Analysis of the Structure and Propagation of a Simulated Squall Line on 14 June 2009

Squall lines are an important type of organized mesoscale convective system (MCS) that are often accompanied by disastrous weather conditions, such as thunderstorms, strong winds, hail, and tornados. Thus, squall line behavior merits widespread research.

Some overseas investigators (Newton, 1950, Fujita, 1955) began to study squall lines as early as the 1950s. (Fujita, 1955) identified structural features, such as the pre-squall low, meso-high, and wake-low pressure system, behind squall lines. In the 1960s, (Browning and Ludlam, 1962) proposed a 3D structural model of a typical thunderstorm. With improvements in science and technology, the structures and features of squall lines have been documented in detail using Doppler radar observations (Roux et al., 1984; Smull and Houze, 1987; Biggerstaff and Houze, 1991, 1993). (Houze et al., 1989) developed a refined conceptual model, describing in detail the circulation within a squall line. (Weisman, 1992) studied the role of rear-inflow jets in a long-lived meso-convective system through an idealized 3D simulation. (Yang and Houze, 1995b) explored the influence of microphysical processes on squall lines through various sensitivity tests. (Trier et al., 1996) used a numerical cloud model to simulate an oceanic tropical squall line and investigate the impact of surface fluxes and ice microphysics on its structure and evolution. (Fovell, 2002) examined the impact of organized convection on a squall line's upstream environment using a traditional cloud model and a dramatically simplified PM (parametrized moisture) model. (Parker and Johnson, 2000) and (Gallus et al., 2008) classified convective systems based on the number of radar-detected cases.

Chinese scholars have also published several studies on squall lines based on model simulations and radar observations. (Cai et al., 1988) analyzed cloud and divergence features of squall lines based on observational data. (He et al., 1992) studied squall line processes in the warm sector of the Jiang-Huai area and described the evident pre-squall low and weak mesoscale low behind the squall lines. (Yao et al., 2005) concluded that strong vertical wind shear and the feedback between strong updrafts and downdrafts during a storm sustain squall lines. Many other scholars have further studied squall line behavior using high resolution numerical models (Wang et al., 2010; Sun et al., 2011; Wu et al., 2013).

In terms of squall line propagation, Newton (1950, 1966) and Fujita (1955) first discovered the crucial impact of vertical wind shear on squall line development. The traditionally cited mechanism for squall line propagation is the forcing of new cells by cold outflow convergence (Smull and Houze, 1985; Johnson and Hamilton, 1988). (Rotunno et al., 1988) and (Weisman et al., 1988) used a 3D numerical model to investigate the effect of vertical wind shear on squall line structure and evolution, i.e., the RKW theory. This theory states that the combination of the positive horizontal vorticity induced by low-level vertical wind shear and the negative horizontal vorticity induced by cold outflow sustains squall line development. Later, (Weisman, 2004) and (Weisman and Rotunno, 2005) confirmed the RKW theory based on a simplified 2D vorticity streamfunction model. Other researchers also investigated the theory that cold outflow promotes squall line development (Wilhelmson and Chen, 1982; Fovell and Ogura, 1989; Bryan et al., 2006). (Chen and Wang, 2012) analyzed low-level dynamic and thermodynamic effects on a squall line occurrence in North China using RKW theory and the effects of a buoyant environment with high convective available potential energy (CAPE) and a low level of free convection. In addition, several scholars have found a close relationship between gravity waves and squall line development. (Stobie et al., 1983) described a severe storm occurrence in the north central United States, where the storm's spatial distribution and movement corresponded to observed gravity waves. (Zhang and Fritsch, 1987) investigated the interaction between gravity waves and a squall line and stated that the gravity waves were initiated by a supergeostrophic low-level jet and enhanced by intense convection. (Yang and Houze, 1995a) suggested that the multicellular structure of a storm was associated with gravity waves, and the commonly described "cut-off" process was actually a gravity wave phenomenon. (Zhang et al., 2001) used wavelet analysis to investigate the evolution of gravity wave structures and indicated that a train of gravity waves was continuously generated by geostrophic adjustment. Li (1976, 1978, 1981) proposed that gravity waves helped trigger heavy precipitation and analyzed the nonlinear effect of gravity waves on the squall line. (Xu and Sun, 2003) studied the effect of gravity waves on rainstorms during the mei-yu front. (Gong et al., 2005) investigated wave-convection interactions and verified the theory of gravity wave propagation in a severe thunderstorm. (Zhu et al., 2009), based on wavelet analysis, found that the lee wave generated from the Taihang Mountains was one possible squall line initiation mechanism.

It is difficult to study a squall line using conventional observation and reanalysis data because of its small scale and short duration. In this paper, high-resolution spatial and temporal data from the Advanced Regional Prediction System (ARPS) model are used to analyze the characteristics of a squall line. Section 2 provides a description of the model. Section 3 verifies the simulation results. Section 4 discusses the thermodynamic and dynamic features of the squall line at various stages. Section 5 explores the mechanisms of the squall line propagation, and section 6 proposes a conceptual model of the case study. The final section presents the conclusions.

ARPS (Advanced Regional Prediction System) is a non-hydrostatic mesoscale simulation model developed by the Center for Analysis and Prediction of Storms (CAPS) at the University of Oklahoma. The model is suitable for small spatial and temporal scales, such as meso- and storm-scale systems. In this study, ARPS is used to simulate the case of a severe squall line on 14 June 2009. The initial and lateral boundary conditions of the model were obtained from the National Centers for Environmental Prediction/National Center for Atmospheric Research (NCEP/NCAR) Global Forecast System (GFS) reanalysis dataset, with a resolution of 0.5^{°× 0.5°}. The radial velocity and reflectivity of eight radars in the provinces of Shandong, Jiangsu, Anhui and Zhejiang were assimilated into ARPS model. Domain 1 had a spatial resolution of 3 km; it was initiated at 0600 UTC 14 June 2009 and was continuously integrated until 0600 UTC 15 June 2009. The model has 53 layers in the vertical direction, with a grid size of 500 m. Domain 1 used a nudging method to assimilate radar observations every 12 minutes, along with an ice microphysics parameterization scheme (the Lin-Tao scheme).

Domain 2 had a grid size of 1 km (803× 803 grid points); it was integrated for 8 hours starting at 0800 UTC. The following parameterization schemes were used: a 3-moment bulk microphysics parameterization (MYTM); a 1.5-order turbulent kinetic energy-based (TKE) closure scheme; an atmospheric radiation transfer parameterization scheme; and a two-layer force-restore soil scheme (Noilhan/Planton scheme). The model was set up to output results every 10 minutes. The detail descriptions about the model were displayed in table 1.

Mesoscale convective systems can be classified into two types: linear and nonlinear systems. Based on radar-observed characteristics of 88 linear MCSs, Parker and Johnson (2000) proposed a new taxonomy comprising convective lines with trailing stratiform (TS), leading stratiform (LS), and parallel stratiform (PS) types. The TS archetype was found to be the dominant mode of linear MCS organization. On this basis, (Gallus et al., 2008) introduced two new linear convection types: bow echoes (BE) and non-stratiform (NS). In this case, a TS archetype was present in the initial and mature stages, and a PS archetype was present during the decaying stage.

Figure 1.  Spatial distribution of composite reflectivity (units: dBZ) at (a) 0830 UTC, (c) 1030 UTC, and (e) 1300 UTC from the radar and at (b) 0830 UTC, (d) 1030 UTC, and (f) 1300 UTC from the simulations.

Figure 1 compares the observed and simulated radar reflectivity at 0830, 1030 and 1300 UTC, representing the initial stage (0600-0850 UTC), the mature stage (0900-1150 UTC), and the decaying stage (1410-1520 UTC) of the storm, respectively. A number of convective cells were generated at the junction of the provinces of Shandong and Anhui at 0600 UTC and moved southeastward. At 0830 UTC (Fig. 1a), convective cells strengthened and organized into a linear convective system with a length of 300 km and a width of 50 km in the provinces of Jiangsu and Anhui (labeled #1). The radar echo intensity exceeded 60 dBZ. Ahead of the squall line, new convective cells were continuously produced due to convergence of the cold pool outflow; these cells joined the moving squall line. During the southward shift and development, there was an ongoing cycle of new convective cell generation, development, and dissipation in the squall line. Figure 1c (at 1030 UTC) shows the mature stage of the squall line. The convective line at the leading edge intensified and moved southward, with a broad stratiform region at the rear; this setup is characterized as a mature TS archetype. At the same time, another mesoscale convective system occurred at the provinces of Henan and Shandong. The convective cells shifted southward and organized into a squall line at 1200 UTC (labeled #2). By the late stage (Fig. 1e), the first squall line had weakened and changed into a PS archetype, in which the stratiform region was parallel to the convective line. The intense radar echo contracted, weakened and finally broke up. The second squall line behind the first squall line strengthened and then weakened during this stage. The first squall line lasted for approximately 9 hours, and the second lasted for approximately 6 hours. The first squall line was stronger and longer lasting than the second one, and it had a much more severe influence than the second squall line. Here, we mainly discuss the first squall line.

Comparing the simulations (Figs. 1b, d and f) with the observations (Figs. 1a, c and e), although the radar echo region in the simulation was slightly broader and stronger, the center of the intense radar echo, the movement velocity, and the distribution were all consistent with the observations. The archetype transition from a TS to a PS and the new squall line generation behind the original were successfully reproduced. The first squall line generated in the provinces of Anhui and Jiangsu was enhanced and moved southeastward over time. New convective cells were continuously produced ahead of the squall line and were integrated into the system. At the same time, the second squall line intensified and organized into a mesoscale convective system. As mentioned, the simulation results successfully reproduced the severe convective processes and storm evolution. Next, the simulation data are used to analyze the structure and propagation mechanism of the squall line in detail.

A complete understanding of the structural features of a squall line provides a foundation for further study on the mechanisms of squall line evolution and propagation. The dynamic and thermodynamic structure must first be calculated, as demonstrated below.

The squall line moved from northwest to southeast, with a faster meridional velocity than zonal velocity. Here, we look at a meridional cross section through 119.8^°E (approximately 520 grid points). A squall line consists of two parts. One part is the convective zone at the leading edge of the system, where the most intense vertical velocity exists. The other part is the stratiform zone at the rear of the squall line, where there is weaker radar reflectivity and a large region of trailing stratiform precipitation. The squall line was most intense and had the greatest impact on its surroundings during the mature stage of the TS archetype, while it weakened during the PS stage; thus, the mature stage is the focus of this study. Note that the PS stage and the decaying stage were merged into one category.

Figure 2 shows the evolution of the storm-relative meridional wind. Initially (Fig. 2a), there was strong inflow in the boundary layer ahead of the system in the convective zone, which was divided into two branches in the squall line. One branch was in the convective zone, with outflow at the upper rear of the squall line. The other branch had upper-level outflow ahead of the squall line. Notably, a negative region existed at the midlevel of the convective zone, which can be explained by RKW theory (Weisman et al., 1988; Rotunno et al., 1988). In the initial stage, the cold pool was weak, so the positive horizontal vorticity generated by the vertical environmental wind shear at the low level was stronger than the negative horizontal vorticity generated by the cold pool. Therefore, the updraft tilted downwind, which caused a negative meridional velocity. In the stratiform region, there were negative values of weak descending rear inflow at the midlevel (RTF flow), and a positive value of strong ascending rear outflow at the upper level (FTR flow). The FTR flow had an extreme jet-like area that dominated the squall line. A weak boundary rear outflow was located below the midlevel RTF flow.

Figure 2.  A meridional cross section of the storm-relative meridional wind along 119.8^°E (shading and vectors, units: m s^-1) during (a) the initial stage at 0840 UTC, (b) the mature stage at 1000 UTC, and (c) the decaying stage at 1250 UTC. The contour is the water mixing ratio of 0.2 g kg^-1.

As the squall line matured (Fig. 2b), the negative zone at the midlevel in the convective region disappeared; thus, the cold pool had become stronger and competed with the vertical environmental wind shear, which is an important factor for squall line development. In the stratiform region, the ascending FTR flow became weaker but broader. The RTF flow became stronger and developed a double-core structure. One core was in the low-level convective region, mainly due to the superposition of the outflow ahead of the cold pool. The other core was in the midlevel (4-6 km) at the rear of the storm and was attributed to the positive horizontal vorticity generated by the rear outflow in the boundary from the cold pool and the negative horizontal vorticity generated by the FTR jet flow. The two counter-rotating vorticities caused flow from the rear of the system to move into the storm (Lafore and Moncrieff, 1989; Weisman, 1992). The RTF flow was important for the squall line's development: it not only transported cold and dry air from the environment into the system to increase the stratified instability, but also enhanced the cold pool strength. The strengthened cold pool enhanced the rear outflow at the low levels, increased the vorticity, and increased the RTF flow. Thus, the RTF flow and the cold pool formed a positive feedback, which was conducive to the squall line's development.

Figure 3.  As in Fig. 2 but for vertical velocity (shading, units: m s^-1) and the storm-relative wind (vectors, units: m s$-1$).

Figure 4.  As in Fig. 2 but for potential temperature perturbation (shading, units: k) and the storm-relative wind (vectors, units: m s^-1). The black line at 4-6 km is the isoline for zero degrees.

Figure 5.  (a-c) As in Fig. 2 but for the pressure perturbation (shading, units: Pa) and storm-relative wind (vectors, units: m s^-1). (d) The same cross section of the pressure perturbation (contours) and ∂ ρ B/∂ z (shading) at 1000 UTC.

By the late stage (Fig. 2c), the FTR flow and RTF flow had both decreased, and they were oriented horizontally in the stratiform region. In the convective zone, the positive wind area narrowed and dissipated over time; thus, the rear inflow carrying the cold, dry flow moved through the convective region. In this situation, the cold, dry air gained control of the squall line and disrupted its development; this was the most important cause of the squall line's decay.

Figure 3 illustrates the different stages of the vertical velocity. Initially (Fig. 3a), intense updrafts occurred in the convective zone surrounded by downdrafts due to mass compensation. The area of upward motion was narrow, which contributed to the intense updraft. Below the intense updrafts, precipitation-induced downdrafts were present at low levels. In the stratiform region, the ascending motion and the descending motion were weak, narrow, and scattered.

During the mature stage (Fig. 3b), two updraft maxima existed in the convective region. One maximum, which was in the boundary layer at the leading edge of the squall line, was created by the convergence at the front of the cold pool. The other maximum, which was at the midlevel, was the result of the positive feedback between the latent heat release and a gravity wave. The area of upward motion became broader and connected with the FTR flow in the rear. The ascending and descending flows visibly strengthened and became well organized in the stratiform region.

In the late stage (Fig. 3c), the ascending and descending motions were much weaker and less organized in the expanding stratiform region.

Figure 4 shows the potential temperature perturbations for an analysis of the thermodynamic structure. During the lifecycle of the squall line, a persistent center of warm air occurred in the mid and upper levels due to latent heat release in the updraft. At the south end of the squall line, warm and moist air was dominant over the region; thus, positive potential temperature perturbations were common. In the initial stage (Fig. 4a), a weak precipitation-induced cold pool was produced by evaporative cooling in the convective region and enhanced by the cold, dry air transported by the RTF flow. A midlevel warm core persisted due to the latent heating. In the stratiform region, a weak cold core was present at the melting level (4-6 km) due to ice-phase particles, and a weak warm core existed below due to adiabatic heating during descent. The weak warm core played a crucial role in the wake low behind the squall line at the surface (Johnson and Hamilton, 1988). As the system matured (Fig. 4b), the cold pool became broader, deeper, and stronger, with a minimum value of -12 K, while the warm core simultaneously strengthened. In the decaying stage (Fig. 4c), the cold pool broadened but weakened due to decreased convection. The warm core also weakened but drifted rearward due to the FTR flow.

The pressure perturbation in Fig. 5a indicates high pressure occurred in the boundary layer due to the thermodynamic effect of the cold pool and the dynamic effect of descending motion (Wakimoto, 1982). A mass movement caused by an updraft with latent heating and a downdraft with precipitation drag resulted in a midlevel low-pressure region above the high-pressure region (which can be observed in Fig. 3a). The pre-squall low pressure was evident at this stage. In the mature stage (Fig. 5b), the high pressure intensified, reaching a maximum strength of 4 hPa. The pre-squall low pressure on the ground weakened, but the wake low at the back edge of the stratiform region increased due to adiabatic heating of the strong descending rear inflow (Zipser, 1977; Brown, 1979). The midlevel low pressure weakened but broadened. The comparison of the observations shows that part of the low-pressure area in the stratiform region was collocated with the RTF flow, prompting many researchers to note that the pressure gradient force enhanced or even generated the rear inflow (Smull and Houze, 1987). During the late stage (Fig. 5c), the high pressure at the surface remained strong, but the low pressure in the midlevel weakened. The pre-squall low and the surface wake low in the rear decreased.

The pressure perturbation in the mid and upper levels was mainly caused by buoyancy. Because of the hydrostatic state in the mid and upper levels (Lemone, 1983; Fovell and Ogura, 1988; Braun and Houze, 1994), the motion equation in the vertical direction is as follows: \begin{eqnarray} \label{eq1} 0&=&-\dfrac{1}{\rho}\dfrac{\partial p'}{\partial z}+B ,\\ \label{eq2} B&=&g\left[\dfrac{\theta'}{\overline{\theta}}+\dfrac{p'}{\overline{p}\gamma}-\dfrac{q'_{\rm v}}{\overline{q_v}+\varepsilon}-\dfrac{q'_v+q_w}{1+\overline{q_v}}\right] ,\\ \label{eq3} q_{w}&=&q_{\rm c}+q_{\rm r}+q_{\rm i}+q_{\rm s}+q_{\rm g}+q_{\rm h} , \end{eqnarray} where B is buoyancy; q _c, q _r, q _i, q _s, q _g and q _h represent cloud water, rain water, ice, snow, graupel, and hail, respectively; γ=c_p/c_v is the ratio of the specific heat of air at a constant pressure and volume; and ε=R _d/R _v≈ 0.622. Differentiating Eq. (2) with respect to height produces \begin{equation} \label{eq4} \dfrac{\partial^2p'}{\partial z^2}=\dfrac{\partial \rho B}{\partial z} . \end{equation} The Laplacian operator of a wavelike variable away from boundaries tends to be positive where the perturbations of the variable are negative. Thus, \begin{equation} \label{eq5} \dfrac{\partial^2 p'}{\partial z^2}\propto-p' . \end{equation} Then, \begin{equation} \label{eq6} -p'\propto\dfrac{\partial \rho B}{\partial z} . \end{equation} The equation illustrates that when buoyancy increases with height, the pressure perturbation decreases; this is the most significant reason for the generation of the midlevel low pressure in the squall line.

Figure 5d is the distribution of the term on the right in Eq. (7) and the pressure perturbation. The negative buoyancy as a function of height corresponds to the positive pressure perturbations at 8-12 km, and the positive buoyancy as a function of height is collocated with negative pressure perturbations at 3-6 km. This relationship demonstrates the effect of buoyancy on pressure perturbations in which high pressure occurs in the upper levels and low pressure occurs in the midlevels. Below 3 km (near the surface), the pressure was non-hydrostatic because of obvious mass accumulation and divergence. Thus, the pressure perturbation at the surface resulted from both dynamic and thermodynamic effects.

At present, squall line propagation is mainly divided into two theories. One theory states that the spreading cold outflow enhances convergence and triggers the formation of a new cell at the leading edge of the gust front (Wilhelmson and Chen, 1982, Fovell and Ogura, 1989), while the other theory supports the idea that gravity wave propagation is the primary reason for squall line propagation (Stobie et al., 1983, Zhang and Kaplan, 1987). Here, by analyzing a particular example, we find that the interaction between gravity waves and the cold pool outflow plays a crucial role in squall line development and propagation.

(Li, 1978) noted that the front, the squall line, and the vortex all have non-geostrophic balance, which can stimulate gravity waves. Under the assumption of thermal isolation, Li obtained a solution for gravity waves by solving basic atmospheric equations; he described the gravity wave as the vorticity located one-quarter of a wavelength behind the divergence. Furthermore, the pressure center coincided with the vorticity center but with the opposite phase. The convergence also matched the updraft, with a wavelike propagation form.

Figure 6 shows the vertical distribution of vorticity and divergence at 0900 UTC. In Fig. 6a, there are clearly positive and negative changes in the vorticity in the squall line system; the vorticity spread from the low levels in the rear to the upper levels at the front and moved forward with the squall line. At the same time (Fig. 6b), a similar divergence distribution was found, corresponding with the vorticity. Comparing the divergence with the vorticity, the divergence region was one-quarter of a wavelength ahead of the positive vorticity, as typically seen with gravity waves.

The evolution of vertical velocity with time at a height of 4.25 km is displayed in Fig. 6c. A line of positive and negative changes in the vertical velocity is apparent; thus, the convective updraft cells were associated with gravity waves. The most intense vertical velocity occurred at 33.5^°N at the

Figure 6.  A meridional cross section along 119.8^°E of (a) vorticity (units: 10-3 s-1) at 0900 UTC, (b) divergence (units: 10-3 s-1) at 0900 UTC, and (c) the time-latitude cross section of the vertical velocity (units: m s^-1) at 4.25 km. The contour is the water mixing ratio of 0.2 g kg^-1.

Figure 7.  A meridional cross section of the vertical velocity (shading, units: m s^-1) and wind vectors (vectors, units: m s^-1) along 119.8^°E every 4 min from 0906 UTC to 0922 UTC. The contour is the water mixing ratio of 0.2 g kg^-1.

initial time and moved southward; this pattern is consistent with a squall line. The phase speed of the gravity waves can be determined by the slope of the constant phase line, i.e., approximately 19 m s^-1. There were two additional fluctuations, but they were short-lived and weak. Hence, the time-space plot of the vertical velocity demonstrates the southward propagation of the gravity waves.

To analyze the mechanism of the squall line's spread, we set up the simulation to output results every 4 minutes. Figure 7 shows the vertical velocity and wind field during 0906-0922 UTC. In Fig. 7a, there are three evident convective cells (labeled A, B and C) in the midlevel and several weak cells in the rear, which exhibit the features of the gravity waves. At the surface, convective cell D was produced by the outflow convergence ahead of the cold pool. After 4 minutes (Fig. 7b), convective cells A, B and C were enhanced and shifted forward. According to wave-CISK theory (Raymond, 1984), organized convection is forced by convergence associated with a gravity wave while the latent heat release within the convection provides a source of wave energy. Furthermore, cell D moved upward and strengthened. The phenomenon of upward cell motion at the gust front was also found by (Fovell and Ogura, 1989) and (Yang and Houze, 1995a). One explanation is that the updraft over the gust front is large enough to lift the air parcel to the level of free convection. Because the vertical acceleration was zero in the mid and upper levels (i.e., hydrostatic), the air parcel could continue to move upward without resistance. At 0914 UTC (Fig. 7c), with the reinforcement of cells A, B, C and D, two new convective cells (E and F) were generated ahead of cell D due to the spreading cold outflow convergence. At 0918 UTC (Fig. 7d), cells D and F increased in intensity and moved up. When the D and F convective cells were in phase with the upward branch of the gravity waves, they merged and caused intense convection, with a maximum vertical velocity of 20 m s^-1. This process accelerated the development and propagation of the squall line. Then (Fig. 7e), the gravity wave spread forward with the weakened convective cells in the rear and enhanced cells in the front, and convective cell E strengthened and shifted. Afterward, the newly produced cells at the gust front grew and moved upward, then joined the persistently spreading gravity wave, which promoted squall line development. The cycle was approximately 30 minutes. This cycle occurred until the environment changed with the transition from TS to PS, the coupling was disrupted, and the squall line began to decay.

It can be concluded from the above discussion that the propagation of the squall line was caused by mutual reinforcement between the gravity waves in the midlevel and outflow of the cold pool at the surface. In the middle atmosphere, the forward spread of the gravity wave helped organize deep convection, while the convection released latent heat that tended to enhance the gravity wave. In the boundary layer, new cells were continuously generated by the convergence of the outflow along the gust front. The new intensified cells moved upward and combined with the updraft of the gravity wave; thus, an intense vertical updraft was formed. The strong convection promoted the spread and evolution of the squall line. Thus, the gravity wave's propagation and cold outflow spread interacted to strongly boost the squall line's development and forward-shift; these processes were significant for the squall line's evolution.

There are a number of physical processes responsible for the generation of gravity waves. These processes include vertical shear instability (Mastrantonio et al., 1976; Bosart and Sanders, 1986), ageostrophic adjustment associated with unbalanced flow (Zack and Kaplan, 1987; Koch and Dorian, 1988), intense convection (Curry and Murty, 1974, Raymond, 1983), and terrain effects (Kaplan and Karyampudi, 1992; Zulicke and Peters, 2006). Here, the squall line developed in the provinces of Anhui and Jiangsu, where the topography is flat; thus, the terrain effect can be excluded. The shear instability and unbalanced flow will be discussed in the following section.

First, we explored the effect of the vertical wind shear and atmospheric stability on gravity waves. (Miles, 1961) and (Howard, 1961) studied shear instability in the atmosphere and found that a Richardson number of less than 0.25 signified gravity wave instability. (Fritsch and Chappell, 1980) noted that a gravity wave can absorb energy from basic flow when the gravity wave instability condition is satisfied. The Richardson number is defined as (Shou et al., 2003; Koch et al., 2005): \begin{equation} \label{eq7} Ri=\dfrac{N^2}{S^2} , \end{equation} where N² is the Brunt-Vaisala frequency, and S²=(∂ u/ ∂ z)²+(∂ v/∂ z)² is the vertical wind shear. Because the atmosphere is non-uniformly saturated, we introduced the generalized potential temperature θ^* (Gao et al., 2004, 2005) into N², which is more appropriate for non-uniformly saturated flow (Gao et al., 2010). Thus, N² is expressed as: \begin{eqnarray} \label{eq8} N^2&=&\dfrac{g}{\theta^\ast}\dfrac{\partial\theta^\ast}{\partial z} , \end{eqnarray} \begin{eqnarray} \label{eq9} \theta^\ast&=&\theta\exp\left[\dfrac{L_{\rm v}q_{{\rm vs}}}{c_pT_{\rm c}}\left(\dfrac{q_{\rm v}}{q_{{\rm vs}}}\right)^k\right] , \end{eqnarray} where q _vs is the saturated specific humidity, q _v is the specific humidity, T _c is the lifting condensation level, and k is an empirical constant.

The Richardson number represents the connection between the available potential energy and kinetic energy. A lower Richardson number corresponds to a stronger shear instability. Figure 8 is the vertical distribution of the Richardson numbers at 0900 UTC. Small Richardson numbers are mainly located at the low levels and midlevels at approximately 33^°N, which is located downstream of the gravity wave source. Therefore, vertical wind shear and atmospheric instability were not the primary reasons for gravity wave generation.

According to (Rossby, 1938) and (Cahn, 1945), when the geostrophic balance is not met and ageostrophic wind occurs, the atmosphere relieves the imbalance between the mass and momentum via geostrophic adjustment. At that moment, a gravity wave is likely to be triggered. As the gravity wave disperses, the wind and pressure fields re-establish a balance, i.e., the geostrophic adjustment. (Zhang et al., 2000) summarized different methods for defining and diagnosing the flow imbalance, including the Lagrangian Rossby number (Ro), the residual of the nonlinear balance equation, the omega equation, and PV inversion. Here, we mainly used the first two methods to diagnose the ageostrophic motion.

The Lagrangian Rossby number proposed by (Koch and Dorian, 1988) is defined as the ratio of the parcel acceleration to the Coriolis force. A small value represents geostrophic motion, and a large ratio represents non-geostrophic motion. Some studies have indicated that values of Ro >0.9 represent unbalanced flow, in which gravity waves are easily generated.

Ro is defined as: \begin{equation} \label{eq10} {\it Ro}=\left|\dfrac{d\bm{v}}{dt}\right|\dfrac{1}{f|\bm{v}|}=\dfrac{|f\bm{v}_{\rm ag}\times\bm{k}|}{f|\bm{v}|}= \dfrac{|\bm{v}_{\rm ag}|}{|\bm{v}|}\approx \dfrac{|\bm{v}_{\rm \perp ag}|}{|\bm{v}|} , \end{equation} where \(\bmv_\rm \bot ag\) is the ageostrophic wind perpendicular to the wind vector. (Koch and Dorian, 1988) argued that only the ageostrophic wind perpendicular to the flow contributes to the flow imbalance and that along-stream ageostrophic wind is governed by the gradient wind balance.

Figure 8.  A meridional cross section of the Richardson number at 0900 UTC along 119.8^°E. The contour is the water mixing ratio of 0.2 g kg^-1.

Figure 9.  A meridional cross section of (a) the Lagrangian Rossby number (Ro) and nonlinear balance equation terms (units: 10^-6 s^-2), (b) ∆ NBE, (c) -∇²φ, (d) 2J(u,v), and (e) \(f\xi -\beta u\) (units: 10^-6 s^-2) at 0900 UTC along 119.8^°E. The contour is the water mixing ratio of 0.2 g kg^-1.

Figure 9a shows the vertical distribution of Ro at 0900 UTC. There is clear evidence of imbalance within the squall line, given the pronounced maximum of Ro at a height of 2-4 km at approximately 33.5^°N at 0900 UTC. Compared with Fig. 6, the location of the maximum Ro corresponds to the location of gravity wave generation, indicating that the unbalanced flow played a crucial role in triggering the gravity waves. An hourly analysis of the Ro shows that the maximum Ro shifted southward over time and that it was collocated with the gravity wave motion. Therefore, gravity waves were produced continuously by the imbalanced flow in the squall line and spread downstream. The strong imbalanced flow was largely generated by the divergence produced at the interface of the FTR ascending flow and the RTF descending flow at the back edge of the squall line.

The nonlinear balance equation (NBE) has been widely applied to definitions of unbalanced flow. Because the NBE is quite similar to the gradient wind balance, it is more suitable for shorter time scales and greater curvature in flows (Davis and Emanuel, 1991). The NBE residual is expressed as \begin{equation} \label{eq11} \Delta {\rm NBE}=-\nabla^2\phi+2J(u,v)+f\xi-\beta u , \end{equation} where φ is the geopotential height, J is the Jacobian operator, and \(\xi\) is the relative vorticity. A significant non-zero summation of the NBE residual (10^-8 s^-2) has been used by (Moore and Abeling, 1988) to indicate the "breakdown" of mass and momentum balance in convection regions. Based on scale analysis, the underlying assumption of nonlinear balance is that the magnitude of the NBE residual is smaller than the three terms on the right side of Eq. (12). However, when the magnitude of the NBE residual is comparable to or greater than the magnitude of any individual terms on the right side of Eq. (12), the nonlinear balance assumption is violated, i.e., the flow is unbalanced (Zhang et al., 2000, 2001). In this case (Fig. 9), it can be clearly observed that the maximum residual is greater than those three individual terms; thus, the flow was strongly unbalanced.

The vertical distribution of the NBE residual and the three terms (the Laplacian, Jacobian, and vorticity terms) at 0900 UTC are shown in Figs. 9b-e. The largest NBE residual was found at 4-6 km at 33-33.5^°N within the squall line and was collocated with the maximum Ro above; this further verifies that the strong unbalanced flow in the squall line provided favorable conditions for gravity wave generation in this case. The Laplacian term contributed the most to the imbalance shown in Fig. 9c. The Jacobian and vorticity terms display features of positive and negative changes (Figs. 9d and e), similar to the gravity wave distribution; thus, a close relationship existed between the horizontal wind shear and gravity wave generation.

Based on the combination of gravity waves and the cold pool outflow, we discuss the development and propagation of the squall line. Figure 10 summarizes the squall line process and provides a conceptual model of this case. At the midlevel, two intense convective cells, A and B, were produced in the Wave-CISK process. The convection released latent heat that tended to enhance the gravity wave, while the forward spread of the gravity wave helped organize deep convection. The outflow convergence along the gust front forced the generation of cells C and D, in which cell C was generated earlier than cell D. When cell C matured and moved upward, driven by the intense updraft, a new cell D was produced ahead of cell C as the gust front continuously moved forward. As cell C ascended, it merged with the updraft of the gravity wave, thereby amplifying the gravity wave and strengthening the upward motion. The interaction between the gravity wave and the cold pool outflow was sustained, which enhanced the squall line's development; the spread and reinforcement of these features caused the squall line's propagation.

Figure 10.  A conceptual model of the squall line's development and propagation. The green line is the wind direction and the blue clouds are the convective cells.

A squall line event on 14 June 2009 in the provinces of Jiangsu and Anhui was reasonably simulated by the ARPS model. Based on high resolution spatial and temporal data, a detailed analysis of the structure and propagation of the squall line was conducted. The following results were obtained.

(2) Using ARPS modeling with a nudging method, the squall line process was successfully reproduced. The results successfully simulated the transition from the TS to PS archetype and the secondary squall line generation behind the original squall line. The dynamic and thermodynamic characteristics of the squall line and their causes were analyzed in detail; these features provide the foundation for further squall line research.

(3) The distributions of the vorticity and divergence verified the generation of a mesoscale gravity wave, which was consistent with the movement of the squall line. The gravity wave generation was assessed with the Richardson number, the Lagrangian Rossby number, and the nonlinear balanced equation; it was found that the unbalanced flow was the primary factor in initiating the gravity waves.

(4) The causes of the squall line's spread and development were mainly the combined effect of gravity waves at the midlevel and cold outflow at the ground level. The gravity waves were enhanced by latent heating associated with convection, and the circulation associated with the gravity waves maintained the convection. This positive feedback sustained the propagation and development of the gravity waves. At the same time, new cells were continuously produced along the gust front and were enhanced and lifted by the intense updraft. Eventually, the new cells merged with the gravity waves, leading to an intense updraft that strengthened the squall line. The positive feedback between the spreading gravity waves and the movement of the new cells along the gust front caused the forward movement of the squall line.