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
JF  - 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
U6  - https://doi.org/10.1175/JAS-D-19-0057.1
SN  - 0022-4928
SN  - 1520-0469
VL  - 76
IS  - 12
SP  - 3883
EP  - 3892
PB  - American Meteorological Soc.
CY  - Boston
ER  - 
TY  - JOUR
A1  - Trauth, Martin H.
T1  - Spectral analysis in quaternary sciences
JF  - Quaternary science reviews : the international multidisciplinary research and review journal
N2  - Spectral analysis is a technique of time-series analysis that decomposes signals into linear combinations of harmonic components. Rooted in the 19th century, spectral analysis gained popularity in palaeoclimatology since the early 1980s. This was partly due to the availability of long time series of past climates, but also the development of new, partly adapted methods and the increasing spread of affordable personal computers. This paper reviews the most important methods of spectral analysis for palaeoclimate time series and discusses the prerequisites for their application as well as advantages and disadvantages. The paper also offers an overview of suitable software, as well as computer code for using the methods on synthetic examples.
KW  - Spectral analysis
KW  - Paleoclimate
KW  - Orbital forcing
KW  - MATLAB
Y1  - 2021
U6  - https://doi.org/10.1016/j.quascirev.2021.107157
SN  - 0277-3791
SN  - 1873-457X
VL  - 270
PB  - Elsevier
CY  - Oxford
ER  -