Abstract

In Part I, the vorticity sources of midlevel and low-level mesocyclones in the 6 May 2012 Tsukuba City, Japan, tornadic supercell were investigated by using high-resolution simulation results with a 50-m horizontal grid spacing. In Part II, the analyses are extended to the mechanisms of tornadogenesis. The tornado was generated at the leading edge of a rear-flank downdraft (RFD) outflow surge. Backward-trajectory and vortex line analyses revealed that the RFD outflow surge was a triggering factor for tornadogenesis and that horizontal vorticity around the strong RFD outflow region was ingested into the tornado. To identify the vorticity source of the tornado, the evolution of circulation along a material circuit surrounding the tornado was investigated. Owing to baroclinity at the tip of a hook-shaped distribution of hydrometeors (hereafter hook echo), the circulation increased rapidly from a negative value when the core of the hydrometeors was descending, about 10 min prior to tornadogenesis. Analysis of the buoyancy field as well as a sensitivity experiment without diabatic cooling showed that baroclinity associated with cooling due to evaporation of rain and melting of ice-phase hydrometeors around the tip of the hook echo was the dominant vorticity source responsible for tornadogenesis.

1. Introduction

Important unresolved issues pertaining to supercell tornadogenesis include its triggering factor and vorticity sources. Although the development of a low-level mesocyclone in a supercell often precedes tornadogenesis, the existence of the low-level mesocyclone is not a sufficient condition for tornadogenesis (e.g., Burgess et al. 1993; Trapp 1999; Trapp et al. 2005; Markowski et al. 2011). To address these issues, extensive field observations have been conducted over the past few decades by, for example, the Verification of the Origins of Rotation in Tornadoes Experiment (VORTEX; Rasmussen et al. 1994) and VORTEX2 (Wurman et al. 2012) projects.

Numerous previous studies have revealed that the rear-flank downdraft (RFD) associated with the “hook echo” is closely linked to tornadogenesis in a supercell [see Markowski (2002) for a review]. Recent studies using high-resolution Doppler radar data and mobile mesonet observations (Wurman et al. 2007, 2010; Finley and Lee 2008; Marquis et al. 2008; Lee et al. 2011, 2012; Kosiba et al. 2013; Skinner et al. 2014) and numerical models (Mashiko et al. 2009; Schenkman et al. 2014, 2016; Skinner et al. 2015) have detected multiple small-scale RFD surges with small potential temperature deficits in the vicinity of a tornado. Although the near-surface thermodynamic field around gust fronts in supercells is becoming clear (e.g., Weiss et al. 2015), few observations of the three-dimensional thermodynamic field around the RFD region associated with the hook echo have been obtained.

In the absence of vertical vorticity and vertical vorticity production by baroclinity or horizontal gradients of surface friction, a downdraft is crucial for the creation of vertical vorticity near the surface (Davies-Jones 1982; Davies-Jones and Brooks 1993; Davies-Jones and Markowski 2013). If horizontal vorticity is generated baroclinically, a descending parcel can acquire vertical vorticity through tilting during its descent (Davies-Jones and Brooks 1993). Previous observational and numerical studies (Adlerman et al. 1999; Straka et al. 2007; Markowski et al. 2008, 2012a, 2012b) have suggested that baroclinity around the RFD region plays a crucial role in the formation of a vorticity source for a near-surface vortex in supercells. Marquis et al. (2012) performed a dual-Doppler wind data analysis using data assimilation and demonstrated through a vortex line analysis that the RFD surge might contribute to tornado maintenance by providing baroclinically generated vorticity. However, these studies targeted a large-scale low-level mesocyclone rather than a tornado and focused on intensification of the vortex.

Wicker and Wilhelmson (1995) successfully simulated a supercell tornado by using a model with a tornado-resolving fine mesh (horizontal grid spacing 120 m) under free-slip lower boundary conditions. Their simulation results indicated that the strong vertical vorticity of a tornado originated predominantly from baroclinically generated horizontal vorticity along the forward-flank gust front (FFGF). The horizontal vorticity was tilted into the vertical and stretched by strong dynamical lifting associated with a low-level mesocyclone, and it subsequently evolved into a tornado. This result is quite similar to the formation mechanism of low-level mesocyclones in supercell storms suggested by previous idealized numerical studies (Klemp and Rotunno 1983; Rotunno and Klemp 1985). However, the strong baroclinity along the FFGF found in these simulation results is controversial, because it is thought that the unsophisticated cloud microphysics scheme used in these simulations likely produced an excessively strong cold pool as a result of the excessive rain production and evaporation from rain (e.g., Davies-Jones 2006; Shabbott and Markowski 2006). In fact, using idealized simulations with a 100-m grid spacing, Snook and Xue (2008) reported that drop size distributions in the cloud microphysics significantly affected cold pool intensity and tornadogenesis. Moreover, some trajectories from the inflow region near the surface might have resulted from interpolation errors, as suggested by Dahl et al. (2012). More recent idealized numerical studies focusing on the onset of surface rotation (Markowski and Richardson 2014; Dahl et al. 2014; Parker and Dahl 2015) have analyzed the vorticity forcings along a number of trajectories and have showed that baroclinic vorticity generation by horizontal buoyancy gradients is crucial for the creation of vertical vorticity of a near-surface vortex.

However, because these previous numerical studies were conducted under idealized conditions with a free-slip boundary and a horizontally homogeneous environmental field, the frictional effect on supercell tornadogenesis remains an important unresolved issue. Surface friction is likely to have various effects on a near-surface vortex. Cyclonic rotation affected by surface friction has a radially inward-directed (crosswise) vorticity. Frictional convergence may enhance preexisting vertical vorticity near the surface (Davies-Jones 2006). Davies-Jones (2015) suggested that frictional stress at the ground surface is crucial for tornadogenesis because a cyclostrophic imbalance caused by the surface friction drives a strong radial inflow in the boundary layer, resulting in intensification of the vortex. However, the net effect of friction is to weaken the vortex if the frictional loss of angular momentum is not offset by radial inflow. In fact, waterspouts often dissipate when making landfall (e.g., Hagemeyer 1997). Furthermore, the frictional effect influences the low-level environmental wind field and creates strong horizontal vorticity within the boundary layer, which might affect tornadogenesis (Walko 1993; Markowski and Richardson 2014).

A recent numerical study by Mashiko et al. (2009) was the first to simulate tornadogenesis in a supercell storm under realistic environmental conditions including surface friction. They concluded that the simulated tornado originated dominantly from the environmental streamwise vorticity at low levels. The frictional effect on the vorticity source of tornadogenesis was small compared with the other effects. The RFD surge contributed to tornadogenesis by transporting the additional vorticity toward the surface and enhancing horizontal convergence. However, their study dealt with a typhoon-associated minisupercell over the sea in an environment with highly humid air and strong low-level wind shear; these conditions differ from those associated with a “classic” supercell storm such as occurs on the Great Plains in the United States. Schenkman et al. (2014) examined tornadogenesis in a classic supercell of the 2003 Oklahoma City, Oklahoma, storm using a 50-m grid spacing simulation that included surface friction. By using a vorticity budget analysis along a parcel trajectory, they found that frictionally generated crosswise vorticity near the surface was the dominant vorticity source responsible for tornadogenesis. This result is contrary to the results of most previous studies of classic supercell tornadogenesis, and the surface effect on tornadogenesis is still controversial.

Mashiko (2016, hereafter Part I) analyzed the overall structure and evolution of a midlevel mesocyclone, a low-level mesocyclone, and a low-level mesoanticyclone in a numerical simulation of the 6 May 2012 Tsukuba City, Japan, tornadic supercell. Vortex line and circulation analyses were also performed for these vortices to elucidate the vorticity sources. In the present paper, these analyses are extended to the generation mechanisms of the supercell tornado. As shown in Part I, a 50-m horizontal grid spacing simulation successfully reproduced the tornado with a slight displacement compared to the observed Tsukuba tornado and it formed about 25 min earlier in the simulation. The 50-m grid spacing simulations in this study were conducted using the Japan Meteorological Agency Nonhydrostatic Model (JMA-NHM; Saito et al. 2006) under realistic environmental conditions, including surface friction, as in Mashiko et al. (2009). Vertical grid spacing is 20 m near the surface. The surface flux scheme based on the bulk method (Beljaars and Holtslag 1991) was employed. A 1.5-order turbulent kinetic energy closure model formulated by Deardorff (1980) was used to calculate subgrid-scale turbulent mixing. The bulk-type cloud microphysics predicts the mixing ratios of water vapor, cloud water, rain, cloud ice, snow, and hail/graupel (Ikawa et al. 1991; Murakami 1990). Details of the numerical model and calculation techniques of vortex line and circulation analyses are given in sections 3 and 6a of Part I. The main objective of Part II is to quantitatively clarify the vorticity sources responsible for tornadogenesis by evaluating baroclinic and frictional effects on the circulation along a material circuit. In addition, the buoyancy field was analyzed to elucidate the cause of the baroclinity responsible for tornadogenesis.

The remainder of this paper is structured as follows: in section 2, the triggering factor and vorticity sources of the tornado are examined by analyzing the trajectories, vortex lines, and the evolution of circulation of a tornadic vortex at the preonset stage of tornadogenesis and the fully developed tornadic stage. In section 3, the results of an investigation of the baroclinity around the tip of the hook-shaped pattern of hydrometers (hereafter referred to as hook echo) responsible for tornadogenesis are presented. Section 4 presents the results of a sensitivity experiment without diabatic cooling due to cloud microphysics processes. In section 5, the descending precipitation core at the tip of the hook echo is discussed. Finally, the main results of this study are summarized in section 6.

2. Generation processes of the tornado

a. Triggering factor of tornadogenesis

To clarify the triggering factors of tornadogenesis, the evolution of the kinematic and thermodynamic fields near the surface was carefully examined until just after tornadogenesis. As noted in Part I, the Tsukuba City supercell storm, which had the characteristics of a typical classic tornadic supercell such as occurs on the Great Plains, moved toward the east-northeast at a speed of about 60 km h−1. A sudden drop in pressure and rapid increases in vertical vorticity and wind velocity near the surface at around 1208 Japan standard time (JST = UTC + 9 h) (Fig. 1) defined the timing of tornadogenesis.

Fig. 1.

Time series of vertical vorticity (blue line) and horizontal wind velocity (green line) maxima at z* = 10 m and minimum sea level pressure (red line) within a radius of 2.5 km from the low-level mesocyclone center. The low-level mesocyclone center was defined as the point of maximum vertical vorticity at 1-km height averaged over a 500 m by 500 m area (same as in Fig. 4 in Part I).

Fig. 1.

Time series of vertical vorticity (blue line) and horizontal wind velocity (green line) maxima at z* = 10 m and minimum sea level pressure (red line) within a radius of 2.5 km from the low-level mesocyclone center. The low-level mesocyclone center was defined as the point of maximum vertical vorticity at 1-km height averaged over a 500 m by 500 m area (same as in Fig. 4 in Part I).

Figures 2a–l show the evolution of vertical vorticity, potential temperature, and vertical velocity, along with horizontal wind vectors, at 150-m height from 1205 JST until just after tornadogenesis. The north–south-oriented FFGF and rear-flank gust front (RFGF) separated warm south-southeasterly environmental winds from the storm-generated westerly flows associated with cold pools. The FFGF and RFGF correspond to the leading edges of the westerly outflows from the forward-flank downdraft (FFD) and the RFD, respectively, as shown in a conceptual diagram of a supercell storm reported by Lemon and Doswell (1979). However, because the orientation and location of the FFGF in this study were different from those of a traditional FFGF (e.g., Lemon and Doswell 1979), the FFGF might correspond to a “left-flank convergence boundary” (Beck and Weiss 2013), as noted in Part I. The point at which the FFGF and RFGF intersect is discernible by a kink in the boundary zone. Large vertical vorticity and a strong updraft were present along the FFGF and RFGF, particularly along the RFGF near the storm center. A horseshoe-shaped strong updraft region formed along the RFGF. The horizontal difference of potential temperature across the FFGF and RFGF was 2–3 K. In the storm-relative wind field (Figs. 2i–l), the FFD was accompanied by northerly winds along the FFGF. In the RFD region, divergent flow from the locally intensified RFD was evident, and westerly winds associated with the RFD outflow were present behind the RFGF. The locally intensified RFD outflow surge moved eastward and eventually encroached on the RFGF region (Figs. 2i–l). This RFD outflow surge enhanced the horseshoe-shaped updraft by strong horizontal convergence. This small-scale RFD outflow surge within the RFD region likely corresponds to the secondary RFD surge recently found by high-resolution Doppler radar and mobile mesonet instruments (Wurman et al. 2007, 2010; Finley and Lee 2008; Marquis et al. 2008; Lee et al. 2011, 2012; Kosiba et al. 2013; Skinner et al. 2014) and numerical simulations (Mashiko et al. 2009; Schenkman et al. 2014, 2016; Skinner et al. 2015).

Fig. 2.

Horizontal distributions of (a)–(d) vertical vorticity, (e)–(h) potential temperature, and (i)–(l) vertical velocity (color scales) at 150-m height from 1205 to 1208 JST (just after tornadogenesis); “T − No. min” at the left corner of the panels denotes the number of minutes prior to tornadogenesis. Isobars are drawn at intervals of 1 hPa. Arrows in (a)–(h) are ground-relative wind vectors, and those in (i)–(l) are storm-relative wind vectors. The broken red lines in (a)–(d) represent the gust fronts. The RFD outflow surge is indicated by a broken pink line in (i) and (j). The black rectangles in (b)–(d) correspond to the region shown in Figs. 3a–c.

Fig. 2.

Horizontal distributions of (a)–(d) vertical vorticity, (e)–(h) potential temperature, and (i)–(l) vertical velocity (color scales) at 150-m height from 1205 to 1208 JST (just after tornadogenesis); “T − No. min” at the left corner of the panels denotes the number of minutes prior to tornadogenesis. Isobars are drawn at intervals of 1 hPa. Arrows in (a)–(h) are ground-relative wind vectors, and those in (i)–(l) are storm-relative wind vectors. The broken red lines in (a)–(d) represent the gust fronts. The RFD outflow surge is indicated by a broken pink line in (i) and (j). The black rectangles in (b)–(d) correspond to the region shown in Figs. 3a–c.

As the RFD outflow surge approached the horseshoe-shaped strong updraft region along the RFGF, a weak vortex on the RFGF close to its intersection with the FFGF intensified rapidly and evolved into the tornado at about 1208 JST (Figs. 2d, 2h, and 2l). The tornado was generated at the northern periphery of the RFD outflow surge. The arrival of the RFD outflow surge at a weak incipient vortex on the RFGF was likely the triggering factor of tornadogenesis, which is consistent with recent studies suggesting that RFD outflow surges are crucial to tornadogenesis and tornado maintenance (Mashiko et al. 2009; Lee et al. 2011, 2012; Marquis et al. 2012; Kosiba et al. 2013; Schenkman et al. 2014).

To understand the effect of the RFD outflow surge on tornadogenesis more clearly, backward trajectories initiated at the different stages of the tornadic vortex were compared, using an approach similar to that of Mashiko et al. (2009). The tornadic vortex at 150-m height was targeted at three different stages: the preonset stage of tornadogenesis at 1206 JST, until when the vertical vorticity maximum of about 0.1 s−1 was nearly constant (Fig. 3a); the onset stage of tornadogenesis at 1207 JST, when there were slight pressure drop and vertical vorticity increase (Fig. 3b); and the tornadic stage at 1208 JST, when the vertical vorticity was more than 0.3 s−1 and there was a distinct pressure drop of about 5 hPa (Fig. 3c). A total of 21 parcels were initially placed at regular intervals of 50 m in and around the vertical vorticity maximum on the vortex at each stage. Note that several initial parcels in the western side at each stage were located at the inflow region with high potential temperature, especially at the preonset stage of tornadogenesis (Figs. 3d–f).

Fig. 3.

Backward trajectory analyses initiating at 1206 (preonset stage of tornadogenesis), 1207 (onset stage of tornadogenesis), and 1208 JST (tornadic stage). (a)–(c) Distributions of the origins of 21 trajectories at 1206, 1207, and 1208 JST, respectively. All parcels were placed in and around the vertical vorticity maximum at 150-m height. The areas shown in (a)–(c) correspond to the black rectangular regions in Figs. 2b–d, respectively. Vertical vorticity (color shading), isobars (1-hPa interval), and storm-relative winds (arrows) are also shown. (d)–(f) As in (a)–(c), but that the color shading is potential temperature. Note that the color scale differs from that in Figs. 2e–h. (g)–(i) Backward trajectories of the parcels in (a)–(c) during 5 min, respectively. Trajectory locations are shifted to a storm-relative frame by taking storm motion into account. Colors along each trajectory indicate parcel heights. Isobars (1-hPa interval) and storm-relative winds (arrows) at the initial time of each trajectory analysis are also drawn. The red rectangles in (g)–(i) enclose the regions shown in (a)–(c), respectively.

Fig. 3.

Backward trajectory analyses initiating at 1206 (preonset stage of tornadogenesis), 1207 (onset stage of tornadogenesis), and 1208 JST (tornadic stage). (a)–(c) Distributions of the origins of 21 trajectories at 1206, 1207, and 1208 JST, respectively. All parcels were placed in and around the vertical vorticity maximum at 150-m height. The areas shown in (a)–(c) correspond to the black rectangular regions in Figs. 2b–d, respectively. Vertical vorticity (color shading), isobars (1-hPa interval), and storm-relative winds (arrows) are also shown. (d)–(f) As in (a)–(c), but that the color shading is potential temperature. Note that the color scale differs from that in Figs. 2e–h. (g)–(i) Backward trajectories of the parcels in (a)–(c) during 5 min, respectively. Trajectory locations are shifted to a storm-relative frame by taking storm motion into account. Colors along each trajectory indicate parcel heights. Isobars (1-hPa interval) and storm-relative winds (arrows) at the initial time of each trajectory analysis are also drawn. The red rectangles in (g)–(i) enclose the regions shown in (a)–(c), respectively.

To calculate the backward trajectories, a second-order Runge–Kutta scheme with an integration time step of 0.4 s was employed; this is the same procedure as that used for the circulation analysis in Part I. As Dahl et al. (2012) have suggested, backward trajectories using wind data with a coarse spatiotemporal resolution are more likely to be affected by calculation errors near a strong and confluent vortex such as a tornado, especially in the RFD outflow region. In this study, the three-dimensional model outputs of wind components at 0.8-s intervals were used to accurately compute backward trajectories. The temporal resolution was extraordinarily high because the integration time step of the numerical simulation was 0.4 s (see section 3 of Part I). However, Dahl et al. (2012) showed that backward trajectories are susceptible to errors in a certain case even when the model time step is used to output the wind data for the purposes of trajectory interpolation. Moreover, in this study several parcels descended below the lowest full level at z* = 10 m (10, 6, and 6 of 21 parcels at the preonset, onset, and tornadic stages, respectively). To assess the validity of the backward trajectories, therefore, forward trajectories were also computed from the 1-min backward trajectory points. These forward trajectories were nearly identical to the original backward trajectories (not shown). The detailed trajectory calculation method was presented in section 6a of Part I.

Figures 3g–i show the three sets of trajectories that were integrated backward for 5 min from the tornadic vortex at each stage. Note that the trajectory locations are shifted to the storm-relative frame by taking the storm motion1 into account. Most parcels in the weak vortex at the preonset stage of tornadogenesis at 1206 JST came from the east or northeast near the surface in the inflow sector of the storm environment, and some parcels traveled along the FFGF (cf. Figs. 2 and 3g). Only two parcels descended from the rear (western) side of the storm and then rose again into the vortex. The trajectory distributions for the vortex at the onset stage of tornadogenesis at 1207 JST were quite different from those at the preonset stage. About half of the parcels traveled from a high altitude of about 400 m through the RFD region and wrapped around the low-level cyclonic center (Fig. 3h). These parcels descended to near the surface and then were rapidly ingested into the vortex. Trajectories from the fully developed tornado just after genesis showed similar distributions, except for the parcels traveling along the FFGF (cf. Figs. 3h and 3i). The evolution of the trajectory distributions for the tornadic vortex suggests that the RFD outflow surge was crucial for intensification of the near-surface vortex and was a triggering factor of tornadogenesis. It is of great interest that the trajectory analysis results and the near-surface wind fields are quite similar to those reported for a minisupercell tornado in a typhoon-associated environment (Mashiko et al. 2009, see their Figs. 11 and 12). Note also that the inflow trajectories near the surface from the east or north are not erroneous despite their similarity to backward trajectories resulting from spatiotemporal interpolation errors shown in the simulation results of Dahl et al. (2012).

b. Vorticity sources of the tornado

To elucidate the vorticity sources of the vortex at the preonset stage of tornadogenesis and the tornadic stage, in addition to a vortex line analysis, the evolution of circulation about material circuits surrounding the vortex was investigated by the method described in section 6a of Part I.

1) Preonset stage of tornadogenesis

Figures 4b and 4c depict the vortex lines passing through the region of large vertical vorticity in the weak vortex on the RFGF at 150-m height at the preonset stage of tornadogenesis (Fig. 4a). The large vertical vorticity within the vortex was located in a narrow region with a marked horizontal vertical velocity gradient at the inner edge of the horseshoe-shaped strong updraft region along the RFGF rather than in the maximum updraft region (cf. Figs. 4a and 4b). The vortex lines first rise and then turn horizontally to the southwest, with some vortex lines forming arches (Fig. 4c), indicating that the vortex had a shallow structure. The near-surface vortex lines that were ingested into the vortex are directed northward in the RFD outflow region and then turn upward at the inner edge of the horseshoe-shaped strong updraft region along the RFGF (Fig. 4b). Note that the near-surface northward-directed vortex lines are normal to the strong westerly winds (i.e., crosswise vorticity) associated with the RFD outflow; this result is consistent with vorticity being generated by surface friction.

Fig. 4.

(a) Origins of vortex lines (dots) passing through the weak vortex on the RFGF at 150-m height at the preonset stage of tornadogenesis (1206 JST). Vertical vorticity (color shading), isobars (0.5-hPa interval), and storm-relative winds (arrows) are also shown. The displayed area corresponds to the region in the black rectangle in Fig. 2b. (b) Horizontal projection of the vortex lines overlaid on Fig. 2j. Vortex lines are shown only on the side to the rear of their origins. Note that the storm-relative wind vectors in Fig. 2j have been changed to ground-relative wind vectors and that the color scale of vertical velocity differs from that in Fig. 2j. (c) Three-dimensional perspective of the vortex lines. The direction of the vortex lines is indicated by the black arrow. The horizontal plotted area is the same as that in Fig. 2. Black dots in (b) and (c) indicate origins of the vortex lines.

Fig. 4.

(a) Origins of vortex lines (dots) passing through the weak vortex on the RFGF at 150-m height at the preonset stage of tornadogenesis (1206 JST). Vertical vorticity (color shading), isobars (0.5-hPa interval), and storm-relative winds (arrows) are also shown. The displayed area corresponds to the region in the black rectangle in Fig. 2b. (b) Horizontal projection of the vortex lines overlaid on Fig. 2j. Vortex lines are shown only on the side to the rear of their origins. Note that the storm-relative wind vectors in Fig. 2j have been changed to ground-relative wind vectors and that the color scale of vertical velocity differs from that in Fig. 2j. (c) Three-dimensional perspective of the vortex lines. The direction of the vortex lines is indicated by the black arrow. The horizontal plotted area is the same as that in Fig. 2. Black dots in (b) and (c) indicate origins of the vortex lines.

To clarify whether surface friction was indeed a crucial vorticity source for the vortex at the preonset stage of tornadogenesis, the evolution of the circulation and production terms (in a manner similar to that used in Part I) of the material circuit surrounding the vortex at 150-m height at 1206 JST (Fig. 5a) were investigated. The approach to circulation analysis used in this study is summarized in the following. Circulation C(t) and its change with time can be written as

 
formula
 
formula

where v is a three-dimensional wind vector, dl denotes a displacement vector tangent to the circuit, is density, p is pressure, and F represents the frictional forcing including turbulent mixing and numerical diffusion. The first and second terms on the right-hand side of Eq. (2) represent baroclinic and frictional effects, respectively. Counterclockwise integration is performed around the material circuit surrounding the targeted vortex. The circuit can be traced by using backward trajectory analysis of the parcels on the circuit. A total of 1600 parcels were used at the start and integrated backward in time, adopting the same method as that described in section 2a. If adjacent parcels on the circuit were more than 50 m apart, an additional parcel was added on the circuit at the middle point. Further details are given in section 6a of Part I.

Fig. 5.

(a) The initial position of a material circuit surrounding the vortex at 150-m height at the preonset stage of tornadogenesis (1206 JST). Vertical vorticity (color shading), isobars (0.5-hPa interval), and storm-relative winds (arrows) are also shown as in Fig. 4a. (b) Time series of the circulation (solid black line) and the baroclinic (solid red line), and frictional (dotted blue line) terms in Eq. (2) for the circuit traced backward in time from 1206 to 1153 JST. The dashed purple line represents the integrated circulation, which was calculated by integrating the sum of the baroclinic and frictional terms backward from 1206 JST. Vertical pink lines correspond to the times shown in Fig. 6.

Fig. 5.

(a) The initial position of a material circuit surrounding the vortex at 150-m height at the preonset stage of tornadogenesis (1206 JST). Vertical vorticity (color shading), isobars (0.5-hPa interval), and storm-relative winds (arrows) are also shown as in Fig. 4a. (b) Time series of the circulation (solid black line) and the baroclinic (solid red line), and frictional (dotted blue line) terms in Eq. (2) for the circuit traced backward in time from 1206 to 1153 JST. The dashed purple line represents the integrated circulation, which was calculated by integrating the sum of the baroclinic and frictional terms backward from 1206 JST. Vertical pink lines correspond to the times shown in Fig. 6.

The time series of the circulation and each production term on the right-hand side of Eq. (2) are shown in Fig. 5b. Unfortunately, a large discrepancy between the circulation calculated by integrating the baroclinic and frictional terms on the right-hand of Eq. (2) and the circulation calculated directly with Eq. (1) was found before 1203 JST. This discrepancy indicates that the backward tracing of the circuit and/or the evaluation of the circulation and its production terms of the circuit are unreliable. This is probably because most parts of the circuit originates from the near surface (Fig. 6a), as shown by the backward trajectories from the vortex at the preonset stage of tornadogenesis, in contrast to those at the tornadic stage (Fig. 3). As a result, the horizontal wind velocity under the assumption of a logarithmic profile and the constant frictional forcing below the lowest model level were used in much of the calculation and might lead to large errors. However, the increase in circulation after 1203 JST is quite reliable. Sensitivity tests using different circuit sizes were also performed and the results were qualitatively the same (not shown). As expected from the result of vortex line analysis, the frictional term was dominant and responsible for the increase in circulation after 1202 JST, whereas the baroclinic term was relatively small.

Fig. 6.

Horizontal projections of the circuit traced backward in time from the vortex at the preonset stage of tornadogenesis: (a) 1203 and (b) 1206 JST. At the initial time, shown in (b) and Fig. 5a, the circuit surrounds the vortex at the preonset stage. Each circuit was drawn by using 200 parcels; the circuit in (a) was smoothed. The color scale indicates circuit heights, and the gray shading indicates the mixing ratio of hydrometeors at 1-km height. Ground-relative wind vectors (arrows) and potential temperature (broken contours, 2-K interval) at 100-m height are also shown.

Fig. 6.

Horizontal projections of the circuit traced backward in time from the vortex at the preonset stage of tornadogenesis: (a) 1203 and (b) 1206 JST. At the initial time, shown in (b) and Fig. 5a, the circuit surrounds the vortex at the preonset stage. Each circuit was drawn by using 200 parcels; the circuit in (a) was smoothed. The color scale indicates circuit heights, and the gray shading indicates the mixing ratio of hydrometeors at 1-km height. Ground-relative wind vectors (arrows) and potential temperature (broken contours, 2-K interval) at 100-m height are also shown.

Figure 6a shows the configuration of the circuit at 1203 JST, when the frictional term contributed significantly to the increase in circulation. Most parts of the circuit were located in the inflow region, except for the southwestern portion of the circuit in the RFD outflow region, which is consistent with the result of trajectory analysis (Fig. 3g). Since the southwestern side of the circuit was located at a higher altitude, the northward-directed crosswise vorticity associated with westerly winds near the surface pierced the vertical projection of the circuit, which contributes to positive circulation of the circuit. It is inferred that the friction in the strong RFD outflow region played an important role in generating the vorticity of the vortex at the preonset stage of tornadogenesis, considering the result of vortex line analysis; this generation mechanism is somewhat similar to that of a simulated tornado of the 2003 Oklahoma City supercell in Schenkman et al. (2014). Concerning the inflow parcels, the vorticity budget analyses along the trajectories demonstrated that some parcels acquired vertical vorticity directly through the frictional effect (turbulent mixing) near the vortex (not shown), which implies that the vortex lines do not behave like material lines. Other parcels already had a small vertical vorticity below the lowest model level in the inflow sector or achieved the vertical vorticity through tilting during its ascent (not shown).

2) Tornadic stage just after genesis

Similar analyses were conducted for the tornado just after genesis. Figures 7b–d show vortex lines passing through the large vertical vorticity region in the tornado at 150-m height just after tornadogenesis (Fig. 7a). In contrast to the vortex at the preonset of tornadogenesis, the location of the vertical vorticity maximum at the tornadic stage nearly coincides with the strong updraft region (cf. Figs. 7a and 7d). The vortex lines drawn from the origins within the tornado are almost vertical through the low-level mesocyclone and ascend densely below about 1000 m (Fig. 7c).

Fig. 7.

(a) Origins of vortex lines (dots) passing through the tornado at 150-m height at 1208 JST (just after tornadogenesis). Vertical vorticity (color shading), isobars (1-hPa interval), and storm-relative winds (arrows) are also shown. The displayed area corresponds to the region in the black rectangle in Fig. 2d. (b) Horizontal projection of the vortex lines overlaid on Fig. 2l. The vortex lines are shown only on the side to the rear of their origins. Note that the color scale of vertical velocity differs from that in Fig. 2l. (c) Three-dimensional perspective of the vortex lines. The direction of the vortex lines is indicated by the black arrow. The horizontal plotted area is the same as that in Fig. 2. (d) Close-up of the pink rectangular area in (b), but that vortex lines are shown only below 300-m height. Black dots in (b)–(d) indicate origins of the vortex lines.

Fig. 7.

(a) Origins of vortex lines (dots) passing through the tornado at 150-m height at 1208 JST (just after tornadogenesis). Vertical vorticity (color shading), isobars (1-hPa interval), and storm-relative winds (arrows) are also shown. The displayed area corresponds to the region in the black rectangle in Fig. 2d. (b) Horizontal projection of the vortex lines overlaid on Fig. 2l. The vortex lines are shown only on the side to the rear of their origins. Note that the color scale of vertical velocity differs from that in Fig. 2l. (c) Three-dimensional perspective of the vortex lines. The direction of the vortex lines is indicated by the black arrow. The horizontal plotted area is the same as that in Fig. 2. (d) Close-up of the pink rectangular area in (b), but that vortex lines are shown only below 300-m height. Black dots in (b)–(d) indicate origins of the vortex lines.

On the side to the rear of their origins, some vortex lines pierce the ground2 and others turn horizontally near the surface and extend to the southwest. These vortex lines were directed to the east-northeast, which is nearly the same horizontal direction as not only the ground-relative winds (Fig. 2h) but also the storm-relative winds associated with the RFD outflow near the tornado (i.e., streamwise vorticity for the storm-relative flow on the horizontal plane) (Fig. 7d). The horizontally streamwise vortex lines near the tornado are located roughly along the northern edge (left side) of the strong downdraft in the RFD outflow region (Figs. 7b and 7d).

Time series of the circulation and each production term are shown in Fig. 8b for a material circuit traced backward in time from the tornado at 150-m height just after genesis (Fig. 8a). The circuit was also traced forward in time for 1 min from the tornado vortex. In contrast to the result for the vortex at the preonset stage of tornadogenesis, this result is reliable throughout the period of the analysis, as verified by the comparison between the integrated circulation of the right-hand side in Eq. (2) and circulation calculated directly with Eq. (1). The robustness of the results was also tested with respect to the size of the initial material circuit, and the results were qualitatively the same (not shown). The location of the circuit traced forward for 1 min is shown in Fig. 9f. Most of the circuit was located at about 750-m height owing to the strong updraft within the tornado. The circuit encircled the region of large vertical vorticity associated with the tornado, which indicates that the circulation of the circuit represents the area-averaged vorticity of the entire tornado vortex.

Fig. 8.

(a) The initial position of a material circuit surrounding the tornado at 150-m height at 1208 JST. Vertical vorticity (color shading), isobars (1-hPa interval), and storm-relative winds (arrows) are also shown as in Fig. 7a. (b) Time series of the circulation (solid black line) and the baroclinic (solid red line) and frictional (dotted blue line) terms in Eq. (2) for the circuit traced backward from 1208 to 1153 JST and forward from 1208 to 1209 JST. The dashed purple line represents the integrated circulation, which was calculated by integrating the sum of the baroclinic and frictional terms backward and forward from 1208 JST. Vertical pink lines correspond to the times shown in Fig. 9.

Fig. 8.

(a) The initial position of a material circuit surrounding the tornado at 150-m height at 1208 JST. Vertical vorticity (color shading), isobars (1-hPa interval), and storm-relative winds (arrows) are also shown as in Fig. 7a. (b) Time series of the circulation (solid black line) and the baroclinic (solid red line) and frictional (dotted blue line) terms in Eq. (2) for the circuit traced backward from 1208 to 1153 JST and forward from 1208 to 1209 JST. The dashed purple line represents the integrated circulation, which was calculated by integrating the sum of the baroclinic and frictional terms backward and forward from 1208 JST. Vertical pink lines correspond to the times shown in Fig. 9.

Fig. 9.

Horizontal projections of the circuit traced backward and forward in time from the tornado: (a) 1156, (b) 1159, (c) 1202, (d) 1205, (e) 1208, and (f) 1209 JST. At the initial time, the circuit, shown in (e) and Fig. 8a, surrounds the tornado. Each circuit in (b)–(f) was drawn by using 200 parcels, and that in (a) was drawn by using 400 parcels. The circuits were smoothed except in (e) and (f). The color scale indicates height along each circuit. The mixing ratio of hydrometeors at 1-km height (gray shading) and potential temperature at 150-m height (broken contours, 2-K interval) are also shown in (a)–(e). The gray shading and contour lines in (f) denote vertical vorticity and isobars (2-hPa interval), respectively, at 750-m height. The areas enclosed by the dashed and solid black rectangles in (a) correspond to the regions shown in (b)–(e) and (f), respectively. The pink rectangles in (a) and (b) enclose the areas shown in Figs. 10a and 10b, respectively.

Fig. 9.

Horizontal projections of the circuit traced backward and forward in time from the tornado: (a) 1156, (b) 1159, (c) 1202, (d) 1205, (e) 1208, and (f) 1209 JST. At the initial time, the circuit, shown in (e) and Fig. 8a, surrounds the tornado. Each circuit in (b)–(f) was drawn by using 200 parcels, and that in (a) was drawn by using 400 parcels. The circuits were smoothed except in (e) and (f). The color scale indicates height along each circuit. The mixing ratio of hydrometeors at 1-km height (gray shading) and potential temperature at 150-m height (broken contours, 2-K interval) are also shown in (a)–(e). The gray shading and contour lines in (f) denote vertical vorticity and isobars (2-hPa interval), respectively, at 750-m height. The areas enclosed by the dashed and solid black rectangles in (a) correspond to the regions shown in (b)–(e) and (f), respectively. The pink rectangles in (a) and (b) enclose the areas shown in Figs. 10a and 10b, respectively.

It is noteworthy that during 1155–1202 JST, the circulation of the circuit increased rapidly from a negative value, which indicates that the storm generated the circulation for the tornado vortex. This trend is quite similar to that of the low-level mesocyclone of the 2009 Goshen County storm, described by Markowski et al. (2012b). Most of the rapid increase in circulation during 1155–1200 JST resulted from the baroclinic term. The frictional term also contributed to the increase in circulation until around 1205 JST; however, its sign changed to negative at that time, which caused a small drop in circulation during 1205–1208 JST near the origin of the circuit surrounding the tornado vortex. Thus, although the frictional term had a net positive effect on vorticity generation for tornadogenesis, it had a negative impact when the vortex intensified. This result differs from that found by Schenkman et al. (2014) 3 in a simulation of the 2003 Oklahoma City supercell tornado.

The configurations of the circuit traced backward in time are shown in Figs. 9a–d. Although the western portion of the circuit traveled over the FFGF at 1202 and 1205 JST (Figs. 9c and 9d), the baroclinic term was quite small (Fig. 8b), which indicates that the FFGF contributed little to the vorticity source of the tornado. The rapid increase in circulation was produced principally by the significant baroclinity during 1156–1159 JST (Fig. 8b), at which time the southwestern edge of the circuit was located at a higher altitude on the tip of the hook echo (Figs. 9a and 9b). It is noteworthy that during this time large amounts of hydrometeors were present at the tip of the hook (Figs. 10a and 10b). The hook echo was likely a key factor for the baroclinity responsible for the vorticity source of the tornado. This is discussed further in section 5.

Fig. 10.

(a) Horizontal vorticity vectors (arrows) and the mixing ratio of hydrometeors (bold solid contours) at 1500-m height at 1156 JST. Broken lines indicate potential temperature (2-K interval) at 150-m height. The displayed area corresponds to the region in the pink rectangle shown in Fig. 9a, and the circuit in Fig. 9a is overlaid. (b) As in (a), but at 500-m height at 1159 JST in the area enclosed by the pink rectangle in Fig. 9b. The pink broken-line arrow denotes the clockwise orientation of the vorticity vectors around the hook.

Fig. 10.

(a) Horizontal vorticity vectors (arrows) and the mixing ratio of hydrometeors (bold solid contours) at 1500-m height at 1156 JST. Broken lines indicate potential temperature (2-K interval) at 150-m height. The displayed area corresponds to the region in the pink rectangle shown in Fig. 9a, and the circuit in Fig. 9a is overlaid. (b) As in (a), but at 500-m height at 1159 JST in the area enclosed by the pink rectangle in Fig. 9b. The pink broken-line arrow denotes the clockwise orientation of the vorticity vectors around the hook.

Figures 10a and 10b depict horizontal vorticity vectors around the tip of the hook at heights of 1500 and 500 m at 1156 and 1159 JST, respectively. In addition to the southward-directed horizontal vorticity vectors along the FFGF at 500-m height (Fig. 10b), clockwise-directed horizontal vorticity vectors encircle the tip of the hook, as shown in Part I. These correspond to vortex rings produced baroclinically by the horizontal gradient of buoyancy around the RFD, as discussed by Straka et al. (2007) and Markowski et al. (2008). The eastward- or east-southeastward-directed horizontal vorticity vectors on the northeast side of the hook echo pierced the area encircled by the circuit in the southwest at 1159 JST, resulting in a positive contribution to the circulation of the circuit (Fig. 10b). Although the distribution of horizontal vorticity vectors around the hook echo at 1156 JST is also suggestive of baroclinically generated vorticity, the configuration of the circuit is quite complicated, making it difficult to evaluate the contribution of the baroclinity around the hook echo (Fig. 10a).

3. Baroclinity around the tip of the hook echo

The buoyancy field was examined to clarify the vorticity source for tornadogenesis. Buoyancy around the hook echo at 1156 JST, which rapidly generated significant circulation for the tornado (Fig. 8b), was determined by diagnostically evaluating the buoyancy term in the vertical momentum equation, following the approach of Mashiko et al. (2009). The Boussinesq version of the vertical momentum equation can be written as follows:

 
formula

where w is vertical velocity, g is gravity acceleration, and is the density deviation from ; is a local horizontal average of the density, computed over a 5 km by 5 km region centered on each point. Base-state pressure is then computed to be in hydrostatic balance with , and p′ is the deviation from this base-state pressure. The first term on the right-hand side represents the vertical perturbation pressure gradient force, and the second term is buoyancy. The resulting buoyancy and perturbation pressure fields are different from those used in the model, which are computed using a base state averaged over the entire outermost domain at the initial time (NHM1km, see Table 1 in Part I), but their sums will be the same. As shown by Doswell and Markowski (2004), the contributions from each term on the right-hand side depend on what base state is chosen. Because this study focused on the baroclinity around the tip of the hook echo, is determined as a horizontal average of the density over a 5 km by 5 km region.

Figure 11 shows horizontal distributions of each term on the right-hand side of Eq. (3) at 1500-m height at 1156 JST, when circulation for the tornado was increasing rapidly because of the baroclinity (Fig. 8b). The vertical perturbation pressure gradient was the dominant forcing for the acceleration of vertical velocity; the forcing was strongly negative in the RFD region and strongly positive in the warm sector of the storm to the east. It can be inferred that the perturbation pressure gradient force was caused mainly by dynamical effects, as shown in previous studies (e.g., Lemon and Doswell 1979; Klemp and Rotunno 1983; Finley et al. 2001; Noda and Niino 2010), although it included a contribution from the buoyancy. It is noteworthy that buoyancy was also negative in the RFD region, and the buoyancy field had a horizontal gradient, especially at the tip of the hook echo (cf. Figs. 11b and 9a). These results imply that air parcels can acquire baroclinically generated vorticity even in the dynamically driven occlusion downdraft.

Fig. 11.

The distribution of (a) vertical perturbation pressure gradient term and (b) buoyancy term in Eq. (3) at 1500-m height at 1156 JST (color scale). Bold solid contour lines denote the mixing ratio of hydrometeors of 0.6 g kg−1. Arrows indicate storm-relative winds at 150-m height. The area displayed in each panel corresponds to the region in the pink rectangle shown in Fig. 9a.

Fig. 11.

The distribution of (a) vertical perturbation pressure gradient term and (b) buoyancy term in Eq. (3) at 1500-m height at 1156 JST (color scale). Bold solid contour lines denote the mixing ratio of hydrometeors of 0.6 g kg−1. Arrows indicate storm-relative winds at 150-m height. The area displayed in each panel corresponds to the region in the pink rectangle shown in Fig. 9a.

In addition to diabatic processes such as cooling due to the evaporation of rain, the melting of ice-phase hydrometeors, and other phase changes of the cloud microphysics, the weight of hydrometeors affects the buoyancy field. To quantify the effect of precipitation loading caused by the weight of rain, snow, and hail/graupel on the buoyancy field around the hook echo, the loading contribution was evaluated separately (Fig. 12a). As expected, the distribution of negative forcing due to the precipitation loading was practically coincident with the hook-echo pattern. However, the precipitation loading effect was quite small compared with the strong negative forcing due to the remnant of the buoyancy term, especially at the tip of the hook echo (cf. Figs. 12a and 12b). Since the contribution of water vapor to the buoyancy field was negligible (not shown), it can be inferred that diabatic cooling due to cloud microphysics processes contributed significantly to the formation of negative buoyancy and the horizontal gradient of buoyancy around the tip of the hook echo (discussed in section 4). This result is notably different from that for a typhoon-associated minisupercell in a highly humid environment (Mashiko et al. 2009, see their Fig. 15).

Fig. 12.

Horizontal distributions of (a) precipitation loading and (b) the remnant of the buoyancy term at 1500-m height at 1156 JST (color scale). Bold solid contour lines denote the mixing ratio of hydrometeors of 0.6 g kg−1. The area displayed in each panel corresponds to the region in the pink rectangle shown in Fig. 9a. Arrows indicate storm-relative winds at 150-m height.

Fig. 12.

Horizontal distributions of (a) precipitation loading and (b) the remnant of the buoyancy term at 1500-m height at 1156 JST (color scale). Bold solid contour lines denote the mixing ratio of hydrometeors of 0.6 g kg−1. The area displayed in each panel corresponds to the region in the pink rectangle shown in Fig. 9a. Arrows indicate storm-relative winds at 150-m height.

4. Sensitivity experiment

A sensitivity experiment was conducted to test the effects of diabatic cooling associated with hydrometeors on tornadogenesis. The focus was on diabatic cooling due to evaporation of rain and melting of ice-phase hydrometeors because such microphysical processes are the dominant contributors to cooling, as discussed by Snook and Xue (2008).

Figure 13 shows the diabatic cooling rate by evaporation from rain and melting of snow and hail/graupel at heights of 2500 and 250 m at 1156 JST in the control run. The cooling rate due to the melting of hail/graupel was significantly larger than that due to snow melting, owing to the small amount of snow and its virtual absence below 3000 m (not shown). Evaporative cooling from rain was most effective at 250-m height, whereas cooling due to the melting of ice-phase hydrometeors was weak at low levels and more effective at midlevel.

Fig. 13.

Diabatic cooling rate by evaporation of rain at heights of (a) 2500 and (c) 250 m at 1156 JST in the control run (color scale). Bold solid contour lines denote the mixing ratio of hydrometeors of 1.0 g kg−1 in (a) and 0.3 g kg−1 in (c). Storm-relative wind vectors (arrows) and potential temperature (broken-line contours, 2-K interval) at 150-m height are also shown. The plotted area in each panel corresponds to the region in the pink rectangle in Fig. 9a. (b),(d) As in (a),(c), respectively, but for the diabatic cooling rate due to the melting of snow and hail/graupel.

Fig. 13.

Diabatic cooling rate by evaporation of rain at heights of (a) 2500 and (c) 250 m at 1156 JST in the control run (color scale). Bold solid contour lines denote the mixing ratio of hydrometeors of 1.0 g kg−1 in (a) and 0.3 g kg−1 in (c). Storm-relative wind vectors (arrows) and potential temperature (broken-line contours, 2-K interval) at 150-m height are also shown. The plotted area in each panel corresponds to the region in the pink rectangle in Fig. 9a. (b),(d) As in (a),(c), respectively, but for the diabatic cooling rate due to the melting of snow and hail/graupel.

In the sensitivity experiment, evaporation of rain and diabatic cooling owing to the melting of ice-phase hydrometeors (snow and hail/graupel) were disabled in the nesting runs with horizontal grid spacings of 250 (NHM250m) and 50 m (NHM50m). (See the experimental design in section 3 of Part I for further details.) Figure 14 shows the time series of vertical vorticity and horizontal wind velocity maxima at z* = 10 m and minimum sea level pressure in the sensitivity experiment. A much weaker vortex occurred compared with that in the control run, and the vortex maintained its intensity for a shorter period (cf. Figs. 14 and 1). As in the control run, the vortex was generated near the intersection point between the RFGF and FFGF (Fig. 15a), and a strong RFD was present behind the RFGF (Fig. 15c). However, the sensitivity experiment results exhibited almost no potential temperature deficit behind the gust fronts (Fig. 15b), in contrast to the control run, and this more highly buoyant air near the surface might be expected to be favorable for tornadogenesis and tornado intensification compared to the control run (e.g., Markowski et al. 2002, 2003; Shabbott and Markowski 2006; Grzych et al. 2007; Hirth et al. 2008; Snook and Xue 2008; Markowski and Richardson 2014).

Fig. 14.

As in Fig. 1, but for the experiment without evaporation of rain or diabatic cooling due to melting of snow and hail/graupel.

Fig. 14.

As in Fig. 1, but for the experiment without evaporation of rain or diabatic cooling due to melting of snow and hail/graupel.

Fig. 15.

Horizontal distributions of (a) vertical vorticity, (b) potential temperature, and (c) vertical velocity at 150-m height at 1209 JST in the experiment without evaporation of rain or diabatic cooling due to melting of snow and hail/graupel. Isobars are drawn at intervals of 1 hPa. Arrows indicate ground-relative wind vectors in (a) and (b), and storm-relative wind vectors in (c). Broken red lines in (a) indicate the gust fronts. The rectangular area in (a) corresponds to the region shown in Fig. 16a.

Fig. 15.

Horizontal distributions of (a) vertical vorticity, (b) potential temperature, and (c) vertical velocity at 150-m height at 1209 JST in the experiment without evaporation of rain or diabatic cooling due to melting of snow and hail/graupel. Isobars are drawn at intervals of 1 hPa. Arrows indicate ground-relative wind vectors in (a) and (b), and storm-relative wind vectors in (c). Broken red lines in (a) indicate the gust fronts. The rectangular area in (a) corresponds to the region shown in Fig. 16a.

To investigate the cause of the much weaker vortex simulated in the sensitivity experiment, an analysis of the circulation about the material circuit surrounding the vortex at 150-m height just after genesis (Fig. 16a) was conducted. Figure 16b shows the time series of the circulation and its production terms. Friction was the only dominant forcing, although the integrated circulation did not match the actual circulation well. The baroclinic term was nearly zero throughout the period. The configuration of the circuit is shown in Fig. 17. Most of the circuit originated from the inflow region near the surface, and the circuit area was displaced from the hook echo, in contrast to the control run (cf. Figs. 17 and 9). Although the western portion of the circuit overlapped the gust fronts, there was very little baroclinity along the gust fronts. The vorticity budget analyses along the inflow parcels show that some parcels acquired the vertical vorticity through tilting of the frictionally generated horizontal vorticity while descending near the vortex (not shown). Other parcels achieved the vertical vorticity through tilting of horizontal vorticity during its ascent or already had a slight vertical vorticity below the lowest model level in the inflow sector (not shown).

Fig. 16.

(a) The initial position of a material circuit around the vortex at 150-m height in the experiment without evaporation of rain or diabatic cooling due to melting of snow and hail/graupel. Vertical vorticity (color scale), isobars (1-hPa interval), and storm-relative winds (arrows) are also shown. The displayed area corresponds to the region in the black rectangle in Fig. 15a. (b) Time series of the circulation (solid black line), baroclinic term (solid red line), and frictional term (broken blue line) in Eq. (2) for the circuit traced backward in time from 1209 to 1154 JST. The dashed purple line represents the integrated circulation, which was calculated by integrating the sum of the baroclinic and frictional terms backward from 1209 JST. The vertical pink lines correspond to the times shown in Fig. 17.

Fig. 16.

(a) The initial position of a material circuit around the vortex at 150-m height in the experiment without evaporation of rain or diabatic cooling due to melting of snow and hail/graupel. Vertical vorticity (color scale), isobars (1-hPa interval), and storm-relative winds (arrows) are also shown. The displayed area corresponds to the region in the black rectangle in Fig. 15a. (b) Time series of the circulation (solid black line), baroclinic term (solid red line), and frictional term (broken blue line) in Eq. (2) for the circuit traced backward in time from 1209 to 1154 JST. The dashed purple line represents the integrated circulation, which was calculated by integrating the sum of the baroclinic and frictional terms backward from 1209 JST. The vertical pink lines correspond to the times shown in Fig. 17.

Fig. 17.

Horizontal projections of the circuit traced backward in time from the vortex at 1209 JST in the experiment without evaporation of rain or diabatic cooling due to melting of snow and hail/graupel: (a) 1201, (b) 1205, and (c) 1209 JST. At the initial time, the circuit, shown in (c) and Fig. 16a, surrounds the vortex at 150-m height. Each circuit was drawn by using 200 parcels; the circuits were smoothed except in (c). Colors indicate the height along each circuit. Gray shading indicates the mixing ratio of hydrometeors at 1-km height. Ground-relative wind vectors (arrows) and potential temperature (broken contours, 2-K interval) at 150-m height are also shown.

Fig. 17.

Horizontal projections of the circuit traced backward in time from the vortex at 1209 JST in the experiment without evaporation of rain or diabatic cooling due to melting of snow and hail/graupel: (a) 1201, (b) 1205, and (c) 1209 JST. At the initial time, the circuit, shown in (c) and Fig. 16a, surrounds the vortex at 150-m height. Each circuit was drawn by using 200 parcels; the circuits were smoothed except in (c). Colors indicate the height along each circuit. Gray shading indicates the mixing ratio of hydrometeors at 1-km height. Ground-relative wind vectors (arrows) and potential temperature (broken contours, 2-K interval) at 150-m height are also shown.

The results of the sensitivity experiment suggest that the simulated vortex weakened compared to the control run, in spite of the greater potential positive buoyancy near the vortex, because the main vorticity source associated with baroclinity due to diabatic cooling, as shown in the diagnostic evaluation of the buoyancy in section 3, was not supplied to the vortex.

5. Descending precipitation core at the tip of the hook echo

Baroclinity associated with diabatic cooling around the tip of the hook echo has been shown to be a dominant vorticity source for tornadogenesis thus far. Figure 18 shows the evolution of the hook echo during the time at which the baroclinity responsible for the vorticity sources of the tornado increased rapidly in the control experiment. At 1155 JST, the core, which contained a large amount of hydrometeors, especially at higher altitude, was located at the tip of the hook echo. At 1159 JST, the precipitation core became prominent and it had large amounts of hydrometeors even at low levels (Figs. 18d and 18f).

Fig. 18.

Mixing ratio of hydrometeors (sum of rain, snow, and hail/graupel) at heights of (a) 3000, (c) 2000, and (e) 1000 m at 1155 JST in the control run. Arrows denote storm-relative wind vectors. Note that the storm motion is defined as the movement of the low-level mesocyclone center (see Part I). Solid black contour lines denote vertical velocity (10 m s−1 interval); the zero and negative contours are omitted. (b),(d),(f) As in (a),(c),(e), respectively, but at 1159 JST. The broken circle in each panel indicates the location of the precipitation core at the tip of the hook echo.

Fig. 18.

Mixing ratio of hydrometeors (sum of rain, snow, and hail/graupel) at heights of (a) 3000, (c) 2000, and (e) 1000 m at 1155 JST in the control run. Arrows denote storm-relative wind vectors. Note that the storm motion is defined as the movement of the low-level mesocyclone center (see Part I). Solid black contour lines denote vertical velocity (10 m s−1 interval); the zero and negative contours are omitted. (b),(d),(f) As in (a),(c),(e), respectively, but at 1159 JST. The broken circle in each panel indicates the location of the precipitation core at the tip of the hook echo.

Figure 19 depicts a time–height diagram of the maximum mixing ratio of hydrometeors around the low-level mesocyclone in the control experiment. Local maxima associated with the core of hydrometeors descended from above the 3-km level to the surface in the 1155–1201 JST period, during which time the baroclinic term of circulation for the tornado was significantly increased. The evolution of the simulated hydrometeor core is quite similar to that of an observed descending reflectivity core (DRC) documented in recent studies (e.g., Rasmussen et al. 2006; Kennedy et al. 2007a,b; Byko et al. 2009; Markowski et al. 2012a,b). DRCs have been recently suggested to be a potential precursory phenomenon of supercell tornadogenesis, because they are occasionally detected by radar observations prior to the development of low-level rotation, including tornadoes (e.g., Rasmussen et al. 2006; Kennedy et al. 2007a,b). It is noteworthy that in this study the occurrence of the descending precipitation core (hereafter DRC) preceded tornadogenesis by about 10 min and was tied to the baroclinic vorticity generation (Figs. 10 and 12) that later contributed directly to the tornadogenesis.

Fig. 19.

Time–height diagram of maximum mixing ratio of hydrometeors (sum of rain, snow, and hail/graupel) from 1155 to 1220 JST in the control run. The maximum was calculated at each model level within a radius of 2.5 km from the low-level mesocyclone center at 1-km height. The descending precipitation core at the tip of the hook echo is encircled by a broken-line oval. Time series of the baroclinic term in Fig. 8b are overlaid (solid line). The black arrow denotes the timing of tornadogenesis.

Fig. 19.

Time–height diagram of maximum mixing ratio of hydrometeors (sum of rain, snow, and hail/graupel) from 1155 to 1220 JST in the control run. The maximum was calculated at each model level within a radius of 2.5 km from the low-level mesocyclone center at 1-km height. The descending precipitation core at the tip of the hook echo is encircled by a broken-line oval. Time series of the baroclinic term in Fig. 8b are overlaid (solid line). The black arrow denotes the timing of tornadogenesis.

A strong updraft exceeding 20 m s−1 prevailed at the front (eastern) side of the storm above the 2-km level, and over time it took on a horseshoe-shaped distribution (Fig. 18). At the rear (western side) of the storm, a strong westerly flow existed at the southern side of the hook echo above the 2-km level. The westerly winds decelerated and a couplet of cyclonic and anticyclonic vortices was present at the western flank of the strong updraft region, which appeared to be similar in structure to the “stagnation zone” noted by Rasmussen et al. (2006) and Byko et al. (2009). Accumulated hydrometeors were present within both of the counter-rotating vortices. However, the anticyclonic vortex on the southern side contained fewer hydrometeors, particularly at low levels. With the exception of location (i.e., in a cyclonic rather than anticyclonic vortex), the evolution of the core of hydrometeors is similar to the type-I DRC formation discussed by Byko et al. (2009). DRC formation mechanisms and the relationship between DRC development and the RFD outflow surge still require clarification, for which further investigations are needed using high-resolution simulation results over much longer periods prior to tornadogenesis.

6. Summary and conclusions

Generation mechanisms of the 6 May 2012 Tsukuba City supercell tornado were investigated by using the results of high-resolution simulation with a 50-m-mesh nested grid. The simulation in this study was conducted under a realistic experimental design that included surface friction. The model successfully simulated a “classic” supercell tornado.

The locally intensified RFD outflow surge moved eastward behind the RFGF near the surface. As the RFD outflow surge approached a strong updraft along the RFGF, a weak vortex on the RFGF near its intersection with the FFGF intensified rapidly and evolved into a tornado. Backward-trajectory analysis also revealed that trajectory distributions changed drastically just before tornadogenesis. An intensifying vortex at the onset stage of tornadogenesis ingested about half of the parcels from the RFD outflow region, in contrast to the weak vortex at the preonset stage of tornadogenesis, which had mostly inflow trajectories; this result suggests that the RFD outflow surge was a triggering factor for tornadogenesis.

Vortex line configurations indicated that the weak vortex on the RFGF at the preonset stage of tornadogenesis arose from horizontal crosswise vorticity produced by surface friction in the RFD region. In contrast, the vortex lines on the northern side (left side) of the intensified RFD outflow, which were oriented in the streamwise direction on the horizontal plane, were ingested into the tornado just after genesis.

To quantify the vorticity sources responsible for tornadogenesis, the evolution of circulation and its production terms were investigated for material circuits surrounding the tornadic vortex at the preonset stage of tornadogenesis and the tornadic stage. This is the first study to utilize a circulation analysis to quantify the sources of circulation for a tornado by directly evaluating the frictional effect. Circulation is not identical to vorticity, but the vorticity sources of an entire tornado-scale vortex were able to be clarified by the circulation analysis. Although the analysis of the weak vortex at the preonset stage suffered from some calculation error, the frictional effect was found to be dominant and responsible for the increase in circulation. In contrast, the circuit encircling the tornado just after genesis acquired much of its circulation baroclinically around the tip of the hook echo in a short period, during which time the core of hydrometeors descended about 10 min prior to tornadogenesis. Although the frictional effect also had a net positive effect on the increase in circulation, it caused a small drop that lasted 3 min near the origin of the circuit surrounding the tornado, which implies that surface friction was likely to make a negative contribution to the vorticity source when the vortex intensified. The finding that the storm-generated baroclinic vorticity was a dominant source for a tornado differs from the results of previous numerical studies using realistic conditions (Mashiko et al. 2009; Schenkman et al. 2014). It is of great interest that the RFD outflow surge triggered tornadogenesis in all of these studies even though the vorticity sources of the tornadoes seemed to be completely different among these studies.

To clarify the cause of the baroclinity responsible for tornadogenesis around the tip of the hook echo, the buoyancy term in the vertical momentum equation was investigated. The cooling effect was found to be dominant in the formation of the negative buoyancy around the tip of the hook echo, whereas the effect of precipitation loading was minor. A sensitivity experiment confirmed that baroclinity associated with cooling due to evaporation of rain and melting of ice-phase hydrometeors was the primary vorticity source responsible for tornadogenesis.

This study focused on the vortices at 150-m height in the control and sensitivity experiments. It remains a challenge for future research to clarify the vorticity sources of the tornadic vortex at lower levels and how the inflow parcels achieve vertical vorticity near the surface by using a high-vertical-resolution model.

Acknowledgments

The author acknowledges helpful comments by Hiroshi Niino, Teruyuki Kato, and Hiroshi Yamauchi. The author thanks Yvette Richardson and two anonymous reviewers for their valuable and constructive comments that greatly improved the manuscript. The simulations were performed with the HITACHI SR16000 computer system at Meteorological Research Institute. This work was partly supported by JSPS KAKENHI Grants 23540518 and 15K05295.

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Footnotes

1

In Part I, storm motion was defined as the movement of the low-level mesocyclone at 1-km height. However, the movement of the tornadic vortex near the surface differed slightly from that of the low-level mesocyclone. In this paper (Part II), with its focus on tornadogenesis, the movement of the near-surface vertical vorticity maximum in the tornadic vortex (12.5 m s−1, 0.0 m s−1) was used to define the storm motion (except in the case of the storm-relative wind vectors shown in Fig. 18).

2

As noted in Part I, vortex lines were calculated above z* = 10 m (lowest level in the model); as a result, many vortex lines are likely to have their ends near the surface and appear to pierce the ground.

3

Schenkman et al. (2014) investigated supercell tornadogenesis in a simulation by a model with a 50-m grid spacing and found that frictionally generated crosswise vorticity near the surface was a dominant vorticity source of the tornado. They focused on pretornadic vortices and performed vorticity budget analyses along trajectories for several parcels with a vertical vorticity of about 0.1 s−1 (their Figs. 12, 13, 14, and 17), which is comparable to the magnitude of vertical vorticity in the vortex at the preonset stage of tornadogenesis in section 2b(1) of this paper. The results of Schenkman et al. (2014) might be applicable to a vortex at the preonset stage of tornadogenesis rather than to a fully developed tornado in the present paper.