Toward combining data assimilation and machine learning to improve weather prediction models

Machine learning (ML) surrogate models of the atmosphere have recently been shown to produce forecasts of similar accuracy as compared to state-of-the-art NWP models [1-3]. ML surrogate models are trained, in large part, using high-resolution reanalysis data, which can cause the model to inherit biases from the numerical model used to produce the reanalysis. Hybrid models, which combine an ML component with a knowledge-based model, have been trained using this same data and can encounter similar difficulties [4, 5]. A promising alternative training technique is to use cyclic data assimilation to simultaneously train the ML model and estimate the model state, allowing one to train the ML model online using partial and noisy observations. We propose a technique for using cyclic data assimilation to simultaneously (a) train a hybrid ML model that corrects an existing numerical forecast model and an existing observation operator and (b) estimate the system state. We test this technique using a "reservoir computer" as our model's ML component and the ensemble transform Kalman filter (ETKF) as our cyclic data assimilation technique. In our tests using toy atmospheric models, we find that ML models trained online using data assimilation produce a more accurate analysis and more accurate forecasts than those trained offline using analyses generated with an imperfect numerical model and/or an imperfect observation operator. We finally explore techniques for reducing the required ensemble size when this technique is implemented using ensemble-based DA techniques.

[1] Pathak J., Subramanian S., Harrington P., Raja S., Chattopadhyay A., Mardani M., Kurth T., Hall D., Li Z., Azizzadenesheli K., Hassanzadeh P., Kashinath K., and Anandkumar A., “FourCastNet: A Global Data-driven High-resolution Weather Model using Adaptive Fourier Neural Operators”, arXiv:2202.11214 (2022).

[2] Lam R., Sanchez-Gonzalez A., Willson M., Wirnsberger P., Fortunato M., Alet F., Ravuri S., Ewalds T., Eaton-Rosen Z., Hu W., Merose A., Hoyer S., Holland G., Vinyals O., Stott J., Pritzel A., Mohamed S., and Battaglia P., “GraphCast: Learning skillful medium-range global weather forecasting”, arXiv:2212.12794 (2022).

[3] Bi K., Xie L., Zhang H., Chen X., Gu X., and Tian Q, “Accurate medium-range global weather forecasting with 3D neural networks”, Nature 619, 533-538 (2023).

[4] Arcomano T., Szunyogh I., Wikner A., Hunt B., and Ott E., “A Hybrid Atmospheric Model Incorporating Machine Learning Can Capture Dynamical Processes Not Captured by Its Physics-Based Component”, Geophysical Research Letters, 50 (2023).

[5] Wikner, A., Pathak, J., Hunt B., Szunyogh, I., Girvan, M., and Ott E., “Using data assimilation to train a hybrid forecast system that combines machine-learning and knowledge-based components”, Chaos, 31, 053114 (2021).