# Determining Groundwater Drought Relative to the Opening of a River Barrage in Korea

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## Abstract

**:**

## 1. Introduction

## 2. Methods

#### 2.1. Cross-Correlation Analysis

_{xy}is expressed as follows:

_{i}and x

_{i+k}in the time series, n is the total number of time series, and $cov({x}_{i},{y}_{i+k})$ is the covariance between the overlapping portions of sequences x and y. ${\sigma}_{{x}_{i}}$ and ${\sigma}_{{y}_{i+k}}$ are x

_{i}and y

_{i+k}in the time series, respectively. The lag time (or delay time), calculated using Equation (1) uses the time lag between k = 0 and the time of the maximum cross-correlation, indicating a faster response and stress transfer in a system with a shorter lag time [28].

#### 2.2. K-Means Cluster Analysis

_{1}, …, S

_{i}, …, S

_{Ns}} and R = {R

_{1}, …, R

_{j}, …, R

_{Ns}}), dynamic time warping finds an appropriate matrix that is applied to both local distortions (stretched and compressed parts) and phase correction of the total parts by minimising the W* cumulative squared distance:

#### 2.3. Standardized Groundwater Level Index (SGLI)

_{1}, x

_{2}, …, x

_{n}, h is the bandwidth of the kernel density function (KDF) and is a parameter that adjusts the smoothness of the kernel. For the PDF f(x), the probability P (a ≤ x ≤ b) that the probability variable x will be included in the interval [a, b], is:

_{i}= 1, …, N represents the groundwater level data. The mean E

_{d}and standard deviation ${\sigma}_{d}$ are as follows:

_{x}(x):

## 3. Study Area

#### 3.1. Data Acquisition

#### 3.2. Geological and Hydrological Settings

## 4. Results

#### 4.1. Characteristics of Groundwater Level and River Stage Fluctuation

#### 4.2. Clustering of Groundwater Levels

#### 4.3. KDE and CKDE of Groundwater Level

#### 4.4. Estimation of the SGLI Values

#### SGLI Values Depending on the Opening of the Changnyeong–Haman River Barrage

## 5. Discussion

## 6. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 5.**Stages of Nakdong River at Changnyeong–Haman River barrage from 2012 to 2020, with indication of the five barrage openings (red triangle).

**Figure 6.**Representative groundwater-level fluctuations belonging to (

**a**) Group 1, (

**b**) Group 2, and (

**c**) Group 3 in 2012–2020.

**Figure 7.**Cross correlation of the river level and groundwater level on (

**a**) H004 (Group 1), (

**b**) H007 (Group 2), and (

**c**) H046 (Group 3).

**Figure 8.**KDE and CKDE versus groundwater level of the wells (

**a**) H004, (

**b**) H014, and (

**c**) H021 for the total period of July 2012−October 2020 (red colour) and those for the periods excluding the opening of the barrage (blue colour).

**Figure 9.**KDE versus groundwater level of H004 (Cluster 1), H014 (Cluster 2), and H007 (Cluster 3) on an annual basis from July 2012 to June 2020.

**Figure 10.**SGLI values of (

**a**) H004, (

**b**) H014, and (

**c**) H007, respectively belonging to Cluster 1, 2, and 3, for the periods of 2012−2020. Red line indicates 25th percentile (−0.674) of SGLI values. The vertical dash line in green colour indicates the time of the barrage opening.

Cluster | Monitoring Wells |
---|---|

Cluster 1 | H004, H010, H011, H022, H040, H041, H047, H092, H101 |

Cluster 2 | H014, H019, H038, H046, H105 |

Cluster 3 | H007, H102, H104, H106 |

Cluster 4 | H021 |

Cluster 5 | H103 |

**Table 2.**Statistic of SGLI for the period before the opening of the barrage (July 2012 to February 2017).

Static. | H004 | H007 | H010 | H011 | H014 | H019 | H021 | H022 | H038 | H040 |
---|---|---|---|---|---|---|---|---|---|---|

Min. | −1.34 | −0.46 | −1.59 | −2.52 | −1.92 | −0.90 | −1.82 | −1.17 | −3.15 | −1.48 |

Max. | 3.54 | 2.95 | 2.42 | 3.10 | 3.10 | 3.55 | 2.18 | 2.42 | 2.79 | 3.54 |

Mean | 0.46 | 0.59 | 0.42 | 0.39 | 0.41 | 0.58 | 0.40 | 0.56 | 0.51 | 0.47 |

Static. | H041 | H046 | H047 | H092 | H101 | H102 | H103 | H104 | H105 | H106 |

Min. | −0.85 | −2.33 | −1.54 | 1.29 | - | - | - | - | - | - |

Max. | 3.40 | 3.56 | 3.56 | 1.90 | - | - | - | - | - | - |

Mean | 0.54 | 0.32 | 0.49 | 1.62 | - | - | - | - | - | - |

Static. | H004 | H007 | H010 | H011 | H014 | H019 | H021 | H022 | H038 | H040 |
---|---|---|---|---|---|---|---|---|---|---|

Min. | −2.93 | −2.73 | −3.05 | −3.23 | −3.37 | −3.02 | −3.19 | −3.06 | −3.26 | −3.55 |

Max. | 3.27 | 2.81 | 0.74 | 1.46 | 1.93 | 3.12 | 1.42 | 1.63 | 0.70 | 3.27 |

Mean | −0.60 | −0.83 | −0.59 | −0.51 | −0.56 | −0.81 | −0.55 | −0.74 | −0.73 | −0.64 |

Static. | H041 | H046 | H047 | H092 | H101 | H102 | H103 | H104 | H105 | H106 |

Min. | −3.19 | −3.37 | −3.41 | −3.04 | −3.02 | −2.97 | −2.15 | −1.48 | −3.03 | −3.17 |

Max. | 3.35 | 2.46 | 3.11 | 2.81 | 3.18 | 2.48 | 1.10 | 3.18 | 2.40 | 2.53 |

Mean | −0.72 | −0.42 | −0.67 | −0.04 | −0.01 | −0.03 | −0.04 | 0.03 | −0.02 | −0.02 |

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## Share and Cite

**MDPI and ACS Style**

Yun, S.-M.; Jeong, J.-H.; Jeon, H.-T.; Cheong, J.-Y.; Hamm, S.-Y.
Determining Groundwater Drought Relative to the Opening of a River Barrage in Korea. *Water* **2023**, *15*, 2658.
https://doi.org/10.3390/w15142658

**AMA Style**

Yun S-M, Jeong J-H, Jeon H-T, Cheong J-Y, Hamm S-Y.
Determining Groundwater Drought Relative to the Opening of a River Barrage in Korea. *Water*. 2023; 15(14):2658.
https://doi.org/10.3390/w15142658

**Chicago/Turabian Style**

Yun, Sul-Min, Ji-Hye Jeong, Hang-Tak Jeon, Jae-Yeol Cheong, and Se-Yeong Hamm.
2023. "Determining Groundwater Drought Relative to the Opening of a River Barrage in Korea" *Water* 15, no. 14: 2658.
https://doi.org/10.3390/w15142658