Articles | Volume 25, issue 2
https://doi.org/10.5194/npg-25-387-2018
© Author(s) 2018. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
https://doi.org/10.5194/npg-25-387-2018
© Author(s) 2018. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Research article
| 
28 May 2018
Research article |
| 28 May 2018
| 28 May 2018
Exploring the Lyapunov instability properties of high-dimensional atmospheric and climate models
Royal Meteorological Institute of Belgium, Brussels, Belgium
Sebastian Schubert
Meteorological Institute, CEN, University of Hamburg, Hamburg, Germany
Jonathan Demaeyer
Royal Meteorological Institute of Belgium, Brussels, Belgium
Valerio Lucarini
Meteorological Institute, CEN, University of Hamburg, Hamburg, Germany
Department of Mathematics and Statistics, University of Reading, Reading, UK
Centre for the Mathematics of Planet Earth, University of Reading, Reading, UK
Stéphane Vannitsem
Royal Meteorological Institute of Belgium, Brussels, Belgium
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- Computing Covariant Lyapunov Vectors in Hilbert spaces F. Noethen https://doi.org/10.3934/jcd.2021014
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- Strongly Coupled Data Assimilation in Multiscale Media: Experiments Using a Quasi‐Geostrophic Coupled Model S. Penny et al. https://doi.org/10.1029/2019MS001652
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29 citations as recorded by crossref.
- Inferring the instability of a dynamical system from the skill of data assimilation exercises Y. Chen et al. https://doi.org/10.5194/npg-28-633-2021
- Large deviations in chaotic systems: Exact results and dynamical phase transition N. Smith https://doi.org/10.1103/PhysRevE.106.L042202
- Computing Covariant Lyapunov Vectors in Hilbert spaces F. Noethen https://doi.org/10.3934/jcd.2021014
- Local dimension and recurrent circulation patterns in long-term climate simulations S. Buschow & P. Friederichs https://doi.org/10.1063/1.5031094
- Backpropagation in hyperbolic chaos via adjoint shadowing A. Ni https://doi.org/10.1088/1361-6544/ad1aed
- Impacts of the Lagrangian Data Assimilation of Surface Drifters on Estimating Ocean Circulation during the Gulf of Mexico Grand Lagrangian Deployment L. Sun et al. https://doi.org/10.1175/MWR-D-21-0123.1
- End-to-end Artificial Intelligence to analyze dynamical processes: A linear benchmark test E. Salgarollo et al. https://doi.org/10.1016/j.physd.2025.134880
- Remarkable similarities in distributions of dynamical observables in chaotic systems L. Defaveri & N. Smith https://doi.org/10.1103/2j32-wxjz
- A new mathematical framework for atmospheric blocking events V. Lucarini & A. Gritsun https://doi.org/10.1007/s00382-019-05018-2
- Increasing model vertical resolution may not necessarily lead to improved atmospheric predictability S. Moon et al. https://doi.org/10.1063/5.0081734
- The onset of chaos in nonautonomous dissipative dynamical systems: a low-order ocean-model case study S. Pierini et al. https://doi.org/10.5194/npg-25-671-2018
- Application of a local attractor dimension to reduced space strongly coupled data assimilation for chaotic multiscale systems C. Quinn et al. https://doi.org/10.5194/npg-27-51-2020
- Lyapunov analysis of multiscale dynamics: the slow bundle of the two-scale Lorenz 96 model M. Carlu et al. https://doi.org/10.5194/npg-26-73-2019
- Multiscale fractal dimension analysis of a reduced order model of coupled ocean–atmosphere dynamics T. Alberti et al. https://doi.org/10.5194/esd-12-837-2021
- Extratropical Low‐Frequency Variability With ENSO Forcing: A Reduced‐Order Coupled Model Study S. Vannitsem et al. https://doi.org/10.1029/2021MS002530
- Applications of large deviation theory in geophysical fluid dynamics and climate science V. Gálfi et al. https://doi.org/10.1007/s40766-021-00020-z
- Impact of tropical teleconnections on the long-range predictability of the atmosphere at midlatitudes: a reduced-order multi-scale model perspective S. Vannitsem https://doi.org/10.1088/2632-072X/ad04e8
- Strongly Coupled Data Assimilation in Multiscale Media: Experiments Using a Quasi‐Geostrophic Coupled Model S. Penny et al. https://doi.org/10.1029/2019MS001652
- Routes to long‐term atmospheric predictability in reduced‐order coupled ocean–atmosphere systems: Impact of the ocean basin boundary conditions S. Vannitsem et al. https://doi.org/10.1002/qj.3594
- A large deviation theory-based analysis of heat waves and cold spells in a simplified model of the general circulation of the atmosphere V. Gálfi et al. https://doi.org/10.1088/1742-5468/ab02e8
- Statistical Significance of Small Ensembles of Simulations and Detection of the Internal Climate Variability: An Excitable Ocean System Case Study S. Pierini https://doi.org/10.1007/s10955-019-02409-x
- Heterogeneity of the attractor of the Lorenz ’96 model: Lyapunov analysis, unstable periodic orbits, and shadowing properties C. Maiocchi et al. https://doi.org/10.1016/j.physd.2023.133970
- The physics of climate variability and climate change M. Ghil & V. Lucarini https://doi.org/10.1103/RevModPhys.92.035002
- An ensemble based approach for the effect of climate change on the dynamics of extremes M. Herein et al. https://doi.org/10.3389/feart.2023.1267473
- Adjoint sensitivity analysis on chaotic dynamical systems by Non-Intrusive Least Squares Adjoint Shadowing (NILSAS) A. Ni & C. Talnikar https://doi.org/10.1016/j.jcp.2019.06.035
- A quest for precipitation attractors in weather radar archives L. Foresti et al. https://doi.org/10.5194/npg-31-259-2024
- On Temporal Scale Separation in Coupled Data Assimilation with the Ensemble Kalman Filter M. Tondeur et al. https://doi.org/10.1007/s10955-020-02525-z
- Deep learning-enhanced ensemble-based data assimilation for high-dimensional nonlinear dynamical systems A. Chattopadhyay et al. https://doi.org/10.1016/j.jcp.2023.111918
- A Note on the Role of the Initial Error Structure in the Tropics on the Seasonal-to-Decadal Forecasting Skill in the Extratropics S. Vannitsem & W. Duan https://doi.org/10.1007/s00376-025-4521-7
Saved (final revised paper)
Latest update: 19 Jul 2026
Short summary
The predictability of weather models is limited largely by the initial state error growth or decay rates. We have computed these rates for PUMA, a global model for the atmosphere, and MAOOAM, a more simplified, coupled model which includes the ocean. MAOOAM has processes at distinct timescales, whereas PUMA surprisingly does not. We propose a new programme to compute the natural directions along the flow that correspond to the growth or decay rates, to learn which components play a role.
The predictability of weather models is limited largely by the initial state error growth or...
