Wednesday, 14 January 2004: 9:00 AM
Singular vectors with an analysis error variance metric
There are several areas of research in numerical weather prediction and atmospheric predictability, such as targeted observations and ensemble perturbation generation, where it is desirable to combine information about the uncertainty of the initial state with information about potential rapid perturbation growth. Singular vectors (SVs) provide a framework to accomplish this task in a mathematically rigorous and computationally feasible manner. In this study, a follow-up of Gelaro, Rosmond and Daley (2002), the analysis error variance information produced by the NRL Atmospheric Variational Data Assimilation System is used as the initial-time SV norm (the final-time norm is total energy). These VAR SVs are compared to SVs for which total energy is both the initial and final time norms (TE SVs). The structures of the VAR SVs and TE SVs are examined as a function of wave number and altitude and their effectiveness in explaining forecast error is compared. Despite significant structural difference, the TE and VAR SVs explain comparable amounts of forecast error in both linear and nonlinear experiments. For both the TE and VAR SVs, nonlinear pseudo-inverse corrections are better than the expected linear corrections. When projecting the VAR SV pseudo-inverse perturbation onto the TE SVs, it is found that the component inside the TE-SV subspace accounts for most of the forecast error reduction. The effectiveness of the TE and VAR SVs in explaining forecast error at forecast times other than the optimization time is also examined. The utility and implications of such experiments in assessing the analysis error variance estimates will be explored.