Evolution of Instability before and during a Torrential Rainstorm in North China

A torrential rain event occurred over Beijing and Hebei Province in China on 21 July 2012. Being the most severe event of the past 60 years, it attracted great attention. Its strength exceeded expectations, and it caused major losses of life and property. Many researchers have analyzed the mechanism of this extreme event from different points of view. (Sun et al., 2013a) found that the train-effect phenomenon was obvious during the precipitation, and connected it with the propagation of an inertial gravity wave. (Sun et al., 2013b) explored the effect of the interaction of multi-scale weather systems on the torrential rain over Beijing. (Wang et al., 2014) analyzed the water vapor transport features over Beijing. (Ran et al., 2014) developed a dynamical element forecast equation with the moist thermodynamic advection parameter, the convective vorticity vector, the thermodynamic wave-activity density, and so on, to predict the torrential rain. However, these previous studies focused mainly on the circulation structure, vapor conditions or multi-scale interactions, while relatively few studies have examined the physical mechanism of the instability evolution. Strengthening the analysis on the physical mechanism of instability is important and helpful for improving understanding of the generation and development of torrential rain.

Scholars both home and abroad began researching instability and precipitation many years ago. (Charney, 1947) and (Eady, 1949) put forward the idea of baroclinic instability and used it to explain the constant dynamic instability of midlatitude westerly flow. Stone (1966, 1970, 1971) explored the baroclinic instability in the non-geostrophic atmosphere, and then (Hoskins, 1974) noted that symmetric instability was one of the trigger mechanisms for frontal rainfall. (Bennetts and Hoskins, 1979) found that the perturbation of mesoscale symmetric instability played a significant role in organizing precipitation. By investigating the relationship between symmetric instability and precipitation, (Seltzer et al., 1985) proved that symmetric instability was an important mechanism for the formation of precipitation. (Xu, 1986) re-examined the linear theory of conditional symmetric instability in a rigorous framework and proposed two types of conditional symmetric instability. Zhang (1988a, b) investigated symmetric instability and transversal instability in baroclinic basic flow and explored the effect of baroclinicity on ageostrophic inertial flow. (Wu et al., 1995), (Wu and Cai, 1997), (Wu and Liu, 1999) diagnosed the conditional symmetric instability with the moist potential vorticity (MPV) and found that the slant of the moist isentropic surface caused by the enhanced vertical wind shear or the increased horizontal moist baroclinic wind would strengthen the vertical vorticity, thus causing heavy rainfall. (Zhang and Zhang, 1992) researched the influence of the wave-CISK (conditional instability of the second kind) mechanism on symmetric instability and revealed the feature of symmetric instability perturbation. In the actual atmosphere, convective instability often occurs simultaneously with symmetric instability. (Seman, 1994) proposed the theory of nonlinear convective-symmetric instability. (Schultz and Schumacher, 1999) reviewed the applicability of symmetric instability to various atmospheric situations. (Gao, 2000) and (Gao and Zhou, 2001) hypothesized that when the horizontal wind shear is strong the shear line becomes the instability of the vortex sheet rather than the traditional shear instability. Starting from nonlinear equations containing frictional dissipation under the Boussinesq approximation, (Lu and Shao, 2003) proposed a new type of generalized energy, resulting in a new criterion of generalized nonlinear symmetric instability. (Schultz and Knox, 2007) explored the relationship between banded convection and a combination of conditional, symmetric and inertial instability. Based on the aforementioned work, the theory of atmospheric instability has been widely applied to weather analysis, and great progress has been made.

Building on previous research, this study aims to explore the characteristics and evolution mechanism of instability before and during a precipitation event that occurred in Beijing on 21 July 2012, in the hope of providing significant insight for further heavy rainfall of a similar nature. Section 2 introduces the background situation of the case and the characteristics of the precipitation. Section 3 analyzes the convective and symmetric instability in detail. Section 4 deduces the tendency equation of convective instability and examines the effect of various elements on the convective instability before the precipitation. Section 5 deduces the tendency equation of symmetric instability and discusses its variation during the precipitation. Section 6 summarizes the key conclusions of the study.

During the period 21-22 July 2012 a torrential precipitation event occurred over northern China. The heavy rainfall occurred at about 0200 UTC and had generally vanished by 1800 UTC 21 July. The rain band was oriented from southwest to northeast (Fig. 1). The center of the precipitation was over Beijing (40^°N, 116^°E) and northern Hebei Province, where the 24-h accumulated precipitation reached 200 mm. Before 0800 UTC 21 July there was precipitation generated in the warm region in the front of the front. The center of precipitation scattered. Then, after 0800 UTC 21 July, the front moved into the Beijing area, and the scattered center gradually organized into a marked rain band oriented from southwest to northeast.

In this study, the period before and during the precipitation were both considered to explore the evolution of the instability.

Figure 1.  The 24-h accumulated precipitation (units: mm) from 0000 UTC 21 to 0000 UTC 22 July. The black box represents the location of Beijing (39.5$^\circ$-41$^\circ$N, 115.5$^\circ$-117.3$^\circ$E).

In this study, global forecast system (GFS) reanalysis data from the National Centers for Environment Prediction (NCEP) were used to calculate and explore the spatial and temporal evolution of atmospheric instability and its physical mechanism. The GFS data were collected at four times (0000, 0600, 1200 and 1800 UTC), with a horizontal resolution of 0.5^°×0.5^° and a vertical resolution of 26 levels.

The precipitation formed in an environment with a well-defined trough, surface shear line, low-level jet, high-level jet, and sufficient moisture. At 500 hPa (Fig. 2a), the westerly wind trough was located over Lake Baikal; meanwhile, there were ridges at Barr Kersh Lake (60^°-90^°E) and eastern Asia, forming a "two ridge and one trough" environment. The 588 (gpm) line of the subtropical high jumped from 33^°N to 36^°N, shaping a "high-pressure dam", which typically favors an "east-high-west-low" situation for northern torrential precipitation. At the moment of the storm's approach (0000 UTC 21 July), the westerly wind trough merged with another trough over northwestern China, moving into northern China. There was a wide range of southwesterly warm and moist airflow in front of the trough impacting on Beijing (40^°N, 116^°E) and Hebei Province. At 1200 UTC 21 July (Fig. 2b), the 588 (gpm) line of the subtropical high maintained stability, blocking the westerly trough from moving eastward, and thus the system was detained over northern China, causing the persistent precipitation.

Figure 2.  The distribution of (a) geopotential height at 500 hPa (red line; units: gpm) and wind vector (units: m s$^-1$) at 1200 UTC 20 July; (b) geopotential height at 500 hPa (red line; units: gpm) and wind vector (units: m s$^-1$) at 0600 UTC 21 July; (c) geopotential height at 700 hPa (black line; units: gpm), the low-level jet at 850 hPa (shaded) and positive relative vorticity (red line; units: 10$^-4$ s$^-1$) at 0000 UTC 21 July; (d) geopotential height at 700 hPa (black line; units: gpm), the low-level jet at 850 hPa (shaded) and positive relative vorticity (red line; units: 10$^-4$ s$^-1$) at 0600 UTC 21 July; (e) wind vector (units: m s$^-1$) and the high-level jet (shaded) at 200 hPa at 1200 UTC 21 July; and (f) relative humidity (shaded) and wind vector (units: m s$^-1$) at 925 hPa at 1200 UTC 21 July.

At 700 hPa, before the heavy rainfall, the low-level trough over northwestern China moved eastward along with steering flow. At the moment of the storm's approach (0000 UTC 21 July), the low-level trough developed intensively and formed a closed vortex. At 0600 UTC, the vortex moved to Beijing. The southwesterly airflow in front of the trough increased, reaching 16 m s^-1. At 1200 UTC 21 July (Fig. 2d), the vortex was over the Beijing area and the low-level jet had enhanced, reaching 20 m s^-1. Beijing was located on the left side of the exit of the low-level jet. There was strong cyclonic shear and upward motion over the Beijing area. At 200 hPa (Fig. 2f), from 0600 UTC to 1800 UTC 21 July, the Beijing area was at the entrance of the high-level jet, where there was strong divergence. In accordance with the low-level jet, there was a favorable situation of divergence at the high level, and convergence at the low level, over northern China.

Figure 3.  Vertical distribution (hPa) of pseudo-equivalent potential temperature ($\theta_ se$; contours; units: K) and vertical velocity (shaded; units: hPa s$^-1$) along 40$^\circ$N at (a) 1800 UTC 20 July and (b) 1200 UTC 21 July. (c) Temporal evolution (UTC) of the vertical gradient of pseudo-equivalent potential temperature (shaded; units: K) and 6-h accumulated precipitation (line; units: mm). (d) Temporal evolution (UTC) of vorticity (contours; 10$^-5$ s$^-1$) and divergence (shaded; units: 10$^-5$ s$^-1$) over the Beijing area (39.8$^\circ$-40.0$^\circ$N, 115.8$^\circ$-116.2$^\circ$E).

Figure 2g shows the vapor conditions at 850 hPa. The main water vapor channel was from the Bay of Bengal, transported by a strong southwesterly low-level jet. Furthermore, there was another channel from the South China Sea, which was transported by the southeasterly wind formed between the tropical storm "Vicente" and the subtropical high. These two primary channels provided sufficient vapor for the heavy rainfall, causing the Beijing area to be in a near saturated state for a long time.

During the period from 0000 UTC 20 to 0600 UTC 21 July (Fig. 3) a wide range of area with an isentropic surface decreased with height, which meant the convective instability (∂θ_se/∂p>0) occurred over Beijing (115.5^°-117.3^°E). The region of strong convective instability extended to 700 hPa. At 1200 UTC 20 July (figure omitted), the isolines of pseudo-equivalent potential temperature (θ _se) under 700 hPa were dense when the convective instability reached its maximum. Meanwhile, there was weak downward motion over Beijing, so no convection was triggered. At 1800 UTC 20 July (Fig. 3a), the convective instability was sustained over Beijing. It is worth noting that there was an obvious thermal inversion layer at 900 hPa, which suppressed the convection and was helpful for accumulating enough unstable energy. When the triggering condition was fulfilled, the convection occurred and torrential rain poured down. During 0600-1800 UTC 21 July the cold front moved across the Beijing area. The convective instability weakened and its height lowered. At the same time, the isentropic surfaces became oriented downward because of the latent heat released, enhancing the θ _se suddenly at one place; thus, the isentropic surface became concave. At 1200 UTC 21 July (Fig. 3b) the convective instability decreased and the isentropic surface tilted to almost upright. Beijing was right at the bottom of the funnel-shaped isentropic surface. Strong upward motion occurred over Beijing, tilted westward with height. As shown in Fig. 3d, the vertical vorticity increased significantly due to the tilting of the isentropic surface (Wu et al., 1995), causing positive vorticity in the whole troposphere. The positive vorticity cooperated with divergence in the upper level and convergence in the lower level, bringing about the extreme precipitation.

Figure 4.  (a) CAPE on the surface and wind vector (units: m s$^-1$) at 850 hPa and (b) CIN on the surface and wind vector (units: m s$^-1$) at 850 hPa, at 0000 UTC 21 July.

Figure 3c shows the change over time of the vertical gradient of the pseudo-equivalent potential temperature and the vertical motion. From 0000 UTC 20 July a positive region occurred at 900-700 hPa, with the strongest center at 900 hPa, which was the convective instability. During 0600-1200 UTC 20 July the convective instability reached a maximum. Because there was no triggering condition active at this moment, no convection happened. From 0200 UTC 21 July the precipitation began and the convective unstable energy was released. So, the convective instability weakened and the atmosphere changed into neutral stratification. Furthermore, due to the release of latent heat the baroclinicity strengthened, causing the slantwise isentropic surface, which was favorable to formation of symmetric instability. At 0000 UTC 22 July there was convective instability again, the center of which was at 800 hPa. However, because of the corresponding downward motion, there was no convection. It can be concluded that the production of convection was premised on convective instability and then aided by dynamical triggering conditions. The precipitation did not necessarily occur during the strongest convective instability.

Accumulating convective unstable energy in the atmosphere is one of the necessary conditions for producing strong convection. Convective available potential energy (CAPE) can represent the atmospheric buoyancy instability energy:

\begin{equation} \label{eq1} { CAPE}=\int_{Z_{ LFC}}^{Z_{ EL}}\left(\dfrac{T_{ VP}-T_{ VE}}{T_{ VE}}\right)dz , (1)\end{equation}

where T _VP and T _VE are the air parcel and environment virtual temperature, respectively. Z _LFC and Z _EL are the levels of free convection and balance, respectively. CAPE is the buoyancy work performed on an air parcel during the process of air rising from free height to the height of buoyancy balance, representing the intensity of unstable energy stored in the atmosphere. Furthermore, the strong convective instability needs to release unstable energy, which requires storage of sufficient unstable energy before the strong convection occurs. Convective inhibition energy (CIN) is a measure of convective inhibition quantities, representing the air parcel work performed on the environment during the rising of the air parcel from the ground (Z₀) to the height of free convection (Z₁):

\begin{equation} \label{eq2} { CIN}=\int_{Z_0}^{Z_1}\left(\dfrac{T_{ VP}-T_{ VE}}{T_{ VE}}\right)d{ z} . (2)\end{equation}

Usually, the CIN cannot be so small that the unstable energy releases piecemeal, but it also cannot be so large that it cannot produce deep convection. As shown in Fig. 4, before the precipitation (0000 UTC 21 July), high values of CAPE extended gradually from the southwest to Beijing; its maximum was located in the southwestern region of Beijing, reaching to approximately 1200 J kg^-1. Because a low-level jet controlled the Beijing region, conveying the warm moist airflow with huge unstable energy to the storm continuously, it was an important reason for the maintenance and development of the convective instability. At the same time, the CIN was high, about -80 J kg^-1, and it was not easy to trigger the convection. Thus, during this period of time, unstable energy accumulated for heavy rainfall. At 0600 UTC 21 July high values of CAPE covered the Beijing area, reaching a maximum of 1400 J kg^-1. At this moment there was obvious moisture convergence in the lower level. The surrounding moist air continued to target the storm area, enhancing the atmospheric unstable energy (figure omitted). Meanwhile, the CIN weakened significantly, reducing to -20 J kg^-1, so the convective unstable energy could be easily released without strong, dynamic lifting conditions. With the development of convection, the wind direction turned southerly; thus, the transportation of unstable energy broke off and the CAPE deceased rapidly.

The analysis mentioned above shows that before 0600 UTC 21 July there was convective instability in the lower level, which gradually weakened with time. In this subsection, we show how the atmosphere changed into symmetric instability after the occurrence of rainfall.

As is well-known, symmetric instability generally refers to the instability of the air parcel during the slantwise upward performance. The MPV can be represented as:

\begin{equation} \label{eq3} { MPV}=\dfrac{\zeta_{ a}\nabla\theta_{ se}}{\rho}=-g(\zeta+f)\dfrac{\partial\theta_{ se}}{\partial p} +g\dfrac{\partial v}{\partial p}\dfrac{\partial\theta_{ se}}{\partial x}-g\dfrac{\partial u}{\partial p}\dfrac{\partial\theta_{ se}}{\partial y} , (3)\end{equation}

where ζ _a is the absolute vorticity. θ _se is pseudo-equivalent potential temperature. MPV can be divided into two portions:

\begin{eqnarray} \label{eq4} { MPV}_1&=&-g(\zeta+f)\dfrac{\partial\theta_{ se}}{\partial p} , (4)\end{eqnarray} \begin{eqnarray} \label{eq5} { MPV}_2&=&g\dfrac{\partial v}{\partial p}\dfrac{\partial\theta_{ se}}{\partial x}- g\dfrac{\partial u}{\partial p}\dfrac{\partial\theta_{ se}}{\partial y} , (5)\end{eqnarray}

where MPV₁ is the coupling of the vertical component of absolute vorticity and the vertical gradient of the pseudo-equivalent potential temperature (θ _se), which is the barotropic component. It represents the cooperation of inertial instability and convective instability. Because the absolute vorticity of large-scale motion is positive in the Northern Hemisphere, the negative or positive of MPV₁ is only dependent on ∂θ _se/∂p. When the atmosphere is in convective instability, ∂θ _se/∂p>0 and MPV₁<0. MPV₂ is the baroclinic component of MPV, representing the coupling effect of moist baroclinity and the vertical shear of the horizontal wind. When MPV₁>0 and MPV<0, the atmosphere is in symmetric instability.

Figure 5 shows the change over time of MPV, MPV₁ and MPV₂. From 0000 UTC 20 to 0600 UTC 21 July there was negative MPV₁ at a height of 900-800 hPa (Fig. 5a), signifying a convective unstable atmosphere, which was consistent with the aforementioned results. Meanwhile, MPV was also negative (Fig. 5c), signifying a symmetric unstable atmosphere. However, (Bennetts and Sharp, 1982) noted that when convective instability and symmetric instability coexist, the atmosphere is mainly dominated by convective instability because the growth rate of convective instability is larger than symmetric instability. During the period 0600-1800 UTC 21 July, due to the precipitation, the convective unstable energy was released and the atmosphere changed into neutral stratification. At this moment, MPV₁≥ 0. Meanwhile, the baroclinicity and the horizontal gradient of potential temperature strengthened at 900-800 hPa due to the enhanced low-level jet and the incursion of a cold front over Beijing. Thus, MPV₂ was enhanced and became negative, causing MPV<0. The condition of MPV₁>0 and MPV<0 was met, so the atmosphere displayed symmetric instability during this period. In addition, it is worth noting that the strongest negative MPV₂ corresponded with the maximum precipitation.

Furthermore, based on the definition that the atmosphere is a symmetric unstable atmosphere when the slope of the isentropic surfaces is greater than the slope of the momentum, the steeper the isentropic surfaces were, the easier it was for symmetric instability to occur. Before the heavy rainfall (Fig. 3a) the isentropic surface was gentle, almost horizontally distributed. Then, at 1200 UTC 21 July (Fig. 3b) the front moved into the Beijing area, corresponding to the strongest frontal rainfall. The latent heat released redistributed the moisture and temperature, resulting in steeply inclined isentropic surfaces. This allowed the atmosphere to form the symmetric instability. Figure 6 shows the slope difference between the isentropic surface and the momentum surface over the Beijing area. There was an obvious positive region during the precipitation at 700 hPa, indicating the occurrence of the symmetric instability.

Analysis of the convective instability and symmetric instability indicates that approximately 12-24 hours before the storm, the atmosphere was mainly in convective instability in the lower level. The convective instability experienced a weak-strong-weak process, but the heavy precipitation did not occur at the moment of strongest convective instability. With the occurrence of heavy rain, the convective instability energy was released and the convective instability weakened. At the same time, the symmetric instability was strengthened by the enhancement of atmospheric baroclinicity. The results are consistent with the conclusion of (Liu et al., 2014), who used WRF (Weather Research and Forecasting Model) simulation data to analyze the instability during precipitation.

Figure 5.  Temporal evolution of (a) $ MPV_1$, (b) $ MPV_2$, (c) $ MPV$ (units: 10$^-5$ K m$^2$ s$^-1$ kg$^-1$) over Beijing (39.8$^\circ$-40.0$^\circ$N, 115.8$^\circ$-116.2$^\circ$E), where the black contour denotes the observation of 6-h accumulated rainfall (units: mm).

Figure 6.  Temporal evolution of the slope difference between the isentropic surface and the momentum surface over the Beijing area, where the black contour denotes the observation of 6-h accumulated rainfall (units: mm).

To explore the factors affecting the evolution of convective instability before the rainstorm and provide a theoretical basis for forecasting convective precipitation, the convective instability tendency equation was deduced.

The thermodynamic equation in pressure coordinates is as follows:

\begin{equation} \label{eq6} \dfrac{d\theta_{ se}}{dt}=0 . (6)\end{equation} Take the partial derivative of both sides of Eq. (7), \begin{eqnarray} \label{eq7} &&\dfrac{\partial}{\partial t}\left(\dfrac{\partial\theta_{ se}}{\partial p}\right)+ \left(\dfrac{\partial u}{\partial p}\dfrac{\partial\theta_{ se}}{\partial x}+ \dfrac{\partial v}{\partial p}\dfrac{\partial \theta_{ se}}{\partial y}+ \dfrac{\partial \omega}{\partial p}\dfrac{\partial\theta_{ se}}{\partial p}\right)+\nonumber\\ &&{v}\cdot\nabla\left(\dfrac{\partial\theta_{ se}}{\partial p}\right)=0, (7)\end{eqnarray} and substitute the mass continuity equation (∂ u/∂ x)+(∂ v/∂ y)+(?ω/∂p)=0 into Eq. (8), \begin{equation} \label{eq8} \dfrac{\partial}{\partial t}\left(\dfrac{\partial\theta_{ se}}{\partial p}\right)=-{v}\cdot\nabla\left(\dfrac{\partial\theta_{ se}}{\partial p}\right)+M , (8)\end{equation}

where M=-(∂ u/∂p)(∂θ_se/∂ x)-(∂ v/∂p)(∂θ_se/∂ y)+ [(∂ u/∂ x)+(∂ v/∂ y)](∂θ_se/∂p) is the potential divergence equation (Ran et al., 2013). M represents the curl of horizontal wind rotated 90^° and projected on the direction of the pseudo-equivalent potential temperature, indicating the coupling of horizontal divergence and the vertical shear of the horizontal wind. [(∂ u/∂p)(∂θ_se/∂ x)+ (∂ v/∂p)(∂θ_se/∂ y)] is the baroclinic component of M, and it also represents the vertical component of the convective vorticity vector. It reflects the coupling of vertical wind shear and atmospheric baroclinicity. [(∂ u/∂ x)+(∂ v/∂ y)](∂θ_se/∂p) is the barotropic component of M, representing the coupling of horizontal divergence and convective instability. -v ·▽(∂θ_se/∂p) is the advection of convective instability. Thus, the local variation of convective instability is mainly influenced by advection and potential divergence.

Figure 7.  Vertical distribution of the forcing terms in Eq. (9) affecting the convective instability along 40$^\circ$N at 1200 UTC 20 July: (a) $\partial\theta_ se/\partial p$; (b) $M$; (c) $v\nabla\cdot(\partial\theta_ se)/\partial p$; (d) $-(\partial u/\partial p)(\partial\theta_ se/\partial x)-(\partial v/\partial p)(\partial\theta_ se/\partial y)$; (e) $(\partial u/\partial x+\partial v/\partial y) (\partial\theta_ se/\partial p)$ (units: 10$^-8$ K s$^-1$ m$^-1$).

Figure 8.  Temporal evolution of the forcing terms in Eq. (9) affecting the convective instability over Beijing area (39.8$^\circ$-40.0$^\circ$N, 115.8$^\circ$-116.2$^\circ$E): (a) $\partial\theta_ se/\partial p$; (b) $M$; (c) $v\nabla\cdot(\partial\theta_ se)/\partial p$; (d) $-(\partial u/\partial p)(\partial\theta_ se/\partial x)- (\partial v/\partial p)(\partial\theta_ se/\partial y)$; (e) $(\partial u/\partial x+\partial v/\partial y)(\partial\theta_ se/\partial p)$ (units: 10$^-8$ K s$^-1$ m$^-1$).

Figure 7 is the vertical distribution of the forcing terms in Eq. (9) affecting the convective instability at 1200 UTC 20 July. As shown in Fig. 7a, there were two unstable areas in the troposphere. One was located at 110^°-114^°E at 700 hPa. At this location the advection (Fig. 7c) was positive but the potential divergence (Fig. 7b) was primarily negative, so the convective instability here was mainly caused by the advection term. The other unstable area was at 116^°-118^°E at 900 hPa, which had a major effect on the heavy rainfall in Beijing. Analysis of the vertical distribution, the potential divergence (Fig. 7b) and the advection (Fig. 7c) indicates both had a positive area that overlapped with the convective unstable area. Thus, potential divergence and advection both played an important role in the development of convective instability. The potential divergence can be divided into barotropic and baroclinic components, as shown in Figs. 7d and e. The baroclinic termin the unstable region was negative and the barotropic term was positive, meaning that the convective instability was mainly dominated by the barotropic term, and the baroclinic term played an offsetting role.

The temporal evolution of the forcing terms (Fig. 8) shows the convective instability from 0000 UTC 20 to 0600 UTC 21 July. Then, the convective instability weakened and the atmosphere changed into neutral stratification. Figure 8b indicates that the potential divergence was mainly positive at 900-800 hPa before the rainstorm, helping to develop and maintain the convective instability. The advection also played an important role in convective instability development, but it was relatively weaker before the rainstorm and stronger during the approaching rainfall process. Thus, the potential divergence contributed more to the convective instability. Figures 8d and e show that the barotropic component of potential divergence was primarily positive before the heavy rainfall, so it actively promoted the development of convective instability. The baroclinic component of potential divergence was weak and negative before the precipitation, having an offsetting influence. However, it gradually became stronger during precipitation, having a great impact on inhibiting the convective instability. The barotropic component of potential divergence played the most significant role in affecting the convective instability before the rainstorm. During the period of precipitation from 0000 UTC 21 to 0000 UTC 22 July the convective instability weakened, primarily due to the baroclinic component of the potential divergence mentioned above. The reason might have been that the low-level jet strengthened during the precipitation, bringing about the vertical shear of horizontal wind and the atmosphere's baroclinic enhancement. Meanwhile, the moist, warm air climbed along the cold air in front and the cold and warm airs converged, causing the slantwise isentropic surface and the horizontal gradient of pseudo-equivalent potential temperature to increase. Thus, the baroclinic component was enhanced, partially offset by the effects of the barotropic component, ultimately causing the convective instability to decrease. On the other hand, it was also an important reason for the enhancement of the symmetric instability, which can be seen in the next part.

It can be concluded that the barotropic component of potential divergence played the leading role in promoting the development of convective instability before the rainstorm. After the storm had occurred the baroclinic term of the potential divergence suppressed the convective instability development.

According to the above analysis symmetric instability occurred over Beijing from 0200 UTC 21 to 1800 UTC 21 July. It reached a peak at 1200 UTC 21 July, which corresponded with the maximum precipitation.

Further analysis is made to explore the factors affecting the evolution of symmetric instability during precipitation. Under adiabatic and frictionless conditions the potential vorticity is conservative (Wu et al., 1995):

\begin{equation} \label{eq9} \dfrac{d{ MPV}}{dt}=0 . (9)\end{equation} Equation (10) can be rewritten as: \begin{equation} \label{eq10} \dfrac{d{ MPV}_1}{dt}+\dfrac{d{ MPV}_2}{dt}=0 . (10)\end{equation} Then, \begin{eqnarray} \label{eq11} \dfrac{d{ MPV}_2}{dt}&=&-\dfrac{d{ MPV}_1}{dt} =g\dfrac{\partial\theta_{ se}}{\partial p}\left(\dfrac{\partial\omega}{\partial y}\dfrac{\partial u}{\partial p}- \dfrac{\partial\omega}{\partial x}\dfrac{\partial v}{\partial p}\right)-\nonumber \end{eqnarray} \begin{eqnarray} &&g(\xi+f)\left(\dfrac{\partial\theta_{ se}}{\partial x}\dfrac{\partial u}{\partial p}+ \dfrac{\partial\theta_{ se}}{\partial y}\dfrac{\partial v}{\partial p}\right) ,\\[-10mm]\nonumber (11)\end{eqnarray}

where d MPV₁/dt and d MPV₂/dt are the individual variations of MPV₁ and MPV₂, respectively. Under the premise of MPV conservation, there is a certain mutual conversion between MPV₁ and MPV₂. According to Eq. (10), when d MPV₁/dt increases d MPV₂/dt will decrease, and when d MPV₁/dt decreases d MPV₂/dt will increase. The conditions of MPV₁>0 and MPV<0 signify symmetric instability in the atmosphere. Thus, when d MPV₁/dt>0 MPV₁ increases and when d MPV₂/dt<0 MPV₂ decreases, and the symmetric instability would be maintained and would develop. In Eq. (11), g(∂θ _se/∂p)[(∂ω/∂ y)(∂ u/∂p)- (∂ω/∂ x)(∂ v/∂p)] is the coupling of the vorticity tilting term and vertical gradient of pseudo-equivalent potential temperature, and \(g(\xi +f)[(\partial\theta_ se/\partial x)(\partial u/\partial p)+ (\partial\theta_ se/\partial y)(\partial v/\partial p)]\) is the coupling of vertical vorticity and the baroclinic component of potential divergence. Thus, the individual variation of MPV₂ is mainly affected by the two terms above.

Figure 9 shows the vertical distribution of the two forcing terms of MPV₂ at the moment of strongest precipitation (1200 UTC 21 July). The maximum 6-h accumulated precipitation in Beijing reached 80 mm and the gradient of each forcing term was strong in the precipitation region. The coupled term of vertical vorticity and potential divergence was relatively strong (Fig. 9b) compared with the other terms. There was a negative area at 800 hPa over Beijing, indicating d MPV₂/dt decreased, thus causing MPV₂ to become negative and enhancing the symmetric instability. At the same time, there was a weaker negative area to the south of the positive area. There was a wide positive zone of the first term on the right-hand side of Eq. (11) over Beijing (Fig. 9a), which was weaker than the second term, inhibiting the development of symmetric instability.

Further analysis on the temporal evolution of the three forcing terms is shown in Fig. 10. Because there was no precipitation during the period 0000 UTC 20 to 0000 UTC 21 July, the forcing terms were all weak. From 0200 UTC 21 the heavy rain occurred in the Beijing area, and so the symmetric instability strengthened. During the precipitation, the contribution of the coupled term of vertical vorticity and potential divergence was significant (Fig. 10b). There was a strong negative area at the lower level of 900-800 hPa from 0000 UTC to 1800 UTC 21 July, corresponding to the heavy rain. The negative area caused MPV₂ to decrease with time, contributing to the enhancement of symmetric instability. This term was strongest at 1200 UTC 21, corresponding to the maximum precipitation and strongest symmetric instability.The first coupled term of vorticity tilting and the vertical gradient of pseudo-equivalent potential temperature (Fig. 10a) were weak and positive, having an impact on inhibiting the development of the symmetric instability.

Figure 9.  Vertical distribution of the forcing terms in Eq. (11) affecting the individual variation of MPV2 along 40$^\circ$N, where the black contour denotes the observation of 6-h accumulated rainfall (units: mm): (a) $g(\partial\theta_ se/\partial p)[(\partial\omega/\partial y)(\partial u/\partial p)-(\partial\omega/\partial x)$$(\partial v/\partial p)]$; (b) $-g(\xi+f)[(\partial\theta_ se/\partial x)(\partial u/\partial p)+(\partial\theta_ se/\partial y)(\partial v/$ $\partial p)]$ (units: 10$^-10$ K m$^2$ s$^-2$ kg$^-1$).

Figure 10.  Temporal evolution of the forcing terms in Eq. (11) affecting the individual variation of MPV2 along 40$^\circ$N over the Beijing area (39.8$^\circ$-40.0$^\circ$N, 115.8$^\circ$-116.2$^\circ$E), where the black contour denotes the observation of 6-h accumulated rainfall (units: mm): (a) $g(\partial\theta_ se/\partial p)[(\partial \omega/\partial y) (\partial u/\partial p)-(\partial \omega/\partial x)$$(\partial v/\partial p)]$; (b) $-g(\xi+f)[(\partial\theta_ se/\partial x) (\partial u/\partial p)+ (\partial\theta_ se/\partial y) (\partial v/$ $\partial p)]$ (units: 10$^-10$ K m$^2$ s$^-2$ kg$^-1$).

As seen from the analysis above, the coupling of vertical vorticity and the baroclinic component of potential divergence made the most remarkable contribution to maintaining and developing the symmetric instability during the precipitation. The reason for the anomaly of this term was the tilting of the isentropic surface due to the release of latent heat, causing rapid development of vertical vorticity. Meanwhile, the enhancement of the low-level jet increased the vertical wind shear. Moreover, a cold front moved into the Beijing area and the cold and warm air masses converged, enhancing the three-dimensional spatial gradients of the pseudo-equivalent temperature. These factors synthetically caused \(-g(\xi +f)[(\partial\theta_ se/\partial x)(\partial u/\partial p)+ (\partial\theta_ se/\partial y)(\partial v/\partial p)]\) to decrease, thus contributing to the development of symmetric instability.

Comparing the effect of factors on convective instability and symmetric instability showed some correlation.The baroclinic component of potential divergence is the key point, which weakened the convective instability and enhanced the symmetric instability during the precipitation.

In this paper, using a heavy rain event that occurred in Beijing on 21 July 2012 as an example, GFS reanalysis data from NCAR-NCEP were used to analyze the characteristics and evolution mechanism of convective and symmetric instability before and during the North China rainstorm. The main conclusions can be summarized as follows:

(1) Approximately 12 hours before the rainstorm the atmosphere was mainly dominated by convective instability in the lower level of 900-800 hPa. The strong southwesterly low-level jet conveyed the moist and warm airflow continuously to the torrential rain area, maintaining and enhancing the unstable energy. When the precipitation happened and the unstable energy was released, the convective instability weakened. Meanwhile, due to baroclinic enhancement in the atmosphere, the symmetric instability strengthened, maintaining and promoting the development of the torrential rain.

(2) By deriving the convective instability tendency equation, the evolution characteristics and impact factors on convective instability were analyzed. Before the rainstorm the barotropic component of potential divergence and the advection of convective instability played a major role in promoting the development of convective instability. After the precipitation occurred the convective instability weakened due mainly to the baroclinic component of the potential divergence.

(3) The primary factors affecting the development of the symmetric instability during the precipitation were the cooperation between vertical vorticity and the baroclinic component of potential divergence, as established by analyzing the MPV tendency equation. Importantly, the baroclinic component of potential divergence was the key point, which weakened the convective instability and enhanced the symmetric instability during the precipitation. When the convective instability decreased and the symmetric instability increased, the rainfall event occurred. Thus, the baroclinic component of potential divergence may be an important signal for forecasting, which needs further investigation and discussion.