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In this paper, a new method of dual-Doppler radar wind analysis based on a three-dimensional variational data assimilation (3DVAR) approach is proposed. In it, a cost function, including background term and radial observation term, is minimized through a limited memory, quasi-Newton conjugate-gradient algorithm with the mass continuity equation imposed as a weak constraint. In the method, the background error covariance matrix, though simple in this case, is modeled by a recursive filter. Furthermore, the square root of this matrix is used to precondition the minimization problem.The current method is applied to Doppler radar observation of a supercell storm, and the analysis results are compared to a conceptual model and previous research. It is shown that the horizontal circulations, both within and around the storms, as well as the strong updraft and the associated downdraft, are well analyzed. Because no explicit integration of the anelastic mass continuity equation is involved, error accumulation associated with such integration is avoided. As a result, the method is less sensitive to the vertical boundary uncertainties.

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In this two-part paper, the impact of level-II Weather Surveillance Radar-1988 Doppler (WSR-88D) reflectivity and radial velocity data on the prediction of a cluster of tornadic thunderstorms in the Advanced Regional Prediction System (ARPS) model are studied. Radar reflectivity data are used primarily in a cloud analysis procedure that retrieves the amount of hydrometeors and adjusts in-cloud temperature, moisture, and cloud fields, while radial velocity data are analyzed through a three-dimensional variational (3DVAR) scheme that contains a mass divergence constraint in the cost function. In Part I, the impact of the cloud analysis and modifications to the scheme are examined while Part II focuses on the impact of radial velocity and the mass divergence constraint.The case studied is that of the 28 March 2000 Fort Worth, Texas, tornado outbreaks. The same case was studied by Xue et al. using the ARPS Data Analysis System (ADAS) and an earlier version of the cloud analysis procedure with WSR-88D level-III data. Since then, several modifications to the cloud analysis procedure, including those to the in-cloud temperature adjustment and the analysis of precipitation species, have been made. They are described in detail with examples.The assimilation and predictions use a 3-km grid nested inside a 9-km one. The level-II reflectivity data are assimilated, through the cloud analysis, at 10-min intervals in a 1-h period that ends a little over 1 h preceding the first tornado outbreak. Experiments with different settings within the cloud analysis procedure are examined. It is found that the experiment using the improved cloud analysis procedure with reflectivity data can capture the important characteristics of the main tornadic thunderstorm more accurately than the experiment using the early version of cloud analysis. The contributions of different modifications to the above improvements are investigated.

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In this two-part paper, the impact of level-II Weather Surveillance Radar-1988 Doppler (WSR-88D) radar reflectivity and radial velocity data on the prediction of a cluster of tornadic thunderstorms in the Advanced Regional Prediction System (ARPS) model is studied. Radar reflectivity data are used primarily in a cloud analysis procedure that retrieves the amount of hydrometeors and adjusts in-cloud temperature, moisture, and cloud fields, while radial velocity data are analyzed through a three-dimensional variational (3DVAR) data assimilation scheme that contains a 3D mass divergence constraint in the cost function. In Part I, the impact of the cloud analysis and modifications to the scheme are discussed. In this part, the impact of radial velocity data and the mass divergence constraint in the 3DVAR cost function are studied. The case studied is that of the 28 March 2000 Fort Worth tornadoes. The addition of the radial velocity improves the forecasts beyond that experienced with the cloud analysis alone. The prediction is able to forecast the morphology of individual storm cells on the 3-km grid up to 2 h; the rotating supercell characteristics of the storm that spawned two tornadoes are well captured; timing errors in the forecast are less than 15 min and location errors are less than 10 km at the time of the tornadoes. When forecasts were made with radial velocity assimilation but not reflectivity, they failed to predict nearly all storm cells. Using the current 3DVAR and cloud analysis procedure with 10-min intermittent assimilation cycles, reflectivity data are found to have a greater positive impact than radial velocity. The use of radial velocity does improve the storm forecast when combined with reflectivity assimilation, by, for example, improving the forecasting of the strong low-level vorticity centers associated with the tornadoes. Positive effects of including a mass divergence constraint in the 3DVAR cost function are also documented.

Probabilistic quantitative precipitation forecasts (PQPFs) from the storm-scale ensemble forecast system run by the Center for Analysis and Prediction of Storms during the spring of 2009 are evaluated using area under the relative operating characteristic curve (ROC area). ROC area, which measures discriminating ability, is examined for ensemble size n from 1 to 17 members and for spatial scales ranging from 4 to 200 km.Expectedly, incremental gains in skill decrease with increasing n. Significance tests comparing ROC areas for each n to those of the full 17-member ensemble revealed that more members are required to reach statistically indistinguishable PQPF skill relative to the full ensemble as forecast lead time increases and spatial scale decreases. These results appear to reflect the broadening of the forecast probability distribution function (PDF) of future atmospheric states associated with decreasing spatial scale and increasing forecast lead time. They also illustrate that efficient allocation of computing resources for convection-allowing ensembles requires careful consideration of spatial scale and forecast length desired.

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