# Analysis of Carrying Capacity and Obstacle Factors of Water Resources in Longnan City, China, Based on Driving–Pressure–State–Response and Technique for Order Preference by Similarity to an Ideal Solution Models

^{1}

^{2}

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## Abstract

**:**

## 1. Introduction

## 2. Data Sources and Research Methods

#### 2.1. Overview of the Research Area

^{2}, an average annual temperature of higher than 12 °C, average annual precipitation of 450~800 mm, and a frost-free period of 280 days. It is rich in water resources, belonging to the Jialing River system. The per capita water resources and per mu water resources have been higher than the average levels of Gansu Province for many years. However, it is challenging to manage water resources due to a low utilization rate and prominent engineering water shortage. It is mainly reflected in inadequate agricultural irrigation facilities, small scales of rural water supply projects, low guaranteed degrees of water supply, and the arduous task of allocating water resources across counties and districts. Therefore, it is urgent to promote water reform in the city.

#### 2.2. Data Sources

#### 2.3. Research Methods

#### 2.3.1. Indicator System Construction

#### 2.3.2. Entropy Weight Method

- Construct a matrix of i rows and j columns:$$\mathrm{A}=\left[\begin{array}{ccc}{x}_{11}& \dots & {x}_{1j}\\ \dots & \dots & \dots \\ {x}_{i1}& \dots & {x}_{\mathit{ij}}\end{array}\right]$$
_{ij}is the j-th indicator of the i-th year. - Calculate the proportion of the j-th indicator P
_{j}:$${P}_{j}=\frac{{X}_{\mathit{ij}}}{{\sum}_{i=1}^{m}{X}_{\mathit{ij}}}(i=1,2,\dots ,m)$$ - Calculate the entropy of the j-th indicator E
_{j}:$${E}_{j}=-{\mathrm{ln}\left(n\right)}^{-1}{\sum}_{1}^{n}{P}_{\mathit{ij}}\xb7\mathrm{ln}{P}_{\mathit{ij}}$$ - Determine the weights of indicators w
_{j}:$${w}_{j}=\frac{1-{E}_{j}}{n-\sum {E}_{j}}(j=1,2,\dots ,n)$$

#### 2.3.3. TOPSIS Model

- Normalize the raw data to obtain a normalized matrix X = (X
_{ij})_{m×n}:The larger, the better the type of indicator:$${X}_{\mathit{ij}}=\left({x}_{\mathit{ij}}-{x}_{\mathit{jmin}})/({x}_{\mathit{jmax}}-{x}_{\mathit{jmin}}\right)$$The smaller, the better the type of indicator:$${X}_{\mathit{ij}}=\left({x}_{\mathit{jmax}}-{x}_{\mathit{ij}})/({x}_{\mathit{jmax}}-{x}_{\mathit{jmin}}\right)$$ - Multiply the normalized matrix with the weights of indicators w
_{j}to obtain the weighted standard matrix R = (r_{ij})_{m}_{×n}:$$R={\left({r}_{\mathit{ij}}\right)}_{m\times n}=\left[\begin{array}{ccc}\begin{array}{cc}{x}_{11}^{\prime}\times & {w}_{1}^{\prime}\end{array}& \cdots & \begin{array}{cc}{x}_{1n}^{\prime}& {w}_{n}^{\prime}\end{array}\\ \u22f0& \ddots & \u22f0\\ \begin{array}{cc}{x}_{m1}^{\prime}\times & {w}_{1}^{\prime}\end{array}& \cdots & \begin{array}{cc}{x}_{\mathrm{mn}}^{\prime}& {w}_{n}^{\prime}\end{array}\end{array}\right]$$ - Determine the positive ideal solution R
_{j}^{+}and the negative ideal solution R_{j}^{−}:$$\left\{\right)separators="|">\begin{array}{c}{R}_{j}^{+}=max{\displaystyle \left\{{r}_{1j}{,r}_{2j}{,\cdots ,r}_{\mathrm{mj}}\right\}}\\ {R}_{j}^{-}=min{\displaystyle \left\{{r}_{1j}{,r}_{2j}{,\cdots ,r}_{\mathrm{mj}}\right\}}\end{array}$$ - Determine the distances between the evaluation object and the positive and negative ideal solutions, D
_{i}^{+}and D_{i}^{−}:$$\left\{\right)separators="|">\begin{array}{c}{D}_{i}^{+}=\sqrt{\sum _{j=1}^{n}{\left[\left({R}_{j}^{+}-{r}_{\mathit{ij}}\right)\right]}^{2}}\\ {D}_{i}^{-}=\sqrt{\sum _{j=1}^{n}{\left[\left({R}_{j}^{-}-{r}_{\mathit{ij}}\right)\right]}^{2}}\end{array}$$

_{i}

^{+}, the farther the evaluation object is from the positive ideal solution, and the less ideal the result is; the larger D

_{i}

^{−}, the farther the evaluation object is from the negative ideal solution, and the better the result.

- 5.
- Calculate the closeness K:$$K={D}_{i}^{-}/({D}_{j}^{+}+{D}_{j}^{-})$$The closer K is to 1, the better the evaluation result.

#### 2.3.4. Obstacle Model

- The factor contribution degree F
_{ij}:$${F}_{\mathit{ij}}={w}_{j}\times {W}_{i}$$ - The indicator deviation V
_{ij}:$${V}_{\mathit{ij}}=1-{X}_{\mathit{ij}}$$ - The obstacle degree of an indicator p
_{ij}:$${p}_{\mathit{ij}}={F}_{\mathit{ij}}{V}_{\mathit{ij}}/{\sum}_{1}^{n}{F}_{\mathit{ij}}{V}_{\mathit{ij}}$$ - The obstacle degree of a subsystem P
_{ij}:$${P}_{\mathit{ij}}=\sum {p}_{\mathit{ij}}$$

_{i}denotes the weight of the ruler layer, X

_{ij}refers to the standardized value of an indicator, and n is the number of indicators.

## 3. Results and Discussion

#### 3.1. Evaluation of Water Resource Carrying Capacity of Longnan City

#### 3.1.1. Evaluation of Water Resource Carrying Capacity of DPSR Comprehensive System

_{i}

^{+}and D

_{i}

^{−}) in Longnan City from 2009 to 2019 (Figure 2), D

_{i}

^{+}decreased from 0.22 in 2009 to 0.16 in 2019, and D

_{i}

^{−}increased from 0.17 in 2009 to 0.24 in 2019. D

_{i}

^{+}and D

_{i}

^{−}achieved the maximum and the minimum in 2016, respectively, indicating that the carrying capacity in 2016 was the lowest. It is consistent with the results in Figure 2. Overall, the two showed great fluctuations. During 2012–2014 and 2015–2016, D

_{i}

^{+}increased, while D

_{i}

^{−}decreased. The distance from the positive ideal solution tended to grow, and the distance from the negative ideal solution presented a reducing tendency, implying poor water resource carrying capacity in this period. The main reason may be that from 2012 to 2014, the per capita water resources decreased, the degree of groundwater development and utilization gradually increased, and the proportion of eco-environmental water use was low from 2015 to 2016.

#### 3.1.2. Evaluation of Water Resource Carrying Capacity of DPSR Subsystems

- (1)
- The driving force subsystem

- (2)
- The pressure subsystem

^{3}/10,000 CNY in 2009 to 4286 m

^{3}/10,000 CNY, with a decrease of 74.95%, which may be the main reason for the gradual improvement of carrying capacity. In addition, a significant decrease in the proportion of eco-environmental water use from 2012 to 2018 may also cause a decline in carrying capacity in that year. The low carrying capacity in 2019 may be due to the remarkable enhancement in the per capita urban daily living water consumption, the decrease in ecological environment water utilization, and a large volume of wastewater discharge.

- (3)
- The state subsystem

- (4)
- The response subsystem

#### 3.2. Obstacle Factor Determination of Water Resource Carrying Capacity in Longnan City

#### 3.2.1. Obstacle Analysis of Indicators

_{3}(natural population growth rate) has the highest obstacle degree (26.26%), followed by x

_{13}(popularity rate of urban water, 20.18%). The obstacle degree of x

_{8}(water consumption per 10,000 CNY of GDP) is 14.50%, and those of other indicators are all less than 10%, implying that they had little influence on the water resource carrying capacity in Longnan City.

_{3}(natural population growth rate) increased continuously from 26.26% in 2009 to 28.59% in 2012; the obstacle degrees of x

_{15}(unconventional water resource utilization) and x

_{16}(water-saving irrigation area) gradually decreased to 0; and the obstacle degree of x

_{13}(popularity rate of urban water) slowly declined to 14.67%. However, the impacts of x

_{5}(per capita urban daily water consumption), x

_{6}(proportion of eco-environmental water use), and x

_{7}(wastewater discharge volume) on water resource carrying capacity were gradually enhanced. Among them, x

_{6}(proportion of eco-environmental water use) increased from 0.16% in 2009 to 6.79% in 2012, with the largest amplification. The obstacle degree of x

_{7}(wastewater discharge volume) increased to 7.80%, with an amplification of 6.58% compared to 2009.

_{3}(natural population growth rate), x

_{9}(per capita water resources), and x

_{15}(unconventional water resource utilization). Among them, the impact of x

_{15}(unconventional water resource utilization) on water resource carrying capacity gradually increased, with an obstacle degree of 14.36%. Between 2012 and 2016, the utilization of unconventional water resources in Longnan City presented a downward trend. Unconventional water resources can replace some conventional water resources, thus alleviating the contradiction between water supply and demand to some extent. The obstacle degrees of x

_{2}(urbanization rate), x

_{7}(wastewater discharge volume), and x

_{8}(water consumption per 10,000 CNY of GDP) declined to a certain degree, while x

_{13}(population rate of urban water) decreased significantly from 14.67% to 1.00%.

_{6}(proportion of eco-environmental water use) on water resource carrying capacity gradually increased, with an obstacle degree of 21.27%. In recent years, the proportion of eco-environmental water use in Longnan City has gradually decreased. Ensuring eco-environmental water use is the first step in Longnan City’s ecological environment construction. The obstacle degree of x

_{16}(unconventional water resource utilization) increased significantly (24.90%). The utilization of unconventional water resources was still relatively low. However, the obstacle degrees of some indicators were still reduced gradually. Among them, indicators of x

_{1}(per capita GDP), x

_{2}(urbanization rate), and x

_{3}(per capita natural growth rate) gradually declined to 0.

#### 3.2.2. Obstacle Analysis of Subsystems

## 4. Conclusions and Suggestions

- (1)
- From 2009 to 2019, the overall water resource carrying capacity of Longnan City showed an upward trend;
- (2)
- From 2009 to 2019, the closeness of the driving force subsystem increased continuously, possessing the optimal carrying capacity; the closeness of the pressure subsystem presented a tendency of increase-decrease-increase; the carrying capacity of the state subsystem reached the peak of 0.85; and the carrying capacity of the response subsystem tended to decrease;
- (3)
- From the perspective of obstacle factors, the stress subsystem had the highest obstacle degree, followed by the subsystems of response, driving force, and state. The primary obstacle factors to the carrying capacity of water resources in Longnan City are the utilization of unconventional water resources, the proportion of eco-environmental water use, the volume of wastewater discharge, and the per capita urban daily water consumption.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Comprehensive evaluation of water resource carrying capacity in Longnan City from 2009 to 2019.

**Figure 4.**Obstacle degrees of indicators to water resource carrying capacity in Longnan City. Note: Figures (

**a**–

**d**) represent the obstacle degrees of indicators in Longnan City in 2009, 2012, 2016, and 2019, respectively.

**Table 1.**Evaluation indicator system and weights of water resource carrying capacity in Longnan City.

Target Layer | Ruler Layer | Indicator Layer | Code | Unit | Indicator Definition | Indicator Property | Weight |
---|---|---|---|---|---|---|---|

Water resource carrying capacity | Driving | per capita GDP | x_{1} | CNY | reflecting the level of economic development | + | 0.0147 |

urbanization rate | x_{2} | % | reflecting the level of urbanization | − | 0.0425 | ||

natural population growth rate | x_{3} | ‰ | reflecting the growth of population | − | 0.1507 | ||

urban population density | x_{4} | per/km^{2} | reflecting the magnitude of population pressure | − | 0.0585 | ||

Pressure | per capita urban daily water consumption | x_{5} | L | reflecting the situation of water utilization by urban residents | − | 0.0114 | |

proportion of eco−environmental water use | x_{6} | % | reflecting the demand and importance of ecological water utilization | + | 0.0785 | ||

wastewater discharge volume | x_{7} | 10,000 t | reflecting the pollution of the environment by wastewater | − | 0.0391 | ||

water consumption per 10,000 CNY of GDP | x_{8} | m^{3}/10,000 CNY | reflecting the relationship between economic development and water consumption | − | 0.0750 | ||

State | per capita water resources | x_{9} | m^{3}/per | reflecting the number of regional water resources | + | 0.0957 | |

rate of the development and utilization of groundwater | x_{10} | % | accessing the development and utilization of groundwater resources | − | 0.0761 | ||

water production modulus | x_{11} | 10,000 m^{3}/km^{2} | representing regional water production capacity per unit area | + | 0.0850 | ||

annual precipitation | x_{12} | mm | reflecting regional precipitation | + | 0.0165 | ||

Response | popularity rate of urban water | x_{13} | % | reflecting the popularity level of urban water utilization | + | 0.1151 | |

daily capacity of wastewater treatment | x_{14} | 10,000 m^{3} | reflecting the capacity of regional wastewater treatment | + | 0.0063 | ||

unconventional water resource utilization | x_{15} | a hundred million m^{3} | reflecting the treatment and utilization of regional unconventional water resources | + | 0.1060 | ||

water-saving irrigation area | x_{16} | hm^{2} | reflecting the degree of regional agricultural water-saving | + | 0.0288 |

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## Share and Cite

**MDPI and ACS Style**

Dang, X.; Zhao, X.; Kang, Y.; Liu, X.; Song, J.; Zhang, Y.
Analysis of Carrying Capacity and Obstacle Factors of Water Resources in Longnan City, China, Based on Driving–Pressure–State–Response and Technique for Order Preference by Similarity to an Ideal Solution Models. *Water* **2023**, *15*, 2517.
https://doi.org/10.3390/w15142517

**AMA Style**

Dang X, Zhao X, Kang Y, Liu X, Song J, Zhang Y.
Analysis of Carrying Capacity and Obstacle Factors of Water Resources in Longnan City, China, Based on Driving–Pressure–State–Response and Technique for Order Preference by Similarity to an Ideal Solution Models. *Water*. 2023; 15(14):2517.
https://doi.org/10.3390/w15142517

**Chicago/Turabian Style**

Dang, Xiaofeng, Xuerui Zhao, Yanxia Kang, Xianyun Liu, Jiaqi Song, and Yuxuan Zhang.
2023. "Analysis of Carrying Capacity and Obstacle Factors of Water Resources in Longnan City, China, Based on Driving–Pressure–State–Response and Technique for Order Preference by Similarity to an Ideal Solution Models" *Water* 15, no. 14: 2517.
https://doi.org/10.3390/w15142517