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272 MONTHLY WEATHER REVIEW VOLUME 143

Supercell Low-Level Mesocyclones in Simulations with a Sheared Convective Boundary Layer

CHRISTOPHER J. NOWOTARSKI,* PAUL M. MARKOWSKI, AND YVETTE P. RICHARDSON Department of Meteorology, The Pennsylvania State University, University Park, Pennsylvania

GEORGE H. BRYAN 1 National Center for Atmospheric Research, Boulder, Colorado

(Manuscript received 2 May 2014, in ﬁnal form 5 September 2014)

ABSTRACT

Simulations of supercell thunderstorms in a sheared convective boundary layer (CBL), characterized by quasi-two-dimensional rolls, are compared with simulations having horizontally homogeneous environments. The effects of boundary layer convection on the general characteristics and the low-level mesocyclones of the simulated supercells are investigated for rolls oriented either perpendicular or parallel to storm motion, as well as with and without the effects of cloud shading. Bulk measures of storm strength are not greatly affected by the presence of rolls in the near-storm environment. Though boundary layer convection diminishes with time under the anvil shadow of the supercells when cloud shading is allowed, simulations without cloud shading suggest that rolls affect the morphology and evolution of supercell low-level mesocyclones. Initially, CBL vertical vorticity perturbations are enhanced along the supercell outﬂow boundary, resulting in nonnegligible near-ground vertical vorticity regardless of roll orientation. At later times, supercells that move perpendicular to the axes of rolls in their environment have low-level mesocyclones with weaker, less persistent circulation compared to those in a similar horizontally homogeneous environment. For storms moving parallel to rolls, the opposite result is found: that is, low-level mesocyclone circulation is often enhanced relative to that in the corresponding horizontally homogeneous environment.

1. Introduction Klemp and Rotunno 1983; Rotunno and Klemp 1982, 1985; Wicker and Wilhelmson 1995; McCaul and Most numerical investigations of supercell thunder- Weisman 2001; Naylor et al. 2012)thisapproachdoes storms have used idealized, horizontally homogeneous not account for the inherent inhomogeneity of the environments without surface fluxes of heat, moisture, turbulent convective boundary layer (CBL) found in and momentum. Though fruitful in exposing basic many severe-storm environments. Increased comput- supercell dynamics and the relationship between storm ing power now allows for inclusion of more physical type and the characteristics of the environment (e.g., processes (such as radiation and land surface parame- Schlesinger 1975; Klemp and Wilhelmson 1978a,b; terizations) and better resolution of boundary layer turbulence than in earlier idealized simulations. With this expanded capability, we investigate how meso- * Current affiliation: Department of Atmospheric Sciences, g-scale horizontal variability in a CBL interacts with Texas A&M University, College Station, Texas. 1 The National Center for Atmospheric Research is sponsored supercell thunderstorms. by the National Science Foundation. Because the vast majority of significant tornadoes are spawned by supercell thunderstorms (Trapp et al. 2005), much of our research is concerned with their Corresponding author address: Christopher J. Nowotarski, Department of Atmospheric Sciences, Texas A&M University, low-level mesocyclones (LLMs). Numerous studies 3150 TAMU, College Station, TX 77843-3150. have demonstrated the importance of environmental E-mail: [email protected] properties such as low-level wind shear and moisture

DOI: 10.1175/MWR-D-14-00151.1

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(e.g., Kerr and Darkow 1996; Rasmussen and Blanchard that it might draw inflow from both roll updraft and 1998; Craven and Brooks 2004) in discriminating be- downdraft simultaneously, resulting in equal ingestion tween tornadic and nontornadic supercells, but it re- of air parcels with favorable and unfavorable thermo- mains unclear how the horizontal variability of these dynamic quantities. Yet, Crook and Weisman showed quantities in a CBL may affect the potential of a su- that inhomogeneities in the storm environment may percell to become tornadic. Moreover, inviscid dy- disrupt aspects of supercell evolution, including the namical arguments regarding tornadoes that form in gust front occlusion process. Other studies have noted supercell LLMs generally assume there is no preexist- the appearance of ‘‘feeder clouds’’ in the inflow envi- ing vorticity (z ) near the surface in supercell environ- ronment of supercells and have noted that these clouds ments; thus, the development of rotation next to the may be related to rolls and could signal storm in- surface (a prerequisite for tornadogenesis) requires tensification (Weaver et al. 1994; Weaver and Lindsey a downdraft to reorient and redistribute ambient hor- 2004; Mazur et al. 2009). izontal vorticity and/or horizontal vorticity generated Building upon these previous studies, this article pres- baroclinically within a supercell (e.g., Davies-Jones ents the results of simulations of supercells in a CBL, 1982; Davies-Jones and Brooks 1993; Markowski et al. focusing primarily on characteristics and evolution of 2008). As Nowotarski et al. (2014, hereafter NMRB14) LLMs. We compare these simulations against simulations and others (Arnottetal.2006; Markowski and Hannon that have horizontally homogeneous environments hav- 2006; Marquis et al. 2007) have shown, CBLs typically ing similar overall conditions (e.g., CAPE and shear). do contain patches of significant vertical vorticity that Given the quasi-linear organization of a CBL composed would precede storm development if it occurs. The extent of rolls, it is likely that the orientation of rolls relative to which this vorticity might affect the development to storm motion may, in part, dictate their effects on and evolution of LLMs in supercells has been an un- supercell LLMs. As such, we use two different hodo- answered question. graphs that result in sets of simulations with storm motion Previous studies have found sensitivity of low-level perpendicular to the boundary layer vertical shear and rotation to horizontal variations in the storm environ- convective rolls (hereafter ‘‘perpendicular-shear’’ simu- ment on the meso-b scale (;100 km). Richardson lations) or parallel to the boundary layer vertical shear (1999) found that isolated supercells in areas of in- and convective rolls (hereafter ‘‘parallel shear’’ sim- creased low-level moisture exhibited both stronger ulations). The following section describes our methods, updrafts and low-level rotation. Observations (Maddox including the experiment design and the model configu- et al. 1980; Weaver and Purdom 1995; Markowski et al. ration. Sections 3 and 4 present results and analysis from 1998; Rasmussen et al. 2000) have shown that many the perpendicular-shear and parallel-shear simulations tornadoes develop within supercells interacting with (respectively). Sensitivity to the initiation location of the mesoscale thermal boundaries. Atkins et al. (1999) supercells relative to the rolls is discussed in section 5.We found that stronger low-level rotation develops when offer concluding remarks in section 6. a simulated supercell moves along a mesoscale boundary, and that the mechanism for the development 2. Methods of the LLM is altered when a boundary is present. Wheatley and Trapp (2008) showed in real-data simu- NMRB14 describe the methodology used herein for lations that preexisting boundaries could also affect the simulating a realistic CBL composed of boundary layer strength and development mechanism of mesovortices rolls. The modeled rolls have aspect ratios (i.e., the in quasi-linear convective systems (QLCSs). horizontal distance between rolls divided by the Studies examining the effects of small-scale (order boundary layer depth) of ;3 and they are associated 1 km) horizontal variability on deep moist convection with quasi-periodic horizontal fluctuations in variables are limited (Carpenter et al. 1998; Crook and Weisman that are relevant to severe convective storms, such as 1998), and none have examined the specific case of temperature, moisture, convective available potential CBL rolls (often referred to as ‘‘horizontal convective energy (CAPE), convective inhibition (CIN), vertical rolls’’) interacting with supercells. Considering that the velocity, vertical wind shear, and storm-relative helicity horizontal scale of the perturbations associated with (SRH) throughout the boundary layer. The boundary rolls (,5 km) is smaller than that of a supercell thun- layer development and magnitude of the environmen- derstorm updraft (.10 km), bulk measures of storm tal variations are generally consistent with observa- strength (e.g., maximum updraft speed, maximum z) tions of rolls (e.g., LeMone and Pennell 1976; Reinking may be relatively unaffected by the CBL. The hori- et al. 1981; Atlas et al. 1986; Weckwerth et al. 1996, zontal extent of a supercell updraft is large enough such Markowski and Richardson 2007). Conditions in the

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TABLE 1. Summary of differences in conﬁguration of supercell simulations in each experiment.

Simulation name CBL FRAD CBL INVRAD CONTROL Radiation Full radiation No interaction of radiation with No radiation liquid water or ice Initial state Restart file from BASE Restart file from BASE with Horizontally homogeneous with resolved CBL resolved CBL domain average from BASE Surface fluxes Full surface fluxes Full surface fluxes No heat or moisture fluxes with constant surface drag Base-state nudging Not required Not required Yes updraft branches of roll circulations tend to be warmer FRAD has full radiation and surface fluxes so that and more moist, resulting in greater CAPE, whereas subsequent development of deep moist convection af- conditions in downdraft branches tend to be cooler and fects shortwave and longwave radiation fluxes at the less moist, resulting in less CAPE. NMRB14 also found ground through modifications in atmospheric optical that the simulated CBL comprises alternating bands of depth by cloud water, cloud ice, and precipitation. CBL 2 2 positive and negative vertical vorticity [z, O(10 3)s 1] INVRAD is identical to CBL FRAD, except that the located at the interface between roll updrafts and radiation parameterization was modified such that downdrafts, which originate from tilting of the ambient deep moist convection is ‘‘invisible’’ to radiation in this vertical wind shear by the roll circulations. With time simulation. The CBL INVRAD simulation prevents and continued heating of the model surface, the CBL cloud-shading effects from weakening boundary layer deepens, rolls become less organized (i.e., boundary convection so that the effects of rolls in the near-storm layer convection becomes more three dimensional), environment may be determined clearly. This simula- 2 2 and stronger z extrema O(10 2)s 1 occasionally de- tion is also used in a comparison with the CBL FRAD velop. simulation to understand the effects of cloud shading on the rolls. These effects are discussed in Nowotarski a. Overview (2013) and forthcoming publications. The effects of rolls and their orientation relative to The CONTROL simulation is initialized with a hor- storm motion are studied in two suites of simulations izontally homogeneous thermodynamic and kinematic using the cloud model CM1, release 15 (Bryan and profile that is determined by horizontally averaging Fritsch 2002; Bryan 2002). Each suite contains four output from the BASE simulation at t ’ 3 h. Thus, the main simulations. In the first simulation, BASE, a CBL domain-average initial conditions in all three supercell composed of rolls develops owing to the inclusion of simulations are identical. The CONTROL simulation solar radiation and surface physics (i.e., a soil model does not include surface fluxes of heat and moisture or and surface fluxes). The environment is initially stably radiation. Consequently, there is no temporal change stratified and horizontally homogeneous, but as sensi- to the environment as in the CBL FRAD and CBL ble surface heat fluxes destabilize the boundary layer, INVRAD simulations, which complicates the com- dry convection develops and quickly organizes into parison between them. To make the simulations more rolls. The details of the simulated CBL and its evolu- comparable, some variables are constantly nudged to- tion are presented NMRB14. The BASE simulation is ward the domain-average values from the CBL simu- run for 8 h (480 min) as a basis for comparison of the lations (as described below). Surface drag is applied to evolution of the CBL with and without the presence of the CONTROL simulation with a constant drag co- deep convection. efficient (cd 5 0.005) representative of the average Once the BASE simulation develops robust bound- value in the CBL simulations. ary layer convection,1 three supercell simulations are b. Numerical model configuration initialized and run for 2 h (7200 s). Table 1 summarizes the differences between these simulations. The first two For all simulations, CM1 is run with the same con- simulations, CBL FRAD and CBL INVRAD, are ini- figuration as the ‘‘supercell ready’’ simulations dis- tialized with restart files from the BASE simulation cussed by NMRB14 and further detailed in Nowotarski with a horizontally heterogeneous CBL with rolls. CBL (2013). The domain size is 250 km 3 200 km 3 18 km, with constant horizontal grid spacing of 200 m and vertical grid spacing stretched from 50 m below 3 km 1 Boundary layer convection is determined to be ‘‘robust’’ when to 500 m above 8.5 km. In horizontal grid-spacing 2 the maximum vertical velocity at 100 m AGL exceeds 1 m s 1. sensitivity tests, NMRB14 found that, though not

Unauthenticated | Downloaded 09/29/21 04:52 AM UTC JANUARY 2015 N O W O T A R S K I E T A L . 275 ideal for LES, the flow was qualitatively turbulent at this To keep the average storm environment of the grid spacing, similar to simulations with 100-m horizontal CONTROL simulation similar to that in the CBL sim- grid spacing, and sufficiently representative of the char- ulations, potential temperature (u), water vapor mixing acteristics and evolution of boundary layer convection. ratio (qy), and horizontal wind components (u, y) over Though NMRB14 did not explicitly test the sensitivity of the lowest 3 km are continually nudged toward the av- LLMs to grid spacing, they are of a similar (if not larger) erage environment of the CBL simulations. The nudging length scale as boundary layer convection, such that we for each variable, Danudge(z), depends only on height expect this grid spacing to adequately resolve the effects and is computed by dividing the difference in the of rolls on LLMs. The large (small) time step is 0.75 domain-average (denoted with overbars) profile of (0.125) s, which is sufficient to maintain computational variables in the BASE simulation over the same period stability throughout the simulations. The upper and lower that the supercells are simulated (tstart to tend), by the boundaries are rigid walls with a Rayleigh sponge layer number of large model time steps in that period, Nsteps, applied above 14 km and all lateral boundary conditions as follows: are periodic. a (z, t ) 2 a (z, t ) Precipitation microphysics is parameterized with D 5 BASE end BASE start anudge(z) . (1) the National Aeronautics and Space Administration Nsteps (NASA) Goddard formulation (Tao and Simpson 1993)oftheLin et al. (1983) single-moment bulk ice The nudging from (1) is added to every grid point in the microphysical scheme. When required, radiation is CONTROL simulation at each height level during every parameterized using a vertical column model with the large integration time step along with the other model- NASA Goddard Cumulus Ensemble formulations for calculated changes to that variable during the time step, both longwave and shortwave interactions with air and Damodel(x, y, z, t), as follows: water species (Chou et al. 1998; Tao et al. 1996; Chou and Suarez 1999; Chou et al. 1999). For CBL INVRAD a(x, y, z, t) 5 a(x, y, z, t 2Dt) simulations, mixing ratios of liquid and solid water 1Da (x, y, z, t) 1Da (z). (2) species are set to zero within the radiation scheme, such model nudge that optical thickness within the column is not affected 2 by the presence of clouds or precipitation. Total nudging [aBASE(z, tend) aBASE(z, tstart)] for both the perpendicular- and parallel-shear CONTROL c. Base states and initialization simulations is shown in Fig. 2. In general, nudging is The initial sounding used for the BASE simulation most prominent over the lowest 1 km of the model is described in NMRB14. The CBL FRAD and CBL domain and acts to deepen the boundary layer with INVRAD simulations are started with restart files time. Potential temperature within the boundary layer taken from the BASE simulation at the time when rolls is nudged by about 3 K (Fig. 2a) with cooling of the begin to organize (165 min) with radiation corre- capping inversion as the mixed layer deepens. Bound- sponding to a local time of 0945 UTC 15 May in north- ary layer moisture is increased, with little change above central Oklahoma. The CONTROL simulation is the boundary layer (Fig. 2b). Momentum nudging started with a sounding that is the horizontal average of generally acts to decrease the magnitude of the wind in the BASE simulation at this time (Fig. 1a; black ho- the entrainment zone as the boundary layer deepens dographs in Figs. 1b,c). At this point, boundary layer and to increase the magnitude of the wind near the convection has mixed the lowest ;500 m of the model ground as rolls mix higher momentum air downward in domain, increasing surface-based CAPE from 1385 to the CBL simulations (Fig. 2c). 2 2 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 3. Perpendicular-shear simulation results 2 from 506 to 580 m2 s 2 in the perpendicular-shear en- a. General characteristics vironment, and decreasing 0–3-km SRH from 379 to 2 323 m2 s 2 in the parallel-shear environment (Figs. 1b,c). After 60 min in each simulation, a dominant, right- Deep convection is initialized in all supercell simula- moving supercell develops after storm splitting. The right- tions using a 10-km (1 km) horizontal (vertical) radius moving supercells have an average storm motion over the 21 bubble centered 1 km above the ground with a maxi- last hour of the simulation of (cx, cy) 5 (18, 5) m s . mum potential temperature perturbation of 3 K. These Figures 3a–c show the supercells at 90 min (during their simulations are run for 120 min (2 h). mature state) from the three perpendicular-shear

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FIG. 1. (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. simulations. In all three cases, the simulated reflectivity than in the CBL INVRAD simulation. Initially, severe field exhibits supercell structure (e.g., Lemon and Doswell winds are confined to the precipitation core northwest of 1979) with most precipitation located north of the main the LLMs, but severe winds also develop in the southern updraft and an appendage of higher reflectivity wrapping portion of the low-level mesocylone at 100 min in the around the rear (western) flank of the updraft. CONTROL and CBL FRAD simulations and at To assess the effect of rolls on overall storm strength, 105 min in the CBL INVRAD simulation. Total liquid we compare several bulk measures of storm intensity. and ice water mass is generally 5%–10% higher in the The maximum updraft at any height or any time in CONTROL than the CBL simulations over the last 2 the CONTROL simulation is 85 m s 1 compared with hour. 2 2 84 m s 1 in the CBL INVRAD simulation and 81 m s 1 Time series of maximum integrated updraft helicity in the CBL FRAD simulation. The strongest wind speed over any column in the domain (UHmax, Kain et al. 2 at the lowest scalar grid level (z 5 25 m) was 42 m s 1 in 2008), where 21 the CONTROL compared with 37 m s in both CBL ð 2 simulations. Severe winds (.27 m s 1) at the lowest grid 6km UH 5 wz dz, (3) level first occur at 75 min in the CBL FRAD simulation 1km and at 85 min in the CONTROL and CBL INVRAD simulations. In general, the area of severe wind gusts is are shown in Fig. 4 for the right-moving supercell in larger in the CONTROL and CBL FRAD simulations all three perpendicular-shear simulations. Despite a

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stronger initial peak in the CONTROL simulation,

UHmax is similar among all three simulations, with var- 2 iations between runs usually less than 1000 m2 s 2. Time series (not shown here, see Nowotarski 2013) of maxi-

mum vertical vorticity zmax and vertical velocity wmax are similar between the CONTROL or CBL INVRAD simulations. Over the last hour, the CBL FRAD simu-

lation tends to have weaker wmax (by ;5%) at midlevels (z 5 4 km; Fig. 3c) and weaker zmax (by ;30%) at the lowest grid level. 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 sup- presses rolls (evident in the relative lack of inflow z perturbations near the updraft and precipitation core in 2 Fig. 3c). Appreciable cyclonic z (.0.01 s 1) first develops near the ground in the CONTROL supercell on the im- mediate 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 z . 2 0.08 s 1 by 106 min (Fig. 5a). The CONTROL LLM is associated with protrusions, or ‘‘feeders’’ of positive z 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). In contrast, low-level z develops at multiple locations along the CBL INVRAD supercell outflow boundary earlier than z develops in this region of the CONTROL supercell as ambient z 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 z perturbations persist at 90 min; Fig. 3b). These vorticity extrema con- solidate 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 morphol- ogyoftheLLMsat106mininFigs. 5a,b. After 110 min, FIG. 2. Total nudging over 120 min in the perpendicular- (blue) and parallel- (red) shear CONTROL simulations for (a) potential tem- the initial CONTROL LLM weakens, and is soon re- perature, (b) water vapor mixing ratio, and (c), horizontal velocity. placed with a new LLM by 120 min. By this time a stronger, concentrated area of z, more similar to the

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21 FIG. 3. Plan views of reﬂectivity at z 5 1 km (color shaded), vertical velocity at z 5 4 km (gray contours, 5 m s 2 interval), and vertical vorticity at the lowest grid level (z 5 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 5 90 min. The 20.5-K perturbation potential temperature isentrope at z 5 25 m is shown as a blue line with close dashes. For horizontal scale, see legend in the lower-left corner of (a).

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FIG. 4. Time series of maximum integrated updraft helicity in the right-moving supercell of each perpendicular-shear simulation.

CONTROL LLM, has emerged in the CBL INVRAD effects) are most prominent in the CBL INVRAD simulation. The low-level morphology of the CBL simulation. Before proceeding to the analysis, how- FRAD supercell (Figs. 3c and 5c) generally lies be- ever, it is helpful to define a few of the mathematical tween that of the CONTROL and CBL INVRAD su- quantities and methods employed. percells, but the CBL FRAD supercell does not develop Circulation is an integrated measure of vorticity, de- a clear strong, persistent LLM as in the CONTROL fined about a closed material circuit of fluid parcels as simulation and even fails to achieve the maximum low- þ level vertical vorticity at the end of the CBL INVRAD C [ v Á dl, (4) simulation (not shown). To understand the means by which rolls affect LLMs, where v is the velocity vector and l is the position vector we turn to circulation and trajectory analyses of the of a point on the material circuit. By convention, the in- LLMs in each simulation. The location of the center of tegral is performed moving counterclockwise around the the LLM was subjectively determined at 5-min in- circuit. Circulation is related to vorticity as follows: tervals over the last hour of the simulations. For the ð CONTROL supercells, the center of the LLM is gen- 5 v Á erally the location of the highest z at the lowest vertical C n dA, (5) A grid level beneath the main updraft in close proximity to an inflection in the outflow boundary. For the CBL where A is the area of a surface bounded by the circuit, simulations and at times in the CONTROL when v is the vorticity vector, and n is the unit vector normal multiple vorticity maxima exist in this area, the center to the surface. For a circuit lying in a horizontal plane, of the LLM was estimated through a visual inspection the circulation is proportional to the average vertical of the storm-relative wind, pressure, and temperature vorticity in the region enclosed by the circuit. fields over the depth of the boundary layer. In such Vorticity alone cannot adequately diagnose rotation in situations, the area of cyclonic vorticity collocated with a fluid. For instance, areas with large shear deformation the greatest pressure drop2 and/or largest inflection in also have large vorticity. By subtracting the squares of the the outflow boundary, and located near the center of stretching deformation (D ) and shearing deformation rotation in the storm-relative wind field, was selected 1 (D ) from the square of the vertical vorticity (z), we ar- as the center of the LLM. Though the forthcoming 2 rive at the Okubo–Weiss parameter (OW; Okubo 1970; analysis was performed for all three simulations in each Weiss 1991): suite, as before, we will focus on the CONTROL and CBL INVRAD simulations because rolls (and their ›y ›u 2 OW 5 z2 2 D2 2 D2 5 2 1 2 ›x ›y ›u ›y 2 ›y ›u 2 2 Rotation is associated with a dynamic pressure drop (e.g., 2 2 2 1 . (6) Rotunno and Klemp 1985; Markowski and Richardson 2010). ›x ›y ›x ›y

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Large positive OW parameter3 occurs where vorticity Consequently, circulation is weaker in the vicinity of dominates deformation, implying a negative dynamic the LLM. perturbation pressure (Markowski and Richardson To assess the influence of rolls on the development of 2010). Patches of large positive OW parameter have vertical vorticity in the LLM, we initiated backward often been used to identify vortices in geophysical flows trajectories (see the appendix for details) at points 6 (e.g., Wang et al. 2010; Markowski et al. 2011). every 400 m within 2.5 km of the LLM center at z 5 21 Time series of circulation about a 2-km-radius4 hori- 125 m where z . 0.01 s in the CONTROL and CBL zontal ring centered on the LLM5 at the lowest grid level INVRAD simulations at 106 min (Fig. 8). Parcels en- were computed for each perpendicular-shear simulation tering the LLM at this time have three main streams: (Fig. 6). Before 90 min, the circulation for all three ‘‘downdraft parcels’’ originatingintheforwardflank 2 simulations is similar and never exceeds 3 3 104 m2 s 1. either aloft and descending, or originating closer to Over their last half hour, circulation increases more the ground, ascending, and subsequently descending; rapidly in the CONTROL and CBL INVRAD simula- ‘‘forward-flank parcels’’ that travel along the forward- tions, but the CONTROL LLM consistently has stronger flank outflow boundary near the ground before ascending circulation than the CBL supercells. By this measure, the to 125 m; and ‘‘inflow parcels’’ originating in the inflow CONTROL supercell has a stronger LLM for a longer near the ground before crossing the outflow boundary 7 duration than when rolls are present in the near-storm and abruptly ascending. environment (CBL INVRAD). It should be noted that The evolution of z along parcel trajectories as they the LLM circulation in the CBL INVRAD simulation enter the LLM reveals the basis for the stronger, more still increases with time and occasionally approaches the persistent CONTROL mesocyclone. All of the parcels strength of the CONTROL circulation (120 min). On entering the CONTROL mesocyclone exhibit a nearly average, the CBL FRAD simulation has the weakest low- monotonic increase in z along their paths (Figs. 8a,b) level circulation. This is likely attributable to near-storm into the large, centralized area of positive z (Fig. 7a). decreases in CAPE and a decrease in baroclinicity along The forward-flank parcels tend to pass through the the forward flank associated with anvil shading rather ‘‘vorticity feeder’’ regions discussed previously. In con- than roll effects—rolls likely have less influence because trast, though still divided in three main streams, the near-storm boundary layer convection is diminished in source regions of parcels entering the CBL INVRAD this simulation (see Fig. 3c). mesocyclone are more varied, with frequent fluctuations We focus on low-level rotation at 106 min to under- in z along their paths (Figs. 8c,d). Moreover, parcels in stand why circulation tends to be stronger in the the downdraft stream have a maximum height of CONTROL supercell. At this time, there are distinct ;0.25 km in the CONTROL supercell versus a typical differences between the CONTROL and CBL INVRAD apex of 0.5–1 km in the CBL INVRAD supercell at this LLMs. Maxima of vertical vorticity and OW parameter time (cf. Figs. 8b,d). These CBL INVRAD downdraft are collocated in the CONTROL mesocyclone (Fig. 7a) parcels pass through a small, but relatively intense 2 in an area of relatively strong (.5 3 104 m2 s 1) circula- downdraft on the western flank of the LLM (Fig. 5b, x 5 tion, indicating a well-organized LLM. In contrast, z and 112, y 5 121) that is apparently driven by a localized OW parameters are weaker and more widely scattered increase in rainwater content (not shown). over a larger area and several local maxima in the CBL Example trajectory paths (Fig. 9) and z budgets 8 INVRAD mesocyclone (Fig. 7b) with areas of anticy- (Fig. 10) are shown for each stream. Downdraft parcels clonic vorticity interspersed among the vorticity maxima. in both simulations (A and B) begin with slightly

6 This height level was chosen rather than a lower level in order to decrease the amount of time parcels spent below the lowest grid 3 This formulation of the OW parameter is opposite from the level, where velocities were approximated based on the previously original formulation, wherein vorticity is subtracted from the described assumptions. deformation, but it has precedents in other applications to geo- 7 There has been some suggestion in the literature that inﬂow physical ﬂows (e.g., Isern-Fontanet et al. 2003; Wang et al. 2010). parcel trajectories are not realistic (e.g., Dahl et al. 2012). As such, 4 Several different radii were tested, but there were not qualitative we have chosen not to analyze these parcels. changes in the results. 8 These parcels are representative of the vorticity evolution for 5 There are no major qualitative changes when plotting the other parcels in their streams for the CONTROL simulation. Be- maximum low-level circulation around a circuit centered on any cause of the variations in individual parcels in the CBL INVRAD grid point at the lowest grid level, because the subjectively de- simulation, no single parcel is representative of any other parcels in termined LLM is generally (but not always) associated with the its stream for that simulation; however, the magnitude of z varia- maximum low-level circulation. tions along the parcel are similar to other parcels in these streams.

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21 FIG. 5. Plan views of vertical velocity (color shaded) and vertical vorticity (black contours of 60.005, 0.01, 0.02, 0.03 s , ...)nearthe ground (z 5 25 m for z; z 5 225 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 5 1km(solidgreen)and20.5-K perturbation potential temperature isentrope at z 5 25 m (blue with close dashes) are also shown. Vectors are storm-relative winds at z 5 25 m. negative z. Vertical vorticity consistently increases in the (C and D) show a similar pattern, with vorticity increasing CONTROL downdraft parcel (A) over its path, becom- through both positive tilting of horizontal vorticity in the ing positive first through tilting around 100 min, followed forward-flank buoyancy gradient (Fig. 9,shading)and by an abrupt increase through stretching around 105 min. subsequent stretching over most of the parcel’s trajectory In contrast, the CBL INVRAD downdraft parcel (B) (before 103.5 min) in the CONTROL parcel (C) and obtains higher z earlier, but oscillations in tilting and oscillations (though of a smaller magnitude than in the stretching along its path result in z fluctuations with two downdraft parcel) in tilting, stretching, and z in the CBL short periods of negative z. The forward-flank parcels INVRAD parcel (D).

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FIG. 6. Time series of circulation around a 2-km-radius horizontal ring centered on the mesocyclone at z 5 25 m for the perpendicular-shear CONTROL (black), CBL INVRAD (red), and CBL FRAD (blue) simulations.

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 FIG. 7. Plan views of circulation around a 2-km-radius horizontal ring centered at each grid point (color shading), vertical vorticity 2 reference frame. Yet, the vorticity budgets confirm that (black contours, 60.005, 0.01, 0.02, 0.03 s 1, ...), Okubo–Weiss 2 the parcels encounter some heterogeneity caused by parameter (red contours, 0.001, 0.005, 0.01, 0.02, 0.03 s 2, ...), rolls along their trajectories, presumably owing to dif- storm-relative winds, and the 20.5-K perturbation potential tem- ferent parcel and roll translation speeds. This is im- perature isentrope (blue with close dashes) all at z 5 25 m for the portant because, although all the parcels shown perpendicular-shear (a) CONTROL and (b) CBL INVRAD simulations at 106 min. eventually develop positive z, many other parcels terminate in the same region with negative z, weakening the overall circulation of the LLM. Such parcels ac- 4. Parallel-shear simulation results quire negative z because of oscillations in the vorticity a. General characteristics forcing terms, presumably caused by their roll-relative motion as they approach the LLM region. This process As in the perpendicular-shear environment, deep does not occur in the CONTROL parcels. Thus, the convection develops into a dominant right-moving presence of rolls perpendicular to storm motion (and supercell by 60 min in all three parallel-shear simula- across trajectories entering the LLM) disrupts the de- tions. The right mover has an average storm motion over 21 velopment of the persistent, coherent LLM that develops the last hour of (cx, cy) 5 (7, 0) m s in the CONTROL when rolls are absent. and CBL FRAD simulations. Interestingly, the storm

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FIG. 8. (a),(c) Plan views and (b),(d) perspective views from the southeast of parcel backward, storm-relative trajectories terminating in 2 the low-level mesocyclone at z 5 125 m and t 5 106 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- 2 relative winds and vertical vorticity (thin black contours at 60.01 s 1 increments) at z 5 125 m are plotted in plan views along with the outline of reﬂectivity .10 dBZ at z 5 1 km (thick black contour), and the 20.5-K perturbation potential temperature isentrope at z 5 25 m (blue with close dashes contour).

2 2 motion of the CBL INVRAD supercell is approximately 38 m s 1 in CBL INVRAD and 41 m s 1 in CBL FRAD. 21 21 1ms slower (cx, cy) 5 (6, 0) m s . The reflectivity field Severe winds in all three simulations are confined to shows a core of increased reflectivity on the southwest or small pockets within the precipitation core and are rear flank of the storm that resembles a hook echo, but it not associated with an LLM. The integrated liquid and is generally less pronounced than in the perpendicular- ice water mass is nearly identical throughout the shear simulations (Figs. 3d–f). The parallel-shear storms CONTROL and CBL INVRAD simulations, but by the have smaller midlevel updrafts and more compact end of the CBL FRAD simulation it is about 5% lower areas of often more intense precipitation than their than in the others. perpendicular-shear counterparts. Time series (Fig. 11) reveal that UHmax is more variable The maximum updraft at any time or height in the and often stronger for all three storms with the parallel- 2 CONTROL simulation is 90 m s 1 compared with shear hodograph than those in the perpendicular-shear 21 21 87 m s in CBL INVRAD and 85 m s in CBL FRAD. environment. Within each simulation, UHmax may vary 2 The CONTROL simulation has a maximum wind speed by as much as 4000 m2 s 2 over less than 10 min of 2 at the lowest grid level of 43 m s 1 compared with simulation time, but none of the supercells display

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21 FIG. 9. Plan view of buoyancy (color shaded), convergence (red contours of 0.005, 0.01, 0.02, 0.03 s , ...), vertical vorticity (black 2 contours of 0.01, 0.03, 0.05, 0.07 s 1, ...), and storm-relative winds at z 5 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.

consistently stronger or weaker UHmax from each that seen in the CONTROL supercell (akin to the strong other. As with the perpendicular-shear simulations, downdraft and vortex sheet in Fig. 12a). This results in time series of wmax and zmax (see Nowotarski 2013)are a line of cyclonic vorticity along the rear-flank outflow similar between simulations. boundary with local z enhancements but no obvious LLM (Fig. 13b). By the end of the simulation, the northernmost b. Parallel-roll effects on the low-level mesocyclone of these enhancements has organized into a single, co- The morphology and evolution of the LLMs in the herent LLM. Environmental perturbations associated parallel-shear simulations is quite different than in the with rolls persist into the forward-flank precipitation re- perpendicular-shear simulations. In the CONTROL gion of the CBL INVRAD supercell, unlike the relatively supercell, the LLM has a cyclic evolution, apparently homogeneous CONTROL forward-flank region. driven by pulses of a rear-flank downdraft (RFD). At Again, the CBL FRAD supercell shares similarities 60 min (Fig. 12a), a broken ring of z surrounds a strong with both the CONTROL and CBL INVRAD super- RFD. Eventually the weak vortex sheet at the leading cells. In its early stages, before cloud shading fully sup- edge of the outflow on the eastern flank of the RFD presses boundary layer convection near the storm, the wraps up and intensifies into a short-lived LLM, before low-level vorticity structure is similar to the CBL a reinforcing downdraft pulse creates a new vortex sheet INVRAD simulation, though the vorticity extrema are in its place. This cycle continues through the duration of generally weaker (Fig. 12c). Over later times, the evo- the CONTROL simulation with the strongest LLMs lution of low-level vorticity is more similar to the occurring at 90 (Fig. 3d) and 115 min (Fig. 13a). CONTROL supercell with downdraft pulses resulting in Where a weak vortex sheet exists in the CONTROL vortex sheets that occasionally roll up into discrete supercell at 60 min, stronger discrete vorticity extrema vorticity extrema (Fig. 13c). develop in the CBL INVRAD supercell as z perturba- Time series of circulation about the LLMs of the tions associated with the rolls in the inflow are in- parallel-shear supercells are shown in Fig. 14. The hodo- tensified along the outflow boundary (Fig. 12b). These graph used for this simulation is less conducive to the 2 quasi-periodic vortices, with z as high as 0.05 s 1, persist development of sustained low-level rotation than the over the next 40 min of the simulation as the storm moves perpendicular-shear hodograph. Indeed, at times it was along rolls. A downdraft pulse develops at 100 min, re- often difficult to determine which circulation, if any, placing the periodic vortices with a vortex sheet similar to was the dominant LLM. Because multiple, transient,

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21 2 22 2 22 FIG. 10. Time series of vertical vorticity interpolated to parcels (black, s ), tilting (red, 310 s ), stretching (green, 310 s ), and 2 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. often-overlapping low-level circulations evolve at differ- Plan views of circulation, the OW parameter, and z ent stages of each storm, separate circulation centers were are shown at 115 min, a time with similar circulation but tracked with their individual circulations plotted. Unlike distinct low-level morphological differences between in the perpendicular-shear supercells, there is not a con- the CONTROL and CBL INVRAD supercells (Fig. 15). sistent upward trend in circulation over the last half hour At this time, the CONTROL mesocyclone (Fig. 15a) of the simulations. The CONTROL supercell has a circu- remains isolated from other areas of vorticity, whereas lation that tends to oscillate around a steady value, with the CBL INVRAD mesocyclone (Fig. 15b) is part of an a peak circulation of only ;40% of the peak value in the area of greater z at the northern end of a sheet of vertical perpendicular-shear CONTROL case. Moreover, the vorticity. Though there is a local maximum in circulation CBL INVRAD simulation-LLMs often achieve stronger associated with this mesocyclone, the strongest circula- circulation at multiple locations than the CONTROL tion is associated with another area of strong rotation supercell over this period, despite occasional decreases on to the southwest.9 The CBL INVRAD mesocyclone 2 the order of 4 3 104 m2 s 1. This ﬁnding implies that, when has two main branches of vertical vorticity to the north, 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 circu- 9 This other vortex might also be described as a mesocyclone; lation over the last half hour, though it attains circulation however, it is not associated with an occlusion in the outﬂow comparable to the peak in CBL INVRAD circulation at boundary or under the core of the main updraft like the northern the end of the simulation. vortex.

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FIG. 11. As in Fig. 4, but for parallel-shear simulations. reminiscent of the vorticity feeders found in the forward-flank parcels (C) approach the mesocyclone perpendicular-shear CONTROL mesocyclone. The near the ground with near-zero z, before they rise northeast feeder is linked to a line of vorticity maxima and acquire positive z first through tilting and later associated with the remnants of a roll in the forward- through stretching after 112 min. The CBL INVRAD flank precipitation region. forward-flank parcels (D) often have slightly positive 2 As before, storm-relative backward trajectories of z (.0.001 s 1) along much of their path, which is in- parcels entering the mesocyclones with significant posi- creased first through tilting after 106.5 min and then tive vorticity were computed and are plotted in Fig. 16 at through a gradual increase in stretching after 110 min. 115 min. For the parallel-shear supercells, there are two Figure 17 shows that forward-flank parcels tend to follow characteristic streams of trajectories: a downdraft stream a path along an area of increased low-level convergence and a forward-flank stream. In the CBL INVRAD sim- associated with the remnants of a roll. A comparison with ulation (Figs. 16c,d), three parcels in the inflow terminate other parcels in this stream (Figs. 16c,d) suggests that with positive z near the mesocyclone, but these parcels most parcels in this stream follow the same roll and de- never cross the gust front. These parcels depict air that velop cyclonic vorticity earlier than CONTROL forward- has a near-steady position in the portion of a roll with flank parcels. Unlike in the perpendicular-shear case, positive z. This suggests that, for this hodograph and roll parcel trajectories lie along rolls, rather than across orientation, parcels approaching the LLM remain in them. Thus, air parcels entering the LLM may remain a similar roll-relative position over their paths, unlike in inthesamebandofpositivez (or convergence) asso- the perpendicular-shear simulations. ciated with a roll for a longer period of time than with Example downdraft and forward-flank parcels were perpendicular rolls. Furthermore, rolls are relatively chosen for the CONTROL (parcels A, C) and the CBL stationary in the storm-relative reference frame when INVRAD (parcels B, D) trajectory streams (Fig. 17) compared with their perpendicular counterparts, such and vorticity budgets were calculated along their paths that the mesocyclone encounters less temporally varying (Fig. 18). In the CONTROL supercell, downdraft par- environmental conditions. If conditions are favorable, cels (A) tend to originate at low levels in the forward rolls may enhance low-level circulation relative to a ho- flank, acquiring positive z as they ascend, before z de- mogeneous environment. creases to negative values during descent, and finally Apart from the difference in roll-relative storm motion, reacquiring positive z as they re-ascend to 125 m from this mean hodograph tends to be less supportive of strong near the ground. In contrast, CBL INVRAD downdraft LLMs than the perpendicular-shear mean hodograph— parcels (B) tend to continuously descend from above the the homogeneous-environment storm with this hodo- boundary layer with smaller z oscillations driven mostly graph has a considerably weaker low-level circulation by changes in the tilting term before stretching domi- than with the perpendicular-shear hodograph. The rea- nates after 112 min. It is not clear, however, how (or if) son for this discrepancy is unclear, but perhaps the large rolls influence these parcels. amount of crosswise vorticity in the boundary layer The influence of rolls is clearer when examining (Fig. 1c) is detrimental to low-level rotation as suggested the trajectories of forward-flank parcels. CONTROL by other studies (e.g., Wicker 1996; Nowotarski and

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FIG. 12. As in Fig. 5, but for parallel-shear simulations at 60 min.

Jensen 2013). The supercells with the parallel-shear ho- particularly when the hodograph (and the resulting storm dograph tend to be characterized by pulsing of the RFD, dynamics) are not conducive to a steady LLM. which causes outﬂow surges that periodically replace the LLM with a vortex sheet. When rolls are present, cyclonic 5. Sensitivity to perturbations in initiation (anticyclonic) roll vorticity perturbations locally enhance mechanism (suppress) the background cyclonic vorticity, resulting in periodic vorticity extrema. Thus, it seems that the steady For both the perpendicular and parallel-shear CBL storm-relative position of roll perturbations provides INVRAD simulations, we ran a small ensemble of four consistently favorable regions for the development and additional simulations to verify that trends in low-level intensiﬁcation of persistent low-level cyclonic vortices, circulation when rolls are present (Figs. 6 and 14) are

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FIG. 13. As in Fig. 12, but at 115 min. a robust result, rather than artifacts of initial warm in each member. We calculated the circulation about bubble placement relative to rolls in the environment. In a 2-km-radius ring at z 5 25 m for every grid point. Time each ensemble member the center of the initial warm series of the maximum circulation at any grid point for bubble perturbation was translated either 5 km north, each CBL INVRAD ensemble member, the ensemble south, east, or west of the warm bubble in the previously average, and the CONTROL simulation are shown for discussed CBL INVRAD simulations. Despite some the last hour of each simulation in Fig. 19. minor differences in the timing, location, and strength The perpendicular-shear circulation trends (Fig. 19a) of low-level vorticity maxima in each of the ensemble are similar to those seen in Fig. 6. The CONTROL cir- member supercells, the general characteristics and culation is similar to or weaker than the CBL INVRAD evolution described in the previous section are observed ensemble average circulation over the time period

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FIG. 14. As in Fig. 6, but for multiple circulation centers (numbered) in the parallel-shear simulations. 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 FIG. 15. As in Fig. 7, but for parallel-shear simulations at 115 min. apparent dependence of circulation on initiation location, rolls parallel to storm motion almost always in- effects of environmental heterogeneity rather than sim- crease the maximum circulation in each supercell over ply the result of varying turbulent realizations produced the horizontally homogeneous environment in the by random perturbations. CONTROL simulation. We also tested the sensitivity of the CONTROL 6. Conclusions simulation to random thermal perturbations in the initiating warm bubble in two additional simulations Supercell thunderstorms were simulated in an idealized for each hodograph (not shown). Though there is spread environment with resolved boundary layer convection in in the time series of maximum circulation between the form of quasi-two-dimensional rolls and compared the three CONTROL simulations, the general evolution with those simulated with a horizontally homogeneous of low-level mesocyclones and the ensemble average base state. The principal intent of the numerical simula- maximum low-level circulation are qualitatively consis- tions was to determine if rolls have a considerable effect tent with the CONTROL simulations shown here. This on the evolution of mature supercells, and if any such suggests that the differences between the CONTROL effects are dependent on the orientation of rolls relative and CBL INVRAD simulations are robust signals of the to the supercell motion. Two sets of simulations were

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FIG. 16. As in Fig. 8, but for parallel-shear simulations at 115 min. performed with different hodographs such that right- misocyclone development and the potential for non- moving-supercell motion was either perpendicular or mesocyclone tornadoes will be explored in forthcoming parallel to the boundary layer vertical shear and roll axes publications. (when present). Within each set of simulations, rolls were At later times, differences in the evolution of the low- found to have only small effects on bulk measures of level mesocyclone (LLM) are dependent on the orien- supercell strength such as wmax, zmax, maximum surface tation of the low-level shear and rolls. These differences wind speed, or liquid and ice water mass. When differ- are most clear between the CONTROL supercell and the ences in these quantities did occur, the horizontally ho- simulation wherein cloud shading effects are removed mogeneous (CONTROL) supercells had higher values, (CBL INVRAD). For a hodograph with boundary layer regardless of hodograph. shear perpendicular to storm motion, the CONTROL In the early stages of storm evolution (in the first hour), supercell has a stronger, more persistent near-ground more intense vertical vorticity maxima develop in the circulation associated with its mesocyclone, whereas the supercells with rolls in the near-storm environment, re- vorticity maxima beneath the updraft in the simulated gardless of their orientation relative to storm motion. These supercell with rolls have weaker circulation and are more are associated with the amplification of vertical vorticity transient in nature—at least over the first hour in which perturbations in the boundary layer where they encounter an LLM is present. For a hodograph with boundary layer the supercell outflow boundaries. The interaction between shear parallel to storm motion, the pattern of low-level rolls and the supercell outflow boundary in the context of circulation is more cyclic in nature, with maximum

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FIG. 17. As in Fig. 9, but for parallel-shear simulations at 115 min. circulation that is generally weaker than with the near-surface rotation. This source of z is present both perpendicular-shear hodograph; however, when rolls with and without rolls (i.e., the ‘‘downdraft parcels’’), are present in the near-storm environment, low-level such that the role of rolls is likely an enhancement or circulationvaluesareoftenenhancedrelativetothe suppression (depending on roll orientation) of the low- CONTROL supercell. These trends are further sup- level circulation created through this process. In other ported by a small ensemble of additional simulations words, rolls influence the evolution of LLMs (as con- wherein the initiating warm bubble position is varied ceptualized in Fig. 20), but they do not seem to create relative to rolls in the environment. LLMs. When the storm moves perpendicular to rolls Though these effects appear to be dependent on the (Fig. 20a), air parcels entering the mesocyclone from the quasi-periodic organization and orientation of boundary forward-flank provide inconsistent z to the LLM as it layer heterogeneity, it is possible that the presence of moves across environmental perturbations that persist boundary layer convection in any form may alter LLM even into the forward-flank precipitation region. By evolution, and these effects may vary based on the av- contrast, when the supercell moves parallel to rolls erage low-level wind profile. We also stress that these (Fig. 20b), forward-flank parcels may provide an addi- results and the conclusions drawn from them may only tional source of positive z if an LLM moves along apply to the first two hours of supercell evolution sim- a positive z perturbation associated with a roll for an ulated here. It is possible that differences in LLMs may extended period. change at later stages of storm evolution. Owing to the limited number of simulations allowed In both the perpendicular- and parallel-shear cases, by the computational demands of this problem, the the effects of the rolls are most prominent along generality of these findings remains uncertain. Regard- the forward-flank outflow boundary. Both advection less, these results indicate the potentially diverse and of preexisting vertical vorticity associated with the situation-dependent influences of rolls on supercells. boundary layer convection and modifications to tilting These simulations did not explicitly resolve tornadoes, and stretching of horizontal vorticity in the forward- but under the assumption that increased low-level ver- flank baroclinic zone by rolls appear to influence the tical vorticity and circulation are favorable conditions amount and location of positive z present in the LLM. for tornadoes, we might reasonably speculate some Previous studies (e.g., Davies-Jones and Brooks 1993; implications of this research regarding tornadoes asso- Straka et al. 2007; Markowski et al. 2008), however, ciated with supercell mesocyclones. Regardless of have postulated that the baroclinic generation of roll orientation, it appears that rolls provide a source horizontal vorticity and its subsequent reorientation of preexisting near-ground vertical vorticity that is am- by a downdraft are critical to the development of plified in convergent regions along supercell gust fronts.

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FIG. 18. As in Fig. 10, but for parallel-shear simulations at 115 min.

Such effects have generally been neglected in hypothe- on the near-storm environment are further discussed in ses regarding the development of near-ground rotation Nowotarski (2013) and forthcoming publications. and tornadogenesis in supercells. In our experience, it Future research on this topic is required before any seems that most observed tornadic supercells tend to hypotheses regarding roll influence on tornadogenesis cross rolls (akin to our perpendicular-shear simula- can be verified with certainty and recommendations for tions), such that rolls might be expected to disrupt LLM considerations of boundary layer convection can be intensification, perhaps delaying tornadogenesis or in- made to forecasters. Subsequent investigations might terfering with tornado maintenance. In the seemingly extend the methodology of this study to other hodo- rarer case that supercells move parallel to rolls, the graphs and thermodynamic profiles to investigate the mean hodograph is probably less supportive of torna- robustness of our conclusions for a range of environ- does, but our results imply that tornadogenesis would be ments, or decrease grid spacing such that tornadoes more likely with rolls than without them. may be explicitly resolved. For instance, in a less capped Even if these suppositions are true, at least some part environment, CBL motions themselves may initiate of supercell inflow is often shaded by the anvil (e.g., deep convection (in contrast to the warm-bubble per- Figs. 3c,f), such that the direct influence of rolls may be turbation employed herein). The role of boundary negated. When cloud shading is included (CBL FRAD) layer convection in deep convection initiation (CI) is in our simulations, the LLM circulation tends to be beyond the scope of this study, but it is possible that smallest regardless of hodograph, and rolls were weak- CBL effects on CI could also, in part, determine future ened in the near-storm environment as it became shaded LLM evolution. Comparison of numerical simulations by the supercell anvil cloud. The effects of anvil shading to observations is a logical progression of this work to

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FIG. 19. Time series of maximum circulation about a 2-km-radius ring centered on any grid point at z 5 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.

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FIG. 20. Conceptual model of the effects of rolls on supercell low-level mesocyclones. Bands of environmental z perturbations are associated with rolls (black lines, solid is positive z and dashed is negative z), 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 z [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) z [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 z 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. confirm that the effects of boundary layer rolls on APPENDIX supercells are adequately represented by these simulations; isolating the effects of rolls in observations, Trajectory and Vorticity Budget Calculations however, may be difficult. Despite uncertainty regarding specific situational effects, these results sug- Backward trajectories were calculated from the gest that boundary layer convection can meaningfully C grid (Arakawa and Lamb 1977) using model output influence supercell LLMs. These impacts should con- stored every 15 s. Parcel locations were determined us- tinuetobeconsideredinfutureinvestigationsoflow- ing the fourth-order Runge–Kutta (RK4) method with level rotation in supercell thunderstorms. a 3-s time step. Vorticity and vorticity forcing terms were calculated along trajectories using buoyancy and Acknowledgments. The authors thank Drs. Nels velocity gradients interpolated to every parcel location. Shirer, Lyle Long, Morris Weisman, Jim Marquis, and For parcels traveling below the lowest scalar grid level, Ryan Hastings for many helpful suggestions through- buoyancy equivalent to the value at the lowest grid level out the course of this project. We also thank Dr. David was assumed. Lewellen and two anonymous reviewers for providing Horizontal winds [u(x, y, z, t), y (x, y, z, t)] are assumed careful reviews and suggestions that improved this to vary below the lowest grid level following a loga- manuscript. This work was primarily supported by NSF rithmic profile such that Grant AGS-0644533. Y. Richardson’s time was sup- ln(z/z ) ported by NSF Grant AGS-1157646. Computational 5 0 u(x, y, z, t) uz (x, y, t) (A1) resources and travel support were provided by the 1 ln(z1/z0) National Center for Atmospheric Research. Many of the figures in this manuscript were created using the and Grid Analysis and Display System (GrADS) de- ln(z/z ) veloped by the Center for Ocean–Atmosphere–Land 5 0 y(x, y, z, t) yz (x, y, t) , (A2) Studies. 1 ln(z1/z0)

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