ALBERT

Description: Gibbs oscillation can show up near flow regions with strong temperature gradients in the numerical simulation of nonhydrostatic mesoscale atmospheric flows when using the high-order discontinuous Galerkin (DG) method. The authors propose to incorporate flow-feature-based localized Laplacian artificial viscosity in the DG framework to suppress the spurious oscillation in the vicinity of sharp thermal fronts but not to contaminate the smooth flow features elsewhere. The parameters in the localized Laplacian artificial viscosity are modeled based on both physical criteria and numerical features of the DG discretization. The resulting numerical formulation is first validated on several shock-involved test cases, including a shock discontinuity problem with the one-dimensional Burger’s equation, shock–entropy wave interaction, and shock–vortex interaction. Then the efficacy of the developed numerical formulation on stabilizing thermal fronts in nonhydrostatic mesoscale atmospheric modeling is demonstrated by two benchmark test cases: the rising thermal bubble problem and the density current problem. The results indicate that the proposed flow-feature-based localized Laplacian artificial viscosity method can sharply detect the nonsmooth flow features, and stabilize the DG discretization nearby. Furthermore, the numerical stabilization method works robustly for a wide range of grid sizes and polynomial orders without parameter tuning in the localized Laplacian artificial viscosity.

Description: Airborne adaptive observations have been collected for more than two decades in the neighborhood of tropical cyclones, to attempt to improve short-range forecasts of cyclone track. However, only simple subjective strategies for adaptive observations have been used, and the utility of objective strategies to improve tropical cyclone forecasts remains unexplored. Two objective techniques that have been used extensively for midlatitude adaptive observing programs, and the current strategy based on the ensemble deep-layer mean (DLM) wind variance, are compared quantitatively using two metrics. The ensemble transform Kalman filter (ETKF) uses ensembles from NCEP and the ECMWF. Total-energy singular vectors (TESVs) are computed by the ECMWF and the Naval Research Laboratory, using their respective global models. Comparisons of 78 guidance products for 2-day forecasts during the 2004 Atlantic hurricane season are made, on both continental and localized scales relevant to synoptic surveillance missions. The ECMWF and NRL TESV guidance identifies similar large-scale target regions in 90% of the cases, but are less similar to each other in the local tropical cyclone environment (56% of the cases) with a more stringent criterion for similarity. For major hurricanes, all techniques usually indicate targets close to the storm center. For weaker tropical cyclones, the TESV guidance selects similar targets to those from the ETKF (DLM wind variance) in only 30% (20%) of the cases. ETKF guidance using the ECMWF ensemble is more like that provided by the NCEP ensemble (and DLM wind variance) for major hurricanes than for weaker tropical cyclones. Minor differences in these results occur when a different metric based on the ranking of fixed storm-relative regions is used.

Description: 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.