The spectra of singular values in a regional model

Large portions of the spectra of singular values are determined for both moist and dry versions of a tangent linear, regional model for 4 different synoptic cases. Norms considered include the usual energy norm and versions of a norm measuring only the energy in some set of rotational mode perturbations. At most, only a few percent of the singular vectors possible with any of the norms are growing ones. Inclusion of moist physics in the tangent linear model greatly affects the leading singular vectors but does not increase the number of growing singular vectors much. Most singular vectors are damping ones, and therefore random perturbations drawn from a white-noise distribution will likely damp during the 24-h forecast periods considered. Only a few singular vectors are required to explain a significant portion of the final-time variance of such perturbations, however, because the leading singular values are so large compared with the rest. The truncated rotational mode norm is shown to be very useful for investigating these properties.