## No full-text available

To read the full-text of this research,

you can request a copy directly from the authors.

To read the full-text of this research,

you can request a copy directly from the authors.

... Critical water resources management issues all over the world require such information in order to reduce risks of resource depletion and degradation. Identifying hydraulic connections in the subsurface is thus one of the primary goals of numerous hydrogeological studies, covering a wide range of applications such as well capture zone delineation (e.g., Javandel & Tsang, 1986;Kinzelbach et al., 1992), the characterization of regional groundwater flow and groundwater-surface water interaction (e.g., Ameli et al., 2018;Cardenas et al., 2004;Tóth, 1963;Wang et al., 2016;Winter, 1999;Wroblicky et al., 1998), and in situ groundwater remediation (e.g., Bolster et al., 2009;Luo et al., 2006). Recently, the significance of characterizing groundwater flow patterns to understand solute mixing and reactivity-and thus groundwater quality-has also been emphasized (Chiogna et al., 2014;Cirpka et al., 2015;de Barros et al., 2012;Hidalgo et al., 2015;Hidalgo & Dentz, 2018;Marzadri et al., 2016). ...

... The lack of familiarity with stagnation points in three dimensions indicates a generally poor understanding of how groundwater flows in three dimensions. This may, for instance, explain difficulties encountered when trying to apply the classical concept of groundwater flow systems (Tóth, 1963)-which is very much linked to the occurrence of stagnation points-in three dimensions (Batelaan et al., 2003;Bresciani et al., 2016;Gleeson & Manning, 2008;Goderniaux et al., 2013;Vissers & van der Perk, 2008;Wang et al., 2016;Wang et al., 2017b). Furthermore, the bulk of the groundwater literature discussing stagnation points focused on specific examples of groundwater flow; in contrast, very few studies discussed the general (theoretical) properties of stagnation points. ...

... Indeed, although well established in hydrogeological sciences, this concept has so far mostly been developed through the analysis of two-dimensional (vertical) models . Several authors proposed definitions of groundwater flow systems in three dimensions, but these are different to the original definition by Tóth (1963) and different from one another, while the equivalence between these definitions has not been rigorously analyzed (Batelaan et al., 2003;Gleeson & Manning, 2008;Goderniaux et al., 2013;Vissers & van der Perk, 2008;Wang et al., 2016;Wang et al., 2017b). The occurrence of different flow systems in a groundwater flow field is known to be very much linked to the occurrence of stagnation points (Jiang et al., 2011;Winter, 1976). ...

The importance of stagnation points for characterizing groundwater flow patterns has long been recognized. However, the possible streamline configurations near stagnation points under the constraints of Darcy's law have not been thoroughly investigated. We fill this gap by conducting a systematic analysis of groundwater flow patterns near stagnation points in two and three dimensions. The approach borrows ideas from dynamical systems theory, as often done in fluid mechanics. The most general form of Darcy's law, which applies to variable-density, compressible fluids flowing through heterogeneous, anisotropic, compressible porous media, is first considered. Under these conditions, there are no major restrictions on the possible flow patterns near stagnation points. The common types of stagnation points are thus minimums (spiral or nonspiral), maximums (spiral or nonspiral), and saddles (in three dimensions, these can be converging or diverging and spiral or nonspiral). The implications of dealing with more restrictive fluid and porous medium properties are then systematically investigated. In particular, important restrictions on the possible types of stagnation points exist when the flow is constant density or divergence free. The theoretical analysis is complemented by a series of examples of groundwater flow fields in which different types of stagnation point arise. The findings highlight key differences between two-dimensional and three-dimensional flows and provide new insights on the patterns of variable-density groundwater flow. The fundamental knowledge on groundwater flow patterns gained from this study will benefit both theoretical and applied studies of groundwater flow and solute transport.

... Specifically, the reference for the synthetic periodic basin is based on the exact analytical solution derived by J. Z. Wang et al. (2016), and the reference for the synthetic sandy bedforms and the natural mountainous basin is based on a high-resolution finite element numerical solution implemented in COMSOL Multiphysics. To have a fair comparison, the same number of Fourier coefficients are used for both approaches. ...

... and are characteristic length scales in x-direction and y-direction, respectively. The exact analytical solution for the hydraulic head field in this case is given by J. Z. Wang et al. (2016): ...

Analytical solutions for the three‐dimensional groundwater flow equation have been widely used to gain insight about subsurface flow structure and as an alternative to computationally expensive numerical models. Of particular interest are solutions that decompose prescribed hydraulic head boundaries (e.g., Dirichlet boundary condition) into a collection of harmonic functions. Previous studies estimate the frequencies and amplitudes of these harmonics with a least‐square approach where the amplitudes are fitted given a pre‐assigned set of frequencies. In these studies, an ad hoc and structured discretization of the frequency domain is typically used, excluding dominant frequencies while assigning importance to spurious frequencies, with significant consequences for estimating the fluxes and residence times. This study demonstrates the advantages of using a pre‐assigned frequency spectrum that targets the dominant frequencies based on rigorous statistical analysis with predefined significance levels. The new approach is tested for three hydrologic conceptualizations: (a) a synthetic periodic basin, (b) synthetic bedforms, and (c) a natural mountainous watershed. The performance of the frequency spectrum selection is compared with exact analytical or approximate numerical solutions. We found that the new approach better describes the fluxes and residence times for Dirichlet boundaries with well‐defined characteristics spatial scales (e.g., periodic basins and bedforms). For more complex scenarios, such as natural mountainous watersheds, both pre‐assigned frequency spectrums present similar performance. The spectral solutions presented here can play a central role in developing reduced‐complexity models for assessing regional water and solute fluxes within mountain watersheds and hyporheic zones.

... The existing numerical approach ( Matanga, 1993 ), however, requires an iteration process on solving one stream function from the other beginning with presumed distributions of the stream functions on boundaries, which is very difficult to be implemented and convergent for arbitrary water table shape. Several indirect methods that do not consider stagnation points have been proposed in the literature ( Engelen and Kloosterman, 1996 ;Batelaan et al., 20 03 ;Gleeson and Manning, 20 08 ;Vissers and van der Perk, 2008 ;Goderniaux et al., 2013 ;Wang et al., 2016 ). Some of these methods classified flow systems by characterizing the connections between the recharge and discharge areas with "flow branches" ( Engelen and Kloosterman, 1996 ), "the recharge over discharge area ratio" ( Batelaan et al., 2003 ) or "the perpendicular flow" ( Gleeson and Manning, 2008 ). ...

... Particle tracking of flow paths to continuous discharge areas was also applied ( Vissers and van der Perk, 2008 ). Recently, the residence time distribution (RTD) of groundwater was proposed to partition 3D basin groundwater flow ( Goderniaux et al., 2013 ;Wang et al., 2016 ). However, all these methods yielded approximate classifications of flow systems that were not exactly equivalent to the local, intermediate and regional flow systems defined initially with distinct hydraulic boundaries. ...

Nested groundwater flow systems have been revealed in Tóth's theory as the structural property of basin-scale groundwater circulation but were only well known with two-dimensional (2D) profile models. The method of searching special streamlines across stagnation points for partitioning flow systems, which has been successfully applied in the 2D models, has never been implemented for three-dimensional (3D) Tóthian basins because of the difficulty in solving the dual stream functions. Alternatively, a new method is developed to investigate 3D nested groundwater flow systems without determination of stagnation points. Connective indices are defined to quantify the connection between individual recharge and discharge zones along streamlines. Groundwater circulation cells (GWCCs) are identified according to the distribution of the connective indices and then grouped into local, intermediate and regional flow systems. This method requires existing solution of the flow velocity vector and is implemented via particle tracking technique. It is applied in a hypothetical 3D Tóthian basin with an analytical solution of the flow field and in a real-world basin with a numerical modeling approach. Different spatial patterns of flow systems compared to 2D profile models are found. The outcrops boundaries of GWCCs on water table may significantly deviate from and are not parallel to the nearby water table divides. Topological network is proposed to represent the linked recharge-discharge zones through closed and open GWCCs. Sensitivity analysis indicates that the development of GWCCs depends on the basin geometry, hydraulic parameters and water table shape.

... The configuration of the water table, which is generally dependent on such factors as topography, geology and climate (Gleeson et al. 2011;Haitjema and Mitchell-Bruker 2005), is usually the output of most groundwater flow models. In basin-scale groundwater flow models, it has been found useful to use the water table as a prior known boundary condition to obtain the pattern of groundwater flow (Lazer 2006;Tóth et al. 2016;Wörman et al. 2007;Wang et al. 2016;Zijl 1999). In some situations where measurements of water-table elevations are limited, the topography of a basin can be used to represent the undulating water table (Wörman et al. 2007); however, it is acknowledged that a topography-controlled water table is only applicable in regions with humid climates (Haitjema and Mitchell-Bruker 2005). ...

... Due to the different types of groundwater in the shallow, middle and deep parts, Wang et al. (2015a) inferred that C1 could be from intermediate flow systems and C2 could be from regional flow systems. Numerical simulations of groundwater flow in the Dosit River Watershed by Wang et al. (2016) indicate that C1 belongs to the shallow part of regional flow systems and C2 belongs to deep part of regional flow systems in discharge areas. ...

The Ordos Basin is one of the most intensively studied groundwater basins in China. The Ordos Plateau, located in the north part of the Ordos Basin, is ideal to study the pattern of regional groundwater circulation induced by water-table undulations due to the wavy topography and the relatively simple aquifer systems with macroscopically homogeneous sandstone. In catchments located near the first-order divide, the water table is found to be a subdued replica of the topography, and the nonclosed water-table contours in topographic highs of a catchment are indicative of regional groundwater outflow to other catchments. In topographic lows, groundwater-fed lakes/rivers, topography-driven flowing wells, water-loving and/or salt-tolerant vegetation, and soap holes are all indicative of discharge areas. In discharge areas, although groundwater inflow from recharge areas is relatively stable, seasonal variations in groundwater recharge and evapotranspiration lead to significant seasonal fluctuations in the water table, which can be used to estimate groundwater inflow and evapotranspiration rates based on water balance at different stages of water-table change. In the lowest reaches of a complex basin, superposition of local flow systems on regional flow systems has been identified based on groundwater samples collected from wells with different depths and geophysical measurements of apparent resistivity, both of which can be used for characterizing groundwater flow systems. This study enhances understanding of the pattern of regional groundwater circulation in the Ordos Plateau, and also tests the effectiveness of methods for groundwater flow-system characterization.

... Groundwater discharge from the deeper aquifers mostly takes place in river channels and recharge to these aquifers mostly takes place at a distance from major rivers. The groundwater of these flow systems contributes to baseflow in the Dosit River (Wang et al. 2016). ...

... Conversely, if a factor score is less than 0, it means that the component was not significantly affected by the water chemistry at the site (Banoeng-Yakubo et al. 2009). In Fig. 3a, Cluster A is to some extent influenced by Factor 2. Cluster C is to some extent affected by Factor 1. Clusters B and D are influenced by both Factors 1 and 2. As well, Fig. 3b indicates that Clusters A and B are affected by Factor 3. Factor 3 has less influence on Clusters C and D. According to the local and regional groundwater flow systems of the Dosit River Watershed (Wang et al. 2016) and evolution, samples of Clusters A and B are located at different sites but in the same aquifer (depth less than 200 m; local flow system). Samples of Cluster A are located in the upstream area as opposed to that of Cluster B (Fig. 4). ...

A better understanding of the hydrogeochemical evolution of groundwater in vulnerable aquifers is important for the protection of water resources. To assess groundwater chemistry, groundwater sampling was performed from different representative aquifers in 2012–2013. A Piper trilinear diagram showed that the groundwater types can be classified into Na–SO4 and Na–Cl types. Only one groundwater sample was Na–HCO3 type. The dominant cations for all samples were Na+. However, the dominant anions varied from HCO3− to SO42−, and as well Cl−. The mean total dissolved solid (TDS) content of groundwater in the region was 1889 mg/L. Thus, only 20% of groundwater samples meet Chinese drinking water standards (< 1000 mg/L). Principal component analysis (PCA) combined with hierarchical cluster analysis (HCA) and self-organizing maps (SOM) were applied for the classification of the groundwater geochemistry. The three first principal components explained 58, 20, and 16% of the variance, respectively. The first component reflects sulfate minerals (gypsum, anhydrite) and halite dissolution, and/or evaporation in the shallow aquifer. The second and third components are interpreted as carbonate rock dissolution. The reason for two factors is that the different aquifers give rise to different degree of hydrogeochemical evolution (different travel distances and travel times). Identified clusters for evolution characteristic and influencing factors were confirmed by the PCA–HCA methods. Using information from eight ion components and SOM, formation mechanisms and influencing factors for the present groundwater quality were determined.

... A criterion is proposed to determine whether circulations are topographically-or recharge controlled. Starting from the configuration of the much larger and deeper regional aquifer of the Dosit river from northwestern China (1 km depth over 100 km scale), Wang et al. (2016) determine with a calibrated groundwater flow and transport model that the RTD has a late time peak indicative of regional circulations deeper than the local circulations classically defined in Tothian systems (Tóth, 1962). They propose the RTD as an effective and quantitative criterion to identify local, intermediary and regional circulations. ...

... Therefore, it is difficult to find cross sections parallel to the principal direction of groundwater flow. Moreover, due to the increasingly developing computation ability, 3-D models of groundwater flow using a specified-head boundary condition at the water table are increasingly popular to understand the nature of groundwater circulation (e.g., Lazear, 2006;Marklund & Wörman, 2011;Tóth et al., 2016;Wang et al., 2016;Wang et al., 2017;Winter, 1978;Wörman, Packman, Marklund, Harvey, & Stone, 2006, 2007Zijl, 1999). Similarly, hyporheic flow induced by 3-D bed form has been examined by some researchers (e.g., Caruso, Ridolfi, & Boano, 2016;Marion, Bellinello, Guymer, & Packman, 2002;Tonina & Buffington, 2007;Marzadri, Tonina, Bellin, Vignoli, & Tubino, 2010). ...

Although it has been increasingly acknowledged that groundwater flow pattern is complicated in the three-dimensional (3-D) domain, two-dimensional (2-D) water table-induced flow models are still widely used to delineate basin-scale groundwater circulation. However, the validity of 2-D cross-sectional flow field induced by water table has been seldom examined. Here, we derive the analytical solution of 3-D water table-induced hydraulic head in a Tóthian basin and then examine the validity of 2-D cross-sectional models by comparing the flow fields of selected cross sections calculated by the 2-D cross-sectional model with those by the 3-D model, which represents the “true” cases. For cross sections in the recharge or discharge area of the 3-D basin, even if head difference is not significant, the 2-D cross-sectional models result in flow patterns absolutely different from the true ones. For the cross section following the principal direction of groundwater flow, although 2-D cross-sectional models would overestimate the penetrating depth of local flow systems and underestimate the recharge/discharge flux, the flow pattern from the cross-sectional model is similar to the true one and could be close enough to the true one by adjusting the decay exponent and anisotropy ratio of permeability. Consequently, to determine whether a 2-D cross-sectional model is applicable, a comparison of hydraulic head difference between 2-D and 3-D solutions is not enough. Instead, the similarity of flow pattern should be considered to determine whether a cross-sectional model is applicable. This study improves understanding of groundwater flow induced by more natural water table undulations in the 3-D domain and the limitations of 2-D models accounting for cross-sectional water table undulation only.

... The residence time of a groundwater sample since its recharge can be determined by a numerical model of groundwater flow (de Dreuzy and Ginn, 2016). Based on Wang et al.'s (2016) three-dimensional groundwater flow model of the Dosit River Watershed, the mean residence time of G1 (samples D5 through D8) is around 14,000 years, while that of G2 (samples D1 through D4) is around 18,000 years. This is in accordance with the fact that G2 has longer distances away from the divide of the Dosit River Watershed (Fig. 2). ...

Compared with the numerous studies on river and soil waters, studies on Mg isotopes of groundwater are limited. In this study, a sandstone aquifer in the Ordos Basin, China with contrast contents of Mg in shallow and deep groundwater is selected to examine the behavior of Mg isotopes during groundwater circulation. The δ²⁶Mg values of shallow groundwater are within the range of widely reported results of groundwater, while those of deep groundwater are found to be as light as −3.30‰ to −2.13‰. Assuming that shallow groundwater is an endmember, ⁸⁷Sr/⁸⁶Sr ratios show that calcite dissolution has contribution to low δ²⁶Mg of deep groundwater, but mixing alone cannot explain the coupled low δ²⁶Mg and low Mg contents. The removal of Mg in deep groundwater is found to be mainly caused by incorporating into neoformed clay minerals, which further lowers δ²⁶Mg. For the deep groundwater samples denoted as G1 and G3, the relationship between δ²⁶Mg and 1/Mg has been quantitatively explained by the superposition of calcite dissolution and clay formation with a fractionation factor (αclay–water) of 1.0003. For samples denoted as G2, in addition to calcite dissolution and clay formation, high proportion of Mg in the residual solution are further removed via precipitation of low-Mg calcite, which leads to increased δ²⁶Mg. There are increasingly stronger degrees of clay formation in G3, G1, and G2 due to the increasingly longer travel distances and travel times of groundwater from recharge to discharge areas. This study enhances understanding on the factors controlling Mg isotopes of groundwater, as well as the geochemical processes of subsurface water-rock interactions in sandstone aquifers.

... However, in most aquifer settings, recharge varies spatially across a catchment due to variations in soil and vegetation cover (Cook et al., 1998), topographic relief (McGuire et al., 2005), localized recharge sources such as surface waters, wetlands or mountain front (Fulton et al., 2012;Siade et al., 2015;Wilson & Guan, 2004), and the variability of vadose zone processes (Scanlon et al., 2002;Wood et al., 2015Wood et al., , 2017. This can result in adjacent groundwater flow paths of very different residence times, which could be expected to create substantial mixing of tracer concentrations indicating distinctively different ages where these flow paths converge, such as in long-screen wells (Wang et al., 2016). To consider how these recharge processes could influence the spatial evolution and interpretation of environmental tracer concentrations, we present a scenario where recharge is distributed over the domain via multiple distinct recharge zones. ...

Understanding groundwater ages within an aquifer system has the potential to better constrain estimates of groundwater recharge and flow rates, and therefore increase the reliability of groundwater models. Groundwater ages are generally interpreted from field-observed environmental tracer concentrations, but in many cases in which multiple groundwater age tracers have been analyzed simultaneously the results show significant disparities among tracer-specific estimated ages. The disparities are generally attributed to physical mixing between waters of different ages. However, especially in the geochemical literature environmental tracer concentrations are often analyzed with simplistic models in which the degree of the simulated mixing might be considered unrealistic for natural heterogeneous geologic media. In this study we use numerical experiments to examine under which physical conditions measured concentrations of selected environmental tracers (CFC-12, 39Ar, 14C) may return discrepant ages. Our model simulations suggest that matrix diffusion has the greatest potential to cause mixing of different-aged water and to generate age biases between tracers. The multi-tracer simulations also suggest that there is a limit to the magnitude of the discrepancies that can be attributed to physical processes. When comparing data collected from the Pilbara region of Western Australia with our numerical modeling studies, it was found that a dual-domain mass transfer model was required to explain the field-observed age-discrepancies.

... Even more fundamentally, relating the shape of RTDs to aquifer structure requires some concepts of groundwater flow organizations. Topography-driven flow and transport have been historically organized in nested local, intermediary and regional circulation patterns (Cardenas, 2007;Tóth, 1963;Welch et al., 2012) resulting in multiple exponential or power-law RTDs (Goderniaux et al., 2013;Kirchner et al., 2001;Wang et al., 2016). While relevant for thick unconfined aquifers under high recharge rates, shallower systems result in stronger correlations between climate, geology and geomorphology to shape the organization of flows under free-surface controls uphill and topographic controls downhill (Bresciani et al., 2016a;Condon and Maxwell, 2015;Gleeson et al., 2011;Haitjema and Mitchell-Bruker, 2005). ...

Residence Times in aquifers result from their internal structure, from the hydrodynamic transport processes and from the recharge conditions to which they are exposed. Beyond the already known residence time distributions (RTD) for either constant aquifer thickness and/or uniform recharge, we investigate the effect of both distributed aquifer thickness and distributed recharge. We develop a semi-analytical approximation of the RTD for generic trapezoidal aquifers exposed to linearly-variable recharges. The solution is derived for a homogeneous 2D cross-sectional aquifer in steady-state conditions following the Dupuit-Forchheimer assumption according to which the vertical head gradients are much smaller than the horizontal head gradients. Close agreement with 2D numerical simulations demonstrates the relevance of the Dupuit-Forchheimer assumption to estimate RTDs as long as the aquifer thickness remains an order of magnitude smaller than the aquifer length. At equivalent aquifer volume, geometrical structure and recharge conditions result in non-trivial and complex RTD shapes that may be uniform, Gamma-like, power-law-like shapes as well as any intermediary shapes. The variety of RTD shapes encountered show the need to systematically include the aquifer structure and recharge conditions in the assessment of RTDs and for their subsequent use for problematics related to water quality. The semi-analytical approximation can be further used in a variety of aquifer systems in complement with other existing solutions as a Lumped Parameter Model for RTDs.

... However, until now, no quantitative analysis has been presented of the properties of these flow systems (i.e., volume, flow rate, etc.). This knowledge gap is partly due to the lack of efficient and accessible tools to segment a groundwater flow field into its different flow systems (notwithstanding several research efforts in this direction [48], [49]). ...

... This argument is supported by Gassiat et al. (2013), who recited that the role of layered aquifer systems which are common in both consolidated and unconsolidated sediments has not been systematically explored in groundwater flow modeling. The identification of the volumes occupied by different orders of flow systems in 3D is yet another prime area of research in the field of basin-scale groundwater flow systems modeling (Wang et al. 2016(Wang et al. , 2017. Two-dimensional rather than three-dimensional models have mostly been preferred because of the high computational demands of 3D models. ...

Decision-makers require correct and adequate information on groundwater flow systems in a basin in order to formulate sustainable water resources development strategies. However, the practicality and realism of groundwater flow system models depend on the validity, reliability and availability of quality data and information, and how they are used in model development and calibration. This goes hand in hand with how the underlying theories, tenets and assumptions are understood, interpreted and applied. The more uncertain and contentious the information is, the wider are the knowledge and theoretical gaps, and thus the less useful the model results are for decision-making. The understanding of water table types in groundwater basins has become one of the additional factors for an in-depth understanding and modeling of nested groundwater flow systems. The classification of water table types using a water table ratio provides that if the ratio is more than 1, this depicts a topography-controlled area and a ratio of less than 1 depicts a recharge-controlled terrain. Log transformation of the water table ratio proved the same interpretation. This paper therefore reviews the evolution of groundwater flow systems theory, the prevailing knowledge and theoretical gaps by specifically pinpointing the theoretical and conceptual contentions and additional factors which can possibly limit the application of groundwater flow theories in regional groundwater modeling studies. The implications of how the conceptual and theoretical contentions affect groundwater modeling for decision-making in groundwater development and management are also pinpointed in this paper.

... The results showed a substantial difference in the sizes 460 of the discharge areas of the regional groundwater and hyporheic flows at the streambed interface (Figure 9), in which the groundwater flow discharge area is significantly fragmented into smaller areas under the influence of hyporheic fluxes. Hence, in addition to the previously determined characteristics such as groundwater trajectories (Vissers and van der Perk, 2008;Wang et al., 2014) and the groundwater residence time distribution (Wang et al., 2016), the sizes of the discharge areas of subsurface flows at the streambed interface can be used to distinguish the regional and hyporheic flows in hierarchically nested 465 groundwater flow systems. The investigation of hierarchical nested groundwater flow systems improves our understanding of quantitative and qualitative groundwater flow-related phenomena, including the fate and transport of solutes and contaminants (Zijl, 1999). ...

The importance of hyporheic water fluxes induced by hydromorphologic processes at the streambed scale and their consequential effects on stream ecohydrology have recently received much attention. However, the role of hyporheic water fluxes in regional groundwater discharge is still not entirely understood. Streambed-induced flows not only affect mass and heat transport in streams but are also important for the retention of solute contamination originating from deep in the subsurface, such as naturally occurring solutes as well as leakage from the future geological disposal of nuclear waste. Here, we applied a multiscale modeling approach to investigate the effect of hyporheic fluxes on regional groundwater discharge in the Krycklan catchment, located in a boreal landscape in Sweden. Regional groundwater modeling was conducted using COMSOL Multiphysics constrained by observed or modeled representations of the catchment infiltration and geological properties, reflecting heterogeneities within the subsurface domain. Furthermore, streambed-scale modeling was performed using an exact spectral solution of the hydraulic head applicable to streaming water over a fluctuating streambed topography. By comparing the flow fields of watershed-scale groundwater discharge with and without consideration of streambed-induced hyporheic flows, we found that the flow trajectories and the distribution of the travel times of groundwater were substantially influenced by the presence of hyporheic fluxes near the streambed surface. One implication of hyporheic flows is that the groundwater flow paths contract near the streambed interface, thus fragmenting the coherent areas of groundwater upwelling and resulting in narrow “pinholes” of groundwater discharge points.

... To avoid the uncertainty induced by the insufficient geological information in the upper Selke catchment, and to focus on stream-groundwater interactions in the lower Selke catchment, the average of the observed discharge at the Meisdorf gauging station from 2011 to 2018 is used as the inflow rate of the lower Selke River. Meanwhile, the lower Selke River and its main tributaries are treated with STR package (Prudic, 1989) while the upper Selke River and the other rivers are treated with Drain package by setting a high conductance value of 0.115 m 2 /s and setting the drain elevation equal to the elevation of the land surface, which is a common approach used by previous studies (Goderniaux et al., 2013;Wang et al., 2016). The vadose zone is not considered in the current study. ...

The exchange of water and solutes between the stream and groundwater along a stream network affects the source composition of discharge and solute load in the stream. To date, this hydrologic turnover has only been analyzed with respect to the exchange of water. In this study, we extend the concept of hydrologic turnover to solutes and analyze the effects of different hydrologic conditions on the spatial patterns and magnitude of exchange fluxes. Based on a coupled stream‐groundwater model built in MODFLOW using the Streamflow‐routing package, we simulated stream‐groundwater exchange along a stream of 30 km in length and evaluated the evolution of stream water source composition under different precipitation and streamflow conditions. Results show that even for highly variable hydrologic conditions, the direction of stream‐groundwater exchange (loss/gain) remained unchanged in consistently gaining or losing reaches, but changed in interspersed transitional reaches. The comparison between the source composition of discharge and nitrate load in stream water revealed a decoupling of discharge and solute load contribution from groundwater to the stream, as zones of high water gains do not necessarily coincide with zones of high solute concentrations. Overall, nearly 80% of total groundwater contributions to the outflow of water from the catchment were generated over only 20% of the total stream length. Our research highlights the importance of distinguishing water and solute load contributions to streams. This in turn implies that to reduce groundwater‐borne nutrient loads to streams, measures need to focus on the specific reaches with highest load contributions.

... Identifying, delineating and analyzing these different regions sheds light on groundwatersurface water interactions, the capture zone of pumping wells, and solute transport in groundwater flow systems [38][39][40]. Yet, until recently, this type of analysis has principally been conducted in simplistic configurations in 2D [41][42][43]. Our code will hence allow for tackling long-standing questions about the structure of groundwater flow in more realistic configurations. ...

A myriad of physical phenomena, such as fluid flows, magnetic fields, and population dynamics are described by vector fields. More often than not, vector fields are complex and their analysis is challenging.
Vector field topology is a powerful analysis technique that consists in identifying the most essential structure of a vector field. Its topological features include critical points and separatrices, which segment the domain into regions of coherent flow behavior, provide a sparse and semantically meaningful representation of the underlying data.
However, a broad adoption of this formidable technique has been hampered by the lack of open source software implementing it. The Visualization Toolkit (VTK) now contains the filter vtkVectorFieldTopology that extracts the topological skeleton of 2D and 3D vector fields. This paper describes our implementation and demonstrates its broad applicability with two real-world examples from hydrology and space physics.

Hydrogeochemistry and environmental isotopes were used to gain insight into the recharge processes, water–rock interactions, and groundwater residence time, and to identify groundwater flow systems (GFSs) in an interfluve between the Han River and Yangtze River in the eastern Jianghan Plain (China), an alluvial-lacustrine plain in the middle reaches of the Yangtze River. Because of carbonate mineral weathering, groundwater in the plain is predominantly HCO3-Ca or HCO3-Ca-Mg type. The decrease in typical ions and isotopic depletion with increasing depth indicates that the GFSs were divided into local and regional GFSs with an approximate depth limitation of 20 m. The consistent variations are attributable to complex anthropogenic activities, water–rock interactions and groundwater flow patterns. The multiple independent local GFSs exhibited a pattern in which groundwater was discharged into surface waters during the non-flood season. Groundwater age of local GFSs is modern according to the ³H concentrations, so the hydrodynamic circulation is active. Furthermore, the regional GFS pattern is controlled by slow lateral flow from west or northwest to east, eventually discharging into the Yangtze and Han rivers. The distribution of δ¹⁸O indicated three zones in regional GFSs that are likely dominated by the altitude effect of recharge areas. The groundwater age of regional GFSs varied from hundreds of years to 5000 years, estimated by ¹⁴C isotope data, revealing that the hydrodynamic circulation of regional GFSs is slow to relatively stagnant. The hydrodynamic characteristics and hydrochemical distributions corroborated the mixing zones of differently hierarchical GFSs in the discharge area of the Jianghan Plain.

Numerical models with spatially-varying head as top boundary conditions were used in previous studies to understand topography-driven groundwater flow. The head boundary conditions could cause artifacts of extremely large, but unrealistic recharge rates owing to unlimited supply of water. This study adopted a fully-coupled surface–subsurface hydrologic modeling approach to simulate transient topography-driven groundwater flow and also surface-water flow under homogeneous and isotropic settings. Two 100-year climate datasets and five hydraulic conductivities (K, 0.01 - 100 m/d) were tested in numerical experiments. In the base case with a wet climate (annual precipitation 1696 mm/y) and K of 1 m/d, groundwater head at two different locations close to both lateral boundaries fluctuates only within 5.1 m and 9.6 m, respectively, during the 100-year period. Despite the local water table fluctuations caused by the variability in the climatic record, large-scale groundwater flow systems can be assumed in dynamic equilibrium provided stationary climate. Long-term average exchange fluxes are spatially constant and limited by precipitation infiltration when surface water is absent, whereas they vary from positive to negative values (i.e., recharge to discharge) spatially when surface water is present. Sensitivity analysis suggests that wetter climate and smaller K lead to more inundation of the land surface, stronger hierarchical nesting of groundwater flow systems and more variable exchange fluxes. Overall, our first fully-coupled modeling of topography-driven groundwater flow implies that attention must be paid to causality between head and flow, and climatic record as boundary conditions may be more appropriate due to its relaxed manner.

Study region
Three karst regions in Hungary and Slovakia.
Study focus
Time series of environmental tracers both in the groundwater recharge and discharge provide important insights into how a karst water system works. The aim of the present work was to study the response of discharging karst waters to recharge using time series of environmental tracers, such as tritium, stable water isotopes, noble gases and SF6.
New hydrological insights for the region
Our results show that sampling frequency plays a significant role in detecting short residence times (months): the seasonality of ¹⁸O isotope composition of a selected karst spring indicates a 10 % contribution of recent water with a residence time of half a year. The contribution of an older component can be proven by the decrease of the tritium content of the waters, which compares to the decreasing trend of the tritium time series of the precipitation. However, the tritium concentrations are just slightly lower than those of the precipitation and the recharge water, hence the residence times of these shallow springs are supposed to be short. ³H/³He and SF6 apparent ages confirm this to be between 0 and 10 years, with a median of 1.4 years. Our study demonstrates that long-term time series are preferable to provide better estimation to the age distribution than individual, short-term investigations.

To realize and accelerate the pace of intelligent manufacturing, this paper presents a novel tool wear assessment technique based on the integrated radial basis function based kernel principal component analysis (KPCA_IRBF) and Gaussian process regression (GPR) for real-timely and accurately monitoring the in-process tool wear parameters (flank wear width). The KPCA_IRBF is a kind of new nonlinear dimension-increment technique and firstly proposed for feature fusion. The tool wear predictive value and the corresponding confidence interval are both provided by utilizing the GPR model. Besides, GPR performs better than artificial neural networks (ANN) and support vector machines (SVM) in prediction accuracy since the Gaussian noises can be modeled quantitatively in the GPR model. However, the existence of noises will affect the stability of the confidence interval seriously. In this work, the proposed KPCA_IRBF technique helps to remove the noises and weaken its negative effects so as to make the confidence interval compressed greatly and more smoothed, which is conducive for monitoring the tool wear accurately. Moreover, the selection of kernel parameter in KPCA_IRBF can be easily carried out in a much larger selectable region in comparison with the conventional KPCA_RBF technique, which helps to improve the efficiency of model construction. Ten sets of cutting tests are conducted to validate the effectiveness of the presented tool wear assessment technique. The experimental results show that the in-process flank wear width of tool inserts can be monitored accurately by utilizing the presented tool wear assessment technique which is robust under a variety of cutting conditions. This study lays the foundation for tool wear monitoring in real industrial settings.

Although it has been reported that flowing artesian wells could be topographically-controlled, there is no quantitative research on artesian flow conditions in unconfined aquifers. In this study, the water table, which has a lower amplitude than the land surface, is damped from the topography and used as the boundary condition to obtain the analytical solution of hydraulic head of a unit basin with a single flow system. The term artesian head is defined to characterize the condition of flowing artesian wells. The zone with positive artesian head is called artesian zone while with negative artesian head is non-artesian zone. The maximum artesian head and the size of artesian zones are found to increase with the damping factor and the anisotropy ratio, and decrease with the ratio of basin width to depth and the depth-decay exponent of hydraulic conductivity. Moreover, the artesian head increases with depth nearby the valley and decreases with depth near by the divide, and the variation rates are influenced by the decay exponent and the anisotropy ratio. Finally, the distribution of flowing artesian wells and the artesian head measurements in different depths of a borehole in a small catchment in the Ordos Plateau, Northwestern China is used to illustrate the theoretical findings. The change in artesian head with depth was used to estimate the anisotropy ratio and the decay exponent. This study opens up a new door to analyze basin-scale groundwater flow. This article is protected by copyright. All rights reserved.

Analytical studies on release/capture zones are often limited to a uniform background groundwater flow. In fact, for basin-scale problems, the undulating water table would lead to the development of hierarchically nested flow systems, which are more complex than a uniform flow. Under the premise that the water table is a replica of undulating topography and hardly influenced by wells, an analytical solution of hydraulic head is derived for a two-dimensional cross section of a drainage basin with horizontal injection/pumping wells. Based on the analytical solution, distributions of hydraulic head, stagnation points and flow systems (including release/capture zones) are explored. The superposition of injection/pumping wells onto the background flow field leads to the development of new internal stagnation points and new flow systems (including release/capture zones). Generally speaking, the existence of n injection/pumping wells would result in up to n new internal stagnation points and up to 2n new flow systems (including release/capture zones). The analytical study presented, which integrates traditional well hydraulics with the theory of regional groundwater flow, is useful in understanding basin-scale groundwater flow influenced by human activities.

The use of environmental tracers to characterize time scales when investigating groundwater is a technology that has been in use for half a century. Its usefulness is beyond controversy. However, the use of the word “age” for groundwater connected with these techniques is misleading due to its inherent connection to the general understanding of human age. “Age” as in the understanding of human age cannot be determined for groundwater, although it is a useful zero-order concept abundantly used in this context. This paper describes three basic definitions of “age” for groundwater (1: idealized age as in particle tracking and piston flow, 2: mean residence time involving an age distribution and 3: apparent age) and discusses their context in view of recent developments in numerical groundwater modelling. It further gives arguments why the term is “age” unnecessary in modern hydrology and groundwater management and how not using it can enhance efficiency in system understanding: not using age needs less modelling effort and allows comparing models directly with measured values instead of comparing models with models.

The distribution of groundwater fluxes in aquifers is strongly
influenced by topography, and organized between hillslope and regional
scales. The objective of this study is to provide new insights regarding
the compartmentalization of aquifers at the regional scale and the
partitioning of recharge between shallow/local and deep/regional
groundwater transfers. A finite-difference flow model was implemented,
and the flow structure was analyzed as a function of recharge (from 20
to 500 mm/yr), at the regional-scale (1400 km2), in three
dimensions, and accounting for variable groundwater discharge zones;
aspects which are usually not considered simultaneously in previous
studies. The model allows visualizing 3-D circulations, as those
provided by Tothian models in 2-D, and shows local and regional
transfers, with 3-D effects. The probability density function of transit
times clearly shows two different parts, interpreted using a
two-compartment model, and related to regional groundwater transfers and
local groundwater transfers. The role of recharge on the size and nature
of the flow regimes, including groundwater pathways, transit time
distributions, and volumes associated to the two compartments, have been
investigated. Results show that topography control on the water table
and groundwater compartmentalization varies with the recharge rate
applied. When recharge decreases, the absolute value of flow associated
to the regional compartment decreases, whereas its relative value
increases. The volume associated to the regional compartment is
calculated from the exponential part of the two-compartment model, and
is nearly insensitive to the total recharge fluctuations.

The stagnant zones in nested flow systems have been assumed to be critical to accumulation of transported matter, such as metallic ions and hydrocarbons in drainage basins. However, little quantitative research has been devoted to prove this assumption. In this paper, the transport of age mass is used as an example to demonstrate that transported matter could accumulate around stagnation points. The spatial distribution of model age is analyzed in a series of drainage basins of different depths. We found that groundwater age has a local or regional maximum value around each stagnation point, which proves the accumulation of age mass. In basins where local, intermediate and regional flow systems are all well developed, the regional maximum groundwater age occurs at the regional stagnation point below the basin valley. This can be attributed to the long travel distances of regional flow systems as well as stagnancy of the water. However, when local flow systems dominate, the maximum groundwater age in the basin can be located around the local stagnation points due to stagnancy, which are far away from the basin valley. A case study is presented to illustrate groundwater flow and age in the Ordos Plateau, northwestern China. The accumulation of age mass around stagnation points is confirmed by tracer age determined by 14C dating in two boreholes and simulated age near local stagnation points under different dispersivities. The results will help shed light on the relationship between groundwater flow and distributions of groundwater age, hydrochemistry, mineral resources, and hydrocarbons in drainage basins.

In this paper, we investigate the effects of systematic and local heterogeneity on groundwater flow, transport, and residence time distributions (RTDs) of basins where groundwater flow is topography driven. Systematic heterogeneity is represented by an exponentially depth-decreasing hydraulic conductivity and porosity, and local heterogeneity is represented by the dispersivity. The RTDs for both a simple basin with one flow system and a basin with nested local and regional systems gradually evolve to a power law RTD with more pronounced systematic heterogeneity. Exponential decrease of poromechanical properties enhances shallow circulation and subdues deep and regional flows leading to longer flushing times for the large part of the domain, while the shallower portions flush solutes rapidly. Therefore, deeper basins lead to more persistent and pronounced power law RTDs when the poromechanical properties systematically decrease with depth. Separate contributions to the RTD due to stagnation zones associated with local flow cells and due to deeper immobile zones were identified; each leads to a different tailing behavior. Local heterogeneity slightly enhances the power law RTD by causing the tailing to begin earlier but does not affect the late time portion of the RTD. Systematic depth-dependent heterogeneity is an important factor controlling the circulation and associated RTDs of subsurface fluids. It contributes significantly to generation of power law RTDs.

Theoretical analysis and field observations suggest that the depth-dependent trend of permeability anisotropy is a nature of the geological media accompanying the depth-decaying permeability. However, the effect of depth-dependent anisotropy has not been investigated in previous studies of regional groundwater flow. A more general analytical solution of topography-driven flow in drainage basins is derived in this study. Exponential trend of permeability with depth is assumed, and different decay rates of horizontal permeability (k x) and vertical permeability (k z) are included to account for the depth-dependent anisotropy. It is found that the shape of the nested flow systems in a drainage basin depends on not only the depth-dependent permeability but also the depth-dependent anisotropy ratio (k x/k z). For stagnation points between the flow systems, the number of stagnation points is not influenced by the depth-dependent permeability and anisotropy; however, an increase in k x/k z can lead to a decrease in the depth of their location. When k x is smaller than k z on the top boundary, this phenomenon is especially significant.

The existence of stagnation points in nested flow systems is relevant to a range of geologic processes. There has been no analytical study on the characteristics and locations of stagnation points in nested flow systems. We derived analytical solutions for hydraulic head and stream function in basins with isotropic and depth-decaying hydraulic conductivity. The solutions of hydraulic head and stream function are used to identify the positions of stagnation points and discuss the dynamics of groundwater around the stagnation points. Three types of stagnation points are identified by analytical and graphical means. For stagnation points on the basin bottom below the valley, only two regional flow systems converge from opposite directions. For stagnation points on the basin bottom below the regional high, only two regional flow systems part toward opposite directions. In contrast, for stagnation points under counterdirectional local flow systems, flow systems converging from and parting toward opposite directions coexist, and these stagnation points move deeper as the water table configuration becomes more rugged and the decay exponent of hydraulic conductivity increases. Moreover, the dividing streamlines around stagnation points under counterdirectional local flow systems are used to divide the local, intermediate, and regional flow systems accurately, from which the penetration depths of local and intermediate flow systems are precisely determined. A clear understanding of the location of stagnation points is critical for characterizing the pattern of hierarchically nested flow systems and has potential implication in studying solute and mineral concentration distributions in drainage basins.

The age of groundwater is a manifestation of the temporal scale of groundwater flow in basins, whose pattern was recently found to be influenced by depth-dependent hydraulic conductivity (K). In this paper, we show through numerical simulations how well-documented depth-decaying K and porosity ($\theta$) influence groundwater age. In the unit basin, depth-decaying K and $\theta$ cause aging in deeper parts and rejuvenation near the discharge zones, and the size of rejuvenated zones decreases with the decay exponent (A). In the Tóth basin, the geometry and size of rejuvenated zones, which are generally located at the interfaces between flow systems in the mid to lower reaches of the basin, are sensitive to A. In both basins, the maximum relative age and the relative age of groundwater at the lowest discharge point are dependent on A. Therefore, the depth-decaying K and $\theta$ cannot be ignored when interpreting groundwater age distribution. Bibtex entry for this abstract Preferred format for this abstract (see Preferences) Find Similar Abstracts: Use: Authors Title Keywords (in text query field) Abstract Text Return: Query Results Return items starting with number Query Form Database: Astronomy Physics arXiv e-prints

Steady flow regimes for three-dimensional lake-aquifer systems are
studied via idealized mathematical models that are extensions of earlier
simplified vertical section models of interaction between shallow lakes
and underlying aquifers. The present models apply to a shallow circular
lake at the surface of a rectangular aquifer of finite depth, yielding a
truly three-dimensional representation of the resulting flow system.
Flux boundary conditions are applied at the ends of the aquifer, with
net vertical recharge or evapotranspiration at the water table. The lake
is defined by a region with constant head. By determining and
visualizing solutions to the discretized saturated flow equations, a
range of possible flow regimes is identified, and their topological
properties are studied. Tools for analyzing flow regimes are described,
including a method for locating and mapping three-dimensional dividing
surfaces within steady flow fields. Results show strong similarities
between two- and three-dimensional systems, including a large number of
flow-through, recharge, and discharge regimes and reverse flow cells.
Flow lines calculated on a vertical plane through the middle of a lake
resemble but are not identical to two-dimensional streamlines for a
range of aquifer flow and recharge conditions. Estimates of the widths
and depths of capture and release zones for various lake-aquifer
geometries are asymptotic to earlier results for two-dimensional
systems. Numerical predictions are compared with analytical results for
certain limiting flow regimes.

This study uses numerical simulations to define the salient controls on regional groundwater flow in 3-D mountainous terrain by systematically varying topographic and hydrogeologic variables. Topography for idealized multiple-basin mountainous terrain is derived from geomatic data and literature values. Water table elevation, controlled by the ratio of recharge to hydraulic conductivity, largely controls the distribution of recharged water into local, regional, and perpendicular flow systems, perpendicular flow being perpendicular to the regional topographic gradient. Both the relative (%) and absolute (m3/d) values of regional flow and perpendicular flow are examined. The relationship between regional flow and water table elevation is highly nonlinear. With lower water table elevations, relative and absolute regional flow dramatically increase and decrease, respectively, as the water table is lowered further. However, for higher water table elevations above the top of the headwater stream, changes in water table elevation have little effect on regional flow. Local flow predominates in high water table configurations, with regional and perpendicular flow <15% and <10%, respectively, of total recharge in the models tested. Both the relative and the maximum absolute regional flow are directly controlled by the degree of incision of the mountain drainage network; the elevation of mountain ridges is considerably less important. The percentage of the headwater stream with perennial streamflow is a potentially powerful indicator of regional flow in all water table configurations and may be a good indicator of the susceptibility of mountain groundwater systems to increased aridity.

The objective of the present paper is to show that groundwater is a general geologic agent. This perception could not, and did not, evolve until the system nature of basinal groundwater flow and its properties, geometries, and controlling factors became recognized and understood through the 1960s and 1970s.
The two fundamental causes for groundwater's active role in nature are its ability to interact with the ambient environment and the systematized spatial distribution of its flow. Interaction and flow occur simultaneously at all scales of space and time, although at correspondingly varying rates and intensities. Thus, effects of groundwater flow are created from the land surface to the greatest depths of the porous parts of the Earth's crust, and from a day's length through geologic times. Three main types of interaction between groundwater and environment are identified in this paper, with several special processes for each one, namely: (1) Chemical interaction, with processes of dissolution, hydration, hydrolysis, oxidation-reduction, attack by acids, chemical precipitation, base exchange, sulfate reduction, concentration, and ultrafiltration or osmosis; (2) Physical interaction, with processes of lubrication and pore-pressure modification; and (3) Kinetic interaction, with the transport processes of water, aqueous and nonaqueous matter, and heat. Owing to the transporting ability and spatial patterns of basinal flow, the effects of interaction are cumulative and distributed according to the geometries of the flow systems.
The number and diversity of natural phenomena that are generated by groundwater flow are almost unlimited, due to the fact that the relatively few basic types are modified by some or all of the three components of the hydrogeologic environment: topography, geology, and climate. The six basic groups into which manifestations of groundwater flow have been divided are: (1) Hydrology and hydraulics; (2) Chemistry and mineralogy; (3) Vegetation; (4) Soil and rock mechanics; (5) Geomorphology; and (6) Transport and accumulation. Based on such a diversity of effects and manifestations, it is concluded that groundwater is a general geologic agent.

Flow-system analysis is based on the concept of hierarchical groundwater flow systems. The topography of the water table, which is strongly related to the topography of the land surface, is a major factor in the hierarchical nesting of gravity-driven groundwater flow, resulting in flow systems of different orders of magnitude in lateral extent and depth of penetration. The concept of flow systems is extremely useful in the analysis of spatial and temporal scales and their mutual relationships. Basic equations on the laboratory scale are extended to larger, regional scales. Making use of Fourier analysis further develops Tóth's original idea of topography-driven flow systems. In this way, the different spatial scales of the water table are separated in a natural way, leading to a simple expression for the penetration depth of a flow system. This decomposition leads also to the relationship between spatial and temporal scales.
Analogous to flow systems, water bodies with different water quality may be called 'transport systems.' Field studies, numerical micro-scale modeling over macro-scale domains, and stochastic dispersion theory indicate that between systems with steady transport, the interfaces are relatively thin. The interfaces are much thinner than the relatively large mixing zones predicted by the conventional engineering approach to macrodispersion, in which relatively large, time-independent macrodispersion lengths are applied. A relatively simple alternative engineering approach is presented. For macrodispersion of propagating solute plumes, the alternative dispersion term gives the same results as the conventional engineering approach and gives correct results for steady-state transport.

The dynamic nature of groundwater is not readily apparent, except where discharge is focused at springs or where recharge
enters sinkholes. Yet groundwater flow and storage are continually changing in response to human and climatic stresses. Wise
development of groundwater resources requires a more complete understanding of these changes in flow and storage and of their
effects on the terrestrial environment and on numerous surface-water features and their biota.

This book recognises groundwater flow as a fundamental geologic agent, and presents a wide-ranging and illustrated overview of its history, principles, scientific consequences and practical utilization. The author, one of the founding fathers of modern hydrogeology, highlights key interrelationships between seemingly disparate processes and systems by tracing them to a common root cause - gravity-driven groundwater flow. Numerous examples demonstrate practical applications in a diverse range of subjects, including land-use planning, environment protection, wetland ecology, agriculture, forestry, geotechnical engineering, nuclear-waste disposal, mineral and petroleum exploration, and geothermal heat flow. The book contains numerous user-friendly features for a multidisciplinary readership, including full explanations of the relevant mathematics, emphasis on the physical meaning of the equations, and an extensive glossary. It is a key reference for researchers, consultants and advanced students of hydrogeology and reservoir engineering. © J. Tóth 2009 and Cambridge University Press, 2009. All rights reserved.

Mathematical models of varying complexity have been developed since the 1960s to interpret environmental tracer concentrations in groundwater flow systems. This review examines published studies of model-based environmental tracer interpretation, the progress of different modelling approaches, and also considers the value of modelling tracer concentrations directly rather than estimations of groundwater age. Based on citation metrics generated using the Web of Science and Google Scholar reference databases, the most highly utilised interpretation approaches are lumped parameter models (421 citations), followed closely by direct age models (220 citations). A third approach is the use of mixing cell models (99 citations). Although lumped parameter models are conceptually simple and require limited data, they are unsuitable for characterising the internal dynamics of a hydrogeological system and/or under conditions where large scale anthropogenic stresses occur within a groundwater basin. Groundwater age modelling, and in particular , the simulation of environmental tracer transport that explicitly accounts for the accumulation and decay of tracer mass, has proven to be highly beneficial in constraining numerical models. Recent improvements in computing power have made numerical simulation of tracer transport feasible. We argue that, unlike directly simulated ages, the results of tracer mass transport simulation can be compared directly to observations, without needing to correct for apparent age bias or other confounding factors.

Theoretically, three types of flow systems may occur in a small basin: local, intermediate, and regional. The local systems are separated by subvertical boundaries, and the systems of different order are separated by subhorizontal boundaries. The higher the topographic relief, the greater is the importance of the local systems. The flow lines of large unconfined flow systems do not cross major topographic features. Stagnant bodies of groundwater occur at points where flow systems meet or branch. Recharge and discharge areas alternate; thus only part of the basin will contribute to the baseflow of its main stream. Motion of groundwater is sluggish or nil under extended flat areas, with little chance of the water being freshened. Water level fluctuations decrease with depth, and only a small percentage of the total volume of the groundwater in the basin participates in the hydrologic cycle.

Numerical simulation of three-dimensional groundwater flow near lakes
shows that the continuity of the boundary encompassing the local
groundwater flow system associated with a lake is the key to
understanding the interaction of a lake with the groundwater system. The
continuity of the boundary can be determined by the presence of a
stagnation zone coinciding with the side of the lake nearest the
downgradient side of the groundwater system. For most settings modeled
in this study the stagnation zone underlies the lakeshore, and it
generally follows its curvature. The length of the stagnation zone is
controlled by the geometry of the lake's drainage basin divide on the
side of the lake nearest the downgradient side of the groundwater
system. In the case of lakes that lose water to the groundwater system,
three-dimensional modeling also allows for estimating the area of lake
bed through which outseepage takes place. Analysis of the effects of
size and lateral and vertical distribution of aquifers within the
groundwater system on the outseepage from lakes shows that the position
of the center point of the aquifer relative to the littoral zone on the
side of the lake nearest the downgradient side of the groundwater system
is a critical factor. If the center point is downslope from this part of
the littoral zone, the local flow system boundary tends to be weak or
outseepage occurs. If the center point is upslope from this littoral
zone, the stagnation zone tends to be stronger (to have a higher head in
relation to lake level), and outseepage is unlikely to occur.

The classic work of Tóth in 1963 on 2D, steady state, isotropic, basinal, flow modelling is revisited with a stagnation point and critical streamline analysis. It is found that narrow channels of groundwater flow may exist which have previously been undiscovered. Although these channels do not change the overall concept of dividing basinal flow into regional, intermediate and local flow zones, they do show that small portions of recharge areas in regional zones connect with predominantly intermediate discharge zones and also intermediate recharges connect with predominantly local discharge zones. Depending on basin depth and surface potential parameters, the size and capacity of these channels is determined by the existence of paired stagnation points relative to the basin vertical centreline and the degree of asymmetry of stream functions. These channels are likely to occur in other basinal models and will affect the assessment of discharge water temperature, age and chemical composition.

Natural systems are driven by dynamic forcings that change in time as
well as space, behavior that is inherited by the system flow field and
results in time-varying age distributions (ADs). This work presents a
review of the mathematical tools and solution approaches used to model
ADs in dynamic time-varying flow systems. A simple conceptual, numerical
model is then used to explore the role of flow dynamics in ADs for
topography-driven flow systems. This model is an analog for regional
groundwater systems and hyporheic zones. This model demonstrates that
relatively small fluctuations in the forcing, even though importantly
affecting the flow in the system, can have minimal effects in ADs.
However, as the intensity of fluctuation increases, still within the
bounds observed in natural systems, ADs in shallow parts of the system
become highly sensitive to dynamic flow conditions, leading to
considerable changes in the moments and modality of the distributions
with time. In particular, transient flow can lead to emergence of new
modes in the AD, which would not be present under steady flow
conditions. The discrepancy observed between ADs under steady and
transient flow conditions is explained by enhancement of mixing due to
temporal variations in the flow field. ADs in deeper parts of the system
are characterized by multimodality and tend to be more stable over time
even for large forcing fluctuations.

Topographic influences on groundwater flow processes that contribute to
baseflow and mountain block recharge (MBR) are conceptually investigated
using three-dimensional numerical models of saturated groundwater flow.
Model domains for conceptual and real topographies are developed as
"mountain groundwatershed units" (MGUs) to represent regional-scale
watershed systems. Results indicate regularity in groundwater flow
patterns that reflect consistency of prominent topographic features,
providing a basis for conceptualizing three-dimensional groundwater
flow. Baseflow is generated mainly from recharge within the watershed
area. MBR is produced primarily from recharge that is focused across
triangular facets near the mountain front (˜73%-97% of total MBR),
with additional contributions originating within the watershed (up to
˜27% of MBR). MBR contributions originating from recharge near the
highest-elevation watershed boundaries are minimal but are greater for
topography with less stream incision. With orographic influences, more
MBR originates within the watershed. MBR rates are relatively consistent
between models because of similarities in mountain front topography,
while baseflow is variable. Gains and losses to systems via
cross-watershed groundwater flux, generated because of topographic
differences between adjacent watersheds, cause baseflow to vary by up to
˜10% but do not significantly influence MBR. In data-sparse
regions such as mountains, a basic numerical modeling approach, using
the MGU concept with topography data and mapped watershed boundaries,
can be used to develop site-specific conceptual models to constrain
water budgets, to delineate recharge areas, and to guide further
investigation and data collection.

It is critical that stakeholders are aware of the lag time necessary for conservation practices to demonstrate a positive impact on surface water quality. For solutes like nitrate that are transported primarily by the groundwater pathway, the lag time is a function of the groundwater travel time distribution (TTD). We used three models of varying levels of complexity to estimate the steady-state TTD of a shallow, unconfined aquifer in a small Iowa watershed: (a) analytic model, (b) GIS approach, and (c) MODFLOW model. The analytic model was the least input-intensive, whereas the GIS and MODFLOW approach required detailed data for model development. The resulting TTDs displayed an exponential distribution with good agreement among all the three methods (mean travel times ranging from 16.2 years in the analytic model, 19.6 years in GIS model and 20.5 years in MODFLOW model). The greater deviation in the analytic model was attributed to the difficulty in estimation of a representative saturated thickness in an unconfined aquifer. The correspondence between the spatial travel time distributions generated by GIS and MODFLOW was a function of the landscape position, with greater correspondence in uplands compared to floodplains. In the floodplains the land surface slope is a poor approximation of the water table gradient that is captured by the MODFLOW model but not the GIS that uses the land surface as a surrogate for the water table. Study results indicate that except for cases where there are marked differences between water table surface and land surface, simpler approaches (analytic and GIS) can be used to estimate TTDs required for the design and optimal placement of conservation practices and communicating lag times issues to the public. Published by Elsevier B.V.

In this chapter, we try to mathematically describe how groundwater ages obtained by various methods-as described in the previous three chapters-can be different from or similar to the real ages of each groundwater particle we sample in groundwater dating researches. Groundwater age dating by various tracers gives us an average value for a given sample. This value is certainly very instructive and useful, but gives no information at all on the actual age distribution and its possible complex features, which remain unknown. Using the mean ages to evaluate aquifer characteristics such as recharge rates and flow velocities should therefore be made very carefully, and in principle only for relatively simple hydrogeological configurations for which standard age distributions can be enforced. New mathematical approaches are introduced in this chapter to model age and residence time distributions in samples comprising billions of water molecules originating from various groundwatersheds.

The age of groundwater, the time since the water recharged the subsurface, is a fundamental characteristic of groundwater that impacts diverse geologic processes and practical applications. The distribution of groundwater age depends on many factors including permeability, recharge rate, aquifer geometry, and topography. Seminal work simulated topography-driven regional groundwater flow with various topographies, localized high-permeability zones, and more recently with permeability decreasing with depth, but the role of layered aquifer systems which are common in both consolidated and unconsolidated sediments has not been systematically explored. Here we show that high age zones with predictable locations occur in layered geologic systems across a wide range of hydraulic gradients, basin geometries, and permeabilities. Numerical simulations of a generic three-layer aquifer system indicate that high age zones consistently form in the low-permeability layer near the middle of the basin. The zones of older groundwater result from low groundwater velocities in the low-permeability layer and the rejuvenation of the groundwater through mixing of different flow paths near discharge zones. The high age zones are not hydraulic stagnation points but are associated with areas of low velocity. Formation and location of zones of high groundwater ages in low-permeability units are important as these units are targeted for radioactive waste disposal and shale gas extraction. High age zones are also likely to affect geologic processes that depend on groundwater or solute fluxes and may serve as archives of past hydrological or climatological conditions.

[1] We know little regarding how geomorphological features along the surface-groundwater interface collectively affect water quality and quantity. Simulations of surface water-groundwater exchange at increasing scales across bed forms, bars and bends, and basins show that groundwater has a power-law transit time distribution through all these features, providing a purely mechanistic foundation and explanation for temporal fractal stream chemistry. Power-law residence time distributions are almost always attributed to spatial variability in subsurface transport properties- something we show is not necessary. Since the different geomorphological features considered here are typical of most landscapes, fractal stream chemistry may be universal and is a natural consequence of water exchange across multifaceted interfaces.

Several researchers have observed seasonal reversals in the direction of
groundwater flow around lakes. If these reversals are prolonged and are
accompanied by the formation of a stagnation point, they may have a
significant effect on a lake's water and nutrient budgets. The formation
of a stagnation point at a flow-through lake (i.e., a lake that receives
groundwater through part of the lake basin and recharges the groundwater
system over the rest of the lake basin) is accomplished by the formation
of a groundwater mound on the downgradient side of the lake. In this
paper the seasonal formation of a stagnation point at Snake Lake,
Wisconsin, is investigated with the aid of two-dimensional transient
computer models applied in cross section and areally. The analysis
demonstrates the potential for the seasonal formation of a stagnation
point at a flow-through lake and provides some insight into the
transient development of the stagnation point.

Details of steady-state flow in regional groundwater basins can be investigated using digital computer solutions of appropriately designed mathematical models. The factors that must be considered are: (1) ratio of depth to lateral extent of the basin; (2) Watertable configuration; and (3) stratigraphy and resulting subsurface variations in permeability. The results of this study provide a theoretical basis for the following properties of regional flow systems: (1) groundwater discharge will tend to be concentrated in major valleys; (2) recharge areas are invariably larger than discharge areas; (3) in hummocky terrain, numerous sub-basins are superposed on the regional system; (4) buried aquifers tend to concentrate flow toward the principal discharge area, have a limiting effect on sub-basins, and need not outcrop to produce artesian flow conditions; (5), stratigraphic discontinuities can lead to distributions of recharge and discharge areas that are difficult to anticipate and that are largely independent of the water-table configuration. (Key words: Groundwater; computers, digital; drainage basin characteristics)

The relative cumulative frequency distribution of residence times F(T) is calculated for an entire groundwatershed under steady-state conditions and assuming Dupuit-Forchheimer flow. It appears that F(T) is always the same: F(T) = 1 -exp(−TT), provided that the aquifer recharge rate and T are constant over the groundwatershed. T is the weighted mean residence time for the groundwatershed and is defined at T = nHN, where n is the aquifer porosity, H is the saturated aquifer thickness, and N the areal recharge rate owing to precipitation. In such an idealized groundwatershed the function F(T) appears independent of the groundwatershed size, shape, and nature of the stream network. It is also independent of regional variations in the hydraulic conductivity, provided the aquifer is locally homogeneous. Under unconfined flow conditions, where H varies, the relative frequency distribution of the residence time does depend on all of these parameters, but may be approximated by F(T), as demonstrated for the case of a one-dimensional groundwatershed. The frequency distribution of the residence times, dFdT, is the response curve for an instantaneous unit pulse of a conservative tracer, applied over the entire groundwatershed. The findings are of significance for studying the effects of non-point source pollution on the scale of one or more watersheds.

Among the numerous processes that will cause anomalous temperature distributions in geologic basins is the spatial redistribution of heat by moving ground water. This problem is examined by solving the energy equation for the simultaneous transport of water by hydraulic gradients and heat by forced convection. The factors that affect the temperature distribution in a given basin include the intrinsic properties of the medium and contained fluid-namely, the thermal diffusivity of the solid-fluid complex and the hydraulic conductivity, the water-table configuration, and the ratio of basin depth to basin length. The severity of an anomalous geothermal gradient or temperature measurement depends primarily on the relative magnitude of the ratio of hydraulic conductivity to thermal diffusivity, and on the geometry of the flow field. A dimensionless group may be formulated from these parameters, and provides a relative measure of the simultaneous transport of heat by the bulk motion of the fluid to that by pure conduction. Solutions to the equation itself indicate that convective heat losses in ground-water recharge areas are balanced by convective heat gains in discharge areas. The geothermal gradient accordingly increases with increasing depth in recharge areas, decreases with increasing depth in discharge areas, and is a manifestation of pure conduction at the hinge line separating areas of recharge and discharge.

Because groundwater flow is the dominant mechanism for transporting chemical mass in sedimentary basins, knowledge of the hydrodynamics and geochemistry of flow and transport is a fundamental prerequisite to understanding geologic processes. One goal of this article, therefore, is to review the basic theory that bears on modeling coupled fluid, heat, and mass transport in sedimentary basins. Another goal is to survey specific examples of the geologic role of continental-scale groundwater flow. -from Author

1] Groundwater and surface water are interconnected. Tóth's analysis of topography-driven groundwater flow, presumably exiting in lakes or streams, is one of the first illustrations of this connection. Recently, fractal behavior in time-series observations of stream chemistry, implying a power-law residence time distribution (PLRTD) has been attributed to heterogeneity in subsurface flow paths and mass exchange processes. We show through numerical simulations that topography-driven groundwater flow, i.e., Tóth flow, and transport under homogeneous aquifer conditions results in PLRTDs and may therefore contribute to fractal behavior in surface water chemistry. For the first time, PLRTDs are explained with a purely physical basis. Heterogeneity, accounted for by a large dispersivity value, makes the PLRTD more pronounced and persistent. Late-time arrival of solutes from surround-ing watersheds results in multi-modality in the RTD, but these late peaks also follow a PLRTD after arrival. Citation: Cardenas, M. B. (2007), Potential contribution of topography-driven regional groundwater flow to fractal stream chemistry: Residence time distribution analysis of Tóth flow, Geophys. Res. Lett., 34, L05403, doi:10.1029/2006GL029126.

1] Surface-subsurface flow interactions are critical to a wide range of geochemical and ecological processes and to the fate of contaminants in freshwater environments. Fractal scaling relationships have been found in distributions of both land surface topography and solute efflux from watersheds, but the linkage between those observations has not been realized. We show that the fractal nature of the land surface in fluvial and glacial systems produces fractal distributions of recharge, discharge, and associated subsurface flow patterns. Interfacial flux tends to be dominated by small-scale features while the flux through deeper subsurface flow paths tends to be controlled by larger-scale features. This scaling behavior holds at all scales, from small fluvial bedforms (tens of centimeters) to the continental landscape (hundreds of kilometers). The fractal nature of surface-subsurface water fluxes yields a single scale-independent distribution of subsurface water residence times for both near-surface fluvial systems and deeper hydrogeological flows. Citation: Wörman, A., A. I. Packman, L. Marklund, J. W. Harvey, and S. H. Stone (2007), Fractal topography and subsurface water flows from fluvial bedforms to the continental shield, Geophys. Res. Lett., 34, L07402, doi:10.1029/2007GL029426.

1] It has been long known that land surface topography governs both groundwater flow patterns at the regional-to-continental scale and on smaller scales such as in the hyporheic zone of streams. Here we show that the surface topography can be separated in a Fourier-series spectrum that provides an exact solution of the underlying three-dimensional groundwater flows. The new spectral solution offers a practical tool for fast calculation of subsurface flows in different hydrological applications and provides a theoretical platform for advancing conceptual understanding of the effect of landscape topography on subsurface flows. We also show how the spectrum of surface topography influences the residence time distribution for subsurface flows. The study indicates that the subsurface head variation decays exponentially with depth faster than it would with equivalent two-dimensional features, resulting in a shallower flow interaction. Citation: Wörman, A., A. I. Packman, L. Marklund, J. W. Harvey, and S. H. Stone (2006), Exact three-dimensional spectral solution to surface-groundwater interactions with arbitrary surface topography, Geophys. Res. Lett., 33, L07402, doi:10.1029/2006GL025747.

Hydrologic landscapes are multiples or variations of fundamental hydrologic landscape units. A fundamental hydrologic landscape unit is defined on the basis of land-surface form, geology, and climate. The basic land-surface form of a fundamental hydrologic landscape unit is an upland separated from a lowland by an intervening steeper slope. Fundamental hydrologic landscape units have a complete hydrologic system consisting of surface runoff, ground-water flow, and interaction with atmospheric water. By describing actual landscapes in terms of land-surface slope, hydraulic properties of soils and geologic framework, and the difference between precipitation and evapotranspiration, the hydrologic system of actual landscapes can be conceptualized in a uniform way. This conceptual framework can then be the foundation for design of studies and data networks, syntheses of information on local to national scales, and comparison of process research across small study units in a variety of settings. The Crow Wing River watershed in central Minnesota is used as an example of evaluating stream discharge in the context of hydrologic landscapes. Lake-research watersheds in Wisconsin, Minnesota, North Dakota, and Nebraska are used as an example of using the hydrologic-land-scapes concept to evaluate the effect of ground water on the degree of mineralization and major-ion chemistry of lakes that lie within ground-water flow systems.

Groundwater is a valuable resource in the semiarid Ordos Plateau region where abundant mineral resources, such as coal, natural
gas, and halite, are present. With resources development, groundwater demand will increase dramatically. The origin identification
and recharge estimates of groundwater are significant components of sustainable groundwater development in the Ordos Plateau.
Groundwater and precipitation samples were taken and the isotopic compositions δ2H, δ18O, and chloride were analyzed to identify groundwater origins and to estimate recharge rates. The δ2H and δ18O of the groundwater show that the groundwater recharge is of meteoric origin. The chloride mass balance (CMB) method was
used to quantify recharge rates of groundwater in the Ordos Plateau, which varies from 2.93 to 22.11% of the effective annual
rainfall. Recharge rates estimated by CMB were compared with values obtained from other methods and were found to be in good
agreement. This study can be used to develop effective programs for groundwater management and development.
KeywordsGroundwater origin-Recharge estimate-Ordos Plateau

Spectral analysis enhances the ability to analyze groundwater flow at a steady state by separating the top boundary condition into its periodic forms. Specifically, spectral analysis enables comparisons of the impact of individual spatial scales on the total flow field. New exact spectral solutions are presented for analyzing 3D groundwater flow with an arbitrarily shaped top boundary. These solutions account for depth-decaying, anisotropic and layered permeability while utilizing groundwater flux or the phreatic surface as a top boundary condition. Under certain conditions, groundwater flow is controlled by topography. In areas where the groundwater flow is controlled by the topography, the unknown water table is often approximated by the topography. This approximation induces a systematic error. Here, the optimal resolution of digital elevation models (DEMs) is assessed for use as a top boundary in groundwater flow models. According to the analysis, the water-table undulation is smoother than the topography; therefore, there is an upper limit to the resolution of DEMs that should be used to represent the groundwater surface. The ability to represent DEMs of various spectral solutions was compared and the results indicate that the fit is strongly dependent on the number of harmonics in the spectral solution.

Isotopic and major-ion analyses of 130 fresh and brackish groundwater samples reveal a strikingly consistent pattern of variation over 28,000 km2 of the western Canada sedimentary basin. Hydrodynamic interpretations based on drill-stem tests and piezometric data reveal a pattern of broad, regional flow from south to north. However, there is some evidence to suggest that patterns of groundwater flow have been influenced in the past by Wisconsin glaciation. All the permeable units appear to be recharged by meteoric water in the south where they outcrop or come close to the surface. Samples of groundwater collected down dip in each of six major sandstone units are progressively enriched in D, 18O, Na+ and Cl−. For example, the deepest waters of the artesian Milk River aquifer are enriched by up to 70‰ and 15‰ with respect to the δD and δ18O of the modern recharge waters. The pattern of chemical evolution is strongly related to the hydraulic characteristics of individual units. The isotopic composition is determined by the extent to which hydraulic conductivity has facilitated meteoric water flushing of connate water. Thus, more permeable units and permeable zones within a unit tend to be isotopically lighter because of a more complete and more rapid invasion of meteoric water. Interestingly, the largest conductivity values are found in some of the deepest units (1500 m). Consequently, water in these deeper units have δD- and δ18O-values which approach that of the recharge. The major-ion chemistry is controlled both by this process and a complex set of rock-water interactions. In addition to providing information about the chemical evolution of groundwater, this study can begin to quantify the complex pattern of flushing in a large sedimentary basin.

The relationship between groundwater recharge and discharge is one of the most important aspects in the protection of ecologically valuable areas. Knowledge of groundwater systems is therefore a pre-requisite for up-to-date integrated land and water management. A methodology is presented for assessing the relative importance of different recharge–discharge systems, with respect to ecological status or development, including mapping of regional groundwater systems, and recharge and discharge areas. This methodology is applied to a land-use planning project in the Grote-Nete basin, Belgium. Discharge regions are delineated on the basis of their spatial discharge contiguity, position in the landscape and alkalinity of the plants habitat. The simulated discharge areas are verified by field mapping of phreatophytic vegetation. Particle tracking is used to delineate the recharge area associated with each discharge area, and to characterize each recharge–discharge groundwater system. Three groundwater flow and two vegetation parameters are used in a cluster analysis to obtain four different clusters of groundwater discharge systems. It is shown that the discharge clusters are significantly different in discharge intensity and alkalinity. The effects on the groundwater system due to anthropogenic impacts on the land-use are studied by simulation of the present, pre-development, and future situation. The results indicate the sensitivity and impact of the changes on the recharge and discharge areas, and groundwater discharge fluxes. The impact of the changes for the different areas for both the pre-development and the future situation appears to differ from large decrease to large increase in total groundwater discharge. Of additional ecological importance is the fact that some areas show an opposite behaviour regarding the changes in groundwater discharge area and fluxes. The delicate shifts in the groundwater systems, which cause the changes in the recharge and discharge, clearly show the need for hydrological modelling. The synergy of hydrological modelling and vegetation mapping proves advantageous and reveals some of the ecological differences in the catchment.

Until recent years knowledge of chemical processing was descriptive and qualitative.
In 1810 modern chemical theory was born and process description became quantitative.
Then about 1900 the quantitative engineering approach was developed, first for physical changes, called the Unit Operations, and somewhat later for chemical operations. This we call the American approach.
In 1957 European chemical engineers brought together the design of chemical and their related physical operations under the name of Chemical Reaction Engineering, or CRE. This approach and name received practically universal acceptance.
Today the methods of CRE are widely used in the processing of biochemical and all sorts of other systems,
This talk wanders through this development.

Various subsurface flow systems exhibit a combination of small-scale to large-scale anisotropy in hydraulic conductivity (K). The large-scale anisotropy results from systematic trends (e.g., exponential decrease or increase) of K with depth. We present a general two-dimensional solution for calculation of topography-driven groundwater flow considering both small- and large-scale anisotropy in K. This solution can be applied to diverse systems with arbitrary head distribution and geometry of the water table boundary, such as basin or hyporheic flow. In a special case, this solution reduces to the well-known Tóth model of uniform isotropic basin. We introduce an integral measure of flushing intensity that quantifies flushing at different depths. Using this solution, we simulate heads and streamlines and provide analyses of flow structure in the flow domain, relevant to basin analyses or hyporheic flow. It is shown that interactions between small-scale anisotropy and large-scale anisotropy strongly control the flow structure. In the classic Tóth flow model, the flushing intensity curves exhibit quasi-exponential decrease with depth. The new measure is capable of capturing subtle changes in the flow structure. Our study shows that both small- and large-scale anisotropy characteristics have substantial effects that need to be integrated into analysis of topography-driven flow.

Groundwater flow is temporally variable and uncertain, due to climatologically or anthropogenically induced variation in boundary conditions that result in changes in the drainage network, and uncertainties in hydraulic model parameters used in the quantification of groundwater flow. The quantification and mapping of the variation and uncertainty in groundwater flow is especially essential in relatively flat areas where flow direction is sensitive to decimetre-scale head variations. In these areas, the variability and uncertainty of groundwater flow directions may therefore have important implications for the uncertainties in the spatial configuration of groundwater flow systems. In this study we aim to quantify and map the sensitivity of shallow groundwater flow systems to uncertainties in aquifer anisotropy and drainage resistance, and variations in drainage level and groundwater recharge for a sandy unconfined aquifer in the Salland region, the Netherlands. For this purpose, the most probable configuration of current groundwater flow systems was mapped using particle tracking and Monte Carlo analysis. Sensitivity was represented by the membership of each model cell to the defined groundwater flow systems given the uncertainties and variations in the hydraulic parameters and boundary conditions. In addition, the current configuration of groundwater flow systems was compared to the historical situation without artificial drainage. The average groundwater flow system size was found to be in the order of a few square kilometres, with a relatively stable configuration. In contrast to the intrinsic and temporally invariant hydraulic parameters, which were shown to have a minor influence on the spatial configuration of groundwater flow systems, natural variation in recharge and variations in drainage level management exert a large influence.

Groundwater Investigation in the Ordos Basin

- G C Hou

Hou, G.C. et al., 2008. Groundwater Investigation in the Ordos Basin [in Chinese].