SINGULAR VECTORS - THE EFFECT OF SPATIAL SCALE ON LINEAR GROWTH OF DISTURBANCES

The scale dependence of rapidly growing perturbations is investigated by studying the dominant singular vectors of T21 and T42 versions of t he ECMWF model, which show the most linear energy growth in a 3-day pe riod. A spectral filter is applied to the optimization process to dete rmine which spatial scales are most effective in promoting energy grow th. When the initial perturbation is confined to the top half of the t otal spherical harmonic wavenumber spectrum (high wavenumber end), the growth rates and final structures of the disturbances are changed ver y little from the case in which all wavenumbers are included. These re sults indicate that synoptic waves that become fully developed in a pe riod of three days can arise from initial perturbations that are entir ely contained at subsynoptic scales. Rapid growth is associated with i nitial perturbations that consist of smaller spatial scales concentrat ed near the effective steering level. The linear evolution of these in itial perturbations in a highly complex basic flow leads to disturbanc es of synoptic scale that extend through most of the depth of the trop osphere. Growth rates are approximately doubled when the model resolut ion is increased from T21 to T42, which is consistent with greater gro wth being associated with smaller spatial scales. When the initial per turbation is confined to the lower half of the total wavenumber spectr um, which describes the larger horizontal scales, the growth rates are significantly reduced and the initial and final structures are very d ifferent from the case in which all wavenumbers are included. These lo w wavenumber perturbations tend to be more barotropic in structure and in growth characteristics. As expected from their linear growth rates , when the low-wavenumber perturbations are inserted in the T63 foreca st model, they grow more slowly and result in less forecast dispersion than the high wavenumber perturbations.