Vertical velocity is the most difficult wind component to accurately retrieve from dual- Doppler observations. Typical radar scans are conducted with shallow elevation angles and therefore, the radial velocity observations poorly constrain the vertical velocity in retrievals. Traditional dual-Doppler analysis (DDA) uses the anelastic mass conservation equation as a constraint to retrieve vertical velocity. However, procedures that integrate the anelastic mass conservation equation can have large errors in the vertical velocities due to missing low-level data, errors in boundary specification, and the compounding of horizontal divergence errors in the integration. In recent years, it has been proposed to use a vertical vorticity equation as a weak constraint in addition to the mass conservation equation in order to improve vertical velocity retrievals. Prior observation simulation experiments have found that the vorticity equation constraint can improve vertical velocity retrievals in situations with missing low-level data and radar volume scan times that are sufficiently short to calculate the vorticity tendency accurately.

In this study, the vertical vorticity equation constraint DDA was tested using real observations from rapid-scan radars. A dual-Doppler dataset of a convective storm was collected on 4 Sept 2018 with a maximum volume scan time of 30 seconds. An additional radar was positioned under the storm and conducted near-vertical planned-position indicator scans (PPIs), which were used as a verification dataset. In general, the vorticity equation DDA was able to improve vertical velocity retrievels, but the improvement was dependent on the time between volume scans and the technique used to calculate the vorticity tendency. When the time between volume scans was 30 seconds, a simple centered difference of the vorticity calculated from provisional wind retrievals was sufficient for estimating the vorticity tendency, but with greater time between volume scans this method resulted in significantly degraded vertical velocities. A technique that used advection correction to shorten the time difference in the centered difference improved the vertical velocities of these longer volume scan times, but caused the DDAs with 30 seconds between volume scans to become slightly worse. A new three-dimensional advection correction technique that was developed for the vorticity tendency estimation produced slightly better vertical velocity retrievals than those that used two-dimensional advection correction. One key difference between these results and those of the prior OSSE experiments is that the improvement in the retrieved vertical velocities occurred even though there was not a large data void between the lowest data level and the ground. Additionally, the vorticity equation constraint DDA was more forgiving to radar data errors as it did not produce unphysical vertical velocities in a region of sidelobe contamination that was present in the other DDAs. Considering that observation errors are a common occurrence in radar datasets, these results suggest that the vorticity equation constrained DDA could be more beneficial than what the original OSSE studies indicated.

Another analysis technique that has gained popularity in recent years is ensemble Kalman filter (EnKF) analysis. Prior OSSEs have suggested that EnKF analyses can be more accurate than DDAs. Unfortunately, in this study the EnKF analyses were hampered by catastrophic filter divergence. The adaptive inflation that was used to maintain ensemble spread due to the large number of radial velocity observations being assimilated caused large ensemble spread to develop in data sparse regions, which led to extremely large analysis increments through correlations with regions that had radial velocity observations. Despite the catastrophic filter divergence, EnKF analyses that used radar observations that were thinned to 150-s intervals produced vertical velocities that had better verification statistics than the best DDA. This indicates that if the filter divergence issue is controlled, EnKF analyses could have more accurate vertical velocities than those obtained by DDA.

Most importantly, the results shown in this dissertation highlight that rapid-scan radar data is beneficial to vertical velocity retrievals when that data is paired with a vorticity equation constrained DDA. This DDA technique and the use of rapid-scan radars should be prioritized in future observational studies of convective storms.