2.3.3. The Objective Function of Coordinated Development

In order to demonstrate the principle of water–ecology–energy–food coordinated development in the process of water rights allocation, the existing coordinated development status can be quantified into a specific value, which is called the coordinated development index. The greater the coordinated development index is, the better the coordinated development status of the four resources is. The maximum index of coordinated development is taken as the objective function. The comprehensive evaluation method is used to calculate the coordinated development index. The comprehensive evaluation method [27,28] can select objective indicators from the regional economic, social, and ecological environment. Multiple indicators can be evaluated systematically and normatively at the same time, and the evaluation results can be quantified. Finally, a general numerical value is formed, and the evaluation purpose is achieved through numerical comparison.

(1) The selection of comprehensive evaluation indicators for coordinated development is shown in Table 1.


**Table 1.** The comprehensive evaluation indicators of water–ecology–energy–food coordinated development.


#### **Table 1.** *Cont.*


$$y\_{ij} = \frac{\mathbf{x}\_{ij} - \min(\mathbf{x}\_j)}{\max(\mathbf{x}\_j) - \min(\mathbf{x}\_j)},\tag{5}$$

when the indicator is negative

$$y\_{ij} = \frac{\max(\mathbf{x}\_j) - \mathbf{x}\_{ij}}{\max(\mathbf{x}\_j) - \min(\mathbf{x}\_j)},\tag{6}$$

where *yij* is normalized data; max(*x<sup>j</sup>* ) is the maximum indicator *j* in *n* years; and min(*x<sup>j</sup>* ) is the minimum indicator *j* in *n* years.

(B) The calculation of the index Calculate the weight of the indicator in the year *i* under the index *j*:

$$P\_{ij} = \left(\frac{y\_{ij}}{\sum\_{i=1}^{n} y\_{ij}}\right), i = 1, 2, \dots, n. \tag{7}$$

Calculate the information entropy of indicator *j*:

$$E\_{\vec{l}} = -\frac{1}{\ln n} \times \sum\_{i=1}^{n} \left( P\_{\vec{l}\vec{j}} \times \ln \left( P\_{\vec{l}\vec{j}} \right) \right). \tag{8}$$

Determine the weight of indicator *j*:

$$M\_{\vec{j}} = \left(\frac{1 - E\_{\vec{j}}}{k - \sum\_{j=1}^{k} E\_{\vec{j}}}\right), \vec{j} = 1, 2, \dots, l. \tag{9}$$

Calculate the coordinated development indicator *G<sup>i</sup>* in the year *i*:

$$G\_{l} = \sum\_{j=1}^{k} \left( M\_{j} \times y\_{lj} \right). \tag{10}$$

(C) The objective function of coordinated development

$$\text{maxRG} = \text{maxG}\_{\prime} \tag{11}$$

where *RG* is the objective function of the coordinated development on water–ecology– energy–food.

#### 2.3.4. The Constraints of Industry Water Rights

The current water rights security for industrial and agricultural production and the water rights security for future life are taken, as constraints in this model. Domestic water is the sum of water for the daily life of residents and urban public water. Ecological water includes artificial lake replenishment, urban road sprinkler, and green space irrigation. The energy industry includes coal mining, coal washing, coking, crude oil refining (including gasoline, diesel, kerosene and other crude oil processing industries), and thermal power generation. Food planting includes the cultivation of rice, corn, wheat, and beans (potatoes do not grow in Yinchuan). Other agriculture includes planting industries other than food crops, as well as timber, livestock products, and fishery products. Other agriculture includes farming other than food crops, as well as timber, animal, and fish products.

(1) The constraints of water rights of life:

$$\mathcal{W}\_{\rm L} \ge \left(1 + \mathcal{N}\_{\rm II}\right)^{a} \mathcal{P}\_{\rm U} \times Q\_{\rm II} + \left(1 + \mathcal{N}\_{\rm R}\right)^{a} \mathcal{P}\_{\rm R} \times Q\_{\rm R} + \mathcal{G} \mathcal{D} \mathcal{P}\_{\rm UP} \left(1 + \mathcal{N}\_{\rm UP}\right)^{a} \times M\_{\rm GDP\prime} \tag{12}$$

where *W<sup>L</sup>* is the water rights of life (m<sup>3</sup> ); *PU*, *P<sup>R</sup>* are the number of urban people and rural people; *NU*, *N<sup>R</sup>* are the population growth rate of urban and rural; *QU, Q<sup>R</sup>* are the per capita domestic water quota for urban and rural; *GDPUP* is the *GDP* of urban public industry; *NUP* is *GDP* growth rate of urban public industry; and *MGDP* is the water consumption per CNY 10,000 *GDP*; *a* is the year for future domestic water security.

(2) The constraints of water rights of ecology:

$$\mathcal{W}\_{\rm E} \ge \mathcal{S}\_{\rm G} \times \mathcal{M}\_{\rm G} + \mathcal{S}\_{L} \times (\mathcal{E}\_{L} + \mathcal{K}\_{L}) + \mathcal{S}\_{R} \times \mathcal{M}\_{R\prime} \tag{13}$$

where *W<sup>E</sup>* is the water rights of ecology (m<sup>3</sup> ); *S<sup>G</sup>* is the greening coverage area; *M<sup>G</sup>* is the quota for greening irrigation; *S<sup>L</sup>* is the area of artificial lake; *E<sup>L</sup>* is the evaporation supply quota of local lakes; *K<sup>L</sup>* is the infiltration supply quota of local lakes; *S<sup>R</sup>* is the area of urban roads; and *M<sup>R</sup>* is quota of urban road sprinkling.

(3) The constraints of water rights of energy industry:

$$\mathcal{W}\_{\rm N} \ge \sum (\mathcal{R}\_{\rm Nk} \times \mathcal{M}\_{\rm Nk})\_{\prime} \tag{14}$$

where *W<sup>N</sup>* is the water rights of energy industry (m<sup>3</sup> ); *RNk* is the production of energy *k*; *MNk* is the water quota for the exploitation or processing of energy *k*.

(4) The constraints of water rights of food planting:

$$\mathcal{W}\_{\mathcal{F}} \ge \sum (\mathcal{R}\_{Fk} \times \mathcal{M}\_{Fk}).\tag{15}$$

(5) The constraints of water rights of other agriculture:

$$\mathcal{W}\_{\mathcal{O}} \ge \sum (\mathcal{R}\_{\mathcal{O}k} \times \mathcal{M}\_{\mathcal{O}k})\_{\prime} \tag{16}$$

where *W<sup>O</sup>* is the water rights of other agriculture (m<sup>3</sup> ); *ROk* is the production of other agriculture *k*; *MOk* is the water quota of other agriculture.

(6) The constraints of water rights of general industry:

$$\mathcal{W}\_{\rm I} \ge \sum (\mathcal{R}\_{\rm Ik} \times \mathcal{M}\_{\rm Ik})\_{\prime} \tag{17}$$

where *W<sup>I</sup>* is the water rights of general industry (m<sup>3</sup> ); *RIk* is the production of general industry *k*; *MIk* is the water quota of general industry.

(7) The constraints of total water rights:

$$\mathcal{W}\_L + \mathcal{W}\_\mathcal{E} + \mathcal{W}\_\mathcal{N} + \mathcal{W}\_\mathcal{F} + \mathcal{W}\_\mathcal{O} + \mathcal{W}\_\mathcal{I} \le \mathcal{W}\mathcal{R}\_\mathcal{\epsilon} \tag{18}$$

where *WR* is the total water rights in this city.

(8) The method to solve model

The MATLAB software and particle swarm optimization algorithm are used to solve the water rights allocation model in this study.

#### **3. Results**

According to the water rights allocation model proposed above, Yinchuan in 2019 is taken as an example to calculate the water rights allocation of coordinated development on water–ecology–energy–food. Among the data required for calculation, the water resources data are from Ningxia Water Resources Bulletin (2013–2019) [29–35], and social and economic data are from Yinchuan Statistical Yearbook (2014–2020) [36–42]. The total amount data of water rights allocation in Yinchuan comes from the Yellow River Institute of Hydraulic Research. We put the data into Equations (1) to (18), using MATLAB software to compile the particle swarm optimization algorithm for iterative solution. The result of water rights allocation for the coordinated development on water–ecology–energy–food in Yinchuan is obtained, as shown in Table 2:

**Table 2.** Water rights allocation scheme of the coordinated development of water–ecology–energy– food in Yinchuan.


#### **4. Discussion**

*4.1. Results Analysis of Water Resources Value in Various Industries*

It can be seen from Figure 2, after the allocation of water rights for the coordinated development on water- ecology-energy-food, the value of water resources in various industries in Yinchuan has changed. The water resources value in the living system it increased by 2.10 <sup>×</sup> <sup>10</sup><sup>8</sup> CNY, in the ecosystem it increased by 0.22 <sup>×</sup> <sup>10</sup><sup>8</sup> CNY, in the energy industry system it decreased by 0.70 <sup>×</sup> <sup>10</sup><sup>8</sup> CNY, in the food planting system it decreased by 0.32 <sup>×</sup> <sup>10</sup><sup>8</sup> CNY, it increased by 0.14 <sup>×</sup> <sup>10</sup><sup>8</sup> CNY in other agricultural systems, and it increased by 0.86 <sup>×</sup> <sup>10</sup><sup>8</sup> CNY in general industrial systems. The total water resources value increased by 2.31 <sup>×</sup> <sup>10</sup><sup>8</sup> CNY compared with before allocation. It can be seen that after the allocation of water rights, the overall value of water resources in Yinchuan city has increased, and the efficiency of water resources utilization has improved. When Li et al. [43] optimized the regional water use structure based on water resource vulnerability, they also took the industrial water resource value as an important influencing factor to allocate water resources. In this paper, emergy method is used to quantify the water resources value in various industries, which is conducive to obtain the objective and reliable allocated results. (1) Comparison of the water resources value in various industries under current water rights and allocated water rights. In the efficiency objective of city-industry water rights allocation model, the emergy method is used to calculate the value of water resources in various industries in this paper. The comparison of water resources value in various industries before and after water rights allocation is shown in Figure 2: rights and allocated water rights. In the efficiency objective of city-industry water rights allocation model, the emergy method is used to calculate the value of water resources in various industries in this paper. The comparison of water resources value in various industries before and after water rights allocation is shown in Figure 2:

(1) Comparison of the water resources value in various industries under current water

*Water* **2022**, *14*, x FOR PEER REVIEW 10 of 15

*4.1. Results Analysis of Water Resources Value in Various Industries*

**4. Discussion**

**Figure 2.** Comparison chart of water resources value in various industries under different water rights. **Figure 2.** Comparison chart of water resources value in various industries under different water rights.

It can be seen from Figure 2, after the allocation of water rights for the coordinated development on water- ecology-energy-food, the value of water resources in various industries in Yinchuan has changed. The water resources value in the living system it increased by 2.10 × 108 CNY, in the ecosystem it increased by 0.22 × 108 CNY, in the energy industry system it decreased by 0.70 × 108 CNY, in the food planting system it decreased by 0.32 × 108 CNY, it increased by 0.14 × 108 CNY in other agricultural systems, and it increased by 0.86 × 108 CNY in general industrial systems. The total water resources value increased by 2.31 × 108 CNY compared with before allocation. It can be seen that after the allocation of water rights, the overall value of water resources in Yinchuan city has increased, and the efficiency of water resources utilization has improved. When Li et al. [43] optimized the regional water use structure based on water resource vulnerability, they also took the industrial water resource value as an important influencing factor to allocate water resources. In this paper, emergy method is used to quantify the water resources value in various industries, which is conducive to obtain the objective and reliable allocated results. (2) Comparison of the value of water resources per cubic meter in various industries. (2) Comparison of the value of water resources per cubic meter in various industries. According to the calculation of the value of water resources and the allocation results of water rights in various industries, the value of water resources per cubic meter in Yinchuan city can be obtained. The value of water resources per cubic meter of the living system is the highest, reaching 15.54 CNY/m<sup>3</sup> , followed by that of the energy industry system, reaching 10.28 CNY/m<sup>3</sup> , and that of the food production system is the lowest, only 0.67 CNY/m<sup>3</sup> . The value of water resources per cubic meter in the ecosystem is 2.05 CNY/m<sup>3</sup> , that of other agricultural systems is 4.94 CNY/m<sup>3</sup> , and that of general industrial systems is 5.37 CNY/m<sup>3</sup> . Wang Yu et al. [44] used the emergy method to calculate the value of water resources per cubic meter of the four sectors (life, industry, extra-river ecology, and agriculture) in nine provinces and autonomous regions in the Yellow River Basin. They also obtained the result that the value of water resources per cubic meter of life sector is the largest and that of the agriculture sector is the smallest. Li et al. [43] also suggested that the value of water resources per cubic meter of agriculture is minimal. The food planting industry is faced with the problem of low water efficiency, and it is a trend that accelerates the development of regional water-saving agricultural engineering renovation.

#### According to the calculation of the value of water resources and the allocation results of water rights in various industries, the value of water resources per cubic meter in *4.2. Results Analysis of Coordinated Development Index G*

Yinchuan city can be obtained. The value of water resources per cubic meter of the Through the optimal allocation of the right to use water resources of various industries in Yinchuan in 2019, the change of water rights of various industries will directly affect the values of some comprehensive evaluation indicators. It will thus change the size of the coordinated development index on water–ecology–energy–food. The trend and

*Water* **2022**, *14*, x FOR PEER REVIEW 11 of 15

*4.2. Results Analysis of Coordinated Development Index G*

comparative analysis of that in Yinchuan from 2013 to 2019 under the condition of current water rights and allocated water rights are shown in Figure 3: comparative analysis of that in Yinchuan from 2013 to 2019 under the condition of current water rights and allocated water rights are shown in Figure 3:

Through the optimal allocation of the right to use water resources of various industries in Yinchuan in 2019, the change of water rights of various industries will directly affect the values of some comprehensive evaluation indicators. It will thus change the size of the coordinated development index on water–ecology–energy–food. The trend and

opment of regional water-saving agricultural engineering renovation.

living system is the highest, reaching 15.54 CNY/m3, followed by that of the energy industry system, reaching 10.28 CNY/m3, and that of the food production system is the lowest, only 0.67 CNY/m3. The value of water resources per cubic meter in the ecosystem is 2.05 CNY/m3, that of other agricultural systems is 4.94 CNY/m3, and that of general industrial systems is 5.37 CNY/m3. Wang Yu et al. [44] used the emergy method to calculate the value of water resources per cubic meter of the four sectors (life, industry, extra-river ecology, and agriculture) in nine provinces and autonomous regions in the Yellow River Basin. They also obtained the result that the value of water resources per cubic meter of life sector is the largest and that of the agriculture sector is the smallest. Li et al. [43] also suggested that the value of water resources per cubic meter of agriculture is minimal. The food planting industry is faced with the problem of low water efficiency, and it is a trend that accelerates the devel-

**Figure 3.** Trend and comparison of the water–ecology–energy–food coordinated development index **Figure 3.** Trend and comparison of the water–ecology–energy–food coordinated development index in Yinchuan city from 2013 to 2019 under different water rights conditions.

in Yinchuan city from 2013 to 2019 under different water rights conditions.

As can be seen from Figure 3, in terms of the extended development trend of the water–ecology–energy–food coordinated development index, except that the current As can be seen from Figure 3, in terms of the extended development trend of the water–ecology–energy–food coordinated development index, except that the current water rights declined in 2017, the current indexes and the allocated indexes basically showed an upward trend from 2013 to 2018. Both dropped significantly in 2019 compared to the previous year. Through the analysis of comprehensive evaluation indicators data, it is found that natural annual precipitation (*B1*) decreased significantly in Yinchuan in 2019, and the energy exploitation and food crop yield was decreased. As the result, the per capita water resources (*A1*), energy self-sufficiency rate (*C3*) and food self-sufficiency rate (*D4*) and other positive indicators decreased significantly, which has an impact on the coordinated development index in this year. The coordinated development index under the current water rights condition has a slight decline in 2017, which is due to the obvious decline of annual precipitation (*B1*) in this year compared with 2016.

It can also be seen from Figure 3 that in 2014 and 2016, the coordinated development index under current water rights is slightly larger than that under allocated water rights, which is mainly caused by the changing trend of the proportion of water rights in food planting (*AD1*). The proportion of water rights of food planting (*AD1*) peaked in 2014 and 2016, at 52.36% and 51.54%. Compared with the situation of current water rights in 2019, it is 30.90%, and the proportion of water rights of food planting (*AD1*) under allocated water rights is even smaller, only 27.62%. Under the condition of allocated water rights, the proportion of water rights of food planting (*AD1*) is more discrete than the current water rights, which leads to the decrease of the coordinated development index of water–ecology–energy–food.

From 2013 to 2016, the coordinated development index under the condition of allocated water rights was basically equal to that under the condition of current water rights. From 2017 to 2019, the coordinated development index under the condition of allocated water rights was significantly higher than that under the condition of current water rights. It can be shown that the regional water–ecology–energy–food coordinated development state obtained by water rights allocation in this paper is superior to the current situation. The water rights allocation model established in this paper can provide reference and help to promote the coordinated development of regional water–ecology–energy–food. From 2013 to 2016, the coordinated development index under the condition of allocated water rights was basically equal to that under the condition of current water rights. From 2017 to 2019, the coordinated development index under the condition of allocated water rights was significantly higher than that under the condition of current water rights. It can be shown that the regional water–ecology–energy–food coordinated development state obtained by water rights allocation in this paper is superior to the current situation. The water rights allocation model established in this paper can provide reference and help to promote the coordinated development of regional water–ecology–energy–food.

water rights declined in 2017, the current indexes and the allocated indexes basically showed an upward trend from 2013 to 2018. Both dropped significantly in 2019 compared to the previous year. Through the analysis of comprehensive evaluation indicators data, it is found that natural annual precipitation (*B1*) decreased significantly in Yinchuan in 2019, and the energy exploitation and food crop yield was decreased. As the result, the per capita water resources (*A1*), energy self-sufficiency rate (*C3*) and food self-sufficiency rate (*D4*) and other positive indicators decreased significantly, which has an impact on the coordinated development index in this year. The coordinated development index under the current water rights condition has a slight decline in 2017, which is due to the obvious

It can also be seen from Figure 3 that in 2014 and 2016, the coordinated development index under current water rights is slightly larger than that under allocated water rights, which is mainly caused by the changing trend of the proportion of water rights in food planting (*AD1*). The proportion of water rights of food planting (*AD1*) peaked in 2014 and 2016, at 52.36% and 51.54%. Compared with the situation of current water rights in 2019, it is 30.90%, and the proportion of water rights of food planting (*AD1*) under allocated water rights is even smaller, only 27.62%. Under the condition of allocated water rights, the proportion of water rights of food planting (*AD1*) is more discrete than the current water rights, which leads to the decrease of the coordinated development index of water–

#### *4.3. Results Analysis of Water Rights Allocation 4.3. Results Analysis of Water Rights Allocation*

ecology–energy–food.

A comparative analysis is made between the current water rights of various industries in Yinchuan in 2019 and the allocated water rights in various industries based on the coordinated development of water–ecology–energy–food in this paper, as shown in Figure 4. A comparative analysis is made between the current water rights of various industries in Yinchuan in 2019 and the allocated water rights in various industries based on the coordinated development of water–ecology–energy–food in this paper, as shown in Figure 4.

*Water* **2022**, *14*, x FOR PEER REVIEW 12 of 15

decline of annual precipitation (*B1*) in this year compared with 2016.

**Figure 4.** Comparison of the percentage of current water rights and allocated water rights in various industries. **Figure 4.** Comparison of the percentage of current water rights and allocated water rights in various industries.

As can be seen from Figure 4, the allocated water rights of life in Yinchuan increased by 1.07%, the allocated water rights of ecology increased by 1.85%, the allocated water rights of energy industry decreased by 1.09%, that of food planting decreased by 3.27%, that of other agriculture increased by 0.83%, and general industry increased by 0.65% compared with the current water rights. Water rights of life and ecology have increased, while agricultural water rights have decreased and industrial water rights have little change, which is consistent with the optimization trend of water resources in the Yellow River Basin proposed by Xia et al. [45]. In addition, according to Yinchuan's future economic and social development focus, urban planning and industrial and agricultural construction characteristics, the water rights allocation scheme based on coordinated development of water–ecology–energy–food in this paper is reasonable and sustainable, which can provide some reference for the reasonable allocation of regional water rights.

#### **5. Conclusions**

In this paper, the water resource is taken as the object of control, and a municipalindustry water rights allocation model for the coordinated development of water–ecology– energy–food is established. The fairness objective of the model is established by satisfaction function, the efficiency objective is established by the emergy method, and the coordinated development objective is calculated by comprehensive evaluation method. We calculate the water security for each industry as constraints of the water right allocation model. The conclusions are as follows:


There are still some shortcomings in this paper: It is difficult to completely distinguish the cross industries when dividing the industries, and it is also difficult to make comprehensive statistics of all water use units in the industry. Further research is needed in the future.

**Author Contributions:** All authors contributed to the study conception and design. Data curation, H.Y.; formal analysis, W.Z.; methodology, Y.H.; writing—original draft, Y.H.; writing—review and editing, W.Z. All authors commented on previous versions of the manuscript. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by Basic R&D Special Fund of Central Government for Nonprofit Research Institutes (HKY-JBYW-2020-17) and National Natural Science Foundation of China (No. 51979119).

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** The original data used during the study were provided by a third party. The data that support the findings of this study are available in "Ningxia Water Resources Bulletin" and "Yinchuan Statistical Yearbook". These data were derived from the following resources available in the public domain: Ningxia Water Resources Bulletin: http://slt.nx.gov.cn/xxgk\_281/fdzdgknr/ gbxx/szygb/ accessed on 20 June 2022. Yinchuan Statistical Yearbook: http://www.yinchuan.gov. cn/xxgk/zfxxgkml/tjxx/tjnj/ accessed on 20 June 2022. The authors have made sure that all data and materials as well as software application or custom code comply with field standards.

**Conflicts of Interest:** The authors have no conflict of interest to declare that are relevant to the content of this article.

## **References**

