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Atmospheric predictability: revisiting the inherent finite-time barrier

Leung, T. Y. ORCID: https://orcid.org/0000-0003-0056-284X, Leutbecher, M., Reich, S. and Shepherd, T. G. (2019) Atmospheric predictability: revisiting the inherent finite-time barrier. Journal of the Atmospheric Sciences, 76 (12). pp. 3883-3892. ISSN 1520-0469

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To link to this item DOI: 10.1175/JAS-D-19-0057.1

Abstract/Summary

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 skilfully 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 re-examines 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.

Item Type:Article
Refereed:Yes
Divisions:Faculty of Science > School of Mathematical, Physical and Computational Sciences > Department of Mathematics and Statistics
Faculty of Science > School of Mathematical, Physical and Computational Sciences > Department of Meteorology
ID Code:86240
Publisher:American Meteorological Society

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