# Case Study: Reconstruction of Runoff Series of Hydrological Stations in the Nakdong River, Korea

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## Abstract

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^{2}= 0.92 and RMSE = 99.3 in the validation year (2019). Abnormal runoff series for 2012 to 2013 at the Yulji bridge station in Hapcheon County are also reconstructed. Using the suggested method, a well-matched result with the observations for the period from 2014 onwards is produced and a reconstructed abnormal series is obtained.

## 1. Introduction

## 2. Methods

#### 2.1. Study Material

^{2}and the river widths at the stations are approximately 150 m, 350 m, and 550 m, respectively. The runoff amount at the median water level is 79.2, 93.4, and 101.0 m

^{3}/s for each station from 2014 onwards. The start year of the observations for each station was February 1968 for station A, February 2006 for station B, and June 1980 for station C. However, flow characteristics were significantly changed by the Four Major Rivers Restoration Project [43], which caused the unmatched historical record of runoff from 2012 to the present. Table 1 shows the general flow conditions and changed characteristics before and after the project. Overall, the flow amount of each quantile was approximately increased by 10~20 m

^{3}/s, and the kurtosis coefficient, which is highly correlated with the shape of distribution, was also increased. Stations A, B, and C are considered to be very important points due to being: (i) runoff observatories in the middle part of the Nakdong River, (ii) validation points of the inflow amount from the Hwang River, which is one of the main tributaries, and (iii) the official check points for green algal blooms of the Nakdong River [43]. So, all of them are essential for water resources management, including flood, drought, and water quality. However, station B has abnormal data from 2012 to 2013 that show approximately 3200 m

^{3}/s for the average runoff amount, despite stations A and C showing averages of 208 m

^{3}/s and 259 m

^{3}/s, respectively. So, the historical runoff record of 2012 to 2013 is insignificant and the official approval of hydrological data for the target stations has not been implemented due to the runoff consistency problem. The daily runoff series data of the three hydrological stations and their properties were obtained from the Water Resources Management Information System [44].

#### 2.2. Variational Mode Decomposition (VMD)

#### 2.3. Artificial Neural Network (ANN)

## 3. Application and Discussion

#### 3.1. Runoff Series Characteristics and Its Decomposition

#### 3.2. Establishment of Reconstruction Model

^{2}) and root mean square error (RMSE), which are widely known and used as measures and evaluation for model performance or selection criteria [68]. In comparison, the ANN with raw runoff and multiple regression has 0.93, 0.88 for R

^{2}and 59.3, 116.7 for the RMSE, respectively. Therefore, both ANN models showed similar and better performance than multiple regression. Station B has 15,053 km

^{2}of upper basin area and 350 m of river width, therefore, the station measures the runoff from a relatively large basin. It would be reasonable to regard it as an abnormal observation when station B shows a low flow rate of approximately 20 m

^{3}/s or less [61]. Having too little runoff is a problem in observation. The ANN with raw runoff and multiple regression shows several relatively small runoffs during both periods, such as 0.1–1.0m

^{3}/s in September 2015, 0.5–8.0 m

^{3}/s in August 2016, and 1.0–7.2 m

^{3}/s in March 2017. Station B has 51.8 m

^{3}/s at the drought water level, which is equal to 0.97 in percentiles [41]. Approximately 24 m

^{3}/s or less of runoff amount, which is 0.995 in percentiles in station B at the drought water level and is the confidence boundary for proper observation percentiles [69], has the probabilities of abnormal observation. In the periods of validation (2019), the ANN with raw runoff and multiple regression shows 0.84, 0.81 for R

^{2}and 127.3, 219.2 for the RMSE, respectively. The ANN with VMD shows a more stable result with 0.91 for R

^{2}and 99.3 for the RMSE. Above all, it does not show an abnormal trend or too little runoff during the whole period. Therefore, the suggested method based on VMD shows its applicability.

#### 3.3. Reconstruction Results and Discussion

^{2}and 55.9 for the RMSE from 2014 to 2019 (Figure 7b). Additionally, the reconstructed runoff series was identified to have the same distribution as the two-variable Kolmogorov–Smirnov test with a 95% significance level [70]. Of course, there is no “true value” of observations for 2012 to 2013, but the reconstructed series (red line) seems to be well matched with the observed runoff (blue line) after 2013. In fact, the reconstructed series shows a similar trend with the runoff boundary in stations A and C. Additionally, other evidence could be found in 2014 to 2019. In Figure 7b, there are three periods with wide range of runoff boundaries and abnormal runoff observations in station B: (i) the period (marked as “Missing data”) during March 2017 has a zero value of runoff in station A and was identified as missing data due to the failure of measuring equipment, (ii) period A during November 2018 to February 2019, with approximately a 65.0 m

^{3}/s difference with stations A and C and abnormal runoff (minus runoff value) in station B, and (iii) period B during October 2019, with approximately a 81.6 m

^{3}/s difference between stations A and C and abnormal runoff (1.0–10 m

^{3}/s) in station B. Technically, there is a relatively more constant low runoff amount in station C than stations A and B, therefore, it is insignificant since station C is the downstream station. Station C is located about 7 km downstream from the Hapcheon-Changnyeong weir and about 35 km upstream from the Changnyeong-Haman weir, and therefore it was influenced by the weirs (see the Figure 1). The Korean government established and carried forward the plan that tries to open and monitor the multi-purpose weir for environmental restorations (the Ministry of Environment 2019) [43]. As part of the plan, the Hapcheon-Changnyeong and Changnyeong-Haman weir were also opened twice to evaluate the effect of continuous discharge. The opening periods were from 10 October 2018 to 22 February 2019 and 17 October 2019 to the end of that year, with Height above sea level (EL.) 9.2 to 4.8 m for the Hapcheon-Changnyeong weir, and EL.4.8 to 2.2 m for the Changnyeong-Haman weir, respectively. Therefore, the abnormal observation of stations B and C in these periods (A and B) could be explained by the gate operation of the weirs. It is one of the pieces of evidence proving that the ANN model with VMD is appropriate. Consequently, the suggested method could be used to reconstruct the abnormal data in the river section, which are influenced by hydraulic structures.

^{3}/s as the median value of runoff, and have 150 to 550 m in river width, with approximately a 10 m depth [43]. This means that the flow velocity in the Nakdong River is inevitably low, at 0.05–0.08 m/s, even at median water level, and since the accuracy of ADVM is 1% of the measure velocity or 0.005 m/s [42], this suggests that there is 10% uncertainty or more under the median water level. That is the reason for this study and why the daily runoff time series was selected. Thus, with the help of the methodology suggested in this study, a reconstruction of abnormal data would be possible and can later be used as a basis for accurate quality control in the Nakdong River region.

## 4. Conclusions

^{2}and 55.9 for the RMSE, thereby proving its applicability. Considering the importance of target stations, inaccurate or missing observations could cause problems in managing water resources, especially in times of flood, drought, and even algal blooms. Since different flow characteristics of target stations tend to make quality control more difficult, the method suggested in this study could be used as an alternative to reconstruct or control the quality of the hydrological data for both missing and abnormal data. Finally, with further study, VMD is an effective way to separate or remove white noise in signals, and it could also be a good alternative to remove uncertainties in observed series. This topic can be a subject for further studies.

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 1.**The target stations of the study in the main stream of the Nakdong River; red inverted triangles indicate water level stations, and gray blocks indicate multi-purpose weirs which were completed in 2012 by the Four Major Rivers Restoration Project [43].

**Figure 2.**Overall framework of the reconstruction method for daily runoff time series with three stages: (

**i**) decomposing runoff series, (

**ii**) training an artificial neural network (ANN) using intrinsic mode functions (IMFs), (

**iii**) summing up each reconstructed IMF and residual.

**Figure 3.**Historical record in stations A, B, C from 2012 to 2019. Station B has abnormal data from 2012 to 2013; (

**a**) historical record of daily runoff at each station, (

**b**) flow duration curve at each station.

**Figure 4.**Scatter plot of historical daily runoff record (2012 to 2019): (

**a**) scatter plot of runoff in the Hyeongsan River (Seochoen bridge and Kangdong large bridge at Gyeongju City in Figure 1), (

**b**) scatter plot of stations A and B in the Nakdong River.

**Figure 5.**Decomposed result with variational mode decomposition (VMD): (

**a**) station A, (

**b**) station B, (

**c**) station C, and each runoff series decomposed into two modes and residual mode.

**Figure 6.**Simulated result with two ANN models: (

**a**) learning periods, (

**b**) validation periods; black line indicates observed runoff, green line indicates simulated runoff with multiple regression, blue line indicates simulated runoff with raw runoff, and red line indicates simulated runoff with modes and residual.

**Figure 7.**Reconstructed results for station B: (

**a**) reconstructed periods, (

**b**) observed periods; gray boundary indicates high and low flow at stations A and C, blue line indicates observed runoff, and red line indicates reconstructed (simulated) runoff using the suggested method.

**Table 1.**The general flow condition at target stations before and after the Four Major Rivers Restoration Project.

Station | Before the Project (Until 2012) | After the Project (2012 Onward) | ||||||||
---|---|---|---|---|---|---|---|---|---|---|

Runoff at Quantile (m^{3}/s) | Standard Deviation | Kurtosis Coefficient | Runoff at Quantile (m^{3}/s) | Standard Deviation | Kurtosis Coefficient | |||||

0.75 | 0.5 | 0.25 | 0.75 | 0.5 | 0.25 | |||||

Station A | 132.0 | 53.6 | 23.5 | 602.0 | 70.1 | 152.1 | 85.3 | 52.5 | 343.0 | 110.9 |

Station B | 140.8 | 70.0 | 48.6 | 355.7 | 58.4 | 155.5 | 94.3 | 61.1 | 309.1 | 57.1 |

Station C | 181.7 | 85.9 | 53.3 | 819.7 | 89.3 | 174.5 | 107.4 | 71.7 | 447.9 | 144.9 |

Evaluation Criteria | Training Period (2014~2018) | Validation Period (2019) | ||
---|---|---|---|---|

R^{2} | RMSE (m^{3}/s) | R^{2} | RMSE (m^{3}/s) | |

ANN with Raw | 0.93 | 59.3 | 0.84 | 127.3 |

ANN with VMD | 0.93 | 80.3 | 0.91 | 99.3 |

Multiple Regression | 0.88 | 116.7 | 0.81 | 219.2 |

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**MDPI and ACS Style**

Kwak, J.; Lee, J.; Jung, J.; Kim, H.S.
Case Study: Reconstruction of Runoff Series of Hydrological Stations in the Nakdong River, Korea. *Water* **2020**, *12*, 3461.
https://doi.org/10.3390/w12123461

**AMA Style**

Kwak J, Lee J, Jung J, Kim HS.
Case Study: Reconstruction of Runoff Series of Hydrological Stations in the Nakdong River, Korea. *Water*. 2020; 12(12):3461.
https://doi.org/10.3390/w12123461

**Chicago/Turabian Style**

Kwak, Jaewon, Jongso Lee, Jaewon Jung, and Hung Soo Kim.
2020. "Case Study: Reconstruction of Runoff Series of Hydrological Stations in the Nakdong River, Korea" *Water* 12, no. 12: 3461.
https://doi.org/10.3390/w12123461