This research investigates the dynamics of a simulated training line/adjoining stratiform (TL/AS) mesoscale convective system (MCS), with composite atmospheric fields used as initial and lateral boundary conditions for the simulation.
An initial forward-propagating MCS developed within a region of elevated convective instability and low-level lifting associated with warm-air advection along the terminus of the low-level jet. The environmental conditions external to the MCS continued to provide lift, moisture, and instability to the western side of the forward-propagating MCS, and these conditions were initially responsible for backbuilding on the system’s western side. Most parcels that encountered the southwestern outflow boundary were lifted insufficiently far to reach their levels of free convection (LFCs), and their LFC heights were increased by latent heating above them. These parcels continued northeastward beyond the surface outflow boundary (OFB), were gradually lifted, and initiated convection 80–100 km beyond encountering the OFB. Eventually the surface cold pool became sufficiently deep so that gradual ascent of parcels with moisture and instability over the OFB began initiating new convection close to the OFB—this drove backbuilding during the later portion of the MCS lifetime. These results disentangle the relative contributions of large-scale environmental factors and storm-scale processes on the quasi-stationary behavior of the MCS and show that both contributed to upstream backbulding at different times during the MCS life cycle.
Mesoscale convective systems (MCSs)—specifically those that propagate upwind and involve repetitive motion of individual convective cells over a fixed geographic region—are responsible for a large percentage of warm-season extreme rainfall events (e.g., Maddox et al. 1979; Doswell et al. 1996; Moore et al. 2003; Schumacher and Johnson 2005; Peters and Roebber 2014; Peters and Schumacher 2014). The typical MCS archetypes associated with these behaviors are known as backbuilding (BB; Schumacher and Johnson 2005) and training line/adjoining stratiform (TL/AS; Schumacher and Johnson 2005). These types of convective systems are often quasi stationary and, thereby, deliver large amounts of rain to a localized geographic area.
For the purposes of determining why an MCS may remain quasi stationary, it is useful to conceptualize the motion of the system as a vector sum of an advective component (usually taken to be the mean wind through a cloud-bearing layer) and a propagation component (i.e., the tendency for new convective cells that constitute the larger MCS to preferentially regenerate in a particular direction) (Corfidi et al. 1996; Corfidi 2003). Whereas the notion of a convective system “blowing with the wind” (advection) is an intuitive concept, the mechanisms for propagation vary significantly among different circumstances and are understood to a lesser extent than advection. Previous authors (e.g., Rotunno et al. 1988; Weisman and Rotunno 2004) have shown that robust dynamically forced lifting along the edge of a cold pool [herein the cold pool edge is referred to as an outflow boundary (OFB)] often serves as a focal point for continuous regeneration of new convective cells (this mode of propagation is hereby referred to as “kinematically driven”). Following Corfidi (2003), we hereby differentiate forward propagation, where the direction of this component is downwind (usually a similar direction to advection) from upwind propagation (which may sometimes completely cancel advection). The forward propagation of MCSs is frequently kinematically driven in both surface-based [characterized by the maximum environmental convective available potential energy (CAPE) and minimum environmental convective inhibition (CIN) at ground level] and elevated (characterized by maximum CAPE and minimum CIN above ground level) convective environments (Parker 2008; French and Parker 2010; Trier et al. 2010; Billings and Parker 2012; Keene and Schumacher 2013; Peters and Schumacher 2015a). In contrast, the upstream flank of upwind-propagating MCSs often decouples from, or propagates in the absence of, outflow boundaries.
Various factors associated with meso-α [O(100–1000) km] to synoptic [O(1000–2000) km]-scale atmospheric circulations play a role in the upstream backbuilding of MCSs (these are referred to as “external factors”). Indeed, Peters and Roebber (2014) showed that a significant portion of the variability in the simulated placement of TL/AS MCSs is explained by uncertainty in analyses of the meso-α- to synoptic-scale atmosphere. Specific influencing processes include frontogenetic lift along quasi-stationary frontal boundaries (Maddox et al. 1979; Augustine and Caracena 1994; Moore et al. 2003; Schumacher and Johnson 2005) and low-level lifting associated with warm-air advection as a low-level jet (LLJ) encounters isentropic upslope associated with a frontal zone (e.g., Trier and Parsons 1993; Fritsch and Forbes 2001; Moore et al. 2003; Schumacher and Johnson 2005; Trier et al. 2014; Peters and Schumacher 2014). Slow-moving mesoscale convective vortices (MCVs; e.g., Schumacher and Johnson 2009) are another example of an external factor that may localize warm-air advection and serve as a mechanism for persistent low-level lifting.
Processes that occur within MCSs, or as a result of the influence of MCSs on their surrounding environments, also contribute to upstream backbuilding (these are referred to as “internal factors”; Johnson and Mapes 2001). Schumacher and Johnson (2008) showed that latent heating associated with a BB type MCS produced a stationary upstream gravity wave—the upward branch of which lifted parcels to their levels of free convection (LFCs) and continuously triggered new convection; Marsham et al. (2010) showed observations of a similarly structured wave. Enhanced upward isentropic slope resulting from the presence of a convective cold pool may also enhance low-level lifting and bring parcels to their LFCs (Trier et al. 2010; Keene and Schumacher 2013; Peters and Schumacher 2015a,b). Since MCSs frequently occur along existing baroclinic zones, enhanced isentropic upglide over a cold pool often occurs in conjunction with an ambient environmental meso-α-scale isentropic slope (i.e., an external factor), and it is unclear whether the slope enhancement resulting from the presence of a cold pool is necessary for backbuilding.
Warm-season type TL/AS MCSs [described by Peters and Schumacher (2014)] constitute perhaps the least understood upstream backbuilding scenarios, where forward-propagating shear-parallel (we are referring to deep tropospheric shear in this context) convective lines often occur immediately prior to, and sometimes in conjunction with, shear-perpendicular convective lines that exhibit upstream backbuilding (Corfidi 2003; Trier et al. 2010; Keene and Schumacher 2013; Peters and Schumacher 2014, 2015a,b). For instance, warm-season TL/AS MCSs often undergo rearward off-boundary development (ROD; Peters and Schumacher 2014), which is characterized by the simultaneous development (i.e., the line develops all at once) of a convective line upstream (usually to the west) of an eastward-moving MCS and offset (usually to the north) from the OFB left by the initial system. Keene and Schumacher (2013) and Peters and Schumacher (2015a) showed that resurgence of elevated high-CAPE air into the region convectively overturned by a forward-propagating MCS, and the enhanced isentropic upglide and baroclinicity associated with the cold pool, facilitated ROD.
The goal of the present study is to improve our understanding of the external and internal factors that drive the upstream backbuilding of warm-season TL/AS MCSs. We also seek to better understand the unique morphological characteristics of this MCS archetype, such as rearward off-boundary development, and the presences of adjacent forward-propagating and quasi-stationary convective lines. To conduct our analysis, we use the numerical modeling framework of Peters and Schumacher (2015b), where a progression of composite atmospheric fields was used as the initial and lateral boundary conditions (ICs and LBCs, respectively) to a convection-permitting numerical simulation of a TL/AS system. The organization of this paper is as follows: Section 2 details the experiment design and the precipitation characteristics of the simulated MCSs. Section 3 disentangles the external and internal factors that contributed to upstream propagation. Section 4 investigates factors that regulated the location of training convection on the western flank of the MCS, and section 5 summarizes our results and discusses their impact on our understanding of TL/AS MCSs.
2. Numerical modeling experiments
a. CNTL and NOMP runs
A thorough documentation of the modeling framework for two simulations—abbreviated CNTL for control and NOMP for no microphysics—is provided by Peters and Schumacher (2015b). These model configurations used version 3.4.1 of the Advanced Research version of WRF (ARW; Klemp et al. 2007; Skamarock et al. 2008), with composite atmospheric conditions [generated from 26 observed warm-season TL/AS cases—see Peters and Schumacher (2014)] used as initial and lateral boundary conditions. Other attributes of the CNTL simulation are included in Table 1. We increased the 900–800-hPa relative humidity by 5%–10%—without this addition, convection initiated too late in the simulation for a mature MCS to develop (Parker and Johnson 2004; Naylor and Gilmore 2012). The purpose of using composite ICs and LBCs was to retain the horizontally heterogeneous structures on meso-α to synoptic scales that are suspected to influence the evolution of TL/AS MCSs (discussed in section 1), while excluding (by means of the smoothing that results from composite analysis) the meso-β [O(10–100) km] to meso-γ [O(1–10) km] variability that is common in case study simulations (such as the effects of convective episodes concurrent with, or prior to, the MCS of interest) as well as other complexities such as heterogeneities in the underlying land surface. The CNTL simulation reproduced many of the salient characteristics of warm-season TL/AS MCSs. The structures of the kinematic and thermodynamic fields of the simulated MCS were analyzed in detail by Peters and Schumacher (2015b). In section 2c, we briefly reiterate these characteristics. The outer domain of the simulation was run for 30 h, and the inner one-way nested domain was initialized 10 h after the outer domain to allow for spinup time. Simulation times (tsim) are hereby referred to in terms of hours elapsed since the outer domain simulation began. All subsequent analyses and figures are constructed with fields from the inner model domain.
The NOMP simulation was restarted from the CNTL simulation at tsim = 10 h with the microphysics parameterization turned off, and an otherwise identical model configuration to the CNTL. The results of this second simulation allowed the authors to isolate the processes within the CNTL simulation that specifically resulted from latent heating (since no such heating was permitted the NOMP run). As in Peters and Schumacher (2015b), perturbation fields, denoted by primes, are defined as , where F is any arbitrary scalar or vector quantity. This definition provides us with a rudimentary method for separating external processes (which are associated with fields) from internal processes (which are associated with fields).
b. NOEV run
We ran a third simulation called the no evaporation (or NOEV) run with the temperature tendency due to evaporation turned off in the Thompson microphysics scheme and with all else identical to the CNTL simulation. Previous authors (e.g., Schumacher 2009) have shown that such a configuration prevents the formation of a surface cold pool and may fundamentally alter the behavior of an MCS. Hence, the purpose of the NOEV simulation here is to test the sensitivity of the convective evolution to the presence/absence of a surface cold pool. We recognize that evaporation may play a critical role in mitigating updraft strength via entrainment and the intrusion of rain-cooled air into updraft regions. The absence of evaporative cooling in a simulation may therefore lead to unrealistically strong updrafts, since the deleterious effect of entrainment is mitigated without evaporative cooling, and convective downdrafts are presumably weaker. Our primary interests here, however, are the processes that lead to convection initiation (CI) within the region of upstream backbuilding (e.g., lift bringing parcels with nonzero CAPE to saturation). When interpreting the results of the NOEV simulation, we assume that evaporation plays a negligible role (aside from the presence or absence of a cold pool) in differentiating whether parcels reach their levels of free convection in regions that are not convectively modified prior to CI. Perturbation fields in the NOEV runs were defined such that .
c. Precipitation characteristics of the simulated MCSs
Here we review simulated radar reflectivity characteristics of the CNTL and NOEV simulations. Geographic features (such as Lake Michigan) are included in figures and referenced in the text. These features are only used to give a sense of spatial scale; there is no land surface variability of any kind within the simulation.
The simulated TL/AS system began as a grouping of individual convective cells that grew upscale into a southeastward-moving trailing stratiform (TS; Houze et al. 1990; Parker and Johnson 2000) type MCS between tsim = 14 and 18 h (Figs. 1a,b). This system produced a surface cold pool, which is evident in Fig. 1 as a general south and southeastward movement of the 22° and 23°C surface isotherms beneath the MCS. The second evolutionary stage (between tsim = 18 and 22 h) was characterized by ROD, where a discrete grouping of new convective cells developed in the wake of this initial progressive MCS and north of the OFB left by the initial system (Fig. 1c; the OFB is roughly coincident with the 23°C isotherm). Repeated backbuilding ensued at the upstream end of this new grouping of convection, with individual cells training from the region of backbuilding (Figs. 1d,e) eastward between tsim = 20 and 24 h (evident in Figs. 1d–f). Beyond simulation hour 25, the MCS gradually moved southward away from the region where training of convection occurred (Fig. 1f). By this time, the MCS had produced a vast surface cold pool, with the OFB evident along the 23°C isotherm, and the center of the cold pool located near the south end of Lake Michigan (where a large area of < 21°C is evident).
The NOEV simulation also produced a long-lived MCS, with notable differences in behavior from the CNTL simulation. The initial NOEV convection developed in the same location as the CNTL run (cf. Fig. 2a to Fig. 1a); however, convective coverage increased faster than, and moved eastward faster than, the CNTL simulation (cf. Figs. 2a,b to Fig. 1a). No surface cold pool was produced by the NOEV MCS, with the surface isotherms remaining generally undisturbed between tsim = 12 and 22 h. The initial eastward-moving convection in the NOEV simulation tracked more northerly (evident in Fig. 2c over southern Lake Michigan) than the analogous feature in the CNTL simulation (evident in Fig. 1c immediately south of the southern tip of Lake Michigan). A continuous convective line extended westward from the southern extent of the initial eastward-moving MCS to a region over north central Illinois, where upstream backbuilding occurred between tsim = 14 and 20 h (Figs. 2b–e)—convective echoes trained along this line for over 6 h. Interestingly, the NOEV “training line” occurred in nearly the identical location to the analogous feature in the CNTL simulation; however, the CNTL MCS featured a large latitudinal jump between the southern extent of the initial eastward-moving convection. The NOEV MCS training line, on the other hand, connected with the southern edge of the initial eastward-moving convection (cf. Figs. 2d to 1d). The location of upstream backbuilding was also nearly identical between the CNTL and NOEV simulations.
The CNTL MCS produced a swath of precipitation totals greater than 200 mm that was collocated with the approximate axis of the training line, with maximum point totals near 250 mm (Fig. 3a). The maximum precipitation produced by the NOEV simulation was displaced northward by roughly 10 km from the CNTL simulation (Fig. 3b), with maximum totals having been significantly larger in the NOEV run than the CNTL run (this is presumably a result of higher-precipitation production rates in the NOEV run from stronger updrafts).
3. Processes governing backbuilding
a. An ingredients-based propagation index
Given that three ingredients are necessary for deep moist CI—that is, moisture, CAPE, and lift (e.g., Beebe and Bates 1955)—it is safe to assume that an MCS will propagate toward external regions where these requirements for deep moist CI are satisfied. We also assume that parcels with nonzero CAPE that are near saturation with respect to water vapor are more likely to initiate convection than parcels that are farther from their LFCs and LCLs. Finally, we assume that parcels with less convective inhibition (CIN) are more likely to initiate convection than parcels with more CIN.
CAPE, CIN, and RH are easily computed given a vertical atmospheric profile of temperature, moisture, and pressure at given geopotential heights. Vertical velocity is readily available as a standard WRF model output field; however, modeled vertical velocity fields are often noisy and must be spatially smoothed for the interpretation of regions of meso-α- to meso-γ -scale lift. Local values of smoothed vertical velocity in regions of nonconvective lift [e.g., w O(10) cm s−1] are frequently “saturated” by the signal from nearby ongoing convection, where w can exceed 10 m s−1. Since we are specifically interested in lift within regions where convection is not currently ongoing but that are adjacent to ongoing convection (since we are looking for where the ongoing convection will propagate toward), we seek to devise a strategy that excludes the influence of convective lift while retaining the influence of meso-α- to meso-γ -scale nonconvective lift.
Parcels that are not initially saturated, and that are eventually lifted to the point of saturation and subsequent CI, must undergo adiabatic lift prior to the point of saturation. If we recognize that potential temperature (θ) is conserved following a parcel that travels within flow with nonzero horizontal velocity, and that lifts adiabatically, contours of constant θ must slant upward in the direction of the flow velocity ahead of the parcel (since the parcel ascends as it travels horizontally, conserves θ, and therefore traces an upward slanting path). It follows that
if we position ourselves at a fixed location along the path of the parcel that is undergoing adiabatic ascent, where is the horizontal wind velocity and is the horizontal gradient operator. A positive value of implies a warm-air advection (WAA) regime, which is commonly associated with lower-tropospheric lift.
We define an ingredients-based propagation index (IPI) in order to consolidate the aforementioned principles, where
and and are normalization parameters, and are defined later in this section. IPI is evaluated at every grid point within the domain and is set to zero for RH < 95%, CIN < −10 J kg−1, and where the right-hand side (rhs) of Eq. (2) returns a negative value. The RH and CIN thresholds are arbitrarily defined, and their values in this study are justified a posteriori by our later success at identifying processes that address our primary research questions.
For an air parcel that is within a buoyant convective updraft and traveling toward the updraft center, at a fixed location along the parcel’s path into the updraft, since the temperature within the updraft is higher than outside the updraft, and the gradient in temperature is therefore oriented toward the updraft (along the velocity direction). This yields a negative rhs value in Eq. (2) and IPI is therefore zero for this parcel. Likewise, for a parcel within a convective updraft traveling away from the center of the updraft, CAPE is presumably small given that the parcel is within a convectively overturned region. It is safe to assume that in this region; however, IPI will usually be small given that CAPE is small. By these arguments, IPI should be small within regions of ongoing convection (where parcels are undergoing buoyant ascent or are within convectively overturned air) and large within regions where parcels with high CAPE are undergoing adiabatic ascent (this assertion is demonstrated in our analysis in forthcoming sections). This suggests that our usage of as a proxy for lifting achieves our goal of excluding regions of ongoing convection from our analysis of the vertical velocity field.
We make use of our definition of perturbation fields to further differentiate between lift resulting from processes external to the MCS (e.g., broadscale warm-air advection) from lift produced by the influence of the MCS on the surrounding environment (e.g., lifting of parcels over a convective cold pool). We therefore divide Eq. (2) into its contributions from internal (subscript int) and external (subscript ext) processes:
If we define (where only is included), with for RH < 95%, CIN < 10 J kg−1, and , we may isolate the contribution to IPI resulting from as
We may also isolate the contribution to IPI resulting from as
An obvious question here may be “Why not simply use parameters from the NOMP simulation to compute (e.g., )?” There are instances where the NOMP simulation features a WAA signature (suggesting large-scale lift); however, convective processes have rearranged the temperature and/or wind fields such that there is actually a cold-air advection signature in the CNTL simulation. Lift is unlikely to be occurring in the CNTL simulation in these areas, and we seek to remove them from our , so that only regions where WAA is occurring in both the NOMP and CNTL simulations yield nonzero . The formulation of in Eq. (5) accomplishes this. We define and , where is the spatial maximum of a field at a given time. Spatial maps of the maximum column values of and are analyzed hereafter.
The intersection of the terminus of the low-level jet and a frontal zone is an example of a region where may be maximized. Analogous examples for include flow encountering and being lifted over an OFB or gravity wave that was produced by convection. It is important to emphasize that these features (e.g., the terminus of the low-level jet, outflow boundaries, or gravity waves) must coincide with parcels that are close to saturation and have little CIN and nonzero CAPE (thus these parcels are “primed” or “ready” for CI). If, for instance, a cold pool is below the layer of maximum CAPE, saturation, and minimum CIN, may not be evident since the maximum WAA signature no longer coincides with the maximum CAPE. This result is desirable since the strongest lifting presumably coincides with the strongest WAA signature—if this lifting does not coincide with the parcels that are most ready to trigger convection, CI is unlikely.
The IPI parameters bear similarities to two other indices used to forecast MCS motion and maintenance: the MCS maintenance parameter (MMP; Coniglio et al. 2007) and the MCS index (MI; Jirak and Cotton 2007). The MMP focuses on wind shear and convective instability, excluding a representation of large-scale lift. The MI, on the other hand, only investigates horizontal overlap between WAA and nonzero CAPE and does not explicitly determine whether lift associated with WAA is occurring on the same vertical levels that contain nonzero CAPE. Furthermore, it does not distinguish regions where parcels are near their LFCs from regions where they are not.
b. Effective inflow-layer shear vectors
The IPI parameter may not sufficiently identify regions where robust kinematic lift is produced along an OFB [e.g., the lifting described by Rotunno et al. (1988), referred to herein as “RKW lift”]. This lifting often occurs over small spatial scales (e.g., of order 1 km) and does not produce a broad WAA signature—in fact, the ground relative wind is often oriented from the cold pool toward warm air, producing a cold-air advection signature [e.g., imagine Rotunno et al. (1988), their Fig. 18d, with the storm motion vector added to the storm relative wind vectors in the schematic—the ground relative wind would be characterized by increasing westerly wind speed with height and would blow from cold to warm].
In proceeding, we recognize that RKW lift requires a component of the wind shear vector through the depth of the cold pool to point away from the center of the cold pool and that the relevant air parcels to consider when estimating the aforementioned shear vector are those that are capable of undergoing deep, moist ascent—that is, parcels that have nontrivial CAPE and nonprohibitive CIN. In keeping with previous authors (e.g., Thompson et al. 2007), we define the “effective inflow layer” (EIL) as the layer with CAPE > 100 J kg−1 and CIN > 250 J kg−1 and define effective inflow-layer shear (EILS) vectors as
where and are the wind vectors at the top and bottom of the EIL, respectively. Ideally, the component of the EILS vector normal to the OFB, and oriented away from the cold air, should be equal to the theoretical cold pool speed c, where (Rotunno et al. 1988) and is the depth of . As will be shown in the next subsection, the theoretical cold pool speed in our simulation is often larger than the EILS vector, so that the most “RKW optimal” state possible for kinematically driven propagation along the OFB are EILS vectors oriented away from, and perpendicular to, the OFB.
c. The relative influences of internal and external lift on MCS behavior
The large-scale environment in the NOMP–CNTL simulations featured a synoptic-scale anticyclone centered to the south-southeast of the MCS location and an LLJ along the northwestern periphery of the anticyclone with the terminus of the jet at the MCS location (Figs. 4a–d). The interaction of the LLJ with a zonally aligned low-level temperature gradient produced a persistent meso-α-scale local maximum in WAA immediately to the west of the MCS location through tsim = 21 h (Figs. 4a–d). A broad plume of locally maximized most unstable CAPE (MUCAPE) coincided with the LLJ (the northeastern flank of this plume coincided with the western flank of the MCS; Figs. 5a–d), and meso-α-scale region of saturated air coincided with the terminus of the LLJ and the MCS. These ingredients (e.g., lift associated with WAA, CAPE, and near-saturated air) overlapped in the region immediately to the west of the MCS.
We examined horizontal plots of column maximum and to better illustrate this “overlap” between the aforementioned ingredients for convection. All IPI fields are horizontally smoothed by a Gaussian filter with a radius of influence of 20 km for ease of interpretation. The initial convective cells that would eventually become an MCS initiated along the northeastern side of a region of locally maximized (Figs. 6a,b), suggesting that the lifting within the region of WAA along the terminus of the LLJ (which is evident in Figs. 4a–c) was responsible for CI. These cells were initially transported northeastward by the mean tropospheric steering flow between tsim = 12 and 14 h (Figs. 6b,c). A cohesive surface cold pool had developed by tsim = 14 h (Figs. 6c,f); however, values in the vicinity of the MCS were small at this point, suggesting that the cold pool was shallower than the level where parcels were most primed for convection and were therefore insufficiently deep to trigger new convective cells (Figs. 6d–f).
Convection organized into a southwest–northeast-oriented line along the southeastern OFB by tsim = 16 h (Fig. 7a), and the surface cold pool continued to expand through tsim = 20 h (Figs. 7a–c). The intensified along the western flank of the surface cold pool produced by the MCS (Figs. 7a–c) as a response to the “nose” of 2000 J kg−1 MUCAPE approaching the western flank of the MCS (Figs. 5a–d) and better overlap of the highest CAPE with the strongest large-scale WAA (cf. Figs. 4a–d to Figs. 5a–d). New convective cells developed along the eastern flank of the region of high between tsim = 16 and 20 h and were initially transported northeastward over the existing cold pool by the mean tropospheric steering flow. This repeated generation of cells on the western flank of the system occurred in a region where was small compared to during the tsim = 16–18-h timeframe (Figs. 7a,b), suggesting that externally driven lift was predominantly responsible for their initiation. These cells had apparently intensified the surface cold pool by tsim = 20 h (note the increase in cold pool intensity from 5 to 10 m s−1 between tsim = 18 and 20 h beneath cells along the system’s western flank; Figs. 7e,f). The magnitude of increased to a comparable value to that of along the western flank of the MCS by tsim = 20 h, suggesting that the intensified cold pool began to play a role in lifting parcels to their LFCs.
The cold pool was more intense along the southeastern flank (beneath the initial convective line) than the southwestern flank (Figs. 7d–f) through the tsim = 16–20-h timeframe. EILS vector magnitudes along the southeastern flank of the cold pool were in the 15–20 m s−1 range, and their orientations were eastward. Given that maximum cold pool intensities along the eastern and southeastern flank of the system were 15–20 m s−1 (Figs. 7d–f), the optimal direction for kinematically driven MCS propagation was eastward (in the direction of EILS vectors, where the ratio of the cold pool intensity to the magnitude of EILS vectors was closest to unity), which is corroborated by the persistence of >3 m s−1 vertical velocities on the far eastern OFB through the tsim = 16–20-h timeframe (Figs. 7d–f). A pronounced maximum in was present along the southeast flank of the MCS at (Fig. 7e) and then along the southern flank of the system between tsim = 18 and 20 h (Fig. 7f). This suggests that, in contrast with the southwestern and western OFBs, the cold pool intensity and depth here was sufficient to lift parcels to their LFCs (despite RKW suboptimal conditions along all cold pool flanks except the far eastern periphery) throughout the tsim = 16- and 20-h timeframe. In general, the southeastward movement of the initial convective line appears to have been driven by a combination of strong kinematic lifting along the OFB’s eastern flank and a sufficiently deep cold pool along the southern flank to lift parcels within the southwesterly LLJ to their LFCs. This contrasts with the “externally” driven backbuilding on the western flank of the system where the cold pool was weaker and shallower.
The magnitude of along the western flank of the system gradually decreased between tsim = 22 and 26 h (Figs. 8a–c) as the region of maximum WAA and maximum CAPE ceased to overlap (Figs. 9a–d). At the same time, the cold pool intensity along the western side of the system increased dramatically as a response to persistent training convection over that region. The along the southwestern flank of the MCS also increased dramatically between tsim = 20 and 26 h (Fig. 7f and Figs. 8d–f). This suggests that the cold pool became sufficiently deep here to lift parcels with nonzero CAPE to their LFCs and that this cold-pool-driven lift became the dominant mechanism for upstream backbuilding beyond tsim = 20 h. The cold pool gradually advanced southward beyond tsim = 26 h (not shown), resulting in the gradual southward movement of the MCS during this timeframe.
The time evolutions of , , and 1-h precipitation (Fig. 10a) from the CNTL simulation illustrates the initial externally driven westward backbuilding (tsim = 15–21 h), a short period of both externally and internally driven westward and southwestward backbuilding (tsim = 22–23 h), and then a transition to a southwestward internally driven backbuilding regime (tsim = 23 h onward). On the other hand, the NOEV simulation (which did not produce a surface cold pool) featured much weaker (Fig. 10b). In fact, the backbuilding process between tsim = 15 and 23 h was almost entirely driven by external lift—after which the MCS moved eastward (in contrast, the CNTL MCS continued to backbuild through tsim = 29 h). This corroborates our earlier assertion that external lift dominated the backbuilding process through tsim = 21 h in the CNTL simulation and suggests that this backbuilding process was minimally influenced by the presence of the surface cold pool (since it happened in the NOEV simulation without a cold pool). Conversely, backbuilding in the CNTL simulation after tsim = 23 h likely required cold pool–driven lift, given that backbuilding ceased during this timeframe in the NOEV simulation where no cold pool was present.
4. The geographic and temporal offset of ROD from the southwestern outflow boundary
a. Cross-sectional analysis
In this subsection, we determine why the training convective line on the western side of the MCS in the CNTL simulation was offset significantly northward of the southwestern OFB. We investigate vertical cross sections that bisect the southwestern OFB and the training convective line to begin our analysis. Such analyses are only included for tsim = 21 h (Fig. 11a); however, the processes that we elucidate in this section were coherent in time and representative of the timeframe with the most substantial separation between the training line and the southwestern OFB (≈tsim = 18–22 h). The quantity is introduced, which is the distance a parcel must be lifted to reach its LFC (, where z is the height of a parcel and is the parcel’s LFC height). The is correlated with |CIN|, whereby parcels that need to be lifted large (small) distances to reach their LFCs usually have high (low) convective inhibition. This quantity is useful in our analysis, since it allows us to compare a parcel’s initial value to its subsequent vertical displacement to see if the actual displacement was—in theory—sufficient to trigger convection. In this and later sections “convective stabilization” is defined as an increase in the of a parcel over time. Convective stabilization contrasts with dry static stabilization—the latter of which we define as an increase in ∂θ/∂z.
The cold pool along the southwest flank at tsim = 21 h was 1–1.5 km deep (cold pool depth is inferred as the depth of < −0.5 K) between the surface OFB and the region of training convection that was approximately 100 km north of the surface OFB (Fig. 11b). A small region of >30 cm s−1 was present directly above OFB (Fig. 11b); however, lifting between −10 and −80 km was comparatively weak (<10 cm s−1). The largest CAPE values south of the OFB were in the 0.75–1.5-km- AGL layer (layer A), whereas the smallest values and largest RH values were above the maximum CAPE layer, between 1.5 and 2 km (Figs. 11c,d; layer B). The increased and CAPE decreased in both layers A and B as parcels within these layers interacted with, and passed, the OFB (Fig. 11c). Clouds were present in and above layer B and directly above the OFB; however, cloud water concentrations generally decreased within parcels as they moved between the OFB and the training line (Fig. 11d). Finally, RH values in layer B, which were near 100% prior to parcels within this layer interacting with the OFB, decreased into the 80%–90% range between the OFB and the training line (Fig. 11d). Conversely, RH values above layer B generally increased 5%–10% as parcels within these layers passed through the cloudy region above the OFB (Fig. 11d).
Our analysis of the cross section in Fig. 11 leads to the following hypotheses: 1) Air parcels approaching the southwestern OFB within layer A (e.g., between 20 and 0 km in Fig. 11) experienced insufficient vertical displacement to reach their LFCs as they interacted with the OFB, as inferred by the apparently large values (100–500 m; Fig. 11c) and the apparently weak vertical velocities along the OFB (Fig. 11b). Though parcels with nonzero CAPE and small values in the 1.25–2.0-km layer were likely lifted to their LFCs (as presumed by cloud development along the OFB in Fig. 11d). 2) These parcels did not transition into deep convection because they mixed with comparatively drier parcels above them. This presumes that the increase in RH in the air above layer B as it crossed the OFB resulted from detrained moisture from the cloud produced by parcels in layer B. 3) Warming from latent heating in and above layer B increased of parcels in layer A as these layers passed over the OFB, as inferred from the 1–1.5-K increase in above 1.5 km between 20 and −20 km (Fig. 11b). We evaluate these hypotheses with trajectory analyses, combined with comparisons of the temperature profiles south and north of the OFB in the next subsection.
b. Trajectory analysis
To further address our hypotheses from the previous subsection, we released three-dimensional trajectories approximately 35 km southwest of the southwestern OFB at tsim = 20 h . These trajectories moved northeastward across the OFB and eventually into the training convective line (Fig. 12a), having followed a qualitatively similar path to the cross-sectional path in Fig. 11a. All trajectories were computed from 5-min model history interpolated onto 1-min intervals, and with trajectory position updates every 1 min. Trajectories were disseminated into four populations based on their initial heights (): 500-, 1000-, 1750-, and 2500-m initializations. Their characteristics (e.g., RH, θ) were examined as a function of their northeastward displacement from their initial positions, where northeast is assumed to be the direction perpendicular to the OFB. Distances (e.g., “15 km”) refer to the northeastward displacement from initial trajectory positions. Here 35 km denotes the approximate location of the surface OFB, and trajectory properties at 55 km are compared to analogous properties at 0 km to gauge the impact of the OFB interaction on these properties.
We test hypothesis 1 by comparing the actual vertical displacements of air parcels within layer A as they interacted with the OFB to their initial values. Trajectories with m required nearly a kilometer (not shown in figure) of vertical displacement to reach their LFCs but were only lifted a maximum distance of approximately 280 m by 55 km (Fig. 12b). Likewise, trajectories with required approximately 450 m of vertical displacement (Fig. 11) to reach their LFCs but were only lifted a maximum distance of approximately 175 m by 55 km (Fig. 12b). Neither the trajectories with or m reached saturation by 55 km (Fig. 12c), and both of these trajectory populations approximately conserved their θ (Fig. 13b) and water vapor mixing ratio () (Fig. 13a) values between their initializations and 55 km. This evidence supports hypothesis 1, demonstrating that parcels in layer A did not reach their LFCs—furthermore, they were not lifted to saturation and ascended adiabatically between their initializations and 55 km.
Trajectories with m experienced greater upward displacement than trajectories with m, implying that ∂w/∂z < 0 at and below 1000 m (the w field in Fig. 11b supports this assertion). This resulted in dry static stabilization of the layer below 1.5 km, whereby isentropes were vertically “compressed” (resulting in a greater ∂θ/∂z) within an atmospheric column as it translated from south of the OFB to north of the OFB. For instance, the parcel-following budget for the vertical gradient of θ (γ ≡ ∂θ/∂z) for adiabatic motions can be expressed as
where the positive x direction is defined as the OFB-perpendicular direction toward cold air and boundary parallel gradients in θ have been neglected. Assuming ∂u/∂z > 0 (based on Fig. 11), ∂θ/∂x < 0 (based on Fig. 11b), ∂w/∂x < 0, and γ > 0, both terms A and B in Eq. (7) are positive and, therefore, statically stabilize the flow. This dry static stabilization may have locally dampened vertical motions and prevented parcels in these layers from being perturbed to their LFCs.
Thermodynamic and moisture budgets for trajectories with m and m were analyzed to address hypothesis 2. Trajectories with m required less than 50 m of vertical displacement to reach their LFCs at their initial positions and their actual median upward displacement was approximately 125 m by 55 km, suggesting that a large percentage of them reached their LFCs (Fig. 12b). Furthermore, the median RH of these trajectories was at or above 100% until after 35 km, after which RH steadily dropped into the 90%–95% range (the maximum RH among this population was still supersaturated until just after 55 km; Fig. 12c). The range of upward displacements for trajectories with m expanded well beyond the range of displacements for other initialization heights (Fig. 12d), suggesting that the trajectories with m underwent some degree of convective overturning as they passed over the surface OFB (hence more vigorous upward and downward motion within this population). Water vapor mixing ratios for trajectories with and m initializations remained relatively constant until approximately 65 km, whereas trajectories with m steadily lost water vapor (presumably via condensation), and trajectories with m gained a comparable amount of water vapor between 35 and 55 km to what was lost from the 1750-m trajectories (Fig. 13b). This suggests that convective overturning within the trajectory population with m detrained water into the population with m.
The potential temperature budget following an air parcel and neglecting shortwave radiative effects and surface fluxes (the latter of which were turned off) is
where Q is latent heating and D is the difference between the actual change in θ and the change in θ due to latent heating alone. The quantity D contains turbulent diffusion (e.g., mixing), longwave radiative heating, and errors in trajectory calculations; however, we assume that errors in trajectory calculations and longwave radiative effects are small compared to mixing given that the median θ only changed on the order of 0.125 K for the trajectories with and m as they traveled adiabatically before 75 km (and assuming that for adiabatic motions is an approximate upper bound for errors and longwave radiative effects). The relative contributions to the change in θ over time (denoted as Δθ) following an air parcel by Q and D are therefore obtainable as (Fig. 13c) and (Fig. 13d), respectively (where t* is a dummy variable of integration). Latent heating contributed steady warming in the trajectories with m between 15 and 45 km and brief cooling in the trajectories with m between 35 and 55 km (Fig. 13c). This suggests that as parcels with m detrained cloud water into the trajectories with m, evaporation occurred in the trajectories with m (increasing the water vapor mixing ratio; Fig. 13a). Finally, contributed a negative θ change in the trajectories with m between 15 and 50 km, whereas contributed a positive θ change between 35 and 45 km of comparable magnitude to the negative change in the trajectories with m (Fig. 13d). This suggests that as the parcels with m decreased θ from evaporation, they increased θ via mixing with the parcels ascending from m that had warmed from latent heating. Conversely, this increase in theta for the parcels with m was temporarily mitigated by the mixing of these parcels with the m parcels which had the lower-θ characteristic of the ambient environment. This mixing apparently shut off positive latent heating in the trajectories with m population between 45 and 65 km (Fig. 13c), and the subsequent absence of latent heating prevented this trajectory population from producing widespread deep convective updrafts near the OFB. Finally, the limited height variances of the trajectories with and m, when compared to those with and m, suggests that momentum associated with convective overturning within the populations with and m was not readily communicated into the 500- and 1000-m layers—potentially owing to the static stabilization discussed earlier in this section.
We address hypothesis 3 by comparing the θ, temperature, and dewpoint profiles 20 km south of the boundary (the “preboundary profile”) to the analogous profiles 20 km north of the boundary (the “postboundary profile”; these profiles were obtained from the cross section in Fig. 11). The preboundary profile was cooler below 1.25 km and warmer above 1.25 km than the postboundary profile (Fig. 14a), and ∂θ/∂z was larger in the postboundary profile than the preboundary profile (as discussed earlier). While the adiabatic affects below 1000 m lead to static stabilization (Fig. 14b) in that layer, latent heating predominantly caused static stabilization between 1.5 and 2 km. Furthermore, adiabatic lift alone cannot change a parcel’s lifted path and . The latent heating above 1000 m were therefore responsible for the increasing by moving the environmental temperature more to the right of a parcel’s lifted path relative to the environmental profile south of the OFB (Figs. 14c,d). This increased and slightly reduced CAPE. The pre- and postboundary profiles were nearly identical above 800 hPa, which suggests that processes aloft were not responsible for the CAPE and changes (Fig. 14c).
c. Comparison with later times where convection initiated near the OFB
As discussed in section 3, the lifting of flow over the cold pool began to directly initiate convection beyond tsim = 22 h, as evident in the widespread convection over the cold pool and near the OFB at tsim = 26 h (Fig. 15a). An analogous cross-sectional analysis to Fig. 11b reveals a deeper cold pool at tsim = 26 h (≈1.5–2 km; Fig. 15b) than at tsim = 21 h (≈1–1.5 km; Fig. 11b) and comparatively stronger lifting along the boundary (>40 cm s−1). The distributions of CAPE and southwest of the OFB were similar at tsim = 26 h (Figs. 15c,d) to tsim = 21 h (Figs. 11c,d); however, the cold pool depth at tsim 26 h was higher than the height of the maximum CAPE southwest of the OFB (this was not the case for tsim = 21 h). This presumably facilitated the lifting of parcels below 1.5 km to their LFCs (these parcels did not reach their LFCs at tsim = 21 h when the cold pool was shallower).
Trajectories were released at the same locations and heights as those in the previous subsections, but at tsim = 24 h (Fig. 16a; they encountered the OFB at approximately ). Their vertical displacements—especially those with , , and m—were considerably greater than the analogous displacements for those initialized at tsim = 20 h (cf. Fig. 16b to Fig. 12b), with maximum vertical displacements having exceeded values for all trajectory populations by the 55–65-km range. The 500- and 1000-m trajectories reached saturation at approximately 50 km, whereas the analogous trajectory populations from the tsim = 20 h-initializations approached and/or reached saturation at approximately 85 km. This comparison supports the earlier assertion that the increase in cold pool depth—which contributed to parcels below 1500 m reaching saturation near the boundary—was responsible for the cold pool becoming a source of CI.
5. Summary and discussion
In this research, a simulation of a training line/adjoining stratiform (TL/AS) MCS [conducted by Peters and Schumacher (2015b)] was further analyzed in order to elucidate the system’s governing dynamics. Composite atmospheric fields were used as ICs and LBCs for this simulation. These ICs and LBCs included the meso-α- to synoptic-scale features that are typically present in heavy-rain-producing quasi-stationary MCS events, including a low-level jet terminus, a quasi-stationary low-level frontal zone, an upper-level jet entrance region, and a region of locally maximized low-level warm-air advection. The simulation produced an MCS that well emulated the typical observed characteristics of TL/AS events and produced rainfall totals in excess of 200 mm.
An initial forward-propagating MCS developed along the nose of the low-level jet and was driven southeastward by a combination of kinematic lifting along the eastern flank of the OFB and southwesterly flow being lifted to saturation over the deep cold pool here. The large-scale environment persistently lifted parcels with high CAPE and RH to their levels of free convection upstream of the initial MCS (where the cold pool was too shallow to directly trigger convection), and this large-scale lifting drove upstream propagation of the system through the initial portion of its life cycle. The western flank of the cold pool eventually deepened as a response to persistent backbuilding convection there and eventually became deep enough to directly trigger convection. At the same time, large-scale warm advection weakened on the western flank of the system. The mechanism for upstream backbuilding late in the system’s lifetime therefore transitioned from synoptically driven lift to lifting of parcels over the convectively generated cold pool.
A heating-over-cooling pattern over the southwestern OFB stabilized flow as it passed the OFB and prohibited convective development along the southwestern OFB during the first portion of the systems’ lifetime. Latent heat release in the upper portion of the high CAPE layer reduced CAPE and increased convective inhibition in this flow, and adiabatic cooling from ascent in the lower portion of the high CAPE layer increased dry static stability. The flow then traveled 80–100 km north of the OFB, was gradually lifted by large-scale processes to the point of saturation, and entered convective updrafts within the training line. This additional northward travel and lift required to destabilize parcels explains the geographic separation between the southwestern OFB and the training line. As the cold pool deepened later in the MCS’s lifetime, lift over the OFB became sufficiently strong to overcome the thermodynamic stabilization process, and convection directly triggered along the boundary.
Several previous studies that have analyzed similar types of MCSs have alluded to the combination of large-scale forcing and upscale convective feedbacks (such as the generation of a mesoscale cold pool) in the upstream backbuilding process (e.g., Maddox et al. 1979; Trier et al. 2010; Keene and Schumacher 2013; Peters and Schumacher 2015a) that we have demonstrated here. However, to the authors’ knowledge, these results are the first to have disentangled the relative contributions of large-scale “external” lifting and lifting resulting from upscale convective feedbacks, respectively. The presence of backbuilding and heavy rainfall production in the NOEV simulation suggests that the cold pool may not have been necessary for upstream backbuilding and a heavy rainfall event, though it likely prolonged heavy rainfall in the CNTL simulation. The cold pool did significantly influence the behavior of the initial MCS—for instance, it was necessary for the rearward off-boundary development phenomena. The location and depth of convective cold pools is notoriously difficult to predict when compared to the location of large-scale lifting. This study therefore yields promising results from a predictability standpoint, since the potential for heavy rainfall is likely identifiable in forecasts even if a forecast model incorrectly predicts the character of the low-level cold pool development (owing to the large-scale contribution to backbuilding identified here).
The thermodynamic stabilization affect that prohibited convective development along the southwestern OFB is also a novel finding and underscores the sensitivity of MCS behavior to the profile of low-level moisture and temperature [this sensitivity is well demonstrated by Schumacher (2015)]. Some evidence of a similar process is evident in the simulation of the 28 July 2011 Iowa MCS by Peters and Schumacher (2015a) (see their Fig. 14), though the process is not explicitly discussed in that study. One may envision that small changes in low-level temperature and moisture (e.g., more moisture near the surface) may have allowed convection to trigger directly along the OFB much earlier in our simulation and may have repositioned the region of heaviest rainfall production. Ongoing work seeks to apply the experimental strategy of Schumacher (2015) to the quasi-idealized modeling framework used here. Additional runs will be conducted and analyzed with variable low-level moisture profiles in order to test the sensitivity of the MCS behaviors to the low-level moisture distribution.
This research was supported by National Science Foundation Grants AGS-1157425 and AGS-PRF 1524435, and NASA Grant NNX15AD11G. NARR data were obtained from the NCDC/NOMADS server. Special thanks go out to Clark Evans and two other anonymous peer reviewers for extremely thoughtful suggestions that substantially improved the quality of the manuscript. We also give thanks to Morris Weisman, Stan Trier, Sue van den Heever, and Richard Johnson for helpful comments and feedback and to Claire Moore for serving as an external editor.