14th Conference on Atmospheric and Oceanic Fluid Dynamics

Thursday, 12 June 2003: 10:15 AM
Evolution of analysis error and adjoint-based optimal perturbation in a quasigeostrophic model
Hyun Mee Kim, University of Wisconsin, Madison, WI; and M. C. Morgan
Poster PDF (251.7 kB)
A diagnosis of error evolution in the National Center for Atmospheric Research quasigeostrophic (QG) model is performed using potential vorticity (PV) inversion and localized Eliassen-Palm flux diagnostics following the ideal cyclone development under the perfect model assumption. The error evolution is compared with the evolution of the adjoint-based perturbations such as singular vector (SV) and perturbation derived from the weighted gradient sensitivity (WGS).

The diagnostics reveal that the mechanisms for error growth and propagation depend upon projection of error onto SVs of the flow. The error which projects onto these SVs during the evolution (identified as a ``Type A error'') is initiated by the barotropic propagation of wave activity from regions of small PV gradient to regions of large PV gradient (i.e., near the jet in the middle of the domain) along the upper and lower boundaries of the QG model followed by the baroclinic interactions between errors along the upper and lower boundaries. That error which is initially large and does not project onto SVs during the evolution (``Type B error'') is sustained by baroclinic processes between the interior PV and boundary potential temperatures without growth or propagation. Adjoint-based perturbations, including SVs and WGS, correspond with the Type A error very well during the evolution.

In the view of adaptive observations, the sensitive regions can be identified by the error growth and propagation mechanism. A forecast measure may be considered sensitive in some regions if the forecast measure exhibits a large response to a small change in the initial conditions in those regions. Because of the barotropic error growth and propagation mechanism along the upper and lower boundaries at the early stage of the evolution, adaptive observations concentrated in the sensitive regions indicated by the adjoint-based strategies remote from the baroclinically unstable region of the flow would be effective in reducing a subsequent forecast error.

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