Deep learning-enhanced ensemble-based data assimilation for high-dimensional nonlinear dynamical systems

Data assimilation (DA) is a key component of many forecasting models in science and engineering. DA allows one to estimate better initial conditions using an imperfect dynamical model of the system and noisy/sparse observations available from the system. Ensemble Kalman filter (EnKF) is a DA algorithm that is widely used in applications involving high-dimensional nonlinear dynamical systems. However, EnKF requires evolving large ensembles of forecasts using the dynamical model of the system. This often becomes computationally intractable, especially when the number of states of the system is very large, e.g., for weather prediction. With small ensembles, the estimated background error covariance matrix in the EnKF algorithm suffers from sampling error, leading to an erroneous estimate of the analysis state (initial condition for the next forecast cycle). In this work, we propose hybrid ensemble Kalman filter (H-EnKF), which is applied to a two-layer quasi-geostrophic turbulent flow as a test case. This framework utilizes a pre-trained deep learning-based data-driven surrogate that inexpensively generates and evolves a large data-driven ensemble of the states to accurately compute the background error covariance matrix with smaller sampling errors. The H-EnKF framework outperforms EnKF with only dynamical model or only the data-driven surrogate, and estimates a better initial condition without the need for any ad-hoc localization strategies. H-EnKF can be extended to any ensemble-based DA algorithm, e.g., particle filters, which are currently too expensive to use for high-dimensional systems. (c) 2023 Elsevier Inc. All rights reserved.

Automated summary

Data assimilation (DA) is a crucial part of forecasting models, allowing for better estimation of initial conditions in imperfect dynamical systems using observations. Ensemble Kalman filter (EnKF) is a widely-used DA algorithm, but its computational complexity is problematic for large systems. In this study, a hybrid ensemble Kalman filter (H-EnKF) is proposed, utilizing a data-driven surrogate to generate a large ensemble and accurately compute the background error covariance matrix. H-EnKF outperforms EnKF without the need for ad-hoc localization strategies, making it applicable to high-dimensional systems.