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    Input conditions to the low-shear case 2D frontal integration, as a function of height AGL (km). (a) Base-state east–west wind U(z) (m s−1). (b) Potential temperature (K, solid), mixing ratio (g kg−1, dashed), and relative humidity (%, inset figure on right).

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    (a) Skew T–logp sounding on the immediate warm side of the surface cold front, with the temperature trace (solid) and dewpoint (dashed). Wind barbs are in m s−1. (b) Hodograph of (a), with heights (km AGL) labeled along the curve. Scale is in m s−1.

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    2D frontal fields used to initialize the 3D model. The 298-K isentrope passing through the surface front (pressure minimum) is shown with a thick black line. (a) Front-relative wind (vertical component exaggerated by a factor of 40) and potential temperature (every 2 K). Maximum in-plane wind is +8.9 m s−1 at top-right corner. (b) Vertical velocity (contoured and positive values shaded every 5 cm s−1, with negative values dashed) and mixing ratio (every 1 g kg−1). Critical level near 5 km is shown with a heavy dashed line. (c) Meridional velocity (every 2 m s−1); local maximum at 5 km shown. (d) Relative vertical vorticity (contoured every 5 × 10−5 s−1; shaded exceeding 1, 2, 3, 4, 5 × 10−4 s−1).

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    Surface and layer properties across the cold front. (a) Vertical velocity (solid, cm s−1) and relative vertical vorticity (dashed, 10−4 s−1). (b) CAPE (solid) and CIN (dashed, J kg−1), with CIN decreasing upward. (c) Lifted index (solid, °C) and bulk Richardson number (BRI, dashed). (d) Temperature (solid) and dewpoint (dashed, °C). SCF denotes the surface cold front (surface pressure minimum).

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    Peak updraft speed (exceeding 20 m s−1) in 75-min single-cell simulations, as a function of forcing and initial temperature perturbation. Frontal convective cases are shown solid; isolated convective results are shown by dashed and dash–dotted lines, based on frontal surface pressure minimum (Pmin) and maximum low-level updraft (Wmax) soundings. Full-scale (of maximum updraft speed) graph is shown in lower-right corner.

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    Time series of maximum updraft speed (m s−1) as a function of forcing and initial temperature perturbation (magnitude shown by small boxed text) in single-cell experiments. (a) Frontal convection; (b) isolated convection for Wmax sounding. Thermal perturbations in (a) include 0.25°, 0.5°, 0.75°, 1°, 1.5°, 2°, 4°, and 6°C [(b) omits 0.25° and 0.5°C].

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    Time series of maximum updraft speed (m s−1) for full-domain experiments, with simulations (identified by small boxed text) referring to Table 1 in text. Maxima represent the peak updraft among all cells in the domain.

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    RN case at 2.1 h. Shown are surface wind vectors (every third), potential temperature deviation from initial warm-side sounding (every 1°C), and 1.9-km rainwater mixing ratio, contoured at (and shaded exceeding) 0.2 and 2.5 g kg−1.

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    Time series for identical moisture experiments; FB represents the frontal series, and IB (dashed) the isolated case. (top) Peak updraft speed (m s−1). (middle) Maximum downdraft at 2 km AGL (m s−1). (bottom two) Maximum rainwater mixing ratio (g kg−1) and surface vertical vorticity (10−4 s−1).

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    Plan view of (top) frontal (FB) and (bottom) isolated (IB) squall lines at 20-min intervals. Shading: 1.9 km AGL rainwater mixing ratio (0.5 and 4.0 g kg−1). Contours: 3.9 km AGL updraft speed (at 5, 10, and 15 m s−1). Solid lines trace the path of initial and cyclonic-split cells; dashed lines follow anticyclonic-split cells; and dotted lines follow secondary cells forming ahead of the initial frontal convection. A large (50 m s−1) eastward motion component was added after T = 25 for clarity. Inset: time–space representation of peak (all X, Z) rainwater mixing ratio, shaded exceeding 2, 6, and 10 g kg−1.

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    Plan view of storm splitting in the (left) isolated and (right) frontal cases. Cloud + rainwater mixing ratio (shaded at 0.5, 1.5, and 4.0 g kg−1), vertical velocity (contoured at ±2, 6, and 10 m s−1, negative values dashed), and perturbation wind vectors at 2.1 km AGL are shown, with the eastern edge of the surface temperature gradient drawn as a cold front. Vertical vorticity maxima and minima at 2.1 km in regions of updraft are denoted with a circle and center dot (cyclonic) and circle with an X (anticyclonic).

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    Close-up plan view and cross sections at 75 min through (left) isolated and (right) frontal convection: (top) 2.1-km cloud + rainwater (shaded exceeding 0.5, 1.5, and 4 g kg−1), vertical velocity at 125 m AGL (hatched exceeding ±0.5 and 1.5 m s−1), surface perturbation wind vectors, and frontal/gust front boundaries (bold lines). (bottom) Cross sections taken along bold dashed line above. Rainwater (shaded exceeding 0.5, 2, 4, 6, and 8 g kg−1), V (normal velocity contoured every 2 m s−1), in-plane velocity vectors, and 298-K isentrope (bold solid line) for the lowest 12 km are shown. Prominent local maxima and minima are indicated with a + or −.

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    Hodographs near (top) frontal and (bottom) isolated convection. (left) Hodographs taken near LM anticyclonic storms, and (right) the environment of RM storms. Each circle represents 10 m s−1, arrows denoting the appropriate cell motion are shown with a boldface arrow, and the height along the hodograph is listed in km.

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    Vertical velocity–vertical vorticity correlation for all cell updrafts exceeding 2.5 m s−1 as a function of time for (left) isolated and (right) frontal convection. Updraft speeds below (above) 12.5 m s−1 are marked with a plus sign (a filled square). Inset at lower right of each figure: scatterplot of correlation vs peak updraft speed (m s−1). Inset at top: cell count vs time for each case.

  • View in gallery

    Time variation of averaged and peak positive relative vertical vorticity (×10−4 s−1). (a) Vertical vorticity for frontal (solid) and isolated (dashed) cases; positive values averaged over the lowest 3 km (boldface) and 8 km (thin lines). (b) Vorticity maxima and minima below 3 km for frontal (solid) and isolated (dashed) cases.

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    (a) Higher-shear case skew T–logp, with the temperature trace (solid) and dewpoint (dashed). Wind barbs are in m s−1. (b) Hodograph of (a), with heights (km AGL) labeled along the curve. Scale is in m s−1. Dashed line shows hodograph from Fig. 2.

  • View in gallery

    Vertical velocity–vertical vorticity correlation for all cell updrafts exceeding 2.5 m s−1 for three increased shear cases. (top) Results for drier sounding with (a) frontal forcing and (b) isolated convection. (c) Results for isolated convection with deeper near-surface moisture. (d) Time series of (top) maximum vertical velocity, (middle) minimum vertical velocity at 2 km AGL, and (bottom) peak surface vorticity (×10−4 s−1, bottom) for cases in (a), (b), and (c). As in Fig. 14, updraft speeds below (above) 12.5 m s−1 are marked with a plus sign (a filled square).

  • View in gallery

    Vertical velocity–vertical vorticity correlation r as a function of (top) peak updraft speed and (bottom) vs storm height for higher (lower) shear on left (right) side of figure.

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The Role of Forcing in Cell Morphology and Evolution within Midlatitude Squall Lines

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  • 1 Department of Atmospheric Sciences, University of Illinois at Urbana–Champaign, Urbana, Illinois
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Abstract

This study assesses the role of mesoscale forcing on cell morphology and early evolution of midlatitude squall lines. The forcing chosen was a cold front, simulated to frontal collapse to produce a specific set of thermodynamic profiles at the leading edge of the front. Use of a realistic, balanced, and persistent forced state allowed a unique evaluation of its importance in thunderstorm evolution compared with a traditional homogeneous environment without forcing. Three-dimensional squall lines were modeled with and without the front present, in low and high bulk Richardson number environments. The forced convection evolved in significantly different ways than their isolated, unforced counterparts. In low-shear conditions, the line of isolated convective cells split, with the adjacent split cells interfering destructively with neighboring cells in the line. With forcing present, differences in anticyclonic cell intensity and propagation prevented this interaction from occurring, leading to longer-lived cyclonic convection despite a near-normal orientation between cloud-bearing shear and the convective line. The split-cell interaction also failed to occur under higher-shear conditions due to anticyclonic cell decay given the greater cyclonic hodograph curvature. In both low- and higher-shear environments, a strong bias toward cyclonic storms was noted with forcing present, due to shallower anticyclonic cells with the front present and to preexisting vorticity in the environment; updraft–vorticity correlations were skewed accordingly. Forcing also reduced the sensitivity of the evolving convection to detailed aspects of the initialization.

Corresponding author address: Brian F. Jewett, Department of Atmospheric Sciences, 105 S. Gregory St., Urbana, IL 61801. Email: bjewett@uiuc.edu

Abstract

This study assesses the role of mesoscale forcing on cell morphology and early evolution of midlatitude squall lines. The forcing chosen was a cold front, simulated to frontal collapse to produce a specific set of thermodynamic profiles at the leading edge of the front. Use of a realistic, balanced, and persistent forced state allowed a unique evaluation of its importance in thunderstorm evolution compared with a traditional homogeneous environment without forcing. Three-dimensional squall lines were modeled with and without the front present, in low and high bulk Richardson number environments. The forced convection evolved in significantly different ways than their isolated, unforced counterparts. In low-shear conditions, the line of isolated convective cells split, with the adjacent split cells interfering destructively with neighboring cells in the line. With forcing present, differences in anticyclonic cell intensity and propagation prevented this interaction from occurring, leading to longer-lived cyclonic convection despite a near-normal orientation between cloud-bearing shear and the convective line. The split-cell interaction also failed to occur under higher-shear conditions due to anticyclonic cell decay given the greater cyclonic hodograph curvature. In both low- and higher-shear environments, a strong bias toward cyclonic storms was noted with forcing present, due to shallower anticyclonic cells with the front present and to preexisting vorticity in the environment; updraft–vorticity correlations were skewed accordingly. Forcing also reduced the sensitivity of the evolving convection to detailed aspects of the initialization.

Corresponding author address: Brian F. Jewett, Department of Atmospheric Sciences, 105 S. Gregory St., Urbana, IL 61801. Email: bjewett@uiuc.edu

1. Introduction

Research into the key processes responsible for and modulating the behavior of multicell and supercell storms has revealed much about the relationship between the vertical buoyancy and shear profiles and the subsequent character of the convection. At the same time, it is known that mesoscale variations in the large-scale environment can be crucial in determining not only the location of thunderstorm initiation but also the mature structure and longevity of the convection. This is true for storms forming along a dryline or front as well as convection encountering a boundary after initiation (e.g., Markowski et al. 1998a, hereafter M98; Gilmore and Wicker 2002).

The environment in the vicinity of severe thunderstorms is often very complex. Local forcing and the associated horizontal gradients in thermodynamic conditions and shear have been documented on meso-γ scales (Mueller et al. 1993; Thompson and Edwards 2000). Contributions to the local vertical shear profile may include Ekman turning, large-scale baroclinicity, a low-level jet, and/or circulations associated with fronts, drylines, outflow boundaries, and horizontal convective rolls. Boundaries are often accompanied by low-level moisture convergence and ascent, are a frequent location for convective initiation (Wilson and Schreiber 1986; Lee et al. 1991; Wilson and Megenhardt 1997), exhibit considerable horizontal vorticity, may alter storm motion (Weaver and Nelson 1982) and squall-line alignment (Fankhauser et al. 1992), and can modulate storm type and severity, including the likelihood of tornadogenesis (M98; Rasmussen et al. 2000).

Metrics defining the storm environment include convective available potential energy (CAPE), vertical wind shear, and the bulk Richardson number (BRN), which may be computed from a single sounding or model vertical column. However, observational evidence of significant small-scale gradients in CAPE, convective inhibition (CIN; Mueller et al. 1993), and helicity (Markowski et al. 1998b, hereafter M98b) makes identifying a “representative” sounding problematic (Weisman et al. 1998): the representativeness is highly localized. Considerable variations in storm type have been documented within similar “environments” (M98b; Rasmussen and Straka 1998), suggesting high spatial variability (Bluestein and Parker 1993; Rasmussen and Blanchard 1998; M98b), or that parameters other than those commonly quantifying that “environment” are important.

Numerical simulation of deep convection has often been posed in highly idealized, horizontally uniform environments without mesoscale and synoptic-scale structure. Early modeling studies strongly correlated storm behavior to the local buoyancy and deep-layer shear (Weisman and Klemp 1982, hereafter WK82). WK82 used weak thermal perturbations to initiate convection—perturbations weak enough to have a deliberately short-lived influence on convection. They stated, however, that “synoptic or mesoscale forcing . . . may be equally important in influencing convective storm structure.”

Modeling research has also identified the importance of low-level buoyancy and shear (McCaul and Weisman 2001) in determining storm evolution, and the roles of midlevel (Brooks et al. 1994) and anvil-level (Rasmussen and Straka 1998) storm-relative winds in determining supercell type. Later work delineated the instability and shear parameter space associated with weak mesoscale convective systems (MCSs) from those of bow echoes (Weisman 1993) and strong bowing segments and mesovortices (Weisman and Trapp 2003; Trapp and Weisman 2003). Modeling studies with horizontally uniform environments are most applicable to storms forming well away from boundaries, and do not address how environmental variations or forcing might modulate the convection.

Squall-line evolution has been shown using numerical models to be related to the environment in which the line exists as well as to the organization of and interaction between cells within the line. Interaction among cells may have consequences for convective evolution (Bluestein and Parker 1993; Bluestein and Weisman 2000, hereafter BW00; Jewett et al. 2002). If the mean wind (and shear) is normal to a line of cells, the split-cell members will move laterally apart along the line, interfering with one another (often destructively), resulting in a short-lived squall line due to the difficulty of establishing steady cells (Weisman et al. 1988; Rotunno et al. 1988, hereafter RKW). Most of the aforementioned numerical studies considered isolated convective modes, in which perturbations responsible for storm initiation were short-lived. The role of long-lived forcing and its thermodynamic and shear structure on early and long-term cell and line behavior was not addressed. This motivates the following research questions: How does sustained forcing modulate squall-line behavior, and why? Does the local instability and shear of a “representative” inflow sounding still largely determine the outcome? Does long-lived forcing matter once the convection has formed, with its attendant strong updrafts, downdrafts, and cold pool?

This study addresses the role of persistent forcing in the early development and structure of deep convective squall lines. Two-dimensional forcing was selected for its relative simplicity (conceptually and through numerical simulation), here taken to be a cold front, formed and evolving as an idealized baroclinic wave. The methodology is discussed in section 2, the two-dimensional forcing in section 3, 3D results in section 4, and the results are summarized in section 5.

2. Methodology

The initial state for the 3D squall-line simulations was designed to provide

  • realistic cross-frontal structures at small spatial scales;
  • deep moisture maximized at the surface cold front;
  • substantial instability, appropriate for deep convection;
  • realistic tropopause and ambient shear;
  • two-dimensional (slab symmetric) forcing but with alongfront velocity predicted, resulting in curved hodographs.

We sought to merge aspects of high-resolution frontal simulations (e.g., Bénard et al. 1992; Snyder et al. 1993; Zhang and Cho 1995) with idealized studies of deep midlatitude convection (e.g., WK82; RKW; BW00). Earlier idealized frontal simulations were often carried out in 2D with a rigid (∼8 km) lid, while deep convection simulations were typically modeled in 3D under horizontally uniform conditions with a superimposed thermal, line of thermals, or cold source. The goal here is a more complete, but idealized and variable, initial state for simulating realistic midlatitude squall lines.

Models of frontal formation or structure include deformation frontogenesis (Garner 1989; Snyder et al. 1993, hereafter S93) and the density current (discussed by Braun et al. 1997; Moncrieff and Liu 1999; Wakimoto and Bosart 2000). Some frontal models were initialized using a dry semigeostrophic solution to shear frontogenesis (Koch et al. 1995; Keyser and Anthes 1982; Bénard et al. 1992), with constant thermal stratification and constant relative humidity often assumed for the initial state (Bénard et al. 1992 used 98%). Crook (1987) specified the base-state in-plane velocity and plane-normal jet structure and determined the temperature structure assuming thermal wind balance.

In this study, the cold front was initialized using shear-type frontogenesis (Eady 1949; Hoskins and Bretherton 1972; Pedlosky 1987; Holton 2004) in which an out-of-plane (meridional) temperature gradient was acted upon by the evolving slab-symmetric meridional velocity field. The Eady model reasonably approximates mature fronts, with some limitations. The inviscid model produces an unrealistically high height for the updraft maximum (Ogura and Portis 1982; Orlanski et al. 1985) and large alongfront velocities as the front forms (Hoskins and Bretherton 1972; Reeder and Smith 1986). The Eady model assumptions of inviscid, Boussinesq flow with constant base-state static stability and vertical shear were relaxed to allow a realistic tropopause, temperature, and shear profile, and vertical velocity structure.

The Collaborative Model for Multiscale Atmospheric Simulation (COMMAS) model (Wicker and Wilhelmson 1995; Skamarock et al. 1989) was used for the 2D frontal and 3D convective simulations. COMMAS is a nonhydrostatic, nested-grid model used in high-resolution convective and mesoscale applications. The version applied here incorporated second-order momentum advection, warm-rain microphysics, and a semislip surface layer. While ice microphysics were not employed in the shorter-term simulations carried out here, future work should include ice processes.

The 2D, f-plane frontal simulation was carried out in a 4000 km long by 18 km tall domain, with 16 km (X) and 250 m (Z) grid spacing1 and periodic lateral boundaries. Two nested grids resulted in 1.8-km grid spacing, adequate for modeling general convective behavior in weak–moderate shear (Weisman et al. 1997) but not for small-scale, highly transient phenomena. The 2D model grids were 255 (16 km), 48 (5.3-km nest), and 125 (1.78-km nest) points wide, with 73 vertical levels. The vertical resolution did not meet the very stringent criteria (Δzxf/N) of Pecnick and Keyser (1989) and Lindzen and Fox-Rabinovitz (1989), making possible spurious gravity waves (Persson and Warner 1991; S93). Our results near and following frontal collapse exhibited only small-amplitude gravity waves near and above the surface cold front (SCF), which were also seen in high-resolution inviscid simulations by S93. We saw no evidence of spurious waves, possibly due to the semislip surface layer and added vertical and horizontal filtering not used by S93.

The form of the most unstable mode was determined numerically, using a specified initial temperature, relative humidity, and wind shear profile (Fig. 1). In a “cycling” procedure, all perturbation fields were periodically rescaled (reduced) to small values to allow the emergence of this mode, a westward-tilted baroclinic wave with ascent, southerly winds, and positive temperature and moisture advection (Hsie et al. 1984) occupying half of the domain. Once the most unstable mode was established, the 2D integration proceeded normally. Over time, the separation between the northerly and southerly low-level jets diminished, and a distinct low-level “updraft jet” developed. This jet is known to be important for low-level frontogenesis (Orlanski et al. 1985).

The integration was continued until the front approached the minimum resolvable horizontal scale (“frontal collapse”), which was diagnosed with an empirically determined 2D area of the vertical vorticity maximum, by which time the frontal width
i1520-0493-134-12-3714-eq1
(Williams 1967) reached 9Δx (Vmax and Vmin here refer to the maximum and minimum meridional wind υ). Two nested grids were placed and integration continued to collapse on each grid. The horizontal damping was then increased to halt collapse as in S93, and the integration continued for 12 h to stabilize the inner grid solution. The expected decrease in meridional velocity accompanying frontal equilibration (Nakamura and Held 1989) occurred later, beyond the time in which we moved from 2D to 3D.

After the frontal solution was stabilized, the conditions at the SCF were compared to a chosen thermodynamic profile based on that used by WK82. Corrections were made to the initial 2D thermal stratification, and the above sequence was repeated, until the final SCF thermal profile approached the chosen one. Short (3 h) integrations after collapse were repeated until the water vapor profile also approached the desired sounding. The chosen sounding included a sharp tropopause, moderate (2470 J kg−1) instability, and near-neutral conditions just above the surface. Compared to the conditions ahead of a severe frontal squall line with distinct 3D cells studied by Heymsfield and Schotz (1985), this sounding was cooler and more moist at low levels and lacked their inversion. This sounding was also drier in the middle and upper troposphere than in WK82, and somewhat closer to the composite squall-line soundings of Bluestein and Jain (1985). The in-plane and plane-normal winds were determined by the intensifying baroclinic wave, with a curved hodograph forming by the time of frontal collapse. The final temperature and mixing ratio profiles at the SCF (Fig. 2) differed from the desired sounding by at most 0.3°C and 0.1 g kg−1. A curved hodograph was present with modest shear (note the height scale in Fig. 2).

3. Two-dimensional structure and convective initiation

Following frontal collapse, the low-level relative vorticity on the inner grid reached 12 × 10−4 s−1 [12f, versus 4f for the strong front analyzed by Sanders (1955, hereafter S55)].Thepeaksurfacetemperaturegradientwas0">, hereafter S55)]. The peak surface temperature gradient was 27 K (100 km)−1, versus 33–56 K (100 km)−1 for S55. The low-level updraft (21 cm s−1) was comparable to S55 (25 cm s−1) and Ogura and Portis (1982) (−7 μbar s−1) but much weaker than in tower data (5 m s−1; Shapiro et al. 1985) and aircraft observations by Bond and Fleagle (1985) (6 m s−1) and Wakimoto and Bosart (2000) (over 4 m s−1). The vertical mixing and 250-m vertical grid may have limited the updraft jet intensity; Gall et al. (1987) found vertical resolution strongly controlled the horizontal scale of fronts in their inviscid simulations as the front collapsed.

The 2D structure of the frontal fields on the innermost grid is depicted in Fig. 3, for the lowest 8 km. The location of the SCF is defined as the surface pressure minimum, and the isentrope at the SCF is highlighted in all figures. The front-relative wind field (Fig. 3a) shows deep easterly flow ahead of the SCF with relatively weak westerly flow behind it, as noted by Bond and Fleagle (1985), Fankhauser et al. (1992), and others. The vertical velocity in Fig. 3b exhibits the split updraft found by S93, wherein the frontal updraft (e.g., S93’s semigeostrophic solution) is modulated by a stationary gravity wave, leading to the pattern seen in Fig. 3b. The vertical extent of the wave is limited by the critical level indicated with the dashed line. While weak, broad ascent is found ahead of the front, the primary frontal updraft jet is only 10 km wide. The mixing ratio in Fig. 3b exceeds 15 g kg−1 near the SCF, with moist air transported above and behind the SCF.

A 28 m s−1 midlevel meridional jet is centered behind the SCF while a 24 m s−1 low-level jet is located farther east. The 12f vorticity maximum in Fig. 3d reflects the strong near-surface shear in Fig. 3c. The maximum vorticity axis is nearly collocated with the isentrope passing through the SCF, with which we approximate the location of the front.

The near-surface conditions and stability parameters appear in Fig. 4. The pressure minimum leads (is east of) the near-surface vertical velocity maximum, which leads the vorticity peak, as in Smith and Reeder (1988). Orlanski et al. (1985) showed that displacement of the locations of peak vorticity and updraft limits intensification by stretching, thereby helping halt frontal collapse. Given significant instability (lifted index of −8) and modest shear, the bulk Richardson number is clearly in the multicell regime.

The frontal conditions described above, depicted prior to the formation of clouds or precipitation, became the initial condition for 3D simulations described in the next section. If this 2D state was instead integrated forward in 2D, clouds formed in 30 min, and by 4 h the storm top reached 13 km. Compared to Fig. 4, the surface temperature gradient increased by a factor of 8, and the near-surface frontal/outflow boundary slope steepened significantly. The leading edge convection tilted upshear later in a pattern of weakening consistent with low shear versus buoyancy (Weisman et al. 1988). No trailing stratiform structure was evident in these or later 3D simulations, presumably due to the absence of ice processes, although an extensive downwind anvil developed.

4. Three-dimensional convective evolution

a. Idealized single-cell experiments in a limited domain

The innermost nested-grid fields (alone) shown in Fig. 3 were expanded in the out-of-plane (Y, or meridional) direction for use in single-grid simulations. The 2D frontal solution thus represented the initial condition for the subsequent 3D simulations. Use of a single 3D grid avoided unrealistic cell propagation differences noted near nested-grid boundaries in earlier tests. No Y gradients were assumed; the meridional expansion was slab symmetric. Had we incorporated plane-normal temperature and [relative humidity RH(Y) constant] moisture gradients assumed in the 2D model, locations 200 km to the south (north) of the original 2D plane would have CAPEs of 3340 (1750) J kg−1, with comparable CIN. Neglect of these gradients allowed study of 3D convective development apart from the influence of north–south buoyancy gradients on line behavior (e.g., Skamarock et al. 1994).

Highly idealized experiments were first used to assess sensitivity of early convection to changes in initial conditions, with or without the front present. We considered an infinitely long line of storms, simulated with one cell in a periodic north–south (N–S) framework, as in Wilhelmson and Klemp (1983). A domain only 18 km long was chosen from cell spacing seen in a simulation with a 140-km-long N–S domain with random temperature perturbations superimposed on the initial frontal fields. Since cells would not retain this scale or identity for long, these simulations were limited to 75 min.

In the first part of this experiment (“frontal forcing”), a warm thermal was placed at the SCF. In the second part, “isolated cell” simulations used conditions at the SCF to initialize a new horizontally homogeneous domain. In separate experiments, the isolated “sounding” was taken from both the location (Fig. 4) of the peak low-level updraft (Wmax) and the surface pressure minimum (Pmin). Though only 3.5 km apart, the Wmax location had 200 J kg−1 greater CAPE and 20 J kg−1 less CIN than found at Pmin.

For all three cases, the thermal magnitude was varied from 0.25° to 6°C. In each case, the thermal was centered at the lowest 125-m model level, with a 1400-m vertical radius, and 10-grid-point (18 km) horizontal radius. The peak updraft speed was tabulated as a function of thermal magnitude and initial condition type: frontal forcing, or isolated convection using Wmax or Pmin soundings (Fig. 5). No deep convection formed with either sounding in the homogeneous tests for temperature perturbations under 1°C. Convection, with updrafts exceeding 25 m s−1, formed in all frontal cases, consistent with lifting and warm advection at the SCF and earlier 2D tests without imposed perturbations. Frontal convective updrafts were stronger than the isolated cases regardless of thermal magnitude but particularly for small perturbations.

When the time evolution of the updraft maxima are considered (Fig. 6), the sensitivity to initial conditions is evident. Early convection in the frontal environment is highly ordered and more predictable, in these simulations, than that forming in isolation. Each frontal convective updraft peak is stronger and occurs earlier for larger thermal magnitude, followed by a similar trend in weakening. If the traces in Fig. 6a are overlaid to match the initial updraft timing (not shown), the behavior among various perturbations is nearly identical. The isolated Wmax convective cases show greater variability. Thus, this sensitivity is not simply a time lag, as 4° and 2°C tendencies are notably different in the isolated cases.

Lilly (1990) noted “surprising long-term sensitivities to simple changes in idealized initial conditions” in simulations by McPherson and Droegemeier (1991, their Table 1). Two cases, identical but for their initial warm thermal radius, underwent cell splitting at nearly the same time with the left mover dominating in one case and the right-mover persisting in the other. The aforementioned idealized experiments suggest some of this sensitivity is due to an underdetermined initial state, given that convection often occurs in the presence of mesoscale forcing (Wilson and Schreiber 1986; Roberts and Rutledge 2003). The presence of the front restricts the range of solutions, resulting in more consistent behavior over a range of thermal forcing in these highly simplified settings. This is consistent with studies showing reduced sensitivity to initial conditions for strong forcing (Zhang and Fritsch 1986) and the concomitant importance of detailed mesoscale data for forecasts with weak forcing (Stensrud and Fritsch 1991; Brooks et al. 1992).

b. Full-domain simulations

We next consider full-domain experiments with less limited convection. The innermost 2D domain was expanded to be 149 km long (N–S, alongfront), with periodic conditions on the N–S boundaries. The resulting single domain size was 103 × 85 × 73 (181 km wide × 149 km long). These cases, listed in Table 1, were used to assess the impact of variations in forcing (frontal convection versus “isolated” storms forming in horizontally uniform conditions), initial temperature perturbations (randomly placed, with or without additional warm thermals), N–S thermal spacing (5 or 8 thermals, for 28- or 18-km separation), perturbation magnitude (2° or 6°C thermals, and up to 0.5°C random perturbations), east–west boundary treatment (open boundaries, tendencies from the 2D model, or specification of boundary heat/moisture fluxes), and initial moisture fields (frontal mixing ratio fields or horizontally uniform). Random temperature perturbations were always included to permit along-line differences. Individual thermals used in all cases were typically 2°C warmer than the environment. While unnecessary for frontal convective initiation, this assured initiation without the front present (Fig. 5). In the case of frontal forcing, the thermals were placed along the axis of strongest low-level vertical velocity. Prefrontal soundings were characterized by 2470 J kg−1 CAPE, 50 J kg−1 CIN, 40 m2 s−2 bulk BRN shear (BRNSHR), and a BRN of 62.

We now summarize the results of the first six experiments in Table 1 before describing the last two in detail. In all experiments with 2° or 6°C thermals, an initial updraft peak was followed by weakening and an unsteady plateau, consistent with multiple updrafts and high BRN (Fig. 7). As in earlier idealized single-cell experiments, larger initial perturbations led to more rapid growth and stronger initial updrafts (cases I5, I6). In frontal (F8, F5) and isolated (I8, I5) environments, closer cell spacing resulted in lower initial updraft maxima as adjacent cell influence occurred earlier. Frontal convection was stronger than isolated convection in the first hour, as in Fig. 5, but weaker thereafter.

Convection developed slowly in the frontal case (RN) with random temperature perturbations (Fig. 7). After splitting, left-moving cells moved west of the front, atop the cold air, where they persisted but remained generally weaker than the right-moving cells at the leading edge of the front as a broken squall line. The surface outflow/frontal boundary was driven eastward by postfrontal convective downdrafts, and extended westward where enhanced inflow was present, yielding the sinusoidal pattern of front-normal wind and temperature (Fig. 8). As in Wakimoto and Bosart (2000), gap regions between precipitation cores were just south of the updrafts, but our modeled convection was much deeper (12 km) than their narrow cold-frontal rainband (3 km). At later times (not shown) the storms became more elevated and further removed from warm air and weakened, as in other frontal cases in Fig. 7, but lagged due to delayed initiation.

The frontal case with an imposed line of eight cells (F8) produced rain within 20 min. The storms split with the left-moving cells remaining weaker and elevated, as in case RN. A cyclic pattern developed in leading-line convection with new cells forming, moving rearward, and decaying, resulting in rainfall events every 35–40 min. Increasing the cell spacing by using 5 rather than 8 thermals (case F5) along the front increased the initial line updraft strength but did not significantly alter the behavior. After 90 min, cases F5 and F8 were similar (Fig. 7).

The convection without the front present (cases I5 and I8) was initially weaker but eventually stronger than frontal convection. As in the forced case, larger initial cell spacing led to stronger initial updrafts. Use of warmer initial thermals (6°C; case I6) produced stronger initial updrafts (Fig. 7) and earlier rainfall, as in the single-cell tests.

The consistently stronger isolated convection after the first hour was due to differences in moisture availability and weakening of the cold front. The isolated convection retained inflow (east and west of the line) of more buoyant air late in the simulation, while frontal convection remained in an environment of diminishing moisture due in part to the use of a single grid, the lateral boundary conditions, and a weakening front. The intensity differences between frontal and isolated convection complicates any assessment of the role of forcing in storm morphology.

c. Identical-moisture experiments

Two additional series of experiments (FB, IB) were made to allow comparison of convection of comparable strength. First, the isolated case was run using the frontal moisture field. This artificial construct assured that isolated storms did not have an inherent buoyancy advantage through greater low-level moisture, particularly later in the lifetime of the squall line. Second, the east–west lateral boundary tendencies were changed to advect the original boundary heat and moisture values into the domain, rather than maintaining the original tendencies. Together, these changes provided similar instability to both cases, and maintained the frontal intensity in a manner consistent with the original nested 2D evolution. Both frontal (FB) and isolated (IB) cases made use of five 2°C thermals at 28-km spacing with superimposed random temperature fluctuations.

The FB updraft maxima were nearly identical to the original (F5) case for the first 2 h, and slightly stronger thereafter (Fig. 7 versus Fig. 9). The IB case was notably weaker than the old IB case (simulation I5) after 50 min as a result of limited low-level moisture availability. In terms of maximum updraft and downdraft intensity and rainfall, the FB and IB cases were now of comparable strength (Fig. 9). Beyond these statistics, however, significant differences were found.

The general evolution of the frontal and homogeneous cases (Fig. 10) is as follows: significant downdrafts developed by 40 min; splitting began at 50 min; split cells were distinct by 70 min; and interaction with neighboring split cells started at 80 min. Two clear differences between frontal and isolated convection are apparent in Fig. 10: frontal convection was typically longer lived (note the inset rainwater time–space diagrams), and the pattern of splitting was notably different (cf. dashed anticyclonic tracks to solid cyclonic tracks). Although frontal and isolated cell behavior was quite similar for 40 min, marked differences developed soon after, as splitting began.

The isolated convective cells split in a straightforward manner. After an initial updraft peak of 25–30 m s−1, deep downdrafts formed by 40 min (Fig. 11). The 2-km rainwater and 4-km updraft fields elongated northwestward before splitting by 70 min. As adjacent right-moving (RM) and left-moving (LM) split cells approached one another, the vertical velocity aloft elongated and merged by 80 min (not shown). The RM and LM rainwater fields joined in a manner similar to the reflectivity bridge described by Westcott (1994) and Lee et al. (2006a,b), and in simulations by BW00. As in Westcott and Kennedy (1989), new cell growth occurred in the low-level convergence zone between the older RM and LM cells (Fig. 10, t = 105 min). The new cells then intensified rapidly and merged with the RM storms; LM cells never fully merged and weakened as they propagated northward away from the other storms after 105 min. The merged RM cells also decayed, for four of the five cells in the line. As seen in the time–space diagram (Fig. 10, inset lower right), the rainwater production for the isolated storms was largest until shortly after splitting, and again briefly after merging occurred.

In contrast, frontal convective behavior was modulated by the wind shear and thermal gradients across the front, along with the production of additional cells through frontal lifting. The initial frontal cells also split, but in a different manner than in the isolated case (Fig. 11). The downdraft originating northeast of each updraft descended to the surface as splitting began, as in the isolated case. However, instead of the updraft extending westward, forming a “U” with the incipient left mover ingesting warm surface air, the elongated LM updrafts remained elevated above the front, clearly not ingesting high-θe air, though they eventually grew/redeveloped into deeper anticyclonic cells under the influence of persistent lifting and forcing by the convective downdrafts.

The environment in which the frontal LM cells existed was appreciably different from the isolated case. The cross-front gradient in meridional wind from 1 to 3 km AGL and the presence of stronger, deeper easterly winds above and west of the SCF (Fig. 3) meant that the shallow frontal LM cells propagated northeastward (Fig. 2) more slowly, falling behind the RM cells. The frontal LM cells remained south of and behind their cyclonic counterparts, never affecting the next cell north in the line. This illustrates one consequence of the forcing: environmental differences across the boundary affected split-cell behavior, such that the type of cell interaction seen in the isolated line never occurred. We note this occurred despite the same alongfront sounding conditions in the warm sector, and the presence of a storm-generated cold pool in both cases. The differences in cell environment are considered of first-order importance in explaining differences in evolution between the forced and unforced squall lines. The isolated behavior here is similar to line-normal shear findings by RKW, wherein neighboring split cells interfered destructively, weakening the line. However, we have shown here that the large-scale forcing and environment fundamentally altered the cell and line development.

At 75 min (Fig. 12), differences between forced and isolated convection included 1) stronger cross-frontal wind shear, 2) the position and propagation of the anticyclonic split cell with respect to the right mover, 3) the westward extent of convective outflow—greater without the frontal boundary, and 4) stronger cyclonic shear along outflow boundaries in the frontal case (see time series, Fig. 9). Enhanced, elongated convergence zones were between cells (isolated case) and between convective outflow and pre- or postfrontal air masses (forced case). Most cells at 75 min, for either case, were near a plateau in updraft intensity with gradually weakening downdrafts (Fig. 9).

Comparing hodographs taken near RM and LM split cells (Fig. 13), enhanced shear is evident behind the boundary, as expected, for frontal LM cells. Right-moving cell hodographs generally lengthened (increasing mean shear) with time as storm inflow strengthened and outflow aloft increased. These differences were exaggerated in the frontal case, with strong northerly flow behind the front. A time series of linear correlation coefficients r,
i1520-0493-134-12-3714-eq2
between updraft velocity (w) and vorticity (ζ) appears in Fig. 14. Cells with weaker updrafts are denoted with a plus sign and stronger updrafts are denoted with a black square. These statistics were generated for each cell at 5-min intervals, with minimum, average, and peak correlation computed for a 15 km × 15 km domain centered on each updraft for the lowest 8 km (similar to Weisman and Klemp 1984). Cells were identified based on local maxima within a 2D field of peak vertical velocity for each vertical column. Cells with vertical velocities exceeding 2.5 m s−1 are plotted in Fig. 14. Correlation values do not exceed ±0.5 as a consequence of horizontal averaging for each cell, and updraft tilt with height. Peak correlations of 0.7–0.9 (both cyclonic and anticyclonic) were common.

As cells intensified, tilting of ambient shear produced ζ couplets oriented normal to the vertical shear vector, yielding low correlation; high r in the first 15 min resulted from weak waves triggered by the thermals. The correlation increased significantly with splitting, and anticyclonic updrafts appeared as increasingly negative r after 1 h, particularly for isolated convection where updrafts evolved in a more straightforward manner. These patterns were found in both isolated and forced cases, though the weaker and initially shallow frontal LM cells produced a less prominent signature in Fig. 14.

The interaction of split-cell pairs (isolated case) and new frontal cell development (forced case) occurred by 1.5 h. The number of cells increased sharply (Fig. 14, top), to 3x (5x) the original number of isolated (frontal) storms. Accompanying this increase was a brief decrease in correlation magnitude in both cases, and a wide variety of r for the far greater number of frontal convective cells. This is in contrast to the trend of generally increasing r seen by Weisman and Klemp (1984), where such cell interaction did not take place. Reintensification occurred followed by gradual decay for most cells, particularly among isolated storms (Fig. 14; see also time–space plots in Fig. 10). In both cases, the strongest updrafts were often characterized by the highest r (Fig. 14, inset). A smaller w versus r subspace was found for frontal convection than in the unforced case.

In Fig. 15a, vertical vorticity for isolated (dashed lines) and frontal (solid) convection indicates the lasting influence of the forcing. By design, the forced case has nonzero vertical vorticity in the initial state, unlike the isolated environment, and this difference persists and grows. Because the 0–3- or 0–8-km averaging is of only positive ζ, the rapid rise in deep-layer vorticity in the frontal case can be attributed to tilting by intensifying updrafts, and later to emergence of split RM storms. The growth of cells able to stretch preexisting ζ along the front likely contributes to these statistics, since averaging over 0–1 km (not shown) exaggerates forced/unforced differences. We conclude from the peak ζ data (Fig. 15b) that the differences are attributable to both areal extent (far more cells in the frontal case) as well as storms acting upon preexisting horizontal shear.

d. Increased shear results

A limited number of simulations were carried out under increased vertical shear and reduced instability to contrast forced and unforced convective evolution under conditions of reduced BRN (Fig. 16). Compared to the earlier cases, these had lower CAPE (approximately 1500 versus 2500 J kg−1), lower CIN (15 versus 50 J kg−1), and reduced BRN (35 versus 60). The BRNSHR and 0–6-km hodograph length were greater—the latter now in the range in which supercells may occur (Bunkers 2002). The largest difference in wind, as evident from Fig. 16, was an increased westerly component at upper levels.

Three simulations will be discussed here. A somewhat drier sounding characterized the first two, with slightly less (1400 versus 1600 J kg−1) instability. Correlation and time series data for these experiments appear in Figs. 17a and 17b. The higher shear and reduced CAPE led to a short lifetime for unforced convection (Fig. 17b). A subsequent simulation was made, one with identical shear but slightly deeper low-level moisture. This sounding, with a BRN of 36 (versus frontal 32), is shown in Fig. 16. A corresponding frontal simulation was not made; the results from this “isolated–deeper moisture” case are summarized in Fig. 17c. The time series (Fig. 17d) shows the isolated convection to be initially stronger than frontal storms, given slightly greater instability, but comparable in updraft and downdraft intensity after the first hour. Note that the isolated convective cases described here used horizontally uniform (not frontal) initial moisture fields.

No significant anticyclonic cells developed in the higher-shear frontal case. Weak LM split cells formed but immediately decayed given the reduced instability, cyclonically curved hodograph, and location above and behind the SCF. The result was a series of long-lived storms with cyclonic updrafts exhibiting high r (Fig. 17a). Irregular updraft pulses characterized new cell growth on the south side of each RM frontal storm.

In contrast, isolated convection (Fig. 17c) had more similarities to its lower-shear counterpart (Fig. 14), forming deep RM and LM cells. Storm splitting took place in 1–1.5 h, and rapid growth of LM storms from 1.5 to 2 h. The scatter of low (0–0.25) r near 1.5 h accompanied storm splitting and tilting by the downdrafts and anticyclonic updrafts, while increasingly negative r followed as LM storms intensified and deepened, and stretching became important. The anticyclonic LM cells ultimately weakened, as expected given the hodograph in Fig. 16b, before any interaction with adjacent RM cells could occur. The result, as in the frontal case, was a series of long-lived RM storms.

A summary of w′–ζ′ correlation statistics for prior (low shear) and later experiments, evaluated versus updraft strength and storm height, appears in Fig. 18. Looking first at the top row (r versus w), we note increased scatter for 1) low versus increased shear (and lower CAPE), and 2) isolated versus frontal storms under low shear. In addition, fewer, stronger cyclonic storms occurred with higher shear, and cyclonic storms predominated for frontal versus isolated convection. There exists a tail to the r–w distribution for frontal convection, where a range of updraft speeds of 10–20 m s−1 are characterized by high w′–ζ′ correlation; unforced storms are less “focused.” The bias toward cyclonic over anticyclonic frontal storms may be attributed to the development of weaker, shallower LM cells with the front present, and to preexisting vertical vorticity in the environment (Fig. 17d).

The r–storm height relationship (Figs. 18e–h) was examined given potentially disparate storm motion under different cloud-bearing winds for different storm depths. The storm top was defined as the top height at which the rainwater mixing ratio met or exceeded 0.05 g kg−1. In unforced convection in low shear, the potential for long-lived cyclonic and anticyclonic storms was more equal, with a “<” pattern (Fig. 18h) as more strongly rotating storms of either sign possessed larger updrafts and storm tops. Cyclonic storms were favored for larger shear. For frontal storms, a bias toward cyclonic updrafts occurred in either environment, though most dramatically in the presence of higher shear.

5. Summary and discussion

Weisman and Rotunno (2004) noted, “it is difficult to differentiate the impact of external versus internal forcing mechanisms.” The degree to which internal mechanisms for storm behavior are modified or play a greater or lesser role in the presence of forcing is a question addressed here by defining and selectively removing a realistic mesoscale state. We find a significant role for forcing not only in storm initiation but also in the evolution and persistence of the modeled squall-line system. “Forcing” need not be limited to larger scales; indeed, the forcing here has large-scale organization but also meso-γ detail; the key is that this forcing is persistent. While this is no guarantee it will have a lasting influence on convective behavior, our findings indicate, at least in this setting, that it does.

Our use of the word “forcing” could imply a clear and lasting distinction between convective and preconvective scales and structures. This distinction is clearly blurred once convection is underway. The scale interaction discussed here is strongest among phenomena of similar (convective) scales, and the forcing is taken to be the larger-scale setting in which convection evolves. Storms are often known to have a longer-term, large-scale influence, for example, via convectively generated gravity waves (Balachandran 1980) or mesoscale convective vortices (e.g., Davis and Trier 2002). A surprising result here is that a front and updraft jet of modest intensity can have such a lasting influence on storm morphology, when convective updrafts, downdrafts, and temperature deficits are so much larger than in the preconvective environment. This influence is evident as greater vertical vorticity, at the surface into the midtroposphere; the bias toward longer-lived cyclonic storms; and (particularly at lower shear) a stronger convective system.

Several studies (e.g., Lilly 1990; Crook 1996; Elmore et al. 2002) have revealed considerable sensitivity of modeled storms to details of their initialization. Our findings suggest that such sensitivity may be exaggerated in idealized, horizontally homogeneous simulations, compared to the more typical severe convective environment in which mesoscale and storm-scale forcing plays a more significant role (e.g., Moller et al. 1994). This is consistent with results of Stensrud and Fritsch (1991), who found heightened sensitivity and concomitant lowered predictability in weakly forced settings. We also find limitations in modeling of squall lines initialized with short-lived perturbations, since external forcing appears to be important in evolution as well as initiation, as hypothesized by Weisman and Klemp (1982).

Squall-line evolution is a consequence of many factors, including the relative strength of the cold pool and ambient shear (Weisman and Rotunno 2004), the orientation of the convective line to the vertical shear (Bluestein and Weisman 2000), and line end and Coriolis effects (Skamarock et al. 1994). An important component of line morphology is storm cell interaction, which is related to line orientation (Bluestein and Weisman 2000), cell strength, position, and propagation (Jewett et al. 2002), and cell spacing versus boundary layer depth (Stalker and Knupp 2003). Factors important in storm propagation include the mean cloud-bearing wind, and thus storm depth; gust front propagation (Weaver and Nelson 1982); and vertical perturbation pressure gradients related to storm rotation and to the mean shear acting upon the updraft (Rotunno and Klemp 1982).

We find that boundary forcing here plays an important role in storm propagation and cell behavior, due to (a) changes in the mean wind across the boundary, (b) changes in storm intensification with the boundary present, and thus storm height and cloud-bearing wind, and (c) subsequent changes in split-cell behavior and storm merging. The frontal ascent and enhanced moisture convergence along the front, though important for additional cell growth (Fig. 14) and weak stretching of ambient vertical vorticity, are believed to be of secondary importance to the cell interaction and line morphology found in this study. The key role of the forcing here is the cross-frontal environmental differences and the concomitant changes in split-cell behavior and interaction.

This paper has emphasized cell interaction and squall line evolution in homogeneous and heterogeneous environments. Among the logical extensions to this work are 1) inclusion of ice processes; 2) utilizing the same model, for example, the Weather Research and Forecast model (WRF), for single-sounding versus fully 3D simulations in other mesoscale settings; 3) modeling large, long-lived MCSs, known for their significant role in long-term precipitation; and 4) other aspects of storm interaction and severity. We are pursuing the latter in expanded numerical modeling studies of supercell–supercell and supercell–developing cell interaction.

Acknowledgments

This work was supported by the National Science Foundation under Grants ATM-9986672 and ATM-0449753. Computational and other support was provided by National Center for Supercomputing Applications (NCSA). Discussions with Drs. William Skamarock and Chris Snyder of NCAR/MMM are gratefully acknowledged.

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Fig. 1.
Fig. 1.

Input conditions to the low-shear case 2D frontal integration, as a function of height AGL (km). (a) Base-state east–west wind U(z) (m s−1). (b) Potential temperature (K, solid), mixing ratio (g kg−1, dashed), and relative humidity (%, inset figure on right).

Citation: Monthly Weather Review 134, 12; 10.1175/MWR3164.1

Fig. 2.
Fig. 2.

(a) Skew T–logp sounding on the immediate warm side of the surface cold front, with the temperature trace (solid) and dewpoint (dashed). Wind barbs are in m s−1. (b) Hodograph of (a), with heights (km AGL) labeled along the curve. Scale is in m s−1.

Citation: Monthly Weather Review 134, 12; 10.1175/MWR3164.1

Fig. 3.
Fig. 3.

2D frontal fields used to initialize the 3D model. The 298-K isentrope passing through the surface front (pressure minimum) is shown with a thick black line. (a) Front-relative wind (vertical component exaggerated by a factor of 40) and potential temperature (every 2 K). Maximum in-plane wind is +8.9 m s−1 at top-right corner. (b) Vertical velocity (contoured and positive values shaded every 5 cm s−1, with negative values dashed) and mixing ratio (every 1 g kg−1). Critical level near 5 km is shown with a heavy dashed line. (c) Meridional velocity (every 2 m s−1); local maximum at 5 km shown. (d) Relative vertical vorticity (contoured every 5 × 10−5 s−1; shaded exceeding 1, 2, 3, 4, 5 × 10−4 s−1).

Citation: Monthly Weather Review 134, 12; 10.1175/MWR3164.1

Fig. 4.
Fig. 4.

Surface and layer properties across the cold front. (a) Vertical velocity (solid, cm s−1) and relative vertical vorticity (dashed, 10−4 s−1). (b) CAPE (solid) and CIN (dashed, J kg−1), with CIN decreasing upward. (c) Lifted index (solid, °C) and bulk Richardson number (BRI, dashed). (d) Temperature (solid) and dewpoint (dashed, °C). SCF denotes the surface cold front (surface pressure minimum).

Citation: Monthly Weather Review 134, 12; 10.1175/MWR3164.1

Fig. 5.
Fig. 5.

Peak updraft speed (exceeding 20 m s−1) in 75-min single-cell simulations, as a function of forcing and initial temperature perturbation. Frontal convective cases are shown solid; isolated convective results are shown by dashed and dash–dotted lines, based on frontal surface pressure minimum (Pmin) and maximum low-level updraft (Wmax) soundings. Full-scale (of maximum updraft speed) graph is shown in lower-right corner.

Citation: Monthly Weather Review 134, 12; 10.1175/MWR3164.1

Fig. 6.
Fig. 6.

Time series of maximum updraft speed (m s−1) as a function of forcing and initial temperature perturbation (magnitude shown by small boxed text) in single-cell experiments. (a) Frontal convection; (b) isolated convection for Wmax sounding. Thermal perturbations in (a) include 0.25°, 0.5°, 0.75°, 1°, 1.5°, 2°, 4°, and 6°C [(b) omits 0.25° and 0.5°C].

Citation: Monthly Weather Review 134, 12; 10.1175/MWR3164.1

Fig. 7.
Fig. 7.

Time series of maximum updraft speed (m s−1) for full-domain experiments, with simulations (identified by small boxed text) referring to Table 1 in text. Maxima represent the peak updraft among all cells in the domain.

Citation: Monthly Weather Review 134, 12; 10.1175/MWR3164.1

Fig. 8.
Fig. 8.

RN case at 2.1 h. Shown are surface wind vectors (every third), potential temperature deviation from initial warm-side sounding (every 1°C), and 1.9-km rainwater mixing ratio, contoured at (and shaded exceeding) 0.2 and 2.5 g kg−1.

Citation: Monthly Weather Review 134, 12; 10.1175/MWR3164.1

Fig. 9.
Fig. 9.

Time series for identical moisture experiments; FB represents the frontal series, and IB (dashed) the isolated case. (top) Peak updraft speed (m s−1). (middle) Maximum downdraft at 2 km AGL (m s−1). (bottom two) Maximum rainwater mixing ratio (g kg−1) and surface vertical vorticity (10−4 s−1).

Citation: Monthly Weather Review 134, 12; 10.1175/MWR3164.1

Fig. 10.
Fig. 10.

Plan view of (top) frontal (FB) and (bottom) isolated (IB) squall lines at 20-min intervals. Shading: 1.9 km AGL rainwater mixing ratio (0.5 and 4.0 g kg−1). Contours: 3.9 km AGL updraft speed (at 5, 10, and 15 m s−1). Solid lines trace the path of initial and cyclonic-split cells; dashed lines follow anticyclonic-split cells; and dotted lines follow secondary cells forming ahead of the initial frontal convection. A large (50 m s−1) eastward motion component was added after T = 25 for clarity. Inset: time–space representation of peak (all X, Z) rainwater mixing ratio, shaded exceeding 2, 6, and 10 g kg−1.

Citation: Monthly Weather Review 134, 12; 10.1175/MWR3164.1

Fig. 11.
Fig. 11.

Plan view of storm splitting in the (left) isolated and (right) frontal cases. Cloud + rainwater mixing ratio (shaded at 0.5, 1.5, and 4.0 g kg−1), vertical velocity (contoured at ±2, 6, and 10 m s−1, negative values dashed), and perturbation wind vectors at 2.1 km AGL are shown, with the eastern edge of the surface temperature gradient drawn as a cold front. Vertical vorticity maxima and minima at 2.1 km in regions of updraft are denoted with a circle and center dot (cyclonic) and circle with an X (anticyclonic).

Citation: Monthly Weather Review 134, 12; 10.1175/MWR3164.1

Fig. 12.
Fig. 12.

Close-up plan view and cross sections at 75 min through (left) isolated and (right) frontal convection: (top) 2.1-km cloud + rainwater (shaded exceeding 0.5, 1.5, and 4 g kg−1), vertical velocity at 125 m AGL (hatched exceeding ±0.5 and 1.5 m s−1), surface perturbation wind vectors, and frontal/gust front boundaries (bold lines). (bottom) Cross sections taken along bold dashed line above. Rainwater (shaded exceeding 0.5, 2, 4, 6, and 8 g kg−1), V (normal velocity contoured every 2 m s−1), in-plane velocity vectors, and 298-K isentrope (bold solid line) for the lowest 12 km are shown. Prominent local maxima and minima are indicated with a + or −.

Citation: Monthly Weather Review 134, 12; 10.1175/MWR3164.1

Fig. 13.
Fig. 13.

Hodographs near (top) frontal and (bottom) isolated convection. (left) Hodographs taken near LM anticyclonic storms, and (right) the environment of RM storms. Each circle represents 10 m s−1, arrows denoting the appropriate cell motion are shown with a boldface arrow, and the height along the hodograph is listed in km.

Citation: Monthly Weather Review 134, 12; 10.1175/MWR3164.1

Fig. 14.
Fig. 14.

Vertical velocity–vertical vorticity correlation for all cell updrafts exceeding 2.5 m s−1 as a function of time for (left) isolated and (right) frontal convection. Updraft speeds below (above) 12.5 m s−1 are marked with a plus sign (a filled square). Inset at lower right of each figure: scatterplot of correlation vs peak updraft speed (m s−1). Inset at top: cell count vs time for each case.

Citation: Monthly Weather Review 134, 12; 10.1175/MWR3164.1

Fig. 15.
Fig. 15.

Time variation of averaged and peak positive relative vertical vorticity (×10−4 s−1). (a) Vertical vorticity for frontal (solid) and isolated (dashed) cases; positive values averaged over the lowest 3 km (boldface) and 8 km (thin lines). (b) Vorticity maxima and minima below 3 km for frontal (solid) and isolated (dashed) cases.

Citation: Monthly Weather Review 134, 12; 10.1175/MWR3164.1

Fig. 16.
Fig. 16.

(a) Higher-shear case skew T–logp, with the temperature trace (solid) and dewpoint (dashed). Wind barbs are in m s−1. (b) Hodograph of (a), with heights (km AGL) labeled along the curve. Scale is in m s−1. Dashed line shows hodograph from Fig. 2.

Citation: Monthly Weather Review 134, 12; 10.1175/MWR3164.1

Fig. 17.
Fig. 17.

Vertical velocity–vertical vorticity correlation for all cell updrafts exceeding 2.5 m s−1 for three increased shear cases. (top) Results for drier sounding with (a) frontal forcing and (b) isolated convection. (c) Results for isolated convection with deeper near-surface moisture. (d) Time series of (top) maximum vertical velocity, (middle) minimum vertical velocity at 2 km AGL, and (bottom) peak surface vorticity (×10−4 s−1, bottom) for cases in (a), (b), and (c). As in Fig. 14, updraft speeds below (above) 12.5 m s−1 are marked with a plus sign (a filled square).

Citation: Monthly Weather Review 134, 12; 10.1175/MWR3164.1

Fig. 18.
Fig. 18.

Vertical velocity–vertical vorticity correlation r as a function of (top) peak updraft speed and (bottom) vs storm height for higher (lower) shear on left (right) side of figure.

Citation: Monthly Weather Review 134, 12; 10.1175/MWR3164.1

Table 1.

Summary of full-domain 3D simulations—low shear.

Table 1.

1

The 4000-km-wide domain was slightly larger than that for the most unstable mode in a Boussinesq, constant static-stability atmosphere (λ ≈ 3600 km).

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