Abstract

To identify important factors for supercell tornadogenesis, 33-member ensemble forecasts of the supercell tornado that struck the city of Tsukuba, Japan, on 6 May 2012 were conducted using a mesoscale numerical model with a 50-m horizontal grid. Based on the ensemble forecasts, the sources of the rotation of simulated tornadoes and the relationship between tornadogenesis and mesoscale environmental processes near the tornado were analyzed. Circulation analyses of near-surface, tornadolike vortices simulated in several ensemble members showed that the rotation of the tornadoes could be frictionally generated near the surface. However, the mechanisms responsible for generating circulation were only weakly related to the strength of the tornadoes. To identify the mesoscale processes required for tornadogenesis, mesoscale atmospheric conditions and their correlations with the strength of tornadoes were examined. The results showed that two near-tornado mesoscale factors were important for tornadogenesis: strong low-level mesocyclones (LMCs) at about 1 km above ground level and humid air near the surface. Strong LMCs and large water vapor near the surface strengthened the nonlinear dynamic vertical perturbation pressure gradient force and buoyancy, respectively. These upward forces made contributions essential for tornadogenesis via tilting and stretching of vorticity near the surface.

1. Introduction

Most strong tornadoes are generated in supercells (Browning 1964), a special type of convective storm with persistent mesocyclones, which are rotations having diameters of 2–10 km and vertical vorticities of O(10−2) s−1. Midlevel mesocyclones [MMCs, generally at 1–5 km above ground level (AGL)] are known to develop primarily in a preexisting environment with unstable stratification and strong veering wind shear (Weisman and Klemp 1982; Rotunno and Klemp 1982). In contrast, low-level mesocyclones (LMCs, generally below 0.5–1 km AGL) are known to be generated in association with a downdraft in a storm (Davies-Jones 1982; Rotunno and Klemp 1985; Wicker and Wilhelmson 1995; Adlerman et al. 1999). The horizontal buoyancy gradient associated with the outflow of the storm generates horizontal vorticity baroclinically; this vorticity can be tilted upward (even as air descends through a downdraft), and has been shown in prior simulations to be the main source of LMCs (Markowski et al. 2002, 2003, 2008; Straka et al. 2007). Because this horizontal vorticity and convective updraft are intensified by environmental low-level vertical shear and water vapor, respectively, the preexisting low-level environment is especially important for tornadogenesis (Thompson et al. 2003; Craven and Brooks 2004; Markowski and Richardson 2014; Parker and Dahl 2015).

Even in the presence of MMCs and LMCs, however, tornadoes are not necessarily generated. Trapp et al. (2005) have shown that only 15% of MMCs and 40% of LMCs detected with the Weather Surveillance Radar-1988 Doppler (WSR-88D) in the United States result in tornadogenesis. The source of the vorticity and circulation of tornadoes and the near-tornado mesoscale factors required for tornadogenesis have therefore been the subjects of extensive research.

Previous studies based on high-resolution numerical simulations of observed tornadoes have suggested that various mechanisms can be responsible for the rotation of tornadoes: Mashiko et al. (2009) first succeeded in reproducing an observed tornado with a numerical model. They used a numerical model with a 50-m horizontal grid interval to simulate the tornado of 17 September 2006, which struck the city of Nobeoka, Japan, and showed that the vorticity and circulation of the tornado originated from the streamwise vorticity associated with strong, low-level vertical wind shear in Typhoon Shanshan (Fig. 1a). In contrast, Schenkman et al. (2012, 2014) examined the sources of vertical vorticity of tornadoes in a quasi-linear convective system and in a typical supercell that struck Oklahoma City, Oklahoma, on 8–9 May 2007 and on 8 May 2003, respectively. They used numerical models with 100- and 50-m horizontal grid intervals, respectively, and showed that the tornadoes were mainly originated from frictionally generated crosswise vorticity (Fig. 1b). Mashiko (2016b) reproduced the typical supercell tornado that struck the city of Tsukuba, Japan, on 6 May 2012 by using a numerical model with a 50-m horizontal grid interval. He showed that frictionally generated circulation was the main source of the weak vortex before development of the tornado, but that baroclinically generated circulation was the main source of the rapidly developing tornado (Fig. 1c).

Fig. 1.

Schematic illustrations of three possible sources of tornado rotation: (a) preexisting environmental streamwise vorticity, (b) frictionally generated crosswise vorticity, and (c) baroclinically generated horizontal vorticity. Red and blue arrows denote directions of velocity and vorticity vectors, respectively.

Fig. 1.

Schematic illustrations of three possible sources of tornado rotation: (a) preexisting environmental streamwise vorticity, (b) frictionally generated crosswise vorticity, and (c) baroclinically generated horizontal vorticity. Red and blue arrows denote directions of velocity and vorticity vectors, respectively.

These studies seem to suggest that the vorticity and circulation of a tornado can be originated from various sources in a numerical experiment. This conclusion also seems to be the case for idealized numerical experiments. Although Roberts et al. (2016) have found that crosswise vorticity mainly generated by friction and streamwise vorticity mainly exchanged from crosswise vorticity can be sources of tornadoes, Markowski (2016) has shown that the main source of the circulation of near-surface mesocyclones in idealized simulations is variable and depends on the magnitudes of the winds and frictional forces.

If tornadogenesis occurs regardless of the source of the circulation, low-level convergence (vertical stretching) that increases vertical vorticity while conserving the circulation may be more important for tornadogenesis than the way the circulation is generated. Because such low-level convergence can be intensified by an LMC-induced vertical perturbation pressure gradient force (VPPGF), tornadoes are more likely to be generated when a strong LMC is located directly above a high-vorticity area near the surface (e.g., Wicker and Wilhelmson 1995; Noda and Niino 2005, 2010; Markowski and Richardson 2014).

Although there have been extensive studies of tornadogenesis, the conditions essential for tornadogenesis have not been satisfactorily identified. This may be partly because most previous studies of tornadogenesis have been based on observational case studies (e.g., Markowski 2002; Markowski et al. 2002, 2008), deterministic simulations of observed cases (e.g., Mashiko et al. 2009; Schenkman et al. 2012, 2014; Mashiko 2016a,b), sensitivity studies in idealized simulations (e.g., Roberts et al. 2016; Markowski 2016), and statistical studies using observations or reanalysis data (e.g., Craven and Brooks 2004; Trapp et al. 2005). Observations and reanalysis data have limited spatiotemporal resolutions, simulations of observed cases have uncertainties with respect to initial and boundary conditions, and idealized simulations may generate tornadoes through unconfirmed processes because of overly simplified configurations.

In view of various uncertainties involved in these studies, one of the efficient ways to identify the conditions important for actual tornadogenesis may be to perform ensemble experiments with reliable initial and boundary conditions that take into consideration possible observational errors. An ensemble Kalman filter (EnKF; Kalman 1960; Evensen 1994) is useful for generating initial and boundary conditions for such ensemble experiments. An EnKF can create multiple atmospheric fields within the range of analysis error via assimilation of dense observations around the tornadoes. Ensemble forecasts from EnKF analyses therefore enable ensemble-based analyses of tornadogenesis, statistical clarification of the relationship between tornadoes and the near-tornado environment, and examination of the conditions essential for tornadogenesis (e.g., ensemble-based sensitivity analyses; Ancell and Hakim 2007; Torn and Hakim 2008).

Seko et al. (2015) and Yokota et al. (2016, hereafter Y16) have conducted ensemble-based analyses of the tornadic supercell generated in Japan on 6 May 2012 based on ensemble experiments with an EnKF. Their results revealed that low-level water vapor and convergence near the storm were important factors for low-level mesocyclogenesis. However, they did not show which physical variables were essential for tornadogenesis because their models did not have enough resolution to reproduce tornadoes. Coffer et al. (2017) selected 30 environmental soundings for observed tornadic and nontornadic supercells, and made idealized ensemble experiments with 125-m horizontal grid intervals in which storms were initiated in a horizontally uniform basis field given by each environmental sounding. They found not only all soundings for tornadic supercells but also 40% of soundings for nontornadic supercells produced tornadoes, suggesting that tornadogenesis has some stochastic nature. They also showed that the tornadic supercells feature a strong VPPGF caused by the steady LMC. However, they did not examine a quantitative relationship between the strength of the tornado and the near-tornado environment. In this study, we conducted ensemble forecasts of tornadoes with 50-m horizontal grid intervals to clarify the conditions required for supercell tornadogenesis. For the first time we analyzed the sources of the circulation of simulated tornadoes and the correlation between tornadogenesis and the near-tornado mesoscale variables based on the ensemble forecasts of tornadoes in a realistic environment.

The remainder of the paper is structured as follows: the design of the ensemble experiments to clarify the mechanisms of tornadogenesis is described in section 2, and the results are presented in section 3. Section 4 examines the sources of circulation of simulated tornadoes, and section 5 examines correlations between tornadoes and near-tornado environmental conditions. In section 6, the conditions for tornadogenesis and the potential for tornado forecasts are discussed. Finally, section 7 presents conclusions and remarks.

2. Experimental design

The tornado simulated in this study was an F3 supercell tornado generated on the Kanto Plain, Japan, at about 1230 Japan standard time (JST; 0900 JST corresponds to 0000 UTC) on 6 May 2012 (Japan Meteorological Agency 2012). The synoptic-scale environment around the supercell was favorable for midlevel mesocyclogenesis: conditionally unstable stratification and a strong veering wind shear (cf. Seko et al. 2015; Mashiko 2016a). This tornado passed through the city of Tsukuba, Ibaraki prefecture (about 60 km northeast of Tokyo), and caused serious damage. In the present study, it is hereafter called the Tsukuba tornado. The near-surface vortex associated with the Tsukuba tornado was located at the southern tip of a mesoscale precipitation system moving northeastward over the Kanto Plain and was observed by the Meteorological Research Institute advanced C-band solid-state polarimetric radar (MACS-POL; Yamauchi et al. 2013).

In this study, we conducted 33-member ensemble forecasts of the Tsukuba tornado with a 50-m horizontal grid interval (hereafter referred to as 50m-EXPs) with the Japan Meteorological Agency (JMA) nonhydrostatic model (Saito et al. 2006)1 to identify the physical conditions that directly affect tornadogenesis. The vertical grid interval was varied from 10 m near the surface to 445 m near the top of the calculation domain. The number of vertical levels was 90, and the lowest level for scalar variables was at 5 m AGL. We adopted a 1.5-order turbulence closure scheme based on Deardorff (1980) and used no cumulus parameterization. In total, 33-member ensemble forecasts with a 350-m horizontal grid interval were conducted as a part of Y16 (hereafter referred to as the 350m-EXPs) and successfully forecasted the LMC associated with the Tsukuba tornado. Those same forecasts were used as the initial and boundary conditions for the 50m-EXPs. The initial and boundary conditions of the 350m-EXPs were made with the nested four-dimensional local ensemble transform Kalman filter (nested 4D-LETKF; Hunt et al. 2004, 2007; Seko et al. 2013) with horizontal grid intervals of 15 km (outer LETKF) and 1.875 km (inner LETKF). Conventional observations were assimilated with the outer LETKF every 6 hours, and dense surface and C-band Doppler radar (including MACS-POL) data observed in the Kanto Plain were assimilated with the inner LETKF every hour. Figure 2a outlines the calculation procedures, Fig. 2b shows the computational domains of the experiments, and Table 1 summarizes the settings.

Fig. 2.

(a) Outline of the calculation procedure and (b) the calculation domains of the nested 4D-LETKF system. Shading is altitude in each model (m).

Fig. 2.

(a) Outline of the calculation procedure and (b) the calculation domains of the nested 4D-LETKF system. Shading is altitude in each model (m).

Table 1.

Setting of the nested 4D-LETKF.

Setting of the nested 4D-LETKF.
Setting of the nested 4D-LETKF.

3. Tornadoes generated in the ensemble forecasts

a. Tornado characteristics

The 50m-EXPs produced a wide range of tornadic vortices: the highest vertical vorticity at 30 m AGL, , exceeded 2.0 s−1 in one member but did not exceed 1.0 s−1 in some other members (Fig. 3). In total, 7 of the 33 members spawned tornadoes, where a tornado was defined as a vortex that had a 5-min moving average of around the time of (hereafter denoted by ) that exceeded 1.0 s−1. These values were 2.35, 1.53, 1.19, 1.16, 1.07, 1.05, and 1.03 s−1 for the members with the seven largest values, hereafter designated as members 01–07, respectively. The smallest value among the 33 members is 0.37 s−1 (designated as member 33).

Fig. 3.

Time series of (s−1) within the region bounded by 35.75°–36.45°N, 139.3°–140.1°E in 50m-EXPs output at 1-min intervals for the seven tornadic (thick color lines) and 26 nontornadic (thick gray line and thin black lines) members; additionally, at 1-s intervals during the 20-min surrounding peak for the eight members 01–07 (thin color lines) and 33 (thin gray lines). Blue, red, green, purple, orange, sky blue, and pink lines are ensemble members 01–07, respectively.

Fig. 3.

Time series of (s−1) within the region bounded by 35.75°–36.45°N, 139.3°–140.1°E in 50m-EXPs output at 1-min intervals for the seven tornadic (thick color lines) and 26 nontornadic (thick gray line and thin black lines) members; additionally, at 1-s intervals during the 20-min surrounding peak for the eight members 01–07 (thin color lines) and 33 (thin gray lines). Blue, red, green, purple, orange, sky blue, and pink lines are ensemble members 01–07, respectively.

For member 01, was <0.5 s−1 until 1127 JST, but it rapidly increased and exceeded 2.0 s−1 by 1129 JST (Fig. 3). For the other members that spawned tornadoes, rapidly increased (by as much as 0.5 s−1 in a few minutes) after 1130 JST and exceeded 1.0 s−1 as late as 1150 JST. The time of occurrence of varied greatly among these members (1132–1149 JST). It was earlier than that of the actual tornadogenesis because the low-level mesocyclogenesis simulated in 350m-EXPs occurred also earlier (Y16). However, the duration of in member 01 (17 min for 1128–1145 JST), which was longest among the 33 members, was fairly consistent with the duration of the Tsukuba tornado (16 min for 1235–1251 JST) estimated by the MACS-POL observations (Yamauchi et al. 2013). The locations of in the 33 members (35.84°–36.26°N, 139.44°–140.03°E) were also fairly consistent with the path of the Tsukuba tornado (36.11°–36.18°N, 139.94°–140.09°E; Yamauchi et al. 2013).

The predicted tornado in member 01 was located in a zone with a steep gradient of near-surface temperature (Fig. 4). The vortex near the surface was stronger and smaller than that at about 1 km AGL. The diameter of the high-vorticity region [>1.0 s−1 at 30 m AGL (Fig. 5a)] was less than 500 m.

Fig. 4.

Three-dimensional structure of the predicted tornadic vortex at 1132 JST in member 01. Red isosurfaces show vertical vorticities of 0.2 s−1 (translucent) and 0.6 s−1 (opaque). White isosurfaces are 1 g kg−1 cloud water mixing ratio. Color shading shows temperature (K) at 1.5 m AGL. Arrows are horizontal winds (m s−1) at 30 m AGL, where black and white arrows show <30 and >30 m s−1, respectively.

Fig. 4.

Three-dimensional structure of the predicted tornadic vortex at 1132 JST in member 01. Red isosurfaces show vertical vorticities of 0.2 s−1 (translucent) and 0.6 s−1 (opaque). White isosurfaces are 1 g kg−1 cloud water mixing ratio. Color shading shows temperature (K) at 1.5 m AGL. Arrows are horizontal winds (m s−1) at 30 m AGL, where black and white arrows show <30 and >30 m s−1, respectively.

Fig. 5.

Horizontal winds (arrows, m s−1), potential temperature (color shading, K), pressure (thin white contours, every 5 hPa), and vertical vorticity (black contours, every 0.5 s−1) at 30 m AGL at the time of . The results of members (a) 01, (b) 02, (c) 03, (d) 04, (e) 05, (f) 06, (g) 07, and (h) 33 are shown. The centers of the panels are the points corresponding to . The thick white circle in (h) is the circuit around which the circulation was analyzed in Fig. 8h.

Fig. 5.

Horizontal winds (arrows, m s−1), potential temperature (color shading, K), pressure (thin white contours, every 5 hPa), and vertical vorticity (black contours, every 0.5 s−1) at 30 m AGL at the time of . The results of members (a) 01, (b) 02, (c) 03, (d) 04, (e) 05, (f) 06, (g) 07, and (h) 33 are shown. The centers of the panels are the points corresponding to . The thick white circle in (h) is the circuit around which the circulation was analyzed in Fig. 8h.

b. Near-tornado environment

In member 01, the time of was earlier and the potential temperature around the tornado at that time was higher than those in members 02–07, but those in member 02 were not earlier and higher than those in members 03–07 (Figs. 5a–g). In member 33, no strong vortices were generated at 30 m AGL and the gradient of the potential temperature was not steep even at the time of (Fig. 5h).

At , the time when exceeded 0.6 s−1 and was continuing to increase (Fig. 6a),2 the vortex at 30 m AGL in member 01 was in the weak gradient zone of high potential temperature. However, a similar development of a tornado vortex was not apparent in members 02–07, in which the vortices at 30 m AGL at were close to the steep gradient zone of relatively low potential temperature (Figs. 6b–g).

Fig. 6.

Horizontal winds (arrows, m s−1), potential temperature (color shading, K), pressure (thin white contours, every 2 hPa), and vertical vorticity (black contours, every 0.2 s−1) at 30 m AGL at . The results of members (a) 01, (b) 02, (c) 03, (d) 04, (e) 05, (f) 06, and (g) 07 are shown. The centers of the panels are the points corresponding to . The thick white circles are the circuits around which the circulations were analyzed in Figs. 8a–g.

Fig. 6.

Horizontal winds (arrows, m s−1), potential temperature (color shading, K), pressure (thin white contours, every 2 hPa), and vertical vorticity (black contours, every 0.2 s−1) at 30 m AGL at . The results of members (a) 01, (b) 02, (c) 03, (d) 04, (e) 05, (f) 06, and (g) 07 are shown. The centers of the panels are the points corresponding to . The thick white circles are the circuits around which the circulations were analyzed in Figs. 8a–g.

In contrast, the vertical pressure difference between heights of 30 m AGL and 1 km AGL became larger near the point of maximum vertical vorticity at 1 km AGL at , especially in members with larger (Figs. 7a–g). Although in all seven members 01–07 at the times corresponding to Figs. 7a–g, the vertical pressure difference was very different among the members: it was larger in member 01 than in members 02–07 (Fig. 7a), was small near the point of maximum vertical vorticity at 1 km AGL in member 05 (Fig. 7e) and member 07 (Fig. 7g), and was small near the point of in member 06 (Fig. 7f). Therefore, the distribution and magnitude of the vertical pressure gradient are likely to be important determinants of tornado intensification, as they affect the VPPGF below 1 km AGL (Markowski et al. 2012; Markowski and Richardson 2014; Coffer and Parker 2017).

Fig. 7.

Horizontal winds (arrows, m s−1), potential temperature (color shading, K), vertical vorticity (black contours, every 0.2 s−1) at 1 km AGL, and vertical pressure difference between heights of 30 m AGL and 1 km AGL (thin white contours, every 2 hPa) at . The results of members (a) 01, (b) 02, (c) 03, (d) 04, (e) 05, (f) 06, and (g) 07 are shown. The centers of the panels are the points corresponding to .

Fig. 7.

Horizontal winds (arrows, m s−1), potential temperature (color shading, K), vertical vorticity (black contours, every 0.2 s−1) at 1 km AGL, and vertical pressure difference between heights of 30 m AGL and 1 km AGL (thin white contours, every 2 hPa) at . The results of members (a) 01, (b) 02, (c) 03, (d) 04, (e) 05, (f) 06, and (g) 07 are shown. The centers of the panels are the points corresponding to .

4. Circulation analysis to clarify the source of the rotation of tornadoes

One of the useful methods to clarify the source of the rotation of tornadoes is to analyze of budgets of streamwise, crosswise, and vertical vorticity for the backward trajectories of parcels placed near tornadoes (cf. Lilly 1982; Adlerman et al. 1999; Mashiko et al. 2009; Schenkman et al. 2014; Roberts et al. 2016). We found that the vorticity of the tornadoes mainly originated from frictionally generated crosswise vorticity in the vorticity budget analysis for one parcel of each member of 01 and 02 (see the  appendix). However, each tornado consists of a large number of parcels that are located in various parts of the vortex and can have different vorticity budgets. Furthermore, the results of the vorticity budget are complicated by the fact that three components of vorticity change through various generation terms. To clarify important factors for tornadogenesis more reliably, therefore, we conducted circulation analyses. Circulation is the curvilinear integral of velocity along a closed circuit and is defined as

 
formula

Its time rate of change is given by

 
formula

which shows that circulation changes are due only to baroclinic and frictional effects, where is density and is the frictional force resulting from subgrid turbulence calculated by 1.5-order turbulence closure scheme (Deardorff 1980) and empirical closure function of land surface momentum flux (Beljaars and Holtslag 1991). We calculated and the baroclinic and frictional terms on the right-hand side (rhs) of Eq. (2) along the circuits backtracked from the 100-m-radius circle around the point corresponding to at in members 01–07 (thick white circles in Figs. 6a–g) and at the time of in member 33 (thick white circle in Fig. 5h). Backward trajectories of the circuits were calculated using velocity data saved every 1.0 s and a fourth-order Runge–Kutta scheme with a time step of 0.5 s.3 Initially, 500 parcels were used to calculate the circulations for each circuit, but additional parcels were introduced at each midpoint of adjacent parcels on the circuit when separations between adjacent parcels exceeded 50 m (cf. Mashiko 2016a,b; Markowski 2016). The variables , , and of the parcels below the lowest model height of 5 m AGL were linearly extrapolated from above assuming the same vertical gradient between 5 and 15 m AGL.4

Figures 8a–h show time series of and the baroclinic and frictional terms during the 8 min before for members 01–07 and the time of for member 33. In all eight members, time series of (black lines in Figs. 8a–h) were fairly consistent with the sum of time-integrated baroclinic and frictional terms (red lines in Figs. 8a–h), and the change of the circulation caused by the frictional term (green lines in Figs. 8a–h) was generally much larger than that caused by the baroclinic term (blue lines in Figs. 8a–h).

Fig. 8.

Time series of the circulation (black), baroclinic (blue), and friction (green) terms calculated along the circuits backtracked from the thick white circles shown in Figs. 6a–g and,5h. The results of members (a) 01, (b) 02, (c) 03, (d) 04, (e) 05, (f) 06, (g) 07, and (h) 33 are shown. Red lines are the sum of time-integrated baroclinic and friction terms (integrated circulation).

Fig. 8.

Time series of the circulation (black), baroclinic (blue), and friction (green) terms calculated along the circuits backtracked from the thick white circles shown in Figs. 6a–g and,5h. The results of members (a) 01, (b) 02, (c) 03, (d) 04, (e) 05, (f) 06, (g) 07, and (h) 33 are shown. Red lines are the sum of time-integrated baroclinic and friction terms (integrated circulation).

Figure 9 shows a three-dimensional view of the magnitude of the frictional term per unit length on the circuit at in member 01 (white circle in Fig. 6a). On this circuit, the largest values of the frictional term occurred on portions of the circuits near the surface (Fig. 9). Thus, parts of the circuit needed to pass near the surface to have frictionally generated circulation, which is consistent with the finding of Roberts and Xue (2017).

Fig. 9.

The friction term per unit length (color, m s−2) on the circuit in member 01 shown in Fig. 6a and on the circuit backtracked for 1 min from that time.

Fig. 9.

The friction term per unit length (color, m s−2) on the circuit in member 01 shown in Fig. 6a and on the circuit backtracked for 1 min from that time.

However, the members in which friction contributed the most to the increase of were not necessarily the members with relatively large . In fact, time-integrated baroclinic and frictional terms seemed to be hardly correlated with (Fig. 10). For example, the frictional term in member 02 was negative at (Fig. 8b), and in member 05, the frictional term clearly decreased from (Fig. 8e). Even in member 33, the magnitude and time fluctuations of the baroclinic and frictional terms were similar to those in members 01, 03, and 05 (Fig. 8h).

Fig. 10.

The 480-s time-integrated baroclinic (blue) and friction (green) terms (m2 s−1) shown in Figs. 8a–h. Vertical axis is (s−1).

Fig. 10.

The 480-s time-integrated baroclinic (blue) and friction (green) terms (m2 s−1) shown in Figs. 8a–h. Vertical axis is (s−1).

Furthermore, the results of the circulation analyses were sensitive to the locations and times the target circuits were selected. For example, we found that the baroclinic term was as large as the frictional term on the circuit backtracked from the 250-m-radius circle at 140 m AGL around the point corresponding to at in member 05 (Figs. 11a,b). The baroclinic term was especially large along the part of the circuit that extended vertically (Fig. 11c). This result demonstrates that the circuit needed to be advected vertically for circulation to be generated via baroclinity. Note that baroclinic terms of circuits backtracked from the circle above 30 m AGL at were not necessarily larger than those at 30 m AGL at (not shown). Because the main generation term depended on the locations and times of the analyzed circuits, however, friction was not always the principal contributor to the circulation of supercell tornadoes.

Fig. 11.

(a) As in Fig. 6e, but at 140 m AGL at in member 05. (b) As in Fig. 8e, but along the circuit backtracked from the thick white circle of (a). (c) The baroclinic term per unit length (color, m s−2) on the circuit shown in (a) and on the circuit backtracked for two minutes from that time.

Fig. 11.

(a) As in Fig. 6e, but at 140 m AGL at in member 05. (b) As in Fig. 8e, but along the circuit backtracked from the thick white circle of (a). (c) The baroclinic term per unit length (color, m s−2) on the circuit shown in (a) and on the circuit backtracked for two minutes from that time.

5. Correlation between the strength of tornadoes and physical characteristics of the near-tornado environment

As shown in section 4, the source of circulation does not seem to be closely related to whether the vortices near the surface develop into tornadoes or even the intensity of tornadoes that do develop. However, stretching of vorticity that causes the circuit to shrink is likely to be important for tornadogenesis.

To identify the mesoscale factors associated with stretching of vorticity that are essential for tornadogenesis, we calculated the Pearson correlation coefficients (r values) between (5-min moving average of centered at , the time corresponding to ) and several physical variables in the composite fields across the full 33-member ensemble of 50m-EXPs. The composite fields were constructed with respect to the point and time () corresponding to by using the output data of the 33 members at 1-min intervals. In the t test for 33 samples, |r| > 0.344 is significant correlation (confidence level >95%). To examine the relationship between tornadogenesis and near-tornado mesoscale characteristics without convective-scale variations, variables in this composite field were horizontally smoothed over 350 m × 350 m (7 × 7 grids) in the present analysis. These smoothed fields were then analyzed over a 30 km (along the east–west direction) × 30 km (along the north–south direction) square region surrounding the LMC.5

In this section, we focus on r between and the maximum vertical vorticity . The value of corresponds to the strength of the mesocyclone, which causes VPPGF (Markowski et al. 2012; Markowski and Richardson 2014; Coffer and Parker 2017). Additionally, we also focus on r between and near-tornado environmental variables associated with buoyancy: water vapor mixing ratio and potential temperature . In the present analysis, and were quantified in terms of their horizontal averages over a 30 km × 30 km square region.

Figure 12a shows that, as approached, there was an increase of the ensemble mean of , especially below 1 km AGL. On the other hand, the ensemble mean of both and decreased. These decreases were especially apparent in the lower layer (height < 1 km AGL) as convective instability was eliminated in this region (Figs. 12b–c).

Fig. 12.

Distribution of the ensemble mean of (a) (contours, s−1), (b) (contours, g kg−1), and (c) (contours, K). Color shows their correlations with (s−1). The red contour shows confidence level >95% (r > 0.344.).

Fig. 12.

Distribution of the ensemble mean of (a) (contours, s−1), (b) (contours, g kg−1), and (c) (contours, K). Color shows their correlations with (s−1). The red contour shows confidence level >95% (r > 0.344.).

The r between and below 4 km AGL was positive, and the r at about 1 km AGL just before was especially large (Fig. 12a). At , the r between and was much larger at 1 km AGL (r = 0.71; Fig. 13a) than at 5 km AGL (r = 0.25; Fig. 13b). These results show that the strength of the LMC at 1 km AGL was more related to near-surface vertical vorticity, and thus potentially a better predictor of tornadogenesis, than the strength of the MMC. The r between and the maximum updraft was also higher at 1 km AGL (r = 0.68; Fig. 13c) than at 5 km (r = 0.46; Fig. 13d), and the r between and the maximum vertical pressure difference between heights of 30 m AGL and 1 km AGL was also significant (r = 0.52; Fig. 13e). Moreover, in all members that spawned tornadic vortices (), the horizontal position of at 1 km AGL was particularly close to the center of the near-surface vortex at (horizontal distance ; Fig. 13f).

Fig. 13.

Scatterplots of (s−1) and variables at : (a),(b) at 1 km AGL and 5 km AGL, respectively (s−1); (c),(d) at 1 km AGL and 5 km AGL, respectively (m s−1); (e) between heights of 30 m AGL and 1 km AGL (hPa); (f) horizontal distance between the points of at heights of 30 m AGL and 1 km AGL (km); (g) averaged below 100 m AGL (g kg−1); and (h) averaged below 100 m AGL (K). The numbers at the top right are correlation coefficients. Red numerical characters and lines show necessary conditions for tornadogenesis (, seven members as shown by red solid circles).

Fig. 13.

Scatterplots of (s−1) and variables at : (a),(b) at 1 km AGL and 5 km AGL, respectively (s−1); (c),(d) at 1 km AGL and 5 km AGL, respectively (m s−1); (e) between heights of 30 m AGL and 1 km AGL (hPa); (f) horizontal distance between the points of at heights of 30 m AGL and 1 km AGL (km); (g) averaged below 100 m AGL (g kg−1); and (h) averaged below 100 m AGL (K). The numbers at the top right are correlation coefficients. Red numerical characters and lines show necessary conditions for tornadogenesis (, seven members as shown by red solid circles).

The r between and below 1 km AGL was greater than 0.4, and it was especially large below 100 m AGL just before (Fig. 12b). At , the average r between and below 100 m AGL was 0.49 (Fig. 13g). The r between and was negative below 1 km AGL, but it was not significant at any height below 4 km AGL: confidence level <95% (Figs. 12c and 13h).

6. Discussion

a. Dynamics of tornadogenesis

The values of and at 1 km AGL and of between heights of 30 m AGL and 1 km AGL are dynamic factors that are important for tornadogenesis (cf. Wicker and Wilhelmson 1995; Noda and Niino 2005, 2010; Markowski and Richardson 2010, 2014). By taking the divergence of the governing equations of motion in the Boussinesq approximation, the following diagnostic equation for the perturbation pressure can be derived (Rotunno and Klemp 1982):

 
formula

where and are the reference density and buoyancy, respectively; and the velocity field comprises horizontally averaged fields and deviations therefrom . Because we were interested in phenomena with a small horizontal scale, the Coriolis force was neglected. If the vertical vorticity of the LMCs (n.b., ) is strong, vertical shear , fluid extension , deformation , and the vertical gradient of buoyancy may also be neglected and Eq. (3) may be approximated by

 
formula

where is assumed to be proportional to (Klemp and Rotunno 1983). Equation (4) means that pressure drops at the centers of strong LMCs, and upward acceleration is generated owing to the nonlinear dynamic VPPGF below the LMCs. This upward acceleration strengthens the low-level updraft and convergence near the surface, and this strengthening in turn stretches vertical vorticity near the surface and contributes to tornadogenesis.

Figures 14a–c show vertical velocity, VPPGF , and buoyancy at the point of maximum vertical velocity vertically averaged below 1 km AGL in the 50m-EXPs. Both VPPGF and buoyancy contributed to intensify vertical velocity below 1 km AGL (Fig. 14a), and VPPGF was stronger than buoyancy there (Figs. 14b and 14c). Although all correlations between and vertical velocity, VPPGF, and buoyancy were generally positive, and often strongly positive (Figs. 14a–c), the correlation with VPPGF was significant only after the LMC intensified (; Fig. 14b).

Fig. 14.

As in Fig. 12, but for (a) vertical velocity (m s−1), (b) VPPGF (m s−2), and (c) buoyancy (m s−2) at the point corresponding to the maximum vertical velocity averaged below 1 km AGL. Pressure and density averaged in a 30 km × 30 km square region were used as the base state in (b) and (c). The thick black contour is the ensemble mean of LCL of the parcel at 30 m AGL and the dotted contour is the minimum LCL among 33 members. Red and blue contours show confidence level >95% (|r| > 0.344).

Fig. 14.

As in Fig. 12, but for (a) vertical velocity (m s−1), (b) VPPGF (m s−2), and (c) buoyancy (m s−2) at the point corresponding to the maximum vertical velocity averaged below 1 km AGL. Pressure and density averaged in a 30 km × 30 km square region were used as the base state in (b) and (c). The thick black contour is the ensemble mean of LCL of the parcel at 30 m AGL and the dotted contour is the minimum LCL among 33 members. Red and blue contours show confidence level >95% (|r| > 0.344).

This VPPGF was due to mainly the nonlinear dynamic perturbation pressure (Figs. 15a–c) because was negative at 1 km AGL and positive near the surface, and the absolute value of was much larger than those of and . The height of the boundary between negative and positive lowered (Fig. 15b), resulting in lowering of the height of maximum VPPGF (Fig. 14b). Similar to the correlation between and VPPGF, the correlation between and was also significant (confidence level >95%) only after (Fig. 15b).

Fig. 15.

As in Fig. 12, but for (a) (10−3 s−2), (b) (10−3 s−2), and (c) (10−3 s−2) at the point corresponding to the maximum vertical velocity averaged below 1 km AGL. Red and blue contours show confidence level >95% (|r| > 0.344).

Fig. 15.

As in Fig. 12, but for (a) (10−3 s−2), (b) (10−3 s−2), and (c) (10−3 s−2) at the point corresponding to the maximum vertical velocity averaged below 1 km AGL. Red and blue contours show confidence level >95% (|r| > 0.344).

The below 100 m AGL was another important factor for tornadogenesis. It is also related to upward acceleration: a more humid parcel near the surface has larger buoyancy because of its (i) larger potential temperature due to reduced evaporative cooling and (ii) larger virtual potential temperature due to the smaller mass density of water vapor than dry air. It also has (iii) the stronger potential instability due to lower lifted condensation level (LCL). In addition, buoyancy VPPGF is positive near the LCL because the buoyancy perturbation pressure derived via Eq. (3) is negative above the LCL and positive below the LCL in the conditional instability.6 Therefore, a lower LCL also (iv) enhances buoyancy VPPGF in the lower layer. All four of these factors (i.e., i–iv) may contribute to generating upward acceleration.

We now examine the four factors in more detail. In the 50m-EXPs, the r between and buoyancy was always large (Fig. 14c). However, factor (i), reduced evaporative cooling, is thought to have hardly affected tornadogenesis because the r between and was small and negative below 1 km AGL (Fig. 12c). Factor (ii), the smaller mass density of water vapor, was not essential either, because the r between and the near-tornado environmental virtual potential temperature was also small and negative below 1 km AGL (not shown).

In contrast, factor (iii), increase of the potential instability (buoyancy above the LCL) because of lowering of the LCL, seems to be important because the r between and buoyancy was strongly positive above the LCL (Fig. 14c). Factor (iv), increase of buoyancy VPPGF in the lower layer, also seems to be important because the negative r between and was significant (confidence level >95%) above the LCL (Fig. 15c). Because the buoyancy above the LCL was smaller than the VPPGF (Figs. 14b–c) and the absolute value of above the LCL was much smaller than that of (Figs. 15b and 15c), buoyancy and the buoyancy VPPGF are unlikely to have been the main causes of tornadogenesis, although they may have facilitated it.

This analysis suggests that (i) the large nonlinear dynamic VPPGF (Figs. 14b and 15b) associated with the strong LMC at about 1 km AGL (Fig. 12a) and (ii) the large buoyancy (Fig. 14c) and buoyancy VPPGF (Figs. 14b and 15c) associated with humid parcels near the surface (Fig. 12b) were especially important for tornadogenesis. Particularly, (i) is consistent with the finding of Markowski and Richardson (2014) and Coffer et al. (2017). Note that these factors were not directly related to the source of rotation near the surface.

b. Conditions for tornadogenesis

In this subsection, we discuss the characteristics of observable or forecastable mesoscale variables that are necessary and sufficient for tornadogenesis () based on the results of the 50m-EXPs. In particular, we focus on the dynamic conditions associated with LMCs (strong vertical vorticity and updrafts, and low pressure) at about 1 km AGL because the correlation analysis in section 5 showed that tornadoes were likely to be generated directly below relatively strong LMCs at about 1 km AGL (Figs. 13a–f) because of the nonlinear dynamic VPPGF (Fig. 15b).

At , the dynamic conditions necessary for tornadogenesis for the 7 members were more than 0.077 s−1 for at 1 km AGL (Fig. 13a), more than 14.6 m s−1 for at 1 km AGL (Fig. 13c), and more than 113.5 hPa for between heights of 30 m AGL and 1 km AGL (Fig. 13e). In total, 17 members satisfied the necessary condition of at 1 km AGL, while 7 of those 17 members spawned tornadoes (Fig. 13a). Therefore, the success ratio (SR)7 of tornadoes with the criterion of at 1 km AGL was 7/17 = 41%. This SR is larger than the SR with the criterion of at 1 km AGL (7/26 = 27%; Fig. 13c) and the SR with the criterion of between heights of 30 m AGL and 1 km AGL (7/29 = 24%; Fig. 13e).

As a surrogate for thunderstorms containing mesocyclones, updraft helicity (UH; Kain et al. 2008) has often been used. UH is defined as the vertical integral of the product of vertical velocity and vertical vorticity, and a UH in the lower layer related to LMCs is expected to be associated with a high SR of tornadoes. However, the SR associated with the maximum UH at 0–1 km AGL (7/18 = 39%, not shown) was not larger than the SR of 41% associated with the criterion of at 1 km AGL.

The foregoing discussion indicates that it would be difficult to identify appropriate criteria for tornadogenesis using only dynamic conditions such as . Thermodynamic variables, which are not directly related to the strength of LMCs, therefore, need to be included among the necessary conditions for tornadogenesis. However, the correlation between and near-surface at was too weak to forecast tornadogenesis (Fig. 13h). This poor linear correlation probably reflects the fact that a too-weak cold pool (too high ) is not suitable for LMCs that generate baroclinically, whereas a too-strong cold pool (too low ) is not suitable for intensifying LMCs via updrafts (Markowski and Richardson 2014).

The was a more appropriate thermodynamic variable than for predicting tornadogenesis (Fig. 13g). Requirements for tornadogenesis () were values of averaged below 100 m AGL that exceeded 10.6 g kg−1 (Fig. 13g). Although the SR with only (7/18 = 39%; Fig. 13g) was no greater than the SR with the criterion of at 1 km AGL, the SR with both and was 58% (7/12; Fig. 16). This higher SR indicates that the mechanism by which higher near-surface water vapor favors tornadogenesis are not limited strictly to enhancing the LMC; in principle, if this were the case, the SR using both criteria ( and ) would be equal to the SR using only one of the criteria alone. Therefore, higher near-surface water vapor seems to be favorable for tornadogenesis due not only to strengthening of LMCs but also to strengthening of tornadoes directly through strengthening of near-surface buoyancy and buoyancy VPPGF.

Fig. 16.

Scatterplot of at 1 km AGL (s−1) and averaged below 100 m AGL (g kg−1) at in 33 ensemble members. The number written at the top-right corner is the correlation coefficient. Gray, black, red, and large red solid circles show that was <0.7, 0.7–1.0, 1.0–2.35, and 2.35 s−1, respectively. Red numerical characters and lines show conditions required for tornadogenesis ().

Fig. 16.

Scatterplot of at 1 km AGL (s−1) and averaged below 100 m AGL (g kg−1) at in 33 ensemble members. The number written at the top-right corner is the correlation coefficient. Gray, black, red, and large red solid circles show that was <0.7, 0.7–1.0, 1.0–2.35, and 2.35 s−1, respectively. Red numerical characters and lines show conditions required for tornadogenesis ().

The values of at 1 km AGL and averaged below 100 m AGL therefore provide useful dynamic and thermodynamic necessary conditions, respectively, for tornadogenesis. Moreover, tornadoes were spawned in all members that satisfied both at 1 km AGL and averaged below 100 m AGL. Four of the seven members that spawned tornadoes satisfied this sufficient condition (Fig. 16).

c. Possibilities for improving tornado forecasts

The values of at about 1 km AGL and near the surface, which were found to be useful variables for detecting the potential for tornadogenesis, were not directly related to the source of the rotation of tornadoes: baroclinity associated with downdrafts and friction near the surface. In fact, the vorticity and circulation analyses in the 50m-EXPs showed that the terms that generated the vorticity and circulation of the tornadoes depended very much on the ensemble member, the time, and the position of the analyzed parcels. Furthermore, the relationship between the generation terms and was unclear (Fig. 10).

Therefore, forecasting the strength of LMCs at about 1 km AGL and the amount of water vapor near the surface appears to be a more efficacious way to improve tornado forecasts than forecasting baroclinity and friction, which depend on small-scale processes. This conclusion implies that high-resolution numerical forecasts that resolve tornadoes may not be indispensable for improving tornado forecasts. In fact, in the 50m-EXPs was strongly correlated not only to the strength of LMC values in the 50m-EXPs (Figs. 12a and 13a) but also to the vertical vorticity of LMCs in the 350m-EXPs (not shown). This result shows that the strengths of LMCs predicted with 350m-EXPs, which do not resolve tornadoes, also have good potential for tornado forecasting.

Y16 has shown that forecasts of the strengths of LMCs at about 1 km AGL are sensitive to the low-level convergence of horizontal winds on the forward side of the storm and to low-level water vapor on the rear side of the storm. Improved estimates of local low-level winds and water vapor through assimilation of dense surface observations will therefore be an important step toward enabling more accurate tornado predictions through improvements of LMC forecasts.

7. Conclusions and remarks

a. Conclusions

Ensemble-based analyses were used to identify mechanisms responsible for supercell tornadogenesis. The case studied was the Tsukuba tornado of 6 May 2012. A total of 33-member ensemble forecasts were made with a horizontal grid interval of 50 m (50m-EXPs). Seven members of the 50m-EXPs spawned tornadoes near the path of the Tsukuba tornado. A tornado was defined as a vortex with a 5-min averaged vertical vorticity exceeding 1.0 s−1.

Circulation analyses of seven members of the 50m-EXPs showed that the circulation of the tornado was changed mainly by the friction term near the surface (Fig. 8). However, the friction term did not always increase the circulation, and depending on the locations and times that the circuits were analyzed, the baroclinic term was sometimes as large as the friction term (Fig. 11).

In the ensemble-based correlation analysis, tornadogenesis was especially well correlated with the strength of LMCs at about 1 km AGL and water vapor near the surface several minutes before (Fig. 12). These dynamic and thermodynamic factors were related mainly to upward accelerations caused by the VPPGF and buoyancy. Strong LMCs at about 1 km AGL intensified the nonlinear dynamic VPPGF below 1 km (Fig. 17a), and large near-surface water vapor intensified both the buoyancy above the LCL and the VPPGF because of the vertical buoyancy gradient near the LCL (Fig. 17b). Both of these upward accelerations made important contributions to tornadogenesis via tilting and stretching of vorticity near the surface (Fig. 17c). Therefore, strong LMCs at about 1 km AGL and near-surface humid air are both essential factors for tornadogenesis in a three-dimensional environment in the realistic atmosphere, where the importance of the former is consistent with the finding of Markowski and Richardson (2014) and Coffer et al. (2017). The implication is that low-level convergence and water vapor, which contribute to intensifying LMCs (Y16), are also important for tornadogenesis.

Fig. 17.

Schematic illustrations of upward accelerations required for tornadogenesis: (a) nonlinear dynamic VPPGF, (b) buoyancy and buoyancy VPPGF, and (c) the tornado caused by these upward accelerations.

Fig. 17.

Schematic illustrations of upward accelerations required for tornadogenesis: (a) nonlinear dynamic VPPGF, (b) buoyancy and buoyancy VPPGF, and (c) the tornado caused by these upward accelerations.

These dynamic and thermodynamic factors, however, are not directly related to the processes that increase the circulation of tornadoes: baroclinity and friction. Circulation analyses showed that the strength of tornadoes was not clearly related to the way vorticity and circulation were generated (Figs. 8 and 10). This result suggests that the source of near-surface rotation is not a strong predictor of tornadogenesis. High-resolution forecasts that reveal the source of the rotation of tornadoes may therefore not be necessary for improving tornado forecasts if the strength of LMCs is accurately predicted.

b. Final remarks

To our knowledge, this is the first study to have used reliable, high-resolution ensemble forecasts to examine the relationship between a predicted tornado and mesoscale processes in the realistic atmosphere. This study confirmed that the processes suggested by previous studies, including low-level mesocyclogenesis, are important for tornadogenesis (e.g., Markowski and Richardson 2014). For the first time, moreover, the ensemble forecasts revealed that correlation between tornadogenesis and the sources of near-surface rotation is weak. Because the present study is based on a single case study, however, it is desirable to perform similar studies for cases of different tornadoes.

Because of the limited computational resources available in the present study, ensemble-based analyses to identify relationships between tornadogenesis and mesoscale processes were conducted with only 33 members. In these analyses, only linear relationships between variables near the tornadoes were identified. Although the present analyses showed that mesoscale vertical vorticity at about 1 km AGL and water vapor near the surface were potentially useful tools for predicting tornadogenesis, a tornado cannot be reliably predicted more than several minutes prior to its genesis, even if these two variables are used. Therefore, nonlinear relationships between tornadogenesis and mesoscale variables such as potential temperature (Fig. 13h) should also be taken into consideration. Such an analysis might be carried out, for example, by least squares fitting of quadratic functions using a large number of high-resolution ensemble forecasts that can resolve tornadoes although it has not been reported yet.

Acknowledgments

The authors thank Dr. Wataru Mashiko for important advice about tornado dynamics and how to perform vorticity and circulation analyses, and anonymous reviewers for thoughtful comments on the original manuscript. This work was supported in part by the research projects “HPCI Strategic Program for Innovative Research (SPIRE) Field 3,” “social and scientific priority issues (Theme 4) to be tackled by using post K computer of the FLAGSHIP2020 Project,” “Tokyo Metropolitan Area Convection Study for Extreme Weather Resilient Cities (TOMACS),” Japan Society for the Promotion of Science KAKENHI Grants JP24244074 and JP16K17804, and the Cooperative Program (Grants 131, 2014; 136, 2015; 138, 2016; 137, 2017; and 141, 2018) of the Atmosphere and Ocean Research Institute, The University of Tokyo. Outer and inner LETKFs were conducted using the Fujitsu PRIMEHPC FX10 System (Oakleaf-FX, Oakbridge-FX) at the Information Technology Center, The University of Tokyo. The 350m-EXPs and 50m-EXPs were conducted using the K computer at the RIKEN Advanced Institute for Computational Science through the HPCI System Research Project (Project ID: hp120282, hp130012, hp140220, hp150214, hp150289, hp160229, hp170246, and hp180194). The C-band Doppler radar data were obtained from the JMA and a second laboratory, the Meteorological Satellite and Observation System Research Department, Meteorological Research Institute. The surface data were from JMA and NTT DOCOMO, Inc.

APPENDIX

Vorticity Budget Analysis

Budgets of ground-relative streamwise vorticity , crosswise vorticity , and vertical vorticity can be analyzed based on the following equations (cf. Lilly 1982; Adlerman et al. 1999; Mashiko et al. 2009; Schenkman et al. 2014; Roberts et al. 2016):

 
formula
 
formula
 
formula

where s, n, and z denote streamwise, crosswise, and vertical directions, respectively; is the magnitude of the ground-relative horizontal wind; is the direction of the ground-relative horizontal wind; and is the frictional force due to the streamwise, crosswise, and vertical components of subgrid turbulence, respectively. The first term on the rhs of Eqs. (A1)(A3) represents stretching caused by convergence. The second and third terms represent tilting of the other two vorticity components. The fourth term is baroclinic generation of vorticity, mainly caused by the horizontal gradient of density that partly depends on temperature. The fifth term is frictional generation of vorticity, mainly caused by the vertical gradient of the horizontal frictional force near the surface. The sixth term in Eqs. (A1) and (A2) represents exchange from the other component of horizontal vorticity resulting from the change of direction of the parcel.

We calculated all terms in Eqs. (A1)(A3) on the backward trajectories of parcels placed at points near at . The backward trajectories of the parcels were calculated in the same way as the circulation analysis in section 4. The variables , , and below the lowest model height of 5 m AGL were calculated with linearly extrapolated from above assuming the same vertical gradient between 5 and 15 m AGL. In this  appendix, we focused on members 01 and 02, which appeared to spawn strong tornadoes. The calculated backward trajectories over an 8-min period in members 01 and 02 are shown in Figs. A1a and A1b, respectively.

Fig. A1.

Backward trajectory of the 13 parcels within the circle with a radius of 100 m centered around the point corresponding to (origin of coordinates) at in members (a) 01 and (b) 02. Color is potential temperature (K). The thick line is where vorticities were analyzed in Fig. A2.

Fig. A1.

Backward trajectory of the 13 parcels within the circle with a radius of 100 m centered around the point corresponding to (origin of coordinates) at in members (a) 01 and (b) 02. Color is potential temperature (K). The thick line is where vorticities were analyzed in Fig. A2.

Time series of , , and on the parcel in member 01 (Fig. A2a) showed that , , and were intensified at , , and , respectively. Because these time series of , , and were fairly consistent with the sum of the time-integrated generation terms on the rhs of Eqs. (A1)(A3) (Fig. A2a), these generation terms provided information that was useful for identifying the sources of the rotation of the tornadoes.

Fig. A2.

(a),(e) Time series of vertical (red, s−1), streamwise (blue, s−1), and crosswise (green, s−1) vorticities and the height of the parcel (black, m), and generation terms (s−2) of (b),(f) vertical; (c),(g) streamwise; and (d),(h) crosswise vorticities on the thick lines in Figs. A1a (member 01) and A1b (member 02). Dashed lines in (a) and (e) are the sum of the time-integrated generation terms on the rhs of Eqs. (A1)(A3).

Fig. A2.

(a),(e) Time series of vertical (red, s−1), streamwise (blue, s−1), and crosswise (green, s−1) vorticities and the height of the parcel (black, m), and generation terms (s−2) of (b),(f) vertical; (c),(g) streamwise; and (d),(h) crosswise vorticities on the thick lines in Figs. A1a (member 01) and A1b (member 02). Dashed lines in (a) and (e) are the sum of the time-integrated generation terms on the rhs of Eqs. (A1)(A3).

At , was intensified mainly by stretching (light blue in Fig. A2b) and tilting of (pink line in Fig. A2b) and (orange line in Fig. A2b). Tilting of was caused by the updraft located in the forward direction of the parcel motion because is parallel to the parcel motion. In contrast, tilting of was caused by updraft near the center of counterclockwise rotation of the parcel because is directed to the left of the parcel motion.

Because was generated mainly by tilting of and , the sources of both and are of interest. When was intensified (), was generated mainly by friction (green line in Fig. A2d). When was intensified (), was generated mainly by tilting of (orange line in Fig. A2c) and exchange from (gray line in Fig. A2c).

Because the following processes (i–iv) were suggested in the vorticity budget analysis, the friction seemed to be the major source of , , and in member 01: (i) was initially generated by friction, (ii) was then tilted and exchanged to generate , (iii) and were tilted to generate , and then (iv) was stretched (Fig. A3). Among all the terms that generated , , and , the baroclinic terms were generally small and negligible. The genesis process (i–iv) that emerged from our analysis is similar to the process described by Roberts et al. (2016) and consistent with Schenkman et al. (2014).

Fig. A3.

Schematic of transformation from frictionally generated vorticity to vertical vorticity of the tornado. Red arrows denote directions of storm-relative velocity vectors. Blue and green arrows denote directions of vorticity vectors that are generated baroclinically and frictionally, respectively.

Fig. A3.

Schematic of transformation from frictionally generated vorticity to vertical vorticity of the tornado. Red arrows denote directions of storm-relative velocity vectors. Blue and green arrows denote directions of vorticity vectors that are generated baroclinically and frictionally, respectively.

This vorticity budget was based on only one parcel that originated from the cold region in member 01 (Fig. A1a). However, the process (i–iv) was found to be important for other parcels. The , , and of a parcel in member 02 (Fig. A1b) were also found to have originated mainly from friction (Figs. A2e–h). In both members 01 and 02, the friction term was large when the parcel was near the surface. Moreover, the process (i–iv) was also found for the parcels that originated from warm inflow regions in members 01 and 02 (not shown). Finally, it should be noted that main sources of the vorticity were not necessarily analyzed completely in these vorticity analyses because it was based on only 240-s trajectories and , , and of the parcels at were not zero. To quantify the contribution of each vorticity from the environment, baroclinity, and friction, the vorticity budget analysis of each partial vorticity (Markowski 2016) started from before may be useful.

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Footnotes

© 2018 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

1

In this model, a hybrid terrain-following vertical coordinate system (Ishida 2007) was used. Hereafter, height (written as z*) is given in this coordinate system, as in Y16.

2

Because the vertical vorticity in each member exceeded 0.6 s−1 several times, the time of the last exceedance before the occurrence of was considered here.

3

Fine spatiotemporal resolution is required to calculate backward trajectories of the parcels near strongly confluent intensifying vortices (Dahl et al. 2012). The 50-m horizontal grid interval and 0.5-s time step used in this study were half of those used by Markowski (2016).

4

Logarithmic vertical profile of v may prevail in a constant flux layer in the neutral stratification. Generally, however, the neutral stratification cannot be assumed. In the present analysis, time series of C(t) and the sum of time-integrated baroclinic and frictional terms calculated with logarithmic vertical profile of v below the lowest model height were less consistent than those calculated with simple linear extrapolation from above (not shown), suggesting that the stratification was not neutral and the boundary layer condition used in this study might not be suitable near the tornado (cf. Markowski 2016).

5

We chose 5 km west of the center of the composite field as the center of this square to focus on the near-tornado environment in the storm that moved eastward.

6

If the environmental lapse rate around the LCL is more than the saturated adiabatic lapse rate and less than the dry adiabatic lapse rate, because the lifted parcel is unsaturated (saturated) below (above) the LCL, the adiabatic lapse late of the parcel below (above) the LCL is larger (smaller) than the environmental lapse rate. It means that difference between the temperature of the lifted parcel and the environmental temperature is the maximum at the LCL. Therefore, its buoyancy B below (above) the LCL decreases (increases) with altitude.

7

The SR is defined by the number of hits divided by the total number of event forecasts [(hits)/(hits + false alarms)].