1 Introduction

The surface water and groundwater resources are limited and unevenly distributed in time and space in the Loess hilly region, where the climate is predominantly arid and semi-arid. Even so, groundwater is, in some regions, the only freshwater source for the production and life of the inhabitants, such as drinking water and irrigation water (Xia et al., 2008). However, due to the insufficient precipitation and the high evapotranspiration in this area, groundwater recharge rate tends to be relatively low (Scanlon et al., 2010), while unreasonable abstraction of groundwater continues to occur. The overexploitation of groundwater compared to its renewal and recharge rate will cause the fast depletion of groundwater, thereby threatening the ecological restoration as well as the production and life of the residents. The sustainable management of groundwater resources must, therefore, requires an accurate quantitative analysis of groundwater recharge mechanism (Shen et al., 2015). It is nonetheless particularly difficult to provide a quantitative estimate of groundwater recharge given its relatively low rate in the region.Various methods have been used in previous studies to conduct an in-depth exploration of the groundwater recharge mechanism in this region. Zhu et al. (2009a; 2010b) quantitatively estimated the groundwater recharge ratio and the residence time of Wuding River Basin in the Loess Plateau, based on the water withdrawal analysis method. Gates et al. (2011) estimated the impact of land use on groundwater recharge in the Loess Plateau using a tracer method combining chloride ion, stable hydrogen and oxygen isotopes. They concluded that concentrated water infiltration in gullies and other low-lying areas was the main groundwater recharge mechanism in this region. Hui et al. (2015) evaluated the effect of reforestation on groundwater recharge in the Loess Plateau by applying the RHESSys model.
The hydrogen and oxygen isotope tracers have been widely used to examine groundwater recharge in arid and semi-arid regions due to the numerous advantages this technique presents (Emam et al., 2015; Qin et al.,2011). Amongst these advantages, these tracers do not interact with other substances in the water molecule migration process, they directly participate in groundwater circulation, they do not pollute the environment, and they can track long-term groundwater movements. Regional water cycle and the mixing process of multi-terminal water body could be traced by measuring δ D and δ 18O in precipitation, soil water and groundwater in order for some of the main hydrological processes to be revealed, which include the precipitation composition, infiltration, evaporation, migration (Kendall; Tan et al., 2016). Peng et al.(2005) investigated the effect of vapour water from the continental evaporation on hydrogen and oxygen isotopes composition in precipitation based on hydrogen and oxygen isotope tracer method. Liu et al.(1995) explored the seasonal soil water movement in the top meter of undisturbed desert soil in the southern Arizona using δ D and δ 18O, the results indicate repeated seasonal cyclic movement of soil water mainly occurred in the top layer of 60–80 cm. Several previous studies have applied the hydrogen and oxygen isotope tracer method in the groundwater research field. For example, the seasonal recharge pattern of the Huanlia river basin in Taiwan, China was quantitatively analysed by Yeh et al. (2014) using the hydrogen and oxygen isotope tracer technique. Earman et al. (2006) used these tracers to explore the groundwater recharge characteristic caused by snowmelt in the southwest of the United States. Thoma et al. (1979) calculated the amount of groundwater recharge by atmospheric precipitation through the analysis of the seasonal variation of δ 18O in the atmospheric precipitation in Pelat dune, Israel. However, because of a lack of temporal water monitoring data of hydrogen and oxygen isotope, The mechanisms governing loess groundwater recharge in such a climatic and topographic environment still remain unclear (Tan et al., 2016). Existing studies in this field mainly focused on the analysis of groundwater source and recharge mechanism (Xiang et al., 2019; Tan et al., 2017; Zhi et al., 2017). Limited studies have focused on the spatial-temporal distribution characteristics of groundwater recharge in a small watershed of this region.
Water transmission time refers to the time-lapse that water molecules have experienced from when they enter the small watershed system until they leave it. The transmission time could not only reveal some information about the water storage, the flow path and the water source but is also closely related to some of the internal hydrological processes in the watershed (Sivapalan, 2010; Mcguire et al., 2004). Numerous studies have investigated water transmission time in small watersheds. Asano et al. (2002) calculated the mean water transmission time of precipitation to groundwater in Rachdani region using the index of δ D, which was equivalent to a year. LEE et al. (2007) evaluated the water residence time at different depths of soil layers in Puji Island, South Korea, using deuterium surplus. Their results showed that the mean residence time at 30cm and 60-80cm depths were about 74 and 198 days, respectively. However, due to the Loess Plateau, China is predominantly covered by loess deposits ranging from 30 to 80 m in thickness (Wang et al., 2010), there is a slower groundwater recharge rate and the recharge period can be up to several decades, hundreds of years or even longer in the process of groundwater recharged by rainfall through unsaturated loess layers (Huang et al.,2013; Lin and Wei, 2006). Few studies have explored water transmission time in the Loess Hilly Region for relatively concealed water flow path and the insufficiency temporal monitoring data of isotope.
In this study, over 17 months in the Zhifanggou watershed and over 7 months in the Bangou watershed of stable D and O isotope composition monitoring were performed in precipitation, surface water and groundwater in the Loess hilly region. The results could provide a basis for the scientific research and rational development and utilisation of groundwater resources in this region. Therefore, the overall objectives of this study were threefold: (1) to analyze the spatial-temporal variation characteristics of hydrogen and oxygen isotopes in different water bodies at small watersheds in the Loess hilly region, and identify the main recharge sources of groundwater; (2) to quantitatively estimate the recharge ratio and the water transmission time of precipitation and surface water to groundwater in the small watershed; (3) uncover the temporal and spatial distribution model of groundwater recharge in small watershed of the Loess hilly region.