Abstract
Adaptive observing guidance products for Atlantic tropical cyclones are compared using composite techniques that allow one to quantitatively examine differences in the spatial structures of the guidance maps and relate these differences to the constraints and approximations of the respective techniques. The guidance maps are produced using the ensemble transform Kalman filter (ETKF) based on ensembles from the National Centers for Environmental Prediction and the European Centre for Medium-Range Weather Forecasts (ECMWF), and total-energy singular vectors (TESVs) produced by ECMWF and the Naval Research Laboratory. Systematic structural differences in the guidance products are linked to the fact that TESVs consider the dynamics of perturbation growth only, while the ETKF combines information on perturbation evolution with error statistics from an ensemble-based data assimilation scheme. The impact of constraining the SVs using different estimates of analysis error variance instead of a total-energy norm, in effect bringing the two methods closer together, is also assessed. When the targets are close to the storm, the TESV products are a maximum in an annulus around the storm, whereas the ETKF products are a maximum at the storm location itself. When the targets are remote from the storm, the TESVs almost always indicate targets northwest of the storm, whereas the ETKF targets are more scattered relative to the storm location and often occur over the northern North Atlantic. The ETKF guidance often coincides with locations in which the ensemble-based analysis error variance is large. As the TESV method is not designed to consider spatial differences in the likely analysis errors, it will produce targets over well-observed regions, such as the continental United States. Constraining the SV calculation using analysis error variance values from an operational 3D variational data assimilation system (with stationary, quasi-isotropic background error statistics) results in a modest modulation of the target areas away from the well-observed regions, and a modest reduction of perturbation growth. Constraining the SVs using the ETKF estimate of analysis error variance produces SV targets similar to ETKF targets and results in a significant reduction in perturbation growth, due to the highly localized nature of the analysis error variance estimates. These results illustrate the strong sensitivity of SVs to the norm (and to the analysis error variance estimate used to define it) and confirm that discrepancies between target areas computed using different methods reflect the mathematical and physical differences between the methods themselves.
Note on Analyzing Perturbation Growth in a Tropical Cyclone–Like Vortex Radiating Inertia–Gravity Waves
