Preprints
https://doi.org/10.5194/gmd-2019-136
https://doi.org/10.5194/gmd-2019-136
Submitted as: development and technical paper
 | 
21 May 2019
Submitted as: development and technical paper |  | 21 May 2019
Status: this preprint was under review for the journal GMD but the revision was not accepted.

Combining data assimilation and machine learning to emulate a dynamical model from sparse and noisy observations: a case study with the Lorenz 96 model

Julien Brajard, Alberto Carrassi, Marc Bocquet, and Laurent Bertino

Abstract. A novel method, based on the combination of data assimilation and machine learning is introduced. The new hybrid approach is designed for a two-fold scope: (i) emulating a hidden, possibly chaotic, dynamics and (ii) predicting its future states. The method applies alternatively a data assimilation step, here an ensemble Kalman filter, and a neural network. Data assimilation is used to combine optimally a surrogate model with sparse noisy data. The resulting analysis is spatially complete and can thus be used as a training set by the neural network to upgrade the surrogate model. The two steps are then repeated iteratively. Numerical experiments have been carried out using the chaotic Lorenz 96, a 40-variables model, proving both convergence and statistical skills. The skill metrics include the short-term forecast skills out to two Lyapunov times, the retrieval of positive Lyapunov exponents and the power density spectrum. The sensitivity of the method to critical setup parameters is also presented: forecast skills decrease smoothly with increased observational noise but drops abruptly if less then half of the model domain is observed. The synergy demonstrated with a low-dimensional system is encouraging for more sophisticated dynamics and motivates further investigation to merge data assimilation and machine learning.

Julien Brajard, Alberto Carrassi, Marc Bocquet, and Laurent Bertino
 
Status: closed
Status: closed
AC: Author comment | RC: Referee comment | SC: Short comment | EC: Editor comment
Printer-friendly Version - Printer-friendly version Supplement - Supplement
 
Status: closed
Status: closed
AC: Author comment | RC: Referee comment | SC: Short comment | EC: Editor comment
Printer-friendly Version - Printer-friendly version Supplement - Supplement
Julien Brajard, Alberto Carrassi, Marc Bocquet, and Laurent Bertino

Model code and software

GMD Code v1.1 J. Brajard, A. Carrassi, M. Bocquet, and L. Bertino https://doi.org/10.5281/zenodo.2925547

Julien Brajard, Alberto Carrassi, Marc Bocquet, and Laurent Bertino

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Latest update: 27 Mar 2024
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Short summary
We explore the possibility of combining data assimilation with machine learning. We introduce a new hybrid method for a two-fold scope: (i) emulating hidden, possibly chaotic, dynamics and (ii) predicting its future states. Numerical experiments have been carried out using the chaotic Lorenz 96 model, proving both the convergence of the hybrid method and its statistical skills including short-term forecasting and emulation of the long-term dynamics.