## 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 × 10^{4}m^{3} 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. *R*^{2} 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 ^{222}Rn (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 km^{2}. 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).

## 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.

### 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.

*Q*

_{S-G}is the SGW interaction in 10

^{4}m

^{3};

*Q*

_{RE}is the recharge of the study area in 10

^{4}m

^{3};

*Q*

_{D}is the discharge of the study area in 10

^{4}m

^{3};

*Q*

_{ZX}is the actual measured runoff at the ZhenXi Hydrological Station in 10

^{4}m

^{3};

*Q*

_{WB}is the actual measured runoff at the WuBen Hydrological Station in 10

^{4}m

^{3};

*Q*

_{H}is the runoff of the Emutai River in 10

^{4}m

^{3};

*Q*

_{RI}is the direct recharge of rainwater to the river in 10

^{4}m

^{3};

*Q*

_{TN}is the actual measured runoff at the TaoNan Hydrological Station in 10

^{4}m

^{3};

*Q*

_{E}is the evaporation from the river surface in 10

^{4}m

^{3}; and

*Q*

_{C}is the water diversion from the canal in 10

^{4}m

^{3}.

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 × 10^{4} m^{3} 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.

### 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 (*γ*_{1}), and irrigation infiltration coefficient (*γ*_{2}). *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 *γ*_{1} and *γ*_{2} (Table 1).

Zone . | Area (km^{2})
. | Permeability coefficient (K) (m/d)
. | Specific yield (μ)
. | Precipitation infiltration coefficient (α)
. | Phreatic water evaporation coefficient (β)
. | Channel infiltration coefficient (γ_{1})
. | Irrigation infiltration coefficient (γ_{2})
. |
---|---|---|---|---|---|---|---|

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 |

Zone . | Area (km^{2})
. | Permeability coefficient (K) (m/d)
. | Specific yield (μ)
. | Precipitation infiltration coefficient (α)
. | Phreatic water evaporation coefficient (β)
. | Channel infiltration coefficient (γ_{1})
. | Irrigation infiltration coefficient (γ_{2})
. |
---|---|---|---|---|---|---|---|

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

*Δt*= 1a is used for calculations. The ‘a’ means one year. The formulae are: where

*ΔQ*is the amount of phreatic water storage in 10

^{4}m

^{3};

*F*is the area of the study region in m

^{2};

*ΔH*is the rate of groundwater level change in one year in the study region in m;

*Q*

_{r}is the amount of recharge for phreatic water in 10

^{4}m

^{3}; and

*Q*

_{d}is the amount of discharge for phreatic water in 10

^{4}m

^{3}.

*Q*

_{r}are: where

*Q*

_{pr}is the amount of groundwater recharge for precipitation in 10

^{4}m

^{3};

*P*is the amount of precipitation in mm;

*Q*

_{cr}is the amount of groundwater recharge for canal water in 10

^{4}m

^{3};

*Q*

_{c}is the amount of canal water;

*Q*

_{ir}is the amount of water recharged to the underground for mining groundwater in 10

^{4}m

^{3};

*Q*

_{i}is the amount of mining groundwater;

*Q*

_{lr}is the amount of groundwater recharge for groundwater runoff in 10

^{4}m

^{3};

*I*is the dimensionless hydraulic gradient of groundwater;

*M*is the aquifer thickness in m;

*L*

_{i}is the cross-section of groundwater inflow into the study area in m; and

*Q*

_{S–G}is the amount of SGW interaction in 10

^{4}m

^{3}.

*Q*

_{d}are: where

*Q*

_{pd}is the amount of groundwater for artificial mining in 10

^{4}m

^{3};

*Q*

_{ed}is the amount of water evaporation for phreatic water in 10

^{4}m

^{3};

*Q*

_{e}is the evaporation in mm;

*Q*

_{ld}is the amount of groundwater discharged for groundwater runoff in 10

^{4}m

^{3}; and

*L*

_{o}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

*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: where

*β*

_{0},

*β*

_{1},

*β*

_{2}, …

*β*are

_{n}*n*

*+*1 unknown parameters;

*β*

_{0}is the regression constant;

*β*

_{1},

*β*

_{2}…

*β*are the regression coefficients;

_{n}*Y*is the explained variable; and

*X*

_{1},

*X*

_{2}, …

*X*are

_{n}*n*+ 1 explanatory variables.

*R*

^{2}is used to express the fitting degree of the regression equation to the original data. The values of

*R*

^{2}lie in the range of [0,1]. The closer

*R*

^{2}is to 1, the better the fitting degree of the prediction equation. The formula is: where

*R*

^{2}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 × 10^{4} m^{3} (in 1998), and the minimum value was 9,222.7 × 10^{4} m^{3} (in 2002), with an average of 27,848.4 × 10^{4} m^{3} over the entire period spanned by the data (Figure 4).

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.

### Groundwater balance method

Calculations indicate that the amount of SGW interaction changed greatly from 2000 to 2013, with a maximum of 49,052.7 × 10^{4} m^{3} (in 2012), a minimum of 9,994.7 × 10^{4} m^{3} (in 2002), and an average value of 29,056 × 10^{4} m^{3} (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.

### 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.

### 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)
- (2)

*Q*

_{S–G}is the interaction of SGW in 10

^{4}m

^{3};

*Q*

_{S}is the total runoff of the river in 10

^{4}m

^{3};

*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 *Q*_{S–G} are positive, which shows that *Q*_{S–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.

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). *R*^{2}, 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 *R*^{2} 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 × 10

^{4}m^{3}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.