The Behavior of Squall Lines in Horizontally Heterogeneous Coastal Environments

Kelly Lombardo Department of Marine Sciences, University of Connecticut, Groton, Connecticut

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Tristan Kading Department of Marine Sciences, University of Connecticut, Groton, Connecticut

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Abstract

Inland squall lines respond to the stable marine atmospheric boundary layer (MABL) as they move toward a coastline and offshore. As a storm’s cold pool collides with the marine layer, characteristics of both determine the resulting convective forcing mechanism over the stable layer and storm characteristics. Idealized numerical experiments exploring a parameter space of MABL characteristics show that the postcollision forcing mechanism is determined by the buoyancy of the cold pool relative to the MABL. When the outflow is less buoyant, storms are forced by a cold pool within the marine environment. When the buoyancies are equivalent, a hybrid cold pool–internal gravity wave develops after the collision. The collision between a cold pool and less buoyant MABL initiates internal waves along the stable layer, regardless of MABL depth. These waves are inefficient at lifting air into the storm, and ascent from the trailing cold pool is needed to support deep convection. Storm intensity decreases with deeper and less buoyant MABLs, in part due to the reduction in elevated instability. Precipitation is enhanced just prior to the collision between a storm and the deepest marine layers. Storms modify their environment downstream, leading to the development of a moist adiabatic unstable layer and a lowering of the level of free convection (LFC) to below the top of the deepest marine layer. An MABL moving as a sea breeze into the storm-modified air successfully lifts parcels to the new LFC, generating convective towers ahead of the squall line. This mechanism may contribute to increased coastal flash flooding risks during observed events.

© 2018 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Kelly Lombardo, kelly.lombardo@uconn.edu

Abstract

Inland squall lines respond to the stable marine atmospheric boundary layer (MABL) as they move toward a coastline and offshore. As a storm’s cold pool collides with the marine layer, characteristics of both determine the resulting convective forcing mechanism over the stable layer and storm characteristics. Idealized numerical experiments exploring a parameter space of MABL characteristics show that the postcollision forcing mechanism is determined by the buoyancy of the cold pool relative to the MABL. When the outflow is less buoyant, storms are forced by a cold pool within the marine environment. When the buoyancies are equivalent, a hybrid cold pool–internal gravity wave develops after the collision. The collision between a cold pool and less buoyant MABL initiates internal waves along the stable layer, regardless of MABL depth. These waves are inefficient at lifting air into the storm, and ascent from the trailing cold pool is needed to support deep convection. Storm intensity decreases with deeper and less buoyant MABLs, in part due to the reduction in elevated instability. Precipitation is enhanced just prior to the collision between a storm and the deepest marine layers. Storms modify their environment downstream, leading to the development of a moist adiabatic unstable layer and a lowering of the level of free convection (LFC) to below the top of the deepest marine layer. An MABL moving as a sea breeze into the storm-modified air successfully lifts parcels to the new LFC, generating convective towers ahead of the squall line. This mechanism may contribute to increased coastal flash flooding risks during observed events.

© 2018 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Kelly Lombardo, kelly.lombardo@uconn.edu

1. Introduction

Coastal and offshore regions are frequently impacted by mesoscale convective systems organized into lines of deep convective cells that initiate and mature over land. These storms, known as squall lines, occur in coastal regions ubiquitously across the globe, including the eastern United States (Heymsfield et al. 1999; Lombardo and Colle 2012, 2013), Mediterranean (Kömüşçü et al. 1998; van Delden 1998; Cohuet et al. 2011), China and South China Sea (Wang and Carey 2005; Meng et al. 2013), South America (Garstang et al. 1994; Greco et al. 1994; Cohen et al. 1995; Pereira de Oliveira and Oyama 2015), and Australia (Drosdowsky et al. 1989). Coastal squall lines pose threats of high wind, hail, heavy precipitation, tornadoes, and frequent lightning (Ashley and Mote 2005; Schumacher and Johnson 2005; Lombardo and Colle 2011; Colle et al. 2012; Corfidi et al. 2016) to coastal communities and metropolitan cities, recreational and industrial maritime activities, and military coastal ports and their offshore activities.

Squall lines often respond to the stable marine boundary layer as they move toward the coast and offshore. The impact of the marine layer on squall-line evolution is not confined to offshore regions, however, as the stable layer can progress tens to hundreds of kilometers inland as a sea breeze during certain synoptic regimes (e.g., Tijm et al. 1999; Lombardo et al. 2016). Some coastal storms decay within kilometers or tens of kilometers after encountering the marine atmospheric boundary layer (MABL), while others remain intense and move more than 100 km offshore (Lombardo and Colle 2012, 2013). Mesoscale simulations of northeastern U.S. squall lines showed that a successful coastline crossing can be supported by the development of a bore-like feature resulting from the collision of the storm cold pool and MABL (Lombardo and Colle 2013). The authors hypothesized that the deep, stable MABL supported the development of the bore-like structure that advanced the storm offshore. However, only one storm that successfully moved over the coastal waters was examined in this case study analysis, leaving open questions regarding the conditions that support wave development following the collision of a cold pool and marine layer, as well as their role in determining storm characteristics.

Bore development resulting from a cold pool–MABL collision has been observed in the subtropics (Wakimoto and Kingsmill 1995; Kingsmill and Crook 2003). During the Convection and Precipitation/Electrification (CaPE) Experiment over east-central Florida (Gray 1991), analysis of a collision between a less dense gust front and a denser sea breeze showed the generation of a bore that propagated ahead of the storm outflow, opposing the sea breeze motion (Wakimoto and Kingsmill 1995). A few small convective cells developed in association with the bore, though it was unable to support deep convection over the coastal waters. A climatology of 10 gust front–MABL collisions during CaPE reported that in 7 of the events, a bore or bore–density current hybrid resulted and convection was initiated or enhanced along the bore in a majority of these events (Kingsmill and Crook 2003). Metrics used in the study to predict bore development, specifically the relative speed of the gust front versus the sea breeze, were unsuccessful.

The goal of this study is to understand the conditions that support the development of waves following the interaction between a squall line and marine layer, as well as the impact of the offshore convective forcing mechanism on storm structure and dynamics. Idealized numerical simulations allow for a controlled experiment exploring a parameter space of MABL characteristics and isolate the impact of the stable layer on the storms. Section 2 presents the numerical modeling configuration used in the experiments, a description of the MABL sensitivity experiments, and methods used for diagnostics. Results from the sensitivity experiments are presented in section 3. Section 4 characterizes the collision-generated internal waves. Processes surrounding the collision of the cold pool and marine layer are discussed in section 5, including a mechanism for precollision precipitation enhancement. A comparison between coastal and inland nocturnal squall lines is presented in section 6, with a summary provided in section 7.

2. Methods

a. Numerical model and configuration

Numerical simulations are performed with the nonhydrostatic Cloud Model 1, version 18 (CM1; Bryan and Fritsch 2002), in two dimensions, with a 600 km (horizontal) × 20 km (vertical) domain. Sensitivity experiments using 800- and 1000-km (horizontal) domains indicate that storm evolution is insensitive to domain size. Movement to the left (right) in the domain is referred to as westward (eastward). Horizontal grid spacing is 200 m. The vertical grid is stretched from 50-m spacing below 3 km to 250-m spacing above 10 km, resulting in 148 vertical levels. To simulate a coastal region, the frictional property of a wooded-wetland surface is applied to the bottom boundary of the left 300 km of the domain, while the right 300 km was designated as a water surface. Microphysics processes are parameterized with the Morrison double-moment scheme (Morrison et al. 2009), which predicts number concentrations and mixing ratios of cloud droplets, cloud ice, rain, snow, and graupel. Subgrid-scale turbulence is parameterized using a TKE scheme. No radiation and surface heat and moisture fluxes are included to prevent the convolution of a storm’s response to the MABL and time-varying environmental parameters [e.g., convective available potential energy (CAPE), boundary layer temperature and moisture].

The horizontal boundaries are open radiative to minimize reflection off the lateral edges (Klemp and Wilhelmson 1978). A free-slip condition is applied to the upper boundary, with a Rayleigh damping sponge layer above 15 km. The bottom boundary is semislip to allow for the land to ocean surface transition. The advection of velocities and scalars is integrated with fifth-order horizontal and vertical advection schemes with implicit diffusion (Wicker and Skamarock 2002), with a Klemp–Wilhelmson time-splitting, vertically implicit, horizontally explicit pressure solver. Time stepping follows a Runge–Kutta scheme, with a large time step of 0.75 s and a small time step of 0.125 s (Klemp and Wilhelmson 1978). A weighted essentially non-oscillatory (WENO) scheme is applied to velocity advection on the final step of each Runge–Kutta time step (Shu 2001).

b. Base-state environment

All simulations are initialized with the Weisman and Klemp (1982) analytic sounding (Fig. 1, top) as it supports long-lived, robust squall lines capable of traversing the full horizontal domain. This thermodynamic vertical profile has been used in a number of idealized squall-line process studies (Rotunno et al. 1988; Weisman et al. 1988; Weisman 1992, 1993; Bryan et al. 2003; Weisman and Rotunno 2004; Bryan 2005; Bryan et al. 2006; Morrison et al. 2009; Seigel et al. 2013; Alfaro and Khairoutdinov 2015). The ambient surface-based CAPE (SBCAPE) is 1923 J kg−1 with 44 J kg−1 of convective inhibition (CIN), with a most unstable CAPE (MUCAPE) and most unstable CIN (MUCIN) of 1935 and 42 J kg−1, respectively. The surface-based lifting condensation level (LCL) is 1021 m, with a level of free convection (LFC) at 1796 m. The moisture profile is modified by reducing the water vapor mixing ratio qυ by 10% above 1 km to prevent convective initiation by the MABL (Fig. 1, top). A decrease in environmental humidity above the boundary layer has been shown to reduce updraft strength, total condensation, and rainfall for organized deep convective storms in low- and moderate-CAPE environments (Takemi 2006; James and Markowski 2010; Alfaro and Khairoutdinov 2015). The initiation of deep convective storms is also sensitive to the relative fraction of dry air aloft (not shown). Therefore, a reduction in moisture limits the ability of the MABL to initiate deep convective storms as it traverses the domain. Moisture modifications are restricted to above the LCL to prevent SBCAPE variations. The base-state vertical wind profile increases linearly from 0 to 10 m s−1 from the surface to 2500 m, with constant values above (Fig. 1, top).

Fig. 1.
Fig. 1.

(top) Analytic sounding used for the numerical experiments, with temperature (°C) and mixing ratio (g kg−1) shown in black (from Weisman and Klemp 1982) and mixing ratio reduced by 10% shown in red. (bottom) Profiles of temperature (°C) used in the sensitivity experiments, with the control in black, 250-m-deep MABL in red, 500-m-deep MABL in blue, and 1000-m-deep MABL in gray. The −8-K-θ′ MABL is shown as an example.

Citation: Journal of the Atmospheric Sciences 75, 4; 10.1175/JAS-D-17-0248.1

c. Squall-line initiation

Storms are initiated at time t = 0 using an elliptical +2-K warm bubble, centered at 150 km from the left boundary and 1.5 km above the surface, with horizontal and vertical radii of 10 and 1.5 km, respectively. Within the warm bubble, qυ is modified (increased) to maintain a constant relative humidity (RH) with respect to the base-state environment. Storms develop and mature over land, and move eastward toward the idealized coastline and MABL.

d. Marine atmospheric boundary layer initiation and sensitivity experiments

A series of numerical experiments quantify the sensitivity of deep convective ascent mechanisms and storm structure to varying MABL characteristics, specifically the depth and thermal perturbation. Values constraining the MABL structure are based on observations at mid-Atlantic coastal stations [e.g., Chatham, Massachusetts (CHH); Upton, New York (OKX); Wallops Island, Virginia (WAL); Newport, North Carolina (MHX)] during the warm season [June–August (JJA)] and are documented in the literature (e.g., Keyser and Anthes 1997; Lombardo and Colle 2013; Nunalee and Basu 2014; Lombardo et al. 2016). Potential temperature perturbation θ′ values of −2, −5, and −8 K are used, with the perturbation based on the potential temperature θ of the uniform base-state air adjacent to the MABL. Generally, observed MABL temperature deficit values decrease through the season, with a −8-K-θ′ deficit more common in June and a −2-K-θ′ deficit more common in August. The qυ was decreased, keeping the MABL RH constant relative to the base state to prevent the development of clouds near the top of the MABL and a modification of the environment downstream of the convection. Within the MABL, the temperature T decreases with height and increases at the top of the inversion layer (Fig. 1, bottom). The depths of the MABL in the experiments are 250, 500, and 1000 m. Observational evidence suggests that the most extreme values during JJA are typically about 1300 m.

The MABL is initiated simultaneously with the convection, as a rectangular region of negative temperature perturbation over the water surface. This technique results in the westward movement of the MABL as a density current, which is characteristic of observed sea breezes in the mid-Atlantic during JJA (e.g., Simpson et al. 1977; Simpson 1997; Galvin 1997; Lombardo et al. 2016, 2018). The speed of a density current is a function of its depth and buoyancy. Therefore, the location of the left boundary of each MABL rectangle was positioned such that the squall line would intercept the MABL at an inland point <30 km from the coast (275–290 km in the x direction) at 175–210 min into all simulations. MABL speeds range between 2.0 and 10.6 m s−1, with larger values for increasing depth and decreasing θ′ (Table 1). Movement of the MABL results in a reduced depth at the leading edge, though this does not impact the overall conclusions (section 6).

Table 1.

Average speed of the MABL (m s−1) calculated between initialization and cold pool collision. Values represent the speed toward the left in the domain.

Table 1.

e. Vertical momentum equation diagnostics

A pressure decomposition technique is used to quantify changes in the vertical acceleration associated with squall-line offshore movement. The foundation of this method has been presented and discussed in detail, as well as applied in the analysis of deep convective storms (Das 1979; Davies-Jones 2003; Jeevanjee and Romps 2015; Schenkman et al. 2016; Dawson et al. 2016). Historically, parcel theory has attributed the vertical acceleration of an air parcel to the density difference between the air parcel and the surrounding environment (thermal buoyancy force). It has been shown that this interpretation of the contributing source(s) to vertical momentum is incomplete (Das 1979; Houze 1993; Emanuel 1994; Doswell and Markowski 2004). First, the vertical acceleration due to buoyancy is dependent on the choice of the base-state environment, implying that buoyancy is a relative quantity. Second, the dynamic contribution of the vertical perturbation pressure gradient force to the vertical momentum is neglected. A more complete description of the vertical momentum involves the contribution from the vertical perturbation pressure gradient force and contribution from the thermal buoyancy force, the combination of which are independent of the base state (Doswell and Markowski 2004). The following discussion briefly describes the method that provides unique solutions for the static and dynamic components of the vertical momentum equation (Davies-Jones 2003; Dawson et al. 2016; Schenkman et al. 2016).

The total pressure perturbation p′ can be separated into a dynamic component due to variations in the flow field and a buoyant component due to variations in density. Using these components, the anelastic Lagrangian vertical momentum equation
e1
where is the total density of the horizontally homogeneous hydrostatic base-state environment, p′ is the total perturbation pressure relative to the base state, and F represents friction and diffusive processes (i.e., physical and computational mixing), can be expressed as
e2
the sum of the contribution from the dynamic vertical perturbation pressure gradient force [DVPPGF; first term on the rhs of Eq. (2)], the vertical acceleration due to the combination of the standard Archimedean buoyancy
e3
and the vertical perturbation pressure gradient due to B [second term on the rhs of Eq. (2)]. The effective buoyancy is defined as
e4
where the term in parentheses is the buoyant contribution to the vertical momentum (Jeevanjee and Romps 2015; Dawson et al. 2016). The combination of the DVPPGF and the buoyant contribution are the locally nonhydrostatic vertical pressure gradient force (NHVPGF; Davies-Jones 2003). Calculation of the total effective buoyancy eliminates the ambiguities introduced in the calculation of B due to the choice of an arbitrary base state and can be calculated as follows:
e5
where ∇2β is the 3D Laplacian of the effective buoyancy, g is the acceleration due to gravity, and is the horizontal Laplacian of total density including moisture and hydrometeors (Davies-Jones 2003). Using this approach implies that the buoyant acceleration is the acceleration that results to compensate for horizontal motions generated by horizontal density variations and the associated hydrostatic pressure gradient (Jeevanjee and Romps 2015).

To numerically solve for the buoyant acceleration, model output is interpolated to a uniform domainwide 50-m gridcell width and height prior to the calculation of −∇2β. Additionally, a mirror image of the model domain is concatenated to the right edge of the domain to create periodic lateral boundaries in the presence of the MABL. A homogeneous Dirichlet condition of β = 0 is imposed on the top (z = 20 km) and bottom (z = 0 km) boundaries, forcing the total vertical acceleration to zero at these boundaries (Davies-Jones 2003; Schenkman et al. 2016). The choice of the homogeneous Dirichlet condition at the bottom boundary has been shown to be distinctly correct (Jeevanjee and Romps 2015). The effective buoyancy is solved for using successive overrelaxation (e.g., Fulton et al. 1986). The buoyant acceleration is calculated as the effective buoyancy divided by the base-state density.

Following Dawson et al. (2016), the dynamic vertical perturbation pressure gradient acceleration (DVPPGA) is calculated as the residual of the vertical perturbation pressure gradient acceleration (VPPGA) and the buoyancy terms. The VPPGA is approximated from numerical output using a central-differencing scheme, imposing the condition that the domainwide average p′ = 0. The values of p′ at the upper and lower domain boundaries are determined by linear interpolation through the two levels nearest to the domain edge. Buoyancy B is calculated following Eq. (3) and the vertical acceleration Dw/Dt is calculated following Eq. (1). The frictional acceleration term is negligible.

3. Results

a. Coastal squall-line control simulation

A control simulation is performed excluding the MABL to quantify storm evolution in a thermodynamically and kinematically uniform domain, while including coastal surface friction variations. Sensitivity experiments show that the inclusion of a land surface causes the lowest 100–200 m of the cold pool to lag 5–10 km behind a cold pool over an ocean surface, slowing the storm speed by ~0.03% (not shown), which does not impact the overall conclusions (section 6). In the MABL sensitivity experiments, the average cold pool–MABL collision time is near 190 min. The control experiment is analyzed beginning at this time as a benchmark for later discussions.

At 190 min, the storm is well developed and located 15 km west of the coastline, illustrated in the 10-min time-averaged mixing ratio (Fig. 2). The squall line reaches a quasi-steady state prior to crossing the land–water surface friction boundary. As it moves over the water surface at 16.9 m s−1 (Table 2), convection remains robust and the anvil continues to expand horizontally (Fig. 2).

Fig. 2.
Fig. 2.

Control simulation at (left) 190, (center) 370, and (right) 450 min, with (top) 10-min time-averaged mixing ratio (g kg−1, shaded; includes qrain, qsnow, qgraupel, qice, and qcloud), potential temperature perturbation (contoured every −1 K), and uz wind vectors (reference vector 10 m s−1), (middle) instantaneous equivalent potential temperature (K, shaded) and precipitation mixing ratio (0.04 g kg−1 contours), and (bottom) instantaneous buoyancy (m s−2, shaded) and vertical motion (m s−1; positive contours in black at 1, 6, 11, and 16 m s−1 and negative contours in gold at −16, −11, −6, and −1 m s−1). Note that the z axis is consistent among plots, though the x axis telescopes down, moving from the top to bottom row.

Citation: Journal of the Atmospheric Sciences 75, 4; 10.1175/JAS-D-17-0248.1

Table 2.

Average storm speed (m s−1) calculated from 370 to 450 km, while the storm is located over the water surface. Values represent the speed toward the right in the domain. The control storm speed is 16.9 m s−1.

Table 2.

The environmental instability remains relatively constant in space and time in the absence of radiative forcing and surface fluxes, with potential instability values near −12°C km−1 between 1–5 km (Fig. 2), conditional instability from the surface to 4 km (not shown), and 1512 J kg−1 of SBCAPE (1872 J kg−1 of MUCAPE) averaged 40 km downstream of the cold pool (Table 3). The CAPE values here are slightly different than the point values from the initialization profile, since these are 40-km-wide averaged values and the environment immediately ahead of the squall line is modified by the storm (Fovell 2002; Fovell et al. 2006). The LFC is 1.5 km above the surface, and the head of the 2–2.5-km-deep cold pool located 3–8 km downstream of the precipitation is efficient at lifting air parcels to this level (Fig. 2). Ascent associated with the cold pool is as large as 6 m s−1 through the lowest 4 km (Fig. 2).

Table 3.

SBCAPE (J kg−1) [with CIN (J kg−1) in brackets] and MUCAPE (J kg−1) averaged over 40 km downstream of the storm cold pool, when the cold pool is located at 450 km. Control values are 1512 [38] and 1872, respectively.

Table 3.

b. Coastal squall-line sensitivity experiments

1) Storm cloud and precipitation structure

Storms successfully move across the idealized coastline in all sensitivity experiments (Fig. 3), which will be addressed in section 3b(2). Discussion of cloud and precipitation structure focuses on 450 min into the simulation. The storms are approximately 200 km offshore and have moved over the MABL for more than 4 h, allowing storms to reach a quasi-steady state over the stable layer, except for the storm moving over the −8-K-θ′ 1000-m-deep MABL, which is decaying and intentionally highlighted. This is the only storm that decays within the domain. Storm decay in this simulation may result from internal storm physical processes, addressed in sections 4 and 5a. Decay may also be a consequence of the proximity of the storm to the eastern boundary of the domain. Numerical artifacts may have impacted storm evolution leading to decay, rather than independent physical processes associated with the storm. At this time, the storms are over MABLs with depths near the initialized values (250, 500, and 1000 m).

Fig. 3.
Fig. 3.

Time-averaged mixing ratio (g kg−1, shaded; includes qrain, qsnow, qgraupel, qice, and qcloud) over 10 min beginning at 450 min, time-averaged potential temperature perturbation (contoured every −3 K starting at −1 K) over 10 min beginning at 450 min, and instantaneous uz wind vectors (reference vector 10 m s−1) at 450 min for the (left) 250-, (center) 500-, and (right) 1000-m-deep MABL and the (top) −2-, (middle) −5-, and (bottom) −8-K-θ′ MABL experiments.

Citation: Journal of the Atmospheric Sciences 75, 4; 10.1175/JAS-D-17-0248.1

For storms moving over a −2-K-θ′ MABL, precipitation structures are similar to the control experiment (Fig. 2), though the convective cores are weaker and shallower for storms over the 1000-m-deep MABL (Fig. 3). Convection weakens further for storms over a −5-K-θ′ MABL. Deep convection is more vigorous for storms over the shallower MABLs, with notably weaker convective and stratiform precipitation for the storm moving over the deepest MABL. The squall lines over the coldest MABL are even less intense, especially while over the deepest MABL.

2) Thermodynamic properties and convective forcing mechanisms

Presentation of equivalent potential temperature θe and buoyancy within the lower troposphere (surface to 4 km) provides initial insights into the offshore convective forcing mechanism and associated ambient thermodynamics in the presence of the MABLs (Figs. 4, 5). Given that potential instability exists in an elevated layer of 1–5 km, the inclusion of even the deepest MABL does not impact its magnitude. The presence of this elevated layer of potential instability likely supports the successful movement of all storms over the stable layers. Such elevated layers of high equivalent potential temperature have been shown to sustain observed organized, intense nocturnal convection (Trier et al. 2006). The inclusion of an MABL does impact the potential stability below 1 km, creating a region of enhanced ∂θe/∂z > 0 through the depth of the MABL (not shown), as well as the vertical profile of CAPE (Fig. 6).

Fig. 4.
Fig. 4.

Equivalent potential temperature (K, shaded) and mixing ratio (0.04 g kg−1, contours) at 450 min for the (left) 250-, (center) 500-, and (right) 1000-m-deep MABL and the (top) −2-, (middle) −5-, and (bottom) −8-K-θ′ MABL experiments.

Citation: Journal of the Atmospheric Sciences 75, 4; 10.1175/JAS-D-17-0248.1

Fig. 5.
Fig. 5.

Buoyancy (m s−2, shaded) and vertical motion (m s−1; positive contours in black at 1, 6, 11, and 16 m s−1 and negative contours in gold at −16, −11, −6, and −1 m s−1) at 450 min for the (left) 250-, (center) 500-, and (right) 1000-m-deep MABL and the (top) −2-, (middle) −5-, and (bottom) −8-K-θ′ MABL experiments. Note the z axis is from 0 to 10 km with the x axis from 500 to 570 km.

Citation: Journal of the Atmospheric Sciences 75, 4; 10.1175/JAS-D-17-0248.1

Fig. 6.
Fig. 6.

CAPE (J kg−1, shaded) and CIN (50 J kg−1 contoured in black) at 450 min for the (left) 250-, (center) 500-, and (right) 1000-m-deep MABL and the (top) −2-, (middle) −5-, and (bottom) −8-K-θ′ MABL experiments. Note the z axis is from 0 to 6 km with the x axis from 500 to 600 km.

Citation: Journal of the Atmospheric Sciences 75, 4; 10.1175/JAS-D-17-0248.1

Squall lines over a −2-K-θ′ MABL are forced by a cold pool efficient at lifting surface air parcels to their LFC as they advance over the ocean surface (Fig. 4; Table 4). The equivalent potential temperature associated with the MABL is 333 K, which is 2–3 K greater than the storm outflow (Fig. 4), and the buoyancy of the cold pool (−0.3 to −0.2 m s−2) is less than that of the MABL (−0.1 to −0.05 m s−2; Fig. 5). Ascent depth and magnitude for the storm over shallowest MABL is similar to the control (Fig. 3), with a reduction in magnitude and depth for progressively deeper MABLs (Fig. 5). Despite the presence of a −2-K-θ′ MABL, SBCAPE of 539–603 J kg−1 is available (Table 3; Fig. 6). Additionally, there is CAPE above the MABLs with values over 2000 J kg−1 (Fig. 6). The vertical profile of instability, in part, constrains the intensity of squall lines (Alfaro and Khairoutdinov 2015). Environments with the greatest vertically integrated CAPE (as deduced from Fig. 5) support storms with the deepest and most intense convective cores (Fig. 3). Since the greatest CAPE is above the MABL to 1.5 km, storms moving over the shallower MABLs are the most intense (Figs. 3, 6).

Table 4.

Surface-based LFC (km) and the elevated LFC calculated using the level of the maximum equivalent potential temperature (km) in brackets. The control value is 1.5 km.

Table 4.

For simulations with a −5-K-θ′ MABL, the θe and buoyancy of the cold pool and MABL are similar (Figs. 4, 5), contributing to a modification in convective forcing mechanism following the collision. At 450 min, the cold pool is noticeably ahead of the convective line (Fig. 4), with a pronounced dome of negatively buoyant air (Fig. 5). While over the 250-m MABL, cold pool ascent is elevated and weaker than prior experiments, though the structure is similar. For storms over the deeper MABLs, circulatory motions of the individual convective cells (Yang and Houze 1995; Fovell and Tan 1998) above the cold pool–driven ascent are visible, suggesting more upright ascent at the leading edge (Fig. 5). There is no CAPE from the surface to just below the top of the MABL, with CAPE < 100 J kg−1 near the top of the stable layer (Table 3; Fig. 6), though the vertical profile of instability above the MABL is similar to the −2-K-θ′ MABL experiments. The reduced vertically integrated CAPE supports storms that are weaker than those over the −2-K-θ′ MABL, with a similar relationship to MABL depth (Fig. 3).

A new convective forcing mechanism emerges following the collision of the storm outflow and the −8-K-θ′ MABL, a regime where the MABL is less buoyant than the storm outflow (Figs. 4, 5). For all MABL depths, internal gravity waves form along the top of the stable layer. The waves are composed of stable boundary layer air, with buoyancy values that of the MABL (Fig. 5). These features are discernable as early as 20 min after the collision and 10 km from the coast (not shown). At 450 min, the waves are 15–25 km downstream of the precipitation, though the structure in the 1000-m-deep MABL experiment is more complex given that the storm is undergoing decay (Fig. 4). Postcollision wave development impacts squall-line speed, with storms forced by an internal gravity wave moving 2–3.5 m s−1 faster than other storms (Table 2). There is periodic ascent and descent associated with the waves, with rising motion ahead of the wave crest and sinking motion behind (Fig. 5). As expected, there is no CAPE from the surface through the depth of the MABL, with elevated instability similar to the other experiments (Table 3; Fig. 6). The reduced vertical instability supports the weakest storms within the MABL parameter space (Fig. 3; Alfaro and Khairoutdinov 2015).

3) Vertical acceleration

Analysis of the time-averaged vertical acceleration provides insight into the physical mechanisms associated with storm ascent as storms move over the MABLs, including evidence supporting the transition from cold pool to internal wave forcing within the MABL parameter space. Ten-minute time-averaged fields are presented, though averages were performed over 30 min to test the robustness of these results, showing only minor differences. Quantities are calculated beginning at 370 min to illustrate the vertical acceleration for mature squall lines over the MABL prior to decay (i.e., the storm over the −8-K-θ′ 1000-m MABL is decaying at 450 min). Diagnostics for the control experiment illustrate the structure of the vertical acceleration and the relative contribution of each component in the absence of an MABL (Fig. 7). Vertical acceleration along the cold pool boundary extends from the surface to 2.5 km and is maximized in the lowest kilometer (0.01–0.15 m s−2; Fig. 7a). Accelerations are dynamically driven due to variations in the flow field along the cold pool boundary (i.e., diffluence, deformation, rotation), with a minimal contribution from effective buoyancy (Fig. 7b). The DVPPGA is largest in the lowest kilometer associated with the greatest confluence at the cold pool edge.

Fig. 7.
Fig. 7.

The control experiment time-averaged (a) DVPPGA (m s−2, shaded), vertical acceleration (m s−2; positive contours in black at 0.01, 0.05, 0.1, 0.15, and 0.2 m s−2 and negative contours in gold at −0.2, −0.15, −0.1, −0.05, −0.01 m s−2), and uz wind vectors (reference vector 10 m s−1) and (b) buoyant contribution to the vertical acceleration (m s−2, shaded) and vertical acceleration (m s−2; positive contours in black at 0.01, 0.05, 0.1, 0.15, and 0.2 m s−2 and negative contours in gold at −0.2, −0.15, −0.1, −0.05, −0.01 m s−2). Averages are calculated over 10 min beginning at 370 min.

Citation: Journal of the Atmospheric Sciences 75, 4; 10.1175/JAS-D-17-0248.1

Analysis of only the 250- and 1000-m-deep MABL experiments are presented for the two more buoyant marine layers to highlight the greatest contrasts in vertical acceleration. For the case with a −2-K-θ′ 250-m-deep MABL, the total vertical acceleration associated with the cold pool is shallower and smaller than the control (Fig. 2 and Figs. 8, 9), implying weaker convergence at the leading edge. This may result from a reduction in the horizontal pressure gradient force (PGF) due to a smaller horizontal density gradient across the cold pool boundary in the presence of the MABL. For storms over the 1000-m-deep MABL, the vertical accelerations are more comparable to the control experiment (Fig. 2 and Figs. 8, 9), potentially because of the larger easterly u component of the wind associated with the deeper, faster MABL contributing to increased convergence (Fig. 10; Table 1).

Fig. 8.
Fig. 8.

Time-averaged DVPPGA (m s−2, shaded), vertical acceleration (m s−2; positive contours in black at 0.01, 0.05, 0.1, 0.15, and 0.2 m s−2 and negative contours in gold at −0.2, −0.15, −0.1, −0.05, −0.01 m s−2), and uz wind vectors (reference vector 10 m s−1) for the (left) 250- and (right) 1000-m-deep MABL and the (top) −2- and (bottom) −5-K-θ′ MABL experiments. Averages are calculated over 10 min beginning at 370 min.

Citation: Journal of the Atmospheric Sciences 75, 4; 10.1175/JAS-D-17-0248.1

Fig. 9.
Fig. 9.

Time-averaged buoyant contribution to the vertical acceleration (m s−2, shaded) and vertical acceleration (m s−2; positive contours in black at 0.01, 0.05, 0.1, 0.15, and 0.2 m s−2 and negative contours in gold at −0.2, −0.15, −0.1, −0.05, −0.01 m s−2) for the (left) 250- and (right) 1000-m-deep MABL and the (top) −2- and (bottom) −5-K-θ′ MABL experiments. Averages are calculated over 10 min beginning at 370 min.

Citation: Journal of the Atmospheric Sciences 75, 4; 10.1175/JAS-D-17-0248.1

Fig. 10.
Fig. 10.

The u component of the wind at 450 min averaged 40 km downstream of the cold pool, with the control in black, 250-m-deep MABL experiments in red, 500-m-deep MABL experiments in blue, and 1000-m-deep MABL experiments in gray. The −2- (dotted), −5- (dashed), and (bottom) −8-K-θ′ MABL (solid) experiments are shown.

Citation: Journal of the Atmospheric Sciences 75, 4; 10.1175/JAS-D-17-0248.1

For a moderately cool MABL (θ′ = −5 K), the vertical acceleration is elevated above 250 m and weaker than the other experiments (Figs. 8, 9). The similar buoyancy values of the cold pool and MABL likely contribute to a further reduction in the PGF across the cold pool boundary, reflected in the smaller wind magnitudes at the lowest levels behind the cold pool boundary (Fig. 8). Vertical accelerations are primarily dynamically driven, though there is a weak reflection of a buoyancy acceleration positive–negative couplet between 1 and 2 km (Fig. 9). This and the minimal acceleration below 250 m may be a reflection of the transition from cold pool convective forcing to a hybrid surface cold pool–elevated wave regime.

The structure of the vertical acceleration changes when the −5-K-θ′ MABL is deepened to 1000 m (Figs. 8, 9). The depth of the acceleration is the greatest among experiments with two maxima, which again may reflect the transition to a hybrid convective forcing regime (Figs. 8, 9). DVPPGA is dominant with weak opposing accelerations due to buoyancy above 1 km (Figs. 8, 9). The relatively large MABL speed and the associated depth and strength of the u component of the wind (Table 1; Fig. 10) may contribute to the slightly larger low-level DVPPGA maximum compared to the shallower MABL experiment (Fig. 8).

As storms move over the coolest MABLs (−8-K-θ′), convective forcing for ascent is supported by an internal gravity wave, with oscillating positive and negative vertical accelerations (Fig. 11). Though the total vertical acceleration is primarily due to the DVPPGA, there are positive–negative couplets of accelerations due to buoyancy, visible for storms over the −5- and −8-K-θ′ MABL at this time. The positive and negative values correspond to upward and downward vertical motion, respectively (Fig. 5), sometimes leading the vertical accelerations due to dynamics. As the waves propagate eastward, air experiences the positive buoyancy vertical acceleration just prior to, or at the same time as, the positive dynamic acceleration. Therefore, vertical accelerations may be initially driven by buoyancy processes and are subsequently reinforced by the strong dynamical component. The speed of the internal waves increases with increasing wave amplitude, addressed in section 4, with the most waves visible along the top of the deepest MABLs at this time.

Fig. 11.
Fig. 11.

For the −8-K-θ′ MABL experiment, (left) time-averaged DVPPGA (m s−2, shaded), vertical acceleration (m s−2; positive contours in black at 0.01, 0.05, 0.1, 0.15, and 0.2 m s−2 and negative contours in gold at −0.2, −0.15, −0.1, −0.05, −0.01 m s−2), and uz wind vectors (reference vector 10 m s−1), and (right) the time-averaged buoyant contribution to the vertical acceleration (m s−2; positive contours in black at 0.01, 0.05, 0.1, 0.15, and 0.2 m s−2 and negative contours in gold at −0.2, −0.15, −0.1, −0.05, −0.01 m s−2), with a (top) 250-, (middle) 500-, and (bottom) 1000-m-deep MABL. Averages are calculated over 10 min beginning at 370 min.

Citation: Journal of the Atmospheric Sciences 75, 4; 10.1175/JAS-D-17-0248.1

4) Passive tracer motion

To complement the vertical acceleration diagnostics, passive tracers quantify air parcel trajectories into the storm originating from different vertical levels within the MABL. Tracers are released at 370 min between 0 and 500 m, 500 and 1800 m, and 1800 and 2500 m (Fig. 12). The 0–500-m layer highlights the movement of air parcels originating within the full depth of the intermediate (500 m) MABL and least buoyant layer of the deepest (1000 m) MABL. The 500–1800-m layer highlights trajectories of air originating above the intermediate MABL and within the more buoyant layer of the deepest MABL to the base-state LFC. The 1800–2500-m layer highlights trajectories of air originating above the base-state LFC and within the vertical wind shear layer (0–2.5 km). A 10-km-wide block of tracers is released immediately ahead of the storm (e.g., Fig. 12).

Fig. 12.
Fig. 12.

Passive tracer concentration for the control experiment released between (top) 0 and 500 m (blue), (middle) 500 and 1800 m (black), and (bottom) 1800 and 2500 m (red). Tracers were released at (left) 370 min and allowed to travel for 30 min, with snapshots of (center) 385 and (right) 400 min shown. The −1-K potential temperature perturbation surface is contoured in black to highlight the location of the cold pool.

Citation: Journal of the Atmospheric Sciences 75, 4; 10.1175/JAS-D-17-0248.1

Passive tracer analysis for the control experiment provides insight into air trajectories in the absence of an MABL (Fig. 12). As expected, all parcels ascend into the storm updrafts associated with the surface-based vertical acceleration that extends through the LFC (Fig. 7; Table 4). Similarly, all air parcels within and above the −2-K-θ′ MABL, including those within the 1000-m-deep MABL (Fig. 13a), rise into the storms, indicating that the system is still surface based in the presence of the relatively warm MABL.

Fig. 13.
Fig. 13.

Passive tracer concentration between (top) 0 and 500 m (blue), (middle) 500 and 1800 m (black), and (bottom) 1800 and 2500 m (red) for the experiments (a) −2-K-θ′ 1000-m-deep MABL at 400 min, (b) −5-K-θ′ 250-m-deep MABL at 400 min, (c) −5-K-θ′ 500-m-deep MABL at 400 min, (d) −5-K-θ′ 1000-m-deep MABL at 400 min, (e) −8-K-θ′ 500-m-deep MABL at 400 min, (f) −8-K-θ′ 1000-m-deep MABL at 385 min, and (g) −8-K-θ′ 1000-m-deep MABL at 400 min. The −1-K potential temperature perturbation surface is contoured in black to highlight the location of the cold pool and MABL.

Citation: Journal of the Atmospheric Sciences 75, 4; 10.1175/JAS-D-17-0248.1

Storms moving over a −5-K-θ′ MABL are partially elevated, consistent with the elevated vertical acceleration (Figs. 8, 9) and the lack of convective instability through most of the MABL (Fig. 6): the air source becomes increasingly elevated as the depth of the MABL increases. For storms over a 250-m-deep MABL, 38% of the air from the lowest 500 m ascends above 3 km, with the majority originating between 250 and 500 m (Fig. 13b). For a 500-m-deep MABL, most air parcels originating within the MABL remain in the boundary layer, with only 4.5% rising above 3 km (Fig. 13c). For a 1000-m-deep MABL, less than 3% of the air parcels originating below 500 m rise into the storm, though most parcels from above 500 m rise into the storm, indicating that the storm is elevated but not above the MABL (Fig. 13d), supported by the vertical profile of CAPE (Fig. 6).

Most air parcels originating within the least buoyant MABL are unable to rise into the storm. A negligible amount (2%) of air within the 500-m MABL rises above 3 km (Fig. 13e), and none of the air within the bottom half of the 1000-m-deep MABL ascends above the stable layer (Figs. 13f,g). As indicated by the passive tracers, the waves are inefficient at lifting stable surface air parcels into a storm, which favors the maintenance of squall lines over stable boundary layers. The ingestion of MABL air into the storm would diminish the deep convective latent heating, resulting in a reduction in storm intensity and potentially decay (Alfaro 2017).

Air above the 1000-m-deep MABL struggles to ascend into the storm as well because of internal wave motions (Figs. 13f,g). Parcels initially rise associated with the upward ascent and acceleration of the approaching wave, but descend down the back side of the wave associated with the downward motions and accelerations (Fig. 13f). Air ascending over the wave crest rises through and above the LFC[θe(max)] (Table 4), though fails to rise freely. Subsequently, air successfully ascends into the storm in response to the trailing cold pool (Fig. 13g). Therefore, the waves are insufficient at lifting air into the storms and lift from the trailing cold pool is necessary. In a case study event observed during the Cooperative Oklahoma Profiler Studies field program in May 1991 (COPS-91), ascent associated with the passage of a bore was insufficient to initiate convective storms (Koch and Clark 1999). The authors hypothesized that the bore-induced vertical motion was either too shallow or the duration was too short. In our study, ascent appears to be sufficiently deep with air rising above the elevated LFC. Additionally, elevated CAPE extends for several kilometers vertically above the waves, indicating that ascent is not inhibited by a lack of instability (Fig. 6).

4. Internal gravity wave characteristics

The internal gravity waves resulting from the collision of the cold pool and the −8-K-θ′ MABL manifest initially as atmospheric bores (Wood and Simpson 1984; Rottman and Simpson 1989; Klemp et al. 1997; Parker 2008) and appear to evolve into a family of solitary waves (Christie et al. 1978, 1979; Maxworthy 1980; Crook 1988). A bore is a gravity wave disturbance that can form as a density current encounters a stably stratified boundary layer and propagates along the low-level inversion advancing ahead of the density current (Haase and Smith 1984; Rottman and Simpson 1989; Koch et al. 1991). Unlike density currents, classical bores transport no mass, though observational and numerical studies illustrate the existence of hybrid structures with density current air within the leading edge of the bore, indicating mass transport (e.g., Fulton et al. 1990; Haase and Smith 1989). Following the cold pool–MABL collision, the waves propagate as type A undular, laminar bores (1 < h1/h0 < 2) or type B with mixing along the leading undulation (2 < h1/h0 < 4), where h0 is the depth of the MABL and h1 is the mean height of the bore (Rottman and Simpson 1989; Klemp et al. 1997; Table 5).

A bore can evolve into a family of solitary waves, known as a soliton, in the presence of a sufficiently deep, stable waveguide to trap the vertical propagation of wave energy (Christie et al. 1979; Fulton et al. 1990; Knupp 2006; Koch et al. 2008). Observations and numerical modeling studies have shown that solitary wave energy can become trapped when there exists a relatively deep, weakly stratified layer above the stable boundary layer as well as a favorable curvature vertical profile in the low-level winds (Doviak and Ge 1984; Crook 1986, 1988; Fulton et al. 1990). Doviak and Ge (1984) observed that 7 m s−1 winds at 500 m opposing the direction of wave motion transitioning to 5 m s−1 at 1 km in the direction of wave motion was sufficient to trap wave energy within the boundary layer. Similarly, the numerical modeling study of Crook (1988) showed that 6 m s−1 winds below 1.3-km opposing wave motion and 6 m s−1 wind above in the wave propagation direction supported the development of solitary waves.

The vertical thermodynamic and wind profiles support the development of a soliton for internal waves propagating along the −8-K-θ′ MABL. The static stability is relatively weak, θ−1θ/∂z ≅ 1 × 10−5 m−1, within several kilometers above the MABL. The curvatures and magnitudes of the vertical wind profile are similar to those seen in Doviak and Ge (1984), Crook (1988), and Fulton et al. (1990). For example, in the 500 (1000)-m MABL experiment, winds are 3 (5) m s−1 opposing the wave propagation direction near 200 (250) m and 4 (9) m s−1 in the same direction as the waves at 600 m (750 m; Fig. 10).

Doviak and Ge (1984) noted that solitary waves have supercritical speeds that allow for wave propagation ahead of storm outflows. In the −8-K-θ′ simulations, the undular bores that appear to have evolved into a soliton propagate at somewhat similar speeds, as predicted by theory (Table 5), though there is little difference in wave speed among the experiments (Table 2). Based on hydraulic theory, the theoretical propagation speed of a bore cbore can be expressed as (Rottman and Simpson 1989; Knupp 2006)
e6
where gravity wave speed cgw is (Simpson 1997; Knupp 2006)
e7
where θυ is the average virtual potential temperature through the depth of the inversion and Δθυ is the difference in average θυ across the inversion. At 370 min, the propagation speed of the waves along the 250 (1000)-m-deep MABL is about 3.7 m s−1 lower (4.8 m s−1 higher) than the theoretical speed (Tables 2,5). For waves propagating along the 1000-m-deep MABL, the soliton is no longer clearly visible at 450 min (Figs. 4, 5). One hypothesis, as posed by Christie et al. (1979), is that for large-amplitudes waves, nonlinearity dominates over dispersion, causing the waves to steepen, break, and evolve into a turbulent internal bore.
Table 5.

Depth of the MABL h0 (m) and mean height of the bore h1 (m) at 370 min for the −8-K-θ′ MABL simulations. Type A undular, laminar bores are produced when 1 < h1/h0 < 2, while type B bores with mixing along the leading undulation are produced when 2 < h1/h0 < 4 (Rottman and Simpson 1989). The theoretical gravity wave speed cgw (m s−1) and the theoretical bore speed cbore (m s−1) are calculated at 500 km in the x direction, θυ is calculated through depth h0, and Δθυ is calculated as the difference in the average θυ over 250 m above the stable layer and the average θυ of the stable layer. It is worth noting that the type B bore in the 250-m-deep MABL experiment evolves into a type A bore by 450 min, with h1/h0 = 1.8.

Table 5.

Representative time series from the −8-K-θ′ 500-m-deep MABL experiment illustrate elevated potential temperature, pressure, and water vapor mixing ratio, as well as surface temperature and wind associated with the passage of the waves (Fig. 14). As the wave crest approaches, pressure and mixing ratio above the surface increase, while potential temperature decreases (Fig. 14). The MABL is disrupted by the passage of the wave, resulting in downward mixing of warmer air from above the stable layer and upward mixing of cooler air from within the stable layer (Koch and Clark 1999). Consequently, air above the surface cools, leading to a hydrostatic pressure jump, while the surface temperature increases (Fig. 14). As the wave trough passes, potential temperature increases about 3 K, while mixing ratio and pressure decrease approximately 6 g kg−1 and 0.3 hPa, respectively, due to subsidence. Temperature at the surface remains constant following the initial mixing. These time series parallel observed surface and elevated flight level data during bore and solitary wave events (e.g., Koch and Clark 1999; Koch et al. 2008). Passage of the trailing cold pool is indicated by cooling at the surface, an increase in wind speed, and a higher mixing ratio associated with the deeper convection. There is evidence of another wave behind the cold pool, though the signatures are dampened, highlighting the complexity of motions at the cold pool interface.

Fig. 14.
Fig. 14.

Time series from the −8-K-θ′ 500-m-deep MABL experiment at 470 km in the x direction and 250 m in the vertical of (a) potential temperature (K), (b) pressure (hPa), (c) water vapor mixing ratio (g kg−1), (d) surface temperature (°C), and (e) surface wind (m s−1). The light (dark) gray small dashed line(s) marks the approximate time of the passage of a wave crest (trough). The thick black dashed line marks the passage of the cold pool.

Citation: Journal of the Atmospheric Sciences 75, 4; 10.1175/JAS-D-17-0248.1

For comparison, time series illustrating the passage of a cold pool–wave hybrid from the −5-K-θ′ 500-m-deep MABL experiment are presented (Fig. 15). As expected, the collective signal of the elevated and surface variables depicting the passage of the hybrid feature is more complex. The initial response of the above-surface potential temperature, pressure, and mixing ratio is consistent with a wave passage, through there is variability in the surface temperature and a notable increase in wind speed (Fig. 15). It is challenging to identify the passage of the wave trough, though there is weak evidence in the elevated variables. At the surface, there is the signal of two cold pool boundaries. The initial boundary is collocated with the wave trough, associated with a decline in surface temperature and increasing winds. Combined trends in the elevated and surface variables at this time likely indicate a hybrid passage of a cold pool and a wave. Following a weak rebound in temperature and wind, the second cold pool passage occurs approximately 10 min later.

Fig. 15.
Fig. 15.

As in Fig. 14, but for the −5-K-θ′ 500-m-deep MABL simulation. The light (dark) gray small dashed line marks the approximate time of the passage of the leading edge of the hybrid cold pool–wave crest (trough). The thick black dashed line marks the passage of the leading edge of the precipitation.

Citation: Journal of the Atmospheric Sciences 75, 4; 10.1175/JAS-D-17-0248.1

5. Processes surrounding cold pool–MABL collisions

a. Precollision precipitation enhancement

Precipitation enhancement occurs for storms interacting with the deepest MABL, illustrated by time series of domain total accumulated precipitation (Fig. 16). This enhancement is directly related to MABL depth, with a secondary dependence on temperature. The total accumulated precipitation is greatest within 20–40 min of the average collision time (Fig. 16) for storms colliding with the deepest marine layers. The signal is the most robust for storms encountering the coldest MABL and lessens for smaller thermal perturbations, with no obvious signal as storms interact with the −2-K-θ′ MABL. Following the increase in total accumulated precipitation, there is a reduced trend in accumulated precipitation, and by the end of the experiments, storms interacting with the deepest marine layers have the lowest accumulated precipitation values.

Fig. 16.
Fig. 16.

Time series of domain accumulated precipitation (109 kg) for the control (black), 250-m-deep MABL (red), 500-m-deep MABL (blue), and 1000-m-deep MABL (gray) for the (a) −2-, (b) −5-, and (c) −8-K-θ′ MABL experiments. The black dashed line marks the average collision time between the storm cold pools and MABLs. The gray dashed line marks the reduction in the postcollision enhanced precipitation accumulation rate for the 1000-m-deep MABL experiments.

Citation: Journal of the Atmospheric Sciences 75, 4; 10.1175/JAS-D-17-0248.1

The precipitation enhancement is, in part, due to the modification of the environment downstream of the squall line by the storm, decreasing the LFC to a height below the top of the MABL, allowing the approaching MABL to successfully lift air parcels into the storm. Prior to collision, convective towers develop downstream of the squall line at the leading edge of the 1000-m MABLs, though these towers do not form ahead of the 250- and 500-m-deep marine layers (Fig. 17). Downstream of the squall line, a moist absolutely unstable layer (MAUL; Bryan and Fritsch 2000) develops due to the storm in all experiments (e.g., Fig. 18). Compiled observations and numerical simulations illustrate that MAULs can exist tens of kilometers downstream of mesoscale convective systems, hundreds of kilometers along the axis of the storm, and for more than 30 min (Bryan and Fritsch 2000). Soundings 3–5 km ahead of the squall lines show MAULs between 800–900 m and 2.3–2.8 km while the storms are over land prior to collision (Fig. 18). The surface LFC decreases to 840–890 m in conjunction with MAUL development. The encroaching 1000-m-deep MABLs are capable of lifting air parcels to the new, lower LFC promoting convective development in advance of the squall line, though the shallower MABLs (250, 500 m) are insufficient (Fig. 17).

Fig. 17.
Fig. 17.

Mixing ratio (g kg−1, shaded; includes qrain, qsnow, qgraupel, qice, and qcloud), potential temperature perturbation (contoured every −1 K), and uz wind vectors (reference vector 10 m s−1) at 190 min for the (left) 250-, (center) 500-, and (right) 1000-m-deep MABL and the (top) −2-, (middle) −5-, and (bottom) −8-K-θ′ MABL experiments.

Citation: Journal of the Atmospheric Sciences 75, 4; 10.1175/JAS-D-17-0248.1

Fig. 18.
Fig. 18.

Profile of temperature (°C) and mixing ratio (g kg−1) at 275 km in the x direction for the (a) −2-K-θ′ 1000-m-deep MABL experiment at 186 min, (b) −5-K-θ′ 1000-m-deep MABL experiment at 187 min, and (c) −8-K-θ′ 1000-m-deep MABL experiment at 178 min. Profiles are from 3 to 5 km downstream of the squall line within the ambient air over land, uncontaminated by the MABL.

Citation: Journal of the Atmospheric Sciences 75, 4; 10.1175/JAS-D-17-0248.1

Bryan and Fritsch (2002) hypothesized that MAULs develop because of dynamically driven layer lifting by the storm cold pool (Figs. 7, 8, 11) in the presence of a conditionally unstable environment (Figs. 1a, 2, 4). However, Fovell et al. (2006) showed that low-frequency gravity waves that form in response to storm latent heating can propagate downstream of the squall line, contributing to the development of a cooler and moister lower troposphere. Both processes may contribute to the development of these MAULs. The moist unstable layers develop periodically downstream of the squall lines (not shown). The deepest instability layer forms approximately 5 km ahead of the storm, above the boundary layer but over a similar vertical depth as the dynamic vertical acceleration (e.g., Fig. 7). At 10–15 km, no MAUL is visible, though it reforms near 20 km downstream, over a shallower, more elevated layer. Further downstream, no moist unstable layers develop, though the atmosphere approaches saturation about 40 km ahead of the storm, with a uniform thermodynamic profile beyond. The cyclic MAUL development may indicate that gravity wave–induced ascent supports their development. However, the depth over which they form could be constrained by the level of dynamic layer lifting closer to the storm and/or gravity wave energy trapping further downstream, indicating that the may develop due to both dynamically driven and gravity wave ascent. The intermittent development of convective towers downstream of the squall lines (e.g., Fig. 17; −5-K-θ′ 1000-m MABL) may be a consequence of the horizontally heterogeneous presence of moist instability.

The secondary dependence of the precipitation enhancement on MABL buoyancy may be a consequence of the greater speed associated with the denser, less buoyant MABL (Table 1) promoting greater convergence (e.g., Fig. 8) and more vigorous ascent. Ascent associated with the −8-K-θ′ 1000-m-deep MABL is 4 m s−1, twice as large as the −5-K-θ′ MABL (2 m s−1) and 4 times as large as the −2-K-θ′ MABL (1 m s−1). The vertical depth is greater as well, extending to 3 km, which is 1.5 (6) times deeper than for the −5 (−2)-K-θ′ MABL. Air parcels lifted by the −8-K-θ′ MABL may be less impacted by entrainment processes because of the more vigorous, deeper ascent contributing to more intense precipitation and greater accumulations.

The subsequent decrease in the trend of accumulated precipitation occurs following the reorganization of the storms following the collision, which will be discussed in section 5b. For the storm moving over the coldest marine layer, the decline may be due to greater entrainment of ambient low-θe air into the buoyant air parcels as they move over the waves prior to rising into the storm. Since the air parcels oscillate vertically over the internal waves, they are exposed to lower-θe air for a longer period of time relative to more efficiently lifted air parcels, likely increasing the entrainment of less buoyant into the air parcels, leading to an overall reduction in parcel buoyancy. Subsequently, the air parcels are lifted by the trailing cold pool and ascend through sloped updrafts, potentially due to the reduced effective shear above the stable layer, allowing for additional entrainment. Squall-line updrafts become more sloped in the presence of weaker vertical wind shear (e.g., Bryan et al. 2003). Additionally, the reduction in the vertical profile of instability after the collision likely contributed to the decline in accumulated precipitation, associated with the decrease in storm intensity (Alfaro and Khairoutdinov 2015). Therefore, while internal gravity waves are a mechanism to advance storms offshore, they contribute to less intense precipitation because of their inefficiency at lifting air into the storms.

b. Storm characteristics surrounding collision

As storms collide with the marine layer, their structure and speed are altered for a subset of interactions, while there is little change in storm characteristics for others. There are minimal differences in storm structure and speed as they encounter the shallower marine layers (i.e., 250, 500 m), with the exception of storms colliding with the −8-K-θ′ 250- and 500-m-deep MABLs, which move 4–5 m s−1 faster than storms over land due to the development of internal waves immediately following the collision. As storms interact with the deepest MABL, there is an apparent increase in storm translational speed due to the development of MABL-generated convective towers downstream of the squall lines and a reorganization of the systems by 230 min (Fig. 19). The easternmost convective elements that develop in association with MABL precollision (210 min) become the leading edge of the reorganized squall line as the convection to the west (230 min), including that associated with the original squall line, weakens. This discrete propagation results in an apparent acceleration of the storms, with speeds 6–9 m s−1 greater than storms over land. Fovell et al. (2006) described a similar discontinuous jump in translation for nocturnal squall lines associated with the development of convection downstream of the organized systems, though convection was triggered by gravity waves generated in response to latent heating from the squall lines. Storms colliding with the −8-K-θ′ MABL move faster than those interacting with the warmer MABLs given the added influence of the internal waves that develop as the MABL and cold pools collide during storm reorganization. Following 230 min, the storms are in a quasi-steady state.

Fig. 19.
Fig. 19.

Mixing ratio (g kg−1, shaded; includes qrain, qsnow, qgraupel, qice, and qcloud), potential temperature perturbation (contoured every −1 K), and uz wind vectors (reference vector 10 m s−1) for the 1000-m-deep MABL experiments at (left) 210, (center) 220, and (right) 230 min with a (top) −2-, (middle) −5-, and (bottom) −8-K-θ′ MABL. New convection highlights deep convective towers that form in association with the MABL downstream of the squall line.

Citation: Journal of the Atmospheric Sciences 75, 4; 10.1175/JAS-D-17-0248.1

6. Comparison to inland nocturnal squall lines

A number of studies have examined and quantified the impact of a gradually developing nocturnal stable boundary layer on inland deep convective storms (e.g., Knupp 2006; Parker 2008; Schumacher 2009; French and Parker 2010; Marsham et al. 2011; Trier et al. 2011; Schumacher 2015). Given that these inland storms and the coastal storms presented in this study move over stable boundary layers, it is instructive to discuss the processes supporting inland nocturnal storms compared to those interacting with a marine layer. There is at least one notable difference regarding the interaction between a storm and each type of stable layer. In coastal regions, storm outflow encounters abrupt horizontal gradients in environmental boundary layer conditions, at times resembling a horizontal elastic collision, that occurs in the presence or absence of solar radiation. During nocturnal cooling events, a storm vertically perturbs a gradually evolving boundary layer during the decline and eventual absence of insolation. The resulting forcing mechanisms that sustain convection over the stable layer in these two regimes are similar, though the conditions that support the development of these physical processes as well as the storm characteristics surrounding the stable-layer interactions appear to be different.

Observational (Knupp 2006; Marsham et al. 2011) and numerical (Parker 2008; Schumacher 2009; Trier et al. 2011; Schumacher 2015) studies of nocturnal MCSs report the development of convectively generated waves along stable boundary layers that support storm maintenance and at times are capable of initiating new deep convection. During the International H2O project, convectively generated downdrafts were observed to initiate waves and bores that propagated along the stable nocturnal boundary layer ahead of the cold pool and initiated new convection downstream (Marsham et al. 2011). The idealized numerical experiments of Parker (2008) showed that squall lines can become forced by an elevated, simple internal bore as the temperature difference between a cold pool and a gradually cooling boundary layer of comparable depths approached zero. This regime is similar to storms moving over the −5-K-θ′ MABL, where the temperature and buoyancy of the cold pool and marine layer are similar, though convection is supported by a cold pool–wave hybrid rather than a simple bore, especially for storms over the deeper MABLs. When both the nocturnal boundary layer and cold pool were cooled at the same rate (i.e., cold pool temperature deficit preserved), forcing transitioned from a density current to a gravity wave as the nocturnal layer cooled and deepened, and the gravity wave speed exceeded that of the density current (Parker 2008). Postcollision gravity waves form only when the marine layer is less buoyant than the cold pool, with no dependence on MABL depth. Furthermore, a “stalling” phase occurred (i.e., the system’s speed decreased) as the temperature of the nocturnal boundary layer approached that of the cold pool (Parker 2008). No such stalling is observed during the interaction of a storm and a marine layer, though there is a reorganization as storms interact with the deepest MABLs. These differences may be a consequence of the differing MABL and cold pool relative depths, type of storm–boundary layer interaction (collision versus gradual cooling), or characteristics of the stable layer (static versus evolving), and suggest that the relationship between the system conditions (i.e., storm and stable layer) and the resulting convective forcing mechanism in coastal and inland regions differs.

Schumacher (2015) discussed an additional complexity regarding the relationship between cold pools and convectively generated gravity waves in a 3D numerical study of elevated heavy-rain-producing MCSs. Convective development by storm-generated internal gravity waves ceased as the storm cold pool strengthened through the addition of dry air into the stable boundary layer. The stronger cold pool moved farther away from the MCS, disrupting the gravity wave low-level lifting on the upstream flank of the storm, limiting back building, storm intensity, and storm accumulated precipitation. This emphasizes the importance of examining both the processes in the leading convective line as well as those in the upstream regions of the storm when assessing the impact of the cold pool–stable layer relationship on precipitation. Additionally, both Parker (2008) and Schumacher (2015) emphasized that storms may still be surface based in the presence of a stable boundary layer, with consistent findings for storms moving over some stable marine layers (Fig. 13)

7. Summary

As squall lines approached the coastline and collided with marine atmospheric boundary layers (MABLs), the postcollision storm characteristics and the mechanism for convective lift over the stable layer were determined by the MABL depth and buoyancy relative to the storm cold pool. When the cold pool was less buoyant than the MABL (−2-K-θ′ MABL experiments), the storm remained forced by a cold pool over the stable layer, as it was over land. The convection was less intense compared to a control experiment with no MABL, in part due to the decrease in the vertical profile of instability in the presence of the stable marine layer. When the buoyancy values were equivalent (−5-K-θ′ MABL experiments), the collision between the marine layer and storm cold pool resulted in the development of a cold pool–wave hybrid, with forcing depth directly proportional to the depth of the marine layer. The further reduction in vertically integrated instability supported weaker convection, with decreasing storm intensity for increasing MABL depth.

The collision of the cold pool and marine layer initiated internal gravity waves on top of the stable marine layer, specifically atmospheric bores that evolved into a soliton, when the storm outflow was more buoyant than the MABL (−8-K-θ′ MABL experiments). These waves formed regardless of MABL depth. Wave development supported storm maintenance over the marine layer, as they were inefficient at lifting stable boundary layer air into the storm: the ingestion of marine layer air into the storm would diminish the convective intensity or promote storm decay. However, the waves were also inefficient at lifting the unstable air above the marine layer into the storm. Wave motions forced air parcels downward on the backside of the waves, and lift from the trailing storm cold pool was needed for parcels to ascend into the storms updrafts. Convection was the weakest among experiments, likely due to a combination of several factors. The vertical profile of instability was further reduced by the presence of the coldest MABL. Air parcels may have been more impacted by entrainment processes prior to ascending into the storm given that lift from the waves was inefficient, exposing the air to turbulence within the lower levels for a larger amount of time. The effective vertical shear experienced by the trailing cold pool was reduced, leading to sloped updrafts, which could have contributed to additional entrainment. Therefore, the waves were a mechanism to support the maintenance of storms over stable layers, though the convective intensity was diminished. Storm speed over the marine layer was the fastest among experiments, constrained by characteristics of the waves.

Precipitation enhancement occurred just prior to the collision of the storm cold pool and only the deepest marine layers (i.e., 1000 m). In an unperturbed environment, the deep marine layer was unable to initiate convection. However, in all experiments, the squall line modified the ambient environment downstream. Dynamic lift and gravity wave processes associated with the storm led to the development of a moist adiabatic unstable layer (MAUL) ahead of a system and a lowering of the level of free convection (LFC) below the top of the deep MABL. As the marine layer moved into the storm-modified environment, it successfully lifted air parcels to the new lower LFC and generated convective towers downstream of the squall line, leading to an increase in accumulated precipitation. The MABLs with shallower depths remained ineffective at initiating convection, and precipitation was not enhanced in these experiments. This mechanism may indicate a greater coastal flash-flooding risk during certain observed squall-line events.

Finescale thermodynamic and kinematic observations of the storm cold pool, as well as the marine and storm-modified environment, are needed to test the robustness of these results during observed coastal squall-line events. Observing and quantifying the vertical profile through these environments at high spatial and temporal resolutions will be especially important. These environments change with time as the storm and marine layer evolve, and therefore, the timing of the cold pool – MABL interaction may be an important component in determining the collision outcome. Ongoing and future work explores the evolution of coastal squall lines in less favorable, more realistic environments representative of the mid-Atlantic United States. Simulations will also expand beyond 2D to evaluate 3D storm processes as squall lines collide with stable marine layers.

Acknowledgments

The authors thank the editor Dr. Robert G. Fovell, three anonymous reviewers, and George H. Bryan for the use and continuous support of his cloud-resolving numerical model, Cloud Model 1 (CM1), as well as for the many insightful conversations regarding squall-line simulations. This research would not have been possible without the generous support of the National Science Foundation (Grant ASG-1514115).

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