# Impact of Input Filtering and Architecture Selection Strategies on GRU Runoff Forecasting: A Case Study in the Wei River Basin, Shaanxi, China

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## Abstract

**:**

## 1. Introduction

## 2. Methodology

#### 2.1. Preprocessing

#### 2.1.1. Principal Component Analysis (PCA) Denoising

#### 2.1.2. Normalization

#### 2.1.3. Sliding Window Sampling

#### 2.2. Gated Recurrent Unit (GRU)

#### 2.3. Stacked and Bi-Directional GRU (bi-GRU)

#### 2.4. Model Evaluation

^{3}/s in this study), the lower the RMSE and MAE are, the better the model performs. The RMSE is more sensitive to abnormal values than the MAE.

## 3. Case Study and Materials

#### 3.1. Research Area and Data

#### 3.2. Scenarios and Traning Process

#### 3.3. PCA Denoised Data

## 4. Results and Discussions

#### 4.1. Robustness Evaluation

#### 4.1.1. Overall Evaluation

#### 4.1.2. Time Step Standard Deviation of the Evaluation Metrics

#### 4.2. Accuracy Evaluation

#### 4.2.1. Overall Evaluation

^{3}/s and 19.868 m

^{3}/s, respectively. The NSE values in all the scenarios exceed 0.9 for T + 1 forecasting, and in most of the scenarios exceed 0.8 for T + 2 forecasting, which means that either of the input filtering strategies can have an acceptable prediction accuracy after the optimization of hyperparameters. However, there are still some differences determining which kind of strategy is better.

#### 4.2.2. Accuracy of Flood Peak Forecasts

^{2}compared with 135,900 Km

^{2}), the time lag effect caused by the distance would not as evident as that in the Wei River basin. The rainfall in that basin is also more intensive. Additionally, the flood event evaluated in that study has a peak flow of over 10,000 m

^{3}/s, indicating a much shorter duration compared with the one in this study. Thus, the rainfall data in the Da River basin does not explain the flood event well. Hence, significant differences in the characteristic of the research area would partially make the patterns vary. The mean error of the flood peaks in S1 and S2 is correspondingly higher than in S3 and S4, revealing that the inclusion of the runoff data from the Beiluo River basin significantly increased the prediction deviation. These phenomena show that, though the rainfall data acts as a noise for T + 1 forecasts, it can explain the runoff two days later; some information contained in the runoff data in the adjacent region is valuable for the T + 1 forecasts since the similarity to the data at the prediction target but acts as a noise for the T + 2 forecasts. The comparison between S5, S6, and other scenarios, suggesting that the models with PCA denoising can have a better performance on the peak flow forecasts when the lead time increases. The PCA has effectively filtered the noise and remained valuable information. Similar to that in the T + 1 forecasting, the bi-directional architecture has enhanced the peak flow forecasts’ accuracy.

#### 4.3. Recommendations Based on the Evaluation Results

## 5. Conclusions

- Based on the premise that the rainfall data is sufficient, its inclusion can enhance the model’s robustness when the hyperparameters vary. Additionally, when the lead time increases, this enhancement effect becomes more pronounced. For optimized accuracy, the rainfall data has a negative impact on the forecasts with a short lead time but is valuable for the forecasts with a longer one in either the overall forecasting process or the flood peak forecasting process. Therefore, the rainfall data is recommended to be included in long-lead-time forecasts.
- Though a relative high relevance to the prediction target, the runoff data at the adjacent tributary introduces noise that significantly hinders the robustness of the model and will increase the difficulty of the optimization of hyperparameters. Nevertheless, this runoff data also contains valuable information for the flood peak forecasts with a short lead time and, thus, the exclusion of it should be carefully considered according to the purpose of use. For the forecasts with a more extended lead time, this data acts as noise and should be excluded.
- The model uses PCA denoising as the input filtering strategy has comparable robustness to the model that uses well manually filtered data as the input. Thus, it can reduce much effort in the data filtering stage. Meanwhile, the model with PCA denoising operation can provide accurate forecasts, especially for the flood peak forecasts when the lead time increases. Thus, the PCA denoising can be an efficient substitution for the manual input filtering process and is recommended to be considered as an alternative preprocessing method in the future.
- Despite a slightly lower time-step robustness, the bi-directional architecture has higher prediction accuracy than the single directional architecture for runoff forecasting, therefore, it is suggested to be utilized.

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 1.**An example of the sliding window method, F denotes the feature column, and t denotes a record (or sample).

**Figure 3.**The typical structure of a double layer stacked GRU network, the second layer obtains the state of the first layer for further calculation.

**Figure 5.**The research area with the locations of hydrological and meteorological stations, in addition to the prediction target. The whole basin can be divided into three main sub-basins, which are the main channel basin of the Wei River, the Jing River basin, and the Beiluo River basin.

**Figure 6.**Scree plot of the components, the green line represents the accumulative explained variance ratio, the red line represents the explained variance ratio of each component.

**Figure 7.**Box plots of the distribution of evaluation metrics in the validation stage. (

**a**) Box plot of the distribution of NSE; (

**b**) box plot of the distribution of RMSE; (

**c**) box plot of the distribution of MAE.

**Figure 8.**Scatter plots of the fitting results for the best models. (

**a**) Fitting result of one-day-ahead (T + 1) forecasting in the training, validation, and testing stage; (

**b**) Fitting result of two-day-ahead (T + 2) forecasting in the training, validation, and testing stage.

**Figure 9.**Hydrographs of the forecasting results for the best models. The green bars represent the rainfall data at the Pucheng meteorological station. (

**a**) Hydrograph of one-day-ahead (T + 1) forecasting in the training, validation, and testing stage; (

**b**) Hydrograph of two-day-ahead (T + 2) forecasting in the training, validation, and testing stage.

Stations | Sub-Basin | Distance (Km) | Max (m^{3}/s) | Mean (m^{3}/s) | Grey Relation | R |
---|---|---|---|---|---|---|

Huaxian | W | 0.0 | 4410.0 | 171.7 | 1.000 | 1.000 |

Nanronghua | B.L. | 23.5 | 250.0 | 12.5 | 0.993 | 0.763 |

Zhuangtou | B.L. | 49.4 | 440.0 | 15.5 | 0.993 | 0.757 |

Lintong | W | 53.3 | 4570.0 | 182.0 | 0.996 | 0.888 |

Taoyuan | J | 72.8 | 906.0 | 32.7 | 0.993 | 0.703 |

Xianyang | W | 100.3 | 2890.0 | 94.9 | 0.995 | 0.809 |

Zhangcunyi | B.L. | 158.5 | 147.0 | 2.8 | 0.990 | 0.409 |

Weijiabao | W | 186.7 | 1830.0 | 64.9 | 0.992 | 0.727 |

Yuluoping | J | 188.8 | 687.0 | 10.1 | 0.990 | 0.194 |

Zhuyuan | W | 263.9 | 59.5 | 2.0 | 0.992 | 0.536 |

Fenggeling | W | 299.8 | 114.0 | 3.7 | 0.993 | 0.545 |

Beidao | W | 348.2 | 959.0 | 22.8 | 0.991 | 0.365 |

Gangu | W | 398.5 | 90.7 | 0.6 | 0.987 | 0.098 |

Wushan | W | 439.6 | 699.0 | 12.1 | 0.991 | 0.274 |

Stations | Sub-Basin | Distance (Km) | Max (mm) | Mean (mm) | Grey Relation | R |
---|---|---|---|---|---|---|

Pucheng | W | 37.3 | 60.8 | 1.4 | 0.979 | 0.114 |

Yaoxian | W | 105.6 | 69.0 | 1.6 | 0.979 | 0.120 |

Luochuan | B.L. | 109.1 | 107.5 | 1.7 | 0.979 | 0.096 |

Jinghe | W | 115.2 | 117.3 | 1.5 | 0.979 | 0.109 |

Qindu | W | 126.3 | 158.5 | 1.5 | 0.979 | 0.093 |

Yongshou | W | 151.9 | 100.1 | 1.6 | 0.979 | 0.106 |

Wugong | W | 155.3 | 101.4 | 1.7 | 0.979 | 0.124 |

Changwu | J | 213.7 | 142.2 | 1.6 | 0.980 | 0.089 |

Fengxiang | W | 232.6 | 76.2 | 1.7 | 0.979 | 0.097 |

Longxian | W | 296.9 | 214.6 | 1.6 | 0.980 | 0.094 |

Prediction Target | Scenario | RNN Cell | Pre-Processing | Hydrological Stations (Runoff Data) | Meteorological Stations (Rainfall Data) |
---|---|---|---|---|---|

T + 1 | S1 | GRU | MMN | all included | all included |

S2 | GRU | MMN | all included | all excluded | |

S3 | GRU | MMN | B.L. excluded | all included | |

S4 | GRU | MMN | B.L. excluded | all excluded | |

S5 | GRU | PCA + MAN | all included | all included | |

S6 | bi-GRU | PCA + MAN | all included | all included | |

T + 2 | S1 | GRU | MMN | all included | all included |

S2 | GRU | MMN | all included | all excluded | |

S3 | GRU | MMN | B.L. excluded | all included | |

S4 | GRU | MMN | B.L. excluded | all excluded | |

S5 | GRU | PCA + MAN | all included | all included | |

S6 | bi-GRU | PCA + MAN | all included | all included |

Num. of Layers | Input Time Steps | Num. of Hidden Units | ||
---|---|---|---|---|

Layer 1 | Layer 2 | Layer 3 | ||

1 | 5~10 | 1 | - | - |

2 | 10, 20, 30 | 1 | - | |

3 | 10, 20, 30, 40 | 10 | 1 |

**Table 5.**Time step standard deviation of each scenario for one-day-ahead and two-day-ahead forecasting in the validation set.

Prediction Target | Scenario | NSE | RMSE (m^{3}/s) | MAE (m^{3}/s) |
---|---|---|---|---|

T + 1 | S1 | 0.045 | 9.552 | 7.790 |

S2 | 0.046 | 10.225 | 7.355 | |

S3 | 0.023 | 5.634 | 6.849 | |

S4 | 0.037 | 8.915 | 8.325 | |

S5 | 0.023 | 5.713 | 4.693 | |

S6 | 0.028 | 7.409 | 5.436 | |

T + 2 | S1 | 0.116 | 15.080 | 7.983 |

S2 | 0.148 | 15.370 | 13.799 | |

S3 | 0.061 | 10.062 | 6.825 | |

S4 | 0.110 | 14.560 | 10.106 | |

S5 | 0.057 | 9.825 | 5.762 | |

S6 | 0.068 | 11.105 | 5.143 |

**Table 6.**The overall evaluation metrics of the validation and testing set for the best models in each scenario.

Prediction Target | Scenario | NSE | RMSE (m^{3}/s) | MAE (m^{3}/s) |
---|---|---|---|---|

T + 1 | S1 | 0.937 | 50.088 | 24.089 |

S2 | 0.945 | 47.449 | 21.276 | |

S3 | 0.927 | 54.695 | 28.848 | |

S4 | 0.951 | 44.132 | 19.868 | |

S5 | 0.941 | 48.402 | 24.178 | |

S6 | 0.946 | 46.511 | 20.147 | |

T + 2 | S1 | 0.835 | 82.436 | 38.032 |

S2 | 0.745 | 98.346 | 42.062 | |

S3 | 0.836 | 81.469 | 39.625 | |

S4 | 0.801 | 89.179 | 37.733 | |

S5 | 0.828 | 84.130 | 39.014 | |

S6 | 0.836 | 81.069 | 36.293 |

**Table 7.**The relative error of the simulated flood peaks in each scenario for T + 1 and T + 2 forecasting.

Lead Time | Case (Year/Month/Day) | Flow (m^{3}/s) | Relative Error (%) | |||||
---|---|---|---|---|---|---|---|---|

S1 | S2 | S3 | S4 | S5 | S6 | |||

T + 1 | 2012/9/3 | 2020 | 16.75 | 4.12 | 13.94 | 14.48 | 4.30 | 17.95 |

2013/7/24 | 2200 | 9.97 | 8.75 | 2.63 | 11.81 | 24.40 | 1.81 | |

2014/9/17 | 1520 | 6.77 | 7.44 | 31.15 | 1.22 | 9.32 | 7.19 | |

Mean | - | 11.17 | 6.77 | 15.90 | 9.17 | 12.68 | 8.99 | |

T + 2 | 2012/9/3 | 2020 | 38.85 | 57.00 | 18.58 | 17.83 | 14.66 | 18.89 |

2013/7/24 | 2200 | 35.74 | 54.11 | 46.29 | 26.52 | 16.18 | 11.80 | |

2014/9/17 | 1520 | 19.63 | 31.87 | 11.23 | 33.44 | 33.64 | 32.70 | |

Mean | - | 31.41 | 47.66 | 25.37 | 25.93 | 21.49 | 21.13 |

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**MDPI and ACS Style**

Wang, Q.; Liu, Y.; Yue, Q.; Zheng, Y.; Yao, X.; Yu, J.
Impact of Input Filtering and Architecture Selection Strategies on GRU Runoff Forecasting: A Case Study in the Wei River Basin, Shaanxi, China. *Water* **2020**, *12*, 3532.
https://doi.org/10.3390/w12123532

**AMA Style**

Wang Q, Liu Y, Yue Q, Zheng Y, Yao X, Yu J.
Impact of Input Filtering and Architecture Selection Strategies on GRU Runoff Forecasting: A Case Study in the Wei River Basin, Shaanxi, China. *Water*. 2020; 12(12):3532.
https://doi.org/10.3390/w12123532

**Chicago/Turabian Style**

Wang, Qianyang, Yuan Liu, Qimeng Yue, Yuexin Zheng, Xiaolei Yao, and Jingshan Yu.
2020. "Impact of Input Filtering and Architecture Selection Strategies on GRU Runoff Forecasting: A Case Study in the Wei River Basin, Shaanxi, China" *Water* 12, no. 12: 3532.
https://doi.org/10.3390/w12123532