivity are identified. To this end, a random forest model is trained on a dataset consisting of more than 1000 hydraulic conductivity measurements of core-scale sediment samples from a wide range of stratigraphic units and depths in the Netherlands. The dataset contains textural properties, such as the grain size distribution and porosity, as well as structural data, such as location, sampling depth, stratigraphical unit, lithofacies, organic carbon content, carbonate content and groundwater chloride concentration. Results show that clay fraction, stratigraphic unit, depth, lithofacies and x-coordinate are the most important features for predicting the hydraulic conductivity. Here, x-coordinate is presumably a proxy for distance from marine influence. Using a more detailed grain size distribution or using derived parameters such as the grain size percentiles does not improve the model any further. Our findings indicate that structural properties play a significant role in predicting aquitard conductivity, as they serve as indicators of processes such as compaction and soft-sediment deformation. The model is furthermore an effective method to estimate hydraulic conductivity for sediment samples without conducting costly and time-consuming hydraulic conductivity measurements. [ABSTRACT FROM AUTHOR]

• The effect of tunnel drainage in heterogeneous media is significantly different from the homogeneous model, and it aligns more closely with reality. • The water discharge distributes unevenly along the tunnel in heterogeneous realizations and is relatively higher compared to that in homogeneous media. • The drawdown caused by tunnel drainage is higher in homogeneous model, while large drawdown in specific small regions is observed in heterogeneous simulations. The mountainous tectonic zone exhibits high formation heterogeneity, which significantly affects groundwater seepage around the excavated tunnel. Traditional modeling methods that assume the surrounding rock to be a homogeneous field face challenges in accurately predicting and evaluating water discharge within the tunnel. To gain a better understanding of how heterogeneity influences tunnel water discharge, synthetic heterogeneous fields are conducted based on the conceptualization and parameters of the Daxuecheng Tunnel in Chongqing, southwest China. In the heterogeneous modeling, we consider four standard deviations of hydraulic conductivity distribution (0.21, 0.37, 0.55, 0.72) and four dip angles (0°, 30°, 60°, 90°). The results reveal that formation heterogeneity leads to localized instances of significant water inrush and irregular head drawdown distribution, which closely resemble the actual situation compared to the homogeneous model. Generally, the total water discharge into the tunnels increased with increasing heterogeneity and dip angles. Furthermore, the head drawdown in the tunnel region decreased with heterogeneity and increased with dip angles. These findings emphasize the importance of considering formation heterogeneity in tunnel zones and offer valuable guidance for evaluating engineering and environmental challenges in tunnel construction. [ABSTRACT FROM AUTHOR]

• Groundwater mounds resulting from nearshore recharge is identified in a sandy hillslope. • The thickness of vadose zone determines fluxes across water table along the hillslope. • Nearshore recharge temporarily changes streamlines and increases tortuosity of flowpaths. • Flowpaths near the wetland are mainly controlled by regional GW discharge and strong ET. Groundwater mounds and depressions induced by rainfall and evapotranspiration near wetlands/lakes have been widely observed, but their effects on groundwater flow field are poorly known. Here, a sandy hillslope near a wetland in the Ordos Plateau, China, which has a semi-arid climate, is selected for investigation. After identifying temporary groundwater mounds/depressions based on three water level observation wells, a HYDRUS-2D model is setup to obtain the highly transient daily flow field. The variable thickness of unsaturated zone near the wetland, which controls soil water content and unsaturated hydraulic conductivity, is found to be responsible for groundwater mounds resulting from focused recharge and groundwater depressions resulting from nonuniform evapotranspiration. On nonrainy days, evapotranspiration in the lowland is supported by flowpaths from regional groundwater discharge, and in the slope is supported by a flow cell from the upland to the upper part of the slope, which causes water table recession in the upland. On rainy days, focused recharge in the lowland leads to two temporary local flow cells, which break the regional groundwater discharge flowpaths into two temporary flow cells. The two temporary flow cells toward the upland contribute to water table rises in the uplandMoreover, we find focused recharge in rainy days does not change the overall direction of flowpaths controlled by regional groundwater discharge and strong evapotranspiration, but only increase the tortuosity of flowpaths. By coupling daily atmospheric conditions and regional groundwater discharge, this study has implications for groundwater recharge estimation and future groundwater modelling in arid regions. [ABSTRACT FROM AUTHOR]

• First-time examination of the effect of aquifer anisotropy on dam efficiency. • Higher hydraulic conductivity anisotropy enhances fresh groundwater discharge. • Optimizing dam design for environmental mitigation in anisotropic coastal aquifers. Hydraulic conductivity is a key parameter controlling groundwater flow and solute transport, and anisotropy in hydraulic conductivity is common in aquifers. Previous studies have investigated the effectiveness of subsurface dams in combating seawater intrusion (SWI) and associated environmental concerns. However, the quantitative impact of hydraulic conductivity anisotropy on the performance of subsurface dam has not been explored. This study goes beyond previous research by examining, for the first time, the effects of subsurface dams on SWI prevention in anisotropic settings. Furthermore, the study optimized subsurface dam designs in anisotropic coastal aquifers through numerical simulations that take into account the environmental impact. Our findings reveal the mechanism of hydraulic conductivity anisotropy's influence on the discharging zone and demonstrate that as the anisotropy ratio (r k) decreases, the coastal discharging zone expands landward, reducing SWI and ultimately lowering the minimum effective dam height (MEDH). This process effectively prevents SWI while maximizing fresh groundwater discharge. Increasing the r k values simultaneously expands both the MEDH and the peak fresh groundwater discharge (PFGD). Additionally, increasing the horizontal hydraulic conductivity of the aquifer significantly increases the range of PFGD, while the distance between the dam and shoreline emerges as the main factor influencing the extent of the MEDH. [ABSTRACT FROM AUTHOR]

• DNAPL accumulations indicate subtle vertical hydraulic conductivity contrasts. • shallow, fractured sedimentary rock aquitards are moderately to highly anisotropic. • bulk K h may not identify thin aquitards typical in shallow sedimentary rock systems. • fracture termination horizons can create poor vertical hydraulic connectivity. Aquitard assessment poses a challenge for practitioners and researchers managing dense non-aqueous phase liquid (DNAPL) contaminants in sedimentary rock aquifer systems. Within these systems, DNAPL migration and bulk hydraulic properties are controlled by fracture networks which are difficult to characterize at relevant scales with conventional methods. A previous study at a DNAPL contaminated site used contrasts in high-resolution vertical gradients to delineate four aquitards and two surfaces with poor vertical connectivity within a thick (>200 m) sedimentary rock aquifer system primarily composed of layered sandstones. In this study, we corroborate that method by using the existing DNAPL contamination as a tracer to identify and characterize the aquitards in the sequence and assess aquitard integrity. Closely spaced samples of rock from four continuous cores were collected and analyzed for volatile organic compounds (VOCs). The cores were collected along a transect perpendicular to groundwater flow and 75 m downgradient of the DNAPL source zone. Dissolved phase contaminant concentrations were collected using high-resolution multilevel systems placed along the plume centerline, downgradient from the source. The rock core and groundwater VOC concentration profiles suggest a primary aquitard limits vertical migration of both DNAPL and the associated dissolved phase contaminants, despite relatively large, downward gradients across its lower boundary. A calibrated, three-dimensional numerical groundwater flow model indicates an anisotropy factor of 1,000 for this aquitard. The K v values for all four aquitards are only slightly lower than the values for the aquifers. However, the aquitard K v values are 1–3 orders of magnitude less than their K h values, and the aquitard K h values are often similar to or even greater than the K h values for the aquifers. Therefore, large anisotropy, rather than exceptionally low K v values, distinguish the aquitards from the aquifers in this system. Fracture network characterization of nearby outcrops showed the anisotropy of the aquitards can be attributed to laterally extensive, bedding parallel partings coupled with short, frequently terminating, and poorly connected vertical fractures. In addition, the rock VOC profiles combined with fracture network data show that fracture termination surfaces can be powerful inhibitors of downward DNAPL migration providing additional evidence for the importance of these features in sedimentary rock flow systems. Ultimately, this study reveals the important influence of anisotropic aquitards on DNAPL migration, accumulation, and persistence, as well as associated plume migration. Furthermore, it demonstrates that subtle contrasts critical to aquitard integrity may be easily missed with long screened wells and other conventional, low resolution site characterization methods. [ABSTRACT FROM AUTHOR]

• Transience of a variable is treated as 1D spatial heterogeneity for optimization. • Transience of streambed K can be identified via geostatistical inverse modeling. • The new methodology is validated through synthetic and field data investigations. Quantitative investigation of the interaction between surface water and groundwater relies on the determination of transience of streambed hydraulic conductivity (K sb). The commonly used successive inversion approach (i.e., the inversion is repeated over successive time steps) of interpreting aquifer hydraulic response data belongs to different optimization windows consists of a sizable number of inversion sub-processes and tends to lose sharp changes in K sb. This study treats the transience of a parameter in the time domain as the heterogeneity in 1D space domain and uses geostatistical inverse modeling to characterize such transience. The methodology is first tested through a group of ten synthetic cases with independently generated random transient patterns of K sb. Results of these synthetic cases reveal the capability of geostatistical inverse modeling to effectively characterize the general varying pattern as well as sharp changes in K sb. Subsequently, the methodology is applied to interpret the aquifer hydraulic response data measured at the Rhône River site, Town of Fully, Switzerland. A significant improvement in model calibration is observed when the methodology is compared to the successive inversion approach. The field investigation reveals that the transience of in-situ K sb is closely related to stream stage variations. Particularly, multiple occurrences of sharp increases and decreases in K sb appear when the stream stage lowers below and rises above the aquifer head. The driving mechanism for these sharp variation events is that fine-grained sediments within the streambed can be partly washed away when the aquifer water flows toward the river, and vice versa. The geostatistical approach has the potential to help investigate other physical or chemical processes in groundwater hydrology associated with transient changes in K sb. [ABSTRACT FROM AUTHOR]

• Advective travel time along streamlines is analytically found for phreatic aquifers. • The Laplace/Poisson equations are solved in polygon's exterior/interior. • The water table, flownet, hydraulic gradients, and discharge streamlines are obtained. • Ecohydrology of parks and desert oases in arid zones is discussed. • Isoperimetric problems travel time – park's area are formulated. Strack's (1984, 2017) analysis of infiltration from a pond into a shallow aquifer, with a generated groundwater mound, is modified for steady phreatic groundwater flows in perched aquifers, typical for arid/hyperarid environments, with a zone of intensive transpiration and induced groundwater trough. The interior of an urban phreatophytic park is an n -polygon (in an aerial view), which degenerates into a circle at n → ∞. Transpiration acts as an areal groundwater sink. The water table drawdown is hydrologically symmetric with Strack's drawup. In the exterior of the park, the ground surface is phyto-sterile (e.g. a desert in Arabia or a paved megapolis) and evapotranspiration from the water table there is ignored. The travel (residence) time of advected marked particles along the flowpaths (streamlines) towards the park and under it are analytically evaluated. In terms of the Dupuit-Forchheimer model of a vertically averaged hydraulic head, the Strack potential obeys the Laplace and Poisson equations in polygon's exterior and interior (correspondingly), with a hydraulic commingling along the park boundary. The tracer particles start their topologically converging journey from a remote circular zone of contamination (e.g. sewage from urban septic tanks recharging the water table). Porosity, hydraulic conductivity of the aquifer, evapotranspiration rate and a piezometric head in a remote observational well are given. For a circular park flow is 1-D radial. In the park exterior, the Schwarz-Christoffel formula maps conformally the physical domain (an infinite trigon) onto a half-strip in the complex potential plane. Strack's potential is expressed via hypergeometric functions, whose parameters depend on n. The flow net is reconstructed with the help of the stream function. For a triangular park interior, there is no stream function and the Saint-Venant solution to the Poisson equation is engaged to find the water table, hydraulic gradients, and discharge streamlines. The total dewatered volume and groundwater storage under the water table and "gross travel time" are evaluated for circular parks. Implications for ecohydrology of parks and desert oases in the Gulf countries and intuitive isoperimetric problems are discussed. [ABSTRACT FROM AUTHOR]

• A novel deep learning model guided by analytical model was developed. • Analytical model helps the neural network to improve the accuracy of prediction. • The proposed model performs satisfactorily even with sparse training data. Deep learning models exhibit good interpolating ability, but their performance is often hindered by the scarcity of data in groundwater problems. Analytical models (solutions) provide a first-order physical principle for groundwater flow, but they are only applicable under specific conditions, such as when the aquifer is homogeneous. This study introduces a novel framework for deep transfer learning that integrates the strengths of both methods and overcomes their limitations. Specifically, we propose a deep learning model guided by a simple analytical model to predict groundwater flow in heterogeneous aquifers. It differs from previous deep learning model by incorporating the knowledge from the simple analytical model and utilizing transfer learning technique to improve the prediction in relatively complicated problems where the analytical model is not applicable. The model is tested against the traditional deep learning model Deep Back Propagation Neural Network (DBPNN) in the scenarios with unknown hydraulic conductivity fields. The results show that the proposed model significantly improve the accuracy of hydraulic head predictions by fusing analytical knowledge with neural networks. The hydraulic conductivity mainly affects the parameters of the shallow layers in the neural network, which enables the use of transfer learning techniques in more complex problems. In all test scenarios, the prediction errors of the proposed model are much smaller than those of the DBPNN. Additionally, the proposed model performs satisfactorily even with limited training data. [ABSTRACT FROM AUTHOR]

• Hydrochar derived from food waste was reused as a soil amendment. • Saturated hydraulic conductivity was increased by hydrochar. • Unsaturated hydraulic conductivity and sorptivity were decreased by hydrochar. • Infiltration was limited due to the soil water repellency induced by hydrochar. Hydrothermal carbonization of food waste (FW) and application of the solid product (hydrochar, HC) in agriculture, is expected to be an effective way to promote the circulation in food-energy-water nexus. However, little is known on the effects of applying FW-derived HC as a soil amendment on soil properties and functions. The current study investigated the effects of FW-derived HC on soil hydraulic properties and infiltration process. Two types of FW-derived HC were mixed into the top 0–20 cm soil layer at a rate of 1 % and 2 % (w/w) in a soil column experiment with grass growth. In-situ infiltration experiment was conducted within the soil column using a disc infiltrometer at different negative pressure (−20 cm, −6 cm, and −2 cm water head). Unsaturated hydraulic conductivity (K 0) and sorptivity (S 0) at each negative pressure head was estimated by fitting experimental cumulative infiltration data to a 4-terms infiltration model. Saturated hydraulic conductivity (K s) and soil water retention curve (SWRC) were measured using undisturbed soil cores taken from the soil column. Soil pore size distribution and soil water constants were estimated from the SWRCs. The results indicate that application of FW-derived HC significantly (p < 0.05) affected soil structure by increasing meso (0.03–0.0002 mm) and macro (> 0.03 mm) pores, which can be attributed to the promoted soil aggregation. Saturated hydraulic conductivity was significantly increased and water retention characteristics were changed with significantly (p < 0.05) increased soil water holding capacity and plant available water content. Besides, FW-derived HCs were found hydrophobic and can render wettable sandy soil water repellent. The K 0 and S 0 were significantly (p < 0.05) decreased and cumulative infiltration was reduced when soil was wetted from an initial dry condition. Negative effect was found on grass growth with significantly (p < 0.05) decreased aboveground biomass after HCs application. Our study indicates that agriculture application of FW-derived HC as a soil amendment could effectively improve soil fertility by recycling nutrient elements and improving soil structure. However, attention should be paid to the hydrophobicity and phototoxicity of FW-derived HC to avoid the related detrimental influences on plant growth and environment. [ABSTRACT FROM AUTHOR]

• Lognormal, unsaturated hydraulic conductivity model not requiring K s as input. • K s model derived from hydraulic parameters describing bimodal soil water retention function. • The novel hydraulic conductivity model does not require the use of integrals. • The model considers the clay-water interaction without using clay content data. • Lognormal distribution function parameters were constrained for physical consistency. We developed a novel, lognormal, pore-scale, unsaturated hydraulic conductivity model, K(ψ) M odel , which does not require saturated hydraulic conductivity, K s , as an input parameter. K(ψ) M odel is derived solely from hydraulic parameters describing a bimodal, lognormal, pore-scale, soil water retention curve θ(ψ). The K(ψ) M odel is based on the Hagen-Poiseuille equation, which represents the soil as a bundle of parallel, non-intersecting capillary tubes. To improve the modelling of fine-textured soils we introduced a novel model to consider the clay-water interaction. This model assumes that clay-water interaction occurs for soils having more than 30% of clay and an effective matrix porosity greater than 35%. Compared to previously developed models, the K(ψ) M odel does not require the use of integrals and can be computed from a spreadsheet and distinguishes between macropore (non-equilibrium) and matrix (equilibrium) flows. The K(ψ) M odel gives improved results when the hydraulic parameters are dynamically constrained and when θ(ψ) describes a bimodal, lognormal distribution. [ABSTRACT FROM AUTHOR]

• First hydrogeological model established for URL site of HLW disposal in China. • The effect of the hydraulic influence zones of faults is incorporated in the numerical model. • Different variations in the horizontal and vertical directions of hydraulic conductivity are considered. • A total of 120 stochastic parameterized models are presented. • Hydraulic conductivity < 10−9 m/s at high-level radioactive waste disposal depth. Deep geological disposal is internationally accepted as a feasible and safe approach for high-level radioactive waste (HLW) disposal. To evaluate hydrogeological conditions in support of safety assessments for HLW disposal at the Xinchang preselected site in China, stochastic inverse models of site-scale groundwater flow were developed in this study to generate highly parameterized hydraulic conductivity fields for the fractured medium by adopting pilot point and null-space Monte Carlo methods. The hydraulic influence zones of the faults were carefully considered to have homogenous parameter values across the zones. A total of 120 multiple random realizations were generated to characterize the 3D spatial variations in hydraulic conductivity by conditioning to 1218 fixed pilot points. The simulated hydraulic heads of the realizations were in good agreement with observational data. The hydraulic conductivity fields close to the boreholes could be characterized in detail and had relatively low uncertainties. Furthermore, the hydraulic conductivity (K) values around underground research laboratory (URL) at the HLW disposal zone depth were less than 10−9 m/s. The K values obtained for most of the influence zones of these faults at this depth were consistent with hydraulic test data and ranged from 10−10 to 10−9 m/s, thereby indicating that the surrounding rock has low permeability and is suitable for HLW disposal. These findings offer new insights into hydrogeological conditions by providing key information on the permeability characteristics that need further focus on HLW disposal. [ABSTRACT FROM AUTHOR]

• A modified KC equation is proposed to calculate hydraulic conductivity in nanopores. • Influence of surface activity and pore size on nano-flow is modelled by MD simulations. • A specific function is proposed to quantify the adsorbed proportion based on MD simulation results. • The modified KC equation is valid to be applied to both sandy and clayey soils. Hydraulic conductivity is a critical parameter for studying the behavior of clay-water systems. However, accurately estimating saturated hydraulic conductivity k in clayey soil by using the Kozeny-Carman (KC) equation is challenging due to the neglect of its active surface properties and nanoscale pores. Clay surfaces can have diverse characteristics resulting from various physicochemical processes such as isomorphous substitution and are typically characterized by the Cation Exchange Capacity (CEC). These properties can significantly impact fluid transport through the clay matrix. To address this issue, this study modifies the KC equation by incorporating an adsorbed water proportion φ that considers the occurrence state of pore water and its correlation with pore diameter, making it applicable to clayey soils. Molecular dynamics (MD) models are established to investigate the influence of surface interaction (CEC) and nanopore size (r) on saturated hydraulic conductivity k of seepage flow in clayey soils. Based on the MD results, a specific function is proposed to quantify the adsorbed proportion φ , which is linearly related to the root of CEC and reciprocal of pore size (r), and then incorporated into a proposed hydraulic correction ratio k * to modify the classical KC equation. The modified KC equation is validated using experimental data from literature, showing a high R 2 value of 0.96. This result demonstrates that the proposed correction ratio k * can extend the application scope of the classical KC equation to clayey soils. [ABSTRACT FROM AUTHOR]

• The magnitude of the increase in the matrix hydraulic conductivity affects the karstic water storage variation estimation accuracy. • The impact of the variation path of matrix specific yield on the karstic water storage variation estimation accuracy varies, specifically manifested in the amplitude of estimation accuracy. • The findings could provide greater insights for estimating the karstic water storage variation error in karst areas under different parameter changes and offer scientific support for water resource management and utilization. Karst water plays a crucial role as a freshwater source, which provides drinking water for millions of people worldwide. Accurate assessment of karst water resources and prediction of the impact of rainfall events on karst systems require a comprehensive understanding of medium parameters, such as the karst matrix hydraulic conductivity and specific yield. Therefore, in this paper, we investigated the effects of karst matrix hydrogeological parameters on the estimation accuracy of karstic water storage variation using a numerical modelling approach. Specifically, we considered matrix–conduit coupled karst systems and analysed the spring flow recession hydrograph following rainfall events. The objective of this study was to explore the vertical and horizontal variations in karst matrix parameters and their effects on the estimation accuracy of karstic water storage variation and to provide insights into the role of the hydraulic conductivity and specific yield in controlling groundwater dynamics. The results of this study have important implications for karst water resource management, highlighting the necessity for improved characterization of karst aquifer medium properties. [ABSTRACT FROM AUTHOR]