UNIVERSITY OF OKLAHOMA
GRADUATE COLLEGE
TORNADOGENESIS IN HIGH-RESOLUTION IDEALIZED NUMERICAL
SIMULATIONS
A THESIS
SUBMITTED TO THE GRADUATE FACULTY
in partial fulfillment of the requirements for the
Degree of
MASTER OF SCIENCE IN METEOROLOGY
By
BRETT JULIAN ROBERTS
Norman, Oklahoma
2012
TORNADOGENESIS IN HIGH-RESOLUTION IDEALIZED NUMERICAL
SIMULATIONS
A THESIS APPROVED FOR THE
SCHOOL OF METEOROLOGY
BY
______________________________
Dr. Ming Xue, Chair
______________________________
Dr. Howard Bluestein
______________________________
Dr. Alan Shapiro
© Copyright by BRETT ROBERTS 2012
All Rights Reserved.
iv
Acknowledgements
Financial support for this research came from NSF grant AGS-0802888 and an
AMS Graduate Fellowship. The Extreme Science and Engineering Discovery
Environment (XSEDE) provided supercomputing resources for this project, including
systems administered by the National Institute for Computational Sciences (NICS) and
Pittsburg Supercomputing Center (PSC).
I am grateful to everyone who made this research and degree possible. Thanks
are in order for Dr. Ming Xue, Dr. Howard Bluestein, and Dr. Alan Shapiro, who served
on my committee. Dr. Xue, my primary advisor, obtained the funding for this project
and provided much-needed perspective and experience through all its trials and
tribulations. Drs. Bluestein and Shapiro reviewed this thesis and helped immensely in
improving its quality through their insightful questions and comments. In addition,
discussions with several of my fellow students were of great help as I attempted to
analyze and make sense of my results. Alex Schenkman, in particular, spared significant
time in assisting my progress and collaborating on areas of overlap between our
respective projects. Daniel Betten also provided invaluable insight into my results, as
did Dan Dawson, who in addition allowed me to use his code as the basis for many of
the plots included in this thesis.
I appreciate Scott Hill and Yunheng Wang of CAPS for helping to ensure the
many computing resources I employed for this work ran as smoothly as is possible in
the world of supercomputer-based modeling. Eileen Hasselwander and Debra Farmer in
the CAPS office, along with Celia Jones and Marcia Pallutto in the School of
Meteorology office, are thanked for their assistance in matters of scheduling and
v
making sure the considerable paperwork entailed in the degree-seeking process reached
its proper destination! Finally, I would be remiss not to thank all of my family and
friends for their companionship and moral support as I worked toward this degree. My
parents, in particular, have provided much encouragement and assistance (financial and
otherwise!) over the years, and I would not be where I am today without it.
vi
Table of Contents
Acknowledgements ........................................................................................................ iv
List of Tables ................................................................................................................ viii
List of Figures ................................................................................................................ ix
Abstract ......................................................................................................................... xii
Chapter 1: Introduction and Organization .................................................................. 1
Chapter 2: Background ................................................................................................. 3
1. Initial development of a mid-level mesocyclone ............................................ 3
2. Subsequent development of a near-ground mesocyclone .............................. 4
a. Low-level vertical shear of the horizontal wind ....................................... 5
b. Baroclinic generation of horizontal vorticity ........................................... 6
c. Role of mid-tropospheric flow ................................................................. 7
d. Dynamic pipe effect ................................................................................. 8
e. Frictional effects ....................................................................................... 9
3. Tornadogenesis ............................................................................................. 10
Chapter 3: Methodology and Motivation ................................................................... 13
1. Model configuration ..................................................................................... 13
2. Experiments .................................................................................................. 15
a. Control experiment ................................................................................. 15
b. Microphysics experiments ...................................................................... 17
c. Low-level shear experiments .................................................................. 20
3. Definitions .................................................................................................... 26
a. Mesocyclone ........................................................................................... 26
vii
b. Tornado ................................................................................................... 26
Chapter 4: Analysis of Control Simulation ................................................................ 28
1. Storm morphology ........................................................................................ 28
2. Low-level mesocyclone intensification and tornadogenesis ........................ 33
a. Evolution of model fields ....................................................................... 33
b. Trajectory analysis .................................................................................. 42
3. Summary and Conclusions ........................................................................... 54
Chapter 5: Sensitivity to Low-Level Shear ................................................................ 56
1. Comparison of mesocyclone intensity and tornadogenesis timing .............. 56
2. Qualitative comparison and storm morphology ........................................... 60
3. Summary and Conclusions ........................................................................... 68
Chapter 6: Sensitivity to Microphysics Parameterization ........................................ 70
1. Comparison of low-level mesocyclone intensity and tornadogenesis timing
...................................................................................................................... 70
2. Qualitative comparison and storm morphology ........................................... 74
3. Summary and Conclusions ........................................................................... 78
Chapter 7: Comments on High-Resolution Model Trajectory Calculations .......... 80
1. Accuracy in the presence of noise ................................................................ 80
2. The use of Eularian temporal interpolation for trajectory calculations ........ 82
References ..................................................................................................................... 86
Appendix A: Sounding Wind Data for Shear Experiments ..................................... 90
Appendix B: Numerical Methods for Trajectory Calculations ................................ 91
viii
List of Tables
Table 1. ARPS model configuration (universal to all experiments). ............................. 14
Table 2. Summary of soundings and intercept values for all experiments. .................... 23
Table 3. Low-level vertical wind shear magnitudes for all shear experiments. ............. 24
Table 4. Trajectory experiments for temporal interpolation comparison. ...................... 83
Table 5. Median initial position error for 300 s backward trajectories. ......................... 84
Table 6. Mean initial position error for 300 s backward trajectories. ............................ 84
Table 7. Zonal (u) wind for sounding points below 2 km AGL, in m s-1
. ...................... 90
Table 8. Meridional (v) wind for sounding points below 2 km AGL, in m s-1
. ............. 90
ix
List of Figures
Figure 1. Sounding “may20” utilized for the control experiment (CTRL). ................... 17
Figure 2. Graphical depiction of parameter space covered by all experiments. ............. 23
Figure 3. Zonal (u) wind component for the six initial soundings. ................................ 24
Figure 4. Meridional (v) wind component for the six initial soundings. ........................ 25
Figure 5. Average zonal (u) and meridional (v) wind components for strongly-tornadic
(solid), weakly-tornadic (dashed), and nontornadic (dotted) supercell environments as
derived from 413 RUC proximity soundings. Adapted from Markowski et al. (2003). 25
Figure 6. Perturbation potential temperature (shading; K) and 1 g kg-1
rainwater mixing
ratio contour at 10 m AGL for (a) 3000 s, (b) 4800 s, (c) 7200 s, and (d) 10200 s. ...... 30
Figure 7. As in Fig. 5, but for vertical velocity (shading; m s-1
) at 4265 m AGL. ......... 31
Figure 8. Close-up (moving) view of low-level mesocyclone at 10 m AGL. Perturbation
potential temperature (shading; K) and 0.1 s-1
vertical vorticity contour (orange solid)
are plotted at (a) 9000 s, (b) 9420 s, (c) 9600 s, and (d) 9900 s. Gust fronts are indicated
by solid red (FFGF), dark blue (RFGF), and purple (occluded) curves. Black “T”
indicates tornado position. .............................................................................................. 34
Figure 9. Zoomed (moving) view of the tornado in CTRL. (a-d) Horizontal wind speed
(shading; m s-1
) and perturbation pressure at 3 hPa increments below -3 hPa (contour),
at 10 m AGL. (e-h) Vertical velocity (shading; m s-1
) and p’ (contour; -5 hPa) at 1039 m
AGL. Pretornadic vortices are denoted by “PV1” and “PV2” in (a). ............................. 36
Figure 10. Vertical cross-section through (a) pretornadic vortex PV1 at 9180 s, and (b-
d) the tornado at 9480, 9600, and 9720 s. Vertical velocity (shading; m s-1
) is shown,
along with positive vertical vorticity contours (s-1
) at 0.1 s-1
intervals starting at 0.1 s-1
.
The horizontal endpoints of each slice are indicated as (xs, ys)...................................... 39
Figure 11. Conceptual model of a two-cell vortex associated with subcritical flow.
Adapted from Trapp (2000). ........................................................................................... 39
Figure 12. Time-height cross-section of (a) maximum vertical velocity, (b) maximum
vertical vorticity, and (c) minimum perturbation pressure over the model domain from
7200-12600 s. ................................................................................................................. 41
Figure 13. Parcel trajectories initialized in the vortex at (a) 9480 s, (b) 9600 s, and (c)
9780 s; and in the low-level mesocyclone center at (d) 10080 s. Parcels were initialized
at 50 m AGL and integrated backward in time for 480 s. Parcel height is indicated by
color, providing a pseudo-3D visualization. ................................................................... 44
x
Figure 14. Simulated reflectivity at 1 km AGL at (a) 9240 s, (b) 9360 s, (c) 9480 s, and
(d) 9600 s. Black circles denote the leading edge of the RFD surge at this height. ....... 46
Figure 15. Horizontal cross-sections of simulated reflectivity following a representative
tornado-entering parcel. The height of each slice is the parcel height at the indicated
time. The black curve is the projection of the parcel path into the xy-plane, while the
large dot is its current location. ...................................................................................... 47
Figure 16. Horizontal projection of the trajectory path for the representative parcel.
Color indicates parcel height, allowing for a pseudo-3D visualization. The remaining 20
parcels which were also initialized at 9480 s are shown in gray. Stars denote original
parcel locations (at 9000 s). ............................................................................................ 49
Figure 17. Diagnostic quantities calculated along the representative trajectory from
9000-9480 s. (a) Vertical and horizontal-streamwise vorticity components, (b) source
terms for horizontal-streamwise vorticity, and (c) parcel height.................................... 50
Figure 18. Horizontal cross-sections of equivalent potential temperature (shading; K)
for 9240 s and 9300 s. The projection of the parcel path into the xy-plane is indicated by
the black curve, while the large black dot is its current location. The height plotted at
each time is the parcel height at that time. ..................................................................... 53
Figure 19. Timeseries of (a) minimum perturbation pressure, and (b) maximum surface
wind speed, for all low-level shear experiments over the period 7200-12600 s. ........... 58
Figure 20. Time-height cross sections of minimum perturbation pressure for all low-
level shear experiments over the period 7200-12600 s. ................................................. 59
Figure 21. Timeline of tornado occurrence for the low-level shear experiments. ......... 60
Figure 22. Perturbation potential temperature (shading; K) and 1 g kg-1
rainwater
mixing ratio contour at 10 m AGL and 8400 s for all low-level shear experiments. ..... 61
Figure 23. Perturbation potential temperature (shading; K) at the time of peak tornado
intensity for all low-level shear experiments containing a tornado. The RFGF is denoted
by a dark blue curve, while the occluded portion of the gust front is purple. Red “T”
indicates tornado position. Note that for IS2, the first of two tornadoes is shown. The
plotted time varies by experiment and is indicated below the experiment name. .......... 62
Figure 24. Backward parcel trajectories initialized in tornadoes from four low-level
shear experiments; see Section 4.2b for complete methodology description. Trajectories
were integrated backward in time for 480 s. For each experiment, the initialization time
(from which backward integration was performed) is listed below the experiment name.
........................................................................................................................................ 64
Figure 25. Vertical cross-section through the strong tornado in IS2 at (a) 10740 s and
(b) 10920 s. Vertical velocity (shading; m s-1
) is plotted, along with contours for
positive vertical vorticity at 0.1 s-1
increments starting at 0.1 s-1
. .................................. 66
xi
Figure 26. Horizontal path for the representative parcel entering the strong tornado in
IS2 at 10740 s. Parcel height is indicated by color. The remaining 20 parcels calculated
for this initial time are plotted in gray. Stars indicate original positions after backward
integration. ...................................................................................................................... 66
Figure 27. Diagnostic calculations of (a) vertical and horizontal streamwise vorticity,
(b) horizontal streamwise vorticity source terms, and (c) parcel height, for the
representative parcel entering the strong tornado in IS2. ............................................... 67
Figure 28. Timeseries of (a) minimum perturbation pressure, and (b) maximum surface
wind speed, for all microphysics experiments over the period 7200-12600 s. .............. 72
Figure 29. Time-height cross sections of minimum perturbation pressure for all
microphysics experiments over the period 7200-12600 s. ............................................. 73
Figure 30. Timeline of tornado occurrence for the microphysics experiments. ............. 74
Figure 31. Perturbation potential temperature (shading; K) and 1 g kg-1
rainwater
mixing ratio (solid contour) at 8400 s for all microphysics experiments. ...................... 77
Figure 32. Perturbation potential temperature (shading; K) and wind vectors at 10 m
AGL for (a) R86, (b) R45, (c) CTRL, and (d) R45H43. Tornado centers at 10 m AGL
are denoted by “T,” mid-level mesocyclone centers at 2925 m AGL are denoted by
“M,” and RFGF positions are highlighted by dark blue curves. Note that the position of
the plotted subdomain within the model domain varies for each experiment. ............... 78
Figure 33. Timeseries of Eulerian and Lagrangian horizontal streamwise vorticity for
the representative parcel in Section 4.2b. ....................................................................... 81
Figure 34. Timeseries of (a) Eulerian and Lagrangian horizontal streamwise vorticity,
and (b) vertical velocity, for Parcel B. Red and orange ellipses denote two periods in
which disagreement between Eularian and Lagrangian time tendency for streamwise
vorticity is very large. ..................................................................................................... 81
xii
Abstract
For several decades, idealized numerical simulations wherein an initial thermal
bubble induces deep moist convection have been an important tool for understanding
supercells. Several such studies in the literature have utilized the 20 May 1977 “Del
City storm” sounding for their initial environment, often employing nested grids to
attain higher resolution over some spatiotemporal subdomain of interest. In this study,
simulations are conducted at uniform 50 m horizontal resolution using this sounding in
the Advanced Regional Prediction System (ARPS) with Lin ice microphysics. Under
this configuration, the initial right-moving supercell fails to produce a tornado within
the first 2 h of model integration. However, a second convective cell develops to its
southwest, and an eventual merger of the two storms leads to tornadogenesis later in the
simulation. The resulting tornado is a two-cell vortex with central downdraft throughout
its life cycle, likely owing to the lack of surface friction in the model. Diagnostic
calculations along a representative tornado-entering trajectory reveal that both
baroclinic generation and tilting of background vorticity contribute in comparable
measures to positive streamwise vorticity before the parcel turns upward near the
vortex.
In addition to the control simulation, two sets of sensitivity experiments are
performed. In the first set, the rain and hail intercept parameter values are varied to test
sensitivity to precipitation microphysics. In the second set, the distribution of vertical
shear within the lowest 2 km AGL is varied around the original 20 May 1977 wind
profile. In both cases, a clear temporal trend in overall storm evolution is identified:
faster evolution for weaker 0-1 km AGL shear and for smaller intercept parameter
xiii
values. However, the effect upon tornado occurrence, intensity and duration is nonlinear
in both cases. Finally, some issues relating to trajectory accuracy in high-resolution
supercell simulations are briefly explored.
1
Chapter 1: Introduction and Organization
This study presents a suite of high-resolution idealized numerical simulations of
supercell thunderstorms. There are two primary goals. The first is to understand in a
general sense the storm evolution and how it leads to low-level mesocyclogenesis and
tornadogenesis. The second is to explore the sensitivity of this evolution to a parameter
space in both low-level shear distribution and microphysics parameterization. As
detailed in Chapter 3, a key strength of this study is the use of a very high (50 m)
uniform horizontal grid spacing. This allows the identification of tornadoes within the
simulations, where earlier studies either could only identify tornado cyclones (owing to
lower resolution) or relied on nested subdomains to resolve tornadoes themselves.
This thesis is organized as follows. Chapter 2 presents a brief literature review
of supercells, mesocyclogenesis and tornadogenesis. Chapter 3 introduces the
experimental design and motivation for this work.
Chapter 4 presents an analysis of the control simulation. First, the storm-scale
evolution over the course of the simulation is described and illustrated. Then, the period
in which the low-level mesocyclone intensifies and a tornado occurs is analyzed in
more detail. Trajectories entering the low-level mesocyclone and tornado are examined,
and a vorticity budget is calculated along one representative parcel.
Chapter 5 compares the experiments in which low-level shear was varied from
the control run. Similarly, Chapter 6 compares the microphysics-varying experiments.
In both cases, temporal trends in storm evolution – particularly with respect to the
development of a low-level mesocyclone – are identified within the parameter space.
Furthermore, the relative tendency for storm features to become configured in a manner
2
favoring tornadogenesis over the parameter space is explored. In the case of the low-
level shear experiments, one experiment produces a tornado that is explored in some
detail due to important differences from the others.
Chapter 7 adds a few comments on the use of trajectories as a diagnostic tool in
model simulations, particularly at spatial resolutions considered high at the time of this
study (Δx < 100 m). It is demonstrated that such trajectories may sometimes contain
significant position errors when passing through fast, complex flow, as exemplified by
the region near a tornado. Within the context of trajectory calculations, the value of
employing temporal interpolation between model output times is also explored.
3
Chapter 2: Background
Despite receiving considerable attention from the research community in recent
decades, our understanding of the physical processes responsible for supercell
tornadogenesis remains relatively poor. One need look no further for evidence of this
inadequacy than in the operational setting, where forecasters continue to issue tornado
warnings in a primarily reactive fashion upon detection by radar or spotters (Stensrud et
al. 2009). Recent observational and numerical studies have made progress in supporting
or refuting mechanisms hypothesized to be responsible for the generation of tornadic-
strength vorticity within supercell thunderstorms, serving to guide current research
towards the most likely candidates. Nevertheless, the roles and relative contributions of
these candidates remain greatly in question.
Numerical and observational work has identified three processes which typically
occur sequentially leading up to supercell tornadoes: first, the development of a mid-
level mesocyclone; second, the development of a low-level (or near-ground)
mesocyclone; and finally, tornadogenesis itself. Each stage is reviewed below.
1. Initial development of a mid-level mesocyclone
Observations indicate that supercells first develop a mid-level mesocyclone
several km above ground level (AGL), and only afterwards gain a near-ground
mesocyclone at or below 1 km AGL (Davies-Jones et al. 2001). In his summary of the
current state of tornadogenesis research, Davies-Jones (2006) suggested that the
development of this near-ground mesocyclone is the least-understood process in the
chain of events which leads to supercell tornadoes – as such, it will be the main focus of
this review The preceding development of a mid-level mesocyclone is understood to
4
result from tilting of environmental horizontal streamwise vorticity into the vertical by a
supercell’s updraft (Rotunno and Klemp 1985). Davies-Jones (1984) derived the
theoretical correlation coefficient between perturbation vertical velocity (w’) and
vertical vorticity (ζ’), showing that it varies directly with the proportion of
environmental vorticity which is streamwise:
where is the streamwise component of the environmental vorticity vector. The
physical significance of this expression is that larger environmental streamwise vorticity
implies a greater tendency for updrafts (positive w’) to rotate cyclonically (positive ζ’).
This idea is supported by the finding by Droegemeier et al. (1993) that 0-3 km storm-
relative environmental helicity (SREH), a vertical integral of environmental streamwise
vorticity, is useful in discriminating between supercell and nonsupercell thunderstorms
in a numerical model.
2. Subsequent development of a near-ground mesocyclone
Near-ground mesocyclones are unlikely to share the direct vorticity-tilting mode
of formation, however. Such a mechanism would require near-ground parcels bearing
horizontal streamwise vorticity to turn upward quite sharply in order to produce strong
vertical vorticity close to the ground, and observations do not support the existence of
such extreme horizontal gradients in near-ground vertical velocity prior to
tornadogenesis (Bluestein 2007). Therefore, other sources for either creating or
amplifying existing near-ground vertical vorticity must be identified.
5
a. Low-level vertical shear of the horizontal wind
The robust correlation observed by forecasters and formally established by
Rasmussen (2003) between high values of 0-1 km SREH and the likelihood that a
supercell will produce a tornado seems curious, given that near-ground mesocyclones (a
prerequisite for supercell tornadoes) probably do not form as a direct result of an
updraft tilting horizontal streamwise vorticity into the vertical. Davies-Jones (2006)
proposed that the base of a mid-level mesocyclone may be relatively low when 0-1 km
SREH is high, perhaps encouraging or hastening the formation of a near-ground
mesocyclone in some way. This idea is supported by Schumacher and Boustead (2011),
who associated an increasing magnitude of 0-1 km shear during one outbreak with an
abrupt increase in the number and strength of tornadoes. Another possibility is that
horizontal streamwise vorticity associated with low-level environmental shear is
amplified by stretching as parcels descend in the rear-flank downdraft (RFD), and upon
reaching the surface these parcels exhibit high enough streamwise vorticity that only
modest tilting and stretching near the ground by an updraft is necessary to instigate a
near-ground mesocyclone.
Mashiko et al. (2009), hereafter M09, numerically simulated a minisupercell
associated with a typhoon’s outer rain band, and found through trajectory analysis that
about half the parcels entering the storm’s intensifying low-level mesocyclone 18 s
prior to tornadogenesis originated in the RFD. The vorticity budget for a representative
parcel was analyzed, and stretching of already-substantial streamwise vorticity from the
environmental shear was found to be the primary contributor to its large value after
descending toward the near-ground mesocyclone center. While tropical minisupercells
6
typically form in environments of notably weaker buoyancy and stronger low-level
shear than classic supercells, the findings of M09 lend credence to the more general
idea that the RFD aids near-ground supercell mesocyclogenesis through barotropic
downward transport of large environmental streamwise vorticity. Moreover, earlier
numerical studies of classic supercells have demonstrated evidence that some parcels
entering the low-level mesocyclone originate from the RFD and experience stretching
of streamwise vorticity during descent (Adlerman et al. 1999).
b. Baroclinic generation of horizontal vorticity
Another hypothesized mechanism for near-ground mesocyclogenesis is the
baroclinic generation of horizontal vorticity which is tilted into the vertical and
stretched. Clearly, this explanation faces the same obstacle regarding the need for
unrealistically sharp horizontal gradients in low-level vertical motion discussed in the
preceding section. Proposed sources for baroclinic generation include the storm-scale
forward-flank downdraft (FFD) gust front, as well as mesoscale and synoptic-scale
outflow boundaries and fronts. The former was found to be of significant importance in
the numerical simulations of Klemp and Rotunno (1983). However, observations during
the VORTEX field experiment in 1994-95 revealed an unexpected lack of baroclinicity
along the FFD gust fronts of many significantly tornadic supercells. In fact, Shabbott
and Markowski (2006) analyzed mobile mesonet data from 12 supercells and found
those whose FFD had large θ deficits at the surface (and therefore a relatively strong
gradient of buoyancy along the gust front) were actually less likely to be tornadic than
those with smaller θ deficits in the FFD. Moreover, Markowski et al. (2002) observed a
similar pattern for the thermodynamics of the RFD. These studies and others have cast
7
significant doubt on the role of baroclinic streamwise vorticity generated at the storm
scale in low-level rotation, prompting researchers to look elsewhere over the past
decade.
Markowski et al. (1998), hereafter M98, noted that a large proportion of the
tornadoes observed during VORTEX occurred when supercells interacted with
mesoscale boundaries, a phenomenon also frequently observed by operational
meteorologists. As such, unlike the FFD buoyancy gradient, the causal role of this form
of baroclinic vorticity generation in tornadogenesis cannot easily be dismissed.
Reconciling this fact with the need for very abrupt upward turning of parcels traveling
along these boundaries in order to produce a near-ground mesocyclone remains a
challenge facing research meteorologists. It is possible that inflow parcels which travel
along the baroclinic boundary and acquire enhanced streamwise vorticity enter the
updraft, wrap around it cyclonically in the mid-level mesocyclone, and are later
processed by the RFD, ultimately descending and converging into the low-level
mesocyclone. Another potential factor noted by M98 is that updraft intensity may
increase due to enhanced low-level convergence along mesoscale boundaries, which
could at the very least increase vertical stretching of parcels in an incipient tornado
given a pre-existing near-ground mesocyclone.
c. Role of mid-tropospheric flow
In addition to the generation of vorticity discussed in 3a, vertical shear of the
horizontal wind likely influences the development of a low-level mesocyclone in other
capacities. Brooks et al. (1994) found that the development and longevity of near-
ground rotation in a supercell depends in part upon a complex balance between mid-
8
level storm-relative winds and low-level vertical shear (and resultant mid-level
mesocyclone intensity). In cases with very strong mid-level winds, precipitation may be
advected far downshear from the updraft, which is rich in streamwise vorticity. Hence,
the precipitation-induced downdraft will form in a location well removed from a major
vorticity source, unable to transport it downward efficiently for near-ground
mesocyclogenesis. Conversely, weak mid-level winds can result in precipitation falling
into and weakening the updraft, or at least falling close enough to the updraft that cold
outflow undercuts it (and the near-ground mesocyclone) more quickly. An optimal
balance between the two ensures that the RFD is close enough to the updraft to deliver
vorticity-rich parcels, but not so close that updraft intensity is adversely affected.
It is important to note that this finding implies the vertical wind profile
throughout a large depth of the troposphere, not just the lowest few kilometers, is a
control on the formation of low-level mesocyclones.
d. Dynamic pipe effect
A theoretical means by which an atmospheric vortex in cyclostrophic balance
may build downward with time through the “suction” of vorticity-bearing air below was
proposed by Leslie (1971), who termed it the dynamic pipe effect (DPE). In this
situation, the pre-existing vortex acts much like a pipe, drawing up air from below
through the vertical perturbation pressure gradient force (VPPGF) associated with
rotationally-induced low pressure in the vortex. The horizontal convergence of inflow
air at the bottom of the vortex would amplify any existing vertical vorticity through
stretching, and if this effect were strong enough, downward propagation of the vortex
9
would occur. Once established, this process would continue at successively lower levels
until the vortex reached the ground.
While it might seem tempting to employ this explanation as the mechanism for
near-ground mesocyclogenesis following the establishment of mid-level rotation,
Davies-Jones et al. (2001) assert that mid-level mesocyclones are not in cyclostrophic
balance, and are thus not resistant to parcel displacements in the radial direction. The
consequence of this idea is that air may enter the mesocyclone through its sides,
precluding the formation of a vacuum at its base (or top). Recent observations from
mobile phased-array radars with high temporal data frequency have revealed further
weaknesses in the DPE hypothesis. French (2012) found that despite the appearance of
a descending TVS in five-minute WSR-88D radar data for the 5 June 2009 tornado in
Goshen Co., WY, there actually was none in mobile phased array data. Instead, high-
frequency velocity data revealed many short-lived mid-level TVS signatures which
might easily be mistaken for one continuous TVS (and therefore a descending vortex
with time) in the 88D data. As such, the DPE is unlikely to explain near-ground
mesocyclogenesis, and other sources of enhanced low-level vorticity (such as those
described in 3a-b) must be considered.
e. Frictional effects
Alongside baroclinic generation and tilting of environmental shear, another
possible source of vorticity for low-level mesocyclones is that generated by surface
friction. Although this factor has been remained somewhat unstudied relative to the
former two, some recent work is beginning to shed light on it. In the observational
realm, Markowski et al. (2012) examined vortex lines and material circuits derived from
10
dual-Doppler analyses of the 5 June 2009 tornadic supercell. When they were unable to
reconcile a calculated increase in circulation about a tornado-enclosing circuit with the
value expected from baroclinic generation, the possibility that surface friction
accounted for the discrepancy was raised.
Schenkman et al. (2012) demonstrated the critical importance of surface friction
in the development of a tornado-like vortex within a mesoscale convective system
(MCS). Specifically, the inclusion of friction in their simulations led to a horizontal
rotor and associated strong low-level updraft which enhanced vortex stretching.
Although the broader convective system which produced this vortex differs from a
classic supercell in some important respects, the authors note the presence a low-level
mesovortex which resembles a supercellular low-level mesocyclone in structure and
spatiotemporal scale. Thus, their work shows convincingly that surface friction can
strongly influence tornadogenesis in at least some circumstances. It must be
emphasized, however, that its role as a vorticity source was found to be secondary to
that of augmenting the low-level updraft and stretching existing vorticity.
3. Tornadogenesis
Following the establishment of a strong near-ground mesocyclone, locating the
source of vorticity for tornadogenesis becomes much easier. Bluestein (2007)
demonstrates through scale analysis that convergence of O(10-2
s-1
) acting upon a low-
level mesocyclone ~5 km in horizontal diameter could produce vorticity of tornado
strength, O(1 s-1
), on a timescale of 1000 s. Because the specified magnitude of
convergence is typical of values found beneath intense supercell updrafts, and the
specified timescale is consistent with that of tornadoes, it is easily seen that
11
convergence/stretching of mesocyclonic vertical vorticity alone can account for
tornadogenesis.
The Tornado Vortex Signature (TVS), first described by Brown et al. (1978), is
a radar signature indicative of strong azimuthal wind shear a few kilometers AGL and is
associated with many tornadoes. Trapp and Davies-Jones (1997) distinguished between
cases in which a TVS precedes tornadogenesis by at least 5 min. (mode I
tornadogenesis) and cases in which a TVS appears nearly simultaneously with
tornadogenesis (mode II). Mode I corresponds to a situation in which mid-level rotation
is initially stronger than near-ground rotation, possibly necessitating the DPE in order to
build the tornado vortex downwards to the ground. (Note that, unlike a mesocyclone,
the tornado vortex is in cyclostrophic balance and resists parcel motion in the radial
direction, so the DPE is plausible). Thus, in cases where low-level convergence beneath
the updraft is initially insufficient to instigate a tornado, the DPE may provide the extra
convergence needed to begin the process.
Interestingly, Trapp et al. (1999) examined the TVS character associated with 52
tornadoes and found roughly an equal number of descending and nondescending
signatures. This conflicts with the assumption that supercell tornadoes are usually of the
descending variety, since most tornadoes are supercellular; indeed, closer examination
of the sample set by the authors revealed various supercell tornado cases with
nondescending TVS behavior. This is a confirmation that the DPE is not always
necessary for tornadogenesis, and more generally, that supercell tornadoes may not
always build down from above. The idea that existing low-level convergence is
sufficient in some instances also has implications for the role of mesoscale boundaries
12
in tornadogenesis described in 3b: the role of enhanced convergence along such
boundaries must be carefully considered as an alternative or complement to their
baroclinic vorticity generation in explaining why tornadoes are frequently associated
with them.
13
Chapter 3: Methodology and Motivation
1. Model configuration
This study examines a set of numerical simulations conducted using the
Advanced Regional Prediction System (ARPS), a three-dimensional non-hydrostatic
model developed at the Center for Analysis and Prediction of Storms (Xue et al. 2000).
Version 5.2.12 of the ARPS package was used for model integration, and the message-
passing interface (MPI) system was employed by splitting the model domain into 1024
equally-sized horizontal patches, with one CPU core assigned to each patch (Johnson et
al. 1994).
A summary of the model configuration for these simulations is found in Table 1.
The horizontal resolution is uniform at 50 m; this is considered sufficient to resolve
tornadoes (albeit not their detailed internal structure), which distinguishes this study
from most work in the existing literature based upon the Del City sounding. The vertical
resolution varies with height from 20 m near the ground to 400 m at the top of the
domain (16 km AGL), and there are 83 vertical levels. Lateral boundary conditions are
radiation, while top and bottom boundary conditions are free-slip rigid wall. A Rayleigh
sponge layer is present from 12 km AGL upward in order to minimize the effects of
waves reflecting off the top of the domain.
All simulations herein are idealized, i.e., they are initialized in a horizontally-
homogeneous manner from a single sounding and otherwise do not assimilate any real
data, nor do they contain terrain at the model surface. The Coriolis force and surface
physics (including friction) are neglected. Deep moist convection is induced by
introducing a “bubble” with an initial positive perturbation in potential temperature of
14
magnitude 4 K. The bubble has a radius of 5x5x1.5 km, and within the 64x64x16 km
model domain, is centered at (x, y, z) = (46, 28, 1.5) km. This position was determined
through trial and error with the goal of keeping the entire storm of interest inside the
domain after several hours of integration.
Integration was allowed to proceed for 12600 s (3.5 h), with history files saved
every 60 s. For some experiments, a period of interest was identified for which higher
temporal resolution was desired, particularly for the purpose of trajectory analysis. In
these cases, a restart file written during the initial run was used to re-initialize the model
at or near the beginning of the period in question and write 3 s output. Due to the
relatively small model time step and use of MPI, the model solution during this
subsequent integration diverges from the original solution slightly with time, but the
results were found to be qualitatively similar even at tornado scale.
Parameter Value
Domain size 64x64x16 km
Grid size 1283x1283x83
Horizontal resolution, Δx 50 m
Vertical resolution, Δz 20 m ≤ Δz ≤ 400
m Large time step, Δt 0.25 s
Small time step, Δτ 0.08 s
Microphysics parameterization Lin ice
Turbulence parameterization 1.5-order TKE
Mixing coefficient, horiz. (4th
order) 20x10-4
s-1
Mixing coefficient, vert. (4th
order) 10x10-4
s-1
Table 1. ARPS model configuration (universal to all experiments).
15
2. Experiments
a. Control experiment
A control run (CTRL) was initialized using the same 20 May 1977 sounding
employed in numerous earlier supercell modeling studies, notably Klemp et al. (1981),
Adlerman et al. (1999) (hereafter A99), and Noda and Niino (2010) (hereafter NN10).
This sounding is a blend of observations from Ft. Sill and Elmore City, OK, during the
evening of a tornado event in central Oklahoma, and features a classic Great Plains
supercell environment with surface-based convective available potential energy
(SBCAPE) of approximately 4000 J kg-1
, effective storm-relative helicity (SRH) of 101
m2 s
-2, and a veering vertical wind profile which produces a hodograph shape
resembling a semicircle. Figure 1 presents this sounding graphically. The horizontal
resolution of 50 m is finer than any published study with this sounding to the author’s
knowledge, with the closest (and most recent) contender being NN10, who used Δx =
70 m. As with previous ARPS model studies, the sounding has been interpolated above
the surface to 500 m vertical resolution, with state variables defined between 250 m and
16250 m AGL. Note that upon model initialization the sounding data is then re-
interpolated to the grid itself, which is stretched in the vertical. The 20 May 1977
observed storm motion of (u,v) = (3,14) m s-1
is subtracted from the wind data
throughout the sounding. This results in a model domain that effectively follows the
storm motion without the need to handle explicitly a moving domain. As such, any
references to cardinal directions and speeds regarding motion hereafter must be
interpreted in a quasi-storm-relative, rather than ground-relative, framework.
16
The second major difference between CTRL and earlier, comparable work is the
microphysics treatment. Whereas A99 and NN10 both employed the Kessler warm rain
parameterization, this simulation (and indeed all others herein) instead uses Lin ice,
which is further detailed in the next subsection. Though this choice carries some
computational expense, the inclusion of a hail species in particular should improve the
accuracy of storm thermodynamics and cold pool evolution, an important factor for
tornadogenesis. For CTRL, rain and hail intercept parameter values are 8x10-4
m-4
and
4x10-4
m-4
, respectively. See Table 2 for a summary of the differences between all
experiments. Figure 2 provides a graphical description of the parameter space covered
by the experiments herein.
17
Figure 1. Sounding “may20” utilized for the control experiment (CTRL).
b. Microphysics experiments
The six-species bulk microphysics parameterization described in Lin et al.
(1983) (hereafter LFO83) was used for all experiments in this study. This scheme
predicts mixing ratio for rain, hail, snow, graupel, cloud water, and cloud ice. For each
species, the number concentration is given by
18
where the subscript x represents the species (e.g., rain, hail, etc.), D is the particle
diameter, n0 is the intercept parameter, and Λ is the slope parameter. Because the
LFO83 scheme in ARPS is single-moment, the intercept parameter n0x is specified as a
constant, and only the slope parameter is computed as a function of state variables.
Multi-moment schemes in which the intercept parameters vary spatiotemporally have
shown significant improvements in terms of thermodynamic realism in supercell
modeling studies (Dawson et al. 2009), but carry too high a computational cost at the
grid size employed herein to justify their inclusion in this study.
Among the six species treated in LFO83, parameterizations of rain and hail are
considered the most important for continental deep moist convection in the
midlatitudes. Numerous modeling studies, notably Gilmore et al. (2004), van den
Heever and Cotton (2004), and Snook and Xue (2008) (hereafter SX08), have
demonstrated a large sensitivity to rain and hail intercept parameters in numerical
simulations of such convection. Moreover, observational studies such as Waldvogel
(1974) and Sauvageot and Lacaux (1995) illustrate that these intercept values can vary
widely in nature, even within a storm. Hence, the choice of n0r and n0h for supercell
simulations is a nontrivial issue.
With this in mind, five experiments were performed alongside CTRL whose rain
and/or hail intercept parameters were varied. These experiments are labeled R86, R85,
R45, R45H43, and H43, and their respective settings are described in Table 2. The suite
of Lin ice microphysics experiments in this study follows the general methodology of
SX08, who also varied the rain and hail intercept parameters in idealized ARPS
simulations based on the 20 May 1977 sounding and explored the effects on
19
tornadogenesis. The primary differences here are that we use double the horizontal
resolution, and the rain and hail intercept parameter values tested in this study cover a
lower range of values for reasons explained below.
Note that CTRL does not use the default value for n0r specified in LFO83
(8x106 m
-4); instead, it uses a value two orders of magnitude lower than the default
(8x104 m
-4). Thus, the labels for the microphysics experiments should be interpreted
with caution, as CTRL was so labeled simply because its intercept parameter values
were re-used in all the shear experiments (described in the next subsection), as shown in
Figure 2. This is because the full set of microphysics experiments was conducted as the
first stage of this research; afterwards, the experiment with the strongest and most
persistent low-level mesocyclone was chosen as the control run upon which the shear
experiments would be based. Comparative plots of domain-wide minimum perturbation
pressure and maximum low-level vertical vorticity indicated the run with n0r = 8x104
mm-4
to be the strongest candidate, resulting in its CTRL designation.
Experiment R86 uses the default intercept parameter for all species as specified
in LFO83, and was the first simulation conducted in the present study. In SX08, this is
regarded as the control experiment, and yields one of the more pronounced tornadic
vortices within their parameter space. In the present 50 m study, the LFO83-specified
intercept values in R86 result in very cold and persistent low-level outflow from any
convective cells developing in the domain. Although focused low-level mesocyclones
are evident, they are rather brief and contained within air that is quite negatively-
buoyant. For this reason, the remaining parameter space was chosen to extend only
20
toward smaller intercept values from R86 with the goal of containing the “ideal” values
for tornadogenesis within.
c. Low-level shear experiments
The literature contains ample evidence linking low-level wind shear with
tornado potential in supercell environments. In the context of supercells, the low-level
shear is typically characterized by one of two means which are related but distinct. The
first uses the perspective of storm-relative helicity (SRH), which quantifies
environmental streamwise vorticity over a specified depth of the atmosphere. SRH,
which is a function of both the environmental shear and storm motion, has been a
popular tool to discriminate between tornadic and nontornadic storms over the past few
decades, and as such many studies have explored its utility in this regard, e.g.
Markowski et al. (1998). One practical issue with using SRH diagnostically, particularly
before a storm has even formed, is its strong sensitivity to storm motion, which may
vary widely in time and space (Weisman and Rotunno 2000). A second, and perhaps
currently less-popular, means to characterize low-level shear is simply its magnitude as
a vector difference per unit depth. The shear value itself does not incorporate the effects
of streamwise vorticity, which can be both an advantage (less spatiotemporally variable
and complex to calculate) and disadvantage (may fail to identify tornado likelihood
when or if environmental vorticity is an important source). Though the body of work
relating this quantity to tornadogenesis is comparatively smaller than that for SRH, a
few pertinent studies are addressed below.
Using a relatively low-resolution numerical simulation, Weisman and Klemp
(1982) (hereafter WK82) explored the relationship between vertical shear magnitude
21
and storm behavior for unidirectional westerly flow, finding a distinct maximum in low-
level vertical vorticity production at a 0-10 km vector wind difference of 25 m s-1
. Of
significance is that even higher shear values (35 m s-1
and 45 m s-1
) yielded drastically
less intense cyclonic vertical vorticity near the ground, despite stronger midlevel
cyclonic vorticity. Note that in the experiments of WK82, the wind speed was
proportional to the hyperbolic tangent of height AGL, placing most of the shear in the
lowest few kilometers. As such, their results can be interpreted primarily as describing a
“sweet spot” at which low-level wind shear maximizes low-level vorticity within
supercells.
Markowski et al. (2003) examined an extensive dataset of RUC model proximity
soundings for strongly-tornadic, weakly-tornadic and nontornadic supercells. They
explored both SRH and shear magnitude in relation to these categories, finding both to
be convincingly correlated with tornado likelihood and strength in the 0-1 km AGL
layer. They do note that “[n]o robust differences in hodograph curvature exist” among
these three categories, implying that the bulk shear’s contribution to SRH could
potentially be more important than the precise orientation of the shear. In the same vein,
Esterheld and Giuliano (2008) examined proximity soundings which revealed that in the
10-1000 m AGL layer, shear magnitude better discriminated between strongly- and
weakly-tornadic supercells than SRH.
Schumacher and Boustead (2011) (hereafter SB11) examined the 24 June 2003
tornado outbreak in Nebraska and South Dakota, and found in particular that an increase
in the magnitude of the 0-1 km AGL shear vector played a crucial role in the transition
from nontornadic or weakly tornadic supercells early in the event to strongly tornadic
22
supercells later. They emphasize that even when total shear through the storm-bearing
layer (0-6 km AGL) remained steady or decreased slightly, a redistribution of vertical
wind shear into the lowest kilometer proved quite favorable for significant tornadoes.
In order to shed further light on the role of low-level shear on supercell tornado
formation, five experiments were performed alongside CTRL whose initial
environments were characterized by kinematic modifications to the “may20” sounding
in the lowest 2 km AGL. These experiments (and their respective soundings) are labeled
IS1 (may20_lls2), IS2 (may20_lls3), IS3 (may20_lls4), DS1 (may20_lls5), and DS2
(may20_lls6). Figure 3 and Figure 4 display vertical profiles below 2 km AGL for the
u- and v-components of the horizontal wind, respectively, for these soundings. For
numerical values, reference Appendix A. Comparable vertical profiles for the supercell
cases of Markowski et al. (2003) discussed earlier in this subsection are presented in
Figure 5, though the plots extend upward to 12 km AGL and values are ground-relative
(rather than storm-relative).
The kinematic differences amongst these initial soundings are characterized by
varying vertical distributions of wind shear in the lowest 2 km of the model domain,
while preserving approximately the same hodograph shape. The surface wind vector is
held constant for all experiments. Experiments IS1, IS2 and IS3 feature additional wind
shear in the 0-1 km AGL layer, with a compensating decrease in the 1-2 km AGL layer.
Conversely, experiments DS1 and DS2 feature weaker wind shear in the 0-1 km AGL
layer, with a compensating increase in the 1-2 km AGL layer. All wind values are
identical between experiments at and above 1750 m AGL (note that some are identical
to one another at levels lower than 1750 m AGL; consult Figure 3 and Figure 4 for
23
details). To facilitate comparisons with the aforementioned work in the literature,
vertical shear magnitude in the 0-500 m AGL and 0-1000 m AGL layers was calculated
for each experiment and presented in Table 3.
Experiment Sounding n0r (m-4
) n0h (m-4
)
CTRL may20 8x104
4x104
R86 may20 8x106
4x104
R45 may20 4x105
4x104
R85 may20 8x105 4x10
4
R45H43 may20 4x105
4x103
H43 may20 8x104
4x103
IS1 may20_lls2 8x104
4x104
IS2 may20_lls3 8x104
4x104
IS3 may20_lls4 8x104
4x104
DS1 may20_lls5 8x104
4x104
DS2 may20_lls6 8x104
4x104
Table 2. Summary of soundings and intercept values for all experiments.
Figure 2. Graphical depiction of parameter space covered by all experiments.
24
Experiment 0-500 m AGL shear (s-1
) 0-1000 m AGL shear (s-1
)
CTRL 0.0026 0.0067
IS1 0.0032 0.0067
IS2 0.0040 0.0070
IS3 0.0057 0.0075
DS1 0.0018 0.0055
DS2 0.0010 0.0043
Table 3. Low-level vertical wind shear magnitudes for all shear experiments.
Figure 3. Zonal (u) wind component for the six initial soundings.
25
Figure 4. Meridional (v) wind component for the six initial soundings.
Figure 5. Average zonal (u) and meridional (v) wind components for strongly-tornadic
(solid), weakly-tornadic (dashed), and nontornadic (dotted) supercell environments as
derived from 413 RUC proximity soundings. Adapted from Markowski et al. (2003).
26
3. Definitions
a. Mesocyclone
Wicker and Wilhelmson (1995) (hereafter WW95) define a mesocyclone, at any
horizontal slice through a supercell thunderstorm, as the region within which vertical
vorticity exceeds 0.01 s-1
. Owing to the high horizontal resolution of simulations in our
study relative to earlier modeling-based work, however, this definition is somewhat
problematic in application. Through the life cycles of our modeled supercells, the
presence of noise and other small-scale features on the order of 100 m (2Δx) often
precludes the identification of contiguous regions inside the ζ = 0.01 s-1
contour which
are of a radius consistent with observed low-level mesocyclones (i.e., a few kilometers).
Even where the flow pattern features a circulation suggestive of a mesocyclone, the
embedded vertical vorticity distribution typically contains small patches of low (and
even negative) values. For this reason, the identification of mesocyclones hereafter is
somewhat qualitative, while attempting to conform to the spirit of the vorticity-based
definition.
b. Tornado
Identification of tornadoes within these simulations presents similar challenges
to those regarding mesocyclones. A wind speed threshold alone is of limited utility
because it fails to account for the presence of strong circulation and vorticity. A
vorticity threshold, while more pertinent, is impractical due to the high dependence of
derivative quantities (e.g., du/dx) upon grid spacing. Pressure deficit is a more attractive
and practical choice for setting a threshold, as it is predicted explicitly by the model and
27
not as sensitive to grid spacing. WW95 demonstrate that for a Rankine combined vortex
in cyclostrophic balance,
where Δp is the central pressure deficit, ρ is the air density, and Vt is the maximum
tangential wind speed. Clearly, the vortices which develop in our simulations will
neither be in perfect cyclostrophic balance nor contain uniform tangential winds at a
given radius. Nevertheless, this approximation is useful for choosing a threshold which
introduces an objective element into the tornado-identification process. WW95 set a
minimum surface wind speed threshold of 30 m s-1
; considering this value for Vt in the
equation and assuming ρ ~ 1 kg m-3
yields a pressure deficit of 9 hPa. Taking this into
consideration, the following criteria are used in order to classify a vortex as tornadic:
1) The maximum surface pressure deficit is at least 10 hPa.
2) The maximum embedded surface wind speed is at least 30 m s-1.
3) The radius of the vortex is less than 750 m.
4) The surface flow pattern is approximately circular.
Criterion 3 is supported by Bluestein (2007), an extensive literature review
which found a generally-accepted maximum tornado diameter of ~1.5-2 km. It must be
clarified that Criterion 4 references only the wind vector directions; there is no
expectation that the distribution of wind speeds will be axisymmetric. Criteria 3 and 4
introduce subjectivity due to the nebulous definitions of “radius” and “circular,”
respectively, but this is necessary in order to avoid classifying diffuse and/or
disorganized low-level mesocyclones (which might contain transient vortices with
substantial pressure drops) as tornadoes.
28
Chapter 4: Analysis of Control Simulation
1. Storm morphology
The initial thermal bubble initiates deep moist convection rapidly in CTRL, and
the domain-wide maximum reflectivity exceeds 30 dBZ by 600 s. This cell initially
translates rapidly to the northwest, influenced primarily by flow in the lowest few
kilometers owing to its shallow vertical extent. A convective storm with ground-level
reflectivity exceeding 60 dBZ is evident by 1800 s near the center of the domain (x = 32
km, y = 32 km).
As early as 3000 s, the initially-unicellular updraft appears to have split in the
manner described by Klemp and Wilhelmson (1978), with one cell to the west and
another to the east (Figure 6a,Figure 7a). While the eastern cell slows significantly
during the period 3000-4200 s, the western cell continues translating rapidly to the
west-northwest, eventually reaching the western boundary of the domain. The western
cell during this period is considered to be the left-moving split of the initial convective
storm, while the eastern cell is the right-moving split. The left split later weakens and
ultimately dissipates at the northwest corner of the model domain by 8000 s,
presumably owing in large part to its advection out of the domain. The right split is the
focus of the analysis hereafter, and will be labeled “Cell A.”
Cell A propagates westward to a position near (x = 24 km, y = 36 km) by 3600
s. At this time, supercellular characteristics are already evident, including a well-defined
FFD and RFD in the ground-level reflectivity field. The horizontal extent of the storm,
as defined by the 30 dBZ reflectivity contour at ground level, is approximately 30x16
km. A surge of relatively cold outflow at ground level emanates from the storm’s FFD
29
around 4500 s, and this outflow expands southward and westward away from the storm
over the next several minutes.
During the period 4800-5400 s, a new convective cell initiates near the
southwest corner of the domain, which will hereafter be called “Cell B.” Based upon a
movie of ground-level potential temperature and wind vectors (not shown), it appears
that outflow from early in Cell A’s life cycle was the source of low-level convergence
that instigated this development. Between 5400 s and 8000 s, Cell B remains nearly
stationary, with its precipitation core at ground-level centered near (x = 12 km, y = 20
km). Meanwhile, Cell A propagates south-southwestward, and its own precipitation
core eventually begins to merge with Storm B around 8400 s. Their respective mid-level
updrafts also merge around 9000-9600 s, coinciding with significant intensification of
the low-level mesocyclone originally associated with Cell A. This raises the possibility
that the storm merger played a role in tornadogenesis, perhaps by modulating the
strength and storm-relative position of the primary updraft. This issue is further
explored in the next subsection.
Prior to the storm merger, the Cell A exhibits well-defined supercell structure,
including a hook echo in the ground-level reflectivity field around 4800-5400 s (Figure
6b). Despite this precipitation configuration, the surface flow pattern is not indicative of
a well-formed ground-level mesocyclone; accordingly, positive surface vertical
vorticity is not present in noteworthy quantity or concentration at the hook. Above the
surface, the flow pattern at 1039 m AGL does suggest the presence of a mesocyclone,
and a concentrated region of vertical vorticity exceeding 0.01 s-1
exists at the tip of the
30
hook. Therefore, this first hook echo is associated with a low-level mesocyclone, but
one which does not reach the ground.
Figure 6. Perturbation potential temperature (shading; K) and 1 g kg-1
rainwater mixing
ratio contour at 10 m AGL for (a) 3000 s, (b) 4800 s, (c) 7200 s, and (d) 10200 s.
31
Figure 7. As in Fig. 5, but for vertical velocity (shading; m s-1
) at 4265 m AGL.
The initial hook echo becomes ill-defined by 6000 s as precipitation in the RFD
of Cell A expands in horizontal extent. During this period leading up to the storm
merger, positive values of low-level vertical vorticity are found in a broad zone along
the primary storm’s forward- flank and rear-flank gust front (FFGF and RFGF,
respectively). This period also marks a transition in the storm’s spatial configuration.
Initially, the RFD and FFD storm-relative locations approximately followed the
conceptual model of Lemon and Doswell (1979): to the west and northeast of the main
updraft, respectively. By 7200 s, however, the entire supercell appears rotated 45 to 90
degrees counterclockwise from the classic conceptual model: specifically, the FFGF
32
extends northward from its intersection with the RFGF, rather than northeastward or
eastward (Figure 6c). Indeed, the highest reflectivity marking the FFD core is located
northwest of the gust front intersection, rather than northeast. The strongly-meridional
environmental mid-level wind on the initial sounding likely helps to account for this, as
the entire (ground-relative) wind profile is somewhat more backed than the classic
southwest flow environment upon which conceptual models were built. This rotated
configuration persists for the remainder of the simulation.
Immediately after the storm merger and associated low-level mesocyclone
intensification of the 9300-9600 s period, a surge of cold air stronger than previous
episodes (surface potential temperature perturbations on the order of -12 to -15 K)
emanates from the RFD at ground-level and spreads quickly in the horizontal. This
rapidly occludes a much longer segment of the gust front, with deep-layer downdraft
concurrently overspreading the mesocyclone. By 10200 s, cold air at the surface covers
much of the southwest quadrant of the domain behind the RFGF, which surges well
southeast of the low-level mesocyclone (Figure 6d). Simultaneously, the mid-level
updraft appears less cellular, instead becoming elongated and bow-shaped
approximately above the length of the RFGF (Figure 7d). For the remainder of the
simulation, the mid-level updraft is relatively weak and cold air at the surface extends to
the southern boundary of the domain south of the storm, indicating it is no longer
containing its own outflow.
33
2. Low-level mesocyclone intensification and tornadogenesis
a. Evolution of model fields
In CTRL, a mid-level mesocyclone is detected as early as 1800 s, even before
the initial convective cell has split. Given effective-layer storm-relative helicity (SRH)
exceeding 100 m2 s
-2, this is expected, as updraft is correlated with positive vertical
vorticity in such an environment. As described by Davies-Jones et al. (2001), only
afterwards does a low-level mesocyclone develop. The first evidence of a low-level
mesocyclone appears around 4800 s, when a region of positive vertical vorticity at 1039
m AGL becomes concentrated near the tip of Cell A’s hook echo. This region of
vorticity persists in some form for the remainder of the period leading up to the storm
merger, but at times grows more diffuse and elongated along the gust front.
As the storm merger begins in earnest around 9000 s, numerous compact lobes
of > 0.1 s-1
vertical vorticity are present along Cell A’s FFGF and RFGF at the surface,
with several in close horizontal proximity to the gust front intersection (Figure 8a).
Over the 300 s that follow, lobes of vorticity continue to advect southward down the
FFGF and concentrate vorticity at the intersection with the RFGF; simultaneously, a
surge of relatively strong northwesterly flow develops in the RFD just to the northwest
of the gust front intersection. Plots of perturbation potential temperature reveal this
surge to be associated with air that is slightly warmer than the surrounding FFD and
RFD. Between 9300-9500 s, this surge begins to wrap cyclonically around the south
and east sides of the low-level mesocyclone. This forces the northernmost segment of
the RFGF to pivot northwestward, resulting in an occlusion on the north side of the
mesocyclone (Figure 8b).
34
Figure 8. Close-up (moving) view of low-level mesocyclone at 10 m AGL.
Perturbation potential temperature (shading; K) and 0.1 s-1
vertical vorticity contour
(orange solid) are plotted at (a) 9000 s, (b) 9420 s, (c) 9600 s, and (d) 9900 s. Gust
fronts are indicated by solid red (FFGF), dark blue (RFGF), and purple (occluded)
curves. Black “T” indicates tornado position.
Just to the southeast of the occlusion point, a tornado develops around 9480 s. A
24x24 km subdomain centered approximately on the tornado track was extracted from
the 64x64 km model domain, and all spatial references for the remainder of this section
pertain to this subdomain, denoted by xs and ys. (The subdomain is not a nested grid nor
does it contain finer-scale interpolation, and was produced simply to reduce the
computational demands of reading data for plots and trajectory calculations). The
tornado develops near (xs = 11.0 km, ys = 13.6 km) in the subdomain. This vortex
35
results from the merger of two pretornadic vortices which can be identified as early as
9180 s, or three minutes before tornadogenesis (Figure 9a). At this stage, low-level
updraft is present above the southern portion of the stronger pretornadic vortex (labeled
“PV1”), but the strongest updraft remains on the west side of the mesocyclone (Figure
9e). By 9480 s, the low-level updraft has become more cellular and the strongest portion
has advanced cyclonically to a position over the southern portion of the incipient
tornado (Figure 9f). The tornado initially has a horizontal radius of approximately 200
m and tightly-concentrated pressure drop at the surface at 9480 s (Figure 9b), but with
time evolves into a broader circulation with a radius around 400 m by 9600 s (Figure
9c). This evolution coincides with the RFGF continuing to surge outward from the low-
level mesocyclone, forcing its occlusion point with the FFGF farther to the north
(Figure 8c). By 9720 s, despite maintaining a surface pressure deficit exceeding 10 hPa,
the vortex is no longer considered tornadic due to its radius appearing to exceed 750 m
(Figure 9d). Low-level updraft over the southern half of the vortex has eroded, while
downdraft has expanded and strengthened over its northern half (Figure 9h). While
surface wind speeds at that time exceed 35 m s-1
at the radius of maximum winds, a
large circular zone (radius around 500 m) of winds less than 15 m s-1
exists at the vortex
center. Between 9600-9700 s, immediately prior to this expansion of the vortex into a
more diffuse and disorganized entity, a second, colder RFD surge appears to wrap
cyclonically around and into the surface circulation.
36
Figure 9. Zoomed (moving) view of the tornado in CTRL. (a-d) Horizontal wind speed
(shading; m s-1
) and perturbation pressure at 3 hPa increments below -3 hPa (contour),
at 10 m AGL. (e-h) Vertical velocity (shading; m s-1
) and p’ (contour; -5 hPa) at 1039 m
AGL. Pretornadic vortices are denoted by “PV1” and “PV2” in (a).
37
To compliment the horizontal plots, vertical cross-sections in the xz-plane are
presented in Figure 10. Note that the position and orientation of these slices are chosen
manually at each time to follow the vortex tilt with height. At 9180 s, three minutes
before the time at which we declare tornadogenesis to occur, the stronger of the two
pretornadic vortices appears formidable in its own right. A vertical slice from (xs = 8, ys
= 15) to (xs = 14, ys = 14.6) reveals the vortex (as defined by the 0.1 s-1
vertical
vorticity contour) to extend from the surface up to around 3 km AGL, with a 20-30° tilt
toward the west with height (Figure 10a). While vertical velocity inside the vortex is
small in magnitude, strong updraft exceeding 35 m s-1
is found in the mid-levels
immediately above. By 9360 s, however, an equivalent cross-section following the
vortex (not shown) shows that this vortex has weakened in the 1-3 km AGL layer; the
0.1 s-1
vertical vorticity contour only extends up to about 900 m AGL, though mid-level
updraft immediately above remains strong. Entering the tornadic stage at 9480 s, the
vortex regains a depth of nearly 3 km, while mid-level updraft immediately above has
weakened slightly (Figure 10b). Given the somewhat broken, patchy distribution of
vertical vorticity, it might be inferred that the tornado is comprised of multiple vortices.
However, close inspection of the horizontal wind field at grid scale confirms that the
circulation, while broad, is a single, continuous entity, with no embedded sub-vortices
apparent. Local vorticity maxima within owe largely to small shear zones, which could
hint at subvortices the 50 m horizontal grid spacing is unable to resolve explicitly.
Significant changes appear by 9600 s, when the tornado is best-organized and
exhibits the strongest surface pressure deficit. A vertical slice through from (xs = 9, ys =
10.3) to (xs = 15, ys = 15) shows the tornado contains deep, strong downdraft driven by
38
its own downward-directed perturbation pressure gradient force, signaling its imminent
demise (Figure 10c). Indeed, by 9720 s, a vertical slice reveals this downdraft has
further strengthened and that the original vortex has weakened substantially near the
surface (Figure 10d). A strong low-level mesocyclone exists through the 1-3 km AGL
layer, but it contains significant downdraft which is likely contributing to the
divergence and less-organized structure at the surface.
Some degree of central downdraft is observed throughout the tornado’s life
cycle, and there exists a core of relatively weak tangential flow which expands radially
outward with time until the vortex can no longer be considered tornadic. It is speculated
that the lack of surface friction in the simulation may be a primary driver of this
structure. Trapp (2000) observed similar structure when simulating a vortex using a
free-slip lower boundary condition, labeling it a “two-celled vortex." In such a vortex,
friction is not allowed to disrupt cyclostrophic balance near the surface, and low-level
updraft is confined to just outside the vortex core. A schematic is presented in Figure
11, revealing a vertical velocity distribution analogous to that seen in Figure 10 (in
particular, Figure 10c). Thus, the vortex in CTRL from 9480-9720 s is considered a
two-celled vortex. Observations indicate this configuration is typically seen late in the
life cycles of some tornadoes, after vortex breakdown has occurred (Trapp 2000). In
CTRL, however, no such breakdown occurs. Observations of two-celled tornadoes in
nature do exist (Lee and Wurman 2005), but appear somewhat rare. An issue to explore
in future work is why such structure is seen here, while some other free-slip simulations
using the 20 May 1977 sounding (e.g., NN10) produce central updraft until late in the
tornado life cycle.
39
Figure 10. Vertical cross-section through (a) pretornadic vortex PV1 at 9180 s, and (b-
d) the tornado at 9480, 9600, and 9720 s. Vertical velocity (shading; m s-1
) is shown,
along with positive vertical vorticity contours (s-1
) at 0.1 s-1
intervals starting at 0.1 s-1
.
The horizontal endpoints of each slice are indicated as (xs, ys).
Figure 11. Conceptual model of a two-cell vortex associated with subcritical flow.
Adapted from Trapp (2000).
40
Time-height cross sections are presented for subdomain-wide maximum vertical
vorticity (Figure 12a) and maximum updraft (Figure 12b). In light of the analyses
performed via instantaneous cross sections above, it is immediately apparent that
caution must be exercised when interpreting these time-height plots for a couple
reasons. First, the presence of two distinct supercells (Cell A and Cell B) in close
proximity complicates interpretation of domain-wide maximum and minimum values,
potentially masking important trends in one storm or the other. (Furthermore, choosing
separate subdomains for each cell over which to compute extrema is impractical, since
they merge with time). This may explain why any individual updraft pulses and
vorticity maxima prior to the merger at 9000 s appear fairly nondescript in the extrema
plots. Second, the strongest low-level vertical vorticity in the simulation occurs from
9960-10200 s, but horizontal cross-sections reveal this maximum owes to transient,
shallow vortices along the FFGF; these might be considered strong gustnadoes. The
more sustained tornado we follow between 9480-9720 s is coincident with another,
weaker maximum in vertical vorticity below 1 km AGL, as well as a period of relatively
strong low-level updraft exceeding 30 m s-1
. One notable difference between Figure 12
and comparable plots in NN10 and others is the relatively abrupt appearance of the
primary pressure drop over a deep layer around 9100 s. Whereas earlier studies
examining prototypical supercell evolution found a mid-level mesolow which expanded
vertically with time (over tens of minutes) to support tornadogenesis, the low-level
updraft and deep-layer perturbation pressure minimum here appear quite suddenly, only
a few minutes before tornadogenesis. It appears the merger of updraft associated with
Cell A and Cell B around this time aided in this abrupt transition.
41
Figure 12. Time-height cross-section of (a) maximum vertical velocity, (b) maximum
vertical vorticity, and (c) minimum perturbation pressure over the model domain from
7200-12600 s.
42
The precise means by which the storm merger enhanced low-level
mesocyclogenesis and ultimately led to tornadogenesis will require further work in the
future, although both time-height and instantaneous horizontal cross sections clearly
reveal low-level updraft intensification coincident with the merger. Lee et al. (2006)
documented a significant temporal association between storm mergers and tornado
incidence during an Illinois outbreak in 1996, speculating that perhaps outflow
boundaries separating air with relatively small differences in θe (which were observed in
their case) could provide constructive interference to a mature supercell. In this study,
however, the younger storm (Cell B) does not appear to feature a well-formed, distinct
gust front antecedent to the merger with which the more mature storm (Cell A) could
interact. Wurman et al. (2007) also observed repeated tornadogenesis during mergers in
a 1997 supercell episode in Oklahoma, hypothesizing a corresponding increase in low-
level convergence and updraft to be the causal factor; the results modeled in this study
would support this idea.
b. Trajectory analysis
To investigate the spatial origins of air parcels entering the low-level
mesocyclone and tornado, backward time-dependent parcel trajectories were calculated.
The model was re-run to obtain 3 s data within the time period of interest (9000-10200
s), and several initial times were selected from which to integrate backward trajectories.
For each initial time chosen, 20 trajectories were initialized along a ring centered within
the low-level mesocyclone (or tornado, if it was present at the initial time), along with
one trajectory initialized at the center of that ring. The ring radius was 200 m, and initial
parcel heights were 50 m. Backward calculations were carried out in time to 480 s prior
43
to initialization using Heun’s method and trilinear spatial interpolation between grid
points; see Appendix B for a complete description of the trajectory calculation
procedure. These calculations utilized wind data dumped every 3 s from the model with
no temporal interpolation. Some implications of this choice are discussed in Chapter 7.
Figure 13a illustrates 21 representative parcels entering the tornado at 9480 s,
near the time of tornadogenesis. All but one of these parcels originates from the
northwest of the tornado in the FFD region; the lone exception appears to be a parcel
which followed the stronger pretornadic vortex for several minutes prior. At 8 min prior
to initialization, there is a substantial range of original parcel heights in the FFD.
Several parcels originate from above 1000 m AGL, while others move primarily in the
horizontal near the ground. Most parcels in the latter group exhibit spiraling paths in the
horizontal as they approach the tornado which suggest they may have entered the
pretornadic vortex a minute or two prior; by contrast, the only parcels with a relatively
straight path into the tornado at 9480 s originated from above 1000 m AGL. Thus, it is
hypothesized that the wide disparity in original heights owes significantly to a
corresponding disparity in the time at which parcels entered the vortex, and that
ultimately most parcels participating in the tornado descended in the FFD at some time
prior. The typical parcel path can then be described as first descending in the FFD, then
moving southeast below 100 m AGL through the RFD region and ultimately into the
tornado from the south and west.
44
Figure 13. Parcel trajectories initialized in the vortex at (a) 9480 s, (b) 9600 s, and (c)
9780 s; and in the low-level mesocyclone center at (d) 10080 s. Parcels were initialized
at 50 m AGL and integrated backward in time for 480 s. Parcel height is indicated by
color, providing a pseudo-3D visualization.
Figure 13b shows parcels within the tornado at 9600 s, around the time of its
peak strength. A few notable changes are evident. First, a relatively high proportion of
the parcels appear to have followed the tornado over the preceding minutes, rather than
entering it at this time. Additionally, there are now two parcels with “inflow
trajectories” from the east of the vortex, where none existed at 9480 s. In an intensive
study of trajectory calculation methodology in the context of supercell mesocyclones
and tornadoes, Dahl et al. (2012) found that such trajectories often result from artifacts
of the backward-integration methodology, and are not present when more-accurate,
45
equivalent forward trajectories are calculated using the model time step. For this reason,
the validity of these parcel trajectories is called into question and they will be
discounted. Among the remaining parcels, the group originating above 500 m AGL
appears now to descend from west of the vortex in the RFD, rather than northwest in the
FFD, as was seen at 9480 s. This trend continues at 9780 s (Figure 13c), at which time
the vortex has become diffuse and nontornadic. Thus, over the lifespan of the tornado,
the area of origin for descending participating parcels moves cyclonically around the
low-level mesocyclone, from northwest to west-southwest of the tornado. As illustrated
in Figure 13d, parcels entering the broad, divergent low-level mesocyclone at 10080 s
descend sharply from nearly overhead, as strong downdraft has now overtaken the
entire low-level mesocyclone.
To clarify the reason for the cyclonic wrapping of the parcel-origin region, plots
of vertical pressure gradient force (not shown) were inspected, and did not reveal
significant dynamic forcing for descent in the parcel-origin areas. However, a maximum
in the reflectivity field at 1 km AGL was observed to wrap cyclonically around the low-
level updraft between 9000-9600 s, coinciding with the evolution of parcel origin
(Figure 14). Horizonta
