Characteristics of δ¹⁸O and δ²H and their implication for the interaction between precipitation, groundwater and river water in the upper River Tuojiang, Southwest China

‘Isotope’ refers to an element with the same number of protons and different numbers of neutrons; they can be divided into radioisotopes and stable isotopes. With the development of measurement technology, the stable isotope has been widely applied and developed in different fields and plays an important role, especially in the study of food, chemistry, biology and hydrology, etc. (Meitinger et al. 2014; Stout et al. 2014; Zhao et al. 2014; Xia et al. 2019a). The research and application of the stable isotope in hydrology began in the 1950s. Craig (1961) proposed the global meteoric water line (δ²H = 8δ¹⁸O – 10) by analysing the oxygen and hydrogen isotopic compositions (δ¹⁸O and δ²H) in different waters all around the world; then, Dansgaard (1964) gave a definition to the deuterium excess (d-excess = δ²H −8δ18O); Gat (1996) found that when the ocean or other water bodies evaporate, they will undergo isotope fractionation, and the light isotopes in the water will escape first, thus increasing the specific heavy isotopic content, resulting in the constant accumulation of heavy isotopes.

Due to the fractionation, natural stable isotopes in different waters have different composition characteristics and evolution laws and vary greatly at the spatial-temporal level. The natural stable isotope is viewed as the fingerprint of water, thus in some remote areas where hydrological data are insufficient, the isotope data can be studied as a way of supplementation. For example, Crawford et al. (2017) studied the isotopic composition of the precipitation of Macquarie Marsh in New SouthWales, Australia, and found that a large portion of the local precipitation comes from inland. Biggs et al. (2015) compared the isotopic compositions of four lakes in the arid region of the western Himalayas and found that lakes with a deeper depth have a greater evaporation ratio. With the development of modern industry and the increase in population, there is a growing demand for water resources. In some arid areas, water resources have already become a limiting factor for social development. So, the assessment of water quantity and quality appears important. The introduction of stable water isotopes as a tool for investigating storm hydrographs in a watershed started in the late 1960s (Crouzet et al. 1970). In the past 30 years, changes in oxygen and hydrogen isotopic compositions (δ¹⁸O and δ²H) in watershed water have been proved to be able to identify the water source and hydrological paths under different flow conditions (Ogrinc et al. 2008, 2018; Zhao et al. 2011). Subsequently, the method was widely applied in various regions by many researchers; for example, Vasil'chuk et al. (2017) studied the contribution of snow meltwater, precipitation and groundwater to the runoff in different seasons of the Dzhankuat R. glacier. It was found that a considerable portion of Dzhankuat R. total runoff in June originated from spring snowfall, while in August and September, the contribution of runoff is mainly from groundwater, snow and glacial meltwater. Liu et al. (2008) performed hydrograph separation analysis on the Heishui River and its tributaries in the upper reaches of the Yangtze River by stable isotopes. The result shows that the base flow in the Heishui River Basin is mainly derived from snow and glacial melt water. Zhao & Li (2017) found by analyzing stable isotopes that with the increasing distance from the Yellow River, the supply from the Yellow River decreases and the supply from groundwater increases in the rivers in the Dezhou region. The interaction between precipitation, surface water, and groundwater plays an important role in the elaboration of water cycle mechanisms, which are of great significance in scientifically developing and managing water resources. However, it is difficult to investigate this cycle process by traditional methods (Hao et al. 2019). The stable oxygen and hydrogen isotopes are ideal conservative tracers to provide insight for investigating this cycle process as they are components of water molecules and remain unchanged except in instances of water phase changes or isotope fractionation in the hydrological cycle. In recent years, the pollution problems of lakes and rivers such as the Tuojiang River and Lake Taihu have become more and more serious (Chen et al. 2020a). Estimating the mean residence time and evaporation of lakes and rivers by analyzing stable isotope values can provide some insightful suggestions to understand the pollution situation and the renewal rate of water. By studying the stable isotope values of water in more than 1,000 lakes in the United States, Brooks et al. (2014) found that the lake water chemistry has a strong correlation with evaporation and a poor correlation with residence time, and the evaporation capacity of lakes with a good biological state is weaker than lakes with a poor biological state.

Located in southwest China, the Sichuan Basin has varied and complicated topography, a low-lying West and a high East. It is the source area of many important tributaries of the Yangtze River. Affected by multiple monsoons, complex water vapor source, and unique geographical and climatic characteristics, a complicated water circulation mechanism is observed in this region. Previous studies on the stable isotope in Sichuan Basin mainly were on the hydrological mechanism of mountain rivers and changes in rainfall isotope under the influence of monsoon (Xia et al. 2019b, 2019c). Isotopic study of the rivers in the Chengdu Plain is still rare. Furthermore, previous studies on the evaporation and replenishment of natural water bodies in the Plain are quite limited in both the sampling frequency and the duration of time. The mutual replenishment mechanism between different water bodies has been analyzed in many past studies (Yeh et al. 2010; Banks et al. 2011; Martinez 2015). However, few studies focused on tributary replenishment to the mainstream. The Tuojiang River is a typical river affected by human activities with complex water sources and seriously polluted water, flowing through densely populated and industrial areas. From May 2018 to April 2019, the authors conducted a one-year continuous sampling and measurement of isotopes in river water and groundwater along the upper reaches of the Tuojiang River. It provided high-precision isotope data for river water and groundwater as well as an important supplement to the isotope data set of the Tuojiang River Basin. The main purposes of this paper are: (1) to understand the variations of stable isotopes in rivers, precipitation, and groundwater in the upper reaches of the Tuojiang River Basin; (2) to identify the interaction between the river, groundwater, and precipitation in the upper reaches of the Tuojiang River Basin; (3) to obtain the contribution ratios of tributaries' recharge to the mainstream of the Tuojiang River; (4) to calculate and compare the MRT (mean residence time) of the mainstream of the Tuojiang River and its tributaries. The results of this paper will prove the usefulness of stable isotopes for separating components of the hydrological system and indicating the potential pollution situation in medium catchments with complicated sources and serious pollution problems.

Tuojiang River is an upstream tributary of the Yangtze River (104 °E ∼ 105.5 °E, 29 °N ∼ 31.5 °N) (Figure 1). The Tuojiang River has five different tributaries in its upper reach. The upper tributaries include the Yazi River, Shiting River and Mianyuan River. These three tributaries flow southward and merge into the mainstream of Tuojiang River in Jintang County. The middle tributaries include the Pihe River and Qingbai River. The Qingbai River drains into the Pihe River before entering into Tuojiang River. The Qingbai River and Pihe River are derived from the Minjiang River system; thus, the water source of the Tuojiang River is complicated. The Tuojiang River has a total length of 712 kilometers and a drainage area of 32,900 square kilometers. The study region of this paper mainly includes the upper part of the Tuojiang River. The Tuojiang River Basin is located in a humid monsoon region with annual mean precipitation about 1,200 mm. Annual precipitation amount in the middle part of the river tends to be low (800 mm) and annual precipitation amount in the northwest mountains is much higher (1,300 mm). The Tuojiang River has a distinct dry and wet season, and the precipitation in the wet season accounts for more than 80% of the annual total (Figure 2).

Water samples in the study area were collected from May 2018 to April 2019. During the wet season (May-October), the sampling was performed at a weekly frequency, and in the dry season (November-April), the sampling was performed at a bi-weekly frequency. A total of 30 sampling activities were conducted, with 714 samples overall, including 117 groundwater samples, 597 river water samples and 102 precipitation samples. A total of 20 sampling sections were laid in the study area, of which 16 were river water sampling sections and four were groundwater sampling sections. The sampling locations and names are shown in Table 1.

The water samples collected from the upper reaches of the Tuojiang River include surface water, groundwater, and precipitation. The surface water samples were collected from the mainstream of the Tuojiang River and its four tributaries. The river water was collected in a one-liter plastic bottle, which was connected to a rope, and the river water 20 cm below the surface was selected via measuring the length of rope. Groundwater samples were pumped from residential wells along the Tuojiang River, which comes from a Quaternary phreatic aquifer with a depth of 5–20 metres. Because of the logistical limitations, it was difficult to collect the high-frequency precipitation in the study area. Therefore, the precipitation data collected from the State Key Laboratory of Hydraulics and Mountain River Engineering of Sichuan University were employed instead. The shortest distance between the precipitation sampling point (104.08 °E, 30.63 °N) and the Tuojiang River is 38 kilometers. The precipitation sampling device was made with reference to the recommended method of the Global Precipitation Isotope Network (GNIP) (http://www-naweb.iaea.org/napc/ih/IHS_resources_gnip.html).

In this equation, A_Z1 is the amplitude of rainfall, A_Z2 is the amplitude of river water and c is the radial frequency of the annual amplitude of Equation (5).

The detailed process of each model can be seen as follows (Figure 3).

Based on the stable isotope data of precipitation in Chengdu from May 2018 to April 2019, the temporal variations of δ¹⁸O and δ²H in precipitation are investigated. The isotopic composition of precipitation can be highly variable. The negative values for δ¹⁸O and δ²H are throughout the whole year and the d-excess value is positive. Isotopic contents range from −12.01 to −0.83 ‰ for δ¹⁸O, from −85.95 to −0.99 ‰ for δ²H and from 7.42 to 22.28 ‰ for d-excess. Average values for the stable isotope in precipitation in the catchment are δ¹⁸O=−6.45 ‰, δ²H=−38.93 ‰ and d-excess= 13.35 ‰ (Table 2). A significant seasonal variation of the isotope in precipitation is observed. In the wet season (May to October), precipitation shows depleted isotopes and fluctuates greatly. In detail, the average δ¹⁸O, δ²H and d-excess values of precipitation are −8.45 ‰, −56.49 ‰, and 11.14 ‰ respectively. Its isotope value decreases from May to July and increases from July to October. The extremely low δ¹⁸O and δ²H values are observed in July (δ¹⁸O = − 12.01‰, δ²H = − 85.95 ‰) (Figure 4). In the dry season (November to April), the isotope values gradually enrich from November to April and reach the maximum in February (δ¹⁸O = − 0.83 ‰, δ²H = − 0.99 ‰). The average δ¹⁸O, δ²H and d-excess values of precipitation are −4.05 ‰, −17.85 ‰, and 15.56 ‰, respectively.

In the wet season, the isotope value of precipitation shows a wide variation range and obviously precipitation amount effect (i.e. isotope value shows a reverse trend with precipitation amount). This phenomenon is also observed in other regions in China and shows the same trend in the wet season (Ma et al. 2016; Wan et al. 2018). In this region, we found that extreme precipitation events are also reflected in the isotopic composition of precipitation. According to the record, the total precipitation amount is 556 mm in July. The extremely low δ¹⁸O and δ²H values in July may be related to the extremely high precipitation amount caused by the East Asian monsoon and Indian monsoon in Sichuan (Yu et al. 2017). In the dry season, the relative humidity is low with a decrease in precipitation amount. During the precipitation process, the rainwater is easily influenced by evaporation before reaching the ground. As a result, the isotope kinetic fractionation effect occurs and enriches the isotope values in precipitation. Another reason for the different isotope values in precipitation between δ¹⁸O and δ²H are the sources of water vapor. To prove that, the d-excess, which is affected by the relative humidity in the water vapor source area and could be used for indicating the source of water vapor (Jouzel & Merlivat 1984; Bershaw et al. 2020), is investigated. The d-excess value of precipitation in the dry season is higher than that in the wet season. Usually, the d-excess value is low in the water vapor from the low latitude ocean surface, which leads to a low d-excess value in the precipitation. On the contrary, water vapor from arid areas will lead to a high d-excess value in the precipitation (Shi et al. 2020). Chengdu belongs to the East Asian monsoon region where air masses are mainly derived from the low latitude ocean in the wet season. In the dry season, water vapor mainly comes from the arid inland areas in the west. This is consistent with the finding of other precipitation studies in Southwestern China (e.g. Zhang et al. 2008; Hu et al. 2018).

In all river water, its isotope values show a medium variation range comparable to that of precipitation and groundwater. Specifically, the annual δ¹⁸O, δ²H and d-excess values in all river water vary from −12.06 to −6.37 ‰, −81.94 to −46.81 ‰ and −5.62 to 24.41 ‰ respectively. The temporal variation in δ¹⁸O and δ²H of all river water also show a similar season variation like that in precipitation (Figure 4). The isotopic composition of river water decreased from May 2018 to August 2018 and increased from September 2018 to April 2019. This variation indicates river water in the Tuojiang river catchment is recharged by precipitation and the isotopic characteristics of precipitation are inherited. In the wet season, the average δ¹⁸O, δ²H and d-excess values of all river waters are −9.77 ‰, −68.65 ‰, and 9.15 ‰ respectively. The δ¹⁸O and δ²H values of all river waters in the wet season are larger than those of river water in the dry season. This variation is in contrast to our expectation that the isotope-depleted precipitation input to river water will lead to lower δ¹⁸O and δ²H value of river water in the wet season than that of the dry season. The possible reason is that in Tuojiang River Basin, the river mainly receives more isotope-depleted groundwater in the dry season, which leads to the depleted isotope value of river water relative to that of the wet season. By comparing the isotope value between river water and groundwater (Figure 4), it can be found that the isotopic composition of river water in winter (December to February) is close to that of groundwater in autumn (September to November). It is indicated that the groundwater stored in autumn recharges river water in winter. The variation in the isotopic composition of river water collected from four tributaries are investigated (Table 1 and Figure 5).

Among the four tributaries of Tuojiang River, the average δ¹⁸O and δ²H values are in the order of the Mianyuan River ( − 9.05 ‰, −62.51 ‰) > Shiting River ( − 9.35 ‰, −65.38 ‰) > Yazi River (−10.04 ‰, −69.65 ‰) > Pihe River ( − 10.84 ‰, −76.3 ‰). In August 2018, an increasing trend in δ²H values of four river waters is observed, but δ¹⁸O values show a decreasing trend in Yazi River, Mianyuan River and Pihe River. However, the increasing δ¹⁸O and δ²H values of precipitation are observed in August compared with the previous month. It indicates that the opposite trends of stable isotope measurements of oxygen and hydrogen in river water are not the result of precipitation input but the replenishment effect of depleted-isotope ice and snow meltwater. Because of the influence of equilibrium fractionation and kinetic fractionation at low temperature, the ice-snow meltwater contains a relatively depleted δ¹⁸O value and enriched δ²H value. Glacier water and snowmelt amount reach the annual peak in August at the headwater area, while the precipitation is significantly lower than that in July. The increase in the supply ratio of ice-snow meltwater to the river leads to the isotopic fingerprint of the ice-snow meltwater being observed in the downstream river water. The same phenomena are also found in the study of the Hailuogou river (Meng & Liu 2018) and the mountainous Bringi catchment of Kashmir Himalaya (Bhat & Jeelani 2018). In the Tuojiang River Basin, the δ¹⁸O and δ²H values of river water fluctuate along the river but are enriched generally. Generally, the source of the river is in the mountainous area. Affected by the precipitation amount effect and temperature effect as it has a high rainfall and low temperature, the isotope value of the upstream river water is low. Instead, in the downstream of the river, the isotope value of the river water increases along the river due to the evaporation enrichment effect (Ogrinc et al. 2008; Zhao & Li 2017). The decrease in δ¹⁸O and δ²H values are due to the inflow of the Minjiang River into the Tuojiang River (Wu et al. 2020) (Figure 6). The study of the Heishui River in the upper reaches of the Minjiang River shows that even in the rainy season, the main supply source of the Minjiang River water is meltwater. So the isotope values of Minjiang River water are generally depleted compared with those of Tuojiang River (Liu et al. 2008). Moreover, S2, S4 and T4 are river junctions, affected by the inflow of isotope-depleted river water, the isotope values of the river water decrease after the junctions.

The groundwater from the upper reaches of the Tuojiang River contains a relatively small magnitude of variations. Its δ¹⁸O, δ²H and d-excess values range from −10.46 to −6.12 ‰ for δ¹⁸O, from −71.43 to −43.93 ‰ for δ²H and from −16.41 to 1.33 ‰ for d-excess. The average values of δ¹⁸O, δ²H and d-excess are −8.34 ‰, −59.81 ‰, −6.92 ‰, respectively. In the wet season, the average values of δ¹⁸O, δ²H and d-excess are −8.18 ‰, −58.63 ‰ and −6.77 ‰, compared with the values of −8.55 ‰, −61.29 ‰ and −7.11 ‰ in the dry season, respectively. The isotope value of groundwater is enriched in the wet season and depleted in the dry season, and it is enriched compared with the river water in the same period (Table 2). The average value of δ¹⁸O in the wet season is only 0.37 ‰ away from the dry season, which suggests that the groundwater is relatively stable between the wet season and dry season, resulting from the long-term recharge of surface water and precipitation. The isotope variation ranges of groundwater (δ¹⁸O are −10.46 to −6.12‰ and δ²H are −71.43 to −43.93 ‰ ) is within the range of river water (δ¹⁸O are −12.06 to −6.37 ‰ and δ²H are −81.94 to −46.81 ‰) and precipitation (δ¹⁸O are −12.01 to −0.83 ‰ and δ²H are −85.95 to −0.99 ‰). Its temporal variation trend is basically the same as that of precipitation and river water, indicating that groundwater is recharged by precipitation and river water simultaneously. The relatively small isotope variations of groundwater reflect the retention effect of groundwater, which is not obvious over time. Comparing Figure 4 (a)–4(d), it can be seen that the isotopic composition of groundwater throughout the year is very nearly to that of river water. This phenomenon indicates that the groundwater may exchange frequently with river water and the river water is the major recharge source of groundwater rather than precipitation. The well we collected groundwater sample is close to the river bank. In this region, there are close hydraulic relations between groundwater and river water. The isotopic composition of groundwater and river water provides evidence for this close hydraulic relation (Shamsuddin et al. 2018). This close hydraulic relationship among groundwater and river water will be weak with the increase in the distance to the river (Zhao & Li 2017; Kong et al. 2018).

Craig (1961) found a linear relationship between δ¹⁸O and δ²H in precipitation by analyzing the stable isotopic compositions of oxygen and hydrogen in different water bodies around the world and proposed a global meteoric water line equation (GMWL): δ²H = 8δ¹⁸O + 10. According to the Rayleigh fractionation model, stable isotopes of hydrogen and oxygen in water are enriched and depleted in the process of water distillation. The kinetic effect in fast evaporation can disturb the above-mentioned parallelism between the δ¹⁸O and δ²H variations, resulting in different relationships between δ¹⁸O and δ²H values of precipitation in different regions (i.e. the slope and intercept of the local meteoric water line (LMWL) are different). For example, Lide & Yao (2001) obtained LMWL from north to south Delingha, Tuotuohe and Lhasa on the Tibet Plateau, in which δ²H = 8.47δ¹⁸O + 15.2 (R² = 0.98), δ²H = 8.21δ¹⁸O + 17.46 (R² = 0.967), δ²H = 7.90δ¹⁸O + 6.29 (R² = 0.97). Ansari et al. (2020) obtained the LMWL of Mumbai which is given by δ²H = (8.90 ± 0.5) δ¹⁸O + (10.5 ± 0.9) (r = 0.95). Based on the weighted average δ¹⁸O and δ²H values of monthly precipitation during the study period, the LMWL equation in Chengdu is calculated as δ²H = 8.394δ¹⁸O + 15.3 (R² = 0.98, P < 0.01). Its slope and intercept are slightly larger than the GMWL. This may be attributed to the fact that Chengdu belongs to the Sichuan Basin, with an annual rainfall of 1,000 mm–1,300 mm and low evaporation. Most of the precipitation is concentrate in the wet season and the meteoric water line equation for the wet season is δ²H = 8.2522δ¹⁸O + 13.277 (R² = 0.99, P < 0.01), which is closer to the slope and intercept of the GMWL. The meteoric water line equation for the dry season is δ²H = 7.8157δ¹⁸O + 13.837 (R² = 0.879, P < 0.01). Its slope and intercept are smaller than those of the rainy season and the LMWL (Figure 7).

Most of the isotopic data collected from groundwater are located between the LMWL and river line (RL) (Figure 8), which indicates that groundwater is mainly recharged by river and precipitation throughout the year. The intersection of the RL and the LMWL can reveal the average isotopic composition of the precipitation entering the river. According to the intersection points of the SL in the wet season and LMWL, and the intersection points of the SL in the dry season and the LMWL, it is found that the δ¹⁸O and δ²H values at the intersection points are close to the δ¹⁸O and δ²H values of precipitation in July, August and September. It indicates that most of the river water in both wet and dry season comes from the precipitation in July, August and September. Precipitation has a seasonal lag in the recharge of the river. The precipitation in the wet season is divided into two parts, one part is directly transferred into the river through the overland flow, and the other part is stored in a shallow aquifer by interflow. On the seasonal scale, the GL in the wet season lies between the LMWL and the RL in the wet season and the slope of the GL in the wet season is close to that of the wet season RL. It indicates that the groundwater is mainly recharged by the river water during the wet season. The slope of the GL during the dry season is close to that of the wet season and the slope of the RL in the wet season is relatively larger than the slope of GL in the dry season. It suggests that the groundwater in both the dry season and wet season mainly comes from the replenishment of river water during the wet season and has experienced evaporation to some extent.

The Tuojiang River catchment has developed industries and frequent irrigation activities, so there is a large demand for water resources. There are close hydraulic relations among precipitation, river water, and groundwater. Quantifying the process of precipitation and river water recharge to groundwater in different periods is important to manage and utilize water resources in the catchment. However, the interactions among precipitation, river water and groundwater in the upper reaches of the Tuojiang River have not been investigated in detail in previous studies. The isotope value and GL of groundwater are both between those of precipitation and river water, indicating that groundwater is recharged by precipitation and river water together. Then, seasonal changes in groundwater sources are further calculated based on δ²H and δ¹⁸O data (Table 3).

In spring and autumn, results calculated by δ²H and δ¹⁸O both show the recharge from river water is higher than precipitation. In Spring, the temperature rises lead to the melting of snow and ice in the headwater region. This increases the amount of water coming from upstream of the river, thus leads to the increase of the lateral recharge from river water to the groundwater. A similar recharge ratio of precipitation and river water to groundwater is observed between spring and autumn. This is because of the precipitation amount in the Tuojiang River region during the spring (March to May) and autumn (June to April). In autumn, the results calculated by ¹⁸O and ²H are beyond our expectation that a different trend is observed in oxygen and hydrogen isotopes. Autumn is the season of rice maturity, local residences pump well or river water for irrigation. During this process, the evaporation of water ponded after irrigation increases, resulting in non-equilibrium fractionation. The concentrations of ¹⁸O and ²H in water change to different degrees. The distinct variation trend between δ²H and δ¹⁸O in groundwater from August to October proved this process. In summer, the recharge ratio of precipitation to groundwater increases significantly and surpasses the river water. Influenced by the water vapor transported by the southwest and southeast monsoon, the precipitation amount and frequency increase significantly. Heavy precipitation falls on the catchment and recharges the groundwater by interflow. During the winter, because of the influence of Mongolia High, this region is controlled by the dry cold terrigenous water vapor carried by the inland monsoon. The precipitation amount and temperature decrease, which results in decreasing precipitation and meltwater from the upstream. As a result, the value of the river stage reduces. When the river level is lower than the adjacent groundwater level, the groundwater no longer accepts the supply from the river. Groundwater in winter mainly consists of two components, namely groundwater stored in Autumn and replenishment of precipitation in winter. This result is contrary to the conclusion that the groundwater in the Pihe River still accepts river water during winter (Chen et al. 2020b). This is because of the existence of the Dujiangyan Irrigation Project in the upper reaches of the Pihe river. This regulates the water resource of the Pihe River, thus maintaining the river level. In the whole year, the fraction of precipitation recharge to groundwater is consistent with the variation trend of the precipitation amount. It means that the groundwater responds harmoniously to precipitation in the upper reaches of Tuojiang River. The fraction of river water recharge to groundwater is significant all year round except for winter. In winter, because the Tuojiang River water significantly decreases and its pollutant discharge, the concentration of organic matter is seriously over standard. Rational use of groundwater to recharge river water may help to relieve the pollution problem in the Tuojiang River. Given the uncertainty in measure δ²H and δ¹⁸O concentrations, we calculate how this uncertainty is propagated into our result by using Equation 4. The result (Table 3) shows the uncertainty W_f is small and cannot affect the accuracy of our calculated result. Comparing the W_f of δ²H and δ¹⁸O, it can be seen that the uncertainty of δ¹⁸O is higher than δ²H, though both are small. This may indicate that using the end-member mixing model by δ²H will obtain a more accurate result. Compared to the results of other studies (Meng & Liu 2016; Chen et al. 2020b) using the same model in southwest China, the result shows a similar trend. Distinct isotopic compositions of precipitation, river water, and groundwater are observed and it is possible to use the end-member mixing model based on isotope data. The results all show the same variation trend with precipitation and different variation trends between the wet and dry season. This indicates that precipitation shows strong seasonal variation in southwest China and this variation will also be reflected in other water bodies like groundwater and river water.

To better understand the seasonal variations in the water sources of the Tuojiang River, a dual-end member mixing model based on ²H data is used in each section to calculate quantitatively the contribution rate of each tributary volume over the total river. The results show that in the spring, the contribution rate of the tributaries to the Tuojiang River is in the order of Pihe (65.6%) > Yazi River (21.3%) > Shiting River (7.5%) > Mianyuan River (5.6%). In summer, the order of contribution rate of each tributary to the Tuojiang River is Pihe River (63.8%) > Yazi River (20.2%) > Mianyuan River (12.7%) > Shiting River (3.3%). In autumn, the order is Pihe River (43.4%) > Mianyuan River (29.3%) > Shiting River (17.4%) > Yazi River (9.9%). In winter, the contribution rate of the Yazi River and Shiting River is less than zero (Table 4).

This is because the water quantity before and after the river confluence is assumed to be in balance and fully mixed when using the end-member mixing model. However, this assumption is not completely accurate for most rivers due to the difference in water flow conditions, which brings about deviation from the actual situation. The division ratio can't be negative, so the calculation result of winter is taken as zero here. Therefore, the Mianyuan River and Pihe River contribute 54.5% and 45.5% to Tuojiang River in winter, respectively. Among the four tributaries of the Tuojiang River, the Pihe River has the largest contribution rate to the Tuojiang River, and the ratio is higher in spring and summer, lower in autumn and winter. The Shiting River contributes the least to the Tuojiang River. Its minimum value is only 3.28% in summer, but its contribution in autumn is more significant. The contribution rate of the Mianyuan River to Tuojiang River water volume varies significantly throughout the year. The contribution ratio of the Mianyuan River is small in spring and summer, while the contribution ratio is large in autumn and winter. The contribution of the Yazi River to Tuojiang River is relatively stable among the three seasons of the year. These results indicate that the Mianyuan River and Pihe River have a higher contribution rate to the entire Tuojiang River. Compared to the Mianyuan River, the variation in contribution ratio of the Pihe River to the Tuojiang River is stable. The reason is the regulating effect of the existence of the Dujiangyan Irrigation Project in the upper reaches of the Pihe river. This indicates that the water conservancy project is useful to manage the water resource in the river. The Tuojiang River is a river with serious pollution problems and its water resource shortage is severe = in dry winters. Thus, building a water conservancy project is an effective measure to maintain the river level in the dry season and relieve the pollution problem.

MRT is a basic descriptor for the basin, which reflects the water storage capacity, flow path and water source information. The MRT value is directly related to the internal process of the basin. The distribution of the MRT describes how the watershed maintains and releases water and solutes, thus controlling the biogeochemical cycle and the migration of pollutants. Therefore, it is important to study MRT for water resources management and environmental protection in the basin (Sivapalan 2003). In this study, δ¹⁸O seasonal trends in precipitation and river water can be qualitatively used to fit seasonal sinusoidal waves to simulate annual δ¹⁸O changes in the river water and precipitation. During the sample period, the model A_z1 = 5.577 ‰ described the precipitation data well (R² = 0.54). The simulated δ¹⁸O values of river water are well described in the Mianyuan River (R² = 0.33) and Pihe River (R² = 0.32). Especially in Tuojiang River mainstream (R² = 0.46), Yazi River (R² = 0.56) and Shiting River (R² = 0.47), the simulated δ¹⁸O values of river water have a good correlation with actual values (Figure 9).

The estimated annual amplitude of simulated δ¹⁸O in river water is lower than that of precipitation. The results of these simulations are then converted to an estimate of the water MRT by Equation (6). The MRT of the Tuojiang River is estimated to be 1.07 years, which is similar to the MRT of the Shiting River (1.02 years) and Yazi River (0.92 years). While the MRT of Mianyuan River and Pihe River are relatively long, with estimated values of 1.49 years and 1.35 years respectively (Table 2). The δ¹⁸O value of river water is mainly controlled by the seasonal rainstorm runoff (freshwater) and stable groundwater (older water). So MRT can indicate the mixing degree of different sources, thus providing a valuable overall assessment of the differences in runoff processes in the Tuojiang River Basin as well as the management and regulation of water resources in the Tuojiang River. The MRT can also reflect the storage volumes of basin reservoirs to some extent. In the areas with low groundwater storage, the MRT is usually shorter (Małoszewski et al. 1983). The MRT of the Tuojiang River mainstream is 1.07 years, which is relatively short, indicating that there is not much groundwater storage in the basin. This can be attributed to the fact that the type of groundwater in the Tuojiang River Basin is mainly loose rock pore water. Its aquifer lithology is mainly gravel pebbles and silt pebbles, with strong permeability, small thickness and average water yield. MRT of each tributary of Tuojiang River varies greatly, ranging from 0.95 to 1.49 years. The MRT difference of these tributaries is due to the influence of topographical, geological and soil conditions and other factors. For example, Dewalle et al. (1997) compared the hydrological characteristics of two forest watersheds, West Virginia (WV 34–39 hectares) and Pennsylvania (PA 1134 hectares). Then, Dewalle et al. (1997) found that the mean transportation time of the base flow is longer for watersheds with smaller slopes. Rodgers et al. (2005) found that in the Feshie River Basin of the Cairngorm Mountains in Scotland, the MRT values are shorter in the headwater area covered with peat and shallow plateau soils, while longer MRT is observed in other tributaries with free-draining soil on the surface and larger groundwater storage in shallow aquifers. Along the flow path of Tuojiang River, the MRT of each tributary is gradually increasing, with the order of Yazi River < Shitingjiang < Pihe River < Mianyuan River. This result is in contrast to the result found in the Mandava catchment (Soulsby et al. 2010). The upper reaches of Tuojiang River Basin have steep slopes in mountain areas, while the middle reaches are described as gentle plain. Considering the cumulative effect of aquifers along the river flow path and the existence of older groundwater recharge, the MRT values of tributaries from the upper reaches to the lower reaches show an increasing trend. The shortest MRT is 0.95 years in Yazi River, where the δ¹⁸O annual variation reaches the largest with a lower annual average δ¹⁸O value. The shortest MRT and the close isotope value between Yazi River and precipitation both reflect that the Yazi River is greatly affected by rainfall. The MRT of Shiting River is relatively short, which could be attributed to more middle and upper Pleistocene peat cover in this basin, which makes it respond quickly to the input of precipitation. Moreover, after a storm, runoff can carry large amounts of pollutants into the river, causing the deterioration of river water quality. Therefore, when designating environmental protection, we should pay attention to the sensitivities of the two rivers, Shiting River and Yazi River, to pollutants. The MRT of Pihe River and Mianyuan River are both long. A long MRT means that the input of rainfall takes a long time to flow into the river channel through the watershed, which also means that rainfall has a longer biochemical reaction time with the river basin (Burns et al. 2003). On the other hand, the Pihe River and Mianyuan River contribute a large proportion to the water volume of the Tuojiang River. Therefore, we should conduct a water resources plan and environmental protection management according to the specific conditions of different tributaries of the Tuojiang River.

• Isotopic composition of precipitation, groundwater, and river water show strong seasonal variation, enriching in the dry season and depleting in the wet season. Isotope variation between wet and dry season reflect the different water vapor source in the different seasons. Extreme precipitation events can be reflected in the isotopic composition of precipitation. The δ¹⁸O and δ²H values of the tributaries of the Tuojiang River are in the order of the Mianyuan River > Shiting River > Yazi River > Pihe River. Along the flow path, the isotope value of river water is gradually enriched and fluctuates in the river junction.

• Compared with the local meteoric water line in the wet season, the slope of the dry season is small, which indicates the precipitation in the dry season is affected by evaporation. The intersection of the RL and the LMWL indicated the majority of river water in the wet and dry seasons both come from the precipitation in July, August and September.

• Based on the isotopic composition of river water and precipitation, the relative contribution of river water and precipitation to groundwater is calculated. The results show that river water is the main source of groundwater and precipitation is the auxiliary source of groundwater throughout the year. In winter, groundwater receives little external recharge. Groundwater replenishes river water, which plays an important role in maintaining river stability and meeting ecological water demand. Therefore, we should be rational in development and employment of groundwater in the upper reaches of the Tuojiang River, especially in winter.

• The contribution of the tributaries to Tuojiang River water volume varies significantly with different space and time. The contribution of the Pihe River is the largest, reaching 65.6% and 63.8% in spring and summer, respectively, while that of the Shiting River is the smallest.

• The MRT of the Tuojiang River, Yazi River, Shiting River, Mianyuan River and Pihe River are 1.09, 0.95, 1.03, 1.49 and 1.35 years, respectively. The MRT of the river is both controlled by groundwater (older water) and precipitation (freshwater), thus the shorter MRT of the Tuojiang River Basin indicates that the groundwater storage is relatively low in Tuojiang River Basin. The MRT of the Yazi River and Shiting River is relatively small compared to other tributaries. Therefore, these two rivers respond quickly to rainfall, which makes it easy for a large number of pollutants to flow into the river and thus threatens the water environment. This study further proves the usefulness that the hydrological characteristics can be investigated and the environmental sensitivity can be evaluated by using stable isotopes even in a medium catchment with a complex source. It also provides a valuable application for calculating MRT by stable isotope in a medium catchment.

This research was funded by the China Scholarship Council (CSC) (No. 201806245015).

Data cannot be made publicly available readers should contact the corresponding author for details.