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    (a) Thermodynamic profile and (b) hodograph used for the simulations, created using the method of Weisman and Klemp (1982). In (a), the gray line represents the dewpoint profile (°C), whereas the black line represents the temperature profile (°C). The dashed line indicates the ascending surface-based parcel trajectory. Wind barbs are in knots.

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    Simulated reflectivity (shaded, dBZ) overlaid with horizontal velocity (every eighth vector shown, m s−1, scale at bottom left) at 50 m AGL for 8700 s into the control simulation. Arrows indicate the location of the main boundaries associated with the supercell.

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    Convergence values (shaded, s−1) with horizontal velocity (vectors, m s−1, scale at bottom left) and simulated reflectivity (contoured at 20, 30, 40, 50, and 60 dBZ) at 50 m AGL for 8700 s into the simulation.

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    (a) Equivalent potential temperature (colored, K) with horizontal velocity (every tenth vector shown, m s−1, scale at bottom left) and simulated reflectivity (contoured at 20, 30, 40, 50, and 60 dBZ) at 50 m AGL for 8700 s into the simulation, and (b) density potential temperature perturbation (colored, K) overlaid with 15-min backward trajectories from either side of the northeastward-directed boundary at 8700 s and 50 m AGL. Green parcel paths indicate consistent heights of 50–100 m AGL. The white box in (a) indicates the domain of (b).

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    Perturbation density potential temperature (colored, K) with LFCB and FFCB boundaries outlined in black at 50 m AGL for 6300 s into the simulation, and 30-min backward trajectories terminating on either side of the LFCB. Colors along the trajectories depict height, with black, green, blue, red, yellow, light blue and magenta signifying higher heights, respectively, from the surface up to >400 m AGL (legend inset at bottom right). Refer to section 3b for a description of the dashed line.

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    Perturbation density potential temperature (shaded, K) with horizontal wind (every seventh vector shown, m s−1, scale at bottom left) and simulated reflectivity (contoured at 20, 30, 40, 50, and 60 dBZ) at 8700 s for 50 m AGL.

  • View in gallery

    Perturbation pressure (colored, Pa), with horizontal wind vectors (every seventh vector shown, m s−1, scale at bottom left), and simulated reflectivity (contoured at 20, 30, 40, 50, and 60 dBZ) at 8700 s for 50 m AGL.

  • View in gallery

    Steady-state conceptual model of the low-level boundaries and flow in the simulated supercell. The thick solid line represents the radar reflectivity boundary, whereas the relatively thinner lines represent the boundary locations and strength of convergence, with thicker lines representing stronger convergence. Dashed lines represent the areas where the boundaries become weak and begin to dissipate. Arrows show typical streamlines.

  • View in gallery

    Positive convergence (shaded, s−1) with simulated reflectivity (contoured at 20, 30, 40, 50, and 60 dBZ) and horizontal wind (vectors, m s−1, scale at bottom left) at (a) 8700 and (b) 5700 s for 50 m AGL for rain intercept values (a) 8.0 × 105 and (b) 8.0 × 107 m−4.

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    Convergence (colored, s−1) with simulated reflectivity (contoured at 20, 30, 40, 50, and 60 dBZ) and horizontal wind (every eighth vector shown, m s−1, scale at bottom left) at 3900 s for 50 m AGL.

  • View in gallery

    Liquid water mixing ratio tendency/evaporation rate (shaded, kg kg−1 s−1) with simulated reflectivity (contoured at 20, 30, 40, 50, and 60 dBZ) and horizontal wind vectors (every eighth vector shown, m s−1, scale at bottom left) at 5700 s for 1000 m AGL.

  • View in gallery

    Convergence (colored, s−1) with simulated reflectivity (contoured at 20, 30, 40, 50, and 60 dBZ) and horizontal wind vectors (every eighth vector shown, m s−1, scale at bottom left) at 5700 s for 50 m AGL. Arrows point to the four LFCBs present at this time and to the developing FFCB.

  • View in gallery

    Perturbation density potential temperature (colored, K) with simulated reflectivity (contoured at 20, 30, 40, 50, and 60 dBZ) and 10-min backward trajectories ending at 50 m AGL at 4200 s on either side of transient LFCBs. The solid black line indicates the main LFCB position, whereas dashed lines indicate developing LFCBs.

  • View in gallery

    Conceptual model of the evolution of low-level boundaries within the simulated supercell. The thick solid line represents the radar reflectivity boundary, whereas the other lines represent the RFGF (thick line), the LFCBs (evolving boundaries associated with the counterclockwise arrow), and the FFCB (thinnest line). Dashed segments indicate weak, developing, or dissipating portions of the boundaries.

  • View in gallery

    Averaged vertical vorticity (s−1, colored) time–height plot for the control simulation and for the area directly encompassing the low-level mesocyclone from the surface to 6 km AGL and from 3600 to 10 800 s. The black line indicates the time at which ancillary outflow affects the analyzed storm, after which vorticity analysis is stopped.

  • View in gallery

    Horizontal vorticity (vectors), absolute magnitude shaded (s−1, scale at bottom left), and simulated reflectivity (contoured at 20, 30, 40, 50, and 60 dBZ) for 8700 s at 150 m AGL within the region of the low-level vertical vorticity maximum.

  • View in gallery

    (a) Solenoidal generation of horizontal vorticity (colored, s−2) with simulated reflectivity contours (at 20, 30, 40, 50, and 60 dBZ), horizontal solenoidal tendency (vectors, s−2, scale at bottom left), and 15-min backward trajectories preceding 8700 s. Termination points of the trajectories are bordered by two white boxes. Selected times are indicated with arrows for trajectories 8 and 13. (b) Zoomed in on region of the low-level mesocyclone. Trajectories 8 and 13 are displayed.

  • View in gallery

    All for trajectory 8 ending at 8700 s: (top left) x component of horizontal vorticity (s−1), (top right) y component of horizontal vorticity (s−1), (bottom right) y components of horizontal vorticity tendency terms (s−2), and (bottom left) x components of horizontal vorticity tendency terms (s−2).

  • View in gallery

    All for trajectory 13 at time 8700 s: (top left) x component of horizontal vorticity (s−1), (top right) y component of horizontal vorticity (s−1), (bottom right) y components of horizontal vorticity tendency terms (s−2), and (bottom left) x components of horizontal vorticity tendency terms (s−2). Note scale of x and y components of horizontal vorticity tendency: 10−4 and 10−5, respectively.

  • View in gallery

    (top left) Vertical vorticity (s−1) and (top right) vertical vorticity tendency terms (s−2) for trajectory 8 ending at 8700 s, (bottom right) vertical vorticity (s−1) and (bottom left) vertical vorticity tendency (s−2) terms for trajectory 13 ending at 8700 s. Note scales on images [(bottom left) 10−3; (bottom right) 10−5].

  • View in gallery

    Streamwise horizontal vorticity (dashed, s−1) and total horizontal vorticity (solid, s−1) along both trajectories (left) 8 and (right) 13 ending at 8700 s.

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An Assessment of Low-Level Baroclinity and Vorticity within a Simulated Supercell

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  • 1 Centre National de Recherches Météorologiques, Météo-France, Toulouse, France
  • | 2 Atmospheric Science Group, Texas Tech University, Lubbock, Texas
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Abstract

Idealized supercell modeling has provided a wealth of information regarding the evolution and dynamics within supercell thunderstorms. However, discrepancies in conceptual models exist, including uncertainty regarding the existence, placement, and forcing of low-level boundaries in these storms, as well as their importance in low-level vorticity development. This study offers analysis of the origins of low-level boundaries and vertical vorticity within the low-level mesocyclone of a simulated supercell. Low-level boundary location shares similarities with previous modeling studies; however, the development and evolution of these boundaries differ from previous conceptual models. The rear-flank gust front develops first, whereas the formation of a boundary extending north of the mesocyclone undergoes numerous iterations caused by competing outflow and inflow before a steady-state boundary is produced. A third boundary extending northeast of the mesocyclone is produced through evaporative cooling of inflow air and develops last. Conceptual models for the simulation were created to demonstrate the evolution and structure of the low-level boundaries. Only the rear-flank gust front may be classified as a “gust front,” defined as having a strong wind shift, delineation between inflow and outflow air, and a strong pressure gradient across the boundary. Trajectory analyses show that parcels traversing the boundary north of the mesocyclone and the rear-flank gust front play a strong role in the development of vertical vorticity existing within the low-level mesocyclone. In addition, baroclinity near the rear-flank downdraft proves to be key in producing horizontal vorticity that is eventually tilted, providing a majority of the positive vertical vorticity within the low-level mesocyclone.

Corresponding author address: Jeffrey R. Beck, Centre National de Recherches Météorologiques, Météo-France, DT/AD/RH, 42 Avenue G. Coriolis, 31057 Toulouse CEDEX 1, France. E-mail: jeff.beck@meteo.fr

Abstract

Idealized supercell modeling has provided a wealth of information regarding the evolution and dynamics within supercell thunderstorms. However, discrepancies in conceptual models exist, including uncertainty regarding the existence, placement, and forcing of low-level boundaries in these storms, as well as their importance in low-level vorticity development. This study offers analysis of the origins of low-level boundaries and vertical vorticity within the low-level mesocyclone of a simulated supercell. Low-level boundary location shares similarities with previous modeling studies; however, the development and evolution of these boundaries differ from previous conceptual models. The rear-flank gust front develops first, whereas the formation of a boundary extending north of the mesocyclone undergoes numerous iterations caused by competing outflow and inflow before a steady-state boundary is produced. A third boundary extending northeast of the mesocyclone is produced through evaporative cooling of inflow air and develops last. Conceptual models for the simulation were created to demonstrate the evolution and structure of the low-level boundaries. Only the rear-flank gust front may be classified as a “gust front,” defined as having a strong wind shift, delineation between inflow and outflow air, and a strong pressure gradient across the boundary. Trajectory analyses show that parcels traversing the boundary north of the mesocyclone and the rear-flank gust front play a strong role in the development of vertical vorticity existing within the low-level mesocyclone. In addition, baroclinity near the rear-flank downdraft proves to be key in producing horizontal vorticity that is eventually tilted, providing a majority of the positive vertical vorticity within the low-level mesocyclone.

Corresponding author address: Jeffrey R. Beck, Centre National de Recherches Météorologiques, Météo-France, DT/AD/RH, 42 Avenue G. Coriolis, 31057 Toulouse CEDEX 1, France. E-mail: jeff.beck@meteo.fr

1. Introduction

Conceptual models of supercell thunderstorm structure were developed in the late 1970s (Brandes 1978; Lemon and Doswell 1979) and have remained relatively unchanged. While these conceptual models have generally been accepted, verification of boundaries and air masses through in situ measurements has been limited because of the difficulty and potential hazards of recording direct measurements within the storm itself (Shabbott and Markowski 2006). Specifically, measurements of low-level thermodynamics have been lacking, particularly within the downshear region of the storm. Therefore, the necessity exists for more research of low-level dynamics to assess the development and impact of vorticity generated in different parts of the storm.

One of the pioneering modeling studies documenting the dynamics of a supercell in detail (with 1-km horizontal grid spacing) was performed by Klemp et al. (1981). The simulation contained features and structure that compared well with observations. The ability to replicate an observed supercell through model simulation solely via a proximity sounding led Klemp et al. (1981) to suggest that the larger-scale environment plays an important role in the structure and dynamics of these storms. Using similar modeling methods, Klemp and Rotunno (1983) discovered a mechanism through which low-level vertical vorticity is strengthened and subsequently repositioned around the simulated low-level mesocyclone. Analysis revealed that low-level air northeast of the mesocyclone flowed parallel to the “cold frontal boundary” as it moved toward the low-level mesocyclone. This boundary was identified by the −1°C perturbation isotherm; therefore, a quantifiable amount of solenoidally produced horizontal vorticity was present in this region of the simulation. A parcel traversing this boundary acquires significant (mesocyclonic) values of horizontal vorticity in a short period of time (e.g., ~300 s). Klemp and Rotunno (1983) found that this horizontal vorticity, with a magnitude comparable to that within the environmental inflow, is subsequently tilted within the gradient of vertical velocity near the mesocyclone, thus enhancing low-level vertical vorticity. Rotunno and Klemp (1985) found a buoyancy gradient associated with this cold-air boundary, concluding that it is important to the solenoidal generation of horizontal vorticity.

Wicker and Wilhelmson (1995) found two separate origins for parcels with trajectories terminating in the mesocyclone: one northeast of the mesocyclone, with the other aloft, northwest of the mesocyclone, near the forward-flank gust front (defined by the authors as the −1-K potential temperature isotherm) extending north from the center of rotation. Parcels originating from the northeast were found to contribute most significantly to the vertical vorticity budget of the low-level mesocyclone. These parcels then traverse a portion of the cold-air boundary immediately north of the mesocyclone, acquiring baroclinically produced horizontal vorticity.

An earlier paper by Davies-Jones and Brooks (1993) found that the method in which the baroclinity associated along the cold-air boundary is tilted ultimately proved fundamental in the production of positive vertical vorticity near the ground. Specifically, in the presence of a rear-flank downdraft, solenoidal generation of horizontal vorticity would allow the vorticity vector within the downdraft to depart from trajectory paths, resulting in a positive component of vertical vorticity as the parcel reaches the surface within the downdraft. In this sense, the authors’ findings, concerning the importance of baroclinity along the boundary north of the mesocyclone, mirror those found by Rotunno and Klemp (1985) and Wicker and Wilhelmson (1995). These results are corroborated by Adlerman et al. (1999), who found parcels entering the mesocyclone originate from regions northwest, north, and northeast of the mesocyclone and experience positive vertical vorticity tendency upon descent in the rear-flank downdraft (RFD).

Established observational conceptual models, along with past numerical supercell simulations, have not always agreed on low-level baroclinity/boundary strength and position, specifically within the forward flank. In addition, a spectrum of supercell types exists (Beatty et al. 2008), depending upon many variables, including vertical wind shear, hodograph shape, and sounding profile. The many different environments in which supercells form most certainly change the low-level evolution and boundaries within these storms. Moreover, recent observational studies using Doppler-on-Wheels (DOW) and Shared Mobile Atmospheric Research and Teaching Radar (SMART-R) data (e.g., French et al. 2004; Beck et al. 2006; Wurman et al. 2007a,b) have shown variability in low-level boundary strength within the forward flank of observed storms [many showing the absence of a forward-flank gust front (FFGF) in the convergence field]. While these studies lacked thermodynamic data, project Verification of the Origins of Rotation in Tornadoes Experiment (VORTEX) collected mobile mesonet measurements within a number of supercells. Using the data collected during this project, Markowski et al. (2002) documented the virtual potential temperature perturbations and equivalent potential temperature values around hook echoes and the near-mesocyclonic region of supercells. Both tornadic and nontornadic storms were sampled, with evidence of a gradual east-to-west increase in the virtual potential temperature deficit north of each mesocyclone. The conceptual model presented at the conclusion of the study showed a north–south boundary extending out of the low-level vertical vorticity maximum, separate from the rear-flank gust front (RFGF), very similar to Brandes (1978). These results mirror those found in Markowski et al. (2011), where again a north–south-oriented boundary was found to exist separate from the RFGF in a number of nontornadic supercell thunderstorms. Finally, Shabbott and Markowski (2006) studied similar mobile mesonet-collected thermodynamic properties from the forward flank of supercells. A gradual east-to-west increase in density potential temperature deficit was found to exist in many of the storms, but no sharp thermodynamic or kinematic boundary was found. Therefore, given the discrepancies in forward-flank characteristics and implied low-level dynamics between many of these studies, it is important to focus additional research to determine how this region of the storm impacts the development of the low-level mesocyclone.

A common thread throughout these research papers is a lack of a mutual definition for a baroclinic boundary within a supercell. Terms such as cold-frontal or cold-air boundary, in addition to gust front, are used, sometimes defined using values of perturbation potential temperature, or in other cases, the convergence of the wind field. However, general consensus is now to use the term “gust front” as the primary description of a baroclinic boundary within a supercell thunderstorm. Per the Glossary of Meteorology (Glickman 2000), a gust front is defined as having a strong wind shift, with delineation between inflow and outflow air, and a strong pressure gradient across the boundary. Furthermore, outflow air is defined to specify an advancing cold pool with relatively higher pressure than the air it is displacing, and is therefore linked to the definition of a gust front within a supercell thunderstorm.

In this study, a simulated supercell is generated to analyze the low-level evolution and dynamics as the storm evolves. A conceptual model of the simulated supercell is defined to describe each low-level feature or boundary found within the storm. This conceptual model shows three types of low-level boundaries associated with the simulated thunderstorm, with each boundary produced via different means. Trajectory analyses are conducted to assess the importance of horizontal vorticity along these boundaries and any impact on vertical vorticity development. Baroclinity along these boundaries is shown to be of importance to the development of the horizontal (and, ultimately, vertical) vorticity, so long as parcels parallel these boundaries for a sufficient amount of time, typically near the end of trajectories terminating in the low-level mesocyclone. Findings from this research show that a consensus is needed when defining baroclinic boundaries within the low levels of supercells. In addition, differences between the conceptual models of this simulated storm and previous research indicate a potential spectrum of boundary position, evolution, and dynamics.

2. Methodology

a. Simulation description

An idealized supercell simulation was created using the Weather Research and Forecasting (WRF) model. A base state sounding was developed (Fig. 1a) using analytical equations of potential temperature and relative humidity, as detailed by Weisman and Klemp (1982). An L-shaped hodograph was chosen (Fig. 1b) as the wind profile for this study. Storm motion was calculated from Bunkers et al. (2000) and was subtracted uniformly from the initial hodograph to obtain a stationary storm (Fig. 1b), making all variables storm relative.

Fig. 1.
Fig. 1.

(a) Thermodynamic profile and (b) hodograph used for the simulations, created using the method of Weisman and Klemp (1982). In (a), the gray line represents the dewpoint profile (°C), whereas the black line represents the temperature profile (°C). The dashed line indicates the ascending surface-based parcel trajectory. Wind barbs are in knots.

Citation: Monthly Weather Review 141, 2; 10.1175/MWR-D-11-00115.1

In the horizontal, 501 grid points exist in both the x and y direction, with 250-m grid spacing, creating a horizontal domain of 125 km × 125 km. In the vertical, 51 levels exist, beginning near the surface at 50 m AGL, extending to 17 km AGL. Because of the Arakawa C-grid employed by the WRF model, vertical velocity values a half grid point below and above each vertical level are averaged, along with horizontal wind components at the sides of the grid to arrive at the values of u, υ, and w at the center of the grid. The vertical grid is explicitly defined, beginning at 50-m spacing and terminating at 150-m spacing at the top of the domain. Owing to stretching of grid points in the vertical, 20 vertical levels exist below 2 km, allowing for high resolution in the boundary layer. An importance is placed on this region, specifically for sufficient depiction of cold pool dynamics, in relation to low-level boundary structure, development, and evolution.

The simulation is run for 3 h to include the full evolution of the storm. Data are saved every 5 min for the first hour, after which, data are archived every 60 s for improved tendency calculations and trajectories. The WRF single-moment 6-class (WSM6) scheme is chosen for the microphysics parameterization, with five classes of hydrometeors: rain, snow, cloud ice, cloud water, and graupel. The varying impact of microphysical schemes on the strength of the supercell cold pool has been well documented (e.g., Gilmore et al. 2004; Dawson et al. 2010). Acknowledging that the use of different microphysics schemes could change the strength of the cold pool sufficiently to alter the low-level dynamics discussed in forthcoming sections, sensitivity to the WSM6 scheme was investigated in this study through alterations to the drop size distribution for rain—the hydrometeor of interest in the region studied within the storm. While these sensitivity simulations produced different cold-pool strengths, the overall evolution of low-level features remained very similar (further discussed in section 3a). The domain utilizes open lateral boundary conditions with rigid upper and lower boundaries. Rayleigh damping is employed near the top of the domain to help control vertical reflection; divergence damping is used to control sound waves. For subgrid-scale turbulent mixing, a three-dimensional 1.5-order turbulent–kinetic mixing closure scheme is used. No Coriolis forcing, surface fluxes, surface friction, or radiation are included in the simulation. The initial convective thermal perturbation of 5 K has a horizontal radius of 10 km, vertical radius of 500 m, and is centered at 1 km AGL. A summary of the model characteristics can be found in Table 1.

Table 1.

WRF model simulation specifications.

Table 1.

b. Calculation of variables, tendency equations, and trajectories

The u, υ, and w components of the wind, temperature, mixing ratio of all hydrometeor species, evaporation tendency, potential temperature, and total pressure are all variables output by the WRF model. However, postprocessing is necessary for other variables. Specifically, horizontal gradients and vertical advection of theta are calculated in a Cartesian framework based on the calculated x, y, and z positions of the grid points within the domain. Furthermore, the density potential temperature is computed using contributions from the mixing ratios of water vapor, rain, and graupel. However, it should be noted that graupel only exists (and therefore impacts the density potential temperature) at levels above 2 km AGL in the analyzed forward-flank region of the storm. The density potential temperature perturbation is computed by subtracting the initial uniform density potential temperature field from the time-specific density potential temperature. Equivalent potential temperature is also calculated (Bolton 1980) and is a psuedoadiabatically conserved quantity allowing for retrieval of the approximate origin height of air parcels (Markowski 2002). Vorticity and vorticity tendency (both vertical and horizontal) are computed as well (Bluestein 1992). The equations for the x and y components of horizontal vorticity tendency are (respectively):
e1
and
e2
where ζx and ζy are horizontal vorticity in the x and y directions (respectively), ζ is the vertical vorticity, f is the Coriolis parameter, α is inverse density, and Fx and Fy are the forces of friction in the x and y directions (respectively). However, surface friction is not included in the analysis. Finally, to better compare simulated storms to observational research, a simulated reflectivity field was generated, calculated using the formula outlined by Smith et al. (1975). This formulation includes the contribution from both rain and graupel.
The thermodynamic tendency equation (e.g., Bluestein 1993) is used as the basis for calculations of air mass origin, comparison, and transport, and is defined as
e3
where ω is vertical velocity, Cp is the specific heat of air at constant pressure, and dQ/dt is the rate of heat transfer. Over small vertical and horizontal distances (hundreds of meters), where pressure and height surfaces are relatively parallel, it is possible to rewrite this equation in terms of height in a finite difference framework:
e4
Density potential temperature, rather than potential temperature, tendency is used in the context of this research. A scale analysis of the density potential temperature tendency equation was conducted, indicating that terms involving absolute values and time tendencies of hydrometeor species and water vapor were negligible in comparison to that of potential temperature. Therefore, it can be shown that .

Trajectory analyses for parcels terminating in the low-level mesocyclone are performed using the Read/Interpolate/Plot (RIP) program developed by the National Center for Atmospheric Research (NCAR) and the University of Washington, which incorporates an Eulerian integration scheme. During the time of the trajectory analysis, data are input every 60 s, and velocity data are linearly interpolated in time every 5 s throughout the duration of each trajectory. Accuracy assessment of each trajectory was conducted to ensure the location and variable quantities along all trajectories were reasonable. To accomplish this assessment, sample trajectories were selected with model data saved every second, instead of every 60 s. Trajectories acquired from the 1-s data were compared to those from the 60-s data and were found to be nearly identical. In addition, summation of vertical vorticity tendency quantities were conducted along each trajectory, with total vertical vorticity values matching well with instantaneous values along each trajectory and at the origin points.

3. Analysis

a. Established thermodynamic and kinematic low-level structure

Initial consideration is given to the evolution of the supercell and a representative time is chosen for analysis of the main features of the low-level flow. After 3600 s into the simulation, the storm has formed supercellular features at low levels, including a hook echo in simulated reflectivity and remnants of a left-split storm moving off to the northwest (not shown). In addition, a broad area of vertical vorticity of mesocyclonic strength O(10−2 s−1) has formed at low levels just east of the hook echo. Later in the evolution, the low-level features become nearly steady state in nature. Therefore, a time from this period (8700 s into the simulation) is chosen for analysis as it is representative of mature low-level supercell structure (Fig. 2).

Fig. 2.
Fig. 2.

Simulated reflectivity (shaded, dBZ) overlaid with horizontal velocity (every eighth vector shown, m s−1, scale at bottom left) at 50 m AGL for 8700 s into the control simulation. Arrows indicate the location of the main boundaries associated with the supercell.

Citation: Monthly Weather Review 141, 2; 10.1175/MWR-D-11-00115.1

At this time, three main boundaries within the wind field can be observed. One boundary extends northeast from the mesocyclone, south of the reflectivity gradient of the forward flank. Another boundary extends due north from the mesocyclone into the core of the storm. A final boundary, the RFGF, runs south from the mesocyclone. The boundaries are associated with differing amounts of low-level convergence (Fig. 3). The strongest convergence is associated with the RFGF (~2 × 10−2 s−1), followed by weaker convergence along the boundary extending north out of the low-level mesocyclone (~1.5 × 10−2 s−1). The weakest convergence is associated with the boundary extending northeast out of the mesocyclone, with values around ~1 × 10−2 s−1 or less. Only this latter boundary shows distinct spatial variation in both strength and breadth of convergence, with strength decreasing eastward, away from the low-level mesocyclone. On either side of the boundary extending northeast from the hook, the equivalent potential temperature values are identical (Fig. 4a), indicating a common air mass origin, as equivalent potential temperature is conserved for both dry and moist adiabatic processes. Backward trajectory analyses at 50 m AGL confirm this conclusion (Fig. 4b), with air parcels on either side originating from the inflow region. However, the westernmost parcels are influenced by increasing amounts of evaporative cooling (calculated from the microphysics scheme), as rain falls into this inflow air, with density potential temperature decreasing from east to west (Fig. 4b). Specifically, a parcel traveling along a trajectory through this region for 15 min experiences an average density potential temperature change of approximately −2 K due to evaporative cooling based on Eq. (4), comparing well with simulation results at the western termination points of the trajectories (Fig. 4b).

Fig. 3.
Fig. 3.

Convergence values (shaded, s−1) with horizontal velocity (vectors, m s−1, scale at bottom left) and simulated reflectivity (contoured at 20, 30, 40, 50, and 60 dBZ) at 50 m AGL for 8700 s into the simulation.

Citation: Monthly Weather Review 141, 2; 10.1175/MWR-D-11-00115.1

Fig. 4.
Fig. 4.

(a) Equivalent potential temperature (colored, K) with horizontal velocity (every tenth vector shown, m s−1, scale at bottom left) and simulated reflectivity (contoured at 20, 30, 40, 50, and 60 dBZ) at 50 m AGL for 8700 s into the simulation, and (b) density potential temperature perturbation (colored, K) overlaid with 15-min backward trajectories from either side of the northeastward-directed boundary at 8700 s and 50 m AGL. Green parcel paths indicate consistent heights of 50–100 m AGL. The white box in (a) indicates the domain of (b).

Citation: Monthly Weather Review 141, 2; 10.1175/MWR-D-11-00115.1

Given the findings of a weak gradient in both perturbation pressure and density potential temperature across this portion of the forward flank and a lack of strong convergence, the latter evident from horizontal velocity vectors and trajectories in Figs. 4a,b, this boundary may not be considered a gust front, using the traditional definition of the term. Instead, the term “forward-flank convergence boundary” (FFCB) is deemed more appropriate, and is used through the remainder of this paper.

For the boundary extending north out of the low-level mesocyclone, a strong eastward-directed gradient in equivalent potential temperature exists (Fig. 4a). This result is consistent with air parcels descending from aloft to the west of the boundary. Keeping in mind that an exact parcel origin cannot be found because of diabatic effects, an estimation can be made using the equivalent potential temperature. Air descending west of this boundary has equivalent potential temperature values of ~327–333 K (Fig. 4a). Comparing these values to the initialization sounding (Fig. 1a), approximate origin heights are around 2–3 km AGL. Indeed, backward trajectories across the boundary extending north out of the mesocyclone support the conclusion that air is descending west of the boundary, while to the east, air parcels originate from just above the surface (Fig. 5), with equivalent potential temperatures of 343 K.

Fig. 5.
Fig. 5.

Perturbation density potential temperature (colored, K) with LFCB and FFCB boundaries outlined in black at 50 m AGL for 6300 s into the simulation, and 30-min backward trajectories terminating on either side of the LFCB. Colors along the trajectories depict height, with black, green, blue, red, yellow, light blue and magenta signifying higher heights, respectively, from the surface up to >400 m AGL (legend inset at bottom right). Refer to section 3b for a description of the dashed line.

Citation: Monthly Weather Review 141, 2; 10.1175/MWR-D-11-00115.1

To assess the impact of evaporative cooling on density potential temperature, backward trajectories are used. Trajectories terminating west of the boundary at 6300 s are utilized in this sense to compute the diabatic term in Eq. (4) in a Lagrangian framework. Considering an average evaporation rate of approximately −2 × 10−6 kg kg−1 s−1 for the first 20 min of the trajectories, the first part of the trajectory experiences a density potential temperature tendency rate of −2.4 × 10−3 K s−1, equating to a change of approximately −3 K. For the last 10 min of the trajectory, the density potential temperature tendency rate is −7.2 × 10−3 K s−1, resulting in a change of approximately −4 K. Therefore, over the path of the trajectory, evaporation of rainwater results in ~7 K of density potential temperature cooling. The computed amount of cooling matches well with density potential temperature perturbations seen in the simulation west of the boundary and north of the mesocyclone (Fig. 6). Yet, while temperature varies little north of the mesocyclone, a density gradient does exist, owing to differences in water vapor content across the boundary, resulting in the convergence that is seen (Fig. 3).

Fig. 6.
Fig. 6.

Perturbation density potential temperature (shaded, K) with horizontal wind (every seventh vector shown, m s−1, scale at bottom left) and simulated reflectivity (contoured at 20, 30, 40, 50, and 60 dBZ) at 8700 s for 50 m AGL.

Citation: Monthly Weather Review 141, 2; 10.1175/MWR-D-11-00115.1

While convergence is evident along this boundary, the change in wind vector orientation across it is minor, with no strong outflow on either side (inferred from pressure field). In addition, this boundary does not separate outflow from environmental air, such that use of the term gust front is not accurate in this case. Therefore, hereafter, this boundary will be referred to as the “left-flank convergence boundary” (LFCB).

Evaluating the RFGF, equivalent potential temperatures in the region just west of the boundary are ~333 K, resulting in an approximate parcel height origin of ~3 km AGL. This result suggests that air is not descending from very high levels within the RFD (similar results were found in a number of other studies, including Knupp 1987 and Adlerman et al. 1999, for example, and summarized in Markowski 2002); however, the air west of the RFGF is colder and moister than west of the LFCB. In this case, there is an area of enhanced evaporative cooling in the hook echo, therefore it is likely that evaporative cooling is the main forcing term acting in this case (similar to the LFCB). Further trajectory analysis (not shown) indicates that parcels terminating within the northeastern portions of the RFD arrive from the north, and traverse an area of strong evaporative cooling west of the RFGF. However, values of liquid water mixing ratio are nearly ~7 × 10−3 kg kg−1 in this region, indicating a high concentration of rainwater and therefore a strong contribution from water loading in addition to evaporative cooling. The RFGF is the only boundary of the three presented to display a sharp boundary in perturbation pressure (Fig. 7), a distinct wind shift, and a separation of environmental from storm-altered, outflow air, therefore making it a true gust front.

Fig. 7.
Fig. 7.

Perturbation pressure (colored, Pa), with horizontal wind vectors (every seventh vector shown, m s−1, scale at bottom left), and simulated reflectivity (contoured at 20, 30, 40, 50, and 60 dBZ) at 8700 s for 50 m AGL.

Citation: Monthly Weather Review 141, 2; 10.1175/MWR-D-11-00115.1

Having identified the origin of these surface boundaries, it is useful to quantify the strength of the frontogenetical forcing that results (frontogenesis can be defined as a measure of the tendency of a horizontal gradient in density or temperature for a given boundary). Of the three boundaries analyzed, the RFGF shows the strongest frontogenetical forcing (~5 × 10−5 K m−1 s−1), as descending air is strongly impacted by evaporative cooling and spreads out near the surface and meets inflow air from the east. This frontogenetical forcing is uniform along the length of the RFGF. Frontogenesis for the LFCB is slightly weaker than that for the RFGF (2–3 × 10−5 K m−1 s−1), but is also uniform in strength for a fair extent along the boundary toward the north. Finally, the forcing for the FFCB is the weakest of all three boundaries (1–2 × 10−5 K m−1 s−1), and trails off in strength toward the northeast, in relation to the amount of evaporation cooling a parcel experiences traversing north of the boundary. The strength of the frontogenetical forcing analysis matches well with the previous descriptions of the development of each boundary.

Based on the analyzed low-level structure, a conceptual model for this simulation (Fig. 8) is created to depict the position, orientation, and strength of the three low-level boundaries. Each boundary is shown as a solid line, with the thickness of each line representing the strength of convergence associated with each boundary. For the FFCB and the LFCB, dashed lines represent the portion of the boundary that is less defined and becomes less distinguishable from the general flow, farther away from the low-level mesocyclone. Arrows represent the general low-level flow near and around the boundaries and mesocyclone.

Fig. 8.
Fig. 8.

Steady-state conceptual model of the low-level boundaries and flow in the simulated supercell. The thick solid line represents the radar reflectivity boundary, whereas the relatively thinner lines represent the boundary locations and strength of convergence, with thicker lines representing stronger convergence. Dashed lines represent the areas where the boundaries become weak and begin to dissipate. Arrows show typical streamlines.

Citation: Monthly Weather Review 141, 2; 10.1175/MWR-D-11-00115.1

A number of sensitivity studies were conducted regarding changes to the low-level and cloud-level specific humidity within the initialized sounding, as well as changes to the rain drop size distribution within the WSM6 microphysics package. Regarding the microphysical sensitivity tests, alterations were made to the intercept value within the drop size distribution of rain. The default value (used for this study) was 8.0 × 106 m−4; therefore, two sensitivity studies were conducted at intercept values of 8.0 × 105 m−4 and 8.0 × 107 m−4 (Fig. 9) to analyze the impact this change might have on the conceptual model. Alterations to the rain intercept value produce differences in the low-level dynamics for each storm. For the 8.0 × 105 m−4 rain intercept value simulation, convergence associated with the FFCB is weakened at 8700 s, but still present. In the 8.0 × 107 m−4 simulation, an intense unified cold pool develops that overtakes all three boundaries by 8700 s. Therefore, analysis of this simulation was conducted at 5700 s, showing that while convergence along the LFCB is stronger than in the control simulation, the FFCB, LFCB, and RFGF all coexist at this time.

Fig. 9.
Fig. 9.

Positive convergence (shaded, s−1) with simulated reflectivity (contoured at 20, 30, 40, 50, and 60 dBZ) and horizontal wind (vectors, m s−1, scale at bottom left) at (a) 8700 and (b) 5700 s for 50 m AGL for rain intercept values (a) 8.0 × 105 and (b) 8.0 × 107 m−4.

Citation: Monthly Weather Review 141, 2; 10.1175/MWR-D-11-00115.1

In addition, forward-flank boundary orientation is altered in both the 8.0 × 105 m−4 and 8.0 × 107 m−4 simulations, compared to the control simulation. However, all three boundaries—the FFCB, the LFCB, and the RFGF—are present in the sensitivity simulations and baroclinity remains similar to the initial simulation, lending credence to the representativeness of the conceptual model presented previously. However, this model should not be necessarily considered to be applicable to all modeled or observed supercells.

b. Evolution of low-level structure

During the early portion of the simulation, the supercell undergoes large fluctuations in terms of downdraft structure and strength and boundary development, position, and strength. Initially, around 3600 s, of the three boundaries discussed previously, only the RFGF is present (Fig. 10). During the time analyzed in the previous section of the paper, one strong region of evaporative cooling exists within the upshear portion of the forward-flank downdraft, around 400–1000 m AGL. However, earlier in the simulation, many discrete regions of evaporative cooling are present (Fig. 11). These regions are not as strong or as large in aerial coverage as that seen later during the steadier evolution. Surface outflow is not as prominent, and any westerly outflow generated by downdrafts behind recurrent LFCBs is countered by the stronger easterly flow north of the low-level mesocyclone. This fact can be seen in the second hour of the simulation, as the easterly flow in the upshear region of the FFD is still stronger than the outflow caused by these discrete pockets of evaporative cooling. Therefore, as a downdraft nears the surface, an LFCB forms via convergence between these downdrafts (Fig. 12), but is then advected westward and dissipates. New LFCBs develop and follow a similar pattern. This process creates as many as four LFCBs simultaneously (Fig. 12) at 5700 s into the simulation. A backward trajectory analysis through these boundaries confirms that there is descent from differing heights occurring on either side of the LFCBs, where pockets of evaporative cooling exist (Fig. 13).

Fig. 10.
Fig. 10.

Convergence (colored, s−1) with simulated reflectivity (contoured at 20, 30, 40, 50, and 60 dBZ) and horizontal wind (every eighth vector shown, m s−1, scale at bottom left) at 3900 s for 50 m AGL.

Citation: Monthly Weather Review 141, 2; 10.1175/MWR-D-11-00115.1

Fig. 11.
Fig. 11.

Liquid water mixing ratio tendency/evaporation rate (shaded, kg kg−1 s−1) with simulated reflectivity (contoured at 20, 30, 40, 50, and 60 dBZ) and horizontal wind vectors (every eighth vector shown, m s−1, scale at bottom left) at 5700 s for 1000 m AGL.

Citation: Monthly Weather Review 141, 2; 10.1175/MWR-D-11-00115.1

Fig. 12.
Fig. 12.

Convergence (colored, s−1) with simulated reflectivity (contoured at 20, 30, 40, 50, and 60 dBZ) and horizontal wind vectors (every eighth vector shown, m s−1, scale at bottom left) at 5700 s for 50 m AGL. Arrows point to the four LFCBs present at this time and to the developing FFCB.

Citation: Monthly Weather Review 141, 2; 10.1175/MWR-D-11-00115.1

Fig. 13.
Fig. 13.

Perturbation density potential temperature (colored, K) with simulated reflectivity (contoured at 20, 30, 40, 50, and 60 dBZ) and 10-min backward trajectories ending at 50 m AGL at 4200 s on either side of transient LFCBs. The solid black line indicates the main LFCB position, whereas dashed lines indicate developing LFCBs.

Citation: Monthly Weather Review 141, 2; 10.1175/MWR-D-11-00115.1

It should be noted that each boundary starts as a weak convergence line farther east within the forward flank, then strengthens as it moves west, peaks in magnitude of convergence (~0.015 s−1), and then gets progressively weaker with time. This process continues until a larger, stronger region of evaporative cooling (and, therefore, near-surface divergence) develops, from which the eastward outflow counters the prevailing mesocyclonic flow. At this point (7200 s into the simulation), the sequence of LFCBs evolves into one relatively stationary LFCB. After the evolution of the LFCBs commences, the FFCB begins to develop (Fig. 12), but is still very weak (convergence from 10−3 to 10−4 s−1) at 5700 s into the simulation. The FFCB becomes more convergent with time. The evolution of the low-level boundaries and other features of the simulation at this time are shown in a conceptual model (Fig. 14). The portion of the simulation conceptual model at 7200 s represents the steady-state structure of the supercell outlined in section 3a.

Fig. 14.
Fig. 14.

Conceptual model of the evolution of low-level boundaries within the simulated supercell. The thick solid line represents the radar reflectivity boundary, whereas the other lines represent the RFGF (thick line), the LFCBs (evolving boundaries associated with the counterclockwise arrow), and the FFCB (thinnest line). Dashed segments indicate weak, developing, or dissipating portions of the boundaries.

Citation: Monthly Weather Review 141, 2; 10.1175/MWR-D-11-00115.1

c. Vorticity and trajectory analysis

Persistent, but discrete midlevel mesocyclones (~5 km AGL) exist throughout the duration of the time analyzed, with pulses of strong (>6 × 10−2 s−1) vertical vorticity (Fig. 15). Near the surface, however, appreciable rotation (vertical vorticity >4 × 10−3 s−1) is absent from the storm until approximately 8000 s. At this point, a near-ground maximum in vertical vorticity is present with magnitude of about 0.05 s−1 (another occurs at 8700 s with vertical vorticity of about 0.06 s−1). This time also marks the first connection of vertical vorticity between low levels and midlevels. The strongest near-ground vertical vorticity associated with the low-level mesocyclone (~0.07 s−1) occurs just prior to the interaction of the analyzed storm with outflow originating from the initial left-split storm (Fig. 15).

Fig. 15.
Fig. 15.

Averaged vertical vorticity (s−1, colored) time–height plot for the control simulation and for the area directly encompassing the low-level mesocyclone from the surface to 6 km AGL and from 3600 to 10 800 s. The black line indicates the time at which ancillary outflow affects the analyzed storm, after which vorticity analysis is stopped.

Citation: Monthly Weather Review 141, 2; 10.1175/MWR-D-11-00115.1

The impact of preexisting environmental and baroclinically produced horizontal vorticity on low-level vertical vorticity maxima is next examined. Assessment of the low-level horizontal vorticity field at 8700 s shows that environmental horizontal vorticity within the inflow air has an average value of 8 × 10−3 s−1 (Fig. 16). The horizontal vorticity associated with the three persistent boundaries identified within the supercell (RFGF, LFCB, and FFCB) is substantially larger than that in the environmental inflow (Fig. 16). Horizontal vorticity values of 0.04 s−1 are intrinsic to both the FFCB and LFCB, with values of 0.06 s−1 associated with the RFGF. The horizontal vorticity vectors are directed parallel to each boundary and in a direction that suggests that solenoidal generation of horizontal vorticity is impacting the orientation of the vector. At 8700 s, the RFGF has the strongest values of solenoidal horizontal vorticity tendency (~5 × 10−4 s−2), followed by the LFCB (~3 × 10−4 s−2) and then the FFCB (~2.5 × 10−4 s−2). The amount of solenoidally generated horizontal vorticity that is tilted and stretched within the vertical vorticity maximum is related to the residence time of parcels that move along these boundaries.

Fig. 16.
Fig. 16.

Horizontal vorticity (vectors), absolute magnitude shaded (s−1, scale at bottom left), and simulated reflectivity (contoured at 20, 30, 40, 50, and 60 dBZ) for 8700 s at 150 m AGL within the region of the low-level vertical vorticity maximum.

Citation: Monthly Weather Review 141, 2; 10.1175/MWR-D-11-00115.1

Backward trajectories at 8700 s reveal that parcels originate in separate groups to the east and west of the vertical, low-level rotation (Fig. 17a). Parcels that arrive from the east, entering the mesocyclone, do not vary much in elevation and traverse the low-level inflow directly into the area of maximum vertical vorticity. However, parcels arriving from the west follow a much more complicated path. All of these parcels pass through the RFD; however, some arrive from aloft, and descend to the ground, whereas others originate near the surface, ascend first, and then descend in the RFD (Fig. 17a). Parcels that descend from aloft contain positive vertical vorticity from the start of their descent, whereas parcels beginning at the surface contain solely horizontal vorticity. Only certain parcel trajectories briefly parallel the LFCB/RFGF before entering the region of low-level vorticity situated along the RFGF.

Fig. 17.
Fig. 17.

(a) Solenoidal generation of horizontal vorticity (colored, s−2) with simulated reflectivity contours (at 20, 30, 40, 50, and 60 dBZ), horizontal solenoidal tendency (vectors, s−2, scale at bottom left), and 15-min backward trajectories preceding 8700 s. Termination points of the trajectories are bordered by two white boxes. Selected times are indicated with arrows for trajectories 8 and 13. (b) Zoomed in on region of the low-level mesocyclone. Trajectories 8 and 13 are displayed.

Citation: Monthly Weather Review 141, 2; 10.1175/MWR-D-11-00115.1

A final analysis at 9400 s shows a strong similarity to that at 8700 s. Two source regions of parcels, both west and east of the low-level rotation, converge as before (not shown). However, at 9400 s, a few parcels originate east of the rotation, translate west of the rotation, and then are enveloped by the RFD. One specific parcel traverses the FFCB for a brief period of time, close to the low-level circulation, before curving back to the east. While these few parcel trajectories differ slightly in location from those seen at 8700 s, their horizontal and vertical vorticity tendencies and impact on the vertical, low-level rotation at 9400 s are similar to trajectories at 8700 s (described later). Parcels passing through the RFD at 9400 s again have two origins. One group of trajectories originates near the surface, whereas a few originate from aloft. Overall, the two analyses at 8700 and 9400 s show remarkable resemblance.

Keeping in mind that trajectory analyses inherently contain some error, it is informative to look at vorticity tendency terms along specific trajectories to assess the forcing of each low-level vertical vorticity maxima. Assessing the amount of streamwise vorticity that exists along each trajectory is important, as streamwise vorticity directly impacts the amount of vertical vorticity that can be stretched within the low-level mesocyclone (Davies-Jones 1984; Rotunno and Klemp 1985). Two representative trajectories were chosen for the main vertical vorticity maximum at 8700 s in an attempt to quantify vorticity generation. Trajectory 13 was chosen for the easterly inflow, while trajectory 8 was chosen for the westerly flow (Fig. 17b).

Looking at trajectory 8 first (Fig. 18), a general increase exists in both the positive x and negative y components of horizontal vorticity owing to the proximity and impact of stretching and production of solenoidal horizontal vorticity associated with the LFCB aloft (which exists west of the LFCB at the surface). This effect increases as parcels accelerate, descending toward the low-level mesocyclone. Specifically, the strong increase in negative y solenoidal vorticity tendency at 8300 and 8600 s is noted as the trajectory approaches the west side of the low-level LFCB (see termination point of trajectory 8 in Fig. 17b).

Fig. 18.
Fig. 18.

All for trajectory 8 ending at 8700 s: (top left) x component of horizontal vorticity (s−1), (top right) y component of horizontal vorticity (s−1), (bottom right) y components of horizontal vorticity tendency terms (s−2), and (bottom left) x components of horizontal vorticity tendency terms (s−2).

Citation: Monthly Weather Review 141, 2; 10.1175/MWR-D-11-00115.1

Analysis of trajectory 13 reveals less horizontal vorticity fluctuation for the air parcel coming from the inflow (Fig. 19). Horizontal vorticity forcing and parcel height change little over the first 600 s of the parcel path. However, as parcels near the low-level mesocyclone, they are exposed to the strong solenoidal generation of horizontal vorticity (8500 s) along the RFGF. The production of horizontal vorticity along this boundary is in the opposite sense of the horizontal vorticity already existing in the inflow environment. In turn, the horizontal vorticity of air parcels along the trajectory is altered drastically by the end of the trajectory (~8650 s), resulting in a strongly east–southeastward-directed horizontal vorticity vector about equal in magnitude, but opposite in direction to that found in the storm-relative inflow air. Whether or not these inflow parcels attain horizontal vorticity opposite to that prescribed by the background environment is clearly a function of residence time along the RFGF. The east–southeastward horizontal vorticity vector in this case is tilted downward by the RFD, generating positive vertical vorticity (Fig. 20).

Fig. 19.
Fig. 19.

All for trajectory 13 at time 8700 s: (top left) x component of horizontal vorticity (s−1), (top right) y component of horizontal vorticity (s−1), (bottom right) y components of horizontal vorticity tendency terms (s−2), and (bottom left) x components of horizontal vorticity tendency terms (s−2). Note scale of x and y components of horizontal vorticity tendency: 10−4 and 10−5, respectively.

Citation: Monthly Weather Review 141, 2; 10.1175/MWR-D-11-00115.1

Fig. 20.
Fig. 20.

(top left) Vertical vorticity (s−1) and (top right) vertical vorticity tendency terms (s−2) for trajectory 8 ending at 8700 s, (bottom right) vertical vorticity (s−1) and (bottom left) vertical vorticity tendency (s−2) terms for trajectory 13 ending at 8700 s. Note scales on images [(bottom left) 10−3; (bottom right) 10−5].

Citation: Monthly Weather Review 141, 2; 10.1175/MWR-D-11-00115.1

Analysis of the vertical vorticity along trajectory 8 (Fig. 20) shows a gradual decrease in positive vertical vorticity over time as parcels descend to the surface, owing to a negative value of stretching as the parcel decelerates (especially beginning at 7800 s). Eventually, the stretching term reverses sign (8500 s), and vertical vorticity increases sharply through convergence as parcels reach the low-level updraft and are stretched in the vertical direction. Vertical vorticity is never negative as the parcel descends from aloft to the surface. In addition, the vertical tilting term does not drop below zero for long over the duration of the trajectory (Fig. 20), indicating that the vorticity associated with these parcels is not being tilted downward appreciably during descent.

In interpreting the ability of the principal storm updraft to stretch tilted horizontal vorticity, it is important to assess the streamwise component of this vorticity for both trajectories (Fig. 21). Though there are fluctuations along the path, the horizontal vorticity along trajectory 8 ultimately becomes mostly streamwise by the time the parcel reaches the low-level vertical vorticity maximum. The vorticity of the parcel in trajectory 13 initially starts out streamwise to the storm-relative inflow, but is altered by the strong solenoidal generation of horizontal vorticity along the RFGF and becomes mostly antistreamwise as it is tilted by the RFD into the vertical as the parcel reaches the interface between the RFGF and the downdraft air. Therefore, it is clear that both parcels impart positive vertical vorticity to the low-level vertical vorticity maximum, even though one trajectory exhibits streamwise horizontal vorticity and the other antistreamwise horizontal vorticity.

Fig. 21.
Fig. 21.

Streamwise horizontal vorticity (dashed, s−1) and total horizontal vorticity (solid, s−1) along both trajectories (left) 8 and (right) 13 ending at 8700 s.

Citation: Monthly Weather Review 141, 2; 10.1175/MWR-D-11-00115.1

Another trajectory analysis is conducted for a low-level vertical vorticity maximum (LLVVM) at 9400 s. However, for brevity, only a brief discussion will be included here. As before, two representative trajectories were chosen for the two different air mass origins affecting the LLVVM. For the selected trajectory originating from the storm-relative inflow, parcels experience a similar reversal of streamwise to antistreamwise horizontal vorticity as they reach the RFGF. However, in this case, their interaction with the boundary is limited in time, resulting in extremely weak antistreamwise vorticity that is then tilted into positive vertical vorticity by the RFD. For the trajectory originating from aloft within the RFD (~400 m AGL), parcels descend cyclonically and, on average, undergo an increase in the strength of vertical vorticity, with solenoidal generation of horizontal vorticity remaining positive for the majority of the trajectory. As a result, inflow trajectory parcels provide about one-third the positive vertical vorticity of those descending in the RFD to the LLVVM.

In summary, a remarkably varied set of processes influence the LLVVM along incoming trajectories. Trajectory paths are critical in identifying not only the origin of air parcels interacting with the low-level mesocyclone but also how these air parcels impart vertical vorticity to the LLVVM. For example, the RFGF has a dramatic influence on the horizontal vorticity of any inflow air parcels that move through it. Downdraft tilting of antistreamwise vorticity created from this interaction is a prominent source of positive vertical vorticity, tempered by the direction and strength of the solenoidal production of horizontal vorticity, a strong function of residence time within baroclinic zones. All trajectories from the north and northwest of the LLVVM move through the RFD and are associated with solenoidal generation of horizontal vorticity along the LFCB as they descend, with vertical vorticity remaining positive, and at periods even increasing with time. The updraft/downdraft interface is the ultimate source for the tilting seen in these low-level vertical vorticity maxima.

4. Comparison of simulation to past findings

While the supercell simulation presented shows a varied distribution and evolution of boundaries and air mass origins, there are similarities to past observational and numerical modeling work. Keeping in mind that the three-boundary conceptual model is only being directly inferred from this simulated storm, it is in many ways a combination of past work. The observational studies of Lemon and Doswell (1979) and Brandes (1978) show the presence of what could possibly be a FFCB and LFCB, respectively, but both boundaries together are not present in either of these papers. The presence of both an LFCB and FFCB has not been previously identified or discussed as such in the literature. In fact, confusion may exist as to whether a specific boundary identified in a previous paper could be either the LFCB or the FFCB, as north–south boundaries have been defined previously only as FFGFs before.

Some observational papers have found supcrcells without a LFCB (e.g., Dowell and Bluestein 2002a,b; Beck et al. 2006), while Brandes (1984) and many of the recent mobile Doppler radar papers (e.g., Wurman et al. 2007a,b) show no evidence for any boundary aside from the RFGF (it should be noted that these recent mobile radar papers lack thermodynamic data). Dowell et al. (2002) found evidence of a transient north–south boundary north of the investigated mesocyclone prior to tornadogenesis and full hook echo development. This feature could have been an early LFCB that quickly dissolved, as in the conceptual model of the three-boundary evolution in this research (Fig. 13). In addition, boundaries similar to the LFCB, extending northward out of the low-level mesocyclone, were identified in both Markowski et al. (2002) and Markowski et al. (2011). Shabbott and Markowski (2006) found an east–west gradient in in a number of supercells comparable to that found in the simulated supercell in this study.

Past modeling studies have identified a boundary extending north from the low-level mesocyclone (e.g., Klemp and Rotunno 1983; Wicker and Wilhelmson 1995; Adlerman et al. 1999). These boundaries appear to most likely correspond to LFCBs, both because of their location and the indication of descending air west of their position, as revealed by trajectory analyses. Wicker and Wilhelmson (1995) and Adlerman et al. (1999) show times where the boundaries could be identified as either FFCBs or LFCBs, if analyzed solely on their orientation and position relative to the low-level mesocyclone. Both papers also show evidence of two boundaries coexisting in the forward flank of their modeled storm.

Many numerical modeling studies of supercells have used a potential temperature perturbation contour to mark the leading edge of outflow in supercell thunderstorm simulations (e.g., Klemp and Rotunno 1983; Rotunno and Klemp 1985; Wicker and Wilhelmson 1995; Adlerman et al. 1999). In addition, simulations have shown that multiple kinematic and baroclinic gradients can be associated with boundaries north of the mesocyclone. For example, a distinct wind shift (associated with a strong gradient in potential temperature) is evident north and southeast of the mesocyclone presented by Adlerman et al. (1999, their Fig. 8a), yet the −1-K potential temperature perturbation contour is displaced farther to the east. In addition, terms such as cold front and gust front have been used in previous research to define forward-flank boundaries found using perturbation potential temperature contours. A gust front is defined as having a strong wind shift, with delineation between inflow and outflow air, and a strong pressure gradient across the boundary. Past observational research (e.g., Beck et al. 2006; Wurman et al. 2007a,b) has documented mainly minor wind shifts when these boundaries are present, and modeling studies have not found them to be coincident with strong gradients of temperature or vertical motion (e.g., Wicker and Wilhelmson 1995; Adlerman et al. 1999).

The simulation shows two distinct regions of parcel origins for the low-level mesocyclone: east and west/northwest of the low-level vertical vorticity maxima, with the latter origin containing parcels descending from aloft. The disparate location of these parcel origins is similar to findings from Klemp and Rotunno (1983), Rotunno and Klemp (1985), Wicker and Wilhelmson (1995), and Adlerman et al. (1999). However, the generation, direction, and impact of parcel horizontal vorticity along trajectories inbound to the low-level mesocyclone from the inflow differs from that of Rotunno and Klemp (1985). The simulation in the current study shows that environmental inflow horizontal vorticity along trajectories is mostly eradicated upon reaching the LLVVM.

The simulation shows that the RFD does not produce significant tendencies in negative vertical vorticity within descending parcels at the time analyzed, and that parcels originating west of the LLVVM maintain their positive vertical vorticity throughout the path and descent of the trajectory. This maintenance of positive vertical vorticity during the descent of an air parcel within the RFD has been explained theoretically by Davies-Jones and Brooks (1993). They showed that if baroclinity is present during such descent, the generation of horizontal vorticity when tilted just before reaching the surface will produce a positive component of vertical vorticity. This finding has been corroborated in past modeling studies (e.g., Adlerman et al. 1999), and the theory applies very well to the results of the simulation, where baroclinic generation of horizontal vorticity is present along the LFCB and RFGF during the descent of parcels through the RFD.

5. Conclusions

The purpose of this study is to use a high-resolution simulation of a supercell thunderstorm to identify and investigate the development, evolution, and impact of low-level boundaries, assign an appropriate naming convention, and elucidate the role of these boundaries in the generation of both horizontal and vertical vorticity. Each of these boundaries is identified and named accordingly, based on their location relative to the primary updraft, and the dynamics associated with the creation and maintenance of each boundary. Conceptual models have been developed to define the low-level position (Fig. 8) and evolution (Fig. 14) of the boundaries in this case.

The RFGF is created early in the evolution of the storm as precipitation drag and evaporative cooling within the RFD develop quickly, generating a strong region of higher pressure relative to the inflow air. The LFCB is created later, as modified environmental inflow (low-level inflow impacted by precipitation) meets downdraft air to the west of the boundary, originating from hundreds of meters aloft. A dominant LFCB develops much more slowly than the RFGF, with an evolution including development and dissipation of many precursor boundaries, as cyclonic storm-relative flow dominates transient bursts of outflow in the forward flank. Ultimately, enough outflow develops for an LFCB to become relatively stationary (Fig. 14). Lastly, the FFCB develops as precipitation in the northeastward extent of the forward flank cools inflow air and begins to produce a broad pressure gradient. This air in turn meets inflow air that has not been modified by the storm and creates the FFCB.

The term “gust front,” as it has been used in previous studies, is not applicable when used to describe anything but the RFGF. Therefore, the term “convergence boundary” has been used to replace gust front in the conceptual models put forth in this research. In the case of the LFCB, horizontal pressure gradients are weak and the boundary does not separate outflow from unmodified storm inflow. The FFCB is also not a gust front, as it does not exist within a sharp horizontal pressure gradient and does not contain descending air west of the boundary.

The baroclinity and solenoidally generated horizontal vorticity associated with the FFCB contribute weak low-level vertical vorticity to the LLVVMs, as trajectory analyses show few parcels parallel this boundary. Trajectories do reveal, however, that environmental horizontal vorticity within inflow parcels reaching the updraft is reduced or totally reversed in sign owing to the production of solenoidally generated horizontal vorticity along the RFGF. Trajectories traversing the RFD originate from aloft (>500 m AGL), containing parcels which, during descent, can maintain positive vertical vorticity. These parcels acquire solenoidally generated streamwise horizontal vorticity along the LFCB and RFGF during descent, which is converted into positive vertical vorticity upon reaching the surface ahead of the LLVVMs. This process has been described through theoretical study by Davies-Jones and Brooks (1993) and confirmed in other supercell modeling studies (Wicker and Wilhelmson 1995; Adlerman et al. 1999). However, when inflow parcels parallel the RFGF for enough time, just as much antistreamwise vorticity can be tilted negatively by the RFD, also producing positive vertical vorticity. The residence time for parcels paralleling boundaries with solenoidally generated horizontal vorticity ultimately controls the amount of positive vertical vorticity generated as tilting and stretching take place within the updraft.

The ability to determine whether the conceptual models put forth in this study can be confirmed using in situ measurements within supercells is an important future goal for understanding the impact of baroclinity within these regions of the storm and, potentially, their impact on mesocyclogenesis and tornadogenesis. Detection of any temporal variation of these boundaries during the lifespan of the supercell, as described in the conceptual models presented within this paper, is crucial. Findings from the recent field phase of the VORTEX2 project may be significant to this end. In addition, use of different microphysics schemes (such as double-moment schemes) and environmental soundings/hodographs is of particular interest to identify changes that occur within the development and evolution of the low-level boundaries.

Acknowledgments

Portions of this research were supported by National Science Foundation Grant AGS-0800542, the Texas Tech Wind Science and Engineering Research Center, the Visiting Graduate Student program at the National Center for Atmospheric Research, and from supercomputing allocations donated by the National Center for Supercomputing Applications. Thanks are due to David Dowell, Curtis Alexander, Morris Weisman, George Bryan, and Sylvie Lorsolo for their constructive input during this research. David Schultz and the other anonymous reviewers of this manuscript are also due thanks for their comments during the publication process.

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