9.3 THE NUMERICAL SIMULATION OF NON-SUPERCELL TORNADOGENESIS
Bruce D. Lee and Robert B. Wilhelmson Department of Atmospheric Sciences and National Center for Supercomputing Applications University of Illinois at Urbana-Champaign
1. INTRODUCTION
Until this past decade most attention in tornado research has been placed on understanding supercell tornadogenesis due to the severity of this type of tornado. Non-supercell tornadoes (NST's) have attracted more recent attention as they affect geographical areas of increasing population density such as the High Plains just east of the Front Range and the Florida peninsula, two regions where NST's are quite common. The term "non-supercell tornado" (NST) as given by Wakimoto and Wilson (1989) or "non-mesocyclone tornado" as given by Brady and Szoke (1989) has been used to describe tornadoes associated with storms not displaying the strong pre-tornadic mid-level rotation found in supercell storms. NST's are usually associated with deep convection found along lower tropospheric boundaries possessing significant across-front horizontal shear. Although most NST's fall in the F0-F1 range on the Fujita scale (see Fujita, 1981), this type of tornado can, on occasion, demonstrate considerable strength. Wakimoto and Wilson (1989) report damage rated at F2 and F3 for two of the four NST's which hit the Denver, Colorado area on 15 June 1988.
During the past decade several observational studies have produced a better understanding of NST's along with some general forecast rules. Observationally studying NST-genesis is inherently difficult due to the small time and space scales of this phenomenon; however, the NST-genesis problem is well suited for investigation with high resolution numerical modeling. In this research, we focus on the "landspout" type NST's, a name coined by Howard Bluestein (1985) for their similarity to waterspouts. The present research effort was motivated by the fact that although we know substantially more about non-supercell tornadoes than a decade ago, there is much to be learned. The process by which a misocyclone (i.e., the pre-cursor and parent circulation of an NST) initiates, develops, interacts with neighboring misocyclones and ultimately intensifies to tornadic strength is poorly understood. As defined by Fujita (1981), misocyclones are circulations with diameters less than 4 km. The relationship of these low-level circulations to the initiation of moist convection is also largely unknown. Further, the relationship of the NST circulation to storm structure and storm processes is not well understood. Results from dry model simulations investigating the initiation and evolution of misocyclones along an outflow boundary are presented in an upcoming article (Lee and Wilhelmson, 1995). In this paper, some results from moist model runs are reported and a "refined" schematic model for NST-genesis is presented.
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Corresponding author address: Bruce D. Lee, University of Illinois, Dept. of Atmospheric Sciences 105 South Gregory St., Urbana, IL 618012. CONCEPTUAL MODEL
The current "observational model" became established as more NST cases, most of which occurred near the National Center for Atmospheric Research's observational network in northeast Colorado, were analyzed. Studies by Wilson (1986), Wakimoto and Wilson (1989) and Brady and Szoke (1989) built the foundation for this model of NST-genesis. The necessary conditions appear to include: 1) a lower tropospheric boundary possessing significant across-front horizontal shear, 2) misocyclones developing along the boundary, possibly as a result of horizontal shearing instability, 3) rapidly deepening convection along the boundary, and 4) an atmosphere having only weak vertical shear (by supercell standards). If a fortunate juxtaposition of moist convective updraft and misocyclone occurs, the vortex may be stretched to tornadic intensity. Wilczak et al. (1992) has suggested that vertically tilting baroclinically produced horizontal vorticity along boundaries may also be important in some NST cases.
3. NUMERICAL MODEL
A three-dimensional, non-hydrostatic, quasi-compressible, convective cloud model called MSTFLOW is employed to simulate NST-genesis along a weak outflow boundary. This model is a hybrid spin-off of the Klemp and Wilhelmson (1978) cloud model and the COMMAS model (Wicker and Wilhelmson, 1995) and was designed to utilize the massively parallel Connection Machine (CM-5) at the National Center for Supercomputing Applications. The high speed, large memory CM-5 proved to be an ideal platform for the high resolution necessary for this type of investigation.
The primary simulation employed a 384 x 64 x 50 point grid with 60 m horizontal resolution and a stretched vertical grid yielding 40 m resolution at the surface and 700 m resolution near the top of the domain. This stretched vertical grid configuration places 23 grid points in the dynamically critical surface to 2 km layer. The model domain (23 x 3.8 x 14 km) is shown in Fig. 1. The lateral boundary conditions are open on the east/west sides and periodic on the north/south sides. The domain top is a rigid lid. A semi-slip surface layer parameterization is used to represent surface friction.
The initial conditions are designed to represent a typical northeast Colorado NST scenario involving an outflow boundary. A weak outflow boundary is created in the model via a quasi "dam break" initialization whereby a cold reservoir is allowed to collapse, creating an outflow-like density current in the model domain (Fig. 1). The maximum temperature deficit in this reservoir is -2.5deg.K, a value typical of weak summer outflow boundaries in northeast Colorado
Fig. 1 Model domain configuration at t = 0 s featuring the cold reservoir (-2.5 deg K), the vertical shear profile of u and the southerly wind region. Peak southerly wind at the surface is 15 m s-1 while westerly winds range from -6 m s-1 at the surface to 16 m s-1 at the 14 km level.
(Mahoney, 1988). Heterogeneous initial conditions in the model wind fields shown in Fig. 1 are utilized such that as the outflow propagates forward, a region of significant horizontal shear (a vertical vortex sheet) is created at the leading edge. The model domain wind field contains a vertical shear profile in u such that outflow leading edge and the misocyclones residing there are vertically erect (Xu and Moncrieff, 1994; Rotunno et al., 1988). A thermodynamic profile composited from several northeast Colorado NST cases is used (Fig. 2) which features a convective available potential energy of 1100 m2s-2 and an L.I. of -4 deg C. A small thermal impulse (0.3 deg C) that acts as a short term quasi-stationary perturbation is placed along the front of the cold reservoir to introduce initial three-dimensionality to the outflow.
Fig. 2 Skew-T diagram for model thermodynamic conditions outside of the cold reservoir region.
4. RESULTS
To gain a three dimensional perspective of the evolving ensemble of misocyclone(s), the storm and the outflow boundary, an isosurface based rendering of select model fields covering the pre-tornadic and tornadic phases of the simulation is shown in Fig. 3. As the simulated outflow encounters the southerly wind regime, a vertical vortex sheet is created in the region of horizontal shear at the outflow leading edge. The initial thermal impulse within the outflow leading edge serves to trigger horizontal shearing instability growth along this vertical vortex sheet. These instabilities represent the inaugural circulations of the young misocyclones. Similar to dry simulations of this misocyclone developmental process (Lee and Wilhelmson, 1995), the vortex sheet dynamics operating at the leading edge initially concentrates vertical vorticity along the sheet at discrete centers by preferential advection (vortex sheet roll-up phase). Figure 3a shows these initial misocyclones at 1200 s as the three vertical vortices located at the center of the circulations seen in the leading edge thermal field. The strongest of the misocyclones exhibits a 28 m s-1 differential velocity across the circulation. The initial misocyclone wavelength is approximately 1.3 km. At this time the young convective line at the outflow leading edge is nearly two-dimensional with the cloud base at 2 km AGL. By 1440 s (Fig. 3b), the southern two misocyclone circulations have merged via a sub-harmonic interaction whereby the stronger southern vortex extruded the vorticity from its weaker northerly neighbor (coalescence phase). The convective line is beginning to show more three-dimensionality as misocyclone induced updraft maxima establish asymmetric moist convective forcing along the line. Maximum cloud top at 1440 s is 6 km. By 1680 s (Fig.3c), the remaining two misocyclones have paired off and then merged into one consolidated vortex (a continuation of the coalescence phase). Concurrent with this merger, a prominent convective tower has developed near the unified misocyclone position with the maximum cloud top ascending rapidly to 8.6 km. Peak differential velocity in the misocyclone reaches 37 m s-1 at this time. Between 1680 and 1920 s, the NST vortex continues to intensify as the growing cumulonimbus matures (maximum cloud height 10 km). We designate this the NST early mature phase. At 1920 s (Fig. 3d), the beginning of the NST mature phase is shown with the vortex located at the center of the obvious circulation along the leading edge of the original outflow boundary (delineated by the band of light gray shading running north/south and wrapping into the tornadic circulation). The new dark areas east and west of the original outflow leading edge represents new precipitation induced cold pools from the ongoing convection. The vortex is erect in orientation and deep, reaching the storm's mid-levels (vertical vorticity of 0.05 s-1 reaching the 5 km level). A swirl structure in the cloud base has developed, consistent with the deepening circulation. Maximum ground relative wind speed at this time is 33 m s-1 and maximum differential velocity is 44 m s-1. Between 1980 and 2100 s, the tornadic vortex enters its most intense stage which coincides with the pronounced appearance of the new cold pools previously mentioned. The peak ground relative wind speed during this period reaches 42 m s-1 and peak across-vortex differential velocity reaches 54 m s-1. The simulated NST goes into the NST dissipation phase after 2160 s as negatively buoyant air from the new western cold pool both encircles the low-level vortex and
Fig. 3: Three-dimensional perspective of the evolving ensemble of leading edge misocyclones (and NST vortex), the storm and the outflow boundary for a) 1200 s, b) 1440 s, c) 1680 s and d) 1920 s. At the domain base the gray shading delineates the outflow boundary (darker = colder). The vertical vortex tube is representative of vertical vorticity greater than 0.07 s-1. The cloud isosurface represents cloud water greater than 0.5 g kg-1 for panels a, b, c and 0.37 g kg-1 for 1920 s. View is from an elevated position looking east.
vertically tilts the vortex creating a brief "rope stage" before the near-surface portion of the vortex becomes decoupled from the "in-cloud" portion of the NST vortex, a demise similar to that observed by Wakimoto and Martner (1992). We subjectively define the tornadic phase of this event as that time when the across-vortex differential velocity exceeded 40 m s-1. By this standard, the simulated NST had a life span of 7 min. Within this span, ground relative wind speeds meet F1 severity criteria for a 4.5 min period, while vertical vorticity values near the surface reach the 0.3-0.4 s-1 range. Peak pressure falls of nearly 7 mb as measured with respect to the air mass surrounding the vortex are realized.
5. DISCUSSION
Non-supercell tornadogenesis, at least along weak outflow boundaries, appears highly dependent upon the vortex sheet dynamics leading up to the NST early-mature phase. Each step prior to this point serves to concentrate vertical vorticity at fewer discrete centers, thus providing a large circulation pool that may ultimately undergo vortex stretching. Several observational papers dealing with NST's or addressing misocyclone circulations along convergence boundaries have suggested the possibility that horizontal shearing instability was responsible for the observed circulations (Carbone, 1982; Wilson, 1986, Mueller and Carbone, 1987;; Wakimoto and Wilson, 1989; Kingsmill, 1995). Our simulations confirm this horizontal shearing instability activity, and further, these model runs illustrate the process by which the vortex dynamics select longer length scales and create larger circulations. Misocyclone merger events (coalescence phase), prominent in our simulations, have been documented in the NST observational literature (Wilson, 1986; Roberts and Wilson, 1989; Wilczak et al., 1992).
A by-product of the ongoing scale selection process involves the asymmetry in the leading edge updraft distribution created by the misocyclone circulations (also found in the dry simulations of Lee and Wilhelmson, 1995). In this moist NST simulation, the strongest deep convective forcing was associated with the misocyclone circulations, and most notably, after a coalescence event. The rapid storm growth in this simulation was positionally associated with the final coalescence event occurring between 1440 and 1680 s. To verify that the north/south dimension of the model domain was not artificially influencing both the outflow leading edge principal wavelength and the positioning of the dominant convective tower with respect to the misocyclone, a model domain three times wider (11.5 km) was used with identical resolution. Several simulations with this model domain size with randomized small thermal perturbations along the entire outflow leading edge revealed a dominant wave 3 or wave 4 pattern (wavelength ~ 2.9 - 3.8 km) existing at the outflow leading edge upon entering the NST early mature phase. This wavelength range is consistent with wavelength observed in the smaller domain simulation (wavelength ~ 3.8 km). A similar pattern of deep convection positionally consistent with the misocyclone locations was observed in these large domain simulations. As a side note, three-dimensional renderings of these large domain runs comparable to that shown in Fig. 3d (but with 3 or 4 NST's) look strikingly similar to the 4 June 1995 multiple landspout event captured on film near Muleshoe, Texas. In this video sequence which was widely shown by the television media, 6 landspouts were simultaneously occurring under a line of growing cumulonimbus. Convection initiation by horizontal shearing instability has been hypothesized (Kingsmill, 1995) but never observationally or numerically verified. The results of this modeling effort provide a direct locational link between the pre-tornadic misocyclone and deep convection initiation.
An examination of the vortex intensification process employing a vertical vorticity tendency analysis has revealed that through most of the NST early mature and mature stages the stretching term was much larger than the tilting term near the NST circulation at low-levels (at times, nearly an order of magnitude difference just above the surface). The NST vortex entered its most intense stage when new cold pools developed on either side. To understand the importance of the new precipitation induced cold pools, a simulation was conducted with the rain microphysics turned off. The resulting NST vortex was significantly weaker as illustrated by a 26 percent reduction in the across-vortex differential velocity and an approximate 30 percent reduction in both the maximum ground relative surface winds and the pressure deficit. Further analysis of the role the new cold pools play indicates that as the these pools spread out (especially the stronger western pool), they establish a pattern of additional peripheral low-level convergence around the NST vortex. This leads to a slightly narrower and stronger surface vortex with a ring of enhanced vortex stretching encircling the NST present from 2000 to 2120 s which corresponds to the time of maximum NST intensity.
To illustrate the refinements we have made to the NST-genesis model, a schematic presentation of this process is provided in Fig. 4. Horizontal shearing instability is triggered along an outflow boundary with significant across-front horizontal shear. The vortex sheet residing there rolls up along with the outflow leading edge (vortex sheet roll-up phase - I). Vortex interactions scale select a longer wavelength misocyclone pattern which produces larger circulations (coalescence phase - II). These larger misocyclones produce an asymmetric moist convective forcing along the outflow such that the largest deep convective towers grow adjacent to the misocyclones. As the cumulonimbus rapidly deepen, the young NST vortices intensify as they undergo stretching and extend above cloud base (NST early mature phase - III). The most intense phase occurs concurrent with the emergence of new precipitation induced cold pools which bound the NST, temporarily increasing the low-level convergence (stretching) on the periphery of the vortex (NST mature phase - IV). The NST life cycle concludes when the dominant new cold pool sharply tilts the NST vertically and encircles the near-surface vortex with negatively buoyant air (dissipation stage - V).
A more detailed analysis of this simulation and comparison to observed NST cases will be forthcoming in Part 2 of a three part series of articles on numerically simulating NST-genesis.
6. ACKNOWLEDGMENTS
The numerical simulations were carried on the massively parallel Connection Machine (CM-5) at the National Center for Supercomputing Applications. This work is supported by ATM92-14098.
7. REFERENCES
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Fig. 4 Schematic diagram showing the five phases of NST-genesis along the leading edge of an outflow boundary. View is from an elevated position looking northwest. See text for additional details.