Significant wave height forecasts integrating ensemble empirical mode decomposition with sequence-to-sequence model

Lina Wang Yu Cao Xilin Deng Huitao Liu Changming Dong

Lina Wang, Yu Cao, Xilin Deng, Huitao Liu, Changming Dong. Significant wave height forecasts integrating ensemble empirical mode decomposition with sequence-to-sequence model[J]. Acta Oceanologica Sinica, 2023, 42(10): 54-66. doi: 10.1007/s13131-023-2246-y
Citation: Lina Wang, Yu Cao, Xilin Deng, Huitao Liu, Changming Dong. Significant wave height forecasts integrating ensemble empirical mode decomposition with sequence-to-sequence model[J]. Acta Oceanologica Sinica, 2023, 42(10): 54-66. doi: 10.1007/s13131-023-2246-y

doi: 10.1007/s13131-023-2246-y

Significant wave height forecasts integrating ensemble empirical mode decomposition with sequence-to-sequence model

Funds: The Project Supported by Southern Marine Science and Engineering Guangdong Laboratory (Zhuhai) under contract No.SML2020SP007; the National Natural Science Foundation of China under contract Nos 42192562 and 62072249.
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    Corresponding author: E-mail: cmdong@nuist.edu.cn;leader author, E-mail: wangln@nuist.edu.cn
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  • Figure  1.  Location of Buoys 41040, 41044, 41046 and 41047 (data acquired from National Data Buoy Center).

    Figure  2.  The flow chart of the ensemble empirical mode decomposition algorithm. m is the mean of the upper and lower envelope; IMF: intrinsic mode function.

    Figure  3.  The structure of the sequence-to-sequence prediction model with attention mechanism. LSTM: long short-term memory; CA: encoded attention vector. The meanings of symbols refer to formula in the text.

    Figure  4.  The structure of long short-term memory neuron.

    Figure  5.  The structure of the ensemble empirical mode decomposition sequence-to-sequence (EEMD-Seq-to-Seq) prediction model. IMFs: intrinsic mode functions.

    Figure  6.  The flowchart of ensemble empirical mode decomposition sequence-to-sequence (EEMD-Seq-to-Seq) prediction model.

    Figure  7.  Comparison of significant wave height (SWH) forecasts of different models for Buoy 41040 at the 3-h (a), 6-h (b), 12-h (c) and 24-h (d) windows. LSTM: long short-term memory; EEMD-Seq-to-Seq: ensemble empirical mode decomposition with the sequence-to-sequence model.

    Figure  8.  Comparison of significant wave height (SWH) forecasts of different models for Buoy 41044 at the 3-h (a), 6-h (b), 12-h (c) and 24-h (d) windows. LSTM: long short-term memory; EEMD-Seq-to-Seq: ensemble empirical mode decomposition with the sequence-to-sequence model.

    Figure  9.  Comparison of significant wave height (SWH) forecasts of different models for Buoy 41046 at the 3-h (a), 6-h (b), 12-h (c) and 24-h (d) windows. LSTM: long short-term memory; EEMD-Seq-to-Seq: ensemble empirical mode decomposition with the sequence-to-sequence model.

    Figure  10.  Comparison of significant wave height (SWH) forecasts of different models for Buoy 41047 at the 3-h (a), 6-h (b), 12-h (c) and 24-h (d) windows. LSTM: long short-term memory; EEMD-Seq-to-Seq: ensemble empirical mode decomposition with the sequence-to-sequence model.

    Figure  11.  Comparison of empirical mode decomposition-long short-term memory (EMD-LSTM) and EMD-sequence-to-sequence significant wave height forecast errors at the 3-h (a), 6-h (b), 12-h (c) and 24-h (d) forecast windows for Buoy 41047.

    Figure  12.  Comparison of significant wave heights (SWHs) of the 2nd, 3rd, 4th and 5th intrinsic mode functions through empirical mode decomposition model (a–d) and ensemble empirical mode decomposition model (e–h).

    Figure  13.  Scatter diagram of the observed and predicted significant wave height (SWHs) obtained by different algorithms at Buoy 41040. a–d for 3-h forecast window, e–h for 6-h forecast window, i–l for 12-h forecast window, m–p for 24-h forecast window.

    Table  1.   Data statistics of the selected buoys from January 1, 2019 to December 31, 2020 (data acquired from National Data Buoy Center)

    Buoy IDLatitudeLongitudeWater depth/mNumber of observations
    (before interpolation)
    Number of observations
    (after interpolation)
    4104014.542°N53.341°W5 15917 27317 520
    4104421.582°N58.630°W5 41917 28017 520
    4104623.822°N68.384°W5 54916 92417 520
    4104727.514°N71.494°W5 32117 23417 520
    下载: 导出CSV

    Table  2.   Comparisons of error statistics among four algorithms at the 3-h, 6-h, 12-h, 24-h, 48-h and 72-h forecast windows for Buoy 41040

    Time spanLSTMEMD-LSTMEMD-Seq-to-SeqEEMD-Seq-to-Seq
    RMSE/mMAE/mMAPE/%RRMSE/mMAE/mMAPE/%RRMSE/mMAE/mMAPE/%RRMSE/mMAE/mMAPE/%R
    3 h0.170.126.550.950.080.063.250.980.080.063.250.990.080.063.180.99
    6 h0.220.158.120.920.100.073.92240.980.100.073.790.980.090.063.330.99
    12 h0.290.2111.080.840.140.105.320.970.140.105.180.930.110.084.320.98
    24 h0.390.2814.930.690.210.157.930.920.200.147.450.930.160.126.040.96
    48 h0.480.3418.430.470.310.2111.500.830.310.2211.660.830.270.189.320.87
    72 h0.510.3720.020.360.380.2615.240.740.380.2915.280.700.380.2914.890.70
    Note: RMSE: root mean square error; MAE: mean absolute error; MAPE: mean absolute percentage error; R: Pearson correlation coefficient; LSTM: long short-term memory; EEMD: ensemble empirical mode decomposition; Seq-to-Seq: sequence-to-sequence deep learning model.
    下载: 导出CSV

    Table  3.   Comparisons of error statistics among four algorithms at the 3-h, 6-h, 12-h, 24-h, 48-h and 72-h forecast windows for Buoy 41044

    Time
    span
    LSTMEMD-LSTMEMD-Seq-to-SeqEEMD-Seq-to-Seq
    RMSE/mMAE/mMAPE/%RRMSE/mMAE/mMAPE/%RRMSE/mMAE/mMAPE/%RRMSE/mMAE/mMAPE/%R
    3 h0.210.137.250.950.110.073.590.990.110.084.240.990.080.052.930.99
    6 h0.270.179.230.920.140.084.420.980.140.094.980.980.090.063.630.99
    12 h0.380.2413.220.820.210.126.330.970.200.137.080.960.130.094.990.98
    24 h0.540.3418.900.520.330.2010.950.880.330.2014.610.890.210.147.440.91
    48 h0.650.4223.930.310.510.3118.320.720.470.3015.160.750.320.2110.850.88
    72 h0.680.4425.730.160.530.3218.790.720.510.3317.140.730.480.3216.870.72
    Note: RMSE: root mean square error; MAE: mean absolute error; MAPE: mean absolute percentage error; R: Pearson correlation coefficient; LSTM: long short-term memory; EEMD: ensemble empirical mode decomposition; Seq-to-Seq: sequence-to-sequence deep learning model.
    下载: 导出CSV

    Table  4.   Comparisons of error statistics among four algorithms at the 3-h, 6-h, 12-h, 24-h, 48-h and 72-h forecast windows for Buoy 41046

    Time spanLSTMEMD-LSTMEMD-Seq-to-SeqEEMD-Seq-to-Seq
    RMSE/mMAE/mMAPE/%RRMSE/mMAE/mMAPE/%RRMSE/mMAE/mMAPE/%RRMSE/mMAE/mMAPE/%R
    3 h0.230.158.590.950.110.074.030.990.120.084.610.990.080.063.130.99
    6 h0.290.1911.120.910.130.095.090.980.130.095.130.980.090.063.440.99
    12 h0.410.2615.920.830.190.137.310.960.180.126.680.970.120.094.810.99
    24 h0.550.3722.640.660.300.2011.380.910.270.1810.420.930.210.158.090.96
    48 h0.670.4628.750.410.420.3116.840.830.380.2715.320.850.320.2212.350.90
    72 h0.710.4930.600.300.470.3418.480.770.460.3318.660.770.420.3016.540.83
    Note: RMSE: root mean square error; MAE: mean absolute error; MAPE: mean absolute percentage error; R: Pearson correlation coefficient; LSTM: long short-term memory; EEMD: ensemble empirical mode decomposition; Seq-to-Seq: sequence-to-sequence deep learning model.
    下载: 导出CSV

    Table  5.   Comparisons of error statistics among four algorithms at the 3-h, 6-h, 12-h, 24-h, 48-h and 72-h forecast windows for Buoy 41047

    Time spanLSTMEMD-LSTMEMD-Seq-to-SeqEEMD-Seq-to-Seq
    RMSE/mMAE/mMAPE/%RRMSE/mMAE/mMAPE/%RRMSE/mMAE/mMAPE/%RRMSE/mMAE/mMAPE/%R
    3 h0.250.169.390.960.130.073.970.990.110.074.120.990.100.063.910.99
    6 h0.330.2112.430.930.130.094.950.980.120.084.740.990.110.074.560.99
    12 h0.450.3018.130.850.210.137.350.970.190.126.900.970.150.116.160.98
    24 h0.630.4326.430.680.390.2613.010.910.370.2412.530.910.250.1710.030.96
    48 h0.790.5534.010.400.580.3820.850.790.550.3822.030.780.390.2716.810.89
    72 h0.830.5936.520.250.620.4323.760.710.600.4224.950.720.490.3619.850.82
    Note: RMSE: root mean square error; MAE: mean absolute error; MAPE: mean absolute percentage error; R: Pearson correlation coefficient; LSTM: long short-term memory; EEMD: ensemble empirical mode decomposition; Seq-to-Seq: sequence-to-sequence deep learning model.
    下载: 导出CSV
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出版历程
  • 收稿日期:  2023-06-10
  • 录用日期:  2023-08-15
  • 网络出版日期:  2023-10-12
  • 刊出日期:  2023-10-01

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