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Using a representative station as an example, the daily lake level and river discharge data in a typical normal year (2007) are first selected. Statistical characteristics of the input and the output variables are shown in Table 3. After the normalization procedure, the input and output data are randomly divided into a training group (70% data) and a testing group (30% data). The training data are used to establish the regression relationship and calibrate the critical parameters (Table 4). The site-specific relationship models are successfully developed at all stations, and the performance is shown in Table 5. After that, the testing data are applied to quantitatively validate the model performance. The scatter plots of observed and predicted lake levels, for example, at 3 representative stations are shown in Figure 7 together with the coefficients of determination. In general, they all show good agreement of the model results with the measured values: at Lujiao in the eastern region, R2 = 0.9930; at Yangliutan in the southern region, R2 = 0.9963; and at Xiaohezui in the western, R2 = 0.9933. The relationship models are also successfully developed at all stations for the typical dry year (2006), with all mean squared errors (MSEs) less than 0.01 and R2 larger than 0.99. The merit of the SVR-based relationship models is that they may forecast the response of lake levels at different stations accurately and quickly, thus providing an efficient predictor for optimization modeling.
Table 3

Statistics of the input (m3/s) and output (m) variables in the relationship model

Input indexTGR (x1)Qingjiang (x2)Xiangjiang (x3)Zishui (x4)Yuanjiang (x5)Lishui (x6)
Mean value 15,889 392 2,025 797 2,012 434 
Minimum 3,210 77 287 160 333 
Maximum 61,000 889 8,420 8,130 17,600 3,820 
Standard deviation 13,380 239 1,644 801 2,102 591 
Output indexLujiaoYingtianYangliutanNanzuiXiaohezui
Mean value 28.24 28.48 28.57 30.96 31.24 – 
Minimum 26.04 26.06 26.32 28.74 29.67 – 
Maximum 31.97 32.15 32.16 34.85 34.57 – 
Standard deviation 1.58 0.085 1.56 0.083 1.13 – 
Input indexTGR (x1)Qingjiang (x2)Xiangjiang (x3)Zishui (x4)Yuanjiang (x5)Lishui (x6)
Mean value 15,889 392 2,025 797 2,012 434 
Minimum 3,210 77 287 160 333 
Maximum 61,000 889 8,420 8,130 17,600 3,820 
Standard deviation 13,380 239 1,644 801 2,102 591 
Output indexLujiaoYingtianYangliutanNanzuiXiaohezui
Mean value 28.24 28.48 28.57 30.96 31.24 – 
Minimum 26.04 26.06 26.32 28.74 29.67 – 
Maximum 31.97 32.15 32.16 34.85 34.57 – 
Standard deviation 1.58 0.085 1.56 0.083 1.13 – 
Table 4

Critical parameters for the relationship model

ParameterLujiaoYingtianYangliutanNanzuiXiaohezui
Error threshold (ε3.82 × 10−4 5.63 × 10−7 1.90 × 10−4 3.17 × 10−6 5.65 × 10−2 
Regularization parameter (C13.4114 11.1012 5.2005 36.8999 12,968.4523 
Kernel parameter (γ0.17279 0.21613 0.26582 0.12718 0.058089 
ParameterLujiaoYingtianYangliutanNanzuiXiaohezui
Error threshold (ε3.82 × 10−4 5.63 × 10−7 1.90 × 10−4 3.17 × 10−6 5.65 × 10−2 
Regularization parameter (C13.4114 11.1012 5.2005 36.8999 12,968.4523 
Kernel parameter (γ0.17279 0.21613 0.26582 0.12718 0.058089 
Table 5

Performance of the training and testing for the relationship model

Performance (training)LujiaoYingtianYangliutanNanzuiXiaohezui
Coefficient of determination 0.998847 0.998955 0.998590 0.999900 0.998356 
Correlation coefficient 0.999441 0.999493 0.999315 0.999951 0.999178 
Root-mean-square error (m) 0.053918 0.051663 0.057776 0.015482 0.045924 
Mean absolute error (m) 0.014989 0.013051 0.017115 0.004078 0.0424472 
Performance (testing)LujiaoYingtianYangliutanNanzuiXiaohezui
Coefficient of determination 0.993006 0.996524 0.996286 0.997902 0.993348 
Correlation coefficient 0.996617 0.998356 0.998177 0.998988 0.997165 
Root-mean-square error (m) 0.124307 0.091084 0.09300 0.069147 0.084161 
Mean absolute error (m) 0.076960 0.059425 0.057600 0.042857 0.063450 
Performance (training)LujiaoYingtianYangliutanNanzuiXiaohezui
Coefficient of determination 0.998847 0.998955 0.998590 0.999900 0.998356 
Correlation coefficient 0.999441 0.999493 0.999315 0.999951 0.999178 
Root-mean-square error (m) 0.053918 0.051663 0.057776 0.015482 0.045924 
Mean absolute error (m) 0.014989 0.013051 0.017115 0.004078 0.0424472 
Performance (testing)LujiaoYingtianYangliutanNanzuiXiaohezui
Coefficient of determination 0.993006 0.996524 0.996286 0.997902 0.993348 
Correlation coefficient 0.996617 0.998356 0.998177 0.998988 0.997165 
Root-mean-square error (m) 0.124307 0.091084 0.09300 0.069147 0.084161 
Mean absolute error (m) 0.076960 0.059425 0.057600 0.042857 0.063450 
Figure 7

Scatter plots of observed and predicted lake levels at 3 representative stations: Lujiao (the eastern), Yangliutan (the southern) and Xiaohezui (the western).

Figure 7

Scatter plots of observed and predicted lake levels at 3 representative stations: Lujiao (the eastern), Yangliutan (the southern) and Xiaohezui (the western).

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