1. Introduction
The seminal numerical modeling studies of Weisman and Klemp (1982, 1984) demonstrated the critical role that vertical wind shear plays in the organization of deep, moist convection. In particular, they showed that increasing shear promotes a transition in storm mode from short-lived single cells to multicell clusters and, ultimately, to supercells. This transition is typically explained in terms of three key changes in the storm-scale flow (e.g., Markowski and Richardson 2010, chapter 8). The first is increasing separation of the storm updraft and downdraft by means of the downshear advection of growing hydrometeors. The second is an increase in low-level storm-relative (SR) flow that prevents negatively buoyant outflow air from undercutting the updraft. The third is the development of vertical perturbation pressure gradient accelerations (VPPGAs) in association with vertical vorticity (formed via the tilting and stretching of horizontal vorticity by the updraft) and the so-called updraft-in-shear effect (Rotunno and Klemp 1982). In supercells, these accelerations contribute significantly to updraft strength, particularly at low levels (Weisman and Klemp 1984), and give rise to the characteristic deviant motion of these storms relative to the mean flow (Rotunno and Klemp 1985; Davies-Jones 2002).
Weisman and Klemp primarily considered shear below about 6 km and subsequent idealized modeling studies have largely done the same (e.g., Weisman and Rotunno 2000; James and Markowski 2010; Nowotarski et al. 2011; Verrelle et al. 2015; Hastings and Richardson 2016). Shear in the first few kilometers above the surface is particularly relevant to supercells because it determines the horizontal vorticity of air ingested by the storm and thus the strength of the low-level mesocyclone (Coffer and Parker 2015). This, in turn, strongly influences the potential for tornadogenesis, which seems to require strong dynamic lifting near cloud base (Markowski and Richardson 2014). However, upper-level shear (ULS), defined here as the shear above 6 km, has also been suggested to modulate the likelihood of severe weather via its effect on supercell morphology (Rasmussen and Straka 1998, hereinafter RS98).
Observed supercells are typically classified into one of three types based on the intensity and updraft-relative distribution of their associated precipitation (Doswell et al. 1990; Moller et al. 1994; RS98; Beatty et al. 2008). Classic (CL) supercells are characterized by intense precipitation in the forward-flank region, with some rain and possibly hail wrapping around the mesocyclone to produce the familiar hook-echo signature in radar imagery (Browning 1964; Lemon and Doswell 1979). Low-precipitation (LP) supercells feature little to no rainfall in close proximity to the updraft and, therefore, generally lack a hook echo, while light to moderate rain and large hail may fall ahead of the storm from the anvil (Bluestein and Parks 1983; Bluestein 1984). At the other end of the spectrum, high-precipitation (HP) supercells are characterized by significant precipitation around the updraft and mesocyclone, giving them a kidney bean shape in radar imagery (Moller et al. 1990). Studies suggest that the three types of supercell differ in their propensity to produce particular hazards (Doswell et al. 1990; Moller et al. 1994). For example, CL storms are the most prolific tornado producers, while LPs are rarely tornadic but can produce large hail. HPs are less likely than CLs to spawn strong (EF 2–3) and violent (EF 4–5) tornadoes, but can produce flash flooding, large hail, and damaging outflow winds. These differences have motivated research into environmental controls on supercell morphology.
RS98 classified 43 isolated supercells as CL, LP, or HP and then compared their environments using representative proximity soundings. The most striking difference they identified was in the wind shear above 7 km, with LP and HP storms being associated with the strongest and weakest shear, respectively, and CL storms falling in between (their Figs. 6 and 7). Their composite LP hodograph also featured notable backing of the flow at upper levels while the equivalent hodograph for HPs showed slight veering. The average storm motion for CLs and LPs was found to be comparable, while HPs moved slightly faster. Together, these differences suggest that upper-level SR flow increases across the supercell spectrum from HP to LP. RS98 argued that this factor could explain the differences in precipitation intensity and distribution between the morphologies via its effects on hydrometeor advection within the storm’s anvil. Specifically, they hypothesized that in environments with strong upper-level SR flow, hydrometeors descending from the forward anvil are displaced farther from the updraft and thus are less likely to be reingested by it. This limits their growth, promoting weak precipitation concentrated primarily in the storm’s forward flank (i.e., an LP storm). Conversely, in environments with weak upper-level SR flow, hydrometeors descend in close proximity to the updraft and thus are more readily recycled, leading ultimately to more intense precipitation, which wraps around the mesocyclone (i.e., an HP storm). Earlier modeling work by Brooks et al. (1994) had suggested a similar mechanism, albeit focused on mid- rather than upper-level winds; however, the realism of their simulations was compromised by a lack of ice microphysics. RS98 had planned to undertake their own modeling study, which would form the basis of a follow-up paper; however, the work was never undertaken (E. Rasmussen 2015, personal communication).
Since RS98, the issue of environmental controls on supercell morphology has received very little attention. Beatty et al. (2009) found some support for RS98’s hypothesis, with their “rear-reflectivity mode” storms (HPs in the traditional classification) featuring slightly weaker upper-level SR flow than “forward-reflectivity mode” storms (CLs and LPs); however, their sample size was very small (just six storms). More recently, Grant and Van den Heever (2014) found that they could simulate LP-like storms in the absence of strong ULS, simply by introducing dry layers into the idealized thermodynamic sounding of Weisman and Klemp (1982). In agreement with RS98, these storms featured stronger SR flow at upper levels; however, this was associated with changes in storm motion and storm-scale circulation rather than the background shear. The authors’ conclusion, that midlevel humidity is a key factor separating CL and LP supercells, is consistent with the tendency for the latter to form close to the Great Plains dryline (Bluestein and Parks 1983). However, RS98 did not find any significant difference in 0–5-km mean relative humidity between LP and CL environments or, indeed, between LP and HP environments.
Clearly, further work is needed to elucidate fully the environmental factors that influence supercell morphology. To this end, the present study seeks to test the hypothesis of RS98 by simulating supercells across a range of ULS profiles. This also provides an opportunity to investigate more generally the impact of variations in ULS on simulated storms, a question that has thus far been overlooked in the literature on supercell–environment interactions. We begin in section 2 by detailing the numerical experiments performed. Eight primary simulations are conducted, exploring changes in ULS magnitude, vertical distribution, and direction. In addition we consider the sensitivity of our main findings to variations in other environmental parameters that have been shown to influence supercell characteristics. Results from all of these runs are presented in section 3 with a summary and discussion provided in section 4.
2. Methodology
a. Model configuration
Idealized simulations of supercells were performed using the cloud model CM1, release 17 (Bryan and Fritsch 2002; Bryan 2016). The model was configured to solve the compressible governing equations on a three-dimensional domain with rigid, free-slip upper and lower boundaries and open–radiative lateral boundaries. To prevent domain-total mass loss and pressure falls, the restricted outward flux option was enabled, where at the end of each time step the boundary-normal wind components are rescaled to balance the inward and outward mass fluxes. For temporal integration, a Klemp–Wilhelmson time-splitting scheme (Klemp and Wilhelmson 1978) was employed with a vertically implicit solver and eight acoustic time steps per full time step. Implicitly diffusive fifth-order advection was used in both the horizontal and vertical with no additional artificial diffusion applied. Subgrid turbulence was parameterized using a turbulent kinetic energy scheme similar to that of Deardorff (1980), while microphysical processes were represented by the double-moment scheme of Morrison et al. (2005) with hail (rather than graupel) as the rimed ice category. Surface fluxes, the Coriolis force, and radiation were all neglected. All of the simulations were run for 3 h and output files were saved every 5 min.
Storms were initiated in a time-invariant horizontally homogeneous environment (detailed below) using a warm bubble centered at an altitude of 1.5 km, with horizontal and vertical radii of 10 and 1.5 km, respectively, and a maximum potential temperature perturbation of 2 K. The bubble was placed at (x, y) = (50, 50) km in a domain with horizontal dimensions of 240 km × 180 km; these values were chosen to ensure that storms and their associated outflow did not impinge on the lateral boundaries during the simulations. The model top was placed at 20 km with Rayleigh damping applied in the uppermost 4 km to limit spurious reflection of wave energy. A uniform horizontal grid length of Δx = 500 m was employed, together with a stretched vertical grid, with Δz increasing from 100 m at the surface to 500 m above 12 km (giving a total of 56 levels). It is recognized that horizontal grid lengths of 250 m or less are required to properly capture the turbulent nature of deep convection, in particular the processes of entrainment and detrainment (Bryan et al. 2003; Petch 2006; Lebo and Morrison 2015). To verify that our findings were not strongly influenced by the choice of grid spacing, two sensitivity runs with Δx = 250 m were performed: one without ULS and one with moderate ULS (SU00 and SU20, described below). Similar tests were also performed using higher vertical resolution and different microphysics schemes. While significant differences were seen in the absolute values of certain quantities (such as updraft area and condensate mass), the changes in storm characteristics associated with increasing shear were found to be consistent with the main findings of this paper.
b. Initial conditions
The initial thermodynamic conditions were specified using the method of McCaul and Weisman (2001). This allows for independent variations of the CAPE, height of maximum buoyancy, mixed-layer depth, relative humidity, and temperature—variables which all uniquely influence supercell characteristics (McCaul and Weisman 2001; McCaul and Cohen 2002; McCaul et al. 2005; James and Markowski 2010; Kirkpatrick et al. 2011). Vertical profiles of potential temperature and mixing ratio are derived based on the first 10 input variables defined in Table 1. Details of the method are given in the appendix. Figure 1 shows the default sounding on a skew T–logp diagram. Similar to the canonical Weisman and Klemp (1982) sounding, it features a 1-km-deep nearly well-mixed boundary layer, surface-based CAPE (SBCAPE) of 2000 J kg−1, negligible convective inhibition (CIN), a low lifting condensation level (LCL), and relative humidity that decreases steadily from the mixed-layer top (where the air is close to saturation) to the tropopause at 12 km.
Parameters used to define the thermodynamic and wind profiles used in our simulations. Default values of variable parameters are indicated with boldface font.
Skew T–logp diagram showing the default thermodynamic sounding used in our simulations. Thick solid, dashed, and dotted lines show the environmental temperature, dewpoint temperature, and virtual temperature, respectively. The thin solid line shows the virtual temperature of a parcel lifted from the surface, with areas of positive and negative buoyancy above the LCL shaded light and dark gray, respectively (the latter area is very small).
Citation: Monthly Weather Review 145, 7; 10.1175/MWR-D-16-0412.1
The 0–6-km wind profile used in our simulations is the quarter-circle profile of Weisman and Rotunno (2000), but with a slightly smaller shear magnitude (hodograph length) of 30 m s−1 (compared to 35 m s−1). Eight configurations of upper-level (6–12 km) shear were considered. The full profiles for each of these are shown as hodographs in Fig. 2. Each run is given a four-character identifier. The first four simulations (SU00–30) were designed to examine the sensitivity of simulated supercells to variations in ULS magnitude. The shear in these runs is unidirectional and constant over the 6–12-km layer, with the hodograph length varying from 0 to 30 m s−1 in 10 m s−1 increments (Figs. 2a–d). Using the intermediate ULS magnitude of 20 m s−1, two additional pairs of simulations were then performed. In the first, the vertical distribution of ULS was varied, with shear concentrated in the lower portion of the layer in one simulation (CONL; Fig. 2e) and the upper portion of the layer in the other (CONU; Fig. 2f). In the second, the shear vector was rotated by 90° over the layer, clockwise in one simulation (VEER; Fig. 2g) and counterclockwise in the other (BACK; Fig. 2h). Each wind profile is defined by five variables (Table 1); details of their construction are provided in the appendix.
Hodographs showing the eight configurations of ULS used in our simulations. The 0–6- and 6–12-km wind profiles are plotted in dark and light gray, respectively, with height markers (diamonds) every 1 km. Blue circles show the simulated storm motion for t = 1–3 h, while green squares and red triangles show predictions obtained using the original (0–6-km mean wind) and modified (0–8-km mean wind) Bunkers et al. (2000) method, respectively (the former prediction is identical in every case). The magnitude of the vector error associated with each prediction is given in the top-right corner of each panel.
Citation: Monthly Weather Review 145, 7; 10.1175/MWR-D-16-0412.1
To explore the impact of variations in ULS across a range of environmental conditions, a total of 14 sensitivity tests were performed using different configurations of CAPE, height of maximum buoyancy, mixed-layer depth, temperature, free-tropospheric humidity, and low-level shear (hodograph length and shape). Details are provided in Table 2. In each run only a single parameter was perturbed, apart from in the decreased and increased CAPE runs where the height of the maximum buoyancy, zB, was also modified. (A decrease in CAPE necessitated a decrease in zB in order to prevent the rapid decay of storms, while an increase in CAPE necessitated an increase in zB to prevent the low-level lapse rate from becoming superadiabatic.) To reduce computational and storage requirements, all of these experiments were only performed for the SU00 and SU20 configurations of ULS.
Details of simulations used to investigate the sensitivity of our results to variations in environmental parameters. Each of these was performed twice, with the SU00 and SU20 configurations of ULS.
To verify the realism of our environmental conditions, values of key parameters were compared against those derived from the proximity sounding dataset of Thompson et al. (2007). These soundings were obtained from hourly Rapid Update Cycle (RUC) model analyses in the vicinity of 835 supercells observed over the contiguous United States during 1999–2005. A total of 70 profiles, featuring SBCAPE of less than 100 J kg−1, were considered unrepresentative and excluded from our analysis. The results of this comparison, shown in Fig. 3, indicate that the parameters used in this study all fall within their observed range. Critically, the range of values considered here for ULS (quantified by the 6–12-km bulk wind difference; Fig. 3h) spans over 95% of the observed distribution (without producing unrealistically high anvil-level winds; Fig. 3i).
Histograms showing the probability density function for nine parameters derived from the supercell proximity sounding dataset of Thompson et al. (2007): (a) SBCAPE; (b) height of maximum buoyancy zB; (c) LCL; (d) 0–6-km mean relative humidity (RH); (e) 6–12-km mean RH; (f) precipitable water (PW); (g) 0–6 km bulk wind difference (BWD); (h) 6–12-km BWD; and (i) 9–12-km mean wind speed. Note that BWD was computed using wind components averaged over 500 m at either end of the layer (e.g., 0–500 and 5500–6000 m for the 0–6-km BWD). Solid black, blue, and red vertical lines show, respectively, the default, minimum, and maximum values considered in our simulations. Since there is no default setting for upper-level winds, black lines are not included in (h) and (i). The blue line in (h) is at x = 0 and is thus obscured by the y axis. Dashed black vertical lines in (a)–(f) show values for the canonical Weisman and Klemp (1982) sounding (with a surface mixing ratio of 14 g kg−1). Numbers in each panel give the percentage of observed values that fall within the simulated range.
Citation: Monthly Weather Review 145, 7; 10.1175/MWR-D-16-0412.1
It must be noted, however, that our soundings are considerably moister than the majority of those characterizing supercell environments in the United States, particularly in the bottom half of the troposphere (Fig. 3d). In fact, the low-level humidity of the driest sounding we consider (FH05; Table 2) is still around 10% higher than the largest value in RS98’s sample of proximity soundings from the Great Plains (cf. their Fig. 5). It was found that storms could not be sustained in simulations with drier profiles (lower values of the parameter F; Table 1), which is typical when using a warm bubble to initialize convection, at least in horizontally homogeneous environments (McCaul and Cohen 2004; Bunkers 2010; Naylor and Gilmore 2012). This difference between simulated and observed storm environments may limit the relevance of our findings to the hypothesis of RS98, a possibility that is discussed further in section 4. Nevertheless, Fig. 3 suggests that our results should, at the very least, be relevant to real supercells in moist environments. Investigation of the role of ULS in drier environments, using a more sophisticated method of convection initiation (e.g., Loftus et al. 2008; Naylor and Gilmore 2012), is deferred to future work.
3. Results
In all simulations, the initial warm bubble triggers an isolated convective cell that splits during the first hour into left- and right-moving storms. As a result of the clockwise turning of the low-level shear vector, the latter becomes the dominant supercell while the former develops more multicellular characteristics (not shown). Our analysis focuses exclusively on the right-moving storm during the final 2 h of the simulations. To this end, the storm is tracked and its characteristics analyzed using moving windows centered on its location at each output time. Specifically, we track the midlevel updraft core, defined here as a contiguous region with 3–6-km mean vertical velocities above a threshold. To account for temporal variations in updraft intensity, a percentile-based threshold is used; namely, the 95th percentile of velocities above 1 m s−1. Following Lakshmanan et al. (2015), the u and υ components of storm motion are estimated by applying a Theil–Sen fit to the storm centroid coordinates as a function of time. This calculation is performed three times for each simulation: once for the full final 2 h (t = 1–3 h) and separately for t =1–2 and 2–3 h.
Analysis of the 36 simulations is divided into three sections. In the first, we consider those runs where the magnitude of ULS was varied (SU00, SU10, SU20, and SU30), while the second deals with cases of nonuniform and directionally varying shear (CONL, CONU, VEER, and BACK). In the final section, we explore the sensitivity of our findings to variations in other environmental parameters. Summary diagnostics for the first two sets of runs, computed over the final 2 h of simulation time are given in Table 3. Storm severity is quantified by the maximum values and “swath widths” of accumulated rainfall, R, and surface wind speed, U. Swath widths are computed by applying a minimum threshold to each quantity (R = 25 mm, U = 26 m s−1; the former is arbitrary while the latter corresponds to the Storm Prediction Center’s definition of severe winds), computing the area impacted by that hazard (within the portion of the domain containing the right-moving storm), and normalizing by the track length.
Summary diagnostics for all simulations with variations in ULS. SRH is storm-relative helicity and the symbols R and U denote rainfall accumulation and surface wind speed, respectively. For SU10, SU20, and SU30, numbers in parentheses give the percentage change compared to SU00; for CONL, CONU, VEER, and BACK, they give the percentage change compared to SU20.
a. Variations in upper-level shear magnitude
We first note that as ULS increases in magnitude from 0 to 30 m s−1, the simulated storm speed also increases (Table 3). This suggests that supercell motion is not solely governed by the 0–6-km winds, a result that stands in contrast to the majority of observationally based methods developed to predict it (Davies and Johns 1993; Davies 1998; Rasmussen and Blanchard 1998; Bunkers et al. 2000). An exception is Ramsay and Doswell (2005), who found that the accuracy of the widely used Bunkers et al. (2000) method could be improved by using the 0–8-km (rather than 0–6 km) mean wind in the calculation. Their assertion is supported by our results: estimates of storm motion obtained using the modified algorithm have consistently smaller errors (Fig. 2). However, more recent observational studies, utilizing larger datasets, have agreed with Bunkers et al. (2000), finding 0–6 km to be the optimal mean-wind layer (Thompson et al. 2007; Bunkers et al. 2014). This disaccord may be related to our idealized shear profiles, but could also reflect a systematic model bias, a possibility we return to in section 4.
The increase in storm motion with increasing ULS may simply be a consequence of enhanced advection due to the stronger upper-level flow. However, mature supercells also move through continuous propagation associated with dynamic VPPGAs and discrete new updraft development along the leading edge of their outflow (Zeitler and Bunkers 2005). It is likely that the changes in storm characteristics detailed below act to enhance these forcing mechanisms, driving a feedback on the storm motion in the latter portion of the simulations. Evidence for such a feedback is provided in Table 4, which shows that acceleration of the storm between the second and third hours of the simulation generally increases with increasing ULS.
Comparison of calculated storm speeds Us for t = 1–2 and 2–3 h, and the difference between the two, ΔUs, for the SU00, SU10, SU20, and SU30 runs.
It should be noted that despite the increase in storm motion, there is still a pronounced increase in upper-level SR flow with increasing ULS. At 9 km, the SR wind speed increases from 15.3 m s−1 in SU00 to 27.5 m s−1 in SU30 (Table 3). These values approximately span the 18–28 m s−1 range over which RS98 observed a transition in supercell morphology from predominantly HP to predominantly LP. We might thus expect a similar transition to occur across our four simulations.
Figure 4 summarizes the evolution of the SU00–30 runs through two diagnostics computed over the full 3-h simulation time: the 5-km updraft “swath” (maximum vertical velocity at 5 km, computed at every horizontal grid point across all model time steps) and the accumulated surface rainfall. The updraft intensity appears to be quite consistent among the first three runs; however, in SU30 it is noticeably reduced between t = 90 and 155 min. Further analysis suggests that this weakening is associated with surging rear-flank outflow, which temporarily disrupts the supply of potentially buoyant air at low levels (not shown). Similar behavior in SU20 is responsible for the brief weakening of the updraft around t = 90 min. It thus appears that there is a tendency toward outflow dominance as ULS is increased from 0 to 30 m s−1. This tendency is explained by a dramatic increase in rainfall intensity (right column in Fig. 4; Table 3), which, through enhanced evaporative cooling, promotes lower cold-pool temperatures and stronger outflow winds (Table 3). These are surprising results; based on the observations of RS98, we would expect a decrease in precipitation and outflow intensity with increasing ULS.
(left) Swath of 5-km updraft velocity (m s−1) and (right) accumulated rainfall (mm) for (top to bottom) the SU00, SU10, SU20, and SU30 runs. The storm track for t = 1–3 h is shown in each panel with small and large circles marking 5- and 60-min intervals, respectively. The domain shown extends from x = 50 to 200 km and y = 40 to 80 km, with tick marks on the axes spaced at 10-km intervals.
Citation: Monthly Weather Review 145, 7; 10.1175/MWR-D-16-0412.1
Figures 5 and 6 illustrate the changes in storm structure that accompany variations in ULS magnitude. Both show composite fields produced by averaging the 5-min output over the second and third hours of the simulation using domains that follow the tracked midlevel updraft. This averaging allows for a fairer comparison between the runs as it smoothes out short-time-scale fluctuations in storm structure and intensity, which can mask systematic differences at a particular time step.
Composites plan views for (left to right) the SU00, SU10, SU20, and SU30 runs, computed over (a)–(d) t = 1–2 and (e)–(h) t = 2–3 h. Variables shown are surface rain rate (colors; mm h−1), 3–6-km average vertical velocity (thin black contours; 5, 10, and 20 m s−1), cold-pool boundary (thick black contour; θ′ = −1 K at z = 50 m), θ′ = −5 K at z = 50 m (blue contour), and ground-relative winds at z = 50 m (vectors, plotted every 2.5 km; reference vector in bottom right).
Citation: Monthly Weather Review 145, 7; 10.1175/MWR-D-16-0412.1
Composite vertical cross sections for (left to right) SU00, SU10, SU20, and SU30 runs, computed over (a)–(d) t = 1–2 and (e)–(h) t = 2–3 h. Variables shown are total condensate mixing ratio (colors; g kg−1), vertical velocity (thin black contours; 5, 10, and 20 m s−1), cloud boundary (gray contour; qc + qi = 0.01 g kg−1), and storm-relative winds (vectors, plotted every 2.5 km in the horizontal and 1.5 km in the vertical). Cross sections are taken from west to east at ysr = 0 with values averaged over a width of 5 km.
Citation: Monthly Weather Review 145, 7; 10.1175/MWR-D-16-0412.1
The increase in rainfall and outflow intensity with increasing shear is clearly seen in Fig. 5, as is the associated reduction in cold-pool temperatures (shown by the areal expansion of the −5-K perturbation-potential-temperature contour). These differences are slight for t = 1–2 h, but substantial for t = 2–3 h. Overall, the simulated storm tends toward a more HP-like structure with increasing ULS, with heavy precipitation concentrated in the rear flank of the storm, which is precisely the opposite of what RS98 hypothesized. We also note an increase in updraft area with increasing ULS, although in the final hour the trend is reversed between SU20 and SU30 because of the aforementioned temporary weakening of the storm in the latter simulation. At this time, a secondary area of ascent can be seen to the north of the main updraft in SU30 (Fig. 5h). This feature is associated with the development of multiple small updrafts (visible in Fig. 4g) along the storm’s forward-flank gust front. It appears that the strong outflow in this run ultimately promotes a storm mode that lies between the HP-supercell and multicell archetypes. Similar “hybrid” storms (e.g., Nelson 1987) have been simulated in other environments that favor outflow dominance, such as those with a high LCL (McCaul and Cohen 2002).
The composite cross sections in Fig. 6 reveal the presence of a more tilted updraft in the runs with ULS, with enhanced downshear advection of condensate at upper levels. In SU00, the storm quickly develops a back-sheared anvil as strong divergence around the tropopause overwhelms the background westerly flow (Fig. 6a). For t = 1–2 h, this feature is less pronounced in SU10 (Fig. 6b) and completely absent in SU20 and SU30 (Figs. 6c,d). Over time, all four storms become more upright as the upper-level flow is decelerated and deflected by the updraft. A back-sheared anvil ultimately develops in SU10 and SU20 (Figs. 6f,g) but is still absent in the SU30 composite for t = 2–3 h (Fig. 6h). This may be explained by the combination of even stronger upper-level SR winds and a narrower updraft (with associated weaker cloud-top divergence) compared to the other runs. Figure 6 also shows an increase in both the maximum and area-averaged total condensate mixing ratio with increasing ULS, at least up to SU20.
Further insight into the vertical structure of the storms is provided in Figs. 7 and 8, which show composite vertical profiles computed over a 20 × 20 km2 domain centered on the midlevel updraft centroid at each output time. Figure 7 shows the area-integrated mass flux (mass flow rate), area, average velocity, and average effective buoyancy (defined below) of the primary updraft, defined as the largest contiguous volume where w ≥ 5 m s−1. Figure 8 shows the mass of each of the model’s five liquid and ice water species: cloud water, cloud ice, rain, snow, and hail. Interpretation of changes in condensate mass is aided by Fig. 9, which shows, for each species, the contribution from all other water species (including water vapor) to increases in their mass, computed over the same 20 × 20 km2 moving domain.
Composite vertical profiles for the SU00, SU10, SU20, and SU30 runs, computed over (a)–(d) t = 1–2 and (e)–(h) t = 2–3 h. Variables shown are (left to right) updraft-total mass flow rate, updraft area, updraft-average vertical velocity, and updraft-average effective buoyancy. The updraft is defined as the largest contiguous volume with w ≥ 5 m s −1 within a 20 × 20 km2 moving domain centered on the midlevel updraft centroid.
Citation: Monthly Weather Review 145, 7; 10.1175/MWR-D-16-0412.1
As in Fig. 7, but for cloud water and cloud ice mass (solid and dotted lines, respectively), rain mass, snow mass, and hail mass.
Citation: Monthly Weather Review 145, 7; 10.1175/MWR-D-16-0412.1
Stacked bar chart showing the time-averaged contribution of each of the model’s six water species to the rate of increase in mass of cloud water, cloud ice, rain, snow, and hail for (a) t = 1–2 and (b) t = 2–3 h. The bars for each variable show values for (left to right) the SU00, SU10, SU20, and SU30 runs, each scaled by the total rate of increase in mass for SU00. Values were computed over a 20 × 20 km2 moving domain centered on the midlevel updraft centroid.
Citation: Monthly Weather Review 145, 7; 10.1175/MWR-D-16-0412.1
Turning to Fig. 8, we note a large, monotonic increase in cloud water mass with increasing shear for t = 1–2 h (Fig. 8a), associated with the increase in updraft area (a larger region of adiabatic cooling and condensation). The opposite trend is observed for cloud ice, reflecting both the reduced mass flux at upper levels and enhanced advection of this species away from the updraft (and out of the 20 × 20 km2 box) under stronger SR flow. The same processes contribute to a reduction in snow and hail mass at upper levels (Figs. 8c,d). Meanwhile, rain mass is increased in the presence of ULS (Fig. 8b), primarily as a result of enhanced accretion of cloud water within the larger updrafts (Fig. 9a). In the final hour of the simulations (t = 2–3 h), the trend for cloud water persists (consistent with the trend in updraft area), but the cloud ice mass in SU10 and SU20 recovers to about the same magnitude as in SU00 (Fig. 8e). This recovery is associated with the aforementioned development of a back-sheared anvil in these runs. In contrast, the cloud ice mass remains significantly lower for the persistently downshear-tilted SU30 storm. Snow and hail mass now show a pronounced increase, with ULS up to 20 m s−1 (Figs. 8g,h), reflecting enhanced growth of these species through deposition and collection processes within the larger updraft (Fig. 9b). Rain mass also increases across these runs (Fig. 8f), again via enhanced accretion, but also via the melting of a larger mass of hail (Fig. 9b). In SU30, intermediate mass values are found for rain and, below 9 km, snow and hail because of the similarly intermediate updraft area (Fig. 7f) and associated differences in hydrometeor growth (Fig. 9b); however, at higher levels the snow and hail mass remain smaller than in SU00.
The foregoing analysis suggests that the increase in precipitation intensity as ULS is increased from 0 to 20 m s−1 results from an increase in updraft area that promotes enhanced cloud water production and hydrometeor growth. The increase in updraft area appears to originate in the lowest few kilometers of the storm, in association with enhanced inflow and convergence on the leading (eastern) edge of updraft (Fig. 10). For t = 1–2 h, the low-level SR flow in this region increases monotonically with increasing shear (by about 2 m s−1 between SU00 and SU30). Later, we observe a more substantial increase for ULS of 0–20 m s−1 but a decrease as the shear is increased further to 30 m s−1. The changes in SR flow also appear to contribute to variations in updraft shape and orientation during the final simulation hour (e.g., the elongated, southeast-to-northwest-orientated updraft in SU20) via similar variations in the regions of low-level convergence.
Composite plan views for (left to right) the SU00, SU10, SU20, and SU30 runs, computed over (a)–(d) t = 1–2 and (e)–(h) t = 2–3 h. Variables shown are 0–3 km-average storm-relative wind speed (colors; m s−1), 3–6 km-average vertical velocity (thin black contours; 5, 10, and 20 m s−1), 10 mm h−1 surface rain-rate outline (thick gray contour), and 0–3 km-average storm-relative winds (vectors, plotted every 2.5 km; reference vector in bottom right). Black box shows the area used to compute the hodographs in Fig. 11.
Citation: Monthly Weather Review 145, 7; 10.1175/MWR-D-16-0412.1
To what extent are these changes in SR flow due to the previously noted increase in storm motion with ULS versus perturbations to the low-level background flow? This question is addressed in Fig. 11, which shows composite hodographs of the 0–3-km winds averaged over a 5 × 5 km2 area immediately northeast of the updraft (shown in Fig. 10) for t = 1–2 and 2–3 h. It is apparent that the flow in this region is strongly perturbed, with northwesterly winds at the surface (associated with the storms’ outflow; Fig. 5) veering to south-southeasterly at 3 km (approximately the top of the inflow layer; Fig. 6). For t = 1–2 h, the wind profiles for each run are very similar, indicating that the slight increase in SR flow with ULS during this time is largely due to the enhanced storm motion (Table 4). However, for t = 2–3 h, the winds in SU10 and SU20 have an enhanced easterly component at all levels compared to SU00, while the opposite is true for SU30. Thus, in the final hour of the simulations, changes in both storm motion and the ambient wind contribute to the observed trends in SR flow with increasing ULS.
Composite hodographs showing 0–3-km ground-relative winds (lines) and storm motion (circles) for the SU00, SU10, SU20, and SU30 runs, computed over (a) t = 1–2 and (b) t = 2–3 h. The thin black line shows the background 0–3-km wind profile. Diamonds indicate heights of 1, 2, and 3 km. Winds were averaged over the 5 × 5 km2 box shown in Fig. 10.
Citation: Monthly Weather Review 145, 7; 10.1175/MWR-D-16-0412.1
Composite plan views for (left to right) the SU00, SU10, SU20, and SU30 runs, computed over (a)–(d) t = 1–2 and (e)–(h) t = 2–3 h. Variables shown are 1–3-km average pressure perturbation (colors; hPa), 3–6-km average vertical velocity (thin black contours; 5, 10, and 20 m s−1), 10 mm h−1 surface rain-rate outline (thick gray contour), and 1–3-km average perturbation winds (vectors, plotted every 2.5 km; reference vector in bottom right).
Citation: Monthly Weather Review 145, 7; 10.1175/MWR-D-16-0412.1
The perturbation pressure components were obtained following the method outlined by Coffer and Parker (2015). Unfortunately, the resulting solutions are not unique (they are only determined up to an arbitrary additive constant) and therefore cannot be compared quantitatively. We therefore examined the zonal perturbation pressure gradient accelerations (which are unique), calculated as (1/
The calculated perturbation pressure terms also allow us to assess the contribution of dynamic lifting to variations in storm motion between the runs. To this end the linear-, nonlinear-, and total-dynamic VPPGAs were computed as (1/
Composite plan views for (left to right) the SU00, SU10, SU20, and SU30 runs, computed over (a)–(d) t = 1–2 and (e)–(h) t = 2–3 h. Variables shown are 0–6-km dynamic VPPGA (colors; 10−2 m s2) and its linear and nonlinear components (thick solid and dotted lines, respectively; positive in red, negative in blue; same contour levels as color bar), and 3–6-km average vertical velocity (thin black contours; 5, 10, and 20 m s−1). Black box shows the area used to compute the mean dynamic VPPGA given in the top-right corner.
Citation: Monthly Weather Review 145, 7; 10.1175/MWR-D-16-0412.1
In summary, we find that an increase in 6–12-km shear from 0 to 20 m s−1 drives significant changes in simulated supercell characteristics, including wider updrafts, more intense precipitation, and stronger outflow winds. These changes result from an increase in low-level inflow, initially driven by faster storm motion but later enhanced by accelerations associated with a low-level perturbation pressure minimum. The initial increase in storm motion can be explained as a combination of enhanced advection and increased dynamic lifting, although we are unable to quantify the relative contribution of these two effects. However, as the storms mature, it is likely that the stronger cold pools contribute additional accelerations through discrete propagation at the gust front. With a further increase in ULS, from 20 to 30 m s−1, the storm weakens slightly, as the even stronger outflow begins to undercut the updraft.
This final result suggests that there is an optimal ULS magnitude, of around 20 m s−1, for which storm intensity is maximized. However, simulated convective cold pools are remarkably sensitive to other environmental characteristics, such as mixed-layer depth (McCaul and Cohen 2002), and various aspects of the microphysics parameterization (Adlerman and Droegemeier 2002; van den Heever and Cotton 2004; Cohen and McCaul 2006; Dawson et al. 2010; Morrison and Milbrandt 2011; Van Weverberg et al. 2012). We would therefore expect this optimal ULS threshold to show similar sensitivity. Additional sets of runs performed using (i) a shallower mixed-layer and (ii) the Lin microphysics scheme (Lin et al. 1983; Tao and Simpson 1993) confirm this expectation: in both cases, weaker outflow allows the SU30 storm to remain more intense than its counterparts in the lower-shear runs (not shown). Based on these simulations, we conclude that there is no universal optimal ULS magnitude; however, if the environment is already conducive to the formation of strong cold pools, increasing ULS may ultimately tip the balance in favor of outflow dominance.
b. Variations in upper-level shear distribution and direction
The characteristics of the CONL, CONU, VEER, and BACK runs are illustrated in Fig. 14, which shows plan-view composites for the final simulation hour. The top, middle, and bottom rows show the same fields as in Figs. 5, 10, and 12, respectively, and should be compared with the corresponding plots for SU20. Comparisons with SU20 are also made in Table 3.
Composite plan views for (left to right) the CONL, CONU, VEER, and BACK runs, computed over t = 2–3 h. Variables shown in the top, middle, and bottom rows are the same as in Figs. 5, 10, and 12, respectively.
Citation: Monthly Weather Review 145, 7; 10.1175/MWR-D-16-0412.1
We first note that CONL features more intense precipitation, colder cold pools, and stronger outflow than SU20 (Fig. 14a; Table 3). These changes are associated with an increase in storm speed (Table 3) and low-level inflow (Fig. 14e). Storm speed is unchanged in CONU; however, the motion is slightly backed with respect to that of the SU20 storm, resulting in weaker low-level SR flow, less precipitation, and weaker outflow (Figs. 14b,f; Table 3). In both cases, there are again feedbacks on the low-level pressure field and associated perturbation flow that act to amplify initially small differences (Figs. 14i,j). Overall, the CONL and CONU runs are consistent with the results presented in the previous section and highlight the fact that winds in the lower portion of the 6–12-km layer exert greater influence on storm motion than those farther aloft.
The introduction of veering or backing into the ULS profile leads to little change in storm speed (a slight decrease in both cases) but does impact the direction of storm motion (Table 3). As one might expect, the motion vector rotates in the same sense as the shear vector: clockwise for VEER and counterclockwise for BACK. This influences both the magnitude and direction of the low-level inflow (Figs. 14g,h), which, in turn, modifies the shape of the updraft (by promoting low-level convergence in different storm-relative locations) and the distribution of surface precipitation (Figs. 14c,d). Specifically, in VEER the updraft and precipitation are elongated toward the northwest, while in BACK the updraft is more circular with heavy precipitation concentrated in the storm’s rear flank, similar to the HP archetype. This result again stands in contrast to the observations of RS98, which showed veering and backing ULS in HP and LP environments, respectively.
A final conclusion that can be drawn from these simulations is that changing the vertical distribution and direction of ULS has a far smaller impact on storm characteristics than changing the magnitude of ULS. This can be seen by comparing the percentage-change values in columns 2–4 and 5–8 in Table 3. For example, the swath width for strong winds is 3.5 times larger in SU20 than SU00 but only changes by around 20% in CONL and CONU and 15% in VEER and BACK.
c. Sensitivity to environmental conditions
In this section we seek to address the question of whether variations in ULS impact simulated supercells differently under different environmental conditions. This is achieved through the sensitivity tests listed in Table 2, all of which were performed using the SU00 and SU20 ULS configurations. Figure 15 concisely summarizes the results of these simulations using a selection of relevant diagnostics computed over t = 1–3 h. One can observe some dramatic changes in the storm properties, which are largely consistent with expectations and previous studies. For example, a deeper mixed layer (ML15) favors colder and stronger outflow (McCaul and Cohen 2002), a lower LCL temperature (T285) increases the updraft mass flux (McCaul et al. 2005), and reduced free-tropospheric humidity (FH05) promotes lower condensate mass (James and Markowski 2010). However, our focus here is not on comparing the storm properties themselves but the trends associated with increasing ULS (i.e., the slope of the lines in Fig. 15).
Summary diagnostics for the control runs (CNTL) and the 14 sensitivity runs listed in Table 2. Variables plotted are (a) storm speed, (b) 0–3-km average storm-relative flow, (c) updraft mass flow rate at z = 6 km, (d) updraft area at z = 6 km, (e) total cloud water mass, (f) total rain mass, (g) area-averaged surface cold-pool perturbation potential temperature, and (h) area-averaged surface cold-pool (outflow) wind speed. All of these were computed for t = 1–3 h over a 20 × 20 km2 moving domain centered on the midlevel updraft centroid. The updraft is defined as the largest contiguous area with w ≥ 5 m s−1 and the surface cold pool is defined as all points with θ′ ≤ −1 K at z = 50 m. The lower and upper circles in each panel show values for the SU00 and SU20 runs, respectively; thus, the lines connecting them indicate the trend associated with increasing ULS.
Citation: Monthly Weather Review 145, 7; 10.1175/MWR-D-16-0412.1
It is immediately apparent that the effects of ULS (on storm speed, updraft width, outflow strength, etc.) are consistent across almost the full parameter space considered. The magnitude of the change (slope of the lines) varies somewhat—for example, the 6-km updraft area increases much more dramatically for T285 compared to T295—but the direction is the same. The only exception is C1Z6, the configuration with SBCAPE reduced to 1000 J kg−1 (and the height of maximum buoyancy reduced to 6 km). In this case, storm motion decreases slightly with increasing ULS, with the other parameters showing either very little change or a change opposite to that in the other runs.
The anomalous nature of C1Z6 can be explained by considering Fig. 16, which shows composite west-to-east vertical cross sections of the SU00 and SU20 runs for this case. In agreement with previous studies, lower CAPE promotes a smaller and shallower supercell with a narrower updraft and reduced condensate mass (Weisman and Klemp 1982; Kirkpatrick et al. 2011). Weaker divergence at cloud top means the storm remains downshear tilted throughout the simulation, even in the absence of ULS (Fig. 16a). With the introduction of moderate ULS, the tilt amplifies while storm-top height decreases (Fig. 16b), similar to what was seen in SU30 (Fig. 6). With less condensate mass above 6 km, the component of storm motion associated with advection is reduced while the contribution of dynamic VPPGAs to propagation is largely unchanged (not shown). Through the chain of processes set out in section 3a, this ultimately leads to less intense surface precipitation, a warmer cold pool, and weaker outflow winds.
Composite vertical cross sections for the (a) SU00 and (b) SU20 runs with the C1Z6 sounding, computed over t = 2–3 h. Variables shown are the same as in Fig. 6. Cross sections are taken from west to east at ysr = 0 with values averaged over a width of 5 km.
Citation: Monthly Weather Review 145, 7; 10.1175/MWR-D-16-0412.1
In addition to verifying the robustness of our results, these sensitivity tests give context to the simulated changes in storm characteristics. For example, increasing ULS from 0 to 20 m s−1 leads to an increase in midlevel updraft area that is comparable to that associated with a 10 m s−1 increase in 0–6-km shear (from 25 to 35 m s−1) or a doubling of CAPE (from 1000 to 2000 J kg−1).
4. Summary and discussion
A series of idealized simulations have been conducted to explore the impact on supercell characteristics of variations in the magnitude, direction, and vertical distribution of upper-level (6–12 km) shear (ULS). A key objective was to test the observationally based hypothesis of RS98 that increasing ULS reduces precipitation formation through enhanced advection of growing hydrometeors away from the updraft, promoting a transition from HP to LP morphology. Our main findings are as follows:
An increase in the magnitude of ULS promotes faster simulated storm motion. This is initially associated with a combination of enhanced advection (due to stronger upper-level flow) and enhanced propagation (due to stronger dynamic vertical perturbation pressure gradient accelerations). However, subsequent changes in cold-pool characteristics likely contribute to a further increase in propagation later in the storms’ evolution.
As ULS magnitudes increase from 0 to 20 m s−1, storms produce more intense surface precipitation and stronger outflow winds. This trend is associated with an increase in updraft width that promotes enhanced mass flux and condensate production. This in turn can be related to the increase in storm speed via stronger low-level storm-relative (SR) flow. Toward the end of the simulations, inflow is further enhanced through feedbacks that drive a reduction in low-level perturbation pressure.
When ULS is increased further to 30 m s−1, the above noted trends are reversed as a result of the occurrence of rear-flank gust front surges, which promote intermittent weakening of the low-level mesocyclone. It thus appears that the increase in outflow strength with increasing ULS ultimately acts as a buffer on storm intensity. However, the strong sensitivity of convective cold pools to numerous environmental and model parameters precludes the definition of a universal optimal ULS magnitude.
As hypothesized by RS98, the increase in upper-level SR flow with increasing ULS initially transports anvil-level hydrometeors farther downstream. However, strengthening cloud-top divergence, associated with the aforementioned increase in updraft mass flux, ultimately reverses this trend in all but the strongest shear case.
Variations in the vertical distribution of ULS reveal that shear in the lower portion of the 6–12-km layer has a more pronounced impact on storm motion and characteristics than does shear farther aloft.
The introduction of veering or backing into the ULS profile leads to a slight change in storm direction, which modifies the distribution of the surface precipitation via changes in low-level SR flow and convergence. Specifically, a backing shear vector appears to favor enhanced precipitation in the rear-flank region, while, under veering ULS, the precipitation area is elongated toward the northwest (for approximately westerly storm motion).
Sensitivity tests reveal that the changes in storm properties (such as updraft area, rain mass, and cold-pool temperature) resulting from the introduction of 20 m s−1 of ULS are comparable to those associated with realistic variations in parameters such as CAPE, mixed-layer depth, and 0–6-km shear.
Clearly, RS98’s hypothesis is not supported by our results. Rather than limiting the growth of hydrometeors, the introduction of ULS into our simulations actually leads to more intense precipitation via an increase in storm motion and low-level inflow. Thus, we observe a transition to a more HP-like structure with increasing ULS, the precise opposite of what RS98 predicted.
Can we reconcile these disparate findings? One possibility is that the differences in ULS between CL, LP, and HP supercells observed by RS98 are simply a by-product of the environments that favor these morphologies. For example, it has been observed that, in the Great Plains, LP storms tend to form in close proximity to the dryline (Bluestein and Parks 1983). Strong drylines typically form ahead of an upper-level short-wave trough (Schultz et al. 2007), and jet maxima, associated with these troughs, are well known to favor convective development through induced secondary circulations (e.g., Uccellini and Johnson 1979). Thus, it may be that the stronger ULS in LP-supercell environments reflects a tendency for stronger upper-level flow in the vicinity of convectively active drylines.
An alternative explanation is the high relative humidity of our idealized soundings compared with those observed by RS98. As noted in section 2b, such moist environmental conditions were required to produce sustained convection, which is most likely due to our use of a warm-bubble initialization (Naylor and Gilmore 2012). It is possible that the impact of increasing ULS is reversed in drier environments; that is, stronger shear promotes a reduction in storm speed, leading ultimately to a more LP-like (or, at least, less HP like) structure (similar to the low-CAPE case, C1Z6). The fact that the trends in storm characteristics associated with increasing ULS are reduced in the slightly drier FH05 simulations (Fig. 15) lends some support to this hypothesis. However, further experimentation is needed to determine whether the trends are actually reversed in even drier environments.
A final possibility that must be entertained is that our simulations fail to accurately represent relevant dynamical and/or microphysical processes that govern the evolution of real supercells. Recent work has shown that high-resolution numerical weather prediction models tend to move storms too fast (e.g., Yussouf et al. 2015; Snook et al. 2016; Supinie et al. 2016). This has been hypothesized to be the result of assimilation errors (Yussouf et al. 2015) or cold-pool biases (Supinie et al. 2016); however, it may be that the influence of upper-level winds on storm motion is exaggerated. In particular, the absence of resolved turbulent entrainment and associated excessive updraft velocities (e.g., Lebo and Morrison 2015) may promote both faster advection, via enhanced condensate mass at upper levels, and faster propagation, via stronger linear-dynamic forcing. Such a bias could explain the disagreement between our results and the observations, which mostly suggest that winds above 6 km do not influence supercell motion (e.g., Bunkers et al. 2014). Another aspect of model fidelity that should be considered is the ability to represent the full supercell spectrum. It is notable that all of the supercells simulated here, together with the vast majority of those in past idealized modeling studies, most closely resemble the HP archetype, with heavy precipitation concentrated to the rear of the mesocyclone. While this tendency may again be a consequence of overly moist input soundings, it could also reflect a systematic model bias, perhaps related to the representation of certain microphysical processes.
The disparate hazards associated with LP, HP, and CL supercells provide strong motivation for continued research into the environmental factors that distinguish these morphologies. In the near term, we intend to repeat the primary simulations presented herein using drier input soundings (combined with a more sophisticated method of storm initialization) to provide a more appropriate comparison with the observations of RS98. Further investigation into the impact of variations in the vertical profile of relative humidity on simulated supercells is also required. From an operational perspective, there is a need to ascertain whether convection-permitting numerical weather prediction models can reliably forecast supercell morphology and, if so, at what lead time. A pertinent question is whether the above-noted overrepresentation of HP storms in idealized simulations also occurs in full-physics operational-type runs. All of these efforts must be supported by continued work on model verification, particularly with regard to precipitation microphysics. Finally, we suggest that, given the ever-expanding archives of radar and near-storm environment data for severe weather events (e.g., Thompson et al. 2012), the time is right to revisit RS98’s hypothesis from an observational standpoint.
Acknowledgments
RAW was funded by Australian Research Council Linkage Project Grant LP130100679. Simulations were performed on the National Computing Infrastructure’s Raijin supercomputer. We would like to acknowledge Brice Coffer, for invaluable assistance with the pressure perturbation analysis, and Dave Kinniburgh and Paul Markowski, for additional useful discussions on this subject. We also thank George Bryan, for providing and maintaining CM1, and Rich Thompson, for furnishing us with the supercell proximity dataset. Finally, we gratefully acknowledge Matt Bunkers and three anonymous reviewers for their detailed and insightful comments on an earlier draft of this manuscript.
APPENDIX
Construction of Environmental Profiles
a. Thermodynamic profiles
The base-state thermodynamic soundings used in our simulations were all created following the approach of McCaul and Weisman (2001). Three layers—a mixed layer, free troposphere, and stratosphere—are specified using the first 10 parameters listed in Table 1. The mixed layer is defined by its depth, zml; a prescribed potential temperature lapse rate, γml; the air properties at its top (temperature, Tml; relative humidity, Hml; and pressure, pml); and the assumption of constant equivalent potential temperature. The pressure at the mixed-layer top is selected to give a surface pressure of approximately 1000 hPa in all experiments. Profiles of potential temperature and water vapor mixing ratio over this layer are determined by integrating down from zml to the surface.
Above the tropopause, the temperature and mixing ratio are taken to be constant. This truncates the buoyancy profile, resulting in CAPE that is lower than the specified value. To obtain the correct value, the calculations above the mixed layer are repeated iteratively, with the buoyancy profile at step n scaled by E/En−1. For the values of SBCAPE considered here, 5–10 iterations were required to obtain a precision of ±0.5 J kg−1.
b. Wind profiles
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