Introduction

Research on groundwater/surface-water (GW–SW) interaction can provide valuable information on water supply, water quality and environmental health (Winter et al. 1998; Sophocleous 2002), which is critical for assessing water budget and contaminant fate and to quantify the interactions (Choi and Harvey 2000; Harvey et al. 2004; Rosenberry and LaBaugh 2008). Published studies on GW–SW interactions have mostly concentrated on the exchange between streams and “directly connected” aquifers composed of high-permeability sediments (Krause et al. 2007; Garrett et al. 2012; Guzman et al. 2016). Some other studies have also focused on the interactions between streams and aquifers through a low-permeability streambed layer (Barlow et al. 2000; Brunner et al. 2010; Xian et al. 2017); however, hydrogeologic conditions at many sites indicated that the low-permeability streambed layer could be extensive laterally and significantly thick vertically, and that the streambed also functioned as an aquitard layer in terms of regional-scale hydrogeology. In spite of the low permeability, aquitards are always leaky to varying degrees (Cherry and Parker 2004), especially the water flow, which would be considerable when aquitards were linked with fractures or matrix windows (Martin and Frind 1998). However, there has been little concern with regard to exchange between streams and aquifers through an extensive aquitard thus far.

Lots of methods have been successfully applied in quantifying GW–SW interactions such as various environmental or thermal tracers (Anibas et al. 2011; Cartwright and Gilfedder 2015; Cartwright and Morgenstern 2016), hydrogeologic calculation (Harvey et al. 2004) and modeling (Brunner et al. 2010; Guay et al. 2013). Each method may be applicable in a specific range of time scales; even so, combining multiple approaches can obtain more reliable results and more comprehensive explanations for the characteristics and controls of GW–SW interactions. Existing studies on the interactions have included smaller-scale and larger-scale interactions and there have been some successful applications with multiple approaches on smaller-scale interactions, mainly focusing on the exchange between streams and groundwater in hyporheic zones (González-Pinzón et al. 2015; Rosenberry et al. 2016). However, reports of the combined application of multiple approaches for larger-scale interactions are relatively rare.

The Jianghan Plain (JHP) in central China, an alluvial plain of the Yangtze River, is the world’s third largest river that originates from the Tibet Plateau (Chen et al. 2001). In recent decades, JHP has seen a massive reclaiming of land through construction of aquaculture ponds, rice paddies, ditched channels and large hydraulic management projects such as the Three Gorges Project located at the JHP’s upper reaches. As a result of coupled natural conditions and anthropogenic activities, the plain is facing a set of environmental problems such as wetland degradation (Zhang 2009), water quality anomalies (Gan et al. 2014; Du et al. 2017) and ecological damage (Wang et al. 2016). GW–SW interactions may be integral to understanding water quality and ecological processes on the JHP; however, there have been few systematic studies of groundwater in JHP, such that the characteristics and controls on GW–SW interactions are poorly known. In order to effectively guide local water resource management, a better understanding of GW–SW interactions is needed in this area.

The shallow sediments in JHP are mainly composed of an upper silty-clay with silt layer functioning as an aquitard and an underlying fine-to-coarse sand, functioning as an aquifer (Guo 2014). In the large rivers of JHP, Yangtze River and Han River may be directly connected with the lower aquifer in some areas (Zhao 2005). The significantly influencing horizontal distance of these two rivers is around 3 km (HBHEGB 1990); therefore, for most areas of JHP, surface waters in the interior are hypothesized to affect groundwater recharge and discharge. In the interior of JHP, there are abundant stream networks of interior rivers and ditched channels, with different depths of cuttings in the upper aquitard, which do not penetrate into the aquifer.

The present study aims to quantify interactions between surface waters and the aquifer in the interior of JHP using a combination of groundwater simulation, hydrogeologic calculation and environmental tracer (i.e., tritium) modeling, to assess the general characteristics and controls of GW–SW interactions in JHP. The results from this study could reveal unexpected links with water pollution and improve water-resources management practices in JHP. In addition, the issues addressed here are generally applicable to other sites as well because hydrogeologic conditions similar to JHP are quite common globally.

Study area

The Jianghan Plain is located in the middle reach of the Yangtze River of China (Fig. 1), encompassing an area of >55,000 km2 downstream of the Three Gorges Project. It was formed by alluvial deposits of Yangtze River which is the third largest river in the world and Han River which is the largest tributary of Yangtze River, coupled with lacustrine deposits in recent tens of thousands of years. The JHP has a sub-tropical monsoonal climate with an annual precipitation and evaporation of about 1,208 and 1,379 mm, respectively, and an annual average temperature of 16.8 °C (Deng et al. 2014). The geomorphology of JHP can be grouped into two categories, the hilly area just at the western boundary and the widespread low plain in the interior. The low plain area is very flat and vast with a slope of 1/20000–1/30000 and the elevation decreases from 30 to 40 m above sea level in the northwest and 20–27 m in the southeast (Zhou et al. 2013).

Fig. 1
figure 1

The geographic location of the Jianghan Plain in China. a Locations of groundwater sampling sites for tritium measurement, where groups 1 and 2 represent samples close to and away from the TSR, respectively; b a typical monitoring site (Shahu Site) near the TSR; c a typical section from the Han River to the Yangtze River

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The low plain is comprised of the upper Pleistocene (Qp3) or Holocene (Qh) alluvial and lacustrine sediments at the surface (Gan et al. 2014). Quaternary unconsolidated sediments form porous media for groundwater storage and flow. The groundwater systems in the present study can be divided into two groups. The shallower sediments are composed of Holocene sediments (clay, silty clay and silt, interlaced mud), functioning as an upper aquitard with thickness ranging from 10 to 35 m, mostly around 20 m. The underlying sediments are composed of upper and mid Pleistocene alluvial sediments with a thickness of 50–80 m, functioning as a lower aquifer, the primary layer for local water supply. The upper aquitard and lower aquifer together are referred to as the shallow groundwater system. Below the aquifer, there is a continuous aquitard with a thickness of about 10 m and an underlying deeper confined aquifer that will not be discussed in this paper due to their weak relation to surface waters.

The upper aquitard is hypothesized to be recharged from rainfall, as well as through exchange with streams and ponded water. A recent survey indicated there was a vertical gradient between surface waters and the aquifer (Duan et al. 2015; Schaefer et al. 2016), providing an opportunity for leakage through the aquitard. The aquifer is hypothesized to be recharged from leakage of the overlying aquitard and lateral groundwater flow (Zhao 2005). The general groundwater flow direction in the aquifer is from northwest to southeast, nearly consistent with that of rivers, both of which follow the topographic slope (Zhao 2005). The horizontal hydraulic gradient in the aquifer is fairly low with a magnitude of 0.0001 (Zhou 2009; Schaefer et al. 2016), resulting in quite slow groundwater flow.

The present study focuses on the interactions between the aquifer and surface water through an intermediate aquitard in the extensive interior areas of JHP. Tongshun River (TSR), an important river in the interior, was targeted for study of interaction with the aquifer. The TSR begins as a distributary channel (a branch of a river that flows away from the main stream) of the Han River that flows for 191 km until reaching Yangtze River (Fig. 1) but does not penetrate into the aquifer; however, the cutting depth of TSR relative to the ground is around 6–8 m, shortening the vertical flow path to the aquifer.

Methodology

Before all the approaches were applied, it was necessary to make some basic assumptions. Firstly, the thicknesses of the upper aquitard and the lower aquifer are assumed to be constant within the TSR watershed. Secondly, the cutting depth (i.e., vertical distance between TSR and the underlying aquifer) is assumed to be constant as well. Although there must be heterogeneity for Quaternary sediments, those basic assumptions are believed to be relatively reasonable in a fairly low-slope plain area, especially for a regional-scale study.

Groundwater simulation

A numerical model, MODFLOW-2000, was used to assess the magnitudes and ways of lateral influence of TSR on the aquifer head change. Detailed introduction for this model can be found in Harbaugh et al. (2000). One two-dimensional cross-sectional simulation of transient flow was conducted (Fig. S18 of the electronic supplementary material (ESM), in which there were 500 columns horizontally (20 m for each column) and 15 layers vertically (10 and 5 constant-thickness layers for the aquitard and aquifer, respectively). The reason for multiple layers created in the aquitard is that the hydraulic head does vary vertically under a river (Brunner et al. 2010) and it is also the case for aquitards (Cherry and Parker 2004). The reason for multiple layers set in the lower aquifer is for the purpose of achieving higher resolution of simulation. The left and right boundaries were both assigned as the constant-head boundaries. A river with similar geometry to TSR was added in the middle of the model. At first, all the cells were assigned the same initial head. Then, the river stage was instantaneously assigned as a distinct value (i.e., a sudden elevation or decline, representing the case for the wet or dry season, respectively). The initial head and river stage given in the model were based on average measured values of the aquifer head and the TSR stage during the wet or dry season in a typical monitoring site (Fig. 1b). Each simulation was run for a period of 6 months, which is a common cycling period for both wet and dry season.

Hydraulic conductivity (K) of the lower aquifer was cited from a recent hydrogeological survey report about JHP (GEC-HB 2016) based on large numbers of pumping tests, where horizontal and vertical K values were 6.74 and 0.74 m/day, respectively. The K value of the aquitard was obtained through infiltration experiments in superficial sediments, which were then extrapolated to the whole aquitard sediments. Those experiments were conducted in 40 randomly selected sites within Xiaotao Reach of TSR, resulting in an average saturated K value of 0.13 m/day, which was also used in the horizontal direction by assuming the aquitard sediments to be isotropic. The pumping tests or slug tests were not chosen for the aquitard because domestic wells and drilled piezometers in the upper aquitard were often screened in local silt layers. This would be expected to produce a significantly higher value. The laboratory measurements based on core samples were also not chosen because they often had a low probability of containing preferential pathways, which were believed to often provide minimum values (Cherry and Parker 2004). All parameters used in the simulation coupled with data sources can be found in Table S1 of the ESM.

Hydrogeologic calculation

Hydrogeologic calculation aimed to quantify vertical fluxes between surface waters and the aquifer based on the collected hydrogeologic parameters mentioned in section ‘Groundwater simulation’. This work was conducted in a typical field site (Shahu) near TSR (Fig. 1b), which consists of 13 multilevel monitoring points with three piezometers of 10, 25 and 50-m depth at each point. The water samples from piezometers with 10 and 25-m depth can represent the groundwater at an intermediate depth of the upper aquitard and the uppermost part of the aquifer, while those with 50-m depth can represent the groundwater in a relatively deeper part of the aquifer. Further details of this field site can be seen in Duan et al. (2015) and Schaefer et al. (2016).

The groundwater level monitoring data from this field site, from June 2012 to November 2013, were collected at half-month intervals. The monitoring data of the main surface waters (TSR and two channels) were also recorded, correspondingly. The detailed monitoring information for surface waters and all monitoring points can be seen in Figs. S1–S14 of the ESM. The 50-m piezometers have nearly the same water level as the 25-m piezometers (Duan et al. 2015; Schaefer et al. 2016), but this will not be discussed in this paper. The vertical hydraulic gradients were calculated by dividing the water-level difference between TSR and the nearest 25-m piezometers by the vertical distance between the river bottom and the aquifer top. In this field site, three points (SY05, SY06 and SY10) were selected to calculate vertical hydraulic gradients between them and TSR. The vertical fluxes were calculated by multiplying hydraulic gradients by the hydraulic conductivity of the upper aquitard sediments based on Darcy’s Law. Another ten monitoring points (SY01-SY04, SY07-SY09 and SY11-SY13) are relatively far from TSR, with rice paddies, ponds or quite shallow channels nearby; therefore, vertical fluxes between the 25 and 10-m piezometers might better represent the vertical fluxes for those points. A conceptual scheme for the flux calculation is shown in Fig. 2a.

Fig. 2
figure 2

a A conceptual scheme for the calculation of vertical fluxes. Δh1 represents the water-level difference between the aquifer and surface water, while L1 is vertical flow distance. Δh2 represents the water-level difference between 25 and 10-m piezometers, while L2 is vertical flow distance. The vertical fluxes near the river were calculated based on Darcy’s Law (q = K1·Δh1/L1), and those farther from the river were calculated based on q = K1·Δh2/L2. The resulting positive fluxes indicate discharge and negative ones represent recharge. b A conceptual model showing one-dimensional transport and decay of tritium in TSR and its exchange with groundwater. d average surface-water depth; d GW depth of water storage with detectable tritium; θ porosity; q E vertical exchange flux; d GW θ−1 depth of interactive groundwater

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Collection and modeling of tritium data

Collection of tritium data

Tritium data were used to quantify groundwater residence time near the river and away from the river, and resulting exchanging flux between TSR and the aquifer. In total, 14 shallow groundwater samples were collected in June 2015 for tritium measurement, of which seven were quite close to TSR, within 200 m (group-1 samples), and another seven were away from the TSR, beyond 1,000 m (group-2 samples). In the field, the unfiltered water samples for tritium analysis were collected by filling up 600-ml HDPE bottles, and were stored in a refrigerator immediately until analyses were conducted. The sampling locations are shown in Fig. 1a.

The tritium analyses of water samples were completed in the experimental center of School of Environmental Studies, China University of Geosciences, with a liquid scintillation counting method (1220 Quantulus Ultra Low Level LSC), after enrichment by electrolysis. The tritium concentration is expressed in tritium units (TU), where 1 TU indicates a T/H abundance ratio of 10−18. The accuracy of low-level tritium measurement is 0.1 TU coupled with an average standard deviation of about 0.6 TU. For this study, the sum of accuracy and average standard deviation (0.7 TU) were regarded as the best estimate of a tritium minimum detection limit. The measured tritium concentrations are all more than 0.7 TU (Table 2), suggesting validity for all tritium data.

The relatively complete tritium data for historical precipitation close to the study area were only available from Hong Kong station from 1961 to 2010 (IAEA 2016); however, there would be a considerable difference for the record of tritium concentrations between the study area and Hong Kong due to the latitude effect. In order to fill this gap, a relationship of tritium concentrations in precipitation between the study area and Hong Kong can be established based on the model by Zhang et al. (2011; Fig. S15 of the ESM). As a result of correlation analysis for modeled concentrations in these two locations, a relation equation was established—CJ = 1.4CH + 1.5, where CJ and CH represent the concentrations of tritium for JHP (J) and Hong Kong (H)—(Fig. S16 of the ESM). Based on the equation and measured tritium concentrations in Hong Kong, the tritium concentrations in historical precipitation of JHP were calculated (Fig. S17 of the ESM). Although there is a 5-year gap between the last tritium record in precipitation and the sampling period, the analysis would not be influenced a lot because the tritium concentration in precipitation had been very low and decreased extremely slowly since 2005. For the present study, the last tritium value (2015) was set as the nearest tritium record (2010) in precipitation.

Tritium modeling

Two tritium modeling methods were used for different groups of groundwater samples. Because groundwater flow paths near TSR did vary over time and were mainly affected by the river rather than precipitation, for group-1 samples, a transient storage model was used (tritium modeling-1). However, for group-2 samples, because groundwater flow paths away from TSR were relatively invariable and received relative uniform recharge through the unsaturated zone, a lumped parameter model was used (tritium modeling-2).

Group-1 samples were regarded as “actively interactive groundwaters” and a tritium transport simulation was conducted using the numerical code OTIS (Runkel 1998). Several additional assumptions were necessary to run the model in this case: (1) the groundwater flow along the direction of TSR corridor dominated over the flow perpendicular to TSR; (2) the historical tritium concentrations of TSR were equal to those for historical precipitation; (3) the tritium concentrations of samples close to TSR were extrapolated to those strictly under the river. The rationality for those assumptions will be further discussed in section ‘General characteristics of GW–SW interactions in the interior JHP’. The model, for which major components are illustrated in Fig. 2b, simulated transport and decay of tritium in TSR and its exchange with shallow groundwater. The related equations for the stream and storage zone are as follows (Harvey et al. 2006):

$$ \frac{\partial C}{\partial t}=-\frac{Q}{w\cdot d}\frac{\partial C}{\partial x}+\frac{1}{w\cdot d}\frac{\partial }{\partial x}\left(w\cdot d\cdot D\frac{\partial C}{\partial x}\right)+\frac{q_{\mathrm{E}}}{w\cdot d}\left({C}_{\mathrm{GW}}-C\right)-\lambda \cdot C $$
(1)
$$ \frac{\partial {C}_{\mathrm{GW}}}{\partial t}=\frac{q_{\mathrm{E}}}{w\cdot {d}_{\mathrm{GW}}}\left(C-{C}_{\mathrm{GW}}\right)-\lambda \cdot {C}_{\mathrm{GW}} $$
(2)
$$ {q}_{\mathrm{E}}=\frac{d_{\mathrm{GW}}w}{t_{\mathrm{GW}}} $$
(3)

where Q is the average volumetric flow rate of surface water [m3/s]; t is time [s]; x is distance [m]; C is the concentration of tritium [TU] in surface water; CGW is the concentration of tritium [TU] in the “interactive groundwater” layer; D [m2/s] is the longitudinal dispersion coefficient in surface water; w [m] is the width of the modeled cross-section in surface water and groundwater; d [m] is the average depth of the surface water; dGW [m] is the average depth of water storage in the layer of interactive groundwater; λ [s−1] is the first-order coefficient of radioactive decay of tritium in surface water and groundwater (1.8 × 10−9 s−1); and qE [m2/s] is the coefficient describing bi-directional exchange that occurs between surface water and groundwater by vertical fluxes; tGW [s] is the groundwater residence time. The residence time is the only parameter that needs to be adjusted to fit observed tritium data. The average fluxes per unit cross-sectional width are estimated by dividing qE by w. The main parameters used in the simulation can be found in Table S2 of the ESM.

For group-2 samples, an interactive Excel program (TracerLPM, version 1) was used to assess their residence time through a lumped parameter model (Jurgens et al. 2012). The dispersion model was selected because the surficial aquitard is leaky with relatively constant thickness and receives uniform recharge, while the sampling did not include the flow lines with short transit times (Maloszewski and Zuber 1982), owing to the short-screened wells used in the sampling undertaken as part of this study. In addition, dispersion is often an important process and even a dominant process in aquitards (Cherry and Parker 2004). The dispersion model is based on the one-dimensional advection-dispersion equation for which the system response function is:

$$ g\left(\tau \right)=\frac{n}{\tau \sqrt{4\uppi {D}_{\mathrm{P}}\tau /{\tau}_{\mathrm{m}}}}{e}^{-\left(\frac{{\left(1-\tau /{\tau}_{\mathrm{m}}\right)}_2}{4{D}_{\mathrm{P}}\tau /{\tau}_{\mathrm{m}}}\right)} $$
(4)

where Dp is the dispersion parameter. Dp is the inverse of the Peclet Number and equivalent to D/(vx), where v is velocity (m/day), x is distance (m), and D is the dispersion coefficient (m2/day). τ is the transit time and τm is the mean transit time. Coupling the sample concentrations with the tritium input history (Fig. S17 of the ESM), the best fit of the residence time for each sample was obtained with a random dispersion coefficient. The results of modeled residence time can be seen in Table 2.

Results

Results from groundwater simulation

Six observation piezometers screened at the uppermost part of the aquifer with gradually increasing lateral distances from the river were added to the model to observe temporal variations of the water levels. The average measured values of the aquifer head during the wet season and dry season were 21.06 and 20.76 m, and those of the TSR stage were 22.27 and 19.15 m. Those values produced a head difference of −1.21 and +1.61 m between the aquifer and TSR during the wet and dry season, respectively; the simulating results are shown in Fig. 3. It was clear that the influence of TSR on aquifer head change decreased sharply with increasing lateral distance. When the distance was less than 500 m, the increase or decline of the aquifer head in a half-year period was more than 0.20 m. When the distance was more than 1,000 m, the change of water level in that period was not significant. When the distance was 2,000 m, hardly any change of water level could be observed. In summary, the influencing lateral distance from TSR was about 1,000 m, with the area within 500 m being much more significant.

Fig. 3
figure 3

The temporal water-level change with different lateral distances from TSR due to a sudden stage elevation or decline of TSR based on the MODFLOW procedure. a–b Represented are the cases in the wet and dry season, respectively. The solid and dashed lines represent the case with (original simulation) and without (“new simulation”) lateral flow in the aquitard, respectively

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The influence of the TSR stage on the aquifer head could result from (1) vertical flow in the aquitard between the riverbed and aquifer, and following lateral flow in the aquifer (component 1); and (2) lateral exchange between the river and the aquitard, and following infiltration into the aquifer (component 2). The horizontal conductivity was set approaching zero for the aquitard and the same simulation was conducted as described in section ‘Groundwater simulation’ (“new simulation”), which could rule out the contribution of component 2 and assess the contribution of component 1. The quantitative contribution of component 1 was calculated by dividing the aquifer head change (increase for the wet season or decrease for the dry season) from the beginning to the end of the new simulation by that with the original simulation (Fig. 3). In the case for the wet season, the calculated contribution of component 1 was 91.13, 90.58, 89.87 and 87.74% for the piezometer with lateral distance of 1, 10, 100 and 500 m, respectively. In the case for the dry season, the corresponding contributions were 93.40, 92.94, 92.57 and 91.50%, respectively. In summary, the quantitative contribution of component 1 to the aquifer head change is around 90%. Relatively less contribution (about 10%) from component 2 was believed to result from lateral bank storage.

In the simulation, the aquitard sediments were assumed to be isotropic. Although the horizontal hydraulic conductivity could be different from the vertical one, it may not be an issue as vertical flow in the aquitard is primary and horizontal flow only plays a minor part.

Vertical fluxes based on hydrogeologic calculation

Vertical fluxes reported by percentile were summarized in Table 1. The fluxes between the aquifer and TSR tended to be bidirectional (i.e., seasonal recharge and discharge) and variable (Fig. 4), whereas the vertical fluxes farther from TSR tended to be unidirectional with time (i.e., mostly recharge). Bidirectional and variable fluxes between the aquifer and TSR could result from significant seasonal stage fluctuation of TSR, with difference of about 5.6 m between the wet season and dry season. The relatively unidirectional and stable fluxes farther from TSR could result from relatively small stage variations of channels or ponded waters.

Table 1 Vertical fluxes reported by percentile for all sites. The positive flux represents the groundwater discharge and the negative represents the groundwater recharge
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Fig. 4
figure 4

Cumulative distribution of calculated vertical fluxes. Among them, three points (SY05, SY06 and SY10) near TSR were used to calculate the fluxes based on the level difference between TSR and the aquifer; other points farther from TSR were used to calculate the fluxes based on the level difference between the 10 and 25-m piezometers

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For the points near TSR, the average behavior of vertical fluxes was better represented by the 25th and 75th percentile fluxes. This was because those sites experienced reversals in the direction of fluxes that tended to balance one another, resulting in a median value near zero (Harvey et al. 2004). The 25th percentile fluxes between the aquifer and TSR ranged from −0.0156 to −0.0116 m/day, with an average of −0.0144 m/day, and the 75th percentile fluxes ranged from +0.0135 to +0.0182 m/day, with an average of +0.0152 m/day. The 25th and 75th percentile fluxes could represent the average behavior of recharge and discharge, respectively. As a whole, the vertical fluxes near the river were on the order of 0.01 m/day.

For the points farther from TSR, the average behavior of those relatively unidirectional vertical fluxes was better represented by the 50th percentile fluxes. Those fluxes exhibited a wide range of −0.0186 to −0.0006 m/day, with a median value and an average value of −0.0095 and −0.0083 m/day, respectively, a little lower than those near TSR but both approaching an order of −0.01 m/day as well. The wide range of fluxes could be attributed to different recharge from the surface end members (precipitation, channels and ponded waters). For example, two points near the Kuige Channel (SY01 and SY02) exhibited the least recharge, which was consistent with quite low stage of the Kuige Channel (Fig. S1 of the ESM). Whereas, three points near the Lvfeng Channel (SY11–SY13) exhibited the most recharge, which was consistent with quite high stage of the Lvfeng Channel (Fig. S1 of the ESM).

Groundwater residence time and exchanging flux based on OTIS model

Near the river, the tritium concentrations in sampled groundwater were from 2.2 to 5.3 TU, with an average value of 3.6 TU. Based on the data set, there was a good liner deceasing trend (R2 = 0.77) for tritium concentrations from the aquitard to the aquifer (Fig. 5a). Based on the resulting trend line, tritium concentrations would be lower than 0.7 TU (minimum detection limit) when the depth is over 40 m; as an estimate, groundwater samples in the top 40 m were regarded as representing interactive groundwater. Firstly, the average storage depth was calculated based on the porosity–depth relationship. The vertical distance between the riverbed and aquifer top was 11 m with a porosity of 0.51 (HBHEGB 1985), whereas the vertical distance between the aquifer top and the lower boundary for detectable tritium was 22 m with a porosity of 0.40 (Schaefer et al. 2016). As a result, the average storage depth was 14.41 m (21.41 m relative to the ground surface), which was just located in the uppermost part of the aquifer, suggesting that most of the water storage was accounted for by water storage in the upper aquitard, with the remaining in the top few meters of the aquifer. Then, based on the same trend line, the average tritium concentration in the interactive groundwater was estimated to be 3.3 TU.

Fig. 5
figure 5

a Relationship between the tritium concentration and sampling depth near TSR, where a liner equation was established (Y = −7.18X + 45.06) with an R2 of 0.77; b modeled tritium concentrations in interactive groundwater, and results from seven simulations with varying groundwater residence times (1, 10, 30, 50, 100, 300 and 1,000 years) are shown. ATC represents the average tritium concentration in interactive groundwater for fitting

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Through the OTIS model, a range of results for the simulated tritium concentrations in the interactive groundwater using different given groundwater residence times (1, 10, 30, 50, 100, 300 and 1,000 years) are shown in Fig. 5b. The best-fit simulation to the average tritium concentration was determined to have a residence time of about 15 years. The best fit simulation is not shown, but the close fit of the simulation with about a 15-year residence time is apparent in Fig. 5b. Dividing the water storage depth in the interactive groundwater (14.41 m, under the riverbed) by the best-fit residence time (15 years) resulted in an exchange flux of 0.0026 m/day.

Groundwater residence time and vertical flux based on the lumped parameter model

The tritium concentrations in collected groundwater samples away from the river were from 0.9 to 5.5 TU, with an average value of 2.3 TU. Six of the seven samples were determined to have tritium concentrations lower than 3.0 TU (Fig. 6a), which could suggest a relatively weak hydrologic cycle away from the river, in which most areas were recharged from precipitation, waterlogged rice paddies or quite shallow ponds and channels, resulting in a relatively longer vertical flow path from the surface end members. Vertically, there was a relatively weak linear varying trend (R2 = 0.40) for tritium concentrations, which was probably caused by various exchange with the surface end members in different sites.

Fig. 6
figure 6

a Relationship between the tritium concentrations and sampling depth away from TSR, where a liner equation was established (Y = −3.20X + 23.86) with an R2 of 0.40. b Relationship between modeled residence times and sampling depth away from TSR, where a liner equation was established (Y = 0.14X + 3.55) with an R2 of 0.32

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The residence time for shallow groundwater away from the river was assessed with a dispersion model. The modeled groundwater residence times ranged from 50.1 to 136.0 years, with an average value of 91.8 years (Table 2). A liner relationship of the residence time and depth was established as well although not very significant (R2 = 0.32; Fig. 6b). Multiplying the slope of the trend line mentioned previously by a depth-weighted porosity (0.47) resulted in a vertical flux of 0.0002 m/day.

Table 2 Tritium concentrations and modeled residence times of sampled groundwater
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Discussion

General characteristics of GW–SW interactions in the interior of JHP

The simple groundwater simulation suggested that the influencing lateral distance of TSR on the aquifer head was within 1,000 m, especially within 500 m. The tritium concentrations also exhibited remarkable difference for groundwater near the river (< 200 m) and away from the river (> 1,000 m). Vertical flow in the aquitard between the riverbed and the aquifer followed by lateral flow in the aquifer contributed significantly more than lateral bank storage in the aquitard and following infiltration to the aquifer head change near the river. Based on this knowledge, the magnitude of vertical fluxes between the surface waters and the aquifer can be discussed in the case near the river and away from the river, separately.

Near the river

The average flux based on the OTIS simulation was 0.0026 m/day, approaching an order of 0.001 m/day, coupled with a residence time of about 15 years. In contrast, the vertical recharge or discharge flux near the river based on hydrogeologic calculation was on the order of 0.01 m/day, an order of magnitude higher than the simulated fluxes from the OTIS model. Here the influence of assuming conditions on the simulated results through the OTIS model should be discussed. Firstly, as suggested from the groundwater simulation, vertical flow in the aquitard between the riverbed and the aquifer dominated over lateral bank storage in the aquitard near the river. In addition, as mentioned in the introduction to the study area, the general groundwater flow direction in the aquifer is nearly consistent with that of rivers, following the topographic slope. Therefore, it is reasonable to assume the groundwater flow along the direction of TSR corridor dominated the flow perpendicular to TSR. Secondly, patterns of temporal variation in the TSR stages were significantly consistent with those of precipitation (Duan et al. 2015). In addition, based on hydrochemical survey results from the project of CUG (2016), the δ18O and δ2H values of TSR in the wet season (−39.5 and −6.0‰ respectively, n = 18) were somewhat lower than those in the dry season (−31.1 and −4.3‰ respectively, n = 8). This was consistent with the “rainfall amount effect” for this study area, meaning lower δ2H and δ18O values of rainfall coupled with the greater amount of rainfall (Wang 1991), regardless of additional influence from evaporation. Those values could indicate that precipitation is the dominant source of the TSR discharge, which also makes it reasonable to assume the historical tritium concentrations of the TSR were equal to those for historical precipitation. The remaining possible influence derives from the assumption that the tritium concentrations of samples close to TSR were extrapolated to those just under the river. However, it could not explain an order of magnitude difference between the OTIS-based estimates and the calculated fluxes because there would be no significant difference between tritium concentrations within 200 m from TSR and those strictly under the riverbed.

It should be noted that groundwater samples for tritium measurements were from the aquitard and the uppermost part of the aquifer; therefore, the results from tritium modeling could represent the spatially average fluxes across the boundary of the aquitard and aquifer. In addition, tritium modeling was consistent with long time-scale (i.e., decadal) GW–SW interactions. The results from it could represent the decadally average fluxes (long-lived flux), whereas, the hydrogeologic calculation based on Darcy’s Law were characterized by a relatively short time scale (i.e., half-monthly). The shorter time-scale exchange could be more significant between the river and the aquitard rather than the subsurface area across the aquitard and aquifer, and exchanging direction converted frequently, producing a short-lived flux.

Away from the river

The groundwater away from the river was mainly exchanged with precipitation and ponded waters, which was characterized by a longer flow path prior to reaching the aquifer top. The modeled residence time from a lumped parameter model showed a vertical flux of 0.0002 m/day, with an average residence time of 91.8 years. Similar to the OTIS model, tritium modeling based on the lumped parameter model was also consistent with a long time-scale (i.e., decadal) exchange between groundwaters and the surface end members. The results suggested an order of magnitude difference for long-lived vertical fluxes near and away from the river; however, the average vertical fluxes away from the river based on hydrogeologic calculation exhibited an order approaching 0.01 m/day, despite a quite variable magnitude. This order is the same as the order for calculation-based fluxes near the river. In general, the water level fluctuation of 10-m piezometers was much more variable comparing to the 25-m piezometers (seen in the ESM), suggesting a significant influence from the surface end members. The order of 0.01 m/day probably represented the short-lived fluxes within the aquitard, which were affected a lot by the surface end members. In summary, there was no observable difference for the short-lived (half-monthly) fluxes near and away from the river, whereas there was an order of magnitude difference for the long-lived (decadally) fluxes. A conceptual model of the hydrologic cycle between the surface waters and groundwaters, with labeled fluxes in the interior of JHP, is shown in Fig. 7.

Fig. 7
figure 7

Conceptual model showing the general characteristics of GW–SW interactions in the interior of JHP. Several numbers about the vertical fluxes are labeled. The thin dashed arrows represent the short-lived fluxes, whereas the solid thick arrows represent the long-lived fluxes. All red lines or arrows represent the case for the wet season and blue lines or arrows represent the case for the dry season. The long-term horizontal flow direction is perpendicular to the page

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Links to water quality in JHP

There are two types of water quality problems in JHP: water pollution for which pollutants come from anthropogenic input, and natural groundwater anomaly (high As, Fe, NH4+, etc). In general, the interactions between the river and the aquifer with a long-lived vertical flux around 0.001 m/day are active. The active exchange could result from common preferential pathways in the aquitard, coupled with the considerably large vertical hydraulic gradient. The industrial discharge into TSR has taken place only in the last 10 to 20 years. In the context of an average groundwater residence time around 15 years near the river, shallow groundwater could be expected to face a contamination risk from recent anthropogenic activities. According to a recent broad-scale survey of the interior of JHP (CUG 2016), the conservative chloride has reached a significant concentration in the upper aquitard, and even in a handful of samples from the uppermost part of the aquifer (Fig. 8a). If the pollutants from anthropogenic activities continue to be input into the subsurface, a contamination risk to deeper groundwater could be expected despite a small vertical hydraulic gradient in the aquifer; however, in general, the current contamination state of the aquifer is not very serious. The possible reasons include: (1) most of areas are relatively far away from large interior rivers, resulting in longer residence time comparing to 10–20 years; and (2) the upper aquitard has a good capacity to remove some reactive pollutants such as nitrate and sulfate prior to entering the aquifer.

Fig. 8
figure 8

The vertical distribution of a dissolved chloride and b arsenic in groundwater samples. The data are from a broad-scale hydrochemical survey in the JHP (CUG 2016)

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More interesting is the problem about high As content in groundwater, coupled with high iron, ammonium, etc. Spatially, high arsenic sites are mainly located near the river (Gan et al. 2014). Temporally, As content in groundwater changes significantly in different seasons. The redox change owing to hydrologic change (seasonal recharge and discharge) was commonly believed to account for the seasonal variation of As concentrations (Deng et al. 2014; Duan et al. 2015; Schaefer et al. 2016); however, there is no sufficient explanation for the spatial distribution of As concentrations. It is still unclear whether arsenic in the lower aquifer comes from local sediments or upper aquitard sediments. An indoor compaction experiment coupled with a core sediment profile from JHP suggested that arsenic could come from the release from upper organic-rich muddy sediments (Xiao et al. 2016). From Fig. 8b, it can be observed clearly that As contents are high mainly in the uppermost part of the aquifer, which is a depth where most extensive and intensive groundwater pumping is conducted. The pumping could be expected to further enhance the soluble As releasing into the lower aquifer. In general, the groundwater As concentrations have a significant bell-shaped profile, which is quite similar to the case in Bangladesh, where pumping is believed to have caused arsenic transport into the shallow groundwater coupled with degradable organic carbon (Neumann et al. 2009). Based on the results from the present study, the long-lived vertical fluxes near the river are significantly higher than those away from the river. The higher vertical fluxes can enhance more arsenic transport into the aquifer, which could also explain the higher arsenic concentration in groundwater near the river. The much lower arsenic concentration below the uppermost part of the aquifer could be attributed to the quite weak vertical flow in the aquifer. In summary, it is clear that the spatial distribution of arsenic in groundwaters is related to the groundwater dynamics at JHP; further study linking the hydrologic cycle and arsenic distribution would result in interesting knowledge on the genesis of high arsenic groundwater in JHP.

Conclusion

Hydrogeologic calculation coupled with tritium modeling was jointly applied to quantify the interactions between the surface waters and the aquifer through an extensive aquitard in the interior of JHP. First of all, a simple groundwater simulation suggested that the influencing lateral distance by TSR was about 1,000 m, with the area within 500 m being much more significant; vertical flow in the aquitard between the riverbed and aquifer followed by lateral flow in the aquifer contributed significantly more (~90%) than lateral bank storage in the aquitard and following infiltration to the aquifer head change near the river.

Calculation-based vertical fluxes between TSR and the aquifer tended to be bidirectional (i.e., seasonal recharge and discharge) and variable, whereas those fluxes away from TSR tended to be unidirectional and stable. Despite distinct behavior, vertical fluxes near and away from the river were both in an order of 0.01 m/day. The hydrogeologic calculation was consistent with a relatively short time scale (i.e., half-monthly), and an order of 0.01 m/day could represent the short-lived fluxes between the river and the aquitard near the river, and between the surface end members and the aquitard farther from the river.

Near the river, the tritium modeling based on the OTIS model produced an average storage depth of 14.41 m (21.41 m under the ground surface), just located in the uppermost part of the aquifer. The best-fit simulation to the average tritium concentration in interactive groundwater was determined to have a residence time of about 15 years and a resulting vertical flux of 0.0026 m/day. Away from the river, the tritium modeling based on a lumped parameter model produced a vertical flux of 0.0002 m/day, with an average residence time of 91.8 years. The tritium modeling was consistent with a long time-scale (i.e., decadal) exchange between groundwaters and surface waters. The order of 0.001 and 0.0001 m/day represented the long-lived average vertical fluxes close to and away from the river.

The time (10–20 years) since which the industrial discharge into the river had taken place in JHP is approximated to the average groundwater residence time of 15 years near the river, posing an existing potential contamination risk to the lower aquifer. The spatial distribution of arsenic in groundwaters is related to the groundwater dynamics at JHP; however, more work is needed to understand the link of the hydrologic cycle with arsenic distribution.