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R. Buizza and T. N. Palmer

Abstract

The impact of ensemble size on the performance of the European Centre for Medium-Range Weather Forecasts ensemble prediction system (EPS) is analyzed. The skill of ensembles generated using 2, 4, 8, 16, and 32 perturbed ensemble members are compared for a period of 45 days—from 1 October to 15 November 1996. For each ensemble configuration, the skill is compared with the potential skill, measured by randomly choosing one of the 32 ensemble members as verification (idealized ensemble). Results are based on the analyses of the prediction of the 500-hPa geopotential height field. Various measures of performance are applied: skill of the ensemble mean, spread–skill relationship, skill of most accurate ensemble member, Brier score, ranked probability score, relative operating characteristic, and the outlier statistic.

The relation between ensemble spread and control error is studied using L 2, L 8, and L norms to measure distances between ensemble members and the control forecast or the verification. It is argued that the supremum norm is a more suitable measure of distance, given the strategy for constructing ensemble perturbations from rapidly growing singular vectors. Results indicate that, for the supremum norm, any increase of ensemble size within the range considered in this paper is strongly beneficial. With the smaller ensemble sizes, ensemble spread does not provide a reliable bound on control error in many cases. By contrast, with 32 members, spread provides a bound on control error in nearly all cases. It could be anticipated that further improvement could be achieved with higher ensemble size still. On the other hand, spread–skill relationship was not consistently improved with higher ensemble size using the L 2 norm.

The overall conclusion is that the extent to which an increase of ensemble size (particularly from 8 to 16, and 16 to 32 members) improves EPS performance, is strongly dependent on the measure used to assess performance. In addition to the spread–skill relationship, the measures most sensitive to ensemble size are shown to be the skill of the best ensemble member (particularly when evaluated on a point-wise basis) and the outlier statistic.

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W. Bourke, R. Buizza, and M. Naughton

Abstract

The performance of two ensemble prediction systems, that of the European Centre for Medium-Range Weather Forecasts (EC-EPS) and that of the Australian Bureau of Meteorology (BM-EPS) are compared over the Southern Hemisphere annulus (20°–60°S) and over the Australian region. Ten-day ensemble forecasts for 152 daily cases (from 2 April to 31 August 2001) of 500-hPa geopotential height are examined.

A comprehensive set of verification measures documents the different spread and skill characteristics of the BM-EPS and EC-EPS. Overall, EC-EPS deterministic (i.e., unperturbed control) products and the probabilistic ensemble-based products are more skillful than the corresponding BM-EPS products. The utility of the BM-EPS for the Australian region is indicated.

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C. A. Reynolds, M. S. Peng, S. J. Majumdar, S. D. Aberson, C. H. Bishop, and R. Buizza

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.

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S. J. Majumdar, S. D. Aberson, C. H. Bishop, R. Buizza, M. S. Peng, and C. A. Reynolds

Abstract

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.

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