Vortex Lines Within Low-Level Mesocyclones Obtained From

SEPTEMBER 2008 MARKOWSKI ET AL. 3513

Vortex Lines within Low-Level Mesocyclones Obtained from Pseudo-Dual-Doppler Radar Observations PAUL MARKOWSKI,* ERIK RASMUSSEN, JERRY STRAKA,# ROBERT DAVIES-JONES,@ YVETTE RICHARDSON,* AND ROBERT J. TRAPP& *Department of Meteorology, The Pennsylvania State University, University Park, Pennsylvania Rasmussen Systems, Mesa, Colorado #School of Meteorology, University of Oklahoma, Norman, Oklahoma @National Severe Storms Laboratory, Norman, Oklahoma &Department of Earth and Atmospheric Sciences, Purdue University, West Lafayette, Indiana

(Manuscript received 24 July 2007, in final form 4 January 2008)

ABSTRACT

Vortex lines passing through the low-level mesocyclone regions of six supercell thunderstorms (three nontornadic, three tornadic) are computed from pseudo-dual-Doppler airborne radar observations obtained during the Verification of the Origins of Rotation in Tornadoes Experiment (VORTEX). In every case, at least some of the vortex lines emanating from the low-level mesocyclones form arches, that is, they extend vertically from the cyclonic vorticity maximum, then turn horizontally (usually toward the south or southwest) and descend into a broad region of anticyclonic vertical vorticity. This region of anticyclonic vorticity is the same one that has been observed almost invariably to accompany the cyclonic vorticity maximum associated with the low-level mesocyclone; the vorticity couplet straddles the hook echo of the supercell thunderstorm. The arching of the vortex lines and the orientation of the vorticity vector along the vortex line arches, compared to the orientation of the ambient (barotropic) vorticity, are strongly suggestive of baroclinic vorticity generation within the hook echo and associated rear-flank downdraft region of the supercells, and subsequent lifting of the baroclinically altered/generated vortex lines by an updraft. Dis- cussion on the generality of these findings, possible implications for tornadogenesis, and the similarity of the observed vortex lines to vortex lines in larger-scale convective systems are included as well.

1. Introduction ponent at a time. For example, the dynamics of midlevel mesocyclogenesis in supercell thunderstorms Vortex lines (also sometimes called vortex filaments) is easily demonstrated by way of vortex lines (Davies- are lines tangent to the vorticity vector, analogous to Jones 1984; Rotunno and Klemp 1985; Fig. 1). Vortex the streamline in a velocity vector field (Dutton 1986, p. line analyses in phenomena like thunderstorms are 364; Pedlosky 1987, p. 25; Kundu 1990, p. 120).1 Vortex complicated by the baroclinic generation of vorticity by lines can aid the visualization of the three-dimensional the horizontal buoyancy gradients that accompany pre- vorticity field. The three-dimensional perspective pro- cipitation regions and vertical drafts. In the presence of vided by vortex lines can expose dynamics that may not significant baroclinic vorticity generation, vortex lines be as apparent in inspections of only one vorticity com- may not even closely approximate material lines (Helmholtz’ theorem). Nonetheless, vortex line analyses can be enlightening in that they can suggest plau- 1 What are referred to as “vortex lines” herein are termed “vor- sible methods of vorticity generation and reorientation ticity lines” by Lugt (1996, p. 90). Lugt defines a vortex line as an (e.g., observations of vortex rings might lead one to isolated vorticity line within a wind field that is otherwise irrota- surmise that a local buoyancy extremum is present and tional. responsible for the generation of the rings). Although the vertical component of vorticity tends to be empha- Corresponding author address: Dr. Paul Markowski, 503 sized in supercell thunderstorm and tornado studies, Walker Building, University Park, PA 16802. there is some merit in systematically inspecting the dis- E-mail: [email protected] tribution and orientation of three-dimensional vortex

DOI: 10.1175/2008MWR2315.1

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FIG. 1. (a) Effect of a localized vertical displacement “peak” (i.e., hump in an isentropic surface) on vortex lines when the mean vorticity ␻ and mean storm-relative flow v c are perpendicular (purely crosswise vorticity). The peak draws up loops of vortex lines (shown slightly above, instead of in, the surface for clarity), giving rise to cyclonic vorticity on the right side of the peak (relative to the shear vector S) and anticyclonic vorticity on the left side. [Solenoidal effects (not included in the drawing) actually divert the vortex lines around the right (left) side of a warm (cool) peak, relative to the mean vorticity vector, but do not alter the result.] The environmental flow across the expanding peak produces maximum updraft upstream (storm-relative frame) of the peak due to the upslope component of the vertical velocity. In this case, there is no correlation between vertical velocity and vertical vorticity. (b) As in (a), but for the other extreme when vorticity is purely streamwise (i.e., ␻ is parallel to v c). Here, the upslope (downslope) side of the peak is also the cyclonic (anticyclonic) side, and the vertical velocity and vertical vorticity are positive correlated. (From Davies-Jones 1984.) lines in observed and simulated storms. A lengthier dis- wind fields) with the exception of the recent supercell cussion on the benefits of vortex line analysis appears in thunderstorm studies by Majcen et al. (2006) and Straka et al. (2007). Straka et al. (2007). Vortex line analyses appear relatively infrequently The origins of midlevel and low-level rotation in su- within the body of severe local storms literature. In percell thunderstorms have been reviewed by Davies- addition to the previously cited theoretical and numeri- Jones and Brooks (1993), Rotunno (1993), and Davies- cal modeling studies of midlevel mesocyclogenesis by Jones et al. (2001). [Herein, “low level” refers to alti- Davies-Jones (1984) and midlevel and low-level meso- tudes nominally Յ1000 m AGL. Davies-Jones et al. cyclogenesis by Rotunno and Klemp (1985), respec- (2001) referred to these altitudes as “near ground.” The tively, Walko (1993) and Wicker and Wilhelmson distinction between low-level and midlevel mesocy- (1995) presented vortex lines in their three-dimensional clones is discussed further in section 4.] Midlevel verti- simulations of tornadogenesis. As one would expect, cal vorticity having relatively high correlation with ver- the vortex lines were nearly erect in the tornadoes, tical velocity (negative correlation, in the case of a “left- turned horizontally at the base of the tornadoes, and moving” storm)—what most would probably consider then extended horizontally several kilometers from the the defining characteristic of a supercell thunderstorm tornadoes along the surface. Weisman and Davis (1998) (i.e., a rotating updraft)—can be envisioned as arising presented vortex lines in their investigation of the gen- from the tilting of vortex lines having a significant esis of line-end vortices in mesoscale convective sys- streamwise component by an “isentropic mountain” tems. The counterrotating mesoscale vortices com- (Davies-Jones 1984; Fig. 1). The vortex lines are quasi- monly found at opposite ends of quasi-linear convective horizontal in the ambient environment owing to the line segments were joined by “arching” vortex lines that presence of large mean vertical wind shear. On the rose out of the cyclonic vortex to the north (in the case other hand, baroclinic vorticity generation is present in of westerly mean vertical shear and a north–south con- convective storms, at least somewhere, owing to the vective line orientation), turned horizontally and ex- presence of horizontal buoyancy gradients (if there tended many tens of kilometers to the south, and then were no buoyancy gradients there could be no buoyant descended into the anticyclonic vortex. More recently, updraft in the first place). In addition to the updraft, the Nolan (2004) showed that three-dimensional Lagran- evaporation of rain, the melting of graupel and hail, and gian vortex methods (Chorin 1996) could be used to even the direct contribution to negative buoyancy by simulate mesocyclogenesis as an alternative to the tra- the mass of hydrometeors themselves unavoidably lead ditional approach of simulating the dynamics with an to horizontal buoyancy gradients and baroclinic vortic- Eulerian grid. We are unaware of any attempts to con- ity generation. Given this addition of baroclinic vortic- struct vortex lines in observed convective storms (using ity (Dutton 1986, p. 390; Davies-Jones 1996; Davies- presumably dual-Doppler–derived three-dimensional Jones et al. 2001) to the barotropic vorticity (defined as

Unauthenticated | Downloaded 09/27/21 04:08 AM UTC SEPTEMBER 2008 MARKOWSKI ET AL. 3515 the vorticity that has resulted from the amplification storm-scale horizontal vorticity and is crucial for the and reorientation of the initial ambient vorticity of the development of low-level mesocyclones (Klemp and vertically sheared environment over the lifetime of the Rotunno 1983; Rotunno and Klemp 1985) [although storm), particularly at low levels within the rain-cooled recent observations (e.g., Shabbott and Markowski outflow of storms where significant buoyancy gradients 2006; Beck et al. 2006; Frame et al. 2008) have raised would most likely be found [prior modeling and obser- questions about the extensiveness of horizontal vortic- vational evidence that at least some of the air feeding ity generation within some storms]. We believe, how- mesocyclones near the ground originates in the rain- ever, that the much stronger downward velocities of the cooled outflow (e.g., Klemp and Rotunno 1983)], one RFD, in contrast to those in the FFD (the forward- probably would not expect the vortex lines passing flank outflow is more nearly hydrostatic), particularly through low-level mesocyclones necessarily to have the in the lowest kilometer (e.g., dramatic cloud erosion is same configuration or orientation as those passing commonly observed in conjunction with intensifying through the midlevel mesocyclone, such as in Fig. 1. RFDs; Markowski 2002a), lend the RFD to be a more Along these lines, Davies-Jones (1982a,b) proposed likely mechanism for the generation of near-ground cy- that a downdraft was actually a prerequisite for the clonic vertical vorticity. In the absence of preexisting development of low-level rotation in environments in vertical vorticity at the ground, the development of ro- which vertical vorticity was initially negligible near the tation at the ground requires positive vorticity tilting ground [also see the reviews by Davies-Jones and within air parcels that are sinking toward the ground Brooks (1993) and Davies-Jones et al. (2001)], a notion (Davies-Jones 1982a,b; Davies-Jones and Brooks 1993; that has been verified in numerical simulations (e.g., Davies-Jones et al. 2001). Rotunno and Klemp 1985; Walko 1993) and is consis- In this paper we present vortex lines in the low-level tent with the nearly countless observations of rear-flank mesocyclone regions of supercells using data obtained downdrafts (RFDs), hook echoes, and “clear slots” in from airborne Doppler radars during the Verification close proximity to tornadoes (Lemon and Doswell of the Origins of Rotation in Tornadoes Experiment 1979; Markowski 2002a). (VORTEX; Rasmussen et al. 1994). This work is in- If downdrafts are important for the amplification of tended to provide insight into the likely importance of low-level vertical vorticity in supercell thunderstorms, baroclinic versus barotropic vorticity, particularly in the the vortex line distribution in the vicinity of low-level RFD region, in the amplification of low-level rotation mesocyclones should provide insights into the role of in supercells. The data and wind retrieval method are the downdrafts. Dual-Doppler wind syntheses and described in section 2. The observations are presented three-dimensional numerical simulations of supercells in section 3. Some discussion and interpretation of the almost invariably have revealed a region of anticyclonic findings are provided in section 4. A summary and vorticity on the opposite side of the hook echo as the some final remarks appear in section 5. cyclonic vorticity region associated with the low-level mesocyclone or tornado (Markowski 2002a). These ob- 2. Data and methodology servations may be indications that vorticity tilting in the vicinity of the RFD, which has a close association with Six supercells were analyzed, all of which were ob- the hook echo, is important in the intensification of served during VORTEX-95 (Table 1). Of these, three low-level rotation within supercell storms. A vortex line were nontornadic (29 April, 12 May, 22 May) and three analysis should shed insight into how this couplet is were tornadic (16 May, 31 May, 8 June). All six cases produced, and in turn, the likely means by which low- have been documented by a number of investigators level rotation is intensified near the time of tornado- using airborne Doppler radar observations (Table 1 genesis. The RFD is emphasized in this article, hope- provides a complete listing). The analyses of the 12 fully not unduly, because the horizontal gradient of ver- May, 16 May, 31 May, and 8 June cases utilized data tical velocity commonly found in proximity to low-level from the Electra Doppler Radar (ELDORA) system mesocyclones and tornadoes (Markowski 2002a) is a on the National Center for Atmospheric Research maximum along the interface separating the RFD and (NCAR) Electra aircraft (Hildebrand et al. 1994). The updraft. We do not wish to imply that forward-flank analyses of the 29 April and 22 May cases relied on data downdrafts (FFDs; Lemon and Doswell 1979) are un- obtained by the National Oceanic and Atmospheric important to the overall vorticity budget of low-level Administration (NOAA) P-3 tail radar. The relatively mesocyclones. In numerical simulations of supercell small unambiguous velocity of the P-3 tail radar (12.9 thunderstorms, the horizontal buoyancy gradient along ms1; by comparison, the unambiguous velocity of the forward-flank gust front is an important source of ELDORA was 78.8 m s1) resulted in severe speck-

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TABLE 1. Listing of the six supercell thunderstorms analyzed herein.

Case Tornadic/nontornadic Airborne radar system Prior documentation 29 Apr 1995 Nontornadic NOAA P3 Trapp (1999) 12 May 1995 Nontornadic ELDORA Trapp (1999); Wakimoto and Cai (2000) 16 May 1995 Tornadic ELDORA Wakimoto and Liu (1998); Wakimoto et al. (1998); Trapp (1999); Cai and Wakimoto (2001) 22 May 1995 Nontornadic NOAA P3 Trapp (1999); Bluestein and Gaddy (2001) 31 May 1995 Tornadic ELDORA Wakimoto et al. (2004) 8 Jun 1995 Tornadic ELDORA Dowell and Bluestein (2002a,b); Wakimoto et al. (2003)

ling of radial velocities in the middle to upper portions were not contaminated by ground clutter was generally of the storms observed by the P-3 tail radar. Dealiasing 300–500 m AGL. Data positions were corrected for was not attempted at altitudes above 5.5 km. storm motion as recommended by Gal-Chen (1982), In the cases using ELDORA data, the radar data except here the mean mesocyclone motion averaged were objectively analyzed to a 30 30 18 km3 Car- over a 30-min period centered on the analysis period tesian grid having horizontal and vertical grid spacings was used. of 400 and 250 m, respectively. In the cases using The three-dimensional pseudo-dual-Doppler wind NOAA P-3 data, the radar data were objectively ana- syntheses were performed using the variational tech- lyzed to a 30 30 4km3 Cartesian grid having the nique with weak constraints presented by Gamache same grid spacings. The objective analyses were per- (1997) [this method is fairly similar to that described by formed using the technique described by Barnes (1964). Gao et al. (1999)]. The three components of the wind A smoothing parameter of 0.61 km2 was used, field were obtained by minimizing a cost function that based on the recommendation of Pauley and Wu (1990) considers the radial velocity projections, anelastic mass to use (1.3)2, where is the data spacing. Al- continuity, upper and lower boundary conditions (in though Pauley and Wu’s recommendation strictly ap- the 29 April and 22 May cases, only a lower boundary plies to uniformly distributed data, at the range of the condition could be specified due to the fact that radar storms, the distribution of radar observations tends to data were not processed above 5.5 km as stated earlier), be fairly regular. A conservative approach was taken in and degree of smoothing [see Gamache (1997) for fur- the determination of , whereby was specified based ther details]. Precipitation fall speeds were parameter- on the coarsest data spacing of all of the cases rather ized in terms of radar reflectivity factor using the pa- than the mean data spacing. For the four ELDORA rameterization used by Dowell and Bluestein (2002a). cases, the along-track data spacing was 300 m, and the The theoretical response of the objective analyses is beamwidth in the mesocyclone regions, which were ob- 0.01, 0.22, 0.51, 0.69, 0.79, and 0.94 for wavelengths of served at a range of 10–16 km, was 310–496 m. For the 1, 2, 3, 4, 5, and 10 km, respectively. Given that the two NOAA P-3 cases, the along-track data spacing was objective analyses employed a fairly large (conserva- 600 m and the beamwidth at 10–16 km ranges was tive) degree of smoothing prior to the wind synthesis, 366–586 m. Using 600 m (the coarsest data spacing) the additional smoothing applied in synthesizing the results in 0.61 km2 using the Pauley and Wu (1990) three-dimensional wind fields [i.e., the smoothing that recommendation. The ELDORA data were perhaps a is included in the Gamache (1997) cost function] is rela- bit oversmoothed (i.e., using 496 m yields a rec- tively minor. Features having scales larger than ap- ommended of 0.42 km2). It was deemed most desir- proximately 3 km probably can be viewed as being rea- able to use the same degree of smoothing for all of the sonably well-resolved. cases, with the smoothing parameter dictated by the The reader is referred to Jorgensen et al. (1983), worst resolution of all of the cases. [The reader is re- Hildebrand and Mueller (1985), Ray and Stephenson ferred to Koch et al. (1983) and Trapp and Doswell (1990), and Wakimoto et al. (1998) for general discus- (2000) for additional discussion on the choice of sions of the errors in airborne pseudo-dual-Doppler smoothing parameter.] Data farther than 1.7 km from a wind retrievals. It is worth stating that the wind synthe- grid point [which corresponds to (5)1/2] had their ses constructed herein are qualitatively very similar to weights set to zero in the interest of computational ex- those that have been derived by previous investigators pediency. No extrapolation of the observations was (Table 1) using slightly different techniques. Although permitted in the assignment of grid values, as is com- it certainly would have been possible to compute vortex monly allowed. The height of the lowest wind data that lines from the wind syntheses produced by the previous

Unauthenticated | Downloaded 09/27/21 04:08 AM UTC SEPTEMBER 2008 MARKOWSKI ET AL. 3517 investigators, it was deemed desirable to use identical cyclone-scale kinematic features. Only the vortex lines objective analysis and wind synthesis methods and pa- clustered around the mesocyclone center were com- rameters for all of the vortex line analyses presented puted; no attempt to construct vortex lines through the herein, given the sensitivity of vorticity (and even center of the tornado was undertaken since the torna- greater sensitivity of vortex lines) to small-scale details does were not resolved by the airborne radars. in the wind field. The three-dimensional vorticity components were 3. Observations computed at each grid point using second-order, centered differences, except along data boundaries where a. Nontornadic supercell cases: 12 May, 29 April, one-sided differences were used. The vorticity compo- 22 May nents were lightly smoothed with a one-step Leise filter Figures 2–5 depict the radar reflectivity, storm- (Leise 1982), after which vortex lines were computed relative wind vectors, and vertical vorticity at 1 km using a fourth-order Runge–Kutta integration. The AGL, in addition to vortex lines passing through and finescale structure of the vortex lines is, as one would near to the low-level vertical vorticity maximum, for the surmise, fairly sensitive to the degree to which the vor- 12 May, 29 April, and 22 May nontornadic supercell ticity components are smoothed; however, the qualita- cases, respectively. A vortex line originating in the am- tive characteristics of the vortex lines (e.g., whether bient boundary layer south of the gust front also is vortex lines form loops, arches, or erupt vertically from shown for the 12 May and 29 April cases (lack of dual- near the ground to mid- to upper levels) are fairly ro- Doppler observations in the ambient environment pre- bust for reasonable degrees of smoothing (see appen- cluded the calculation of an environmental vortex line dix). in the 22 May case). The environmental hodographs for The vortex lines presented in section 3 pass through each case are presented in Fig. 6. and near to the center of the vertical vorticity maximum In all three nontornadic supercell cases, the low-level at 1 km AGL, which we also occasionally refer to as the mesocyclones are associated with vertical vorticity low-level mesocyclone; one vortex line passes through maxima well in excess of 1 10 2 s 1. The strongest the vertical vorticity maximum, and four additional vor- low-level mesocyclone is analyzed in the 12 May storm, tex lines pass through points surrounding the vertical with a peak vertical vorticity of approximately 5 10 2 vorticity maximum (these points form a 1 km 1km s 1 at 1 km AGL (Fig. 2a).3 The weakest low-level square centered on the vorticity maximum, with the mesocyclone at the time of tornadogenesis failure is exception of the 22 May case, for which a 2 km 2km analyzed in the 22 May case, with a peak vertical vor- square was used owing to the mesocyclone core being ticity of approximately 2 10 2 s 1 at 1 km AGL (Fig. nearly twice as large as in the other cases). When pos- 5a), although it is worth noting that the core radius of sible, an additional, sixth vortex line originating in the the low-level mesocyclone of the 22 May storm is al- ambient environment ahead of the storm gust fronts most twice as wide as that analyzed in the 12 May storm also is shown for each case. In the nontornadic cases, at the times analyzed herein; thus, the 12 May and 22 vortex lines are shown at the time of maximum low- May mesocyclones have more similar circulations. level vertical vorticity (tornadogenesis “failure”) iden- Almost all of the vortex lines passing through the tified by prior investigators [Wakimoto and Cai (2000) low-level mesocyclone in the 12 May storm extend a for the 12 May case (0034:39–0041:15 UTC 13 May);2 few kilometers upward from the cyclonic vorticity Trapp (1999) in the 29 April (0026:22–0030:59 UTC 30 maximum, but then turn southwestward and descend April) and 22 May (2355:11–0000:58 UTC) cases]. For into a broad region of low-level anticyclonic vertical the tornadic cases, vortex lines are shown prior to tor- vorticity found in the trailing portion of the hook echo nadogenesis (generally 10–20 min before tornadogen- (Figs. 2b,c). In other words, the couplet of oppositely esis) as well as at the time of tornadogenesis. It also is signed vertical vorticity (reviewed in section 1) that worth mentioning that the location of the tornado is not seems to be a ubiquitous characteristic of supercell necessarily coincident with the vertical vorticity maxi- hook echo regions is joined by vortex line “arches.” mum retrieved in the three-dimensional wind syntheses These vortex lines bear a striking resemblance to the (e.g., Wakimoto et al. 2004), which only retain meso- vortex lines originating in the cold pools of mesoscale

2 Trapp (1999) analyzed the 12 May 1995 case at earlier times (2252 and 2256 UTC analysis times were presented) using NOAA 3 The maximum low-level (0–1 km AGL) vertical vorticity ana- P-3 data (the 0034–0041 UTC period is analyzed herein using lyzed by Trapp (1999) in his 2252 and 2256 UTC analyses of the ELDORA data). 12 May case was approximately 2.5 102 s1.

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convective systems simulated by Weisman and Davis (1998), which are subsequently drawn upward by updrafts, leading to the formation of counterrotating line- end vortices. This similarity will be revisited in section 4. The vortex lines that originate in the boundary layer of the ambient environment south of the gust front in the 12 May case point generally toward the north (Figs. 2b,c), consistent with the environmental hodograph obtained from inflow soundings (Fig. 6a; excluding a shallow layer within 200 m of the ground, in which the environmental horizontal vorticity points toward the southwest). The environmental vortex line displayed in Fig. 2c ascends abruptly from south to north, entering the midlevel updraft and mesocyclone region several kilometers above the ground. The differences in the configurations of the environmental vortex line and the vortex lines passing through the low-level vorticity maximum (e.g., the horizontal component of the environmental vorticity points in roughly the opposite direction to the horizontal component of the vorticity that defines the vortex line arches emanating from the low-level vertical vorticity maximum) might imply that different dynamical processes were important to the production of vertical vorticity at different altitudes. This issue also is reserved for section 4. Additional vortex lines also are constructed at select locations northwest (upstream) of the aforementioned vortex lines (Fig. 3). These vortex lines also form arches, but the apexes of the arches extend to progres- sively lower altitudes the farther northwest one looks. The vortex line farthest northwest in Fig. 3 is inclined very little with respect to the horizontal, and the view from above (Fig. 3a) indicates that this vortex line nearly forms a closed loop (the endpoints of this vortex line extend below the data horizon), with the orientation of the vorticity along this vortex line suggestive of a local maximum of downdraft and/or negative buoyancy being nearly encircled by this vortex line. Indeed,

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FIG. 2. (a) Equivalent radar reflectivity factor (dBZe; shaded) at 1.0 km AGL at 0034:39–0041:15 UTC 13 May 1995. Storm-relative wind vectors and vertical vorticity contours (102 s1 contour interval; the zero contour is suppressed and negative contours are dashed) at the same altitude also are overlaid. (b) Equivalent radar reflectivity factor and isovorts at 1.0 km AGL as in (a), along with the projections of select vortex lines (bold solid lines) onto the ground. The region enclosed by the square in (a) is enlarged. The direction of the vorticity vector is indicated by the arrow heads. Five of the vortex lines pass through points centered on and surrounding the vertical vorticity maximum at 1.0 km. A sixth vortex line originates in the environment ahead of the gust front. (c) As in (b), but a three-dimensional perspective is shown.

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FIG. 3. As in Figs. 2b,c, but only a pair of select vortex lines in the outflow to the west of the low-level mesocyclone are shown, in addition to the vortex line passing through the center of the vorticity maximum at 1 km AGL and a vortex line originating in the environment (cf. Figs. 2b,c). In (a), select vertical velocity contours at 1 km AGL also are overlaid to show the position of a local downdraft maximum (white dashed contours of 2.5, 5.0, 7.5, and 10.0 m s1 are shown). a local downdraft maximum was observed in this location (Fig. 3a). In the 29 April and 22 May nontornadic cases, similar FIG. 4. As in Fig. 2, but for 0026:22–0030:59 UTC 30 Apr 1995. evidence of vortex line arches is present, although per-

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haps to a lesser degree. In the 29 April case (Figs. 4b,c), only the vortex line passing through the southeastern part of the low-level mesocyclone forms an arch in a manner similar to the majority of vortex lines constructed for the 12 May case. In the 22 May case (Figs. 5b,c), only the vortex lines passing through the western part of the low-level mesocyclone form such arches (because of overlapping vortex lines, it might be somewhat difficult to see that the vortex line arches enter the western part of the low-level mesocyclone in Figs. 5b,c). The differences in the exact number of vortex lines that form arches should not be overinterpreted (the number of vortex lines passing through even a tiny area is infi- nite unless a convention is applied that relates the spacing of lines to the strength of the field), as it is somewhat arbitrary in that more vortex line arches could have been drawn if the points surrounding the low-level vertical vorticity maximum through which the vortex lines passed were adjusted from case to case, depending on the size and horizontal structure of the low-level mesocyclone. Instead, vortex lines were drawn through the exact same arrangement of points surrounding the low-level mesocyclones in each case (one point centered on the vertical vorticity maximum, with four additional points surrounding the vertical vorticity maximum, as discussed in section 2). Furthermore, and perhaps more importantly, recall that the top of the data region in the 29 April and 22 May cases was 4 km, compared to 18 km in the 12 May case. One cannot know where the vortex lines that exit the relatively shallow domains in the 29 April and 22 May cases would go after reaching an altitude of 4 km. Similar to the 12 May case, the horizontal component of the environmental vorticity in the 29 April case (which points toward the northeast; Fig. 6b) points in roughly the opposite direction as the horizontal component of the vorticity that defines the vortex line arch emanating from the low-level vertical vorticity maximum (Fig. 4b). In the 22 May case, although no ambient vortex line in the near-storm environment could be computed from the dual-Doppler observations, hodographs obtained from soundings launched in the storm inflow showed a horizontal vorticity orientation that veered significantly with height, from southwestward pointing in the lowest few hundred meters to north- northeastward pointing at 1 km (Fig. 6c); the orientation of the horizontal vorticity in the vortex line arches

FIG. 5. As in Fig. 2, but for 2355:11–0000:58 UTC 22–23 May evident in Fig. 5c was approximately parallel to the 1995. A vortex line originating in the environment ahead of the horizontal vorticity at 500 m but differed substantially gust front could not be drawn owing to limited observations. from the orientation of the environmental horizontal vorticity in the 0–300-m layer and above 800 m (Fig. 6c).

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FIG. 6. Storm-relative hodographs depicting the environmental winds in the following cases: (a) 12 May, (b) 29 Apr, (c) 22 May, (d) 16 May, (e) 31 May, and (f) 8 Jun 1995. Numerals along the hodographs indicate heights above ground level in km. Open circles are placed on the hodographs at an altitude of 500 m. The orientation of the ␻ environmental horizontal vorticity vector ( h) at 1 km AGL is indicated with a bold arrow in (a)–(f). The 12 May, 22 May, 16 May, and 8 Jun 1995 cases are identical to those presented by Wakimoto and Cai (2000), Bluestein and Gaddy (2001), Wakimoto et al. (1998), and Dowell and Bluestein (2002a), respectively.

b. Tornadic supercell cases: 16 May, 31 May, larities at scales larger than the tornado (e.g., the me- 8 June socyclone scale) (Trapp 1999; Wakimoto and Cai 2000). Vortex line arches are observed in all of the tornadic Figures 7–12 depict vortex lines and low-level radar reflectivity, storm-relative wind vectors, and vertical cases, just as they are for the nontornadic cases. In all vorticity for the 16 May, 31 May, and 8 June tornadic three tornadic cases, as is found for the nontornadic supercell cases. The supercells produced F3, F0, and F2 cases, the orientation of the low-level environmental tornadoes, respectively.4 horizontal vorticity (Fig. 6d–f), relatively isolated ex- For each case, analyses are presented both at the ceptions in shallow layers aside, differs significantly time of tornadogenesis as well as at an earlier time (the from the orientation of the horizontal vorticity associ- exact lead time varies from case to case). The reader ated with the vortex line arches. The environmental may find it interesting that the vertical vorticity maxima vorticity tends to point northward, whereas the vortex at 1 km AGL are not systematically larger in the tor- lines that form arches tend to turn southward or west- nadic cases, even at the time of tornadogenesis (Figs. ward after emanating from the low-level vertical vor- 8a, 10a, 12a), compared to the nontornadic cases (Figs. ticity maxima (Figs. 7–12b,c). 2a, 4a, 5a). In fact, this might be considered one of the Some tendency exists for the arches to be more com- most important findings of VORTEX: tornadic and mon prior to tornadogenesis. In the 16 May case, an nontornadic supercells have surprising kinematic simi- analysis derived approximately 29 min prior to tornadogenesis (2301:40–2307:00 UTC) reveals that the vortex lines passing through the center and to the south of 4 The 8 June 1995 supercell produced a number of significant the low-level vertical vorticity maximum abruptly turn tornadoes (the most intense was rated F5 by R. Wakimoto) in cyclic fashion. The analyses presented herein were obtained dur- southwestward below 3 km AGL, where they then de- ing and just prior to the development of the first tornado. See scend and exit the bottom of the data domain 3–7km Dowell and Bluestein (2002a) for further details. from the vertical vorticity maximum (Figs. 7b,c). Dur-

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FIG. 7. As in Fig. 2, but for 2301:40–2307:00 UTC 16 May 1995. FIG. 8. As in Fig. 2, but for 2331:00–2336:00 UTC 16 May 1995.

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FIG. 9. As in Fig. 2, but for 2218:00–2222:00 UTC 31 May 1995. FIG. 10. As in Fig. 2, but for 2236:40–2244:32 UTC 31 May 1995.

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FIG. 11. As in Fig. 2, but for 2239:42–2245:18 UTC 8 Jun 1995. FIG. 12. As in Fig. 2, but for 2246:47–2250:33 UTC 8 Jun 1995.

Unauthenticated | Downloaded 09/27/21 04:08 AM UTC SEPTEMBER 2008 MARKOWSKI ET AL. 3525 ing the analysis period in which tornadogenesis oc- encircled a relative maximum in the midlevel vertical curred (2331:00–2336:00 UTC), the vortex lines on the velocity field (not shown) that apparently was associ- eastern flank of the low-level mesocyclone form arches, ated with a flanking line updraft. The orientation of the whereas the vortex line passing through the center of horizontal vorticity along the “looping” portion of the the low-level vertical vorticity maximum is fairly up- vortex line is consistent with the presence of a relative right and extends all the way to the storm summit (Figs. maximum of buoyancy and updraft at the center of the 8b,c). loop. This vortex line serves as a nice example of how In the 31 May case, almost all of the vortex lines complex vortex line distributions and configurations passing through the low-level vertical vorticity maxi- can be. mum 19 min before tornadogenesis (2218:00–2222:00 Regarding the tendency for arches to be more com- UTC) form short arches, with the vertical planes con- mon prior to tornadogenesis, as the low-level vorticity taining the arches being oriented from east-southeast to intensifies, the vortex lines passing through the vorticity west-northwest, or approximately normal to the major maximum ought to become more vertical, with the sum- axis of the echo appendage on the rear flank of the mits of the arches extending to higher altitudes. [Straka storm (Figs. 9b,c). During the analysis period contain- et al. (2007) also found that arches give way to vortex ing tornadogenesis (2236:40–2244:32 UTC), almost all lines extending deeply and vertically as their vortices of the vortex lines reach the storm summit (Figs. 10b,c). intensified, with the prominence of the arch structures The lone vortex line arch originates in the northwestern being a function of time in their simulation.] Two pos- flank of the low-level mesocyclone and extends above 8 sible reasons for why arching vortex lines are less com- km before turning back toward the ground, where it monly observed as tornadogenesis nears might be that enters a broad region of anticyclonic vertical vorticity the apexes of the arches are simply too high for us to to the rear of the hook echo. The environmental vortex observe, or that by the time the arches are lifted to such line displayed during this analysis period enters the high altitudes, their configurations have been signifi- midlevel updraft and mesocyclone (Fig. 10c) in a man- cantly modified by additional baroclinic effects or tur- ner similar to that observed in the 12 May case (Fig. 2c). bulence, the latter of which can cause vortex lines to be Relatively limited vortex line arching appears in the severed and reattached to other lines instantaneously as 8 June pretornadic analysis period (2239:42–2245:18 long as there are no loose ends at any time (additional UTC; Figs. 11b,c), which is only 7 min prior to the discussion is provided in section 4e). Both effects pre- analysis period (analyses are not available at earlier vent the vortex lines from behaving as material lines. times) during which tornadogenesis occurred (2246:47– Furthermore, in each case, vortex lines have been 2250:33 UTC; Fig. 12). The vortex line originating in drawn through the same 1 km 1 km lattice of grid the southwestern portion of the low-level vertical vor- points centered on the vorticity maximum at 1 km. If ticity maximum rises to an altitude of nearly 4.5 km, this region is extended to the periphery of the vortex, then turns toward the west and descends into a region where vertical vorticity is not as large, additional arch- of anticyclonic vertical vorticity to the rear of the storm ing vortex lines are observed, even at the time of tor- (Figs. 11b,c). Another vortex line during the pretor- nadogenesis (e.g., Fig. 13). nadic analysis period, originating in the southeastern portion of the low-level mesocyclone, turns toward the north-northwest and descends within the main precipi- 4. Discussion tation core, exiting the domain approximately 3 km a. Vortex line arches observed in prior supercell AGL. During the analysis period in which tornadogen- studies esis occurs, almost all of the vortex lines reach the storm summit (although these vortex lines tilt north- These are not the first observations of vortex line eastward with height), with the lone exception being arches. Similar vortex line configurations have been the vortex line that originates in the southwestern por- found in the Dimmitt, Texas, tornadic supercell inter- tion of the low-level mesocyclone (Figs. 12b,c). This cepted during VORTEX on 2 June 1995 (Straka et al. vortex line erupts vertically out of the low-level vertical 2007), in a nontornadic supercell observed by a pair of vorticity maximum, then abruptly turns horizontally Doppler On Wheels (Wurman et al. 1997) radars on 12 and makes one and a half counterclockwise loops hav- June 2004 (Majcen et al. 2006), and even in the simu- ing a radius of roughly 1.5 km before descending to the lations of the 20 May 1977 Del City, Oklahoma, super- bottom of the data domain and entering a region of cell by Rotunno and Klemp (1985), as evidenced by the anticyclonic vertical vorticity immediately west of the vortex line shown in their Fig. 9 (Fig. 14). [Presumably cyclonic vertical vorticity maximum. The vortex line other investigators who have simulated supercells using

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FIG. 14. Three-dimensional perspective (looking to the northwest) of the e 331 K isosurface and the vortex line that passes through the location of maximum vertical vorticity at t 90 min in the simulation of the Del City, OK, supercell by Rotunno and Klemp (1985, their Fig. 9). The vertical scale is exaggerated by a factor of 2. The cold frontal boundary indicates the location of the 1°C perturbation surface isotherm.

a e surface if Ertel’s potential vorticity is conserved and is zero), enters the low-level vertical vorticity maximum, and then rises and descends toward the southwest to form an arch like those observed in section 3. In the present study, we cannot determine where the vortex lines go after passing below approximately 300–500 m AGL owing to the limitations of the data (see section 2). Thus, we cannot say whether the observed vortex line arches, if extended, would reach into the forward- flank baroclinic zone near the ground, and ultimately even into the ambient environment, as in the analysis of Rotunno and Klemp (Fig. 14). It is possible that the horizontal extension of the vortex line from the low- level vertical vorticity maximum into the forward-flank region and ambient environment in the analysis of Ro- tunno and Klemp should not be interpreted too “liter- ally”; the lowest model grid level was 250 m AGL, the same level at which the vertical vorticity maximum was identified through which the vortex line was drawn. Not only would the configuration of the vortex line at the lowest grid level depend on the (unrealistic) free-slip lower boundary condition, but the vortex line passing through the vertical vorticity maximum at the lowest grid level should have passed below the lowest model FIG. 13. As in Fig. 8, but the 1 km 1 km lattice of grid points grid level. Its horizontal extension into the forward- through which vortex lines are drawn has been shifted 3 km south flank region and ambient environment is therefore ex- and 2 km east of the vorticity maximum at 1 km. The environ- trapolated. mental vortex line is overlaid as in Fig. 8. Although the sample of observed and simulated supercells displaying arching vortex lines is very small, the 20 May 1977 proximity sounding (e.g., Klemp et al. vortex line calculations, when done, have never failed 1981; Klemp and Rotunno 1983; Grasso and Cotton to reveal arches that connect the counterrotating vor- 1995; Adlerman et al. 1999; Adlerman and Droege- tices that straddle the hook echo. The fact that such meier 2002) would find a similar vortex line configura- vorticity couplets have been observed in essentially ev- tion in the low-level mesocyclone region.] This vortex ery dual-Doppler and numerical modeling study of su- line originates in the ambient environment, is “de- percells (Markowski 2002a; also refer to section 1) flected” from the south toward the west upon encoun- might lead one to wonder whether vortex line arches tering outflow having a relatively low equivalent poten- are as common to supercell RFD regions as are these tial temperature ( e; the vortex line cannot pass through vorticity couplets (i.e., it is tempting to wonder whether

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generated by buoyancy gradients in the RFD region, assuming the buoyancy isopleths in the RFD region are approximately parallel to the rear-flank gust front; (iii) if only the tilting of barotropic vorticity by a downdraft were involved in the production of the observed low- level mesocyclones, vortex lines should form U shapes rather than arches. Let us expand a bit on this last point below. If the ambient, barotropic vorticity is dominated by the horizontal component (in the limit of a horizontally homogeneous environment, ambient vertical vorticity is absent and vortex lines are horizontal), the tilting of vortex lines by an updraft produces midlevel vertical vorticity (the degree to which the cyclonic vertical vor- FIG. 15. Vortex line structure in a numerical simulation of a ticity maximum is in phase with the midlevel vertical quasi-linear convective system with line-end vortices, from Weis- velocity maximum depends on the degree to which the man and Davis (1998, their Fig. 9). The vortex lines are denoted by the thick solid lines, with the direction of the vorticity vector ambient horizontal vorticity is streamwise, as shown in indicated by the arrow heads. Vectors denote the surface wind Fig. 1) but no significant vertical vorticity near the flow. The surface cold pool (potential temperature perturbations ground (Fig. 16a). Tilting of the ambient vorticity by less than 1 K) is shaded. the horizontal vertical velocity gradients associated with an updraft alone is not effective at producing ver- vortex line arches are a ubiquitous trait of supercell tical vorticity near the ground because air is rising away thunderstorms). from the surface as horizontal vorticity is tilted into the vertical. But if a downdraft is involved in the tilting b. Inferences about baroclinic vorticity generation process, then vertical vorticity can be advected toward the surface as it is produced via tilting (Davies-Jones The vortex line arches evident in all six supercells and Brooks 1993; Grasso and Cotton 1995; Adlerman bear a striking resemblance to the vortex lines com- et al. 1999), yielding significant vertical vorticity next to puted by Weisman and Davis (1998) in their numerical the ground (Fig. 16b), and perhaps even a tornado if the modeling study of the formation of line-end vortices in vorticity is further amplified by stretching. For these mesoscale convective systems (Fig. 15). Weisman and reasons, as pointed out in section 1, it has been argued Davis found that counterrotating vortices arise on op- that a downdraft is needed for tornadogenesis when posite ends of a finite-length convective line owing to preexisting rotation is absent near the ground (Davies- the lifting of vortex lines that are baroclinically gener- Jones 1982a,b). (This conclusion depends on eddies be- ated within the horizontal buoyancy gradient of the ing too weak to transport vertical vorticity downward 5 cold pool. It is tempting to draw the same conclusion in against the flow. Furthermore, once a tornado is estab- the present study: baroclinic vorticity generation almost lished, the tilting of surface-layer horizontal vorticity by certainly led to the development of the vortex line the extreme vertical velocity gradient associated with arches observed in the supercell low-level mesocyclone the tornado updraft itself probably contributes to the and RFD region. This conclusion is supported by a near-ground vertical vorticity in a significant way. How- number of observations: (i) the environmental vorticity ever, such abrupt upward turning of streamlines, strong points in markedly different directions (often in the pressure gradients, and large vertical velocities are not exact opposite direction) compared to the orientation present next to the ground prior to tornadogenesis; of the horizontal vorticity component that defines the thus, such tilting in the absence of a downdraft cannot vortex line arches emanating from the low-level vertical be invoked to explain the amplification of near-ground vorticity maxima; (ii) the horizontal vorticity compo- vertical vorticity that results in tornadogenesis.) If only nent at the apexes of the arches tends to point in the ambient, barotropic vorticity is involved in the afore- same direction as vorticity that would be baroclinically mentioned process, then the vortex lines that pass through the low-level mesocyclone and connect the counterrotating vorticity extrema that are routinely ob- 5 Weisman and Davis (1998) also found that when environmental horizontal vorticity is large, tilting of environmental vortex served to straddle the hook echo and RFD would form lines also can produce significant vertical vortices in the same way U shapes, not arches [Fig. 16b; also see Fig. 5 of Weis- that supercell thunderstorm updrafts acquire vertical vorticity. man and Davis (1998)]. Thus, although it is dynamically

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FIG. 16. (a) Tilting of ambient (barotropic) horizontal vorticity by an updraft produces midlevel vertical vorticity. In the above case, the ambient horizontal vorticity has a significant streamwise component so that the midlevel vertical vorticity maximum lies within the updraft. Vertical vorticity cannot arise next to the ground because air is rising away from the ground as vertical vorticity is being generated by the tilting effect. (b) If a downdraft develops, vertical vorticity can be advected toward the surface as it is produced via tilting, resulting in significant vertical vorticity next to the ground. If baroclinity is absent (and turbulent diffusion is ne- glected), vortex lines are frozen in the fluid and are redistributed by the downdraft as material lines. In this case, the vortex line passing through the low-level vertical vorticity maximum takes a U shape rather than an arch. A couplet of counterrotating vortices straddles the downdraft maximum. Of course, the very presence of a downdraft implies that at least some solenoidal effects are unavoidable, even if the downdraft is driven solely by dynamic pressure perturbations. Just as the presence of a warm isentropic peak in Fig. 1 actually diverts vortex lines toward the right as the lines are lifted by the peak (refer to the Fig. 1 caption), vortex lines would actually be diverted toward the left (i.e., in the opposite direction) in the case above. This is not easily shown in the figure above, nor does it dramatically alter the main result, which is a U-shaped vortex line at low levels. possible to develop strong near-ground rotation and an arch that straddles the hook echo unless the trajec- even a tornado from the tilting of ambient, barotropic tory of an air parcel coming out of the forward-flank vorticity, as has been shown by Davies-Jones (2000a, outflow follows an arch itself [i.e., this trajectory would 2007) and Markowski et al. (2003),6 the observations of have to exit the updraft to the rear (typically west or vortex lines arches, if they apply generally, would indi- southwest) after rising a short distance]. In our consid- cate that baroclinic vorticity generation in the RFD re- eration, this would require a rather exotic three- gion is important in the amplification of low-level ver- dimensional wind field. Forward-flank baroclinity cer- tical vorticity in observed supercells. tainly could extend the “foot” of the cyclonic “leg” of a Three-dimensional numerical simulations have vortex line arch into the forward-flank baroclinic zone shown that baroclinic vorticity generation within the along the ground, but we cannot envision how a vortex forward-flank outflow also is important in the genera- line arch that straddles the hook echo could result from tion of low-level rotation (Klemp and Rotunno 1983; anything other than the lifting of baroclinic vortex lines Rotunno and Klemp 1985), as reviewed in section 1; that originate in the RFD outflow. The reader also is however, the orientation of the vortex line arches ob- referred back to Fig. 3, for example, which shows vortex served in the present sample of supercells, while cer- lines upstream of the arches. The vortex lines, one of tainly not excluding the possibility of significant hori- which nearly forms a closed loop around a relative zontal vorticity generation in the forward-flank out- downdraft maximum, are suggestive of baroclinic vor- flow, strongly suggest baroclinic generation in the RFD ticity generation in the RFD/hook echo region. region [refer to (ii) in the third paragraph of this sec- The idea that baroclinic vorticity generation in the tion]. Forward-flank baroclinity alone cannot produce RFD/hook echo region is important to the development of near-ground rotation in supercells has been advanced by Davies-Jones and Brooks (1993), Davies- 6 Baroclinic vorticity was present in the Davies-Jones (2000a, Jones (1996, 2000b), Adlerman et al. (1999), and 2007) and Markowski et al. (2003) simulations, but only barotro- Davies-Jones et al. (2001). More recently, Davies-Jones pic vorticity contributed to the tornadoes in these simulations. The baroclinic vorticity could not be converted to vertical vortic- (2006), in agreement with numerical simulations by ity via tilting owing to the axisymmetry used in these idealized Straka et al. (2007), demonstrated how a relative mini- simulations. mum in the buoyancy field, like that observed within

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FIG. 17. One possible way by which a couplet of vertical vorticity can be produced by a purely baroclinic process in an environment containing no ambient vorticity (neither vertical nor horizontal). (a) Baroclinically generated vortex rings encircle a buoyancy minimum that extends throughout a vertical column (such a region of negative buoyancy might be found in the hook echo/RFD region of a supercell, for example); the presence of negative buoyancy causes the rings to sink toward the ground as they are generated. (b) If the vortex rings are swept forward as they descend toward the ground owing to the additional presence of rear-to-front flow through the buoyancy minimum, the vortex rings become tilted upward on their downstream sides (a vertical velocity gradient is present within the column because buoyancy is a minimum in the center of the column and increases with increasing distance from the center of the column). (c) If the leading edge of the vortex rings can be lifted by an updraft in close proximity to the buoyancy minimum (an updraft is typically found in close proximity to the hook echo/RFD region of a supercell, for example), then the vortex rings can be tilted further and stretched upward, leading to arching vortex lines and a couplet of cyclonic (“C”) and anticyclonic (“A”) vertical vorticity that straddles the buoyancy minimum and associated downdraft. Note the similarity to Fig. 15. (Adapted from Straka et al. 2007.) the RFD/hook echo region of a supercell, produces loops, as if encircling a local buoyancy minimum in the baroclinic vortex rings that descend to the ground (Figs. RFD (e.g., Fig. 17), the arching process does not de- 17a,b) and, if they interact with a nearby updraft, the pend on the vortex lines forming closed loops. The re- leading edges of the rings subsequently can be lifted sults would be qualitatively similar in the case of a such that the vortex lines form arches (Fig. 17c). The buoyancy minimum in the hook echo/RFD that was vortex line arches that arise from this baroclinic process conterminous with the negative buoyancy and down- are similar to those found in the supercells we have draft in the forward reaches of the storm, such that the observed, which lends much credence to the aforemen- vortex lines that ultimately formed arches were not tioned hypothesis for the role of RFD/hook echo baro- closed loops on their rear sides, but rather extended far clinity in the generation of near-ground rotation in su- into the precipitation region and out of the photograph. percells. In some ways, these ideas are similar to one of We take the opportunity here to discuss what occa- Fujita’s (1985) microburst conceptual models (Fig. 18), sionally has been, in our experience, a confusing or but in Fujita’s model, the vortex rings spread out at the misunderstood relationship between the low-level and ground and do not interact with a localized updraft such midlevel mesocyclone. We prefer to avoid rigid distinc- that the leading edges of the vortex rings are lifted to tions between the two if at all possible. We believe the produce a vorticity couplet. c. Relationship between midlevel mesocyclones and low-level mesocyclones A generalized depiction of vortex lines in the vicinity of a low-level mesocyclone is shown in Fig. 19. The portrayal has been inferred from the sample of supercells surveyed herein (Figs. 2–12, particularly Fig. 3, which displays vortex lines upstream of the vortex line arches that emanate from the low-level vertical vorticity maximum), and is superimposed on a photograph of a generic supercell thunderstorm in order to facilitate visualization. The portrayal also conforms to the observational and numerical modeling findings of Straka et al. (2007). Although the descending, baroclinically gen- FIG. 18. Fujita’s (1985) conceptual model of a microburst and erated vortex lines shown in Fig. 19 are drawn as closed an attendant vortex ring.

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FIG. 19. Idealized evolution of vortex rings and arches inferred from the sample of supercells surveyed herein, superimposed on a photograph of a supercell thunderstorm (courtesy of Jim Marquis; view is from the south). The numerals 1–4 can indicate either a single vortex line seen at four different times in a sequence, or four different vortex lines at a single time but in different stages of evolution. An environmental vortex line also is shown to illustrate, sche- matically, the relationship between the midlevel and low-level mesocyclone. None of the vortex lines have been derived from an actual three-dimensional wind synthesis of the storm appearing in the photograph; the vortex lines simply have been drawn atop a photo of a supercell thunderstorm (one that could easily represent a number of generic supercell thunderstorms) by compositing vortex lines computed from actual three-dimensional wind syntheses in the sample of supercells herein. The evolution also conforms with the evolution found in the Straka et al. (2007) idealized numerical simulations. Although the descending, baroclinically generated vortex lines shown above are drawn as closed loops, as if encircling a local buoyancy minimum in the RFD, the arching process does not depend on the vortex lines forming closed loops. The results would be qualitatively similar in the case of a buoyancy minimum in the hook echo/RFD that was conterminous with the negative buoyancy and downdraft in the forward reaches of the storm, such that the vortex lines that ultimately formed arches were not closed loops on their rear sides, but rather extended far into the precipitation region and out of the photograph. more meaningful distinction in the generation of verti- from the tilting of environmental horizontal vorticity if cal vorticity is between the tilting of horizontal vorticity the horizontal vorticity is very large and the updraft that involves only an updraft versus tilting that involves very strong. On the other hand, if a downdraft is in- both an updraft and a downdraft. When only an updraft volved in the tilting process, air can be sinking toward is involved in the tilting of horizontal vorticity (whether the ground while tilting is producing vertical vorticity it be environmental horizontal vorticity or storm- (section 4b). Thus, significant vertical vorticity can be generated horizontal vorticity, e.g., that which might be achieved at the ground. generated in the forward-flank region), air is rising as Summarizing, in the early stages of a supercell’s life, tilting produces vertical vorticity (the vertical advection vertical vorticity in the mesocyclone comes from the of vertical vorticity has the opposite sign of the tilting), tilting of environmental horizontal vorticity (the as discussed in section 4b. Significant vertical vorticity “midlevel” versus “low-level” distinction is somewhat can be generated above the ground, but not at the arbitrary—the altitude at which “significant” vertical ground. Even a low-level mesocyclone, if one defines vorticity appears decreases as the environmental hori- “low-level” nominally as 500–1000 m AGL, could arise zontal vorticity increases and is subjective anyway). In

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Fig 19 live 4/C SEPTEMBER 2008 MARKOWSKI ET AL. 3531 later stages, once storm-scale buoyancy gradients arise tribution to outflow strength from the evaporation of at low levels but before significant vertical vorticity is rain within the boundary layer, as evidenced by signif- present at the ground, the vertical vorticity in the icant correlations between observed cold pool strength midlevel mesocyclone as well as low-level mesocyclone and environmental boundary layer relative humidity likely comes from tilting of the ambient environmental (Markowski et al. 2002; Shabbott and Markowski horizontal vorticity as well as additional horizontal vor- 2006).] We are not in a position to answer this question ticity that might be generated baroclinically by way of at this point, but perhaps supercell baroclinity is an- storm-scale buoyancy gradients. Once a mature super- other “Goldilocks” problem whereby at least some cell is established, with significant rotation extending all baroclinity is crucial (all thunderstorms have at least the way to the surface (and downdrafts necessarily hav- some baroclinity, as discussed in section 1), but too ing played a critical role in arriving at this state), the much, especially near the ground, is detrimental in that vertical vorticity in the midlevel mesocyclone as well as large near-ground baroclinity would imply very cold air low-level mesocyclone comes from both the ambient near the ground and thus rapid gust front motion rela- environment as well as from near the ground via verti- tive to the main updraft, which might undercut it cal advection. Some of the vortex lines traced backward (Brooks et al. 1993) or inhibit the vorticity stretching from the midlevel vertical vorticity maximum extend required by tornadogenesis (Leslie and Smith 1978; horizontally into the ambient environment and others Markowski et al. 2003). In terms of Fig. 17, if the down- extend vertically through the vertical vorticity maxi- draft air containing the vortex rings is too negatively mum at the lowest data level. Some of the vortex lines buoyant, then perhaps the end result is something re- traced forward from the midlevel vertical vorticity sembling Fujita’s microburst model (Fig. 18) rather maximum extend to the storm summit and others form than significant lifting of the leading edge of the vortex arches that bend back toward the trailing part of the rings to produce vertical vorticity (Fig. 17c). It goes hook echo where anticyclonic vertical vorticity is without saying that thermodynamic observations above present. Notice that the illustration in Fig. 19 depicts a the ground would be invaluable in trying to assess the midlevel mesocyclone that contains a vortex line that overall importance of baroclinic vorticity generation extends into the ambient environment as well as one within supercell thunderstorms. We currently lack a that forms an arch. three-dimensional, let alone four-dimensional, conceptual model of the range of thermodynamic characteris- d. Paradoxical observations of weak cold pools in tics in supercell thunderstorms and how these would tornadic supercells impact vorticity generation and reorientation in ways What we believe to be one of the outstanding mys- that might be important for tornadogenesis. teries is why, if baroclinic generation of vorticity in the e. Effects of turbulence on the vortex lines RFD region is as important as the vortex line analyses seem to suggest, there is so much growing evidence Finally, a few comments regarding the effects of tur- from field observations that strong cold pools and ex- bulence on the vortex lines are warranted. Although cessive negative buoyancy at the surface are detrimen- the effects of subgrid-scale turbulence on supercell dy- tal to tornadogenesis (Markowski 2002b; Markowski et namics are of secondary importance (if they were not, al. 2002; Shabbott and Markowski 2006; Grzych et al. numerical simulations would be very sensitive to the 2007). For example, the 8 June 1995 tornadic supercell turbulence parameterization), turbulence can have an studied herein has been shown to have possessed only important effect on the vortex lines. As described by very small (2 K) temperature deficits at the surface Morton (1984), cross-diffusion of vorticity allows “sur- (Dowell and Bluestein 2002a; Markowski et al. 2002). gery” of vortex lines (see his Figs. 10i, iii). Lines can be Moreover, climatological studies (Rasmussen and severed and reattached to other lines instantaneously as .(␻ 0 • ١) Blanchard 1998; Thompson et al. 2003) show that tor- long as there are no loose ends at any time nadic supercells are favored in environments having a Although Morton is dealing with viscous diffusion, a large boundary layer relative humidity, which would similar process can occur with subgrid-scale turbulence. tend to limit the production of exceptionally cold out- We cannot observe what is happening locally with the flow and associated baroclinity. [Of course, cold out- vortex lines at the unresolved scales, thus when two flow can be produced by the entrainment of potentially oppositely directed lines come very close together, the cold midlevel environmental air, independent of the surgery may be performed on our “smooth lines.” The boundary layer relative humidity. Moreover, the melt- likelihood of cross-diffusion of vortex lines altering our ing of ice is enhanced in humid conditions. However, simple concept of their configuration increases with these effects do not appear to completely mask the con- time after the rings of baroclinic vorticity are gener-

Unauthenticated | Downloaded 09/27/21 04:08 AM UTC 3532 MONTHLY WEATHER REVIEW VOLUME 136 ated; as time increases, there is a greater likelihood for magnitude, distribution, etc., we believe that vortex line having a lifted arching vortex line find itself in close analysis can provide a beneficial perspective. We ea- proximity to midlevel vortex lines that might have a gerly await future analyses in order to evaluate whether different orientation. This effect might partly contrib- the findings of the present study extend to a larger ute to the greater tendency to observe prominent sample of supercells. We also believe that a priority of arches early in the tornadogenesis process. future field experiments should be the collection of thermodynamic observations above the ground (perhaps even extending several kilometers above the sur- 5. Summary and conclusions face) to better characterize the three-dimensional Pseudo-dual-Doppler radar observations were used buoyancy field, given the apparent importance of baro- to construct vortex lines within the low-level mesocy- clinic processes despite the general lack of strong cold clone regions of six supercells (three nontornadic, three pools beneath the most prolific tornadic storms. Finally, tornadic) near the time of maximum low-level rotation. it also is interesting to ponder whether the dynamics The main findings and conclusions are summarized as shown by Davies-Jones (1996) and Weisman and Davis follows: (1998) to lead to mesoscale vortices in larger-scale convective systems operate on a wide range of scales; that 1) Some vortex lines originating in the low-level verti- is, is it possible that the same fundamental dynamical cal vorticity maximum extended to the storm sum- process (baroclinic vortex lines generated in a cool mit, whereas others formed arches that connected downdraft and subsequently lifted by an updraft) can the vertical vorticity maximum to the commonly ob- produce vortices that range in size and intensity from served region of anticyclonic vertical vorticity on the bookend vortices to near-ground mesocyclones to tor- opposite flank of the hook echo of the supercell. nadoes? 2) At least some vortex line arches emanate from the low-level mesocyclone in every case at every analy- Acknowledgments. We are grateful to Drs. David sis time; vortex line arches are a robust trait of the Dowell, Hanne Murphey, and Roger Wakimoto for sample of supercells studied herein. providing edited ELDORA data for the 12 May 1995, 3) The arching of the vortex lines and the orientation 16 May 1995, 31 May 1995, and 8 June 1995 cases. We of the vorticity vector along the vortex line arches, thank the three anonymous reviewers for their sugges- compared to the orientation of the ambient (baro- tions for improving the paper. Support from the Na- tropic) vorticity, are strongly suggestive of baro- tional Science Foundation (Grants ATM-9617318, clinic vorticity generation within the hook echo and ATM-0003689, ATM-0338661, ATM-0340693, ATM- associated rear-flank downdraft region of the super- 0437512, and ATM-0644533) also is acknowledged. cells, and subsequent lifting of the baroclinically altered vortex lines by an updraft, rather than ambient APPENDIX vortex lines alone being tilted by either an updraft or downdraft to produce a low-level vertical vorticity maximum.7 Sensitivity of Vortex Lines to Smoothing and Grid Parameters Although the tornadogenesis problem is horribly nonlinear and is complicated by the presence of both The sensitivity of the vortex line configurations to the barotropic and baroclinic vorticity, each likely varying smoothing and grid parameters was explored exten- significantly from case to case in terms of orientation, sively. Figure A1 presents some examples, whereby the Barnes smoothing parameter was doubled (to 1.22 km2), the horizontal grid spacing was doubled (to 800 7 Environmental vortex lines might be tilted abruptly by the m), and vorticity components were left unsmoothed rear-flank gust front to produce significant low-level vertical vorticity along a fairly long corridor extending (typically southward, prior to vortex line calculations (i.e., a one-step Leise in the Northern Hemisphere in the case of a cyclonically rotating filter was not applied to the vorticity components after supercell) far from the low-level mesocyclone center. Our conclu- deriving them from the three-dimensional wind re- sion refers to the vortex lines that pass through or near to the trieval). Not surprisingly, the finescale structure of the center of the low-level vertical vorticity maximum found at or vortex lines is fairly sensitive to the smoothing and grid near the low-level mesocyclone center, rather than the environmental vortex lines that are lifted by the trailing gust front to spacing; however, the qualitative characteristics of the produce a relative maximum in vertical vorticity along a signifi- vortex lines (e.g., whether vortex lines form loops or cant length of the trailing gust front. arches) are fairly robust.

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FIG. A1. Three-dimensional perspective of vortex lines at 0034:39–0041:15 UTC 13 May 1995 for a variety of smoothing and grid parameters. Equivalent radar reflectivity factor 2 1 (dBZe; shaded) and vertical vorticity contours (10 s contour interval; the zero contour is suppressed and negative contours are dashed) at 1.0 km AGL also are plotted: (a) 0.61 km2, 400-m horizontal grid spacing, vorticity components smoothed with one-step Leise filter (as in Fig. 2c); (b) 0.61 km2, 400-m horizontal grid spacing, vorticity components received no additional smoothing prior to vortex line calculations; (c) 0.61 km2, 800-m horizontal grid spacing, vorticity components smoothed with one-step Leise filter; (d) 1.22 km2, 400-m horizontal grid spacing, vorticity components smoothed with one-step Leise filter.

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