# Exploring the Effect of Meteorological Factors on Predicting Hourly Water Levels Based on CEEMDAN and LSTM

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Study Area Description

#### 2.2. Data Collection and Analysis

#### 2.3. Machine Learning Algorithms for Predicting Water Level References

#### 2.3.1. Support Vector Machine (SVM)

#### 2.3.2. Random Forest (RF)

#### 2.3.3. Extreme Gradient Boosting (XGBoost)

#### 2.3.4. Light Gradient Boosting Machine (LightGBM)

#### 2.4. Deep Learning Algorithms for Predicting Water Level Reference

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

#### 2.4.2. Stack Long Short-Term Memory (StackLSTM)

#### 2.4.3. Bi-Directional Long Short-Term Memory (BiLSTM)

#### 2.5. Input Portfolio Strategy

#### 2.6. Complete Ensemble Empirical Mode Decomposition Adaptive Noise (CEEMDAN)

#### 2.7. Model Comparison Statistical Analysis

#### 2.8. Hyperparameter Tuning

## 3. Results

#### 3.1. Compare the Accuracy of Each Model Prediction for Different Combinations of Inputs

#### 3.2. Compare the Stability of Each Model

#### 3.3. Seasonal Analysis of Predicted Water Levels

#### 3.4. Application of CEEMDAN to the Prediction Accuracy of Individual Models Based on All Meteorological Combinations

## 4. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Appendix A

**Figure A1.**Residual scatter plots of predicted water levels at the Burlington site under seven models with all meteorological factors as inputs.

**Figure A2.**The prediction results for each IMF mode and residual obtained from the CEEMDAN decomposition of water level data at site Burlington.

## Appendix B

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**Figure 2.**Violin analysis plots of meteorological (WS, WG, AT)—water level data for two stations, (

**a**,

**b**): Kahului and La Jolla stations, respectively.

**Figure 6.**CEEMDAN-LSTM forecasting process; note that the LSTM part of it can be replaced with other models for the prediction task.

**Figure 7.**Prediction curves of each model for three stations when all meteorological factors are used as inputs. The right histogram’s L-G, B-L, S-L, and L represent LightGBM, BiLSTM, StackLSTM, and LSTM, respectively.

**Figure 8.**RMSE thermal analysis of each model’s prediction results for all seasons under all combinations of meteorological factors.

**Figure 10.**CEEMDAN-BiLSTM predictions of water level at the La Jolla site based on input combinations of all meteorological factors.

Burlington | ||||||
---|---|---|---|---|---|---|

Variable | Wind Speed (m/s) | Wind Dir (deg) | Wind Gust (m/s) | Air Temp (°C) | Baro (mb) | Water Level (m) |

$\mathbf{Mean}$ | 2.674 | 197.173 | 4.212 | 13.279 | 1017.397 | 1.316 |

$\mathbf{Std}$ | 1.954 | 103.032 | 2.895 | 10.174 | 7.619376 | 0.793 |

$\mathbf{Min}$ | 0.000 | 0.000 | 0.000 | −13.400 | 985.000 | −0.595 |

$\mathbf{Q}\mathbf{1}$ | 1.200 | 93.000 | 1.900 | 5.3000 | 1012.700 | 0.621 |

$\mathbf{Q}\mathbf{2}$ | 2.300 | 229.000 | 3.700 | 13.600 | 1016.900 | 1.307 |

$\mathbf{Q}\mathbf{3}$ | 3.800 | 283.000 | 5.800 | 21.800 | 1022.300 | 2.028 |

$\mathbf{Max}$ | 13.100 | 360.000 | 21.300 | 35.000 | 1040.600 | 3.278 |

Site | Kahului | La Jolla | ||
---|---|---|---|---|

Variable | Wind Dir (deg) | Baro (mb) | Wind Dir (deg) | Baro (mb) |

$\mathbf{Mean}$ | 94.608 | 1016.683 | 198.091 | 1015.177 |

$\mathbf{Std}$ | 90.115 | 2.348 | 102.664 | 3.867 |

$\mathbf{Min}$ | 0.000 | 997.700 | 0.000 | 998.600 |

$\mathbf{Q}\mathbf{1}$ | 45.000 | 1015.400 | 114.000 | 1012.500 |

$\mathbf{Q}\mathbf{2}$ | 66.000 | 1016.800 | 213.500 | 1014.700 |

$\mathbf{Q}\mathbf{3}$ | 82.000 | 1018.200 | 286.000 | 1017.700 |

$\mathbf{Max}$ | 360.000 | 1023.100 | 360.000 | 1027.600 |

**Table 3.**Combination of meteorological water level variable inputs for different machine learning models and deep learning models.

Input Combinations | SVM | RF | XGB | LightGBM | LSTM | StackLSTM | BiLSTM |
---|---|---|---|---|---|---|---|

WS, WD, WG, AT, Baro, WL | SVM1 | RF1 | XGB1 | LightGBM1 | LSTM1 | StackLSTM1 | BiLSTM1 |

WS, WD, WG, WL | SVM2 | RF2 | XGB2 | LightGBM2 | LSTM2 | StackLSTM2 | BiLSTM2 |

AT, Baro, WL | SVM3 | RF3 | XGB3 | LightGBM3 | LSTM3 | StackLSTM3 | BiLSTM3 |

WL, WS, AT | SVM4 | RF4 | XGB4 | LightGBM4 | LSTM4 | StackLSTM4 | BiLSTM4 |

Site | Models | Parameters |
---|---|---|

Burlington, Kahului, La Jolla | SVM | Kernel: RBF |

RF | N_Estimators: 50, Oob_Score: True, N_Jobs: −1, Random_State: 50, Max_Features: 1.0, Min_Samples_leaf: 10 | |

XGB | Objective: reg:squarederror, N_Estimatorsl: 50 | |

LightGBM | Boosting Type: Gbdt, Objective: Regression, Num_Leaves: 29, Learning_Rate: 0.09, Feature_Fraction: 0.9, Bagging_Fraction: 0.8, Bagging_Freq: 6 | |

LSTM | Layers: 1, Number of Neurons: 200, Dense: 1, Activation: ReLU, Optimizer: Adam, Loss Function: MSE, Epochs: 40, Batch Size: 1 | |

StackLSTM | Layers: 2, Number of Neurons: 200 (2×100), Dense: 1, Activation: ReLU, Optimizer: Adam, Loss Function: MSE, Epochs: 40, Batch Size: 1 | |

BiLSTM | Layers: 2, Number of Neurons: 200 (2×100), Dense: 1, Activation: ReLU, Optimizer: Adam, Loss Function: MSE, Epochs: 40, Batch Size: 1 |

Model | Statistical Indicators | Model | Statistical Indicators | ||||||
---|---|---|---|---|---|---|---|---|---|

Input | ${\mathit{R}}^{2}$ | MAEmh ^{−1} | RMSEmh ^{−1} | nRMSE | ${\mathit{R}}^{2}$ | MAEmh ^{−1} | RMSEmh ^{−1} | nRMSE | |

WS, WD, WG, AT, Baro, WL | WS, WD, WG, WL | ||||||||

SVM1 | 0.688 | 0.358 | 0.389 | 0.111 | SVM2 | 0.696 | 0.361 | 0.387 | 0.110 |

RF1 | 0.692 | 0.357 | 0.398 | 0.110 | RF2 | 0.686 | 0.356 | 0.395 | 0.112 |

XGB1 | 0.680 | 0.359 | 0.412 | 0.110 | XGB2 | 0.658 | 0.363 | 0.409 | 0.116 |

LightGBM1 | 0.689 | 0.347 | 0.393 | 0.110 | LightGBM2 | 0.682 | 0.351 | 0.390 | 0.110 |

LSTM1 | 0.695 | 0.346 | 0.392 | 0.112 | LSTM2 | 0.686 | 0.350 | 0.387 | 0.110 |

StackLSTM1 | 0.721 | 0.367 | 0.391 | 0.110 | StackLSTM2 | 0.719 | 0.356 | 0.384 | 0.109 |

BiLSTM1 | 0.681 | 0.350 | 0.390 | 0.116 | BiLSTM2 | 0.699 | 0.357 | 0.386 | 0.109 |

WS, AT, WL | AT, Baro, WL | ||||||||

SVM3 | 0.682 | 0.364 | 0.391 | 0.111 | SVM4 | 0.698 | 0.362 | 0.390 | 0.110 |

RF3 | 0.689 | 0.362 | 0.401 | 0.113 | RF4 | 0.678 | 0.368 | 0.409 | 0.116 |

XGB3 | 0.674 | 0.366 | 0.419 | 0.119 | XGB4 | 0.662 | 0.371 | 0.428 | 0.121 |

LightGBM3 | 0.698 | 0.353 | 0.399 | 0.113 | LightGBM4 | 0.691 | 0.360 | 0.402 | 0.114 |

LSTM3 | 0.698 | 0.353 | 0.388 | 0.110 | LSTM4 | 0.704 | 0.357 | 0.386 | 0.109 |

StackLSTM3 | 0.695 | 0.346 | 0.392 | 0.111 | StackLSTM4 | 0.689 | 0.347 | 0.391 | 0.110 |

BiLSTM3 | 0.702 | 0.353 | 0.389 | 0.110 | BiLSTM4 | 0.704 | 0.358 | 0.385 | 0.109 |

Model | Statistical Indicators | Model | Statistical Indicators | ||||||
---|---|---|---|---|---|---|---|---|---|

Input | ${\mathit{R}}^{2}$ | MAEmh ^{−1} | RMSEmh ^{−1} | nRMSE | ${\mathit{R}}^{2}$ | MAEmh ^{−1} | RMSEmh ^{−1} | nRMSE | |

WS, WD, WG, AT, Baro, WL | WS, WD, WG, WL | ||||||||

SVM1 | 0.843 | 0.073 | 0.090 | 0.077 | SVM2 | 0.838 | 0.075 | 0.093 | 0.079 |

RF1 | 0.837 | 0.074 | 0.095 | 0.081 | RF2 | 0.831 | 0.076 | 0.096 | 0.082 |

XGB1 | 0.836 | 0.076 | 0.095 | 0.081 | XGB2 | 0.815 | 0.080 | 0.100 | 0.085 |

LightGBM1 | 0.845 | 0.074 | 0.092 | 0.078 | LightGBM2 | 0.840 | 0.075 | 0.093 | 0.079 |

LSTM1 | 0.838 | 0.074 | 0.093 | 0.080 | LSTM2 | 0.835 | 0.074 | 0.094 | 0.080 |

StackLSTM1 | 0.852 | 0.073 | 0.092 | 0.078 | StackLSTM2 | 0.847 | 0.074 | 0.093 | 0.079 |

BiLSTM1 | 0.838 | 0.073 | 0.093 | 0.079 | BiLSTM2 | 0.842 | 0.074 | 0.094 | 0.080 |

WS, AT, WL | AT, Baro, WL | ||||||||

SVM3 | 0.839 | 0.074 | 0.093 | 0.079 | SVM4 | 0.831 | 0.076 | 0.095 | 0.081 |

RF3 | 0.834 | 0.075 | 0.096 | 0.082 | RF4 | 0.839 | 0.075 | 0.095 | 0.081 |

XGB3 | 0.830 | 0.077 | 0.098 | 0.083 | XGB4 | 0.831 | 0.078 | 0.097 | 0.083 |

LightGBM3 | 0.840 | 0.074 | 0.094 | 0.080 | LightGBM4 | 0.832 | 0.076 | 0.096 | 0.082 |

LSTM3 | 0.850 | 0.072 | 0.091 | 0.077 | LSTM4 | 0.836 | 0.074 | 0.094 | 0.08 |

StackLSTM3 | 0.831 | 0.074 | 0.095 | 0.081 | StackLSTM4 | 0.838 | 0.074 | 0.094 | 0.08 |

BiLSTM3 | 0.839 | 0.073 | 0.093 | 0.080 | BiLSTM4 | 0.837 | 0.075 | 0.095 | 0.081 |

Model | Statistical Indicators | Model | Statistical Indicators | ||||||
---|---|---|---|---|---|---|---|---|---|

Input | ${\mathit{R}}^{2}$ | MAEmh ^{−1} | RMSEmh ^{−1} | nRMSE | ${\mathit{R}}^{2}$ | MAEmh ^{−1} | RMSEmh ^{−1} | nRMSE | |

WS, WD, WG, AT, Baro, WL | WS, WD, WG, WL | ||||||||

SVM1 | 0.802 | 0.197 | 0.235 | 0.086 | SVM2 | 0.805 | 0.192 | 0.232 | 0.085 |

RF1 | 0.828 | 0.191 | 0.229 | 0.084 | RF2 | 0.818 | 0.194 | 0.234 | 0.086 |

XGB1 | 0.831 | 0.190 | 0.226 | 0.083 | XGB2 | 0.810 | 0.197 | 0.239 | 0.088 |

LightGBM1 | 0.830 | 0.189 | 0.225 | 0.082 | LightGBM2 | 0.821 | 0.193 | 0.232 | 0.085 |

LSTM1 | 0.820 | 0.189 | 0.227 | 0.083 | LSTM2 | 0.817 | 0.193 | 0.233 | 0.085 |

StackLSTM1 | 0.815 | 0.191 | 0.230 | 0.084 | StackLSTM2 | 0.815 | 0.190 | 0.231 | 0.085 |

BiLSTM1 | 0.826 | 0.189 | 0.229 | 0.084 | BiLSTM2 | 0.808 | 0.193 | 0.235 | 0.086 |

WS, AT, WL | AT, Baro, WL | ||||||||

SVM3 | 0.820 | 0.191 | 0.229 | 0.084 | SVM4 | 0.813 | 0.193 | 0.230 | 0.084 |

RF3 | 0.826 | 0.193 | 0.231 | 0.085 | RF4 | 0.821 | 0.194 | 0.232 | 0.085 |

XGB3 | 0.831 | 0.191 | 0.232 | 0.085 | XGB4 | 0.833 | 0.189 | 0.228 | 0.083 |

LightGBM3 | 0.833 | 0.191 | 0.228 | 0.084 | LightGBM4 | 0.837 | 0.188 | 0.223 | 0.082 |

LSTM3 | 0.824 | 0.191 | 0.229 | 0.084 | LSTM4 | 0.828 | 0.188 | 0.227 | 0.083 |

StackLSTM3 | 0.830 | 0.191 | 0.228 | 0.084 | StackLSTM4 | 0.827 | 0.189 | 0.226 | 0.083 |

BiLSTM3 | 0.830 | 0.190 | 0.227 | 0.083 | BiLSTM4 | 0.835 | 0.188 | 0.225 | 0.082 |

**Table 8.**Water level prediction results for three sites, Burlington, Kahului, and La Jolla, based on the optimal combination of the CEEMDAN algorithm introduced with the input meteorological factors as inputs.

Site | Model | Statistical Indicators | |||
---|---|---|---|---|---|

Input | ${\mathit{R}}^{2}$ | MAEmh ^{−1} | RMSEmh ^{−1} | $\mathit{n}\mathit{R}\mathit{M}\mathit{S}\mathit{E}$ | |

WS, WD, WG, AT, Baro, WL | |||||

Burlington | CEEMDAN-SVM | 0.9652 | 0.1131 | 0.1448 | 0.0397 |

CEEMDAN-RF | 0.9742 | 0.1015 | 0.1245 | 0.0342 | |

CEEMDAN-XGB | 0.9738 | 0.0996 | 0.1255 | 0.0344 | |

CEEMDAN-LightGBM | 0.9755 | 0.0982 | 0.1213 | 0.0333 | |

CEEMDAN-LSTM | 0.9803 | 0.0864 | 0.1088 | 0.0299 | |

CEEMDAN-StackLSTM | 0.9803 | 0.0881 | 0.1089 | 0.0299 | |

CEEMDAN-BiLSTM | 0.9820 | 0.0790 | 0.1040 | 0.0285 | |

Kahului | CEEMDAN-SVM | 0.9317 | 0.0475 | 0.0596 | 0.0474 |

CEEMDAN-RF | 0.9695 | 0.0317 | 0.0399 | 0.0317 | |

CEEMDAN-XGB | 0.9667 | 0.0330 | 0.0416 | 0.0331 | |

CEEMDAN-LightGBM | 0.9676 | 0.0325 | 0.0410 | 0.0326 | |

CEEMDAN-LSTM | 0.9800 | 0.0254 | 0.0322 | 0.0256 | |

CEEMDAN-StackLSTM | 0.9794 | 0.0258 | 0.0327 | 0.0260 | |

CEEMDAN-BiLSTM | 0.9799 | 0.0254 | 0.0323 | 0.0257 | |

La Jolla | CEEMDAN-SVM | 0.9493 | 0.0851 | 0.1164 | 0.0426 |

CEEMDAN-RF | 0.9754 | 0.0630 | 0.0811 | 0.0297 | |

CEEMDAN-XGB | 0.9694 | 0.0683 | 0.0904 | 0.0331 | |

CEEMDAN-LightGBM | 0.9742 | 0.0635 | 0.0831 | 0.0304 | |

CEEMDAN-LSTM | 0.9833 | 0.0514 | 0.0669 | 0.0245 | |

CEEMDAN-StackLSTM | 0.9844 | 0.0503 | 0.0646 | 0.0237 | |

CEEMDAN-BiLSTM | 0.9846 | 0.0501 | 0.0641 | 0.0235 |

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## Share and Cite

**MDPI and ACS Style**

Yan, Z.; Lu, X.; Wu, L.
Exploring the Effect of Meteorological Factors on Predicting Hourly Water Levels Based on CEEMDAN and LSTM. *Water* **2023**, *15*, 3190.
https://doi.org/10.3390/w15183190

**AMA Style**

Yan Z, Lu X, Wu L.
Exploring the Effect of Meteorological Factors on Predicting Hourly Water Levels Based on CEEMDAN and LSTM. *Water*. 2023; 15(18):3190.
https://doi.org/10.3390/w15183190

**Chicago/Turabian Style**

Yan, Zihuang, Xianghui Lu, and Lifeng Wu.
2023. "Exploring the Effect of Meteorological Factors on Predicting Hourly Water Levels Based on CEEMDAN and LSTM" *Water* 15, no. 18: 3190.
https://doi.org/10.3390/w15183190