Many approaches have recently been proposed to combine data assimilation with machine learning for improved forecasts with geophysical models. Here, we focus on combining advanced sequential data assimilation schemes with a generative forecasting model which accounts for complex model errors. This generative model provides a stochastic approximation of the conditional distribution of the successor state given the current state. The proposed variational formulation is a novel one-step weak-constraint 4D-Var scheme in which a learned conditional stochastic forecast replaces the prescribed additive Gaussian model error representation. We derive and implement this formulation as an ensemble variational algorithm, the generative iterative ensemble Kalman filter (IEnKF-G), which generalises the iterative ensemble Kalman filter with additive Gaussian model error (IEnKF-Q). We extend the method to a smoother with an assimilation window spanning multiple time steps and propose a simplified variant. The IEnKF-G is evaluated on a stochastic variant of the Lorenz 1963 model to assess its robustness. It is then tested on a multi-scale variant of the one-dimensional Lorenz 1996 model, in which the resolved variables are affected by model error originating from the hidden small-scale variables. The algorithm is then compared to an ensemble Kalman filter that adaptively mitigates model and sampling errors, and to the IEnKF-Q. The IEnKF-G is generally more accurate in the tested configurations, with substantial gains under partial observations and significant model error. This demonstrates the potential of generative data-driven models when paired with classical data assimilation methods, particularly when model error is substantial.

翻译：暂无翻译