## Abstract

In this paper, we take the Qinhuai River Basin in Nanjing as an example to study the influence of diversion flow ratio on the water environment. The daily precipitation of 20 rainfall stations in the basin was collected from 1962 to 2006, and the rainfall under different assurance rates was calculated by P-III frequency curve to calculate the surface runoff in different typical years. In the meantime, according to the downstream furcated estuary water level in different typical years, the diversion flow ratio under different frequencies was calculated by using a mathematical model of the water environment. The results show that the diversion flow ratio of a branch channel increases with the increase of water level difference, and the growth rate decreases gradually. The other branch channel diversion flow ratio decreases with the increase of water level difference, and the decreasing rate decreases gradually. The pollutant concentrations in the bifurcated rivers are equal, but the concentration decreases exponentially with the increase of the upstream flow. Under different rainfall frequencies, the diversion pollutant ratio and diversion flow ratio are equal in different months of different years.

## INTRODUCTION

A bifurcated river is a kind of plain river landscape, because of the heart beach, the sandbar causing river bed division. Bifurcated rivers are like the main trunk of a tree and branches: the main trunk is the mainstream, a tree branch is a sub-stream. Diversion flow ratio refers to the percentage of a branch channel flow to the mainstream channel flow. The diversion pollutant ratio is the percentage of a single pollutant flux in a branch channel that accounts for the flux of the main stream pollutants. Previous studies have studied the situation of river diversion, but less research has been conducted on the diversion pollutant ratio of branch channels, and moreover, they have not studied the evolution of diversion flow ratio and diversion pollutant ratio. Based on the Qinhuai River, this paper explores the influence of diversion flow ratio on the water environment.

In 1944, Taylor (1944) studied open channel flow structure, considering that the diversion flow ratio is related to estuary hydrodynamics and the reflux conditions of the branches. Grace & Priest (1958) studied the relationship between diversion flow ratio and water depth, taking into account the bifurcation angle and width ratio between the main stream and the branch river. Law & Reynolds (1966) established a relationship between the shunt ratio, contraction coefficient and Froude number in 1966 through the momentum equation, energy equation, and continuity equation into the branch contraction coefficient. Ramamurthy & Satish (1988) and Ramamurthy *et al.* (1990, 1995, 1996) studied the relationship between diversion flow ratio, width ratio and contraction coefficient, and studied the variation law of energy loss before and after branching. Bifurcated river diversion flow ratio from theoretical research to experimental studies and the application of modern commercial software (Zhang *et al.* 2016) have gradually become mature, which has provided more mature theoretical guidance for the current diversion ratio study.

According to the spatial distribution, the mathematical model of the water environment is divided into a one-dimensional river network hydrodynamic and water quality model, planar two-dimensional hydrodynamic and water quality model under a curved coordinate system, and three-dimensional hydrodynamic and water quality model under a curved coordinate system (Di Toro *et al.* 1983; Zhou & Lin 1998; Yuan *et al.* 2005; Zhang *et al.* 2005). One-dimensional river network hydrodynamics and water quality model commonly used numerical methods are: hierarchical solution, combined element solution, and finite element method (Szymkiewicz 1991; Feng & Rui 1999; Sen & Garg 2002; Wu *et al.* 2004; Zhang 2005). Two-dimensional hydrodynamic and planar water quality model commonly used numerical methods are: finite difference method, finite element method, finite analysis, and finite volume method (Sladkevich *et al.* 2000; Duan *et al.* 2001; Chau & Jin 2002; Arega & Sanders 2004; Lu *et al.* 2005). Three-dimensional hydrodynamic and water quality model commonly used numerical methods are: finite difference method, finite analysis, and finite volume method (Fang & Wang 2000; Wilson *et al.* 2003; Jia *et al.* 2004; Chen & Sheng 2005; Chao *et al.* 2006). At present, there are many models to simulate the hydrodynamics and water quality of river courses. Commonly used models such as QUAL2 K (Modeling Framework for Simulating River and Stream Water Quality), MIKE11 (Modeling System for Rivers and Channels), WASP (Water Quality Analysis Simulation Program) and EFDC (Environmental Fluid Dynamics Code) make no significant difference in the calculation results (Zhao *et al.* 2011).

The Qinhuai River Basin is located in the main urban area of Nanjing. It has a population of about 6 million and a total GDP of 134 billion USD. It is also an important political center in East China. The Qinhuai River is an important tributary of the Yangtze River. Preventing floods and water pollution is very important in this region. The water level of the Yangtze River controls the water level of the Qinhuai River estuary. For a single channel, the downstream water level only controls the water level of the whole river and does not affect the upstream water flow. However, for the bifurcated river, a water level change of any of the rivers affects the water level of the whole river and the flow of the branching channel, that is, it changes the diversion flow ratio. The water level of the Yangtze River is constantly changing and is full of uncertainty, which means that the water level and flow of the Qinhuai River are also full of uncertainty. The Qinhuai River runs through the densely populated and economically developed city of Nanjing. We study the relationship between water level difference and diversion flow ratio for the purpose of safeguarding people's lives and property. Assume that the water level difference has a relationship with the split ratio, so that by setting a gate at the estuary to adjust the water level, a suitable diversion flow ratio can be obtained to ensure urban safety. Taking the Qinhuai River Basin typical bifurcated river as an example, based on the daily precipitation data of 20 rainfall stations in the basin from 1962 to 2006, the P-III frequency curve is used to analyze the annual rainfall under different frequencies. After determining different typical frequency years, the water level of these years is collected, and further the runoff under different frequencies is calculated according to the surface runoff coefficient in the basin. By using the Mike11HD hydrodynamic model, the upstream flow rate and the downstream water level are taken as the boundaries, and the monthly flow diversion flow ratio in different years is calculated. The correlation between the diversion ratio and the downstream water level difference is obtained. Then, using the model of Mike11AD to calculate the pollutant concentrations under different diversion flow ratios, the relationship is further analyzed to find out the monthly migration of pollutants in frequency years of the bifurcated river. By studying the relationship between the water level difference between the bifurcated rivers and the diversion ratio, a scientific basis is provided for flood control in the city. At the same time, studying the relationship between the concentration of pollutants in the bifurcated rivers and the water level will provide a scientific basis for the improvement of the water environment in the Qinhuai River Basin.

## METHODOLOGY

### Study area

The Qinhuai River (118° 29′E ∼ 119° 2′E, 31° 35′N ∼ 32° 4′N) is a typical bifurcated river in the lower reaches of the Yangtze River in Nanjing, China (Figure 1). The total area of the basin is 2,659 km^{2}. There are three national water quality sections on the Qinhuai River. Since 2016, water quality has continued to fail to meet the target. Due to the large population density in the main urban area of Nanjing, the urban sewage collection rate is low (≈70%), and some domestic sewage is directly discharged into the river, leading to water pollution. The water quality of the downstream section cannot reach the target and is affected by the whole basin. Therefore, we choose the whole basin for research. The Qinhuai River is the main stream from point E to point D, with 12 tributaries flowing into the main stream and the downstream of the New Qinhuai River (D–A section) and the Outer Qinhuai River (D–B section). In the basin there are four water level stations (ABCD), monitoring the actual water level, with C also as the flow station, monitoring the actual flow. There are 20 rainfall stations in the basin, and daily precipitation data from rainfall stations from 1962 to 2006 have been collected.

### Study method

First, based on the annual precipitation data from various rainfall stations in Qinhuai River Basin from 1962 to 2006, the P-IIIfrequency curve is used for calculation, and the annual average precipitation under different frequencies is further calculated. The typical years of different frequency are selected, and then the average annual runoff of surface water in typical years is calculated according to the runoff coefficient of the basin.

The hydrodynamic model (HD) of the MIKE11 software is used to calculate the diversion flow ratio for different typical years of the bifurcated river (Keupers & Willems 2017; Li *et al.* 2017). The upstream (point E, 1–12) is taken as the boundary of the flow, and the monthly flow of each tributary is calculated from the monthly precipitation, the basin area of each tributary and the surface runoff coefficient (0.5). Downstream (point A, point B) takes the water level as the boundary. By searching the hydrological almanac of the Yangtze River Basin, the average monthly water level at the two points is obtained, and the diversion ratio of New Qinhuai River and Outer Qinhuai River can be calculated.

_{3}-N and total phosphorus (TP) in the upper stream (point E, 1–12) were selected as 15 mg/L, 0.5 mg/L and 0.1 mg/L respectively. At point ⑨, 1 m

^{3}/s pollutant outlet was generalized, at which concentrations of COD, NH

_{3}-N and TP were 300 mg/L, 30 mg/L and 3 mg/L respectively. The degradation coefficients of the three pollutants were 0.06 d

^{−1}. By coupling the hydrodynamic module (HD), the concentration of pollutants at point A and point B is further calculated to further analyze the pollutant flux to obtain the diversion pollutant ratio. Then the calculated diversion flow ratio and pollutant concentrations were compared to study the influence of the diversion flow ratio on the water environment.

The flow of the river was measured by a shipping ADCP (Acoustic Doppler Current Profiler). At the same time, we conducted water sampling at all monitoring sites. We used a 10-litre bucket to collect water samples at the 1/4, 1/2, and 3/4 river-width of the cross-section. The water sample depth was 0.5 m underwater. We filled the water sample in 500 ml volume Plexiglas bottles and dropped 15 drops of 98% concentrated sulfuric acid as a stabilizer in each water sample. The concentration of COD was determined by the acid potassium permanganate method, the concentration of ammonia nitrogen was determined by the spectrophotometric method of nano-reagent, and the total phosphorus concentration was determined by ammonium molybdate spectrophotometry. Some of the older data come from the Statistical Yearbook.

## RESULTS AND DISCUSSION

### Calculation of typical annual monthly runoff

Based on the daily precipitation data from the 20 rainfall stations, the daily average precipitation in the basin from 1962 to 2006 was calculated. The data from the 20 rainfall stations were analyzed to get the annual average rainfall, *C*_{V}, maximum annual rainfall, year of maximum rainfall, minimum rainfall, year of minimum rainfall, and maximum to minimum. Then, we obtained the P-III frequency distribution curve of annual average rainfall in Qinhuai River Basin (Figure 2).

According to the P-III frequency distribution curve (Figure 2), the average annual precipitation under different assurance rates and its typical years are obtained. According to the total area of the basin and the area of each tributary of small watershed, the total runoff and each tributary runoff are calculated. The data of runoff at point E and points 1–12 were used as the flow boundary condition for the hydrodynamic model (Table 1). The yearly concentrations of COD, ammonia nitrogen and total phosphorus at point D are also shown in Table 1.

Precipitation frequency (%) . | 10 . | 25 . | 50 . | 75 . | 80 . | 90 . | 95 . |
---|---|---|---|---|---|---|---|

Precipitation (mm) | 1,391.27 | 1,214.79 | 1,049.76 | 916.82 | 889.32 | 820.56 | 774.72 |

Typical year (year) | 1987 | 2002 | 2005 | 2004 | 1979 | 1966 | 1973 |

Runoff (m^{3}/s) | 58.04 | 50.67 | 43.79 | 38.24 | 37.1 | 34.23 | 32.32 |

E | 11.58 | 10.11 | 8.74 | 7.63 | 7.40 | 6.83 | 6.45 |

1 | 4.15 | 3.62 | 3.13 | 2.73 | 2.65 | 2.45 | 2.31 |

2 | 5.07 | 4.43 | 3.83 | 3.34 | 3.24 | 2.99 | 2.83 |

3 | 1.88 | 1.64 | 1.41 | 1.24 | 1.20 | 1.11 | 1.04 |

4 | 3.20 | 2.79 | 2.41 | 2.11 | 2.04 | 1.89 | 1.78 |

5 | 4.70 | 4.10 | 3.55 | 3.10 | 3.00 | 2.77 | 2.62 |

6 | 1.10 | 0.96 | 0.83 | 0.73 | 0.71 | 0.65 | 0.61 |

7 | 20.74 | 18.10 | 15.65 | 13.66 | 13.26 | 12.23 | 11.55 |

8 | 0.66 | 0.58 | 0.50 | 0.44 | 0.42 | 0.39 | 0.37 |

9 | 2.21 | 1.93 | 1.66 | 1.45 | 1.41 | 1.30 | 1.23 |

10 | 1.85 | 1.62 | 1.40 | 1.22 | 1.18 | 1.09 | 1.03 |

11 | 0.57 | 0.50 | 0.43 | 0.38 | 0.37 | 0.34 | 0.32 |

12 | 0.33 | 0.29 | 0.25 | 0.22 | 0.21 | 0.20 | 0.18 |

COD (mg/L) | 21 | 24 | 23 | 23 | 25 | 24 | 23 |

NH_{3}-N (mg/L) | 1.11 | 1.42 | 1.34 | 1.33 | 1.55 | 1.47 | 1.33 |

TP (mg/L) | 0.158 | 0.189 | 0.180 | 0.181 | 0.202 | 0.194 | 0.181 |

Precipitation frequency (%) . | 10 . | 25 . | 50 . | 75 . | 80 . | 90 . | 95 . |
---|---|---|---|---|---|---|---|

Precipitation (mm) | 1,391.27 | 1,214.79 | 1,049.76 | 916.82 | 889.32 | 820.56 | 774.72 |

Typical year (year) | 1987 | 2002 | 2005 | 2004 | 1979 | 1966 | 1973 |

Runoff (m^{3}/s) | 58.04 | 50.67 | 43.79 | 38.24 | 37.1 | 34.23 | 32.32 |

E | 11.58 | 10.11 | 8.74 | 7.63 | 7.40 | 6.83 | 6.45 |

1 | 4.15 | 3.62 | 3.13 | 2.73 | 2.65 | 2.45 | 2.31 |

2 | 5.07 | 4.43 | 3.83 | 3.34 | 3.24 | 2.99 | 2.83 |

3 | 1.88 | 1.64 | 1.41 | 1.24 | 1.20 | 1.11 | 1.04 |

4 | 3.20 | 2.79 | 2.41 | 2.11 | 2.04 | 1.89 | 1.78 |

5 | 4.70 | 4.10 | 3.55 | 3.10 | 3.00 | 2.77 | 2.62 |

6 | 1.10 | 0.96 | 0.83 | 0.73 | 0.71 | 0.65 | 0.61 |

7 | 20.74 | 18.10 | 15.65 | 13.66 | 13.26 | 12.23 | 11.55 |

8 | 0.66 | 0.58 | 0.50 | 0.44 | 0.42 | 0.39 | 0.37 |

9 | 2.21 | 1.93 | 1.66 | 1.45 | 1.41 | 1.30 | 1.23 |

10 | 1.85 | 1.62 | 1.40 | 1.22 | 1.18 | 1.09 | 1.03 |

11 | 0.57 | 0.50 | 0.43 | 0.38 | 0.37 | 0.34 | 0.32 |

12 | 0.33 | 0.29 | 0.25 | 0.22 | 0.21 | 0.20 | 0.18 |

COD (mg/L) | 21 | 24 | 23 | 23 | 25 | 24 | 23 |

NH_{3}-N (mg/L) | 1.11 | 1.42 | 1.34 | 1.33 | 1.55 | 1.47 | 1.33 |

TP (mg/L) | 0.158 | 0.189 | 0.180 | 0.181 | 0.202 | 0.194 | 0.181 |

According to the annual data from hydrological almanacs in the typical years (1987, 2002, 2005, 2004, 1979, 1966, 1973), we can get the monthly rainfall of a typical year and obtain the monthly runoff by further calculation (Figure 3). And then through all the tributaries of the basin proportion of the total catchment (E, 1–12: 22.89%, 6.88%, 8.42%, 3.11%, 5.31%, 7.80%, 1.83%, 34.42%, 1.10%, 3.66%, 3.08%, 0.95%, 0.55%), get the runoff of tributaries. The two exits of the Qinhuai River Basin are located on the Yangtze River, and the A point is located at the upstream of point B. The perennial flow of the Yangtze River is from A to B, and the water level at point A is higher than at point B. At the same time, we can see that the average monthly water level of the downstream (point A, point B) in a typical year (Figure 3) is used as the water level boundary condition for the calculation of the hydrodynamic model.

### Calculation and analysis of the diversion flow ratio of the bifurcated river

Prior to formally calculating the split ratio, the model is verified. C, D and E point water level, and C point flow rate on July 3, 2014, to July 15 were verified. D point water level and C point flow rate on June 17, 2015, to July 11 were verified. It can be seen from the results (Figure 4) that the model calculation results are in good agreement with the measured results, indicating that the construction of the model is correct, so that we can proceed to the diversion flow ratio calculation.

The flow of New Qinhuai River (Figure 5(b)) and Outer Qinhuai River (Figure 5(a)) of the downstream bifurcated river was calculated by the mathematical model of the water environment. The flow direction of Outer Qinhuai River does not change with other conditions changing in different typical years. The diversion flow in different typical years shows first an increase and then a decrease with the increase of the month, which trend is consistent with the rainfall, total surface runoff, water level and water level difference. If water level difference is small, the upper reaches of the Qinhuai River flow into the Yangtze River. If the water level in AB is relatively large and it is in the wet season, the water in point A will flow to point B, and the upstream runoff will still flow into the Outer Qinhuai River. Therefore, the flow in Figure 5(a) will be negative. In general, the New Qinhuai River backflow occurred in the wet season, and the runoff first increased and then decreased with the increase of the month. The total surface runoff of the mainstream and the annual maximum of the flow rates of the D–A and D–B branches were all advanced with the increase of the rainfall frequency. The total surface runoff of the mainstream was the most obvious, with the maximum reaching from August to April.

The relationship between the bifurcated river diversion flow and AB water-level difference is analyzed. The Outer Qinhuai River diversion flow increases with the increase of water-level difference, and its growth rate also increases gradually (Figure 6(a)). The New Qinhuai River flow decreases with the increase of water level, and the reduction rate also increases gradually. When the water level difference is greater than 0.17 m, New Qinhuai River flows backward and the diversion flow increases with the increase of water level difference, and its growth rate also decreases gradually (Figure 6(c)). The relationship between diversion flow ratio and water level difference is analyzed. The diversion flow ratio of the Qinhuai River increases with the increase of water level, and its growth rate decreases gradually (Figure 6(b)). The diversion flow ratio of New Qinhuai River decreases with the increase of water level, and the reduction rate also decreases gradually (Figure 6(d)).

### Calculation and analysis of diversion pollutant ratio of the bifurcated river

According to the study method described above, the concentrations of COD, NH_{3}-N and TP in the upper stream (point E, 1–12) were selected as 15 mg/L, 0.5 mg/L and 0.1 mg/L respectively. At point ⑨, a 1 m^{3}/s pollutant outlet was generalized, at which the concentrations of COD, NH_{3}-N and TP were 300 mg/L, 30 mg/L and 3 mg/L respectively. Then, the water quality of the bifurcated river under different upstream runoffs was calculated.

According to the calculation results (Figure 7(1–3)), the ratios of COD, NH_{3}-N and TP pollutants between the two branches are both about 1, that is, the upstream pollutant concentration does not change with the river division. The concentrations of COD, NH_{3}-N and TP in the D–B section decrease exponentially with the increase of the upstream flow (Figure 7(4–6)). Similarly, the concentrations of COD, NH_{3}-N, and TP pollutants in the D–A section also decrease exponentially with the increase of upstream flow (Figure 7(7–9)).

The pollutant concentration (g/s) is multiplied by the pollutant concentration and the flow rate in the distributary channel, and the diversion pollutant ratio of the branch channel is further calculated by accounting for the upstream pollutant flux.

The calculated diversion pollutant ratio is related to the diversion flow ratio (Figure 8). The diversion flow ratio of D–B and D–A in the bifurcated river is positively related to the diversion pollutant ratio, and the ratio of flow ratio to pollutant ratio is about 1, that is, the diversion ratio is equal to the fouling ratio. In the analysis of diversion ratios of different months in different years, there is 86.3% probability of the diversion ratio of the D–B section being between 0.3 and 0.8, and 86.3% probability of that of the D–A section being between 0.2 and 0.7.

## CONCLUSION

According to the study of the Qinhuai River watershed in Nanjing, it is found that the diversion flow ratio of a branch channel increases with the increase of water level difference, and the increase rate decreases gradually. The other branch channel diversion flow ratio decreases with the increase of water level difference, and the decreasing rate decreases gradually. In the future, based on different precipitation and downstream water levels, the diversion ratio of the bifurcated river could be predicted, and flood control dispatching in urban areas will be done in a timely manner in wet years to avoid flood disasters in urban areas, and in dry years in a timely manner to replenish the water, to ensure the safety of urban water supply. The pollutant concentrations in the bifurcated rivers are equal, but the concentration decreases exponentially with the increase of the upstream flow. Under different rainfall frequencies, the diversion pollutant ratio and diversion flow ratio are equal at different months of different years. According to the hydrological situation, the water quality of the bifurcated river is predicted. During the wet period, with urban flood control and dispatching, the transport of pollutants in the sub-river should be timely to improve the water quality in urban areas. During the dry season, it is predicted in good time to take good ecological compensation measures in advance to ensure the ecological environment and water quality of the rivers.

## ACKNOWLEDGEMENTS

This research was supported by the Fundamental Research Funds for the Central Universities (Grant No. 2017B613X14), Postgraduate Research & Practice Innovation Program of Jiangsu Province (Grant No. KYCX17_0417), Priority Academic Program Development of Jiangsu Higher Education Institutions, National Natural Science Foundation of China (Grant No. 5187090164), China Scholarship Council (Grant No. 201806710159).