Atmospheric Predictability: Revisiting the Inherent Finite-Time Barrier
- The accepted idea that there exists an inherent finite-time barrier in deterministically predicting atmospheric flows originates from Edward N. Lorenz’s 1969 work based on two-dimensional (2D) turbulence. Yet, known analytic results on the 2D Navier–Stokes (N-S) equations suggest that one can skillfully predict the 2D N-S system indefinitely far ahead should the initial-condition error become sufficiently small, thereby presenting a potential conflict with Lorenz’s theory. Aided by numerical simulations, the present work reexamines Lorenz’s model and reviews both sides of the argument, paying particular attention to the roles played by the slope of the kinetic energy spectrum. It is found that when this slope is shallower than −3, the Lipschitz continuity of analytic solutions (with respect to initial conditions) breaks down as the model resolution increases, unless the viscous range of the real system is resolved—which remains practically impossible. This breakdown leads to the inherent finite-time limit. If, on the other hand, theThe accepted idea that there exists an inherent finite-time barrier in deterministically predicting atmospheric flows originates from Edward N. Lorenz’s 1969 work based on two-dimensional (2D) turbulence. Yet, known analytic results on the 2D Navier–Stokes (N-S) equations suggest that one can skillfully predict the 2D N-S system indefinitely far ahead should the initial-condition error become sufficiently small, thereby presenting a potential conflict with Lorenz’s theory. Aided by numerical simulations, the present work reexamines Lorenz’s model and reviews both sides of the argument, paying particular attention to the roles played by the slope of the kinetic energy spectrum. It is found that when this slope is shallower than −3, the Lipschitz continuity of analytic solutions (with respect to initial conditions) breaks down as the model resolution increases, unless the viscous range of the real system is resolved—which remains practically impossible. This breakdown leads to the inherent finite-time limit. If, on the other hand, the spectral slope is steeper than −3, then the breakdown does not occur. In this way, the apparent contradiction between the analytic results and Lorenz’s theory is reconciled.…
Author details: | Tsz Yan LeungORCiD, Martin LeutbecherORCiDGND, Sebastian ReichORCiDGND, Theodore G. ShepherdORCiDGND |
---|---|
DOI: | https://doi.org/10.1175/JAS-D-19-0057.1 |
ISSN: | 0022-4928 |
ISSN: | 1520-0469 |
Title of parent work (English): | Journal of the atmospheric sciences |
Publisher: | American Meteorological Soc. |
Place of publishing: | Boston |
Publication type: | Article |
Language: | English |
Year of first publication: | 2019 |
Publication year: | 2019 |
Release date: | 2020/09/29 |
Tag: | Atmosphere; Error analysis; Numerical weather prediction; Spectral analysis; Turbulence; distribution; forecasting; models |
Volume: | 76 |
Issue: | 12 |
Number of pages: | 10 |
First page: | 3883 |
Last Page: | 3892 |
Funding institution: | Engineering and Physical Sciences Research Council Grant "EPSRC Centre for Doctoral Training in the Mathematics of Planet Earth at Imperial College London and the University of Reading" [EP/L016613/1]; European Research CouncilEuropean Research Council (ERC) [339390]; Deutsche Forschungsgemeinschaft (DFG)German Research Foundation (DFG) [CRC 1114] |
Organizational units: | Mathematisch-Naturwissenschaftliche Fakultät / Institut für Mathematik |
DDC classification: | 5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik |
Peer review: | Referiert |