A Machine Learning and Data Assimilation forecasting framework for surface waves

In this paper, we combine Deep symbolic regression (DSR) and Ensemble Optimal Interpolation-based Data Assimilation (DA) method to correct the error in the forecasts from the numerical model, WaveWatch III. In our experiments, the DA and DSR training is performed on the hindcasts and then the model is integrated forward in time with both the numerical model and the symbolic expressions generated from the DSR procedure to generate the forecasts. The DSR method is utilized in this paper to generate the symbolic equations that correct the model error in the WaveWatch III/ DA system. The proposed algorithm takes the zonal (u) and meridional (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 SARAL altimeter measurements, and the independent testing uses the in situ buoys The RMSD of the proposed method is better than the numerical model with/without DA for up to 42 hours 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.