3102 MONTHLY WEATHER REVIEW VOLUME 141

A Variational Method for Detecting and Characterizing Convective Vortices in Cartesian Fields

COREY K. POTVIN Cooperative Institute for Mesoscale Meteorological Studies, University of Oklahoma, and NOAA/OAR/National Severe 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 -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 ) 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 , 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- and characteristics, and detecting tornadoes, , and 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 -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 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 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 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 simulations in section 3. divided into 6-km-wide subdomains (these are distinct

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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. 1d). Detected vortices (Fig. 1a). Next, a 5 3 5 grid of first-guess vortex centers is locatedwithin1000mofeachotherandhavingthe constructed over each identified subdomain (Fig. 1b). same direction of rotation (i.e., like-signed VT)are The use of multiple first guesses for the vortex center is assumed to correspond to the same vortex in the input critical to detecting all vortices in the input wind field wind field. In such cases, the characteristics of the (Potvin et al. 2009). Finally, a 6-km-wide analysis domain proximate vortices are averaged together to form a is centered on each first-guess vortex center. Once all the ‘‘mean vortex.’’

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The wind retrieval within each analysis domain pro- was largely motivated by poor retrievals in instances ceeds as follows. A cost function J is computed as the where a strong deformation zone exists north of the sum of the squared differences between the input winds maximum in the rear-flank downdraft outflow (Fig. 3a). uinput, yinput and the model winds: In such cases, the broadscale model parameters in steps 1 and 3 fail to adequately capture the larger-scale flow J [ å å [(u 2 uinput)2 1 (y 2 yinput)2], (4) (Fig. 3b), substantial portions of which consequently i j remain in the residual wind fields input into the vortex retrievals (steps 2 and 4; Fig. 3c). The vortex model where i and j are the zonal and meridional grid indices, parameters subsequently retrieve much of the residual respectively. To optimize (in the least squares sense) the deformation flow (Fig. 3d), resulting in a false vortex fit between the model and input winds and thereby re- detection and, in some cases, failure to detect an em- trieve the low-order model parameters, J is minimized bedded vortex (located at x 5 96 km, y 5 58 km in using the Polak–Ribiere (1969) conjugate-gradient Fig. 3f). The false detection problem is addressed by method. The first guesses for the broadscale model pa- rejecting total wind retrievals (from steps 3 and 4) whose rameters are set to zero. The first guesses for both VT errors within the retrieved vortex core exceed 40% of 21 21 and VR are set to 1 m s (21ms ) to detect cyclonic the mean wind speed over the same region. While ad- (anticyclonic) vortices. The first guesses for R, a, and b mittedly ad hoc, the chosen error threshold worked well are set to 1000 m, 0.7, and 0.7, respectively. for the wide range of wind fields on which the algorithm As in Potvin et al. (2009, 2011), a multiple-step pro- was tested (section 3), suggesting this detection criterion cedure is used to retrieve the wind field within each is fairly robust. To ensure the detection of any vortices analysis domain (Fig. 2). In step 1, VT and VR are fixed at embedded in the deformation flow in such cases, rather zero (i.e., the vortex model parameters are not re- than restarting the retrieval procedure at the next first- trieved) while the broadscale model parameters are re- guess vortex center, broadscale and vortex retrievals covered. The retrieved broadscale wind field (Fig. 2b) is (steps 5 and 6) are performed over an analysis domain subsequently subtracted from the input wind field with the radius (center) set to the retrieved R (x0 and y0) (Fig. 2a). In step 2, using the residual wind field from from step 2 (therefore, steps 5 and 6 are identical to steps step 1 (Fig. 2c) as the new uinput and yinput, the broadscale 3 and 4 except the analysis domain is set to R rather than model parameters are fixed at zero while the vortex 1.5R). Since the nonvortex flow over the modified analysis model parameters are retrieved (Fig. 2d).1 Subtracting domain varies roughly linearly (enough to resemble a the retrieved broadscale flow prior to retrieving the vortex core, leading to the false vortex detection in step 2), vortex parameters was found in preliminary experi- most of the deformation flow is retrieved by the broad- ments and in Potvin et al. (2009) to help prevent the scale model parameters in step 5 (cf. Figs. 3g and 3h), retrieval of unrealistically broad vortices that better allowing the embedded vortex (if present) to be well re- represent the larger-scale flow than the vortex itself. If trieved in step 6 (cf. Figs. 3i and 3j; cf. Figures 3g and 3k). the vortex parameters retrieved in step 2 do not satisfy Retrieval steps 5 and 6 were also occasionally re- the detection criteria (described below), the retrieval quired to detect a vortex embedded in another vortex procedure restarts at step 1 at the next first-guess vortex (Fig. 4). In that scenario, the local minimum in W (not center. If, on the other hand, a vortex is detected, the shown) is typically collocated with the smaller vortex retrieval proceeds to step 3. Steps 3 and 4 (Figs. 2g–j) are (since the latter locally enhances vorticity) and thus is identical to steps 1 and 2 except the analysis domain displaced from the center of the larger vortex. Retrieval center and radius are set to (x0, y0) and 1.5R,respectively, steps 5 and 6 are therefore performed if the minimum W retrieved in step 2. In preliminary experiments and in within the retrieved core (from step 4) of a vortex Potvin et al. (2011), the strategy of repeating the retrieval passing the detection criteria lies more than R/2 from the within an analysis domain customized to a preliminarily retrieved vortex center. Modifying the analysis domain detected vortex improved the retrieval of vortices em- to barely encompass the retrieved core of the larger bedded in high-vorticity flow. vortex in such cases results in much of the latter being The retrieval procedure in the present algorithm has captured and removed in step 5 [since the shear and been expanded from four to six steps. This modification divergence parameters implicitly make provision for solid-body rotation; Potvin et al. (2009)], allowing the embedded vortex to be retrieved in step 6. 1 Retrieving the broadscale model parameters in addition to the As with other minimization problems, multiple min- vortex model parameters in step 2 as in Potvin et al. (2009, 2011) ima in J in the present case can prevent the desired mildly degraded the algorithm performance in the present study. minimum (that associated with an intense vortex in the

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FIG. 2. Representative retrieval from the 333-m simulation at z 5 1.1 km: (a) input (simulated) wind field, (b) step 1 (broadscale) retrieval, (c) residual (input 2 broadscale) wind field, (d) step 2 (vortex) retrieval, (e) total (step 1 1 step 2) retrieval, and (f) difference res between input and total retrieved wind fields (errors). (g)–(l) As in (a)–(f), but for retrieval steps 3 and 4. The retrieved VT and R from steps 2 and 4 are shown in (d) and (j), respectively.

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FIG. 3. Retrieval of a vortex obscured by strong deformation north of the apex of the rear-flank downdraft outflow at z 5 1.1 km: (a) input (simulated) wind field, (b) step 3 (broadscale) retrieval, (c) residual (input 2 broadscale) wind field, (d) step 4 (vortex) retrieval, (e) total (step 3 1 step 4) retrieval, and (f) difference between input and total retrieved wind fields (errors). (g)–(l) As in (a)–(f), but for res retrieval steps 5 and 6. The retrieved VT and R from steps 4 and 6 are shown in (d) and (j), respectively.

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FIG. 4. As in Fig. 3, but for the scenario where a vortex is embedded in a larger vortex. input wind field) from being reached. Local minima in function becomes highly elliptical, in which case even the current problem can result from the nonlinearity of small model violations may be sufficient to produce spu- (1)–(4) and from violations of the low-order model. The rious minima. To reduce the ellipticity of J (and increase threat of local minima increases as the surface of the cost the convergence rate of the minimization algorithm),

Unauthenticated | Downloaded 10/03/21 02:06 PM UTC SEPTEMBER 2013 P O T V I N 3109 the first-guess vector is scaled such that the gradients of (Dx 5 333 m) simulations, respectively. In both simu- J with respect to each of the model parameters become lations, the storm was initiated with a thermal bubble, closer in magnitude (Wang et al. 1997). To accomplish and the base state was provided by the composite this, the scaling factors are set to physically realistic sounding in Potvin et al. (2012). The algorithm was values of each of the parameters. The multiple-minima applied to the simulated wind fields every minute at z 5 problem is further addressed by rejecting retrievals where 100 m, 1.1 km, and ’4 km. This allowed the technique the vortex center in step 4 lies within R/2 of the edge of to be tested with a variety of vortices and flow regimes. the analysis domain, since spurious vortices whose wind Algorithm output was evaluated for cyclonic vortices fields are heavily truncated by the edge of the analysis within the right-moving supercell in each simulation. domain are often associated with local minima (Potvin Cursory inspection of the cyclonic vortex retrievals in et al. 2009). the left-moving supercells, and of the anticyclonic A final way in which the multiple-minima problem is vortex retrievals obtained in another set of experiments 21 mitigated is by adopting vortex detection criteria that (with first guesses for VT and VR set to 21ms ), are insensitive to the solution nonuniqueness that arises supports the assessment of the algorithm performance in R and VT when the vortex is poorly resolved (Potvin given in section 3c. et al. 2011). In cases where R $ Dx, the vortex core b. Retrieval verification procedure (solid-body rotation region) is considered sufficiently well resolved for the retrieved VT to be reliable. Oth- Since the input wind fields were not analytically gen- erwise, the tangential wind speed at r 5Dx, considered erated in these experiments, the vortex model parame- res here to be the maximum ‘‘resolved’’ tangential wind VT ters do not have well-defined ‘‘true’’ or ‘‘optimal’’ is computed: values. This introduces subjectivity into the retrieval  verification process, especially in cases where a vortex is V , R $ Dx, res 5 T embedded within strong, complex flow. Nevertheless, VT D a ,D (5) VT (R/ x) , R x. the algorithm can still be meaningfully evaluated by comparing the retrieved and input wind fields. Figure 2 In the experiments below, a retrieved vortex is retained (introduced in the previous subsection) depicts a repre- res . 21 5 if VT 10 m s . The choice for this threshold was sentative retrieval from the 333-m simulation at z somewhat arbitrary. The optimal threshold value will 1.1 km. While the broadscale model parameters fail to vary according to the minimum size and intensity of the capture the maximum in the rear-flank downdraft out- vortices sought, and the degree to which the smallest and flow in step 1 (cf. Figs. 3a and 3b), comparisons of the weakest vortices are resolved in the input wind analysis. residual wind field (Fig. 3c) with the retrieved vortex field (Fig. 3d) and of the total input wind field (Fig. 3a) with the total retrieved wind field (Figs. 3e and 3f) sug- 3. Tests with supercell simulations gest the vortex core is retrieved reasonably well. Thus, the (x , y ), R, and Vres retrieved in step 2 (Fig. 3e) are a. Experimental setup 0 0 T plausible. Similar assessment of the retrieval from steps The vortex algorithm was tested using two idealized 3 and 4 (Figs. 3g–l) reveals the vortex parameters re- supercell simulations generated using the trieved in step 4 are also reasonable. The retrieval from National Severe Storms Laboratory Collaborative Model steps 3 and 4, however, better matches the input wind for Multiscale Atmospheric Simulation (NCOMMAS; field in the vicinity of the vortex (cf. Figs. 3f and 3l) than Wicker and Skamarock 2002; Coniglio et al. 2006). A does the retrieval from steps 1 and 2, suggesting the fully dual-moment version of the Ziegler (1985) micro- vortex retrieval from step 4 is (as intended) more ac- physics scheme (Mansell et al. 2010) was used. A prog- curate than that from step 2. The vortex retrieved in step nostic turbulent energy equation similar to that of 2 appears slightly too strong, likely due in part to the Deardorff (1980) was used to parameterize the turbu- strong shear along the southern periphery of the vortex lent mixing coefficient. Each simulation proceeded on in the residual wind field from step 1. The flow in the a 200 km 3 200 km 3 20 km domain with vertical spac- same region is less sheared in the residual wind field ing increasing from 200 m over the lowest 1 km to 600 m from step 3 (cf. Figs. 3c and 3i) since the broadscale flow above z 5 13 km. The Dx was set to 333 m in one sim- is more linear over the smaller analysis domain and, ulation and to 1000 m in the other to test whether the thus, better captured by the model parameters. While it algorithm performance is sensitive to the resolution of is also plausible that the low-order model is violated in the input wind field. Large and small time steps of 4 this case such that the stronger vortex in step 2 better and 2/3 s(1and1/6 s) were used for the Dx 5 1000 m represents the true vortex despite the larger errors in the

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FIG. 5. Locations of retrieved cyclonic vortices at z 5 (a) ;4, (b) 1.1, and (c) 0.1 km in a 1000-m simulation (t 5 0–2 h), and the maximum cyclonic vorticity occurring at each grid point (shading). # res , 21 # res , 21 Black symbols show 10 VT 15 m s , green symbols are for 15 VT 20 m s , circles for R , 1000 m, triangles for 1000 # R , 2000 m, and squares for R $ 2000 m.

res total retrieved wind field, this seems the less likely of the The locations, R, and VT of the mean retrieved cy- two possibilities. clonic vortices in each simulation are depicted in Figs. 5 and 6.2 The trends in retrieved vortex size and intensity c. Algorithm performance were found to comport well with the evolution of the For all of the retrieved vortices satisfying the de- simulated vortices, indicating that the intrinsic uncer- tection criteria, the retrieved wind field within the vortex tainty in the retrieved vortex parameters is not so large core (r , R) resembled the input wind field fairly well as to mask identifiable tendencies in input vortices. For (e.g., Fig. 2). Accordingly, all vortex detections corre- example, the much smaller number of detections at z ’ res . 5 sponded to input vortices that plausibly had VT 4 km than at z 1.1 km is consistent with the simulated 2 10 m s 1 (i.e., no obviously false detections occurred). midlevel mesocyclones appearing generally weaker (not Conversely, the algorithm detected all simulated vorti- shown) than the low-level mesocyclones (the number of ’ res ces that, based on visual inspection and/or comparison detections at z 4 km increases dramatically when VT with retrieved wind fields, could be confidently de- res . 21 termined to have VT 10 m s . The ability of the al- gorithm to detect even vortices embedded within strong 2 The detections south of the storm track in Figs. 6c and 9a,b cor- deformation or larger vortices (Figs. 3 and 4) is partic- respond to ‘‘gustnado’’-like vortices along the leading edge of the ularly encouraging. cold pool in the 333-m simulation.

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FIG. 6. As in Fig. 5, but for a 333-m simulation.

2 is decreased to 5 m s 1; not shown). Confidence in the substantial portion of the outer vortex flow, resulting in accuracy of the retrieved vortex centers was increased the latter being truncated in the residual wind field input by their proximity (generally , 500 m) to the local to retrieval step 2. This hypothesis is supported by the Okubo–Weiss number minimum. The locations of the fact that much more realistic a and b estimates (gener- vortices detected at each of the three examined heights ally, 0.5–1.2) were obtained when the 333-m experi- within each simulation are compiled in Fig. 7. Figures 5–7 ments were repeated (not shown) with retrieval steps 1 illustrate the potential utility of the algorithm output and 3 modified to allow both the broadscale and the for examining the evolution of vortex motion, size, and vortex parameters to vary (but with only the retrieved strength at different heights within different simulations/ broadscale flow subtracted from the input winds prior to analyses/forecasts. steps 2 and 4, as in the original procedure). The R and res res While R and VT appear to be retrieved reasonably VT estimates, however, were not substantially changed, well, the wind decay parameters a and b are systemati- and the differences that resulted were generally too cally overestimated, with retrieved values of both param- small to attribute to either increases or decreases in er- eters (especially a) routinely exceeding 2, and occasionally ror. This suggests that the poor retrieval of a and b in the exceeding 5 [estimates of a derived from mobile Doppler presented experiments is not indicative of substantial res observations of tornadoes are generally 0.5–0.8; e.g., errors in R and VT . This hypothesis is consistent with Wurman and Gill (2000); Lee and Wurman (2005); the similarity between the input and retrieved vortex Kosiba and Wurman (2010)]. The corresponding sharp cores (section 2b). The original retrieval procedure was decrease in the outer (r . R) vortex winds is tentatively retained since the modified procedure increased the attributed to the broadscale parameters retrieving a total computational time of the detection algorithm by

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between maximum vorticity and maximum vortex tan- gential winds arises largely from the frequent superposi- tion of vortices with strong linear shear in the simulations. As stated in the introduction, the commonness of this scenario in nature is a major motivation for the vortex- fitting approach. d. Retrieval sensitivity to first-guess R and analysis domain size The values of the first-guess R (1000 m) and analysis domain width (D; 6 km) adopted in the above experi- ments were optimized in preliminary tests using trial and error. That the selected values worked well for the range of vortices and broadscale flows to which the algorithm was applied is encouraging. In applications where the FIG. 7. Locations of vortex detections at z 5 0.1 km (black), 1.1 km vortex radii are highly uncertain or strongly variable, (green), and ;4 km (red) in (a) 1000- and (b) 333-m simulations. however, errors in the first-guess R may occasionally be very large. In addition, larger D than used herein would an order of magnitude without producing detectable likely be required to encompass the largest mesocy- res improvements in R and VT . clones and quasi-linear convective system mesovortices. As suggested by careful inspection of Figs. 5 and 6, It is also possible that smaller D would be required for and confirmed by examination of algorithm output and vortices with R 1000 m. vorticity fields at individual times, there are many in- These considerations motivated additional experi- stances where the maximum vorticity value within an ments in which the first-guess R and D were varied. Only intense vortex at a particular time is exceeded at another results from the 333-m simulation experiments are location–time where no intense vortex is present. For shown in the figures below; sensitivity tests with the example, in Fig. 6b, the vortex detections west of x 5 1000-m simulation (but with the first-guess R varied 70 km are associated with maximum vorticity values from 1000 to 2000 m) yielded qualitatively similar re- 2 2 of ;0.04 s 1, while vorticity values exceeding 0.05 s 1 sults. In the first set of tests, D was held at 6 km and the occur near x 5 120 km in the absence of any vortex first-guess R was set to 500 or 1500 m. The z 5 1.1 km detections. The lack of a one-to-one correspondence results are shown in Fig. 8; all discussion in this section

FIG. 8. As in Fig. 6, but at z 5 1.1 km for first-guess R of (a) 500, (b) 1000, and (c) 1500 m.

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FIG. 9. As in Fig. 6, but at z 5 0.1 km for analysis domain widths of (a) 4, (b) 6, and (c) 10 km. 21 Red symbols indicate 20 # Vres , 25 m s . applies to the algorithm output at all three tested cases where very large vortices may be present (requiring heights. Overall, the mean vortex retrievals were not wider analysis domains), the choice of first-guess R re- excessively sensitive to the first-guess R. In most cases, mains uncritical to the algorithm’s performance. the differences that occurred could not be attributed to increases or decreases in error (due to the uncertainty in 4. Discussion the ‘‘optimal’’ vortex parameter values). Furthermore, res temporal trends in the mean retrieved R and VT were The proposed algorithm appears to effectively retrieve qualitatively similar among the experiments. convective vortices, a nontrivial task given the strong, In the second set of sensitivity tests, the original first- complex wind fields in which they are often embedded. guess R was retained and D was set to 4 or 10 km (Fig. 9). The relative insensitivity of the technique to the first-guess Inspection of the input and retrieved wind fields re- R and analysis domain width suggests it would work well vealed that increasing nonlinearity in the nonvortex flow for a wide range of vortex sizes. The technique may on larger scales occasionally resulted in obviously therefore be useful for both research and operational poorer broadscale flow retrievals in the D 5 10 km ex- activities that require automated detection and charac- periments. In those cases, larger portions of the non- terization of convective vortices. Possible research appli- vortex flow were retained in the residual wind fields and cations include investigations of the relationship between subsequently retrieved by the vortex model parameters, mesocyclone characteristics or environmental parameters res leading to overestimated R and VT . Fortunately, most (e.g., storm-relative helicity) and tornado probability, such retrievals failed the detection criterion that the size, and intensity. Possible operational applications mean error in the total retrieved wind field within the include detecting and characterizing tornadoes and me- vortex core be less than 40% of the mean wind speed socyclones in real-time wind analyses and ensemble over the same region. Consequently, as in the first-guess forecasts (critical for the warn-on-forecast paradigm). R sensitivity experiments, differences among the vortex In some applications, it may be desirable to identify detections obtained using different D were usually too only vortices having a minimum depth and/or duration. small to attribute to increases or decreases in error. Fortunately, the output of the technique at various In a third set of tests (not shown), the analysis domain heights and/or times could be combined in simple, in- width was set to 10 km and the first-guess R varied from tuitive ways to suit user needs. For example, supercell j resj . 21 500 to 1500 m. The sensitivity of the retrievals to the classification could require that VT 5ms over first-guess R was similar to that in the first set of ex- 75% of the 2–5-km AGL layer for 20 min. Alternatively, periments with 6-km-wide domains. This suggests that in it would be relatively straightforward to modify the

Unauthenticated | Downloaded 10/03/21 02:06 PM UTC 3114 MONTHLY WEATHER REVIEW VOLUME 141 technique to retrieve vortex characteristics over 3D anal- Hughes, L. A., 1952: On the low-level structure of tropical storms. J. Meteor., 9, 422–428. ysis domains using height-dependent (x0, y0), R,andVT. An important aspect of any algorithm, particularly for Kain, J. S., S. J. Weiss, J. J. Levit, M. E. Baldwin, and D. R. Bright, 2006: Examination of convective-allowing configurations of real-time applications, is the computational cost. For the the WRF model for the prediction of severe convective Dx 5 333 m (Dx 5 1000 m) experiments, each set of 25 weather: The SPC/NSSL Spring Program 2004. Wea. 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