Modern data-driven surrogate models for weather forecasting provide accurate short-term predictions but inaccurate and nonphysical long-term forecasts. This paper investigates online weather prediction using machine learning surrogates supplemented with partial and noisy observations. We empirically demonstrate and theoretically justify that, despite the long-time instability of the surrogates and the sparsity of the observations, filtering estimates can remain accurate in the long-time horizon. As a case study, we integrate FourCastNet, a state-of-the-art weather surrogate model, within a variational data assimilation framework using partial, noisy ERA5 data. Our results show that filtering estimates remain accurate over a year-long assimilation window and provide effective initial conditions for forecasting tasks, including extreme event prediction.

使用机器学习代理模型和部分、嘈杂观测，本研究调查在线天气预测。我们经验性地证明并理论上证明，尽管代理模型长期不稳定且观测稀疏，但滤波估计在长期时间范围内仍然准确。作为一个案例研究，我们在变分数据同化框架中使用FourCastNet，一种最先进的天气代理模型，使用部分、嘈杂的ERA5数据。我们的结果表明，在一年的同化窗口中，滤波估计保持准确，并为包括极端事件预测在内的预测任务提供有效的初始条件。

使用机器学习代理模型的数据同化研究：以FourCastNet为例