2 Materials and methods

2.1 study area

The study was conducted in the Zhifanggou watershed (36°43′-36°46′N,109°14′-109°16′E) and the Bangou watershed (36°46′-36°44′N,109°24′-109°26′E), in Ansai county on the northern Loess Plateau of China (Fig. 1). The Zhifanggou watershed is the first branch of the lower reaches of the Xingzi River, a tributary of the Yanhe River. The area of the watershed is 8.27 km2, with a narrow and long north-south direction. The watershed has a continental monsoon season climate. The mean elevation is 1425-1041 m, the annual mean temperature is 8.8 °C, the annual mean evaporation is 1463 mm, the annual mean precipitation is approximately 549.1 mm, which is unevenly distributed in the year and can vary considerably from one year to another. The land consists of loessial soil, mainly consisting of silt (0.002-0.05mm). The terrain is broken, and the density of the gully is 8.07 km/km2. Groundwater mainly consists of water flowing in the quaternary alluvial aquifer and the fissured shallow weathering crust, with a mean depth of 13 m. The Bangou watershed (36°46′-36°44′N,109°24′-109°26′E) is located at 14.60 km east of the Zhifanggou watershed and belongs to the first-grade tributary of the Yanhe River. The watershed area is 6.56 km2 with a mean elevation of 1268-1055 m and annual mean precipitation of approximately 534.7 mm. The soil type is mainly loessial, and the mean depth of the phreatic surface is 12 m. The climate type and the hydrogeological conditions of the Bangou watershed are similar to those of the Zhifanggou watershed, but its gully is cut deeper, and the aquifer is more fragmented.

2.2 sampling and analysis

The water sampling point of precipitation, surface water and groundwater were set up in each part of the gully head, upperstream, middlestream and downstream in the Zhifanggou watershed, respectively. Likewise, water sampling point of precipitation, surface water and groundwater were set up in each part of the upperstream, middlestream and downstream in the Bangou watershed, respectively. The elevation, the longitude and the latitude were recorded using a hand-held GPS. The specific sampling points were shown in Fig.1. Form June 2016 to October 2017, three water bodies in the Zhifanggou watershed were continuously sampled at intervals of 15 days. Similarly, three water bodies in the Bangou watershed were sampled from June April to October 2017 at similar intervals. Each sampling was repeated twice, and the samples were sent to the laboratory of water resources research institute, Xi’an University of Technology once the sample collections were completed. All samples were tested for δD and δ18O using DLI-100 liquid isotope laser analyser LGR-LWIA (Los Gatos Research Inc., USA). Sampling methods for each water body were as follows:
Precipitation sampling: an open area was selected near each sampling point, and rain measuring cylinder with of type J16022 was set up to collect precipitation samples. About 8 milliliters of liquid paraffin oil was previously applied to the rainwater collector to prevent water evaporation. During sampling, the water below the paraffin oil layer was extracted with a 15 mL disposable syringe. The collected precipitation samples were filled in 10 ml brown glass reagent bottles, which were tightened and sealed with Membrane seal film. After the collection completed, the water collector was cleaned up, and the liquid paraffin oil reapplied. All the samples were refrigerated at 4 °C. The stable isotope was after that tested to ensure the reliability of the test results. According to statistics, 312 precipitation samples were collected during the experiment.
Surface water sampling: surface water sampling points were set up at the bottom of the gully, near the precipitation sample point. During the collection, the sample bottle was inserted 20 cm below the surface of the water to prevent the influence of evaporation fractionation. The collected surface water samples were filled in 10 ml brown glass reagent bottles, tightened and sealed with Membrane seal film. The samples were after that refrigerated at 4 ℃, before the stable isotope was tested. According to statistics, 312 surface water samples were collected during the experiment.
Groundwater sampling: the sampling of groundwater consisted of withdrawing water from the bottom of a well up to the surface using a bucket, and quickly placing it in a cool place. The sampling and refrigeration methods were similar to those applied in the case of the surface water. Since there were only one groundwater well in the Zhifanggou watershed laocated in the mouth part of this watershed, which is used as a drinking water source, so as to only one groundwater sampling point was set up in the mouth of this watershed. A total of 76 groundwater samples were collected. In the case of the Bangou watershed, three groundwater sampling points were set up. The groundwater sample in upperstream corresponded to seepage water from the rock formation, and groundwater samples in the middlestream and downstream were from wells. A total of 56 groundwater samples were collected.

2.3 Analysis methods

2.3.1 Estimation of water transmission time
A large number of studies showed that the annual (seasonal) isotope characteristics of precipitation, surface water and groundwater followed a certain periodicity, which can be characterised by sinusoidal regression analysis of the following form:
δ=X+A*cos(ct-θ) (1)
where δ corresponds to δ D, δ 18O or d-excess; X is the annual mean of δ D,δ 18O or d-excess; C is the fluctuation frequency of δ D, δ 18O or d-excess (0.017214rad·d-1); T is the time, and θ is the lag time.
The mean water transmission time (T) in the water circulation system is as follows:
T=C-1[(Az2/Az1)-2-1]0.5(2)
Where Az1 is the amplitude of the input signal; Az2 is the amplitude of the output signal; C is the fluctuation frequency of δ D, δ 18O or d-excess (0.017214rad·d-1).
2.3.2 Quantitative estimation of groundwater recharge
The MixSIAR statistical package (Stock and Semmens, 2013) is a general Bayesian framework that was used to quantify the contributions of the different flows relative to the total groundwater recharge. It has been widely used in sourcing plant water, pollutants, soil carbon and in food-web studies. In this study, only two end members were considered: precipitation and surface water (as described in Section 3.1). As for groundwater, the water isotopes of different samples were considered independent consumers (input) as they were collected from different sites. The error structure was set to default, “Resid*Process” and the Markov Chain Monte Carlo length was set to “short” for better predictions of the probability distributions of the sources (e.g. precipitation and surface water). Because there was no prior information, the “Uninformative”/Generalist was selected in this framework. After running MixSIAR, a check diagnostic was conducted according to Stock and Semmens (2013) to confirm the validity of the output (contributions). Finally, the mean values of the runs were considered as the most likely proportions of contributions, and the standard deviation was considered as the uncertainty (Xiang et al., 2019)(Fig. 2).