Abstract

The study of surface water and groundwater (SGW) interaction can be used to improve water resource management. Herein, annual and monthly interactions in the Taoer River alluvial fan were calculated for the 1956–2014 period using the surface water balance method and the groundwater balance method, and a statistical model of interaction was obtained. The SGW interaction is shown in terms of the recharge of groundwater by surface water. From 1956 to 2014, the amount of SGW interaction in the study area varied greatly, averaging 27,848.4 × 104m3 annually. SGW interaction decreased gradually from the 1950s to the 1980s, and increased gradually from the 1980s to the present. During an individual year, SGW interaction increases gradually from January to July, peaking in July, and decreases gradually from August to December. An annual and a monthly multivariate regression statistical model were established. R2 was 0.697 for the annual model and 0.405 for the monthly model; the annual interaction model is more reliable. The model can be used to predict future trends in SGW interaction, which could be of great significance to the management of groundwater resources in the study area.

INTRODUCTION

Surface water and groundwater (SGW) interaction forms one of the important components of research into the groundwater cycle (Winter et al. 2003). This is especially true for inland river basins where, in arid regions of the world, surface water is the main source of groundwater recharge (Manoj et al. 2019). However, there is also often a close hydraulic relationship between groundwater and surface water in near-shore regions. It is important to study mutual SGW interaction for the comprehensive management and utilization of water resources (Yao et al. 2019).

In recent years, the study of SGW has primarily employed three methods. The first is the coupling model of SGW. The existing surface water–groundwater coupling model (Sebok et al. 2013) is mainly used to examine spatial–temporal SGW interaction (Chebud & Melesse 2012; Gejl et al. 2019), the hydrological connectivity model between the SGW aquifer (Barthel & Banzhaf 2016), and the simulation of the impact of climate change on the basin water cycle (Huo et al. 2016). The second method is based on isotope tracing (Lin et al. 2006; Li et al. 2017) mainly using the isotope 222Rn (Zhao et al. 2018; Wang et al. 2019). Both the coupling model and the isotope tracer method focus on the relationship between SGW. The third approach used in studies of groundwater and surface water is to calculate interaction. Widely used methods to do this are the hydrodynamic method (Osei-Twumasi et al. 2016), the water balance model, dynamics model (Barati et al. 2019), a new type of point device (Cremeans et al. 2018), and the water balance method (Ibrakhimov et al. 2018). Although these methods can calculate the amount of SGW interaction, few studies have calculated long-term series of SGW interaction, and few have systematically analyzed the results of the amount of interaction.

The water balance method has been widely used in many fields (Ducci & Sellerino 2015), and has been proved effective (Tozer et al. 2018). Therefore, it is feasible to apply the water balance method to the study of SGW interaction. In this work, surface water balance and groundwater balance are used to calculate the monthly interaction of SGW in the Taoer River alluvial fan from 1956 to 2014, and to create a statistical model of their interaction that incorporates other influencing factors. Each method is used to verify the other and to ensure the accuracy of the results.

This study is the first to be carried out in Jilin Province, and is the first to calculate SGW interaction in the Taoer River alluvial time series to obtain a statistical model of interaction that can be used to predict the SGW interaction (Roushangar & Alizadeh 2018; Roushangar et al. 2018). The main contributions of this work are as follows. First, the annual and monthly groundwater interaction amounts of the long time series in the study area are determined, and the rules governing the annual and monthly variation in the interaction amount are identified. Then, a statistical model of SGW interaction is established, which can provide the basis for the comprehensive management of water resources.

Study area

The Taoer River alluvial fan (45°16′–45°53′ N, 122°8′–123°3′ E) is located in Baicheng City, Jilin Province, China, and occupies an area of about 2,920 km2. The altitude of the study area ranges from 140 m to 215 m, and decreases gradually from the top to the bottom of the alluvial fan. The elevation of the river bed is generally lower than that of both river banks. In some areas near the mountain area in front of the fan, the elevation of the river bed is higher than that of the top of the fan. From the top of the alluvial fan to its edge, the slope of the land decreases; the ratio of the slope at the top of the alluvial fan is about 0.96, and that at the base of the alluvial fan is about 0.19. The study area has a continental monsoon climate in the north temperate zone and an average annual temperature range of –2 to + 5 °C. The average annual precipitation is 395.0 mm. Precipitation is mainly concentrated in the months June–September, which account for 82.59% of the total annual precipitation. The average annual evaporation in the study area is 911.2 mm, and is mainly concentrated in the months April–September, which account for 82.21% of the total annual evaporation.

The main rivers in the study area are the Taoer River, the Jiaoliu River (the tributary of Taoer River) and part of the Emutai River (the tributary of Jiaoliu River). ZhenXi and WuBen hydrological stations are located in the upstream region of the alluvial fan, and control most of the runoff entering the alluvial fan, while TaoNan hydrological station controls all the runoff outside the alluvial fan. The water balance method is based on the principle of calculating the interaction of SGW according to the water quality balance. It is advantageous to use the water balance method to calculate SGW interaction in the study area (Figure 1).

Figure 1

Location map of the study area, with a contour map of the groundwater level. Orange points indicate observations obtained in September 2014. The water level line is based on the water level records of long-term observation wells and a single observation from each short-term observation well. Please refer to the online version of this paper to see this figure in colour: http://dx.doi.org/10.2166/ws.2019.118.

Figure 1

Location map of the study area, with a contour map of the groundwater level. Orange points indicate observations obtained in September 2014. The water level line is based on the water level records of long-term observation wells and a single observation from each short-term observation well. Please refer to the online version of this paper to see this figure in colour: http://dx.doi.org/10.2166/ws.2019.118.

DATA AND METHODS

Data

Daily runoff, river water level, evaporation, precipitation and channel diversion for the 1956–2014 period were provided by ZhenXi, TaoNan and WuBen hydrological stations. These data were mainly sourced from the monitoring data of the Songliao Committee of the Ministry of Water Resources of China.

Data on the groundwater level from 14 observation wells, quantity of water used in surface water irrigation, and groundwater exploitation in the study area for the 2000–2013 period were collected. From June to September 2014, 102 groundwater level detection sites were distributed across the study area.

METHODS

Overview of the method

The process of this study mainly includes three steps: the first is data collection and field investigation; the second is calculation of interaction amount, using methods of surface water balance and groundwater balance; the third is establishment of the statistical model. The flow chart of this work is shown in Figure 2.

Figure 2

Flow diagram of the study.

Figure 2

Flow diagram of the study.

Surface water balance method

The surface water balance and groundwater balance methods are based on the principle of mass conservation (Rezaei & Mohammadi 2017). Although these methods seem outdated, they are based on the most basic and reliable water balance principle, and therefore yield accurate and credible results. This can be used to identify the rules governing the interaction rule of SGW and to establish a statistical model, which needs to be based on accurate calculation results.

SGW interaction is calculated based on the principle of surface water balance. The formulae are: 
formula
(1)
 
formula
(2)
 
formula
(3)
where QS-G is the SGW interaction in 104 m3; QRE is the recharge of the study area in 104m3; QD is the discharge of the study area in 104m3; QZX is the actual measured runoff at the ZhenXi Hydrological Station in 104m3; QWB is the actual measured runoff at the WuBen Hydrological Station in 104m3; QH is the runoff of the Emutai River in 104m3; QRI is the direct recharge of rainwater to the river in 104 m3; QTN is the actual measured runoff at the TaoNan Hydrological Station in 104 m3; QE is the evaporation from the river surface in 104 m3; and QC is the water diversion from the canal in 104 m3.

In Equation (2), there is no measured runoff and precipitation data from the Emutai River. The precipitation runoff from the Emutai River is calculated using the hydrological analogy method (Wulf et al. 2016) based on runoff data from WuBen Hydrological Station. This is because the runoff conditions in the upper reaches of the Emutai River are very similar to those in the upper reaches of the WuBen Hydrological Station, and the underlying surface is the same.

The results of the hydrological analogy method indicate that the annual precipitation runoff from the Emutai River is estimated to be 228.3 × 104 m3 annually. Because the Emutai River is a seasonal river and its runoff is very low, accounting for 1.5% of the total water inflow of the study area, so the error in using the hydrological analogy method to calculate its runoff on the interaction of SGW in the study area is very small.

GROUNDWATER BALANCE METHOD

Hydrogeological zoning

In order to accurately calculate the variation in groundwater in the study area, the study area was divided into five zones based on similarities in hydrogeological and geomorphological conditions. The top and front parts of the alluvial fan were designated as Zones I and II, respectively, for calculation. There were some differences in the landforms and conditions on opposite sides of the river. Thus, Zone I was divided into three calculation zones: I 1 (left river bank), I 2 (interriver block), and I 3 (right river bank). Zone II was divided into two calculation zones: II 1 (left river bank) and II 2 (right river bank). These zones are shown in Figure 3.

Figure 3

Parametric zoning map.

Figure 3

Parametric zoning map.

Hydrogeological parameters

To calculate groundwater balance, it is necessary to determine the permeability coefficient (K), specific yield (μ), precipitation infiltration coefficient (α), phreatic water evaporation coefficient (β), channel infiltration coefficient (γ1), and irrigation infiltration coefficient (γ2). K is calculated using pumping test data, and the permeability coefficient is determined through comprehensive analysis. Calculation of μ involves laboratory experiments, pumping experiments, and groundwater dynamics data deduction. Atmospheric precipitation and groundwater dynamics data are used to calculate α, and β is usually obtained using the ratio of the annual average evaporation of phreatic water to the evaporation of the surface water in the same period. Field tests and data collected in the study area are used to determine γ1 and γ2 (Table 1).

Table 1

Parameters given for each partition in the study area

ZoneArea (km2)Permeability coefficient (K) (m/d)Specific yield (μ)Precipitation infiltration coefficient (α)Phreatic water evaporation coefficient (β)Channel infiltration coefficient (γ1)Irrigation infiltration coefficient (γ2)
I1 1,054 320 0.22 0.28 0.04–0.10 0.2 0.25 
I2 402 280 0.2 0.25 0.05–0.09 0.2 0.24 
I3 260 330 0.18 0.3 0.03–0.08 0.2 0.25 
II1 680 100 0.16 0.23 0.05–0.08 0.2 0.23 
II2 418 110 0.13 0.21 0.05–0.10 0.2 0.26 
ZoneArea (km2)Permeability coefficient (K) (m/d)Specific yield (μ)Precipitation infiltration coefficient (α)Phreatic water evaporation coefficient (β)Channel infiltration coefficient (γ1)Irrigation infiltration coefficient (γ2)
I1 1,054 320 0.22 0.28 0.04–0.10 0.2 0.25 
I2 402 280 0.2 0.25 0.05–0.09 0.2 0.24 
I3 260 330 0.18 0.3 0.03–0.08 0.2 0.25 
II1 680 100 0.16 0.23 0.05–0.08 0.2 0.23 
II2 418 110 0.13 0.21 0.05–0.10 0.2 0.26 

Groundwater balance method

The principle of the groundwater balance method is to calculate the incoming and outgoing amounts of groundwater (phreatic water) according to the law of conservation of mass. The time period of Δt = 1a is used for calculations. The ‘a’ means one year. The formulae are: 
formula
(4)
 
formula
(5)
where ΔQ is the amount of phreatic water storage in 104 m3; F is the area of the study region in m2; ΔH is the rate of groundwater level change in one year in the study region in m; Qr is the amount of recharge for phreatic water in 104 m3; and Qd is the amount of discharge for phreatic water in 104 m3.
The formulae of Qr are: 
formula
(6)
 
formula
(7)
 
formula
(8)
 
formula
(9)
 
formula
(10)
where Qpr is the amount of groundwater recharge for precipitation in 104 m3; P is the amount of precipitation in mm; Qcr is the amount of groundwater recharge for canal water in 104 m3; Qc is the amount of canal water; Qir is the amount of water recharged to the underground for mining groundwater in 104 m3; Qi is the amount of mining groundwater; Qlr is the amount of groundwater recharge for groundwater runoff in 104 m3; I is the dimensionless hydraulic gradient of groundwater; M is the aquifer thickness in m; Li is the cross-section of groundwater inflow into the study area in m; and QS–G is the amount of SGW interaction in 104 m3.
The formulae of Qd are: 
formula
(11)
 
formula
(12)
 
formula
(13)
where Qpd is the amount of groundwater for artificial mining in 104 m3; Qed is the amount of water evaporation for phreatic water in 104 m3; Qe is the evaporation in mm; Qld is the amount of groundwater discharged for groundwater runoff in 104 m3; and Lo is the cross-section of groundwater outflow in the study area in m. The limit of evaporation depth for phreatic water is about 5 m (Mengistu et al. 2018). Using records from 14 observation wells in the study area, the area of groundwater less than 5 m in depth per year in each zone was obtained, and the phreatic evaporation calculated according to the evaporation coefficients corresponding to different zones.

Statistical model

The multivariate linear regression model is a linear regression model with multiple explanatory variables, which is used to explain the linear relationship between the explained variable and other explanatory variables (George et al. 2016). Multivariate linear statistical models have unique characteristics that can meet the needs of this work. First, SGW interaction is influenced by many factors, and the multivariate statistical model can account for each factor. Second, the model has high practical applicability and can play an important role in the rapid prediction and calculation of SGW interaction. The multivariate linear regression equation is: 
formula
(14)
where β0, β1, β2, … βn are n+ 1 unknown parameters; β0 is the regression constant; β1, β2βn are the regression coefficients; Y is the explained variable; and X1, X2, … Xn are n + 1 explanatory variables.
In general, the determinant coefficient R2 is used to express the fitting degree of the regression equation to the original data. The values of R2 lie in the range of [0,1]. The closer R2 is to 1, the better the fitting degree of the prediction equation. The formula is: 
formula
(15)
where R2 is the determinant coefficient; ESS is the sum of the residual squares; and TSS is the sum of the regression squares. The above calculation can be completed automatically by SPSS software.

RESULTS

Surface water balance method

According to the principle of surface water balance, the water balance equation of the study area was established, and the amount of SGW interaction was obtained. The maximum value of SGW interaction was 80,277 × 104 m3 (in 1998), and the minimum value was 9,222.7 × 104 m3 (in 2002), with an average of 27,848.4 × 104 m3 over the entire period spanned by the data (Figure 4).

Figure 4

Annual SGW interaction.

Figure 4

Annual SGW interaction.

Based on the principle of water balance, the monthly SGW interaction from 1959 to 2014 was calculated (Figure 5). For clarity, these data are presented as the average of each decade. During each year from 1959 to 2014, SGW interaction increased gradually from January to July, and decreased gradually from August to December. SGW interaction was greatest between the months of June and September, accounting for 61.8% of the annual total. In other months, SGW interaction was relatively small, that is, the interaction of SGW was much larger in the flood season than in the dry season. In the 1950s, 1990s, and 2010s, the amount of interaction was relatively large compared with other decades.

Figure 5

Monthly SGW interaction.

Figure 5

Monthly SGW interaction.

Groundwater balance method

Calculations indicate that the amount of SGW interaction changed greatly from 2000 to 2013, with a maximum of 49,052.7 × 104 m3 (in 2012), a minimum of 9,994.7 × 104 m3 (in 2002), and an average value of 29,056 × 104 m3 (Figure 6). In 2002, the runoff of the Taoer River was blocked by an upstream reservoir, and its groundwater level was deep, so the river channel interaction in 2002 was small. After 2010, the discharge of upstream reservoirs increased gradually, and the interaction of rivers also showed a significant increasing trend.

Figure 6

Calculation of SGW interaction by the groundwater balance method. Qpr is the groundwater recharge for precipitation; Qcr is the groundwater recharge for canal water; Qir is the groundwater recharged to the underground for mining groundwater; Qlr is the groundwater recharge for groundwater runoff; QS–G is the interaction amount of SGW; Qpd is the groundwater for artificial mining; Qld is the groundwater discharged for groundwater runoff; Qed is the groundwater evaporation; ΔQ is the phreatic water storage.

Figure 6

Calculation of SGW interaction by the groundwater balance method. Qpr is the groundwater recharge for precipitation; Qcr is the groundwater recharge for canal water; Qir is the groundwater recharged to the underground for mining groundwater; Qlr is the groundwater recharge for groundwater runoff; QS–G is the interaction amount of SGW; Qpd is the groundwater for artificial mining; Qld is the groundwater discharged for groundwater runoff; Qed is the groundwater evaporation; ΔQ is the phreatic water storage.

Comparison and selection of calculation results of SGW interaction

The calculated results of SGW interaction are shown in Figure 7. The results obtained by the surface water balance method and the groundwater method are similar. This verifies the reliability of the surface water balance method for the calculation of SGW interaction. Owing to a lack of groundwater observation data and relatively short calculation duration, in the comprehensive analysis of the actual conditions of the relationship between SGW the surface water balance method is used to calculate the main results. The groundwater method is used as a comparison and reference.

Figure 7

Comparison of SGW interaction results obtained using the surface water balance method and the groundwater balance method.

Figure 7

Comparison of SGW interaction results obtained using the surface water balance method and the groundwater balance method.

Establishment of an SGW interaction model

The main factors influencing SGW interaction are river runoff, groundwater level, precipitation and evaporation. By calculating the annual and monthly interaction, a multivariate linear regression statistical model was established to simulate the interactive relationship between SGW in the study area.

  • (1)
    Multivariate linear regression statistical model (year): 
    formula
    (16)
  • (2)
    Multivariate linear regression statistical model (month): 
    formula
    (17)
where QS–G is the interaction of SGW in 104 m3; QS is the total runoff of the river in 104 m3; D is the groundwater level in m; P is precipitation in mm; and E is evaporation in mm.

Two calculation models, annual and monthly, are presented. The groundwater level data are obtained from long-term observation well 26600014 (45° 34′ 00.64″ N, 122° 33′ 49.37″ E) (Figure 1).

DISCUSSION

Interaction relationship between SGW

In the calculation of surface water balance and groundwater balance, the calculation results of QS–G are positive, which shows that QS–G is one of the discharge items of surface water balance and one of the recharge items of groundwater balance. The groundwater level of the three observation wells is perennially lower than the river water level, and the groundwater receives the seepage recharge of the river water. All of the above shows that the interaction relationship between SGW is that surface water recharges groundwater regularly.

Regularity of SGW interaction

From 1956 to 2014, the amount of SGW interaction in the study area varied significantly, influenced greatly by changes in river runoff (Figure 8(a)). To analyze the inter-annual trend of interaction, anomaly and cumulative anomaly evolution trend maps were used. From 1956 to 2014, the total amount of interaction showed an upward trend. From the perspective of inter-annual change, a decreasing trend was seen until 1996, after which an increasing trend was seen (Figure 8(b)). However, the exploitation of groundwater increased gradually, leading to a reduction in groundwater level, so that SGW interaction increased gradually. Furthermore, upstream of ZhenXi Hydrological Station, there are large reservoirs that became operational in the 1990s and are used for water storage. The runoff of the river is controlled artificially, resulting in a large impact on SGW interaction.

Figure 8

Calculation results of SGW interaction (a) and (c); calculation results of SGW interaction of anomaly and cumulative anomaly (b).

Figure 8

Calculation results of SGW interaction (a) and (c); calculation results of SGW interaction of anomaly and cumulative anomaly (b).

Within an individual year, the amount of SGW interaction first increases and then decreases, with the greatest amount of interaction occurring in July (Figure 8(c)). The trend in SGW interaction in the year is similar to that of river runoff. However, in August, when runoff is highest, SGW interaction begins to decrease. At this time, the groundwater level has risen substantially, and the interaction of SGW has been restrained to a great extent. This shows that SGW interaction is mainly affected by runoff and groundwater level.

Influencing factors and mechanisms of SGW interaction

The controlling factor influencing SGW interaction is the difference in water level between SGW. As the level of surface water depends on river runoff, the main factors affecting the interaction of SGW are river runoff and groundwater level. The greater the amount of precipitation, the larger the upstream inflow and corresponding increase of pre-interaction. With an increase in the amount of interaction, the groundwater level rises continuously, thus restraining the flow from surface water to groundwater. As evaporation increases, groundwater will reduce, which is beneficial to the interaction of SGW. Any artificial change in volume (for example from mining) will also be directly reflected as a change in groundwater level.

For the lithology of the stratum, the sand gravel at the top of the alluvial fan in the study area is directly exposed to the surface, the SGW are well connected, and the groundwater runoff is strong, all of which are conducive to the interaction of SGW. Weak, permeable soil layers with different layer thicknesses and relatively slow groundwater runoff greatly reduce SGW interaction.

Established statistical model

Using the calculated results of SGW interaction and incorporating several influencing factors, annual and monthly multivariate regression statistical models were established. In both cases the coefficient test was significant (α < 0.05). R2, which represents the goodness of fit, was 0.697 for the annual model and 0.405 for the monthly model, indicating that the annual interaction model is more reliable and can be used to predict the SGW interaction. The monthly interaction model has a lower R2 value due to periodic changes in runoff and groundwater level burial depth. However, for the influencing factors such as runoff, groundwater level and artificially exploited amount, the annual data are relatively independent, and the degree of interaction is very small, so the statistical model is more reliable. In the statistical analysis of integrated management of SGW, the annual statistical model results should be given priority, while the monthly statistical model results should be used based on the actual situation or as a reference.

CONCLUSION

  • (1)

    The interaction relationship between SGW in the study area is dependent on the infiltration of surface water to recharge groundwater.

  • (2)

    The average annual amount of SGW interaction in the study area is 27,848.4 × 104m3 annually, which shows a decreasing trend before 1996, followed by an increasing trend. Within any single year, the amount of interaction first increases, peaks in July, and then decreases. This variation is mainly influenced by river runoff and groundwater level.

  • (3)

    The statistical model of SGW interaction is suitable for future annual SGW interaction, and can be used as a reference for planning the use of water resources.

  • (4)

    In summary, in order to counter the gradual depletion of groundwater resources, the discharge of reservoirs upstream of the study area can be controlled manually, the river water can be appropriately stored during the flood season, and the amount of groundwater transferred from surface water to groundwater can be increased. Furthermore, the exploitation of groundwater should be strictly controlled, according to the forecast and calculated SGW interaction, extraction, the principles of recharge and balance, and the planned recovery and conservation of groundwater.

ACKNOWLEDGEMENTS

This work was financially supported by the National Natural Science Foundation of China (Project Approval No. 41572216); Project of Provincial-School Co-construction Plan: Frontier Science and Technology Guidance Class (SXGJQY2017-6); Key Projects of Geological Exploration Fund of Jilin Province (2018-13, 2018-11); Shenyang Geological Survey Center Project of China Geological Survey (121201007000150012).

CONFLICT OF INTEREST STATEMENT

The authors declare that they have no conflicts of interest.

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