Marc Bocquet and his co-authors replace the assumption of a Gaussian model error with a stochastic forecast learnt through data assimilation, yielding clear benefits when observations are incomplete.
Data assimilation, which combines observations and models to estimate the state of the atmosphere or ocean, is often based on a simplifying assumption: the model error would be additive Gaussian noise. Marc Bocquet, Tobias S. Finn, and Sibo Cheng propose to replace it with a learned generative model, which provides a stochastic approximation of the next state from the present state, and thus captures much more complex model errors.
A new ensemble Kalman filter
The authors derive a variant of a low-constraint 4D-Var scheme, implemented in the form of an ensemble variational algorithm called IEnKF-G, which generalizes the classical iterative ensemble Kalman filter (IEnKF-Q). They extend it to a straightener covering several time steps and propose a simplified version.
Tested on a stochastic version of Lorenz's 1963 model, then on a multi-scale variant of Lorenz 1996 where small-scale hidden variables perturb the solved variables, IEnKF-G is generally more accurate than reference methods, especially when the observations are partial and the model error is large. This is a way to improve weather and climate model forecasts by combining generative learning and classical methods.
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