TY  - JOUR
A1  - Leung, Tsz Yan
A1  - Leutbecher, Martin
A1  - Reich, Sebastian
A1  - Shepherd, Theodore G.
T1  - Atmospheric Predictability: Revisiting the Inherent Finite-Time Barrier
T2  - Journal of the atmospheric sciences
N2  - 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.
KW  - Atmosphere
KW  - Turbulence
KW  - Error analysis
KW  - Spectral analysis
KW  - models
KW  - distribution
KW  - Numerical weather prediction
KW  - forecasting
Y1  - 2019
UR  - https://publishup.uni-potsdam.de/frontdoor/index/index/docId/47754
SN  - 0022-4928
SN  - 1520-0469
VL  - 76
IS  - 12
SP  - 3883
EP  - 3892
PB  - American Meteorological Soc.
CY  - Boston
ER  -