On 6 May 2012, an F3 supercell tornado, one of the most destructive tornadoes ever recorded in Japan, hit Tsukuba City in eastern Japan and caused severe damage. To clarify the generation mechanisms of the tornadic storm and tornado, high-resolution numerical simulations were conducted under realistic environmental conditions using triply nested grids. The innermost simulation with a 50-m mesh successfully reproduced the Tsukuba City tornadic supercell storm.
In this study (the first of a two-part study), the vorticity sources responsible for mesocyclogenesis prior to tornadogenesis were investigated by analyzing vortex lines and the evolution of circulation of the mesocyclones. Vortex lines that passed through the midlevel mesocyclone (4-km height) originated from the environmental streamwise vorticity, whereas the low-level mesocyclone and low-level mesoanticyclone were connected by several arching vortex lines over the rear-flank downdraft associated with the hook-shaped distribution of hydrometeors (hereafter hook echo). Most of the circulation for the circuit surrounding the midlevel mesocyclone was conserved, although the baroclinity associated with positive buoyancy within the storm led to an up-and-down trend. The circulation of the material circuit encircling the low-level mesocyclone showed a gradual increase caused by baroclinity along the forward-flank gust front. Friction also had a positive net effect on the circulation. In contrast, most of the negative circulation of the low-level mesoanticyclone was rapidly acquired owing to baroclinity around the tip of the hook echo. Just after tornadogenesis, the low-level mesocyclone intensified significantly and developed upward, which caused retrograde motion of the midlevel mesocyclone.
Our understanding of the structure, evolution, and dynamics of supercell storms has been greatly advanced by observational, numerical, and theoretical studies conducted over the past few decades. As many previous studies (e.g., Browning 1964; Lemon and Doswell 1979; Klemp 1987) have indicated, supercells are characterized by the existence of a persistent mesocyclone with a strong updraft within a convective storm. In the early stage of supercell storms, a strong rotating updraft forms at midlevel (~4-km height, hereafter referred to as a midlevel mesocyclone). As the storm develops, a low-level mesocyclone (~1-km height) becomes prominent, and a low-level mesoanticyclone (~1-km height) is sometimes observed on the anticyclonic shear side of the rear-flank downdraft (RFD) outflow as a counterpart of the low-level mesocyclone (e.g., Brandes 1981; Markowski et al. 2008, 2012a; Atkins et al. 2012). Several observational and numerical studies have shown that supercell tornadogenesis is preceded by the intensification of the low-level mesocyclone (Rasmussen et al. 2000; Mashiko et al. 2009; Schumacher and Boustead 2011; Schenkman et al. 2014) because the dynamically induced pressure deficit associated with the low-level mesocyclone intensifies the updraft near the surface (e.g., Wicker and Wilhelmson 1995; Noda and Niino 2010). Although numerous observational studies (e.g., Wakimoto and Cai 2000; Markowski et al. 2002, 2011; Wakimoto et al. 2004) have reported that nontornadic supercell storms are often similar in structure and evolution to tornadic supercells, Trapp et al. (2005) showed statistically that more than 40% of low-level mesocyclones detected by a Doppler radar network in the United States are associated with tornadoes. Thus, an understanding of the formation mechanisms of mesocyclones not only increases scientific knowledge but also is crucial for improving operational tornado warning systems. Nevertheless, the formation mechanisms of low-level mesocyclones remain unclear, and one of the most fundamental uncertainties pertains to the vorticity sources responsible for mesocyclogenesis in supercell storms at low levels.
The vorticity source of midlevel mesocyclones in supercell storms is relatively well understood. Using vortex line analyses, numerous previous studies (Davies-Jones 1984; Rotunno and Klemp 1985; Markowski et al. 2008, 2012a) revealed that midlevel mesocyclones acquire vertical vorticity aloft by the tilting of horizontal vorticity associated with environmental vertical wind shear. Indeed, storm-relative environmental helicity (SREH) (e.g., Davies-Jones et al. 1990), which is calculated by integrating vertically the scalar product of the environmental horizontal vorticity and storm-relative wind vectors, is frequently used as an index of the potential for supercell genesis. Although the possible importance of the baroclinic effect on a midlevel rotation was also acknowledged (Davies-Jones et al. 2001), the contribution of the environmental vertical wind shear to the vorticity source of a midlevel mesocyclone has thus far not been quantified by analyzing the circulation of the material circuit tracked backward from the midlevel mesocyclone.
Numerous studies of low-level mesocyclones have focused on the RFD as the vorticity source. Vortex lines passing through low-level mesocyclones form arches over the RFD region, which suggests that the vorticity is baroclinically generated by horizontal buoyancy gradients in the RFD region (Straka et al. 2007; Markowski et al. 2008, 2012a). If the leading edge of the vortex rings produced by baroclinity associated with the RFD region is lifted by updrafts due to the gust front or the low-level mesocyclone, arching vortex lines form and connect the cyclonic and anticyclonic vortices. These storm-generated vortex lines and the environmental vorticity usually have different orientations (e.g., Markowski et al. 2008).
Using Doppler radar data, Markowski et al. (2012b) quantitatively evaluated the vorticity sources of a low-level mesocyclone in a supercell by analyzing the circulation of the material circuit surrounding the vertical vorticity maximum associated with the low-level mesocyclone. They revealed that the baroclinity associated with the forward-flank downdraft (FFD) in the precipitation region is the primary source of circulation, and that the RFD associated with the descending reflectivity core (e.g., Byko et al. 2009) modulates the low-level rotation and buoyancy field instead of generating vorticity. Numerical studies of supercell storms conducted during the 1990s or earlier (e.g., Klemp and Rotunno 1983; Wicker and Wilhelmson 1995) also suggested that the baroclinity along the forward-flank gust front (FFGF) might be a dominant vorticity source responsible for the development of low-level mesocyclones. Wicker (1996) indicated that the interaction between the environmental horizontal vorticity near the surface and the baroclinically generated horizontal vorticity along gust fronts is crucial for the development of a low-level mesocyclone. Rotunno and Klemp (1985) analyzed the circulation of a material circuit surrounding a low-level vortex and estimated the baroclinic contribution directly. They found that the circulation originated mostly from baroclinity along the gust fronts. However, the finding of strong baroclinity along gust fronts within a storm in the aforementioned simulation results is disputable, because the cold pools simulated behind the gust fronts were excessively strong compared to those reported by observation (e.g., Davies-Jones 2006; Shabbott and Markowski 2006).
More recent idealized numerical studies have indicated that the RFD and/or the FFD plays a dominant role in creating vertical vorticity and bringing it to the ground (Dahl et al. 2014; Markowski and Richardson 2014; Parker and Dahl 2015). The baroclinically generated horizontal vorticity is tilted upward during the parcel descent. Markowski and Richardson (2014) also analyzed the vorticity forcing along a trajectory initiated from a region of negative vertical vorticity associated with a near-surface anticyclonic vortex. The vorticity vector generated by baroclinity is inclined below the descending parcel trajectory. These results are consistent with previous studies showing arching vortex lines over the RFD region (Straka et al. 2007; Markowski et al. 2008, 2012a).
However, these idealized numerical studies of the low-level mesocyclones and mesoanticyclones did not evaluate the frictional effect despite their consideration of near-surface phenomena; the circulation of material circuits was changed solely by baroclinity and turbulent mixing while neglecting surface friction.
In this study, which is the first part of a two-part study, high-resolution simulation results were used to investigate a tornadic supercell that caused severe damage to Tsukuba City, Japan, on 6 May 2012. A simulation with a 50-m horizontal grid spacing was conducted under realistic environmental conditions that included the surface drag. The aim of the study is to quantify the vorticity sources of the low-level and midlevel mesocyclones and the low-level mesoanticyclone in the supercell. In addition to analyzing the configuration of three-dimensional vortex lines, the evolution of circulation about the material circuits surrounding the mesocyclones was examined to directly assess the contributions of baroclinity and frictional drag to mesocyclogenesis. The baroclinic field around the midlevel mesocyclone was also investigated. In Mashiko (2016, manuscript submitted to Mon. Wea. Rev., hereafter Part II) the generation mechanisms of the simulated tornado in the Tsukuba supercell were investigated.
The remainder of this paper is structured as follows: Section 2 presents a brief overview of the 6 May 2012 Tsukuba City tornadic supercell. Section 3 describes the experimental design of the numerical simulations. The simulated environmental fields around the storm are presented in section 4. Section 5 presents an overview of the evolution of the simulated storm, including tornadogenesis. In section 6, mesocyclogenesis of the midlevel mesocyclone, the low-level mesocyclone, and the low-level anticyclonic vortex is described on the basis of analyses of vortex lines and circulation. Section 7 describes the structure changes of the storm before and just after tornadogenesis. Finally, in section 8, the results are summarized and conclusions are presented.
2. Case overview
On 6 May 2012, an F3 tornado, one of the most destructive tornadoes ever recorded in Japan, hit Tsukuba City in eastern Japan (Fig. 1) and caused one fatality and 37 injuries along with severe property damage, with 76 houses completely destroyed (Japan Meteorological Agency 2012). The tornado was generated at about 1235 Japan standard time (JST; JST = UTC + 9 h) near Tsukuba City, and it moved east-northeastward at about 60 km h−1 across Tsukuba City before eventually dissipating at about 1255 JST, when it encountered a mountainous area (Fig. 1b). The damage path was about 17 km long.
The tornadic storm developed at the southern tip of a north–south-oriented rainband that was accompanied by wind shear near the surface. The storm had the typical characteristics of a supercell. A hook-shaped echo pattern (Fig. 2a) and a strong cyclonic rotation associated with a mesocyclone were detected by a C-band Doppler radar about 15 km from the storm (Yamauchi et al. 2013). The storm also had a “vault” structure in the radar reflectivity field, and the height of the echo top exceeded 10 km (not shown). However, the horizontal dimensions of the Tsukuba storm were slightly smaller than those of a typical supercell in the midwestern United States (e.g., Markowski 2002). Using polarimetric radar observations, Yamauchi et al. (2013) performed a detailed dynamical analysis of the supercell storm as well as the tornado itself.
Figure 3 shows the surface synoptic weather map at 0900 JST. A low pressure system was situated over the Japan Sea, and low-level southerly winds with warm and moist air prevailed in eastern Japan. Shoji et al. (2014) estimated the precipitable water vapor around the Tsukuba storm based on observations of ground-based stations of the global navigation satellite system and reported that high precipitable water vapor (more than 40 mm) was present in the inflow region of the storm. Moreover, an upper-level trough accompanied by cold air was approaching eastern Japan and created a favorable condition for tornadic supercell genesis, combining strong static instability and vertical wind shear with veering (as discussed in section 4). In fact, the north–south-oriented rainband contained at least two other tornadic storms to the north of Tsukuba City (Japan Meteorological Agency 2012).
3. Experimental design and brief verification
Numerical simulations of the Tsukuba supercell tornado were conducted using the Japan Meteorological Agency Nonhydrostatic Model (JMANHM; Saito et al. 2006), which is an operational model of the Japan Meteorological Agency (JMA). The JMANHM has performed well in simulating various mesoscale phenomena, including supercell tornadogenesis (Mashiko et al. 2009). The model includes a bulk-type cloud microphysics scheme (Ikawa et al. 1991; Murakami 1990) based on the formulation of Lin et al. (1983), and it predicts the mixing ratios of six water species (water vapor, cloud water, rain, cloud ice, snow, and hail/graupel) and the number concentrations of ice-phase particles (cloud ice, snow, and hail/graupel). The rain intercept parameter is set to 8 × 106 m−4, as in most previous studies (e.g., Schenkman et al. 2014). Subgrid turbulent mixing is treated using a 1.5-order turbulent kinetic energy closure scheme (Deardorff 1980). Surface fluxes are computed by the bulk method formulated by Beljaars and Holtslag (1991). Topography and vegetation datasets with a 50-m mesh provided by the Geospatial Information Authority of Japan were used for the simulations. The terrain-following vertical coordinate of z* is adopted: z* = H(z − zs)/(H − zs), where zs and H are the surface and model-top heights, respectively.1
To explicitly resolve the tornado, which had a scale of a few hundred meters, a high-resolution simulation with a horizontal grid spacing of 50 m (hereafter referred to as NHM50m) was performed by using triply nested one-way grids. Horizontal grid spacings of 1 km and 250 m were adopted for the outermost model (NHM1km) and intermediate model (NHM250m), respectively. The model domains are shown in Fig. 1; the NHM50m domain (1300 × 1100 horizontal grid points) includes the actual tornado path within a 65 km × 55 km area around Tsukuba City. The model designs are summarized in Table 1. The innermost model, NHM50m, included 100 vertical levels with variable grid interval, which increased from 20 m at the surface to 260 m at the model top (H = 15 640 m). The lowest level was at z* = 10 m.
To obtain the realistic environmental conditions around the storm, the JMA mesoscale analysis data with a horizontal grid spacing of 5 km, which are operationally produced by a four-dimensional variational data assimilation technique based on JMANHM (Japan Meteorological Agency 2013), were used for the initial and boundary conditions of NHM1km. The NHM1km simulation was initialized at 0900 JST 6 May, more than 3 h before tornadogenesis. The NHM50m simulation started at 1150 JST and was integrated for 30 min. The initial and lateral boundary data for NHM50m were obtained from the simulation results of NHM250m.
NHM50m successfully simulated both the Tsukuba supercell storm and the tornado, except that the simulated tornado formed about 25 min earlier than the observed tornado (Fig. 2). In this study, the low-level mesocyclone center was defined as the point of maximum vertical vorticity at 1-km height averaged over a 500 m × 500 m area. The storm motion was defined as the averaged movement of the low-level mesocyclone from 1203 to 1213 JST. The simulated supercell exhibited a hook-shaped hydrometeor pattern (hereafter referred to as hook echo), and cyclonic rotation associated with a low-level mesocyclone was evident in the storm-relative wind field (Fig. 2b). The simulated tornado, which had large vertical vorticity of more than 1.0 s−1 and a pressure deficit of about 20 hPa near the surface, was located at the tip of the simulated hook echo.
Figure 4 shows time series of the vertical vorticity and horizontal wind velocity maxima at z* = 10 m and of sea level pressure minimum within a radius of 2.5 km from the center of the low-level mesocyclone. Rapid increases of vertical vorticity and wind velocity together with the abrupt decrease of pressure occurred at around 1208 JST, which can be defined as the timing of tornadogenesis. The vertical vorticity reached 0.78 s−1 at 1208:20 JST, and it was accompanied by an increase in the wind velocity of more than 20 m s−1 in less than a minute. The simulated tornado significantly intensified around 1214 JST, and at its peak the vertical vorticity and wind velocity were 1.63 s−1 and 67.2 m s−1, respectively. Then around 1218 JST, the simulated tornado encountered a mountainous area and suddenly weakened and dissipated, similar to the observed Tsukuba Tornado (Fig. 1b). The simulated track was close to the observed track (Fig. 1b).
4. Environment around the supercell storm
A wind hodograph from 0- to 6-km altitude at a point 20 km south of the storm 10 min prior to tornadogenesis is shown in Fig. 5a. The environmental wind field was characterized by strong vertical shear with veering at low levels; the winds were southerly below 500 m and south-southwesterly to southwesterly above that elevation. The orientation of the near-ground shear is consistent with surface friction. The southerly wind of about 4 m s−1 at the lowest model level nearly matched the surface observation at Tsukuba City. The motion of the low-level mesocyclone at a height of 1 km (Fig. 5a) was 68% of the magnitude of the 0–6-km average wind and deviated by 24° to the right relative to the averaged wind direction. This deviation is a typical characteristic of supercell storms, and it is caused by an upward dynamic pressure gradient force on the right flank of an updraft in the environmental veering shear (Rotunno and Klemp 1982). The 0–3-km SREH value was 554 m2 s−2, which is comparable to or a little smaller than that of a tornadic supercell occurring in a tropical cyclone environment (Molinari and Vollaro 2008; Mashiko et al. 2009), but larger than that in a typical continental supercell environment (e.g., Thompson et al. 2003, 2007).
Vertical profiles of the simulated thermodynamic fields are shown in Fig. 5b. The low-level air below 940 hPa was warm and highly humid, whereas the temperature was relatively low around 400 hPa under the influence of the upper-level trough, leading to the unstable atmospheric condition. The maximum unstable convective available potential energy (MUCAPE) was 2040 J kg−1 for an air parcel at z* = 298 m, which is within the range of typical supercell environments (e.g., McCaul and Weisman 1996; Thompson et al. 2003) and much larger than that of tropical cyclone environments (e.g., McCaul 1991; Mashiko et al. 2009; Molinari and Vollaro 2010). In addition, the atmosphere was unsaturated throughout the troposphere and a dry layer existed around 700–900 hPa, in contrast to the typhoon-associated supercell case (Mashiko et al. 2009). The Tsukuba tornadic supercell formed in an environment with large convective available potential energy (CAPE) and SREH, which provided favorable conditions for a typical supercell storm such as occurs in the midwestern United States.
5. Evolution of the supercell tornado
Figures 6a–c show the time–height diagrams of vertical vorticity maxima, pressure perturbation minima from the initial averaged state at 1150 JST, and updraft maxima around the low-level mesocyclone from 1155 to 1220 JST, which provide an overview of the evolution of a tornadic storm. Throughout the period, a pressure deficit associated with a midlevel mesocyclone was evident around a height of 4 km. From 1204 JST (4 min prior to tornadogenesis), the vertical vorticity and updrafts started to intensify, particularly below 1 km, indicating the development of a low-level mesocyclone. Rapid intensification of vertical vorticity and a sudden pressure drop occurred at a height of around 1 km just before tornadogenesis, resulting in strong updrafts exceeding 20 m s−1 even at 500-m height. After that, the vertical vorticity intensified near the surface, and the tornado was subsequently generated at 1208 JST. After the intensification of the low-level mesocyclone, its associated strong vertical vorticity and significant pressure drop appeared to develop upward toward midlevels with time, indicating that the low-level mesocyclone continued to develop and formed a deep structure. This structure change is discussed in more detail in section 7.
Horizontal distributions of the supercell structures until just after tornadogenesis are shown in Figs. 7 and 8. The hydrometeor distribution became deformed into a distinct hook echo as the cyclonic rotation, along with the strong updraft, intensified with time. The low-level mesocyclone was located inside the hook, and a low-level anticyclonic circulation was present to the southwest of the low-level mesocyclone (Figs. 7d–f). A strong RFD outflow region with northwesterly winds was nearly coincident with the hook echo pattern. The tip of the hook echo and the associated RFD region were located between the counter-rotating vortices. Both the low-level cyclonic circulation with a large positive vertical vorticity and the anticyclonic circulation with a large negative vertical vorticity significantly intensified about 2 min prior to tornadogenesis (Fig. 8e). However, the low-level mesoanticyclone weakened just before tornadogenesis (cf. Figs. 8e and 8f).
The FFGF and rear-flank gust front (RFGF) were directed from north-northeast to south-southwest and separated environmental southerly winds from the storm-generated westerly winds (Figs. 7a–c and 8g–i). The RFGF curved gradually to the southwest by the effect of the strong westerly outflow near the storm center. The FFGF might correspond to the “left-flank convergence boundary” described by Beck and Weiss (2013) because its orientation and location differed from those of a traditional FFGF as analyzed by Lemon and Doswell (1979). The cold pools behind the gust fronts had a 2–3-K deficit in potential temperature. As has been shown in previous studies (e.g., Lemon and Doswell 1979), the tornado was generated on the RFGF close to its intersection with the FFGF, which was almost directly beneath the low-level mesocyclone (Figs. 8f and 8i). The simulated storm shares obvious features with a typical “classic” tornadic supercell (e.g., Noda and Niino 2010; Markowski et al. 2012a). The generation process of the simulated tornado is investigated in further detail in Part II.
At midlevel (~4-km height), a broad mesocyclone with a pressure deficit of more than 4 hPa and large vertical vorticity was present 5 min prior to tornadogenesis (Fig. 8a). This midlevel mesocyclone was located about 3 km ahead (on the east-northeast side) of the low-level mesocyclone until 2 min prior to tornadogenesis (Figs. 8b,e), but it slowly moved and was nearly directly above the low-level mesocyclone by the time of tornadogenesis (Figs. 8c,f).
Hereafter, this paper focuses on the vorticity sources of the midlevel mesocyclone (4-km height) 5 min prior to tornadogenesis (Fig. 8a) and just after tornadogenesis (Fig. 8c), of the low-level mesocyclone (1-km height) 2 min prior to tornadogenesis (Fig. 8e), and of the low-level mesoanticyclone (1-km height) 2 min prior to tornadogenesis (Fig. 8e). In Part II, the vorticity sources and generation mechanisms of the incipient vortex (Fig. 8h) and of the tornado just after its genesis (Fig. 8i) are investigated.
6. Analyses of vortex lines and circulations
a. Analysis techniques
Vortex line analysis was performed to elucidate the vorticity sources and dynamics of each mesocyclone. A second-order Runge–Kutta scheme was used to calculate the vortex lines. They were computed above z* = 10 m [lowest full level in the model adopting the Lorenz grid; Lorenz (1960)]; thus, many vortex lines have their ends near the surface and appear to pierce the ground surface. As Markowski et al. (2008) noted, vortex lines do not behave as material lines in the presence of vorticity production owing to baroclinity and friction; nevertheless, examination of the configurations of vortex lines is helpful for understanding the vorticity field and storm dynamics.
To quantify the contributions of environmental vorticity and storm-generated vorticity to the genesis of each mesocyclone, the evolution of the circulation for each mesocyclone was also analyzed. The circulation C(t) can be written as
where v is the wind vector and dl represents a displacement vector tangent to the circuit. Counterclockwise integration is performed around the circuit. The Coriolis term can be neglected because of its small magnitude. From Stokes’s theorem, the circulation is equal to the area integral of vorticity normal to the circuit area; thus, circulation analysis is better suited to target a vortex having a certain size than a vorticity budget analysis along a parcel trajectory. Moreover, the calculation errors can be reduced by distributing the circuit outside the immediate vicinity of a vortex center accompanied by a large gradient of wind velocity. The material circuit surrounding each mesocyclone can be traced backward in time by a backward trajectory analysis using many parcels along the circuit. In this study, the circulation analysis was performed by using an approach similar to that of Markowski and Richardson (2014). Initially, 1600 parcels were distributed along the circuit surrounding the targeted vortices, and they were integrated backward in time adding a parcel on the circuit at a middle point if adjacent parcels on the circuit were spaced more than 50 m apart. The backward trajectory of each parcel was calculated by using a second-order Runge–Kutta scheme with a time step of 0.4 s. Backward trajectory analysis requires fine spatiotemporal resolution of the velocity field to reduce calculation errors, particularly for a strongly confluent flow such as a tornado (Dahl et al. 2012). In this study, the wind velocities at each parcel location were obtained from the model outputs at 0.8-s intervals by linear interpolation in time and space. A logarithmic wind profile assuming a 0.1-m surface roughness was used to extrapolate the near-surface wind below the lowest model level at z* = 10 m, as in Mashiko et al. (2009).
The time change in circulation can be written as
where is density, p is pressure, and F represents the effect of turbulent mixing and numerical diffusion. The variable F includes the near-surface frictional effect, which is computed by the surface flux scheme. Here, F below the lowest model level at z* = 10 m was assumed to have the same value as that at the lowest level. The first term on the right-hand side of Eq. (2) represents the baroclinic vorticity generation caused by buoyancy torques.
In this study, each term on the right-hand side of Eq. (2) was calculated directly from the model outputs at 0.8-s intervals, unlike in previous studies (Rotunno and Klemp 1985; Mashiko et al. 2009; Markowski et al. 2012b; Markowski and Richardson 2014). Additionally, the circulation analysis result was verified by comparing the evolution of the circulation calculated by integrating the sum of the terms on the right-hand side of Eq. (2) to that of the circulation calculated directly with Eq. (1). Because of the fine spatiotemporal resolution of the datasets used in this study, it was possible to obtain more accurate circulation analysis results for a small vortex such as a tornado, compared with those of previous studies using Doppler radar data (Markowski et al. 2012b) and numerical simulation results (Rotunno and Klemp 1985; Markowski and Richardson 2014).
b. Vorticity sources of the mesocyclones
1) Midlevel mesocyclone
Figures 9b and 9c depict the vortex lines passing through eight points in the midlevel mesocyclone at a height of 4 km, 5 min prior to tornadogenesis (Fig. 9a). Note that the vortex lines are shown only on the side to the rear of their origins. All of the vortex lines drawn backward from the midlevel mesocyclone region turn horizontally toward the south-southwest. Most of the vortex lines eventually turn southward at a height of about 1500 m, but some vortex lines originate in the southeast at about 500-m height. The directions of these vortex lines are nearly coincident with those of the storm-relative wind and horizontal vorticity associated with the environmental vertical wind shear (streamwise vorticity), as shown in the wind hodograph (Fig. 5a).
The time series of the circulation and its production terms on the right-hand side of Eq. (2) are shown in Fig. 10b for a material circuit surrounding the midlevel mesocyclone center accompanied by a pressure minimum at 4-km height, 5 min prior to tornadogenesis (Fig. 10a). The circuit is traced backward in time to 1152 JST. Additionally, the integrated circulation, which was calculated by integrating the baroclinic and frictional terms in Eq. (2) backward from 1203 JST, is compared with the circulation calculated directly with Eq. (1) (cf. the dashed purple and solid black lines in Fig. 10b). The circulations calculated by these two methods are in good enough agreement during their evolution to make qualitative inferences except near the start of the backward time series (around 1202 JST); thus, the calculations of the circulation and each production term in Eq. (2) are considered reliable. It was also confirmed that the results were robust with respect to the size of the initial material circuit (not shown).
The circulation was roughly constant throughout the integration time, although, because of the baroclinic term, it exhibited a slight up-and-down trend in the 1155–1203 JST period. However, the net effect of this baroclinity on the circulation was small. As expected, the frictional term was nearly zero. This result implies that the midlevel mesocyclone originated from preexisting environmental vorticity.
The configuration of the circuit became more complicated as it was integrated backward in time (Figs. 11a–d). Although the circuit was not traced into the far field of the storm (Fig. 11a), the calculated baroclinic production was close to zero at 1152 JST (Fig. 10b). The northern portion of the circuit at the initial time of 1203 JST (Figs. 11d and 12c) descended markedly backward in time (Fig. 12b), so that the northward-directed environmental horizontal vorticity vectors were likely to pierce the inside of the circuit throughout the integration period. These environmental vorticity vectors contributed to the positive circulation of the circuit, which indicates that the vorticity source of the midlevel mesocyclone was the environmental vertical wind shear with veering. However, a horizontal gradient of density was present in and around the circuit from 1155 JST (Fig. 12). When the baroclinic term was contributing to the positive circulation at 1159 JST, a southeastward-directed horizontal density gradient existed within the eastern part of the circuit (Fig. 12a), indicating the presence of northeastward-directed baroclinic vorticity generation there. It is evident from the vertical projection of the circuit that this baroclinity contributed to the positive circulation of the circuit. In contrast, at 1202 JST, southward-directed baroclinic vorticity generation was associated with a westward-directed density gradient within the circuit (Fig. 12b), and as a result the baroclinic term made a negative contribution to the circulation. It can be inferred that this baroclinity was attributable to storm-generated positive buoyancy caused by diabatic warming, because the region of low density coincided closely with the distributions of hydrometeors and high potential temperature (not shown).
2) Low-level mesocyclone
Figures 13b and 13c show the vortex lines passing through 10 points in the low-level mesocyclone at 1-km height, 2 min prior to tornadogenesis (Fig. 13a). After passing through the low-level mesocyclone, some vortex lines form arches on its southwest side. The vortex lines turn horizontally to the southwest, and then descend to the negative vertical vorticity region in and around the anticyclonic vortex a few kilometers southwest of the low-level mesocyclone. These arching vortex lines connecting the counter-rotating vortices are similar to those shown in previous studies (Straka et al. 2007; Markowski et al. 2008, 2012a; Marquis et al. 2012). These studies suggested that the baroclinically generated horizontal vorticity around the RFD associated with the hook echo is the primary vorticity source and is crucial for the development of the couplet of counter-rotating vortices.
However, the arching vortex lines passing through the low-level mesocyclone come from various regions, including the FFGF and the ground surface beneath the low-level mesocyclone. Moreover, some vortex lines extend vertically instead of forming arches after passing through the low-level mesocyclone, as shown by Markowski et al. (2008) and Kosiba et al. (2013). It is very difficult to interpret the configuration of vortex lines because they are not material lines, owing to the effects of baroclinity and friction, as noted by Markowski and Richardson (2014). Thus, this result raises the question of whether the baroclinity around the RFD is the dominant vorticity source of the low-level mesocyclone.
To clarify the origin of vertical vorticity in the low-level mesocyclone, the time series of the circulation and each production term in Eq. (2) is shown in Fig. 14b for a material circuit encircling the large vertical vorticity region of the low-level mesocyclone at a height of 1 km, 2 min prior to tornadogenesis (Fig. 14a). These calculations are also reliable, as verified by comparing the integrated circulation calculated from production terms on the right-hand side of Eq. (2) with the circulation calculated directly with Eq. (1) (Fig. 14b). The results are also robust with respect to the size of the initial material circuit (not shown).
The circulation gradually increased until 1203 JST (5 min prior to tornadogenesis); this result differs from the rapid increase of the circulation of a low-level rotation in the 2009 Goshen County storm shown in Markowski et al. (2012b). This gradual increase was caused mainly by the baroclinic term in the 1154–1203 JST period. The frictional term also had a net positive effect on the gradual increase of the circulation, especially prior to 1157 JST, although at certain times it had a negative effect.
The evolution of the circuit is shown in Fig. 15. The circuit converged on the low-level mesocyclone mainly from the northeast side near the surface, and most parts of the circuit were present in the inflow sector of the storm at 1200–1206 JST. However, the northwestern side of the circuit was located along the FFGF, which was oriented from north-northeast to south-southwest and had a 2–3-K horizontal difference of potential temperature across it.
Figure 16 shows the horizontal vorticity vectors at 250-m height around the western portion of the circuit at 1200 JST, the time at which a gradual increase in circulation was caused principally by the baroclinic term. The large south-southwestward-directed vorticity vectors generated by baroclinity along the FFGF are overlapped by the northwestern portion of the circuit. The northwestern edge of the circuit is at a higher altitude (above 250 m) around the FFGF, which indicates that baroclinity along the FFGF might have contributed to the generation of circulation along the circuit.
To quantify the baroclinic contribution around the FFGF, the baroclinic term on the right-hand side of Eq. (2) was evaluated along a small segment (circuit S in Fig. 16) of the circuit near the FFGF at 1200 JST. The baroclinic term value of circuit S was 31.5 m2 s−2, and that of the total circuit was 29.8 m2 s−2. These results imply that most of the baroclinically generated circulation arose along the FFGF, which contributed substantially to the gradual increase in circulation.
At 1158 JST, the entangled circuit was located at levels higher than 1000 m on the tip of the hook echo (Fig. 15b), which was accompanied by large horizontal buoyancy gradients as shown in Part II. However, the configuration of the circuit at 1158 JST is so complicated that the effects of baroclinity around the hook remain unclear.
The circuit for the low-level mesocyclone maintained about two-thirds of its original circulation value for 14 min backward in time (Fig. 14b), and the baroclinic production was relatively small at the final integrated time (1152 JST). However, the circulation was already increasing at 1152 JST, and the circuit stretched across the weak baroclinic zone associated with the hydrometeor distribution (Fig. 15a). Further investigation using simulation results with longer model integration and a wider model domain is needed to quantify the contribution of environmental vorticity to low-level mesocyclogenesis.
3) Low-level mesoanticyclone
A similar analysis was conducted for the low-level mesoanticyclone with large negative vertical vorticity at 1-km height, 2 min prior to tornadogenesis. This mesoanticyclone and the low-level mesocyclone to its northeast constitute a couplet of counter-rotating vortices. The configuration of five vortex lines passing through the mesoanticyclone (Fig. 17a) is quite similar to that of the low-level mesocyclone vortex lines, including the arches that connect the low-level cyclonic and anticyclonic vortices (Figs. 17b and 17c). In contrast to the low-level cyclone, however, all of the vortex lines form arches. The strong RFD outflow associated with the hook echo is present under these arching vortex lines (Fig. 7). In contrast to the low-level mesocyclone, the vortex lines passing through the mesoanticyclone rise again and do not extend toward the surface. In fact, the region of negative vertical vorticity associated with the mesoanticyclone is ambiguous near the surface (Fig. 8h).
The time series of the circulation and each production term are shown in Fig. 18b for a material circuit surrounding the large negative vertical vorticity region of the mesoanticyclone at a height of 1 km, 2 min prior to tornadogenesis (Fig. 18a). The integrated and directly calculated circulation values are in approximate agreement during their evolution, which indicates that the calculation results are reliable. The results are also robust with respect to the size of the initial material circuit, although calculation errors increased as its size decreased (not shown).
The baroclinic term was dominant around 1158 JST and was responsible for the large negative circulation of the mesoanticyclone. Note that the circulation had a slightly positive value around 1156 JST, which suggests that the mesoanticyclone originated from the storm-generated vorticity rather than the environmental vorticity associated with vertical wind shear, although further backward integration is needed to evaluate the environmental effect properly. After 1200 JST, the baroclinic term changed its sign to positive and weakened the negative circulation (increased the circulation) along with the frictional term.
The evolution of the circuit is shown in Fig. 19. The circuit converged on the mesoanticyclone mainly from the southeast side near the surface during the 1202–1206 JST period, and the horizontal area encircled by the circuit was quite small, in contrast to the area encircled by the circuit for the low-level mesocyclone. At 1158 JST, at the time of the significant enhancement of negative circulation (rapid decrease in circulation) caused principally by the baroclinic term, the northwestern portion of the circuit was convoluted at about 1-km height at the tip of the hook echo (Fig. 19a). Figure 20 shows the horizontal vorticity vectors at 1-km height around the tip of the hook echo and the intricate circuit at 1158 JST. The large horizontal vorticity vectors pointing clockwise that surround the tip of the hook echo appear to be equivalent to the vortex rings produced by baroclinity around the RFD described in previous studies (Straka et al. 2007; Markowski et al. 2008). It is likely that the baroclinity around the tip of the hook predominantly produced the negative circulation of the mesoanticyclone; however, the circuit was too convoluted to infer visually from which side the membrane is punctured by the baroclinic-production vectors. (The buoyancy field around the hook echo is carefully examined in Part II.) It can be inferred that the baroclinity around the tip of the hook contributed to some extent to the generation of the vorticity of the low-level mesocyclone around 1158 JST (see Figs. 14b and 15b) because some vortex lines passing through the anticyclonic vortex form arches and extend to the low-level mesocyclone.
7. Structure changes of the storm before and just after tornadogenesis
As shown in Fig. 8, the midlevel mesocyclone at 4-km height was located about 3 km ahead (east-northeast side) of the low-level mesocyclone until 2 min prior to tornadogenesis. After that, the midlevel mesocyclone accompanied by a pressure minimum moved slowly (cf. to the 140°E longitude line in Fig. 8) and approached the low-level mesocyclone horizontally (Fig. 8c). That is, the center of the midlevel mesocyclone shifted backward slightly even in a ground-relative sense just before tornadogenesis.
To clarify the causes of this retrograde motion of the midlevel mesocyclone, vortex line analyses were performed for two regions of vertical vorticity extrema: one is in the center of the midlevel mesocyclone accompanied by a pressure minimum and the larger vertical vorticity (Fig. 21a), and the other is on the front side of the midlevel mesocyclone (Fig. 21d). Vortex lines drawn backward from the midlevel mesocyclone center with large vertical vorticity of about 0.08 s−1 extend downward toward the surface, passing in the vicinity of the low-level mesocyclone (Figs. 21b,c). Meanwhile, the vortex lines drawn backward from the front side of the midlevel mesocyclone center turn horizontally toward the south and originate in the storm environment at about 1-km height (Figs. 21e,f), similar to those of the midlevel mesocyclone 5 min prior to tornadogenesis (Figs. 9b,c). The vortex lines were directed to the north or north-northeast, which is coincident with the direction of the environmental streamwise vorticity as shown in the wind hodograph (Fig. 5a).
These results suggest that the original midlevel mesocyclone weakened and that the newly generated vortex intensified on the rear side. As the tornado developed, this trend became more prominent, and more vortex lines drawn from the midlevel mesocyclone center pass through the low-level mesocyclone and the tornado (not shown). This implies that the low-level vortex intensified and developed upward. These structure changes of the storm are quite similar to those of the 2009 Goshen County storm as described by Markowski et al. (2012a).
8. Summary and conclusions
On 6 May 2012, an F3 tornado, one of the most destructive tornadoes ever to strike Japan, hit Tsukuba City and caused severe damage. Radar observations revealed that the tornadic storm exhibited typical characteristics of a “classic” supercell, such as a hook echo, a cyclonic rotational wind pattern aloft, a deep structure with echo top exceeding a height of 10 km, and a strong tornado at the tip of the hook echo. Triply nested high-resolution simulations were conducted using the Japan Meteorological Agency Nonhydrostatic Model (JMANHM). The innermost 50-mesh simulation successfully reproduced the typical “classic” supercell storm as well as the tornado, as in the radar observations. This simulation adopted a realistic experimental design that included surface friction and used initial and boundary conditions obtained by the four-dimensional variational data assimilation technique of the JMA.
The simulated storm exhibited the features of a typical tornadic supercell. In the early stage, a broad mesocyclone at midlevel was present about 3 km horizontally ahead of the low-level circulation center before tornadogenesis. The low-level mesocyclone intensified with time at around 1-km height, and the updraft associated with the low-level mesocyclone exceeded 20 m s−1 at 500-m height, 2 min prior to tornadogenesis. A low-level mesoanticyclone also developed to the southwest of the low-level mesocyclone. The tornado was subsequently generated on the RFGF at the tip of the hook echo, which was nearly directly beneath the low-level mesocyclone.
Analyses of vortex lines and circulation were performed to clarify the vorticity sources of the midlevel mesocyclone, low-level mesocyclone, and low-level mesoanticyclone.
All of the vortex lines that passed through the midlevel mesocyclone originated from the environmental streamwise vorticity, where a strong vertical wind shear existed and the 0–3-km SREH value was 556 m2 s−2. In fact, most of the circulation of the material circuit surrounding the midlevel mesocyclone was retained, although the baroclinity due to diabatic warming within the storm led to an up-and-down trend of the circulation. The net effect of this baroclinity on the circulation was relatively small.
In contrast, some vortex lines passing through the low-level mesocyclone 2 min prior to tornadogenesis formed arches and extended to the low-level anticyclonic vortex, as shown in previous studies (Straka et al. 2007; Markowski et al. 2008, 2012a). However, the circulation of a circuit encircling the low-level mesocyclone gradually increased, mainly owing to the baroclinity along the FFGF. The surface friction also had a positive net effect on the circulation. This result differs from that of a low-level mesocyclone shown by Markowski et al. (2012b) and the tornado described in Part II, which showed the rapid increase of circulation caused by baroclinity.
All of the vortex lines that passed through the low-level mesoanticyclone with a large negative vertical vorticity 2 min prior to tornadogenesis formed arches. Most of the negative circulation about the material circuit surrounding the mesoanticyclone was acquired rapidly owing to baroclinity around the tip of the hook echo. This suggests that the mesoanticyclone did not originate from the preexisting environmental vorticity but from the storm-generated vorticity. However, further backward trace of the circuit will be needed to evaluate the environmental effect properly.
The vortex line analysis also revealed that just after tornadogenesis, the low-level mesocyclone intensified significantly and developed upward, which caused retrograde motion of the midlevel mesocyclone.
The author acknowledges helpful comments by Hiroshi Niino, Teruyuki Kato, and Hiroshi Yamauchi. The author also extends thanks to 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 the Meteorological Research Institute. This work was partly supported by JSPS KAKENHI Grants 23540518 and 15K05295.