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• Stream-function-based (SFB) method is developed for 2D particle tracking along exact streamlines. • The branch cut effect of multivariable stream function around wells is avoided. • Unlike existing methods, the SFB method does not lead to accumulative errors in the particle position. Particle tracking is an essential process in analyzing groundwater flow and solute transport in aquifers. A drawback of existing particle tracking methods, which are based on approximate estimations of the velocity in a time step, is the accumulative errors of numerous time steps would lead to deviation of particles away from the exact streamlines, especially when pumping and injecting wells exist. In this study, to improve the accuracy of particle tracking for the two-dimensional (2D) steady-state flow around wells, we propose a stream-function-based (SFB) particle tracking method in which a particle is traced along the exact streamline with a given value of the stream function, and the branch cut effect caused by the multivalued stream function around a well is eliminated. Three synthetic cases are used to demonstrate the advantages of the SFB method over the existing Pollock method and the fourth-order Runge-Kutta method. In the cases of a single pumping well and an injecting-pumping well pair, the Pollock and Runge-Kutta methods yield pathways that may be far away from the exact streamline, but the SFB method performs much better. In the case with a pumping well and two injecting wells, the SFB method successfully delineated a narrow capture zone of the pumping well, which requires a high accuracy particle tracking process. Moreover, the accuracy of particle positions obtained by the SFB method is insensitive to the step-travel distance. The study would be useful for accurate investigation of flow fields in aquifers disturbed by wells. [ABSTRACT FROM AUTHOR]

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

Hierarchically nested groundwater flow systems have been widely investigated by numerical modeling and laboratory experiments but seldom recognized from in situ observations and testing. Groundwater age and geochemical profiles were obtained by the authors using a packer system along two wellbores drilled in the Ordos Plateau, China. Groundwater age profiles were constructed from 3H, 85Kr, 14C, and 81Kr data, with the apparent age generally increasing with depth, while exhibiting several inflection points. These inflection points were compared with geochemical profiles and numerical modeling results to delineate groundwater flow systems. Inflection points with significant increases in the gradients of age and Cl− concentration versus depth may indicate interfaces among flow systems. A concurrent decrease‐increase turning of groundwater age and Cl− concentration is influenced by a stagnation point. The groundwater age profiles are quite different from previous studies, indicating that the method can greatly reduce the uncertainty in model construction. Plain Language Summary: The provision of renewable groundwater, a crucial source of drinking water worldwide, relies on a circulation path from recharge to discharge zones with a subsurface flow in reservoirs (aquifers). Basin‐scale groundwater circulation is speculated to form hierarchically nested flow systems with differing capabilities for renewal. However, flow systems are invisible and difficult to detect through in situ observations on groundwater. In this study, nested groundwater flow systems were identified from groundwater age and geochemical profiles along wellbores. Inflection points on these profiles provide significant insights into the interfaces and stagnation points among nested groundwater flow systems. Uncertainties could be brought by the aquifer heterogeneity in the hydraulic conductivity and localized soluble salts. This adopted method is expected to be improved by incorporating geophysical survey and high‐resolution geochemical analyses to eliminate uncertainties in model construction. Key Points: Groundwater age and geochemical profiles were obtained to investigate groundwater flow systemsInflection points on profiles are used to infer interfaces or stagnation points among different groundwater flow systemsGroundwater flow models constrained by inflection points greatly reduce the uncertainty of flow system characterization [ABSTRACT FROM AUTHOR]

The Badain Jaran Desert (BJD) in China is a desert with impressive sand dunes and a groundwater situation that has attracted numerous researchers. This paper gives an overview of the mysteries of groundwater in the BJD that are exhibited as five key problems identified in previous studies. These problems relate to the origin of the groundwater, the hydrological connection between the BJD and the Heihe River Basin (HRB), the infiltration recharge, the lake-groundwater interactions, and the features of stable isotope analyses. The existing controversial analyses and hypotheses have caused debate and have hindered effective water resources management in the region. In recent years, these problems have been partly addressed by additional surveys. It has been revealed that the Quaternary sandy sediments and Neogene-Cretaceous sandstones form a thick aquifer system in the BJD. Groundwater flow at the regional scale is dominated by a significant difference in water levels between the surrounding mountains and lowlands at the western and northern edges. Discharge of groundwater from the BJD to the downstream HRB occurs according to the regional flow. Seasonal fluctuations of the water level in lakes are less than 0.5 m due to the quasi-steady groundwater discharge. The magnitude of infiltration recharge is still highly uncertain because significant limitations existed in previous studies. The evaporation effect may be the key to interpreting the anomalous negative deuterium-excess in the BJD groundwater. Further investigations are expected to reveal the hydrogeological conditions in more detail. [ABSTRACT FROM AUTHOR]

• Croplands greatly altered the annual E and Q , while have little effect on annual C. • Croplands increased the evapotranspiration sensitivity to E p but decreased to P. • Croplands significantly increased the runoff sensitivity to climate change. Croplands can significantly influence the hydrologic response of catchments to climate change in a region but such influence has not been well investigated and quantified. In this study, we firstly use the conceptual hydrological model to investigate the annual water balance for croplands-altered catchments, and the "natural" state without croplands of the catchment can be traced back by setting a zero area of croplands in the calibrated model. The model results are then applied to a hydrologic sensitivity framework with the Budyko-type relationship between hydrologic ratios (i.e. evapotranspiration ratio and water storage change ratio) and the aridity index (E p / P) to yield the hydrologic sensitivity coefficients for the croplands-altered and "natural" catchments. The method is applied to investigate three catchments that are rarely affected by inter-basin groundwater flow in Illinois. The results show that croplands significantly increase the actual evapotranspiration (E) and decrease the runoff (Q), while changes in water storage (C) are rarely affected by croplands at the annual time scale. The actual evapotranspiration at the annual timescale is much more sensitive to potential evapotranspiration when the croplands exist. Croplands in Illinois significantly increase the sensitivity of streamflow on the climate change, to at least twice of the sensitivity in the "natural" state. The effectiveness of inter-annual hydrologic sensitivity framework is also demonstrated by hydrological model. This study provides a new simple insight to quantify the inter-annual stability with varying climate and land use at the catchment scale. [ABSTRACT FROM AUTHOR]

Abstract: A new solution of transient confined–unconfined flow driven by a pumping well is developed and compared to previous approximate solutions of Moench and Prickett [Moench AF, Prickett TA. Radial flow in an infinite aquifer undergoing conversion from artesian to water table conditions. Water Resour Res 1972;8:494–9] and Hu and Chen [Hu L, Chen C. Analytical methods for transient flow to a well in a confined–unconfined aquifer. Ground Water 2008;46(4):642–6]. The problem is rewritten in dimensionless form with the Boltzmann transform. The nonlinear equation for flow in the unconfined zone is solved with the Runge–Kutta method. Position of the conversion interface is determined with an iteration scheme. This study shows that the confined–unconfined flow depends on three dimensionless parameters that represent the confined–unconfined storativity ratio (a D ), the ratio of the initial hydraulic head over the aquifer thickness (f i ), and the dimensionless pumping rate (q D ). The rate of expansion of the unconfined zone increases with q D , but decreases with a D and f i . Differences between the two previous approximate solutions and the new solution of this study are observable in the estimated position of the conversion interface and the drawdown–time curves. The new solution can be applied to estimate the time for confined–unconfined conversion to occur (critical conversion time), and the time when the pumping well becomes dry (critical drying time). The critical conversion time is found to be very sensitive to the initial hydraulic head. The critical drying time is often much larger than the critical conversion time and may never be observed during a finite pumping period. [Copyright &y& Elsevier]

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. [ABSTRACT FROM AUTHOR]

• Sustainable groundwater development is achievable in Beijing plain. • Substituting groundwater abstraction with transferred surface water has stopped depletion. • Managed aquifer recharge is very effective for sustaining groundwater abstraction. • Climate variation has larger impact on groundwater resources than the anticipated future climate change. To cope with the groundwater depletion problem and achieve sustainable groundwater development, groundwater conservation measures and managed aquifer recharge (MAR) have been implemented worldwide. However, knowledge gaps exit how does the aquifer system respond to these interventions differently and if these interventions are adequate to lead to long-term sustainable groundwater development under future climate change. In Beijing Plain, two measures have been implemented: reduction of groundwater abstraction by substituting groundwater abstraction with transferred surface water and implementation of managed aquifer recharge (MAR) in two major rivers. This study aims to assess how do the shallow and deep aquifers respond to these measures and if these measures can lead to long-term sustainable groundwater development in Beijing Plain under future climate change. A 3-D transient groundwater flow model was calibrated and used to simulate groundwater level and budget changes from 2021 to 2050. The monthly groundwater recharge was estimated using the projected monthly precipitation from three downscaled regional climate models under two scenarios (RCP4.5 and RCP8.5). The results show that declines in groundwater head and storage can be reversed with the combined two measures, thereby contributing to achieve sustainable groundwater development. The reduction of abstractions is a deciding measure to reverse the trend of groundwater depletion, especially in the deep confined aquifers, while large scale MAR schemes can restore the cones of depressions in shallow aquifers and maintain the groundwater abstraction. Climate variation has large impacts on groundwater resources, especially, consecutive dry years can cause rapid groundwater storage depletion. The projected monthly precipitation from 2021 to 2050 is not significantly different from the past. Therefore, the projected future precipitation has minor impacts on groundwater resources in the next 30 years. The findings from the study will support the Beijing municipality to maintain the tight control on groundwater abstraction and to implement large-scale MAR schemes in two rivers. This successful example will encourage managers of other heavily exploited aquifers to take similar measures to achieve sustainable groundwater development. [ABSTRACT FROM AUTHOR]

• We summarize field observations of 14C age showing obvious GW aging in two basins. • Pumping causes not only rejuvenation, but also aging of GW in layered basins. • Although GW rejuvenation is larger in area, aging is greater in magnitude. • We identify two new mechanisms of pumping-induced GW aging in layered basins. • Topography-driven flow is the main cause of GW aging in the discharge area. As an indicator of the renewability of a groundwater basin, the spatial distribution of groundwater age has attracted intensive research. As reported in the literature, 3H measurements in 74 US aquifers showed pumping-induced groundwater rejuvenation, whereas 14C ages in two heavily developed aquifers in France and China indicated pumping-induced groundwater aging. Unfortunately, the mechanisms leading to the seemingly opposite behavior of pumping-induced aging and rejuvenation remain unclear. In this study, we conducted numerical simulations of groundwater age in layered aquifer-aquitard systems under different pumping scenarios and aquitard permeability to show that pumping-induced groundwater rejuvenation and aging always occur simultaneously. Groundwater rejuvenation widely occurs throughout the basin wherever the well is located, whereas groundwater aging mainly occurs to the downgradient parts of the basin. Although groundwater rejuvenation is larger in area, groundwater aging is greater in magnitude, and the magnitude of aging increases with pumping intensity and duration. Moreover, when pumping occurs in the discharge area, aging could occur in almost the entire aquifer to the downgradient of the pumping well, and the magnitude of aging is larger. The large area and large magnitude of aging in the discharge area is a direct result of upward leakage of old groundwater from underlying aquitards/aquifers, which is controlled by the topography-driven groundwater flow. By demonstrating the importance of topography-driven groundwater flow and underlying formations in groundwater age redistribution, this study has implications for determining the bottom of a groundwater flow and solute transport model and interpretation of various tracers. [ABSTRACT FROM AUTHOR]

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

• Field data show the control of soil texture on freezing-induced water table recession. • Ku below the frozen zone is the limiting factor of freezing-induced water flow. • We obtain extinction depths of freezing-induced GW migration for different soils. • The extinction depths of freezing-induced and evaporation-induced GW migration. Although water table recessions associated with seasonal freezing have been widely reported, the conditions that groundwater could respond to seasonal freezing are poorly known. Based on 30 records of winter-time water table recessions reported in the literature, we find the mean water table recession increases from sand to loam to silt to clay. To obtain a quantitative understanding of the conditions of freezing-induced groundwater migration and the role of soil texture, we construct a one-dimensional SHAW model with a dynamic water table that could respond to winter-time atmospheric conditions. By simulating freezing-induced groundwater migration under a series of pre-freezing water table depths, soil textures and freezing indices, we find the extinction depth of freezing-induced groundwater migration, i.e., the limit water table depth beyond which there is negligible freezing-induced groundwater flow, increases from coarse to fine soils and increases with freezing index. Moreover, we find there is a good linear relationship between the distance from the freezing front to the water table corresponding to the extinction depth of freezing-induced groundwater migration and the distance from the land surface to the water table corresponding to the extinction depth of evaporation-induced groundwater migration for different soils. To demonstrate the importance of defining extinction depth, we also show the overestimation of freezing-induced water gain in the frozen zone by the widely used fixed water table condition when the water table depth is shallower than the extinction depth. This study has implications for future hydrologic and engineering studies in critical zones with a cold climate. [ABSTRACT FROM AUTHOR]

As an indispensable component of groundwater circulation, groundwater evapotranspiration rate ( ET G ) estimation using water table fluctuations is a hot research topic in the past decades. However, most existing methods for estimating ET G using either diurnal or seasonal water table fluctuations are based on the assumptions that groundwater recharge equals 0 in the whole period and ET G equals 0 in a specific duration of time. The aim of the current study is to develop a method to estimate ET G when both assumptions do not apply. In the discharge area of a semi-arid catchment in the Ordos Plateau, NW China, it is found out that the water table fluctuations are influenced greatly by recharge, ET G and the vertical inflow rate ( q in ) in the seasonal scale but are controlled by atmospheric pressure instead of evapotranspiration in the diurnal scale, which implies that the existing methods are not applicable. Therefore, we propose a method to estimate ET G and q in using the seasonal water table fluctuations based on the assumptions that q in is stable throughout the year and ET G has a linear relationship to the reference evapotranspiration ( ET 0 ). It is found out that q in is around 1.12 mm/d, and the ratio of ET G to ET 0 is around 0.4. ET G in April through July with the highest ET 0 of the year is found to be around 3 mm/d, which is much larger than q in , thus leads to significant decline in water table. ET G in November with the lowest ET 0 of the unfrozen period is found to be 1.0 mm/d, which is slightly smaller than q in , thus results in a weak increase in water table. The vertical component of regional groundwater inflow is found to exceed precipitation recharge, indicating that regional groundwater inflow plays the major role on maintaining the shallow water table in the discharge area. Groundwater evapotranspiration is also found to exceed precipitation recharge in most time of the unfrozen period, indicating a specified-flux upper boundary with water loss in the discharge area of an arid catchment. The proposed method could be applied to similar study areas and is critical to understand the budget of groundwater. [ABSTRACT FROM AUTHOR]

Summary Previous studies on the characterization of hierarchically nested groundwater flow systems have mainly been based on the spatial distribution analyses of groundwater pathways. In this paper, by considering the discrete nature of the temporal behavior induced by different hierarchical flow systems, a new approach is proposed. The core of this approach is to use the critical residence times defined by the late-time peaks of residence time distributions (RTDs) to divide the groundwater flow field into local, intermediate and regional systems as described by Tóth (1963). We first introduce Tóthian basins of a 2D cross section and a 3D domain as synthetic test cases. The feasibility of the approach is demonstrated by comparing the partitioning results given by the dividing streamlines associated with internal stagnation points in the 2D Tóthian basin and by the hydraulic connections between recharge and discharge zones in the 3D Tóthian basin. Then, the Dosit River Watershed in Northwestern China is introduced as a field case study. Using the calibrated 3D groundwater flow model, one distinct late-time peak is identified from the RTD and indicates that the Dosit River Watershed can generally be regarded as a two-order nested flow structure with local and regional flow systems. This approach can be used to identify the volumes occupied by different orders of flow systems in 3D, and therefore opens up a new perspective in the study of the 3D nature of basin-scale groundwater flow. [ABSTRACT FROM AUTHOR]

• We separate the roles of upward discharge and aquitards in flowing artesian zone. • Basinal flow are coupled with well hydraulics to examine hydraulics of flowing wells. • A low K aquitard causes a large flowing artesian zone but low stable discharge rate. • Baseflow reduction is the main source of groundwater derived in flowing wells. Causes and water sources of flowing artesian wells attracted the interest of many hydrogeologists throughout history, however, a quantitative model that satisfactorily considers the roles of topography, groundwater recharge/discharge and aquitards on hydraulics of flowing wells is still lacking. In this study, a three-layer river-valley basin with a recharge boundary is used to obtain the basinal flow field, spatial distribution and transient discharge rates of flowing wells. Even if there is an aquitard separating the unconfined and the confined aquifers, groundwater discharge to the river still plays a critical role in occurrence of flowing wells. An aquitard with lower permeability would enlarge the zone with flowing wells, implying that flowing wells are more likely to occur in basins with continuous aquitards. By comparing flowpaths and inter-aquifer leakages before and after numerically installing a flowing well in a three-layer basin, we find decreased upward leakage in the discharge limb plays a much larger role than increased downward leakage in the recharge limb in the stable discharge rate of a flowing well. This recognition is different from previous studies where the stable discharge rate is supported only by downward leakage from the overlying aquifer. By considering well hydraulics in a basinal background flow field, this study improves understanding of the mechanisms of flowing artesian wells and the interaction of surface water and deep groundwater, indicating that flowing wells are valuable for sampling deep groundwater representative of deep and old groundwater in the discharge area of a basin. [ABSTRACT FROM AUTHOR]

The theory of regional groundwater flow is critical for explaining heat transport by moving groundwater in basins. Domenico and Palciauskas's () pioneering study on convective heat transport in a simple basin assumed that convection has a small influence on redistributing groundwater temperature. Moreover, there has been no research focused on the temperature distribution around stagnation zones among flow systems. In this paper, the temperature distribution in the simple basin is reexamined and that in a complex basin with nested flow systems is explored. In both basins, compared to the temperature distribution due to conduction, convection leads to a lower temperature in most parts of the basin except for a small part near the discharge area. There is a high-temperature anomaly around the basin-bottom stagnation point where two flow systems converge due to a low degree of convection and a long travel distance, but there is no anomaly around the basin-bottom stagnation point where two flow systems diverge. In the complex basin, there are also high-temperature anomalies around internal stagnation points. Temperature around internal stagnation points could be very high when they are close to the basin bottom, for example, due to the small permeability anisotropy ratio. The temperature distribution revealed in this study could be valuable when using heat as a tracer to identify the pattern of groundwater flow in large-scale basins. Domenico PA, Palciauskas VV (1973) Theoretical analysis of forced convective heat transfer in regional groundwater flow. Geological Society of America Bulletin 84:3803-3814 [ABSTRACT FROM AUTHOR]

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 2 n 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. [ABSTRACT FROM AUTHOR]

A new method based on a graphics processing unit ( GPU) library is proposed in the paper to parallelize MODFLOW. Two programs, GetAb_CG and CG_GPU, have been developed to reorganize the equations in MODFLOW and solve them with the GPU library. Experimental tests using the NVIDIA Tesla C1060 show that a 1.6- to 10.6-fold speedup can be achieved for models with more than 105 cells. The efficiency can be further improved by using up-to-date GPU devices. [ABSTRACT FROM AUTHOR]

Summary: Multi-scale heterogeneity of geological formations is a rule, which consists of random (local-scale) and systematic (large-scale) variability of hydraulic conductivity. The random variability and depth–decaying trend, a systematic variability, have different effects on subsurface flow, thus on groundwater discharge into tunnels. Little research has examined this problem in the past. Using Monte Carlo simulation and information of statistics of heterogeneity, we evaluate the most likely (ensemble average) discharge rate into a tunnel in geologic media with the multi-scale heterogeneity and uncertainty associated with this estimate. We find that the ensemble average discharge rate is larger than the discharge rate predicted by geometric mean of hydraulic conductivity, and smaller than the discharge rate predicted by arithmetic mean of hydraulic conductivity. Moreover, the ensemble average discharge rate decreases with the decay exponent of the depth–decaying trend, and increases with the standard deviation as well as the correlation scale of the stationary log-conductivity fields. We also find that the discharge rate of a tunnel is highly influenced by the hydraulic conductivity near the tunnel. Furthermore, deviation of the true discharge rate from the ensemble average can be large and increases with the decay exponent, standard deviation and correlation scale of log-conductivity fields. The largest uncertainty of discharge rate prediction in the shallow subsurface is controlled by the variability of conductivity fields and the uncertainty at the deep subsurface is by the depth–decaying trend of hydraulic conductivity. Therefore, accurate prediction of groundwater discharge into tunnels requires detailed characterization of multi-scale heterogeneity. [Copyright &y& Elsevier]

• Three alternative conceptual models were constructed. • Each model was calibrated automatically and evaluated statistically. • Hydrogeological interpretations are the basis for the conceptualisation. • Modelling objectives determine the complexity of the conceptual models. Three alternative groundwater flow models were evaluated for Beijing Plain, China. The first model (AM1) was constructed with the "thin layer approach" in which all 9 model layers, including five aquifers separated by four aquitards, are continuously present in the same model area. The second model (AM2) was constructed with the "quasi-3D approach" in which the hydrogeological formations were classified into five aquifer units consisting of mixed permeable and semi-permeable layers at different depth ranges. The third model (AM3) was constructed with the "true layer approach" in which aquifers and aquitards were defined according to hydrostratigraphic properties, and model layers are absent in the area where corresponding hydrogeological formations intersect bedrocks. All 3 models were calibrated with the parameter optimization method under the steady state flow condition with the same hydrological stresses and observation data. All three models fit to observations well with the similar calibration criteria values. Furthermore, AIC and BIC information criteria could not distinguish three alternative models. Only KIC could identify AM3 as the best model. Major differences of the three alternative models were identified from a hydrogeological perspective. The AM1 model depicted an illusion through contour maps that groundwater was present everywhere in the deep aquifers. The model computed larger vertical leakages because more abstraction rates were assigned improperly in deep aquifers. The AM2 model was able to compute regional groundwater balances and depicted spatial groundwater level variations. However, the AM2 model computed longer groundwater travel times around the wellfield and should not be used for the delineation of the well field protection zones and contaminant transport simulation. The AM3 model could not only compute the regional groundwater balances and describe spatial groundwater distribution in deep confined aquifers, but also delineate the capture zone of the wellfield. It can therefore be used for simulating contaminant transport. Furthermore, the AM3 model is suitable to construct a coupled regional and local flow model for simulating a managed aquifer recharge scheme. [ABSTRACT FROM AUTHOR]