# Improving Daily Streamflow Forecasting Using Deep Belief Net-Work Based on Flow Regime Recognition

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## Abstract

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^{2}) of 0.93/0.89 for the integrated framework/DBN model during the validation period, respectively. Additionally, the prediction accuracy of the peak flood was also improved. The relative error of the peak flood derived from the integrated framework was reduced by 4.6%, compared with the single DBN model. Overall, the constructed integration framework, considering the complex characteristic of different flow regimes, could improve the accuracy for daily streamflow forecasting.

## 1. Introduction

## 2. Study Area and Data

^{2}(Figure 1). The Hanjiang River Basin (HJRB) is divided into three regions by the Huangjiagang and Huangzhuang hydrological stations: the upper sub-basin, the middle sub-basin, and the lower sub-basin. The topography in HJRB is high in the west and low in the east. The HJRB is located in a subtropical monsoon region and the rainfall is unevenly distributed throughout the year, with rainfall from May to October accounting for about 75% of the yearly rainfall.

## 3. Methodology

#### 3.1. Streamflow Process Clusters Based on Hydro-Meteorological Conditions

#### 3.2. Integrated Neural Network Framework (SOM-RF-DBN)

#### 3.2.1. Self-Organizing Map (SOM)

#### 3.2.2. Random Forests (RF)

#### 3.2.3. Deep Belief Network (DBN)

#### 3.3. Experiment Setup

#### 3.4. Performance Evaluation Criteria

## 4. Results and Discussion

#### 4.1. Data Clustering

^{3}/s). It is interesting to note that the hydro-meteorological data during the stage of base flows (no rainfall or sprinkling rainfall) were grouped into cluster B. The hydro-meteorological data during the rising limb stage of the streamflow were grouped into Cluster A, which is influenced by the duration and intensity of rainfall. The hydro-meteorological data during the stage of the falling limb were grouped into Cluster C, which is dominated by the sprinkling rainfall and storage characteristics of the basin. The clustering results suggest that the hydro-meteorological data were grouped according to the different hydro-meteorological conditions corresponding to respective streamflow sub-processes.

#### 4.2. Input Variable Selection

#### 4.3. Performance Comparison between the Integrated Framework and Single DBN Model

^{3}/s. Due to the storage characteristics and continuous rainfall in the catchment during the flood season, the validation dataset contained many outliers. In the validation dataset, the upper boundary (3500 m

^{3}/s) was exceeded on 113 days (10.1%), and daily streamflow exceeded 10,000 m

^{3}/s on five days. As shown in Figure 7a, values forecasted by the single DBN model were smaller than those observed when the daily streamflow exceeded 10,000 m

^{3}/s. In contrast, the SOM-RF-DBN framework provided forecasts more consistent with the observation data. The cumulative distribution of the modeled and observed data is shown in Figure 7b. When the cumulative distribution value is less than 0.85, the three curves of cumulative distribution nearly coincide. However, when the value is greater than 0.85, the curve of DBN deviates from the other two curves. The single DBN model and SOM-RF-DBN framework exhibited similar performances in small-volume streamflow forecasting (Figure 7). However, the single DBN model showed poorer performance in large-volume streamflow forecasting. The statistical characteristics of the validation dataset therefore not only showed that the daily streamflow characteristics of the Xiantao hydrological station are highly complex and difficult to forecast but also preliminarily showed that the constructed integrated framework is better than the single DBN model for daily streamflow forecasting.

_{P}value of the SOM-RF-DBN model was only half that of the single DBN model. These results indicate that the SOM-RF-DBN model can accurately forecast peak flow. The accurate forecasting of flood peak streamflow is critical for forecasting hydrological processes.

^{2}values of the DBN and SOM-RF-DBN models were 0.89 and 0.93, respectively. The higher R

^{2}of the SOM-RF-DBN framework indicates its capability in accurately constructing non-linear relationships between the selected input variables and observed streamflow. As shown in Figure 8a, the forecasting results of the single DBN model exhibits more scattering with many abnormal values. In contrast, the results of the SOM-RF-DBN model are less scattered (Figure 8b). Overall, the integrated framework is more suitable for streamflow forecasting than the single DBN model, and it also shows a better correlation with the observation data.

^{3}/s. The SOM-RF-SOM framework could forecast peak streamflow better than the single DBN model. In 2009, 2011, and 2014, the EQ

_{p}values of SOM-RF-SOM framework were approximately half those of the single DBN model, approximately one-third that of the single DBN model in 2006. Even for the remaining years, the EQ

_{p}values of the SOM-RF-SOM framework remained lower than those of the single DBN model. This proves that the single DBN model has weaker ability to forecast flood peaks than the SOM-RF-DBN framework. The forecasted values of the single DBN model fluctuated abnormally compared to the observed values, irrespective of whether the streamflow volume was large or small. In contrast, the SOM-RF-DBN framework did not exhibit such fluctuations. The fluctuations of forecasted values by the single DBN model were especially more pronounced in 2009, 2012, 2013, and 2014, while the flood hydrograph of the SOM-RF-DBN framework almost coincided with the hydrograph of the observation data. The comparison of daily streamflow forecasting between the single DBN model and SOM-RF-DBN framework proved that the SOM based analysis of hydrological data can improve the performance of DBN models in simulating and forecasting daily streamflow.

_{p}values of the SOM-RF-DBN framework at one and two days lead time were also less than those of the DBN model to varying degrees. These results further confirm that the SOM-RF-DBN model has a good performance in flood peak flow forecasting. With the increase of the forecasting period, the performance of the two models decreased, but the values of NSE, R

^{2}, RMSE, MAE, and EQ

_{p}did not show very clear trends. Based on the above results, it can be concluded that the SOM-RF-DBN framework can accurately forecast highly complex streamflow. Accordingly, the integrated SOM-RF-DBN modeling framework can be considered suitable for hydrological research.

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 7.**Box-plots (

**a**) and cumulative distribution function (

**b**) of observed and forecasted streamflow with the validation dataset for the single DBN model and SOM-RF-DBN framework.

**Figure 8.**Scatter plots of the observed and forecasted streamflow with the validation dataset: (

**a**) DBN model; (

**b**) SOM-RF-DBN framework.

**Figure 9.**Hydrographs of observed and forecasted streamflow by the DBN and SOM-RF-DBN models for the validation period (2005–2014).

**Table 1.**Statistical characteristics of datasets (Rainfall, Streamflow, Soil moisture, Evaporation) of the flood seasons from 1980 to 2014 over the Hanjiang Basin.

Datasets | MEAN | CV | SKEW | KURT |
---|---|---|---|---|

Streamflow | 1260 | 0.85 | 2.79 | 9.94 |

Rainfall | 4.2 | 1.51 | 2.41 | 7.22 |

Soil moisture | 0.3 | 0.06 | 0.02 | 0.09 |

Evaporation | 2.6 | 0.30 | −0.09 | −0.67 |

^{3}/s; Unit of Rainfall: mm/d; Unit of Soil moisture: m

^{3}/m

^{3}; Unit of Evaporation: mm/d.

**Table 2.**Performance of the DBN model for four dimensions of SOM during the calibration and validation periods.

Period | Dimension of SOM | NSE | R^{2} | RMSE | MAE |
---|---|---|---|---|---|

Calibration | 5 × 5 | 0.90 | 0.90 | 262.79 | 140.45 |

7 × 7 | 0.94 | 0.95 | 256.12 | 111.71 | |

10 × 10 | 0.72 | 0.87 | 471.45 | 221.42 | |

15 × 1 5 | 0.63 | 0.82 | 612.35 | 361.87 | |

Validation | 5 × 5 | 0.89 | 0.90 | 263.35 | 141.98 |

7 × 7 | 0.91 | 0.93 | 261.66 | 129.17 | |

10 × 10 | 0.73 | 0.86 | 442.13 | 241.67 | |

15 × 15 | 0.65 | 0.80 | 601.23 | 354.13 |

Out Variable | Group | Input Variables and Importance Scores |
---|---|---|

Q (t) | Cluster A | Q (t − 1), 0.67; R (t − 3), 0.10; Q (t − 2), 0.07; R (t − 2), 0.04; Q (t − 3), 0.04; S (t − 3), 0.04; |

Cluster B | Q (t − 1), 0.65; R (t − 3), 0.08; Q (t − 2), 0.08; S (t − 3), 0.05; R (t − 2), 0.04; E (t − 3), 0.04; R (t − 4), 0.03; | |

Cluster C | Q (t − 1), 0.69; Q (t − 2), 0.12; S (t − 3), 0.07; R (t − 3), 0.05; R (t − 2), 0.02; |

**Table 4.**Comparison of the performances of the single DBN and the integrated framework (SOM-RF-DBN) for daily streamflow forecasting during the calibration and validation periods.

Datasets | Models | NSE | R^{2} | RMSE | MAE | EQ_{p} |
---|---|---|---|---|---|---|

Calibration | ||||||

1980–2004 | DBN | 0.85 | 0.89 | 446.20 | 194.83 | 9.95% |

SOM-RF-DBN | 0.94 | 0.95 | 256.29 | 111.71 | 4.84% | |

Validation | ||||||

2005–2014 | DBN | 0.81 | 0.89 | 404.77 | 197.53 | 10.34% |

SOM-RF-DBN | 0.91 | 0.93 | 261.66 | 129.17 | 5.74% |

**Table 5.**Performances of the single DBN model and SOM-RF-DBN framework in streamflow forecasting at different lead times (1–2 d).

Time | Period | Models | NSE | R^{2} | RMSE | MAE | EQ_{p} |
---|---|---|---|---|---|---|---|

t + 1 | Calibration | DBN | 0.80 | 0.83 | 474.83 | 235.13 | 12.81% |

SOM-RF-DBN | 0.86 | 0.88 | 332.54 | 154.67 | 8.42% | ||

Validation | DBN | 0.77 | 0.81 | 464.30 | 228.22 | 12.05% | |

SOM-RF-DBN | 0.87 | 0.89 | 324.45 | 139.27 | 7.89% | ||

t + 2 | Calibration | DBN | 0.68 | 0.70 | 661.08 | 323.73 | 18.30% |

SOM-RF-DBN | 0.72 | 0.74 | 578.45 | 291.78 | 15.64% | ||

Validation | DBN | 0.64 | 0.64 | 658.06 | 317.03 | 18.36% | |

SOM-RF-DBN | 0.70 | 0.71 | 610.76 | 301.21 | 16.81% |

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**MDPI and ACS Style**

Shen, J.; Zou, L.; Dong, Y.; Xiao, S.; Zhao, Y.; Liu, C.
Improving Daily Streamflow Forecasting Using Deep Belief Net-Work Based on Flow Regime Recognition. *Water* **2022**, *14*, 2241.
https://doi.org/10.3390/w14142241

**AMA Style**

Shen J, Zou L, Dong Y, Xiao S, Zhao Y, Liu C.
Improving Daily Streamflow Forecasting Using Deep Belief Net-Work Based on Flow Regime Recognition. *Water*. 2022; 14(14):2241.
https://doi.org/10.3390/w14142241

**Chicago/Turabian Style**

Shen, Jianming, Lei Zou, Yi Dong, Shuai Xiao, Yanjun Zhao, and Chengjian Liu.
2022. "Improving Daily Streamflow Forecasting Using Deep Belief Net-Work Based on Flow Regime Recognition" *Water* 14, no. 14: 2241.
https://doi.org/10.3390/w14142241