# A Case Study: Groundwater Level Forecasting of the Gyorae Area in Actual Practice on Jeju Island Using Deep-Learning Technique

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## Abstract

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## 1. Introduction

## 2. Theoretical Background

#### 2.1. Study Material

#### 2.2. Test Statistics: Cross-Wavelet and Granger Causality

#### 2.3. LSTM Technique

## 3. Application and Proposed New Method

#### 3.1. Predictor Selection for Groundwater Level Forecasting

#### 3.2. Construction of the LSTM Model and Result

^{2}), root mean square error (RMSE, m), and Nash coefficient for determination of the efficiency of hydrological simulation showed high levels at 0.96, 0.02 m, and 0.95, respectively, for the learning period (2012–2020). The same goes for the validation period (2021) with R

^{2}, RMSE (m), and the Nash coefficient remaining high at 0.95, 0.03 m, and 0.95, respectively. Its performance was enabled by the fact that deep learning techniques including the LSTM model use a black-box system where learning is conducted automatically from multidimensional datasets [71], and the simulation result proves that it can be applied for solving complex problems such as forecasting groundwater levels. In particular, considering the delay between the antecedent precipitation and the groundwater level in Jeju Island [67,68], the LSTM model which considers temporal correlation may be more suitable for groundwater level simulation. In addition, the LSTM model does not require a separate calculation of lag time. Rather, it considers the correlation and causality between two time series on its own. Therefore, simulating the groundwater level of the Gyorae area through LSTM has enough applicability.

#### 3.3. Proposed New Method to Forecast Groundwater Levels

## 4. Result and Discussion

^{2}, RMSE(m), and the Nash coefficient for the learning period in Figure 7 were over 0.62, 8.32 m, and 0.60, respectively. Since, the learning and simulation were performed based on derivatives (gradients) of groundwater time series, not the GWL itself, it can be regarded as the learning and simulation based on the gradients of GWL using hydro-meteorological factors. As the constructed model did not learn GWL in accordance with hydro-meteorological data, it is free from the problem of overfitting to the tendency of the GWL time series [85]. The result of the learning period in Figure 7a indicates that, overall, the model simulated GWL change well. However, although the pattern itself was well simulated, over time, there was a consistent gap between the simulated results and the actual observations. This is attributable to the fact that it was simulated through closed-loop learning after the initial observed value of GWL for the learning and validation periods. As long as the simulation accuracy for GWL change is less than 100%, the gaps at previous time stamps are accumulated, and, consequently, the overall gap increases over time, which can explain the consistent gap shown in Figure 7a. Furthermore, an underestimating tendency of the trained LSTM model can be confirmed from Figure 7a, as well as for the validation in Figure 7b. Although the simulation performance was lower for the validation compared to that of the learning period, the overall pattern was determined to be well simulated. However, there was a certain degree of difference in simulation efficiency as the learning period’s evaluation function was ≥0.9, while that of the validation period was 0.6 for R

^{2}and the Nash coefficient. Therefore, it was determined that overfitting occurred during learning. Nevertheless, even after considering accumulated simulation errors and a certain degree of overfitting from the closed-loop learning, an evaluation function higher than 0.6 signifies that it has sufficient applicability. Moreover, as it can prevent overfitting caused by learning the GWL time series itself, it can be used to validate the results produced by other simulation methods.

^{2}, RMSE(m), and the Nash coefficient of the learning period in Figure 8b were 0.92, 2.84 m, and 0.92, respectively, and those of the validation period in Figure 8d were 0.90, 3.95 m, and 0.89, respectively, thus implying that it has applicability.

## 5. Conclusions

- The study analyzed the correlation between JH Gyorae-1′s GWLs and 12 kinds of hydro-meteorological data (maximum temperature, daily minimum temperature, daily mean temperature, dew temperature, relative humidity, precipitation, ground air pressure, sea-level pressure, mean wind speed, total sun hours, insolation, and evapotranspiration) through cross-wavelet and Granger causality analysis for predictor selection. As a result, five factors (mean wind speed, sun hours, evaporation, minimum temperature, and daily precipitation) showed time sequential correlations with GWLs and were selected as predictors.
- An LSTM model, a representative deep learning method, was constructed using the observed GWLs of JH Gyorae-1 from 2012 to 2020, and the model was validated with the events of the year 2021. The simulation demonstrated a highly outstanding performance and applicability with R
^{2}, RMSE(m), and the Nash coefficient, which show the simulation efficiency of a model for its learning and validation periods of ≥0.97, ≤0.03 m, and ≥0.96, respectively. - It proposed (i) derivatives-based learning and assessed the applicability to complement the lack of clarity of process for a particular result that deep-learning-based forecasts have. An LSTM model was constructed through learning based on the derivatives of GWLs and presented convincing results with R
^{2}, RMSE(m), and Nash coefficient of 0.93, 3.92 m, and 0.93, respectively, for the long-term (learning period) simulation, which used only the first observational GWL, and of 0.62, 8.32 m, and 0.60, respectively, for the 1-year validation period (2021). Therefore, it showed that the method can be utilized to aid decision-making when managers review deep learning models. - It also proposed and assessed (ii) ensemble forecasting. As for ensemble forecasting, ±1-month GWL simulation and forecasting were repeated on a daily basis, and the GWLs for the following 2 weeks were forecasted using the medians of the forecasted time series. The result demonstrated that it is sufficiently applicable as R2, RMSE(m), and the Nash coefficient were, respectively, 0.97, 1.84 m, and 0.97 for the learning period and 0.91, 3.75 m, and 0.90 for the validation period.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 2.**Obtained groundwater level and meteorological factors from 2012 to 2021: (

**a**) groundwater level and daily precipitation; (

**b**) daily mean, minimum and maximum air temperature and dew point temperature; (

**c**) daily mean wind speed, Solar insolation, total sun hours and small pen evaporation; and (

**d**) daily mean ground air and sea level air pressure.

**Figure 4.**Cross-wavelet result between groundwater level and each meteorological factor: (

**a**) average temperature; (

**b**) minimum temperature; (

**c**) maximum temperature, (

**d**) precipitation; (

**e**) average wind speed; (

**f**) dew temperature; (

**g**) relative humidity; (

**h**) average air pressure; (

**i**) total sunshine hours; (

**j**) ground temperature; (

**k**) 5 cm underground temperature; (

**l**) small pan evaporation. Bold-lined area indicates that there are correlations with groundwater level.

**Figure 5.**LSTM and ANN simulated results of GWL on Gyorae-1 at daily scale: (

**a**) learning period (2012–2020) and (

**b**) validation period (2021).

**Figure 7.**LSTM-simulated result of GWL with derivatives-based learning in daily scale: (

**a**) learning period (2012–2020) and (

**b**) validation period (2021).

**Figure 8.**Attractor-concept multiple forecasting results of GWL in daily scale: (

**a**) multiple forecasting in the learning period (2012–2020); (

**b**) ensemble result in the learning period; (

**c**) multiple forecasting in the validation period (2021); (

**d**) ensemble result in the validation period. Green-box in (

**a**,

**c**) indicates forecasted series excluded from the estimation of forecasted groundwater level.

Content | U.W.L. → Factor | Factor → U.W.L. | ||
---|---|---|---|---|

F-Value | Cri. Value | F-Value | Cri. Value | |

‘Average Temperature’ | 4.03 | 3.84 | 3.99 | 3.84 |

‘Minimum Temperature’ | 6.70 | 3.00 | 18.06 | 3.84 |

‘Maximum Temperature’ | 1.13 | 3.84 | 8.27 | 3.84 |

‘Precipitation’ | 13.91 | 1.65 | 10.16 | 3.84 |

‘Average Wind Speed’ | 17.83 | 3.00 | 6.22 | 3.00 |

‘Dew Temperature’ | 10.37 | 3.00 | 0.50 | 3.84 |

‘Relative Humidity’ | 11.54 | 3.00 | 0.64 | 3.84 |

‘Average Air Pressure’ | 6.84 | 3.00 | 0.29 | 3.84 |

‘Total Sun Hours’ | 28.61 | 3.84 | 11.87 | 3.84 |

‘Ground Temperature’ | 3.79 | 3.84 | 16.35 | 3.84 |

‘5 cm Underground Temperature’ | 2.37 | 3.84 | 18.86 | 3.84 |

‘Small Pan Evaporation’ | 15.77 | 3.84 | 15.16 | 3.84 |

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## Share and Cite

**MDPI and ACS Style**

Kim, D.; Jang, C.; Choi, J.; Kwak, J. A Case Study: Groundwater Level Forecasting of the Gyorae Area in Actual Practice on Jeju Island Using Deep-Learning Technique. *Water* **2023**, *15*, 972.
https://doi.org/10.3390/w15050972

**AMA Style**

Kim D, Jang C, Choi J, Kwak J. A Case Study: Groundwater Level Forecasting of the Gyorae Area in Actual Practice on Jeju Island Using Deep-Learning Technique. *Water*. 2023; 15(5):972.
https://doi.org/10.3390/w15050972

**Chicago/Turabian Style**

Kim, Deokhwan, Cheolhee Jang, Jeonghyeon Choi, and Jaewon Kwak. 2023. "A Case Study: Groundwater Level Forecasting of the Gyorae Area in Actual Practice on Jeju Island Using Deep-Learning Technique" *Water* 15, no. 5: 972.
https://doi.org/10.3390/w15050972