1. Introduction
In the context of global climate warming, extreme precipitation events have become more frequent, leading to a significant increase in heavy precipitation [
1,
2,
3,
4,
5]. Consequently, associated natural hazards such as flash floods, urban waterlogging, landslides, and debris flows are posing serious threats to society, the economy, and personal safety [
6,
7,
8,
9]. Despite substantial progress in comprehending the structure and lifespan of convective systems, accurately forecasting the convective initiation (CI, which refers to the process by which air particles gain and maintain positive buoyancy after being lifted above the level of free convection, eventually forming deep convective clouds) remains one of the biggest challenges in meteorology [
10,
11,
12,
13,
14,
15,
16,
17,
18,
19,
20,
21].
The mechanisms of the CI and convection development of the extreme precipitation events are influenced by many factors such as atmospheric circulation, solar radiation, terrain, and underlying surface properties, and boundary layer convergence zones, etc., resulting its spatial and temporal distribution characteristics highly complex [
22,
23,
24,
25,
26,
27,
28,
29]. Among these factors, the formation and maintenance mechanisms of terrain-induced precipitation have been extensively studied by many researchers to analyze the impact of terrain on precipitation. Kirshbaum et al. [
22] found that strong precipitation occurs both in the warm front and warm sector when a mid-latitude frontal system passes, with terrain amplifying precipitation more significantly in the warm sector. McMurdie et al. [
23] compared cloud structures over the ocean and the windward slope of the Olympic Mountains in the Unites States, and they observed significantly intense radar echoes within the range of 2–8 km above the windward slope. Mulholland et al. [
24] analyzed a case of heavy rainfall event in northern Argentina, South America, and found that changes in terrain height can significantly affect the blocking effect of the terrain on the cold pool (CP) and modify environmental conditions under certain conditions.
Numerous studies employing numerical simulations have also focused on extreme rainstorms associated with the CP in China [
13,
25,
26,
27,
30]. For example, Du et al. [
21] used dynamic and thermodynamic analysis methods and a number of numerical simulation experiments to explore the effects of the topography, coastline, and CP on the formation of CI. The CP outflows resulting from the evaporation of precipitation propagate southeastward rather than along the background southerlies due to the obstacle of the coastal SW–NE-oriented terrain, which vitally affects the growth and movement of the mesoscale convective system. Xu et al. [
25] discovered that the CP generated by earlier precipitation was trapped by the terrain of Taiwan Island and remained fixed in the lower altitude on the southwest side of the island. This led to the lifting of unstable airflows over the CP during the precipitation process. Wei et al. [
26] analyzed a balance was established between the eastward dispersion of the CP and the easterly inflow, restraining the storm’s eastward progression, resulting in the unprecedented extreme rainfall over Zhengzhou, China. Kang et al. [
27] discovered that the interaction between the mesocyclone and mesoscale topography leads to the CI along a shear line, and it is also influenced by terrain, a CP, and the outer flow of the mesocyclone. This ultimately results in orographic forcing and CP augmentation, intensifying the precipitation event over the Taihang Mountains.
Unstable energy and frontogenetical forcing are important environmental conditions for the CI, and the convergence lifting along the leading edge of a CP can usually cause CI [
31,
32]. The CI and convection development of convective systems is closely related to atmospheric stabilities and moist potential vorticity (MPV, a comprehensive diagnostic physical quantity that characterizes the dynamic and thermal conditions of the atmosphere), which have been widely used in studying the mechanisms of heavy precipitation events in mid-latitude regions to diagnose atmospheric instability [
33,
34,
35]. For instance, Liu et al. [
36] analyzed the characteristics of the MPV in their investigation on the CI mechanisms of a rainstorm event in Bei**g, and they concluded that convective instability (CIns, i.e., an instability due to the buoyancy force of heavy fluid over light fluid overcoming the stabilizing influence of viscous forces) is released after precipitation, while conditional symmetric instability [
37] (CSI, i.e., an instability which is recognized as the contributor to the slantwise convection and which can occur in baroclinic flows in which the slantwise-upward displacement of air parcels, elongated in the direction of the thermal wind, results in a vector combination of buoyancy and Coriolis (or centrifugal) and pressure-gradient accelerations that drive the parcel in the same direction as the displacement) maintains precipitation. Huang et al. [
38] found that negative MPV areas serve as precursors for heavy precipitation in their study of a rainstorm process in the Ili Valley of **njiang. In their research on a rainstorm event in Shanxi, Li et al. [
34] stated that the CSI (calculated based on high resolution simulation data) near the frontogenesis (i.e., the formation process of the front) zone indicates a certain connection between frontogenesis and the release of unstable energy.
Despite there being continuous improvements in weather forecasting and numerical simulation technologies, the prediction of localized short-term heavy precipitation remains a challenge due to the sparse observation stations and complex terrains in **njiang, especially in southern **njiang. Furthermore, in contrast to the relatively comprehensive and thorough investigations on intense rainfall events over the mid-eastern part of China [
10,
13,
38,
39,
40,
41,
42,
43], there are relatively few studies on extreme rainfall events over the northern slope region of the Kunlun Mountains (KLM) in **njiang. In addition, to the authors knowledge, there has been no previous comprehensive and systematic study on the CI mechanisms of heavy rainfall in the northern slope region of the KLM based on high tempo-spatial resolution numerical simulations. Therefore, the present study aims to investigate the mechanisms of CI associated with the interactions between a CP, boundary level jet (BLJ), and unstable energy within an extreme rainfall event, in order to deepen or fill the gap in the understanding of these kinds of CI mechanisms over the northern slope region of the KLM.
The rest of this paper is organized as follows:
Section 2 introduces the data and methodology, and
Section 3 gives a brief overview of the rainfall event along with associated environmental conditions.
Section 4 presents the evaluation of numerical simulation results. The mechanism of CI is documented in
Section 5, according to the analysis of MPV and frontogenetical forcing. Finally, discussions and conclusions are presented in
Section 6 and
Section 7, respectively.
4. Evaluation of Simulation
Figure 6 shows the 3 h accumulated precipitation observed by AWSs and obtained from the model simulation. Because the sparse and uneven distribution of the AWSs over the northern slope of the KLM, the interpolation of accumulated precipitation has poor performance. Hence, distinct colored dots are employed to indicate the value of the accumulated precipitation at each of the stations. As shown in
Figure 6a, during the period from 0500 to 0800 UTC on 15 June, the observed distribution of accumulated precipitation along the northern slope of the KLM exhibits a clear northwest–southeast-oriented banding pattern, and three main areas of high precipitation values can be identified (indicated by red dotted ellipticals in
Figure 6a). It can be seen from the corresponding simulation results (
Figure 6b) that the simulated precipitation band also shows a distinct northwest–southeast-oriented pattern, with three corresponding high-value areas (indicated by the red dotted ellipticals in
Figure 6b). Due to the scarcity of the AWSs over the northern slope of the KLM, the range of high precipitation values shown in
Figure 6a seemed to be less than those in the simulation result. However, the relatively high precipitation may also have occurred over the areas beyond the locations of the AWSs. The pattern and magnitude of the simulated precipitation align well with the observed precipitations, which indicates a good representation of the heavy precipitation event in the simulation.
Figure 7a–c shows the temperature of the black body (TBB) over the top of the precipitation clouds observed by FY-4A at 0300, 0400, and 0500 UTC on 15 June 2021. It can be seen that the rainfall clouds formed at about 0300 UTC and were independent of the convective system on the northwest side of the Tarim basin.
Figure 7d–f displayed the simulated composite reflectivity along with the horizontal wind field at 2500 m ASL at 0330, 0430, and 0530 UTC on 15 June 2021. Similarly, as shown in
Figure 6b, an isolated convective cell (indicated by the red arrow) which corresponds to the region of high precipitation region can be identified. In addition, a distinct mesoscale vortex (roughly indicated by a black dashed arrow) can be identified at this height (2500 m ASL). Although the time of the simulated composite reflectivity and the TBB observed by the FY-4A lag by about half an hour, they still successfully captured the essential features of the convections, which indicates a good performance of the simulation. In order to clearly identify the occurrence of the CI near the Pishan, the major area (indicated by the black rectangular box in
Figure 7d–f) where the CI occurred is further magnified, and this is shown in
Figure 7g–i. The composite reflectivity value above the 35 dBZ is plotted with colors in
Figure 7g–i, because the occurrence of the CI is confirmed when the composite reflectivity reached the value of 35 dBZ for the first time in the newly generated convective cell [
31,
32,
39]. The results showed that although more than one convective cell triggered over Pishan at 0430UTC, only the cell we selected (indicated by the red arrow in
Figure 7h) continuously developed into an intense convective system, causing heavy precipitation in the study area. The convective cell indicated by the red solid arrow in
Figure 7h is believed to the major convective cell that responsible for the heavy precipitation over the Pishan.
5. Convection Initiation
In order to further analyze the CI mechanisms of the convective cell, we conducted a further analysis based on the simulated data from the innermost domain (d03, with horizontal resolution of 1 km) of the model. The convective cell which mainly responsible for the heavy precipitation over the Pishan was initiated at 0430UTC; therefore, we mainly focus on the time period before the CI in the following. It can be seen from the potential temperature fields (
Figure 8a,b) at the lowest layer of the model (
= 0.9970323) (the potential temperature on the lowest mode layer was plotted because the CP often moves and almost sticks to the surface) that a CP generated due to the influence of previous precipitation was moving from north to south (indicated by the black hollow arrow) in the western Tarim Basin. At 0330 UTC on 15 June 2021, the thermal boundary of the leading edge of the CP (i.e., 305 K isoline) had not yet reached the CI area mentioned above. At this time, the movement of the CP was slowed down due to the blocking effect of the terrain, while the leading edge of the CP reached the CI area at 0400 UTC. Meanwhile, the horizontal wind field at 2500 m ASL (horizontal wind fields are affected by topography to some extent, and it varies significantly with height; therefore, the constant-height surface was used to investigate the horizontal wind features) revealed the existence of a boundary layer jet (BLJ) in the region. At 0330 UTC (
Figure 8c), as mentioned in our
Supplementary Materials, areas of high values (exceeding 10 m s
−1) of horizontal wind speeds occur on the windward slopes of the study area due to pressure gradient forces and valley winds. The horizontal wind speeds in the CI area enhanced (indicated by the black hollow arrow) to some extent at 0400 UTC (
Figure 8d). In order to further figure out the roles of the CP and BLJ in the CI mechanisms, the related dynamic and thermal conditions reflected by the vertical cross-sections in the CI area (line segment AB in
Figure 7h) are further investigated in the following (
Figure 9).
Figure 9 shows the potential temperature (
), horizontal wind speed, and divergence on the vertical cross-section along the line AB during a 1 h period before the occurrence of the CI (i.e., 0330–0430 UTC). The vertical cross-section along the line segment AB went through the center of heavy precipitation and the leading edge of the CP (as shown in
Figure 7h and
Figure 8), which helped us to obtain a clearer insight of the CI process in this case. The CP was advancing roughly from the north direction towards the windward slope of the KLM (
Figure 9a–c). The potential temperature within the CP remains below 302 K below an altitude of 2800 m ASL. The 304 K and 305 K isotherms can be identified as the thermal boundary of the leading edge of the CP (represented by a dotted red arrow). Simultaneously, from the vertical distribution of horizontal wind speed (
Figure 9d–f), it can be seen that along with the movement of the CP, there is a region of higher wind speeds (exceeding 10 m s
−1) along the leading edge of the CP below ~1 km AGL (above ground level) during this period. Additionally, there is also a region of higher wind speeds (indicated by the red solid line arrows) at around 2500 m ASL on the windward slope at 0330 and 0400 UTC (it coincides with the analysis of the BLJ mentioned above).
It can be seen from the vertical distribution of the divergence (
Figure 9g–i) that there is a significant convergence (around −1.5 × 10
−3 s
−1) that occurred near the leading edge of the CP, and a similar significant convergence can be found in the area influenced by BLJ. At 0400 UTC, the leading edge of the CP and BLJ are located in almost the same area, and some local rainfall cloud clusters are generated with a vertical velocity up to 1 m s
−1 along the leading edge of the CP. At 0430 UTC, the leading edge of the CP completely reached to the area where the CI occurred, probably due to the combined convergent lifting effect associated with the leading edge of the CP and BLJ, leading to generation of convective clouds accompanied by the vertical velocities reaching to about 1.8 m s
−1. In general, it can be concluded from the characteristics of the vertical cross sections of potential temperature, horizontal wind speed, and divergence that the CP seemed to had provided a dynamical forcing (i.e., convergence) conditions for CI during its movement to the study area, along with the similar dynamic forcing generated due to the convergence near the leading edge of the BLJ over the north slope of the KLM.
MPV is a physical quantity that reflects atmospheric dynamics, thermodynamics, and moisture properties, and it can also characterize the atmospheric instability. In recent years, it has been widely used in the study of heavy precipitation events [
49,
50,
51,
52]. Therefore, in order to further investigate the CI mechanisms, the MPV was calculated and its vertical cross section along the line segment AB is analyzed in the following. The negative MPV values serve as indicators of atmospheric instability, especially in the context of heavy precipitation events, such as frontal systems. According to some previous studies [
36,
38,
51,
52], the negative values of MPV can provide predictive indications for precipitation areas, and negative MPV1 represents the CIns, while negative MPV2 represents the CSI. Therefore, we will mainly focus on the spatial variations of negative values of the MPV during the CI process.
In order to better illustrate the atmospheric instability, we only show the negative values of MPV, MPV1, and MPV2 in
Figure 10. At the early period before the CI (i.e., at 0330 UTC,
Figure 10a), there are mainly two negative MPV maxima regions along the leading edge of the CP. Additionally, there is another negative MPV center (represented by three purple dashed ellipses) within the area influenced by the BLJ on the windward slope. The negative values of MPV in the area affected by the BLJ on the windward slope are relatively weak, while a relatively large negative MPV region (with an intensity of about −10 PVU) exists along the leading edge of CP, extending to an altitude of ~4 km ASL. At 0400 UTC, the movement of the CP caused the convergence near the leading edge of the CP and the area affected by the BLJ, resulting in a relatively large negative MPV center (with an intensity of about −10 PVU). At this time, rainfall cloud clusters started to form, and the intensity of the negative MPV center above the CP weakened (represented by two purple dashed ellipses). When the CI occurred at 0430 UTC, the negative center along the leading edge of the CP significantly weakened compared to the previous two times, while the negative MPV center above the CP still existed. Meanwhile, a large area of negative MPV within the CP continued to transport towards the study area.
At 0400 UTC (
Figure 10e), as the CP moved forward, and the rainfall cloud clusters had further developed, and the intensity and size of the negative MPV1 (represents the CIns) decreased to some extent. The CIns indicates the influence of thermodynamic instability, and as the CP further moved forward, the rainfall cloud clusters continue to develop, leading to the occurrence of the CI at 0430 UTC. At the period of occurrence of the CI (
Figure 10f), the negative values of the MPV1 along the leading edge of the CP further weakened, which indicates that the development of rainfall cloud clusters consumes the CIns energy. In addition, there is an area of persistent and relatively strong negative MPV2 above the CP, with both its height and intensity showing a weakening trend before the CI. It can be deduced that the negative MPV2 area indicated the CSI (suggesting the presence of a strong vertical wind shear above the CP) had played a significant role in supporting the CI.
In general, at the early stages before the CI, the instability energy on the windward slope is mainly controlled by CIns and CSI. The CIns played a significant role mainly in the lower layer below 3 km ASL along the leading edge of the CP, while the CSI makes a certain contribution within the range of 3~5 km ASL above the CP. At the CI period, the intensity and extent of the CIns noticeably weakened compared to that of the period before the CI, while the CSI retains significant values above the CP, providing favorable conditions for the CI of rainfall cloud clusters.
As mentioned in the introduction above, the release of unstable energy is closely related to the frontogenetical forcing, and the leading edge of the CP acts similarly to a small-scale cold front. The convergence of cold and warm air at the leading edge of CP provided favorable conditions for frontogenesis. The frontogenesis process led to upward motion of the thermal circulation, which is one of the important reasons for the CI. In order to further study the frontogenetical forcing mechanisms responsible for the release of those unstable energies, the frontogenesis function (which is a method of quantifying the characteristics of the thermal and dynamic forcing related to the formation of a front) was calculated and analyzed in the vertical cross section along the line AB in the following.
Before the CI (i.e., 0330 UTC), the significant high values of Ft are mainly located near the leading edge and inside of the CP, and in some areas, they are influenced by the BLJ (as indicated by the blue dashed ellipses in
Figure 11a). The overall strength of F
1 is comparatively low, primarily distributed at the leading edge and inside of the CP (as indicated by the blue dashed ellipses in
Figure 11b). The major centers of F
2 are located in the low layers below ~2500 m ASL at the leading edge of the CP, exhibiting a similar distribution pattern as that of F
1. There are no significant high-value centers of F
3 below 4 km ASL. Meanwhile, the overall distribution of F
4 is closely similar to that of the Ft, with two apparent high-value centers inside the CP and at ~2.5 km ASL on the windward slope of the KLM (as indicated by the blue ellipses).
At the CI period (i.e., 0430 UTC), a prominent high-value center of Ft can be identified on the windward slope (as shown in
Figure 11f), while the significant center observed at 0330 UTC has completely disappeared. During this time, the intensity of F
1 (
Figure 11g) remains relatively weak, but there is a relatively high-value center inside the convective cloud cluster (as indicated by the blue dashed ellipse). The distribution of F
2 (
Figure 11h) indicates that the significant high-value center identified at the leading edge of the CP at 0330 UTC has vanished, and only a weak high-value center exists inside the convective cloud cluster (as indicated by the blue dashed ellipse). There are still no significant high-value centers of F
3 in the lower layers. The intensity and distribution range of F
4 (
Figure 11j) are consistent with that of the Ft, with significant high-value centers existing inside the convective cloud cluster over the windward slope and above the CP.
Overall, throughout the entire process of the CI, F4 makes a more significant contribution to the Ft. Before the CI, except for the dominance of F4 at the leading edge of the CP and ~2.5 km ASL on the windward slope, F1 and F2 also make relatively weaker contributions at the leading edge of the CP. F3 makes a minor contribution in the lower layers. During the CI stage, F1 and F2 make relatively weaker contributions inside the convective cloud cluster, while F4 makes significant contributions to the Ft over the windward slope and inside the cloud cluster.
F
1 and F
2 mainly represent the latent heat released by condensation and local convergence, respectively. Based on the above analysis, F
1 may be caused by the latent heat released from condensation inside the rainfall cloud cluster, while F
2 may be attributed to the convergence at the leading edge of the CP and the blocking effect of the windward slope topography. According to Equation (8), F
4 reflects the combined effects of CIns, horizontal gradient of the equivalent potential temperature (i.e.,
, shading, units: K km
−1), and the horizontal gradient of vertical velocity (i.e.,
, denoted as
, indicating the non-uniformity of vertical velocity in the horizontal direction). From the previous analysis, most regions along the vertical profile of the line segment AB show negative CIns values (as shown in
Figure 10d–f). Therefore, the values of F
4 are primarily influenced by
and
. To further investigate the physical processes contributing to F
4, we will analyze the characteristics of
and
in the following passages.
Before the CI (i.e., 0330 UTC), it can be seen from the vertical cross section of the
(
Figure 12a) that there are two high-value centers over the windward slope, one is located near the leading edge of the CP, and the other one is influenced by the BLJ. At the time of CI (i.e., 0430 UTC), two high-value centers are presented inside the cloud cluster (indicated by blue dashed ellipses), which indicates a significant horizontal gradient of vertical velocity at the leading edge of the CP. These high-value centers are highly consistent with the distribution of F
4. In the lower layers below 3 km ASL, there is a prominent high-value center of
near the leading edge of the CP before the CI (i.e., 0330 UTC) (indicated by a blue dashed ellipse). At the CI time (i.e., 0430 UTC), with the southward movement of the CP, the high-value center of the
also moved to above the windward slope (indicated by a blue dashed ellipse). There is also a high-value center inside the rainfall cloud cluster (indicated by a blue dashed ellipse). The high value of
in the lower layers is mainly due to the horizontal gradients of the temperature and humidity at the leading edge of the CP, while the high-value centers inside the rainfall cloud cluster may be caused by the process of latent heat release. During the CI stage, the overall strength of
appears to be higher than that of
, which indicated that the contribution of
may be greater than that of
. In general, the strong convergence area in the leading of the CP and the intense vertical gradient of horizontal equivalent potential temperature near the leading edge of the CP contributed to F
4 together.