Improving Significant Wave Height Forecasts Using a Joint Empirical Mode Decomposition–Long Short-Term Memory Network
Abstract
:1. Introduction
2. Data and Methodology
2.1. Buoy Data and Data Preprocessing
2.2. The Long Short-Term Memory Network
2.3. Empirical Mode Decomposition
- For signal, identify all the maxima and minima.
- Through a cubic spline interpolation, fit upper and lower envelopes of signal . The mean of the two envelopes is the average envelope curve :
- To obtain an IMF candidate, subtract m from :
- If does not satisfy the two IMF conditions, then is set as the original signal and the prior step is repeated k times. Here, can be estimated as follows:
- However, if satisfies the two IMF conditions, then define as . The standard deviation is defined as follows:
- To obtain a new signal , subtract from :
- Repeat steps 1–6 until cannot be further decomposed into IMFs. The residual of the original signal is given by The original signal can finally be presented as a collection of n components and a residual :
2.4. Performance Indicators
3. Results
4. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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Buoy ID | Latitude (°N) | Longitude (°W) | Water Depth (m) | No. of Observations before Interpolation | No. of Observations after Interpolation |
---|---|---|---|---|---|
41046 | 23.822 | 68.384 | 5549 | 17,420 | 17,520 |
41047 | 27.514 | 71.494 | 5321 | 17,402 | 17,520 |
LSTM | EMD-LSTM | Degree of Improvement | ||||||||
---|---|---|---|---|---|---|---|---|---|---|
Forecast Hours | RMSE (m) | MAPE (%) | R | RMSE (m) | MAPE (%) | R | RMSE (%) | MAPE (%) | R (%) | |
41046 | 3 | 0.15 | 6.4 | 0.97 | 0.11 | 1.41 | 0.985 | 30.1 | 77.8 | 1.5 |
6 | 0.22 | 9.2 | 0.92 | 0.12 | 6.68 | 0.979 | 44.6 | 27.4 | 6.4 | |
9 | 0.28 | 11.1 | 0.88 | 0.16 | 10.20 | 0.960 | 42.4 | 7.8 | 9.1 | |
12 | 0.33 | 13.2 | 0.84 | 0.19 | 12.01 | 0.950 | 41.1 | 9.2 | 13.1 | |
24 | 0.45 | 19.0 | 0.67 | 0.26 | 11.41 | 0.900 | 41.8 | 39.9 | 34.3 | |
48 | 0.58 | 31.1 | 0.41 | 0.38 | 18.90 | 0.790 | 33.7 | 39.2 | 92.7 | |
72 | 0.60 | 33.7 | 0.32 | 0.44 | 18.70 | 0.690 | 26.1 | 44.5 | 115.6 | |
41047 | 3 | 0.19 | 7.2 | 0.97 | 0.10 | 3.96 | 0.991 | 46.8 | 44.9 | 2.1 |
6 | 0.28 | 11.3 | 0.93 | 0.14 | 5.51 | 0.982 | 50.2 | 51.2 | 5.6 | |
9 | 0.35 | 13.1 | 0.88 | 0.18 | 7.38 | 0.971 | 49.2 | 43.7 | 10.3 | |
12 | 0.40 | 15.0 | 0.83 | 0.21 | 8.42 | 0.957 | 47.0 | 43.9 | 15.3 | |
24 | 0.55 | 22.0 | 0.67 | 0.28 | 11.76 | 0.922 | 48.2 | 46.5 | 37.6 | |
48 | 0.67 | 33.4 | 0.43 | 0.47 | 20.35 | 0.769 | 29.9 | 39.1 | 78.9 | |
72 | 0.71 | 38.8 | 0.34 | 0.48 | 21 | 0.757 | 32.2 | 45.9 | 122.6 |
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Zhou, S.; Bethel, B.J.; Sun, W.; Zhao, Y.; Xie, W.; Dong, C. Improving Significant Wave Height Forecasts Using a Joint Empirical Mode Decomposition–Long Short-Term Memory Network. J. Mar. Sci. Eng. 2021, 9, 744. https://doi.org/10.3390/jmse9070744
Zhou S, Bethel BJ, Sun W, Zhao Y, Xie W, Dong C. Improving Significant Wave Height Forecasts Using a Joint Empirical Mode Decomposition–Long Short-Term Memory Network. Journal of Marine Science and Engineering. 2021; 9(7):744. https://doi.org/10.3390/jmse9070744
Chicago/Turabian StyleZhou, Shuyi, Brandon J. Bethel, Wenjin Sun, Yang Zhao, Wenhong Xie, and Changming Dong. 2021. "Improving Significant Wave Height Forecasts Using a Joint Empirical Mode Decomposition–Long Short-Term Memory Network" Journal of Marine Science and Engineering 9, no. 7: 744. https://doi.org/10.3390/jmse9070744