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 <br>theories. This concept is studied in the frame of the two-dimensional, <br>quasigeostrophic Eady problem with uniform potential vorticity. <br>Analytical solutions are produced for the relevant physical norms. Exact<br> relations are also derived for the amplifications, which give the lower<br> and upper bounds to any linear development. Results show significant <br>differences in the structure of the singular modes, as well as in the <br>associated amplifications, when the horizontal wavenumber is varied or <br>the inner product is changed. It is found that the singular modes can <br>depart significantly from the normal modes, though the dynamics of the <br>problem are very simple. Comparisons with previous works are also <br>performed. Finally, the derived equations are used to present the linear<br> evolution of error growth within the Eady problem, as predicted by a <br>Kalman filter. Considerations on the spectral space error covariance <br>matrix are made, and a particular case of error dynamics in the 2D <br>physical space is shown. The derivation of the general algebraic <br>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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