Impact of a Vertical Vorticity Constraint in Variational Dual-Doppler Wind Analysis: Tests with Real and Simulated Supercell Data

Abstract

One of the greatest challenges to dual-Doppler retrieval of the vertical wind is the lack of low-level divergence information available to the mass conservation constraint. This study examines the impact of a vertical vorticity equation constraint on vertical velocity retrievals when radar observations are lacking near the ground. The analysis proceeds in a three-dimensional variational data assimilation (3DVAR) framework with the anelastic form of the vertical vorticity equation imposed along with traditional data, mass conservation, and smoothness constraints. The technique is tested using emulated radial wind observations of a supercell storm simulated by the Advanced Regional Prediction System (ARPS), as well as real dualDoppler observations of a supercell storm that occurred in Oklahoma on 8 May 2003. Special attention is given to procedures to evaluate the vorticity tendency term, including spatially variable advection correction and estimation of the intrinsic evolution. Volume scan times ranging from 5 min, typical of operational radar networks, down to 30 s, achievable by rapid-scan mobile radars, are considered. The vorticity constraint substantially improves the vertical velocity retrievals in our experiments, particularly for volume scan times smaller than 2 min.

Assessing Errors in Variational Dual-Doppler Wind Syntheses of Supercell Thunderstorms Observed by Storm-Scale Mobile Radars

“…An overview of the 3DVAR dual-Doppler analysis technique follows; a complete description can be found in Shapiro et al (2009) and Potvin et al (2012b), though it should be noted that the vorticity equation constraint adopted in those studies is not imposed in the present work (this constraint did not help in the present case, largely because of the availability of low-level radar data). The technique minimizes the cost function J 5 J O 1 J M 1 J S , where J O , J M , and J S are the cost functions associated with the observational, mass conservation, and smoothness constraints, respectively.…”

“…Since our primary objective is to examine typical errors in storm-scale 3DVAR dual-Doppler wind syntheses, we did not attempt to use more specialized methods to correct for these processes (e.g., Shapiro et al 2010a,b;Potvin et al 2012b). The errors arising from unaccounted wind field advection and evolution in our case are examined in section 3g.…”

Comparison between Dual-Doppler and EnKF Storm-Scale Wind Analyses: Observing System Simulation Experiments with a Supercell Thunderstorm

“…The simulation proceeded on a stationary 102.4 km 3 102.4 km 3 20 km domain with 200-m horizontal and vertical spacing. Further details about the supercell simulation can be found in Potvin et al (2012b). The storm was initiated with an ellipsoidal 4-K thermal bubble with horizontal and vertical radii of 10 and 1.4 km, respectively.…”

“…These considerations motivated a recent observing system simulation experiment (OSSE) study of threedimensional variational data assimilation (3D-VAR) dual-Doppler analysis (DDA) errors under various observational scenarios (e.g., deep versus shallow radar scanning and optimal versus poor radar cross-beam angle; Potvin et al 2012b). Such knowledge is required to 1) select the technique (and technique settings) most likely to minimize analysis errors for a particular case, 2) estimate analysis errors and determine how much confidence to place in inferences drawn from the analysis, and 3) help design future mobile radar deployment and scanning strategies that address significant sources of analysis error.…”

“…DDA techniques provide a relatively straightforward and sophisticated way to retrieve the 3D storm wind field from radar observations, particularly when the 3D-VAR framework is used (Potvin et al 2012c). However, substantial DDA errors can arise from a number of sources including finite observational resolution, incomplete Doppler velocity coverage due to Earth's curvature and low-reflectivity regions, and rapid flow evolution during the analysis period.…”