# Deep Learning Methods for Predicting Tap-Water Quality Time Series in South Korea

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Related Literature

#### 2.1. Deep Learning-Based Methods

#### 2.2. Statistical Methods

_{4}concentration in the Zhuyi River. The results indicated that ARIMA yields high accuracy for short-term water quality prediction. The vector autoregressive model, an extension of the AR model, captures linear dependencies between different time series. These statistical methods are popular in the field of univariate time series prediction because of their simplicity and interpretability (mobility). However, these approaches are difficult to extend to long-term prediction and multivariate time series prediction problems.

#### 2.3. Comparison of Methods

#### 2.4. Drinking Water Quality Standards

## 3. Methodology

#### 3.1. Scope of Study

#### 3.2. Spatial Range

#### 3.3. Temporal Range

#### 3.4. Data Preprocessing

## 4. Exploratory Data Analysis

#### 4.1. Correlation Analysis

#### 4.2. Anomaly Analysis

## 5. Development of Tap Water Quality Prediction Models

#### 5.1. Deep Learning-Based Methods

#### 5.1.1. LSTM

#### 5.1.2. GRU

#### 5.1.3. SCINet

#### 5.2. Classical Statistical Methods

#### 5.3. Tap Water Quality Prediction Models

#### 5.3.1. Architecture of LSTM, GRU, and SCINet Models

#### 5.3.2. Performance Comparison with the ARIMA Model

## 6. Model Performance Evaluation

#### 6.1. Evaluation Method

#### 6.2. Evaluation Metrics

#### 6.3. Cross-Validation

#### 6.4. Model Construction and Running Time

#### 6.5. Overall Prediction Accuracy in Major River Basins

#### 6.6. Long-Term Forecasting Results

## 7. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

- National Waterworks Information System. Statistics of Waterworks 2020. Available online: https://www.waternow.go.kr/web/ssdoData?pMENUID=8 (accessed on 10 October 2022).
- Lee, C.W.; Lee, Y.J.; Park, J.S. Determination of the sensor placement for detection water quality problems in water supply systems. J. Korean Soc. Hazard Mitig.
**2020**, 20, 299–306. [Google Scholar] [CrossRef] [Green Version] - Ryu, D.; Choi, T. Development of the Smart Device for Real Time Water Quality Monitoring. J. KIECS
**2019**, 14, 723–728. [Google Scholar] [CrossRef] - Wang, J.; Zhang, L.; Zhang, W.; Wang, X. Reliable model of reservoir water quality prediction based on improved ARIMA method. Environ. Eng. Sci.
**2019**, 36, 1041–1048. [Google Scholar] [CrossRef] - Desye, B.; Belete, B.; Asfaw Gebrezgi, Z.; Terefe Reda, T. Efficiency of treatment plant and drinking water quality assessment from source to household, gondar city, Northwest Ethiopia. J. Environ. Public Health
**2021**, 2021, 9974064. [Google Scholar] [CrossRef] [PubMed] - Yi, S.; Ryu, M.; Suh, J.; Kim, S.; Seo, S.; Kim, S.; Jang, S. K-water’s integrated water resources management system (K-HIT, K-water Hydro Intelligent Toolkit). Water Int.
**2020**, 45, 552–573. [Google Scholar] [CrossRef] - Zhou, J.; Wang, Y.; Xiao, F.; Wang, Y.; Sun, L. Water quality prediction method based on IGRA and LSTM. Water
**2018**, 10, 1148. [Google Scholar] [CrossRef] [Green Version] - Dong, Q.; Lin, Y.; Bi, J.; Yuan, H. An integrated deep neural network approach for large-scale water quality time series prediction. In Proceedings of the 2019 IEEE International Conference on Systems, Man and Cybernetics (SMC), Bari, Italy, 6–9 October 2019; pp. 3537–3542. [Google Scholar]
- Hochreiter, S.; Schmidhuber, J. Long short-term memory. Neural Comput.
**1997**, 9, 1735–1780. [Google Scholar] [CrossRef] - Cho, K.; Van Merriënboer, B.; Gulcehre, C.; Bahdanau, D.; Bougares, F.; Schwenk, H.; Bengio, Y. Learning phrase representations using RNN encoder-decoder for statistical machine translation. arXiv
**2014**, arXiv:1406.1078. [Google Scholar] [CrossRef] - Liu, M.; Zeng, A.; Xu, Z.; Lai, Q.; Xu, Q. Time series is a special sequence: Forecasting with sample convolution and interaction. arXiv
**2021**, arXiv:2106.09305. [Google Scholar] [CrossRef] - Ahmed, U.; Mumtaz, R.; Anwar, H.; Shah, A.A.; Irfan, R.; García-Nieto, J. Efficient water quality prediction using supervised machine learning. Water
**2019**, 11, 2210. [Google Scholar] [CrossRef] - Chen, K.; Chen, H.; Zhou, C.; Huang, Y.; Qi, X.; Shen, R.; Liu, F.; Zuo, M.; Zou, X.; Wang, J. Comparative analysis of surface water quality prediction performance and identification of key water parameters using different machine learning models based on big data. Water Res.
**2020**, 171, 115454. [Google Scholar] [CrossRef] [PubMed] - El Bilali, A.; Taleb, A. Prediction of irrigation water quality parameters using machine learning models in a semi-arid environment. J. Saudi Soc. Agric. Sci.
**2020**, 19, 439–451. [Google Scholar] [CrossRef] - Loos, S.; Shin, C.M.; Sumihar, J.; Kim, K.; Cho, J.; Weerts, A.H. Ensemble data assimilation methods for improving river water quality forecasting accuracy. Water Res.
**2020**, 171, 115343. [Google Scholar] [CrossRef] [PubMed] - Solanki, A.; Agrawal, H.; Khare, K. Predictive analysis of water quality parameters using deep learning. Int. J. Comput. Appl.
**2015**, 125, 0975–8887. [Google Scholar] [CrossRef] [Green Version] - Singha, S.; Pasupuleti, S.; Singha, S.S.; Singh, R.; Kumar, S. Prediction of groundwater quality using efficient machine learning technique. Chemosphere
**2021**, 276, 130265. [Google Scholar] [CrossRef] - Zhang, Y.; Gao, X.; Smith, K.; Inial, G.; Liu, S.; Conil, L.B.; Pan, B. Integrating water quality and operation into prediction of water production in drinking water treatment plants by genetic algorithm enhanced artificial neural network. Water Res.
**2019**, 164, 114888. [Google Scholar] [CrossRef] [PubMed] - Liu, P.; Wang, J.; Sangaiah, A.K.; Xie, Y.; Yin, X. Analysis and prediction of water quality using LSTM deep neural networks in IoT environment. Sustainability
**2019**, 11, 2058. [Google Scholar] [CrossRef] [Green Version] - Vadiati, M.; Rajabi Yami, Z.; Eskandari, E.; Nakhaei, M.; Kisi, O. Application of artificial intelligence models for prediction of groundwater level fluctuations: Case study (Tehran-Karaj alluvial aquifer). Environ. Monit. Assess.
**2022**, 194, 619. [Google Scholar] [CrossRef] - Samani, S.; Vadiati, M.; Azizi, F.; Zamani, E.; Kisi, O. Groundwater Level Simulation Using Soft Computing Methods with Emphasis on Major Meteorological Components. Water Resour. Manag.
**2022**, 36, 3627–3647. [Google Scholar] [CrossRef] - Peng, L.; Wu, H.; Gao, M.; Yi, H.; Xiong, Q.; Yang, L.; Cheng, S. TLT: Recurrent fine-tuning transfer learning for water quality long-term prediction. Water Res.
**2022**, 225, 119171. [Google Scholar] [CrossRef] - Wu, J.; Zhang, J.; Tan, W.; Sheng, Y.; Zhang, S.; Meng, L.; Zou, X.; Lin, H.; Sun, G.; Guo, P. Prediction of the Total Phosphorus Index Based on ARIMA. In Proceedings of the International Conference on Artificial Intelligence and Security, Qinghai, China, 15–20 July 2022; pp. 333–347. [Google Scholar]
- Zhang, L.; Xin, F. Prediction model of river water quality time series based on ARIMA model. In Proceedings of the International Conference on Geo-Informatics in Sustainable Ecosystem and Society, Handan, China, 21–25 November 2018; pp. 127–133. [Google Scholar]
- Chen, Y.; Zheng, B. What happens after the rare earth crisis: A systematic literature review. Sustainability
**2019**, 11, 1288. [Google Scholar] [CrossRef] [Green Version] - Abbas, F.; Feng, D.; Habib, S.; Rahman, U.; Rasool, A.; Yan, Z. Short term residential load forecasting: An improved optimal nonlinear auto regressive (NARX) method with exponential weight decay function. Electronics
**2018**, 7, 432. [Google Scholar] [CrossRef] [Green Version] - Lee, J.H.; Song, G.W.; Im, Y.J.; Cho, M.S. Development of Predictive Time-Series Models for Anomaly Detection of Tap-Water Quality. KIISE Trans. Comput. Pract.
**2022**, 28, 465–473. [Google Scholar] [CrossRef] - Fischer, T.; Krauss, C. Deep learning with long short-term memory networks for financial market predictions. Eur. J. Oper. Res.
**2018**, 270, 654–669. [Google Scholar] [CrossRef] [Green Version] - Zhao, Z.; Chen, W.; Wu, X.; Chen, P.C.; Liu, J. LSTM network: A deep learning approach for short-term traffic forecast. IET Intell. Transp. Syst.
**2017**, 11, 68–75. [Google Scholar] [CrossRef] [Green Version] - Box, G.E.; Jenkins, G.M.; Reinsel, G.C.; Ljung, G.M. Time Series Analysis: Forecasting and Control; John Wiley & Sons: Hoboken, NJ, USA, 2015. [Google Scholar]
- Moriasi, D.N.; Gitau, M.W.; Pai, N.; Daggupati, P. Hydrologic and water quality models: Performance measures and evaluation criteria. Trans. ASABE
**2015**, 58, 1763–1785. [Google Scholar] [CrossRef] - Shojaei, A.; Flood, I. Univariate modeling of the timings and costs of unknown future project streams: A case study. Int. J. Adv. Syst. Meas.
**2018**, 11, 36–46. [Google Scholar]

**Figure 2.**Map showing sampling stations in the basins of the Han, Geum, Nakdong, and Seomjin Rivers in the Korean Peninsula.

**Figure 3.**Descriptive statistics of the water quality parameters analyzed in this study: (

**a**) PH, (

**b**) TB, and (

**c**) RC.

**Figure 11.**Overall architecture of SCINet (reproduced from ref. [11]).

**Figure 13.**Visual representation of the cross-validation methods used for model evaluation based on a fixed window rolling forecast.

**Figure 14.**MAE values of (

**a**) PH, (

**b**) TB, and (

**c**) RC, predicted with different prediction lead times and time steps.

**Figure 15.**Comparison of actual and predicted (

**a**) PH, (

**b**) TB, and (

**c**) RC values for ARIMA, LSTM, GRU, and SCINet models.

**Figure 16.**Comparison of actual and predicted water quality values for ARIMA and deep learning models over a 24-h period.

Methods | Advantages | Disadvantages | Ref. |
---|---|---|---|

ARIMA ^{1} | - Suitable for non-stationary time series, stable, high accuracy of the forecast
- Very fast and simple for calculation of indicators
| - Can only work with stationary data
- Less accurate with time series data
- Not reliable, cannot be used alone for decision-making
- Highly sensitive to outliers
| [4,23,25,26] |

LSTM ^{2} | - Able to store multiple layers of data or information and better at finding and exploiting long-range context
- Suitable for processing sequence signals
- Overcomes the vanishing gradient problem occurring on the timeline
| - The form of the LSTM neural network model is more complicated, and there are also problems such as long training and prediction times and high computational costs
- Excessive simplification can lead to inaccurate results.
| [9,19] |

GRU ^{3} | - Makes the structure simpler compared with LSTM but maintains the effect of LSTM
- Computationally efficient
- Reduces the complexity of the network
| - The performance of GRU is inferior to that of LSTM in the case of large datasets
| [10] |

SCINet ^{4} | - Can be applied to real-time application because of high computing efficiency
- Incorporates the predictive power of different combinations of inputs
- Improved forecast accuracy
| - Large number of required parameters for modeling real systems
- Downsampling mechanism may also have difficulty handling data collected at irregular intervals.
| [11] |

**ARIMA = Autoregressive integrated moving average.**

^{1}**LSTM = Long short-term memory.**

^{2}**GRU = Gated recurrent units.**

^{3}**SCINet = Sample Convolution and Interaction Networks.**

^{4}Dataset | Period | Observed Data |
---|---|---|

Modeling (training) | 1 January 2017–31 December 2021 | 4,338,576 |

Model validation (out of sample) | 1 January 2022–31 May 2022 | 358,776 |

Model Configuration | Han River | Geum River | Nakdong River | Seomjin River | |||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|

PH | TB | RC | PH | TB | RC | PH | TB | RC | PH | TB | RC | ||

LSTM | Other parameter | Input node: 128; activation: ReLU; dropout rate: 0.2; loss: mean squared error; optimizer: Adam; learning rate: 0.001; epoch: 200 | |||||||||||

Batch size | 34 | 24 | 39 | 58 | 47 | 32 | 34 | 47 | 39 | 34 | 36 | 39 | |

GRU | Other parameter | Input node: 128; activation: ReLU; dropout rate: 0.2; loss: mean squared error; optimizer: Adam; learning rate: 0.001; epoch: 200 | |||||||||||

Batch size | 21 | 56 | 37 | 21 | 56 | 55 | 21 | 39 | 37 | 21 | 39 | 53 | |

SCINet | Other parameter | Hidden size: 8; stacks: 1; levels: 3; learning rate: 0.007; batch size: 64; dropout: 0.25 |

Location | pH | Turbidity | Residual Chloride |
---|---|---|---|

Han River | ARIMA(2,1,2) | ARIMA(1,1,2) | ARIMA(2,1,1) |

Geum River | ARIMA(1,1,3) | ARIMA(1,1,1) | ARIMA(1,1,3) |

Nakdong River | ARIMA(0,1,2) | ARIMA(2,1,4) | ARIMA(1,1,2) |

Seomjin River | ARIMA(0,1,2) | ARIMA(2,1,1) | ARIMA(1,1,2) |

Parameters | LSTM | GRU | SCINet |
---|---|---|---|

Epochs | 100 | 100 | - |

200 | 200 | ||

Batch size = 64, optimizer = Adam, learning rate = 0.001 | |||

Accuracy (%) Time (min) | 98.75 | 98.75 | 99.58 |

98.71 | 98.73 | 99.55 | |

35 | 27 | 05 | |

27 | 25 | 05 | |

Batch size = 128, optimizer = Adam, learning rate = 0.001 | |||

Accuracy (%) Time (min) | 98.73 | 98.79 | 98.77 |

98.72 | 98.76 | 98.89 | |

33 | 23 | 08 | |

24 | 20 | 07 |

Dataset | Indicator | pH | Turbidity | Residual Chloride | |||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|

Method | ARIMA | LSTM | GRU | SCINet | ARIMA | LSTM | GRU | SCINet | ARIMA | LSTM | GRU | SCINet | |

Han River | |||||||||||||

Goyang | 0.99715 | 0.99281 | 0.99677 | 0.99719 | 0.98477 | 0.98042 | 0.98434 | 0.98719 | 0.98175 | 0.98174 | 0.98398 | 0.98592 | |

Deokso | 0.99735 | 0.99408 | 0.99487 | 0.99728 | 0.96943 | 0.96656 | 0.96879 | 0.97133 | 0.97699 | 0.98065 | 0.98131 | 0.98096 | |

Banwol | 0.98855 | 0.98508 | 0.98725 | 0.99021 | 0.97448 | 0.96857 | 0.97648 | 0.97183 | 0.88134 | 0.89947 | 0.91617 | 0.91870 | |

Seongnam | 0.99795 | 0.98195 | 0.99649 | 0.99795 | 0.90435 | 0.89575 | 0.90255 | 0.91811 | 0.97942 | 0.97722 | 0.98173 | 0.98351 | |

Songjeon | 0.99630 | 0.99501 | 0.99621 | 0.99658 | 0.93905 | 0.94128 | 0.92918 | 0.95416 | 0.95604 | 0.95201 | 0.84342 | 0.95865 | |

Suji | 0.99739 | 0.97795 | 0.97802 | 0.99748 | 0.90199 | 0.90542 | 0.90691 | 0.92447 | 0.94664 | 0.96040 | 0.96033 | 0.96149 | |

Siheung | 0.99712 | 0.98176 | 0.98499 | 0.99727 | 0.95739 | 0.90197 | 0.91485 | 0.96032 | 0.97480 | 0.95683 | 0.97566 | 0.98025 | |

Wabu | 0.99421 | 0.99378 | 0.99430 | 0.99501 | 0.94281 | 0.92375 | 0.93642 | 0.94623 | 0.97491 | 0.98067 | 0.97963 | 0.98131 | |

Ilsan | 0.99732 | 0.99161 | 0.99609 | 0.99717 | 0.97388 | 0.96456 | 0.97542 | 0.98011 | 0.97823 | 0.97697 | 0.97912 | 0.98051 | |

Chungju | 0.99231 | 0.98184 | 0.99282 | 0.99364 | 0.94169 | 0.93293 | 0.92548 | 0.95039 | 0.94928 | 0.95354 | 0.95295 | 0.95361 | |

Hwangji | 0.99660 | 0.99095 | 0.99424 | 0.99702 | 0.99336 | 0.96186 | 0.96387 | 0.98478 | 0.98226 | 0.96071 | 0.97667 | 0.98412 | |

Geum River | |||||||||||||

Gosan | 0.99752 | 0.98970 | 0.99637 | 0.99771 | 0.98707 | 0.96847 | 0.97202 | 0.98703 | 0.97598 | 0.98069 | 0.98072 | 0.98108 | |

Gongju | 0.99886 | 0.98308 | 0.99877 | 0.99894 | 0.97053 | 0.96019 | 0.96550 | 0.97792 | 0.97619 | 0.97714 | 0.97672 | 0.98282 | |

Geumsan | 0.99811 | 0.99553 | 0.99622 | 0.99809 | 0.98579 | 0.98648 | 0.98689 | 0.99071 | 0.96873 | 0.97041 | 0.97156 | 0.97236 | |

Boryeong | 0.99211 | 0.99040 | 0.99352 | 0.99591 | 0.96668 | 0.97149 | 0.97171 | 0.97644 | 0.97996 | 0.98066 | 0.98293 | 0.98338 | |

Buan | 0.99720 | 0.99646 | 0.99663 | 0.99693 | 0.91718 | 0.87630 | 0.86198 | 0.93233 | 0.96897 | 0.98066 | 0.97166 | 0.97172 | |

Sanseong | 0.99481 | 0.99389 | 0.99558 | 0.99581 | 0.94637 | 0.94994 | 0.95021 | 0.95995 | 0.95793 | 0.95959 | 0.95926 | 0.96423 | |

Seokseong | 0.98705 | 0.98603 | 0.98459 | 0.99352 | 0.95065 | 0.95701 | 0.95791 | 0.97192 | 0.94903 | 0.95834 | 0.95849 | 0.96211 | |

Asan | 0.99718 | 0.98874 | 0.99658 | 0.99838 | 0.96649 | 0.96965 | 0.97130 | 0.97317 | 0.97105 | 0.97485 | 0.97517 | 0.97603 | |

Cheonan | 0.99743 | 0.99676 | 0.99740 | 0.99851 | 0.98124 | 0.98108 | 0.98116 | 0.98317 | 0.98004 | 0.97380 | 0.97796 | 0.98036 | |

Cheongju | 0.99855 | 0.98836 | 0.99090 | 0.99797 | 0.90400 | 0.93815 | 0.93884 | 0.93990 | 0.91801 | 0.94180 | 0.94242 | 0.95701 | |

Nakdong River | |||||||||||||

Gucheon | 0.99538 | 0.99373 | 0.99362 | 0.99479 | 0.96746 | 0.97397 | 0.95964 | 0.98098 | 0.93704 | 0.94804 | 0.94934 | 0.95019 | |

Miryang | 0.99810 | 0.99443 | 0.99571 | 0.99810 | 0.96307 | 0.96014 | 0.96695 | 0.97329 | 0.97659 | 0.97299 | 0.97553 | 0.97674 | |

Bansong | 0.99788 | 0.99710 | 0.99469 | 0.99815 | 0.95958 | 0.95697 | 0.94961 | 0.95831 | 0.95668 | 0.95346 | 0.96087 | 0.95867 | |

Sacheon | 0.99497 | 0.99483 | 0.98901 | 0.99638 | 0.94955 | 0.94778 | 0.93498 | 0.96190 | 0.96047 | 0.96836 | 0.96693 | 0.97061 | |

Yangsan | 0.99707 | 0.99387 | 0.99123 | 0.99697 | 0.97905 | 0.95178 | 0.96784 | 0.98221 | 0.97156 | 0.97288 | 0.97249 | 0.97368 | |

Yeoncho | 0.99884 | 0.99774 | 0.99667 | 0.99876 | 0.89065 | 0.66796 | 0.66542 | 0.91065 | 0.97453 | 0.97500 | 0.97446 | 0.97658 | |

Unmun | 0.99754 | 0.99688 | 0.99441 | 0.99780 | 0.97116 | 0.97312 | 0.97816 | 0.98062 | 0.95991 | 0.96270 | 0.96112 | 0.96670 | |

Hakya | 0.99805 | 0.97437 | 0.99602 | 0.99769 | 0.95385 | 0.96060 | 0.95747 | 0.96079 | 0.95745 | 0.95546 | 0.96005 | 0.96117 | |

Seomjin River | |||||||||||||

Deokjeong | 0.99812 | 0.99071 | 0.99716 | 0.99792 | 0.97053 | 0.96247 | 0.97088 | 0.97457 | 0.96917 | 0.97497 | 0.97555 | 0.97590 | |

Donghwa | 0.99604 | 0.98659 | 0.99198 | 0.99614 | 0.99537 | 0.98720 | 0.99090 | 0.99476 | 0.98204 | 0.98277 | 0.98280 | 0.98437 | |

Byeollyang | 0.99886 | 0.99211 | 0.99878 | 0.99868 | 0.96725 | 0.97020 | 0.97592 | 0.97834 | 0.98765 | 0.98611 | 0.98749 | 0.98752 | |

Pyeongnim | 0.99720 | 0.99581 | 0.99261 | 0.99710 | 0.96929 | 0.97500 | 0.97294 | 0.98278 | 0.95703 | 0.95713 | 0.96111 | 0.96322 |

**Table 7.**Baseline comparisons under multi-step setting for best practices of time series forecasting tasks.

Methods | Metrics | pH | Turbidity | Residual Chloride | ||||||
---|---|---|---|---|---|---|---|---|---|---|

Horizon | Horizon | Horizon | ||||||||

6 | 12 | 24 | 6 | 12 | 24 | 6 | 12 | 24 | ||

ARIMA | MAE | 0.0079 | 0.0095 | 0.0113 | 0.0004 | 0.0005 | 0.0008 | 0.0130 | 0.0137 | 0.0146 |

RMSE | 0.0060 | 0.0073 | 0.0086 | 0.0001 | 0.0002 | 0.0003 | 0.0095 | 0.0099 | 0.0104 | |

NSE | 0.9957 | 0.9937 | 0.9909 | 0.9783 | 0.9612 | 0.9124 | 0.6236 | 0.5801 | 0.5276 | |

LSTM | MAE | 0.0490 | 0.0424 | 0.0469 | 0.0008 | 0.0008 | 0.0009 | 0.0113 | 0.0113 | 0.0117 |

RMSE | 0.0505 | 0.0445 | 0.0493 | 0.0009 | 0.0010 | 0.0011 | 0.0151 | 0.0152 | 0.0158 | |

NSE | 0.6895 | 0.6203 | 0.6255 | 0.9549 | 0.9371 | 0.9076 | 0.6015 | 0.5731 | 0.5343 | |

GRU | MAE | 0.0272 | 0.0271 | 0.0329 | 0.0007 | 0.0007 | 0.0009 | 0.0099 | 0.0102 | 0.0107 |

RMSE | 0.0285 | 0.0288 | 0.0348 | 0.0008 | 0.0009 | 0.0011 | 0.0134 | 0.0139 | 0.0146 | |

NSE | 0.8758 | 0.8731 | 0.8657 | 0.9443 | 0.9450 | 0.8808 | 0.5099 | 0.4604 | 0.4069 | |

SCINet | MAE | 0.0068 | 0.0077 | 0.0094 | 0.0002 | 0.0002 | 0.0003 | 0.0095 | 0.0099 | 0.0104 |

RMSE | 0.0087 | 0.0099 | 0.0122 | 0.0004 | 0.0005 | 0.0006 | 0.0130 | 0.0136 | 0.0144 | |

NSE | 0.9948 | 0.9932 | 0.9894 | 0.9801 | 0.9679 | 0.9485 | 0.6254 | 0.5884 | 0.5394 |

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**MDPI and ACS Style**

Im, Y.; Song, G.; Lee, J.; Cho, M.
Deep Learning Methods for Predicting Tap-Water Quality Time Series in South Korea. *Water* **2022**, *14*, 3766.
https://doi.org/10.3390/w14223766

**AMA Style**

Im Y, Song G, Lee J, Cho M.
Deep Learning Methods for Predicting Tap-Water Quality Time Series in South Korea. *Water*. 2022; 14(22):3766.
https://doi.org/10.3390/w14223766

**Chicago/Turabian Style**

Im, Yunjeong, Gyuwon Song, Junghyun Lee, and Minsang Cho.
2022. "Deep Learning Methods for Predicting Tap-Water Quality Time Series in South Korea" *Water* 14, no. 22: 3766.
https://doi.org/10.3390/w14223766