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Geoscientific Model Development An interactive open-access journal of the European Geosciences Union
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Discussion papers
https://doi.org/10.5194/gmd-2019-136
© Author(s) 2019. This work is distributed under
the Creative Commons Attribution 4.0 License.
https://doi.org/10.5194/gmd-2019-136
© Author(s) 2019. This work is distributed under
the Creative Commons Attribution 4.0 License.

Submitted as: development and technical paper 21 May 2019

Submitted as: development and technical paper | 21 May 2019

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This discussion paper is a preprint. It is a manuscript under review for the journal Geoscientific Model Development (GMD).

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 Brajard1,2, Alberto Carrassi1,3, Marc Bocquet4, and Laurent Bertino1 Julien Brajard et al.
  • 1Nansen Center, Thormøhlensgate 47, 5006, Bergen, Norway
  • 2Sorbonne University, CNRS-IRD-MNHN, LOCEAN, Paris, France
  • 3Geophysical Institute, University of Bergen, Norway
  • 4CEREA, joint laboratory École des Ponts ParisTech and EDF R&D, Université Paris-Est, Champs-sur-Marne, France

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 et al.
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Julien Brajard et al.
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 et al.
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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.
We explore the possibility of combining data assimilation with machine learning. We introduce a...
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