# Optimizing Water Distribution in Transboundary Rivers Based on a Synthesis–Dynamic–Harmonious Approach: A Case Study of the Yellow River Basin, China

^{1}

^{2}

^{3}

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## Abstract

**:**

^{3}and 30 billion m

^{3}, upon which calculations were performed. This study should provide a scientific and reasonable scheme for water distribution of transboundary rivers, and rational utilization of water resources. It should lay a solid foundation for the high-quality development of the Yellow River basin.

## 1. Introduction

^{3}and 30 billion m

^{3}of water allocation. The rationality of the scheme is analyzed and demonstrated. This manuscript attempts summarize the theories and technical methods of water distribution in transboundary rivers, assist the formation of systematic water distribution ideas and standards, and provide a basis for water distribution in transboundary rivers across regions and even countries.

## 2. Materials and Methods

#### 2.1. Theoretical System of Water Distribution in Transboundary Rivers

#### 2.1.1. Framework of the Water Distribution System for Transboundary Rivers

#### 2.1.2. Water Distribution Ideas

#### 2.1.3. Water Distribution Principles

#### 2.1.4. Water Distribution Rules

#### 2.2. Water Distribution Calculation Methods for Transboundary Rivers

#### 2.2.1. Rule-Based Calculation to Obtain the Water Distribution Scheme for Each Element

_{kp}is the water distribution under the pth water distribution scheme in the k area; k is the area code, k = 1, 2, …, n; p = 2 (representing rule b); ω is the adjustment coefficient of the current water consumption; Q

_{k}

_{1}is the current water consumption; Q

_{k}

_{2}is future water consumption, obtained by considering the scale of future development. This paper uses ω = 0.5 when calculating the Yellow River water distribution scheme, i.e., the current and future water consumptions will each account for half of the proportion. Note that the value of ω is adjustable to reflect its relative importance.

_{k}is the actual water-using population in the kth area; P

_{t}is the total actual water-using population in the basin; Q

^{1}

_{td}is the distributable water volume; and p = 3 (representing rule b). Other symbols are similar to above.

_{k}is the GDP of the k th area; G

_{t}is the total GDP in the basin; and p = 4 (representing rule d). Other symbols are the same as before.

_{k}is the basin area of the k th area; S

_{t}is the total basin area; and p = 5 (representing rule e). Other symbols are mentioned earlier.

_{k}is the harmony behavior of the kth area, i.e., the actual water consumption; G

_{k}is the harmonious behavior in the kth area that meets the harmony rules, i.e., it does not exceed the water consumption under the allocated water volume. In Equation (5), i and j are the harmony coefficient and the disharmony coefficient, respectively, which are calculated using the function curve given by Zuo (2016) [36].

#### 2.2.2. Consideration of Dynamic Changes for Dynamic Correction

^{1}

_{k}is the new water distribution scheme with the amount of water that can be distributed; Q

^{0}

_{k}is the original water distribution scheme; and Q

^{0}

_{td}is the original water distribution volume.

#### 2.2.3. Consideration of the Water Constraints of Each Area for Correction

_{min}is the minimum water demand to meet the regional ecology, life, and production; Q

_{max}is the maximum water demand under the control of the water efficiency quota; and Q

_{k}is the allocated water volume of the kth area.

#### 2.2.4. Calculation and Determination of the Water Distribution Scheme

_{j}of each water distribution scheme. To comprehensively synthesize the opinions of different scholars, we conducted a survey (through the water science QQ group, the water science WeChat group, and the Yellow River Forum expert WeChat group) to obtain a sum of 180 completed questionnaires. Through a statistical analysis, we finally summarized six weights of the water separation rules (i.e., 0.170, 0.255, 0.130, 0.090, 0.080, and 0.275). For different rivers, similar methods can be used to obtain specific weights.

_{k}, for the kth area.

_{k}according to the same rate of change.

_{k}meets the minimum water demand and water efficiency constraints.

## 3. Case Study

#### 3.1. Overview of the Study Area

^{2}, accounting for only 1.7% of the total basin area. The Yellow River water distribution research scope defined here is based on the natural boundary of the basin. As demonstrated in Figure 5, the research scope includes 70 water distribution units. By processing this set of data, the water distribution results of the nine provinces are calculated according to the water distribution method of transboundary rivers.

#### 3.2. Data Source and Description

^{3}. This study first allocates 37 billion m

^{3}of water available to the Yellow River reasonably among the provinces. If the available water is adjusted, the corresponding water distribution of each province can also be obtained according to the dynamic correction formula. In our calculation, 2017 is the current water-use year. When calculating the degree of harmony, the water consumption in the past 10 years is used as the original data, and the water consumption of each region in the 1987 water distribution scheme is adjusted according to the degree of harmony to achieve the maximum value.

## 4. Results and Discussion

#### 4.1. New Water Distribution Scheme for the Yellow River

#### 4.1.1. Calculation of Water Distribution Corresponding to Each Scheme

^{3}. In this section, a reasonable water distribution among the provinces is performed. If the available water is adjusted, the water distribution of each province can also be calculated by referring to the dynamic adjustment formula. In this calculation, six water distribution schemes are obtained according to Equations (1)–(5) and the original water distribution scheme. Among them, scheme (B) refers to the future water requirement, which is obtained according to the total water consumption control target in the “implementation of the most stringent water resource management system assessment method”, and combined with the comprehensive regional water resource planning and water resource bulletin data. Scheme (F) uses water consumption of the last 10 years as the original data when calculating the degree of harmony. It adjusts the amount of water allocated in the water distribution scheme according to the degree of harmony, to achieve the maximum overall degree of harmony.

^{3}. Secondly, the remaining water supply of 36.024 billion m

^{3}will be distributed to nine provincial administrative regions in the basin, according to six schemes, as shown in Figure 6a. Finally, according to the weight of each scheme obtained (Figure 6b), the final water quantity and water proportion of each province are calculated (Figure 7), and compared with the 1987 water quantity scheme (Figure 8).

#### 4.1.2. Dynamic Adjustment of Water Distribution

^{3}of distributable water of the Yellow River is taken as an example for illustration purposes (refer to Figure 9). Supposing that the distributable water volume is not 30 billion m

^{3}, the calculation can be done similarly.

#### 4.2. Analysis of Changes in the Yellow River Water Distribution Scheme

#### 4.2.1. Changes of Water Volume in Various Provinces

^{3}.

#### 4.2.2. Dynamic Adjustment of the Distributable Water Volume

^{3}to 30 billion m

^{3}. Similarly, a new water distribution scheme can be developed using the given method.

#### 4.2.3. Comparative Analysis of Water Distribution

## 5. Conclusions

- (1)
- According to the related concepts and characteristics of transboundary rivers, we summarized the theoretical system (i.e., ideas of water distribution, principles of water distribution, rules of water distribution) of transboundary river water distribution. Furthermore, we applied the theory of harmony to the water division of transboundary rivers, and laid the foundation for proposing the calculation method for harmonious water distribution.
- (2)
- On the basis of the theoretical system of water distribution in transboundary rivers, we constructed a “synthesis–dynamic–harmonious water distribution method” (SDH). We applied the SDH method to estimate the Yellow River water distribution and establish a new water distribution scheme, the “19ZQT” water distribution scheme.
- (3)
- The new water distribution scheme is calculated by the “SDH” transboundary water distribution method. The results show that in the “19ZQT” water distribution scheme, there are six rules corresponding to the water distribution scheme that can reflect the main influencing factors of water distribution. However, the amount of water available under different water distribution schemes may vary in the same area.
- (4)
- Under the “19ZQT” water distribution scheme, Shandong, Inner Mongolia, and Henan have the largest water distribution, and the three regions account for 50% of the total water distribution. Sichuan has the smallest water distribution, accounting for only 0.3% of the total. Compared with the 1987 water distribution scheme, the water distribution in Hebei and Tianjin has changed greatly, decreasing by 51.2%, whilst in Shaanxi, it has increased by 24.89%.

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

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**Figure 6.**(

**a**) Water distributions of the six water distribution schemes. (

**b**) The weights of the six water distribution schemes.

**Figure 8.**Comparison between the new water distribution scheme and the 1987 water distribution scheme.

**Figure 9.**A water distribution scheme for the Yellow River, with a water supply capacity of 30 billion m

^{3}.

**Figure 10.**Comparison between the proportion of water allocated under the new scheme, and the proportion of water used in 2017, and projected to be used in 2030, in the Yellow River basin.

Key Indicators | Unit | QH | SC | GS | NX | IM | SX | SN | HA | SD | HB TJ |
---|---|---|---|---|---|---|---|---|---|---|---|

2008 water consumption | 100 million m^{3} | 13.82 | 0.24 | 34.46 | 41.76 | 75.24 | 33.18 | 46.95 | 54.22 | 76.37 | 7.30 |

2009 water consumption | 100 million m^{3} | 12.54 | 0.25 | 33.91 | 40.76 | 81.03 | 32.19 | 45.21 | 57.77 | 80.25 | 8.66 |

2010 water consumption | 100 million m^{3} | 12.07 | 0.25 | 34.30 | 38.49 | 80.96 | 35.25 | 43.93 | 58.18 | 81.28 | 10.15 |

2011 water consumption | 100 million m^{3} | 12.15 | 0.24 | 37.21 | 40.27 | 83.14 | 39.03 | 45.37 | 65.30 | 84.96 | 13.60 |

2012 water consumption | 100 million m^{3} | 10.09 | 0.26 | 36.55 | 41.31 | 76.51 | 39.42 | 49.53 | 70.75 | 87.90 | 6.80 |

2013 water consumption | 100 million m^{3} | 10.56 | 0.36 | 34.70 | 42.67 | 85.45 | 40.60 | 51.30 | 70.45 | 87.19 | 3.47 |

2014 water consumption | 100 million m^{3} | 10.50 | 0.33 | 33.97 | 42.55 | 83.67 | 40.89 | 51.14 | 63.26 | 98.37 | 6.38 |

2015 water consumption | 100 million m^{3} | 10.78 | 0.34 | 33.26 | 42.50 | 79.34 | 43.47 | 51.63 | 60.93 | 104.61 | 5.19 |

2016 water consumption | 100 million m^{3} | 11.24 | 0.24 | 33.43 | 39.85 | 76.23 | 44.65 | 51.10 | 60.46 | 91.99 | 3.71 |

2017 water consumption | 100 million m^{3} | 11.17 | 0.21 | 33.78 | 40.95 | 74.97 | 44.79 | 52.68 | 65.32 | 90.92 | 2.30 |

Forecast water consumption in 2030 | 100 million m^{3} | 19.96 | 0.52 | 41.80 | 87.59 | 120.23 | 67.63 | 83.01 | 81.74 | 130.19 | 6.10 |

Total population | 10^{4} persons | 598.58 | 94.01 | 2318.52 | 681.78 | 1265.76 | 3702.39 | 3203.77 | 4397.27 | 5408.92 | —— |

GDP | 100 million yuan | 2656.53 | 295.16 | 5987.29 | 3490.61 | 11,204.35 | 14,911.15 | 19,383.97 | 26,668.66 | 36,479.96 | —— |

Basin area | 10^{4} km^{2} | 15.22 | 1.70 | 14.32 | 5.14 | 5.10 | 9.71 | 13.33 | 3.62 | 1.36 | —— |

**Table 2.**Calculation results of water distribution and weights of the two water distribution schemes. (100 million m

^{3}).

Distribution Scheme | QH | SC | GS | NX | IM | SX | SN | HA | SD | HB TJ | Weights |
---|---|---|---|---|---|---|---|---|---|---|---|

Scheme A | 14.10 | 0.40 | 30.40 | 40.00 | 58.60 | 43.10 | 38.00 | 55.40 | 70.00 | 20 | 0.40 |

Scheme B | 10.92 | 0.26 | 26.49 | 45.04 | 68.40 | 39.39 | 47.55 | 51.53 | 77.48 | 2.94 | 0.60 |

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## Share and Cite

**MDPI and ACS Style**

Qiu, M.; Zuo, Q.; Wu, Q.; Wu, B.; Ma, J.; Zhang, J.
Optimizing Water Distribution in Transboundary Rivers Based on a Synthesis–Dynamic–Harmonious Approach: A Case Study of the Yellow River Basin, China. *Water* **2023**, *15*, 1207.
https://doi.org/10.3390/w15061207

**AMA Style**

Qiu M, Zuo Q, Wu Q, Wu B, Ma J, Zhang J.
Optimizing Water Distribution in Transboundary Rivers Based on a Synthesis–Dynamic–Harmonious Approach: A Case Study of the Yellow River Basin, China. *Water*. 2023; 15(6):1207.
https://doi.org/10.3390/w15061207

**Chicago/Turabian Style**

Qiu, Meng, Qiting Zuo, Qingsong Wu, Binbin Wu, Junxia Ma, and Jianwei Zhang.
2023. "Optimizing Water Distribution in Transboundary Rivers Based on a Synthesis–Dynamic–Harmonious Approach: A Case Study of the Yellow River Basin, China" *Water* 15, no. 6: 1207.
https://doi.org/10.3390/w15061207