1. Introduction
The role of vertical wind shear (hereafter “shear”) in squall-line evolution has been extensively addressed over the last half century. For instance, the strength and direction of low-level (LL) shear that occurs over the depth of the cold pool regulates updraft tilt and speed (e.g., Hane 1973; Thorpe et al. 1982; Rotunno et al. 1988; Fovell and Dailey 1995; Grady and Verlinde 1997; Davis et al. 2004; Coniglio et al. 2006). This connection exists because the ratio of the LL shear magnitude to the integrated cold pool buoyancy (hereafter simply “cold pool intensity”) strongly influences the character of the lifting along the outflow boundary (OFB) that underlies the buoyant updrafts within the squall line (e.g., Rotunno et al. 1988; Weisman and Rotunno 2000; Bryan and Rotunno 2014). When the cold pool intensity overwhelms the LL shear or the LL shear overwhelms the cold pool intensity, ascent occurs in a slantwise manner along the OFB within the squall line’s buoyant updrafts. Alternatively, when LL shear and cold pool intensity approximately balance each other, OFB ascent and buoyant updrafts are comparatively upright. These ideas are encapsulated by “RKW” theory (Rotunno et al. 1988). Updrafts that are more slanted have larger downward-oriented pressure gradient accelerations (PGA) that weaken their ascent rates relative to less slanted updrafts, all else being equal (e.g., Parker 2010; Peters 2016; Peters et al. 2019a). Furthermore, the magnitude of dynamically driven lifting along an OFB positively correlates with the LL shear magnitude, so long as the LL shear magnitude does not “overpower” the cold pool. These studies suggest that squall lines in environments with stronger LL shear should have stronger updrafts than those in environments with weaker LL shear, all else being equal.
Oftentimes, substantial upper-level (UL) shear is also found within squall-line environments (e.g., see Fig. 6 in Davis et al. 2004; see Fig. 21 in Coniglio et al. 2006). Fovell and Dailey (1995) and Coniglio et al. (2006) showed that both LL and UL shear work together to result in a deeper overturning layer, and stronger maximum vertical velocities (wMAX), than would occur if UL shear were absent and only LL shear were present. In addition, Moncrieff and Liu (1999) noted that certain orientations of UL shear result in deep convective updrafts that “anchor” vertically above an OFB, which is an optimal situation for squall-line maintenance. Other UL shear orientations prevent the anchoring of storms along an OFB, which may result in less efficient triggering and maintenance of deep convection. Strong mid- to upper-level winds also influence the cold pool speed via downward momentum transport (Mahoney et al. 2009), which in turn alters the balance between the cold pool and the LL shear. Furthermore, strong UL shear may also influence squall-line motion via changes in steering flows aloft, and thus, LL OFB-relative flow and LL horizontal mass flux. Finally, studies of model-derived soundings taken in proximity to squall lines suggest that their probability of maintenance increases as UL shear increases (e.g., Coniglio et al. 2007). Most of the aforementioned numerical modeling studies varied LL (UL) shear while holding UL (LL) shear fixed, so the importance of variations in both LL and UL shear collectively on squall-line updraft properties is largely unknown, as stated in Coniglio et al. (2006).
One updraft process that has seldom been discussed in the context of squall lines is entrainment. Entrainment involves the mixing of updraft air with surrounding environmental air. Entrainment typically results in dilution of updraft buoyancy (B), leading to a reduction in vertical accelerations and vertical velocities (w). Understanding entrainment within deep convective updrafts is vital, as this process modulates updraft w, in turn influencing how updrafts vertically redistribute heat, moisture, momentum, and chemical constituents. Updraft w also plays a key role in the generation of large hail (e.g., Browning 1963; Wakimoto et al. 2004), damaging winds (e.g., Marion and Trapp 2019), tornadoes (e.g., Markowski and Richardson 2014; Coffer and Parker 2015), lightning (e.g., Lang and Rutledge 2002; Tessendorf et al. 2005; Wiens et al. 2005; Deierling and Petersen 2008), and heavy rainfall (e.g., Doswell et al. 1996; Nielsen and Schumacher 2018).
Canonical studies of squall lines have typically depicted a structure with deep convective updrafts along an OFB that are driven by a “tongue” of high equivalent potential temperature and conditionally unstable air that slopes up and over the cold pool—colloquially known as front-to-rear flow (e.g., Zipser 1977; Houze 1989; Kingsmill and Houze 1999; Bryan and Fritsch 2000). This type of layer lifting is commonly referred to as “slab-like” ascent (e.g., Zipser 1977; Chong et al. 1987; Redelsperger and Lafore 1988; Houze 1989; Jorgensen et al. 1997; Trier et al. 1997; Kingsmill and Houze 1999; Bryan and Fritsch 2000; Mechem et al. 2002; James et al. 2005; Alfaro and Khairoutdinov 2015; Alfaro 2017). The role of entrainment in these regions of slab-like ascent is presently unclear, and it is possible that entrainment minimally affects updraft air because of the laminar flow within these layer-lifting regions. However, this slab-like airstream often breaks down into discrete, quasi-spherical updraft pulses—commonly known as thermals—in the middle to upper troposphere (e.g., Redelsperger and Lafore 1988; Weisman et al. 1988; Fovell and Tan 1998; Bryan and Fritsch 2000; Bryan et al. 2003, 2007; Bryan and Morrison 2012; Lebo and Morrison 2015). The diameters of these thermals are typically on the order of 1–2 km, which is more than an order of magnitude smaller than the horizontal scale of the slab-like airstream; however, it is conceivable that the horizontal scale of the ascending slab-like airstream “sets the stage” for the width of thermal-like updrafts aloft in squall lines, as hypothesized by James et al. (2005). The structure of thermals generally plays an essential role in the entrainment behavior of deep convection, and there is evidence that thermal-like updrafts are more susceptible to the deleterious effects of entrainment-driven dilution of B than other updraft organizational structures, such as plumes (e.g., Morton et al. 1956; Scorer 1957; Morrison 2017; Morrison et al. 2020; Peters et al. 2020a,c). Consequently, the thermal-like structure of middle- to upper-tropospheric squall-line updrafts suggest that they are susceptible to the deleterious effects of entrainment.
It is possible that shear influences squall-line entrainment characteristics, in addition to the dynamical connections that have been described by previous authors and are outlined above, though this potential connection has received little attention in previous literature. For instance, the influence of shear on supercellular updraft width and intensity has received growing attention in recent literature. Studies such as Dennis and Kumjian (2017), Trapp et al. (2017), Warren et al. (2017), Marion and Trapp (2019), Peters et al. (2019b, 2020a,b), and Mulholland et al. (2020) have all shown supercell updraft width to positively scale with shear magnitude (i.e., stronger shear is correlated with wider supercell updrafts). Specifically, Peters et al. (2019b) provided theoretical and idealized numerical model simulation results that showed increasing shear led to increasing LL storm-relative inflow (i.e., greater LL horizontal mass flux) and, through a mass continuity argument (see section 4 therein), resulted in wider supercell updrafts. Wider supercell updrafts were shown to be more resistant to entrainment-driven dilution of B, and therefore had larger vertical accelerations and w (e.g., Peters et al. 2019b, 2020b). It is natural to wonder if this concept also applies to squall lines. An idealized numerical modeling study of squall lines by French and Parker (2010) showed that increasing LL shear in squall line environments equated to larger vertical mass flux in the deep convective line. An idealized numerical modeling study of squall lines by Alfaro (2017) found that increasing LL shear resulted in a greater fraction of inflowing high-CAPE air to the total inflowing air, resulting in greater B aloft in simulated squall lines. Alfaro (2017) argued that the greater fraction of inflowing high-CAPE air to the total inflowing air resulted in less dilution of updrafts aloft in the simulated squall lines, although that study did not explicitly show variations in entrainment-driven dilution and/or changes in updraft width with changes in LL shear. We thus build upon the Alfaro (2017) results and pose the following central research questions: 1) Do environments with stronger shear also foster wider squall-line updrafts than environments with weaker shear, and are squall-line updrafts in stronger-shear environments therefore less susceptible to entrainment-driven dilution? 2) If such a relationship exists, what are the relative influences of LL and UL shear on this relationship? Some of these research questions were further motivated by the pathways for future work outlined in Marinescu et al. (2017) and results shown in Phinney et al. (2017). Specifically, Marinescu et al. (2017) suggested that future squall-line simulation studies use large-eddy-resolving scales to further evaluate how environmental factors, such as wind shear, modulate entrainment within squall lines.
In response to these research questions, we evaluate the following hypothesis: stronger LL shear in squall-line environments equate to stronger LL OFB-relative flow, greater LL horizontal mass flux into the edge of the cold pool, and thus wider squall-line updrafts with less entrainment-driven dilution than in environments where LL shear is comparatively weak. The wider squall-line updrafts in environments with stronger LL shear equate to larger updraft B, and consequently w, when compared to squall-line updrafts amid environments with weaker LL shear. Furthermore, we expect a similar relationship between UL shear, which may alter squall-line steering currents and OFB-relative horizontal mass flux, updraft width, entrainment, and intensity. Here we show that, in addition to the dynamics discussed by previous authors, the specific connection between LL shear, updraft width, and entrainment is an essential missing piece explaining why LL shear tends to modulate the intensity (i.e., wMAX) of deep convective updrafts in squall lines. Finally, although we expect LL and UL shear to have similar impacts on squall-line updraft properties, we hypothesize that LL shear should have a greater influence on these aforementioned processes than UL shear owing to the more obvious connection between LL shear and both LL OFB-relative flow and LL horizontal mass flux (e.g., Parker and Johnson 2004b; French and Parker 2010; Alfaro 2017). To address this hypothesis, we analyzed a suite of idealized numerical model simulations of squall lines with variations solely in the background LL and UL shear profiles for a singular thermodynamic environment (outlined in section 2). Results from the suite of idealized numerical model simulations are detailed in section 3 and a summary, discussion, and conclusions are given in section 4.
2. Experimental design
a. Numerical modeling setup
We conducted idealized numerical model simulations using Cloud Model 1 (CM1; Bryan and Fritsch 2002) release 19.7. All simulations used isotropic grid spacings of 250 m in the horizontal and vertical directions. The domain top was set to 25 km above ground level (AGL) with a Rayleigh dampening layer (coefficient = 3.33 × 10−3 s−1) applied above 20 km AGL. The north–south domain length was 99 km with periodic lateral boundary conditions while the east–west domain length was 420 km with open radiative lateral boundary conditions. Coarser horizontal grid spacing (Δx, Δy = 1 km) simulations (with and without east–west horizontal grid stretching) were conducted with various domain sizes; the results of those simulations were qualitatively similar to those presented in section 3 for the higher-resolution simulations. The lower and upper boundaries were free slip with a rigid domain top. In all simulations, we neglected radiation, surface fluxes, friction, terrain, and Coriolis acceleration. Microphysical processes were parameterized with the Morrison two-moment scheme (Morrison et al. 2009) with hail set as the prognostic rimed ice hydrometeor species. The simulations used a time step of 3.5 s with integration lengths of 8 h and output written every 5 min. A summary of all CM1 settings is given in Table 1.
Summary of the CM1 configuration. LBC—Lateral boundary condition.
b. Description of base-state environments
The thermodynamic base-state environments for all simulations were identical and used the Weisman and Klemp (1982, hereafter WK82) analytic equations (Fig. 1). Modifications to the original WK82 sounding included increasing the surface potential temperature θ from 300 to 302 K and reducing the relative humidity (RH) above 2.5 km AGL to a constant value of 45%. The slight increase in surface θ (from 300 to 302 K) was made to reduce the amount of errant convection that occurred ahead of the squall-line OFB in the simulations, while the reduction in RH above 2.5 km AGL to 45% was to create an environment more in-line with observed squall-line environments (e.g., Fig. 7 in Coniglio et al. 2012). The modified planetary boundary layer (PBL) mixing ratio was set to 14 g kg−1, which resulted in surface-based, 0–1 km mean layer, and most-unstable convective available potential energy (CAPE) [convective inhibition (CIN)] of 2043 (−69), 2191 (−44), and 2615 (−3) J kg−1, respectively—all of which fall within the range of observed values for squall-line environments (e.g., see Fig. 9 in Evans and Doswell 2001; see Fig. 8 in Cohen et al. 2007). The approximate effective inflow layer (EIL; Thompson et al. 2007) depth following the CAPE and CIN criteria of Thompson et al. (2007) (i.e., largest contiguous vertical layer with CAPE > 100 J kg−1 and CIN < −250 J kg−1) was ~2.5 km (cf. Figs. 2c,d).
Input sounding used for the CM1 simulations plotted on a skew T–logP diagram. The rightmost solid lines are the air temperature (°C) and the leftmost solid lines are the dewpoint temperature (°C). Blue solid lines are for a sounding taken at a grid point in the cold pool and the red solid lines are for a sounding taken at a grid point in the warm air ahead of the cold pool. The black dotted line is the parcel trace for an air parcel lifted from the surface in the warm air ahead of the cold pool, and green dots represent the lifting condensation level, level of free convection, and the equilibrium level from bottom to top, respectively, of this lifted surface air parcel.
Citation: Journal of the Atmospheric Sciences 78, 6; 10.1175/JAS-D-20-0299.1
(a) West-to-east-oriented vertical cross section of the initial cold pool (green–blue shading; K), (b) input vertical zonal wind profiles (m s−1) and black dashed horizontal line denoting 2.5 km AGL, (c) vertical profile of CAPE (navy blue line; J kg−1) and the layer over which the PT is placed (orange–red shading), and (d) vertical profile of −CIN (navy blue line; J kg−1) and the layer over which the PT is placed (orange–red shading). The vertical profiles of CAPE and CIN were calculated from the warm air sounding in Fig. 1. Note the different y-axis limits for (a)–(d).
Citation: Journal of the Atmospheric Sciences 78, 6; 10.1175/JAS-D-20-0299.1
Deep convection was initiated in the simulations with a cold pool covering the domain from south to north and extending from the center of the domain westward. The minimum surface θ perturbation of the cold pool was set to −5 K and decreased in magnitude toward 0 K with increasing height through the 2.5 km depth of the cold pool (Fig. 2a). To facilitate the development of turbulence, ±0.25 K random θ perturbations were seeded throughout the depth and horizontal extent of the cold pool in the initial conditions (e.g., as in Parker and Johnson 2004b). Two sensitivity simulations (not shown) with initial ±0.25 K random θ perturbations placed throughout the entire domain below 2.5 km AGL, instead of just confined within the cold pool, yielded nearly identical results as the configuration we used here.
A set of various initial vertical wind profiles were used in the simulations to address our hypothesis. All wind profiles featured unidirectional west-to-east shear. This unidirectional “shear” profile was chosen for its simplicity and extensive use in previous similar squall-line simulations (e.g., Rotunno et al. 1988; Weisman et al. 1988; Fovell and Ogura 1989; Skamarock et al. 1994; Fovell and Dailey 1995; Weisman et al. 1997; Fovell and Tan 1998; Parker and Johnson 2004a,b,c; Weisman and Rotunno 2004; James et al. 2005; Bryan et al. 2006; Coniglio et al. 2006; James et al. 2006; Lane and Moncrieff 2010; Alfaro and Khairoutdinov 2015; Lebo and Morrison 2015; Peters 2016; Alfaro 2017). Three different LL (0–2.5 km AGL) and UL (2.5–10 km AGL) vertical wind shear1 magnitudes constituted our simulation matrix, all of which generally fall within the range of shear magnitudes used in prior squall-line simulation studies (e.g., Parker and Johnson 2004a,b,c; Coniglio et al. 2006; Alfaro and Khairoutdinov 2015; Alfaro 2017) and also in observations (e.g., Bluestein and Jain 1985; Parker and Johnson 2000; Evans and Doswell 2001; Coniglio et al. 2004; Parker and Johnson 2004a; Cohen et al. 2007; Coniglio et al. 2007; Bryan and Parker 2010; Lombardo and Colle 2012; Hitchcock et al. 2019) (Fig. 2b; Table 2). The naming convention for the various simulations uses numbers from 1 to 3 to indicate the relative LL and UL shear magnitudes. For example, the LL1_UL3 simulation is characterized by the weakest LL shear (7 m s−1) and the strongest UL shear (10 m s−1) shown in Table 2. It should be noted that our LL3 shear profile likely represents the far high end of the LL shear spectrum for observed squall lines in environments with substantial CAPE (e.g., see Fig. 13 in Evans and Doswell 2001; see Figs. 1 and 2 in Cohen et al. 2007; see Fig. 2 in Coniglio et al. 2007). Furthermore, our strongest UL shear profile (UL3) is likely at the low to moderate end of the UL shear spectrum for observed squall lines in environments with substantial CAPE (e.g., see Figs. 1 and 2 in Cohen et al. 2007; see Fig. 2 in Coniglio et al. 2007). Finally, to approximately center the squall-line OFBs within the domains throughout the length of the simulations, a unique uniform zonal wind speed was subtracted from the entire domain for each simulation, which included regions inside and outside of the cold pool.
Magnitude of LL (0–2.5 km AGL) and UL (2.5–10 km AGL) shear (calculated as a simple bulk wind difference and expressed in units of m s−1) for all nine squall-line simulations. The naming conventions follow that outlined in section 2.
c. Quantifying entrainment-driven dilution
To quantify entrainment-driven dilution of updraft cores in the squall lines, a passive tracer (PT) was initialized in the base state to the east of the cold pool between 0 and 1.5 km AGL (light red shading in Figs. 2c and 2d), or approximately throughout the lower half of the EIL in which the largest magnitudes of CAPE were located (e.g., Fig. 2c; similar PT setup as in Phinney et al. 2017). In subsequent analyses, the degree to which the PT concentration in updrafts falls below 100% is used to quantify the degree of entrainment-driven updraft dilution.
d. In-line forward parcel trajectories
As a final test of our hypothesis, we computed in-line forward trajectories2 in the simulations with the strongest and weakest LL and UL shear combinations (i.e., LL1_UL1, LL1_UL3, LL3_UL1, and LL3_UL3). At four hours into the simulations, 1000 trajectories were initialized ahead of the squall-line OFBs. Trajectories were placed in a 10 km south-to-north line at 100 km east of the domain center and spanned between 25 and 835 m AGL, covering the lower EIL. Trajectories were calculated with a time step consistent with the model simulations (3.5 s) with output written every time step. To test if alterations in shear affected squall-line updraft B, and ultimately wMAX, we compared the contribution of B versus the contribution of vertical perturbation pressure gradient accelerations (VPG) to wMAX along the trajectories among the four different simulations.
3. Results
a. General attributes of simulations
The 4–7-h3 averaged lowest model level (125 m AGL) reflectivity (computed relative to the OFB4 each 5-min output time) revealed that all nine simulations produced squall lines with many characteristic features of observed squall lines, such as a stratiform region that trailed the leading deep convective line (Fig. 3; also see radar animations in Fig. S1 in the online supplemental material). Simulations with the weakest LL shear displayed notably broken and cellular reflectivity features displaced rearward of their OFBs (e.g., far left column of Fig. 3 and Fig. S1). Increasing LL shear led to more widespread and coherent reflectivity structures with a nearly continuous south-to-north deep convective region that was located closer to the OFB (black dashed lines in Fig. 3 and Fig. S1), in agreement with Hane (1973) and numerous other studies. Conversely, alterations in UL shear had relatively muted impacts on the squall lines’ organizational structures, especially in LL2 simulations. Interestingly, increasing UL shear in the LL1 simulations actually resulted in slightly weaker reflectivity magnitudes closer in proximity to the OFBs (e.g., compare LL1_UL2 and LL1_UL3 in Fig. 3 and Fig. S1). Alternatively, increasing UL shear in the LL3 simulations resulted in slightly stronger reflectivity magnitudes and more three-dimensional structures (e.g., bowing segments in LL3_UL3)—in agreement with the squall-line simulations of Coniglio et al. (2006).
Plan views of average 4–7-h lowest-model-level reflectivity (shaded; dBZ) and the −1 K lowest-model-level θ perturbation contour (x = 25 km; black dashed lines). The titles above each panel indicate the simulation-specific shear combination. Averages were computed relative to the OFB (x = 25 km; black dashed lines) using 5 min model output (see section 3 for additional details). Note that only a portion of the full domain is shown.
Citation: Journal of the Atmospheric Sciences 78, 6; 10.1175/JAS-D-20-0299.1
West-to-east oriented, OFB-relative vertical cross sections of PT concentration, w, and reflectivity averaged −5 to +5 km around the center of the domain (y = 49.5 km) and over the 4–7-h period revealed stark differences in the convective features of the squall lines (Fig. 4; also see animations in Fig. S2). Simulations with weaker LL shear had correspondingly weaker and shallower updrafts whereas simulations with stronger LL shear had stronger and deeper updrafts. Furthermore, as noted in the plan view reflectivity composites (Fig. 3), the low-level OFBs were closer in proximity to the leading deep convective line in the stronger LL shear simulations, whereas the OFBs were effectively detached from the middle- to upper-tropospheric updrafts in LL1 simulations. Last, weaker LL shear simulations displayed greater dilution of the EIL PT aloft compared to the stronger LL shear simulations.
West-to-east-oriented, average 4–7-h (within −5 to +5 km of the domain center at y = 49.5 km relative to the OFB) vertical cross sections of PT concentration (shaded; %), vertical velocity (1 m s−1 contour in light blue), and reflectivity (20 dBZ contour in dark gray). The titles above each panel indicate the simulation-specific shear combination. Note that only a portion of the full domain is shown.
Citation: Journal of the Atmospheric Sciences 78, 6; 10.1175/JAS-D-20-0299.1
To provide context for comparisons with previous studies of squall lines, we assessed the relative “balance” between the cold pool-induced circulation and LL shear-induced circulation for the simulated squall lines. This was accomplished by calculating the C/Δu ratio (Rotunno et al. 1988), where C is the integrated cold pool strength equal to
West-to-east-oriented, average 4–7-h (within −5 to +5 km of the domain center at y = 49.5 km relative to the OFB) vertical cross sections of B (shaded; m s−2), vertical velocity (2 m s−1 contour in green), and in-plane wind vectors (m s−1; scale located below color bar). Note that only a portion of the full domain is shown.
Citation: Journal of the Atmospheric Sciences 78, 6; 10.1175/JAS-D-20-0299.1
b. Influence of shear on updraft width and entrainment-driven dilution
A first step toward evaluating our hypothesis was to determine whether the simulations with stronger shear displayed wider updrafts than the simulations with weaker shear. Updraft area was quantified by first calculating contiguous horizontal regions that met a certain w threshold at each model vertical level. We then took an average of all such updraft area “objects” at each model vertical level and at each time, excluding areas of small-scale vertical motion (i.e., contiguous areas ≤ 1 km2). Finally, we time averaged updraft area “objects” at each model vertical level over the 4–7-h period. Updraft area “objects” were characterized using two different w thresholds: 1) “broad” (w = 5 m s−1) and 2) “core” (w = 20 m s−1) updrafts. Our results were relatively insensitive to small variations (~few meters per second) in these w thresholds. Broad updraft area increased with increasing LL shear, especially below 5 km AGL (Fig. 6a). Differences in broad updraft area due to variations in UL shear were less pronounced than for variations in LL shear, with a slight increase in broad updraft area with stronger UL shear in LL2 and LL3 simulations and a slight decrease in broad updraft area with stronger UL shear in LL1 simulations. Similar to broad updraft area, core updraft area also generally increased with increasing LL shear, with lesser differences due to variations in UL shear (Fig. 6b). The large “spikes” in broad updraft area below ~2.5 km AGL were associated with the front-to-rear slab-like ascending airstreams that characterized these squall lines. The larger regions of slab-like ascent in the stronger LL shear simulations—which likely owe to stronger LL shear and stronger, deeper cold pools (see Fig. 5; e.g., James et al. 2005)—appear to “set the stage” for wider thermals aloft. Statistically significant correlations (linear correlation coefficient CC = 0.81; p value < 0.05) between average 0–5 km AGL broad updraft area and average 5–10 km AGL core updraft area across all simulations over the 4–7-h period show strong support for this idea (Fig. 7). A heat map5 of the median 4–7-h average 0–5 km AGL broad updraft area shows that as LL shear increased, broad updraft area increased (Fig. 8a). A similar trend was noted for median 4–7-h average 5–10 km AGL core updraft area (Fig. 8b). Interestingly, stronger UL shear with LL1 simulations resulted in slightly smaller broad and core updraft area than weaker UL shear with LL1 simulations (far left columns in Figs. 8a and 8b), whereas stronger UL shear with LL2 and LL3 simulations resulted in comparable broad and core updraft area relative to weaker UL shear with LL2 and LL3 simulations. Thus, updraft width appears to be more strongly influenced by LL shear than by UL shear.
Vertical profiles of average 4–7-h average contiguous (a) broad and (b) core updraft areas (km2) by shear experiment. Contiguous areas that were ≤1 km2 were not included in the averaging. Note the different x-axis limits between (a) and (b).
Citation: Journal of the Atmospheric Sciences 78, 6; 10.1175/JAS-D-20-0299.1
Scatterplots of 4–7-h average contiguous 5–10 km AGL core updraft area (y axis; km2) versus 4–7-h average contiguous 0–5 km AGL broad updraft area (x axis; km2). The green line is the linear regression fit and the corresponding CC value is listed in section 3. Each dot represents 5 min output model data.
Citation: Journal of the Atmospheric Sciences 78, 6; 10.1175/JAS-D-20-0299.1
Heat maps of median 4–7-h average (a) 0–5 km AGL broad and (b) 5–10 km AGL core updraft areas (km2) by shear experiment. Darker shading denotes larger magnitudes (see color bar below each panel). The smaller number located to the lower-right-hand side of each block denotes the ±95% confidence interval range around the median values truncated at two decimal places (calculated using the Python SciPy toolkit; available online at https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.t.html).
Citation: Journal of the Atmospheric Sciences 78, 6; 10.1175/JAS-D-20-0299.1
To quantify the potential influence of updraft width on entrainment-driven dilution, we compared PT concentrations aloft across the simulations. A heat map constructed using the median 4–7-h 5–10 km AGL layer maximum PT concentrations show that stronger LL shear equated to larger PT concentrations aloft, relative to weaker LL shear (Fig. 9). In contrast, but in a consistent manner with the trends in updraft width, stronger UL shear in the LL1 simulations actually resulted in smaller PT concentrations aloft when compared to weaker UL shear in the LL1 simulations. However, there was no statistically significant connection between UL shear and PT concentration in the LL2 and LL3 simulations, which is again consistent with the trends in updraft width. Correlations between 4–7-h 5–10 km AGL layer maximum PT concentrations and average 5–10 km AGL core updraft area were statistically significant (i.e., p value <0.05), with a log-scaled CC = 0.83 (Fig. 10). These results reveal that squall-line updrafts in environments with stronger LL shear displayed less entrainment-driven dilution compared to squall-line updrafts in environments with weaker LL shear. The connection between LL shear and updraft width is evident in the statistically significant correlations (CC = 0.79; p value <0.05) between 4–7-h 0–1 km AGL horizontal mass flux and average 5–10 km AGL core updraft area across all simulations (Fig. 11). The LL shear is directly connected to the LL horizontal mass flux (e.g., French and Parker 2010) and, in turn, connected to the vertical mass flux via mass continuity. In an analogous manner to what occurs in supercells (e.g., Peters et al. 2019b), the increase in vertical mass flux equates to wider updrafts.
As in Fig. 8, but for median 4–7-h 5–10 km AGL layer maximum PT concentrations (%).
Citation: Journal of the Atmospheric Sciences 78, 6; 10.1175/JAS-D-20-0299.1
As in Fig. 7, but of 4–7-h 5–10 km AGL layer maximum PT concentration (y axis; %) versus 4–7-h average contiguous 5–10 km AGL core updraft area (x axis; km2). The green line is now the predicted curve for PTTH concentration using Eq. (1) with L set equal to the horizontal grid spacing (Δx, Δy = 250 m) and the gold line is now the predicted curve for PTTH concentration using Eq. (1) with L ~ R, which follows from Morrison (2017); see section 3 for additional details.
Citation: Journal of the Atmospheric Sciences 78, 6; 10.1175/JAS-D-20-0299.1
As in Fig. 7, but of 4–7-h average contiguous 5–10 km AGL core updraft area (y axis; km2) versus 4–7-h 0–1 km AGL horizontal mass flux (x axis; ×103 kg s−1 m−2). Horizontal mass flux was calculated at y = 49.5 km and at a grid point 50 km east of the OFB at each 5 min output time during the 4–7-h period.
Citation: Journal of the Atmospheric Sciences 78, 6; 10.1175/JAS-D-20-0299.1
c. Theoretical support for the relationship between updraft width and entrainment-driven dilution
Axisymmetric updrafts were assumed in deriving the theoretical expression for PTTH concentration. Because our simulations are fully 3D, we assume that R is proportional to the effective radius Reff of a circular region with area equal to the simulated 5–10 km AGL core updraft area A. In other words, R = cReff and Reff = (A/π)1/2. The constant of proportionality c is found by approximately matching the solution for PTTH concentration from Eq. (1) with the PT concentration from the simulation with the largest core A and Reff, and then applying this value of c across the full range of A and Reff from the simulations. Note that modifying c simply shifts the PTTH concentration curve up or down, but does not modify the shape of the relationship between PTTH concentration with A. For simplicity, we set height z in Eq. (1) to 5 km AGL; while there is variability in height of maximum PT concentrations at different times, it generally occurs at ~5 km AGL (e.g., Fig. S3).
The closeness of the PTTH concentration curve (green line in Fig. 10) and the 4–7-h 5–10 km AGL layer maximum PT concentrations from the simulations supports a 1/R2 scaling for fractional entrainment rate and dilution of the simulated updrafts. The theoretical 1/R2 scaling comes directly from the assumption of constant L in Eq. (2). If instead L is assumed to be proportional to R, the classical 1/R scaling of fractional entrainment rate from dimensional analysis of dry plumes and thermals (e.g., Morton et al. 1956; Scorer 1957) is obtained from Eq. (2). However, this scaling gives a much poorer comparison of PTTH concentration to the simulated PT concentration (gold line in Fig. 10). Specific reasons for this behavior are unclear and are beyond the scope of the study. Regardless, this analysis strongly supports an inverse relationship between updraft area and entrainment-driven dilution of the simulated squall-line updrafts, which is in line with our primary hypothesis.
d. Impact of differences in updraft width and entrainment-driven dilution on maximum vertical velocities
Next, we establish a relationship between updraft dilution and wMAX among the simulations, which is a key to our hypothesis. A heat map displaying a matrix of median 4–7-h wMAX magnitudes for the various LL and UL shear combinations was analyzed first (Fig. 12). Visual inspection of the heat map in Fig. 12 reveals that as LL shear increased, wMAX increased. Consistent with earlier analysis, stronger UL with LL1 simulations actually resulted in slightly weaker wMAX relative to weaker UL shear with LL1 simulations (far left column of Fig. 12), whereas the trend between UL shear and wMAX in the LL2 and LL3 simulations was ill defined. To provide a baseline for comparison with parcel theory, the “thermodynamic speed limit” (i.e.,
As in Fig. 9, but for median 4–7-h wMAX (m s−1).
Citation: Journal of the Atmospheric Sciences 78, 6; 10.1175/JAS-D-20-0299.1
Vertical profiles of wMAX averaged over the 4–7-h period depicted an increase in the magnitude and height of wMAX with stronger LL shear (Fig. 13). Stronger LL shear equates to stronger wMAX along the LL OFBs (along and below ~2.5 km AGL) across all simulations when compared to weaker LL shear, as previously shown in numerous studies. Note, however, that the height of wMAX, and the largest variations in wMAX between the various LL and UL shear simulations, corresponded with thermals aloft (>5 km AGL) and not with the dynamically driven low-level ascent along the OFB. Variations in UL shear had the largest impact in LL3 simulations, with a monotonic increase in both the height and magnitude of wMAX with increasing UL shear (red shaded lines in Fig. 13). Furthermore, we examined the maximum forward parcel trajectory displacements, as it is a combination of both w and the time it takes parcels to ascend that determines parcel displacements. Figure 14 displays these results and shows that, in line with the aforementioned wMAX analyses, maximum parcel displacements were substantially larger in the stronger LL shear simulations. Thus, updrafts experiencing stronger LL shear were faster and deeper than those experiencing weaker LL shear. Variations in UL shear had lesser impact on maximum parcel displacements, although there still was a notable shift in the maximum parcel displacements upward between the LL3_UL1 and LL3_UL3 simulations (Fig. 14).
Vertical profiles of average 4–7-h wMAX (m s−1).
Citation: Journal of the Atmospheric Sciences 78, 6; 10.1175/JAS-D-20-0299.1
Violin plot6 of maximum parcel displacements (km) across all usable trajectories (see section 3 for additional details). Horizontal lines in each violin plot represent the 5th (lower) and 95th (upper) confidence intervals around the median values and dots in each violin plot represent the 5th (lower) and 95th (upper) confidence intervals around the 90th-percentile values.
Citation: Journal of the Atmospheric Sciences 78, 6; 10.1175/JAS-D-20-0299.1
The 4–7-h wMAX magnitudes were statistically significantly correlated (CC = 0.71; p value <0.05) with 4–7-h average 5–10 km AGL core updraft areas (Fig. 15), consistent with less entrainment-driven dilution associated with wider updrafts in the stronger LL shear simulations. This suggests that the wider updrafts in the simulations with stronger LL shear were more buoyant because of their decreased dilution, relative to the simulations with weaker LL shear.
As in Fig. 7, but of 4–7-h wMAX (y axis; m s−1) versus 4–7-h average contiguous 5–10 km AGL core updraft area (x axis; km2).
Citation: Journal of the Atmospheric Sciences 78, 6; 10.1175/JAS-D-20-0299.1
Violin plots of wMAX (blue; m s−1) and wB,MAX (orange; m s−1) across all usable trajectories (see section 3 for additional details). Blue (wMAX) and red (wB,MAX) horizontal lines in each violin plot represent the 5th (lower) and 95th (upper) confidence intervals around the median values and dots in each violin plot represent the 5th (lower) and 95th (upper) confidence intervals around the 90th-percentile values.
Citation: Journal of the Atmospheric Sciences 78, 6; 10.1175/JAS-D-20-0299.1
Percentage of acceleration (y axis) from B (solid lines; %) and VPG (dashed lines; %) that contributed to wMAX across all usable trajectories (x axis) (see section 3 for additional details). Each wMAX bin size is 5 m s−1. If a bin had less than 10 occurrences, it was excluded from the calculation.
Citation: Journal of the Atmospheric Sciences 78, 6; 10.1175/JAS-D-20-0299.1
e. Impact of upper-level shear variations on squall-line updraft characteristics
As discussed above, variations in LL shear led to the most drastic changes in updraft width, entrainment characteristics, B, and ultimately wMAX, whereas variations in UL shear had comparatively lesser impacts. LL3 simulations with increasing UL shear generally showed minor increases in updraft area (e.g., Figs. 6–8), PT concentrations aloft (e.g., Figs. 9 and 10), LL horizontal mass flux (e.g., Fig. 11), wMAX (e.g., Figs. 12, 13, 15), and B (e.g., Fig. 5). LL2 simulations with increasing UL shear generally had small changes in squall-line updraft characteristics. Interestingly, LL1 simulations with increasing UL shear had opposite changes in squall-line updraft characteristics compared to the LL3 simulations, including minor decreases in updraft area (e.g., Figs. 6–8), PT concentrations aloft (e.g., Figs. 9 and 10), LL horizontal mass flux (e.g., Fig. 11), wMAX (e.g., Figs. 12, 13, 15), and B (e.g., Fig. 5). Changes in wMAX from variations in UL shear for a given value of strong LL shear (i.e., our LL3 simulations) were generally comparable to the results of Coniglio et al. (2006). For example, the difference in median 3–6-h wMAX between the weak UL shear and moderate-to-strong UL shear simulations in Coniglio et al. (2006) was roughly 40% (see their Fig. 10a). Similarly, the differences in median 4–7-h wMAX between our LL3_UL1 and LL3_UL3 simulations was roughly 27%.
4. Summary, discussion, and conclusions
This study investigated the influence of LL and UL shear variations on squall-line updraft characteristics for a singular thermodynamic environment (i.e., fixed CAPE and CIN). Our simulations revealed that as LL shear increased, LL horizontal mass flux increased, leading to wider squall-line updrafts that were stronger and deeper. Changes in squall-line updraft width, entrainment, and intensity characteristics owing to variations in UL shear were relatively minor. The wider updrafts in stronger LL shear environments displayed the least amount of entrainment-driven dilution of B, consistent with larger concentrations aloft of a PT that originated from the EIL. Statistically significant correlations were found between LL horizontal mass flux (and by extension, LL shear), updraft width, PT transport aloft, and wMAX. Forward trajectory analyses revealed that the larger B in wider, less dilute updrafts resulted in larger vertical accelerations and wMAX when compared to narrower and more dilute updrafts. Thus, our results highlight a previously unexplored mechanism for how shear (especially LL shear) influences squall-line updraft intensity. In an interesting (albeit unsurprising) contrast with previous work that has established the central role of deep-layer shear in regulating supercell updraft width, our results suggest that LL shear is more important than UL shear to determining squall-line updraft width.
Alfaro’s (2017) results are particularly pertinent to our study. He showed that as the ratio of high-CAPE inflowing air to the total inflowing air increased—whether through variations in LL shear and/or LL thermodynamic variations—squall-line updrafts became less dilute, had greater B, and thus were stronger and deeper. Our work adds to this conceptual model by explaining how differences in LL shear affect updraft properties, such as updraft width, within squall lines for a given thermodynamic environment. Finally, we studied possible impacts of varying UL shear on squall line updraft properties, similar to Coniglio et al. (2006). Our results arguably agree with Coniglio et al. (2006); increasing UL shear (in our case, to 10 m s−1 over the 2.5–10 km AGL layer) led to slightly stronger squall-line updrafts in the strongest LL shear simulations. Interestingly, the weakest LL shear simulations in combination with increasing UL shear led to weaker squall-line updrafts. Further exploration into the reasons for this behavior of squall-line updrafts within various LL shear environments in combination with a much more expansive set of UL shear magnitudes (i.e., stronger) is warranted for future work.
Clearly, CAPE is strongly tied to wMAX and future simulations across a range of thermodynamic environments (i.e., various CAPE and CIN magnitudes) are necessary to evaluate the sensitivity of the aforementioned relationship to CAPE. It is also possible that differences in the cold pool propagation speed and the resultant magnitude of cold pool relative flow outside of the cold pool, in addition to vertical wind shear, influence the tilt, entrainment characteristics, and intensity of squall-line deep convective updrafts. This is yet another potential mechanism that may modulate squall-line intensity and structure that future studies should investigate. Furthermore, future simulated squall-line entrainment studies should include stable layers, drier middle- to upper-troposphere environments, stronger UL shear magnitudes, different three-dimensional wind profiles, and modified initial and lateral boundary conditions to see if these trends extend beyond the environments considered herein. We did not examine how the relationship between environmental shear, entrainment, and updraft characteristics might impact severe weather, which is left to future work.
Acknowledgments
The authors thank Chris Nowotarski, Geoff Marion, Bowen Pan, Peter Marinescu, Susan van den Heever, Rachel Phinney, Johana Lambert, and Janice Mulholland for their insightful comments, coding assistance, and stimulating conversations related to the material presented in this article. The authors would also like to thank the exceptionally helpful comments and suggestions from the three anonymous reviewers. We greatly appreciate George Bryan’s tireless efforts in maintaining CM1. We would like to acknowledge high-performance computing support from Cheyenne (doi:10.5065/D6RX99HX) provided by NCAR’s Computational and Information Systems Laboratory, sponsored by the National Science Foundation. Funding for this research was supported by National Science Foundation Grants AGS-1928666 and AGS-1841674 and Department of Energy Atmospheric System Research Grants DE-SC0020104 and DE-SC0000246356.
Data availability statement
All code, model configuration, and model output are available upon request to the corresponding author.
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