Local error growth in a barotropic model

Abstract

The concept of local error growth is considered within the context of the non-viscous barotropic vorticity equation. Using the adjoint equation of the tangent linear barotropic vorticity equation, we determine error patterns in the initial state that result in the maximum linear error growth at some pre-chosen geographical area and prediction time. For some solutions of the nonlinear barotropic vorticity equation, we investigate to what extent error growth depends on the geographical position of the area considered. It appears that for short prediction times (< 3 days), the barotropic growth of kinetic energy of initial perturbations is exponential plus a substantial transient effect due to the non-orthogonality of the eigenmodes of the tangent linear operator with respect to the kinetic energy inner product. The latter mechanism initially causes very rapid perturbation growth, even for neutral flows.