Study of the Interaction between Yellow River Water and Groundwater in Henan Province, China

Abstract

Determining the interaction between surface water and groundwater is crucial for the protection of groundwater resources. Based on the data of natural geography, geological and hydrogeological conditions, environmental isotopes, and groundwater hydrochemical components, we investigated the interaction between Yellow River water and groundwater in Henan Province, China. The recharge range and interaction amount of the groundwater aquifer from the Yellow River lateral seepage were also analysed, and the influence of the lateral seepage of the Yellow River on groundwater hydrochemical type was studied. The results showed that, firstly the transverse seepage range of the north bank of the Yellow River was larger (approximately 20 km) than that of the south bank (approximately 10 km). The main groundwater recharge sources were atmospheric precipitation and the Yellow River, of which the latter accounted for 50.1%. Secondly, in Sections 1–4, the lateral seepage amounts in the north bank were 1476.94, 505.89, 40.88, and 65.7 m³/a·m, respectively. The single-width permeability of typical Section 2 was larger upstream than downstream and larger in the north than in the south. Thirdly, the lateral seepage of the Yellow River significantly influenced the hydrochemical types of groundwater. From upstream to downstream and from proximal to distal location from the Yellow River, the hydrochemical types changed from single to complex and the salinity increased gradually. Fourthly, the annual average lateral seepage groundwater recharge quantity of the Yellow River was 25,114.36 × 10⁴ m³/a between 2001–2019.

1. Introduction

Water is an important natural resource for maintaining ecological development [1]. In recent decades, water resource shortages have become a major factor restricting human development. With rapid economic development and population growth, the demand for water resources is increasing, resulting in a more prominent distinction between such demand and its supply [2], as well as the water cycle process and allocation of water resources [3]. It is of great theoretical and practical significance to study the interaction between surface water and groundwater, establish a water cycle model, study the formation of water resources, reveal the mechanism of the water cycle, and maintain ecosystem stability [4].

The interaction between surface water and groundwater is often accompanied by an exchange of material and energy. The research methods for the interaction relationship between surface water and groundwater include the use of flow gauging [5], base flow separation [6], hydrochemistry methods [7], and numerical modelling [8]. Different methods have different technical advantages and ranges of applications. The study of interactions is mostly determined by the groundwater flow field and environmental isotopes method, and the study of the conversion amount is mostly determined by the water balance method, numerical simulation, and environmental isotopes [9,10,11]. Among these methods, hydrochemistry and isotopic traces are suitable for identifying and quantifying the spatial and temporal patterns of surface water and groundwater interactions on a regional scale [12].

Hydrochemistry and stable isotopes, which are important components of surface water and groundwater, indicate the formation and evolution of water systems to a certain extent. The hydrochemical composition of the surface water and groundwater changes along the flow direction with migration distance. It can fully reflect the hydrochemical reaction of the water body in the process of migration and can judge the interaction and cyclic evolution characteristics of surface water and groundwater [13]. As an important part of atmospheric precipitation, hydrogen and oxygen isotopes can sensitively collect environmental changes, record water cycle information, and identify sources based on their content changes. Many studies have been carried out on the mutual interactions between surface water and groundwater. The International Atomic Energy Agency and World Meteorological Organization established a global precipitation isotope observation network in 1961 to continuously track and monitor the precipitation isotope ratio. Using hydrogen and oxygen stable isotope tracers, Chiogna et al. studied the recharge and discharge relationship between surface water and groundwater in the Vermiliana Basin, Italy, and determined the recharge sources and hydrological cycles of each water system [14]. The basic principles of hydrochemistry and isotopes use to determine the interaction between surface water and groundwater is the migration of solutes in water. Therefore, many scholars have studied the Heihe River, Malian River, Hailiutu River, Bayin River, and other regions by using hydrogen and oxygen isotopes and hydrochemistry as tracers and have conducted sufficient research on the water cycle of the basin and the interaction of surface water and groundwater [15,16,17]. Based on the composition and spatial distribution of hydrogen and oxygen isotopes, combined with hydrochemical characteristics, Sun et al. revealed the interaction relationship between surface water and groundwater and established a groundwater quality equilibrium equation to calculate the interaction between surface water and groundwater [18]. Although much research has been carried out on the interaction between surface water and groundwater, because it is affected by underlying surface conditions, aquifer types and other factors, the theoretical method of the interaction between surface water and groundwater needs further research.

The Yellow River Basin is a vast area and an important source of recharge for shallow groundwater. The groundwater system along the Yellow River was controlled by the hydrological system of the Yellow River, and the long-term water supply from the Yellow River alleviated the current situation of regional water resource shortages to a certain extent. Research on the recharge of groundwater by lateral seepage in the lower reaches of the Yellow River to the surrounding groundwater is of great practical significance to study the joint utilisation of river water and groundwater, control the groundwater level, and improve the utilisation efficiency and water productivity of lateral seepage in the Yellow River. Lin et al. calculated the base flow of several sections of the Yellow River and concluded that the unilateral seepage recharge of groundwater in the suspended reach of the Yellow River was 1500 m³/(km·d) [19]. Han et al. used hydrochemical and isotope methods to study groundwater circulation characteristics and finally used the Modflow-2000 numerical model to study groundwater circulation [20]. At present, the main research method for studying the interaction between surface water and groundwater in the Yellow River is the isotope method, which uses a combination of hydrodynamics, isotopes, hydrochemistry, and Darcy’s law. Therefore, this study determined the range of groundwater recharge by lateral seepage of the Yellow River using the groundwater dynamic field, environmental isotope method, and groundwater numerical simulation. Based on fundamental data such as isotopic data, analysis of the variation law of hydrogen, oxygen, and tritium isotopes in time and space, this paper discusses the interaction ratio of surface water and groundwater, uses Darcy’s law to calculate the typical sections of the lateral infiltration recharge of groundwater seepage quantity, uses the water hydration method to study the lateral seepage influence on hydrochemical types, and uses the groundwater model to study the recharge quantity by lateral seepage of the Yellow River. This provides a scientific basis for the evaluation and utilisation of the Yellow River and groundwater resources.

2. Study Area

The study area was located in the middle and lower reaches of the Yellow River in China. The study area stretches from 112°30′ E to 116°06′ E and 34°42′ N to 36°06′ N, with a total area of 13,616.0 km² (Figure 1). The climate type is warm temperate monsoon. The perennial mean temperature from 1956 to 2020 was 13.1 °C–14.5 °C. The over-year water surface evaporation from 1956 to 2020 was above 1000–1400 mm. The land surface evaporative capacity from 1956 to 2020 was 500–600 mm. In the study area, Cenozoic Neogene and Quaternary loose deposits are widely distributed (disseminated) in the lower Yellow River plain, which is formed (trained) in the Yellow River alluvial strata, including Holocene, Upper Pleistocene, and Middle Pleistocene strata. The aquifer lithology is mainly composed of gravel, medium coarse sand, medium sand, medium fine sand, and fine sand. The aquifer floor depth is generally 60–120 m [21]. According to the basic genetic types of landforms, the area can be divided into three categories: the Yellow River alluvial plain, piedmont alluvial-pluvial plain and bedrock, and loess tableland and hills. The plain of the lower Yellow River has flat terrain, and the main recharge sources of shallow groundwater in this area are atmospheric precipitation and Yellow River water leakage. The water content of the groundwater in this area is loose rock pore water, and the main formation lithology is silty fine sand and medium-fine sand.

3. Methods

3.1. Sample Collection and Testing

Four sections of shallow groundwater dynamic monitoring were established in the study area according to the geological and hydrogeological conditions of the study area. A total of 21 water samples (15 from the north bank of the Yellow River and 6 from the south bank) were collected from the four profiles for hydrochemical composition analysis. Section 2 was selected as the typical research object, and 16 water samples (one from the Yellow River and 15 from shallow groundwater within 60 m) were collected for isotopic analysis (Figure 1). The groundwater level contour maps for October 2019 and May 2020, and October 2020 were determined using the groundwater level survey. Based on the flow field diagram of groundwater in the wet and dry seasons, the relationship between the Yellow River and groundwater was determined, and the recharge range of the lateral seepage in the Yellow River was studied.

3.2. Environmental Isotopic Method

Sixteen water sample monitoring points (one Yellow River water and 15 groundwater samples) were arranged for the determination of δ¹⁸O, δD, and tritium isotopes, which were used to verify the recharge range of the Yellow River lateral seepage. The recharge ratio of the Yellow River water in the groundwater was also determined based on the ¹⁸O isotope mass conservation model.

3.2.1. D and ¹⁸O Isotope Method

The atmospheric precipitation line refers to the linear relationship between precipitation isotopes D and ¹⁸O over a certain period of time, which provides a basis for the composition of local atmospheric precipitation isotopes and is the most commonly used means to identify whether water sources come from atmospheric precipitation. The global meteoric water line equation (GMWL) is as follows [22]:

$$\mathsf{\delta }\mathrm{D}=8.13{\mathsf{\delta }}^{18}\mathrm{O}+10$$

(1)

Based on 57 isotope series data of the atmospheric precipitation line at the IAEA Zhengzhou Monitoring Station from 1985 to 1992, the local meteoric water line equation (LMWL) is as follows [23]:

$$\mathsf{\delta }\mathrm{D}=6.75{\mathsf{\delta }}^{18}\mathrm{O}-2.71$$

(2)

3.2.2. Tritium Isotope Method

Tritium is a short-period radioactive isotope and an ideal tracer for groundwater movement. Its half-life is 12.43 years. Because of the decay characteristics of tritium, its decay law can be used to estimate the age of modern groundwater. According to the existing research results in the study area, the age range corresponding to tritium concentration can be divided into the following three scenarios: (1) 3H > 6.4 TU represents modern circulating water supplying the Yellow River; (2) 6.4 TU > 3H > 1.0 TU represents modern circulating water mainly supplied by atmospheric precipitation; (3) 3H < 1.0 TU represents groundwater before the nuclear explosion, where groundwater age > 60 years [23].

3.2.3. Hydrochemical Method

This study draws a Piper diagram and hydrochemical diagram using groundwater and surface quality data, and analyses the changes in hydrochemical types and ion concentrations. By analysing the degree of correlation between the hydrochemical types of groundwater and surface water, the influence of lateral seepage of the Yellow River on the groundwater chemistry composition was analysed.

3.3. Exchange Capacity of Yellow River Water and Groundwater

3.3.1. ¹⁸O Mass-Conservation Model

The ¹⁸O mass-conservation model was used to calculate the proportion of groundwater recharge by the Yellow River water. Assuming that the total proportion of δ¹⁸O in groundwater samples is 1, the proportion of lateral seepage recharge of the Yellow River water is α, and the proportion of atmospheric precipitation recharge is β, then

$$\mathsf{\alpha }+\mathsf{\beta }=1$$

(3)

$${\mathsf{\delta }}^{18}{\mathrm{O}}_{\mathrm{g}}=\mathsf{\alpha }\left({\mathsf{\delta }}^{18}{\mathrm{O}}_{\mathrm{r}}\right)+\mathsf{\beta }\left({\mathsf{\delta }}^{18}{\mathrm{O}}_{\mathrm{p}}\right)$$

(4)

By combining the above two equations, we can deduce the formula for calculating the proportion $\mathsf{\alpha }$ of the water-side seepage recharge of the Yellow River as follows:

$$\mathsf{\alpha }=\frac{{\mathsf{\delta }}^{18}{\mathrm{O}}_{\mathrm{g}}-{\mathsf{\delta }}^{18}{\mathrm{O}}_{\mathrm{p}}}{{\mathsf{\delta }}^{18}{\mathrm{O}}_{\mathrm{r}}-{\mathsf{\delta }}^{18}{\mathrm{O}}_{\mathrm{p}}}.$$

(5)

where ${\mathsf{\delta }}^{18}{\mathrm{O}}_{\mathrm{g}}$ is the ${\mathsf{\delta }}^{18}\mathrm{O}$ of the groundwater, ${\mathsf{\delta }}^{18}{\mathrm{O}}_{\mathrm{p}}$ is the ${\mathsf{\delta }}^{18}\mathrm{O}$ of the atmospheric precipitation; ${\mathsf{\delta }}^{18}{\mathrm{O}}_{\mathrm{r}}$ is the ${\mathsf{\delta }}^{18}\mathrm{O}$ of the Yellow River.

3.3.2. Darcy’s Law

The recharge ratio of the Yellow River was determined using ¹⁸O, and the exchange amount between the Yellow River and groundwater was calculated using Darcy’s law, which is the theoretical basis of groundwater seepage analysis. Using Darcy’s law, i.e., using the difference between the water level of the Yellow River and the groundwater level, the amount of Yellow River leakage to the groundwater recharge river water was calculated by the following formula:

$$\mathrm{q}=\mathrm{KMI}$$

(6)

where q is the single-width seepage flow of the river channel (m²/a), K is the permeability coefficient of the section aquifer (m/d), M is the aquifer thickness (m), and I is the hydraulic gradient of groundwater determined according to the relationship between the water level of the Yellow River and the groundwater level combined with the groundwater flow field (Figure 2).

3.4. Groundwater Flow Model

3.4.1. Model Discretization

A groundwater flow model in the study area was built using MODFLOW-2000 in the GMS. The area was 13,616.0 km². The grid cells were designated as “inactive” outside the model domain and as “active” inside the model domain. The model was divided into 174 rows and 353 columns, each with a size of each cell being 1000 m × 1000 m (Figure 3a). The model included one layer representing the hydrogeological conditions and data on the porous aquifers at the study site. The simulation period was from 1 May 2001 to 31 December 2019 with 228 stress periods defined for the simulation. Three time-steps were defined for each stress period. Groundwater levels observed in 2001 were used as the initial conditions of the model.

3.4.2. Boundary Conditions

The boundary conditions are shown in Figure 3b. For the lateral boundary conditions, a general head boundary condition and special head boundary condition exist in the model. The Jindi River and the Yellow River in the east and northeast of the study area are generalized as special head boundaries; other boundaries have certain water exchange and are treated as general head boundaries. The river boundary is a Dirichlet boundary condition because there is a good connection between the groundwater and the river. In the places perpendicular to the groundwater flow direction, the boundary is defined as a “no flow” boundary as they are impermeable boundaries. The flow rate is based on hydraulic conductivity (K), thickness (M), and hydraulic gradient (I). For the vertical boundary conditions, the top boundary was defined for the recharge and discharge flux, infiltration of precipitation, irrigation, river leakage, pumping wells, and phreatic water evaporation on the surface of the water table. The bottom boundary condition at the base of the deep aquifer was treated as a no-flow boundary.

3.4.3. Parameters

The formation and distribution of groundwater are controlled by the formation lithology, geological structure, and geomorphologic shape. Field geological observations show that the porous aquifer consists of quaternary sand and is the main aquifer in the study area. Data from more than 60 pumping tests were obtained from previous hydrologic studies and were used to quantify the hydraulic characteristics of the aquifer and identify the boundary conditions [24]. The Theis equation and Cooper–Jacob graphical method were used to calculate parameters such as hydraulic conductivity (K) and specific yield (μ). For the sand and gravel aquifers, the calculated K ranged from 6 to 25 m/d (Figure 3c), and μ ranged from 0.05 to 0.075 (Figure 3d).

3.4.4. Recharge and Discharge

The main recharge items in the study area included atmospheric rainfall infiltration, Yellow River seepage, groundwater runoff recharge, channel leakage, and irrigation infiltration. The main discharge parameters were evaporation, evapotranspiration, groundwater runoff discharge, and groundwater withdrawal. Irrigation is prominent every year from the May to October growing season. Irrigation water is derived from river and groundwater pumping in the irrigation district, but wells in the district are not monitored; therefore, area features were used to simulate the recharge of precipitation and withdrawal of irrigation water with the recharge (RCH) package. The direct evaporation and evapotranspiration (ET) package was based on data from Zhengzhou meteorological stations (Figure 4). The average annual precipitation infiltration, irrigation infiltration and fishpond infiltration in the study area were 175,579.864 m³/a, 34,528.98 × 10⁴ m³/a and 47,365.02 × 10⁴ m³/a, respectively. The average annual evaporation and irrigation discharge of the study area were 73,663.99 × 10⁴ m³/a and 82,520.30 × 10⁴ m³/a, respectively.

3.4.5. Model Calibration and Sensitivity Analysis

It is important to determine the result that is reasonable in the calibration process. Two types of data were used to calibrate the regional groundwater flow model. First, the observed groundwater level contour maps of the aquifer in December 2019 were used to match the computed water levels (Figure 5) as a qualitative step before performing a more comprehensive and quantitative calibration. Second, the variable heads of the 12 observation wells from 2001 to 2019 were used as the calibration targets. As shown in Figure 5, the contour maps of the observed groundwater level and the calculated groundwater level agreed well. The observation wells are distributed throughout the study area and are thus representative of the regional aquifer conditions. The average absolute error between the observed groundwater level and calculated groundwater level of the long observation hole was 1.289 m. The average absolute error of the four observation holes was less than 1 m, the average absolute error of the five observation holes was in the range of 1–2 m, and the average absolute error of the three observation holes was greater than 2 m. The model accuracy is acceptable after identification and verification.

3.5. Technical Procedure

In this paper, Groundwater dynamic field, Environmental isotope method, Hydrochemical method and Groundwater flow model were used for analyzing the interaction between yellow river and groundwater. The technical procedure is shown in Figure 6.

4. Results and Discussion

4.1. Determination of Recharge Rate of Yellow River Lateral Seepage

4.1.1. Recharge Range of Yellow River Lateral Seepage

Figure 7 shows the groundwater level contours for October 2019 and May 2020, and October 2020. From the contour maps of October 2019 and May 2020, it can be seen that the contour density in May 2020 is larger and the flow field changes are complex, indicating that the hydraulic gradient of the phreatic surface and the groundwater flow velocity increased by May 2020. Compared with October 2019, the groundwater flow direction in Fengqiu County in May 2020 was significantly different, changing from northeast to northeast and southwest and forming a groundwater funnel, indicating that the exploitation amount in Fengqiu County in May 2020 was relatively large. Compared with the phreatic water level contour maps of October 2020 and October 2019, it can be seen that there was little difference in the range and density of the Yellow River lateral seepage, indicating that the intensity of the Yellow River lateral seepage recharge was roughly the same in the same season.

In summary, results for the final recharge range of the Yellow River lateral seepage were obtained. The shallow groundwater flow field used the Yellow River as the central axis and flowed radially to the southeast and northeast. The Yellow River recharges groundwater perennially, and the recharge range of seepage measurements is larger in the north bank than in the south bank. The lateral seepage range of the Yellow River was different across the four sections. Section 1 was approximately 26.2 km on the north bank and 3.8 km on the south bank. Section 2 was approximately 20.6 km on the north bank and 14.0 km on the south bank. Sections 3 and 4 were bounded by the Jindi River to the north, and Section 3 was approximately 31.3 km. Section 4 was approximately 9.5 km.

4.1.2. Recharge Range of Yellow River Lateral Seepage in Typical II Section

(1)

Determination using ¹⁸O stable isotope

Section 2 passed through multiple geological and lithologic plates, and the geographical location and hydrogeological conditions were good; therefore, Section 2 was selected as the isotope sampling detection section (Figure 1).

Taking Section 2 as the typical research object, the average values of October 2019, May 2020, and October 2020 were used as the data for this analysis. In Section 2, the δD of groundwater was between −66.1‰ and −54.7‰, δ¹⁸O was between −9.06‰ and −7.3‰, with the average being −8.47‰, the δD of the Yellow River was −52.5‰, and δ¹⁸O was −6.77‰ (

Table 1. Isotope of δD and δ¹⁸O composition of Yellow River and Groundwater samples.

No.	δDV-SMOW‰	δ18OV-SMOW‰	Remark
TY1	−52.5	−6.77	Yellow River
TY2	−59.3	−8.25	Groundwater
TY3	−63.5	−8.78
TY4	−63.1	−8.455
TY5	−62.7	−8.29
TY6	−62	−8.59
TY7	−65.1	−9.06
TY8	−58.8	−7.94
TY9	−59.7	−8.07
TY10	−60.4	−8.29
TY11	−61.2	−8.37
TY12	−61.3	−8.33
TY13	−66.1	−9.02
TY14	−65.4	−8.65
TY15	−61.8	−8.18
TY16	−65.1	−8.82
Groundwater average	−62.37	−8.47

). The isotopic composition of the shallow groundwater was similar to that of the Yellow River, which is located near the local rainwater line. It can be seen that the recharge sources of groundwater in the working area were atmospheric precipitation and the Yellow River (Figure 8). The lower reaches of the Yellow River are semi-arid inland areas affected by evaporation, so the gradient is slightly smaller than that of the Global Meteoric Water Line [24].

It can be seen in Figure 9 that the spatial variation of ¹⁸O and D in the Yellow River and groundwater was the same. On the north bank, sample numbers TY8, TY9, and TY10 were closer to TY1, whereas TY11 and TY12 (both far from the Yellow River) were between −8 and −8.5. On the south bank, the δD and δ¹⁸O of TY2, which were closer to the Yellow River, were larger than those of TY4, TY5, and TY6, which were relatively far away from the Yellow River. This indicates that shallow groundwater near the Yellow River was strongly recharged by the Yellow River. Further away from the Yellow River, the shallow groundwater was recharged by atmospheric precipitation. The curve change was relatively flat 20 km north of the Yellow River and tended to be stable beyond 10 km south, so the influence range of the Yellow River lateral seepage was approximately 20 km from the north bank and approximately 10 km from the south bank.

(2)

Determination of ³H radioactive isotopes

According to the isotopic characteristics of water samples collected on the profile II (

Table 2. Isotope feature list of ³H (TU) of Groundwater and Yellow River samples.

No.	TY1	TY2	TY3	TY4	TY5	TY6	TY7	TY8
3H (TU)	14.37	5.67	1.98	4.53	4.98	1.97	1.98	13.56
No.	TY9	TY10	TY11	TY12	TY13	TY14	TY15	TY16
3H (TU)	9.1	5.85	3.7	4.25	1.98	3.71	3.99	2.55
Remark	TY1 was Yellow River, others were groundwater

), it can be known the ³H concentration of groundwater was between 1.97 TU and 13.56 TU; the ³H of the Yellow River was 14.37 TU. According to the tritium distribution map in Section 2 (Figure 10), the tritium value of the Yellow River was the highest. With an increase in the distance from the sampling point to the Yellow River, the tritium value first decreased and then increased. Combined with hydrogeological conditions and groundwater dynamics, it can be seen that in the area near the Yellow River, shallow groundwater dynamics were hydrological and surface water recharged groundwater. Therefore, the tritium value decreased with an increase in the distance from the Yellow River. In the area far from the Yellow River, the groundwater dynamic was of the meteorological–hydrological type. The groundwater was mainly recharged by atmospheric rainfall, followed by irrigation and lateral infiltration of the Yellow River. Therefore, the tritium values at the corresponding sampling points were significantly affected by atmospheric precipitation. Therefore, the recharge range of the north bank of the Yellow River was south of TY11, 20.4 km from the Yellow River, and the south bank of the Yellow River was north of TY3, 13.7 km from the Yellow River.

Combined with the tritium concentration of groundwater, the ³H of groundwater was between 1.97 TU and 13.56 TU, with an average value of 5.26 TU. Therefore, shallow groundwater is essentially modern circulating water. When ³H was low, it was mainly recharged by atmospheric precipitation, and when the concentration was high, it was mainly recharged by Yellow River infiltration recharge. Figure 10 shows that the tritium concentrations of the TY10, TY9, TY8, and TY2 samples were affected by the Yellow River. On the North Bank, the lateral seepage section was approximately 20 km. On the south bank, after approximately 10 km, the tritium concentration changed little, indicating that the recharge range of the northern bank of the Yellow River was wider than that of the southern bank.

The groundwater flow field diagram showed that the Yellow River lateral seepage recharge range of Section 2 was approximately 20.6 km on the north bank and 14.0 km on the south bank. The recharge range of the Yellow River lateral seepage determined by the stable isotope and radioactive isotope in the Yellow River water and shallow groundwater in Section 2 was 20 km on the north bank and 10 km on the south bank. The groundwater flow field diagram and groundwater recharge range determined by the environmental isotopes were consistent.

4.2. Determination of Lateral Seepage Quantity of the Yellow River on the Typical Sections

4.2.1. Proportion of Groundwater Recharged by Yellow River on the Typical Sections

When calculating the proportion of groundwater recharged by the Yellow River, the average oxygen isotope data of atmospheric precipitation from 1985 to 1992, monitored by Global Network of Isotopes in Precipitation (GNIP) (IAEA) in Zhengzhou City, were selected as ${\mathsf{\delta }}^{18}{\mathrm{O}}_{\mathrm{P}}$ = −6.41‰, and the isotope of the Yellow River was ${\mathsf{\delta }}^{18}{\mathrm{O}}_{\mathrm{r}}$ = −10.2‰. These data were used in place of real-time data obtained by monitoring, because the recharge part of the Yellow River in groundwater was often formed over many years and not instantaneously recharged. It was obviously more accurate to calculate the proportion of groundwater recharged by the Yellow River water with an average of many years, and the Yellow River recharge ratio of shallow groundwater samples in the study area. As only TY2, TY3, TY8, TY9, and TY10 were within the range of lateral infiltration of the Yellow River, the impact of the Yellow River beyond the range of lateral infiltration on groundwater was relatively small and therefore not analysed.

According to the formula,

$$\mathsf{\alpha }=\frac{{\mathsf{\delta }}^{18}{\mathrm{O}}_{\mathrm{g}}-{\mathsf{\delta }}^{18}{\mathrm{O}}_{\mathrm{p}}}{{\mathsf{\delta }}^{18}{\mathrm{O}}_{\mathrm{r}}-{\mathsf{\delta }}^{18}{\mathrm{O}}_{\mathrm{p}}}$$

where ${\mathsf{\delta }}^{18}{\mathrm{O}}_{\mathrm{P}}$ = −6.41‰ and ${\mathsf{\delta }}^{18}{\mathrm{O}}_{\mathrm{r}}$ = −10.2‰, the stable isotope δ¹⁸O_V-SMOW‰ was calculated and summarized in

Table 3. The proportion of Yellow River recharge in shallow groundwater on the typical sections.

North Bank	Proportion	South Bank	Proportion
TY8	0.404	TY2	0.485
TY9	0.438	TY3	0.625
TY10	0.496
average	0.446	average	0.555
Overall average	0.501

.

It can be seen from the calculation results that the proportion of Yellow River supply in shallow groundwater was approximately 50.1%, indicating that the supply source of shallow groundwater was mostly the Yellow River.

4.2.2. Lateral Seepage Quantity of the Yellow River on the Typical Sections

Based on the data of permeability coefficient, aquifer thickness and hydraulic gradient of four typical sections in 2019, using Darcy’s law to calculate the replenishment quantity of groundwater by infiltration of the Yellow River produced the following results (

Table 4. Single-wide lateral leakage recharges groundwater quantity on typical sections.

Location	Permeability Coefficient K (m/d)	Average Aquifer Thickness (m)	Hydraulic Gradient (%)	Single-Width Lateral Seepage (m3/a·m)
I section of the north	28.1	80	0.18	1476.94
I section of the south	22	75	0.11	662.48
II section of the north	22	45	0.14	505.89
II section of the north	13	48	0.18	409.97
III section of the north	14	40	0.02	40.88
IV section of the north	12	25	0.06	65.7

): The single-width lateral seepage was 1476.94 m³/a·m in north Section 1, 662.48 m³/a·m in south Section 1, 505.89 m³/a·m in north Section 2, 409.97 m³/a·m in south Section 2, 40.88 m³/a·m in north Section 3, and 65.7 m³/a·m in north Section 4. According to the calculation results, the lateral seepage of the upper section of the Yellow River is larger than that of the lower section, and the lateral seepage of the north bank is greater than that of the lower section.

4.3. Influence of Yellow River Lateral Seepage on Groundwater Chemistry Composition

Hydrochemical and Piper diagrams of the study area (Figure 1 and Figure 11) show that the closer to the Yellow River, the more single the water’s chemical composition and the lower the salinity. The further away one moves from the Yellow River, the more complex the groundwater chemical composition and the higher the salinity. On the south bank of the Yellow River, the cations were Ca²⁺, Mg²⁺, and Na⁺, while the anion was HCO₃⁻, the hydrochemical type was HCO₃-Ca·Mg·Na, and the salinity was less than 1 g/L. In the north of the Yellow River, the hydrochemical cations were Mg²⁺ and Na⁺ and the anions were HCO₃⁻, SO₄²⁻, and Cl⁻. The hydrochemical type was relatively complex, e.g., HCO₃·Cl-Na·Mg, HCO₃-Ca·Mg·Na, HCO₃·SO₄-Na·Mg, HCO₃·Cl·SO₄-Ca·Mg·Na, etc. Most of the salinity in the upper reaches of the Yellow River was less than 1 g/L, and most of the lower reaches were greater than 1 g/L, especially near the Jindi River, and the salinity ranged between 2 and 4 g/L.

Overall, the distribution of the chemical types of shallow groundwater showed an apparent regularity. From the upper reaches to the lower reaches and from near to faraway from the Yellow River, the hydrochemical types of the Yellow River change from single to complex, and the salinity increases gradually from relatively low. In addition, the water chemical types in cities with high salinity and near the Jindi River in Puyang were more complex due to the pollution in these three cities.

4.4. Recharged by Lateral Seepage of the Yellow River by Groundwater Flow Model

The water balance of the groundwater system from January 2001 to December 2019 was obtained using groundwater flow model water budget analysis. From January 2001 to December 2019, the recharge of the shallow aquifer group in the study area was 315,199.04 × 10⁴ m³/a, the discharge capacity was 310,310.68 × 10⁴ m³/a, and the equilibrium difference was 4888.36 × 10⁴ m³/a. Precipitation infiltration accounted for 55.70%, fishpond infiltration 15.03%, irrigation infiltration 10.95%, Yellow River lateral infiltration recharge 7.97%, boundary lateral recharge 5.74%, and channel leakage 4.61%. Together, these infiltrations and channel leakage accounted for 94.26% of the total infiltration. Precipitation infiltration recharge plays an important role in the amount of recharge. Among the total shallow water discharge, agricultural exploitation, evaporation, fishpond exploitation, industrial exploitation, domestic exploitation, and lateral outflow accounted for 26.59%, 23.74%, 23.45%, 10.72%, 9.05%, and 6.45%, respectively (

Table 5. Average groundwater balance of aquifer from 2001 to 2019.

	Budget Items: 104 m3/a	Quantity	Proportion
Recharge items	Precipitation infiltration recharge	175,579.86	55.70%
	Yellow River seepage recharge	25,114.36	7.97%
	Groundwater lateral runoff recharge	18,089.94	5.74%
	Irrigation recharge	34,528.98	10.95%
	River seepage recharge	14,520.88	4.61%
	Fishpond leakage recharge	47,365.02	15.03%
	Total amount	315,199.04	/
Discharge items	Domestic exploitation	28,078.87	9.05%
	Industrial exploitation	33,258.92	10.72%
	Agricultural Exploitation	82,520.3	26.59%
	Fishpond exploitation	72,783.14	23.45%
	Groundwater lateral runoff discharge	20,005.46	6.45%
	Evaporative discharge	73,663.99	23.74%
	Total amount	310,310.68	/
	groundwater budget difference	4888.36

). The annual average lateral seepage groundwater recharge quantity of the Yellow River from 2001 to 2019 was 25,114.36 × 10⁴ m³/a (Figure 12).

5. Conclusions

Based on the groundwater flow field map, hydrochemistry map, and Piper diagram, the interaction between surface water and groundwater in the Yellow River was studied using isotope analysis and the hydration method. This study can improve the understanding of surface water and groundwater interaction rules, guide the development of a reasonable allocation of local water resources, and the sustainable utilisation of water resources plans.

(1)

It can be determined by analysing the groundwater flow field maps of October 2019 and May 2020, and October 2020, that the transverse seepage range of the north bank of the Yellow River was larger (approximately 20 km) and that of the south bank was smaller (approximately 10 km).

(2)

The main recharge sources of groundwater were atmospheric precipitation and the Yellow River, of which the latter was the main recharge source, accounting for 50.1%.

(3)

In Sections 1·4, the lateral seepage amounts in the north bank were 1476.94 m³/a·m, 505.89 m³/a·m, 40.88 m³/a·m, and 65.7 m³/a·m, respectively. The single-width permeability of typical Section 2 was larger upstream than downstream, and larger in the north than in the south.

(4)

According to the hydrochemical diagram and Piper diagram of the study area, we can see that the lateral seepage of the Yellow River had a great influence on the hydrochemical types of groundwater. The hydrochemical type changed from single to complex from upstream to downstream, and also from near to far proximity of the Yellow River, with the salinity increasing gradually along those two same lineal spectra.

(5)

The annual average lateral seepage recharge groundwater quantity of the Yellow River from 2001 to 2019 was 25,114.36 × 10⁴ m³/a.