Knowledge of the history of the local atmospheric mixing ratios of CFCs in precipitation is required for indicating modern water recharge. The difference between the local and global background atmospheric mixing ratios of CFCs in the Northern Hemisphere – CFC excess – varies substantially based on the industrial development of the area. Elevated CFC concentrations (10 %–15 % higher than those of the Northern Hemisphere as a whole) have been reported in the air of urban environments such as Las Vegas, Tucson, Vienna, and Beijing (Barletta et al., 2006; Carlson et al., 2011; Han et al., 2007; Qin et al., 2007), whereas the atmospheric mixing ratios of CFCs in Lanzhou and Yinchuan (northwestern China) were approximately 10 % lower than those of the Northern Hemisphere (Barletta et al., 2006). Manas River Basin is located in northwestern China (Fig. 1a), has a very low population density, and is far from industrial cities. To evaluate the modern water recharge by CFCs, the time series trend of the Northern Hemisphere atmospheric mixing ratio (Fig. 3; 1940–2014, https://water.usgs.gov/lab/software/air_curve/index.html, last access: 27 October 2017) was adopted in this study.

Measured CFC concentrations (in pmol L-1) can be interpreted in terms of partial pressures of CFCs (in pptv) in solubility equilibrium with the water sample based on Henry's law. The computational process was conducted following Plummer et al. (2006a). In arid northwestern China, estimating the local shallow groundwater temperature as recharge temperature is more suitable than the annual mean surface air temperature (Qin et al., 2011) because the local low precipitation usually cannot reach the groundwater. Studies on the MRB (Ji, 2016; Wu, 2007) have also indicated much less vertical recharge water from the local precipitation compared with abundant groundwater lateral flow recharge and river leakage from the mountain to the piedmont areas. In this study, the measured groundwater temperature, which varied from 11.5 to 15.7 ∘C between wells (Table 1), was used as the recharge temperature to estimate the groundwater input CFC concentrations. Surface elevations of the recharge area vary from 316 to 755 m. The modern water recharge was then determined by comparing the calculated partial pressures of CFCs in solubility equilibrium with the water samples with historical CFC concentrations in the air (Fig. 3).

Carbon-14 (14C, half-life 5730 years) activity in groundwater is often used to estimate groundwater age over time periods of approximately 200 to 30 000 years, and to determine the recharge from mixing water in various climate conditions (Cook et al., 2017; Custodio et al., 2018; Huang et al., 2017). Since groundwater age cannot be measured directly, and the age distribution in the sample is unknown, one can derive an apparent age using a mathematical formula for the groundwater 14C sample (Suckow, 2014). “Apparent” here describes the fact that the age is not corresponding to the time difference between recharge and sampling during which piston flow is assumed for a water parcel (Cartwright et al., 2017; Suckow, 2014). Calculation of groundwater apparent 14C age may be complicated if dissolved inorganic carbon is derived from a mixture of sources, or if 14C originating from the atmosphere or soil zone is significantly diluted by the dissolution of 14C-free carbonate minerals in the aquifer matrix and biochemical reactions along the groundwater flow paths (Clark and Fritz, 1997). Although only minor carbonate dissolution is likely and determination of groundwater residence times requires 14C correction (Atkinson et al., 2014). When the dissolution of carbonate during recharge or along the groundwater flow path may dilute the initial soil CO2, δ13C can be used to trace the process (Clark and Fritz, 1997). An equation for the reaction between CO2-containing water with a carbonate mineral is commonly written as follows (modified after Pearson and Hanshaw, 1970): CO2+H2O+CaCO3(δ13Ccarb=0)→Ca2++2HCO3-(δ13CDIC), where δ13Ccarb is the dissolved carbonate δ13C value (approximately 0; Clark and Fritz, 1997), and δ13CDIC is the measured δ13C value in groundwater.

Depending on knowing the measured 14C activity after adjustment for the geochemical and physical dilution processes in the aquifer (without radioactive decay), the groundwater apparent 14C ages (t) can be calculated from the following decay equation: t=-1λ14C×ln⁡a14Ca014C, where λ14C is the 14C decay constant (λ14C=ln⁡2/5730), and a14C is the measured 14C activity of the DIC in groundwater.

Previous studies in the arid northwest of China (Edmunds et al., 2006; Huang et al., 2017) have concluded that a volumetric value of 20 % “dead” carbon derived from the aquifer matrix was recognised, which is consistent with the value (10 %–25 %) obtained by Vogel (1970). Therefore, the initial 14C activity (a014C) of 80 pMC is used to correct groundwater 14C ages (results are shown in Table 1), although this simple correction makes no attempt to correct the age of individual samples that may have experienced different water–rock interaction histories.

Groundwater mixing may occur both within the aquifer and in the long-screened wells (Cook et al., 2017; Custodio et al., 2018; Visser et al., 2013). A wide range of the groundwater residence times (ages) has been reported in an arid unconfined aquifer because recharge occurs under various climate conditions (Custodio et al., 2018). Furthermore, the groundwater residence time with wide variabilities governed by the distribution of flow paths of varying length cannot be measured directly (de Dreuz and Ginn, 2016; Suckow, 2014). A lumped parameter model may be an alternative approach to describe the distribution of residence times, which at the same time describes a mean residence time for the mixtures of different residence times. With the aid of gaseous tracers (e.g. 3H, CFCs, SF6, and 85Kr) one can describe the distribution of tracer concentrations (Stewart et al., 2017; Zuber et al., 2005) to obtain the groundwater MRTs. For the steady-state subsurface hydrologic system, 3H and CFCs tracers entering groundwater with precipitation are injected proportionally to the volumetric flow rates by natural processes. The output concentration in water at the time of sampling relating to the input 3H and CFCs can be described by the following convolution integrals (Małoszewski and Zuber, 1982): Coutt=∫0∞Cint-τgτe-λ3Hτdτfor3Htracer,Coutt=∫0∞Cint-τgτdτforCFCstracer, where Cout is the tracer output concentration, Cin is the tracer input concentration, τ is the residence time, t-τ is the time when water entered the catchment, λ3H is the 3H decay constant (λ3H=ln⁡2/12.32), and gτ is the system response function that describes the residence time distributions in the subsurface hydrologic system.

In this study, the CFC concentrations from the time series trend of the Northern Hemisphere atmospheric mixing ratio (Fig. 3) and 3H activities in precipitation in Urumqi (Fig. 4) are treated as proxies for CFC and 3H recharge concentrations (Cin), respectively. The historical precipitation 3H activity in the Urumqi station (Fig. 4) was reconstructed with the data available from the International Atomic Energy Agency (IAEA) using a logarithmic interpolation method. The precipitation 3H activity between 1969 and 1983 at Hong Kong and Irkutsk with different latitudes was used (data are available at https://www.iaea.org/, last access: 4 December 2017). The time series of 3H activity (Fig. 4) used as the input data was based on the following considerations. First, the MRB is located in the Northern Hemisphere, where the bomb pulse 3H activity is several orders of magnitude higher than in the Southern Hemisphere (Clark and Fritz, 1997; Tadros et al., 2014) and was superimposed with the China atmospheric nuclear tests from 1964 to 1974 in the arid northwest of China. Thus, the remnant 3H activity remains affected by the tail end of the bomb pulse. Second, the study area is more than 3500 km away from the western Pacific, and hence the atmospheric 3H activity is much higher than that at coastal sites due to the continental effect (Tadros et al., 2014). Furthermore, although the atmospheric 3H activity varies between seasons (Cartwright and Morgenstern, 2016; Morgenstern et al., 2010; Tadros et al., 2014), mean annual values (Fig. 4) were considered in this study.

Several residence time distributions have been described (Małoszewski and Zuber, 1982; Jurgens et al., 2012) and have been widely used in studies of variable timescales and catchment areas (Cartwright and Morgenstern, 2015, 2016; Cartwright et al., 2018; Hrachowitz et al., 2009; Morgenstern et al., 2010, 2015; McGuire et al., 2005). The selection of each model depends on the hydrogeological situations in the hydrologic system to which it is applicable. The exponential piston flow model (EPM) describes an aquifer that contains a segment of the exponential flow followed by a segment of piston flow. The piston flow model assumes minimal water mixing from different flow lines and little or no recharge in the confined aquifer; the exponential flow model assumes that water mixing between flowlines in the unconfined aquifer is minimal and that flowlines have an exponential distribution of transit times (Jurgens et al., 2012; Małoszewski and Zuber, 1982). The weighting function of this model is given by gτ=0forτ<τm1-1/η,gτ=ητme-ητ/τm+η-1forτ≥τm1-1/η. The dispersion model (DM) mainly measures the relative importance of dispersion to advection, and is applicable for confined or partially confined aquifers (Małoszewski, 2000). Its residence time distribution is given by gτ=1τ4πDPτ/τme-1-τ/τm24πDPτ/τm. The weighting function of the exponential mixing model (EMM) is gτ=1τme-τ/τm, where τm is the mean residence time and η is the ratio defined as η=lP+lE/lE=lP/lE+1, where lE (or lP) is the length of area at the water table receiving (or not receiving) recharge. DP is the dispersion parameter, which is the reciprocal of the Peclet number (Pe) and defined as DP=D/vx, where D is the dispersion coefficient (m2 day-1), v is velocity (m day-1), and x is distance (m).

Each residence time distribution has one or two parameters. MRTs (τm) are determined by convoluting the input (the time series of 3H and CFCs input in rainfall) to each model to match the output (the measured 3H and CFC concentrations in groundwater). The other parameters (η and Dp) are determined depending on the hydrogeological conditions. To interpret the ages of the MRB data set, EPM (η=1.5 and 2.2), DM (Dp=0.03 and 0.1), and EMM models were used, after which MRTs were compared.

Stable isotopes (δ2H and δ18O), the components of the water molecule that record the atmospheric conditions at the time of recharge (Batlle-Aguilar et al., 2017; Chen et al., 2003), provide valuable information on groundwater recharge processes (Ma et al., 2017; Stumpp and Małoszewski, 2010; Stumpp et al., 2009). Generally, there are two possible meteoric recharge sources including precipitation in the modern climate and in the paleoclimate. Groundwater whose isotopic values are more depleted than the modern precipitation would usually be ascribed to one or both of two recharge sources, including snowmelt or precipitation at higher elevation and precipitation that fell under cooler climate conditions. Figure 5 shows that the markers of groundwater isotopes are generally distributed along the LMWL but do not define evaporation trend, implying that little evaporation and isotope exchange between groundwater and the rock matrix have occurred (Ma et al., 2018; Négrel et al., 2016). Transpiration is likely to be dominant over evaporation in the soil when infiltration takes place, as soil water uptake by root is not significantly isotope fractionated (Dawson and Ehleringer, 1991).

Three groundwater clusters can be identified in the δ2H–δ18O plot (Fig. 5), suggesting different recharge sources among the upstream, midstream, and downstream areas. The first group of UG has the average δ2H and δ18O values of -68.24 ‰ and -10.08 ‰, respectively. Figure 5a shows that UG is located much closer to the summer rainfall, which reflects more enriched summer rainfall inputs in the upstream area of the Manas River. Negligible evaporation trends are observed in UG, although the recharge is mostly from the fast river leakage in the intermountain depression through highly permeable pebbles and gravel deposits (Fig. 1c). Furthermore, the detectable CFC concentrations and high 3H activity (Table 1) also indicate a modern precipitation recharge. An overlap between surface water and UG indicates the same recharge sources, because some alignment of river water and groundwater isotopic values is a qualitative indication of recharge under climate conditions similar to contemporary conditions (Huang et al., 2017).

The second group has the average δ2H and δ18O values of -73.10 ‰ and -11.0 ‰, respectively, which overlap with the annual amount-weighted mean rainfall isotopic value from MG. Such isotopic values are comparable to the modern annual amount-weighted mean rainfall δ2H and δ18O values (-74.7 ‰ and -11.0 ‰, respectively; Fig. 5a); it probably reflects annual modern precipitation recharge. The mixing of different timescale recharges of variable isotopic values at different aquifers and sites along the groundwater flow paths is another explanation for the highly scattered MG isotopic values in the δ2H–δ18O plot (Fig. 5b). Groundwater isotopes in the piedmont plain are relatively rich in heavy isotopes (Fig. 5b), which overlap with the river water, and indicate fast river leakage recharge within a short time (Ma et al., 2018). Groundwater isotopic values in the oasis plain diverge from those in the piedmont plain (Fig. 5b) and do not align with surface water, indicating recharge with longer flow paths rather than fast river leakage recharge.

The third group, which is most depleted in heavy isotopes (-82.36 ‰ and -12.03 ‰), is from DG and is located much closer to the winter rainfall in the δ2H–δ18O plot (Fig. 5b). Studies (Ji, 2016; Ma et al., 2018) have shown that vertical recharge from the winter rainfall in the downstream area is unlikely. As precipitation recharge from high altitudes (Clark and Fritz, 1997) and paleo-meteoric recharge during the cooler climate (Chen et al., 2003) could collectively account for the depletion of isotopes in groundwater, it is usually not easy to distinguish the precipitation recharge sources at a higher elevation from paleo-meteoric recharge. However, precipitation in the north Tian Shan (Fig. 1a) has a positive isotope altitude gradient due to the moisture recycling (Kong and Pang, 2016); thus sub-cloud evaporation effects will yield more enriched isotopes from higher-altitude precipitation recharge. The isotopically enriched UG (Fig. 5b) in the intermountain depression with higher altitude (Fig. 1c) is recharged from the high mountains. This also demonstrates that DG is unlikely to be from the high mountain recharge. Accordingly, its depleted isotopic values (Fig. 5b) are attributed to the paleo-meteoric recharge in a cooler climate. In the last glacial period, temperatures in the Xinjiang region (Li et al., 2015) and North China Plain (Chen et al., 2003) were cooler by approximately 10 and 6–9 ∘C, respectively, compared with the present day. Groundwater had a depleted δ18O value of -12.0 ‰ from the paleo-meteoric recharge in the arid northwest of China, such as in the Minqin basin (Edmunds et al., 2006), as well as in the east (Li et al., 2015) and west (Huang et al., 2017) Junggar Basin (Fig. 1a).

Table 1 shows that groundwater with well depths of 13–150 m contained detectable CFC concentrations (0.17–3.77 pmol L-1 for CFC-11, 0.19–2.18 pmol L-1 for CFC-12, and 0.02–0.38 pmol L-1 for CFC-113) in both the upstream and midstream areas, indicating at least a small fraction of young groundwater components (post-1940). The highest concentration is observed in the UG (G3), south of the fault. The median and the lowest concentrations are observed in the west and east banks, respectively, of the East Main Canal in the MG, north of the fault. In the midstream area (Fig. 2), CFC concentrations generally decrease with well depth south of the reservoirs (G25, G8, and G9), and increase with well depth north of the reservoirs (G15 and G16), which may indicate different groundwater flow paths (e.g. downward or upward flow directions).

The groundwater aerobic environment (Table 1; DO values from 0.7 to 9.8 mg L-1) makes CFC degradation under anoxic conditions unlikely. Nevertheless, CFC-11 has shown a greater propensity for degradation and contamination than CFC-12 (Plummer et al., 2006b); therefore we use CFC-12 to interpret the modern groundwater recharge in the following discussions. The estimated CFC partial pressure and possible recharge year are shown in Table 2 and Fig. 3. The UG (G3) CFC-113 and CFC-12 both indicate the 1990 precipitation recharge (Table 2), most likely as a piston flow recharge in the upstream area. The MG CFC-11-based modern precipitation recharge is in agreement with that based on CFC-12 concentrations within 2–8 years, whereas the CFC-113-based recharge is as much as 4–11 years later than that of the other two, signifying recharge of a mixture of young and old groundwater components in the midstream area. The most recent groundwater recharge is in the upstream area (G3 with 1990 rainfall recharge), which is most likely because the flow paths from recharge sources here are shorter than those of the piedmont groundwater samples in the midstream area.

G5 and G7 are located in the east bank of the East Main Canal in the midstream area and are closer than G15 and G16 north of the reservoir, showing that the modern recharge is much earlier than that of G15 and G16 (Table 2). This can be explained by the lower groundwater velocities in the east bank of the East Main Canal, where the hydraulic gradient (Fig. 2) is much smaller than that in the west. Furthermore, groundwater recharge south of the reservoir (G25, G8, and G9) becomes much earlier with increasing well depth from 48 to 100 m, whereas that north of the reservoir becomes much later with increasing well depth from 23 to 56 m (G15 and G16; Table 2, Fig. 2). The different trends for the relationship between groundwater recharge year and well depth may be due to the different flow paths between the two sites.

Comparing CFC concentrations helps to identify samples containing young (post-1940) and old (CFC-free) water (Han et al., 2007, 2012; Koh et al., 2012) or exhibiting contamination or degradation (Plummer et al., 2006b). The cross-plot of the concentrations for CFC-113 and CFC-12 (Fig. 7a) demonstrates that all of the groundwater can be characterised as binary mixtures between young and old components, though there is still room for some ambiguity around the crossover in the late 1980s (Darling et al., 2012). As shown in Fig. 7a, all of the MG samples were located in the shaded region, representing no post-1989 water recharge. The UG (G3) sample is clearly relatively modern and seems to have been recharged in 1990 through piston flow or mixed with old water and post-1995 water. Using the method described by Plummer et al. (2006b) with the binary mixing model, the fractions of young water are found to vary from 12 % to 91 % (Table 2) for the MG samples with the relatively low young fractions of 12 % and 18 % in the MG samples from the east bank of the East Main Canal (G5 and G7). These two well water tables are deeper than 40 m, suggesting a relatively slow and deep circulated groundwater flow. This hypothesis is also suggested by the lower DO (3.7–4.6 mg L-1; Table 1) and nitrate concentrations (8.6–9.5 mg L-1 from Ma et al., 2018), and the considerably smaller hydraulic gradient (Fig. 2). Furthermore, a fraction of young water as high as 100 % is obtained from the G3 sample with the recharge water from 1990, and an 87 % fraction is obtained from the binary mixture of post-1989 water and old water (Table 2). The relatively modern recharge for the G3 sample is likewise supported by its high DO (9.8 mg L-1; Table 1) and relatively low nitrate concentration (7.9 mg L-1 from Ma et al., 2018), which represents the contribution of high-altitude recharge rather than old water.

CFC contamination and sorption in the unsaturated zone during recharge considerably influence the interpretation of groundwater recharge. Points off the curves in the cross-plot of CFC concentrations may indicate contamination with CFCs from the urban air during sampling (Carlson et al., 2011; Cook et al., 2006; Mahlknecht et al., 2017) or the degradation or sorption of CFC-11 or CFC-113 (Plummer et al., 2006b). Figure 7 demonstrates that CFC contamination from the urban air, which generally increases CFC concentrations above the global background atmospheric CFC concentrations for the Northern Hemisphere, are unlikely. Elevated CFC concentrations have been reported in the air of urban environments such as Las Vegas, Tucson, Vienna, and Beijing (Barletta et al., 2006; Carlson et al., 2011; Han et al., 2007; Qin et al., 2007), but not in the arid northwest of China (Barletta et al., 2006). Hence, the anomalous ratios of CFC-11 / CFC-12 (Fig. 7b) off the model lines may be attributed to sorption in the unsaturated zone during recharge but not the degradation of CFC-11 (Cook et al., 2006; Plummer et al., 2006b) under anoxic conditions (Table 1; DO values vary from 0.7 to 9.8 mg L-1). Nevertheless, the small deviations (Fig. 7b) indicate a low sorption rate. A higher CFC sorption rate occurs with high clay fraction and high organic matter in soils (Russell and Thompson, 1983), and vice versa (Carlson et al., 2011). Therefore, the hypothesis of a low sorption rate due to the low clay fraction and low organic matter content in the intermountain depression and the piedmont plain (Fig. 1c) is reasonable.

The time lag for CFC transport through the thick unsaturated zone (Cook and Solomon, 1995) and degradation (especially as CFC-11 is common in anaerobic groundwater; Horneman et al., 2008; Plummer et al., 2006b) are both important considerations when interpreting groundwater recharge using CFC concentrations. The time lag for CFC diffusions through the deep unsaturated zone in simple porous aquifers, a function of the tracer solubility in water, tracer diffusion coefficients, and soil water content (Cook and Solomon, 1995), have been widely proved (Darling et al., 2012; Qin et al., 2011). The small differences in CFC-11 and CFC-12 recharge years (Table 2) demonstrate that the time lag should be short in the fault-influenced hydraulic drop alluvium aquifers with the deep unsaturated zone (Fig. 1c). Studies on the MRB (Ma et al., 2018; Zhou, 1992) have shown that groundwater is mainly recharged by fast river leakage in the upstream area and piedmont plain, where the soil texture consists of pebbles and sandy gravel (Fig. 1c). This suggests that the unsaturated zone air CFC closely follows that of the atmosphere, so the recharge time lag through the unsaturated zone is not considered.

Groundwater recharge was determined using 14C activity in groundwater for time intervals from centuries to millennia (Custodio et al., 2018), and 3H has been used for modern precipitation recharge, especially during the nuclear bomb periods (Cook et al., 2017; Huang et al., 2017). Groundwater 3H activity varies from 1.1 to 60 TU (Fig. 4 and Table 1), with the highest value in UG (G4), followed by MG (mean 12.4 TU) and DG (mean 4.5 TU). All of the 3H values in UG (G1, G2, and G4) and G23 (belonging to MG) are higher than 34.3 TU, which indicate input of some fractions of the 1960s precipitation recharge. Groundwater with 3H activity lower than 5.6 TU contains some pre-1950s recharge.

Both 3H and 14C activities show large variations with the distance to the mountainous region along groundwater flow paths in the midstream area (Fig. 8), suggesting recharge over a mixture of short to long timescales. Two different trends for the distribution of 3H activity with distance to the mountainous region (Fig. 8) from the upstream to midstream areas are observed. First, in the upstream area an increase in 3H activity with distance is seen from 41.1 (G1 and G2) to 60 TU (G4), indicating a larger fraction of 1960s precipitation for G4 than for G1 and G2; indeed, as seen in Fig. 2, near-G4 samples exhibited the highest hydraulic gradient values. Second, 3H activity in groundwater in the midstream area show an obvious reduction trend along the Manas River from 37.5 (G23) to 1.1 TU (G14), indicating that more fractions of pre-bomb precipitation recharge may have occurred along the groundwater flow direction north of the fault. Furthermore, 14C activities in the MG show small increases with distance (Fig. 8) from 43.4 to 54.6 pMC, with the exception of sample G12 at approximately 54 km (86.9 pMC with a 14C age of -684 years; modern recharge; Table 1), whereas that in the DG decrease to 23.5 pMC. The presence of detectable 3H (2.9–6.91 TU) in DG with low 14C values (23.5–34.3 pMC) indicates that some mixing with post-bomb precipitation recharge may have occurred.

Combined use of CFCs and 3H may help to resolve even more complicated recharge features due to the large difference of the temporal pattern in the input functions between CFCs and 3H. Compared with plots of tracer ratios, tracer–tracer concentration plots have some advantages because they reflect more directly the measured quantities and potential mixtures (Plummer et al., 2006b), such as mixing with irrigation water (Han et al., 2012, 2015; Koh et al., 2012) or young water mixtures in different decades (Han et al., 2007; Qin et al., 2011). The plot of 3H vs. CFC-12 (Fig. 9; CFC-11 and CFC-113 can substitute for CFC-12) shows that some samples (G9, G15, and G20) are slightly above the piston flow line, whereas in Fig. 7a they are away from the piston flow line but on the binary mixing lines. G15 and G20 have the shallowest well depths of 23 and 13 m, respectively. The G9 sample was collected from the piedmont plain near Manas River (Fig. 2), which features pebbles and sandy gravel deposits. This situation may be explained by (i) binary mixing between post-1989 water and older water recharged between 1950 and 1970 that did not contain CFC-free water (pre-1940), or (ii) mixing of two end-members with one end-member containing various mixtures of young (but pre-1989) and old water and the other having post-1989 water. The second explanation requires samples to contain at least some post-bomb fractions from the 1960s (revealed by 3H activities; Fig. 9) and both post-1989 and pre-1940 water, which is not consistent with CFC data (Fig. 7a). If the first explanation is true, the binary mixing hypothesis and the young water (post-1940) fractions in Table 2 for these three samples should be adjusted accordingly.

Because atmospheric 3H activities have been elevated for a long time, old water components can be identified by 3H activities that are anomalously low compared with those of CFCs (Plummer et al., 2006b). The G5 sample contains very low CFC-113 with a 3H concentration of 3.8 TU (Table 1), indicating that this sample is likely a mixture of the older water (pre-1940) and 1960–1970 water. The low 3H concentration can be attributed to dilution by a high fraction of old water, and thus the “3H bomb peak” cannot be recognised. The G16 sample, outside of the shaded region (Fig. 9), has low 3H but a substantial CFC concentration. This situation may be explained by (i) exposure to the atmosphere before sampling during large water table fluctuations due to groundwater pumping or the addition of excess air to water through the fractured system, or (ii) river water or reservoir water with high CFC concentration but minimal 3H recharge. Furthermore, the relatively high fraction of young water (89 %; Table 2) precludes the dilution effect by old water. Irrigation re-infiltration can cause a shift of CFC concentrations to higher values but does not alter the 3H concentration (Han et al., 2015). However, the relatively low NO3- concentration (4.51 mg L-1; data from Ma et al., 2018) of the G16 sample suggested that irrigation re-infiltration did not have a significant effect. Therefore, river or reservoir water with very low NO3- concentration (2.7–7.3 mg L-1; data from Ma et al., 2018) recharge is possible.

Residence time distribution functions (Eqs. 3 to 5) are suited to several specific hydrogeological situations (Małoszewski and Zuber, 1982). EPM is particularly useful for the interpretation of MRTs in aquifers that have regions of both exponential and piston flow (Cartwright et al., 2017). The unconfined aquifers adjacent to the rivers (Fig. 1c) are likely to exhibit exponential flow, and the recharge through the unsaturated zone (Fig. 1c) will most likely resemble piston flow (Cartwright and Morgenstern, 2015; Cook and Böhlke, 2000). For the time series of 3H and CFCs inputs, MRTs (Fig. 10) are initially calculated using EPM, with an EPM ratio of 1.5 obtained using Eqs. (2) and (3) (lE in Eq. (3) is determined by adding the intermountain depression to the piedmont plain in Fig. 1c). But the river leakage and rainfall input could have come only from the piedmont plain (Ma et al., 2018); thus a smaller proportion of piston flow in the EPM could give an EPM ratio of 2.2 (lE in Eq. (3) would only be for the piedmont plain in Fig. 1c). The veracity of MRTs is tested by Eqs. (2), (4), and (5) using the DM (DP=0.03 or 0.1) and the EMM. Plots of the output concentrations for 3H (Fig. 10a) and CFCs (CFC-11 in Fig. 10b, CFC-12 in Fig. 10c, and CFC-113 in Fig. 10d) vs. MRTs for different lumped parameter models show that the range of MRTs are wide and correspond positively to the increase in MRTs.

Figure 11 presents MRTs determined from the time series of 3H and CFC inputs using different lumped parameter models. MRTs obtained from different lumped parameter models tend to become more discretised with the increase in the MRTs themselves. On the other hand, MRTs estimated from the EPM with an EPM ratio of 1.5 in Fig. 11a vary from 19 to 101 years (median: 51 years) for the CFC-12 rainfall input, 33 to 115 years (median: 62.3 years) for the CFC-11 rainfall input, and 18 to 92 years (median: 50.2 years) for the CFC-113 rainfall input. Good linear relationships for MRTs between the different CFCs rainfall inputs are obtained using the same EPM (EPM 1.5 in Fig. 11a and EPM 2.2 in Fig. 11b). MRTs increase when the EPM ratios decrease from 2.2 to 1.5 in Fig. 11b, implying that the groundwater flow paths recharged from the intermountain depression are much longer. MRTs in the UG, the west and east banks of the East Main Canal of MG are estimated from the different lumped parameter models with different CFC-12 concentrations in Figs. 2 and 11b. The mean values of MRTs in the UG and the west bank of the East Main Canal of MG vary from 28.6 to 64.8 years, and in the east bank of the East Main Canal of MG vary from 129.2 to 173 years. It is seen that the mean values of MRTs in the east bank of the East Main Canal of MG have larger differences than those in the UG and in the west bank of the East Main Canal of MG (see Figs. 2 and 11b, and Table 2). Overall, the youngest value is observed in the G3 sample on the south side of the fault, and the oldest value is observed in the G5 sample on the east bank of the East Main Canal in Fig. 2.

It is seen from Fig. 11 that MRTs determined from the time series of 3H inputs have larger uncertainties and wider ranges than those from CFCs. For EPM with an EPM ratio of 1.5, MRTs estimated from the time series3H inputs vary from 19 to 158 years with a median of 112.2 years (Fig. 11c), which are much longer than those calculated from the CFCs inputs by the same model (Fig. 11b). The reason is that the travel times through the thick unsaturated zone for 3H are much longer than those for CFCs. 3H moves principally in the liquid phase, whereas CFCs travel in the gas phase through the unsaturated zone (Cook and Solomon, 1995). The transport in the gas phase is more rapid than that in the liquid phase in the unsaturated zone, which is expected to give rise to longer residence times from 3H than those determined from CFCs (Cook, et al., 2017). Furthermore, the ranges of MRTs estimated from EPM, DM, and EMM are 16–158 years, 72–285 years, and 30–360 years, respectively. The uncertainties will increase when MRTs increase among different models, especially for MRTs that are higher than 130 years (Fig. 11c), which mainly exist in the DG and the east bank of the East Main Canal of MG.

Groundwater MRTs in the west bank of the East Main Canal show an overall increasing trend with the distance to the mountain in MG and DG (Fig. 11b, c). It has been proven that much longer as well as much deeper flow paths usually give rise to much longer MRTs (Cartwright and Morgenstern, 2015, 2016; McGuire et al., 2005). On the other hand, groundwater MRTs in the east bank of the East Main Canal are much longer than those in the west bank. As shown in Fig. 2, this phenomenon can partly be ascribed to the relatively short distance to the mountain and much smaller hydraulic gradient in the west bank. Previous studies pointed out that groundwater MRTs would vary on account of the interplay of factors, like the uncertainties of the input concentrations and different models (Cartwright and Morgenstern, 2015, 2016), and mixing and dispersion in the subsurface flow systems. Moreover, the assumption of the homogeneous aquifer with a simple geometry may result in significantly different MRTs that are calculated by lumped parameter models to the actual MRTs (Cartwright et al., 2017; Kirchner, 2016; Stewart et al., 2017). Nevertheless, the homogeneous aquifers, being at steady state, justify the use of lumped parameter models to calculate MRTs in this study.

Strong correlations between hydrochemical components and groundwater age permit their use as proxies for, or complementary to, age via previously established relationships in similar lithological conditions. For example, an excellent correlation between silica (SiO2) and MRTs (R2=0.997) has been reported (Morgenstern et al., 2010), which was much better than in Fig. 12 and in other results (Morgenstern et al., 2015). SiO2 (Fig. 12a), sulfate (SO42-), bicarbonate (HCO3-), and TDS (Fig. 12b) all show good correlations with groundwater age, indicating that mineral dissolutions through water–rock interactions dominate hydrochemical changes (Ma et al., 2018), and major ion concentrations increase with groundwater age. However, MRTs determined by the time series of 3H inputs show poor correlations with the ions (data not shown). Moreover, the lithology type that the groundwater flows through within the aquifer and the likely evolutionary path ways play important roles in the hydrochemical compositions. The negative saturation indices with respect to gypsum (Ma et al., 2018) indicate that the high SO42- concentrations (Fig. 12b) are due to gypsum dissolution in the Tertiary stratum. It is also of note that high SO42- can originate from geothermal water (Morgenstern et al., 2015), in contrast to studies such as Guo et al. (2014) and Guo et al. (2017), and can be biased due to anoxic SO42- reduction. However, the groundwater in this study have relatively low temperatures and aerobic environment (Table 1), making the two cases above unlikely.

The combination of hydrochemistry concentrations and groundwater age data is also a powerful tool for investigating the groundwater flow processes and flow-through conditions (McGuire and McDonnell, 2006; Morgenstern et al., 2010, 2015), and for identifying the natural groundwater evolution and the impact of anthropogenic contaminants (Morgenstern et al., 2015; Morgenstern and Daughney, 2012). The pH of the groundwater decreases from 10.1 to 8.6 over the age range from 19 to 101 years, with a log law fit of pH =0.72×ln⁡MRTs+11.85, R2=0.65 (Fig. 12a). In contrast, a trend of increasing pH with increasing groundwater age has been reported in New Zealand (the dashed red line shown in Fig. 12a; Morgenstern et al., 2015), where pH values were all less than 7.2. These two discrepant trends can be explained by the relationship between pH and HCO3- concentrations in water (inserted plot in Fig. 12a). The pH increases with increasing HCO3- concentration only when the pH is less than 8.34; otherwise it decreases with increasing HCO3- concentrations. Therefore, the trend of increasing HCO3- concentrations with increasing groundwater age (Fig. 12b) in this study supports the decreasing trend for the pH (from 10.1 to 8.6).

The soda waters with an overall pH higher than 8.1 (Table 1) are in disequilibrium with primary rock-forming minerals of the host rocks. The incongruent dissolutions of the albite and anorthite through hydrolysis reaction are as follows: 2NaAlSi3O8+11H2O=Al2Si2O5(OH)4+2Na++4H4SiO4+2OH-CaAl2Si2O8+3H2O=Al2Si2O5(OH)4+Ca2++2OH-, where all chemical components of albite and anorthite are released into the solution phase and produce OH- with simultaneous precipitation of kaolinite. A trend of increasing pH with well depth (Table 1) suggests that groundwater whose pH is lower than 9 is likely recharged by CO2-containing water, because OH- generally interacts with CO2 and organic acids in the soil to form HCO3- (Wang et al., 2009). Similarly, the trend of decreasing pH with increasing MRTs (Fig. 12a) indicates that groundwater with much longer MRTs contains much higher CO2 concentrations, which seems to suggest an anthropogenic input. The nitrate (NO3-) concentrations vary from 4.5 to 20.2 mg L-1 with a median of 12.2 mg L-1 (data not shown), which exceed the natural nitrate concentration in groundwater of 5–7 mg L-1 (Appelo and Postma, 2005). The development of the plough after the 1950s, N–NO3 fertiliser (with low 87Sr/86Sr ratios; Ma et al., 2018), and the extensive groundwater withdrawal for irrigation (Ji, 2016) suggest that irrigation infiltration can account for the high groundwater NO3- concentrations in the piedmont plain. On the other hand, little irrigation infiltration was observed in the downstream area with groundwater NO3- concentrations of less than 5 mg L-1 (Ma et al., 2018) due to the water-saving irrigation style, which does not contribute to groundwater recharge in the arid northwest of China.