Satellite data-driven and knowledge-informed machine learning model for estimating global internal solitary wave speed

Internal solitary waves (ISW) are widely distributed worldwide and significantly affect the ocean environment and offshore activities. ISW propagation speed is important for ISW forecasts and varies largely globally. This study collected 810 quasi-synchronous optical satellite images with clear ISW signatures in 13 global hotspots to build a large ISW dataset. ISW speed was calculated using extracted ISW wave crest locations and the time difference between satellite image pairs. The dataset contains 57,196 samples, including extracted ISW wave crests and corresponding ISW phase speed. We developed an ISW propagation speed (IPS) model based on the dataset using machine learning techniques. The model structure includes clustering and regression algorithms. The model adopts two tailored modifications to incorporate the ISW domain knowledge and solve the ISW sample distribution imbalance problems. Implementation domain knowledge (IDK) includes selecting relevant ocean factors and ISW properties based on oceanography theory and remote sensing imaging mechanisms. The second tailored modification is adopting advanced model architecture (AMA) by introducing the Gaussian clustering algorithm to classify ISW samples into several groups beyond the limitation of space and time. The extreme gradient boosting regression algorithm was applied in each group to build the IPS model. We used 47,425 samples as the training dataset and the remaining 9771 samples as the test dataset. The model-predicted ISW speed shows good accuracy, with a root mean square error/relative error rate (RER) of 0.16 (7.9) and 0.30 m/s (12.7%) on the training and test dataset. Analysis shows that IDK and AMA improve the model performance by 19.4% and 13.1%, respectively. With a one-pixel error in the peak-to-peak distance of input parameters, the model results degraded from 0.30 m/s to 0.33 m/s. The IPS model was applied to estimate ISW speeds in ocean regions besides the 13 hotspots, and the average RER is 6.0%. ISW forecast in seven ocean areas was tested, and the results indicate that the IPS model can describe ISW propagation patterns. The model results reveal that the ISW phase speed strongly correlates with the spring and neap tide. The IPS model results show that ISW speed is decreased with a deepening stratification. Model-predicted global ISW propagation speed comparison shows that the Celebes Sea and North-West of South America has the fastest and slowest propagating ISWs all year around, respectively. Discussion on the background current's influence on the IPS model results is presented.