# 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

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**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