Significant wave height forecasts integrating ensemble empirical mode decomposition with sequence-to-sequence model
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Abstract: As wave height is an important parameter in marine climate measurement, its accurate prediction is crucial in ocean engineering. It also plays an important role in marine disaster early warning and ship design, etc. However, challenges in the large demand for computing resources and the improvement of accuracy are currently encountered. To resolve the above mentioned problems, sequence-to-sequence deep learning model (Seq-to-Seq) is applied to intelligently explore the internal law between the continuous wave height data output by the model, so as to realize fast and accurate predictions on wave height data. Simultaneously, ensemble empirical mode decomposition (EEMD) is adopted to reduce the non-stationarity of wave height data and solve the problem of modal aliasing caused by empirical mode decomposition (EMD), and then improves the prediction accuracy. A significant wave height forecast method integrating EEMD with the Seq-to-Seq model (EEMD-Seq-to-Seq) is proposed in this paper, and the prediction models under different time spans are established. Compared with the long short-term memory model, the novel method demonstrates increased continuity for long-term prediction and reduces prediction errors. The experiments of wave height prediction on four buoys show that the EEMD-Seq-to-Seq algorithm effectively improves the prediction accuracy in short-term (3-, 6-, 12-, and 24-h forecast horizon) and long-term (48-, and 72-h forecast horizon) predictions.
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Key words:
- Significant wave height /
- wave forecasting /
- EEMD /
- Seq-to-Seq /
- long short-term memory
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Figure 7. Comparison of SWH forecasts of different models for buoy 41040 at the (a) 3-, (b) 6-, (c) 12- and (d) 24-hwindows.
Figure 8. Comparison of SWH forecasts of different models for buoy 41044 at the (a) 3-, (b) 6-, (c) 12- and (d) 24-h windows
Figure 9. Comparison of SWH forecasts of different models for buoy 41046 at the (a) 3-, (b) 6-, (c) 12- and (d) 24-h windows
Figure 10. Comparison of SWH forecasts of different models for buoy 41047 at the (a) 3-, (b) 6-, (c) 12- and (d) 24-h windows
Figure 11. Comparison of EMD-LSTM(blue) and EMD-Seq-to-Seq (orange) SWH forecast errors at the (a) 3-, (b) 6-, (c) 12- and (d) 24-h forecast windows for buoy 41047
Figure 12. Comparison of SWHs of the second, third, fourth and fifth intrinsic mode functions through EMD model (a)–(d) and EEMD model (e)–(h)
Figure 13. Scatter diagram of the observed and predicted SWHs obtained by different algorithms at buoy 41040. (a)–(d) for 3-h forecast window, (e)–(h) for 6-h forecast window, (I)–(l) of 12-h forecast window, (m)–(p) for 24-h forecast window
Table 1. Data statistics of the selected National Data Buoy Center buoys from January 1, 2019 to December 31, 2020.
Buoy ID Latitude/ °N Longitude/ °W Water depth/m No. of observations before interpolation No. of observations after interpolation 41040 14.542 53.341 5159 17,273 17,520 41044 21.582 58.630 5419 17,280 17,520 41046 23.822 68.384 5549 16,924 17,520 41047 27.514 71.494 5321 17,234 17,520 
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Table 2. Comparisons of error statistics among four algorithms at 3-, 6-, 12-, 24-, 48- and 72-h forecast windows for buoy 41040
Time span LSTM EMD-LSTM EMD-Seq-to-Seq EEMD-Seq-to-Seq RMSE/m MAE/m MAPE/% R RMSE/m MAE/m MAPE/% R RMSE/m MAE/m MAPE/% R RMSE/m MAE/m MAPE/% R 3 0.17 0.12 6.55 0.95 0.08 0.06 3.25 0.98 0.08 0.06 3.25 0.99 0.08 0.06 3.18 0.99 6 0.22 0.15 8.12 0.92 0.10 0.07 3.9224 0.98 0.10 0.07 3.79 0.98 0.09 0.06 3.33 0.99 12 0.29 0.21 11.08 0.84 0.14 0.10 5.32 0.97 0.14 0.10 5.18 0.93 0.11 0.08 4.32 0.98 24 0.39 0.28 14.93 0.69 0.21 0.15 7.93 0.92 0.20 0.14 7.45 0.93 0.16 0.12 6.04 0.96 48 0.48 0.34 18.43 0.47 0.31 0.21 11.50 0.83 0.31 0.22 11.66 0.83 0.27 0.18 9.32 0.87 72 0.51 0.37 20.02 0.36 0.38 0.26 15.24 0.74 0.38 0.29 15.28 0.70 0.38 0.29 14.89 0.70
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Table 3. Comparisons of error statistics among four algorithms at 3-, 6-, 12-, 24-, 48- and 72-h forecast windows for buoy 41044
Time
spanLSTM EMD-LSTM EMD-Seq-to-Seq EEMD-Seq-to-Seq RMSE/m MAE/m MAPE/% R RMSE/m MAE/m MAPE/% R RMSE/m MAE/m MAPE/% R RMSE/m MAE/m MAPE/% R 3 0.21 0.13 7.25 0.95 0.11 0.07 3.59 0.99 0.11 0.08 4.24 0.99 0.08 0.05 2.93 0.99 6 0.27 0.17 9.23 0.92 0.14 0.08 4.42 0.98 0.14 0.09 4.98 0.98 0.09 0.06 3.63 0.99 12 0.38 0.24 13.22 0.82 0.21 0.12 6.33 0.97 0.20 0.13 7.08 0.96 0.13 0.09 4.99 0.98 24 0.54 0.34 18.90 0.52 0.33 0.20 10.95 0.88 0.33 0.20 14.61 0.89 0.21 0.14 7.44 0.91 48 0.65 0.42 23.93 0.31 0.51 0.31 18.32 0.72 0.47 0.30 15.16 0.75 0.32 0.21 10.85 0.88 72 0.68 0.44 25.73 0.16 0.53 0.32 18.79 0.72 0.51 0.33 17.14 0.73 0.48 0.32 16.87 0.72
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Table 4. Comparisons of error statistics among four algorithms at 3-, 6-, 12-, 24-, 48- and 72-h forecast windows for buoy 41046
Time span LSTM EMD-LSTM EMD-Seq-to-Seq EEMD-Seq-to-Seq RMSE/m MAE/m MAPE/% R RMSE/m MAE/m MAPE/% R RMSE/m MAE/m MAPE/% R RMSE/m MAE/m MAPE/% R 3 0.23 0.15 8.59 0.95 0.11 0.07 4.03 0.99 0.12 0.08 4.61 0.99 0.08 0.06 3.13 0.99 6 0.29 0.19 11.12 0.91 0.13 0.09 5.09 0.98 0.13 0.09 5.13 0.98 0.09 0.06 3.44 0.99 12 0.41 0.26 15.92 0.83 0.19 0.13 7.31 0.96 0.18 0.12 6.68 0.97 0.12 0.09 4.81 0.99 24 0.55 0.37 22.64 0.66 0.30 0.20 11.38 0.91 0.27 0.18 10.42 0.93 0.21 0.15 8.09 0.96 48 0.67 0.46 28.75 0.41 0.42 0.31 16.84 0.83 0.38 0.27 15.32 0.85 0.32 0.22 12.35 0.90 72 0.71 0.49 30.60 0.30 0.47 0.34 18.48 0.77 0.46 0.33 18.66 0.77 0.42 0.30 16.54 0.83
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Table 5. Comparisons of error statistics among four algorithms at 3-, 6-, 12-, 24-, 48- and 72-h forecast windows for buoy 41047
Time span LSTM EMD-LSTM EMD-Seq-to-Seq EEMD-Seq-to-Seq RMSE/m MAE/m MAPE/% R RMSE/m MAE/m MAPE/% R RMSE/m MAE/m MAPE/% R RMSE/m MAE/m MAPE/% R 3 0.25 0.16 9.39 0.96 0.13 0.07 3.97 0.99 0.11 0.07 4.12 0.99 0.10 0.06 3.91 0.99 6 0.33 0.21 12.43 0.93 0.13 0.09 4.95 0.98 0.12 0.08 4.74 0.99 0.11 0.07 4.56 0.99 12 0.45 0.30 18.13 0.85 0.21 0.13 7.35 0.97 0.19 0.12 6.90 0.97 0.15 0.11 6.16 0.98 24 0.63 0.43 26.43 0.68 0.39 0.26 13.01 0.91 0.37 0.24 12.53 0.91 0.25 0.17 10.03 0.96 48 0.79 0.55 34.01 0.40 0.58 0.38 20.85 0.79 0.55 0.38 22.03 0.78 0.39 0.27 16.81 0.89 72 0.83 0.59 36.52 0.25 0.62 0.43 23.76 0.71 0.60 0.42 24.95 0.72 0.49 0.36 19.85 0.82
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