A machine‐learning and data assimilation forecasting framework for surface waves

• Published in: Quarterly journal of the Royal Meteorological Society Vol. 150; no. 759; pp. 958 - 975
• Main Authors: Pokhrel, Pujan, Abdelguerfi, Mahdi, Ioup, Elias
• Format: Journal Article
• Language: English
• Published: Chichester, UK John Wiley & Sons, Ltd 01.01.2024; Wiley Subscription Services, Inc
• Subjects: Altimeters; Buoys; Data assimilation; Data collection; Geographical coordinates; Interpolation; Mathematical models; model error; Numerical models; residual correction; Surface waves; Wave height; wave parameters; WaveWatch; Weather forecasting
• ISSN: 0035-9009; 1477-870X
• DOI: 10.1002/qj.4631

In this article, we combine deep symbolic regression (DSR) and ensemble optimal interpolation‐based data assimilation (DA) methods to correct the error in forecasts from the numerical model WaveWatch III. In our experiments, DA and DSR training is performed on hindcasts and then the model is integrated forward in time using both the numerical model and the symbolic expressions generated from the DSR procedure to generate the forecasts. The DSR method is utilized in this article to generate the symbolic equations that correct the model error in the WaveWatch III/ DA system. The proposed algorithm takes the zonal (u$$ u $$) and meridional (v$$ v $$) wind components from Global Forecast System (GFS) forecasts, wave heights from WaveWatch III, and geographical coordinates (latitude and longitude) to model physical relationships not included in the original numerical model. The DA is performed using Jason‐2 and Satellite with ARgos and ALtiKa (SARAL) altimeter measurements, and the independent testing uses in situ buoys. The root‐mean‐squared deviation (RMSD) of the proposed method is better than that of the numerical model with/without DA for up to 42 hr with only 12 days of assimilation spin‐up cycle. The symbolic equation generated from the proposed framework can be used to correct the predictions from WaveWatch III for weather prediction. This paper introduces a deep symbolic regression‐based methodology to correct errors in the Wavewatch III numerical model. The Machine Learning algorithm can be trained during the assimilation period and the residuals can be added during the forward run of the model and added back to the original model to make predictions. The proposed setup outperforms the Wavewatch III free and assimilated runs.