# Simulation of Water Quality in a River Network with Time-Varying Lateral Inflows and Pollutants

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. River Network Hydrodynamic Model

#### 2.1. Improvements to the Control Equation

_{i}and pollutant input q

_{i}C

_{i}to the river network, both of which change with rainfall intensity and runoff. Therefore, the lateral boundary parameters in the hydrodynamic water quality model for a river network are not constant; that is, lateral runoff q

_{i}(t) and pollutant input q

_{i}(t)C

_{i}(t) are time-varying processes. This means that the control equations for the river network model can be improved by the time-varying processes of lateral inflow and pollutant inputs as follows:

_{i}(t) is the time-varying lateral inflow, C

_{i}(t) is the time-varying lateral inflow pollutant concentration, C is the pollutant concentration in the river network, λ is the pollutant degradation coefficient, R is the hydraulic radius, n is the Manning coefficient, and the other symbols are the same as before.

#### 2.2. Time-Varying Process Associated with Lateral Inflow

_{m}(t) is the lateral inflow per unit time and unit width at the node (m

^{3}/sm), P

_{m}(t) is the rainfall intensity of the block around the mth node (mm/h), A

_{mj}is the area of the jth block around the mth node (km

^{2}), α

_{m}is the runoff coefficient of the block around the mth node, β

_{m}is the proportion of the runoff into the mth node in the jth block, that is, the runoff distribution coefficient, and the constant 3.6 is the conversion coefficient of the parameter unit.

_{im}(t) of the mth node into the ith tributary, then the inflow of the ith tributary should be equal to the sum of all the nodes into the tributary, so the time-varying process q

_{i}(t) for the lateral inflow of the ith tributary in Equation (1) can be calculated according to the following formula:

_{i}is the number of computing nodes associated with the ith tributary.

#### 2.3. Calculation Method for Lateral Pollutant Concentration

_{mj}(t) is the pollutant concentration of the jth block of the mth node, then the total amount of pollutants entering the mth node is as follows:

_{im}(t)c

_{im}(t), which can be calculated according to Equation (6), then the lateral pollutant input of the ith tributary should be equal to the sum of the pollutant input of all the nodes into the tributary, that is, q

_{i}(t)C

_{i}(t) in Equation (3) can be calculated using the following equation:

_{i}(t) is the time-varying lateral inflow of the ith tributary, C

_{i}(t) is the time-varying pollutant concentration in the lateral inflow of the ith tributary, and q

_{i}(t)C

_{i}(t) is the time-varying lateral pollutant input into the ith tributary, which includes regional non-point source and point source pollution inputs at the outfall. For the Maozhou River Basin, the time-varying lateral pollutant input q

_{i}(t)C

_{i}(t) is mainly a regional non-point source pollutant input. The term q

_{im}(t) indicates the time-varying lateral inflow at the mth node of the ith tributary, and C

_{im}(t) indicates the time-varying pollutant concentration of the lateral inflow at the mth node of the ith tributary.

## 3. Case Study

#### 3.1. Mainstream and Tributaries of the Maozhou River

^{2}, of which 112.65 km

^{2}is under the jurisdiction of Bao’an. The water system diagram is shown in Figure 1. Bao’an District is densely built-up with a relatively high proportion of industrial land. In addition to scarce background water sources, the river water pollutants seriously exceed the national standard and do not meet surface water class V, which means that the water ecological environment urgently needs to be improved. The water quality of the river network has recently been significantly improved by introducing reclaimed water from the Sewage Treatment Plant in Bao’an District to supplement the main water source. However, the non-point source pollution in the highly built-up area during the rainy season means that it is difficult to continuously and stably comply with the water quality standards.

#### 3.2. Determination of Regional Non-Point Source Chemical Oxygen Demand (COD) Load

#### 3.3. Regional Divisions and Node Pollutant Distribution

## 4. Results and Discussion

#### 4.1. Parameter Calibration of the River Network Hydrodynamic Water Quality Model

_{O}

^{t}is the measured value at time t, Q

_{m}

^{t}is the simulated value at time t, $\overline{{Q}_{O}}$ is the average of the observed values.

^{2}/s. The results of the model calibration are shown in Figure 7. In the Gonghe Village, The NSE values for water level and ammonia nitrogen concentration section were 0.988 and 0.841, and P were 0.88 and 0.99, respectively, indicating that the model could accurately simulate river hydrodynamics and water quality.

#### 4.2. Comparative Analysis of the Improved Model

#### 4.3. Analysis of the River Water Quality Change Law after Rain and Ecological Water Supplements Were Optimized

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

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**Figure 10.**COD concentrations during and after rainfall in the mainstream section and tributaries of the Maozhou River.

**Figure 11.**COD concentration after rainfall in the mainstream section and tributaries of the Maozhou River after water supplement optimization.

**Figure 12.**COD concentration changes in a typical river section following rain and before and after optimization of the water supplement scheme.

Block | Underlay Surface Type |
---|---|

A | Non-urban construction land, park green space |

B | High-end residential areas, public buildings, science and technology parks |

C | Ordinary commercial areas, ordinary residential areas, well-managed factories or industrial areas, municipal roads |

D | Farmers’ markets, garbage transfer stations (houses), food streets, urban villages, village-run industrial zones |

Rivers/Canals | Water Supplement Volume (10,000 m^{3}/d) | Water Quality Recovery Days after Moderate Rain | Remarks | ||
---|---|---|---|---|---|

Current Status | Optimization | Current Status | Optimization | ||

Qizhi Canal | 2 | 2 | 1.25 | 0.75 | The water supplement site is moved upstream |

Wanfeng R. | 2.4 | 2.4 | 1.75 | 0.8 | The water supplement site is moved upstream |

Shajing R. | 6.5 | 6 | 0.9 | 1 | Adjust water supplement volume |

Shangliao R. | 10.6 | 9.1 | 0.75 | 0.9 | Adjust water supplement volume |

Songgang R. | 0 | 1 | 2.7 | 1.5 | Add water supplement sites |

Shiyan Canal | 0 | 1 | 2.5 | 1.2 | Add water supplement sites |

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**MDPI and ACS Style**

Sun, Z.; Cheng, K.; Liu, J.; Guo, W.; Guo, J.
Simulation of Water Quality in a River Network with Time-Varying Lateral Inflows and Pollutants. *Water* **2023**, *15*, 2861.
https://doi.org/10.3390/w15162861

**AMA Style**

Sun Z, Cheng K, Liu J, Guo W, Guo J.
Simulation of Water Quality in a River Network with Time-Varying Lateral Inflows and Pollutants. *Water*. 2023; 15(16):2861.
https://doi.org/10.3390/w15162861

**Chicago/Turabian Style**

Sun, Zhilin, Kaiyu Cheng, Jing Liu, Wenrui Guo, and Jing Guo.
2023. "Simulation of Water Quality in a River Network with Time-Varying Lateral Inflows and Pollutants" *Water* 15, no. 16: 2861.
https://doi.org/10.3390/w15162861