Abstract

Numerical simulations of supercell thunderstorms including parameterized radiative transfer and surface fluxes are performed using the Advanced Regional Prediction System (ARPS) model to investigate how low-level air temperature deficits within anvil shadows affect the simulated storms. The maximum temperature deficits within the modeled cloud shadows are 1.5–2.0 K, which is only about half that previously observed. Within the shadows, the loss of strong solar heating cools and stabilizes the near-surface layer, which suppresses vertical mixing and modifies the near-surface vertical wind shear. In a case of a stationary storm, the enhanced easterly shear present beneath the anvil leads to a thinning of the outflow layer and corresponding acceleration of the rear-flank gust front far ahead of the overlying updraft, weakening the low-level mesocyclone. It is further shown that the direct absorption and emission of radiation by clouds does not significantly affect the simulated supercells. Varying the time of day of model initialization does not prevent the simulated storms from weakening. This behavior is mirrored for storms that slowly move along the major axis of the anvil shadow. If the rear-flank gust front moves into the anvil shadow and the updraft moves normal to the shadow (i.e., northward movement of the updraft), cyclic periods of intensification and decay can result, although this result is likely highly dependent on the storm-relative wind profile. If the gust front does not advance into the shaded region (i.e., southward movement), or if the storm moves rapidly, the storm is relatively unaffected by anvil shading because the rear-flank gust front speed and outflow depth remain relatively unchanged.

1. Introduction

The importance of low-level baroclinic zones on the development of low-level rotation in supercell thunderstorms has been well established. The importance of storm-scale boundaries as a source of baroclinically generated horizontal vorticity to be ingested by the updraft, particularly the forward-flank gust front, has been demonstrated (e.g., Klemp and Rotunno 1983; Rotunno and Klemp 1985; Markowski et al. 2012) by several investigators. Furthermore, Markowski et al. (1998a) and Rasmussen et al. (2000) observed that the low-level mesocyclone within a supercell typically intensified just after a storm passed from the warm to the cool side of a preexisting mesoscale boundary (i.e., a boundary independent of the storm's own gust fronts), presumably owing to enhanced horizontal vorticity present within the baroclinic zone. Similar results were seen in the simulations of Atkins et al. (1999).

Relatively unexplored, however, have been any potential impacts of the low-level baroclinic zone shown to exist along the edges of the anvil shadow owing to differential radiative heating between the shaded region beneath the anvil and the ambient environment. The extinction of the direct solar beam by the anvils of supercell thunderstorms can cause dramatic reductions in the net radiative flux at the surface in as little as 15 min, creating low-level air temperature deficits of approximately 3 K beneath the anvils (Markowski et al. 1998b). Dowell and Bluestein (1997) observed a gradual 5-K temperature decrease between full sun and the onset of light precipitation in instrumented tower measurements of another supercell thunderstorm. These cases suggest that these particular supercell thunderstorms modified their environments via the extinction of shortwave radiation by their anvil clouds.

A pair of numerical simulations of supercell thunderstorms performed by Markowski and Harrington (2005) revealed that surface radiative cooling, coupled with a surface sensible heat flux, led to significant changes in simulated mesocyclone strength. The radiative cooling was admittedly crude, with a constant prescribed cooling rate of 6 K h−1 applied to the skin temperature at any grid point at which cloud was overhead. It was stressed in that study that the size of the anvil was likely underdone because the simulations only considered warm-rain (Kessler 1969) processes and, thus, the anvil likely did not spread as far downwind as it would have had ice microphysics been used. Nevertheless, that study demonstrated that emulated radiative cooling within the anvil shadow could have a possibly significant effect on supercell evolution. Additionally, the presence of cooler air led to a weaker forward-flank baroclinic zone and the development of a radiatively driven baroclinic zone near the edge of the cloud shadow.

Frame and Markowski (2010, hereafter FM10) documented the effects of radiation and surface fluxes on an idealized supercell thunderstorm environment and the development and characteristics of an anvil shadow with a series of numerical simulations. Therein, it was shown that longwave radiative cooling within the anvil shadow forced temperature deficits of up to 2 K within the shaded region. This cooling stabilized the boundary layer and suppressed vertical mixing, preventing air from near the surface that had lost momentum to friction from mixing with higher momentum air from aloft, significantly altering the low-level wind profile within the shaded region. In FM10, these effects were maximized when the near-surface winds were strong and when storm motion was relatively slow, which extended the duration of radiative cooling beneath the anvil. They also determined that longwave radiation alone does not cause any significant modifications to the near-storm environment over the course of a few hours.

In this study, the simulations of FM10 will be used to illustrate the potential dynamical effects of anvil-generated radiative cooling and the subsequent frictional modification of the low-level wind profile on simulated supercells and mesocyclones. Section 2 describes the model setup and methodology. The results of the simulations are presented in section 3, and the sensitivities of these results to varying environmental parameters are found in section 4. A summary of the results and the conclusions are presented in section 5.

2. Model description and methodology

a. Model parameters

The Advanced Regional Prediction System (ARPS) model, version 5.1.5 (Xue et al. 2000, 2001) was employed for all simulations. The configuration of the model is as in FM10, the most salient details of which are reproduced below and also can be found in Table 1. The grid dimensions are 160 km in the east–west direction (x), 150 km in the north–south direction (y), and 18 km in the vertical direction (z). The simulations employ a horizontal grid spacing of 1 km, which is sufficient to capture the basic circulation of a supercell thunderstorm (e.g., Rotunno and Klemp 1982). The vertical grid is a hyperbolic tangent stretched grid with an average spacing of 500 m and a minimum spacing of 50 m at the surface. The large time step is 1.5 s and all simulations were run for 5 h. Open radiation boundary conditions were imposed at all lateral boundaries of the domain as described by Orlanski (1976). A rigid lid exists at the top of the domain, and a Rayleigh sponge layer was imposed within the top 5 km of the model domain to damp any vertically propagating gravity waves (Klemp and Durran 1983). Fourth-order numerical diffusion was employed to remove the spurious 2Δx and 4Δx waves that develop as a result of the leapfrog advection schemes within ARPS.

Table 1.

Model physical and computational parameters.

Model physical and computational parameters.
Model physical and computational parameters.

A six-species cloud microphysics package (Lin et al. 1983) was used, with adjustments made by Tao et al. (1989) and Tao and Simpson (1993). The turbulence routine contains a 1.5-order turbulent kinetic energy (TKE) closure of the Deardorff (1980) subgrid mixing scheme and is anisotropic, owing to the relatively fine vertical resolution near the surface when compared with the horizontal resolution. The fluxes of momentum, heat, and moisture from the surface are determined according to bulk aerodynamic drag laws. The exchange coefficients are prognosed according to stability criteria as defined by the bulk Richardson number Rib. No planetary boundary layer parameterization was utilized in the simulations. The soil model is the two-layer force-restore scheme described by Noilhan and Planton (1989).

The National Aeronautics and Space Administration (NASA) Goddard Cumulus Ensemble radiative transfer model was used for both shortwave (Chou 1990, 1992; Chou et al. 1998) and longwave (Tao et al. 1996; Chou et al. 1999) radiation. This model allows for the absorption, scattering, and emission of radiation by atmospheric constituents, including clouds and gases. The tilted independent column approximation (TICA; Varnai and Davies 1999), in which solar radiation travels along a slant path dictated by the solar zenith and azimuth angles (as opposed to vertically), was incorporated into the radiative transfer model to allow for more correct shading geometry (Frame et al. 2009). FM10 also included TICA in their simulations of cloud shading and demonstrated that it is capable of producing realistic anvil shadows.

b. Model initialization and simulations

The ARPS model is initialized from the same horizontally homogeneous base state used by FM10. This sounding (Fig. 1a) has 2465 J kg−1 of convective available potential energy (CAPE), 47 J kg−1 of convective inhibition (CIN), a 0–3-km storm-relative helicity (assuming stationary storm motion) of 470 m2 s−2, and a bulk Richardson number (Weisman and Klemp 1982) of 11.1 The initial vertical wind profile used for most of the simulations consists of a semicircular hodograph shifted relative to the origin such that the resultant storm motion is approximately stationary (black curve in Fig. 1b). Sensitivity tests were performed in which this hodograph was shifted northward, southward, and eastward by 5 m s−1 and eastward by 25 m s−1. The simulations with the 25 m s−1 eastward translation utilize a domain that extended 500 km in the east–west direction, necessitated by the rapid eastward storm motion. A complete list of the simulations can be found in Table 2. Most simulations, except for a few sensitivity tests, are initialized at 1800 UTC (1200 LST) 20 May. The model grid is centered at 36°N, 100°W, which corresponds to a point on the border between western Oklahoma and the Texas Panhandle.

Fig. 1.

(a) Skew T–logp diagram depicting the initial vertical profiles of temperature (red) and water vapor (green). (b) Hodograph depicting the initial vertical wind profile. The black hodograph results in a stationary storm while the red, blue, and green hodographs are the result of northward, eastward, and southward translations by 5 m s−1, respectively. Winds are shown in m s−1. Speed rings are shown at 5, 15, and 25 m s−1. Elevations in km are shown at selected points on the green wind profile.

Fig. 1.

(a) Skew T–logp diagram depicting the initial vertical profiles of temperature (red) and water vapor (green). (b) Hodograph depicting the initial vertical wind profile. The black hodograph results in a stationary storm while the red, blue, and green hodographs are the result of northward, eastward, and southward translations by 5 m s−1, respectively. Winds are shown in m s−1. Speed rings are shown at 5, 15, and 25 m s−1. Elevations in km are shown at selected points on the green wind profile.

Table 2.

List of simulations and their descriptions.

List of simulations and their descriptions.
List of simulations and their descriptions.

Convection is initiated with an ellipsoidal warm bubble that has a radius of 10 km in each horizontal direction and 1.5 km in the vertical direction. The warm bubble has a maximum amplitude of 4 K, which is necessary to overcome the capping inversion in the initial sounding. The thermal is centered at 1.5 km above ground level for all simulations.

Simulations were performed that include a radiative transfer parameterization that uses either the TICA (e.g., simulation TICA0) or the independent column approximation (ICA; e.g., ICA0) in order to gauge the effect of the correct solar geometry on the storm environment. Other simulations were run with shortwave radiation only (e.g., NoLW0), or with a clear sky (e.g., CS0). In the CS simulations, all radiation was prohibited from interacting with the cloud or any precipitation particles, but not the water vapor field, allowing for a direct examination of the impacts of anvil shading, since radiation was still able to modify the near-storm environment. Several sensitivity tests were also performed and are discussed in section 4, including altering the time of day of model initialization, the radiative cooling rate beneath the anvil, the environmental wind profile, and the soil moisture content.

3. Simulation results

a. Anvil shading

A comparison of the results of the TICA0 simulation to those obtained from the CS0 simulation allows for an analysis how the anvil shadow impacts stationary thunderstorms. As seen in FM10, the near-storm environment outside of the anvil shadow is nearly identical between the TICA0 and CS0 simulations after 3 h of simulation time. This means that any differences between the storms in these two simulations is likely attributable to anvil shading.

The total upward flux of water (including water vapor and all cloud species) is given by

 
formula

where ρa is the air density, w is the vertical velocity, and qw is the total water mixing ratio, given by qw = qυ + qr + qc + qi + qs + qh, the sum of the mixing ratios of water vapor, rainwater, cloud water, cloud ice, snow, and hail–graupel. In this calculation, upward vertical velocities were considered only; if a downdraft occurred at a grid point, the flux at that grid point was set to zero. Time series of total upward water flux at 5 km and maximum vertical vorticity in the lowest 500 m with a 14 km × 14 km square centered on the maximum updraft were used to gauge supercell intensity over time. Care was taken to ensure that the time series always represented the primary supercell thunderstorm within the domain if any secondary convection developed.

The time series of the total upward water flux from the TICA0 and CS0 simulations (Fig. 2a) reveal that the CS0 storm has an upward water flux that is consistently 20%–30% greater than does the TICA0 storm. The time series of the maximum low-level vertical vorticity (Fig. 2b) also indicate that the CS0 storm produces a stronger low-level mesocyclone than the TICA0 storm. Aside from the first hour of the simulation, when the anvil shadow had not yet formed, the maximum low-level vertical vorticity is 20%–25% greater in the CS0 simulation than it is in the TICA0 simulation.

Fig. 2.

(a) Total upward water flux at 5 km (g m−2 s−1) within a 14 × 14 km2 centered on the maximum upward water flux and (b) maximum vertical vorticity (s−1) in the lowest 500 m for the TICA0 (solid), CS0 (dotted), NoLW0 (long dash), and ICA0 (short dash) simulations.

Fig. 2.

(a) Total upward water flux at 5 km (g m−2 s−1) within a 14 × 14 km2 centered on the maximum upward water flux and (b) maximum vertical vorticity (s−1) in the lowest 500 m for the TICA0 (solid), CS0 (dotted), NoLW0 (long dash), and ICA0 (short dash) simulations.

The low-level rainwater, potential temperature, wind, low-level vertical vorticity, and midlevel vertical velocity fields from the TICA0 and CS0 simulations (Figs. 3a and 3b) illustrate that the storm in the CS0 simulation evolves differently than does the storm in the TICA0 simulation. The precipitation core is more intense in the CS0 storm, as expected from the time series, and both the low-level mesocyclone and the midlevel updraft are broader in the CS0 simulation. These features are also nearer to the warm and moist inflow in the CS0 simulation. Since the CS0 storm has no anvil shadow, there is no temperature deficit or slowing of surface winds in the region immediately east of the updraft (FM10).

Fig. 3.

Rainwater mixing ratio (g kg−1, shaded), potential temperature perturbation (K, light contour), and wind vectors (vectors) at 25 m; vertical vorticity at 125 m (s−1, thick black contours); and vertical velocity at 2000 m (m s−1, thick red contours) at t = 3 h for the (a) TICA0, (b) CS0, (c) NoLW0, and (d) ICA0 simulations. Potential temperature perturbation is taken from an area far from the storm and is as indicated. Irregular potential temperature perturbation contours are 0.0, −0.5, −1.0, −1.5, −2.0, −3.0, −4.0, −6.0, and −8.0 K. Vertical vorticity contour interval is 0.0025 s−1. Vertical velocity contour interval is 5 m s−1, beginning at 5 m s−1. Wind vectors are scaled as indicated.

Fig. 3.

Rainwater mixing ratio (g kg−1, shaded), potential temperature perturbation (K, light contour), and wind vectors (vectors) at 25 m; vertical vorticity at 125 m (s−1, thick black contours); and vertical velocity at 2000 m (m s−1, thick red contours) at t = 3 h for the (a) TICA0, (b) CS0, (c) NoLW0, and (d) ICA0 simulations. Potential temperature perturbation is taken from an area far from the storm and is as indicated. Irregular potential temperature perturbation contours are 0.0, −0.5, −1.0, −1.5, −2.0, −3.0, −4.0, −6.0, and −8.0 K. Vertical vorticity contour interval is 0.0025 s−1. Vertical velocity contour interval is 5 m s−1, beginning at 5 m s−1. Wind vectors are scaled as indicated.

The inflow winds east of the updraft roughly parallel the isotherms within the forward-flank baroclinic zone in the CS0 simulation (Fig. 3b), meaning that the baroclinic generation of horizontal vorticity and subsequent tilting into the vertical is likely enhancing the low-level vertical vorticity in that simulation. In contrast, the inflow winds east of the updraft are approximately perpendicular to the isotherms in the TICA0 case, meaning that any baroclinic generation of streamwise horizontal vorticity is likely small in that simulation. This result, however, is likely not generalizable to all simulations of supercell thunderstorms with radiative transfer.

Baroclinic generation of horizontal vorticity also occurs within the temperature gradient on the south side of the anvil shadow (note that the shadow is defined as the region in which downwelling shortwave radiation at the surface is reduced owing to the presence of the anvil cloud). Any such vortex lines would also be orientated such that they would enhance the low-level vertical vorticity in the mesocyclone through tilting. A trajectory analysis2 reveals that none of the air within this anvil-generated baroclinic zone comes near the updraft (the southern two trajectories in Fig. 4). These parcels ascend weakly as they approach the rear-flank gust front, then subside to near 300 m in elevation once they are behind the gust front.3 It is postulated that if the storm-relative inflow winds were from the southeast in the inflow region southeast of the updraft, some of the air within the baroclinic zone along the southern edge of the anvil shadow may feed the updraft. A complete examination of this, however, would require an additional suite of simulations since not only hodograph shape, but also hodograph location relative to the origin would have to be varied since surface fluxes are non-Galilean invariant.

Fig. 4.

Rainwater mixing ratio (shaded; g kg−1) and representative trajectories for the TICA0 simulation. The starting and ending elevations of each trajectory (km) are indicated. Trajectory calculations begin at 9600 s and are terminated at 12 000 s.

Fig. 4.

Rainwater mixing ratio (shaded; g kg−1) and representative trajectories for the TICA0 simulation. The starting and ending elevations of each trajectory (km) are indicated. Trajectory calculations begin at 9600 s and are terminated at 12 000 s.

Vertical cross sections of radiative heating rates show relatively little radiative heating or cooling in cloud-bearing regions in the CS0 simulation (cf. Figs. 5a,b) as expected. The anvil is also thicker and longer in the CS0 simulation, reflective of the stronger storm in that simulation.

Fig. 5.

Vertical west-east cross-sections of radiative heating (K h−1) at t = 3 h for the (a) TICA0, (b) CS0, (c) NoLW0, (d) ICA0 simulations. Thick black contour marks the cloud outline. The cross sections are taken through the maximum updraft in all simulations.

Fig. 5.

Vertical west-east cross-sections of radiative heating (K h−1) at t = 3 h for the (a) TICA0, (b) CS0, (c) NoLW0, (d) ICA0 simulations. Thick black contour marks the cloud outline. The cross sections are taken through the maximum updraft in all simulations.

In FM10, it was demonstrated that that the loss of strong surface heating beneath the anvil modifies the low-level wind shear profile within the shaded region. The suppression of vertical mixing due to the stabilization of the near-surface layer means that surface friction only decelerates the winds in the lowest few model levels; the winds above these levels remain relatively unaffected by friction. The net result is a greater vector difference in winds confined to a shallower layer near the surface. As a consequence of this easterly wind shear, the horizontal vorticity vector points generally southward below this level of maximum winds and northward above this level of maximum winds. These differences in the vertical shear profiles between the shadow and the full sun are apparent in east–west vertical cross sections taken 5 km south of the maximum updraft (Fig. 6). The inflow winds beneath the anvil in the TICA0 simulation (east of x = 65 km in Fig. 6a) are much less than those in the CS0 simulation in this region (Fig. 6b).

Fig. 6.

Vertical west–east cross section of potential temperature (shaded; K) and zonal wind speed (contoured; m s−1) at t = 3 h for the (a) TICA0 and (b) CS0 simulations. The cross sections are taken 5 km south of the maximum updraft in both simulations. Contour interval is 3 m s−1.

Fig. 6.

Vertical west–east cross section of potential temperature (shaded; K) and zonal wind speed (contoured; m s−1) at t = 3 h for the (a) TICA0 and (b) CS0 simulations. The cross sections are taken 5 km south of the maximum updraft in both simulations. Contour interval is 3 m s−1.

Previous simulations of idealized density currents (e.g., Rotunno et al. 1988; Xu et al. 1996) have shown that a density current that moves upshear into a strongly vertically sheared flow develops a shallow head and generates less lift than does a deep density current head (e.g., Xue 2000). A vertical cross section of vertical velocity (Fig. 7), taken along the same plane as Fig. 6, depicts a shallower cold pool head in the TICA0 simulation than in the CS0 simulation, forcing a weaker low-level updraft that slopes back over the cold pool. Numerical simulations of squall lines (e.g., Weisman et al. 1988) have indicated that low-level updrafts that slope rearward over cold pools are not as intense as are erect updrafts owing to increased entrainment of cold air and reduced proximity to the potentially buoyant inflow. Although density current dynamics have not been a major focus of previous supercell research, previous studies (e.g., Bluestein and Gaddy 2001) have speculated that supercells must balance cold pool intensity (i.e., the amount of precipitation and the proximity of the precipitation core to the updraft) with low-level wind shear in order to remain long lived. When too much cold air builds up beneath the storm, the gust front typically surges outward far ahead of the overlying updraft, leading to a weaker low-level mesocyclone. This is likely similar to the inflow–outflow balance hypothesized in recent studies of cyclic mesocyclogenesis (e.g., Trapp 1999; Dowell and Bluestein 2002; French et al. 2008). It is also likely that a deeper cold pool owing to a more robust storm in the CS0 simulation is able to maintain an erect low-level updraft in that case. Though the cooling beneath the anvil results in a slight (nonhomogeneous) reduction in CAPE within the shaded region, such a slight reduction in CAPE (on the order of 1%–2% of the total CAPE) is unable to explain the radically different gust front structure seen between the TICA0 and CS0 simulations.

Fig. 7.

As in Fig. 6, but for vertical velocity (contoured; m s−1). Contour interval is 0.5 m s−1.

Fig. 7.

As in Fig. 6, but for vertical velocity (contoured; m s−1). Contour interval is 0.5 m s−1.

b. Longwave radiation

The effects of longwave radiation on supercell thunderstorms are gauged by comparing the TICA0 simulation to the NoLW0 simulation, run without longwave radiation. The time series of upward water fluxes and maximum low-level vertical vorticity are remarkably similar throughout the entire simulations (Figs. 2a,b), although the NoLW0 storm has a slightly greater upward water flux. A closer inspection of some of the kinematic and thermodynamic fields near the mesocyclone (Figs. 3a,c) also reveals that the storm in simulations TICA0 and NoLW0 are quite similar. After 3 h of simulation time, the rear-flank gust front is far in front of the midlevel updraft and mesocyclone in both simulations, and this persists throughout the simulations. There is also an air temperature deficit of up to 2 K beneath the anvil clouds of both storms, consistent with the findings of FM10. This deficit is slightly larger in the TICA0 simulation because longwave radiation results in additional cooling of the surface.

Longwave radiation increases the storm total precipitation by 5%–8%, depending on the initial wind profile used. The small differences in the upward water fluxes noted above and total precipitation amounts are caused by differing in-cloud radiative heating rates. Vertical cross sections of the radiative heating rates (Figs. 5a,c) illustrate significant radiative heating at cloud top in the presence of shortwave radiation in the NoLW0 simulation, resulting in stabilization of the cloud-bearing layer. These results agree with the findings of Fu et al. (1995), who noted that longwave radiation destabilized cloud layers in simulations of mesoscale convective systems. The simulated longwave radiative heating rates are small, however, when compared to the latent heat released by condensation in intense convective cells.

c. The tilted independent column approximation

Frame et al. (2009) and FM10 established that the TICA models the surface shortwave radiation fluxes near clouds far more accurately than the ICA. It will now be investigated whether this superior representation of the cloud shadows has any dynamical effect on simulated supercell behavior.

The time series of total upward water flux (Fig. 2a) and maximum low-level vertical vorticity (Fig. 2b) from the TICA0 and ICA0 simulations show no consistent differences between the storms throughout the duration of the simulations. The low-level kinematic and thermodynamic fields from the TICA0 and ICA0 simulations (Figs. 3a and 3d) are also remarkably similar, aside from a 0.5 K larger 25-m air temperature deficit beneath the anvil and slightly larger shaded region in simulation TICA0. Given the behavior of the time series, this slight additional cooling has a negligible impact on simulated storm evolution. The vertical cross section of the radiative heating rates from the TICA0 and ICA0 simulations (Figs. 5a and 5d) are similar, apart from the radiative heating on the western side of the cloud in the ICA simulation (Frame et al. 2009).

4. Sensitivity of radiative influences to varying model and environmental parameters

a. Time of day

All of the simulations discussed thus far have been initialized at 1800 UTC (1300 CDT) 20 May. This time was chosen in order to generate a relatively large shortwave flux differential between the sunny and shaded regions and to correspond to the daily and seasonal maximum in convective activity over many areas. Supercells can occur earlier in the day than this, so a pair of simulations (MORN and MORN-CS) was initialized at 1400 UTC (0900 CDT) to investigate how anvil shading effects might change throughout the day.

The time series of the upward water flux at 5 km (Fig. 8a) and low-level maximum vertical vorticity (Fig. 8b) indicate that the simulation that was initialized in the morning (MORN) displays more oscillations in midlevel updraft intensity (as reflected by the upward water flux) and low-level mesocyclone strength than does the simulation initialized in the afternoon (TICA0), but is otherwise generally similar. The MORN-CS storm, however, gradually becomes more intense relative to the MORN storm as the simulations progress and the shortwave flux differential between clear and cloudy skies increases. Inspection of the low-level kinematic and thermodynamic fields from the MORN and MORN-CS simulations (not shown) reveals that the rear-flank gust front does not surge eastward in the MORN-CS simulation, while it has in the MORN simulation, mirroring the behavior seen earlier between the CS0 and TICA0 simulations. Given these similarities, the time of day does not have a substantial effect on the mechanism proposed in section 3, provided the downwelling solar flux is of sufficient strength to create an anvil shadow.

Fig. 8.

As in Fig. 2, but in the lowest 500 m for the primary supercell in the TICA0 (solid), MORN (dotted), MORN-CS (long dash), and MH05 (short dash) simulations.

Fig. 8.

As in Fig. 2, but in the lowest 500 m for the primary supercell in the TICA0 (solid), MORN (dotted), MORN-CS (long dash), and MH05 (short dash) simulations.

b. Increased radiative cooling

As in FM10, the current model configuration does not produce surface temperature deficits beneath the anvil as large as what has been observed (Markowski et al. 1998b). Thus, it is worth investigating how increased surface cooling beneath the anvil affects the parent thunderstorm. An additional simulation (MH05) was performed in which a constant cooling rate of 6.0 K h−1 was applied to the skin temperature at any grid point that was directly below a point that contained hydrometeors. This emulated radiative cooling is the same as that used by Markowski and Harrington (2005). All other radiative heating and cooling is neglected in this simulation.

The upward water flux in the MH05 simulation is similar to the TICA0 simulation (Fig. 8a) for about the first 2 h of the simulation, then it gradually decreases as the MH05 storm eventually dissipates. The decrease in the intensity of the upward water flux is monotonic throughout the second half of the MH05 simulation, implying that the storm steadily weakens. As the MH05 storm begins to weaken, its low-level mesocyclone surprisingly remains stronger than that from the TICA0 simulation (Fig. 8b), although it is unclear precisely why this is the case. It is evident from these time series that the maximum low-level vertical vorticity can lag the upward water flux as a measure of storm intensity.

At t = 3 h, temperature deficits beneath the anvil in the MH05 simulation are unrealistically large (greater than 8 K; not shown). As a result, the surface winds become nearly calm beneath the anvil due to frictional effects, allowing for the cold pool head, even shallower than that in the TICA0 simulation, to translate even farther away from the updraft. This, when combined with the excessive cooling with the storm's inflow beneath the anvil, results in the demise of the simulated storm. A separate simulation was run in which the cooling beneath any cloud was reduced to 3 K h−1 and the primary significant difference between the simulations is that the storm in the simulation with less cooling does not dissipate as quickly as does the MH05 storm.

c. Ground-relative wind profile

It has been shown that anvil shading alters the vertical mixing profile within the atmospheric boundary layer, which in turns modifies the low-level wind shear profile. Because surface fluxes are not Galilean invariant, it is expected that the translation of the hodograph relative to the origin will influence these radiative impacts. It is also likely that surface friction may result in different simulated storm intensities even if radiation is not considered. Three additional initial wind profiles are created by shifting the TICA0 hodograph (black curve in Fig. 1b) 5 m s−1 northward, eastward, and southward and are indicated by the red, blue, and green curves in Fig. 1b. These wind profiles were used to initialize simulations TICAN, TICAE, and TICAS (and CSN, CSE, and CSS), respectively.

1) Slow eastward motion

The time series of upward water flux (Figs. 9a and 10a) and maximum low-level vertical vorticity time series (Figs. 9b and 10b) display considerable variation among these simulations. Simulation CSE possesses a consistently greater upward water flux and a stronger low-level mesocyclone than the corresponding simulation with a shadow (TICAE). This variation is owing to the TICAE storm moving eastward into the anvil-shaded region, where the frictionally modified vertical shear beneath the anvil allows the rear-flank gust front to advance far in front of the midlevel updraft and the mesocyclone. Simulation CSE possesses the strongest mesocyclone of any of the modeled storms considered here because it has the weakest easterly shear (negative component of y vorticity) within its boundary layer. Similarly, the TICAE storm still possesses a stronger low-level mesocyclone than the TICA0 storm (Fig. 9b), although still weaker than the CSE storm.

Fig. 9.

As in Fig. 2, but for the lowest 500 m for the primary supercell in the TICA0 (solid), TICAN (dotted), TICAS (long dash), and TICAE (short dash) simulations.

Fig. 9.

As in Fig. 2, but for the lowest 500 m for the primary supercell in the TICA0 (solid), TICAN (dotted), TICAS (long dash), and TICAE (short dash) simulations.

Fig. 10.

As in Fig. 2, but for the lowest 500 m for the primary supercell in the CS0 (solid), CSN (dotted), CSS (long dash), and CSE (short dash) simulations.

Fig. 10.

As in Fig. 2, but for the lowest 500 m for the primary supercell in the CS0 (solid), CSN (dotted), CSS (long dash), and CSE (short dash) simulations.

2) Slow southward motion

In simulation TICAS, the rear-flank gust front moves southward into a region that has not been shaded by the storm's anvil (Fig. 11), so any radiatively driven effects on the motion of the gust front are minimal. Thus, the storm within simulation TICAS remains in a relatively steady state, like simulations CSS and CS0. Accordingly, simulation TICAS displays a greater upward water flux than does the TICA0 simulation. The relative weakness of the low-level mesocyclones in the CSS and TICAS simulations can be explained in terms of tilting of the ambient horizontal vorticity. The stronger low-level northerly low-level winds in those simulations result in stronger northerly shear just above the surface due to surface friction (i.e., ∂υ/∂z < 0). This yields a more positive x component of the horizontal vorticity vector, which leads to increased generation of negative vertical vorticity through tilting (i.e., ∂w/∂x < 0).

Fig. 11.

As in Fig. 3, but for the (a) TICA0 and (b) TICAS simulations.

Fig. 11.

As in Fig. 3, but for the (a) TICA0 and (b) TICAS simulations.

3) Slow northward motion

Simulation TICAN displays dramatic oscillations in intensity, with upward water fluxes ranging from 10 to 45 g m−2 s−1 (Fig. 9a), which are not present in the CSN (or any other) simulation. To examine this behavior more closely, four plots of the low-level fields near the storm are produced at different times (Fig. 12). After 1.5 h of simulation time, the TICAN storm has a fully developed precipitation core and cold pool (Fig. 12a). The updraft and mesocyclone are surrounded by outflow, which causes the storm to weaken shortly after this time (Figs. 9a,b). The updraft collapses shortly after 1.5 h and the precipitation core weakens substantially by 2 h (Fig. 12b), yielding warmer outflow owing to reduced evaporation. As the updraft reaches the decelerating gust front, it begins to reintensify around 2 h, causing the precipitation core to grow in size and strength by 2.5 h (Fig. 12c). By this time, there is again a large area of outflow with temperature perturbations of −6 to −8 K surrounding the updraft, causing it to subsequently weaken again (Fig. 12d). The temperature deficit beneath the anvil has lessened by 3 h because the weaker updraft lofts fewer hydrometeors upward to form the anvil, and the optical thickness of the anvil is reduced. The rapid regeneration of the updraft again occurs just after this time (Fig. 9a).

Fig. 12.

As in Fig. 3, but for the TICAN simulation at (a) 1.5, (b) 2.0, (c) 2.5, and (d) 3.0 h.

Fig. 12.

As in Fig. 3, but for the TICAN simulation at (a) 1.5, (b) 2.0, (c) 2.5, and (d) 3.0 h.

In simulation TICAN, because the rear-flank gust front moves into a shaded area, it is able to outrun the midlevel updraft. Additionally, the midlevel updraft becomes embedded within the precipitation core, weakening it substantially via evaporative cooling and precipitation drag. A weaker updraft results in a diminished precipitation core, ultimately freeing the updraft of hydrometeors. It also reduces the amount of evaporatively chilled air beneath the storm, slowing the rear-flank gust front relative to the midlevel updraft. Thus, the updraft is able to catch up to the weakening gust front and subsequently reintensify because of the increased low-level convergence at the gust front. This reintensification drives the development of a new precipitation core, reinvigorating the outflow, which again accelerates away from the midlevel updraft. Such behavior is not seen in simulation CSN because there is no slowing of the low-level winds (i.e., strong easterly shear) beneath the anvil in that simulation, preventing the gust front from ever accelerating away from that storm. Cycling is also not seen in simulation TICA0 because the updraft does not move appreciably relative to the gust front, meaning that the midlevel updraft in this simulation never repositions itself over the gust front and reintensifies.

4) Rapid eastward motion

To investigate if rapidly moving storms are affected in similar ways, two additional simulations were performed (TICA5W and CS5W) in which the hodograph used in the TICA0 simulation was translated 25 m s−1 eastward, resulting in an initial surface westerly wind of 5 m s−1, and a rapid eastward storm motion. The domain was enlarged to 500 km in the zonal direction and the simulation time was truncated to 3.5 h for computational reasons.

The upward water fluxes in both 5W storms are much greater than are those in the TICA0 storm (Fig. 13a), or even in the CS0 storm (Fig. 2a). Furthermore, there is a much larger spread in upward water flux between the TICA0 and TICA5W storms than between the TICA5W and CS5W storms, suggesting that radiation may not be nearly as important in modulating simulated supercell intensity. In contrast to the greater upward water fluxes, the low-level mesocyclones are much weaker in both of the 5W storms than in either the TICA0 or CS0 storms, and are again nearly identical to each other (Fig. 13b).

Fig. 13.

As in Fig. 2, but for the primary supercell for the TICA0 (solid), TICA5W (dotted), and CS5W (dash) simulations.

Fig. 13.

As in Fig. 2, but for the primary supercell for the TICA0 (solid), TICA5W (dotted), and CS5W (dash) simulations.

To rectify these somewhat conflicting trends in the time series relative to the TICA0 simulation, selected low-level fields near both 5W storms after 3 h of simulation time are plotted (Fig. 14). Both the TICA5W and CS5W simulations have nearly identical updrafts, mesocyclones and intense precipitation cores, both of which contain rainwater mixing ratios greater than 5 g kg−1. Anvil shading only produces about 0.5 K of cooling in the TICA5W simulation (cf. Figs. 14a,b) because the rapid storm motion means that there is less time over which radiative heating is reduced. The weaker initial surface winds in the 5W simulations mean that surface friction has a reduced effect on the low-level vertical wind shear. For example, the zonal wind component is initially 20 m s−1 in simulation TICA0, and it is reduced to about 10 m s−1 after 3 h of simulation time, which yields a 50% loss of zonal momentum in the lowest model level. A similar 50% reduction occurs in simulation TICA5W, but the initial surface wind speed is only 5 m s−1, meaning that the net loss of momentum to friction is only 2.5 m s−1, or 4 times less than that in simulation TICA0, resulting in weaker low-level vertical wind shear and a weaker low-level mesocyclone in both 5W simulations.

Fig. 14.

As in Fig. 3, but for the (a) TICA5W and (b) CS5W simulations.

Fig. 14.

As in Fig. 3, but for the (a) TICA5W and (b) CS5W simulations.

d. Soil moisture

The moisture concentration in the top layer of the model soil strongly modulates the latent and sensible heat fluxes from the model surface to the atmosphere. As discussed in FM10, a reduction in the latent heat flux forces a corresponding increase in the sensible heat flux. Thus, not only the low-level moisture concentrations, but also the low-level temperatures are influenced by the choice of initial soil moisture. In reality, soil moisture can vary on small spatial and temporal scales, especially during the warm season owing to the often sporadic nature of deep moist convection. It also depends on factors such as vegetation and soil type. To gauge the impact of soil moisture on anvil shading, two simulations were performed that are identical to the TICA0 simulation, except that the initial (dimensionless) soil moisture was changed from 0.3 to 0.1 in simulation SOILQ1 and to 0.2 in simulation SOILQ2.

An examination of the low-level thermodynamic and kinematic fields from these simulations reveals that the storms in these simulations do not remain supercellular owing to environmental changes during the course of the simulations. After 3 h of simulation time in SOILQ1, the storm has lost its supercellular characteristics and is transitioning into a bow echo (Fig. 15a). A quasi-circular updraft no longer exists on the right flank of this storm; instead, a linear updraft is found above the gust front, characteristic of squall lines and bow echoes (e.g., Houze 2004). A vortex couplet straddles the developing bow echo, with the cyclonic member on the northern end of the line and the anticyclonic member on the southern end, matching the bookend vortices described by Weisman (1993). The primary difference between the SOILQ1 and SOILQ2 simulations is that the SOILQ2 storm takes longer to transition into a bow echo (Fig. 15b).

Fig. 15.

As in Fig. 3, but for the (a) SOILQ1 and (b) SOILQ2 simulations.

Fig. 15.

As in Fig. 3, but for the (a) SOILQ1 and (b) SOILQ2 simulations.

The transformation of both of these supercells into bow echoes is caused by the changing environmental conditions that result from the dry model soil. The lack of an appreciable latent heat flux in both simulations results in much larger sensible heat flux, and hence warmer surface air temperatures than in the TICA0 simulation. These warmer temperatures result in a significantly deeper boundary layer, greater mixing of dry air from the free atmosphere, and reduced low-level water vapor mixing ratios (Fig. 16). This yields large surface dewpoint depressions that support colder outflow and faster gust front translation (i.e., bow echoes). Although the results presented in this section are not a direct consequence of anvil shading, this sensitivity test demonstrates a possibly significant modulation of simulated storm behavior by soil moisture and merits future study.

Fig. 16.

Skew T–logp diagrams depicting the domain-averaged vertical profiles of temperature and water vapor after 3 h of simulation time for the (a) TICA0, (b) SOILQ1, and (c) SOILQ2 simulations.

Fig. 16.

Skew T–logp diagrams depicting the domain-averaged vertical profiles of temperature and water vapor after 3 h of simulation time for the (a) TICA0, (b) SOILQ1, and (c) SOILQ2 simulations.

5. Summary and future work

Simulations of supercell thunderstorms were examined that included parameterizations of both surface fluxes and radiative transfer, and a soil model. It was generally found that simulations with anvil shadows yielded weaker storms than simulations in which shading effects were excluded. A brief summary of the results obtained in this study follows below.

Within the anvil shadow, surface cooling of up to 2 K stabilized the boundary layer and suppressed vertical mixing, preventing air from near the surface that had lost momentum to friction from mixing with larger momentum air from aloft. This increased the magnitude of the near-surface easterly vertical wind shear beneath the anvil, allowing the rear-flank outflow to become shallower and accelerate into the anvil-shaded region. In the case of an approximately stationary thunderstorm, the cold outflow was able to advance far in front of the midlevel updraft, weakening it. This process is shown schematically in Fig. 17a. A trajectory analysis indicated that the baroclinic zones that develop along the edges of anvil shadows were not a source of vertical vorticity for the low-level mesocyclone because the air within these zones did not enter the updraft for the wind profiles used herein. If anvil shading was not present (Fig. 17b), the rear-flank gust front did not surge away from the storm, and the stationary supercell was more intense. Changing the time of day of model initialization did not have a significant impact on this behavior. The simulated storms weakened even more if the cooling beneath the anvil was increased, and, in extreme cases, the storms dissipated. It was found that longwave radiation slightly destabilized the cloud layer, resulting in a marginally stronger supercell and greater precipitation rate. The choice of TICA instead of the ICA was found not to have a significant impact on any of the simulated supercell thunderstorms.

Fig. 17.

Schematic diagram illustrating how anvil shading affects simulated storm intensity and rear-flank gust front speed. (a) If anvil shading is considered, the near-surface winds in the shadowed region weaken owing to surface drag and the corresponding loss of vertical mixing; allowing the gust front to advance far in front of the storm and a weaker storm results. (b) Without anvil shading, the gust front is restrained and the storm is stronger. Pink arrows represent horizontal wind vectors at different levels and light pink arrows represent updrafts. Lengths of arrows are scaled relative to the magnitude of the flow. The gust front is denoted using the symbols typically used to identify cold fronts. Horizontal vorticity is also shown. The area shaded by the anvil is indicated in (a) with gray shading.

Fig. 17.

Schematic diagram illustrating how anvil shading affects simulated storm intensity and rear-flank gust front speed. (a) If anvil shading is considered, the near-surface winds in the shadowed region weaken owing to surface drag and the corresponding loss of vertical mixing; allowing the gust front to advance far in front of the storm and a weaker storm results. (b) Without anvil shading, the gust front is restrained and the storm is stronger. Pink arrows represent horizontal wind vectors at different levels and light pink arrows represent updrafts. Lengths of arrows are scaled relative to the magnitude of the flow. The gust front is denoted using the symbols typically used to identify cold fronts. Horizontal vorticity is also shown. The area shaded by the anvil is indicated in (a) with gray shading.

The influences of anvil shading as outlined above are not Galilean invariant because surface fluxes are not Galilean invariant. The initial hodograph was translated relative to the origin and it was determined that a storm that slowly moved along the major axis of its anvil shadow (eastward in the current simulations) evolved similarly to the stationary storm, with a midlevel updraft consistently located atop cold outflow. Any radiatively induced weakening became less noticeable as eastward storm motion increased. Storms that moved normal to the major axis of the anvil (northward or southward) were also investigated. The rear-flank gust front of the northward-moving storm was influenced in the same way as was that of the stationary storm because it advanced into the anvil shadow, but because the updraft moved relative to the rear-flank gust front, it could periodically reintensify, resulting in strongly cyclic behavior. The rear-flank gust front of the southward moving storm did not move into the anvil shadow, and thus it was not accelerated by the modified low-level shear layer beneath the anvil (Fig. 17b), similar to simulations in which anvil shading was not present. If storms moved rapidly, any anvil shading impacts were minimal, allowing for insufficient time for low-level cooling to occur beneath the anvils of these storms. In tests designed to investigate the sensitivity of anvil shading to soil moisture, it was found that if the soil moisture was decreased, strong heating of the model surface resulted in a much deeper boundary layer and decreased low-level water vapor mixing ratios, forcing the simulated supercells to transition into bow echoes.

This is only the first investigation of simulated supercellular convection in the presence of radiation. The present suite of simulations should be extended to include different temperature and moisture profiles, although care must be taken in designing idealized soundings for use in simulations that include radiation. Simulations with different storm-relative wind profiles should also be performed. The weakening of the updraft and mesocyclone in the simulation with anvil shading may be hodograph specific because the supercells examined herein trended toward the high-precipitation end of the spectrum. Air within the anvil-edge baroclinic zones may also enter the updrafts in simulations with different hodograph shapes. Additionally, it is possible that the use of different microphysical parameterizations, such as multimoment ice schemes, which affect outflow temperatures, can influence these results. For example, a warmer cold pool (which typically results from the use of a multimoment scheme) would result in a slower rear-flank gust front and a reduced chance that the outflow would accelerate far in front of the midlevel updraft and mesocyclone. The influence of shortwave and longwave radiation on other convective modes, such as squall lines and ordinary convective storms should be investigated as well. Additional degrees of realism should also be incorporated into future idealized simulations, including boundary layer dry convection, which is the subject of current research (Nowotarski et al. 2011).

It is important to expand upon this research as noted above because some of the results, including the overall weaker storm in the simulation with anvil shading, as well as those conclusions obtained by translating the hodograph, are likely dependent on the storm-relative wind profile. Not all of the results are so limited in scope, however. The conclusion that the direct absorption and emission of radiation by clouds is unimportant to supercell thunderstorms is likely applicable to a wide range of supercells because large latent heating rates exist across the supercell spectrum. Finally, the improvement in the calculation of surface shortwave fluxes offered by the use of the TICA instead of the ICA is generalizable to all simulations that have a sufficient horizontal resolution to resolve cloud shadows.

Acknowledgments

We are grateful to Drs. Yvette Richardson, Jerry Harrington, Bill Frank, and Andrew Carleton whose constructive comments as members of the lead author's dissertation committee improved this work. We also wish to thank Drs. Robert Carver, Jim Marquis, and Jon Petters for their assistance, and Dr. Chuck Pavloski and Mr. Chad Bahrmann for valuable computing help. The constructive comments provided by three anonymous reviewers also greatly improved this manuscript. Calculations of CAPE, CIN, and bulk Richardson number were performed using code made available by Dr. Kerry Emanuel. Many of the plots have been created using the Grid Analysis and Display System (GrADS), developed by the Center for Ocean–Land–Atmosphere Studies. ARPS was developed by the Center for Analysis and Prediction of Storms at the University of Oklahoma. This work has been supported by National Science Foundation Grant ATM-0644533.

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Footnotes

1

CAPE and CIN were calculated for surface parcels, assumed pseudoadiabatic ascent, and included the effects of water vapor on buoyancy.

2

The trajectories were computed using a fourth-order Runge–Kutta technique. The time step of each trajectory was 60 s and model data dump intervals were 300 s. The trajectories presented as a representative sample of dozens computed.

3

Gust fronts were identified subjectively from the simultaneous presence of a temperature gradient and a wind shift.