A Variational Method for Analyzing Vortex Flows in Radar Observed Tornadic Mesocyclones. Part II: Tests with Analytically Formulated Vortices

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  • 1 NOAA/OAR/National Severe Storms Laboratory, Norman, Oklahoma
  • 2 Cooperative Institute for Mesoscale Meteorological Studies, University of Oklahoma
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Abstract

The variational method formulated in part-I for analyzing vortex flow (VF), called VF-Var, is tested with simulated radar radial-velocity observations from idealized and pseudo-operational Doppler scans of analytically formulated benchmark vortices with spiral-band structures to resemble VFs in observed tornadic mesocyclones. The idealized Doppler scans are unidirectional in parallel along horizontal grid lines of a coarse-resolution grid, so they measure only the horizontal components of three-dimensional velocities in the analysis domain. The pseudo-operational Doppler scans mimic a scan mode used by operational WSR-88D radars for severe storms. Paired numerical experiments are designed and performed to test the two-step analysis versus single-step analysis formulated in VF-Var. Both analyses perform very well with dual-Doppler scans and reasonably well with single-Doppler scans. Errors in the analyzed velocities from single-Doppler scans are mainly in the unobserved velocity components and only in fractions of the benchmark velocities. When the vortex is upright or slanted in the direction perpendicular to Doppler scans, the two-step analysis slightly outperforms the single-step analysis for idealized Doppler scans and pseudo-operational dual-Doppler scans. When the vortex becomes slanted in the direction largely along or against Doppler scans, both analyses become less (or more) accurate in analyzing the horizontal (or slantwise vertical) velocity, and the single-step analysis outperforms the two-step analysis especially for single-Doppler scans. By considering the projections of analyzed velocity on radar beams in the original Cartesian coordinates, useful insights are gained for understanding why and how the analysis accuracies are affected by vortex slanting.

Correspondence to: Dr. Qin Xu, National Severe Storms Laboratory, 120 David L. Boren Blvd., Norman, Oklahoma 73072-7326. E-mail: Qin.Xu@noaa.gov

Abstract

The variational method formulated in part-I for analyzing vortex flow (VF), called VF-Var, is tested with simulated radar radial-velocity observations from idealized and pseudo-operational Doppler scans of analytically formulated benchmark vortices with spiral-band structures to resemble VFs in observed tornadic mesocyclones. The idealized Doppler scans are unidirectional in parallel along horizontal grid lines of a coarse-resolution grid, so they measure only the horizontal components of three-dimensional velocities in the analysis domain. The pseudo-operational Doppler scans mimic a scan mode used by operational WSR-88D radars for severe storms. Paired numerical experiments are designed and performed to test the two-step analysis versus single-step analysis formulated in VF-Var. Both analyses perform very well with dual-Doppler scans and reasonably well with single-Doppler scans. Errors in the analyzed velocities from single-Doppler scans are mainly in the unobserved velocity components and only in fractions of the benchmark velocities. When the vortex is upright or slanted in the direction perpendicular to Doppler scans, the two-step analysis slightly outperforms the single-step analysis for idealized Doppler scans and pseudo-operational dual-Doppler scans. When the vortex becomes slanted in the direction largely along or against Doppler scans, both analyses become less (or more) accurate in analyzing the horizontal (or slantwise vertical) velocity, and the single-step analysis outperforms the two-step analysis especially for single-Doppler scans. By considering the projections of analyzed velocity on radar beams in the original Cartesian coordinates, useful insights are gained for understanding why and how the analysis accuracies are affected by vortex slanting.

Correspondence to: Dr. Qin Xu, National Severe Storms Laboratory, 120 David L. Boren Blvd., Norman, Oklahoma 73072-7326. E-mail: Qin.Xu@noaa.gov
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