Daily Runoff Forecasting Model Based on ANN and Data Preprocessing Techniques
Abstract
:1. Introduction
2. Data-Driven Models
2.1. NLPM-ANN Model
2.2. Singular Spectrum Analysis
2.3. Artificial Neural Network
2.4. Proposed SSA-ANN Models
2.5. Evaluation of Model Performances
- (1)
- Determination coefficient (or Nash-Sutcliffe criterion) (R2)
- (2)
- Water balance coefficient (WB)
3. Comparative Study
3.1. Data
Watershed and Datasets | Statistical Parameters | Data Period | |||||
---|---|---|---|---|---|---|---|
μ | Sx | Xmax | Xmin | ||||
Jiahe area: 5578 km2 | rainfall (mm) | whole data | 2.3 | 5.9 | 71.4 | 0 | January 1980–December 1990 |
training data | 2.3 | 6.0 | 68.9 | 0 | |||
cross-validation data | 2.3 | 6.2 | 71.4 | 0 | |||
testing data | 2.1 | 5.3 | 44.2 | 0 | |||
runoff (m3) | whole data | 58.7 | 125.1 | 2620 | 6.5 | ||
training data | 61.9 | 141.6 | 2620 | 6.5 | |||
cross-validation data | 55.3 | 99.6 | 1220 | 7.9 | |||
testing data | 50.7 | 76.4 | 1080 | 10.1 | |||
Laoguanhe area: 4217 km2 | rainfall (mm) | whole data | 2.2 | 6.4 | 69.4 | 0 | January 1980–December 1990 |
training data | 2.3 | 6.8 | 69.2 | 0 | |||
cross-validation data | 2.0 | 5.8 | 56.0 | 0 | |||
testing data | 2.0 | 5.7 | 69.4 | 0 | |||
runoff (m3) | whole data | 27.1 | 73.6 | 1460 | 0.1 | ||
training data | 33.5 | 84.1 | 1460 | 0.4 | |||
cross-validation data | 16.8 | 50.6 | 586 | 0.1 | |||
testing data | 14.8 | 46.1 | 793 | 0.2 | |||
Baohe area: 3415 km2 | rainfall (mm) | whole data | 2.5 | 6.9 | 80.6 | 0 | January 1980–December 1990 |
training data | 2.5 | 7.1 | 80.6 | 0 | |||
cross-validation data | 2.2 | 6.0 | 51.3 | 0 | |||
testing data | 2.6 | 6.8 | 80.5 | 0 | |||
runoff (m3) | whole data | 46.5 | 129.4 | 4020 | 0 | ||
training data | 49.7 | 150.7 | 4020 | 1.2 | |||
cross-validation data | 31.4 | 54.8 | 523 | 3.8 | |||
testing data | 50.3 | 96.8 | 2010 | 0.0 | |||
Mumahe area: 1224 km2 | rainfall (mm) | whole data | 3.2 | 8.8 | 132.8 | 0 | January 1980–December 1990 |
training data | 3.2 | 8.6 | 132.8 | 0 | |||
cross-validation data | 3.3 | 9.3 | 98.6 | 0 | |||
testing data | 2.9 | 9.1 | 94.4 | 0 | |||
runoff (m3) | whole data | 39.3 | 80.3 | 1270 | 1.2 | ||
training data | 41.0 | 80.8 | 1270 | 1.2 | |||
cross-validation data | 40.6 | 82.1 | 796 | 4.6 | |||
testing data | 32.1 | 76.4 | 990 | 2 | |||
Nianyushan area: 924 km2 | rainfall (mm) | whole data | 3.8 | 11.6 | 269.5 | 0 | January 1975–December 1999 |
training data | 3.9 | 12.2 | 269.5 | 0 | |||
cross-validation data | 3.3 | 9.3 | 102.5 | 0 | |||
testing data | 3.7 | 10.8 | 144.7 | 0 | |||
runoff (m3) | whole data | 18.5 | 62.1 | 2095 | 0 | ||
training data | 19.8 | 68.3 | 2095 | 0 | |||
cross-validation data | 13.5 | 33.2 | 508 | 0 | |||
testing data | 17.6 | 55.9 | 822 | 0 | |||
Gaoguan area: 303 km2 | rainfall (mm) | whole data | 4.2 | 12.5 | 179.1 | 0 | January 1984–December 1999 |
training data | 4.4 | 12.8 | 179.1 | 0 | |||
cross-validation data | 3.5 | 11.3 | 143.8 | 0 | |||
testing data | 4.2 | 12.7 | 116.0 | 0 | |||
runoff (m3) | whole data | 5.8 | 15.1 | 246 | 0 | ||
training data | 5.7 | 14.2 | 237 | 0 | |||
cross-validation data | 5.1 | 13.5 | 246 | 0 | |||
testing data | 7.7 | 20.5 | 214 | 0 | |||
Shimen area: 271.25 km2 | rainfall (mm) | whole data | 3.8 | 11.4 | 141.3 | 0 | January 1989–December 1999 |
training data | 3.5 | 10.1 | 114.9 | 0 | |||
cross-validation data | 5.1 | 15.1 | 141.3 | 0 | |||
testing data | 3.8 | 11.8 | 116.8 | 0 | |||
runoff (m3) | whole data | 4.9 | 15.2 | 296 | 0 | ||
training data | 3.7 | 9.9 | 150 | 0 | |||
cross-validation data | 8.7 | 25.1 | 296 | 0 | |||
testing data | 5.5 | 17.9 | 172 | 0 | |||
Tiantang area: 220 km2 | rainfall (mm) | whole data | 3.7 | 12.1 | 193.4 | 0 | January 1973–December 1984 |
training data | 3.6 | 11.6 | 175.0 | 0 | |||
cross-validation data | 3.7 | 11.4 | 151.7 | 0 | |||
testing data | 4.2 | 14.7 | 193.4 | 0 | |||
runoff (m3) | whole data | 6.1 | 18.4 | 535 | 0 | ||
training data | 5.6 | 16.5 | 400 | 0 | |||
cross-validation data | 5.6 | 16.5 | 378 | 0.3 | |||
testing data | 8.2 | 25.6 | 535 | 0.3 |
3.2. Determination of Model Inputs
3.3. Data Preprocessing
Watershed | Decomposed Components | L | p | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|
1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | ||||
Jiahe | rainfall | −0.26 | −0.27 | −0.19 | −0.05 | 0.13 | 0.36 | 0.50 | 0.55 | – | – | 8 | 4 |
runoff | −0.14 | −0.15 | −0.11 | −0.05 | 0.05 | 0.18 | 0.39 | 0.55 | 0.77 | – | 9 | 5 | |
Laoguanhe | rainfall | −0.36 | −0.33 | −0.24 | −0.06 | 0.12 | 0.33 | 0.47 | 0.53 | – | – | 8 | 4 |
runoff | −0.15 | −0.15 | −0.10 | 0.00 | 0.14 | 0.35 | 0.55 | 0.77 | – | – | 8 | 4 | |
Baohe | rainfall | −0.26 | −0.26 | −0.18 | −0.04 | 0.14 | 0.35 | 0.50 | 0.60 | – | – | 8 | 4 |
runoff | −0.18 | −0.20 | −0.16 | −0.08 | 0.04 | 0.16 | 0.33 | 0.54 | 0.76 | – | 9 | 5 | |
Mumahe | rainfall | −0.34 | −0.32 | −0.22 | −0.06 | 0.13 | 0.34 | 0.47 | 0.52 | – | – | 8 | 4 |
runoff | −0.15 | −0.18 | −0.14 | −0.09 | −0.01 | 0.11 | 0.25 | 0.41 | 0.56 | 0.71 | 10 | 5 | |
Nianyushan | rainfall | −0.33 | −0.33 | −0.26 | −0.13 | 0.02 | 0.19 | 0.35 | 0.47 | 0.51 | – | 9 | 5 |
runoff | −0.22 | −0.22 | −0.16 | −0.03 | 0.15 | 0.34 | 0.54 | 0.68 | – | – | 8 | 4 | |
Gaoguan | rainfall | −0.32 | −0.37 | −0.30 | −0.18 | −0.07 | 0.09 | 0.23 | 0.37 | 0.46 | 0.43 | 10 | 5 |
runoff | −0.14 | −0.19 | −0.17 | −0.12 | −0.03 | 0.09 | 0.23 | 0.42 | 0.58 | 0.67 | 10 | 5 | |
Shimen | rainfall | −0.34 | −0.34 | −0.32 | −0.28 | 0.01 | 0.19 | 0.35 | 0.47 | 0.48 | – | 9 | 5 |
runoff | −0.21 | −0.23 | −0.18 | −0.09 | 0.04 | 0.19 | 0.39 | 0.58 | 0.66 | – | 9 | 5 | |
Tiantang | rainfall | −0.32 | −0.34 | −0.19 | 0.03 | 0.28 | 0.46 | 0.53 | – | – | – | 7 | 4 |
runoff | −0.31 | −0.31 | −0.16 | 0.03 | 0.25 | 0.46 | 0.62 | – | – | – | 7 | 4 |
4. Results Analysis
Watershed | ANN | NLPM-ANN | SSA-ANN1 | SSA-ANN2 | |||||
---|---|---|---|---|---|---|---|---|---|
R2 (%) | WB | R2 (%) | WB | R2 (%) | WB | R2 (%) | WB | ||
Jiahe | calibration | 68.19 | 1.023 | 85.46 | 1.015` | 80.97 | 0.982 | 96.09 | 1.013 |
testing | 61.48 | 0.866 | 61.31 | 1.119 | 74.91 | 0.975 | 92.40 | 1.013 | |
Laoguanhe | calibration | 69.72 | 1.048 | 85.66 | 1.042 | 82.29 | 0.972 | 96.31 | 1.186 |
testing | 60.42 | 1.058 | 68.25 | 1.412 | 78.44 | 1.464 | 93.20 | 1.407 | |
Baohe | calibration | 64.75 | 0.975 | 70.93 | 1.039 | 88.50 | 1.029 | 94.01 | 1.006 |
testing | 68.62 | 0.667 | 69.38 | 0.893 | 74.03 | 0.927 | 94.31 | 0.956 | |
Mumahe | calibration | 80.64 | 0.950 | 90.18 | 1.050 | 87.86 | 0.976 | 95.08 | 1.019 |
testing | 80.17 | 0.913 | 85.6 | 1.410 | 92.41 | 1.108 | 94.71 | 1.053 | |
Nianyushan | calibration | 75.8 | 0.941 | 83.44 | 1.084 | 84.89 | 0.910 | 85.86 | 1.020 |
testing | 82.38 | 0.803 | 85.39 | 1.329 | 88.30 | 0.939 | 88.39 | 1.077 | |
Gaoguan | calibration | 66.16 | 1.035 | 77.6 | 1.045 | 80.17 | 1.002 | 93.24 | 1.005 |
testing | 76.38 | 0.957 | 77.97 | 0.894 | 80.43 | 0.840 | 89.85 | 0.962 | |
Shimen | calibration | 65.03 | 0.848 | 64.85 | 1.068 | 73.85 | 1.141 | 94.53 | 1.084 |
testing | 72 | 0.772 | 75.72 | 1.281 | 76.90 | 1.089 | 87.99 | 1.055 | |
Tiantang | calibration | 65.47 | 0.985 | 73.06 | 1.049 | 78.08 | 0.960 | 88.66 | 1.131 |
testing | 59.79 | 0.895 | 81.96 | 0.956 | 79.54 | 1.015 | 91.32 | 1.043 | |
Mean | calibration | 69.47 | 0.976 | 78.41 | 1.046 | 82.08 | 1.00 | 92.97 | 1.06 |
testing | 70.16 | 0.879 | 75.86 | 1.155 | 80.62 | 1.04 | 91.52 | 1.07 |
5. Summary and Conclusions
- (1)
- The performance of the ANN model can be improved by data preprocessing techniques. SSA is more effective and it can improve the learning and training ability of the ANN type model significantly. Results also show that the impact of noise in hydrological time series on model performance is bigger than the seasonal hydrological behavior.
- (2)
- Comparing the SSA-ANN1 model with the NLPM-ANN model, the mean values of R2 and WB for the SSA-ANN1 model are 82.08% and 80.62%, and 1.0 and 1.04, during calibration and testing periods, respectively, which are much better than that of the NLPM-ANN model.
- (3)
- The SSA-ANN2 model performs best for daily runoff forecasting for all selected watersheds. The effective way for increasing daily runoff forecasting accuracy is to preprocess data series by SSA and select both previous related rainfall and runoff as predictive factors.
- (4)
- There are some limitations in this study. The method to select the contributing components relies on liner correlation analysis, which disregards the existence of nonlinearity in the hydrologic process. The sensitivities and uncertainties of model parameters are not analyzed. All of these will be the focus in our future research.
Acknowledgment
Author Contributions
Conflicts of Interest
References
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Wang, Y.; Guo, S.; Xiong, L.; Liu, P.; Liu, D. Daily Runoff Forecasting Model Based on ANN and Data Preprocessing Techniques. Water 2015, 7, 4144-4160. https://doi.org/10.3390/w7084144
Wang Y, Guo S, Xiong L, Liu P, Liu D. Daily Runoff Forecasting Model Based on ANN and Data Preprocessing Techniques. Water. 2015; 7(8):4144-4160. https://doi.org/10.3390/w7084144
Chicago/Turabian StyleWang, Yun, Shenglian Guo, Lihua Xiong, Pan Liu, and Dedi Liu. 2015. "Daily Runoff Forecasting Model Based on ANN and Data Preprocessing Techniques" Water 7, no. 8: 4144-4160. https://doi.org/10.3390/w7084144