14.4 Numerical Simulation Of A Tornadogenesis In A Mini .

c. Generation process of the tornado in themini-supercellThe generation process of the simulatedtornado is carefully examined here. Figures10a-d show the horizontal distributions ofhydrometeors, isobars and horizontal gridvectors at a height of 1 km with an interval of30 sec from 14:26:00 to 14:27:30 JST (justafter the tornadogenesis). At this level, thehydrometeors only consist of rain water. Thedistribution of the RFD (Figs. 10e-h) is collocated well with the hook-shaped hydrometeors (Figs. 10a-d), and propagates aroundthe near-surface circulation center. The mainupdraft lays ahead and to the left of the RFD.The advancing RFD enhances the low-levelconvergence at its leading edge, making theupdraft region in a horseshoe shape with time.A close-up view of the square area surrounded by the dashed line in Figs. 10e-hshows that two bands with strong updraftextend southward from the rotating main updraft near the mesocyclone center (Figs. 10iand 10j). The eastern updraft is associatedwith the rear-flank gust front, while thewestern updraft is located ahead of theadvancing RFD. The outflow from the RFD(a)14:26:00 JST (b)Hydrometeors (H 1 km)14:26:30 JSTenhanced the low-level convergence and resulted in the latter updraft. The leading edgeof the RFD approaches the rear-flank gustfront with time and eventually reached it(Figs. 10k and 10l). The most notable is thatthe tornado is generated at the region of astrong updraft near the mesocyclone centeron the left-front edge of the RFD right afterthe RFD reaches the rear-flank gust front (Fig.10l). Judging from the evolution of the RFD,the RFD instigates the tornadogenesis.Figure 11b illustrates the backward trajectories of twenty-one parcels, which are distributed in the tornado region at a height of 150m at 14:27:30 JST (Fig. 11a). Thethree-dimensional model outputs of 1-secinterval are used for the integration, wherethe Euler scheme with a time step of 0.5 secis adopted. Note that the trajectory calculations were performed with storm-relativewinds. The trajectory analysis reveals thatabout half of the parcels located in the tornado region at 17:27:30 JST originate fromthe RFD (Fig. 11b). These parcels descendcyclonically from the middle level (higherthan 500 m for several parcels) to near thesurface through the RFD and then ascend intothe vortex center sharply.(c)14:27:00 JST (d)14:27:30 JST[g kg-1](e)14:26:00 JST (f)W (H 150 m)14:26:30 JST(g)14:27:00 JST (h)14:27:30 JST14:26:30 JST(k)14:27:00 JST (l)14:27:30 JST[ m s-1 ](i)14:26:00 JST (j)W (H 150 m)[ m s-1 ]Fig. 10. Evolution of (a)-(d) hydrometeors (rainwater, snow and graupel) at a height of 1 km, and (e)-(h) verticalvelocity at a height of 150 m from 14:26:00 to 14:27:30 JST with an interval of 30 sec until the tornadogenesis. (i)-(l) A close-up view of the rectangle area in (e)-(h). Contour lines indicate pressure with an interval of 2 hPa, and arrows denote storm-relative wind vectors.

(a)(b)Fig. 11. (a) Initial locations of parcels for backwardtrajectory analysis at 14:27:30 JST. The displayed areas are shown by the solid frames inFig. 10l. All parcels are disposed at a height of150 m. Shaded color represents vertical vorticity.Contour lines indicate pressure with an intervalof 1 hPa. (b) Projection of the three-dimensionalbackward trajectories. Parcels were integratedbackward for 270 sec. Colors indicate the parcelheights. Contour lines denote pressure with aninterval of 1 hPa at 14:27:30 JST.d. Vorticity budget analysis along the trajectory through the RFDIn order to clarify the mechanism for thetornadogenesis, the source and amplifyingprocess of the vertical vorticity in the tornadomust be identified. Studied in this subsectionis the budget analysis for the vertical andhorizontal components of vorticity along thetrajectory traveling through the RFD. Theequation for vertical vorticity (ζ) is given byDζ u v w v w u 1 ρ p ρ p 1 Fy Fx) () ( ) (1) ζ( ) ( Dt x y x z y z ρ2 x y y x ρ x ywhere u, v, and w are the three-dimensionalvelocity components, ρ is the density, p is thepressure, Fx and Fy are the x and y components of turbulent mixing. The terms on theright-hand side represent horizontal convergence of vertical vorticity, tilting of horizontal vorticity into the vertical, solenoidal term,and frictional term, respectively. Coriolisforce is neglected.Figure 12a shows a representative path of aparcel that is located at a height of 150 mnear the center of the tornado at 14:27:30 JST(just after tornadogenesis) and originatesfrom the RFD. Figure 12b displays the timesequence of the vertical vorticity, parcelheight and terms in Eq. (1) during the final90 sec of the trajectory shown in Fig. 12a.Note that the solenoidal term is not shownsince it is always less than the order of 10-4s-1. The parcel first descends while having asmall negative vertical vorticity. After that,the vertical vorticity increases and changesits sign before the parcel reaches its nadir at14:27:09 JST. Throughout most of its descent,both the tilting term and the convergenceterm have considerably small magnitude.However, the tilting term increases rapidlyright before the parcel reaches the lowest partof its trajectory, and the vertical vorticity hasa positive value of about 0.01 s-1. Once thetrajectory turns upward, the convergenceterm becomes dominant, resulting in a rapidincrease of vertical vorticity. The frictionaleffect works negatively after the vertical vorticity intensifies.We also need to examine the evolution ofthe horizontal vorticity, which is tilted intothe vertical and eventually amplified by thehorizontal convergence. To this end, it isconvenient to write down the equations inseminatural coordinates, where (s, n, k) represent orthonormal basis vectors with thewind vector V (Vh, 0, w) (e.g., Adlerman etal. 1999). The equations for the streamwiseand crosswise horizontal vorticities, ωs andωn, respectively, areDωsDψ ψ w VH w VH ψ 1 ρ p ρ p 1 Fz Fn ωn ωs(VH ) ( VH) () ( ) (2)DtDt n z n s z s ρ2 n z z n ρ n zDωnDψ VH w ψ VH ψ w 1 ρ p ρ p 1 Fs Fz ωs ωn( ) (VH VH ) () ( ) (3)DtDt s z z n s n ρ2 z s s z ρ z swhere Ψ tan-1(v/u) is the horizontal angle ofhorizontal velocity vector that increasescounterclockwise from the east. The firstterm on the rhs of both equations representsan exchange between steramwise and crosswise vorticity due to change in the directionof the horizontal velocity. The second andthird terms in the rhs of each equation represent the rate of change of streamwise/crosswise vorticity from the convergence (horizontal stretching) and tilting of

Figure 12c clearly shows that the large increase in the streamwise vorticity resultsmainly from the convergence term throughout its descent, followed by the exchange andtilting terms. The frictional term is alwaysnegative and works effectively at the lowerlevel (not shown). Note that the baroclinicgeneration term (solenoidal term) is less thanthe order of 10-4 s-1 and is small compared toother dominant terms. The tilting and convergence terms in the streamwise vorticityequation rapidly decrease and become negative right before the parcel reaches the lowesttrajectory location, resulting in a rapid decrease of the streamwise vorticity. At thesame time the streamwise vorticity is tiltedinto the vertical.3.0E-02Parcel Height [m]150Height [ m ]1209060300-2180Terms in Vertical Vorticity Equation [s ]2102.5E-022.0E-020.6(b)Vertical VorticityConvergence TermTilting TermDiffusion TermParcel Height0.41.5E-021.0E-020.5-1(a)(a)0.30.2Parcel height5.0E-030.10.0E 000-5.0E-0314:26:0014:26:30Vertical Vorticity [s ]vortex tubes, respectively. Solenoidal termand frictional term are represented by thefourth and fifth terms in the rhs, respectively.Figures 12c and 12d display time evolutionof horizontal vorticity components and theterms in Eqs. (2) and (3) along the same trajectory for 330 sec until just after the tornadogenesis (14:27:30 JST). The streamwisevorticity is the dominant component ofthree-dimensional vorticity and increasessteadily until the parcel reaches the lowestpart of its trajectory, while the crosswise vorticity increased less rapidly. Note that theparcel originally has a remarkably largestreamwise vorticity of about 0.04 s-1 at14:22:00 JST and it was increased to 0.21 s-1near its nadir.-0.114:27:3014:27:00Time [hh:mm:ss JST]2.00E-03-1Tilting Term1.60E-01Solenoidal Term0.00E 00E-0314:22:3014:23:3014:24:3014:25:30Time [hh:mm:ss JST]14:26:300.00E 0014:27:304.00E-032.00E-01Convergence TermTilting Term2.00E-031.60E-01Diffusion Term0.00E 00E-0314:22:3014:23:3014:24:30-1Convergence Term2.40E-01(d)Crosswise VorticityExchange Term14:25:3014:26:300.00E 0014:27:30Time [hh:mm:ss JST]Fig. 12. Budget analysis of vorticity equation along the trajectory traveling through the RFD. (a) Projection of the 330-sec backward trajectory for the targeted parcel which is located near the tornado centerat 14:27:30 JST. Plotted markers represent the parcel heights with an interval of 30 sec. (b) Time series of the terms in the vertical vorticity equation for the last 90-sec trajectory. Parcel height is alsoshown. (c) Time series of the terms in the streamwise vorticity equation. (d) Time series of the terms inthe crosswise vorticity equation. The vorticity components (ζ, ωs, ωn) are also shown in each figure. Thesolenoidal terms in the vertical and crosswise directions and the frictional term in streamwise direction are omitted since they are relatively small compared to other terms.Crosswise Vorticity [s ]-22.00E-01Exchange TermTerms in Crosswise Vorticity Equation [s ]4.00E-036.00E-032.40E-01(c)Streamwise VorticityStreamwise Vorticity [s ]-2Terms in Streamwise Vorticity Equation [s ]6.00E-03

In the crosswise direction, no single forcingterm is dominant, but most of the crosswisehorizontal vorticity is generated by the convergence and tilting terms. The exchangeterm tends to reduce the crosswise vorticityeffectively with time. The solenoidal term isquite small (not shown). The frictional termdoes not give a significant contribution to thecrosswise vorticity although it increasesaround the lowest part of the trajectory.The analysis revealed that most of thestreamwise vorticity that is tilted andstretched into the vertical arises principallyfrom the amplification of the initial largestreamwise vorticity (about 0.04 s-1) due tothe convergence term, followed by the exchange and tilting terms. Thus, our next concern is what the initial streamwise horizontalvorticity around 14:22:00 JST is. Most parcels traveling through the RFD cyclonicallyaround the mesocyclone originate from thenorthern side of the mini-supercell between200 and 500 m height. The wind hodographin Fig. 4 represents the storm environmentwhich has large horizontal vorticity vectordirected west-southwestward between theselevels. It is apparent that the large streamwisevorticity of the parcels originates in the stormenvironment with strong low-level verticalwind shear.The RFD is important for the tornadogenesis because it transports parcels with significant streamwise horizontal vorticity associated with the environmental vertical shearbarotropically to low levels. In addition,when the RFD associated with thehook-shaped precipitation pattern hits therear-flank gust front it causes locally intensified surface convergence on the left-frontedge of the RFD, which amplifies verticallytilted streamwise vorticity significantly.e. What causes the RFD to wrap around themesocyclone cyclonically?To clarify what caused the RFD to wraparound the mesocyclone cyclonically, whichis a key role in the tornadogenesis, we havecalculated each term in the vertical momentum equation diagnostically. The equation ofa Lagrangian time rate of change is, to theapproximation,DwDt 1 p'ρ z 1ρρ 'g(4)where p’ is the pressure perturbation, ρ’ the-density fluctuation from the basic state of ρ,and g the gravity acceleration.Horizontal plots of the terms in Eq. (4) at aheight of 250 m at 14:26:00 JST are shown inFigs. 13a-c. Figure 13a shows that the perturbation pressure gradient forcing is stronglypositive near the mesocyclone circulationcenter. In the surrounding region around themesocyclone, the perturbation pressure gradient forcing is slightly positive. However, astrong negative forcing exists in a small areato the west of the mesocyclone. In themeanwhile, a region of negative buoyancyspreads from the northwest to the south of themesocyclone. This region is collocated withthe RFD (cf., Fig. 13b and Fig. 10a). Thenegative buoyancy in the northwest quadrantof the low-level mesocyclone contributessignificantly to the downward acceleration ofthe vertical velocity (Fig. 13c), which causesthe trajectories in the RFD to start descendingand accelerate further downward.In order to identify the contribution of precipitation loading to the buoyancy, the buoyancy term in Eq. (4) was decomposed. Figures 14a and 14b show the horizontal distribution of the buoyancy due to the precipitation loading and the other contribution, respectively. The distributions of the two contributions to the buoyancy exhibit quite similar pattern to each other (cf., Fig. 14a and Fig.14b), and the negative buoyancy around themesocyclone is nearly collocated with theRFD (cf., Fig. 14 and Fig. 10e) and thehook-shaped hydrometeors (cf., Fig. 14 andFig. 10a). However, the negative buoyancycaused by the precipitation loading contributes more effectively, especially in thenorthwest quadrant around the mesocyclone.Thus, instead of the evaporative cooling, theprecipitation loading is the determining factorfor the formation of the RFD to wrap aroundthe mesocyclone cyclonically.

(a) 1 p '(b)ρ z 1ρDwDt(c)ρ'gFig. 13. Horizontal cross section of (a) perturbation pressure gradient forcing, (b) buoyancy forcing and (c)acceleration term which is sum of (a) and (b) in the vertical momentum equation at a height of 250 m at14:26:00 JST. The pressure contour lines are drawn for each 1 hPa. Arrows denote storm-relative windvectors.(a)Buoyancy (Qr)(b) Buoyancy (except Qr)Fig. 14. Horizontal cross section of (a) buoyancy due to the precipitation loading, and (b) buoyancy due to theother contributions at a height of 150 m at 14:26:00 JST. The contour lines of pressure are drawn for each 1hPa. Vectors denote storm-relative winds.1.530009911.224009879839799750.9Maximum Vorticity1800Distance from MCMinimum Sea Level Pressure0.60.3014:181200Max-Vor 0.68 s-1Min-Psea 987.9 hPa14:2114:2460014:2714:3014:33Distance from Mesocyclone Center [m]995Maximum Vorticity [s -1]In order to examine the effect of precipitation loading on the RFD and the subsequenttornadogenesis, we have performed sensitivity experiment “NOLOAD” in which theweight of the precipitation (rain, snow andgraupel) is neglected in the density in thegoverning equations of the model simulation.The simulation result shows a remarkabledifference from the control run. A muchweaker tornado (maximum VORmax 0.68 s-1and minimum SLPmin 987.9 hPa), whichbarely satisfies the tornado criteria of thisstudy, is generated about 4 min later compared to the control run and dissipatesquickly (Fig. 15). The remarkable differenceis seen in the behavior of the RFD. The RFDdoes not wrap around the low-level mesocyclone cyclonically and exists only in thesouthwestern portion of the mesocycloneunlike the control run (Fig. 16). The sensitivity experiment indicates that the tornadogenesis is extremely sensitive to the behavior of the RFD. The precipitation loadingassociated with hook-shaped hydrometeorsplays a key role in the behavior of the RFDand the subsequent tornadogenesis.Minimum Sea Level Pressure [hPa]7. Sensitivity experiment014:36Time [hh:mm JST]Fig. 15. Same as Fig. 7 except for the experimentwithout precipitation loading (NOLOAD).Fig. 16. Same as in Fig. 10e except for the experiment without precipitation loading (NOLOAD).

8. SummaryAt least three tornadoes hit the east coast ofKyusyu Island in western Japan during thepassage of an outermost rainband in theright-front quadrant of Typhoon Shanshan on17 September 2006.The simulation well reproduced the outermost rainband on the right-front quadrant ofthe typhoon. The environment around therainband was characterized by stronglow-level veering shear and modest CAPE ofabout 1200 J Kg-1. The rainband consisted ofa number of isolated convective systems witha horizontal scale of 20-40 km. Some of thesystems contained a hook-shaped pattern andvault-like structure of hydrometeors at theirsouthern edge. They had a strong rotatingupdraft of more than 30 m s-1 with verticalvorticity exceeding 0.06 s-1. The horizontaland vertical dimensions of the storms wereboth only about 5 km, and a near-surfacetemperature difference across the gust frontwas very small (about 1 K). These characteristics clearly show that the storms weremini-supercells.The innermost simulation with a horizontalgrid spacing of 50 m successfully reproduceda tornado spawned by the mini-supercell approaching the coast of Nobeoka. The diameter of the tornado in pressure field near thesurface was about 500 m, and the verticalvorticity exceeded 1.0 s-1. The tornado wasgenerated on the rear-flank gust front near themesocyclone center when the left-front edgeof the RFD, which was wrapping around thelow-levelmesocyclone,reachedtherear-flank gust front.We conclude that the RFD, which wrapsaround the mesocyclone cyclonically, plays akey role in the tornadogenesis by barotropically transporting large streamwise horizontalvorticity associated with low-level verticalshear in the environment toward the surface.Moreover, the leading-edge of the RFD enhances the horizontal convergence, especiallyat the left-front edge of the RFD, when theRFD reaches the rear-flank gust front. Thehorizontal convergence rapidly amplifies vertical vorticity tilted from streamwise vorticityand forms a tornado. The behavior of theRFD is largely affected by the negativebuoyancy due to the precipitation loading.The precipitation loading in the area ofhook-shaped precipitation pattern is crucial tothe formation of the RFD to wrap around themesocyclone and the subsequent tornadogenesis.REFERENCESAdlerman, E. J., and K. K. Droegemeier, 1999:A numerical simulation of cyclic mesocyclogenesis. J. Atmos. Sci., 56, 2045-2069.Klemp, J. and R. Rotunno, 1983: A study of

Time [hh:mm JST]-1 Maximum Vorticity [s ] 600 1800 2400 3000 Distance from Mesoc clone Center [m] Maximum Vorticity Distance from MC Minimum Sea Level Pressure 975 979 983 987 991 995 Minimum Sea Level Pressure [hPa]-1 Min-Psea 979.9 hPa (b) Fig. 7. Time series of minimum sea level pressure (SLPmin, solid line), maximum vertical vorticity at