# El Niño Index Prediction Using Deep Learning with Ensemble Empirical Mode Decomposition

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## Abstract

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## 1. Introduction

## 2. Proposed Method

#### 2.1. Problem Formulation

#### 2.2. Ensemble Empirical Mode Decomposition

#### 2.3. Long Short-Term Memory Neural Network

- (1)
- According to Equation (7), the input ${h}_{t-1}$ and ${x}_{t}$ are processed to determine whether to forget the data acquired at the previous moment based on the results of the calculation.
- (2)
- According to Equation (8), the information to be stored in the cell state is calculated. At the same time, according to Equation (9), the input gate is used to determine which input data can be collected in the cell.
- (3)
- Based on Equation (10), the results of steps 1 and 2 are processed to filter out the useless data and absorb the useful ones.
- (4)
- Based on the output gate, this step determines the results of the model. Specifically, according to Equations (11) and (12), the output gate determines whether the latest cell output can be passed forward.
- (5)
- Then repeat the above steps continuously. Finally, the parameters in the LSTM are obtained by maximizing the similarity between the target data and the LSTM output.

#### 2.4. Temporal Convolutional Neural Network

#### 2.5. CNN-LSTM Forecasting Framework

#### 2.6. A Multi-Step El Niño Index Forecasting Strategy

## 3. Experiment Design and Evaluation Methods

#### 3.1. Dataset and Preprocessing

#### 3.2. Parameters Details

#### 3.3. Evaluation of Experiments

## 4. Experiments Result and Analysis

## 5. Discussions

- (1)
- Based on the above experimental results, we find that the model using LSTM was significantly better than ARIMA and SVR. This suggests that LSTM has a significant advantage over conventional methods in time series prediction, especially for the prediction of climate indices with chaotic properties.
- (2)
- Compared with the single LSTM, the CNN-LSTM model has better prediction accuracy. The reason for the difference in prediction accuracy should be CNN. CNN can extract features of complex time series, thus effectively improving the performance of El Niño index predictions. Besides, the performance and robustness of the El Niño index predictions are effectively improved due to the EEMD method, which eliminates noise interference in complex nonlinear time series. However, it should also be noted that we were using the EEMD method to filter out the high-frequency noise on the training set and the test set, respectively. This may cause inconsistencies in the degree of filtering between the test set and the training set, affecting the prediction of the model and causing the training model to perform poorly on the test set. In future work, we will further investigate the use of the EEMD method and parameter optimization.
- (3)
- It is well known that the El Niño index is more random and unstable than other climate indices. However, the method proposed in this study has achieved good results in predicting the El Niño index, so the model can also be used to predict other climate indices, such as the Southern Oscillation Index, East Asian summer monsoon index, etc. In addition, it should not be overlooked that the El Niño event, as a special phenomenon in the Earth system, is inextricably linked to other climate events; hence, in the future, we will train models with data from other climate events in order to obtain better prediction models.
- (4)
- In this study, we focus on the 10 day forecast of the Nino 3.4 index. However, the forecast was not limited to 10 days, as the new forecast results were used as historical data during the forecasting process to continue the forecast forward, culminating in a year of Nino 3.4 index forecasts. In this study, for 2017, the Nino 3.4 index prediction yielded good results, and we will test the effectiveness of our model against other El Niño indices and more time in future studies. On the other hand, the predictability time is a very important parameter in the El Niño predictions. In fact, the spring predictability barrier is the great challenge of El Niño predictions. The methods presented in this study have not been studied on the issue of the spring predictability barrier, and in the future, we will adjust the forecast timing to study this issue in depth.
- (5)
- El Niño is a large-scale sea surface temperature (SST) anomaly phenomenon that is strongly spatially correlated, and the study of El Niño cannot ignore spatial information [66]. In El Niño predictions, the time scale information deficit can be addressed by using more spatial information. Our present study demonstrates that EEMD and neural network-based deep learning methods are effective in predicting indices, suggesting that they should also be useful in predicting other physical quantities of El Niño. Next, we will make predictions about the time series of SST anomalies, which is entirely possible because CNN can easily process the two-dimensional space data. Therefore, the EEMD-CNN-LSTM proposed in our paper should yield good results in the prediction of space SST anomalies.
- (6)
- It should not be overlooked that we used the EEMD method for noise reduction on the test set before making the forecast on the test set. As is known to all, any smoothing process such as EEMD transfers future information to the past, i.e., the spread of information over the entire interval. In this way, some part of the prediction improvement may be caused by the fact that the information about the future is already in the input of the predicting operator. This strategy is difficult to achieve when making real-time predictions because the future is completely unknown.

## 6. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## Abbreviations

LSTM | Long Short-Term Memory |

EMD | Empirical Mode Decomposition |

EEMD | Ensemble Empirical Mode Decomposition |

RNN | Recurrent Neural Network |

CNN | Convolutional Neural Network |

NAO | North Atlantic Oscillation |

ARIMA | Autoregressive Integrated Moving Average |

IMF | Intrinsic Mode Function |

SVR | Support Vector Regression |

SGD | Stochastic Gradient Descent |

RMSProp | Root Mean Square Prop |

Adam | Adaptive Moment Estimation |

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**Figure 5.**The line in the figure represents the original Nino 3.4 index series, starting from 1 September 1980 to 29 February 2020. The red part in the figure represents positive values and the blue part represents the negative values.

**Figure 6.**The test set data are decomposed and reconstructed using the Ensemble Empirical Mode Decomposition (EEMD) method, the two graphs in the first row are the reconstructed time series and the original time series, the rest are Intrinsic Mode Functions (IMFs) and residua.

**Figure 9.**The box-plot of prediction results of Root Mean Square Error (RMSE) with different models.

**Figure 10.**Temporal correlations between predictions and real values for all seasons combined. The different color lines represent different models.

**Figure 11.**The RMSE between predictions and real values for all seasons combined. The different color lines represent different models.

**Table 1.**Descriptive statistics for the training and test sets of the Nino 3.4 index, giving the maximum, minimum, and average values of the set.

Data | Num | Min | Max | Mean |
---|---|---|---|---|

training | 12,176 | −2.467572 | 2.732362 | 0.010560 |

testing | 1885 | −1.763447 | 3.287668 | 0.089556 |

η | MAE | RMSE | EV |
---|---|---|---|

0.01 | 0.3173 | 0.2627 | 0.9124 |

0.02 | 0.2419 | 0.2046 | 0.9512 |

0.03 | 0.2275 | 0.1659 | 0.9645 |

0.04 | 0.2083 | 0.1415 | 0.9727 |

0.05 | 0.2217 | 0.1794 | 0.9651 |

0.1 | 0.4538 | 0.3257 | 0.8796 |

0.15 | 0.6514 | 0.5647 | 0.6275 |

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## Share and Cite

**MDPI and ACS Style**

Guo, Y.; Cao, X.; Liu, B.; Peng, K.
El Niño Index Prediction Using Deep Learning with Ensemble Empirical Mode Decomposition. *Symmetry* **2020**, *12*, 893.
https://doi.org/10.3390/sym12060893

**AMA Style**

Guo Y, Cao X, Liu B, Peng K.
El Niño Index Prediction Using Deep Learning with Ensemble Empirical Mode Decomposition. *Symmetry*. 2020; 12(6):893.
https://doi.org/10.3390/sym12060893

**Chicago/Turabian Style**

Guo, Yanan, Xiaoqun Cao, Bainian Liu, and Kecheng Peng.
2020. "El Niño Index Prediction Using Deep Learning with Ensemble Empirical Mode Decomposition" *Symmetry* 12, no. 6: 893.
https://doi.org/10.3390/sym12060893