Analysis of the Ducted Gravity Waves Generated by Elevated Convection over Complex Terrain in China

Abstract

Gravity waves play a crucial role in the evolution of convective systems. The unique thermal structure of elevated convection occurring above a stable boundary layer facilitates the generation and propagation of gravity waves. This study focuses on an elevated convection event over Central China on the night of 2–3 February 2024. The WRF model, combined with terrain sensitivity experiments, is employed to analyze the characteristics of gravity waves and the effects of terrain variability. The event consists of two elevated convection clusters; the first triggers gravity waves on its southwestern side, which subsequently initiates the second convection cluster. The gravity waves exhibit a horizontal wavelength of 25 km and a period of 17.5 min, propagating eastward. Below an altitude of 3 km, a stable wave duct layer is present, overlain by an unstable overreflective zone. This stratification creates an ideal channel for ducted gravity wave propagation, which is essential for maintaining the waves. Sensitivity experiments confirm that convective forcing alone is sufficient to generate the observed gravity waves. Although the terrain lies within the stable boundary layer, its ruggedness modulates the distribution of waves and indirectly influences the organization of elevated convection.

1. Introduction

Gravity waves are oscillations in a stable atmosphere driven by the combined effects of buoyancy and gravity. They play a crucial role in convective organization and energy transport [1]. The development of severe convective weather events, such as heavy rainfall, hailstorms, and typhoons, is closely linked to the presence of gravity waves [2]. As common atmospheric disturbances, gravity waves often act as triggers for mesoscale severe convective systems [3,4]. Additionally, factors such as mountainous terrain, shear instability, and frontal boundaries can also initiate gravity waves [5,6,7]. The formation of elevated convection involves the interplay of terrain [8,9], inversion layers, and frontal zones [10,11,12]. Observations of gravity waves have been reported in case studies of elevated convection [13,14]. However, few studies have explored the interactions among elevated convection, terrain, and gravity waves simultaneously. Therefore, investigating the interactions between elevated convection and gravity waves in mountainous regions is necessary.

Many studies have demonstrated that convection can generate gravity waves, while gravity waves can in turn act as disturbances that trigger new convection. Wang et al. [2] highlighted that outflows from near-surface cold high-pressure regions formed by convection cause downstream airflow perturbations, which then excite gravity waves and subsequently initiate convection further downstream. For gravity waves to trigger convection, they may interact with convection through a mechanism referred to as “Wave-CISK” (convective instability of the second kind) [15,16]. Du and Fuqing [17] highlighted that gravity waves can initiate and modulate convection, while the latent heat released by convection further amplifies these waves. This interaction between convection and gravity waves can, under certain conditions, trigger squall lines in spring [18].

Topography plays a significant role in the generation and propagation of gravity waves. As airflow encounters terrain, the lifting or blocking effect disturbs the stable atmospheric layers, inducing vertical oscillations that give rise to gravity waves [19]. Variations in the scale and shape of the terrain influence key wave characteristics such as wavelength and period, as well as the altitude to which these waves propagate [20,21,22]. The angle between the mountains and the wind also affects wave propagation. When airflow is parallel to the ridge, disturbances are minimal, allowing gravity waves to break at higher altitudes [23]. In contrast, perpendicular flow generates substantial drag forces [24]. Incorporating terrain-induced gravity wave drag parameterizations into numerical models has been shown to improve the simulation of orographic precipitation [25,26].

The long-term maintenance of gravity waves in the horizontal direction typically requires the presence of a wave duct [17,27]. Lindzen and Tung [28] proposed that the ducted gravity waves travel within a low-level stable layer, which is topped by a reflecting layer characterized by low stability and the presence of a critical level. The near-surface stable layer acts as the core of the wave duct, while the weakly stable or unstable layer above reflects wave energy, limiting its vertical leakage and enabling long-distance horizontal propagation. This mechanism has been confirmed through subsequent observations and simulations [17,29,30,31].

Elevated convection refers to deep, moist convection that occurs above a stable boundary layer [10,11]. Research has primarily focused on elevated convection occurring in the cold sector of frontal systems [12,32,33]. The stable boundary layer beneath the front creates favorable conditions for the generation of gravity waves. The near-surface stable layer required for ducted gravity waves, as proposed by Lindzen and Tung [28], corresponds closely to the stable boundary layer necessary for elevated convection [11]. From this perspective, the banded convection associated with ducted gravity waves studied by Lindzen and Tung [28] and Du and Fuqing [17] can be considered a form of elevated convection.

Currently, research on elevated convection and ducted gravity waves remains limited, and studies linking the two phenomena are even rarer. This study focuses on an elevated convection event that occurred on the poleward side of a cold front in central China from 2–3 February 2024, addressing two key scientific questions: (1) Were gravity waves present during the elevated convection? If so, were these waves propagated in a duct? (2) How do terrain variations influence ducted gravity waves?

2. Data and Methodology

2.1. Data

The data used in this study include ERA5 reanalysis data [34], which serve as the initial and boundary conditions for numerical simulations. ERA5 data are also employed in case analyses for weather pattern assessment. The spatial resolution of ERA5 is 0.25° × 0.25°, with a temporal resolution of 1 h and a vertical resolution of 25 hPa. Additionally, data from the Himawari-9 satellite is utilized primarily for data assimilation to enhance simulation accuracy; this data has a spatial resolution of 0.02° × 0.02° and a temporal resolution of 1 h. To provide a clearer depiction of the development process of the elevated convection event, radar composite images for Central China, issued by the National Meteorological Center, are also incorporated.

2.2. Model Configuration

To investigate the wave characteristics during the elevated convective process, numerical simulations are performed using the Advanced Research Weather Research and Forecasting (WRF) Version 4.4 model. Initial and boundary conditions are derived from ERA5 reanalysis data [34]. To improve the simulation accuracy, the WRF model data assimilation system (WRFDA) is employed to assimilate the 10th and 14th channels of the Himawari-9 satellite data using three-dimensional variational assimilation. Assimilation begins at 08:00 BJT on the 2nd, with updates every three hours. Following assimilation, the model proceeds with standard simulation starting from 17:00 BJT, with updates every six hours. The simulations employ a three-level nested grid configuration with horizontal resolutions of 27 km, 9 km, and 3 km from the outermost to the innermost domain, respectively. The spatial arrangement of these domains is illustrated in Figure 1.

The model physics include the Thompson microphysics scheme [35], the RRTM longwave radiation scheme [36], the Dudhia shortwave radiation scheme [37], the Mellor–Yamada–Janjic planetary boundary layer scheme [38], the Monin–Obukhov surface layer scheme, and the Noah land surface model [39]. Convection parameterization is disabled in the innermost domain, while the outer two domains utilize the Kain–Fritsch scheme [40].

Both convection and terrain can generate gravity waves. To investigate the mechanisms of waves in this case, terrain sensitivity experiments are designed. The focus is primarily on the influence of terrain variations, mainly caused by the Daluo Mountains. In these experiments, the terrain height within the region spanning 27° N−31.5° N and 106° E−112.5° E is subjected to Gaussian filtering (GF experiments), as described by the following formula:

$$G\left(x,y\right)={\displaystyle \frac{1}{2\pi {\sigma }^2}}{e}^{-{\displaystyle \frac{x^2+y^2}{2{\sigma }^2}}}$$

(1)

$G\left(x,y\right)$ is the Gaussian weight at coordinate $\left(x,y\right)$, $x$ and $y$ represent spatial coordinates relative to the kernel’s center, and σ denotes the standard deviation. The smoothing effect is controlled by adjusting σ (

Table 1. Configuration of the terrain sensitivity experiments.

Experiment	Domain	Terrain Adjustment	Purposes
Control run	None	None	True terrain control run
GF-1	27° N−31.5° N 106° E−112.5° E	Gaussian filter (σ = 1)	Exploring the impact of terrain variations
GF-3		Gaussian filter (σ = 3)
GF-5		Gaussian filter (σ = 5)
GF-15		Gaussian filter (σ = 15)
Ter-0	27° N−31.5° N 106° E−112.5° E	Height × 0	Exploring whether waves exist in the absence of terrain

), with values set at 1 (GF-1 experiment), 3 (GF-3 experiment), 5 (GF-5 experiment), and 15 (GF-15 experiment). The Gaussian kernel size is $2\times round\left(4\times \sigma \right)+1$, where $round\left(\bullet \right)$ denotes nearest-integer rounding. Additionally, a sensitivity experiment is conducted in which the terrain within this region is entirely removed (Ter-0 experiment). Detailed configurations and names of all sensitivity experiments are provided in Table 1. Figure 2 illustrates the terrain distribution over the D03 for both the control run and sensitivity experiments. As σ increases, the terrain features east of the Sichuan Basin gradually smooth. At σ = 15, many rugged peaks in this region merge into a single large mountain, effectively eliminating local variations while maintaining the overall terrain trend.

3. Results

3.1. Case Overview

From the night of 2–3 February 2024, a heavy snow event occurred across Chongqing, Hunan, and Hubei provinces in China, resulting in widespread traffic disruptions. Analysis of satellite imagery (Figure 3) and radar composite reflectivity (Figure 4) reveals that this snowfall was associated with two convective clusters. Here, radar composite reflectivity refers to the maximum reflectivity value observed at each horizontal location from all radar elevation scans, effectively indicating the strongest radar return within the vertical column above each point.

The first cluster, with a blocky shape, was predominantly centered over Hubei. The second cluster developed later, triggered southwest of the first. At 23:50 BJT (UTC + 8) 2 February, the second cluster was in its initiation phase, with satellite images showing distinct wave-like clouds (Figure 3a). As convection progressed, by 02:10 BJT on the 3rd, these wave-like clouds evolved into discrete convective clouds (Figure 3c), which were also evident as wave-patterned small convective cells in the radar reflectivity data (Figure 4c). These wave-like convective clouds subsequently intensified and merged into a larger convective system (Figure 3e). After 06:00 BJT on the 3rd, the first cluster gradually dissipated, and the ongoing snowfall was primarily driven by the second cluster (Figure 3f and Figure 4f). This study focuses on the early development stage of the second convective cluster, investigating the nature of the waves and the influence of the first cluster and local topography on these waves.

This snowfall event occurred following the passage of a cold front, which had already advanced to the northern regions of Guangdong and Guangxi provinces. The precipitation was concentrated over the Yangtze River Basin and was influenced by a cold high-pressure system, with near-surface winds predominantly from the north (Figure 5a). This weather pattern exemplifies a classic case of elevated convection occurring on the polar side of a cold front [10,12]. The terrain in Hunan Province, with mountains surrounding it except for a lower-lying plain to the north, induces a southward bulge in the equivalent potential temperature (${\theta }_e$) field. This ${\theta }_e$ bulge extends upward to the 850 hPa level (Figure 5b). At 850 hPa, terrain effects generate a low vortex over southern Sichuan. The eastern flank of this vortex features a trough over the Yangtze River Basin, associated with the precipitation area. South of the trough, a broad low-level jet transports warm, moist air upward toward the frontal zone.

At 700 hPa, this jet stream expands further, forming a wide southwest jet across southern China, encompassing the precipitation region (Figure 5c). At 500 hPa, the precipitation area is situated within a westerly flow ahead of the trough. To the north of this region, a convergence zone with strong horizontal wind shear is present, which favors convection development (Figure 5d). The synoptic pattern during this snowfall aligns well with the previously identified circulation associated with elevated convection on the polar side of cold fronts in Hunan and Hubei provinces [12]. Near the surface, a cold pool associated with the cold front is present, overlain by a low-level jet above the frontal zone, triggering elevated convection. This low-level cold pool provides a stable environment conducive to wave generation. Combined with the mountainous terrain of southwest China, these conditions favor the development of gravity waves. Therefore, investigating gravity waves associated with elevated convection is essential to understanding the dynamics of this event.

The control run successfully reproduces the development of two elevated convective clusters, with their positions and intensities largely consistent with observations (Figure 4 and Figure 6). Here, we focus specifically on the process after the development of the first cluster, during which waves occur in its rear and trigger the second cluster. Overall, the simulated convection initiates approximately 30 min earlier than observed. Analyzing the convection based on its morphology, the control run captures the first cluster as a consolidated cell, while the second cluster initially appears as dispersed cells.

In the sensitivity experiments, the GF experiments produce a first cluster whose location and shape closely resemble those in the control run, though the timing differs somewhat; for instance, the control run initiates convection about one hour earlier than GF-1. The morphology of the second cluster is strongly influenced by terrain variations. Smoother terrain corresponds to fewer scattered cells within the second thunderstorm. As shown in Figure 6 at 02:30 BJT on the 3rd, multiple scattered cells appear within the second cluster in the control run, whereas the GF-15 experiment, featuring the smoothest terrain, exhibits a marked reduction in such scattered cells, resulting in a more consolidated convective cluster. These morphological changes partly reflect the distribution of waves.

Furthermore, in the Ter-0 experiment, which lacks terrain obstacles, the circulation pattern within the simulation region is altered to some extent. This results in a larger positional discrepancy of convection compared to the control run, although both elevated convective clusters are still captured. The first cluster in Ter-0 is weaker than in the control run, while the second is comparatively stronger. Radar composite reflectivity indicates that waves still develop even in the absence of terrain.

3.2. Ducted Gravity Waves

The preceding discussion identifies the presence of wave activity during the snowfall event and demonstrates that numerical simulations effectively reproduce this process. Building on this, the present analysis delves deeper into the wave dynamics using results from control run. Figure 7 illustrates the horizontal distribution of vertical velocity at 2 km altitude. This height is chosen because the convective region and the upper-level frontal zone are located near 2 km (Figure 8). The vertical velocity field provides a clear visualization of wave activity.

At 22:30 BJT on the 2nd, wave disturbances are observed on the southern side of the first convective cluster, propagating east–west. The upper portion of these waves, situated above the frontal surface, coincides with an unstable layer sustained by warm, moist air transported by a low-level jet (Figure 3 and Figure 8). The perturbations induced by these waves facilitate the release of convective instability, triggering convection. Given the relatively weak convective instability at this time, only several weak, small-scale convective cells develop within the wave region. As the initial convective cluster moves eastward, waves generated behind it continuously initiate new small convective cells. Through growth and merger, by 02:30 BJT on the 3rd, these cells have consolidated into a larger convective cluster (Figure 7e). Subsequently, the second cluster continues to evolve eastward, with new waves forming to its south.

Figure 9 illustrates the distribution of vertical velocity, perturbation pressure, and perturbation potential temperature within the wave region to elucidate the polarization relationship of the wave. The perturbation fields are obtained by subtracting the background environment—calculated as the average of hourly environmental fields from 20:00 BJT on the 2nd to 08:00 BJT on the 3rd—from the environmental fields at 23:00 BJT. Both perturbation pressure and potential temperature exhibit clear wave-like variations. As the wave propagates from west to east, the maximum vertical velocity is located downstream of the peak perturbation pressure and upstream of the peak perturbation potential temperature. The phase differences between vertical velocity and perturbation pressure and potential temperature are π/2 and −π/2, respectively. This orthogonal polarization confirms the wave as a gravity wave [17,27,41].

Fourier analysis is performed on the vertical velocity output at one-minute intervals from the D03 control run within the red box region shown in Figure 7, covering 22:30 BJT on the 2nd to 03:30 BJT on the 3rd. The resulting power spectrum (Figure 10a) reveals a gravity wave with a horizontal wavelength of approximately 25 km and a period of 17.5 min. This yields a phase speed of about 23.8 m/s, propagating west to east. Figure 10b presents a vertical cross-section of vertical velocity along the green line in Figure 7b, which aligns with the wave propagation direction. This visualization clearly confirms a horizontal wavelength of approximately 25 km.

In the analysis of gravity waves, the Brunt–Väisälä frequency, also known as the buoyancy oscillation frequency, is commonly used to assess atmospheric stability. This study utilizes the moist Brunt–Väisälä frequency ($N_m$), following the approach adopted in Du and Fuqing [17]. The blue line in Figure 11a represents the vertical profile of the average $N_m^2$ within the red box region in Figure 7b at 23:30 BJT on the 2nd. Below 3 km, $N_m^2$ is greater than zero, indicating stable stratification. This stability mainly results from the influence of the front and the underlying cold air (Figure 8). Around 4 km, $N_m^2$ approaches zero, which is associated with a warm tongue formed by the jet above the front. This leads to convective instability at this level (Figure 8), but the averaging process weakens the apparent instability in $N_m^2$. Above 4.2 km, $N_m^2$ becomes positive again, indicating a return to stable conditions. In this configuration, gravity waves are generated within the lower stable layer, which overlies an unstable layer. This stratification is consistent with the environment proposed by Lindzen and Tung [28] for the generation of ducted gravity waves, where such waves are confined to propagate within a “duct”.

To determine whether the observed waves are ducted gravity waves, it is necessary to examine whether a steering level exists above the near-surface stable layer, as well as whether there is a layer where the Richardson number is less than 0.25. The steering level refers to a weakly stable layer where the component of the environmental wind along the direction of wave propagation matches the phase speed of the ducted gravity waves (23.8 m/s, see Figure 10a). As shown in Figure 11b, the wind speed near 4 km altitude aligns with the phase speed of the waves, indicating the presence of a steering level. The Richardson number is defined as follows:

$$\mathrm{R}\mathrm{i}={\displaystyle \frac{N_m^2}{{\left(\partial u/\partial z\right)}^2+{\left(\partial v/\partial z\right)}^2}}$$

(2)

Here, $u$ and $v$ represent the zonal and meridional components of the horizontal wind, respectively. The layer between 3.1 and 4.1 km satisfies the condition $\mathrm{R}\mathrm{i}<0.25$. Therefore, a steering level is embedded within the weakly stable layer above the stable layer. This region acts as an overreflection zone for gravity waves. It inhibits the upward propagation of gravity waves, allowing them to travel long distances horizontally in duct.

The phase speed of ducted gravity waves is given by [28]:

$$c=C_{D,n}+U={\displaystyle \frac{N_{m}H}{\pi \left(\frac{1}{2}+n\right)}}+U$$

(3)

Here, $C_D$ is the phase speed of the wave relative to the mean flow in the duct. $U$ represents the mean wind speed within the low-level stable layer, which is −2.4 m/s in this case. $H$ denotes the depth of the stable layer, defined where $N_m>0.012{\mathrm{s}}^{-1}$. For this case, this corresponds to the 1.0–2.8 km layer, giving $H$ a value of 1.8 km. $N_m$ is the mean moist Brunt–Väisälä frequency within the stable layer, which is taken as $0.022{\mathrm{s}}^{-1}$ here. The parameter $n=0,1,2,\dots$, represents different wave modes, with $n=0$ corresponding to the longest wavelength ducted gravity waves. Based on these values, the theoretical phase speed of the $n=0$ ducted gravity waves is calculated to be 22.81 m/s, as shown by the red line in Figure 10a. The simulated phase speed is 23.8 m/s, demonstrating good agreement between theory and simulation.

According to the study by Du and Fuqing [17], the theoretical vertical wavelength (${\lambda }_z$) and horizontal wavelength (${\lambda }_x$) of ducted gravity waves can be calculated by:

$${\lambda }_z=4\times H$$

(4)

$${\lambda }_x=T\left({\displaystyle \frac{N_m{\lambda }_z}{2\pi }}+U\right)$$

(5)

Here, $T$ represents the wave period. In the control run, $H$ is set to 1.8 km, resulting in a calculated vertical wavelength (${\lambda }_z$) of 7.2 km. With $N_m$ at $0.022{\mathrm{s}}^{-1}$ and $U$ set to −2.4 m/s, and using the decomposed $T$ value of 17.5 min from Figure 10a, the theoretical horizontal wavelength (${\lambda }_x$) is calculated to be 24 km, which is in good agreement with the observed results shown in Figure 10. Equations (3)–(5) indicate that the phase speed and horizontal wavelength of ducted gravity waves are closely related to the characteristics of the stable layer in the lower levels, while the weakly stable region above mainly acts as a reflector and does not directly affect the properties of the gravity waves.

3.3. Terrain Ruggedness Influence

This elevated convection event occurs on the eastern side of the Dalou Mountains, a region characterized by complex topography. To investigate the influence of terrain ruggedness on ducted gravity waves, sensitivity experiments are carried out. As shown in Figure 6, the control run initiates convection approximately one hour earlier than the sensitivity experiments. Therefore, the following analysis compares the results of the control run at 00:30 BJT on the 3rd and the sensitivity experiments at 01:30 BJT.

Figure 12 illustrates the distribution of vertical velocity at the 2 km level for both the control run and sensitivity experiments. Across all experiments, gravity waves consistently form on the southern flank of the first convective cluster. In the GF experiments (Figure 12b–e), as the terrain becomes smoother, the distribution of these waves grows more organized, and the smaller, irregular disturbances evident in the control run diminish significantly in the GF-15 experiment. When the main topographical features are retained, the overall pattern and location of wave propagation remain similar to those in the control run. However, notable changes emerge when the terrain in the convective region is entirely removed (Ter-0 experiment, Figure 12f). Here, gravity waves still develop, suggesting that convection alone is sufficient to generate them during this event. Furthermore, the absence of terrain alters the direction of gravity wave propagation. In the control run, gravity waves spread eastward, whereas in the Ter-0 experiment, they propagate northeastward. This indicates that while terrain impacts the organization and directionality of gravity waves, convective processes remain a primary driver of their formation in this case.

Equations (4) and (5) indicate that the horizontal wavelength of ducted gravity waves is influenced by $N_m$ and $H$. Figure 13a shows the vertical distribution of $N_m$ across the sensitivity experiments. In the GF experiments, as terrain becomes smoother, the thickness of $H$ gradually decreases, leading to a reduction in the ${\lambda }_z$ of ducted gravity waves. The maximum value of $N_m$ increases as the terrain becomes less rugged, and the height at which this maximum occurs also lowers. This peak in $N_m$ corresponds to the location of the frontal zone, so the height of the frontal zone at the same position decreases as the terrain becomes smoother. The $U$ at low levels does not exhibit a clear trend of change. The decrease in ${\lambda }_z$ and the increase in $N_m$ generally offset each other, resulting in little change in the horizontal wavelength of gravity waves (Figure 12a–e). According to the phase speed formula in Equation (3), the phase speed of gravity waves in the GF experiments should be similar to that in the control run.

In the Ter-0 sensitivity experiment, removing the terrain causes the height of the maximum $N_m$ to decrease significantly compared to the other experiments, indicating that without terrain, the frontal zone lowers. Since only a small area of terrain is altered in the model, the distribution of $N_m$ above 2.5 km in the Ter-0 experiment remains largely consistent with the other simulations. In this experiment, after the northern cold air passes over the Dalou Mountains, the absence of near-surface barriers inhibits cold air accumulation, resulting in smaller near-surface $N_m$ and greater thickness of $H$ compared to the other simulations.

In the GF experiments, the frontal zone is located at approximately 1.6 km, while in the Ter-0 experiment, it is found near 0.9 km (Figure 13a). Figure 14 presents the distributions of potential temperature and horizontal wind fields below the frontal zone for each experiment. Near the surface, convection remains under the control of the cold air mass, with prevailing northeasterly winds. The second convective cluster is situated downwind of the first one, and all simulations display similar circulation patterns near the surface.

In both the control run and GF experiments, a cold center consistently appears behind the convective region, particularly pronounced behind the first convective cell (Figure 14a–e). However, in the Ter-0 experiment, the cold center behind the convective area is less evident (Figure 14f). This suggests that convection tends to form a cold pool in its wake, and the presence of western terrain helps to support the formation of this cold pool.

Additionally, in both the control run and GF experiments, a banded cold region appears along the airflow direction at the location of the second convective event. This cold zone is situated to the east of the Dalou Mountains. Analysis of the airflow source indicates that the formation of this cold region is also related to the first convective cluster. Cold air from the north flows around the eastern side of the Daba Mountains and enters the convective region. At the location of the first convective cluster, the wind is northeasterly, but as it interacts with warm air from the south, the wind direction at the second convective location shifts to easterly (Figure 14). Thus, low-level air ascends along the Daba Mountains, and the terrain ruggedness influences the flow during this ascent.

Figure 15 shows the vertical velocity profiles along the green line marked in Figure 12 and Figure 14. These profiles clearly display the distribution of waves, especially the circulation circles with a wave pattern appearing around 2 km height. This provides a direct visualization of the relationship between the waves and the airflow.

In the control run (Figure 15a), each terrain undulation corresponds to a disturbance in the airflow. When the direction of these disturbances aligns with the flow in the gravity waves, they enhance the airflow associated with the gravity wave, such as the descending motion observed over the peak at 111.1° E. Conversely, when the disturbance opposes the flow in gravity waves, the disturbance dissipates beneath the frontal zone and weakens the gravity wave, as seen at the peak near 109.6° E.

In the GF experiments, as the terrain becomes smoother, the influence of low-level terrain-induced disturbances on the wave pattern diminishes. When the terrain is smoothed into a uniform slope (Figure 15e), disturbances caused by terrain ruggedness disappear entirely. The vertical velocity in both ascending and descending regions forms a spindle-shaped pattern, with the strongest upward and downward motions concentrated at the center of waves. Vertical motion near the surface and in the lower troposphere is relatively weak. However, small convective cells present along the cross section continue to disturb the gravity waves. In the Ter-0 experiment (Figure 15f), the cross section is free from convective disturbances and terrain ruggedness. Here, the upward and downward motions associated with gravity waves show a uniform spindle-shaped distribution.

Therefore, in this case, convection alone is sufficient to generate ducted gravity waves, but terrain influences their distribution. Terrain ruggedness disrupts the otherwise uniform gravity waves produced by convection and alters the low-level circulation, thereby changing the propagation direction and horizontal wavelength of the gravity waves. Elevated convection refers to updrafts that originate entirely above a stable boundary layer [10,11]. Since the terrain lies beneath the frontal zone, it does not directly trigger elevated convection. However, it can indirectly affect elevated convection by modifying the distribution of gravity waves. As observed in Figure 1, the second convective cluster is triggered by the direct influence of gravity waves generated by the first convective cluster, as well as by the indirect effect of the terrain.

4. Summary

Elevated convection on the polar side of a front refers to deep, moist convection that develops above a stable boundary layer formed by a front. In these situations, the air below the frontal boundary is stabilized by cold air from the north, while unstable stratification develops above the front due to warm, moist air from the south. This configuration creates favorable conditions for the formation and propagation of ducted gravity waves. This study examines an elevated convection event north of a cold front that results in widespread snowfall across central China during the night of 2–3 February 2024, with a particular focus on the characteristics of gravity waves and the impact of terrain ruggedness.

The snowfall event consists of two elevated convective clusters. The first convective cluster initiates over southern Chongqing, forming a clustered structure that moves east-northeast. As it travels, wave-like clouds appear on its southwestern flank. Numerous small convective clouds subsequently develop within these clouds, gradually merging to form a second, larger convective cluster. During this process, the surface cold front moves southward into South China, and convection occurs near the 850 hPa trough. Strong southwesterly jets at both 700 hPa and 850 hPa transport warm, moist air into the convective region, while at 500 hPa, convection develops ahead of an upper-level trough.

Throughout the event, gravity waves produced by the first convective cluster propagate from west to east. These waves exhibit a horizontal wavelength of 25 km, a period of 17.5 min, and a phase speed of 23.8 m/s. The maximum vertical velocity occurs downstream (upstream) of the pressure (potential temperature) perturbation maximum. The phase difference between vertical velocity and pressure (potential temperature) perturbation is π/2 (−π/2). This orthogonal polarization confirms the presence of gravity waves. Following the criteria outlined by Lindzen and Tung [28], the duct for ducted gravity waves is located between 1.0 and 2.8 km altitude. Above this, a weakly stable layer caps the waves between 3.1 and 4.1 km, and a steering level appears near 4 km, together forming an overreflection layer. The theoretical phase speed and horizontal wavelength of ducted gravity waves, calculated as 22.81 m/s and 24 km, respectively, closely match the simulated result, corroborating that the simulated gravity wave is indeed a ducted gravity wave.

Sensitivity experiments are designed to assess the impact of terrain ruggedness on convection and gravity wave characteristics. In the GF experiments, Gaussian filtering smooths the terrain in the convective region, while in the Ter-0 experiment, the terrain is completely removed. Results indicate that gravity waves can form with or without orographic influence. However, terrain changes affect the low-level circulation: in the GF experiments, greater terrain smoothing leads to lower frontal positions and higher $N_m$ values at the front; in the Ter-0 experiment, the lack of orographic blocking weakens the near-surface cold pool, resulting in a lower front and smaller $N_m$ values. Terrain-induced disturbances near the surface also lead to uneven gravity wave distributions, which impact the elevated convection above. Without terrain ruggedness, vertical velocity exhibits a uniform, spindle-shaped distribution, with strongest upward and downward motions at the center of waves, while vertical motions are weaker near the surface and in the middle troposphere.

This study establishes a link between elevated convection and ducted gravity waves, suggesting that the unique circulation patterns associated with elevated convection may facilitate the widespread occurrence of ducted gravity waves. Currently, statistical investigations on this relationship remain limited. Elevated convection initiates above the stable boundary layer, so orography does not directly trigger convection but, instead, influences it indirectly by modulating the ducted gravity wave distribution. Furthermore, the interaction between ducted gravity waves and the unstable region above the front resembles the Wave-CISK mechanism. The interplay between stable and unstable layers in elevated convection warrants further investigation.