# Assessment and Prediction of Water Resources Vulnerability Based on a NRS-RF Model: A Case Study of the Song-Liao River Basin, China

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## Abstract

**:**

## 1. Introduction

## 2. Data and Methodology

#### 2.1. Research Area

^{2}. The basin is surrounded by mountains to the west, north and east, and there is a vast plain in the middle of the basin. The specific distribution of rivers is shown in Figure 1. In the Song-Liao River Basin, that is rich in black soil resources, the plains are flat, the soil is fertile, the rainfall is abundant, the climate is suitable, the sunlight is sufficient, and it has good conditions for agricultural development [58]. What’s more, the basin is also a major industrial hub for coal, steel, petrochemical and equipment manufacturing [59,60,61]. In terms of precipitation, the annual average precipitation in the Song-Liao River Basin shows a spatial distribution characteristic of less precipitation in the northwest and more precipitation in the southeast [2]. The spatial distribution of annual average precipitation in Song-Liao Basin is shown in Figure 1. At present, the Song-Liao River Basin is in a stage of extreme precipitation, and the probability of extreme precipitation has increased [62]. What’s more, due to uneven seasonal precipitation and the high-water level of the drainage channel, the internal water cannot be discharged. The mountainous area has serious soil erosion, and a large amount of sediment is discharged and deposited on the drainage channel, which causes that the riverbed has been silted up year by year, the channel is blocked, and the water is urgent in the flood season. Also, poor water leakage in the waterlogged area and low infiltration capacity have led to frequent occurrence of waterlogging in the watershed. As the northwestern part of the basin is in the westerly zone, when a large precipitation front and low-pressure system pass through this area, the rainfall will be significantly reduced or no precipitation. The normal annual precipitation is below 400 mm, and the water surface evaporation capacity is 1100–1200 mm, which caused many droughts [2]. With the development of industrialization and urbanization and the massive discharge of industrial wastewater and domestic sewage, the Song-Liao River Basin is facing a severe situation of aggravated pollution. According to relevant statistical data such as environmental yearbook, since 2014, the chemical oxygen demand (COD) emissions of the Song-Liao River Basin are about 830,400 tons, and the ammonia and nitrogen emissions are about 12.85 tons. Compared with the previous level, the water pollution problem still cannot be ignored. This objectively aggravates the vulnerability of water resources, so research on the vulnerability of water resources is timely.

#### 2.2. Data Sources

#### 2.3. Methodology

#### 2.3.1. Assessment Indicator System

#### 2.3.2. Attribute Reduction Method

**Definition**

**1**

**.**Given the universe$U=\left\{{x}_{1},{x}_{2},\cdots ,{x}_{n}\right\}$, if for any${x}_{i},{x}_{j},{x}_{k}\in U$, there are unique real functions ∆ corresponding to them, and ∆ satisfies:

- 1.
- Non-negative.$\Delta \left({x}_{i},{x}_{j}\right)\ge 0$, if and only if${x}_{i}={x}_{j}$,$\Delta \left({x}_{i},{x}_{j}\right)=0$.
- 2.
- Symmetry.$\Delta \left({x}_{i},{x}_{j}\right)=\Delta \left({x}_{j,}{x}_{i}\right)$.
- 3.
- Triangle inequality. $\Delta \left({x}_{i},{x}_{k}\right)\le \Delta \left({x}_{i},{x}_{j}\right)+\Delta \left({x}_{j},{x}_{k}\right)$.

**Definition**

**2**

**.**For any metric space$<U,\Delta >$and any$U$, the neighborhood$\delta $of any${x}_{i}$can be expressed as:

**Definition**

**3**

**.**In the neighborhood rough set decision-making system$NDS=\left(U,A{{\displaystyle \cup}}^{\text{}}D\right)$, given the universe$U=\left\{{x}_{1},{x}_{2},\dots ,{x}_{n}\right\}$and the neighborhood relationship$N$on it, that is, two-tuple$NS=\left(U,N\right)$, for any $X\subseteq U$, the lower approximation of$X$in the neighborhood approximation space$NS=\left(U,N\right)$is:

**Definition**

**4**

**.**In the decision system$S=\left(U,C{{\displaystyle \cup}}^{\text{}}D\right)$,$c\in C$, the importance of conditional attribute (indicator)$c$is defined as:$Sig\left(c\right)={\gamma}_{C}\left(D\right)-{\gamma}_{C-\left\{c\right\}}\left(D\right)$, where the calculation formula of the dependency${\gamma}_{C}$of the conditional attribute set$C$relative to the decision attribute$D$is:

**Definition**

**5**

**.**Given a knowledge base$S=\left(U,R\right)$and a set of equivalent relations$P\subseteq R$on it, for any$G\subseteq P$, if G satisfies the following conditions:

- (1)
- $G$is independent, that is, every element in$G$ is indispensable.
- (2)
- $IND\left(G\right)=IND\left(P\right)$, so that the positive domains of$G$ and $P$ relative to the decision attribute are the same, that is, $po{s}_{G}D=po{s}_{P}D$, then $G$ is a reduction of $P$, denoted as G ∈ Red (P).

- Step 1: Generate decision tables and determine the values of various model parameters, according to the data set decision system $NDS=\left(U,A{{\displaystyle \cup}}^{\text{}}D\right)$, including discretized decision attributes.
- Step 2: Calculate and search the neighborhood radius. The optimal neighborhood radius of the conditional attributes of each subsystem is determined respectively, and the neighborhood set of the sample is obtained separately according to the definition of the neighborhood radius. The size of the neighborhood radius is calculated based on the standard deviation of the attribute samples and the relative number of neighborhood parameters. The samples under the same neighborhood radius as sought are regarded as the same-attribute neighborhood set.
- Step 3: Calculate the upper and lower approximate set, that is, calculate the upper and lower approximations of the decision attribute set relative to the condition attribute set. The lower approximation set is also the positive domain of the neighborhood rough set.
- Step 4: Calculate the dependency of the decision attribute in each condition attribute subset by the positive domain and calculate the importance of each decision attribute relative to each condition attribute according to the importance solving formula.
- Step 5: Get the reduction set. The samples whose attribute importance degree exceeds the set appropriate lower limit of importance degree are taken as the final attribute reduction set, so as to obtain a satisfactory solution.

#### 2.3.3. Random Forest Models

- Step 1: Randomly select a decision tree with a number of k. The bootstrap method is used to resample the original samples, thereby randomly generating k training sets ${\theta}_{1},{\theta}_{2},{\theta}_{3}\dots {\theta}_{k}$, that is, the number of trees generated is k (that is, the value of parameter ntree). At the same time, each training set trained is used to generate the corresponding decision tree $\left\{Tr\left(x,{\theta}_{1}\right),Tr\left(x,{\theta}_{2}\right),Tr\left(x,{\theta}_{3}\right),\dots ,Tr\left(x,{\theta}_{k}\right)\right\}$.
- Step 2: Randomly extract the dimensional feature set with the number m, that is, randomly extract m features from the dimensional features with the indicator feature number M as the split feature set of the current node (that is, the value of parameter mtry), and use the standardized mean-square error as the standard to judge whether these m features follow the most appropriate split method to carry out splitting, so that the whole after splitting has the best stability.
- Step 3: Calculate the observation value of a single tree. The prediction of a single decision tree is obtained by the weighted average of the dependent variables’ observed values ${Y}_{i}\left(i=1,2,3,\dots n\right)$.
- Step 4: Calculate the predicted value of the random forest. According to the weight of each decision tree ${\omega}_{i}\left(x,{\theta}_{t}\right)\left(t=1,2,3\dots k\right)$, the mean value of the observation value of each decision tree is taken as the final result.

#### 2.3.4. Integration of Neighborhood Rough Set and Random Forest Algorithm

- Step 1: Attribute reduction. After constructing the assessment indicator system of water resources vulnerability, we use the forward greedy algorithm of neighborhood rough set to reduce the dimensionality of the original indicator system to remove redundant attributes. It retains the indicators with the greatest attribute importance, and then starts to select it backwards, while also ensuring that the core is not reduced.
- Step 2: Construction of water resources vulnerability assessment model. We take the standard value of the indicator level threshold of the assessment indicator system after dimensionality reduction as the input vector and the vulnerability level value as the output vector to construct a random forest model.
- Step 3: Assessment of water resources vulnerability. The indicator data of the Song-Liao River Basin from 2000 to 2017 is substituted into the model to obtain the water resources vulnerability evaluation value in the past few years.
- Step 4: Testing of the assessment model. We use the 10-fold cross-validation method to test the trained model to judge the reliability of the results. In order to verify whether the accuracy of the random forest regression model is better than other models in this paper, the neural network model, decision tree and support vector machine regression model with excellent nonlinear regression function are compared with it.
- Step 5: Scenario prediction of water resources vulnerability. The indicator data under different scenarios in 2025 and 2030 is substituted into the random forest model as input data to obtain the predicted value of water resources vulnerability, so as to provide reference for future water resources planning and adaptive management.

## 3. Results and Discussion

#### 3.1. Attribute Reduction of Evaluation Indicators

#### 3.1.1. Correlation Analysis of Evaluation Indicators

_{1}and A

_{8}is up to 0.9, and the repeatability between the two is relatively large. The correlation coefficient diagram of man-made vulnerability is shown in Figure 3b. Among them, the correlation coefficient between B

_{5}and B

_{7}is 0.8, which is the strongest. In addition, the correlations between indicator B

_{3}and other indicators are relatively large. The absolute value of the correlation coefficient between B

_{3}and B

_{5}, B

_{3}and B

_{6}are all greater than 0.7. The correlations between other indicators are not so strong. The correlation coefficient diagram of vulnerability of carrying capacity is shown in Figure 3c. Compared with the indicators in the first two aspects, the redundancy between the indicators in the aspect of the vulnerability of carrying capacity is significantly greater. Among them, the absolute values of the correlation coefficient between C

_{2}and other indicators are all not less than 0.3. In summary, there are more or less correlations among various indicators. At the same time, the definition and connotation of each specific indicator and the actual situation of the evaluation industry explain that there is duplication of information in the indicators initially constructed in the article. This information may have an impact on the final prediction of water resources vulnerability of the river basin. Therefore, it is very important to choose a suitable method to eliminate the impact of the constructed index as much as possible. On the basis of the indicator structure and classification ability unchanged, this article uses the neighborhood rough set theory to reduce the attributes of the remaining indicators for the important indicators selected by the qualitative analysis, which is more conducive to the subsequent assessment and prediction work.

#### 3.1.2. Determination of Decision-Making Attributes

- Step 1: Perform non-dimensional standardization on the original data. The non-dimensional standardization processing formula of the positive indicator is as follows:$${X}_{ij}=\frac{{x}_{ij}-min{x}_{ij}}{max{x}_{ij}-min{x}_{ij}}$$

- Step 2: Determine the weight of the entropy method [75]. First of all, we calculate the information entropy ${E}_{j}$ of the j-th index:$${E}_{j}=-\frac{1}{\mathrm{ln}\left(n\right)}{\displaystyle \sum}_{i=1}^{j}({f}_{ij}ln{f}_{ij})$$

- Step 3: Determine the weight of the CRITIC (criteria importance though intercriteria correlation) law [76]. First of all, we quantitatively calculate the information amount ${C}_{i}$ of the assessment indicator:$${C}_{i}={S}_{j}\ast {R}_{j}=\sqrt{\frac{{{\displaystyle \sum}}_{i=1}^{n}({X}_{ij}-\frac{1}{n}{{\displaystyle \sum}}_{i=1}^{n}{X}_{ij})}{n-1}}\ast {\displaystyle \sum}_{t=1}^{n}\left(1-{r}_{rj}\right)$$

- Step 4: Determine the comprehensive weight of the game theory method. This paper uses the game theory method to integrate the entropy method and the CRITIC method to comprehensively determine the weight of the indicator. At the same time, the relevance, dispersion and relative strength of the indicator data information have also been fully tested. Thereby, the weighting result tends to be balanced, and the scientificity of the indicator weight is improved. The steps for determining the comprehensive weight of the game theory method are as follows:

- Step 5: Use the standardized values of related indicators and the weights of each indicator in the water resources vulnerability assessment indicator system to calculate the final comprehensive evaluation value of vulnerability in the three aspects of natural vulnerability, man-made vulnerability and vulnerability of carrying capacity. The calculation formula is as follows:$${Z}_{i}={\displaystyle \sum}_{j=1}^{n}\left({w}_{j}{X}_{ij}\right)$$

#### 3.1.3. Attribute Reduction of Indicators

_{1}is added to the set A, and C

_{5}, C

_{6}are added to the set C. Finally, a reduced indicator system is formed, as shown in Table 3 below, which serves as the basis for the random forest regression model. In addition, according to the correlation analysis of evaluation indicators in the Section 3.1.1, the absolute values of the correlation coefficient between indicators are controlled below 0.6 after the reduction, that is, the redundancy of the indicator system is further reduced.

#### 3.2. Construction of Water Resources Vulnerability Assessment Model

#### 3.2.1. Interpolation of Regression Samples

#### 3.2.2. Construction of Random Forest Regression

^{2}) of all test results is obtained. The related error test formula is as follows [77]:

#### 3.3. Assessment of Water Resources Vulnerability

#### 3.3.1. Calculation of Current Situation of Water Resources Vulnerability

#### 3.3.2. Current Situation Evaluation of River Basin’s Water Resources Vulnerability

^{3}/km

^{2}, and some years have large fluctuations. There is a big gap between the Song-Liao River Basin and other water-producing areas, such as the Huai River Basin whose average water production modulus is 320,000 m

^{3}/km

^{2}. In the Song-Liao River Basin, basin itself has a vast area, the total amount of water resources is relatively abundant and there is a large gap between regions, which is an important factor that is likely to cause the uncertainty of water resources’ natural vulnerability. At the same time, in some areas, precipitation fluctuates greatly in some years, causing the basin to be affected by external natural climatic conditions. In addition, the imbalance of precipitation in the basin, especially the water shortage in inland areas, cannot be ignored, which will objectively aggravate the natural vulnerability of the Song-Liao basin. Additionally, in terms of water quality, the situation of regional water resources pollution has improved recently, but the extent is not very large. From the water quality qualified rate of the river basin, the relevant rate of Song-Liao River Basin in 2017 has increased by 2.96% compared with the previous year. Therefore, there is room for improvement in the future.

#### 3.4. Scenario Prediction and Analysis of River Basin’s Water Resources Vulnerability

#### 3.4.1. Raw Data under Different Scenarios in the Future

#### 3.4.2. Forecast Result Analysis

## 4. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

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**Figure 2.**Water resources vulnerability assessment model based on the integration of neighborhood rough set and random forest model.

**Figure 3.**Correlation coefficient diagram of the original index system: (

**a**) correlation coefficient diagram of natural vulnerability; (

**b**) correlation coefficient diagram of man-made vulnerability; (

**c**) correlation coefficient diagram of vulnerability of carrying capacity.

**Figure 4.**Random forest model training image: (

**a**) relationship graph between model NMSE and ntree; (

**b**) relationship graph between model error and ntree.

First-Level | Second-Level | Number | Indicator | Attribute ^{1} |
---|---|---|---|---|

Natural vulnerability | Water quantity | A_{1} | Water production modulus | Negative |

A_{2} | Variation coefficient of annual precipitation | Positive | ||

A_{3} | Change rate of annual precipitation | Positive | ||

Water quality | A_{4} | Water quality examination pass rate in water function area | Negative | |

A_{5} | Qualified ratio of water quality of river basin | Negative | ||

A_{6} | Decline rate of water quality examination pass rate | Positive | ||

Disasters | A_{7} | Proportion of area affected by flood and drought | Positive | |

A_{8} | Water production coefficient | Negative | ||

Man-made vulnerability | Water quantity | B_{1} | Proportion of surface water resources being utilized | Positive |

B_{2} | Proportion of groundwater resources being utilized | Positive | ||

Water quality | B_{3} | Total COD emission per 10,000 people | Positive | |

B_{4} | Total ammonia and nitrogen emission per 10,000 people | Positive | ||

Disasters | B_{5} | Proportion of farmland area being the effectively irrigated | Negative | |

B_{6} | Proportion of population under levee protection | Negative | ||

B_{7} | Proportion of soil erosion being controlled | Negative | ||

B_{8} | Water conservancy project storage capacity | Negative | ||

Vulnerability of carrying capacity | Water quantity | C_{1} | Ratio of groundwater supply to total water supply | Positive |

C_{2} | Per capita water consumption | Positive | ||

C_{3} | Water consumption for irrigation per mu | Positive | ||

Water quality | C_{4} | Population density | Positive | |

C_{5} | Wastewater generation per 10,000-yuan GDP | Positive | ||

C_{6} | Ecosystem water consumption rate | Negative | ||

Disasters | C_{7} | Population per 10,000 cubic meters of water | Positive | |

C_{8} | Reclamation index | Positive |

^{1}The positive indicator indicates that the larger the value of the assessment index is, the higher the water resources vulnerability is; the negative indicator indicates that the smaller the value of the assessment index is, the lower the water resources vulnerability is.

Level I | Level II | Level III | Level IV | Level V | Level VI | Level VII | |
---|---|---|---|---|---|---|---|

A1 | (60, 100] | (50, 60] | (40, 50] | (30, 40] | (20, 30] | (10, 20] | (0, 10] |

A2 | (0, 0.1] | (0.1, 0.2] | (0.2, 0.3] | (0.3, 0.4] | (0.4, 0.5] | (0.5, 0.6] | (0.6, 0.8] |

A3 | (0, 0.1] | (0.1, 0.2] | (0.2, 0.3] | (0.3, 0.4] | (0.4, 0.5] | (0.5, 0.6] | (0.6, 0.7] |

A4 | (0.9, 1] | (0.8, 0.9] | (0.7, 0.8] | (0.6, 0.7] | (0.5, 0.6] | (0.4, 0.5] | (0.2, 0.4] |

A5 | (0.8, 1] | (0.7, 0.8] | (0.6, 0.7] | (0.5, 0.6] | (0.4, 0.5] | (0.25, 0.4] | (0.15, 0.25] |

A6 | (−0.8, 0] | (0, 0.05] | (0.05, 0.1] | (0.1, 0.2] | (0.2, 0.3] | (0.3, 0.4] | (0.4, 0.5] |

A7 | (0, 0.05] | (0.05, 0.1] | (0.1, 0.15] | (0.15, 0.2] | (0.2, 0.25] | (0.25, 0.3] | (0.3, 1] |

A8 | (0.7, 0.8] | (0.6, 0.7] | (0.5, 0.6] | (0.4, 0.5] | (0.3, 0.4] | (0.2, 0.3] | (0.1, 0.2] |

B1 | (0, 0.2] | (0.2, 0.25] | (0.25, 0.4] | (0.4, 0.55] | (0.55, 0.7] | (0.7, 0.85] | (0.85, 1] |

B2 | (0, 0.2] | (0.2, 0.25] | (0.25, 0.4] | (0.4, 0.55] | (0.55, 0.7] | (0.7, 0.85] | (0.85, 2] |

B3 | (15, 30] | (30, 45] | (45, 60] | (60, 75] | (75, 90] | (90, 105] | (105, 160] |

B4 | (4, 6] | (6, 8] | (8, 10] | (10, 12] | (12, 14] | (14, 16] | (16, 18] |

B5 | (0.95, 1] | (0.9, 0.95] | (0.85, 0.9] | (0.8, 0.85] | (0.75, 0.8] | (0.7, 0.75] | (0.65, 0.7] |

B6 | (0.9, 1] | (0.8, 0.9] | (0.7, 0.8] | (0.6, 0.7] | (0.5, 0.6] | (0.4, 0.5] | (0.2, 0.4] |

B7 | (0.9, 1] | (0.75, 0.9] | (0.6, 0.75] | (0.45, 0.6] | (0.3, 0.45] | (0.15, 0.3] | (0, 0.15] |

B8 | (0.9, 1.2] | (0.75, 0.9] | (0.6, 0.75] | (0.45, 0.6] | (0.3, 0.45] | (0.15, 0.3] | (0, 0.15] |

C1 | (0, 0.1] | (0.1, 0.2] | (0.2, 0.3] | (0.3, 0.4] | (0.4, 0.5] | (0.5, 0.6] | (0.6, 0.7] |

C2 | (180, 200] | (200, 300] | (300, 400] | (400, 450] | (450, 500] | (500, 550] | (550, 600] |

C3 | (180, 200] | (200, 300] | (300, 400] | (400, 450] | (450, 500] | (500, 550] | (550, 600] |

C4 | (0.008, 0.01] | (0.01, 0.02] | (0.02, 0.03] | (0.03, 0.04] | (0.04, 0.05] | (0.05, 0.06] | (0.06, 0.09] |

C5 | (2, 4] | (4, 6] | (6, 8] | (8, 10] | (10, 15] | (15, 25] | (25, 75] |

C6 | (0.06, 0.09] | (0.05, 0.06] | (0.04, 0.05] | (0.03, 0.04] | (0.02, 0.03] | (0.01, 0.02] | (0, 0.01] |

C7 | (0, 3.34] | (3.34, 5] | (5, 10] | (10, 15] | (15, 20] | (20, 30] | (30, 90] |

C8 | (0, 0.1] | (0.1, 0.2] | (0.2, 0.3] | (0.3, 0.4] | (0.4, 0.5] | (0.5, 0.6] | (0.6, 0.7] |

^{1}The level I is the level of no vulnerability; The level II is the level of mild vulnerability; The level III is the level of moderate to low vulnerability; The level IV is the level of moderate vulnerability; The level V is the level of moderate to high vulnerability; The level VI is the level of highly vulnerability; The level VII is the level of extreme vulnerability.

First-Level Indicator | Third Level Indicator |
---|---|

Natural vulnerability | Water production modulus A_{1} |

Change rate of annual precipitation A_{3} | |

Water quality examination pass rate in water function area A_{4} | |

Proportion of area affected by flood and drought A_{7} | |

Man-made vulnerability | Proportion of groundwater resources being utilized B_{2} |

Proportion of population under levee protection B_{6} | |

Proportion of soil erosion being controlled B_{7} | |

Water conservancy project storage capacity B_{8} | |

Vulnerability of carrying capacity | Ratio of groundwater supply to total water supply C_{1} |

Water consumption for irrigation per mu C_{3} | |

Wastewater generation per 10,000-yuan GDP C_{5} | |

Ecosystem water consumption rate C_{6} |

Number of mtry | NMSE of Training Set | NMSE of Test Set |
---|---|---|

2 | 0.001004 | 0.005345 |

3 | 0.000937 | 0.005332 |

4 | 0.000896 | 0.005255 |

5 | 0.000977 | 0.005369 |

6 | 0.000927 | 0.005399 |

7 | 0.000927 | 0.005318 |

8 | 0.00096 | 0.00506 |

Methods | MSE | NMSE | R-Squared ^{1} |
---|---|---|---|

Random forest | 0.0001529336 | 1.738314 × 10^{−8} | 0.9999968 |

Decision tree | 0.00013895 | 0.01205421 | 0.9999924 |

Support vector machine | 0.001653784 | 1.620705 × 10^{−6} | 0.9999991 |

Neural network | 0.8765589 | 1.414752 | 0.9969101 |

^{1}The greater the R-squared is, the greater the precision of model is.

Vulnerability Value (0–7) | Vulnerability Grade (I–VII) | |||||||
---|---|---|---|---|---|---|---|---|

Basin Vulnerability | Natural Vulnerability | Man-Made Vulnerability | Vulnerability of Carrying Capacity | Basin Vulnerability | Natural Vulnerability | Man-Made Vulnerability | Vulnerability of Carrying Capacity | |

2000 | 4.6439 | 3.8538 | 5.0428 | 4.0412 | V | IV | V | IV |

2001 | 4.7345 | 3.8520 | 5.1176 | 4.0910 | V | IV | V | IV |

2002 | 4.7350 | 3.8148 | 4.9121 | 4.2335 | V | IV | V | IV |

2003 | 4.9053 | 3.7021 | 4.6849 | 5.7085 | V | IV | V | VI |

2004 | 4.9896 | 3.8451 | 4.7396 | 5.6695 | V | IV | V | VI |

2005 | 4.8879 | 3.8350 | 4.6024 | 5.4638 | V | IV | V | V |

2006 | 4.8516 | 3.7702 | 4.5788 | 5.4150 | V | IV | V | V |

2007 | 4.8796 | 3.9211 | 5.1552 | 5.2339 | V | IV | V | V |

2008 | 4.8247 | 3.8551 | 4.9260 | 5.1380 | V | IV | V | V |

2009 | 4.9444 | 3.8665 | 4.9004 | 5.3324 | V | IV | V | V |

2010 | 4.5139 | 3.7642 | 4.5418 | 4.8695 | V | IV | V | V |

2011 | 4.6983 | 4.0618 | 5.2211 | 4.2512 | V | IV | V | IV |

2012 | 4.5862 | 4.4266 | 4.6821 | 4.2025 | V | IV | V | IV |

2013 | 4.6497 | 3.5852 | 5.1762 | 4.5860 | V | IV | V | V |

2014 | 4.8027 | 4.0528 | 5.2035 | 4.6551 | V | IV | V | IV |

2015 | 4.6008 | 3.7439 | 5.0740 | 4.1847 | V | IV | V | IV |

2016 | 4.5366 | 3.7731 | 4.8101 | 4.1949 | V | IV | V | IV |

2017 | 4.7030 | 3.8582 | 5.1625 | 4.3442 | V | IV | V | IV |

Vulnerability Value (0–7) | Vulnerability Grade (I–VII) | |||||||
---|---|---|---|---|---|---|---|---|

Basin Vulnerability | Natural Vulnerability | Man-Made Vulnerability | Vulnerability of Carrying Capacity | Basin Vulnerability | Natural Vulnerability | Man-Made Vulnerability | Vulnerability of Carrying Capacity | |

2025 S1 ^{1} | 3.9930 | 2.6677 | 4.4839 | 4.1512 | IV | III | IV | IV |

2025 S2 ^{1} | 4.5857 | 3.6436 | 4.8763 | 4.6821 | V | IV | V | V |

2025 S3 ^{1} | 5.0388 | 3.8908 | 5.1832 | 5.4807 | V | IV | V | V |

2030 S1 | 3.0448 | 2.3793 | 3.5221 | 2.3116 | III | III | IV | III |

2030 S2 | 3.7156 | 3.3894 | 4.0384 | 3.4934 | IV | IV | IV | III |

2030 S3 | 4.3642 | 3.8460 | 4.2620 | 4.2809 | IV | IV | IV | IV |

^{1}S1, S2 and S3 are short for Scenario 1, Scenario 2 and Scenario 3.

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**MDPI and ACS Style**

Chen, W.; Chen, Y.; Feng, Y.
Assessment and Prediction of Water Resources Vulnerability Based on a NRS-RF Model: A Case Study of the Song-Liao River Basin, China. *Entropy* **2021**, *23*, 882.
https://doi.org/10.3390/e23070882

**AMA Style**

Chen W, Chen Y, Feng Y.
Assessment and Prediction of Water Resources Vulnerability Based on a NRS-RF Model: A Case Study of the Song-Liao River Basin, China. *Entropy*. 2021; 23(7):882.
https://doi.org/10.3390/e23070882

**Chicago/Turabian Style**

Chen, Weizhong, Yan Chen, and Yazhong Feng.
2021. "Assessment and Prediction of Water Resources Vulnerability Based on a NRS-RF Model: A Case Study of the Song-Liao River Basin, China" *Entropy* 23, no. 7: 882.
https://doi.org/10.3390/e23070882