Assessment and Prediction of Water Resources Vulnerability Based on a NRS-RF Model: A Case Study of the Song-Liao River Basin, China
Abstract
:1. Introduction
2. Data and Methodology
2.1. Research Area
2.2. Data Sources
2.3. Methodology
2.3.1. Assessment Indicator System
2.3.2. Attribute Reduction Method
- 1.
- Non-negative., if and only if,.
- 2.
- Symmetry..
- 3.
- Triangle inequality. .
- (1)
- is independent, that is, every element in is indispensable.
- (2)
- , so that the positive domains of and relative to the decision attribute are the same, that is, , then is a reduction of , 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 , 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 , 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 .
- 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 .
- Step 4: Calculate the predicted value of the random forest. According to the weight of each decision tree , 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
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:
- Step 2: Determine the weight of the entropy method [75]. First of all, we calculate the information entropy of the j-th index:
- Step 3: Determine the weight of the CRITIC (criteria importance though intercriteria correlation) law [76]. First of all, we quantitatively calculate the information amount of the assessment indicator:
- 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:
3.1.3. Attribute Reduction of Indicators
3.2. Construction of Water Resources Vulnerability Assessment Model
3.2.1. Interpolation of Regression Samples
3.2.2. Construction of Random Forest Regression
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
3.4. 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
References
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First-Level | Second-Level | Number | Indicator | Attribute 1 |
---|---|---|---|---|
Natural vulnerability | Water quantity | A1 | Water production modulus | Negative |
A2 | Variation coefficient of annual precipitation | Positive | ||
A3 | Change rate of annual precipitation | Positive | ||
Water quality | A4 | Water quality examination pass rate in water function area | Negative | |
A5 | Qualified ratio of water quality of river basin | Negative | ||
A6 | Decline rate of water quality examination pass rate | Positive | ||
Disasters | A7 | Proportion of area affected by flood and drought | Positive | |
A8 | Water production coefficient | Negative | ||
Man-made vulnerability | Water quantity | B1 | Proportion of surface water resources being utilized | Positive |
B2 | Proportion of groundwater resources being utilized | Positive | ||
Water quality | B3 | Total COD emission per 10,000 people | Positive | |
B4 | Total ammonia and nitrogen emission per 10,000 people | Positive | ||
Disasters | B5 | Proportion of farmland area being the effectively irrigated | Negative | |
B6 | Proportion of population under levee protection | Negative | ||
B7 | Proportion of soil erosion being controlled | Negative | ||
B8 | Water conservancy project storage capacity | Negative | ||
Vulnerability of carrying capacity | Water quantity | C1 | Ratio of groundwater supply to total water supply | Positive |
C2 | Per capita water consumption | Positive | ||
C3 | Water consumption for irrigation per mu | Positive | ||
Water quality | C4 | Population density | Positive | |
C5 | Wastewater generation per 10,000-yuan GDP | Positive | ||
C6 | Ecosystem water consumption rate | Negative | ||
Disasters | C7 | Population per 10,000 cubic meters of water | Positive | |
C8 | Reclamation index | Positive |
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] |
First-Level Indicator | Third Level Indicator |
---|---|
Natural vulnerability | Water production modulus A1 |
Change rate of annual precipitation A3 | |
Water quality examination pass rate in water function area A4 | |
Proportion of area affected by flood and drought A7 | |
Man-made vulnerability | Proportion of groundwater resources being utilized B2 |
Proportion of population under levee protection B6 | |
Proportion of soil erosion being controlled B7 | |
Water conservancy project storage capacity B8 | |
Vulnerability of carrying capacity | Ratio of groundwater supply to total water supply C1 |
Water consumption for irrigation per mu C3 | |
Wastewater generation per 10,000-yuan GDP C5 | |
Ecosystem water consumption rate C6 |
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 |
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 |
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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
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 StyleChen, 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
APA StyleChen, W., Chen, Y., & Feng, Y. (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(7), 882. https://doi.org/10.3390/e23070882