the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
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
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 et al.


-
RC1: 'Review of Combining data assimilation and machine learning to emulate a dynamical model from sparse and noisy observations: a case study with the Lorenz 96 model', Peter Düben, 06 Jul 2019
-
AC2: 'reply to reviewer 2', Julien Brajard, 26 Aug 2019
-
AC5: '[ERRATUM] answer to reviewer 1', Julien Brajard, 28 Aug 2019
-
AC5: '[ERRATUM] answer to reviewer 1', Julien Brajard, 28 Aug 2019
-
AC2: 'reply to reviewer 2', Julien Brajard, 26 Aug 2019
-
RC2: 'Review', Anonymous Referee #2, 12 Jul 2019
-
AC1: 'reply to reviewer 2', Julien Brajard, 23 Jul 2019
-
AC3: 'reply to the second reviewer', Julien Brajard, 26 Aug 2019
-
AC1: 'reply to reviewer 2', Julien Brajard, 23 Jul 2019
-
SC1: 'Executive editor comment, code and data availability.', David Ham, 26 Jul 2019
-
AC4: 'reply to editor', Julien Brajard, 26 Aug 2019
-
AC4: 'reply to editor', Julien Brajard, 26 Aug 2019


-
RC1: 'Review of Combining data assimilation and machine learning to emulate a dynamical model from sparse and noisy observations: a case study with the Lorenz 96 model', Peter Düben, 06 Jul 2019
-
AC2: 'reply to reviewer 2', Julien Brajard, 26 Aug 2019
-
AC5: '[ERRATUM] answer to reviewer 1', Julien Brajard, 28 Aug 2019
-
AC5: '[ERRATUM] answer to reviewer 1', Julien Brajard, 28 Aug 2019
-
AC2: 'reply to reviewer 2', Julien Brajard, 26 Aug 2019
-
RC2: 'Review', Anonymous Referee #2, 12 Jul 2019
-
AC1: 'reply to reviewer 2', Julien Brajard, 23 Jul 2019
-
AC3: 'reply to the second reviewer', Julien Brajard, 26 Aug 2019
-
AC1: 'reply to reviewer 2', Julien Brajard, 23 Jul 2019
-
SC1: 'Executive editor comment, code and data availability.', David Ham, 26 Jul 2019
-
AC4: 'reply to editor', Julien Brajard, 26 Aug 2019
-
AC4: 'reply to editor', Julien Brajard, 26 Aug 2019
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.
Viewed
HTML | XML | Total | BibTeX | EndNote | |
---|---|---|---|---|---|
1,607 | 1,132 | 62 | 2,801 | 90 | 55 |
- HTML: 1,607
- PDF: 1,132
- XML: 62
- Total: 2,801
- BibTeX: 90
- EndNote: 55
Viewed (geographical distribution)
Country | # | Views | % |
---|
Total: | 0 |
HTML: | 0 |
PDF: | 0 |
XML: | 0 |
- 1
Cited
6 citations as recorded by crossref.
- Predicting critical transitions in multiscale dynamical systems using reservoir computing S. Lim et al. 10.1063/5.0023764
- The Applicability of LSTM-KNN Model for Real-Time Flood Forecasting in Different Climate Zones in China M. Liu et al. 10.3390/w12020440
- Long-term prediction of chaotic systems with machine learning H. Fan et al. 10.1103/PhysRevResearch.2.012080
- Analysis and Development Enlightenment on Source Term Inversion Technology of Nuclear and Chemical Hazards C. Han et al. 10.1051/e3sconf/202021801007
- Data-driven sparse reconstruction of flow over a stalled aerofoil using experimental data D. Carter et al. 10.1017/dce.2021.5
- Learning earth system models from observations: machine learning or data assimilation? A. Geer 10.1098/rsta.2020.0089