Abstract
Recent studies have shown that it is possible to combine machine learning methods with data assimilation to reconstruct a dynamical system using only sparse and noisy observations of that system. The same approach can be used to correct the error of a knowledge-based model. The resulting surrogate model is hybrid, with a statistical part supplementing a physical part. In practice, the correction can be added as an integrated term (i.e. in the model resolvent) or directly inside the tendencies of the physical model. The resolvent correction is easy to implement. The tendency correction is more technical, in particular it requires the adjoint of the physical model, but also more flexible. We use the two-scale Lorenz model to compare the two methods. The accuracy in long-range forecast experiments is somewhat similar between the surrogate models using the resolvent correction and the tendency correction. By contrast, the surrogate models using the tendency correction significantly outperform the surrogate models using the resolvent correction in data assimilation experiments. Finally, we show that the tendency correction opens the possibility to make online model error correction, i.e. improving the model progressively as new observations become available. The resulting algorithm can be seen as a new formulation of weak-constraint 4D-Var. We compare online and offline learning using the same framework with the two-scale Lorenz system, and show that with online learning, it is possible to extract all the information from sparse and noisy observations.
Highlights
Recent studies have shown that it is possible to combine machine learning methods with data assimilation to reconstruct a dynamical system using only sparse and noisy observations of that system
The accuracy of the model after 8192 is remarkable and in particular the sRMSE is lower than when using the true model! We think that, if we were to extend the experiment with an appropriate tuning for bp, the model would in the end be almost as accurate as if trained offline with the truth, just as in the previous experiment with tendency correction (TC)-CNN-b
The use of data assimilation (DA) is essential here to assimilate sparse and noisy observations, which cannot be rigorously treated with machine learning (ML) methods alone
Summary
Recent studies have shown that it is possible to combine machine learning methods with data assimilation to reconstruct a dynamical system using only sparse and noisy observations of that system. Even though models are affected by errors (e.g., misrepresented physical phenomena, unresolved small-scale processes, numerical integration errors, etc.), they benefit from a long history of modelling and they already provide a solid baseline. For this reason, recent studies focus on using ML techniques for model error correction instead of full model emulation [18,19,20,21,22,23,24,25,26]. The first objective of the present paper is to make an exhaustive comparison of the two methods for both forecast and assimilation experiments in a simplified modelling framework
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