Linear amplification and error growth in the 2-D eady problem with uniform potential vorticity
Fischer, C.
Année de publication
1998
The concept of a singular mode underlies optimal linear amplification
theories. This concept is studied in the frame of the two-dimensional,
quasigeostrophic Eady problem with uniform potential vorticity.
Analytical solutions are produced for the relevant physical norms. Exact
relations are also derived for the amplifications, which give the lower
and upper bounds to any linear development. Results show significant
differences in the structure of the singular modes, as well as in the
associated amplifications, when the horizontal wavenumber is varied or
the inner product is changed. It is found that the singular modes can
depart significantly from the normal modes, though the dynamics of the
problem are very simple. Comparisons with previous works are also
performed. Finally, the derived equations are used to present the linear
evolution of error growth within the Eady problem, as predicted by a
Kalman filter. Considerations on the spectral space error covariance
matrix are made, and a particular case of error dynamics in the 2D
physical space is shown. The derivation of the general algebraic
solutions is included in the <a class="ref" href="http://journals.ametsoc.org/doi/abs/10.1175/1520-0469%281998%29055%3C3363%3ALAAEGI%3E2.0.CO%3B2#saa"><sup>appendix</sup></a>.</div>
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