# Ensemble Empirical Mode Decomposition and a Long Short-Term Memory Neural Network for Surface Water Quality Prediction of the Xiaofu River, China

^{*}

## Abstract

**:**

_{3}-N, pH, DO, COD

_{Mn}) collected from the Xiaofu River and compared with the results of a single LSTM. During the validation period, the R

^{2}values when using LSTM for NH

_{3}-N, pH, DO and COD

_{Mn}were 0.567, 0.657, 0.817 and 0.693, respectively, and the R

^{2}values when using EEMD–LSTM for NH

_{3}-N, pH, DO and COD

_{Mn}were 0.924, 0.965, 0.961 and 0.936, respectively. The results show that the developed model outperforms the single LSTM model in various evaluation indicators and greatly improves the model performance in terms of the hysteresis problem. The EEMD–LSTM model has high prediction accuracy and strong generalization ability, and further development may be valuable.

## 1. Introduction

## 2. Study Area and Data

#### 2.1. Study Area

^{2}. The main tributaries are the Fanyang River, Banyang River, Mansi River, Gan River, Zhulong West River and others [36].

#### 2.2. Data Sources

_{3}-N), permanganate index (COD

_{Mn}), pH, dissolved oxygen (DO), electrical conductivity, turbidity, and water temperature. The data were collected every 24 h from 13 April 2019, to 12 April 2021. There are a total of 1096 groups of data, which fully reflect the periodic changes in water quality. According to the water quality of the Xiaofu River, pH, DO, COD

_{Mn}and NH

_{3}-N were selected in this paper as the water quality prediction indicators. Statistical analysis was performed on the data series to check for missing data. The statistical analysis results are shown in Table 1, including average value, standard deviation value, maximum value, minimum value, and number of missing data. The values of water quality parameters meet the general water quality standards. The discrete degree of the pH and NH

_{3}-N time series is small. The numbers of missing data in the water quality time series are very few.

## 3. Method

#### 3.1. Ensemble Empirical Mode Decomposition (EEMD)

#### 3.2. Long Short-Term Memory (LSTM)

#### 3.3. Data Preprocessing

#### 3.3.1. Data Normalization

#### 3.3.2. Outlier Detection

- (1)
- If the anomaly score is very close to 1, then the data are definitely anomalies.
- (2)
- If the anomaly score is much smaller than 0.5, then it is safe to regard the data as normal instances.
- (3)
- If all the anomaly scores are approximately 0.5, then there are no distinct outliers in the sample.

#### 3.4. Performance Evaluation

^{2}). RMSE is sensitive to errors that are evident in the experimental data. MAE is the average value of absolute error and can truly reflect the state of the model’s error in prediction. MAPE is the expected value of the absolute error and percentage of the true value. The values of RMSE, MAE, and MAPE are all from 0 to +∞. The smaller the RMSE, MAE, and MAEP, the more accurate the prediction result and the better the model effect. The value of the determination coefficient R

^{2}is between 0 and 1, and the closer to 1 the value is, the better the model’s prediction ability of the regression effect. Generally, if the coefficient of determination exceeds 0.8, the model is considered to have high goodness of fit. The specific calculation equation of each loss function is as follows:

^{2}as the main criterion for model selection, with higher values indicating better prediction ability. Additionally, considering other performance evaluators, such as RMSE, MAE, and MAPE, can provide a more comprehensive evaluation of the model’s accuracy and prediction performance.

## 4. Results

#### 4.1. Data Preprocessing

#### 4.2. EEMD Decomposition Results

_{3}-N, pH and DO time series were decomposed into eight IMFs and one residual item Res and arranged in the order of frequency from high to low. The COD

_{Mn}time series was decomposed into seven IMFs and one residual item Res.

_{3}-N and COD

_{Mn}time series have obvious declining trends, indicating that the water environmental control measures of the Xiaofu River achieved some results in recent years.

#### 4.3. Model Training and Parameter Optimization

_{3}-N, pH, DO and COD

_{Mn}are 5, 5, 8 and 7, respectively.

#### 4.4. Water Quality Prediction by EEMD–LSTM

^{2}has improved. The RMSE, MAE, and MAPE of NH

_{3}-N decreased by 80.0%, 82.6%, and 93.7%, respectively, and R

^{2}increased by 63.0%. The RMSE, MAE, and MAPE of pH decreased by 71.3%, 74.3%, and 82.4%, respectively, and R

^{2}increased by 46.9%. The RMSE, MAE, and MAPE of DO decreased by 78.2%, 80.4%, and 78.8%, respectively, and R

^{2}increased by 17.6%. The RMSE, MAE, and MAPE of COD

_{Mn}decreased by 69.8%, 73.9%, and 84.1%, respectively, and R

^{2}increased by 35.1%. These indicators illustrate that the EEMD method can better extract essential features of the water quality time series and reduce the interference of random factors. They also indicate that the prediction performance of the model is greatly improved with the EEMD method. Figure 8 also shows that compared with the single LSTM model, the predicted values of EEMD–LSTM are closer to the observed values in the extreme value prediction.

## 5. Discussion

_{Mn}and NH

_{3}-N in rivers are 0.08–0.15 and 0.2–0.44 day

^{−1}, respectively [47]. Therefore, the residence times of COD

_{Mn}and NH

_{3}-N in water are 6.7–12.5 and 2.3–5 days. The optimal sliding time window widths for NH

_{3}-N, pH, DO and COD

_{Mn}are 5, 5, 8 and 7, respectively. This indicates that the optimal sliding time window width is consistent with the degradation time of pollutants in water. This is because after pollutants are discharged into the water, the concentration of pollutants at any point in the water increases with time and then tends to balance to the equilibrium value. As the number of predicted time steps increases, the prediction accuracy of the model will decline, so the EEMD–LSTM model can only predict short time steps at present. Water quality prediction over long time steps is still a challenging issue.

## 6. Conclusions

_{3}-N, pH, DO, COD

_{Mn}) of the Xiaofu River are predicted. The following conclusions were drawn from this study:

- (1)
- The EEMD method can decompose time series into components arranged from high frequency to low frequency. In this study, it is used to decompose the water quality time series to obtain several single-period components, which can effectively reduce the complexity and nonlinearity of the original time series. Among all components, the high-frequency components have the greatest impact on the accuracy of water quality prediction. Predicting the high-frequency components and the low-frequency components separately when using LSTM can significantly improve model accuracy.
- (2)
- Compared with LSTM, EEMD–LSTM significantly improves the accuracy of water quality prediction and greatly improves the model performance in terms of the hysteresis problem. During the validation period, the RMSE, MAE, MAPE and R
^{2}of EEMD–LSTM for NH_{3}-N were 0.022 mg/L, 0.019 mg/L, 3.150% and 0.924, respectively. The RMSE, MAE, MAPE and R^{2}of EEMD-LSTM for pH were 0.035 mg/L, 0.029 mg/L, 0.273% and 0.965, respectively. The RMSE, MAE, MAPE and R^{2}of EEMD-LSTM for DO were 0.224 mg/L, 0.161 mg/L, 0.994% and 0.961, respectively. The RMSE, MAE, MAPE and R^{2}of the EEMD-LSTM for COD_{Mn}were 0.133 mg/L, 0.085 mg/L, 2.219% and 0.936, respectively. This shows that EEMD–LSTM has high prediction accuracy and strong generalization ability. In addition, the predicted values of EEMD–LSTM are closer to the observed values in the extreme value prediction.

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

- Tang, W.; Pei, Y.; Zheng, H.; Zhao, Y.; Shu, L.; Zhang, H. Twenty years of China's water pollution control: Experiences and challenges. Chemosphere
**2022**, 295, 133875. [Google Scholar] [CrossRef] [PubMed] - Xiong, Y.; Ran, Y.; Zhao, S.; Zhao, H.; Tian, Q. Remotely assessing and monitoring coastal and inland water quality in China: Progress, challenges and outlook. Crit. Rev. Environ. Sci. Technol.
**2020**, 50, 1266–1302. [Google Scholar] [CrossRef] - Liang, Z.; Zou, R.; Chen, X.; Ren, T.; Su, H.; Liu, Y. Simulate the forecast capacity of a complicated water quality model using the long short-term memory approach. J. Hydrol.
**2022**, 581, 124432. [Google Scholar] [CrossRef] - Yu, J.; Kim, J.; Li, X.; Jong, Y.; Kim, K.; Ryang, G. Water quality forecasting based on data decomposition, fuzzy clustering and deep learning neural network. Environ. Pollut.
**2022**, 303, 119136. [Google Scholar] [CrossRef] - Bui, H.H.; Ha, N.H.; Nguyen, T.N.D.; Nguyen, A.T.; Pham, T.T.H.; Kandasamy, J.; Tien, V.N. Integration of SWAT and QUAL2K for water quality modeling in a data scarce basin of Cau River basin in Vietnam. Ecohydrol. Hydrobiol.
**2019**, 19, 210–223. [Google Scholar] [CrossRef] - Bai, J.; Zhao, J.; Zhang, Z.; Tian, Z. Assessment and a review of research on surface water quality modeling. Ecol. Model.
**2022**, 466, 109888. [Google Scholar] [CrossRef] - Qin, Z.; He, Z.; Wu, G.; Tang, G.; Wang, Q. Developing Water-Quality Model for Jingpo Lake Based on EFDC. Water
**2022**, 14, 2596. [Google Scholar] [CrossRef] - Kang, M.; Tian, Y.; Zhang, H.; Wan, C. Effect of hydrodynamic conditions on the water quality in urban landscape water. Water Supply
**2021**, 22, 309–320. [Google Scholar] [CrossRef] - Samaneh, A.; Sedghi, H.; Hassonizadeh, H.; Babazadeh, H. Application of Water Quality Index and Water Quality Model QUAL2K for Evaluation of Pollutants in Dez River, Iran. Water Resour.
**2021**, 47, 892–903. [Google Scholar] [CrossRef] - Obin, N.; Tao, H.; Ge, F.; Liu, X. Research on Water Quality Simulation and Water Environmental Capacity in Lushui River Based on WASP Model. Water
**2021**, 13, 2819. [Google Scholar] [CrossRef] - Shabani, A.; Zhang, X.; Chu, X.; Zheng, H. Automatic calibration for CE-QUAL-W2 model using improved global-best harmony search algorithm. Water
**2021**, 13, 2308. [Google Scholar] [CrossRef] - Mendes, J.; Ruela, R.; Picado, A.; Pinheiro, J.P.; Ribeiro, A.S.; Pereira, H.; Dias, J.M. Modeling dynamic processes of Mondego Estuary and Oacute, Bidos Lagoon using Delft3D. J. Mar. Sci. Technol.
**2021**, 9, 91. [Google Scholar] [CrossRef] - Da Silva Burigato Costa, C.M.; Leite, I.R.; Almeida, A.K.; de Almeida, I.K. Choosing an appropriate water quality model-a review. Environ. Monit. Assess.
**2021**, 193, 38. [Google Scholar] [CrossRef] [PubMed] - Ejigu, M.T. Overview of water quality modeling. Cogent Eng.
**2021**, 8, 1891711. [Google Scholar] [CrossRef] - Achite, M.; Farzin, S.; Elshaboury, N.; Valikhan Anaraki, M.; Amamra, M.; Toubal, A.K. Modeling the optimal dosage of coagulants in water treatment plants using various machine learning models. Environ. Dev. Sustain.
**2022**, 1–27. [Google Scholar] [CrossRef] - Farzin, S.; Anaraki, M.V.; Naeimi, M.; Zandifar, S. Prediction of groundwater table and drought analysis; a new hybridization strategy based on bi-directional long short-term model and the Harris hawk optimization algorithm. J. Water Clim. Chang.
**2022**, 13, 2233–2254. [Google Scholar] [CrossRef] - Valikhan Anaraki, M.; Mahmoudian, F.; Nabizadeh Chianeh, F.; Farzin, S. Dye Pollutant Removal from Synthetic Wastewater: A New Modeling and Predicting Approach Based on Experimental Data Analysis, Kriging Interpolation Method, and Computational Intelligence Techniques. J. Environ. Inform.
**2022**, 40, 84–94. [Google Scholar] [CrossRef] - Kourgialas, N.N.; Dokou, Z.; Karatzas, G.P. Statistical analysis and ANN modeling for predicting hydrological extremes under climate change scenarios: The example of a small mediterranean agro-watershed. J. Environ. Manag.
**2015**, 154, 86–101. [Google Scholar] [CrossRef] - Yang, S.; Yang, D.; Chen, J.; Santisirisomboon, J.; Lu, W.; Zhao, B. A physical process and machine learning combined hydrological model for daily streamflow simulations of large watersheds with limited observation data. J. Hydrol.
**2020**, 590, 125206. [Google Scholar] [CrossRef] - Zema, D.A.; Lucas-Borja, M.E.; Fotia, L.; Rosaci, D.; Sarne, G.M.L.; Zimbone, S.M. Predicting the hydrological response of a forest after wildfire and soil treatments using an Artificial Neural Network. Comput. Electron. Agric.
**2020**, 170, 105280. [Google Scholar] [CrossRef] - Lee, J.H.; Lee, J.Y.; Lee, M.H.; Lee, M.Y.; Kim, Y.W.; Hyung, J.S.; Kim, K.B.; Cha, Y.K.; Koo, J.Y. Development of a short-term water quality prediction model for urban rivers using real-time water quality data. Water Supply
**2022**, 22, 4082–4097. [Google Scholar] [CrossRef] - Seo, I.W.; Yun, S.H.; Choi, S.Y. Forecasting water quality parameters by ANN model using pre-processing technique at the downstream of Cheongpyeong Dam. Procedia Eng.
**2016**, 154, 1110–1115. [Google Scholar] [CrossRef] - An, L.; Hao, Y.; Yeh, T.J.; Liu, Y.; Liu, W.; Zhang, B. Simulation of karst spring discharge using a combination of time-frequency analysis methods and long short-term memory neural networks. J. Hydrol.
**2020**, 589, 125320. [Google Scholar] [CrossRef] - Hochreiter, S.; Schmidhuber, J. Long short-term memory. Neural Comput.
**1997**, 9, 1735–1780. [Google Scholar] [CrossRef] - Rumelhart, D.E.; Hinton, G.E.; Williams, R.J. Learning representations by back-propagating errors. Nature
**1986**, 323, 533–536. [Google Scholar] [CrossRef] - Zheng, L.; Wang, H.; Liu, C.; Zhang, S.; Ding, A.; Xie, E.; Li, J.; Wang, S. Prediction of harmful algal blooms in large water bodies using the combined EFDC and LSTM models. J. Environ. Manag.
**2021**, 295, 113060. [Google Scholar] [CrossRef] [PubMed] - Eze, E.; Halse, S.; Ajmal, T. Developing a novel water quality prediction model for a South African aquaculture farm. Water
**2021**, 13, 1782. [Google Scholar] [CrossRef] - Zhou, J.; Wang, J.; Chen, Y.; Li, X.; Xie, Y. Water quality prediction method based on multi-source transfer learning for water environmental IoT system. Sensors
**2021**, 21, 7271. [Google Scholar] [CrossRef] - Tant, C.J.; Rosemond, A.D.; Helton, A.M.; First, M.R. Nutrient enrichment alters the magnitude and timing of fungal, bacterial, and detritivore contributions to litter breakdown. Freshw. Sci.
**2015**, 34, 1259–1271. [Google Scholar] [CrossRef] - Huang, N.E.; Shen, Z.; Long, S.R.; Wu, M.; Shih, H.H.; Zheng, Q.N.; Yen, N.C.; Tung, C.C.; Liu, H.H. The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis. Proc. R. Soc. London. Ser. A Math. Phys. Eng. Sci.
**1998**, 454, 903–995. [Google Scholar] [CrossRef] - Zhaohua, W.U.; Norden, E.H. Ensemble empirical mode decomposition: A noise-assisted data analysis method. Adv. Adapt. Data Anal.
**2009**, 1, 1–41. [Google Scholar] [CrossRef] - Wang, J.; Wang, X.; Lei, X.H.; Wang, H.; Zhang, X.H.; You, J.J.; Tan, Q.F.; Liu, X.L. Teleconnection analysis of monthly streamflow using ensemble empirical mode decomposition. J. Hydrol.
**2020**, 582, 124411. [Google Scholar] [CrossRef] - Niu, W.; Feng, Z.; Zeng, M.; Feng, B.; Min, Y.; Cheng, C.; Zhou, J. Forecasting reservoir monthly runoff via ensemble empirical mode decomposition and extreme learning machine optimized by an improved gravitational search algorithm. Appl. Soft Comput.
**2019**, 82, 105589. [Google Scholar] [CrossRef] - Huan, J.; Cao, W.; Qin, Y. Prediction of dissolved oxygen in aquaculture based on EEMD and LSSVM optimized by the Bayesian evidence framework. Comput. Electron. Agric.
**2018**, 150, 257–265. [Google Scholar] [CrossRef] - Qingmei, M.; Min, L.; Aiju, L. Spatial variation and contamination assessment of heavy metals in surface sediments of Xiaofu River. Health Environ. Res.
**2013**, 6, 785–790. [Google Scholar] [CrossRef] - Ding, S.; Wang, F.; Sun, X.; Ding, J.; Lu, J. Water environmental functional zoning at county level and environmental contamination carrying capacity accounting in the mainstream of Xiaofu River. Water
**2022**, 14, 615. [Google Scholar] [CrossRef] - Zhang, J.L.; Tang, M.G.; Liu, F.; Zhong, Z.S. Vulnerability analysis of groundwater pollution by mining drainage in Zibo coal mine, Shandong Province, China. In International Symposium on Hydrogeology and the Environment; International Atomic Energy Agency: Vienna, Austria, 2000; pp. 157–162. [Google Scholar]
- Singh, D.; Singh, B. Investigating the impact of data normalization on classification performance. Appl. Soft Comput.
**2020**, 97, 105524. [Google Scholar] [CrossRef] - Guia, S.S.; Espirito-Santo, A.; Paciello, V.; Abate, F.; Pietrosanto, A. A comparison between FFT and MCT for period measurement with an ARM Microcontroller. In Proceedings of the 2015 IEEE International Instrumentation and Measurement Technology Conference, Pisa, Italy, 11–14 May 2015; pp. 1938–1942. [Google Scholar] [CrossRef]
- ArunKumar, K.E.; Kalaga, D.V.; Kumar, C.M.S.; Kawaji, M.; Brenza, T.M. Forecasting of COVID-19 using deep layer Recurrent Neural Networks (RNNs) with Gated Recurrent Units (GRUs) and Long Short-Term Memory (LSTM) cells. Chaos Solitons Fractals
**2021**, 146, 110861. [Google Scholar] [CrossRef] - Liu, F.T.; Ting, K.M.; Zhou, Z. Isolation forest. In Proceedings of the 2008 Eighth Ieee International Conference on Data Mining, Pisa, Italy, 15–19 December 2008; pp. 413–422. [Google Scholar] [CrossRef]
- Ren, Y.; Suganthan, P.N.; Srikanth, N. A comparative study of empirical mode decomposition-based short-term wind speed forecasting methods. IEEE Trans. Sustain. Energy
**2015**, 6, 236–244. [Google Scholar] [CrossRef] - Liu, X.; Zhang, Y.; Zhang, Q. Comparison of EEMD-ARIMA, EEMD-BP and EEMD-SVM algorithms for predicting the hourly urban water consumption. J. Hydroinform.
**2022**, 24, 535–558. [Google Scholar] [CrossRef] - Diederik, P.K.; Jimmy, B. Adam: A method for stochastic optimization. arXiv
**2014**, arXiv:1412.6980. [Google Scholar] - Xiang, Z.; Yan, J.; Demir, I. A rainfall-runoff model with LSTM-based sequence-to-sequence learning. Water Resour. Res.
**2020**, 56, e2019WR025326. [Google Scholar] [CrossRef] - Li, X.J.; Cheng, Z.W.; Yu, Q.B.; Bai, Y.; Li, C. Water-quality prediction using multimodal support vector regression: Case study of Jialing River, China. J. Environ. Eng.
**2017**, 143, 04017070. [Google Scholar] [CrossRef] - Ma, L.; Liu, L.; Song, L.L.; Yan, W.M. A study on water pollutant degradation capability affected by water diversion. J. Environ. Prot. Ecol.
**2014**, 15, 39–47. [Google Scholar]

**Figure 3.**LSTM memory cell unit structure [24].

**Figure 4.**The normalization results of the water quality data: (

**a**) pH, (

**b**) DO, (

**c**) COD

_{Mn}, and (

**d**) NH

_{3}-N.

**Figure 8.**The ANN, LSTM, and EEMD–LSTM prediction results of (

**a**) NH

_{3}-N, (

**b**) pH, (

**c**) DO, and (

**d**) COD

_{Mn}.

**Figure 9.**Scatterplot of the observed and predicted values by ANN, LSTM, and EEMD–LSTM in the validation period. (

**a**–

**d**) represent the observed and predicted values of NH

_{3}-N, pH, DO, COD

_{Mn}by ANN, respectively. (

**e**–

**h**) represent the observed and predicted values of NH

_{3}-N, pH, DO, COD

_{Mn}by LSTM, respectively. (

**i**–

**l**) represent the observed and predicted values of NH

_{3}-N, pH, DO, COD

_{Mn}by EEMD–LSTM, respectively.

Variable Name | Description | Average | Standard Deviation | Maximum Value | Minimum Value | Number of Missing Data |
---|---|---|---|---|---|---|

pH | Pondus hydrogenii | 7.912 | 0.437 | 8.83 | 6.02 | 0 |

DO | Dissolved oxygen (mg/L) | 8.779 | 2.379 | 18.9 | 0.5 | 0 |

COD_{Mn} | Permanganate index (mg/L) | 4.327 | 1.149 | 9 | 1.82 | 1 |

NH_{3}-N | Ammonia nitrogen (mg/L) | 0.472 | 0.415 | 5.16 | 0.028 | 1 |

Variable Name | Period (Day) | |||||||
---|---|---|---|---|---|---|---|---|

IMF1 | IMF2 | IMF3 | IMF4 | IMF5 | IMF6 | IMF7 | IMF8 | |

NH_{3}-N | 3 | 7 | 38 | 41 | 152 | 356 | 534 | 534 |

pH | 3 | 7 | 22 | 53 | 89 | 356 | 534 | 534 |

DO | 5 | 9 | 20 | 42 | 97 | 356 | 356 | 534 |

COD_{Mn} | 4 | 8 | 12 | 59 | 66 | 356 | 356 | - |

Parameter Name | Number |
---|---|

epochs | 100 |

batch size | 16 |

number of LSTM layers | 1 |

number of neurons in the input layer | 1 |

number of neurons in the hidden layer | 50 |

number of neurons in the output layer | 1 |

Water Quality Indicator | Sliding Time Window Width | RMSE (mg/L) | MAE (mg/L) | MAPE (%) | R^{2} |
---|---|---|---|---|---|

NH_{3}-N | 4 | 0.096 | 0.071 | 67.387 | 0.423 |

5 | 0.089 | 0.057 | 31.901 | 0.783 | |

6 | 0.089 | 0.060 | 42.082 | 0.727 | |

7 | 0.089 | 0.059 | 39.477 | 0.746 | |

8 | 0.093 | 0.067 | 60.726 | 0.545 | |

pH | 4 | 0.080 | 0.049 | 1.787 | 0.656 |

5 | 0.078 | 0.045 | 1.425 | 0.741 | |

6 | 0.078 | 0.046 | 1.521 | 0.722 | |

7 | 0.078 | 0.046 | 1.558 | 0.721 | |

8 | 0.087 | 0.059 | 1.908 | 0.656 | |

DO | 4 | 0.590 | 0.420 | 7.831 | 0.769 |

5 | 0.587 | 0.424 | 7.600 | 0.772 | |

6 | 0.594 | 0.434 | 7.741 | 0.763 | |

7 | 0.591 | 0.429 | 7.630 | 0.769 | |

8 | 0.588 | 0.422 | 7.628 | 0.777 | |

COD_{Mn} | 4 | 0.246 | 0.167 | 11.041 | 0.748 |

5 | 0.247 | 0.168 | 12.646 | 0.724 | |

6 | 0.244 | 0.165 | 11.538 | 0.743 | |

7 | 0.249 | 0.170 | 10.615 | 0.752 | |

8 | 0.243 | 0.165 | 11.701 | 0.744 |

Model | Water Quality Indicator | Training | Validation | ||||||
---|---|---|---|---|---|---|---|---|---|

RMSE (mg/L) | MAE (mg/L) | MAPE (%) | R^{2} | RMSE (mg/L) | MAE (mg/L) | MAPE (%) | R^{2} | ||

ANN | NH_{3}-N | 0.268 | 0.148 | 51.028 | 0.615 | 0.018 | 0.017 | 89.344 | 0.315 |

pH | 0.167 | 0.107 | 1.393 | 0.851 | 0.026 | 0.017 | 2.106 | 0.627 | |

DO | 1.311 | 0.889 | 13.245 | 0.713 | 0.031 | 0.022 | 5.022 | 0.757 | |

COD_{Mn} | 0.587 | 0.426 | 8.835 | 0.703 | 0.062 | 0.039 | 19.208 | 0.462 | |

LSTM | NH_{3}-N | 0.169 | 0.111 | 37.694 | 0.754 | 0.110 | 0.109 | 50.381 | 0.567 |

pH | 0.136 | 0.080 | 1.032 | 0.872 | 0.122 | 0.113 | 1.554 | 0.657 | |

DO | 1.151 | 0.826 | 10.807 | 0.733 | 1.027 | 0.820 | 4.685 | 0.817 | |

COD_{Mn} | 0.457 | 0.314 | 7.239 | 0.811 | 0.440 | 0.326 | 13.990 | 0.693 | |

EEMD–LSTM | NH_{3}-N | 0.077 | 0.050 | 5.419 | 0.950 | 0.022 | 0.019 | 3.150 | 0.924 |

pH | 0.047 | 0.032 | 0.321 | 0.988 | 0.035 | 0.029 | 0.273 | 0.965 | |

DO | 0.531 | 0.355 | 2.245 | 0.945 | 0.224 | 0.161 | 0.994 | 0.961 | |

COD_{Mn} | 0.189 | 0.131 | 2.756 | 0.969 | 0.133 | 0.085 | 2.219 | 0.936 |

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## Share and Cite

**MDPI and ACS Style**

Luo, L.; Zhang, Y.; Dong, W.; Zhang, J.; Zhang, L.
Ensemble Empirical Mode Decomposition and a Long Short-Term Memory Neural Network for Surface Water Quality Prediction of the Xiaofu River, China. *Water* **2023**, *15*, 1625.
https://doi.org/10.3390/w15081625

**AMA Style**

Luo L, Zhang Y, Dong W, Zhang J, Zhang L.
Ensemble Empirical Mode Decomposition and a Long Short-Term Memory Neural Network for Surface Water Quality Prediction of the Xiaofu River, China. *Water*. 2023; 15(8):1625.
https://doi.org/10.3390/w15081625

**Chicago/Turabian Style**

Luo, Lan, Yanjun Zhang, Wenxun Dong, Jinglin Zhang, and Liping Zhang.
2023. "Ensemble Empirical Mode Decomposition and a Long Short-Term Memory Neural Network for Surface Water Quality Prediction of the Xiaofu River, China" *Water* 15, no. 8: 1625.
https://doi.org/10.3390/w15081625