3102 MONTHLY WEATHER REVIEW VOLUME 141 A Variational Method for Detecting and Characterizing Convective Vortices in Cartesian Wind Fields COREY K. POTVIN Cooperative Institute for Mesoscale Meteorological Studies, University of Oklahoma, and NOAA/OAR/National Severe Storms Laboratory, Norman, Oklahoma (Manuscript received 14 January 2013, in final form 6 March 2013) ABSTRACT Vortex detection algorithms are required for both research and operational applications in which data volume precludes timely subjective examination of model or analysis fields. Unfortunately, objective de- tection of convective vortices is often hindered by the strength and complexity of the flow in which they are embedded. To address this problem, a variational vortex-fitting algorithm previously developed to detect and characterize vortices observed by Doppler radar has been modified to operate on gridded horizontal wind data. The latter are fit to a simple analytical model of a vortex and its proximate environment, allowing the retrieval of important vortex characteristics. This permits the development of detection criteria tied directly to vortex properties (e.g., maximum tangential wind), rather than to more general kinematical properties that may poorly represent the vortex itself (e.g., vertical vorticity) when the background flow is strongly sheared. Thus, the vortex characteristic estimates provided by the technique may permit more effective detection criteria while providing useful information about vortex size, intensity, and trends therein. In tests with two simulated supercells, the technique proficiently detects and characterizes vortices, even in the presence of complex flow. Sensitivity tests suggest the algorithm would work well for a variety of vortex sizes without additional tuning. Possible applications of the technique include investigating relationships between meso- cyclone and tornado characteristics, and detecting tornadoes, mesocyclones, and mesovortices in real-time ensemble forecasts. 1. Introduction vortex detection algorithms that operate on Cartesian wind output. Such algorithms will become even more Vortex detection methods are critical to severe storms crucial once storm-scale ensemble analysis–forecasting research and operations, for two primary reasons. First, systems are implemented as part of the warn-on-forecast high data volume (e.g., from an ensemble forecast) often paradigm (Stensrud et al. 2009, 2012). precludes timely subjective inspection of output fields. Perhaps the simplest way to identify intense vortices Second, vortices are sometimes obscured by larger-scale in gridded convective storm fields is to threshold the flow, reducing the reliability of visual detection and vorticity field. That approach, however, is prone to error characterization. Existing vortex detection algorithms in noisy wind fields and in regions of strong linear shear. have largely been designed for application to Doppler This has motivated the development of more sophisti- radar data (e.g., Crum and Alberty 1993; Stumpf et al. cated vortex detection methods. For example, Naylor 1998; Mitchell et al. 1998; Smith and Elmore 2004; Liu and Gilmore (2012) identified tornadoes in their 100-m et al. 2007; Wang et al. 2008; Potvin et al. 2009; Potvin grid-spacing simulations using thresholds not just on 1) et al. 2011). With ensemble simulations, analyses, and the vertical vorticity at a provisional vortex center r but forecasts becoming increasingly common in storm-scale 0 also on 2) the maximum horizontal wind speed within research, however, the need has arisen for sophisticated a prescribed radius of r0 and 3) the horizontal pressure gradient between the location of the latter rc, and r0. While this approach appeared to work well in that study, Corresponding author address: Dr. Corey K. Potvin, National Severe Storms Laboratory, National Weather Center, 120 David one limitation (beyond requiring the pressure field to be L. Boren Blvd., Norman, OK 73072. known or reliably analyzed) is that rc may differ sub- E-mail: [email protected] stantially from the azimuthal mean vortex radius of DOI: 10.1175/MWR-D-13-00015.1 Ó 2013 American Meteorological Society Unauthenticated | Downloaded 10/03/21 02:06 PM UTC SEPTEMBER 2013 P O T V I N 3103 maximum wind, and r0 from the vortex center, if the Implications of the results for research and operational total wind field within the vortex exhibits strong axial applications are discussed in section 4. asymmetry. This can occur when the vortex is embedded within strongly (linearly) sheared flow, or contains 2. Vortex detection algorithm smaller-scale structures that are resolved on the input grid. To mitigate the effect of linear shear, Markowski The algorithm employs a time-independent version of et al. (2011) identified low-level mesocyclone centers in the low-order model of Potvin et al. (2009). The model is objectively analyzed mobile radar data with negative the sum of a modified combined Rankine vortex (MCRV; minima in the Okubo–Weiss number (W; Okubo 1970; e.g., Hughes 1952; Brown et al. 2002) and a background Weiss 1991) rather than with maxima in vertical vortic- wind field. The latter is the sum of a spatially constant ity. To reduce the impact of smaller-scale features, the flow, linearly sheared flow, and linearly divergent flow. deformation and vorticity fields were smoothed such The low-order model is 2D; thus, the detection algorithm that the subsequently computed W better represented is best suited to constant-altitude or layer-averaged wind the mesocyclone-scale flow. To the author’s knowledge, fields. The model horizontal winds u and y are given by however, W has not been used as the basis of a vortex 8 > V V detection and characterization algorithm, and so it is yet <>a1by1cx1 R(x2x )2 T (y2y ), r ,R, R 0 R 0 unclear how effective such a technique would be. Up- u5 > b a draft helicity (UH; Kain et al. 2008) thresholds have > R V (x2x ) R V (y2y ) :a1by1cx1 R 0 2 T 0 , r $R, been successfully used to identify the presence and in- rb11 ra11 tensity trends of midlevel mesocyclones in convection- (1) allowing model forecasts (e.g., Sobash et al. 2011; Clark 8 et al. 2012; Carley et al. 2011) and higher-resolution > V V <>d1ex1fy1 R(y2y )1 T (x 2 x ), r ,R, simulations (Naylor et al. 2012). It remains to be seen, R 0 R 0 y5 however, whether UH (computed near the ground > b a > R V (y2y ) R V (x2x ) rather than over the commonly used 2–5-km AGL layer) : 1 1 1 R 0 1 T 0 $ d ex fy b11 a11 , r R, could be effective for detecting lower-level vortices. r r The new detection technique tested herein is a modi- (2) fication of the variational vortex-fitting method of where Potvin et al. (2009, 2011). In the original technique, ra- dial wind observations from two or more Doppler radars qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 5 2 2 1 2 2 are fit to an analytical low-order model of a vortex and r (x x0) (y y0) ; (3) its near environment. This enables the retrieval of useful vortex characteristics, including the radius of maximum a and d are the x and y components of the uniform flow 2 wind and the maximum tangential wind speed. The velocity (m s 1); b and e are the components of the 2 present technique is similar to the original technique horizontal shear (s 1); c and f are the components of the 21 except that it operates on Cartesian horizontal wind data horizontal divergence (s ); (x0, y0) are the vortex cen- rather than on Doppler velocity observations, render- ter coordinates (m); R is the vortex radius of maximum ing it suitable for application to storm-scale simula- wind (m); VT and VR are the maximum tangential and 2 tions, analyses, and forecasts. A major strength of both radial vortex velocities (m s 1), respectively; and a and techniquesisthattheoutputvortexsizeandintensity b are the radial decay exponents for the vortex tan- estimates permit the development of detection criteria gential and radial winds, respectively [see Potvin et al. based directly on vortex properties, rather than on (2009) for the derivation of the MCRV Cartesian wind properties of the total wind field that may not be very components]. High-resolution mobile radar observa- representative of the vortex itself (e.g., vertical vor- tions qualitatively support the use of the MCRV to ticity in the case where a vortex lies within a region of represent tornadoes (Wurman and Gill 2000; Bluestein strong linear shear). Therefore, the vortex-fitting ap- et al. 2003; Lee and Wurman 2005; Kosiba and Wurman proach may improve upon other vortex detection 2010), and it is reasonable to expect that mesocyclones methods while also providing useful estimates of vortex also do not deviate substantially from that model. characteristics. The low-order model parameters are retrieved over The rest of this paper is organized as follows. The square analysis domains, the locations of which are de- proposed vortex detection and characterization algo- termined using the following automated procedure. First, rithm is described in section 2. The technique is tested on the input (i.e., simulation, analysis, or forecast) domain is two high-resolution supercell simulations in section 3. divided into 6-km-wide subdomains (these are distinct Unauthenticated | Downloaded 10/03/21 02:06 PM UTC 3104 MONTHLY WEATHER REVIEW VOLUME 141 FIG. 1. Overview of the vortex detection and characterization procedure: (a) identification of subdomains with vorticity-exceeding threshold, (b) division of each such subdomain into 25 analysis domains centered on first-guess vortex centers (dots), (c) retrieval of low-order model parameters within each analysis domain, and (d) application of detection criteria to retrievals and averaging of characteristics of proximate retrieved vortices passing the detection criteria. from the analysis domains that are eventually identified). wind retrievals (Fig. 1c) have finished for a given time Then, at each time step, subdomains containing at least step, useful characteristics (e.g., R) of retrieved vorti- one grid point where the vertical vorticity (hereafter, ces that pass the detection criteria (described later in 2 simply ‘‘vorticity’’ or z) exceeds 0.01 s 1 are recorded this section) are output (Fig.