Are AI Data-Driven Weather Models Learning Atmospheric Physics? Initial Condition Sensitivity Analysis of Cyclone Xynthia.

A significant portion of atmospheric predictability is determined by initial condition uncertainty. Small errors in the initial condition will continue to grow as a function of forecast lead time amplified by the non-linear nature of the atmosphere (Lorenz 1969). Sensitivity analysis allows us to examine how a target forecast metric of interest (K), e.g., kinetic energy over Western Europe, responds to (infinitesimal) perturbations to the atmospheric patterns at the initial time (Xi), i.e., the gradient ∂K/∂Xi. Similar techniques are also used for parameter estimation, data assimilation and model assessment. Artificial Intelligence (AI) data-driven models based on neural networks provide efficient pathways for the computation of the sensitivities by means of the backpropagation algorithm. While the impressive forecast skill of these global weather models is being thoroughly studied and documented (Pathak et al., 2022; Bonev et al., 2023; Lam et al., 2023; Chen et al., 2023; Lang et al., 2024; Charlton-Perez et al., 2024; Kochkov et al., 2024), their source of predictability has been less explored (Hakim and Masanam 2024; Vonich and Hakim 2024). In this study, initial condition sensitivity fields for Cyclone Xynthia (severe cyclone with high winds that impacted Europe in February 2010) are compared by means of an AI data-driven model —the Spherical Fourier Neural Operator (SFNO)— and a dynamical model (reference), 1) to examine the physical consistency of the relationships learned by the AI model, and 2) to assess the potential of these tools for sensitivity analyses. Our results suggest that both the AI and dynamical models point to a small filament of moisture within an atmospheric river at initial time as playing an important role in the subsequent evolution of the cyclone. Vertical profiles of the sensitivities from the two models are almost identical, tilting against the vertical shear with height. Perturbations in the identified sensitive areas, with magnitudes in accordance with estimates of initial condition uncertainty, suggest the possibility of an even more extreme event than the one actually happened. The remarkable similarity between the sensitivity fields from the AI and dynamical models exemplifies the physically-based relationships relevant for predictability learned by the AI model, fostering confidence in these tools. This study also illustrates the potential of AI models for their use in predictability and sensitivity studies.

References

Bi, K., Xie, L., Zhang, H., Chen, X., Gu, X., & Tian, Q. (2023). Accurate medium-range global weather forecasting with 3D neural networks. Nature, 619(7970), 533-538.

Bonev, B., Kurth, T., Hundt, C., Pathak, J., Baust, M., Kashinath, K., & Anandkumar, A. (2023, July). Spherical fourier neural operators: Learning stable dynamics on the sphere. In International conference on machine learning (pp. 2806-2823). PMLR.

Charlton-Perez, A. J., Dacre, H. F., Driscoll, S., Gray, S. L., Harvey, B., Harvey, N. J., ... & Volonté, A. (2024). Do AI models produce better weather forecasts than physics-based models? A quantitative evaluation case study of Storm Ciarán. npj Climate and Atmospheric Science, 7(1), 93.

Chen, L., Zhong, X., Zhang, F., Cheng, Y., Xu, Y., Qi, Y., & Li, H. (2023). FuXi: A cascade machine learning forecasting system for 15-day global weather forecast. npj Climate and Atmospheric Science, 6(1), 190.

Doyle, J. D., Amerault, C., Reynolds, C. A., & Reinecke, P. A. (2014). Initial condition sensitivity and predictability of a severe extratropical cyclone using a moist adjoint. Monthly Weather Review, 142(1), 320-342.

Errico, R. M. (1997). What is an adjoint model?. Bulletin of the American Meteorological Society, 78(11), 2577-2592.

Hakim, G. J., & Masanam, S. (2024). Dynamical tests of a deep-learning weather prediction model. Artificial Intelligence for the Earth Systems.

Kochkov, D., Yuval, J., Langmore, I., Norgaard, P., Smith, J., Mooers, G., ... & Hoyer, S. (2024). Neural general circulation models for weather and climate. Nature, 1-7.

Lam, R., Sanchez-Gonzalez, A., Willson, M., Wirnsberger, P., Fortunato, M., Alet, F., ... & Battaglia, P. (2023). Learning skillful medium-range global weather forecasting. Science, 382(6677), 1416-1421.

Lang, S., Alexe, M., Chantry, M., Dramsch, J., Pinault, F., Raoult, B., ... & Rabier, F. (2024). AIFS-ECMWF's data-driven forecasting system. arXiv preprint arXiv:2406.01465.

Liberato, M. L. R., Pinto, J. G., Trigo, R. M., Ludwig, P., Ordóñez, P., Yuen, D., & Trigo, I. F. (2013). Explosive development of winter storm Xynthia over the Southeastern North Atlantic Ocean. Nat. Hazards Earth Syst. Sci. Discuss, 1, 443-470.

Lorenz, E. N. (1969). The predictability of a flow which possesses many scales of motion. Tellus, 21(3), 289-307.

Pathak, J., Subramanian, S., Harrington, P., Raja, S., Chattopadhyay, A., Mardani, M., ... & Anandkumar, A. (2022). Fourcastnet: A global data-driven high-resolution weather model using adaptive fourier neural operators. arXiv preprint arXiv:2202.11214.

Vonich, P. T., & Hakim, G. J. (2024). Predictability Limit of the 2021 Pacific Northwest Heatwave from Deep-Learning Sensitivity Analysis. arXiv preprint arXiv:2406.05019.