# Hourly Water Level Forecasting at Tributary Affected by Main River Condition

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Study Area and Used Data

^{2}and a main channel length of 32.5 km. Because many residential (urbanized) districts are situated in the upstream (downstream) area, reliable flood warning is crucial to mitigate damage in this area. Ogeumgyo Bridge, the flood prediction site located 6 km upstream of the junction of the Han River, is significantly affected by the backwater effect from the river. Flood flow in the Han River is largely influenced by the release from Paldang reservoir and the tidal effect from sea water at the end of the river. Moreover, a series of tributaries such as Wangsukcheon, Tancheon, Jungnangcheon, and Anyangcheon streams flow to the Han River.

#### 2.2. Artificial Neural Network Model

#### 2.3. ANN Model Development

^{2}), and Nash–Sutcliffe efficiency (NSE) given by

## 3. Results and Discussion

#### 3.1. ANN Models for Hourly Water Level Forecasting with Lead-Times of 1 to 3 h

_{OG}is the water level at OG, h

_{CH}is the water level at CH, h

_{HG}is the water level at HG, h

_{HJ}is the water level at HJ, h

_{JS}is the water level at JS, and the h

_{JR}is the water level at JR.

^{2}among the primary selections that produced the lowest RMSE (Table 3).

#### 3.2. Performance of ANN Models for 1 h Lead-Time Forecasting

^{2}were closer to unity for all ANN models using training and testing data sets. Of these four network models, ANN1d produced the best forecasting performance for both training and testing sets with the lowest RMSE values, 0.0585m and 0.0502m; the highest NSE, 0.9935 and 0.9864; and the highest R

^{2}, 0.9936 and 0.9868, respectively. The inclusion of upstream water level data resulted in only minor improvement (ANN1b). Inclusion of water level data of the main river after the confluence point (ANN1c and ANN1d) produced significantly improved forecasts.

#### 3.3. Performance of ANN Models for 2 h Lead-Time Forecasting

^{2}above 0.920, and RMSE below 0.152 m using all water level data from both training and testing data sets. The best ANN model for 2 h lead-time forecasting using training (testing) data sets was ANN2d, which had the lowest RMSE value, at 0.1132 m (0.0936 m); the highest NSE, at 0.9754 (0.9533); and the highest R

^{2}, at 0.9758 (0.9542). Consistent good model performance was found for all water level data sets (Table 6).

#### 3.4. Performance of ANN Models for 3 h Lead-Time Forecasting

^{2}of 0.9443 (0.8941) for the training (testing) data set.

^{2}values for the testing data set revealed that considerable differences can occur between the forecasted and observed water levels. To increase the accuracy for longer lead-times, other input variables that could affect stream-flow, such as forecasted rainfall data, need to be included in the network model.

## 4. Conclusions

^{2}, and NSE. However, the models showed unsatisfactory performance in forecasting with a 3 h lead-time.

## Author Contributions

## Conflicts of Interest

## References

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**Figure 5.**Cross-correlation between water level at Ogeumgyo station (OG) and averaged rainfall series.

**Figure 9.**Root mean square error (RMSE) of ANN1a and ANN3c models according to the number of hidden nodes and previous time span. (

**a**) ANN1a; (

**b**) ANN3c.

**Figure 10.**Comparison of observed and forecasted water levels with a lead-time of 1 h. (

**a**) Water level of training and test periods; (

**b**) Water level of some period in testing data set.

**Figure 11.**Scatter plots of observed and forecasted water levels with a lead-time of 1 h. (

**a**) ANN1d; (

**b**) ANN1a.

**Figure 12.**Comparison of observed and forecasted water levels with a lead-time of 2h. (

**a**) Water level of training and testing periods; (

**b**) Water level of some period in testing data set.

**Figure 13.**Scatter plots of observed and forecasted water levels with a lead-time of 2 h. (

**a**) ANN2d; (

**b**) ANN2a.

**Figure 14.**Comparison of observed and forecasted water levels with a lead-time of 3 h. (

**a**) Water level of training and testing periods; (

**b**) Water level of some period in testing data set.

**Figure 15.**Scatter plots of observed and forecasted water levels with a lead-time of 3 h. (

**a**) ANN3c; (

**b**) ANN3a.

Event Number | Event Period | Peak Water Level (El.m) |
---|---|---|

1 | 19:00 07/13 to 22:00 07/16/2009 | 6.93 |

2 | 16:00 07/26 to 03:00 07/29/2011 | 8.06 |

3 | 13:00 07/05 to 19:00 07/06/2012 | 6.95 |

4 | 11:00 08/15 to 17:00 08/15/2012 | 6.71 |

5 | 20:00 07/12 to 11:00 07/13/2013 | 5.45 |

6 | 09:00 07/04 to 00:00 07/06/2016 | 5.18 |

**Table 2.**Four groups of artificial neural network models with input variables (model configuration).

Models | Input Variable | Output Variable |
---|---|---|

ANNia | $\mathrm{R}\left(\mathrm{t}\right),\mathrm{R}\left(\mathrm{t}-1\right),\dots ,\mathrm{R}\left(\mathrm{t}-\mathsf{\tau}\right),{\mathrm{h}}_{\mathrm{OG}}\left(\mathrm{t}\right),{\mathrm{h}}_{\mathrm{OG}}\left(\mathrm{t}-1\right),\dots ,{\mathrm{h}}_{\mathrm{OG}}\left(\mathrm{t}-\mathsf{\tau}\right)$ | ${\mathrm{h}}_{\mathrm{OG}}\left(\mathrm{t}+\mathrm{T}\right)$ |

ANNib | $\mathrm{R}\left(\mathrm{t}\right),\mathrm{R}\left(\mathrm{t}-1\right),\dots ,\mathrm{R}\left(\mathrm{t}-\mathsf{\tau}\right),$ | |

${\mathrm{h}}_{\mathrm{OG}}\left(\mathrm{t}\right),{\mathrm{h}}_{\mathrm{OG}}\left(\mathrm{t}-1\right),\dots ,{\mathrm{h}}_{\mathrm{OG}}\left(\mathrm{t}-\mathsf{\tau}\right),{\mathrm{h}}_{\mathrm{CH}}\left(\mathrm{t}\right),{\mathrm{h}}_{\mathrm{CH}}\left(\mathrm{t}-1\right),\dots ,{\mathrm{h}}_{\mathrm{CH}}\left(\mathrm{t}-\mathsf{\tau}\right)$ | ||

ANNic | $\mathrm{R}\left(\mathrm{t}\right),\mathrm{R}\left(\mathrm{t}-1\right),\dots ,\mathrm{R}\left(\mathrm{t}-\mathsf{\tau}\right),$ | |

${\mathrm{h}}_{\mathrm{OG}}\left(\mathrm{t}\right),{\mathrm{h}}_{\mathrm{OG}}\left(\mathrm{t}-1\right),\cdots ,{\mathrm{h}}_{\mathrm{OG}}\left(\mathrm{t}-\mathsf{\tau}\right),{\mathrm{h}}_{\mathrm{CH}}\left(\mathrm{t}\right),{\mathrm{h}}_{\mathrm{CH}}\left(\mathrm{t}-1\right),\dots ,{\mathrm{h}}_{\mathrm{CH}}\left(\mathrm{t}-\mathsf{\tau}\right),$ | ||

${\mathrm{h}}_{\mathrm{HG}}\left(\mathrm{t}\right),{\mathrm{h}}_{\mathrm{HG}}\left(\mathrm{t}-1\right),\dots ,{\mathrm{h}}_{\mathrm{HG}}\left(\mathrm{t}-\mathsf{\tau}\right),{\mathrm{h}}_{\mathrm{HJ}}\left(\mathrm{t}\right),{\mathrm{h}}_{\mathrm{HJ}}\left(\mathrm{t}-1\right),\dots ,{\mathrm{h}}_{\mathrm{HJ}}\left(\mathrm{t}-\mathsf{\tau}\right)$ | ||

ANNid | $\mathrm{R}\left(\mathrm{t}\right),\mathrm{R}\left(\mathrm{t}-1\right),\dots ,\mathrm{R}\left(\mathrm{t}-\mathsf{\tau}\right),$ | |

${\mathrm{h}}_{\mathrm{OG}}\left(\mathrm{t}\right),{\mathrm{h}}_{\mathrm{OG}}\left(\mathrm{t}-1\right),\dots ,{\mathrm{h}}_{\mathrm{OG}}\left(\mathrm{t}-\mathsf{\tau}\right),{\mathrm{h}}_{\mathrm{CH}}\left(\mathrm{t}\right),{\mathrm{h}}_{\mathrm{CH}}\left(\mathrm{t}-1\right),\dots ,{\mathrm{h}}_{\mathrm{CH}}\left(\mathrm{t}-\mathsf{\tau}\right),$ | ||

${\mathrm{h}}_{\mathrm{HG}}\left(\mathrm{t}\right),{\mathrm{h}}_{\mathrm{HG}}\left(\mathrm{t}-1\right),\dots ,{\mathrm{h}}_{\mathrm{HG}}\left(\mathrm{t}-\mathsf{\tau}\right),{\mathrm{h}}_{\mathrm{HJ}}\left(\mathrm{t}\right),{\mathrm{h}}_{\mathrm{HJ}}\left(\mathrm{t}-1\right),\dots ,{\mathrm{h}}_{\mathrm{HJ}}\left(\mathrm{t}-\mathsf{\tau}\right)$ | ||

${\mathrm{h}}_{\mathrm{JS}}\left(\mathrm{t}\right),{\mathrm{h}}_{\mathrm{JS}}\left(\mathrm{t}-1\right),\dots ,{\mathrm{h}}_{\mathrm{JS}}\left(\mathrm{t}-\mathsf{\tau}\right),{\mathrm{h}}_{\mathrm{JR}}\left(\mathrm{t}\right),{\mathrm{h}}_{\mathrm{JR}}\left(\mathrm{t}-1\right),\dots ,{\mathrm{h}}_{\mathrm{JR}}\left(\mathrm{t}-\mathsf{\tau}\right)$ |

Model | Leadtime (i) | Previous Time (τ) | Number of Hidden Nodes (h) |
---|---|---|---|

(h) | (h) | (EA) | |

ANNia | 1 | 3 | 7 |

2 | 4 | 10 | |

3 | 8 | 6 | |

ANNib | 1 | 3 | 11 |

2 | 9 | 16 | |

3 | 10 | 18 | |

ANNic | 1 | 5 | 16 |

2 | 8 | 17 | |

3 | 8 | 17 | |

ANNid | 1 | 7 | 12 |

2 | 10 | 20 | |

3 | 10 | 19 |

Model | Training | Testing | ||||
---|---|---|---|---|---|---|

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

ANN1a | 0.0793 | 0.9879 | 0.9881 | 0.0630 | 0.9781 | 0.9792 |

ANN1b | 0.0757 | 0.9890 | 0.9892 | 0.0606 | 0.9796 | 0.9804 |

ANN1c | 0.0595 | 0.9932 | 0.9933 | 0.0510 | 0.9858 | 0.9862 |

ANN1d | 0.0585 | 0.9935 | 0.9936 | 0.0502 | 0.9864 | 0.9868 |

Model | Training | Testing | ||||
---|---|---|---|---|---|---|

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

ANN1a | 0.1166 | 0.9936 | 0.9937 | 0.1113 | 0.9511 | 0.9500 |

ANN1b | 0.1064 | 0.9947 | 0.9948 | 0.1078 | 0.9553 | 0.9541 |

ANN1c | 0.0865 | 0.9965 | 0.9965 | 0.0876 | 0.9705 | 0.9700 |

ANN1d | 0.0869 | 0.9964 | 0.9965 | 0.0819 | 0.9737 | 0.9735 |

Model | Training | Testing | ||||
---|---|---|---|---|---|---|

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

ANN2a | 0.1519 | 0.9543 | 0.9563 | 0.1161 | 0.9222 | 0.9292 |

ANN2b | 0.1458 | 0.9583 | 0.9598 | 0.1124 | 0.9267 | 0.9327 |

ANN2c | 0.1156 | 0.9740 | 0.9747 | 0.0955 | 0.9494 | 0.9517 |

ANN2d | 0.1132 | 0.9754 | 0.9758 | 0.0936 | 0.9533 | 0.9542 |

Model | Training | Testing | ||||
---|---|---|---|---|---|---|

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

ANN2a | 0.2654 | 0.9650 | 0.9686 | 0.2100 | 0.8429 | 0.8334 |

ANN2b | 0.2554 | 0.9680 | 0.9706 | 0.2065 | 0.8500 | 0.8401 |

ANN2c | 0.2103 | 0.9786 | 0.9798 | 0.1680 | 0.8998 | 0.8947 |

ANN2d | 0.2070 | 0.9796 | 0.9804 | 0.1660 | 0.9030 | 0.9000 |

Model | Training | Testing | ||||
---|---|---|---|---|---|---|

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

ANN3a | 0.2108 | 0.9091 | 0.9159 | 0.1611 | 0.8472 | 0.8635 |

ANN3b | 0.2046 | 0.9149 | 0.9208 | 0.1528 | 0.8582 | 0.8745 |

ANN3c | 0.1716 | 0.9403 | 0.9443 | 0.1421 | 0.8844 | 0.8941 |

ANN3d | 0.1723 | 0.9398 | 0.9438 | 0.1462 | 0.8792 | 0.8952 |

Model | Training | Testing | ||||
---|---|---|---|---|---|---|

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

ANN3a | 0.4028 | 0.9124 | 0.9301 | 0.2943 | 0.7105 | 0.6881 |

ANN3b | 0.3995 | 0.914 | 0.9313 | 0.2989 | 0.7142 | 0.6870 |

ANN3c | 0.3359 | 0.9422 | 0.9503 | 0.2663 | 0.7768 | 0.7561 |

ANN3d | 0.3366 | 0.9425 | 0.9501 | 0.2637 | 0.7747 | 0.7586 |

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**MDPI and ACS Style**

Sung, J.Y.; Lee, J.; Chung, I.-M.; Heo, J.-H.
Hourly Water Level Forecasting at Tributary Affected by Main River Condition. *Water* **2017**, *9*, 644.
https://doi.org/10.3390/w9090644

**AMA Style**

Sung JY, Lee J, Chung I-M, Heo J-H.
Hourly Water Level Forecasting at Tributary Affected by Main River Condition. *Water*. 2017; 9(9):644.
https://doi.org/10.3390/w9090644

**Chicago/Turabian Style**

Sung, Ji Youn, Jeongwoo Lee, Il-Moon Chung, and Jun-Haeng Heo.
2017. "Hourly Water Level Forecasting at Tributary Affected by Main River Condition" *Water* 9, no. 9: 644.
https://doi.org/10.3390/w9090644