**1. Introduction**

Agriculture accounts for 70% of global water withdrawals, most of which is used for irrigation, so it is particularly important to carry out research on the distribution of agricultural water rights in irrigation areas to alleviate the current water shortage problems [1]. The initial allocation of water rights is the first step in the construction of a water rights system and the key measure to carry out water rights trade and give play to the function of optimal allocation of market resources. Based on the experience at home and abroad, the modern water rights system can be divided into the riparian rights system, the priority occupancy rights system, and the public water distribution rights system according to the initial acquisition and distribution forms of water rights [2]. Currently, China implements an administration-led public water rights allocation system [3]. The distribution system is generally from top to bottom, which distributes the initial water rights in a basin to provinces, cities, counties, industries, and final water users [4].

In recent decades, so many scholars have conducted a lot of research on initial water rights distribution, and early research mainly distributes initial water rights from the perspective of fairness [5,6], comprehensively considering the land area, capital investment, public law, water priority, water licenses, and reasonable collection of water fees, etc. [7–9], which enrich the insufficient system of the authorization and water permission system in the original irrigation area. With the in-depth study, some research on initial water

**Citation:** Guan, X.; Wang, B.; Zhang, W.; Du, Q. Study on Water Rights Allocation of Irrigation Water Users in Irrigation Districts of the Yellow River Basin. *Water* **2021**, *13*, 3538. https://doi.org/10.3390/w13243538

Academic Editors: Qiting Zuo, Xiangyi Ding, Guotao Cui and Wei Zhang

Received: 7 November 2021 Accepted: 8 December 2021 Published: 10 December 2021

**Publisher's Note:** MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

**Copyright:** © 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

rights distribution technology has also been carried out. Based on the conditional value at risk theory and Gini coefficient constraints, Zhang L.N. [10] establishes a two-stage stochastic programming model for water rights distribution, which reduces the unfair risk of local water shortages. Sahebzadeh Ali [11] uses the concept of conditional value at risk (CVaR) in the water distribution model to minimize the water loss index under low flow conditions. Using the automatic biophysical surface energy balance model (BAITSSS), Ramesh Dhungel [12] studies two agriculturally dominated groundwater areas in the northwest of the United States and the irrigation simulated by the model is compared with the report on the water rights management unit (WRMU). Imron F [13] uses linear programming to analyze the optimization of irrigation water distribution. By combining the water evaluation and planning system model and the non-principal sorting genetic algorithm II (NSGA-II) optimization algorithm, Chakraei Iman [14] puts forward a comprehensive simulation optimization model for the Zayanderud River Basin in Iran, and the distribution of surface and groundwater resources to various agricultural regions is optimized. Gebre Sintayehu Legesse [15] studies the application of multi criteria decision making (MCDM) related to water resource allocation. In addition, some scholars consider climate change, reservoir operation capacity, regional economic development, and other factors to establish a multi-objective optimization model to realize the fair distribution of water [16–18].

At present, the initial distribution of water rights is mainly concentrated on the distribution from a basin to regions and industries. It is a multi-objective and multi-level distribution problem that the water rights obtained by provinces are further allocated to cities and counties. When the superior water rights allocation method is applied to the county level, there are problems such as large differences in water use among towns, inapplicability of the allocation index system, and difficulty in collecting specific data and so on [19]. The second layer of allocation of water rights is subject to the principle of priority under the constraint of total control among industries to construct a target planning model based on the principles of priority of domestic water, food security, attention to ecological environment, economic benefits, and reasonable industrial structure [20]. Therefore, in the process of initial water rights distribution in the irrigation area, it is an inevitable requirement to further allocate the irrigation water rights to the main body of irrigation water users to realize the refinement of agricultural water management. The existing agricultural water distribution system mostly takes the irrigation area as the minimum distribution unit.

In this paper, according to the characteristics of multi-level water consumption in irrigation districts, a double-level water rights allocation model of national canals–farmer households in the irrigation district is established. The total amount of water rights distribution in national canals is determined by considering the future water-saving potential of the irrigation area. At the farmer household level, the fairness of water rights distribution is fully considered in combination with the characteristics of asymmetric information of farmers' agricultural population and irrigation area. Finally, the Wulanbuhe Irrigation Area of Hetao Irrigation District in the Yellow River Basin is taken as an example for verification based on the double-level water rights allocation model, and the research results can provide new ideas and methods for regional unit agricultural water rights allocation.

#### **2. Materials and Methods**

#### *2.1. Overview of the Study Area and Data Sources*

#### 2.1.1. Overview of the Study Area

Wulanbuhe Irrigation Area is located in the west of the Hetao Irrigation District of Inner Mongolia, and it mainly involves three administrative districts of Dengkou, Hangjin Houqi, and Azuo Qi. The total population of the irrigation area is 115,100, including a rural population of 69,100, and the irrigation area is 68,100 hm<sup>2</sup> in 2017. Wulanbuhe Irrigation Area belongs to the inland high plain of Hetao basin, located in the northeast of Wulanbuhe Desert. It belongs to the temperate continental monsoon climate, with four

distinct seasons, abundant sunlight, large temperature differences, and rare precipitation. The average annual precipitation is 144.5 mm, and the average annual evaporation is 2377.1 mm. The local water resources are very scarce. In order to meet the local water demand, it is necessary to use the transit Yellow River water, which has a certain water intake index for this area. Wulanbuhe Irrigation Area depends mainly on the Yellow River water for irrigation by the Shenwu main canal; there are a total of 476 main canals and submain canals in the Wulanbuhe Irrigation Area, of which 411 canals diverted directly from national canals are confirmed, because the water rights of the 411 canals will be distributed directly to the corresponding farmers, and so this article focuses on the distribution of the Yellow River water rights for those canals in the irrigation district. The basic situation of Wulanbuhe Irrigation Area is shown in Figure 1. Wulanbuhe Desert. It belongs to the temperate continental monsoon climate, with four distinct seasons, abundant sunlight, large temperature differences, and rare precipitation. The average annual precipitation is 144.5 mm, and the average annual evaporation is 2377.1 mm. The local water resources are very scarce. In order to meet the local water demand, it is necessary to use the transit Yellow River water, which has a certain water intake index for this area. Wulanbuhe Irrigation Area depends mainly on the Yellow River water for irrigation by the Shenwu main canal; there are a total of 476 main canals and sub-main canals in the Wulanbuhe Irrigation Area, of which 411 canals diverted directly from national canals are confirmed, because the water rights of the 411 canals will be distributed directly to the corresponding farmers, and so this article focuses on the distribution of the Yellow River water rights for those canals in the irrigation district. The basic situation of Wulanbuhe Irrigation Area is shown in Figure 1.

gation Area belongs to the inland high plain of Hetao basin, located in the northeast of

in 2017. Wulanbuhe Irri-

*Water* **2021**, *13*, x FOR PEER REVIEW 3 of 15

rural population of 69,100, and the irrigation area is 68,100 hm<sup>2</sup>

**Figure 1.** Wulanbuhe Irrigation Area of Hetao Irrigation District. **Figure 1.** Wulanbuhe Irrigation Area of Hetao Irrigation District.

#### 2.1.2. The Data Source 2.1.2. The Data Source

There are 411 canals diverted directly from national canals that are confirmed in the Wulanbuhe Irrigation Area of Hetao Irrigation District. The administration of the Hetao Irrigation District has made statistics for the five-year water consumption of these canals in the Wulanbuhe Irrigation Area from 2008 to 2013 (excluding 2012 due to a larger water shortage than usual), and the data are true. According to the proposed plan of water-saving irrigation engineering, the water-saving volume of the irrigation fields in the future can be calculated. The population and irrigation area of the corresponding farmer households in these canals were obtained from the actual statistical results of the township. There are 411 canals diverted directly from national canals that are confirmed in the Wulanbuhe Irrigation Area of Hetao Irrigation District. The administration of the Hetao Irrigation District has made statistics for the five-year water consumption of these canals in the Wulanbuhe Irrigation Area from 2008 to 2013 (excluding 2012 due to a larger water shortage than usual), and the data are true. According to the proposed plan of water-saving irrigation engineering, the water-saving volume of the irrigation fields in the future can be calculated. The population and irrigation area of the corresponding farmer households in these canals were obtained from the actual statistical results of the township.

#### *2.2. Double-Level Water Rights Allocation Model of the Irrigation District 2.2. Double-Level Water Rights Allocation Model of the Irrigation District*

The double-level water rights allocation model for the irrigation district includes the distribution method of water rights at the level of the national canal system and the distribution method of water rights among farmer households. Taking the amount of water diversion from the main canal head of the irrigation district as the total amount of water rights allocation, firstly allocate water rights at the national canal system level, and then use those as the total for water rights allocation among farmers. The canal system structure diagram of the irrigation district is shown in Figure 2. The double-level water rights allocation model for the irrigation district includes the distribution method of water rights at the level of the national canal system and the distribution method of water rights among farmer households. Taking the amount of water diversion from the main canal head of the irrigation district as the total amount of water rights allocation, firstly allocate water rights at the national canal system level, and then use those as the total for water rights allocation among farmers. The canal system structure diagram of the irrigation district is shown in Figure 2.

**Figure 2.** National canal system structure diagram of irrigation district. **Figure 2.** National canal system structure diagram of irrigation district.

2.2.1. Water Rights Allocation Model of National Canal System in Irrigation District 2.2.1. Water Rights Allocation Model of National Canal System in Irrigation District


$$
\Delta W\_{\rm l} = \Delta W\_{\rm lc} + \Delta W\_{\rm iq} + \Delta W\_{\rm id} \tag{1}
$$

Water-saving amount of canal lining: Water-saving amount of canal lining:

$$
\Delta \mathcal{W}\_{\rm ic} = \mathcal{W}\_{\rm i} (1 - \eta\_{\rm i}) - \mathcal{W}\_{\rm i}' (1 - \eta\_{\rm i}') \tag{2}
$$

Water-saving amount in border field reconstruction: Water-saving amount in border field reconstruction:

$$
\Delta \mathcal{W}\_{i|q} = \mathcal{W}\_{iqb} - \mathcal{W}\_{iql} \tag{3}
$$

Water-saving amount of drip irrigation: *W W W id idb idl* = (4) Water-saving amount of drip irrigation:

where *W<sup>i</sup>*

$$
\Delta \mathcal{W}\_{id} = \mathcal{W}\_{idb} - \mathcal{W}\_{idl} \tag{4}
$$

respectively, the water-saving amounts of canal lining, border field reconstruction, and drip irrigation of the canal *i* , m<sup>3</sup> ; *W<sup>i</sup>* , *W<sup>i</sup>* are, respectively, the canal head water intakes before and after the lining of the canal *i* , m<sup>3</sup> ; *i* , *i* are, respectively, the canal system water utilization coefficients before and after the lining of the canal *i* ; ( 0< < 1  *i i* ); *Wiq b* , *W i q l* are the field irrigation amounts before and after the renovation of border fields of the canal *i* , m<sup>3</sup> ; *Widb* , *Widl* are the headwater diverwhere ∆*W<sup>i</sup>* is the water-saving amount of the canal *i*, m<sup>3</sup> ; ∆*Wic*, ∆*Wiq*, ∆*Wid* are, respectively, the water-saving amounts of canal lining, border field reconstruction, and drip irrigation of the canal *i*, m<sup>3</sup> ; *W<sup>i</sup>* , *W*0 *<sup>i</sup>* are, respectively, the canal head water intakes before and after the lining of the canal *i*, m<sup>3</sup> ; *η<sup>i</sup>* , *η* 0 *i* are, respectively, the canal system water utilization coefficients before and after the lining of the canal *i*; (0 <*η<sup>i</sup>* < *η* 0 *<sup>i</sup>* < 1); *Wiqb*, *Wiql* are the field irrigation amounts before and after the renovation of border fields of the canal *i*, m<sup>3</sup> ; *Widb*, *Widl* are the headwater diversions before and after drip irrigation reconstruction of the canal *i*, m<sup>3</sup> .

sions before and after drip irrigation reconstruction of the canal *i* , m<sup>3</sup> . (3) Distribution of water rights of national canal system. By analyzing the total amount of current water rights of the canal system in the irrigation district and considering the potential water-saving amount of the canal system in the future, the canal-level water rights allocation model is determined. The calculation formula is as follows: (3) Distribution of water rights of national canal system. By analyzing the total amount of current water rights of the canal system in the irrigation district and considering the potential water-saving amount of the canal system in the future, the canal-level water rights allocation model is determined. The calculation formula is as follows:

$$\mathcal{W}\_{\dot{p}} = \mathcal{W}\_{\dot{\rm is}} - \Delta \mathcal{W}\_{\dot{\rm i}} \tag{5}$$

where *Wip* is the water rights distribution of the canal *i* , m<sup>3</sup> ; *Wis* is the total amount of current water rights of the canal *i* , m<sup>3</sup> . where *Wip* is the water rights distribution of the canal *i*, m<sup>3</sup> ; *Wis* is the total amount of current water rights of the canal *i*, m<sup>3</sup> .

Due to the constraint of the water diversion permit in irrigation districts, the total amount of water rights allocated at the canal level shall not exceed the permitted amount. Under the constraint of the water intake permit, canal-level water rights allocation in irrigation districts is as follows:

When the allowable water intake is more than the actual total water diversion of each canal directly from national canal, that is:

$$\sum\_{i=1}^{n} \mathcal{W}\_{ip} \le \mathcal{W}\_{\mathcal{Q}} \tag{6}$$

$$\mathcal{W}\_{ip} = \mathcal{W}\_{\rm is} - \Delta \mathcal{W}\_{\rm i} \tag{7}$$

When the allowable water intake is less than the actual total water diversion of each canal directly from national canal, that is:

$$\sum\_{i=1}^{n} \mathcal{W}\_{ip} \ge \mathcal{W}\_{\mathcal{Q}} \tag{8}$$

$$\mathcal{W}\_{ip} = \lambda\_{ip} \times \mathcal{W}\_{\mathcal{Q}} \tag{9}$$

$$
\lambda\_{ip} = \frac{\mathcal{W}\_{ip}}{\sum\_{i=1}^{n} \mathcal{W}\_{ip}} \tag{10}
$$

where *W<sup>Q</sup>* is the allowance of water intake in the irrigation district, m<sup>3</sup> ; *λip* is the water distribution coefficient of the canal *i*.

#### 2.2.2. Water Rights Allocation Model among Farmer Households in Irrigation Districts

	- (i) Irrigation area of farmer households

Current agricultural water rights allocation is based on irrigation area. The larger the irrigation area, the more water rights are allocated. The distribution of water rights according to the irrigation area mainly reflects the difference of irrigation water of different farmer households, and the distribution of water rights according to irrigation area is as follows:

$$S\_{\bar{\jmath}} = q \times a\_{\bar{\jmath}} \tag{11}$$

$$q = \frac{\mathcal{W}\_{ip}}{A\_i} \tag{12}$$

where *S<sup>j</sup>* is the water rights of farmer household *j* distributed, m<sup>3</sup> ; *q* is the water rights allocation quota, m3/hm<sup>2</sup> ; *a<sup>j</sup>* is the irrigation area of farmer household *j*, hm<sup>2</sup> ; *A<sup>i</sup>* is the irrigation area confirmed for all farmers in the canal system, hm<sup>2</sup> ; *Wip* is the water rights distributed of the canal *i*, m<sup>3</sup> .

#### (ii) Peasant household agricultural population

Water resources are the public resources of the whole society, so the distribution of water rights should give consideration to the development of all people, and the agricultural population of peasant households should be fully considered in the distribution of water rights. The household with more (less) agricultural population will obtain more (less) water rights. The distribution process is as follows:

$$S\_{\bar{\jmath}} = q \times p\_{\bar{\jmath}} \tag{13}$$

$$q = \frac{\mathcal{W}\_{ip}}{P\_i} \tag{14}$$

where *S<sup>j</sup>* is the water rights distributed for farmer household *j*, m<sup>3</sup> ; *q* is the water rights allocation quota, m3/hm<sup>2</sup> ; *p<sup>j</sup>* is the agricultural population of farmer household *j*; *P<sup>i</sup>* is the agricultural population of all farmer households of the canal *i*; *Wip* is the water rights distributed for the canal *i*, m<sup>3</sup> .

	- (i) Gini coefficient

The Gini coefficient [21], also known as the Lorentz coefficient, was first proposed by Italian mathematician Gini at the beginning of the 20th century. It is mainly used in the field of economics to investigate and measure the inequality of regional residents' income and wealth distribution. It can more directly reflect the income difference between residents.

The value range of the Gini coefficient is [0, 1]. When the Gini coefficient is 0, it represents the absolute average of income distribution. Moreover, 0.4 is usually regarded as the warning line of the income gap in the world, and the evaluation standard of the Gini coefficient can be referred to the following Table 1.

**Table 1.** Gini coefficient evaluation criteria.


#### (ii) Construction of water rights allocation model by Gini coefficient method

When a peasant household's water rights are distributed based on irrigation area and the farmer household's agricultural population are equal, the water rights allocation is considered to be fair. When the water rights allocated are not same, neither of the two distribution patterns can reflect the principle of fairness in the allocation of water rights; meanwhile, the irrigation area of farmer households and the agricultural population of farmer households are asymmetrical. In this article, therefore, the per capita irrigation area of each farmer is used as a measure of the fairness of water rights allocation, and the theory of the Gini coefficient is used to study the distribution relationship between irrigation area of farmer households and their agricultural population. With the cumulative percentage of the agricultural population of each farmer household in the canal system as the abscissa and the cumulative percentage of the irrigated area of each farmer household as the ordinate, the water rights allocation model was built based on minimizing the Gini coefficient. The specific steps are as follows:

Step 1: Building the objective function

$$\min G\_{\text{ini}} \tag{15}$$

$$G\_{\rm ini} = \frac{A}{A+B} = 2A = 1 - 2B = 1 - \sum\_{j=1}^{n} (X\_j - X\_{j-1})(Y\_j + Y\_{j-1}) \tag{16}$$

$$(Y\_j - Y\_{j-1})A\_i = x\_j \times (X\_j - X\_{j-1}) \times P\_i \tag{17}$$

where *X<sup>j</sup>* is the cumulative percentage of agricultural population of farmer household *j*; *Y<sup>j</sup>* is the cumulative percentage of irrigation area after equilibrium of farmer household *j*; *P<sup>i</sup>* is the corresponding total agricultural population of the canal *i*; *A<sup>i</sup>* is the corresponding total irrigation area of the canal *i*, hm<sup>2</sup> ; *x<sup>j</sup>* is the per capita irrigation area after equilibrium of farmer household *j*, hm2/person.

The Lorenz curve of the population and irrigation area is as follows in Figure 3.

corresponding total irrigation area of the canal *i* , hm<sup>2</sup>

after equilibrium of farmer household *j* , hm<sup>2</sup>

**Figure 3.** Population–irrigation area Lorentz curve. **Figure 3.** Population–irrigation area Lorentz curve.

Step 2: Setting constraints: a: Fairness constraints: Step 2: Setting constraints: a: Fairness constraints:

$$\begin{cases} \mathbf{x}\_{j} > \mathbf{x}\_{j}^{\prime} \\ \mathbf{x}\_{j} < \mathbf{x}\_{j}^{\prime} \end{cases}, \qquad \mathbf{x}\_{j} < \overline{\mathbf{x}}\_{i} $$

; *j*

/person.

The Lorenz curve of the population and irrigation area is as follows in Figure 3.

*x* is the per capita irrigation area

where *<sup>j</sup> x* is the per capita irrigation area after equilibrium of farmer household *j* , hm<sup>2</sup> /person; *j x* is the current per capita irrigation area of farmer household *j* , hm<sup>2</sup> /perwhere *x<sup>j</sup>* is the per capita irrigation area after equilibrium of farmer household *j*, hm2/person; *x* 0 *j* is the current per capita irrigation area of farmer household *j*, hm2/person; *x<sup>i</sup>* is the per capita irrigation area of farmers of the canal *i* hm2/person.

son; *<sup>i</sup> x* is the per capita irrigation area of farmers of the canal *i* hm<sup>2</sup> b: Constraints of basic water security:

$$\left| \frac{\mathbf{x}\_j' - \mathbf{x}\_j}{\mathbf{x}\_j'} \right| \le s \tag{19}$$

/person.

*j x* where *s* is the reduction ratio determined by the degree of importance the region atwhere *s* is the reduction ratio determined by the degree of importance the region attaches to the principle of equity.

taches to the principle of equity. Restrictions on the extent of reduction or compensation:

 

$$\left|\mathbf{x}\_{j} - \mathbf{x}\_{j}^{\prime}\right| \ge \left|\mathbf{x}\_{\rho} - \mathbf{x}\_{\rho}^{\prime}\right|, \quad \left|\mathbf{x}\_{j}^{\prime} - \overline{\mathbf{x}}\_{i}\right| \ge \left|\mathbf{x}\_{\rho}^{\prime} - \overline{\mathbf{x}}\_{i}\right|, \ j \ne \rho \tag{20}$$
  $\sim$  constraints of sortiner

c: Constraints of sorting: c: Constraints of sorting:

*xj*−<sup>1</sup> ≤ *x<sup>j</sup>* ≤ *xj*+<sup>1</sup> (21)

d: Constraints on irrigation area:

$$\sum\_{j=1}^{n} x\_j \times p\_j = A\_l \tag{22}$$

*j j j* 1 1 *x x x* (21)

1 *j j i j x p A* (22) is the correspondwhere *p<sup>j</sup>* is the agricultural population of farmer household *j*; *A<sup>i</sup>* is the corresponding total irrigation area of the canal *i*, hm<sup>2</sup> .

where *<sup>j</sup> p* is the agricultural population of farmer household *j* ; *A<sup>i</sup>* e: The Gini coefficient after equilibrium is smaller than before:

$$\mathbf{G}\_{\rm ini} < \mathbf{G}'\_{\rm ini} \textit{ini} \tag{23}$$

f: Non-negative constraints:

$$x\_j > 0\tag{24}$$

Step 3: Determining the water rights of farmers distributed: Step 3: Determining the water rights of farmers distributed: *W*

*Water* **2021**, *13*, x FOR PEER REVIEW 8 of 15

$$\mathcal{W}\_{jp} = \frac{\mathcal{W}\_{ip}}{\sum\_{j=1}^{n} \mathbf{x}\_{j} \times p\_{j}} \times \mathbf{x}\_{j} \times p\_{j} \tag{25}$$

*x* (24)

where *Wjp* is the water rights of farmer j distributed, m<sup>3</sup> ; other symbols are the same as above. above. Step 4: Optimal solution of the model:

0 *<sup>j</sup>*

*ip*

Step 4: Optimal solution of the model: The model is optimized and solved by the genetic algorithm in MATLAB, and the

f: Non-negative constraints:

where *Wjp*

The model is optimized and solved by the genetic algorithm in MATLAB, and the calculation process of the optimized solution is as follows: calculation process of the optimized solution is as follows: a: At the beginning of the genetic algorithm calculation, first set various parameters,

a: At the beginning of the genetic algorithm calculation, first set various parameters, such as setting the population size to 20, the number of iterations, the probability of crossover and mutation, and the termination conditions. such as setting the population size to 20, the number of iterations, the probability of crossover and mutation, and the termination conditions. b: Generate the initial value group for the per capita irrigation area of farmers:

b: Generate the initial value group for the per capita irrigation area of farmers: *pop* = [*z*1, *z*2, *z*3, *z*4, *z*5, *z*6, *z*7, *z*8]. *pop z z z z z z z z* = , , , , , , , 1 2 3 4 5 6 7 8 . *n* 

Define fitness function: *Gini* = " 1 − *n* ∑ *j*=1 (*X<sup>j</sup>* − *Xj*−1)(*Y<sup>j</sup>* + *Yj*−1) # and then calculate Define fitness function: 1 -1 1 1 ( )( ) *ini j j j j j G X X Y Y* and then calculate the fitness of the initial population and compare the fitness value of the population.

the fitness of the initial population and compare the fitness value of the population. c: Set the constraint conditions to see whether the fitness of the initial population

c: Set the constraint conditions to see whether the fitness of the initial population meets the optimization criterion. If it is satisfied, the optimization ends; if not, proceed to step d. meets the optimization criterion. If it is satisfied, the optimization ends; if not, proceed to step d. d: Select, cross, and mutate on the initial population *pop*, to produce offspring pop-

d: Select, cross, and mutate on the initial population *pop*, to produce offspring population *pop*1, and see whether the population *pop*<sup>1</sup> meets the optimization conditions. If it is satisfied, the optimization ends; if it is not satisfied, the selection, crossover, and mutation operations are continued until the conditions are met. ulation <sup>1</sup> *pop* , and see whether the population <sup>1</sup> *pop* meets the optimization conditions. If it is satisfied, the optimization ends; if it is not satisfied, the selection, crossover, and mutation operations are continued until the conditions are met.

The optimization flowchart is as follows in Figure 4, and we complete this part based on MATLAB 2018B. The optimization flowchart is as follows in Figure 4, and we complete this part based on MATLAB 2018B.

**Figure 4.** Genetic algorithm optimization flowchart. **Figure 4.** Genetic algorithm optimization flowchart.

#### **3. Results 3. Results**

*3.1. Distribution Results of Water Rights for the Canals Diverted Directly from the National Canal System 3.1. Distribution Results of Water Rights for the Canals Diverted Directly from the National Canal System*

To allocate canal-level water rights for 411 canals diverted directly from the national canal system that need to be confirmed in the Wulanbuhe Irrigation Area, according to the current situation of water-saving projects in the Wulanbuhe Irrigation Area, Formulas (1)–(4) are used to calculate the water-saving amount of the 411 canals. In addition, based on the five-year average water volume collected for the canals diverted directly

from national canal system, Formula (5) and Formulas (6)–(10) are adopted to calculate the distribution of water rights for the 411 canals. Take one of the 411 canals in the Wulanbuhe Irrigation Area as an example for explanation, as shown in Table 2.

**Table 2.** Results of water rights distribution for canals diverted directly from the national canal system in Wulanbuhe Irrigation Area (ten thousand m<sup>3</sup> ).

