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The accurate prediction of groundwater contamination is challenging due to uncertainties arising from the inherent heterogeneity of aquifers, inadequate site characterization, and limitations in conceptual mathematical models. These factors can result in an underestimation of contaminant concentrations. For effective contaminant prevention and control, it is important to estimate the probability of exceeding the allowed threshold for contaminant concentrations, known as the failure probability of groundwater contamination. Computing small failure probabilities using classical Monte Carlo simulation (MCS) requires computing a large number of samplers to converge to a stationary target value, which is time‐consuming. To address this, in this paper, we develop a novel approach for calculating small failure probabilities, known as subset simulation (SS) coupled with preconditioned Crank‐Nicolson Markov chain Monte Carlo (pCN‐SS), which combines subset simulation with preconditioned Crank‐Nicolson Markov chain Monte Carlo (pCN‐MCMC) to promote computational efficiency. We have tested the performance of the proposed algorithm in both a mathematical example and a numerical case study of groundwater contamination. The results demonstrate that pCN‐SS provides improved accuracy and efficiency for evaluating small failure probabilities for high‐dimensional groundwater contamination, specifically for hydraulic conductivity as a source of uncertainty. Compared to classical MCS and traditional SS, pCN‐SS requires fewer model evaluations but produces stable and accurate results. Key Points: The pCN‐SS is proposed to accurately estimate the small failure probability in high‐dimensional groundwater contaminant transport problemsThe results demonstrate that the pCN‐SS can offer both accuracy and efficiency in estimating small failure probabilitiesThe pCN‐SS surpasses traditional subset simulation in accurately estimating small failure probabilities [ABSTRACT FROM AUTHOR]

Understanding responses of stream discharge to precipitation in a watershed is important in gaining insights into watershed hydrology and estimating hydraulic parameters. Transfer functions in the spectral domain are commonly used to quantify the relationship between precipitation and discharge, and estimate watershed hydraulic parameters. However, previous models have not adequately accounted for the impact of the unsaturated zone. To address this, we have developed a novel analytical model that considers the effect of the unsaturated zone to obtain transfer functions within watersheds. These transfer functions are derived by the spectral method and verified through numerical simulations. The results indicate that the transfer functions are influenced significantly by the relative hydraulic conductivity exponent αk in the moisture characteristic curve. A higher αk results in a lower transfer function, indicating more robust filtering of hydrological signals. A thicker unsaturated zone results in lower transfer functions at higher frequencies. The traditional transfer functions, which neglect the retention capacity of the unsaturated zone, tend to overestimate hydrological responses at high frequencies. Our transfer functions agree well with integrated watershed‐scale flow models and are also applied to observed data from four watersheds in Iowa, providing reasonable estimates for the hydraulic parameters. This study contributes to a deeper understanding of watershed behavior and offers an enhanced tool for estimating hydraulic parameters with practical applications. Key Points: Transfer functions are proposed to quantify hydrological signal filtration considering unsaturated flow described by Richards equationThicker unsaturated zones or higher conductivity exponents enhance the filtration of hydrological signalsUnsaturated zone generally possesses a stronger ability to filter watershed hydrological signals than that of saturated zone [ABSTRACT FROM AUTHOR]

Saturated hydraulic conductivity (Ks) is a crucial parameter that influences water flow in saturated soils, with applications in various fields such as surface water runoff, soil erosion, drainage, and solute transport. However, accurate determination of Ks is challenging due to temporal and spatial uncertainties. This study addresses the knowledge gap regarding the long‐term behavior of Ks in sandy soils with less than 10% fine particles. The research investigates the changes in Ks over a long period of constant head tests and examines the factors influencing its variation. Two sandy samples were tested using a hydraulic conductivity cell, and the hydraulic head and discharge were recorded for over 50 days. The results show a general decline in Ks throughout the test, except for brief periods of increase. At the end of both tests, there are noticeable reductions in the saturated hydraulic conductivities of the samples, with one sample being 96% and the other sample 91% less than the maximum recorded saturated hydraulic conductivity during the tests. Furthermore, the relationship between flow rate and hydraulic head gradient does not follow the expected linear correlation from Darcy's law, highlighting the complex nature of sandy soil saturated hydraulic conductivity. The investigation of soil properties in three different sections of the samples before and after the tests revealed a decrease in the percentage of fine particles and a shift in specific gravity from the bottom to the top of the sample, suggesting particle migration along the flow direction. Factors such as clogging by fine particles and pore pressure variation contribute to the changes in Ks. The findings of this research show the importance of considering changes of saturated hydraulic conductivity during constant‐head laboratory tests. Therefore, this study provides evidence for the requirement to further assess the laboratory methods for measurement of the saturated hydraulic conductivity in sandy soil mixtures. Key Points: The estimation of saturated hydraulic conductivity through constant head tests demonstrates sensitivity to the duration of the testsObservations indicate an alteration in particle size distribution before and after testing within different sections of the samplesFlow rate and hydraulic gradient vary over the test duration, emphasizing the complex hydraulic system within the samples [ABSTRACT FROM AUTHOR]

Geophysical methods have proven to be useful for investigating unstable slopes as they are both non‐invasive and sensitive to the spatial distribution of physical properties in the subsurface. Of particular interest are the links between electrical resistivity and near‐surface moisture content; recent work has demonstrated that it is possible to calibrate hydrological models using geophysical measurements. In this study we explore the use of in‐field electrical resistivity data for calibrating unsaturated soil retention parameters and saturated hydraulic conductivity used for modeling unsaturated fluid flow. We study a synthetic case study, and a well‐characterized site in the northeast of England and develop an approach to calibrate retention parameters for a mudstone and a sandstone formation, the former being an actively failing unit. Petrophysical relationships between electrical resistivity and moisture content (or saturation) are established for both formations. 2D hydrological models are driven by effective rainfall estimations; subsequently these models are coupled with a geophysical forward model via a Markov chain Monte Carlo approach. For the synthetic case, we show that our modeling approach is sensitive to the moisture retention parameters, while less so to saturated hydraulic conductivity. We observe the same characteristics and sensitivities for the field case, albeit with a greater data misfit. Further hydrological simulations suggest that the slope retained high moisture contents in the months preceding a rotational failure. Therefore, we propose that coupled hydrological and geophysical modeling approaches could aid in enhancing landslide monitoring, modeling, and early warning efforts. Plain Language Summary: The electrical properties of the ground can be particularly useful in characterizing and monitoring landslides, as they are dependent on key physical properties including moisture content, soil/rock composition and porosity (voids). First, different rock types in landslides have different resistivity values, which helps map weak geology at depth. Second, as moisture content in the ground increases it becomes less electrically resistive; this means that the resistivity of the ground changes with the addition of water, usually from rainfall. In this research, we use the relationships between electrical resistivity and soil moisture to calibrate models of fluid flow in the subsurface for a known landslide. The issue with unstable slopes is that failure is often associated with increased moisture content, therefore modeling fluid flow in the subsurface is important for assessing slope stability. In this study the electrical properties of the ground were measured using electrodes physically inserted into the landslide surface. We ran several thousand simulations of fluid flow to calibrate our modeling parameters against electrical measurements. We found that the moisture content of the slope was sustained at high levels prior to recorded failure events. Hence, we suggest that electrical measurements on landslides could be useful for landslide early warning systems. Key Points: Geoelectrical methods are useful for investigating moisture content levels inside of unstable slopesUnsaturated hydrological modeling parameters can be calibrated with coupled hydrogeophysical modelingCalibrated hydrological models indicate the studied landslide retained high moisture contents prior to recorded failures [ABSTRACT FROM AUTHOR]

Tidal freshwater marshes are threatened by seawater intrusion globally due to freshwater discharge reduction and sea‐level rise. However, terrestrial nitrate (NO3−) transport responding to seawater intrusion remains poorly understood in tidal marshes. After validation against laboratory experiments, numerical simulations were conducted to analyze seawater intrusion effects on terrestrial NO3− transport and transformation in tidal marsh aquifers. Results reveal that seawater intrusion noticeably affects NO3− transport from the marsh aquifer to the tidal creek. Seawater intrusion results in an upper saline plume and a saltwater wedge within the aquifer, which markedly narrows the discharge outlet width of the NO3− plume and intensifies the peak NO3− flux across the creek bank. Consequently, both the NO3− removal efficiency and total nitrogen gas load to the creek decrease substantially after seawater intrusion. This is because the reduction of the transit time and the mixing zone width of the NO3− plume after seawater intrusion weakens denitrification. Sensitivity analyses indicate that the difference of the NO3− removal efficiency before and after seawater intrusion depends on soil properties. A larger unsaturated flow effect, saturated hydraulic conductivity or effective porosity leads to a greater difference of the NO3− removal efficiency before and after seawater intrusion. The predicted decrease of the NO3− removal efficiency after seawater intrusion is consistent with existing field data. Plain Language Summary: Tidal marshes, including salt marshes and freshwater marshes, are the last barrier to discharging land‐sourced solutes to the ocean. As a result of sea‐level rise and anthropogenic activities, seawater intrusion is a widespread threat to tidal freshwater marshes. Conversely, salt marshes can be freshened by inland freshwater during the flood season. Based on a combination of laboratory experiments and computer simulations, the present study explores how terrestrial nitrate (NO3−) transport responds to seawater intrusion in tidal marsh aquifers. The NO3− removal efficiency and total nitrogen gas load to the tidal creek are calculated to quantify seawater intrusion effects on terrestrial NO3− transport. Both the NO3− removal efficiency and total nitrogen gas load to the tidal creek decrease substantially after seawater intrusion. This study has wide applications while designing strategies for coastal water and marsh management. Key Points: Seawater intrusion plays an important role in terrestrial nitrate transportNitrate removal efficiency and total nitrogen gas load to the tidal creek decrease substantially after seawater intrusionThe difference of the nitrate removal efficiency before and after seawater intrusion depends on soil properties [ABSTRACT FROM AUTHOR]

Identifying highly channelized hydraulic conductivity fields and contaminant source parameters remains a challenging task, primarily due to the non‐Gaussian nature and high dimensionality of the parameter space, as well as the computational burden caused by repeatedly running forward numerical models. This study proposes a novel deep learning parameterization method called AEdiffusion, which combines Diffusion Denoising Probabilistic Model (DDPM) with Variational Autoencoder (VAE) for dimensionality reduction. The method employs a generator‐refiner strategy to generate high‐dimensional aquifer properties from low‐dimensional latent representations. The inversion modeling was performed on a synthetic non‐Gaussian hydraulic conductivity field with line‐source contamination using the Iterative Local Updating Ensemble Smoother (ILUES) algorithm. The results demonstrate that the AEdiffusion‐ILUES framework can accurately identify model parameters. To reduce the computational burden, an AR‐Net‐WL (ARNW) surrogate model was introduced, resulting in an efficient inversion framework (AEdiffusion‐ILUES‐ARNW) with similar prediction accuracy and predictive uncertainty estimation as the AEdiffusion‐ILUES but at a lower computational cost. Plain Language Summary: Identifying highly channelized hydraulic conductivity fields and contaminant source parameters is crucial for developing groundwater remediation strategies. However, this remains a challenging task due to the non‐Gaussian nature and high dimensionality of the parameter space, as well as the computational burden caused by repeatedly running numerical models. We propose a novel deep learning‐based inversion framework to identify hydraulic conductivity fields and contaminant sources from sparse and error‐prone observations. Key Points: A novel and accurate deep learning parameterization method combining DDPM and VAE is proposed to parameterize non‐Gaussian hydraulic conductivity fieldsA deep autoregressive neural network is integrated into the inversion framework as a surrogate to alleviate the high computational cost of the forward numerical modelsThe integrated approach is assessed with inverse problems for the identification of a non‐Gaussian conductivity and line contaminant source parameters [ABSTRACT FROM AUTHOR]

Machine learning (ML) has been extensively applied in various disciplines. However, not much attention has been paid to data heterogeneity in databases and number of samples used to train ML models in hydrology. In this study, we addressed these issues and their impacts on the accuracy and reliability of ML models in the estimation of saturated hydraulic conductivity, Ks. We selected 17,990 soil samples from the USKSAT database and created random subsets N = 2,000, 4,000, 6,000, 8,000, 10,000, 12,000, 14,000, 16,000, and 17,990, 80% of which were used for training. The random subset selection was repeated 50 times. The extreme gradient boosting (XGBoost) algorithm was used to estimate Ks from other soil properties, such as bulk density, soil depth, texture, and organic content. For each subset, we conducted the learning curve analysis on the training and cross‐validation data sets. Results showed that for all training sample sizes the number of samples was not enough for the training and cross‐validation curves to reach a plateau. We also applied the concept of representative elementary volume by plotting the average coefficient of determination, R2, and root mean square log‐transformed error, RMSLE, against the training sample size. For the testing data set, as the number of training sample size increased from 1,600 to 14,392 the average R2 value increased from 0.74 to 0.90, while the average RMSLE value decreased from 1.08 to 0.69. Either the learning curve or representative sample size analysis is required to investigate whether the number of samples is enough or not. Key Points: Learning curves were applied to address effects of data heterogeneity and number of samples on machine learning‐based model estimationsConcept of representative elementary volume was used to determine the representative sample size in machine learningThe number of samples was not enough for the training and cross‐validation curves to reach a plateau [ABSTRACT FROM AUTHOR]

Accurate subsurface soil moisture (SM) estimation is critical for vegetation growth, drought monitoring, and climate change mitigation, yet remains a significant challenge. Previous data assimilation (DA) approaches are limited to only surface SM assimilation. In this study, we utilized the proxy subsurface SM estimated via the exponential filter method (ExpF) as another assimilation variable in our 2‐dimensional DA. Meanwhile, the dual updating DA scheme was implemented to simultaneously update model parameters and states. The two DA pathways were incorporated into the proposed framework (DA_1E_D), which enhanced the subsurface SM accuracy, with the effects of 2‐dimensional assimilation being more significant. Under 2‐dimensional DA, the information transfer between layers was more accurately characterized, leading to overall improvements with unbiased root‐mean‐square error (ubRMSE) reductions of 0.015 and 0.005 m3 · m−3, and Kling–Gupta efficiency (KGE) increases of 0.248 and 0.067 for surface and subsurface SM, respectively, across five SM networks. The soil thickness (d2) and hydraulic conductivity exponent (expt2) are the most influential parameters affecting subsurface SM dynamics through model propagation. DA_1E_D also outperformed ExpF in subsurface SM accuracy, particularly in SM networks with weak surface‐subsurface correlation, achieving an average ubRMSE reduction of 0.003 m3 · m−3 and an average KGE increase of 0.202. It was also applied to Soil Moisture Active Passive data at regional scale, demonstrating significant improvements. The model surface‐subsurface SM coupling was adjusted toward the actual coupling after subsurface assimilation and dual updating. This study may provide new insights into the diagnosis and refinements of the model representation of surface‐subsurface processes. Plain Language Summary: Soil moisture (SM) is a key variable in the fields of hydrology, ecology, and agriculture, and in characterizing Earth's climate. Particularly, accurate subsurface SM estimation remains challenging for the Earth science community. Here, we used the empirical subsurface SM estimates derived from an exponential filter method (ExpF) as another assimilation variable, in combination with the data assimilation (DA) technique which updates model states and parameters simultaneously, to constrain the model estimates. We found these two pathways lead to significant improvements in subsurface SM estimation. The accuracy of subsurface SM was improved with biases (ubRMSE) significantly reduced by 0.005 m3 · m−3 on average over the modeling grid cells, due to the assimilation of empirical subsurface SM. The effects of parameter updating were relatively smaller but also positive. The proposed DA framework demonstrated superior accuracy to ExpF, with an average ubRMSE reduction of 0.003 m3 · m−3 and an average KGE increase of 0.202. This framework was also applicable to regional scale using satellite products. Moreover, both pathways proved effective in adjusting the physical surface‐subsurface correlation in the land surface model toward actual coupling. Our analysis has important implications for future studies on estimating subsurface SM using land surface models at larger spatiotemporal scales. Key Points: A 2‐dimensional data assimilation (DA) framework which accounted for a dual state‐parameter updating scheme was proposedThe accuracy of subsurface soil moisture (SM) was improved by assimilating empirical subsurface estimates and dual updatingThe proposed DA framework can also be applied to Soil Moisture Active Passive data to improve subsurface SM estimation at regional scale [ABSTRACT FROM AUTHOR]

The saltwater‐freshwater mixing zones in coastal aquifers can host complex physical exchange and biogeochemical transformations. The land‐sourced dense contaminant plumes could be transferred into the mixing zone of the saltwater wedge due to the density effect prior to discharge to the sea. However, the mixing process between dense contaminants and the saltwater wedge has not received much attention, largely due to the lack of physical evidence. This study used laboratory experiments and numerical simulations to investigate the transport and discharge behaviors of variable‐density contaminant plumes in tidally influenced unconfined coastal aquifers. Results demonstrate that the highly dense contaminants mix with the underlying saltwater and finally merge with the saltwater wedge. This process significantly extends the contaminant discharge durations, thereby reducing the peak value of contaminant efflux. The dense contaminants are elongated along the landward margin of the saltwater wedge, leading to a larger spreading area (Ms) than that of constant‐density contaminants. The sensitivity analysis indicates that the high density of contaminants acts as a trigger to induce the mixing of them and wedges. The higher hydraulic conductivity, lower dispersivities and reduced inland freshwater flux significantly increase the residence times (Rt) and discharge duration (Dt) by enhancing the mixing of dense contaminants with seawater. In contrast, both Rt and Dt values are not only non‐monotonic functions of tidal amplitudes but also less sensitive to tidal effects. Compared with the non‐tidal condition, however, the addition of tides significantly increases both Rt and Ms values of dense contaminant plumes. The results presented herein provide valuable insights into the mechanisms of dense contaminants mixing into saltwater wedges, which could guide practitioners in designing effective strategies to protect coastal environments from land‐sourced contaminants. Key Points: The process of dense contaminant plumes mixing into the saltwater wedge is experimentally observed for the first timeThe high density of contaminants triggers their mixing with the saltwater wedge, thereby extending their residence timesThe gravity and modified Rayleigh numbers assess how hydrogeological parameters affect the mixing of dense contaminants into saltwater wedges [ABSTRACT FROM AUTHOR]

Characterizing the 3D distribution of hydraulic properties in glacial sediments is challenging due to fine‐scale heterogeneity and complexity. Borehole lithological data provide high vertical resolution but low horizontal resolution. Geophysical methods can fill gaps between boreholes, providing improved horizontal resolution but low vertical resolution. Machine learning can combine borehole and geophysical data to overcome these challenges. However, few studies have compared multiple machine learning methods for predicting hydrofacies in glacial aquifer systems. This study uses colocated airborne electromagnetic resistivity and borehole lithology data to train multiple machine learning models and predict the 3D distribution of hydrofacies in glacial deposits of eastern Nebraska, USA. Random Forest, Gradient Boosting Classifier, Extreme Gradient Boosting, Multilayer Perceptron, and Stacking Classifier were used to model 3D probabilistic distributions of hydrofacies (sand and clay) at a grid size of 200 m × 200 m × 3 m. Comparison of the predicted 3D hydrofacies models shows that the probability distributions and the contrasts between hydrofacies vary. The classification metrics show that the Stacking Classifier model performed better than other machine learning models in predicting hydrofacies. Multi‐Layer Perceptron and Stacking Classifier models show sharp vertical transitions between the low and high sand probability while other machine learning models show gradual transitions. K‐means clustering was used to translate the Stacking Classifier model into a 4‐class hydraulic conductivity model. This study shows that machine learning methods advance our understanding of glacial hydrogeology by improving the vertical and horizontal resolution of hydrofacies distribution and resolving aquifer‐aquifer and stream‐aquifer connections. Plain Language Summary: Sediments deposited by glaciers are host to numerous aquifers globally, including the northern USA, providing an important source of groundwater. The size, shape, and physical properties of these aquifers are highly variable, so predicting groundwater flow and resource availability is a challenge. We used machine learning and data from airborne geophysics and boreholes to generate high‐resolution, 3D models of a glacial aquifer in Nebraska, USA. We compare and contrast five different machine learning models, showing that there are differences in the models' performances and abilities to construct geologically plausible results. These models help estimate the aquifer properties, locate aquifer boundaries, and provide a basis for constructing numerical models of groundwater flow. Key Points: A machine learning approach is presented for 3D probabilistic hydrofacies modeling using AEM and borehole dataThis approach generates clustered probabilistic hydrofacies and estimates aquifer and streambed hydraulic conductivity3D probabilistic hydrofacies allow for characterizing the heterogeneity and continuity of aquifer and aquitard units [ABSTRACT FROM AUTHOR]

Heterogeneity is a natural characteristic of aquifers, which has a profound influence on groundwater flow and solute transport. However, the heterogeneity in an aquifer is difficult to characterize and its impact on groundwater response to Earth tides remains insufficiently explored. A common heterogeneity in thick aquifers is the decrease in porosity and hydraulic conductivity with depth. In the present study, we present an analytical model that includes this particular heterogeneity in both the unsaturated and saturated zones to explore its impact on the tidal response. Our results reveal that, as the hydraulic conductivity decays with depth, the amplitude ratio of the tidal response increases and its phase shift decreases, and the impact of the capillary zone on tidal responses is primarily restricted to the shallow region of the aquifer. Neglecting the decay of conductivity in the previous models would result in underestimation of the amplitude ratio and overestimation of the phase shift. The solutions are applied to the field data to effectively estimate the decay in conductivity with depth. This study highlights the importance of considering aquifer heterogeneity in the analysis of the response of saturated and unsaturated flow to Earth tides. Key Points: Decay in conductivity with depth causes an increase in amplitude ratio and a decrease in phase shiftInfluence of capillary zones on tidal responses is restricted to shallow aquifers due to decrease in conductivity with depthHomogeneous solutions estimate mean conductivity well with smaller decay rates of conductivity, but underestimate with larger decay rates [ABSTRACT FROM AUTHOR]

Characterizing the spatiotemporal variability of water fluxes at the stream‐groundwater interface is extremely challenging due to the lack of methods for estimating hyporheic flows at different scales. To address this, we demonstrate the potential of Active‐Distributed Temperature Sensing (DTS) methods for measuring and mapping hyporheic flow in a lowland stream. Experiments were conducted by burying a few hundred meters of heatable Fiber‐Optic cables within streambed sediments in a large meander, where permanent stream‐losing conditions are observed along the stream reach. We propose a new methodology to filter ambient temperature variations along the heated section of the DTS cable and to extend the application of Active‐DTS to losing streams. After data processing, the results show that, along lateral and longitudinal stream profiles, both thermal conductivity and water flux values follow normal distributions with relatively small standard deviations. Hyporheic fluxes vary by one order of magnitude. The absence of correlation between water fluxes within the hyporheic zone and streambed topography variations suggests that the variability is mainly controlled by local streambed heterogeneities. This means that the spatiotemporal variability of fluxes may be used as a marker of the variability of streambed hydraulic conductivities. The relatively low spatial variability (one order of magnitude) in hyporheic flow suggests a small variability of streambed properties. This is an important result for calibrating models assessing hyporheic processes, in which the hydraulic conductivity distribution is generally assumed. Additionally, measurements made over three years yield similar estimates showing the remarkable stability of hyporheic flows through time. Plain Language Summary: Characterizing the interactions between groundwater and surface water is extremely challenging although such interactions control water quality and ecosystems resilience to climate changes. Here, we used an innovative approach based on heated fiber optic cables, called Active‐Distributed Temperature Sensing, to image the spatial variability of hyporheic fluxes in a lowland stream. Our results show that the instrumental developments as well as the data processing methodology are very robust to accurately measure in‐situ the thermal conductivity of stream sediments and hyporheic fluxes within the streambed. Interestingly, groundwater flux variability was found relatively limited and not correlated to the morphology of the riverbed. In addition, measurements made over three years yield similar estimates showing the excellent reproducibility of the measurements and the remarkable stability of hyporheic flows through time. These results shed new light about the spatial and temporal variability of hyporheic fluxes in a lowland river. Key Points: Active‐Distributed Temperature Sensing was used in a lowland stream to assess and map the spatiotemporal variability of stream infiltrationAn innovative field setup and a new methodology was developed to remove ambient temperature variations from the raw temperature signalResults suggest relatively homogeneous streambed properties and show remarkable stability of hyporheic flow during few years [ABSTRACT FROM AUTHOR]

With modern agricultural practices, it is essential to quantify flow and solute transport fluxes by numerical models and associated predictions. A major challenge in modeling preferential flow settings is the ability to constrain the often numerous parameters needed to physically represent these systems. Following this, there is a lack of understanding of what parameters and observations carry the most worth for a model to reduce its prediction uncertainty. Here, first‐order second moment (FOSM) analyses were used for a heavily monitored clay till field with preferential flow to investigate which parameters and observation types contribute the most to reducing the uncertainty of bromide predictions at various depths. Using a multi‐objective regularized optimization approach, a 1‐D preferential flow model was calibrated and subjected to FOSM analyses. Key parameters contributing to the prediction uncertainty of bromide concentrations in 0.25–3 m were limited to the lower boundary condition, the mass transfer coefficient, the hydraulic conductivity of the micro‐ and macropore, the macropore porosity, and the water content at wilting point. The data with the largest worth and ability to reduce the pre‐calibration prediction uncertainty were concentration observations closest to the sought prediction depth, drain concentrations, and averaged water table measurements from the entire field. The post‐calibration prediction uncertainty was increased primarily by removing concentration observations closest to the prediction depths. While this study provided new insights into parameter importance and data worth further research is required to understand if these findings apply broadly to clay till settings (or any soil setting) with preferential flow. Plain Language Summary: Modeling preferential flow settings is challenging because it involves many parameters, and it's not clear which ones are crucial for accurate predictions. Neither is it known what observations should be gathered to reduce the prediction uncertainty the most. A study in a clay till field with preferential flow used first‐order second moment analyses to identify the most influential parameters and observations for reducing uncertainty in predicting bromide concentrations at different depths. The study found that a few parameters played a significant role in prediction uncertainty, such as the lower boundary condition, mass transfer coefficient, hydraulic conductivity of micro‐ and macropores, macropore porosity, and water content at wilting point. Certain types of observations were also key: concentration data closest to the depth of interest, drain concentrations, and average water table measurements across the field. While this research provides valuable insights, more studies are needed to determine if these findings apply to similar clay till settings with preferential flow paths or other soil conditions. Key Points: Quantifying data worth for reducing prediction uncertainty in structured soilsIdentification of model parameters contributing to prediction uncertainty in structured soils [ABSTRACT FROM AUTHOR]

The interaction between climate and groundwater forms a complex, coupled system that affects land‐atmosphere feedback processes and thus local climatic parameters. We propose an analytical framework that integrates local groundwater information and soil hydrophysical characteristics to identify regions with bidirectional (two‐way) coupling where groundwater is influenced by climatic factors (e.g., precipitation) and may affect local climate (e.g., through surface fluxes). The framework capitalizes on the concept of the evaporation characteristic length to quantify the hydraulic connection of groundwater to the soil surface. To evaluate the framework, we calculate the maximum depth of hydraulic connection (Dmax) between groundwater and the soil surface in Hamburg, Germany. For regions with Dmax exceeding the groundwater depth (d), a bidirectional mode of coupling is defined, while Dmax < d implies a unidirectional coupling mode. Our results indicate that climate driven evaporation changes potentially alter the coupling between groundwater and climate depending on soil texture. Moreover, soil hydraulic properties and shallow groundwater tables could play a crucial role in shifting land‐atmosphere feedback processes by influencing the coupling mode. This research provides insights into the groundwater‐climate interactions under various climatic conditions and soil textures which could contribute to sustainable land‐use management practices, particularly in regions characterized by bidirectional coupling. Plain Language Summary: This study explores the hydraulic connection between climate and groundwater. We developed an analytical framework that combines local groundwater levels and soil hydrophysical characteristics to identify areas with potential two‐way climate‐groundwater interaction. In areas with bidirectional mode of coupling not only the groundwater is influenced by the climate (e.g., through precipitation), but also it may affect climatic parameters by influencing soil moisture and evapotranspiration. We employed the framework to calculate the maximum depth of hydraulic connection (Dmax) linking groundwater and climate in Hamburg, Germany. Results identify bidirectional coupling zones, where climate and groundwater can mutually influence each other. We found that changes in soil properties, evaporation dynamics, and groundwater levels affect the climate‐groundwater coupling thus shedding light on the impact of (shallow) groundwaters on land‐athmosphere feedback processes. Key Points: A physically based framework was proposed to quantify effects of soil hydraulic properties on groundwater and climate interactionsSaturated hydraulic conductivity and groundwater levels are crucial for assessing the coupling modes in the study area (Hamburg, Germany)Combined effects of climatic parameters, soil properties and shallow groundwater influence the mode of coupling in Hamburg, Germany [ABSTRACT FROM AUTHOR]

The non‐Darcy flow behavior in unfilled and fully filled rough fractures has been investigated thoroughly for decades. Natural fractures usually be partially filled with porous media due to long‐term internal and external dynamic disturbances and water flow erosion. However, how to evaluate the nonlinear seepage characteristics of the partially filled rough fracture (PFRF) is never scrutinized. In the present study, 2D direct numerical simulations are conducted to investigate the non‐Darcy behavior for flow through 6 PFRF models under different filling conditions (i.e., filling degree, roughness, and hydraulic conductivity capability of the filling medium), which included coupling between the free and seepage flow in the unfilled and filled region, respectively. The results show that the critical non‐Darcy factor E = 0.02 can be used to judge the onset of the non‐Darcy regime in PFRF, which is also the critical point of eddy region (ER) volume mutation. The higher the filling degree and the weaker the hydraulic conductivity of the filled medium, the more significant the non‐Darcy behavior. Furthermore, the variation of ER volume can be divided into three stages with the increasing inertia effect, that is, stable stage (E < 0.02), slow nonlinear growth stage (0.02 ≤ E ≤ 0.1), and rapid linear growth stage (E > 0.1). In addition, a new model for quantitatively evaluating the non‐Darcy behavior of PFRF is developed via gene expression programming based on 735 simulation data set, which is further employed to establish the relationship between the friction factor. Plain Language Summary: The nonlinear flow behavior in partially filled rough fractures (PFRF) was investigated by using 2D simulations. The simulation results revealed a critical non‐Darcy factor of 0.02 to determine the onset of non‐Darcy behavior in PFRF. Higher filling degrees and weaker hydraulic conductivity of filling region intensified the non‐Darcy effect. The volume of eddy regions exhibited three stages of variation with increasing inertia effect (i.e., stable stage, slow nonlinear growth stage, and rapid linear growth stage). We developed a new model based on gene expression programming to quantitatively evaluate PFRF's non‐Darcy behavior. This study enhances the understanding of fluid flow in partially filled rough fractures, benefiting for advancing the understanding of nonlinear seepage and solute transport in partially filled rough fractures. Key Points: Critical non‐Darcy factor E = 0.02 can be used to determine the onset of the non‐Darcy regimeVolume evolution of eddy region can be classified into stable, slow nonlinear growth, and rapid linear growth stagesA nonlinear seepage model is developed for partially filled rough fractures [ABSTRACT FROM AUTHOR]

Steady flow toward a fully penetrating well takes place in a natural porous formation, where the erratic spatial variations, and the raising uncertainty, of the hydraulic conductivity K are modeled within a stochastic framework which regards the log‐conductivity, ln K, as a Gaussian, stationary, random field. The study provides second order moments of the flow variables by regarding the variance of the log‐conductivity as a perturbation parameter. Unlike similar studies on the topic, moments are expressed in a quite general (valid for any autocorrelation function of ln K) and very simple (from the computational stand point) form. It is shown that the (cross)variances, unlike the case of mean uniform flows, are not anymore stationary due to the dependence of the mean velocity upon the distance from the well. In particular, they vanish at the well because of the condition of given head along the well's axis, whereas away from it they behave like those pertaining to a uniform flow. Then, theoretical results are applied to a couple (one serving for calibration and the other used for validation purposes) of pumping tests to illustrate how they can be used to determine the hydraulic properties of the aquifers. In particular, the concept of head‐factor is shown to be the key‐parameter to identify the statistical moments of the random field K. Plain Language Summary: Flow toward a single well takes place in a porous formation, where the hydraulic conductivity is regarded as a random space function to account for its irregular spatial variability. A simple solution to this difficult problem is achieved by adopting some simplifying assumptions which apply to numerous real settings. Theoretical results are applied to a series of pumping tests in order to demonstrate their utility in the identification of aquifers' hydraulic properties. Key Points: A simple, general formulation to compute second‐order moments is presentedThe head factor is introduced for a robust identification of aquifers' statistical parametersThe application to pumping tests is illustrated and discussed [ABSTRACT FROM AUTHOR]

Understanding the spatio‐temporal dynamics of runoff generation in headwater catchments is challenging, due to the intermittent and fragmented nature of surface flows. The active stream network in non‐perennial rivers contracts and expands, with a dynamic behavior that depends on the complex interplay among climate, topography, and geology. In this work, CATchment HYdrology, an integrated surface–subsurface hydrological model (ISSHM), is used to simulate the stream network dynamics of two virtual catchments with the same, spatially homogeneous, subsurface characteristics (hydraulic conductivity, porosity, water retention curves) but different morphology. We run two sets of simulations to reproduce a sequence of steady‐states at different catchment wetness levels and transient conditions and analyze the joint variations of the stream length (L) and discharge at the outlet (Q) with high spatio‐temporal resolutions. The shape of the L(Q) curves differs in the two catchments but does not depend on the climate forcing, as it is mainly controlled by the underlying topography. We then analyzed the suitability of the topographic wetness index and the contributing area to identify the spatial configuration of the maximum stream length in the two catchments. These two morphometric parameters provided a good estimate of the spatial distribution of the maximum flowing network in both the study catchments. Our numerical simulations indicate that ISSHMs have the potential to accurately describe the spatio‐temporal variations of the stream networks and the processes driving such dynamic behavior and that, overall, they can be useful tools to gain insights into the main physical drivers of non‐perennial streams. Key Points: A physics‐based model is used to reproduce the spatiotemporal stream network dynamics of two virtual catchments with different morphologyThe link between active stream length and outlet discharge is analyzed in steady‐state and transient conditionsWell‐established topographic indices can identify the maximum active network extent in catchments with homogeneous subsurface properties [ABSTRACT FROM AUTHOR]

Lateral subsurface flow plays an essential role in sustaining the terrestrial ecosystem, but it is not explicitly represented in most Earth System Models. In this study, we implemented an explicit lateral saturated flow model into the E3SM land model (ELM). The model explicitly describes lateral flow in the saturated zone by representing, for each model grid, an idealized hillslope consisting of five hydrologically connected soil columns. We conducted three model experiments driven by 0.125° atmospheric forcing data during 1980–2015 over California using models of the default ELM, a modified version of ELM to enhance infiltration, and the model with the lateral saturated flow model. The simulated runoff, evapotranspiration, and terrestrial water storage anomaly (TWSA) from the three simulations were evaluated against available observations, and the model explicitly representing lateral flow performs best. The new model produces greater gridcell‐averaged evapotranspiration especially over the mountainous regions with moderate relief and seasonally dry climates. Most importantly, it improves the modeled seasonal variations, interannual variabilities, and the recent decadal decline of TWSA. Many of these improvements can be attributed to the enhanced ecosystem resilience to droughts as demonstrated by transpiration increases caused by lateral flow. Model sensitivity experiments suggest that subsurface runoff is most sensitive to the ratio between horizontal and vertical saturated hydraulic conductivity, followed by hillslope planforms (convergent, divergent, and uniform), number of columns, and lower boundary conditions. Future work should effectively characterize hillslopes in global models and explore the long‐term influences of lateral water movement on modeled biogeochemical cycle. Plain Language Summary: In this study, we implemented a lateral saturated flow scheme into the Energy Exascale Earth System Model's land model (ELM) to explicitly represent lateral groundwater movement. We applied our newly developed model over California and found better model performance against the original and a revised version of ELM through the explicit yet simplified representation of lateral flow along hillslopes. Most importantly, our new model does a better job at reproducing the seasonal variations, interannual variabilities, and a declining trend of terrestrial water storage anomaly in California. Given the intensified coupling among water, energy, and carbon cycles associated with climate change, our study highlights the need to implement lateral flow in Earth System Models for better climate projections. Key Points: A land model with an explicit lateral saturated flow model produces runoff and evapotranspiration reasonably well in the California basinIt simulates a better declining terrestrial water storage trend during droughts as lateral flow enhances ecosystem resilienceLateral subsurface flow is most sensitive to the ratio between vertical and horizontal hydraulic conductivity followed by hillslope shape [ABSTRACT FROM AUTHOR]

Fractures significantly alter the permeability characteristics of the natural porous media, especially for the multilayered porous medium system. The most direct and effective approach to assess the hydraulic conductivity of a multilayered porous medium with continuous fracture is to determine its equivalent permeability coefficient (EPC). A mathematical model with second‐order accuracy is established to analysis the permeability characteristics of the multilayered porous medium incorporating a continuous fracture. The Navier‒Stokes equation is used to govern the clear fluid motion in the continuous fracture, and the seepage fluid motion in the multilayered porous matrix is governed by the Brinkman‒Darcy equation. The semi‐analytical solutions for the velocity profile and EPC of the present model are derived under the conditions of the jumping stress at the fracture‐matrix interface and the continuous velocity at the matrix(i)‐matrix(i +1) interface. The Lattice Boltzmann method, finite element method, and one domain method simulations are conducted to verify the deduced semi‐analytical solutions of the velocity profile. Furthermore, the calculated EPC of the present multilayered model is in good agreement with that of the existing classic models (i.e., one region: fracture, two regions: fracture‐matrix, three regions: fracture‐matrix1‐matrix2, and multilayered porous medium without fracture). Parameter sensitivity reveals that increasing the thickness, dip angle, and porosity of the fractured porous media increases the flow velocity, while an increase in the stress jump coefficient can result in the opposite effect. This implies that porous layers containing fracture are more susceptible to erosion, particularly under conditions of steep dip angle and strong permeability. Plain Language Summary: Fractures in porous mediums change how fluids flow through them, especially in multilayered porous materials. To accurately evaluate fluid flow within these complex systems, we developed a mathematical model with high accuracy. This model employs both the Navier‒Stokes equations and the Brinkman‒Darcy equation to elucidate the fluid flow in fractures and porous matrices. Consequent to this modeling, solutions for fluid velocity and equivalent permeability coefficient (EPC) of the fractured multilayered porous media were derived. Simulations verified the derived solutions. Compared with existing models, the calculated EPC values matched well. Sensitivity analysis revealed that wider fractures, steeper angles, and higher porosity increased fluid flow, while higher stress jump coefficients reduced it. The approaches in this study will be of significant importance for CO2 geological storage, groundwater contaminant transport, and hydrocarbon extraction. Key Points: The permeability characteristics of fractured porous medium can be assessed by the equivalent permeability coefficientThe coupling of fluid flow between the fracture and matrix is achieved under stress jumping boundary conditionThe existing models including fracture, fracture‐matrix, and multilayered porous medium are special cases of the present model [ABSTRACT FROM AUTHOR]

The accurate characterization of hydraulic conductivity heterogeneities in an aquifer is crucial for predicting flow and transport processes correctly. Hydraulic tomography (HT) experiments are often used to infer the hydraulically relevant features, but the correct inversion of the data remains a challenging task. We implemented a discrete fracture network (DFN) inversion approach that is expanded by considering a nonzero matrix permeability. The hybrid model allows the accurate characterization of fractured‐porous sites by taking into account both matrix and fracture flow. This novel inversion algorithm is successfully applied to HT data acquired at a field site in Goettingen (Germany), and the results are compared with those of a standard travel time inversion. Furthermore, we validate the inversion results by using them as the underlying material parameters for simulating heat tracer experiments and comparing the modeled temperature responses with those of heat tracer tests actually conducted at the site. It is shown that the DFN ensemble predicts the thermal response of the experiments correctly for the two major fractures in terms of location, amplitude, and time‐dependent behavior of the temperature anomaly, as long as the stochastic nature of the results is taken into account. We conclude that considering both matrix and fracture flow in a hybrid DFN inversion approach can lead to significant improvements in flow and transport modeling at fractured‐porous sites. Plain Language Summary: For understanding groundwater processes correctly, precise knowledge about the relevant geological structures in the subsurface is crucial. To infer this information, hydraulic tomography (HT) experiments are often used, which are based on sequential pumping tests in boreholes. The acquired data are usually processed by inversion techniques that allow for computing a subsurface model from the field observations. There are two different conceptual approaches: (a) continuum models, which assume a smooth distribution of the hydraulic parameters, and (b) discrete fracture network (DFN) models, which are based on an impermeable rock matrix, crossed by a limited number of fractures exclusively responsible for groundwater flow. However, certain sites show characteristics of both models, meaning that both the rock matrix and individual fractures are relevant. Therefore, we developed a new inversion technique (hybrid DFN inversion) that combines the two approaches. The method is tested on HT data acquired at a field site in Goettingen (Germany), and the results are validated against data from independent experiments (thermal tracer tests). It is shown that the subsurface models from the new hybrid DFN inversion are more accurate and reliable. We conclude that groundwater modeling at those sites can be improved significantly when using the new inversion method. Key Points: A novel inversion approach for hydraulic tomography (HT) data considering flow in both discrete fractures and porous matrix is introducedThe method is applied to HT data from a fractured‐porous field site in Göttingen (Germany)The results are successfully validated against independent thermal tracer test data [ABSTRACT FROM AUTHOR]

Soil infiltration is critical for water security and related ecosystem services. This infiltration, the ability of soils to absorb water at their surface, is controlled by the soil hydraulic conductivity. Despite recent efforts in assembling measurements of soil hydraulic conductivity, global databases and derived pedotransfer functions lack coverage in the tropics. Here, we present soil infiltration measurements and other indicators of soil and land health collected systematically in 3,573 plots from 83 100 km2 sites across 19 countries in sub‐Saharan Africa. We use these data to (a) determine field‐saturated hydraulic conductivity (Kfs) and (b) explore which variables best predict variation in Kfs. Our results show that sand content, soil organic carbon (SOC), and woody cover had a positive relationship with Kfs, whereas grazing intensity and soil pH had a negative relationship. Our findings highlight that, despite soil texture being important, structure also plays a critical role. These results indicate considerable potential to improve soil hydrological functioning through management and restoration practices that target soil structure. Enhancing SOC content, limiting animal stocking, promoting trees, shrubs, and other vegetation cover, and preventing soil erosion can increase Kfs and improve water security. This data set can contribute to improving Earth system and land surface models for applications in Africa. Key Points: We present field infiltration measurements and accompanying indicators of soil and land health from 3,573 plots across sub‐Saharan AfricaField‐saturated hydraulic conductivity (Kfs) is associated with soil texture and factors related to soil structureOur results suggest that soil hydrological functioning can be enhanced through management practices that target soil structure [ABSTRACT FROM AUTHOR]

The fate of nutrients and contaminants in fluvial ecosystems is strongly affected by the mixing dynamics between surface water and groundwater within the hyporheic zone, depending on the combination of the sediment's hydraulic heterogeneity and dune morphology. This study examines the effects of hydraulic conductivity stratification on steady‐state, two‐dimensional, hyporheic flows and solute residence time distribution. First, we derive an integral transform‐based semi‐analytical solution for the flow field, capable of accounting for the effects of any functional shape of the vertically varying hydraulic conductivity. The solution considers the uneven distribution of pressure at the water‐sediment interface (i.e., the pumping process) dictated by the presence of dune morphology. We then simulate solute transport using particle tracking. Our modeling framework is validated against numerical and tracer data from flume experiments and used to explore the implication of hydraulic conductivity stratification on the statistics and pdf of the residence time. Finally, reduced‐order models are used to enlighten the dependence of key residence time statistics on the parameters characterizing the hydraulic conductivity stratification. Key Points: A new integral transform‐based semi‐analytical solution for hyporheic flows in stratified sediments is provided and tested against dataThe impact of hydraulic conductivity stratification on residence time distribution and its statistics is quantitatively analyzedROMs are used to approximate key residence time statistics in the space of variability of parameters characterizing the conductivity profile [ABSTRACT FROM AUTHOR]

Understanding groundwater resource dynamics is limited by the sparsity of observations of water levels, pumping rates, and hydraulic properties relative to their spatiotemporal heterogeneity. To address some of this complexity, we proposed a new highly parameterized linear inverse method to quantify water table change and groundwater depletion rate in unconfined aquifers that does not require initial or boundary conditions. The method requires linearization, and we tested the performance of six proposed water table functions with three coordinate systems with synthetic models, finding that water table functions by the dimensionless method achieve the lowest errors. Our inverted water table changes and depletion rates remained stable and accurate with head measurement error of 5%. However, inversions became less accurate when head observations contained large temporal gaps. Next, we applied the inversion for water table changes and depletion rates in the Texas High Plains Aquifer (HPA) and the HPA during 2000–2015. To address sparse water levels and uncertain hydraulic conductivity measurements, two modifications were made to improve data constraints for inversion: (a) calculating winter‐time water levels for wells with >1 head observation by linear interpolation and (b) using hydraulic conductivity geostatistical realizations. The inverted water table change and depletion rate expected mean values and uncertainties were reasonable compared to the known pumping records of the Texas HPA. With relatively minor data curation, the new inverse method can quantify spatiotemporally continuous water table change, depletion rates, and their uncertainty for heterogeneous aquifers with temporally sparse and noisy water level observations. Plain Language Summary: Groundwater pumping is causing shallow groundwater levels, or the water table, to lower in unsustainable ways. Because groundwater observations are typically sparse and uncertain, so we do not always know where water tables are dropping or how fast they drop. In this study, we introduced a new mathematical method of accurately estimating water table changes and the related losses in groundwater storage while not needing to know all of the uncertain properties of the ground. We tested this method for make‐up cases and cases of the High Plains Aquifer in the central United States. The results demonstrate that the method is both fast and accurate and can be applied for other aquifers. Key Points: New highly parameterized linear inverse method was developed for unconfined aquifers with unknown initial and boundary conditionsSynthetic and field inversions demonstrate accurate and reasonable results with spatiotemporally sparse and uncertain head observationsThe new inverse method yielded accurate water table change and depletion rates despite large uncertainty in hydraulic conductivity [ABSTRACT FROM AUTHOR]

The amount of fresh water moving through coastal deltas worldwide is controlled by the complex subsurface structures within a delta. Morphodynamic influences produced by the feeding river, waves, and tides, in addition to sea level transgressions and regressions, have resulted in deltaic aquifers that are highly heterogeneous. We use 171 unique two‐dimensional morphodynamic models to explore the range of subsurface permeability, hydraulic gradient, and groundwater flux within three end‐member delta types (fluvial, wave, and tidal). We quantify the connectiveness of the subsurface permeability and estimate the horizontal heterogeneity and anisotropy of the permeability. A distance‐based generalized sensitivity analysis is used to investigate the impact morphodynamic influences (fluvial, wave, and tidal), basin conditions (sediment concentration and bathymetric gradient), and geomorphic characteristics (number of channels, shape of the delta plain, and shoreline rugosity) have on the subsurface permeability, hydraulic gradient, and connectivity. We find that the median permeability in deltaic landforms is 4.0 × 10−12 m2 (relating to a hydraulic conductivity of 2.1 × 10−5 m/s), the average hydraulic gradient is 3.9 × 10−4, and the mean specific discharge is 1.3 × 10−8 m/s. High permeability bodies are highly connected and are associated with channelization. Subsurface permeability, hydraulic gradient, and the connectiveness of high permeability areas are sensitive to morphodynamic influences (fluvial, wave, and tidal) and the geomorphic characteristics (number of channels and shoreline rugosity) within a delta. Since morphodynamic influences and geomorphic characteristics are easily identified by looking at the surface of the delta, we suggest that the deltaic subsurface can be characterized by identifying features on the delta surface. Key Points: Delta morphodynamics controls the permeability, hydraulic gradient, and connectivity of high permeability bodies in coastal deltasHigh permeability bodies are associated with current and previous channelization and are highly connectedWave deltas may be especially susceptible to inundation and groundwater salinization due to high permeability and low hydraulic gradient [ABSTRACT FROM AUTHOR]

Salmon spawning activities alter streambed morphology, forming a dune‐shaped egg nest called a redd. The spawning process increases redd sediment hydraulic conductivity, KD, by removing fines, creating an egg pocket with larger sediment grains such that egg pocket hydraulic conductivity, KEP, may be higher than KD. Salmon females may create one or more egg pockets within a single redd. Although the impact of redd shape and KD on redd‐induced hyporheic fluxes has been studied, the effects of streambed roughness, R, egg pocket permeability, and egg pocket location on egg pocket hyporheic fluxes, q‾ep ${\overline{q}}_{ep}$, (downwelling flows from the stoss side of the redd which may enter egg pockets) have not yet been quantified. This study investigates this knowledge gap with a set of numerical simulations supported by flume experiments. We simulated hyporheic flows for five egg pocket locations, five KEP values from 0.0025 to 0.02 m/s, and 12 rough streambed surfaces. Surface roughness was scaled from a measured streambed surface in two ways—only vertically (R1) and both vertically and horizontally (R2)—with scaling coefficients ranging from 0.5 to 3. The measured streambed surface had a median diameter, D50, of 1 cm and a standard deviation (σD) of 0.77 cm. The results indicate that the dimensionless flux into the egg pocket, q‾ep∗=q‾epKD ${\overline{q}}_{ep}^{\ast }=\frac{{\overline{q}}_{ep}}{{K}_{D}}$ increases noticeably with the downstream distance of egg pockets from the redd pit, and less strongly with KEP∗=KEPKD ${{K}_{EP}}^{\ast }=\frac{{K}_{EP}}{{K}_{D}}$. The near‐surface downwelling fluxes significantly increase with R1, but only negligibly with R2, and for deeper egg pockets, q‾ep∗ ${\overline{q}}_{ep}^{\ast }$ is minimally impacted by surface roughness. Our results suggest that the typical simplification of a smooth redd surface with a single redd hydraulic conductivity provides a good representation of the interstitial flow within the redd, and the effects of surface roughness and egg pocket hydraulic conductivity on q‾ep∗ ${\overline{q}}_{ep}^{\ast }$ fall within the uncertainty of the egg pocket location. Plain Language Summary: Salmonids lay their eggs in the streambed gravel, forming dune‐shaped egg‐nests, called "redds." Here we study water movement through the salmon redd, investigating egg pocket permeability, streambed roughness, and egg pocket locations within the redd. This flow is crucial as it delivers oxygenated water and nutrients to eggs while removing waste, influencing embryo survival. One key finding is that the egg pocket near the downstream end of the redd receives significantly more water, over five times more than the upstream‐most egg pocket. Interestingly, the presence of additional egg pockets within a redd doesn't substantially alter water flow into any specific egg pocket. While higher permeability in the egg pocket can increase the flow, its location has a more substantial impact; an 800% increase in permeability results in only about a 71% increase in flow into the egg pocket. Streambed roughness is less crucial for egg pockets deeper within the redd compared to the effect of redd's shape and egg pocket location. Our results indicate that treating redd as a single, smooth feature helps to understand the key factors affecting water flow into egg pockets. Information on egg pocket location, permeability, and riverbed roughness helps to better estimate the flow variations. Key Points: The interstitial flow toward the egg pocket increases with the distance from the pit, and toward the tailspill crestEgg pocket's higher hydraulic conductivity leads to a modest increase in interstitial flow toward itRedd shape primarily controls flows near egg pockets, with streambed roughness having minimal impact deeper within the redd [ABSTRACT FROM AUTHOR]

Permafrost peatlands are vulnerable to rapid structural changes under climatic warming, including vertical collapse. Peatland water budgets, and therefore peat hydraulic properties, are important determinants of vegetation and carbon fluxes. Measurements of hydraulic properties exist for only a limited number of permafrost peatland locations, primarily concentrated in North America. The impacts of thaw‐induced collapse upon properties such as horizontal saturated hydraulic conductivity (Kh), and thus lateral drainage, remain poorly understood. We made laboratory determinations of Kh from 82 peat samples from a degrading Swedish palsa mire. We fitted a linear mixed‐effects model (LMM) to establish the controls on Kh, which declined strongly with increasing depth, humification and dry bulk density. Depth exerted the strongest control on Kh in our LMM, which demonstrated strong predictive performance (r2 = 0.605). Humification and dry bulk density were influential predictors, but the high collinearity of these two variables meant only one could be included reliably in our LMM. Surprisingly, peat Kh did not differ significantly between desiccating and collapsed palsas. We compared our site‐specific LMM to an existing, multi‐site model, fitted primarily to boreal and temperate peatlands. The multi‐site model made less skillful predictions (r2 = 0.528) than our site‐specific model, possibly due to latitudinal differences in peat compaction, floristic composition and climate. Nonetheless, low bias means the multi‐site model may still be useful for estimating peat Kh at high latitudes. Permafrost peatlands remain underrepresented in multi‐site models of peat hydraulic properties, and measurements such as ours could be used to improve future iterations. Key Points: Depth and humification are important controls for horizontal saturated hydraulic conductivity in a degrading Swedish palsa complexPeat hydraulic properties did not significantly differ between desiccating and collapsed areas of the palsa complexAn existing model, trained on lower‐latitude peatlands, predicted horizontal saturated hydraulic conductivity adequately, with low bias [ABSTRACT FROM AUTHOR]

A new approach for measuring fluxes across surface water—groundwater interfaces was recently proposed. The Automatic Seepage Meter (ASM) is equipped with a precise water level sensor and digital memory that analyzes water level time series in a vertical tube inserted into a streambed (Solomon et al., 2020, https://doi.org/10.1029/2019WR026983). The ability to infer flux values with high temporal resolution relies on an accurate interpretation of water level dynamics inside the tube. Here, we reduce the three‐dimensional hydrodynamic problem that describes the ASM water level in a variety of field conditions to a single ordinary differential equation. This novel general analytical solution for estimating ASM responses is more comprehensive and flexible than previous approaches and is applicable to the entire range of field conditions, including steady or transient stream stages, evaporation, rainfall, and noise. For example, our analysis determines the timing of the nonmonotonic ASM response to a monotonic linear stream stage variation and explains previously used empirical parabolic approximation for estimating fluxes. We present algorithms for simultaneous inference of vertical interface flux and hydraulic conductivity values together with an example code. We quantify how the accuracy of parameter estimation depends on test duration and noise amplitude and propose how our analysis can be used to optimize field test protocols. On this basis, changing the ASM geometry by increasing the radius and decreasing tube insertion depth may enable ASM field test protocols that estimate interface flux and hydraulic conductivity faster while maintaining desired accuracy. Potential applications of joint parameter estimation are suggested. Key Points: A generalized equation of water level dynamics in the Automatic Seepage Meter valid for a variety of field conditionsThe theory considers surface water level fluctuations, evaporation, rainfall, and ambient noiseWater flux and vertical hydraulic conductivity estimation accuracy is analyzed with examples and recommendations [ABSTRACT FROM AUTHOR]

Ponding at the soil surface exerts profound impacts on infiltration. However, the effects of ponding depth on infiltration, especially the development of a saturated zone below the soil surface, have yet to be considered in present infiltration models. A new general Green‐Ampt model solution (GAMS) was derived for a one‐dimensional vertical infiltration problem under a uniform initial moisture distribution with ponding on its surface. An expression was included in the new solution for simulating the saturated layer developed below the soil surface as long as the pressure head at the surface is sufficiently high to saturate the soil. The GAMS simulates the infiltration processes closer to the numerical solution by HYDRUS‐1D than the traditional and the recently improved Green‐Ampt model. Moreover, an inversion method to improve the estimates of soil hydraulic parameters from one‐dimensional vertical infiltration experiments that is based on the GAMS was suggested. The effect of ponding depth (hp), initial soil moisture content, soil texture, and hydraulic soil properties (saturated hydraulic conductivity Ks, water‐entry suction hd and shape coefficient n of soil water retention curve) in the saturated zone was also evaluated. The results indicate that the saturated zone length increased at a comparable rate with the unsaturated wetted zone length during infiltration. Generally, a larger saturated zone was found for soils with higher initial soil moisture contents, coarser texture, higher Ks values, greater n, and lower −hd. Our findings reveal that including the saturated zone in the infiltration model yields a better estimate of the soil hydraulic parameters. The proposed GAMS model can improve irrigation design and rainfall‐runoff simulations. Key Points: An implicit expression was proposed for the development of saturated zone during infiltrationThe newly proposed formula improved the simulation accuracy in all stages of ponded infiltrationThe new approach eliminated the time‐dependency of the estimated soil hydraulic properties [ABSTRACT FROM AUTHOR]

We study the upscaling and prediction of ensemble dispersion in two‐dimensional heterogeneous porous media with focus on transverse dispersion. To this end, we study the stochastic dynamics of the motion of advective particles that move along the streamlines of the heterogeneous flow field. While longitudinal dispersion may evolve super‐linearly with time, transverse dispersion is characterized by ultraslow diffusion, that is, the transverse displacement variance grows asymptotically with the logarithm of time. This remarkable behavior is linked to the solenoidal character of the flow field, which needs to be accounted for in stochastic models for the two‐dimensional particle motion. Here, we derive an upscaled model based on the statistical characterization of the motion of solute particles. To this end, we analyze particle velocities and orientations through equidistant sampling along the particle trajectories obtained from direct numerical simulations. This sampling strategy respects the flow structure, which is organized on a characteristic length scale. Perturbation theory shows that the longitudinal particle motion is determined by the variability of travel times, while the transverse motion is governed by the fluctuations of the space increments. The latter turns out to be strongly anticorrelated with a correlation structure that leads to ultraslow diffusion. Based on this analysis, we derive a stochastic model that combines a correlated Gaussian noise for the transverse motion with a spatial Markov model for the particle speeds. The model results are contrasted with detailed numerical simulations in two‐dimensional heterogeneous porous media of different heterogeneity variances. Plain Language Summary: The hydraulic conductivity of environmental geological formation can exhibit strong spatial variations. This leads to the formation of complex flow fields, where the flow tends to by‐pass low conductivity areas and focuses within preferential flow paths. This complexity controls the transport dynamics of dissolved chemicals. Moreover, due to the lack of knowledge about the details of the formation and its properties, we employ a stochastic approach to predict the fate of transported solutes. We propose a stochastic model for large‐scale solute transport in two‐dimensional heterogeneous Darcy flow in which we incorporate key physical transport mechanisms that occur in the direction aligned with and transverse to the mean direction of flow. Key Points: Flow topology determines transverse particle motionTransverse motion follows a correlated Brownian motionStochastic time‐domain random walk model captures full two‐dimensional particle transport [ABSTRACT FROM AUTHOR]

Clogging of streambeds due to clay deposition influences the stream‐subsurface exchange flux and thus directly modulates hyporheic ecological and biogeochemical processes. Clogging of sandy streambeds has previously been studied under losing and gaining flows and during streambed movement, but not when these two flow conditions coincided. We conducted flume experiments to quantify the combined effect of moving bedforms and losing or gaining flows on kaolinite deposition and streambed clogging. The experiments were conducted by adding pulses of kaolinite in a flume packed with sand under a stream water velocity of 25 cm/s. We measured the deposition rates, dynamics of hyporheic exchange flux (HEF) and vertical hydraulic conductivity (Kv), and the vertical distribution of kaolinite at the end of the experiments under two losing and two gaining flows (Darcy velocity of 10 and 20 cm/day). Kaolinite deposition led to clogging and reduction in Kv and HEF under all flow conditions. Deposition occurred faster under losing flow conditions than under gaining flow conditions. However, the changes in Kv and HEF were similar under losing and gaining flow conditions for similar kaolinite concentrations in the bed. Our results indicate that the deposition patterns of kaolinite were more influenced by bedform movement than by losing or gaining flow conditions, which is markedly different from the behavior observed under losing and gaining conditions for stationary bedforms. This implies that bedform morphodynamics control local‐scale clogging of sandy streambeds and should be accounted for when studying the hydrology of catchments at larger scales. Key Points: Bed movement had a greater influence on kaolinite deposition patterns than either losing or gaining flow conditionsKaolinite accumulated in the bed much more quickly under losing conditions than gaining conditions, causing rapid clogging of the bedHydraulic conductivity and hyporheic flux depended on kaolinite content in the bed and were similar under losing and gaining conditions [ABSTRACT FROM AUTHOR]

Recession analysis is a powerful tool for determining the hydraulic characteristics of a riparian aquifer. The basis of the method relies on two analytical solutions of the nonlinear Boussinesq equation: one applies to a uniform water table profile in a semi‐infinite aquifer while the other pertains to a hypothetical initial profile in a finite aquifer. Both solutions assume that the water depth in the adjoining stream is negligible. In the present work, a nonlinear solution of the one‐dimensional Boussinesq equation is derived using the traveling wave approximation. The solution better represents the field conditions as it pertains to a uniform water table profile in a finite aquifer that is adjoining a stream with a non‐zero water level. It allows the derivation of simple algebraic expressions for the recession of the water table, the flow rate, and the associated drainage volume. Approximations relating the discharge rate to the outflow volume were also obtained for practical implementation in the estimation of the hydraulic parameters of the aquifer. A comparison of the proposed methodology of parameter estimation with the standard method of recession analysis showed that the present approach is superior as it avoids the pitfalls associated with the classical method, especially when daily discharge values with inherent observational errors are used. Application of the recession model to real‐world cases demonstrates its effectiveness in the estimation of the catchment‐scale hydraulic conductivity and drainable porosity. Plain Language Summary: The hydraulic characteristics of aquifers are required for many hydrologic applications and analysis of recession flow is one valuable tool for characterizing an aquifer system. The analysis relies on two solutions of the governing Boussinesq equation, each with restrictive conditions. The present study relaxes those assumptions, derives working relationships, and proposes a more effective method for the estimation of the hydraulic properties of aquifers, the evaluation of the baseflow contribution to streamflow, and the quantification of the aquifer depletion in drought periods. Key Points: Practical expressions for the discharge rate and drainage volume are derivedDischarge‐volume relations for the estimation of the hydraulic parameters are presentedA simple equation for the water table recession is obtained for plausible flow conditions [ABSTRACT FROM AUTHOR]

The western U.S. is experiencing increasing rain to snow ratios due to climate change, and scientists are uncertain how changing recharge patterns will affect future groundwater‐surface water connection. We examined how watershed topography and streambed hydraulic conductivity impact groundwater age and stream discharge at eight sites along a headwater stream within the Manitou Experimental Forest, CO USA. To do so, we measured: (a) continuous stream and groundwater discharge/level and specific conductivity from April to November 2021; (b) biweekly stream and groundwater chemistry; (c) groundwater chlorofluorocarbons and tritium in spring and fall; (d) streambed hydraulic conductivity; and (e) local slope. We used the chemistry data to calculate fluorite saturation states that were used to inform end‐member mixing analysis of streamflow source. We then combined chlorofluorocarbon and tritium data to estimate the age composition of riparian groundwater. Our data suggest that future stream drying is more probable where local slope is steep and streambed hydraulic conductivity is high. In these areas, groundwater source shifted seasonally, as indicated by age increases, and we observed a high fraction of groundwater in streamflow, primarily interflow from adjacent hillslopes. In contrast, where local slope is flat and streambed hydraulic conductivity is low, streamflow is more likely to persist as groundwater age was seasonally constant and buffered by storage in alluvial sediments. Groundwater age and streamflow paired with characterization of watershed topography and subsurface characteristics enabled identification of likely controls on future stream drying patterns. Plain Language Summary: In the western U.S., climate change is causing more precipitation to fall as rain rather than snow and it is currently unclear how, where, and when this shift is going to impact groundwater contributions to streams, which is important for predicting streamflow and many ecosystem services, including stream contaminant processing or thermal refugia for fish habitat. In this study, we instrumented a small, high‐elevation stream in Colorado, USA to determine (a) how much groundwater is contributing to streamflow and (b) how long groundwater spends traveling through the subsurface before doing so. We found that groundwater age ranged from 10 to 55 years, with older groundwater located in areas with flat topography and where water could not move through streambed sediment quickly. We found the areas with steeper topography had more groundwater contributing to streamflow, but this groundwater was younger. We predict that under future climate scenarios, streams in areas with steep topography and young groundwater are more likely to dry. Key Points: Mean groundwater age is youngest in areas with high slope and streambed hydraulic conductivityMean groundwater age shifts older during low flow periodsFuture stream drying is more probable where local slope and streambed hydraulic conductivity are high [ABSTRACT FROM AUTHOR]

Hydraulic tomography (HT) has been demonstrated as a robust approach to characterize subsurface heterogeneity through the inverse modeling of multiple pumping data. However, smooth or even erroneous tomograms can result when insufficient observations are involved in the inversion. In this study, the feasibility of integrating geophysical survey data into HT analysis is investigated. First, k‐means clustering is utilized to extract zonal information from borehole geophysical logs, and a new type of spatial constraints containing geological knowledge is proposed to obtain improved hydrostratigraphic boundaries along boreholes. Next, zonation models are constructed by applying clustering‐based zone geometry and populating zonal estimates of hydraulic conductivity (K) from analyzing pumping data. Afterwards, zonation models are treated as the initial guess of spatial variability in the geostatistical inversion of HT analysis. Additionally, local K measurements can be utilized to further improve HT estimates. Comparative cases of HT analyses are designed for a numerical sandbox experiment to highlight the HT performance integrated with geophysical surveys, in which the geostatistical inversion is initialized with: (a) a homogeneous K field; (b) zonation models built by the clustering of disparate geophysical surveys with/without spatial constraints; and (c) zonation improved by incorporating local K measurements. Based on ln K field comparisons and validation through predictions of drawdowns and tracer plume migration from independent tests not used in the calibration effort, we find that integration of geophysical surveys into HT analysis by clustering with spatial constraints is demonstrated as an effective approach, and local K measurements can further improve HT estimates. Key Points: We propose a new type of spatial constraints for clustering of multiple geophysical survey data to construct more reliable zonation modelsWe establish a framework in which borehole geophysical logs are utilized to improve hydraulic tomography (HT) performanceWe design a numerical sandbox experiment to test the effectiveness of integrating geophysical surveys to improve HT estimates [ABSTRACT FROM AUTHOR]

Unconfined coastal aquifers with a sloping aquifer bed are ubiquitous. However, most analytical solutions previously developed to estimate pumping‐induced seawater intrusion considered a horizontal aquifer bed. In this study, we first developed a steady‐state analytical solution to quantify the maximum safe pumping rate in sloping unconfined coastal aquifers with a fixed‐flux inland boundary condition, using the single potential approach. The analytical solution corrected by an empirical factor is validated against the numerical simulation, which reproduces the corresponding numerical results well. It is found that coastal aquifers with a higher aquifer bed toward inland (i.e., a positive sloping angle) yield a higher maximum safe pumping rate than that of coastal aquifers with a horizontal aquifer base, since the elevated freshwater head prevents seawater intrusion and enhances groundwater pumping. Specifically, for the aquifer bases with the sloping angle of 0.01 and −0.01, the maximum safe pumping rate is increased by 42.6% and decreased by 48.4%, respectively, in comparison to the case of a horizontal aquifer base, suggesting that neglecting the aquifer base slop can result in a significant error in estimating the maximum safe pumping rate. Moreover, the sensitivity analysis reveals that the maximum safe pumping rate increases with a lower hydraulic conductivity and a larger dispersivity. Our results provide valuable insights into the effect of the aquifer base slope on the maximum safe pumping in coastal aquifers, and analytical solutions developed can serve as a powerful tool for quick assessment of pumping‐induced seawater intrusion in sloping unconfined coastal aquifers. Key Points: Analytical solutions for pumping‐induced seawater intrusion in a sloping unconfined coastal aquifer are developedAnalytical solutions of the maximum safe pumping rate are validated through numerical simulationNeglecting the aquifer bed slope would result in a significant error in estimating the maximum safe pumping rate, as expected [ABSTRACT FROM AUTHOR]

Heat as a tracer has received increasing attention in recent decades and has become a popular and widely used tool for quantifying streambed fluxes, among many other applications. Nonvertical flow component is an important parameter for heat transport in riparian zones. However, previous investigations using heat as a tracer in the quantification of streambed fluxes frequently overlooked or simplified nonvertical flow component with erroneous presumptions. In this study, a novelty two‐dimensional closed‐form analytical solution for heat transport with vertical and nonvertical flow components and arbitrary initial and boundary conditions under losing conditions is presented for the first time using Green's function method. The new model is tested by finite‐element solution and stochastic modeling. The capabilities of the new analytical solution are demonstrated using field data. Results show that the nonvertical flow component has a significant impact on heat transport in streambed. The temperature difference between the streambed and the surface water increases as the nonvertical flow component increases, and the amplitude of the temperature curves decreases with increasing horizontal distance from the center of stream at the same depth due to the influences of nonvertical flow. Stochastic modeling shows that an increasing nonuniform flow can result in overestimation of vertical and nonvertical flow components near the bank of stream, and the new analytical model works well in a heterogeneous streambed when the variance of natural logarithm of the streambed hydraulic conductivity is less than 0.10 (σlnK2≤0.10 ${\sigma }_{\mathrm{ln}K}^{2}\le 0.10$). The vertical and nonvertical flow components are more sensitive to temperature‐time data than the other parameters. The new analytical model is a significant advancement of the previous one‐dimensional analytical models which only considered vertical flow. Key Points: A two‐dimensional analytical solution for heat transport with nonvertical flow in riparian zones under losing conditions is developedThe new analytical model works well in the heterogeneous streambed when the variance of natural logarithm of streambed hydraulic conductivity is less than 0.10The new model improves the estimation of streambed fluxes in a two‐dimensional flow field under losing conditions [ABSTRACT FROM AUTHOR]

A new methodology was developed to support contaminant mass discharge (CMD)‐based risk assessment of groundwater contamination downgradient of point source zones. Geoelectrical cross‐borehole induced polarization (IP) data were collected at a site undergoing in situ remediation of chlorinated solvents for determining 2D hydraulic conductivity (K) distributions with an inversion model resolution of 0.15 m (vertically) x 0.50 m (horizontally) in three control planes from 10 to 20 m depth. Additionally, 18 slug tests and 31 grain size distribution analyses (GSA) from the control planes, were used for K‐estimation. The geometric means and variance of the IP, slug test, and GSA derived K‐estimates were consistent with previously studied sandy aquifers. Furthermore, the vertical variation in K between two geological settings, a sandy till and a meltwater sand formation, was clearly identified by the IP K‐estimates. The vertical variation was backed up by hydraulic profiling tool (HPT) measurements. Random realizations of CMD were simulated based on the cross‐borehole IP derived K‐values. For comparison, the CMD was also estimated with a geostatistical conditional simulation approach, using the data from slug tests and GSAs. The high IP resolution captured the small scale variations in K across the transects and led to CMD predictions with a narrow uncertainty interval, whereas slug test and GSA either under‐ or overestimated the magnitude of the areas with the highest CMD. Applying the geophysical cross‐borehole method for estimating K‐distributions in addition to traditional methods would improve CMD‐based risk assessment and evaluation of remediation performance at contaminated sites. Key Points: Cross‐borehole induced polarization (IP) data have successfully been used to infer a high resolution hydraulic conductivity fieldHydraulic conductivity estimates from cross‐borehole IP, slug test, grain size distribution and hydraulic profiling tool compared wellCompared to other hydraulic conductivity estimation methods, application of cross‐borehole IP data enables an improved estimation of contaminant mass discharge [ABSTRACT FROM AUTHOR]

The hyporheic zone (HZ), where surface water and groundwater interact in sediments beneath streams, presents unique conditions for nutrient dynamics, such as carbon and nitrogen (N) cycling. Organic carbon (OC) in aquatic systems has two distinct forms: dissolved organic carbon and particulate organic carbon (POC). OC affects N reduction and controls the occurrence of denitrification, a primary process by which nitrate (NO3−) is removed as gas (N2 or N2O) to the atmosphere. When POC is the predominant form of OC in streams, how POC influences NO3− reduction within a HZ remains unclear. We established a new reactive transport model incorporating POC transport and filtration processes to assess how POC deposition affects NO3− removal. Sediment permeability decreases as POC is filtrated in the streambed. Nitrate influx is reduced due to POC‐induced sediment clogging. The deposited POC in the shallow streambed serves as an OC source and supports higher biogeochemical reaction kinetics because OC is an important substrate promoting microbial activities. The filtrated POC pool enhances denitrification, thus causing a higher NO3− removal efficiency. In contrast, the POC pool is typically assumed to be distributed homogeneously in sediments, potentially causing a significant underestimation of stream‐borne NO3− removal. A lower hydraulic conductivity, a smaller POC grain size, and a larger POC filtration efficiency and in‐stream POC concentration allow for extensive POC deposition within the shallow streambed that favors nitrate removal. This study provides a better understanding of N processing and an accurate estimation of NO3− removal potential in HZs. Key Points: We developed a new hydrobiogeochemical model combining saturated flow, particulate organic carbon (POC) deposition and reactive solute transportDeposited POC near the sediment‐water interface reduces nitrate influx and enhances denitrification, causing a higher N removal efficiencyA higher POC concentration and filtration efficiency and a smaller sediment permeability and POC size enhance POC filtration and N removal [ABSTRACT FROM AUTHOR]

Two conventional experimental procedures for determination of the water permeability of saturated porous medium are the constant and the falling head permeability tests. The first one is more applicable on more permeable materials where the outflow from the sample is measured at variety of constant water heads, while the second one is more convenient for low permeable materials, utilizing the continuous measurements of the water head falling due to filtration through the saturated sample. However, neither of the two is useful for materials of high permeability and large cross‐sectional area. The constant head permeability test faces technical issues since a significant and continuous water discharge is required, while the falling head permeability test has limitations due to neglection of the Forchheimer's high‐velocity flow through the sample, but also the influence of inertia on the fluid mass. Here we proposed an approach for determination of the water permeability of saturated porous medium based on the agreement between the measured water level change in two connected reservoirs containing a porous sample and the new semi‐analytical expression describing that change by accounting for the mentioned theoretical deficiencies. This efficient approach has been tested on four pervious paver samples, and results showed satisfactory agreement with the constant head permeability data. It has been also confirmed the proposed semi‐analytical solution is more accurate than the falling head permeability approach in case of highly pervious materials, while for low permeable materials it reduces to the conventional approach. Key Points: The constant and the falling head permeability tests are not useful for highly pervious porous samples of large sizesA new semi‐analytical model considering Forchheimer's high‐velocity flow through the sample and inertia of the fluid mass is proposed hereThis formula is applied on a new permeability test where water flows through a highly pervious sample located between two reservoirs [ABSTRACT FROM AUTHOR]

Salmonids create an egg nest, called a redd, in hyporheic streambed gravel to bury their eggs, characterized by a pit and a hump topography, resembling a dune. Embryos' survival depends on downwelling oxygen‐rich stream water fluxes, influenced by the redd shape, stream hydraulics, and the hydraulic conductivity of the redd sediment, K. We hypothesize that downwelling fluxes increase with stream discharge and redd aspect ratio (AR = A/L, with A, the redd amplitude and L, its length), and they can be predicted using a set of dimensionless numbers, which include the stream flow Reynolds (Re) and Froude (Fr) numbers, AR, and the redd relative submergence (A/Y0, with Y0, the water depth). We address our goal by simulating the surface and subsurface flows with numerical hydraulic models linked through the near‐bed pressure distribution quantified with a two‐phase (air‐water) two‐dimensional surface water computational fluid dynamics model, validated with experiments. We apply the modeling approach to five redd sizes, which span the field observed range (from ∼1 to ∼4 m long), and by increasing discharge from shallow (0.1 m) and slow (0.15 m/s) to deep (8 m) and fast (3.3 m/s). Results confirm that downwelling fluxes increase with discharge and redd aspect ratio due to the increased near‐bed head gradient over the redd. Averaged downwelling fluxes are a function of Re, Fr, AR, and hydraulic conductivity of the redd and not of the undisturbed streambed material. The derived regression equation may help evaluate regulated and unregulated flow impacts on hyporheic flows during embryo incubation. Key Points: Redd‐induced hyporheic exchange increases with discharge and redd aspect ratioHyporheic downwelling flows are a function of surface Reynolds and Froude numbers and redd aspect ratioDisturbed material hydraulic conductivity can be used to predict the downwelling flux instead of categorical heterogeneity for the sediments [ABSTRACT FROM AUTHOR]

The necessity and rationality of using an impedance factor in the calculation of hydraulic conductivity of frozen soil has been an ongoing debate. To address this issue, ice segregation theory was used to analyze the physical meaning of the impedance factor. Based on assumptions sourced from segregation theory, experimental evidence regarding the hydraulic conductivity of frozen soil and the Gibbs‐Thompson effect, a relationship between the impedance factor and soil parameters was deduced. The necessity of the impedance factor was discussed under closed unsaturated and open saturated freezing systems. Finally, the derived impedance factor was compared with the current empirical impedance factor. The results showed the following: (a) The impact of the impedance factor on closed unsaturated freezing systems was small. However, an impedance factor was necessary for water migration in freezing systems with a high degree of ice segregation, such as open saturated freezing systems. (b) The derived impedance factor combined with the VG model had good performance for simulating water migration under different freezing conditions. (c) Compared with the empirical impedance factors, the derived impedance factors considered the effect of segregation acceleration caused by the pore expansion, improving the simulation accuracy of water migration at the freezing front. The parameters used to derive the impedance factor were only the initial porosity and the accumulative curve of the particle size grading, which was easily applied and combined with a VG model as a general method for computing the hydraulic conductivity of frozen soil. Key Points: Unsaturated systems do not need an impedance factor and can use the relative permeability as calculated from the unfrozen water contentAn impedance factor is necessary for computing water migration in open saturated freezing systems due to pore ice segregationThe impedance factor decreases with decreasing temperature, and this process is accelerated by pore expansion [ABSTRACT FROM AUTHOR]

Hydraulic tomography (HT) has been shown to be a robust approach for the high‐resolution characterization of subsurface heterogeneity. However, HT can yield smooth estimates of hydraulic parameters when pumping tests and drawdown measurements are sparse, thus limiting the utility of characterization results in predicting groundwater flow and solute transport. To overcome this issue, this study integrates cross‐hole flowmeter measurements with HT analysis of steady‐state pumping/injection test data for the three‐dimensional (3‐D) characterization of hydraulic conductivity (K) at a highly heterogeneous glaciofluvial deposit site, which has not been previously attempted. Geostatistical inverse analyses of cross‐hole flowmeter data are conducted to yield preliminary estimates of K distribution, which are then utilized as initial K fields for steady‐state HT analysis of head data. Four cases combining three data types (geological information, cross‐hole flowmeter measurements, and steady‐state head data) for inverse modeling are performed. Model calibration and validation results from all cases are compared qualitatively and quantitatively to evaluate their performances. Results from this study show that (a) geostatistical inverse analysis of cross‐hole flowmeter data is capable in revealing vertical distributions of K at well locations and major high/low K zones between wells, (b) cross‐hole flowmeter data carry non‐redundant information of K heterogeneity compared to geological information and steady‐state head data, and (c) integration of flowmeter data improves characterization results in terms of revealing K heterogeneity details and predicting independent hydraulic test data. Therefore, this study demonstrates the usefulness of cross‐hole flowmeter data in augmenting HT surveys for improved K characterization in 3‐D. Key Points: Geostatistical inverse analysis of cross‐hole flowmeter data is capable in revealing heterogeneity patterns of hydraulic conductivityCross‐hole flowmeter data carry non‐redundant information compared to structural information and head response dataIntegration of cross‐hole flowmeter data with steady‐state hydraulic tomography analysis improves characterization results [ABSTRACT FROM AUTHOR]

Soil unsaturated hydraulic conductivity (K), which depends on water content (θ) and matric potential (ψ), exhibits a high degree of variability at the field scale. Here we first develop a theoretical hydraulic‐electrical conductivity (σ) relationship under low and high salinity cases based on the capillary bundle model and Waxman and Smits model which can account for the non‐linear behavior of σ at low salinities. Then the K‐σ relationship is converted into a K(θ, ψ) model using the Brooks‐Corey model. The model includes two parameters c and γ. Parameter c accounts for the variation of the term (λ + 2)/(λ + 4) where λ is the pore size distribution parameter in the Brooks‐Corey model, and the term m‐n where m and n are Archie's saturation and cementation exponents, respectively. Parameter γ is the sum of the tortuosity factor accounting for the differences between hydraulic and electrical tortuosity and Archie's saturation exponent. Based on a calibration data set of 150 soils selected from the UNSODA database, the best fitting log(c) and γ values were determined as −2.53 and 1.92, −4.39 and −0.14, −5.01 and −1.34, and −5.79 and −2.27 for four textural groups. The estimated log10(K) values with the new K(θ, ψ) model compared well to the measured values from an independent data set of 49 soils selected from the UNSODA database, with mean error (ME), relative error (RE), root mean square error (RMSE) and coefficient of determination (R2) values of 0.02, 8.8%, 0.80 and 0.73, respectively. A second test of the new K(θ, ψ) model using a data set representing 23 soils reported in the literature also showed good agreement between estimated and measured log10(K) values with ME of −0.01, RE of 9.5%, RMSE of 0.77 and R2 of 0.85. The new K(θ, ψ) model outperformed the Mualem‐van Genuchten model and two recently published pedo‐transfer functions. The new K(θ, ψ) model can be applied for estimating K under field conditions and for hydrologic modeling without need for soil water retention curve data fitting to derive a K function. Key Points: A new unsaturated hydraulic conductivity model was developed in terms of independent θ and ψ valuesBest fitting values of two parameters in the new unsaturated hydraulic conductivity model were determined from 150 soils in the calibration data setThe new model provided reliable estimates of hydraulic conductivity for 72 soils from two independent data sets [ABSTRACT FROM AUTHOR]

Predicting catchment stormflow responses after tropical deforestation remains difficult. We used 5‐min rainfall and storm runoff data for 30 events to calibrate the Green–Ampt (GA) and the Spatially Variable Infiltration (SVI) models and predict runoff responses for a small, degraded grassland catchment on Leyte Island (the Philippines), where infiltration‐excess overland flow (IOF) is considered the dominant runoff process. SVI replicated individual stormflow hydrographs better than GA, particularly for events with small runoff responses or multiple peaks. Calibrated parameter values of the SVI model (i.e., spatially averaged maximum infiltration capacity, Im and initial abstraction, F0) varied markedly between events, but were statistically significant and negatively correlated with (mid‐slope) soil moisture content at 10 cm (SWC10)—as did the "catchment‐wide effective" hydraulic conductivity (Ke) of the GA model. Using SWC10‐based estimates of F0 and Im in SVI yielded satisfactory to good simulations for 11 out of 17 events with runoff coefficients ≥15%, but failed to reproduce the hydrographs for events with very small runoff amounts (0.25–1 mm) and low runoff coefficients (3%–6%). The median field‐measured near‐surface Ksat (2 mm hr−1) was distinctly lower than the median Im (32 mm hr−1) and, to a lesser extent, Ke (∼8 mm hr−1), suggesting an underestimation of the spatially averaged Ksat by the field measurements. Application of SVI is expected to give the most realistic results for situations where IOF is dominant, that is, where surface conditions are degraded and rainfall intensities high. Plain Language Summary: It is important to be able to predict the streamflow volume and peak flow rate during intense rainfall events. We used rainfall and streamflow data for a small, degraded tropical grassland catchment on Leyte Island (the Philippines) to calibrate two rainfall infiltration models of comparable complexity: the Green–Ampt model (GA), that describes a decrease in infiltration capacity with time, and the Spatially Variable Infiltration (SVI) model for which the infiltration capacity is a function of the rainfall intensity. SVI generally performed better than GA in simulating observed streamflow responses to rainfall, especially for events with multiple rainfall peaks. Values for the two main parameters of SVI (the amount of rainfall required to initiate stormflow, and the maximum infiltration capacity of the soil) were related to the amount of moisture in the top 10 cm of the soil prior to the rainfall event. Using the measured topsoil moisture contents for 26 rainfall events to estimate the SVI parameter values and predict the stormflow response from the measured rainfall intensity produced satisfactory to good results for most of the larger events. However, it failed to reproduce the stormflow patterns for six events with mostly small to very small runoff responses. Key Points: The Spatially Variable Infiltration (SVI) model outperformed the Green–Ampt model, especially when simulating multi‐peaked storm hydrographsSVI‐model parameter values correlated negatively with antecedent topsoil moisture contentModel‐derived catchment‐scale infiltration capacities were higher than field‐measured Ksat, regardless of the model or field method used [ABSTRACT FROM AUTHOR]

In this study, the random finite element method, a finite element method with random field generation techniques, was applied to investigate the cross correlations between the observed head and hydraulic conductivity and specific storage at different locations and different times in pumping tests. The results show that the two cross correlations between the pumping well and the observation well reach their maximums before pumping reaches a steady state. Specifically, the cross correlation between the observed head and hydraulic conductivity is the greatest when the temporal derivative of the observed head does not change significantly, and that between the observed head and specific storage is the greatest when the temporal derivative (the rate) of the observed head is maximum. Based on the results of cross‐correlation analysis, a short‐term pumping strategy for hydraulic tomography is proposed to obtain the spatial distribution of hydraulic conductivity and specific storage using the successive linear estimator. Furthermore, this strategy was validated by Monte Carlo simulations. This paper points out that the sensitivity and cross‐correlation analyses report the ensemble (averaged) behaviors of any heterogeneous aquifers, which is not necessarily suitable for one realization. Furthermore, Monte Carlo simulation is suggested for validating any groundwater inverse modeling result. Key Points: The cross correlations between the observed head and hydraulic parameters are investigated by a random finite element methodThe cross correlations reach the maximums before flow reaches a steady state in a pumping (or injection) testSuccessive linear estimator can yield good estimations of distributions of hydraulic parameters from short‐term pumping tests [ABSTRACT FROM AUTHOR]

The soil water retention curve is the fundamental soil hydraulic property to characterize soil water movement and solute transport. Many efforts have been devoted in the past decades to developing models to describe soil water retention curves. However, most of them are empirical equations or assume that soil pore size distributions conform to a lognormal distribution. Yet, few effects have been undertaken to systematically propose and compare a series of possible alternative probability density functions to describe the sigmoid retention curves with parameters physically explainable. Here, we proposed a family of five soil water retention models based on sigmoid functions with parameters of clear physical implications coinciding with the statistical measures of soil pore size distribution. Compared with the widely used models (i.e., Brooks & Corey, 1964; Kosugi, 1996; van Genuchten, 1980), the proposed models have somewhat improved performances to characterize water retention data for a wide range of soil textures without introducing additional model parameters. Two of the proposed models are capable of characterizing the observed two local extrema in the moisture capacity curves. The associated unsaturated hydraulic conductivity models of the proposed soil water retention models are also derived, which show superior performance in characterizing the observed hydraulic conductivities compared with competing models, especially in macropore regimes. Additionally, we analyzed the parameter‐equivalent conversion between the proposed and the existing models, and a simple linear regression equation can be used to derive the parameters of the proposed models from the existing and other alternative different proposed models. Key Points: A family of soil water retention models based on sigmoid functions and related relative hydraulic conductivity functions are proposedParameters have statistical implications against pore size distributions and can be converted from existing or alternative new modelsCharacterization of hydraulic properties is improved using new models, especially for macropore properties, without additional parameters [ABSTRACT FROM AUTHOR]

In recent years there has been vigorous debate whether asymptotic transverse macrodispersion exists in steady three‐dimensional (3D) groundwater flows in the purely advective limit. This question is tied to the topology of 3D flow paths (termed the Lagrangian kinematics), specifically whether streamlines can undergo braiding motions or can wander freely in the transverse direction. In this study we determine which Darcy flows do admit asymptotic transverse macrodispersion for purely advective transport on the basis of the conductivity structure. We prove that porous media with smooth, locally isotropic hydraulic conductivity exhibit zero transverse macrodispersion under pure advection due to constraints on the Lagrangian kinematics of these flows, whereas either non‐smooth or locally anisotropic conductivity fields can generate transverse macrodispersion. This has implications for upscaling locally isotropic porous media to the block scale as this can result in a locally anisotropic conductivity, leading to non‐zero macrodispersion at the block scale that is spurious in that it does not arise for the fully resolved Darcy scale flow. We also show that conventional numerical methods for computation of particle trajectories do not explicitly preserve the kinematic constraints associated with locally isotropic Darcy flow, and propose a novel psuedo‐symplectic method that preserves these constraints. These results provide insights into the mechanisms that govern transverse macrodispersion in groundwater flow, and unify seemingly contradictory results in the literature in a consistent framework. These insights call into question the ability of smooth, locally isotropic conductivity fields to represent flow and transport in real heterogeneous porous media. Plain Language Summary: The spreading of solutes, colloids and pollutants in groundwater flow is key to both risk assessment and a fundamental understanding of chemical, biological and geophysical transport in the subsurface. In many scenarios the spreading of solutes transverse to the mean flow direction is dominated by hydrodynamic transport from diverging streamlines and the contribution from local dispersion is relatively small. Although it is well understood that such hydrodynamic transport (termed transverse macrodispersion) is zero in steady two‐dimensional groundwater flow for purely advective transport, there has been much debate in recent years as to whether transverse macrodispersion can occur in steady three‐dimensional groundwater flows. In this study we address this question by considering the kinematics associated with Darcy flow of heterogeneous porous with different conductivity structures and identify the structures that generate non‐zero transverse macrodispersion in the absence of local dispersion. We show that numerical predictions of transverse macrodispersion can be highly sensitive to the details of the numerical solvers used and propose a novel numerical method to mitigate against spurious predictions of transverse macrodispersion. These findings are used to reconcile seemingly contradictory results in the literature and provide insights into the suitability of commonly used models of groundwater flow and transport. Key Points: We prove that the transverse macrodispersion does not exist when the hydraulic conductivity field is smooth and locally isotropicWe show that conventional numerical methods do not preserve this constraint, and propose novel numerical methods that doThese insights reconcile previous contradictory results and question the ability of some conductivity models to represent real porous media [ABSTRACT FROM AUTHOR]

The freshwater lenses ("lenses" hereafter) within saline floodplain aquifers are sensitive to river flooding events. However, the effects of extensive floodplain inundation on saline aquifers are rarely considered and have not been examined previously under controlled laboratory conditions. We conducted laboratory experiments within a two‐dimensional (cross‐section) sand tank (i.e., representing a saline floodplain aquifer) and built both laboratory‐ and field‐scale numerical models to examine lens responses to flood events. Three sets of experiments were performed to explore different lateral extents of floodplain inundation. The temporal behavior of experimental lenses was quantified and compared to variable‐density numerical models that adopted calibrated laboratory parameters, showing good agreement. Results show that more extensive floodplain inundation leads to larger lenses (as expected). The sensitivity analysis was performed based on field‐scale numerical models, demonstrating that the floodplain inundation extent, hydraulic conductivity, and dispersivity are key factors controlling the post‐flood recession in lens extent and volume. In field‐scale simulations of floodplain inundation, the entire lens was significantly salinized during flood recession due to enhanced dispersion accompanying higher groundwater velocities, which may further split into several isolated freshwater bodies before eventually returning to steady‐state conditions. Importantly, field‐scale numerical results indicated that the salt load to the adjacent river increased immediately following the flood event, consistent with reporting of the River Murray (South Australia). These results provide critical new insights into relationships between flood events and the behavior of lenses, highlighting the significance of flooding events on both intermediate and long‐term conditions of saline floodplains. Plain Language Summary: In semi‐arid and arid regions, river‐fed freshwater lenses within saline floodplain aquifers can sustain salt‐sensitive riparian vegetation and the health of floodplain ecosystems, especially during periods of low river flow. The dynamics of these lenses may be significantly altered by the river flooding events that often cause widespread floodplain inundation. Thus, the quantitative analysis of how riparian lenses respond to river flooding events is crucial for the sustainable management of salt‐affected floodplains. In this study, the lens behavior under flooding conditions was directly observed and quantified in laboratory experimentations for the first time. Flood‐induced lens dynamics in real‐world settings were further investigated numerically. The results indicate that the occurrence of floodplain inundation leads to a complex relationship between flood events and the behavior of lenses. The salt load to the adjacent river increased immediately following the flood event. These previously unarticulated outcomes are expected to broaden the understanding of riparian lens dynamics and river salinization associated with flooding events. Key Points: Response of riparian freshwater lenses to flooding is examined using laboratory experimentation and numerical modelingRiparian freshwater lenses formed during floodplain inundation may split into several isolated lenses after flood recessionA rapid increase in saltwater discharge to adjacent rivers occurs following a river flooding event [ABSTRACT FROM AUTHOR]

Because tension infiltrometers apply water through a disk of finite size, the infiltrated water moves laterally as well as downward. Only the vertical component of this flow is indicative of the hydraulic conductivity K, so the algorithm for computing K must include a way of isolating that component from the total flow. Some commonly used formulas correct for the multidimensional effects by subtracting an estimate of the laterally spreading flow. For disks smaller than about 200 mm in diameter, however, lateral spreading constitutes so much of the total flow that these subtractive formulas lose considerable accuracy, and sometimes overcorrect so severely as to produce a negative number for K. Other methods rely on empiricisms that are not completely consistent with unsaturated‐flow theory and that require prior knowledge of certain soil properties. We developed a new formula that uses a multiplicative factor instead of a subtracted term to achieve the needed correction. For testing we conducted numerical experiments with synthetic data produced by solving the Richardson‐Richards equation using the code VS2DRTI, for diverse media and a range of disk sizes, including the widely used 45‐mm diameter. We compared K values calculated from our formula to the actual K used to generate the simulated data, as well as to results from other published formulas. This comparison shows that our method provides an algorithm based in unsaturated‐flow theory that produces more reliable values for small disks without requiring prior knowledge of soil properties. Plain Language Summary: Tension infiltrometers are much‐used devices for field measurement of the hydraulic conductivity of soil. Hydraulic conductivity is a measure of how easily water flows in the soil. If it is high, water at the soil surface can cause more infiltration and less runoff, and can move faster within the soil. Tension infiltrometers apply water over a circular area of the soil surface and measure the flow rate of the water being drawn into the soil. For small infiltrometers, a large fraction of the water spreads laterally within the soil, rather than straight down. Consequently, the amount of water flow measured by the infiltrometer is much greater than just the downward‐flowing portion needed to indicate hydraulic conductivity. This laterally flowing water must be corrected for in the formulas that calculate hydraulic conductivity from the measured data. If the diameter is less than about 200 mm, as it is for the great majority of infiltrometers, the needed correction is so large that large errors result from the approximate corrections applied by commonly used formulas. Our new method uses an estimate of the distance the water spreads laterally to give more accurate results. Key Points: Measurements from small diameter tension infiltrometers require a large correction to account for the lateral spreading of infiltrated waterThe use of a multiplicative, rather than subtractive, correction method provides greater accuracy when the correction is large, as needed for small disksOur proposed method provides a direct estimate of how much flow is going into lateral versus vertical components, thereby yielding additional information for interpretation as well as more accurate hydraulic conductivity results [ABSTRACT FROM AUTHOR]

There is a lack of Ordinary Differential Equation (ODE) formulations in numerical hydrology, contributing to the lack of application of canned adaptive timestep solvers; hence the continued dominance of fixed (e.g., Euler) timestep techniques despite their fundamental problems. In this paper, we reformulate Dynamic-TOPMODEL into a constraint-handling ODE form and use MATLAB's advanced adaptive ODE-solvers to solve the resulting system of equations. For wider applicability, but based on existing research and/or first principles, we developed Generalized Multistep Dynamic TOPMODEL which includes: iso-basin spatial discretization, diffusion wave routing, depth-dependent overland flow velocity, relaxing the assumption of water-table parallelism to the ground surface, a power-law hydraulic conductivity profile, new unsaturated zone flux, and a reference frame adjustment. To demonstrate the model we calibrate it to a peat catchment case study, for which we also test sensitivity to spatial discretization. Our results suggest that (a) a five-fold improvement in model runtime can result from adaptive timestepping; (b) the additional iso-basin discretization layer, as a way to further constrain spatial information where needed, also improves performance; and (c) the common-practice arbitrary Topographic Index (TI) discretization substantially alters calibrated parameters. More objective and physically constrained (e.g., top-down) approaches to TI classification may be needed. [ABSTRACT FROM AUTHOR]

Parameter estimation is one of the most challenging tasks in large‐scale distributed modeling, because of the high dimensionality of the parameter space. Relating model parameters to catchment/landscape characteristics reduces the number of parameters, enhances physical realism, and allows the transfer of hydrological model parameters in time and space. This study presents the first large‐scale application of automatic parameter transfer function (TF) estimation for a complex hydrological model. The Function Space Optimization (FSO) method can automatically estimate TF structures and coefficients for distributed models. We apply FSO to the mesoscale Hydrologic Model (mHM, mhm-ufz.org), which is the only available distributed model that includes a priori defined TFs for all its parameters. FSO is used to estimate new TFs for the parameters "saturated hydraulic conductivity" and "field capacity," which both influence a range of hydrological processes. The setup of mHM from a previous study serves as a benchmark. The estimated TFs resulted in predictions in 222 validation basins with a median NSE of 0.68, showing that even with 5 years of calibration data, high performance in ungauged basins can be achieved. The performance is similar to the benchmark results, showing that the automatic TFs can achieve comparable results to TFs that were developed over years using expert knowledge. In summary, the findings present a step toward automatic TF estimation of model parameters for distributed models. Key Points: This study shows the performance of automatic transfer function (TF) estimation with the Function Space Optimization (FSO) methodWe show that FSO is able to estimate TFs that perform similar to the mesoscale Hydrologic Model TFs in an ungauged settingThis study represents a step toward automatic TF estimation for physically interpretable model parameters [ABSTRACT FROM AUTHOR]