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  1. null (Ed.)
    Abstract Techniques to mitigate analysis errors arising from the nonsimultaneity of data collections typically use advection-correction procedures based on the hypothesis (frozen turbulence) that the analyzed field can be represented as a pattern of unchanging form in horizontal translation. It is more difficult to advection correct the radial velocity than the reflectivity because even if the vector velocity field satisfies this hypothesis, its radial component does not—but that component does satisfy a second-derivative condition. We treat the advection correction of the radial velocity ( υ r ) as a variational problem in which errors in that second-derivative condition are minimized subject to smoothness constraints on spatially variable pattern-translation components ( U , V ). The Euler–Lagrange equations are derived, and an iterative trajectory-based solution is developed in which U , V , and υ r are analyzed together. The analysis code is first verified using analytical data, and then tested using Atmospheric Imaging Radar (AIR) data from a band of heavy rainfall on 4 September 2018 near El Reno, Oklahoma, and a decaying tornado on 27 May 2015 near Canadian, Texas. In both cases, the analyzed υ r field has smaller root-mean-square errors and larger correlation coefficients than in analyses based on persistence, linear time interpolation, or advection correction using constant U and V . As some experimentation is needed to obtain appropriate parameter values, the procedure is more suitable for non-real-time applications than use in an operational setting. In particular, the degree of spatial variability in U and V , and the associated errors in the analyzed υ r field are strongly dependent on a smoothness parameter. 
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  2. null (Ed.)
    Abstract Observation system simulation experiments are used to evaluate different dual-Doppler analysis (DDA) methods for retrieving vertical velocity w at grid spacings on the order of 100 m within a simulated tornadic supercell. Variational approaches with and without a vertical vorticity equation constraint are tested, along with a typical (traditional) method involving vertical integration of the mass conservation equation. The analyses employ emulated radar data from dual-Doppler placements 15, 30, and 45 km east of the mesocyclone, with volume scan intervals ranging from 10 to 150 s. The effect of near-surface data loss is examined by denying observations below 1 km in some of the analyses. At the longer radar ranges and when no data denial is imposed, the “traditional” method produces results similar to those of the variational method and is much less expensive to implement. However, at close range and/or with data denial, the variational method is much more accurate, confirming results from previous studies. The vorticity constraint shows the potential to improve the variational analysis substantially, reducing errors in the w retrieval by up to 30% for rapid-scan observations (≤30 s) at close range when the local vorticity tendency is estimated using spatially variable advection correction. However, the vorticity constraint also degrades the analysis for longer scan intervals, and the impact diminishes with increased range. Furthermore, analyses using 30-s data also frequently outperform analyses using 10-s data, suggesting a limit to the benefit of increasing the radar scan rate for variational DDA employing the vorticity constraint. 
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