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    Representative composite radar reflectivity images from three heavy-rain-producing warm-season TL/AS MCSs (each row constitutes a separate event). Valid dates and times are in the lower-right corner of each panel. From PS2014. The 28 Jul 2011 case was studied in detail by Peters and Schumacher (2015).

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    An 18-h event-centered composite progression from 26 warm-season events of 300-hPa wind speed (m s−1; shading), wind vectors (arrows), and geopotential height (black lines at intervals of 50 m) from (a) 6 h prior, (b) the time of, (c) 6 h after, and (d) 12 h after peak 1-h rainfall accumulation was observed at the event location. A black circle at the center of each panel indicates the point location of maximum 1-h rainfall accumulation. The specific latitudes and longitudes shown are arbitrarily selected to illustrate the spatial scale. From PS2014.

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    An 18-h progression from warm-season events of 850-hPa potential temperature advection (shading) (×10−5 K s−1; values below 2 × 10−5 K s−1 have been removed; derivatives were computed from composite atmospheric fields), wind speed (blue dashed contours at intervals of 2 m s−1, starting at 8 m s−1), wind vectors (black arrows), geopotential height (black lines at intervals of 20 m), and potential temperature (K; dashed gray contours). Panel times are the same as those in Figs. 1 and 2. A solid black circle at the center of each panel indicates the point location of maximum 1-h rainfall accumulation. The specific latitudes and longitudes shown are arbitrarily selected to illustrate the spatial scale. Adapted from PS2014.

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    Plots of the standard deviation [σ; see Eq. (1) in the text] of 850-hPa wind speed for (a) 26 warm-season events (m s−1; shading) and (b) 50 training convective events containing both warm-season- and synoptic-type (m s−1; shading) events; the standard deviation of temperature for (c) warm-season (K; shading) and (d) all events (K; shading). Geopotential height (m, at intervals of 40 m; solid black contours), wind vectors (black arrows), and wind speed (m s−1 starting at 8 m s−1 and at intervals of 2 m s−1; blue dotted contours) are shown in all panels. All panels are valid at the time of maximum 1-h rainfall accumulation from stage IV precipitation analysis (see PS2014). A black circle at the center of each frame indicates the point location of maximum 1-h rainfall accumulation. The specific latitudes and longitudes shown are arbitrarily selected to illustrate the spatial scale. Adapted from PS2014.

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    (top) Time–height diagram of the vertical profile of static stability (; K m−1; shading) below the maximum point wind speed value at 850 hPa in the composite progression. (bottom) Time series of the maximum 850-hPa wind speed (red line) and the magnitude of the horizontal geopotential height gradient on the 850-hPa isobaric surface (blue line) in the composite progression.

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    Comparison of the (a),(b) synoptic-scale environments in the warm-season composites used as ICs and LBCs for WRF simulations to the (c),(d) synoptic-scale solution on the 4-km NOMP domain, valid (left) at and (right) 9 h after the time of heaviest 1-h rainfall accumulation in the composites (note that the corresponding simulation times are also included). Red arrows are 300-hPa wind vectors; dotted red contours are 300-hPa wind speeds (m s−1) at intervals of 2 m s−1, starting at 13 m s−1; blue arrows are 850-hPa wind vectors, and blue dotted contours are 850-hPa wind speeds (m s−1) at intervals of 2 m s−1, starting at 7 m s−1; magenta dotted contours are 850-hPa wind speed (K) at intervals of 1 K. Green circles and black arrows indicate the location of the vertical profiles shown in Fig. 9.

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    As in Fig. 6, but here 850-hPa WAA (K s−1; shading), 850-hPa wind vectors (m s−1; blue arrows), 850-hPa wind speed (m s−1; at intervals of 2 m s−1, starting at 7 m s−1; dashed blue contours), 850-hPa geopotential height (m; black solid contours), 850-hPa temperature (K; dashed magenta contours), and 850-hPa relative humidity (%; solid green contours) are shown to facilitate the comparison of synoptic-scale forcing for ascent between the composites and simulation.

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    As in Fig. 5, but for the NOMP simulation. Here, the maximum wind speed value at 1.25 km AGL has been assessed rather than the maximum wind speed at 850 hPa. (bottom) The blue line subsequently depicts a time series of the horizontal pressure gradient (Pa m−1 × 2) at the location of the maximum 1.25-km-AGL wind speed rather than the horizontal geopotential height gradient on an isobaric surface. The location of the maximum wind speed at this level varied considerably with time; therefore, (top) the stability profile was assessed at the sounding location indicated in Fig. 7d.

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    (top) Skew T–logp diagram depicting vertical profiles [composite (COMP) at the time of peak 1-h rainfall, CNTL outer domain 6 h after peak rainfall] of temperature (red solid line, red dashed line), dewpoint (green solid line, green dashed line), wind barbs (CNTL on the left, COMP on the right), and a hodograph (upper-left inset; units on concentric circles are knots; 1 kt = 0.51 m s−1; blue line, red line). The lifted parcel path for the parcel with maximum MUCAPE from the CNTL simulation is the black dashed line. Sounding locations are black arrows in Fig. 6. (bottom) Vertical profiles of CAPE (J kg−1) (red) and CIN (J kg−1) (green) from the CNTL simulation (solid lines) and COMP (dashed lines).

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    (a) Vertical profile of potential temperature from the CNTL simulation at the same time and location as Fig. 9 (K; solid magenta line) and the analogous profile from the composites at the same time and location as Fig. 9 ± the standard deviation of potential temperature at each level, computed over all warm-season cases (K; red dashed lines). (b) As in (a), but for water vapor mixing ratio (kg kg−1). Vertical profile of the (c) u and (d) υ wind components (m s−1; dashed black lines) from the CNTL simulation at the same time and location as (a) and (b) and the analogous profiles from the NARR for individual cases (m s−1; solid gray lines) at the location of maximum 1-h rainfall accumulation for each case.

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    CAPE from the CNTL outer domain for parcels lifted from the 850-hPa surface (J kg−1; shading), 850-hPa geopotential height (m; at intervals of 10 m; black counters;), and 850-hPa relative humidity (%; magenta dashed contours) for tsim at (a) 12, (b) 15, (c) 18, and (d) 21 h. CAPE is shown for the CNTL, rather than the NOMP, simulation to emphasize the location of the MCS relative to the supply of instability. The analogous CAPE field from the NOMP simulation was nearly identical outside the region obviously affected by the MCS.

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    Simulated composite radar reflectivity images from the CNTL run (dBZ; shading) and the 22°C 2-m surface temperature contour (black line). Simulation times for the 4-km domain are shown in the upper left of each panel.

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    (a) Total simulation accumulated precipitation for the 1.33-km domain (mm; shading). Maximum column vertical velocities at simulation hour 20 (green contours at 2, 3, and 4 m s−1) are included to illustrate the positioning of the training convective line during the life cycle of the MCS. (b) Hovmöller diagram of 1-h north–south gridpoint-averaged precipitation accumulation (mm; shading) computed over the box denoted by a dotted black line in (a).

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    Simulated composite radar reflectivity images from the simulation driven by synoptic-type composite initial and lateral boundary conditions (dBZ; shading; with an otherwise identical model configuration to the CNTL run). Simulation times for the 4-km domain are shown in the lower right of each panel. The peak 1-h rainfall in the composites occurred at simulation hour 12.

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    Quantities at the lowest model level at simulation hours 16 and 18. (a),(c) Surface temperature perturbations [T′; K (with areas of |T′| < 1 K masked in white); shading], defined as TCNTLTNOMP, maximum surface to 300-hPa vertical velocities (green contours at 1, 2, and 3 m s−1), and surface wind vectors from the CNTL run (magenta arrows). (b),(d) Surface pressure perturbations [hPa (with areas of |P′| < 0.5 hPa masked in white); shading] defined as PCNTLPNOMP, maximum surface to 300-hPa vertical velocities (green contours at 1, 2, and 3 m s−1), and surface wind perturbation vectors (magenta arrows) defined as VCNTLVNOMP.

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    As in Fig. 14, but for 1.5 km AGL.

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    As in Fig. 14, but for simulation hours 20 and 22.

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    As in Fig. 15, but for simulation hours 20 and 22.

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    As in Fig. 14, but for simulation hours 24 and 26.

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    As in Fig. 15, but for simulation hours 24 and 26.

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    (a),(b) Surface θ′ [K (with areas of |θ′| < 1 K masked in white); shading], maximum surface to 300-hPa vertical velocities (green contours at 1, 2, and 3 m s−1), and surface wind vectors from the CNTL run (black arrows) for simulation hours (a) 16 and (b) 24. (c),(d) Vertical cross sections [along the dotted magenta boxes in (top), with all quantities averaged along the zonal width of the boxes] of θ from the CNTL simulation (K; shading), θ from the NOMP simulation (gray contours; K), θ′ from the CNTL simulation (magenta dashed contour at 1 K, with values > 1 K above; and cyan dashed contour at −1 K, with values <−1 K below), OFB-orthogonal wind vectors (defined as , where Vh is the horizontal wind vector, is a horizontal unit vector orthogonal to the mean orientation of the OFB within the magenta box, w is the full vertical wind, and is the unit vector in the z direction), and vertical velocities (dotted green contours, starting at 1 m s−1 and at intervals of 1 m s−1). Valid times for cross sections in (bottom) are shown at the top of the panel. Red boxes along the bottom of each cross section correspond to the location of vertical profiles shown in Fig. 22. Wind speeds may be associated with vector lengths by comparing the lengths of vectors in green boxes to the wind speed profiles shown in Fig. 22.

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    (a),(b) Vertical profiles of the magnitude of the horizontal component of OFB-orthogonal wind (m s−1; as defined in the Fig. 18 caption; positive values are toward the cold pool) averaged over the width of the green boxes in the cross sections in Fig. 20 (blue lines), and valid at the left (green) and right (red) sides of the box (with valid times listed on top of the panels). (c),(d) Vertical profiles of box-width mean CAPE (J kg−1; blue lines), box-width mean CIN (J kg−1 × 10; green;), box-width mean Brunt–Väisälä frequency (black dashed lines; ; s−1 × 105), and Brunt–Väisälä frequency profiles valid along the box left (cyan dashed lines) and box right (red dashed lines) flanks.

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    Schematic illustrating the relevance of the concepts of Rotunno et al. (1988) and French and Parker (2010) to the MCS simulated in this study. Red shading indicates the effective inflow layer, characterized by high CAPE and low CIN, and blue shading indicates a stable boundary layer characterized by low CAPE and high CIN. Red arrows show the orientation and relative magnitude of the vertical wind shear component perpendicular to the cold pool boundary in the effective inflow layer. Black arrows represent the relative magnitudes of low-level wind vectors perpendicular to the cold pool boundary, and circular arrows indicate the sense of vorticity tendency from vertical wind shear (black) and horizontal buoyancy gradients (blue). (a) The traditional RKW theory model, where a convective system is surface based, and vertical wind shear through the effective inflow layer is favorably oriented toward warm air from cold air (red arrow). (b) The elevated cold pool–driven situation simulated by French and Parker (2010), in which shear orientation in the elevated effective inflow layer remains favorable for lifting along the cold pool boundary (akin to Fig. 21 at 16 h). (c) As in (b), but the wind shear in the effective inflow layer is now unfavorably oriented from warm air to cold air (akin to Fig. 21 at 24 h).

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The Simulated Structure and Evolution of a Quasi-Idealized Warm-Season Convective System with a Training Convective Line

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  • 1 Department of Atmospheric Science, Colorado State University, Fort Collins, Colorado
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Abstract

This study details the development and use of an idealized modeling framework to simulate a quasi-stationary heavy-rain-producing mesoscale convective system (MCS). A 36-h composite progression of atmospheric fields computed from 26 observed warm-season heavy-rain-producing training line/adjoining stratiform (TL/AS) MCSs was used as initial and lateral boundary conditions for a numerical simulation of this MCS archetype.

A realistic TL/AS MCS initiated and evolved within a simulated mesoscale environment that featured a low-level jet terminus, maximized low-level warm-air advection, and an elevated maximum in convective available potential energy. The first stage of MCS evolution featured an eastward-moving trailing-stratiform-type MCS that generated a surface cold pool. The initial system was followed by rearward off-boundary development, where a new line of convective cells simultaneously redeveloped north of the surface cold pool boundary. Backbuilding persisted on the western end of the new line, with individual convective cells training over a fixed geographic region. The final stage was characterized by a deepening and southward surge of the cold pool, accompanied by the weakening and slow southward movement of the training line. The low-level vertical wind shear profile favored kinematic lifting along the southeastern cold pool flank over the southwestern flank, potentially explaining why convection propagated with (did not propagate with) the former (latter) outflow boundaries.

The morphological features of the simulated MCS are common among observed cases and may, therefore, be generalizable. These results suggest that they are emergent from fundamental features of the large-scale environment, such as persistent regional low-level lifting, and with the vertical environmental wind profile characteristic to TL/AS systems.

Corresponding author address: John M. Peters, Department of Atmospheric Science, Colorado State University, 200 West Lake Street, 1371 Campus Delivery, Fort Collins, CO 80523-1371. E-mail: jpeters3@atmos.colostate.edu

Abstract

This study details the development and use of an idealized modeling framework to simulate a quasi-stationary heavy-rain-producing mesoscale convective system (MCS). A 36-h composite progression of atmospheric fields computed from 26 observed warm-season heavy-rain-producing training line/adjoining stratiform (TL/AS) MCSs was used as initial and lateral boundary conditions for a numerical simulation of this MCS archetype.

A realistic TL/AS MCS initiated and evolved within a simulated mesoscale environment that featured a low-level jet terminus, maximized low-level warm-air advection, and an elevated maximum in convective available potential energy. The first stage of MCS evolution featured an eastward-moving trailing-stratiform-type MCS that generated a surface cold pool. The initial system was followed by rearward off-boundary development, where a new line of convective cells simultaneously redeveloped north of the surface cold pool boundary. Backbuilding persisted on the western end of the new line, with individual convective cells training over a fixed geographic region. The final stage was characterized by a deepening and southward surge of the cold pool, accompanied by the weakening and slow southward movement of the training line. The low-level vertical wind shear profile favored kinematic lifting along the southeastern cold pool flank over the southwestern flank, potentially explaining why convection propagated with (did not propagate with) the former (latter) outflow boundaries.

The morphological features of the simulated MCS are common among observed cases and may, therefore, be generalizable. These results suggest that they are emergent from fundamental features of the large-scale environment, such as persistent regional low-level lifting, and with the vertical environmental wind profile characteristic to TL/AS systems.

Corresponding author address: John M. Peters, Department of Atmospheric Science, Colorado State University, 200 West Lake Street, 1371 Campus Delivery, Fort Collins, CO 80523-1371. E-mail: jpeters3@atmos.colostate.edu

1. Introduction

It has been well established in previous literature that the primary mechanism for heavy rainfall generation in mesoscale convective systems (MCS) involves the continuous motion of individual convective elements within the larger convective system over a fixed geographic region (Chappell 1986; Corfidi et al. 1996; Doswell et al. 1996; Schumacher and Johnson 2005, 2006, hereafter SJ2005, 2006, hereafter SJ2006, 2008; Schumacher 2009; Peters and Schumacher 2014, hereafter PS2014). Two processes—training and backbuilding of convection—are often at work during such MCS behavior. Training involves a convective line comprised of smaller convective-scale updrafts that move in a line-parallel direction, resulting in their repeated motion over a fixed geographic region [often associated with the training line/adjoining stratiform (TL/AS; SJ2005) MCS archetype]. Backbuilding involves the repeated upstream (downstream) redevelopment (decay) of convective updrafts, resulting in a near-zero net motion of the larger convective system that they compose (often associated with the backbuilding (BB; SJ2005) MCS archetype). Note that while the TL/AS and BB MCSs represent the primary archetypes that exhibit these behaviors, they sometimes occur in other MCS types as well [such as the parallel stratiform and leading stratiform archetypes described by Parker and Johnson (2000)].

While these mechanisms for heavy rainfall production occur on relatively small spatial scales (of order 10–100 km), the convective systems that exhibit these behaviors typically occur in conjunction with specific meso-α-to-synoptic-scale (>200 km) phenomena, such as locally maximized low-level warm-air advection (WAA) and convergence along the nose of a low-level jet, a supply of low-level convective available potential energy (CAPE; air with CAPE is herein referred to as “potentially buoyant”), low-level frontal circulations, and upper-level jet streaks (Maddox et al. 1979; Crook and Moncrieff 1988; Augustine and Caracena 1994; Moore et al. 2003; SJ2005; SJ2006; PS2014). The common concurrence of training and backbuilding MCSs with such external forcing for ascent suggest that their existence depends on such processes.

The traditional idealized modeling approach for investigating the dynamics of mesoscale convective processes (such as system propagation) has often involved the simulation of isolated convective systems within an otherwise horizontally homogeneous thermodynamic and kinematic environment (e.g., Weisman and Klemp 1984; Rotunno et al. 1988; Fovell and Dailey 1995; Fovell and Tan 1998; Parker and Johnson 2004a,b). Although such simulations are ideal for isolating specific convective processes, since their signatures easily stand out within an otherwise pristine and noise-free surrounding environment, the simulation framework prohibits the inclusion of large-scale thermodynamic and kinematic horizontal gradients and circulations that are important to particular types of MCSs (such as those that exhibit training and backbuilding behaviors). A more sophisticated idealized modeling approach is therefore required for the generation of a meaningful idealized simulation of training/backbuilding MCSs (while retaining the benefits of traditional idealized simulations).

Several novel methodologies for the inclusion of horizontally inhomogeneous features into idealized environments have been utilized in recent literature. Crook and Moncrieff (1988) and Schumacher (2009) applied forced low-level convergence into an otherwise horizontally homogeneous environment to simulate the effects of large-scale forced ascent. Mahoney et al. (2009) artificially constructed a zonal jet and associated baroclinic zone by varying the meridional tropospheric temperature (and thus the meridional pressure and wind fields by the assumption of thermal wind balance), while retaining zonal homogeneity. These authors successfully simulated a realistic trailing-stratiform-type MCS (TS; e.g., Houze et al. 1989, 1990; Parker and Johnson 2000) in order to ascertain the role of vertical momentum transport in rear-inflow jet generation and cold pool behavior. In an earlier study, Coniglio and Stensrud (2001) simulated a progressive TS-type MCS by constructing a large-scale environment from composite atmospheric fields that were generated from averaging over several observed cases. While both strategies were effective in simulating their intended MCS archetype in a realistic manner, the Coniglio and Stensrud (2001) composite strategy is an ideal starting point for the simulation of training/backbuilding MCSs, since the strategy used by these authors retained both zonal and meridional inhomogeneity, which is required for the presence of structures such as the low-level jet terminus and upper-level jet streaks.

The primary goal of this study is to outline the construction of a model framework that was used to simulate a warm-season-type (see PS2014) TL/AS MCS from atmospheric fields composited over observed cases, with the primary hypothesis being that the basic dynamics of upwind propagation and heavy rainfall production are generalizable among individual events. While the analysis of the simulated system here will focus on the precipitation, thermodynamic, and kinematic anomalies produced by the system, future articles will analyze the dynamics of the simulated MCS discussed in this article. The organization of this paper is as follows: section 2 briefly reviews the compositing procedure of PS2014 and describes the numerical modeling configuration; section 3 documents the evolution of the simulated convective system; and section 4 provides an article summary and concluding remarks and outlines several hypotheses that will be tested in future studies.

2. Experiment design

a. Case selection and composite construction

PS2014 applied rotated principal component analysis (RPCA) to the atmospheric fields associated with a large group of TL/AS events (50 cases subjectively identified as such based on their radar methodology) and found two distinct modes of synoptic organization [see Mercer et al. (2012) for the application of RPCA in a similar context]. These two modes, referred to as “synoptic type” events (24 cases) and “warm season”-type events (26 cases), exhibited considerable differences in their moisture, kinematic, and thermodynamic fields despite similarities in their radar-indicated morphology and evolution. Warm-season events (Fig. 1) were contrasted with synoptic-type events for their typical occurrence during the summer months (with synoptic-type events predominantly occurring during the transition seasons), their association with weaker synoptic-scale forcing for ascent and deep-layer wind shear than synoptic-type events, and their propensity to exhibit both upstream backbuilding and training of convective radar echoes over fixed geographic regions. Additionally, the evolution of warm-season events frequently featured quasi-discrete upstream propagation events characterized by the rearward off-boundary development (ROD) phenomenon (PS2014; Peters and Schumacher 2015; discussed in greater detail later in this section) and sometimes the more specific bow-and-arrow effect (Keene and Schumacher 2013): both phenomena are characterized by the simultaneous development of a convective line to the rear of a progressive MCS and north of the outflow boundary (OFB) left by the initial system.

Fig. 1.
Fig. 1.

Representative composite radar reflectivity images from three heavy-rain-producing warm-season TL/AS MCSs (each row constitutes a separate event). Valid dates and times are in the lower-right corner of each panel. From PS2014. The 28 Jul 2011 case was studied in detail by Peters and Schumacher (2015).

Citation: Journal of the Atmospheric Sciences 72, 5; 10.1175/JAS-D-14-0215.1

Since we are interested in elucidating dynamical mechanisms for such upstream propagation behaviors, this analysis will focus on an idealized simulation of the warm-season-type TL/AS events (simulations and dynamical analyses of synoptic-type events will be described in future articles). A brief overview of the composite fields from warm-season events is provided here, and additional details regarding the methods of their computation and structure can be found in PS2014. Using the North American Regional Reanalysis (NARR; Mesinger et al. 2006), composite atmospheric progressions were spatially centered at the location of the maximum 1-h precipitation accumulation in the stage IV (ST4) precipitation analysis (Lin and Mitchell 2005) and temporally centered at the time of the maximum 1-h accumulation.

Selected composite fields on the 300-hPa isobaric surface are shown for warm-season events in Fig. 2. They typically occurred within the right entrance region to an anticyclonically curved upper-level jet streak (this upper-level jet configuration is common in the summer months over the eastern United States). At 850 hPa (Fig. 3), a broad axis of warm air typically extended to the south, southwest, and west of the event location, with the event having occurred within a meridionally oriented temperature gradient (typically a quasi-stationary or warm front). The heaviest rainfall was typically produced along the northern nose of a southwesterly low-level jet, within a region of locally maximized low-level convergence and WAA.

Fig. 2.
Fig. 2.

An 18-h event-centered composite progression from 26 warm-season events of 300-hPa wind speed (m s−1; shading), wind vectors (arrows), and geopotential height (black lines at intervals of 50 m) from (a) 6 h prior, (b) the time of, (c) 6 h after, and (d) 12 h after peak 1-h rainfall accumulation was observed at the event location. A black circle at the center of each panel indicates the point location of maximum 1-h rainfall accumulation. The specific latitudes and longitudes shown are arbitrarily selected to illustrate the spatial scale. From PS2014.

Citation: Journal of the Atmospheric Sciences 72, 5; 10.1175/JAS-D-14-0215.1

Fig. 3.
Fig. 3.

An 18-h progression from warm-season events of 850-hPa potential temperature advection (shading) (×10−5 K s−1; values below 2 × 10−5 K s−1 have been removed; derivatives were computed from composite atmospheric fields), wind speed (blue dashed contours at intervals of 2 m s−1, starting at 8 m s−1), wind vectors (black arrows), geopotential height (black lines at intervals of 20 m), and potential temperature (K; dashed gray contours). Panel times are the same as those in Figs. 1 and 2. A solid black circle at the center of each panel indicates the point location of maximum 1-h rainfall accumulation. The specific latitudes and longitudes shown are arbitrarily selected to illustrate the spatial scale. Adapted from PS2014.

Citation: Journal of the Atmospheric Sciences 72, 5; 10.1175/JAS-D-14-0215.1

The advantage of the consideration of composite atmospheric fields from the statistically sorted methodology of PS2014 to the analogous composite fields computed over all cases is illustrated when comparing the standard deviation of representative atmospheric fields at each grid point within our domain for the 26 warm-season cases to that for all 50 cases (Fig. 4):
e1
where f is any arbitrary atmospheric field, n is the number of cases considered in the computation, t is the time removed from peak stage IV 1-h rainfall, and ci is a case number (see PS2014, where this quantity is introduced in greater detail). Note that standard deviation values—especially near the event location and along the low-level jet—are considerably lower when computed over the 26 warm-season cases only than when computed over all 50 cases. This indicates less variability in the placement of atmospheric structures relative to the event location among warm-season cases than among all cases.
Fig. 4.
Fig. 4.

Plots of the standard deviation [σ; see Eq. (1) in the text] of 850-hPa wind speed for (a) 26 warm-season events (m s−1; shading) and (b) 50 training convective events containing both warm-season- and synoptic-type (m s−1; shading) events; the standard deviation of temperature for (c) warm-season (K; shading) and (d) all events (K; shading). Geopotential height (m, at intervals of 40 m; solid black contours), wind vectors (black arrows), and wind speed (m s−1 starting at 8 m s−1 and at intervals of 2 m s−1; blue dotted contours) are shown in all panels. All panels are valid at the time of maximum 1-h rainfall accumulation from stage IV precipitation analysis (see PS2014). A black circle at the center of each frame indicates the point location of maximum 1-h rainfall accumulation. The specific latitudes and longitudes shown are arbitrarily selected to illustrate the spatial scale. Adapted from PS2014.

Citation: Journal of the Atmospheric Sciences 72, 5; 10.1175/JAS-D-14-0215.1

b. Control (CNTL) simulation

The numerical simulations in this study were conducted with version 3.4.1 of the Advanced Research Weather Research and Forecasting (WRF) Model (ARW; Klemp et al. 2007; Skamarock et al. 2008). Composites of temperature, geopotential height, specific humidity, and u and υ wind components were horizontally interpolated onto the model domain on the 1000-, 950-, 900-, 850-, 800-, 750-, 700-, 600-, 500-, 400-, 300-, 250-, 200-, and 150-hPa isobaric surfaces. No terrain variation was included, with the surface geopotential height set to 0 m. Surface values for the aforementioned quantities were linearly interpolated to the surface based on their values and geopotential heights on adjacent pressure surfaces. These data were then input into the ARW real data preprocessor [which vertically interpolates data onto the model vertical levels and hydrostatically balances the initial and lateral boundary conditions (Skamarock et al. 2008)].

All simulations were configured in “real” mode [contrasted with the “ideal” mode; see Skamarock et al. (2008)]. Several preliminary runs were conducted on a 4-km grid at differing start times relative to the 1-h peak rainfall time in the composites (e.g., start times of 18, 15, and 12 h prior to peak rainfall to allow for more or less spin-up time) and with different approaches to dealing with model physics (e.g., the choice over whether to use a land surface model) in order to 1) determine whether an MCS would develop at all and 2) determine the model configuration that best reproduced a realistic MCS (i.e., exhibiting characteristics that subjectively resembled observed TL/AS cases). Once this configuration was achieved, the simulation was rerun with the addition of a 1.33-km inner nest initialized 2 h prior to the first observed convection in the 4-km domain and centered at the location of the MCS (see the previous subsection for the inner domain position). The final simulation was run at 4 km from 15 h prior to 15 h after peak rainfall time in the composites and at 1.33 km from 5 h prior to 15 h after peak rainfall (see Table 1). Note that while the inner domain was initialized after the outer domain, we will hereby refer to simulation times on the inner domain in terms of their time elapsed from the start of the 4-km domain. The configuration featured a one-way feedback nested structure with the outer domain having dimensions of 2712 km × 2712 km, the inner domain having dimensions of 1000 km × 800 km, and the lower-left corner of the inner domain positioned at grid point (300, 300) in the outer domain. The outer domain was assigned an arbitrary center latitude of 40°N and a center longitude of 88°W.

Table 1.

Comparison of the timetable of the composite evolution (in terms of time removed from peak 1-h rainfall observed in ST4 precipitation) and outer-domain and inner-domain simulations (in terms of elapsed time from the simulation start).

Table 1.

Though the observed events used to construct composites typically occurred during the early morning hours (PS2014), there was considerable spread among the exact times of the 1-h peak rainfall. Despite this, the evolutions of the low-level stability profile and horizontal pressure gradient at the location of the low-level jet maximum (Fig. 5) show signatures of a diurnal low-level jet intensity cycle, with the temporal low-level jet maxima coincident with the maximum low-level stability (and not perfectly correlated with the low-level horizontal pressure gradient). Surface–atmosphere heat fluxes in preliminary simulations produced spurious near-surface temperature fluctuations, and it was unclear where to align our composite progression within the diurnal radiative cycle. Land–atmosphere fluxes were therefore turned off in our final modeling configuration, resulting in a nearly perpetually stable boundary layer (characteristic of a nocturnal environment) through the course of our simulation (discussed in greater detail in the next subsection). Surface friction was minimized by treating the lower boundary in land-use and surface characteristic categories as that of water (while keeping the land surface flag set to that of land).

Fig. 5.
Fig. 5.

(top) Time–height diagram of the vertical profile of static stability (; K m−1; shading) below the maximum point wind speed value at 850 hPa in the composite progression. (bottom) Time series of the maximum 850-hPa wind speed (red line) and the magnitude of the horizontal geopotential height gradient on the 850-hPa isobaric surface (blue line) in the composite progression.

Citation: Journal of the Atmospheric Sciences 72, 5; 10.1175/JAS-D-14-0215.1

While certain attributes of the simulation configuration here may seem rather arbitrary (e.g., the positioning/size of the inner/outer domains and the choice to turn off land/surface fluxes), the environment associated with the simulated MCS exhibited considerable qualitative similarities to that commonly observed in TL/AS events (as will be discussed later), and we therefore justify the modeling configuration a posteriori given the success of our simulation at producing a realistic MCS within an environment consistent with those observed to support such systems. Certainly other domain sizes, resolutions, and positioning may have yielded equally successful results.

The grid spacing of both domains was sufficiently small to explicitly represent convective processes [although insufficiently small to properly resolve individual convective updrafts (Bryan et al. 2003)], and no cumulus parameterization was used in either domain. Table 2 lists the other model parameters and physics options used in all of the modeling experiments described here.

Table 2.

List of ARW grid resolutions, grid dimensions, physical parameterizations, and nudging configurations used in this study.

Table 2.

The nonlinear relationship between many of the aforementioned quantities over which linear averaging was conducted posed a significant obstacle to conducting simulations from the composite atmospheric fields. For instance, the choice between compositing over specific humidity or relative humidity was not entirely obvious, and the two choices do not yield equivalent results, owing to the nonlinear Clausius–Clapeyron relationship. Likewise, there was no guarantee that the composited atmospheric fields retained their dynamical balances (e.g., gradient wind balance, hydrostatic balance) that are typically characteristic of the synoptic-scale atmosphere (though the WRF real data processor “rebalances” these fields, there was no guarantee that the resulting balanced atmospheric state would emulate states from observed cases sufficiently to produce a realistic simulation). Finally, it was clear that the model solution on the model domain would diverge from the composited atmospheric state as the simulation time increases, though such deviations may be partially constrained by the continuous passage of information into the model lateral boundaries. It was therefore important to comprehensively assess the degree to which such deviations caused the simulated environment to deviate from an environment that is characteristic of the events we aimed to simulate.

All simulations that were conducted from raw composite fields resulted in substantially delayed convection initiation (CIN), with timing approaching the end of the simulation. Model simulations often exhibit unrealistically suppressed convection when they are initialized from observed or composite soundings with any convective inhibition (e.g., Parker and Johnson 2004c; Naylor and Gilmore 2012), and a common solution is to slightly increase relative humidity at low levels. Here, the initial relative humidity was increased in accordance with the following formula, which allowed for more realistic CIN timing in the simulations:
e2
where RHm is the modified relative humidity, RHi is the relative humidity value from the composite data, A is the amplitude of the added perturbation (set to 10%), p is pressure (hPa), pref is the pressure level of the maximum added perturbation (900 hPa), the σ parameter (set to 50 hPa) controls the rate of amplitude decrease as the vertical distance from pref increases, and pcutoff (400 hPa) is the maximum vertical distance (hPa) from pref within which the relative humidity was modified. The relative humidity perturbation in Eq. (2) was added uniformly (i.e., no variation in x and y) across all points within the composite analyses prior to them having been interpolated onto the model domain and processed by the WRF real data processor (all simulations analyzed here featured this added perturbation).

c. No microphysics simulation

We ran a second simulation by restarting WRF 1 h before the first convective updrafts associated with the simulated MCS were observed in the CNTL simulation with the microphysics scheme turned off (all other configuration attributes were the same as the CNTL simulation for this second run). The purpose of this simulation was to assess the similarity between the simulated environment and that of the composites and later to define convective perturbation fields. We hereby refer to this simulation as the no microphysics run (NOMP). Herein, the time removed from peak rainfall in the composites will be referred to as tcomp, and the time removed from the start of the simulations will be referred to as tsim. We reiterate that at tsim = 15 h, composite atmospheric fields from tcomp = 0 h are provided as lateral boundary conditions. Table 1 further facilitates the comparison between tcomp and tsim.

It is worth noting that unrealistic phenomena may arise when simulating an atmosphere where large regions of supersaturation are achieved (such as the region where the MCS developed in the CNTL simulation) and the effects of latent heating are neglected. For instance, regions of combined supersaturation and lift may become unrealistically cool because of adiabatic cooling of ascending parcels without latent heating to compensate for such cooling. If sufficient unrealistic cooling occurred, a corresponding low-level high-pressure anomaly would be expected in the NOMP simulation, which would contaminate the perturbation pressure fields analyzed in subsequent sections. We thoroughly examined temperature and pressure fields in the NOMP simulation (not shown) and found no evidence of such unrealistic anomalies, which suggests that vertical velocities (and adiabatic cooling) in the NOMP simulation were insufficiently strong to produce such unrealistic effects. Furthermore, the patterns and magnitudes of perturbations in later sections are comparable to those commonly observed in simulations and observations of MCSs, and we therefore assume that they (perturbation fields) are dominated by the influence of deep convection associated with the MCS simulated here.

A representative comparison of the atmospheric fields in the NOMP solution to the analogous fields in the composites is shown in Fig. 6. The low-level jet maximum in the simulation was displaced considerably farther northward in relation to the composites and exhibited a peak in wind speed 3–6 h after the analogous wind speed maxima in the composites. The upper-level flow was also slightly stronger, and the low-level flow slightly weaker in the simulation. While the horizontal temperature distributions were qualitatively similar between the simulation and composites, the nose of the low-level jet was displaced northward in the simulation at its peak intensity (cf. Fig. 6d to Fig. 6a), resulting in a northward displacement of the maximum simulated WAA. Although it is difficult to disentangle the various potential contributions to such differences between the model solution and composite progression, it is likely that the highly nonlinear nature of the advective component of the governing equations contributed significantly to such differences (i.e., the average of the instantaneous contributions to the time tendency of variables resulting from advection over many cases differed from the advection of the mean values of quantities by the mean wind once the composite initial and lateral boundary conditions began evolving in the simulation).

Fig. 6.
Fig. 6.

Comparison of the (a),(b) synoptic-scale environments in the warm-season composites used as ICs and LBCs for WRF simulations to the (c),(d) synoptic-scale solution on the 4-km NOMP domain, valid (left) at and (right) 9 h after the time of heaviest 1-h rainfall accumulation in the composites (note that the corresponding simulation times are also included). Red arrows are 300-hPa wind vectors; dotted red contours are 300-hPa wind speeds (m s−1) at intervals of 2 m s−1, starting at 13 m s−1; blue arrows are 850-hPa wind vectors, and blue dotted contours are 850-hPa wind speeds (m s−1) at intervals of 2 m s−1, starting at 7 m s−1; magenta dotted contours are 850-hPa wind speed (K) at intervals of 1 K. Green circles and black arrows indicate the location of the vertical profiles shown in Fig. 9.

Citation: Journal of the Atmospheric Sciences 72, 5; 10.1175/JAS-D-14-0215.1

As noted by various past studies (e.g., Maddox et al. 1979; Doswell et al.1996; Moore et al. 2003; SJ2005; PS2014), persistent low-level lifting associated with low-level WAA and convergence along the nose of a low-level jet is often characteristic of the environment of heavy-rain-producing MCSs. In the composite progression used to drive our simulations, the intensity of low-level WAA had begun to subside between tcomp = 3 and 6 h (see Fig. 13 in PS2014). Figure 7 reveals that, while WAA intensity in the composite progression had decreased considerably by tcomp = 6 h relative to tcomp = 0 h, WAA remained intense through this timeframe in the simulation (tsim = 18–26 h) at the location of the MCS, resulting in a persistent region of saturation at 850 hPa. As will be discussed in greater detail in later sections, the MCS in the CNTL simulation reached a subjectively determined maturity approximately 6 h after peak rainfall in the composites (tsim = 21 h).

Fig. 7.
Fig. 7.

As in Fig. 6, but here 850-hPa WAA (K s−1; shading), 850-hPa wind vectors (m s−1; blue arrows), 850-hPa wind speed (m s−1; at intervals of 2 m s−1, starting at 7 m s−1; dashed blue contours), 850-hPa geopotential height (m; black solid contours), 850-hPa temperature (K; dashed magenta contours), and 850-hPa relative humidity (%; solid green contours) are shown to facilitate the comparison of synoptic-scale forcing for ascent between the composites and simulation.

Citation: Journal of the Atmospheric Sciences 72, 5; 10.1175/JAS-D-14-0215.1

A comparison between Fig. 8 and Fig. 5 suggests that the diurnal low-level jet intensity cycle evident in the composites was not present in the simulation. In fact, two distinct low-level jet maxima are evident in Fig. 8: one at simulation tsim = 7 h, and another at roughly simulation tsim = 26 h (the second maxima occurred during the lifetime of the MCS and may be correlated with the magnitude of the horizontal pressure gradient during this timeframe). There is little evidence in the low-level static stability field of a diurnal stability cycle, with the major temporal changes in the top panel having occurred near the beginning of the simulation (likely related to model spinup). These differences in the low-level jet character between the simulation and composites were likely a result of the combination of a missing diurnal heating cycle in the planetary boundary layer, along with the absence of terrain [both of these factors strongly regulate the plains low-level jet intensity (Du and Rotunno 2014)].

Fig. 8.
Fig. 8.

As in Fig. 5, but for the NOMP simulation. Here, the maximum wind speed value at 1.25 km AGL has been assessed rather than the maximum wind speed at 850 hPa. (bottom) The blue line subsequently depicts a time series of the horizontal pressure gradient (Pa m−1 × 2) at the location of the maximum 1.25-km-AGL wind speed rather than the horizontal geopotential height gradient on an isobaric surface. The location of the maximum wind speed at this level varied considerably with time; therefore, (top) the stability profile was assessed at the sounding location indicated in Fig. 7d.

Citation: Journal of the Atmospheric Sciences 72, 5; 10.1175/JAS-D-14-0215.1

The delayed low-level jet intensity maximum in the simulation relative to the composite progression and persistent intense WAA in the MCS region in the simulation beyond the timeframe were therefore advantageous outcomes, since they resulted in the simulated MCS environment remaining suitably analogous to the timeframe where the MCSs occurred in the composites. Further comparisons will therefore focus on the simulated environment at the northern periphery of the low-level jet in the CNTL simulation at tsim = 21 h (which was a representative example of the low-level inflow region to the simulated MCS) and along the northern periphery of the low-level in the composites at tcomp = 0 h (the time of peak MCS intensity in the observed cases).

Vertical temperature and moisture profiles from the aforementioned locations and times are shown in Fig. 9. Interestingly, the composite sounding lacks a discernible stable layer near the surface and exhibits maximum CAPE values at the lowest analysis level (all the cases used to construct the composite were characterized by most unstable CAPE rooted in an elevated layer; PS2014) and convective inhibition through all potentially buoyant layers. While this is a curious attribute, given the nature of the cases used in composite construction, it is potentially an artifact of differing topographic heights between cases (and reanalysis data being interpolated onto subsurface isobaric levels for some cases) and/or differing depths of the near-surface stable layer. The model sounding, however, does exhibit a stable layer near the surface (which may have been reintroduced during the dynamical balancing conducted by the WRF real data processor and maintained by the lack of fluxes from surface to atmosphere), as well as a maximum (minimum) in CAPE (convective inhibition) above the surface (between 900 and 800 hPa). The shapes of the vertical wind profiles (Fig. 9 hodograph) were qualitatively similar between the simulation and composite times and locations [cf. to SJ2005, where winds were slightly stronger, presumably because of their composite pool containing both warm-season- and synoptic-type events].

Fig. 9.
Fig. 9.

(top) Skew T–logp diagram depicting vertical profiles [composite (COMP) at the time of peak 1-h rainfall, CNTL outer domain 6 h after peak rainfall] of temperature (red solid line, red dashed line), dewpoint (green solid line, green dashed line), wind barbs (CNTL on the left, COMP on the right), and a hodograph (upper-left inset; units on concentric circles are knots; 1 kt = 0.51 m s−1; blue line, red line). The lifted parcel path for the parcel with maximum MUCAPE from the CNTL simulation is the black dashed line. Sounding locations are black arrows in Fig. 6. (bottom) Vertical profiles of CAPE (J kg−1) (red) and CIN (J kg−1) (green) from the CNTL simulation (solid lines) and COMP (dashed lines).

Citation: Journal of the Atmospheric Sciences 72, 5; 10.1175/JAS-D-14-0215.1

The simulated temperature profile resides near the cold periphery of the range of values among composited cases above 2 km (Fig. 10a), whereas the simulated moisture profile resides near/beyond the upper end of the moisture range between 1 and 2 km and gradually approaches the dry edge of this range by 5 km AGL [Fig. 10b; note that the simulated moisture profile contains the added moisture from Eq. (2)]. Differences in the former comparison are a result of the simulated profile we are examining being farther north (and slightly cooler) than the composite profile, and differences in the later comparison predominantly arise from our addition of low-level moisture in the simulation initial conditions (ICs) and lateral boundary conditions (LBCs). The u and υ velocity profiles (Figs. 10c,d) fall well within the range of composited cases. A spike in wind speed values below 500 m is evident in the simulated profiles of both wind components (Figs. 10c,d). Curiously, no analogous feature was present in the composited wind profiles (Figs. 10c,d). We examined observed soundings within the inflow region of warm-season cases and found similar features in nearly half of the observed cases (not shown); the absence of this feature in the composited profiles is likely due to the low vertical resolution of the isobaric NARR data used in this study.

Fig. 10.
Fig. 10.

(a) Vertical profile of potential temperature from the CNTL simulation at the same time and location as Fig. 9 (K; solid magenta line) and the analogous profile from the composites at the same time and location as Fig. 9 ± the standard deviation of potential temperature at each level, computed over all warm-season cases (K; red dashed lines). (b) As in (a), but for water vapor mixing ratio (kg kg−1). Vertical profile of the (c) u and (d) υ wind components (m s−1; dashed black lines) from the CNTL simulation at the same time and location as (a) and (b) and the analogous profiles from the NARR for individual cases (m s−1; solid gray lines) at the location of maximum 1-h rainfall accumulation for each case.

Citation: Journal of the Atmospheric Sciences 72, 5; 10.1175/JAS-D-14-0215.1

The modeled CAPE profile in Fig. 9 exhibits considerable qualitative similarities to the vertical equivalent potential temperature θe (which is often spatially correlated with CAPE) composite profile shown in Fig. 13b from Moore et al. (2003) for elevated heavy-rain-producing MCSs. The horizontal distribution of low-level CAPE (Fig. 11) was characterized by a plume of maximized CAPE extending along the low-level jet to the southwest flank of the MCS (the location of which is noted in Fig. 11) throughout the evolution of the simulated MCS. Persistent low-level transport of such potentially buoyant parcels into the southwest flank of the MCS, along with low-level lifting associated with low-level WAA maintained the three required ingredients for convection throughout the MCS lifetime (i.e., moisture, instability, and lift).

Fig. 11.
Fig. 11.

CAPE from the CNTL outer domain for parcels lifted from the 850-hPa surface (J kg−1; shading), 850-hPa geopotential height (m; at intervals of 10 m; black counters;), and 850-hPa relative humidity (%; magenta dashed contours) for tsim at (a) 12, (b) 15, (c) 18, and (d) 21 h. CAPE is shown for the CNTL, rather than the NOMP, simulation to emphasize the location of the MCS relative to the supply of instability. The analogous CAPE field from the NOMP simulation was nearly identical outside the region obviously affected by the MCS.

Citation: Journal of the Atmospheric Sciences 72, 5; 10.1175/JAS-D-14-0215.1

3. Evolution of precipitation and thermodynamic characteristics of the simulated MCS

In this section, we detail characteristics of the life cycle of the MCS that developed within the CNTL simulation. The three major stages of the life cycle of the system are then identified, and the perturbation temperature, pressure, and wind field are analyzed at the surface and on the 1.5-km-AGL height surface for each stage of evolution. Perturbation fields (denoted by primes) are herein defined as the grid point difference between the value of a particular field in the CNTL solution and the value of that field in the NOMP solution at the identical valid time. These (perturbation) fields are defined in such a way so as to highlight the changes to the environment that are exclusively a result of convective processes.

The first deep convective features developed between tsim = 11 and 12 h on the 1.33-km domain, consisting of an approximately 150-km × 150-km region of scattered convective cells along the terminus of the simulated low-level jet (not shown). By tsim = 14 h, these cells had intensified and organized upscale into an east-southeastward-moving MCS (Fig. 12a). By tsim = 18 h (Fig. 12c), new convection had begun to organize upstream (west-northwest) of the initial progressive MCS and north of the OFB left by the initial system; this is an example of ROD. Geographically fixed upstream backbuilding ensued between tsim = 18 and 24 h, with convective echoes training to the east-southeast of the region of upstream backbuilding toward the rear of the remnants of the initial progressive convective system (Figs. 12c–f). Convection gradually weakened and moved southward beyond the times shown in Fig. 12. Note the visual similarity between the evolutions of the convective system depicted in Fig. 12 to the observed cases in Fig. 1, with all three of the observed cases having exhibited similar initial progressive MCS passages and subsequent ROD, training, and geographically fixed upstream backbuilding (though, as shown by PS2014, not all warm-season cases exhibited ROD). Maximum total simulation accumulated precipitation values for the inner domain solution were greater than 250 mm (Fig. 13), which is comparable to many observed events that produced flash floods [308 mm from the 7 May 2000 eastern Missouri event (Schumacher and Johnson 2008); 333 mm from the 28 July 2011 eastern Iowa event Peters and Schumacher (2015)]. The Hovmöller diagram in Fig. 13b summarizes the convective evolution of the simulated MCS, with the initial progressive MCS evident as a diagonal swath of enhanced precipitation between 14 and 20 h (noted in Fig. 13b), and the training line evident as a vertically oriented swath of precipitation between 20 and 28 h (also noted in Fig. 12b).

Fig. 12.
Fig. 12.

Simulated composite radar reflectivity images from the CNTL run (dBZ; shading) and the 22°C 2-m surface temperature contour (black line). Simulation times for the 4-km domain are shown in the upper left of each panel.

Citation: Journal of the Atmospheric Sciences 72, 5; 10.1175/JAS-D-14-0215.1

Fig. 13.
Fig. 13.

(a) Total simulation accumulated precipitation for the 1.33-km domain (mm; shading). Maximum column vertical velocities at simulation hour 20 (green contours at 2, 3, and 4 m s−1) are included to illustrate the positioning of the training convective line during the life cycle of the MCS. (b) Hovmöller diagram of 1-h north–south gridpoint-averaged precipitation accumulation (mm; shading) computed over the box denoted by a dotted black line in (a).

Citation: Journal of the Atmospheric Sciences 72, 5; 10.1175/JAS-D-14-0215.1

The convective evolution in an analogous simulation driven by synoptic-type composites (Fig. 14) was markedly different from the warm-season-type composite-driven simulation (Fig. 12). In the synoptic-subtype simulation, an MCS with southeast–northwest-oriented convective line, and a higher along-line–across-line axis ratio than the warm-season-type MCSs, moved in a predominantly convective line-parallel direction for over 6 h, producing a broad swath of rainfall totals in excess of 150 mm. While the results of the synoptic-type simulation are not discussed in detail here, it is noteworthy that the primary mechanism for heavy rainfall production in that simulation appears to have been convective line-parallel MCS motion combined with a very long convective line, whereas the warm-season-type MCS encompassed a comparatively smaller geographic region but featured continuous upstream backbuilding: results that are consistent with behavior observed in radar imagery and deduced from analysis of Corfidi vectors (see Corfidi et al. 1996) in PS2014. We analyze temperature, pressure, and wind perturbation fields associated with the warm-season simulation in the following subsections.

Fig. 14.
Fig. 14.

Simulated composite radar reflectivity images from the simulation driven by synoptic-type composite initial and lateral boundary conditions (dBZ; shading; with an otherwise identical model configuration to the CNTL run). Simulation times for the 4-km domain are shown in the lower right of each panel. The peak 1-h rainfall in the composites occurred at simulation hour 12.

Citation: Journal of the Atmospheric Sciences 72, 5; 10.1175/JAS-D-14-0215.1

a. Initial nonstationary convection

The first 6 h (tsim = 12–18 h) of active simulated convection were characterized by a TS-type east-southeastward-moving MCS that exhibited similar radar reflectivity characteristics to those identified in various previous studies of forward-propagating squall lines (e.g., Parker and Johnson 2000; Coniglio and Stensrud 2001; Mahoney et al. 2009).

Despite the system having developed within an environment characterized by a stable boundary layer (see the vertical CAPE profile in Fig. 9), a well-defined surface cold pool (Figs. 15a,c) was evident beneath and to the rear of the forward-moving MCS, with minimum surface temperature perturbations of −5 K near the forward convective flank. The southeastern flank of the cold pool progressed eastward between tsim = 16 and 18 h (Figs. 15a,b), while the southwestern flank remained roughly stationary [the implications of this behavior with respect to MCS motion are further discussed in Corfidi (2003)]. This is potentially explained by a significant OFB-perpendicular flow component within the cold pool and along the southeastern flank (evident within the full wind field), contrasted with a comparatively smaller OFB-perpendicular flow component within the cold pool and along the southwestern flank. Again, despite the preexisting (prior to the cold pool generation) stable boundary layer, the perturbation pressure structure at the surface consisted of locally higher pressure within the cold pool relative to surroundings and subsequent perturbation flow diverging in all directions from the center of the cold pool (Figs. 15c,d). The magnitude of cold-pool mesohigh-pressure perturbations shown here are small relative to some MCSs that have been documented in previous literature (e.g., Bryan and Parker 2010; Marsham et al. 2011). This is likely a result of the system here producing a comparatively shallow cold pool (see section 3d, where the depth is shown to be generally 750–1000 m).

Fig. 15.
Fig. 15.

Quantities at the lowest model level at simulation hours 16 and 18. (a),(c) Surface temperature perturbations [T′; K (with areas of |T′| < 1 K masked in white); shading], defined as TCNTLTNOMP, maximum surface to 300-hPa vertical velocities (green contours at 1, 2, and 3 m s−1), and surface wind vectors from the CNTL run (magenta arrows). (b),(d) Surface pressure perturbations [hPa (with areas of |P′| < 0.5 hPa masked in white); shading] defined as PCNTLPNOMP, maximum surface to 300-hPa vertical velocities (green contours at 1, 2, and 3 m s−1), and surface wind perturbation vectors (magenta arrows) defined as VCNTLVNOMP.

Citation: Journal of the Atmospheric Sciences 72, 5; 10.1175/JAS-D-14-0215.1

A rear-inflow jet structure is developed within the perturbation wind field between tsim = 16 and 18 h (Figs. 16a,b), with strong northerly-to-northwesterly perturbation flow having developed into the rear of the convective front by tsim = 18 h. Such rear-to-front accelerations here were potentially a result of parcel accelerations toward low-pressure anomalies residing along the convective front (evident in Figs. 16c,d). It is noteworthy that the east-southeastward movement of the convective system here, combined with the ambient vertical wind profile, resulted in a significant storm-relative southwesterly inflow to the rear of the progressive convective front (Figs. 16a,b). This low-level storm-relative flow was essential for the supply of potentially buoyant air into the region upstream of the initial convective system (Fig. 11) and facilitated persistent convective redevelopment there [this has been documented by previous authors in the context of heavy-rain-producing MCSs (e.g., Maddox et al. 1979; Chappell 1986; Moore et al. 2003; SJ2005; SJ2008; PS2014)].

Fig. 16.
Fig. 16.

As in Fig. 14, but for 1.5 km AGL.

Citation: Journal of the Atmospheric Sciences 72, 5; 10.1175/JAS-D-14-0215.1

b. Rearward off-boundary development and backbuilding

Between tsim = 18 and 20 h, new convective cells developed to the rear of the progressive MCS and north of the OFB left by this system (ROD). These cells organized into a west-northwest–east-southeast-oriented convective line (evident in Figs. 12d–f), which became the axis of training convective echoes and the corresponding location of heaviest precipitation production (see Fig. 13).

By tsim = 20–22 h, the southeastern flank of the surface cold pool continued to progress southeastward, whereas the southwestern flank moved very little (Figs. 17a,b). This behavior is likely a result of the predominant OFB-parallel flow along the southwestern cold pool flank and predominant OFB-perpendicular flow along the southeastern flank discussed in the previous subsection, which persisted through the timeframe discussed here. ROD remained significantly north of the southwestern cold pool flank during this timeframe, with a curious “development void” (shown in Fig. 18a), where convection was completely absent between the cold pool periphery and the newly training convective echoes (Figs. 1a,b). Note also the absence of a significant high-pressure anomaly within the ROD region of the cold pool, where perturbation flow was weak relative to the progressive southeastern flank of the MCS (Figs. 16c,d).

Fig. 17.
Fig. 17.

As in Fig. 14, but for simulation hours 20 and 22.

Citation: Journal of the Atmospheric Sciences 72, 5; 10.1175/JAS-D-14-0215.1

Fig. 18.
Fig. 18.

As in Fig. 15, but for simulation hours 20 and 22.

Citation: Journal of the Atmospheric Sciences 72, 5; 10.1175/JAS-D-14-0215.1

At 1.5 km AGL, cold anomalies were restricted to the southeastern progressive convective gust front at tsim = 20 h (Fig. 18a), but a second cold anomaly within the upstream training convective line became apparent by tsim = 22 h (Fig. 18n). The bulk of the cold pool (Figs. 17a,b), however, remained below this level during this time frame. A marked horizontal wind shift is apparent at the 1.5-km-AGL height along the training convective line, with southwesterly flow to the south of the line and weaker northwesterly flow to the north of the line (Figs. 18a–d). This flow pattern resulted in convergence into the upstream end of the training convective line, which is especially apparent at tsim = 22 h (Figs. 18b,d). The convective system continued to generate a gradually intensifying regional low-pressure anomaly during this time frame (Figs. 18c,d; presumably a result of latent heating aloft). Locally enhanced low pressure resided within convectively active regions.

c. Cold pool surge and demise

Geographically fixed upstream backbuilding occurred at the western end of the training convective line between tsim = 20 and 24 h (see the region denoted in Fig. 18b). By tsim = 26 h, convection within the region of echo training surged southeastward and weakened in conjunction with the southwestern periphery of the cold pool having begun to move southward.

A noticeable OFB perpendicular surface flow component had redeveloped along the southwestern cold pool flank by tsim =26 h (Fig. 19b) [flow here had been largely OFB parallel here between tsim = 20 and 24 h (Figs. 17a,b, 19a)]. This likely explains why the cold pool surged southward beyond tsim = 26 h—an event that potentially precipitated the southward movement of the convection out of the region where training and upstream backbuilding were occurring at prior simulation hours (as denoted in the figure). A strong (relative to previous simulation hours) high-pressure anomaly was also evident near the center of the cold pool at tsim = 24 h (Fig. 19c) and had propagated southward by tsim = 26 h (Fig. 19d). There is some indication within the perturbation wind field that increasing pressure within the cold pool relative to surroundings had produced stronger (when compared to previous simulation hours) flow in the direction of the OFB within cold air.

Fig. 19.
Fig. 19.

As in Fig. 14, but for simulation hours 24 and 26.

Citation: Journal of the Atmospheric Sciences 72, 5; 10.1175/JAS-D-14-0215.1

At 1.5 km AGL, pronounced flow convergence remained evident on the upstream flank of the convective system through this time period (Fig. 20a), in conjunction with locally minimized pressure within that region (Fig. 20c). A more expansive and intense cold anomaly (relative to prior simulation hours) was evident at 1.5 km AGL by 24 h (Fig. 20a): this anomaly had expanded considerably southward by tsim = 26 h (Fig. 20b). A comparison between regions of cold anomalies at 1.5 km AGL (Figs. 20a,b) and surface high-pressure anomalies (Figs. 19c,d) shows clear correspondence between these features and suggests that the increasing depth of this anomaly likely played a role in the eventual southward surge of the southwestern cold pool flank (owing to increasing net column-integrated negative buoyancy). Strong northerly flow was evident to the north of the eastern part of the convective line (Figs. 20a–d), suggestive of a redeveloping rear-inflow jet, perhaps as a response to locally higher pressure north of the convective line relative to pressure anomalies along the convective line (as noted in the figure). This strengthening rear-inflow jet may have also influenced the southward movement of convection during this time frame.

Fig. 20.
Fig. 20.

As in Fig. 15, but for simulation hours 24 and 26.

Citation: Journal of the Atmospheric Sciences 72, 5; 10.1175/JAS-D-14-0215.1

d. Cross-sectional profiles of temperature, winds, and stability

Convection resided close to the cold pool boundary at tsim = 16 h (Fig. 21a); however, ROD convection at tsim = 24 h was significantly removed northward from the surface cold pool periphery (Fig. 21b). At tsim = 16 h, the cold-pool-perpendicular vertical shear (Figs. 21c, 22a) was predominantly oriented outward from the cold pool (aside from a shear reversal in the lowest 250 m AGL and relatively weak shear between 500 and 1500 m). In contrast, the cold pool–perpendicular shear at tsim = 24 h (Figs. 21d, 22b) was significantly weaker (aside from strong shear oriented toward the cold pool in the 0–250-m AGL layer), and exhibited much weaker orientation toward warm air between 250 and 750 m, and slight orientation toward the cold pool between 750 and 2000 m AGL; in fact, along the side of the averaging box in Fig. 18 closest to the cold pool at tsim = 24 h (Fig. 22b), the shear orientation is exclusively toward the cold pool.

Fig. 21.
Fig. 21.

(a),(b) Surface θ′ [K (with areas of |θ′| < 1 K masked in white); shading], maximum surface to 300-hPa vertical velocities (green contours at 1, 2, and 3 m s−1), and surface wind vectors from the CNTL run (black arrows) for simulation hours (a) 16 and (b) 24. (c),(d) Vertical cross sections [along the dotted magenta boxes in (top), with all quantities averaged along the zonal width of the boxes] of θ from the CNTL simulation (K; shading), θ from the NOMP simulation (gray contours; K), θ′ from the CNTL simulation (magenta dashed contour at 1 K, with values > 1 K above; and cyan dashed contour at −1 K, with values <−1 K below), OFB-orthogonal wind vectors (defined as , where Vh is the horizontal wind vector, is a horizontal unit vector orthogonal to the mean orientation of the OFB within the magenta box, w is the full vertical wind, and is the unit vector in the z direction), and vertical velocities (dotted green contours, starting at 1 m s−1 and at intervals of 1 m s−1). Valid times for cross sections in (bottom) are shown at the top of the panel. Red boxes along the bottom of each cross section correspond to the location of vertical profiles shown in Fig. 22. Wind speeds may be associated with vector lengths by comparing the lengths of vectors in green boxes to the wind speed profiles shown in Fig. 22.

Citation: Journal of the Atmospheric Sciences 72, 5; 10.1175/JAS-D-14-0215.1

Fig. 22.
Fig. 22.

(a),(b) Vertical profiles of the magnitude of the horizontal component of OFB-orthogonal wind (m s−1; as defined in the Fig. 18 caption; positive values are toward the cold pool) averaged over the width of the green boxes in the cross sections in Fig. 20 (blue lines), and valid at the left (green) and right (red) sides of the box (with valid times listed on top of the panels). (c),(d) Vertical profiles of box-width mean CAPE (J kg−1; blue lines), box-width mean CIN (J kg−1 × 10; green;), box-width mean Brunt–Väisälä frequency (black dashed lines; ; s−1 × 105), and Brunt–Väisälä frequency profiles valid along the box left (cyan dashed lines) and box right (red dashed lines) flanks.

Citation: Journal of the Atmospheric Sciences 72, 5; 10.1175/JAS-D-14-0215.1

The theory of Rotunno et al. (1988) (RKW theory) and Weisman and Rotunno (2004) showed that a low-level wind shear vector over the depth of the cold pool oriented from cold pool air toward warm air is favorable for kinematic lifting along the cold pool boundary (Fig. 23a). Specifically, when the vorticity tendency owing to the horizontal gradient in buoyancy across this boundary is approximately balanced by the magnitude of the vertical wind shear (i.e., the ratio of the theoretical cold pool speed C to the vertical wind shear over the depth of the cold pool ΔU is equal to 1). French and Parker (2010) further proposed that for elevated systems with cold pools (such as the case here) the principles of the RKW theory extend to the “effective inflow layer,” where CAPE is maximized and CIN is minimized [i.e., the shear in a stable boundary layer is less important for kinematic lifting along a cold pool boundary than the shear in an elevated layer with maximum CAPE (see Figs. 22b,c)].

Fig. 23.
Fig. 23.

Schematic illustrating the relevance of the concepts of Rotunno et al. (1988) and French and Parker (2010) to the MCS simulated in this study. Red shading indicates the effective inflow layer, characterized by high CAPE and low CIN, and blue shading indicates a stable boundary layer characterized by low CAPE and high CIN. Red arrows show the orientation and relative magnitude of the vertical wind shear component perpendicular to the cold pool boundary in the effective inflow layer. Black arrows represent the relative magnitudes of low-level wind vectors perpendicular to the cold pool boundary, and circular arrows indicate the sense of vorticity tendency from vertical wind shear (black) and horizontal buoyancy gradients (blue). (a) The traditional RKW theory model, where a convective system is surface based, and vertical wind shear through the effective inflow layer is favorably oriented toward warm air from cold air (red arrow). (b) The elevated cold pool–driven situation simulated by French and Parker (2010), in which shear orientation in the elevated effective inflow layer remains favorable for lifting along the cold pool boundary (akin to Fig. 21 at 16 h). (c) As in (b), but the wind shear in the effective inflow layer is now unfavorably oriented from warm air to cold air (akin to Fig. 21 at 24 h).

Citation: Journal of the Atmospheric Sciences 72, 5; 10.1175/JAS-D-14-0215.1

The theories presented by these authors suggest that the shear profile at tsim = 16 h (Figs. 22a,c; compare to Fig. 23b) is more favorable for upright kinematic lifting (and thus triggering of convection) along the cold pool boundary than that at tsim = 24 h (Figs. 22b,d; compare to Fig. 23c). This is supported by the presence of a shallow 0.5 m s−1 vertical jet along the cold pool edge at tsim = 16 h in Fig. 19 [and generally more vertical motion immediately above this boundary relative to the boundary at 24 h (Fig. 21c)], along with the absence of significant lifting along the cold pool boundary at tsim = 24 h (Fig. 21d) [a similar wind shear contrast was identified by Trier et al. (2010) and Peters and Schumacher (2015) in simulations of upwind propagating MCSs]. Additionally, the CAPE (static stability) profiles exhibited the greatest (smallest) magnitudes and least convective inhibition above ~750 m throughout the simulation (Figs. 22c,d), further implicating this elevated CAPE layer as the primary source of unstable air to the MCS.

It is noteworthy that the low-level temperature perturbations associated with the cold pool are superimposed upon a gradual isentropic upslope with northward extent imposed by the large scale (evident in Figs. 22c,d in both the CNTL and NOMP temperature profiles). Any potential enhancement of lifting along the southeastern cold pool flank by large-scale isentropic upglide has a negligible effect on the interpretation of the role of the boundary in driving the motion of the MCS here, since it is apparent that lifting and isentropic slope are both abruptly enhanced along the boundary (suggesting that upward forcing by the boundary is significantly larger than large-scale upward forcing). Along the southwestern boundary (Fig. 22d), isentropic upglide is minimal near the outflow boundary and exhibits considerably greater upward slant north of the boundary. Isentropic in the CNTL simulation remained close to their analogies in the NOMP simulation (both slant upward noticeably near the region of deep convection and to a lesser extent further south), which suggests that the large scale may have ultimately regulated where the preferential region of training convection in this region occurred.

4. Summary and discussion

In this research, a 36-h composite progression of atmospheric fields was used as initial and lateral boundary conditions to a high-resolution quasi-idealized numerical simulation of a quasi-stationary heavy-rain-producing MCS. Composite atmospheric fields were computed from 26 observed heavy-rain-producing MCSs. This strategy added a necessary layer of complexity over fully idealized modeling frameworks, which use horizontally homogeneous initial and lateral boundary conditions and rarely represent the effect of large-scale atmospheric processes (hence the term “quasi idealized” having been used here), yet the results of our simulation retained generalizability (which is often cited as the advantage to fully idealized modeling frameworks) because of the inclusion of information from multiple observed events in the simulated atmospheric state.

Despite noticeable differences in the evolution of mesoscale and synoptic-scale atmospheric fields in the simulated solution relative to the composites used to drive the simulation, a realistic TL/AS MCS initiated and evolved within a simulated environment that was very similar to the environment near the observed MCS locations in the composites.

The evolution of the simulated MCS and the associated low-level thermodynamic, pressure, and velocity full and perturbation fields are then detailed in terms of three main stages of evolution: 1) initial progressive MCS, 2) rearward off-boundary development and backbuilding, and 3) cold pool surge and demise. During stage 1, an eastward-moving trailing-stratiform-type MCS developed, generated a robust cold pool, and produced convergent low-level perturbation flow structures in its wake. Low-level convergence combined with southwesterly potentially buoyant return flow into the wake of the initial system facilitated upstream convective redevelopment north of the surface cold pool boundary left by the initial system, which characterized the onset of stage 2. Upstream convection then organized into a quasi-linear training line with geographically fixed upstream backbuilding on the western end. Low-level convergence persisted in the region of upstream backbuilding, and we hypothesized that such convergence resulted from low-level perturbation pressure gradients associated with existing convection. Eventually, the cold pool deepened and surged southward, resulting in the weakening and slow southward movement of the training line, which marked evolutionary stage 3 and the demise of the convective system.

Separate analyses of the low-level wind shear orientation relative to the southeastern and southwestern cold pool flanks revealed a predominant vertical wind shear orientation toward the cold pool along the southwestern flank (unfavorable for kinematic lift along the boundary), contrasted with a predominant vertical wind shear orientation away from the cold pool along the southeastern flank (favorable for kinematic lift along the boundary). We hypothesize that these differing wind shear conditions resulted in persistent convection along the southeastern cold pool flank, whereas they allowed low-level flow to override the southwestern cold pool flank. This points to a different mechanism for upstream backbuilding from OFB lifting [e.g., Parker (2007) in the context of similar parallel stratiform type systems]. Figure 21 provides some evidence that, despite the presence of a cold pool, large-scale environmental lifting ultimately dictates where convection forms [in particular, these results echo those of Trier et al. (2010) in their Fig. 18].

A noteworthy result here is that the features common among observed TL/AS events—training of convection along a quasi-linear axis, rearward off-boundary development, and fixed upstream backbuilding—were reproduced from an initially smooth (with respect to variability among 10–100-km spatial scales) composite environment broadly characteristic of TL/AS events. Though the MCS-to-storm-scale morphology appears to have “emerged” from the upscale growth and organization of convection comprising the MCS of interest (i.e., processes internal to the MCS), the simulation outcome here suggest that the basic dynamics of the upscale emergence of such features are general among TL/AS events. These results support previous evidence of the synoptic regulation of TL/AS systems (e.g., Lorenz 1969; Roebber et al. 2008; Weisman et al. 2008; Peters and Roebber 2014). The regulatory role of the large scale may simply be to provide a region of low-level lift, saturation, and a vertical wind profile characteristic of TL/AS systems (this hypothesis will be further tested in future articles).

The goal of ongoing and future work will be to dynamically assess the processes observed here in order to determine the general mechanisms of the morphological evolution of TL/AS MCSs.

Acknowledgments

This research was supported by National Science Foundation Grant AGS-1157425. NARR data were obtained from the NCDC NOMADS server. We thank Morris Weisman, Sue van den Heever, Richard Johnson, George Bryan, Kelly Mahoney, and Gary Lackmann for helpful conversations and feedback. We also thank Stan Trier and two anonymous reviewers, who provided insightful and constructive comments that improved the quality of the manuscript.

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