# Research on Runoff Simulations Using Deep-Learning Methods

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Study Area

^{2}, and the outlet is the Chaoan hydrological station (Figure 1). The Meijiang and Tingjiang rivers are called the Hanjiang after meeting. The Hanjiang River flows into the Hanjiang Delta from north to south, and then flows into the South China Sea through Shantou City. The terrain of the Hanjiang River Basin slopes from northwest and northeast to southeast. The landform is dominated by mountains, accounting for 70% of the total area of the basin. The Hanjiang River Basin is located in the subtropical and Southeast Asian monsoon climate zone. The climate is hot and humid with abundant rainfall. The average annual rainfall is approximately 1600 mm, but the annual distribution is uneven, mainly concentrated in April to September. The runoff during this period accounts for 80% of the annual runoff. The mean annual flow is approximately 24.5 billion m

^{3}and the recorded maximum peak flow is 13,300 m

^{3}/s.

#### 2.2. Data Introduction

#### 2.3. Models

#### 2.3.1. Deep Learning

_{t}and historical information of the hidden layer h

_{t}

_{−1}and the gate control unit c

_{t}

_{−1}. First, the forget gate selectively discards cell c

_{t}

_{−1}information. Next, the input gate determines how much current external information x

_{t}is retained, and generates candidate cell $\overline{{c}_{t}}$. Then, the cell c

_{t}is updated. Finally, the output gate decides which features of the cell c

_{t}to output, and generates the hidden layer variable h

_{t}. The corresponding formula of the above process is as follows:

_{f}, W

_{i}, W

_{c}and Wo are the weight vectors of forget gate, input gate, output gate and gate unit, respectively; b

_{f}, b

_{i}, b

_{c}and b

_{o}are the bias vectors of the forget gate, input gate, output gate and gate unit, respectively; σ is sigmoid activation function; and tanh is hyperbolic tangent activation function.

_{i}for each input information x

_{i}, and then to obtain the attention weight ${\alpha}_{i}$ of x

_{i}by normalizing s

_{i}using softmax function [53]. The other is to weight the original input and merge it into the intermediate semantic c, a new expression of information. The corresponding formula for the above process is as follows:

#### 2.3.2. Modeling Process

- (1)
- Convolution layer: The preprocessed data was input into the convolution layer, and a convolution kernel with the size of 1 * k was selected to extract more abstract feature structures of different variables in space. The number of convolution kernels was n and the time steps were T. Then, we output the T *n dimensional feature vector, W
_{CNN}. - (2)
- LSTM layer: W
_{CNN}was used as the input for LSTM, and the significant features of time dimension were extracted by LSTM. The number of hidden layer units in LSTM was m. Specifically, ${x}_{t}$ in formula (2) is W_{CNN}, and the output of W_{CNN}was W_{LSTM}. - (3)
- Attention-mechanism layer: We took W
_{LSTM}as the input of the attention-mechanism layer. The influence degree of different time points on the model was expressed as “weight.” The weight was normalized by softmax function [30], and the numerical value was restricted to 0~1. The weight output was W_{attention}. We performed a weighted summation of W_{attention}and WLSTM to obtain the final comprehensive timing information. Specifically, ${x}_{i}$ is W_{LSTM}and ${\alpha}_{i}$ is W_{attention}in formula (10). - (4)
- Full-connection layer. A full connection layer was set up as the output layer.

#### 2.3.3. Artificial Neural Network

#### 2.3.4. Physical Model

#### 2.3.5. Model Evaluation Criteria

^{2}) and the Nash–Sutcliffe efficiency (NSE). The specific formulas are as follows:

^{2}is the square of sample correlation coefficient between 0 and 1 to evaluate the size of model variance. The NSE is often used to evaluate the simulation results in hydrology fields. The variation range of the NSE is from $-\infty $ to 1. A value approximating to 1 means that the simulation process is perfect and the credibility of the model is high.

## 3. Results

#### 3.1. Optimization of Parameters under Different Inputs

^{2}and RMSE as evaluation indices, the corresponding evaluation results are shown in Figure 8. The common feature was that when there were many input variables, the increase or decrease in the evaluation indexes was relatively gentle.

^{2}reached the highest point when the window size was 6 days. Under the A2 input, the RMSE was the lowest when the window size was 4 days. When the window size was longer than 4 days, the effect of each evaluation index became worse. The window size was shorter (2 days) under the A3 input when the evaluation indices achieved the optimal value.

#### 3.2. Comparison of Different Model Components

^{3}/s in the verification period. Taking A3 input as an example, the influence of the model components on the simulation effect was analyzed.

^{2}(0.84) and NSE (0.83) than the LSTM in the validation period. The R

^{2}and NSE of Conv-TALSTM were 0.1 and 0.2 higher than that of Conv-LSTM, respectively. The RMSE of Conv-TALSTM was 0.1 lower than that of Conv-LSTM. Similarly, LSTM and TALSTM were used as baseline models. Conv-LSTM performed better than LSTM. For example, the R

^{2}of Conv-LSTM was 0.84, while the R

^{2}of LSTM was 0.82. Compared with the TALSTM, the three indicators of Conv-TALSTM are superior. Similar trends were witnessed under the A1 and A2 inputs.

#### 3.3. Comparison of Different Inputs

^{2}were 0.88 and 0.82 for the training period and verification period under the A1 input. The NSE of models except LSTM during the validation period was greater than 0.80. In addition, the RMSE ranged from 210 m

^{3}/s to 232.91 m

^{3}/s. Runoff is formed by precipitation, and other meteorological factors also play an important role in its formation process. Therefore, the simulation results under the A1 input are reliable. Figure 11 shows the comparison of evaluation indicators of all models under three different inputs.

^{3}/s. Conv-LSTM convolutes the input data, which can be understood as giving each variable a certain weight according to the correlation between the variable and the target value. The correlation between upstream and downstream flow is greater than that flow and meteorological variables, so Conv-LSTM is greatly influenced by the input data.

^{2}exceeded 0.80 under any input, but R

^{2}under the A3 input was higher than others, and the highest values in the training and verification periods were 0.90 and 0.85, respectively. The NSE was also the highest under the A3 input, while the RMSE was much smaller than that under A1 and A2, and the maximum difference was 15.77 m

^{3}/s and 14.19 m

^{3}/s, respectively. It can be seen in Figure 8 that each model could simulate the peak value and runoff process more accurately under the A3 input.

#### 3.4. Comparison of Simulation Capability with Other Models

^{3}/s. The error of Wetspa changes from negative value to positive value before and after the peak value, indicating that the simulated flood had a large flow in the process of water-lowering. The ANN also showed a similar trend, but the error at the peak value was smaller than that of Wetspa. In addition, the ANN and Wetspa had a large deviation for the multi-peak flow process in 2017. It was found that the simulation at the largest flood peak was relatively low, while the latter two peaks were relatively high. This can be considered to be caused by the peak time-lag. The simulation process of the ANN was closer to the measured process compared with Wetspa, but it could not accurately reproduce the magnitude of flood peak either. Nevertheless, Conv-TALSTM performed better than both of them.

## 4. Discussion

^{2}/station, which is about six times that of our study (7528 km

^{2}/station). Hu et al. [62] obtained great simulation results when the density of rain-gauging stations was 200 km

^{2}/station. The data conditions and research results of Yin et al. [38] were similar to those of Hu et al. [62]. Jiang et al. [40] simulated runoff based on long series data of 50 years, and the model performance was satisfactory. In future research, we will consider replacing monitored data with other meteorological products such as TRMM (Tropical Rainfall Measuring Mission). Converting the site location information and underlying surface conditions into more abundant input data is also a further research direction. In addition, the deep-learning models proposed in this paper are also suitable for the prediction of water quality, groundwater and other factors, which is of great significance to realize the sustainable development of river basins.

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 2.**The correlation between the meteorological variables and the hydrological variables. Changting, Shanghang1, Meixian and Wuhua represent the rainfall of the meteorological stations; Shanghang2, Xikou, Hengshan and Chaoan represent the flow of the hydrological stations.

**Figure 9.**Performance of the four models during the validation period under different inputs. (

**a**) Conv-TALSTM; (

**b**) TALSTM; (

**c**) Conv-LSTM; (

**d**) LSTM.

**Figure 12.**Comparison of the error using the Conv-TALSTM model, ANN model and Wetspa model in representative years.

Input Data | No. of Inputs | Detailed Inputs | |
---|---|---|---|

Data Information at Time t | History Information at Time t-i (i > = 1) | ||

A1 | 29 | M1_{t}; M2_{t}; M3_{t}; M4_{t} | M1_{t-i}; M2_{t-i}; M3_{t-i}; M4_{t-i}; H4_{t-i} |

A2 | 4 | H1_{t}; H2_{t}; H3_{t} | H1_{t}_{-i}; H2_{t}_{-i}; H3_{t}_{-i}; H4_{t}_{-i} |

A3 | 32 | M1_{t}; M2_{t}; M3_{t}; M4_{t}; H1_{t}; H2_{t}; H3_{t} | M1_{t}_{-i}; M2_{t}_{-i}; M3_{t}_{-i}; M4_{t}_{-i}; H1_{t}_{-i}; H2_{t}_{-i}; H3_{t}_{-i}; H4_{t}_{-i} |

Model | Input Data | Time Length | Calibration Period | Validation Period | ||||
---|---|---|---|---|---|---|---|---|

RMSE | R^{2} | NSE | RMSE | R^{2} | NSE | |||

WetSpa | A3 | 1 | 542.22 | 0.73 | 0.68 | 341.79 | 0.70 | 0.65 |

ANN | A3 | 6 | 324.02 | 0.85 | 0.85 | 237.69 | 0.81 | 0.78 |

LSTM | A1 | 6 | 293.87 | 0.87 | 0.87 | 232.91 | 0.81 | 0.79 |

A2 | 4 | 290.03 | 0.88 | 0.87 | 231.33 | 0.81 | 0.79 | |

A3 | 2 | 289.79 | 0.88 | 0.88 | 217.14 | 0.82 | 0.81 | |

Conv-LSTM | A1 | 6 | 292.41 | 0.88 | 0.87 | 228.56 | 0.81 | 0.80 |

A2 | 4 | 288.30 | 0.88 | 0.88 | 219.16 | 0.83 | 0.81 | |

A3 | 4 | 284.04 | 0.89 | 0.88 | 215.64 | 0.84 | 0.82 | |

TALSTM | A1 | 6 | 286.29 | 0.88 | 0.88 | 220.55 | 0.81 | 0.81 |

A2 | 3 | 281.79 | 0.88 | 0.88 | 216.72 | 0.82 | 0.82 | |

A3 | 3 | 279.06 | 0.89 | 0.88 | 205.70 | 0.84 | 0.83 | |

Conv-TALSTM | A1 | 7 | 283.71 | 0.88 | 0.88 | 210.00 | 0.83 | 0.83 |

A2 | 4 | 280.74 | 0.89 | 0.88 | 208.06 | 0.84 | 0.83 | |

A3 | 2 | 277.70 | 0.90 | 0.89 | 205.11 | 0.85 | 0.84 |

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Liu, Y.; Zhang, T.; Kang, A.; Li, J.; Lei, X.
Research on Runoff Simulations Using Deep-Learning Methods. *Sustainability* **2021**, *13*, 1336.
https://doi.org/10.3390/su13031336

**AMA Style**

Liu Y, Zhang T, Kang A, Li J, Lei X.
Research on Runoff Simulations Using Deep-Learning Methods. *Sustainability*. 2021; 13(3):1336.
https://doi.org/10.3390/su13031336

**Chicago/Turabian Style**

Liu, Yan, Ting Zhang, Aiqing Kang, Jianzhu Li, and Xiaohui Lei.
2021. "Research on Runoff Simulations Using Deep-Learning Methods" *Sustainability* 13, no. 3: 1336.
https://doi.org/10.3390/su13031336