MPST: effective significant wave height prediction method based on multiscale physical space-time-frequency fusion

Abstract

Accurate prediction of significant wave height is crucial for maritime safety, offshore engineering, and disaster mitigation. Recent advancements in deep learning have improved wave height prediction by utilizing historical data. However, ocean waves exhibit highly complex and distinct dynamic characteristics across various temporal and spatial scales, resulting in intricate nonlinear couplings between spatial and frequency components. Since conventional methods primarily rely on feature extraction in the space-time domains, they cannot capture multiscale physical variations in wave dynamics accurately, ultimately limiting predictive accuracy. To address this limitation, we propose an effective wave height prediction method based on multiscale physical space-time-frequency (PSTF) fusion (MPST). The proposed method integrates two key modules: the multiscale feature extraction (MSFE) module, which utilizes atrous spatial pyramid pooling to enhance local-global wave characteristic extraction, and the PSTF information fusion module, which combines a Fourier neural operator and a Transformer to fuse frequency and spatial features dynamically. A gated fusion mechanism further optimizes feature weighting, improving accuracy and robustness. Experimental results on the ERA5 dataset show that MPST reduces overall prediction error by 7.43% compared to state-of-the-art methods. Notably, in high-wave regions (above 2, 4, and 8 m), prediction accuracy improves by 5.86%, 3.46%, and 8.84%, respectively. These findings highlight better stability and adaptability of the MPST in complex ocean environments. Thus, MPST offers a robust solution for precise wave height prediction and supports maritime safety and sustainable ocean engineering.

Keywords

Effective wave height prediction / Multiscale feature extraction / Fourier neural operator / Transformer / Atrous spatial pyramid pooling

References

[1] AhmadZ, MansurovaM. Machine learning approach to predict significant wave height. J Math Mech Comput Sci, 2021, 110(2): 87-96.

[2] Ajeesh K, Deka PC (2015) Forecasting of significant wave height using support vector regression. In: 2015 Fifth International Conference on Advances in Computing and Communications (ICACC). IEEE, pp 50–53. https://doi.org/10.1109/ICACC.2015.109

[3] AtteiaG, CollinsMJ, AlgarniAD, SameeNA. Deep-learning-based feature extraction approach for significant wave height prediction in SAR mode altimeter data. Remote Sens, 2022, 1421. 5569

[4] BadieiP, MousaviS. The third generation spectral wave model, WAVEWATCH-III enhanced for use in nearshore regions. J Civil Surv Eng, 2010, 44(2): 289-302

[5] BojesomoA, AlMarzouqiH, LiatsisP. A novel transformer network with shifted window cross-attention for spatiotemporal weather forecasting. IEEE J Sel Top Appl Earth Observ Remote Sens, 2024, 17: 45-55.

[6] Caeiro N (2017) Simulation of wave climate in the Nazare area using WAVEWATCH-III. Technical Report

[7] CaoHW, LiuGL, HuoJD, GongX, WangYC, ZhaoZG, et al.. Multi factors-PredRNN based significant wave height prediction in the Bohai, Yellow, and East China Seas. Front Mar Sci, 2023, 10. 1197145

[8] ChenJH. Spectrum features analysis of ocean wind and wave based on fast Fourier transform algorithm. J Coast Res, 2018, 83(sp1): 418-422.

[9] Dhanistha WL, Suntoyo Rosyid DM, Akbar R (2024) Design of wave spectrum in the Java Sea. IOP Conf Ser-Earth Environ Sci 1298:012028. https://doi.org/10.1088/1755-1315/1298/1/012028

[10] Domala V, Kim TW (2022) A univariate and multivariate machine learning approach for prediction of significant wave height. In: OCEANS 2022. Hampton Roads. IEEE, pp 1–7. https://doi.org/10.1109/OCEANS47191.2022.9977028

[11] FengXC, XuH. Multi-station collaborative wave height prediction based on multi-feature identification and interpretable analysis. Phys Fluids, 2024, 367. 076617

[12] FengZJ, HuP, LiSQ, MoDX. Prediction of significant wave height in offshore China based on the machine learning method. J Mar Sci Eng, 2022, 106. 836

[13] HanL, JiQY, JiaXY, LiuY, HanGQ, LinXY. Significant wave height prediction in the South China Sea based on the ConvLSTM algorithm. J Mar Sci Eng, 2022, 1011. 1683

[14] HouBY, FuHJ, LiX, SongT, ZhangZY. Predicting significant wave height in the South China Sea using the SAC-ConvLSTM model. Front Mar Sci, 2024, 11. 1424714

[15] HouSY, LiWG, LiuTY, ZhouSG, GuanJH, QinRF, et al.. D2CL: a dense dilated convolutional LSTM model for sea surface temperature prediction. IEEE J Sel Top Appl Earth Obs Remote Sens, 2021, 14: 12514-12523.

[16] Jiang TS, Ren JL, Shen CQ (2014) Simulation of significant wave height in the shallow shelf area by SWAN model and its improvement. Mar Forecast 31(4):9–17. https://doi.org/10.11737/j.issn.1003-0239.2014.04.002

[17] Kousal J, Liu Q, Staneva J, Behrens A, Günther H, Bidlot JR et al (2022) Introducing observation-based physics into the wam wave model. In: International Conference on Offshore Mechanics and Arctic Engineering. American Society of Mechanical Engineers, p V002T02A005

[18] Kwon JW, Chang WD, Yang YJ (2023) Significant wave height prediction from X-band marine radar images using deep learning with 3D convolutions. PLoS One 18(10):e0292884. https://doi.org/10.1371/journal.pone.0292884

[19] Li ZY, Kovachki N, Azizzadenesheli K, Liu B, Bhattacharya K, Stuart A et al (2020) Fourier neural operator for parametric partial differential equations. Preprint at arXiv:2010.08895

[20] Littardi A, Hildeman A, Nicolaou MA (2022) Deep learning on the sphere for multi-model ensembling of significant wave height. In: ICASSP 2022–2022 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP). IEEE, pp 3828–3832. https://doi.org/10.1109/ICASSP43922.2022.9747289

[21] LiuJJ, JinBG, WangL, XuLY. Sea surface height prediction with deep learning based on attention mechanism. IEEE Geosci Remote Sens Lett, 2020, 191501605.

[22] Mahjoobi J, Shahidi AE (2007) Application of decision tree techniques for the prediction of significant wave height. In: 2007 OCEANS Conference. IEEE, pp 935–938

[23] MaseH, KitanoT. Spectrum-based prediction model for random wave transformation over arbitrary bottom topography. Coast Eng J, 2000, 42(1): 111-151.

[24] Muliati Y, Tawekal RL, Wurjanto A, Kelvin J, Pranowo WS (2018) Application of SWAN model for hindcasting wave height in Jepara coastal waters, North Java, Indonesia. Int J GEOMATE 15(48):114–120. https://doi.org/10.21660/2018.48.56067

[25] ObakrimS, AilliotP, MonbetV, RaillardN. Statistical modeling of the space-time relation between wind and significant wave height. Adv Stat Clim Meteorol Oceanogr, 2023, 9(1): 67-81.

[26] OleinikPH, TavaresGP, MachadoBN, IsoldiLA. Transformation of water wave spectra into time series of surface elevation. Earth, 2021, 2(4): 997-1005.

[27] OuyangZX, GaoYT, ZhangXF, WuXY, ZhangDJ. Significant wave height forecasting based on EMD-TimesNet networks. J Mar Sci Eng, 2024, 124. 536

[28] PanigrahiJK, SwainJ. Numerical simulation and validation of deepwater spectral wind-waves. Mar Geod, 2010, 33(1): 39-52.

[29] PariseCK, FarinaL. Ocean wave modes in the South Atlantic by a short-scale simulation. Tellus A-Dyn Meteorol Oceanogr, 2012, 641. 17362

[30] PokhrelP, IoupE, SimeonovJ, HoqueMT, AbdelguerfiM. A transformer-based regression scheme for forecasting significant wave heights in oceans. IEEE J Ocean Eng, 2022, 47(4): 1010-1023.

[31] Qiao BY, Wu ZQ, Tang Z, Wu G (2021) Sea surface temperature prediction approach based on 3D CNN and LSTM with attention mechanism. In: 2021 23rd International Conference on Advanced Communication Technology (ICACT). IEEE, pp 342–347. https://doi.org/10.23919/ICACT51234.2021.9370514

[32] SangalugemeC, LuhungaP, KijaziA, KabelwaH. Validation of operational WAVEWATCH III wave model against satellite altimetry data over South West Indian Ocean off-coast of Tanzania. Appl Phys Res, 2018, 10(4): 55-65.

[33] ShahabiS, KhanjaniMJ, KermaniMrH. Significant wave height forecasting using GMDH model. Int J Comput Appl, 2016, 133(16): 13-16.

[34] SonB, DoK. Optimization of SWAN wave model to improve the accuracy of winter storm wave prediction in the East Sea. J Ocean Eng Technol, 2021, 35(4): 273-286.

[35] SongT, HanRS, MengF, WangJR, WeiW, PengSQ. A significant wave height prediction method based on deep learning combining the correlation between wind and wind waves. Front Mar Sci, 2022, 9. 983007

[36] SongT, WangJR, HuoJD, WeiW, HanRS, XuDY, et al.. Prediction of significant wave height based on EEMD and deep learning. Front Mar Sci, 2023, 10. 1089357

[37] SunJC, WeiZX, XuTF, SunM, LiuK, YangYZ, et al.. Development of a fine-resolution atmosphere-wave-ocean coupled forecasting model for the South China Sea and its adjacent seas. Acta Oceanol Sin, 2019, 38(4): 154-166.

[38] Surapaneni P (2023) Neural network prediction of ocean wave behavior using frequency domain mapping. In: OCEANS 2023–MTS/IEEE US Gulf Coast. IEEE, pp 1–6. https://doi.org/10.23919/OCEANS52994.2023.10337361

[39] Tan JM, Zhu JX, Li XY, Ren XL, Zhao CW (2022) OSP-FEAN: optimizing significant wave height prediction with feature engineering and attention network. In: 2022 IEEE International Conference on Systems, Man, and Cybernetics (SMC). IEEE, pp 2201–2208. https://doi.org/10.1109/SMC53654.2022.9945106

[40] Pushpam PMM, Enigo VSF (2020) Forecasting significant wave height using RNN-LSTM models. In: 2020 4th International Conference on Intelligent Computing and Control Systems (ICICCS). IEEE, pp 1141–1146. https://doi.org/10.1109/ICICCS48265.2020.9121040

[41] Van der Westhuysen AJ (2002) The application of the numerical wind wave model SWAN to a selected field case on the South African coast. PhD thesis, University of Stellenbosch

[42] Wang H, Fu DY, Liao S, Wang GC, Xiao XC (2019) Significant wave height prediction based on MSFD neural network. In: 2019 10th International Conference on Intelligent Control and Information Processing (ICICIP). IEEE, pp 1–5. https://doi.org/10.1109/ICICIP47338.2019.9012194

[43] Wen GG, Li ZY, Azizzadenesheli K, Anandkumar A, Benson SM (2022) U-FNO-an enhanced fourier neural operator-based deep-learning model for multiphase flow. Adv Water Resour 163:104180. https://doi.org/10.1016/j.advwatres.2022.104180

[44] WeynJA, DurranDR, CaruanaR. Improving data-driven global weather prediction using deep convolutional neural networks on a cubed sphere. J Adv Model Earth Syst, 2020, 129. e2020MS002109

[45] Yang YJ (2021) Simulation and modelling for a three-dimensional ocean surface wave using and inverse Fourier transform. Preprint at https://doi.org/10.20944/preprints202105.0134.v1

[46] YuanY, YuFJ, ChenZ, LiXD, HouF, GaoYY, et al.. Towards a real-time modeling of global ocean waves by the fully GPU-accelerated spectral wave model WAM6-GPU v1.0. Geosci Model Dev, 2024, 17(16): 6123-6136.

[47] ZhangXN, DaiH. Significant wave height prediction with the CRBM-DBN model. J Atmos Ocean Technol, 2019, 36(3): 333-351.

[48] ZhouSY, BethelBJ, SunWJ, ZhaoY, XieWH, DongCM. Improving significant wave height forecasts using a joint empirical mode decomposition-long short-term memory network. J Mar Sci Eng, 2021, 97. 744

[49] Zuo SY, Wang DZ, Wang X, Suo LJ, Liu SW, Zhao YQ et al (2024) Wave height and period estimation from X-band marine radar images using convolutional neural network. J Mar Sci Eng 12(2):311. https://doi.org/10.3390/jmse12020311

Funding

Fundamental Research Funds for the Central Universities(202042008)

National Natural Science Foundation of China-Shandong Joint Fund for Marine Science Research Centers(62172376)

Natural Science Foundation of Shandong Province(ZR2024QF040)

RIGHTS & PERMISSIONS

The Author(s)