Generalized VTD Retrieval of Atmospheric Vortex Kinematic Structure. Part I: Formulation and Error Analysis

Abstract

The primary circulation of atmospheric vortices, such as tropical cyclones and tornadoes, can be estimated from single-Doppler radar observations using the ground-based velocity track display (GBVTD) algorithm. The GBVTD algorithm has limitations in the following four areas: 1) distortion in the retrieved asymmetric wind fields, 2) a limited analysis domain, 3) the inability to resolve the cross-beam component of the mean wind, and 4) the inability to separate the asymmetric tangential and radial winds. This paper presents the generalized velocity track display (GVTD) algorithm, which eliminates the first two limitations inherent in the GBVTD technique and demonstrates the possibility of subjectively estimating the mean wind vector when its signature is visible beyond the influence of the vortex circulation. In this new paradigm, the GVTD algorithm fits the atmospheric vortex circulation to a new variable VdD/RT in a linear azimuth angle (θ′), rather than the Doppler velocity Vd in a nonlinear angle (ψ), which is used in GBVTD. Key vortex kinematic structures (e.g., mean wind, axisymmetric tangential wind, etc.) in the VdD/RT space simplify the interpretation of the radar signature and eliminate the geometric distortion inherent in the Vd display. This is a significant improvement in diagnosing vortex structures in both operations and research. The advantages of using VdD/RT are illustrated using analytical atmospheric vortices, and the properties are compared with GBVTD. The characteristics of the VdD/RT display of Typhoon Gladys (1994) can be approximated by a constant mean wind plus an axisymmetric vortex.

The Gradient Velocity Track Display (GrVTD) Technique for Retrieving Tropical Cyclone Primary Circulation from Aliased Velocities Measured by Single-Doppler Radar

“…Note V M is a function of altitude only. Interested readers can find the definitions of variables in LJCD, their appendix A. ApproximatingV d /cosf with V d as in Jou et al (2008), the azimuthal gradient of V d can be obtained by taking the derivative of (3) with respect to azimuth relative to vortex center (referred to as azimuth):…”

“…A series of VTD extensions (referred to as the ''VTD family of techniques'')-including extended VTD (EVTD; Roux and Marks 1996), the ground-based VTD (GBVTD; Lee et al 1999, hereafter LJCD), ground-based extended VTD (GB-EVTD; Roux et al 2004), extended GBVTD (EGBVTD; Liou et al 2006), and generalized VTD (GVTD; Jou et al 2008)-expanded the VTD analysis into multiple flight legs for airborne Doppler radar and multiple ground-based Doppler radars (e.g., Roux and Marks 1996;Lee et al 2000;Harasti et al 2004;Liou et al 2006; Lee and Bell 2007;Zhao et al 2008). Recently, the GBVTD technique has been incorporated into the Vortex Objective Radar Tracking and Circulation (VORTRAC) software for real-time analysis of TCs at the National Hurricane Center (NHC) of the United States.…”

Fitting Parametric Vortices to Aliased Doppler Velocities Scanned from Hurricanes

“…On the other hand, since the Nyquist velocities used by operational weather radars are usually in the range between 20 and 30 m s 21 , radial velocities scanned from intense atmospheric vortices can easily exceed these Nyquist velocities and become severely aliased. Thus, radar velocities had to be dealiased first before they were applied to the aforementioned vortex models and other complex vortex models (Lee et al 1999;Liou et al 2006;Jou et al 2008). Because of this and the reason explained below, it is desirable and useful to develop an alias-robust method that can estimate the vortex intensity and gross structure by directly fitting a parametric vortex model to raw aliased velocity data.…”

Distance Velocity–Azimuth Display (DVAD)—New Interpretation and Analysis of Doppler Velocity

“…While manipulating the Doppler velocity equation to formulate the generalized VTD (GVTD) technique, Jou et al (2008) showed that the atmospheric vortex signatures displayed in rV d (V d scaled by the distance from the radar to the gate, r) had several advantages over those displayed in V d and simplified the governing equations. First, the signature of a constant wind (Fig.…”