Computation of optimal unstable structures for a numerical weather prediction model

Numerical experiments have been performed to compute the fastest growing perturbations in a finite time interval for a complex numerical weather prediction model. The models used are the tangent forward and adjoint versions of the adiabatic primitive-equation model of the Integrated Forecasting System developed at the European Centre for Medium-Range Weather Forecasts and Météo France. These have been run with a horizontal truncation T21, with 19 vertical levels. The fastest growing perturbations are the singular vectors of the propagator of the forward tangent model with the largest singular values. An iterative Lanczos algorithm has been used for the numerical computation of the perturbations. Sensitivity of the calculations to different time intervals and to the norm used in the definition of the adjoint model have been analysed. The impact of normal mode initialization has also been studied. Two classes of fastest growing perturbations have been found; one is characterized by a maximum amplitude in the middle troposphere, while the other is confined to model layers close to the surface. It is shown that the latter is damped by the boundary layer physics in the full model. The linear evolution of the perturbations has been compared to the non-linear evolution when the perturbations are superimposed on a basic state in the T63, 19-level version of the ECMWF model.