Use of a Vertical Vorticity Equation in Variational Dual-Doppler Wind Analysis

Abstract

The utility of the anelastic vertical vorticity equation in a weak-constraint (least squares error) variational dual-Doppler wind analysis procedure is explored. The analysis winds are obtained by minimizing a cost function accounting for the discrepancies between observed and analyzed radial winds, errors in the mass conservation equation, errors in the anelastic vertical vorticity equation, and spatial smoothness constraints. By using Taylor’s frozen-turbulence hypothesis to shift analysis winds to observation points, discrepancies between radially projected analysis winds and radial wind observations can be calculated at the actual times and locations the data are acquired. The frozen-turbulence hypothesis is also used to evaluate the local derivative term in the vorticity equation. Tests of the analysis procedure are performed with analytical pseudo-observations of an array of translating and temporally decaying counterrotating updrafts and downdrafts generated from a Beltrami flow solution of the Navier–Stokes equations. The experiments explore the value added to the analysis by the vorticity equation constraint in the common scenario of substantial missing low-level data (radial wind observations at heights beneath 1.5 km are withheld from the analysis). Experiments focus on the sensitivity of the most sensitive analysis variable—the vertical velocity component—to values of the weighting coefficients, volume scan period, number of volume scans, and errors in the estimated frozen-turbulence pattern-translation components. Although the vorticity equation constraint is found to add value to many of these analyses, the analysis can become significantly degraded if estimates of the pattern-translation components are largely in error or if the frozen-turbulence hypothesis itself breaks down. However, tests also suggest that these negative impacts can be mitigated if data are available in a rapid-scan mode.

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

“…As a result, increasing l S by a given factor had roughly the same effect on the analysis as decreasing l O by the same factor, and vice versa. All of these results are consistent with Shapiro et al (2009).…”

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

“…As a result, increasing l S by a given factor had roughly the same effect on the analysis as decreasing l O by the same factor, and vice versa. All of these results are consistent with Shapiro et al (2009).…”

The Effects of Spatial Interpolation on a Novel, Dual-Doppler 3D Wind Retrieval Technique

“…Future work will be aimed at generalizing these results using further OSSEs and real data examples containing different weather phenomena (e.g., stratiform precipitation, tropical cyclones or mesoscale convective systems). We also aim to assess how the improvements achieved with the RA technique will function alongside other recent 3D wind retrieval developments, such as vertical vorticity constraints (Shapiro et al 2009;Potvin et al 2012b) and spatially variable advection corrections (Shapiro et al 2010). Finally, we aim to verify the results of our OSSEs with vertical velocity measurements from observed cases, as demonstrated recently in Gebauer et al (2022).…”

A Case Study of a Hailstorm in the Shanghai Region: Leveraging Multisource Observational Data and a Novel Single-Polarization X-Band Array Weather Radar

“…At the center of each subplot is one reflectivity factor image from the Qingpu SA radar. Although the wind field retrieval and wind field validation capabilities of the AWR have been previously evaluated [43,44,45,47,49,50,51], the continuous Shanghai AWR data presented in Figure 10a–c further illustrate its ability to continuously detect reflectivity intensity fields and retrieve wind fields within overlapped detection areas.…”

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

“…As a result, increasing l S by a given factor had roughly the same effect on the analysis as decreasing l O by the same factor, and vice versa. All of these results are consistent with Shapiro et al (2009).…”

The Effects of Spatial Interpolation on a Novel, Dual-Doppler 3D Wind Retrieval Technique

“…Future work will be aimed at generalizing these results using further OSSEs and real data examples containing different weather phenomena (e.g., stratiform precipitation, tropical cyclones or mesoscale convective systems). We also aim to assess how the improvements achieved with the RA technique will function alongside other recent 3D wind retrieval developments, such as vertical vorticity constraints (Shapiro et al 2009;Potvin et al 2012b) and spatially variable advection corrections (Shapiro et al 2010). Finally, we aim to verify the results of our OSSEs with vertical velocity measurements from observed cases, as demonstrated recently in Gebauer et al (2022).…”

A Case Study of a Hailstorm in the Shanghai Region: Leveraging Multisource Observational Data and a Novel Single-Polarization X-Band Array Weather Radar

“…At the center of each subplot is one reflectivity factor image from the Qingpu SA radar. Although the wind field retrieval and wind field validation capabilities of the AWR have been previously evaluated [43,44,45,47,49,50,51], the continuous Shanghai AWR data presented in Figure 10a–c further illustrate its ability to continuously detect reflectivity intensity fields and retrieve wind fields within overlapped detection areas.…”

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

“…As a result, increasing l S by a given factor had roughly the same effect on the analysis as decreasing l O by the same factor, and vice versa. All of these results are consistent with Shapiro et al (2009).…”

The Effects of Spatial Interpolation on a Novel, Dual-Doppler 3D Wind Retrieval Technique

“…Future work will be aimed at generalizing these results using further OSSEs and real data examples containing different weather phenomena (e.g., stratiform precipitation, tropical cyclones or mesoscale convective systems). We also aim to assess how the improvements achieved with the RA technique will function alongside other recent 3D wind retrieval developments, such as vertical vorticity constraints (Shapiro et al 2009;Potvin et al 2012b) and spatially variable advection corrections (Shapiro et al 2010). Finally, we aim to verify the results of our OSSEs with vertical velocity measurements from observed cases, as demonstrated recently in Gebauer et al (2022).…”

A Case Study of a Hailstorm in the Shanghai Region: Leveraging Multisource Observational Data and a Novel Single-Polarization X-Band Array Weather Radar

“…At the center of each subplot is one reflectivity factor image from the Qingpu SA radar. Although the wind field retrieval and wind field validation capabilities of the AWR have been previously evaluated [43,44,45,47,49,50,51], the continuous Shanghai AWR data presented in Figure 10a–c further illustrate its ability to continuously detect reflectivity intensity fields and retrieve wind fields within overlapped detection areas.…”