1. Introduction
Most numerical investigations of supercell thunderstorms have used idealized, horizontally homogeneous environments without surface fluxes of heat, moisture, and momentum. Though fruitful in exposing basic supercell dynamics and the relationship between storm type and the characteristics of the environment (e.g., Schlesinger 1975; Klemp and Wilhelmson 1978a,b; Klemp and Rotunno 1983; Rotunno and Klemp 1982, 1985; Wicker and Wilhelmson 1995; McCaul and Weisman 2001; Naylor et al. 2012) this approach does not account for the inherent inhomogeneity of the turbulent convective boundary layer (CBL) found in many severe-storm environments. Increased computing power now allows for inclusion of more physical processes (such as radiation and land surface parameterizations) and better resolution of boundary layer turbulence than in earlier idealized simulations. With this expanded capability, we investigate how meso-γ-scale horizontal variability in a CBL interacts with supercell thunderstorms.
Because the vast majority of significant tornadoes are spawned by supercell thunderstorms (Trapp et al. 2005), much of our research is concerned with their low-level mesocyclones (LLMs). Numerous studies have demonstrated the importance of environmental properties such as low-level wind shear and moisture (e.g., Kerr and Darkow 1996; Rasmussen and Blanchard 1998; Craven and Brooks 2004) in discriminating between tornadic and nontornadic supercells, but it remains unclear how the horizontal variability of these quantities in a CBL may affect the potential of a supercell to become tornadic. Moreover, inviscid dynamical arguments regarding tornadoes that form in supercell LLMs generally assume there is no preexisting vorticity (ζ ) near the surface in supercell environments; thus, the development of rotation next to the surface (a prerequisite for tornadogenesis) requires a downdraft to reorient and redistribute ambient horizontal vorticity and/or horizontal vorticity generated baroclinically within a supercell (e.g., Davies-Jones 1982; Davies-Jones and Brooks 1993; Markowski et al. 2008). As Nowotarski et al. (2014, hereafter NMRB14) and others (Arnott et al. 2006; Markowski and Hannon 2006; Marquis et al. 2007) have shown, CBLs typically do contain patches of significant vertical vorticity that would precede storm development if it occurs. The extent to which this vorticity might affect the development and evolution of LLMs in supercells has been an unanswered question.
Previous studies have found sensitivity of low-level rotation to horizontal variations in the storm environment on the meso-β scale (~100 km). Richardson (1999) found that isolated supercells in areas of increased low-level moisture exhibited both stronger updrafts and low-level rotation. Observations (Maddox et al. 1980; Weaver and Purdom 1995; Markowski et al. 1998; Rasmussen et al. 2000) have shown that many tornadoes develop within supercells interacting with mesoscale thermal boundaries. Atkins et al. (1999) found that stronger low-level rotation develops when a simulated supercell moves along a mesoscale boundary, and that the mechanism for the development of the LLM is altered when a boundary is present. Wheatley and Trapp (2008) showed in real-data simulations that preexisting boundaries could also affect the strength and development mechanism of mesovortices in quasi-linear convective systems (QLCSs).
Studies examining the effects of small-scale (order 1 km) horizontal variability on deep moist convection are limited (Carpenter et al. 1998; Crook and Weisman 1998), and none have examined the specific case of CBL rolls (often referred to as “horizontal convective rolls”) interacting with supercells. Considering that the horizontal scale of the perturbations associated with rolls (<5 km) is smaller than that of a supercell thunderstorm updraft (>10 km), bulk measures of storm strength (e.g., maximum updraft speed, maximum ζ) may be relatively unaffected by the CBL. The horizontal extent of a supercell updraft is large enough such that it might draw inflow from both roll updraft and downdraft simultaneously, resulting in equal ingestion of air parcels with favorable and unfavorable thermodynamic quantities. Yet, Crook and Weisman showed that inhomogeneities in the storm environment may disrupt aspects of supercell evolution, including the gust front occlusion process. Other studies have noted the appearance of “feeder clouds” in the inflow environment of supercells and have noted that these clouds may be related to rolls and could signal storm intensification (Weaver et al. 1994; Weaver and Lindsey 2004; Mazur et al. 2009).
Building upon these previous studies, this article presents the results of simulations of supercells in a CBL, focusing primarily on characteristics and evolution of LLMs. We compare these simulations against simulations that have horizontally homogeneous environments having similar overall conditions (e.g., CAPE and shear). Given the quasi-linear organization of a CBL composed of rolls, it is likely that the orientation of rolls relative to storm motion may, in part, dictate their effects on supercell LLMs. As such, we use two different hodographs that result in sets of simulations with storm motion perpendicular to the boundary layer vertical shear and convective rolls (hereafter “perpendicular-shear” simulations) or parallel to the boundary layer vertical shear and convective rolls (hereafter “parallel shear” simulations). The following section describes our methods, including the experiment design and the model configuration. Sections 3 and 4 present results and analysis from the perpendicular-shear and parallel-shear simulations (respectively). Sensitivity to the initiation location of the supercells relative to the rolls is discussed in section 5. We offer concluding remarks in section 6.
2. Methods
NMRB14 describe the methodology used herein for simulating a realistic CBL composed of boundary layer rolls. The modeled rolls have aspect ratios (i.e., the horizontal distance between rolls divided by the boundary layer depth) of ~3 and they are associated with quasi-periodic horizontal fluctuations in variables that are relevant to severe convective storms, such as temperature, moisture, convective available potential energy (CAPE), convective inhibition (CIN), vertical velocity, vertical wind shear, and storm-relative helicity (SRH) throughout the boundary layer. The boundary layer development and magnitude of the environmental variations are generally consistent with observations of rolls (e.g., LeMone and Pennell 1976; Reinking et al. 1981; Atlas et al. 1986; Weckwerth et al. 1996, Markowski and Richardson 2007). Conditions in the updraft branches of roll circulations tend to be warmer and more moist, resulting in greater CAPE, whereas conditions in downdraft branches tend to be cooler and less moist, resulting in less CAPE. NMRB14 also found that the simulated CBL comprises alternating bands of positive and negative vertical vorticity [ζ, O(10−3) s−1] located at the interface between roll updrafts and downdrafts, which originate from tilting of the ambient vertical wind shear by the roll circulations. With time and continued heating of the model surface, the CBL deepens, rolls become less organized (i.e., boundary layer convection becomes more three dimensional), and stronger ζ extrema O(10−2) s−1 occasionally develop.
a. Overview
The effects of rolls and their orientation relative to storm motion are studied in two suites of simulations using the cloud model CM1, release 15 (Bryan and Fritsch 2002; Bryan 2002). Each suite contains four main simulations. In the first simulation, BASE, a CBL composed of rolls develops owing to the inclusion of solar radiation and surface physics (i.e., a soil model and surface fluxes). The environment is initially stably stratified and horizontally homogeneous, but as sensible surface heat fluxes destabilize the boundary layer, dry convection develops and quickly organizes into rolls. The details of the simulated CBL and its evolution are presented NMRB14. The BASE simulation is run for 8 h (480 min) as a basis for comparison of the evolution of the CBL with and without the presence of deep convection.
Once the BASE simulation develops robust boundary layer convection,1 three supercell simulations are initialized and run for 2 h (7200 s). Table 1 summarizes the differences between these simulations. The first two simulations, CBL FRAD and CBL INVRAD, are initialized with restart files from the BASE simulation with a horizontally heterogeneous CBL with rolls. CBL FRAD has full radiation and surface fluxes so that subsequent development of deep moist convection affects shortwave and longwave radiation fluxes at the ground through modifications in atmospheric optical depth by cloud water, cloud ice, and precipitation. CBL INVRAD is identical to CBL FRAD, except that the radiation parameterization was modified such that deep moist convection is “invisible” to radiation in this simulation. The CBL INVRAD simulation prevents cloud-shading effects from weakening boundary layer convection so that the effects of rolls in the near-storm environment may be determined clearly. This simulation is also used in a comparison with the CBL FRAD simulation to understand the effects of cloud shading on the rolls. These effects are discussed in Nowotarski (2013) and forthcoming publications.
Summary of differences in configuration of supercell simulations in each experiment.
The CONTROL simulation is initialized with a horizontally homogeneous thermodynamic and kinematic profile that is determined by horizontally averaging output from the BASE simulation at t ≈ 3 h. Thus, the domain-average initial conditions in all three supercell simulations are identical. The CONTROL simulation does not include surface fluxes of heat and moisture or radiation. Consequently, there is no temporal change to the environment as in the CBL FRAD and CBL INVRAD simulations, which complicates the comparison between them. To make the simulations more comparable, some variables are constantly nudged toward the domain-average values from the CBL simulations (as described below). Surface drag is applied to the CONTROL simulation with a constant drag coefficient (cd = 0.005) representative of the average value in the CBL simulations.
b. Numerical model configuration
For all simulations, CM1 is run with the same configuration as the “supercell ready” simulations discussed by NMRB14 and further detailed in Nowotarski (2013). The domain size is 250 km × 200 km × 18 km, with constant horizontal grid spacing of 200 m and vertical grid spacing stretched from 50 m below 3 km to 500 m above 8.5 km. In horizontal grid-spacing sensitivity tests, NMRB14 found that, though not ideal for LES, the flow was qualitatively turbulent at this grid spacing, similar to simulations with 100-m horizontal grid spacing, and sufficiently representative of the characteristics and evolution of boundary layer convection. Though NMRB14 did not explicitly test the sensitivity of LLMs to grid spacing, they are of a similar (if not larger) length scale as boundary layer convection, such that we expect this grid spacing to adequately resolve the effects of rolls on LLMs. The large (small) time step is 0.75 (0.125) s, which is sufficient to maintain computational stability throughout the simulations. The upper and lower boundaries are rigid walls with a Rayleigh sponge layer applied above 14 km and all lateral boundary conditions are periodic.
Precipitation microphysics is parameterized with the National Aeronautics and Space Administration (NASA) Goddard formulation (Tao and Simpson 1993) of the Lin et al. (1983) single-moment bulk ice microphysical scheme. When required, radiation is parameterized using a vertical column model with the NASA Goddard Cumulus Ensemble formulations for both longwave and shortwave interactions with air and water species (Chou et al. 1998; Tao et al. 1996; Chou and Suarez 1999; Chou et al. 1999). For CBL INVRAD simulations, mixing ratios of liquid and solid water species are set to zero within the radiation scheme, such that optical thickness within the column is not affected by the presence of clouds or precipitation.
c. Base states and initialization
The initial sounding used for the BASE simulation is described in NMRB14. The CBL FRAD and CBL INVRAD simulations are started with restart files taken from the BASE simulation at the time when rolls begin to organize (165 min) with radiation corresponding to a local time of 0945 UTC 15 May in north-central Oklahoma. The CONTROL simulation is started with a sounding that is the horizontal average of the BASE simulation at this time (Fig. 1a; black hodographs in Figs. 1b,c). At this point, boundary layer convection has mixed the lowest ~500 m of the model domain, increasing surface-based CAPE from 1385 to 2492 J kg−1, and decreasing CIN from 232 to 79 J kg−1. In the mixed layer, surface drag and mixing have modified the wind profiles, increasing 0–3-km SRH from 506 to 580 m2 s−2 in the perpendicular-shear environment, and decreasing 0–3-km SRH from 379 to 323 m2 s−2 in the parallel-shear environment (Figs. 1b,c). Deep convection is initialized in all supercell simulations using a 10-km (1 km) horizontal (vertical) radius bubble centered 1 km above the ground with a maximum potential temperature perturbation of 3 K. These simulations are run for 120 min (2 h).
(a) Skew T–logp diagram showing the temperature (red) and dewpoint temperature (green) profiles used to initialize supercell simulations. The blue line shows the temperature of a lifted surface parcel. Hodographs used as the initial conditions for BASE simulations (blue) and the horizontal average hodograph at the initiation time of supercell simulations (black) for (b) perpendicular and (c) parallel shear simulations. Heights above the ground are labeled in km and red vectors indicate the average motion of mature, right-moving supercells.
Citation: Monthly Weather Review 143, 1; 10.1175/MWR-D-14-00151.1
Total nudging 
Total nudging over 120 min in the perpendicular- (blue) and parallel- (red) shear CONTROL simulations for (a) potential temperature, (b) water vapor mixing ratio, and (c), horizontal velocity.
Citation: Monthly Weather Review 143, 1; 10.1175/MWR-D-14-00151.1
3. Perpendicular-shear simulation results
a. General characteristics
After 60 min in each simulation, a dominant, right-moving supercell develops after storm splitting. The right-moving supercells have an average storm motion over the last hour of the simulation of (cx, cy) = (18, 5) m s−1. Figures 3a–c show the supercells at 90 min (during their mature state) from the three perpendicular-shear simulations. In all three cases, the simulated reflectivity field exhibits supercell structure (e.g., Lemon and Doswell 1979) with most precipitation located north of the main updraft and an appendage of higher reflectivity wrapping around the rear (western) flank of the updraft.
Plan views of reflectivity at z = 1 km (color shaded), vertical velocity at z = 4 km (gray contours, 5 m s−1 interval), and vertical vorticity at the lowest grid level (z = 25 m, black contours of 0.05, 0.01, 0.03, 0.05 s−1, …) for the perpendicular-shear (a) CONTROL, (b) CBL INVRAD, and (c) CBL FRAD simulations, and the parallel-shear (d) CONTROL, (e) CBL INVRAD, and (f) CBL FRAD simulations at t = 90 min. The −0.5-K perturbation potential temperature isentrope at z = 25 m is shown as a blue line with close dashes. For horizontal scale, see legend in the lower-left corner of (a).
Citation: Monthly Weather Review 143, 1; 10.1175/MWR-D-14-00151.1
To assess the effect of rolls on overall storm strength, we compare several bulk measures of storm intensity. The maximum updraft at any height or any time in the CONTROL simulation is 85 m s−1 compared with 84 m s−1 in the CBL INVRAD simulation and 81 m s−1 in the CBL FRAD simulation. The strongest wind speed at the lowest scalar grid level (z = 25 m) was 42 m s−1 in the CONTROL compared with 37 m s−1 in both CBL simulations. Severe winds (>27 m s−1) at the lowest grid level first occur at 75 min in the CBL FRAD simulation and at 85 min in the CONTROL and CBL INVRAD simulations. In general, the area of severe wind gusts is larger in the CONTROL and CBL FRAD simulations than in the CBL INVRAD simulation. Initially, severe winds are confined to the precipitation core northwest of the LLMs, but severe winds also develop in the southern portion of the low-level mesocylone at 100 min in the CONTROL and CBL FRAD simulations and at 105 min in the CBL INVRAD simulation. Total liquid and ice water mass is generally 5%–10% higher in the CONTROL than the CBL simulations over the last hour.
Time series of maximum integrated updraft helicity in the right-moving supercell of each perpendicular-shear simulation.
Citation: Monthly Weather Review 143, 1; 10.1175/MWR-D-14-00151.1
b. Perpendicular-roll effects on the low-level mesocyclone
The influence of rolls on LLMs is most evident through comparison of the morphology and evolution of the CONTROL and CBL INVRAD supercells. The lack of cloud shading in the CBL INVRAD simulation allows rolls to persist in the near-storm environment, unlike in the CBL FRAD simulation where cloud shading suppresses rolls (evident in the relative lack of inflow ζ perturbations near the updraft and precipitation core in Fig. 3c). Appreciable cyclonic ζ (>0.01 s−1) first develops near the ground in the CONTROL supercell on the immediate cool side of the outflow boundary around 90 min (Fig. 3a). This budding LLM, located under the midlevel updraft, steadily intensifies over the next 15 min to ζ > 0.08 s−1 by 106 min (Fig. 5a). The CONTROL LLM is associated with protrusions, or “feeders” of positive ζ located along convergence lines in the forward-flank outflow, suggesting a potential source region of vorticity for the intensifying vortex. Similar features were noted in simulations by Dahl et al. (2014).
Plan views of vertical velocity (color shaded) and vertical vorticity (black contours of ±0.005, 0.01, 0.02, 0.03 s−1, …) near the ground (z = 25 m for ζ; z = 225 m for w) in the right-moving supercell for the (a) CONTROL, (b) CBL INVRAD, and (c) CBL FRAD simulations at 106 min. The 10-dBZ reflectivity contour at z = 1 km (solid green) and −0.5-K perturbation potential temperature isentrope at z = 25 m (blue with close dashes) are also shown. Vectors are storm-relative winds at z = 25 m.
Citation: Monthly Weather Review 143, 1; 10.1175/MWR-D-14-00151.1
In contrast, low-level ζ develops at multiple locations along the CBL INVRAD supercell outflow boundary earlier than ζ develops in this region of the CONTROL supercell as ambient ζ perturbations (both cyclonic and anticyclonic) associated with rolls in the near-storm environment (NMRB14) are amplified in the convergent area along the outflow boundary (similar ζ perturbations persist at 90 min; Fig. 3b). These vorticity extrema consolidate into a larger, more intense vorticity maximum beneath the main updraft where one might expect an LLM to develop, occasionally with vertical vorticity as strong as the developing LLM in the CONTROL supercell. However, these vorticity maxima are often flanked by anticyclonic vorticity on the inflow side, and they are more transient than the steadily strengthening LLM in the CONTROL supercell. This difference in behavior is illustrated by the contrast in the morphology of the LLMs at 106 min in Figs. 5a,b. After 110 min, the initial CONTROL LLM weakens, and is soon replaced with a new LLM by 120 min. By this time a stronger, concentrated area of ζ, more similar to the CONTROL LLM, has emerged in the CBL INVRAD simulation. The low-level morphology of the CBL FRAD supercell (Figs. 3c and 5c) generally lies between that of the CONTROL and CBL INVRAD supercells, but the CBL FRAD supercell does not develop a clear strong, persistent LLM as in the CONTROL simulation and even fails to achieve the maximum low-level vertical vorticity at the end of the CBL INVRAD simulation (not shown).
To understand the means by which rolls affect LLMs, we turn to circulation and trajectory analyses of the LLMs in each simulation. The location of the center of the LLM was subjectively determined at 5-min intervals over the last hour of the simulations. For the CONTROL supercells, the center of the LLM is generally the location of the highest ζ at the lowest vertical grid level beneath the main updraft in close proximity to an inflection in the outflow boundary. For the CBL simulations and at times in the CONTROL when multiple vorticity maxima exist in this area, the center of the LLM was estimated through a visual inspection of the storm-relative wind, pressure, and temperature fields over the depth of the boundary layer. In such situations, the area of cyclonic vorticity collocated with the greatest pressure drop2 and/or largest inflection in the outflow boundary, and located near the center of rotation in the storm-relative wind field, was selected as the center of the LLM. Though the forthcoming analysis was performed for all three simulations in each suite, as before, we will focus on the CONTROL and CBL INVRAD simulations because rolls (and their effects) are most prominent in the CBL INVRAD simulation. Before proceeding to the analysis, however, it is helpful to define a few of the mathematical quantities and methods employed.
Time series of circulation about a 2-km-radius4 horizontal ring centered on the LLM5 at the lowest grid level were computed for each perpendicular-shear simulation (Fig. 6). Before 90 min, the circulation for all three simulations is similar and never exceeds 3 × 104 m2 s−1. Over their last half hour, circulation increases more rapidly in the CONTROL and CBL INVRAD simulations, but the CONTROL LLM consistently has stronger circulation than the CBL supercells. By this measure, the CONTROL supercell has a stronger LLM for a longer duration than when rolls are present in the near-storm environment (CBL INVRAD). It should be noted that the LLM circulation in the CBL INVRAD simulation still increases with time and occasionally approaches the strength of the CONTROL circulation (120 min). On average, the CBL FRAD simulation has the weakest low-level circulation. This is likely attributable to near-storm decreases in CAPE and a decrease in baroclinicity along the forward flank associated with anvil shading rather than roll effects—rolls likely have less influence because near-storm boundary layer convection is diminished in this simulation (see Fig. 3c).
Time series of circulation around a 2-km-radius horizontal ring centered on the mesocyclone at z = 25 m for the perpendicular-shear CONTROL (black), CBL INVRAD (red), and CBL FRAD (blue) simulations.
Citation: Monthly Weather Review 143, 1; 10.1175/MWR-D-14-00151.1
We focus on low-level rotation at 106 min to understand why circulation tends to be stronger in the CONTROL supercell. At this time, there are distinct differences between the CONTROL and CBL INVRAD LLMs. Maxima of vertical vorticity and OW parameter are collocated in the CONTROL mesocyclone (Fig. 7a) in an area of relatively strong (>5 × 104 m2 s−1) circulation, indicating a well-organized LLM. In contrast, ζ and OW parameters are weaker and more widely scattered over a larger area and several local maxima in the CBL INVRAD mesocyclone (Fig. 7b) with areas of anticyclonic vorticity interspersed among the vorticity maxima. Consequently, circulation is weaker in the vicinity of the LLM.
Plan views of circulation around a 2-km-radius horizontal ring centered at each grid point (color shading), vertical vorticity (black contours, ±0.005, 0.01, 0.02, 0.03 s−1, …), Okubo–Weiss parameter (red contours, 0.001, 0.005, 0.01, 0.02, 0.03 s−2, …), storm-relative winds, and the −0.5-K perturbation potential temperature isentrope (blue with close dashes) all at z = 25 m for the perpendicular-shear (a) CONTROL and (b) CBL INVRAD simulations at 106 min.
Citation: Monthly Weather Review 143, 1; 10.1175/MWR-D-14-00151.1
To assess the influence of rolls on the development of vertical vorticity in the LLM, we initiated backward trajectories (see the appendix for details) at points every 400 m within 2.5 km of the LLM center6 at z = 125 m where ζ > 0.01 s−1 in the CONTROL and CBL INVRAD simulations at 106 min (Fig. 8). Parcels entering the LLM at this time have three main streams: “downdraft parcels” originating in the forward flank either aloft and descending, or originating closer to the ground, ascending, and subsequently descending; “forward-flank parcels” that travel along the forward-flank outflow boundary near the ground before ascending to 125 m; and “inflow parcels” originating in the inflow near the ground before crossing the outflow boundary and abruptly ascending.7
(a),(c) Plan views and (b),(d) perspective views from the southeast of parcel backward, storm-relative trajectories terminating in the low-level mesocyclone at z = 125 m and t = 106 min with vertical vorticity >0.01 s−1 for the perpendicular-shear (top) CONTROL and (bottom) CBL INVRAD simulations. Vertical vorticity of each point along each trajectory is shaded according to the legend. Storm-relative winds and vertical vorticity (thin black contours at ±0.01 s−1 increments) at z = 125 m are plotted in plan views along with the outline of reflectivity >10 dBZ at z = 1 km (thick black contour), and the −0.5-K perturbation potential temperature isentrope at z = 25 m (blue with close dashes contour).
Citation: Monthly Weather Review 143, 1; 10.1175/MWR-D-14-00151.1
The evolution of ζ along parcel trajectories as they enter the LLM reveals the basis for the stronger, more persistent CONTROL mesocyclone. All of the parcels entering the CONTROL mesocyclone exhibit a nearly monotonic increase in ζ along their paths (Figs. 8a,b) into the large, centralized area of positive ζ (Fig. 7a). The forward-flank parcels tend to pass through the “vorticity feeder” regions discussed previously. In contrast, though still divided in three main streams, the source regions of parcels entering the CBL INVRAD mesocyclone are more varied, with frequent fluctuations in ζ along their paths (Figs. 8c,d). Moreover, parcels in the downdraft stream have a maximum height of ~0.25 km in the CONTROL supercell versus a typical apex of 0.5–1 km in the CBL INVRAD supercell at this time (cf. Figs. 8b,d). These CBL INVRAD downdraft parcels pass through a small, but relatively intense downdraft on the western flank of the LLM (Fig. 5b, x = 112, y = 121) that is apparently driven by a localized increase in rainwater content (not shown).
Example trajectory paths (Fig. 9) and ζ budgets (Fig. 10) are shown for each stream.8 Downdraft parcels in both simulations (A and B) begin with slightly negative ζ. Vertical vorticity consistently increases in the CONTROL downdraft parcel (A) over its path, becoming positive first through tilting around 100 min, followed by an abrupt increase through stretching around 105 min. In contrast, the CBL INVRAD downdraft parcel (B) obtains higher ζ earlier, but oscillations in tilting and stretching along its path result in ζ fluctuations with two short periods of negative ζ. The forward-flank parcels (C and D) show a similar pattern, with vorticity increasing through both positive tilting of horizontal vorticity in the forward-flank buoyancy gradient (Fig. 9, shading) and subsequent stretching over most of the parcel’s trajectory (before 103.5 min) in the CONTROL parcel (C) and oscillations (though of a smaller magnitude than in the downdraft parcel) in tilting, stretching, and ζ in the CBL INVRAD parcel (D).
Plan view of buoyancy (color shaded), convergence (red contours of 0.005, 0.01, 0.02, 0.03 s−1, …), vertical vorticity (black contours of 0.01, 0.03, 0.05, 0.07 s−1, …), and storm-relative winds at z = 25 m for the perpendicular-shear (a) CONTROL and (b) CBL INVRAD simulations at 106 min. The outline of reflectivity >10 dBZ is plotted in green. Example trajectories from each main trajectory stream are overlaid, shaded according to their height above the ground and labeled with a letter corresponding to the panel with their vorticity budget in Fig. 10.
Citation: Monthly Weather Review 143, 1; 10.1175/MWR-D-14-00151.1
Time series of vertical vorticity interpolated to parcels (black, s−1), tilting (red, ×102 s−2), stretching (green, ×102 s−2), and vertical vorticity derived from integrating forcing terms (blue, s−1) for parcels indicated in Fig. 9. See the appendix for details on trajectory and vorticity budget calculations.
Citation: Monthly Weather Review 143, 1; 10.1175/MWR-D-14-00151.1
The oscillations in vorticity along CBL INVRAD parcels are driven by the heterogeneity associated with rolls. Figure 9 shows distinct heterogeneity in convergence in the inflow as well as the forward-flank outflow caused by rolls (vertical velocity heterogeneity is also evident in these regions in Fig. 5b). Approaching areas of stronger negative buoyancy, the roll-driven perturbations in convergence are diminished by the storm in the forward flank, but this region remains considerably more heterogeneous than in the CONTROL simulation. It is important to note that the overlaid parcel paths in this figure are storm relative, such that parcels do not cross the heterogeneities entirely in the manner suggested by this figure. Rather, both the parcels and rolls travel toward the southwest in the storm-relative reference frame. Yet, the vorticity budgets confirm that the parcels encounter some heterogeneity caused by rolls along their trajectories, presumably owing to different parcel and roll translation speeds. This is important because, although all the parcels shown eventually develop positive ζ, many other parcels terminate in the same region with negative ζ, weakening the overall circulation of the LLM. Such parcels acquire negative ζ because of oscillations in the vorticity forcing terms, presumably caused by their roll-relative motion as they approach the LLM region. This process does not occur in the CONTROL parcels. Thus, the presence of rolls perpendicular to storm motion (and across trajectories entering the LLM) disrupts the development of the persistent, coherent LLM that develops when rolls are absent.
4. Parallel-shear simulation results
a. General characteristics
As in the perpendicular-shear environment, deep convection develops into a dominant right-moving supercell by 60 min in all three parallel-shear simulations. The right mover has an average storm motion over the last hour of (cx, cy) = (7, 0) m s−1 in the CONTROL and CBL FRAD simulations. Interestingly, the storm motion of the CBL INVRAD supercell is approximately 1 m s−1 slower (cx, cy) = (6, 0) m s−1. The reflectivity field shows a core of increased reflectivity on the southwest or rear flank of the storm that resembles a hook echo, but it is generally less pronounced than in the perpendicular-shear simulations (Figs. 3d–f). The parallel-shear storms have smaller midlevel updrafts and more compact areas of often more intense precipitation than their perpendicular-shear counterparts.
The maximum updraft at any time or height in the CONTROL simulation is 90 m s−1 compared with 87 m s−1 in CBL INVRAD and 85 m s−1 in CBL FRAD. The CONTROL simulation has a maximum wind speed at the lowest grid level of 43 m s−1 compared with 38 m s−1 in CBL INVRAD and 41 m s−1 in CBL FRAD. Severe winds in all three simulations are confined to small pockets within the precipitation core and are not associated with an LLM. The integrated liquid and ice water mass is nearly identical throughout the CONTROL and CBL INVRAD simulations, but by the end of the CBL FRAD simulation it is about 5% lower than in the others.
Time series (Fig. 11) reveal that UHmax is more variable and often stronger for all three storms with the parallel-shear hodograph than those in the perpendicular-shear environment. Within each simulation, UHmax may vary by as much as 4000 m2 s−2 over less than 10 min of simulation time, but none of the supercells display consistently stronger or weaker UHmax from each other. As with the perpendicular-shear simulations, time series of wmax and ζmax (see Nowotarski 2013) are similar between simulations.
As in Fig. 4, but for parallel-shear simulations.
Citation: Monthly Weather Review 143, 1; 10.1175/MWR-D-14-00151.1
b. Parallel-roll effects on the low-level mesocyclone
The morphology and evolution of the LLMs in the parallel-shear simulations is quite different than in the perpendicular-shear simulations. In the CONTROL supercell, the LLM has a cyclic evolution, apparently driven by pulses of a rear-flank downdraft (RFD). At 60 min (Fig. 12a), a broken ring of ζ surrounds a strong RFD. Eventually the weak vortex sheet at the leading edge of the outflow on the eastern flank of the RFD wraps up and intensifies into a short-lived LLM, before a reinforcing downdraft pulse creates a new vortex sheet in its place. This cycle continues through the duration of the CONTROL simulation with the strongest LLMs occurring at 90 (Fig. 3d) and 115 min (Fig. 13a).
As in Fig. 5, but for parallel-shear simulations at 60 min.
Citation: Monthly Weather Review 143, 1; 10.1175/MWR-D-14-00151.1
As in Fig. 12, but at 115 min.
Citation: Monthly Weather Review 143, 1; 10.1175/MWR-D-14-00151.1
Where a weak vortex sheet exists in the CONTROL supercell at 60 min, stronger discrete vorticity extrema develop in the CBL INVRAD supercell as ζ perturbations associated with the rolls in the inflow are intensified along the outflow boundary (Fig. 12b). These quasi-periodic vortices, with ζ as high as 0.05 s−1, persist over the next 40 min of the simulation as the storm moves along rolls. A downdraft pulse develops at 100 min, replacing the periodic vortices with a vortex sheet similar to that seen in the CONTROL supercell (akin to the strong downdraft and vortex sheet in Fig. 12a). This results in a line of cyclonic vorticity along the rear-flank outflow boundary with local ζ enhancements but no obvious LLM (Fig. 13b). By the end of the simulation, the northernmost of these enhancements has organized into a single, coherent LLM. Environmental perturbations associated with rolls persist into the forward-flank precipitation region of the CBL INVRAD supercell, unlike the relatively homogeneous CONTROL forward-flank region.
Again, the CBL FRAD supercell shares similarities with both the CONTROL and CBL INVRAD supercells. In its early stages, before cloud shading fully suppresses boundary layer convection near the storm, the low-level vorticity structure is similar to the CBL INVRAD simulation, though the vorticity extrema are generally weaker (Fig. 12c). Over later times, the evolution of low-level vorticity is more similar to the CONTROL supercell with downdraft pulses resulting in vortex sheets that occasionally roll up into discrete vorticity extrema (Fig. 13c).
Time series of circulation about the LLMs of the parallel-shear supercells are shown in Fig. 14. The hodograph used for this simulation is less conducive to the development of sustained low-level rotation than the perpendicular-shear hodograph. Indeed, at times it was often difficult to determine which circulation, if any, was the dominant LLM. Because multiple, transient, often-overlapping low-level circulations evolve at different stages of each storm, separate circulation centers were tracked with their individual circulations plotted. Unlike in the perpendicular-shear supercells, there is not a consistent upward trend in circulation over the last half hour of the simulations. The CONTROL supercell has a circulation that tends to oscillate around a steady value, with a peak circulation of only ~40% of the peak value in the perpendicular-shear CONTROL case. Moreover, the CBL INVRAD simulation-LLMs often achieve stronger circulation at multiple locations than the CONTROL supercell over this period, despite occasional decreases on the order of 4 × 104 m2 s−1. This finding implies that, when parallel to storm motion, rolls may enhance low-level circulation rather than disrupt its development. The CBL FRAD supercell typically has the lowest values of circulation over the last half hour, though it attains circulation comparable to the peak in CBL INVRAD circulation at the end of the simulation.
As in Fig. 6, but for multiple circulation centers (numbered) in the parallel-shear simulations.
Citation: Monthly Weather Review 143, 1; 10.1175/MWR-D-14-00151.1
Plan views of circulation, the OW parameter, and ζ are shown at 115 min, a time with similar circulation but distinct low-level morphological differences between the CONTROL and CBL INVRAD supercells (Fig. 15). At this time, the CONTROL mesocyclone (Fig. 15a) remains isolated from other areas of vorticity, whereas the CBL INVRAD mesocyclone (Fig. 15b) is part of an area of greater ζ at the northern end of a sheet of vertical vorticity. Though there is a local maximum in circulation associated with this mesocyclone, the strongest circulation is associated with another area of strong rotation to the southwest.9 The CBL INVRAD mesocyclone has two main branches of vertical vorticity to the north, reminiscent of the vorticity feeders found in the perpendicular-shear CONTROL mesocyclone. The northeast feeder is linked to a line of vorticity maxima associated with the remnants of a roll in the forward-flank precipitation region.
As in Fig. 7, but for parallel-shear simulations at 115 min.
Citation: Monthly Weather Review 143, 1; 10.1175/MWR-D-14-00151.1
As before, storm-relative backward trajectories of parcels entering the mesocyclones with significant positive vorticity were computed and are plotted in Fig. 16 at 115 min. For the parallel-shear supercells, there are two characteristic streams of trajectories: a downdraft stream and a forward-flank stream. In the CBL INVRAD simulation (Figs. 16c,d), three parcels in the inflow terminate with positive ζ near the mesocyclone, but these parcels never cross the gust front. These parcels depict air that has a near-steady position in the portion of a roll with positive ζ. This suggests that, for this hodograph and roll orientation, parcels approaching the LLM remain in a similar roll-relative position over their paths, unlike in the perpendicular-shear simulations.
As in Fig. 8, but for parallel-shear simulations at 115 min.
Citation: Monthly Weather Review 143, 1; 10.1175/MWR-D-14-00151.1
Example downdraft and forward-flank parcels were chosen for the CONTROL (parcels A, C) and the CBL INVRAD (parcels B, D) trajectory streams (Fig. 17) and vorticity budgets were calculated along their paths (Fig. 18). In the CONTROL supercell, downdraft parcels (A) tend to originate at low levels in the forward flank, acquiring positive ζ as they ascend, before ζ decreases to negative values during descent, and finally reacquiring positive ζ as they re-ascend to 125 m from near the ground. In contrast, CBL INVRAD downdraft parcels (B) tend to continuously descend from above the boundary layer with smaller ζ oscillations driven mostly by changes in the tilting term before stretching dominates after 112 min. It is not clear, however, how (or if) rolls influence these parcels.
As in Fig. 9, but for parallel-shear simulations at 115 min.
Citation: Monthly Weather Review 143, 1; 10.1175/MWR-D-14-00151.1
As in Fig. 10, but for parallel-shear simulations at 115 min.
Citation: Monthly Weather Review 143, 1; 10.1175/MWR-D-14-00151.1
The influence of rolls is clearer when examining the trajectories of forward-flank parcels. CONTROL forward-flank parcels (C) approach the mesocyclone near the ground with near-zero ζ, before they rise and acquire positive ζ first through tilting and later through stretching after 112 min. The CBL INVRAD forward-flank parcels (D) often have slightly positive ζ (>0.001 s−1) along much of their path, which is increased first through tilting after 106.5 min and then through a gradual increase in stretching after 110 min. Figure 17 shows that forward-flank parcels tend to follow a path along an area of increased low-level convergence associated with the remnants of a roll. A comparison with other parcels in this stream (Figs. 16c,d) suggests that most parcels in this stream follow the same roll and develop cyclonic vorticity earlier than CONTROL forward-flank parcels. Unlike in the perpendicular-shear case, parcel trajectories lie along rolls, rather than across them. Thus, air parcels entering the LLM may remain in the same band of positive ζ (or convergence) associated with a roll for a longer period of time than with perpendicular rolls. Furthermore, rolls are relatively stationary in the storm-relative reference frame when compared with their perpendicular counterparts, such that the mesocyclone encounters less temporally varying environmental conditions. If conditions are favorable, rolls may enhance low-level circulation relative to a homogeneous environment.
Apart from the difference in roll-relative storm motion, this mean hodograph tends to be less supportive of strong LLMs than the perpendicular-shear mean hodograph—the homogeneous-environment storm with this hodograph has a considerably weaker low-level circulation than with the perpendicular-shear hodograph. The reason for this discrepancy is unclear, but perhaps the large amount of crosswise vorticity in the boundary layer (Fig. 1c) is detrimental to low-level rotation as suggested by other studies (e.g., Wicker 1996; Nowotarski and Jensen 2013). The supercells with the parallel-shear hodograph tend to be characterized by pulsing of the RFD, which causes outflow surges that periodically replace the LLM with a vortex sheet. When rolls are present, cyclonic (anticyclonic) roll vorticity perturbations locally enhance (suppress) the background cyclonic vorticity, resulting in periodic vorticity extrema. Thus, it seems that the steady storm-relative position of roll perturbations provides consistently favorable regions for the development and intensification of persistent low-level cyclonic vortices, particularly when the hodograph (and the resulting storm dynamics) are not conducive to a steady LLM.
5. Sensitivity to perturbations in initiation mechanism
For both the perpendicular and parallel-shear CBL INVRAD simulations, we ran a small ensemble of four additional simulations to verify that trends in low-level circulation when rolls are present (Figs. 6 and 14) are a robust result, rather than artifacts of initial warm bubble placement relative to rolls in the environment. In each ensemble member the center of the initial warm bubble perturbation was translated either 5 km north, south, east, or west of the warm bubble in the previously discussed CBL INVRAD simulations. Despite some minor differences in the timing, location, and strength of low-level vorticity maxima in each of the ensemble member supercells, the general characteristics and evolution described in the previous section are observed in each member. We calculated the circulation about a 2-km-radius ring at z = 25 m for every grid point. Time series of the maximum circulation at any grid point for each CBL INVRAD ensemble member, the ensemble average, and the CONTROL simulation are shown for the last hour of each simulation in Fig. 19.
Time series of maximum circulation about a 2-km-radius ring centered on any grid point at z = 25 m for the CONTROL (black) and CBL INVRAD ensemble members (dashed red) for the (a) perpendicular- and (b) parallel-shear simulations. The average maximum circulation of the CBL INVRAD ensemble members is shown in solid red and the range of values at each time is color shaded.
Citation: Monthly Weather Review 143, 1; 10.1175/MWR-D-14-00151.1
The perpendicular-shear circulation trends (Fig. 19a) are similar to those seen in Fig. 6. The CONTROL circulation is similar to or weaker than the CBL INVRAD ensemble average circulation over the time period from 60 to 95 min, before circulation intensifies and is consistently stronger than the CBL INVRAD ensemble average. Indeed, after 100 min, the CONTROL circulation lies outside the envelope of maximum circulation in any of the CBL INVRAD ensemble members. This adds confidence to the result that rolls perpendicular to supercell motion may be detrimental to the LLM.
The parallel-roll ensemble-maximum circulation time series (Fig. 19b) also support the results discussed in the previous section. After 85 min, the CBL INVRAD maximum circulation is generally stronger than the CONTROL maximum circulation. The CBL INVRAD ensemble average circulation is consistently stronger than the CONTROL circulation, though individual members occasionally have similar or weaker maximum circulation than the CONTROL simulation. Despite the apparent dependence of circulation on initiation location, rolls parallel to storm motion almost always increase the maximum circulation in each supercell over the horizontally homogeneous environment in the CONTROL simulation.
We also tested the sensitivity of the CONTROL simulation to random thermal perturbations in the initiating warm bubble in two additional simulations for each hodograph (not shown). Though there is spread in the time series of maximum circulation between the three CONTROL simulations, the general evolution of low-level mesocyclones and the ensemble average maximum low-level circulation are qualitatively consistent with the CONTROL simulations shown here. This suggests that the differences between the CONTROL and CBL INVRAD simulations are robust signals of the effects of environmental heterogeneity rather than simply the result of varying turbulent realizations produced by random perturbations.
6. Conclusions
Supercell thunderstorms were simulated in an idealized environment with resolved boundary layer convection in the form of quasi-two-dimensional rolls and compared with those simulated with a horizontally homogeneous base state. The principal intent of the numerical simulations was to determine if rolls have a considerable effect on the evolution of mature supercells, and if any such effects are dependent on the orientation of rolls relative to the supercell motion. Two sets of simulations were performed with different hodographs such that right-moving-supercell motion was either perpendicular or parallel to the boundary layer vertical shear and roll axes (when present). Within each set of simulations, rolls were found to have only small effects on bulk measures of supercell strength such as wmax, ζmax, maximum surface wind speed, or liquid and ice water mass. When differences in these quantities did occur, the horizontally homogeneous (CONTROL) supercells had higher values, regardless of hodograph.
In the early stages of storm evolution (in the first hour), more intense vertical vorticity maxima develop in the supercells with rolls in the near-storm environment, regardless of their orientation relative to storm motion. These are associated with the amplification of vertical vorticity perturbations in the boundary layer where they encounter the supercell outflow boundaries. The interaction between rolls and the supercell outflow boundary in the context of misocyclone development and the potential for non-mesocyclone tornadoes will be explored in forthcoming publications.
At later times, differences in the evolution of the low-level mesocyclone (LLM) are dependent on the orientation of the low-level shear and rolls. These differences are most clear between the CONTROL supercell and the simulation wherein cloud shading effects are removed (CBL INVRAD). For a hodograph with boundary layer shear perpendicular to storm motion, the CONTROL supercell has a stronger, more persistent near-ground circulation associated with its mesocyclone, whereas the vorticity maxima beneath the updraft in the simulated supercell with rolls have weaker circulation and are more transient in nature—at least over the first hour in which an LLM is present. For a hodograph with boundary layer shear parallel to storm motion, the pattern of low-level circulation is more cyclic in nature, with maximum circulation that is generally weaker than with the perpendicular-shear hodograph; however, when rolls are present in the near-storm environment, low-level circulation values are often enhanced relative to the CONTROL supercell. These trends are further supported by a small ensemble of additional simulations wherein the initiating warm bubble position is varied relative to rolls in the environment.
Though these effects appear to be dependent on the quasi-periodic organization and orientation of boundary layer heterogeneity, it is possible that the presence of boundary layer convection in any form may alter LLM evolution, and these effects may vary based on the average low-level wind profile. We also stress that these results and the conclusions drawn from them may only apply to the first two hours of supercell evolution simulated here. It is possible that differences in LLMs may change at later stages of storm evolution.
In both the perpendicular- and parallel-shear cases, the effects of the rolls are most prominent along the forward-flank outflow boundary. Both advection of preexisting vertical vorticity associated with the boundary layer convection and modifications to tilting and stretching of horizontal vorticity in the forward-flank baroclinic zone by rolls appear to influence the amount and location of positive ζ present in the LLM. Previous studies (e.g., Davies-Jones and Brooks 1993; Straka et al. 2007; Markowski et al. 2008), however, have postulated that the baroclinic generation of horizontal vorticity and its subsequent reorientation by a downdraft are critical to the development of near-surface rotation. This source of ζ is present both with and without rolls (i.e., the “downdraft parcels”), such that the role of rolls is likely an enhancement or suppression (depending on roll orientation) of the low-level circulation created through this process. In other words, rolls influence the evolution of LLMs (as conceptualized in Fig. 20), but they do not seem to create LLMs. When the storm moves perpendicular to rolls (Fig. 20a), air parcels entering the mesocyclone from the forward-flank provide inconsistent ζ to the LLM as it moves across environmental perturbations that persist even into the forward-flank precipitation region. By contrast, when the supercell moves parallel to rolls (Fig. 20b), forward-flank parcels may provide an additional source of positive ζ if an LLM moves along a positive ζ perturbation associated with a roll for an extended period.
Conceptual model of the effects of rolls on supercell low-level mesocyclones. Bands of environmental ζ perturbations are associated with rolls (black lines, solid is positive ζ and dashed is negative ζ), which can persist into the forward-flank precipitation region (gray shading). These perturbations are amplified along the storm’s outflow boundary (blue line), causing periodic maxima (minima) in ζ [solid (dashed) black circles]. (a) When supercell motion is perpendicular to roll axes, the low-level mesocyclone (M) crosses these perturbations such that parcels entering the low-level mesocyclone from the forward flank provide an alternating supply of positive (negative) ζ [red arrows, with solid (dashed) segments representing positive (negative) vertical vorticity along the trajectory]. At times, such as that represented here, the vertical vorticity associated with the low-level mesocyclone is weakened. At other times, vertical vorticity in the LLM is similar to that in a horizontally homogeneous environment. The overall result is an LLM with less persistent, often weaker, circulation than in a homogeneous environment. (b) When supercell motion is parallel to roll axes, the low-level mesocyclone encounters more consistent environmental conditions such that trajectories entering the mesocyclone may move along positive ζ perturbations in the forward flank for an extended period, as shown here. In this case, the low-level mesocyclone circulation is enhanced relative to a homogeneous environment.
Citation: Monthly Weather Review 143, 1; 10.1175/MWR-D-14-00151.1
Owing to the limited number of simulations allowed by the computational demands of this problem, the generality of these findings remains uncertain. Regardless, these results indicate the potentially diverse and situation-dependent influences of rolls on supercells. These simulations did not explicitly resolve tornadoes, but under the assumption that increased low-level vertical vorticity and circulation are favorable conditions for tornadoes, we might reasonably speculate some implications of this research regarding tornadoes associated with supercell mesocyclones. Regardless of roll orientation, it appears that rolls provide a source of preexisting near-ground vertical vorticity that is amplified in convergent regions along supercell gust fronts. Such effects have generally been neglected in hypotheses regarding the development of near-ground rotation and tornadogenesis in supercells. In our experience, it seems that most observed tornadic supercells tend to cross rolls (akin to our perpendicular-shear simulations), such that rolls might be expected to disrupt LLM intensification, perhaps delaying tornadogenesis or interfering with tornado maintenance. In the seemingly rarer case that supercells move parallel to rolls, the mean hodograph is probably less supportive of tornadoes, but our results imply that tornadogenesis would be more likely with rolls than without them.
Even if these suppositions are true, at least some part of supercell inflow is often shaded by the anvil (e.g., Figs. 3c,f), such that the direct influence of rolls may be negated. When cloud shading is included (CBL FRAD) in our simulations, the LLM circulation tends to be smallest regardless of hodograph, and rolls were weakened in the near-storm environment as it became shaded by the supercell anvil cloud. The effects of anvil shading on the near-storm environment are further discussed in Nowotarski (2013) and forthcoming publications.
Future research on this topic is required before any hypotheses regarding roll influence on tornadogenesis can be verified with certainty and recommendations for considerations of boundary layer convection can be made to forecasters. Subsequent investigations might extend the methodology of this study to other hodographs and thermodynamic profiles to investigate the robustness of our conclusions for a range of environments, or decrease grid spacing such that tornadoes may be explicitly resolved. For instance, in a less capped environment, CBL motions themselves may initiate deep convection (in contrast to the warm-bubble perturbation employed herein). The role of boundary layer convection in deep convection initiation (CI) is beyond the scope of this study, but it is possible that CBL effects on CI could also, in part, determine future LLM evolution. Comparison of numerical simulations to observations is a logical progression of this work to confirm that the effects of boundary layer rolls on supercells are adequately represented by these simulations; isolating the effects of rolls in observations, however, may be difficult. Despite uncertainty regarding specific situational effects, these results suggest that boundary layer convection can meaningfully influence supercell LLMs. These impacts should continue to be considered in future investigations of low-level rotation in supercell thunderstorms.
Acknowledgments
The authors thank Drs. Nels Shirer, Lyle Long, Morris Weisman, Jim Marquis, and Ryan Hastings for many helpful suggestions throughout the course of this project. We also thank Dr. David Lewellen and two anonymous reviewers for providing careful reviews and suggestions that improved this manuscript. This work was primarily supported by NSF Grant AGS-0644533. Y. Richardson’s time was supported by NSF Grant AGS-1157646. Computational resources and travel support were provided by the National Center for Atmospheric Research. Many of the figures in this manuscript were created using the Grid Analysis and Display System (GrADS) developed by the Center for Ocean–Atmosphere–Land Studies.
APPENDIX
Trajectory and Vorticity Budget Calculations
Backward trajectories were calculated from the C grid (Arakawa and Lamb 1977) using model output stored every 15 s. Parcel locations were determined using the fourth-order Runge–Kutta (RK4) method with a 3-s time step. Vorticity and vorticity forcing terms were calculated along trajectories using buoyancy and velocity gradients interpolated to every parcel location. For parcels traveling below the lowest scalar grid level, buoyancy equivalent to the value at the lowest grid level was assumed.
Comparison of the integrated forcing ζ and interpolated ζ shows relatively good agreement over the lifetime of the trajectories. For the parcels analyzed in this study, the mean percentage error (MPE) in vertical vorticity at the backward trajectory initialization time (i.e., the end point of the trajectory) is 33%, with a mean absolute error of 8.2 × 10−3 s−1. Part of this error is likely due to the neglect of subgrid-scale mixing and surface friction in the vorticity budgets. Indeed, trajectories in the more turbulent CBL INVRAD simulations (MPE = 52%) tended to have a larger error in their vorticity budgets than their counterparts in the CONTROL simulations (MPE = 15%).
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Boundary layer convection is determined to be “robust” when the maximum vertical velocity at 100 m AGL exceeds 1 m s−1.
Rotation is associated with a dynamic pressure drop (e.g., Rotunno and Klemp 1985; Markowski and Richardson 2010).
This formulation of the OW parameter is opposite from the original formulation, wherein vorticity is subtracted from the deformation, but it has precedents in other applications to geophysical flows (e.g., Isern-Fontanet et al. 2003; Wang et al. 2010).
Several different radii were tested, but there were not qualitative changes in the results.
There are no major qualitative changes when plotting the maximum low-level circulation around a circuit centered on any grid point at the lowest grid level, because the subjectively determined LLM is generally (but not always) associated with the maximum low-level circulation.
This height level was chosen rather than a lower level in order to decrease the amount of time parcels spent below the lowest grid level, where velocities were approximated based on the previously described assumptions.
There has been some suggestion in the literature that inflow parcel trajectories are not realistic (e.g., Dahl et al. 2012). As such, we have chosen not to analyze these parcels.
These parcels are representative of the vorticity evolution for other parcels in their streams for the CONTROL simulation. Because of the variations in individual parcels in the CBL INVRAD simulation, no single parcel is representative of any other parcels in its stream for that simulation; however, the magnitude of ζ variations along the parcel are similar to other parcels in these streams.
This other vortex might also be described as a mesocyclone; however, it is not associated with an occlusion in the outflow boundary or under the core of the main updraft like the northern vortex.