Review of data assimilation methods for refining the results of pollution dispersion models af-ter accidental releases

Data assimilation (DA) is a crucial task in pollution forecasting, as it enables the integration of observations with models, improving the accuracy of pollutant dispersion predictions in the atmosphere, ocean, and land. This is particularly important for assessing the impact of accidental emissions and managing environmental risks. This paper reviews and compares four different data assimilation methods for pollution dispersion following accidental releases. The methods include ensemble-based approaches: the ensemble Kalman filter (EnKF), Ensemble Smoother (ES), and two novel approaches based on machine learning (ML). The mathematical foundations of these methods are justified, and their advantages and drawbacks are analyzed. Ensemble data assimilation methods, particularly EnKF, are computationally efficient and can provide good results even in non-linear models. They require fewer resources compared to classical methods while preserving critical information with a limited ensemble size. However, their drawback is the Gaussian approximation, which can lead to numerical instabilities and non-physical results in problems with non-Gaussian distributions. Additionally, the need for multiple reinitializations can increase computational costs. An alternative is ES, which does not require recursive updates and reduces modeling time but may produce worse results in certain cases, despite its higher computational efficiency. Two hybrid methods that combine data assimilation with machine learning have been examined: the first involves correcting tendencies or resolvents, leveraging a compositional structure that outperforms similar methods without corrections in benchmark problems; the second utilizes a neural network with a non-standard loss function. Both methods have demonstrated the ability to correct model errors and account for biases in forecasts. Hybrid approaches that integrate traditional assimilation techniques with machine learning offer high accuracy while reducing the number of DA-ML cycles.