1. Introduction and motivation
The amount of streamwise horizontal vorticity in the background environment is critical in determining the potential for a thunderstorm to develop into a supercell. The midlevel mesocyclone, the defining characteristic of a supercell, forms via tilting of ambient streamwise vorticity (Davies-Jones 1984; Dahl 2017). The low-level mesocyclone forms in a similar manner (e.g., Markowski and Richardson 2014) with baroclinity also playing a role (e.g., Rotunno and Klemp 1985; Dahl et al. 2014). To this end, the amount of streamwise horizontal vorticity is incorporated into forecasting parameters to help predict supercell potential and strength. Storm-relative helicity (SRH) in the 0–1-km, 0–3-km, or effective layer is often used, which is a measure of both horizontal vorticity and storm-relative flow (e.g., Davies-Jones et al. 1990; Rasmussen and Blanchard 1998; Thompson et al. 2003; Craven and Brooks 2004). Given equal storm-relative flow, larger SRH implies larger streamwise vorticity and a stronger supercell.
The amount of streamwise horizontal vorticity, particularly at low levels, is also critical in determining the potential for a supercell to produce a tornado (e.g., Rasmussen 2003). Increased low-level SRH supports a stronger low-level mesocyclone via more efficient tilting (Markowski and Richardson 2014; Coffer and Parker 2017). This results in greater low-level upward dynamic accelerations and vertical vorticity stretching that, all else being equal, increases tornado potential. Recent studies also show that increased near-surface streamwise vorticity may play a more direct role in the tornado vorticity budget by being abruptly tilted and stretched upward into the vortex (Rotunno et al. 2017; Boyer and Dahl 2020). The critical angle, defined as the angle between the 10 m AGL storm-relative wind vector and the 10–500-m shear vector, helps diagnose the degree to which environmental vorticity is streamwise close to the surface (Esterheld and Giuliano 2008). A recent study also showed that using 0–500-m SRH instead of 0–1-km SRH in the calculation of the significant tornado parameter (Thompson et al. 2003) yields increased skill in discriminating between tornadic and nontornadic environments (Coffer et al. 2019).
As focus shifts to the vertical wind profile closer to the ground, the possible influences of friction become important. On the tornado scale, friction is important in disrupting cyclostrophic balance to promote inward radial acceleration and abrupt upward turning in the corner region (e.g., Fiedler and Rotunno 1986; Lewellen and Lewellen 2007). On the storm scale, recent studies show that surface friction can modify preexisting vorticity as well as generate horizontal vorticity that then plays a role in the vorticity budget of the tornado or low-level mesocyclone (Schenkman et al. 2014; Roberts et al. 2016; Markowski 2016; Mashiko 2016; Roberts and Xue 2017). A couple studies have also shown that surface friction influences tornado potential in quasi-linear convective systems (Schenkman et al. 2012; Xu et al. 2015). However, the relative importance of friction on the tornado budget in large-eddy simulations like these may be significantly overestimated due to an unrealistic lack of turbulence in the prestorm boundary layer (Markowski and Bryan 2016); as such, these studies probably represent the maximum extent to which friction modifies storm-scale and tornado vorticity budgets.
These studies motivate this initial work to examine the influence of surface friction on the storm-relative wind profile. In particular, we focus on the lowest hundreds of meters AGL where the relative amount of streamwise and crosswise vorticity may more strongly influence supercell and tornado potential (e.g., Thompson and Edwards 2000; Esterheld and Giuliano 2008; Coffer and Parker 2017; Guarriello et al. 2018). We were inspired by the methods of Markowski (2016) who created their DRAG-CROSSWISE and DRAG-STREAMWISE cases simply by shifting the semicircular, ground-relative wind profile away from the origin [see Markowski’s (2016) Fig. 2]. Assuming a storm motion at the center of the semicircular portion of the hodograph (to be discussed later), the profile with faster ground-relative winds yielded increased streamwise vorticity and storm-relative flow in the near-surface layer influenced by friction. Both of these characteristics contributed to larger near-surface SRH in the DRAG-STREAMWISE experiment. Further examining the influence of increased ground-relative flow on near-surface SRH due to friction may help explain how some storms modify their background environment (e.g., Parker 2014; Wade et al. 2018; Coniglio and Parker 2020).
The influence of the wind profile on supercell morphology is often described as Galilean invariant because storm-internal processes depend on vertical wind shear rather than just the wind (e.g., Bunkers et al. 2000). However, friction is ground-relative, violating Galilean invariance, and will always result in a near-surface wind profile extending to the origin, regardless of where the rest of the wind profile lurks in hodograph space. This yields the following question: how do ground-relative winds and friction influence near-ground SRH?
2. Creating the frictionally induced shear profile
The semicircle hodographs used in this study with no near-surface frictional effects (black) and near-surface frictional effects included below 250 m AGL (red). The black hodograph is identical to the strong-shear simulation (m = 8) of Markowski and Richardson (2014, their Fig. 1b). The profiles are plotted in ground-relative, u–υ space (m s−1) and heights of interested are indicated (km). The 0–1- and 0–3-km SRH values are shown for the half-circle profile as well as 0–250-m SRH for each profile. Different storm motions are used for calculating SRH, including motion at the center of the half-circle (i.e., at the origin for the case plotted here) and Bunkers-right storm motion.
Citation: Journal of the Atmospheric Sciences 78, 7; 10.1175/JAS-D-20-0320.1
The semicircle hodographs used in this study with no near-surface frictional effects (black) and near-surface frictional effects included below 250 m AGL (red). The black hodograph is identical to the strong-shear simulation (m = 8) of Markowski and Richardson (2014, their Fig. 1b). The profiles are plotted in ground-relative, u–υ space (m s−1) and heights of interested are indicated (km). The 0–1- and 0–3-km SRH values are shown for the half-circle profile as well as 0–250-m SRH for each profile. Different storm motions are used for calculating SRH, including motion at the center of the half-circle (i.e., at the origin for the case plotted here) and Bunkers-right storm motion.
Citation: Journal of the Atmospheric Sciences 78, 7; 10.1175/JAS-D-20-0320.1
The semicircle hodographs used in this study with no near-surface frictional effects (black) and near-surface frictional effects included below 250 m AGL (red). The black hodograph is identical to the strong-shear simulation (m = 8) of Markowski and Richardson (2014, their Fig. 1b). The profiles are plotted in ground-relative, u–υ space (m s−1) and heights of interested are indicated (km). The 0–1- and 0–3-km SRH values are shown for the half-circle profile as well as 0–250-m SRH for each profile. Different storm motions are used for calculating SRH, including motion at the center of the half-circle (i.e., at the origin for the case plotted here) and Bunkers-right storm motion.
Citation: Journal of the Atmospheric Sciences 78, 7; 10.1175/JAS-D-20-0320.1
As in Fig. 1, but for the straight hodograph case for Δy = 5 m s−1 for the profiles with (red) and without (black) friction.
Citation: Journal of the Atmospheric Sciences 78, 7; 10.1175/JAS-D-20-0320.1
As in Fig. 1, but for the straight hodograph case for Δy = 5 m s−1 for the profiles with (red) and without (black) friction.
Citation: Journal of the Atmospheric Sciences 78, 7; 10.1175/JAS-D-20-0320.1
As in Fig. 1, but for the straight hodograph case for Δy = 5 m s−1 for the profiles with (red) and without (black) friction.
Citation: Journal of the Atmospheric Sciences 78, 7; 10.1175/JAS-D-20-0320.1
3. Varying the ground-relative winds
a. Semicircular shear profile
The 0–250-m SRH (shading) calculated using the semicircular hodograph with near-surface frictional effects included at each (Δx, Δy) point. The profiles at Δx = Δy = 0 and (Δx, Δy) = (2, 3) are shown as examples (solid white and orange lines, respectively). zf = 250 m for these cases highlighted (white and orange dots), and the assumed storm motion at (Δx, Δy) is shown (white and orange ×). Only positive SRH values are contoured. The thin white line is the value of 0–250-m SRH for the full half-circle profile without any frictional effects at the surface, roughly 45 m2 s−2 (constant for all Δx and Δy). The color bar shown here was chosen to match the color bar in Fig. 7 for ease of comparison.
Citation: Journal of the Atmospheric Sciences 78, 7; 10.1175/JAS-D-20-0320.1
The 0–250-m SRH (shading) calculated using the semicircular hodograph with near-surface frictional effects included at each (Δx, Δy) point. The profiles at Δx = Δy = 0 and (Δx, Δy) = (2, 3) are shown as examples (solid white and orange lines, respectively). zf = 250 m for these cases highlighted (white and orange dots), and the assumed storm motion at (Δx, Δy) is shown (white and orange ×). Only positive SRH values are contoured. The thin white line is the value of 0–250-m SRH for the full half-circle profile without any frictional effects at the surface, roughly 45 m2 s−2 (constant for all Δx and Δy). The color bar shown here was chosen to match the color bar in Fig. 7 for ease of comparison.
Citation: Journal of the Atmospheric Sciences 78, 7; 10.1175/JAS-D-20-0320.1
The 0–250-m SRH (shading) calculated using the semicircular hodograph with near-surface frictional effects included at each (Δx, Δy) point. The profiles at Δx = Δy = 0 and (Δx, Δy) = (2, 3) are shown as examples (solid white and orange lines, respectively). zf = 250 m for these cases highlighted (white and orange dots), and the assumed storm motion at (Δx, Δy) is shown (white and orange ×). Only positive SRH values are contoured. The thin white line is the value of 0–250-m SRH for the full half-circle profile without any frictional effects at the surface, roughly 45 m2 s−2 (constant for all Δx and Δy). The color bar shown here was chosen to match the color bar in Fig. 7 for ease of comparison.
Citation: Journal of the Atmospheric Sciences 78, 7; 10.1175/JAS-D-20-0320.1
As defined in Eq. (10), SRH is a function of the magnitudes of ωh and usr as well as the angle between them. To further quantify the relative influences of these on SRH, we calculated the means of these variables in the 0–250 m AGL layer for all Δx and Δy. The result for the half-circle profile with frictional effects included (i.e., the profile used in Fig. 3) is shown in Fig. 4. By definition, the gradient of the angle between ωh and usr (Fig. 4) points in the opposite direction as the gradient of SRH (Fig. 3), and SRH = 0 m2 s−2 when the angle = 90°. As the angle decreases toward 0°, the projection of ωh onto usr increases, resulting in an increase in positive SRH. A minimum in ωh exists near (Δx, Δy) = (7, −3) because in that case the ground-relative wind at 250 m lies at the origin, resulting in near-zero vertical wind shear from 0 to 250 m AGL. As the angle decreases (e.g., as Δx and Δy generally increase), ωh and usr increase. These influences all lead to increasing SRH (see Fig. 3). As the angle increases (e.g., as Δx and Δy generally decrease), ωh and usr increase, leading to negative SRH. As ωh and usr change but the angle remains constant (i.e., moving parallel to the shaded contours in Fig. 4), SRH remains constant.
Mean storm-relative wind speed (blue, m s−1), horizontal vorticity magnitude (orange, s−1), and the angle between the two (shading, in degrees) in the 0–250 m AGL layer for the half-circle profile with frictional effects (i.e., the same profile used in Fig. 3). The 90° isopleth is highlighted in red, which by definition lies along the 0 m2 s−2 isopleth plotted in Fig. 3.
Citation: Journal of the Atmospheric Sciences 78, 7; 10.1175/JAS-D-20-0320.1
Mean storm-relative wind speed (blue, m s−1), horizontal vorticity magnitude (orange, s−1), and the angle between the two (shading, in degrees) in the 0–250 m AGL layer for the half-circle profile with frictional effects (i.e., the same profile used in Fig. 3). The 90° isopleth is highlighted in red, which by definition lies along the 0 m2 s−2 isopleth plotted in Fig. 3.
Citation: Journal of the Atmospheric Sciences 78, 7; 10.1175/JAS-D-20-0320.1
Mean storm-relative wind speed (blue, m s−1), horizontal vorticity magnitude (orange, s−1), and the angle between the two (shading, in degrees) in the 0–250 m AGL layer for the half-circle profile with frictional effects (i.e., the same profile used in Fig. 3). The 90° isopleth is highlighted in red, which by definition lies along the 0 m2 s−2 isopleth plotted in Fig. 3.
Citation: Journal of the Atmospheric Sciences 78, 7; 10.1175/JAS-D-20-0320.1
In this analytical framework, changes in SRH are only possible if the angle between ωh and usr changes. When the angle changes, the magnitudes of ωh and usr influence the magnitude of the resulting change in SRH. Uniformly increasing ground-relative wind speeds throughout the hodograph (e.g., increasing Δx and Δy) above zf results in larger SRH in the surface–zf layer. This finding complements the analyses of Coniglio and Parker (2020) in showing how enhancements to the storm-relative wind profile in different layers can lead to substantial increases in SRH, and in their case discrimination between tornadic and nontornadic wind profiles. In this case, this is solely due to the influence of surface friction altering the near-ground shear profile.
b. Unidirectional shear profile
Next, Δx and Δy are varied in a similar manner for the straight hodograph under the influence of near-ground friction. As before, this results in identical hodograph shapes above zf for all combinations of Δx and Δy but different shapes below zf. As in Fig. 3, SRH values across the domain are plotted in Fig. 5. Rather than assuming the storm motion lies at the center of the straight hodograph, we use a more relevant assumption of Bunkers-right storm motion (Bunkers et al. 2000). This method has caveats—particularly related to predicting the motion of high-precipitation supercells (Ramsay and Doswell 2005) or supercells within environments with any of the characteristics noted in Bunkers (2018)—but is used here due to its general applicability and wide use. In the example profile plotted in Fig. 5 at (Δx, Δy) = (0, 5), roughly 58 m2 s−2 of 0–250-m SRH exists. At (Δx, Δy) = (0, 0), the profile exists solely on the x axis and contains negative SRH due to the assumed Bunkers-right storm motion. Increasing Δx and Δy eventually overcomes this effect and yields positive 0–250-m SRH.
As in Fig. 3, but for the straight profile with frictional effects included (see Fig. 2). The profile at (Δx, Δy) = (0, 5) is shown as an example (orange line). The orange dot indicates the wind vector at 250 m AGL (zf) and the orange × indicates the Bunkers-right storm motion used to calculate SRH for this profile (roughly 58 m2 s−2).
Citation: Journal of the Atmospheric Sciences 78, 7; 10.1175/JAS-D-20-0320.1
As in Fig. 3, but for the straight profile with frictional effects included (see Fig. 2). The profile at (Δx, Δy) = (0, 5) is shown as an example (orange line). The orange dot indicates the wind vector at 250 m AGL (zf) and the orange × indicates the Bunkers-right storm motion used to calculate SRH for this profile (roughly 58 m2 s−2).
Citation: Journal of the Atmospheric Sciences 78, 7; 10.1175/JAS-D-20-0320.1
As in Fig. 3, but for the straight profile with frictional effects included (see Fig. 2). The profile at (Δx, Δy) = (0, 5) is shown as an example (orange line). The orange dot indicates the wind vector at 250 m AGL (zf) and the orange × indicates the Bunkers-right storm motion used to calculate SRH for this profile (roughly 58 m2 s−2).
Citation: Journal of the Atmospheric Sciences 78, 7; 10.1175/JAS-D-20-0320.1
Much of the discussion above regarding the relative influences of ωh, usr, and the angle between the two on SRH for the half-circle profile also applies to the straight one (Fig. 6). The gradient of SRH (Fig. 5) points opposite the gradient of the angle between ωh and usr. ωh is symmetric about the x axis due to the profile containing unidirectional westerly shear. usr is not symmetric about the x axis due to the Bunkers-right storm motion assumption. The direction of the SRH gradient is driven by the angle between ωh and usr and the magnitude of the SRH gradient is driven by the magnitudes of ωh and usr. Within the same domain of Δx and Δy, a larger range of angles between ωh and usr exists for the straight profile than the half-circle one. The next subsection addresses whether this is due to the different shear profile or storm motion assumption.
As in Fig. 4, but for the straight profile with frictional effects included (i.e., the same profile used in Fig. 5).
Citation: Journal of the Atmospheric Sciences 78, 7; 10.1175/JAS-D-20-0320.1
As in Fig. 4, but for the straight profile with frictional effects included (i.e., the same profile used in Fig. 5).
Citation: Journal of the Atmospheric Sciences 78, 7; 10.1175/JAS-D-20-0320.1
As in Fig. 4, but for the straight profile with frictional effects included (i.e., the same profile used in Fig. 5).
Citation: Journal of the Atmospheric Sciences 78, 7; 10.1175/JAS-D-20-0320.1
c. Sensitivity to storm motion
Given identical ground-relative wind profiles, different storm motions yield different values of SRH. Are the changes to near-ground SRH induced by friction sensitive to the assumed storm motion? Fig. 7 shows the variation in 0–250-m SRH for the half-circle profile with frictional effects included (i.e., the same profile used in Fig. 3) but with storm motion following the Bunkers-right assumption rather than lying at the center of the half-circle. The results are indeed sensitive to storm motion. Within the same range of Δx and Δy, the range of positive 0–250-m SRH increases roughly 50% when Bunkers-right storm motion is used (cf. Figs. 3 and 7). The example profile at Δx = Δy = 0 contains less SRH than the case in Fig. 3 due to the presence of antistreamwise vorticity. However, as Δx and Δy increase, Bunkers-right motion continues to lie well to the right of the center of the half-circle, yielding larger SRH. Also, unlike the assumed motion at the center of the half-circle, Bunkers-right motion is slightly influenced by the changing wind profile from 0 to 250 m AGL. Both of these characteristics yield a larger gradient in SRH within the same range of Δx and Δy than in the original case.
As in Fig. 3, but assuming Bunkers-right storm motion. The profile at Δx = Δy = 0 is shown for reference. The white line is the value of 0–250-m SRH for the full half-circle profile without any frictional effects at the surface, roughly 67 m2 s−2 (constant for all Δx and Δy).
Citation: Journal of the Atmospheric Sciences 78, 7; 10.1175/JAS-D-20-0320.1
As in Fig. 3, but assuming Bunkers-right storm motion. The profile at Δx = Δy = 0 is shown for reference. The white line is the value of 0–250-m SRH for the full half-circle profile without any frictional effects at the surface, roughly 67 m2 s−2 (constant for all Δx and Δy).
Citation: Journal of the Atmospheric Sciences 78, 7; 10.1175/JAS-D-20-0320.1
As in Fig. 3, but assuming Bunkers-right storm motion. The profile at Δx = Δy = 0 is shown for reference. The white line is the value of 0–250-m SRH for the full half-circle profile without any frictional effects at the surface, roughly 67 m2 s−2 (constant for all Δx and Δy).
Citation: Journal of the Atmospheric Sciences 78, 7; 10.1175/JAS-D-20-0320.1
d. Sensitivity to the height of the friction layer
Although Coniglio and Parker (2020) found an average hodograph “kink” height near 250 m AGL, varying atmospheric conditions like nocturnal stabilization or increased boundary layer mixing will alter this height. To assess the sensitivity of our results to variations in the “kink” height (i.e., the height at which hodograph curvature begins), we reproduced our analyses with zf = 100 m and zf = 500 m. Intuitively, profiles that are influenced by surface friction through a deeper layer (e.g., zf = 500 m) exhibit greater SRH reductions. Compared to 24 m2 s−2 0–250-m SRH in the zf = 250-m analysis, setting zf = 500 m resulted in 11 m2 s−2 0–250-m SRH. Conversely, reducing zf to 100 m yielded an increase in 0–250-m SRH to 36 m2 s−2, closer to the value when surface friction is not included (45 m2 s−2). The range of 0–250-m SRH increases due to varying Δx and Δy were similar between the zf = 100-, 250-, and 500-m analyses. However, the direction of the SRH gradient changed depending on the orientation of the frictionally induced near-ground shear profile. For example, for Δx = Δy = 0, reducing the near-ground layer to 100 m yielded large, primarily easterly shear in that layer. As a result, increases in SRH due to enhanced ground-relative flow are larger for increases in Δy than Δx. Conversely, weaker, primarily southeasterly shear is present when the near-ground layer is increased to 500 m, supporting the largest SRH increases for equal increases in Δx and Δy. Although the ideal combination of Δx and Δy resulting in the largest SRH increases changes slightly based on the assumed storm motion, the gradient is largest close to 90° to the right of the frictionally induced shear vector.
4. Discussion
The inspiration for this study was the assumed Galilean-invariant relationship between updraft morphology and the vertical wind profile. Bunkers et al. (2000) described this in detail with respect to storm motion. Using idealized, straight hodographs from the surface to 6 km AGL, they showed that the resulting left and right storm motions always lie in the same hodograph-relative position regardless of where the hodograph exists in u–υ space. This is valid given their assumption that the near-ground profile is not influenced by friction. In this study, we showed that accounting for the influence of surface friction results in Galilean-variant storm-relative parameters. This is consistent with the methodology of Markowski (2016), who simulated the effect of streamwise versus crosswise near-ground vorticity on “pseudo-storm” evolution by simply moving the ground-relative wind profile [Markowski’s (2016) Fig. 2].
As discussed earlier, numerous methods exist to parameterize the influence of surface friction on the vertical wind profile in numerical simulations. These methods were not applied in this study due to its analytical nature. Rather, we parameterize the influence of surface friction using the same approach that we used to create the semicircular and straight hodographs but with the bottom boundary condition that
These results may be relevant for better understanding the impact of storm-environment modifications on the local wind profile. Recent studies have shown that ground- and storm-relative winds strengthen in the vicinity of supercells (Parker 2014; Wade et al. 2018; Coniglio and Parker 2020). The physical processes responsible for this remain mostly unexplored but are probably related to the strength of the supercell updraft (meso-γ scale) and compensating inward horizontal accelerations (meso-β scale). Flournoy et al. (2020) showed that these enhancements to the wind profile can result in a local environment much more conducive for tornado production. The findings shown here represent one way in which these modifications can result in such an environment. In particular, uniformly increasing wind speeds above the near-ground layer—which has no direct impact on storm-relative parameters like SRH within the near-ground layer—was shown to indirectly (and substantially) increase near-ground SRH due to friction (i.e., the no-slip condition at the surface).
This is consistent with recent findings from Wade et al. (2018) and Coniglio and Parker (2020) related to the environments of tornadic supercells. In particular, Wade et al. (2018) found enhanced ground- and storm-relative winds in the near inflow of tornadic supercells but not nontornadic ones [Wade et al.’s (2018) Fig. 7b]. Much of this enhancement is attributable to a relatively uniform increase in the poleward, ground-relative wind component below 2 km AGL. Such a scenario is represented in our study by a positive Δy, yielding increased near-ground SRH even if storm motion also moves poleward. The cause for this enhancement near tornadic supercells rather than nontornadic supercells is likely the presence of a stronger mesocyclone in the tornadic cases (Coniglio and Parker 2020). Additionally, Coniglio and Parker (2020) found larger storm-relative winds and SRH, especially from 1 to 3 km AGL, near tornadic supercells than nontornadic ones due to both stronger ground-relative winds and more rightward-deviant storm motions. These findings are not entirely captured in this study because in our case, storm motion is “latched” to the wind profile. Conversely, Coniglio and Parker (2020) examine changes to the storm-relative wind profile due to changes in storm motion while holding the ground-relative wind profile steady [see Coniglio and Parker’s (2020) Fig. 9]. These analyses are complementary in showing that enhancements to the poleward, ground-relative wind profile (i.e., increasing Δx and especially Δx) combined with increasingly rightward deviations yield increased SRH both in the near-ground layer and aloft. This is because enhanced poleward ground-relative flow permits the same ratio of streamwise vorticity for increasingly rightward deviations.
This is exemplified in Fig. 8 using a wind profile adapted from the composite tornadic profile obtained in Coniglio and Parker (2020, their Fig. 10a); the “original” profile and associated 0–250-m and 1–3-km SRH areas (computed using the Bunkers-right estimate shown) are shown in blue, and the “original” profile with Δy = 5 m s−1 (e.g., the “enhanced” profile) is shown in orange. In this schematic, storm motion is “latched” to each wind profile above the near-ground layer such that 1–3-km SRH is identical in both cases. However, as we have shown analytically, the “enhanced” profile contains more SRH in the near-ground layer (shown here as the 0–250-m layer). Finally, if a storm deviated more to the right in the “enhanced” profile, it would encounter more 0–250-m SRH and more 1–3-km SRH above the near-ground layer than the “original” case, as shown by the red dashed lines (e.g., Coniglio and Parker 2020). This shows how the analytical framework presented here may be realized in observed supercells, along with increasingly rightward deviant motions, to yield increased SRH aloft and in the near-ground layer to support tornadic supercells.
Schematic showing the combined influences of increasing Δy and an increasingly rightward deviant storm motion in ground-relative hodograph space. The “original” profile (blue) is derived from the tornadic composite profile obtained in Coniglio and Parker (2020; their Fig. 10a). The “enhanced” profile (orange) is the “original” profile with Δy = 5 m s−1 added above zf = 250 m. Orange and blue shaded areas indicate 0–250-m and 1–3-km SRH areas for each profile. The orange and blue circles that lie off of the profiles show the Bunkers-right storm motion estimate for each profile from which SRH is computed. The red dashed lines indicate SRH computed for an increasingly rightward deviant storm in an environment characterized by the “enhanced” wind profile. Heights (km AGL) are shown (only orange labels are shown). The 0–250-m and 0–1-km SRH values (m2 s−2) are shown for the original (blue), enhanced (orange), and deviant (red) cases.
Citation: Journal of the Atmospheric Sciences 78, 7; 10.1175/JAS-D-20-0320.1
Schematic showing the combined influences of increasing Δy and an increasingly rightward deviant storm motion in ground-relative hodograph space. The “original” profile (blue) is derived from the tornadic composite profile obtained in Coniglio and Parker (2020; their Fig. 10a). The “enhanced” profile (orange) is the “original” profile with Δy = 5 m s−1 added above zf = 250 m. Orange and blue shaded areas indicate 0–250-m and 1–3-km SRH areas for each profile. The orange and blue circles that lie off of the profiles show the Bunkers-right storm motion estimate for each profile from which SRH is computed. The red dashed lines indicate SRH computed for an increasingly rightward deviant storm in an environment characterized by the “enhanced” wind profile. Heights (km AGL) are shown (only orange labels are shown). The 0–250-m and 0–1-km SRH values (m2 s−2) are shown for the original (blue), enhanced (orange), and deviant (red) cases.
Citation: Journal of the Atmospheric Sciences 78, 7; 10.1175/JAS-D-20-0320.1
Schematic showing the combined influences of increasing Δy and an increasingly rightward deviant storm motion in ground-relative hodograph space. The “original” profile (blue) is derived from the tornadic composite profile obtained in Coniglio and Parker (2020; their Fig. 10a). The “enhanced” profile (orange) is the “original” profile with Δy = 5 m s−1 added above zf = 250 m. Orange and blue shaded areas indicate 0–250-m and 1–3-km SRH areas for each profile. The orange and blue circles that lie off of the profiles show the Bunkers-right storm motion estimate for each profile from which SRH is computed. The red dashed lines indicate SRH computed for an increasingly rightward deviant storm in an environment characterized by the “enhanced” wind profile. Heights (km AGL) are shown (only orange labels are shown). The 0–250-m and 0–1-km SRH values (m2 s−2) are shown for the original (blue), enhanced (orange), and deviant (red) cases.
Citation: Journal of the Atmospheric Sciences 78, 7; 10.1175/JAS-D-20-0320.1
5. Summary
This study addressed the following question: how do ground-relative winds and surface friction influence near-ground SRH? The motivation posing this question was to further analyze relationships between the vertical wind profile and updraft morphology, which are commonly assumed to be Galilean invariant. This assumption relies on the fact that storm morphology depends on the vertical shear profile and not the vertical wind profile. However, we hypothesized that the influence of surface friction, a ground-relative and Galilean variant presence, would meaningfully influence the shear profile.
We used an analytical approach to answer this question. Solutions for idealized semicircular and straight hodographs were drawn from the methods of McCaul and Weisman (2001), Markowski and Richardson (2014), and Markowski (2016). The wind profile influenced by surface friction within the near-ground layer (defined here as 0–250 m AGL) was derived from semicircular and linear components and resembled profiles presented in past numerical and observational studies. Uniform changes to the wind profile were introduced above the friction layer to examine the influence of ground-relative flow and friction on the near-ground, storm-relative wind profile.
We quantified the relationship between the vertical wind profile and near-ground SRH, which is not Galilean invariant when accounting for surface friction. This is because surface friction is a ground-relative process that ultimately influences the shear profile impacting updraft development. Previous studies have shown the importance of storm-relative characteristics in this layer in influencing storm morphology, especially with respect to tornado potential in supercells. For cases featuring idealized semicircular and straight wind profiles, increasing ground-relative wind speeds above the near-ground layer yielded increased SRH within the near-ground layer. The magnitude of the increase in SRH was sensitive to storm motion. This is representative of storm-induced modifications to the background wind profile and highlights one way that these processes may create a local environment more supportive of supercell and tornado potential without changing the shear profile above the friction layer. Furthermore, supercells may be more susceptible to storm-induced SRH enhancements due to their deviant motion.
Should storms evolve differently in different shear and friction regimes even if storm-relative parameters like effective bulk shear, winds, and helicity are equal? And, of course, what is the best way to parameterize surface friction in numerical models? Observations of the boundary layer, like those obtained by lidar and unmanned aerial platforms, will continue to help characterize the near-ground profile. These should better inform the methods of numerical studies in parameterizing the near-ground friction layer and its subsequent influence on storm morphology.
Acknowledgments
We thank Michael Coniglio and three anonymous reviewers for their insightful comments that improved this paper. Funding was provided by NOAA/Office of Oceanic and Atmospheric Research under NOAA–University of Oklahoma Cooperative Agreement NA11OAR4320072, U.S. Department of Commerce. The statements, findings, conclusions, and recommendations are those of the authors and do not necessarily reflect the views of NOAA or the U.S. Department of Commerce.
Data availability statement
The code used for the analysis presented in this paper is available online in a GitHub repository at mdflournoy/friction-srh.
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The choice of 250 m is consistent with the average height of a hodograph kink found in Coniglio and Parker (2020). We discuss the impact of varying zf later.
