3 Results

3.1 Spatial and temporal variation characteristics of hydrogen and oxygen isotopes in water

The values of the hydrogen and oxygen isotope characterisation from June 2016 to October 2017 for different water bodies in the Zhifanggou watershed are shown in Table 1. In different water bodies, the δ D and δ 18O of groundwater was most depleted (-64.95, -9.04 ‰),followed by surface water (-60.80, -8.20 ‰) and then the precipitation was most enriched (-52.12, -7.74 ‰). The hydrogen and oxygen isotope characterisation values from April to October 2017 for the precipitation, the surface water and the groundwater in Bangou watershed are shown in Table 2. The hydrogen and oxygen isotopes of each water body in this watershed follow a similar lawpattern as in the Zhifanggou watershed, i.e. the precipitation isotope was the most abundant with the highest variation coefficient, while the groundwater isotope was the most depleted, with a relatively stable isotope.
At the same time, the hydrogen and oxygen isotopes in the different water bodies exhibited a certain spatial variability. In different parts of the Zhifanggou watershed, The δ D of precipitation in the upperstream was most depleted (-53.49‰), followed by
stream (-43.81‰), then the gully head (-43.12‰) , and the δ D of precipitation in the downstream was most enriched(-36.11‰). Theδ 18O of precipitation in the upperstream was most depleted(-7.72‰), followed by gully head (-6.55‰), then the middlestream (-6.46‰), and theδ 18O of precipitation in the downstream was most enriched(-5.43‰). The δ D of surface water in the downstream was most depleted (-62.55‰), followed by gully head (-61.01‰), then the upperstream (-60.95‰), and theδ D of surface water in the middlestream was most enriched (-57.55 ‰). The δ 18O of surface water in the downstream was most depleted (-8.46 ‰), followed by upper stream (-8.09 ‰), then the gully head (-8.03 ‰), and the δ 18O of surface water in the middlestream was most enriched (-7.64 ‰).
On the other hand, the δ D of precipitation in the downstream of the Bangou watershed was most depleted (-39.85‰), followed by upperstream (-39.77‰), then the middlestream (-39.50‰). Theδ 18O of precipitation in the middlestream was most depleted (-6.07 ‰), followed by upperstream (-6.03 ‰), then the downstream (-5.83 ‰). The δ D and δ 18O of surface water in the upperstream of the Bangou watershed were most depleted (60.13, 7.63 ‰), followed by middlestream (57.93, 7.64 ‰), then the downstream (57.59, 7.16 ‰). The δ D andδ 18O of groundwater in the upperstream of the Bangou watershed were most depleted (-57.55, -7.93‰), followed by middlestream (-59.49, -7.44‰), then the downstream (-57.72, -7.39‰). In summary, the three water bodies were gradually enriched from upperstream to downstream in the watershed, but the difference was not significant. However, due to the influence of the watershed environment, the spatial characteristics of the hydrogen and oxygen isotopes in the surface water of the Zhifanggou watershed and the precipitation of Bangou watershed were not obvious.
The temporal variation characteristics of the hydrogen and oxygen isotopes in different water bodies of the Zhifanggou watershed are shown in Fig. 3. The hydrogen and oxygen isotopes of the precipitation exhibited the largest variation over time, and their δ D andδ 18O were the most enriched in May (-19.45, -3.11‰), and were more depleted in November and December (-94.65, -14.26‰). The δ D and δ 18O of the surface water were relatively stable from June to December 2016, and the fluctuations mainly occurred within the period January - August 2017. Their δ D and δ 18O were the most enriched in May (-19.45, -3.11‰) and were more depleted in February (-71.86, -9.39). The hydrogen and oxygen isotopes of the groundwater were relatively stable, with a δ D and δ 18O the most abundant in August (-61.15, -8.16‰), and the most depleted in March (-67.54‰) as well as in November (- 9.51‰). There was a lag time between the depletion peak of groundwater and the peak of precipitation and surface water, indicating that the groundwater recharge process by precipitation and surface water was mainly through piston flow, with a lower recharge rate and longer recharge period (Tan et al., 2016). The temporal evolution of the hydrogen and oxygen isotopes in the three water bodies of Bangou watershed is shown in Fig. 4. The depletion peaks of the precipitation, the surface water and the groundwater appeared in October in all cases. This indicates that there may be preferential flow channels for water flow in this watershed. Hence, precipitation could recharge groundwater faster, which induced a shorted recharge period. Therefore, there was a possibility that the piston flow and the preferential flow could jointly recharge groundwater in the Loess Hilly region (Xiang et al., 2019; Tan et al., 2017).
At the same time, the d-excess of the precipitation in the two watersheds was analysed. The results showed that the d-excess of the precipitation from June to October remained smaller than 10‰, which means that the precipitation water vapour mainly originated from marine air mass. Also, the d-excess from November to May exceeded 10‰, which indicated that the precipitation was mainly attributed to the continental air mass.

3.2 Analysis of groundwater recharge source

The relationship between the hydrogen and oxygen isotopes in the case of the precipitation in the Zhifanggou watershed was fitted for two periods, as shown in Fig. 5-a. The first period extended from November to May and the second period extended from June to October, The equation of the precipitation line wereδ D=7.50δ 18O+10.14, R2=0.98 andδ D=7.84δ 18O+5.64,R 2=0.96, in the first period and in the second period, respectively. The gradient of the precipitation line was smaller than that of the global atmospheric precipitation line (δ D=8δ 18O+10). Most of the groundwater hydrogen and oxygen isotope points fell on the precipitation fitting line from June to October. Away from the part of the surface water points that fell in the region where the groundwater was located, the rest of points were located at the lower right of the precipitation fitting line. The results indicated that the precipitation from June to October was the main recharge source for the surface water and the groundwater, and there was a possibility that surface water and groundwater could recharge each other. And the points of the surface water and the groundwater were all still located at the lower right of this line from November to May. This indicates that the surface water and the groundwater could be recharged by precipitation in this period, but its hydraulic connection with surface water and groundwater was weaker than during the period from June to October.
The fitting equation of the hydrogen and oxygen isotopes for the precipitation in Bangou watershed wereδD=7.42\(\delta^{18}O\)+8.11 (R2=0.99) andδD=6.72\(\delta^{18}O\)-2.62 (R2=0.96), from April to May and from June to October, respectively. The values of the gradient of these two lines were smaller than that of the global precipitation line. The points of the groundwater and the surface water were both located at the lower right of the precipitation fitting line from June to October, which indicate that the precipitation in this period was the main recharge source for the surface water and the groundwater in Bangou watershed. The region where the locations of the surface water and the groundwater points were coincident indicated that the connection between groundwater and surface water was closer in this period than during the period June-October. Also, this demonstrates that the mutual recharge of surface water and groundwater was more frequent.

3.3 Water transmission time

Sinusoidal fitting was performed for the hydrogen and oxygen isotopes in different water bodies of the Zhifanggou watershed in the period June 2016 - October 2017, as shown in Fig. 6. The results of δ D fitted showed that amplitudes of the precipitation and the groundwater were respectively 18.60‰ and 1.79‰, and the transmission time of the precipitation to groundwater estimated by the model was 510.06 d. Based on the results of δ 18O fitted, the transmission time of the precipitation to groundwater was 376.25 d (Table 3). Therefore, the mean transmission time of the precipitation to groundwater was 443.16 d. Table 4 shows the transformation time between surface water and groundwater in different parts of the watershed. The fitting results of δ D provide evidence that the transformation time of surface water to groundwater was 77.14 d, 55.37 d and 65.53 d, in the gully head, upperstream and middlestream, respectively. Also, the estimated result for the transformation time based on \(\delta^{18}O\)fitted was 64.68 d, 60.13 d and 63.88 d, in the gully head, upperstream and middlestream, respectively. Threrfore, the mean transmission time of surface water to groundwater was 70.91, 57.75 and 64.71 d in the gully head, the upperstream and the middlestream, respectively. The mean transmission time of surface water to groundwater in this watershed was 64.58 d, which was about 15% of the transmission time of the precipitation recharge to groundwater. In the downstream, the surface water was recharged by the groundwater. Based on the fitting results ofδ D and δ D18O, the transmission time of surface water recharged by groundwater were 55.26 and 49.53 d, respectively. The mean transmission time value was 51.10 d. This show that the downstream was the main groundwater discharge area in the small watershed. At the same time, the time of groundwater discharge to the surface water was similar to the time of surface water recharge to groundwater. This indicates that there might be a similar channel through which the groundwater and the surface water could recharge each other simultaneously.

3.4 recharge ratio of groundwater

Based on the Bayesian model, the mean groundwater recharge ratio by precipitation and surface water in Zhifanggou watershed were respectively 34.7% and 65.3%, from June 2016 to October 2017. From April to October 2017, the groundwater recharge ratio by precipitation and surface water in the Bangou watershed were 17.2% and 82.8%, respectively. In the Bangou watershed, the groundwater recharge ratio by precipitation was 22.5%, 6.8% and 14.1%, in the upperstream, middlestream and downstream, respectively (Fig. 7a). The groundwater recharge ratios by surface water were 77.5%, 93.2% and 85.9% in the upperstream, middlestream and downstream, respectively (Fig. 7b). The groundwater recharge ratio by precipitation in the gully head, upperstream, middlestream and downstream of the Zhifanggou watershed were 33.3%、32.7%、46.0% and 10.6%, respectively (Fig. 7a), and the recharge ratio by surface water were 66.7%、67.3%、54.0% and 89.4%, respectively (Fig. 7b). The groundwater ratio by precipitation from the upstream to the downstream in the small watershed gradually decreased, while the recharge ratio by surface water increased. These results show that the upperstream of the small watershed was the main recharge area of groundwater by perciputation. But there were two phenomenons that the groundwater ratio by precipitation in the middlestream of Bangou watershed decreased sharply compared with oter parts, and the ratio increased sharply in the middlestream of Zhifanggou watershed compared with other parts of the watershed. This phenomenon might be related to the regional situation such as topography and vegetation, and the location of the sampling points in the middlestream.
The study period from June to October was classified as rainy season since the d-excess value of precipitation was less than 10‰, and the period from January to May was classified as a dry season. The groundwater recharge ratio by precipitation and surface water in Zhifanggou watershed were estimated in the periods June-October and November- May(Fig. 8). Similarly, the groundwater recharge ratio by precipitation and surface in the Bangou watershed were estimated in the periods June-October and April-May, as shown in Fig. 8. In the rainy season (June-October), the values of the groundwater recharge ratio by precipitation were 37.65% and 28.00% in the Zhifanggou watershed, and the Bangou watershed, respectively (Fig. 8a), and the corresponding ratios by surface water were 62.35% and 72.00%, respectively (Fig. 8b). In the dry season (January-May), the values of the groundwater recharge ratio by precipitation were 24.60% and 8.30% in the Zhifanggou watershed, and Bangou watershed, respectively (Fig. 8a), and the corresponding ratios by surface water were 75.40% and 91.70%, respectively (Fig. 8b). In the rainy season, the values of the groundwater recharge ratio by precipitation were 1.53 and 3.37 times greater than in the dry season, for the Zhifanggou watershed and the Bangou watershed, respectively. These results evidence that the rainy season was the main season in which groundwater was recharged through precipitation. Also, the groundwater in the dry season was mainly recharged by surface water, where the ratio was about 1.21 and 1.27 times greater than in the rainy season, in the Zhifanggou watershed and the Bangou watershed, respectively.