Repository: Freie Universität Berlin, Math Department

Atmospheric Predictability: Revisiting the Inherent Finite-Time Barrier

Leung, T.Y. and Leutbecher, M. and Reich, S. and Shepherd, Th.G. (2019) Atmospheric Predictability: Revisiting the Inherent Finite-Time Barrier. Journal of the Atmospheric Sciences, 76 (12). pp. 3883-3892. ISSN Online: 1520-0469 Print: 0022-4928

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Official URL: https://journals.ametsoc.org/doi/pdf/10.1175/JAS-D...

Abstract

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, 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
Additional Information:SFB1114 Preprint: 04/2019 (Print-Titel weicht ab vom Preprint-Titel: "Atmospheric predictability: the origins of the finite-time behaviour")
Subjects:Physical Sciences > Physics > Environmental Physics > Atmospheric Physics
Mathematical and Computer Sciences > Mathematics > Applied Mathematics
ID Code:2386
Deposited By: Silvia Hoemke
Deposited On:04 Dec 2019 13:57
Last Modified:04 Dec 2019 14:37

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