Singular vectors for moisture-measuring norms

Singular vectors (SVs) are determined for 12-hour forecasts using a regional mesoscale model. Norms used as constraints at the initial time include the usual total-energy norm, a related moisture-measuring norm, and norms using weights equal to the inverse of estimated variances of initial-condition uncertainty. Norms used to measure perturbations at the end of the forecast include either the total energy or mean-squared perturbed rate of precipitation. Four synoptic cases are examined. The locations of the four leading SVs for each pair of norms considered differ widely for some cases but are collocated for others. The initial vertical structures of the SVs are also sensitive to norms and cases. Most importantly, both final-time norms are sensitive to initial perturbations of both moisture and dynamic fields. For some cases, similar structures are optimal for maximizing both perturbation energy and precipitation. When the initial moisture SVs are introduced in the nonlinear forecast model with perturbation magnitudes of the size of initial-condition uncertainties, many of the results remarkably match corresponding tangent-linear estimates. In other nonlinear experiments, however, the matches are poor in terms of either correlation or magnitude measures, or both, indicating that the tangent-linear results are sometimes informative but at other times can be misleading. For the present study the key reported tangent-linear model results were, therefore, all confirmed in the nonlinear context. An implication of the results is that as much attention must be paid to moisture analysis as to analysis of other fields, and that ensemble forecast techniques should consider initial moisture uncertainty.