Circulation Background and Genesis Mechanism of a Cold Vortex over the Tibetan Plateau during Late April 2018

The Tibetan Plateau (TP) has an average altitude of more than 4 km. Many studies have highlighted the substantial impact of the TP on the establishment of regional and global atmospheric circulation (Ye and Gao, 1979; Wu, 1984; Yanai et al., 1992), and attributed the impact to the unique thermodynamic and dynamic effects of the large-scale orography of the TP (Wu et al., 2015). Moreover, as a source region of atmospheric disturbances (Shu et al., 2022), the TP serves as the origin of many severe weather events in both the TP and the downstream region (Tao and Ding, 1981). Such a special environment of the TP has also given rise to a common cyclonic weather system known as the TP Vortex (TPV) (Ye and Gao, 1979; Wang, 1987; Tang et al., 2023).

TPVs are sub-synoptic-scale cyclonic systems with a spatial range of several hundred kilometers and a vertical extent of 2–3 km (Ye and Gao, 1979), significantly affecting local weather changes. More than half of daily extreme precipitation events over the central TP are induced by TPVs (Lin et al., 2022). Some TPVs even lead to intense precipitation over the downstream regions, especially during the summer half-year, when moving off the TP (Zhang et al., 2021; Ma et al., 2022).

About 10% of TPVs can move off the TP under a favorable circulation background (Lin, 2015; Curio et al., 2019; Lin et al., 2020), bringing heavy rains or severe storms to Southwest China directly. These “moving-off TPVs” can also trigger or merge with a local rain-producing system called the Southwest China Vortex (Wang and Orlanski, 1987; Kuo et al., 1988; Li et al., 2017; Zhang et al., 2021), often creating more serious disasters than a single TPV alone. An extreme TPV-related catastrophe occurred during flood events from June to August 1998, when a total of eight flood peaks formed over the Yangtze River Valley, and at least two flood peaks were directly affected by TPVs (Yu, 2000). Therefore, it is of great significance to investigate the genesis mechanism of TPVs for forecasting TPV-related local weather changes and subsequent impacts over downstream regions.

As early as in the late 1970s, based on satellite cloud maps, Chinese meteorologists (Ye and Gao, 1979) speculated that TPVs may generate mostly in the western TP. This speculation has subsequently been progressively verified through a variety of reanalysis datasets (e.g., Lin, 2015; Curio et al., 2019). More recently, Lin et al. (2020) employed an objective identification method and specifically noted that most TPVs originate in the central and western TP, especially the mountainous areas at higher altitudes above 5.5 km, and decay at the relatively low altitudes of the plateau. The existing observational network is unable to capture TPVs effectively, especially those in their generation stage. To address this issue, alternative methods such as numerical modeling and high-resolution reanalysis have gained popularity. These methods offer valuable insights into the complex processes governing the genesis of TPVs and thus lead to a lot of related studies.

Based on their thermal structure, Ye and Gao (1979) categorized TPVs into warm TPVs and cold TPVs. The vast majority of studies have since focused on the formation of warm TPVs because of their frequent occurrences and resultant socioeconomic losses. They have examined the factors conducive to warm TPV genesis such as TP surface sensible heating (Shen et al., 1986a, b; Luo et al., 1991; Luo and Yang, 1992; Wu et al., 2018; Zhang et al., 2019), longwave radiation cooling of the cloud top (Deng et al., 2022), and slantwise vorticity development (Wu et al., 2022). In particular, condensational latent heating has long been considered a factor contributing to TPV development (Dell’Osso and Chen, 1986; Shen et al., 1986b; Wang, 1987; Li et al., 2011), and recent studies have shown that it also contributes to the formation of warm TPVs (Ma et al., 2020; Wu et al., 2022). Although there are still some controversies about the dominant role of different heat sources in warm TPV genesis, most studies show a consensus that the formation of warm TPVs is linked closely with the TP thermodynamic effect. However, whether and how the TP thermodynamic effect influences cold TPV genesis remains unclear, warranting further investigation.

As suggested by Lin (2015) and Lin et al. (2020), 19% of TPVs are initially cold, implying that there are up to about 12 cold TPVs annually. Similar to moving-off warm TPVs, some cold TPVs that move away from the TP can also result in downstream heavy precipitation over southern China. For example, a cold TPV occurred over the northeastern TP on 27 April 2018, which subsequently moved eastward and out of the TP, leading to excessive precipitation over spring farming areas in southern China, which caused problems for spring ploughing. More specifically, according to the Agricultural Weather Forecast broadcast by China Central Television at the time, the soil in these farming areas had already been too wet, with the soil relative humidity even exceeding 90%. As a result, this cold TPV and its induced precipitation exerted an adverse effect on spring sowing and ploughing in southern China. Thus, the formation mechanism and weather effect of such a cold TPV are deserving of serious examination. It should be noted that, although the downstream precipitation over southern China caused by this cold TPV in spring may not have been greater than that caused by warm TPVs in summer, such as the 2016 warm TPV in conjunction with a Southwest China Vortex that led to the record-breaking heavy rainfall over the middle and lower reaches of the Yangtze Basin during the end of June 2016 (Zhang et al., 2021), the excessive spring precipitation inevitably brought potential risks to agricultural production locally.

From fundamental dynamical perspectives, Hoskins et al. (2003) combined the quasi-geostrophic potential vorticity (PV) equation with the vertical motion equation, deducing the constraints relating different components of quasi-geostrophic vertical motion to the weather system movement. They demonstrated that the development of the vertical velocity components associated with both isentropic upgliding and isentropic displacement depends on the vertical distribution of PV advection. Typically, a TPV exhibits a significant positive PV anomaly, which can force a vertical motion in the lower troposphere as it advects eastward and may cause severe weather even in the cold season, as described by Wu et al. (2020). Hence, the formation mechanism of cold TPVs can be understood more clearly from the PV perspective.

Ye (1981) suggested that cold TPVs may share similarities with extratropical cyclones in terms of structure, which has so far been the only study to propose such a perspective. Given the cold TPV that generated over the northeastern TP on 27 April 2018 with adverse weather effects on downstream farming areas in southern China, and considering that it exhibited some similarities to extratropical cyclones forced by the equatorward-intruding PV streamer within the upper-tropospheric wave train during the genesis stage, this cold TPV was selected as a case study. Therefore, the objective of the present study is to investigate the formation mechanism of the cold TPV under a quasi-geostrophic framework, exploring the role of the TP thermodynamic effect in cold TPV genesis via numerical experiments, and thus providing a theoretical basis for improving the forecasting skill for cold TPVs.

The remainder of this paper is organized as follows. Section 2 outlines the data, definitions, and model used in this study. Section 3 introduces the normalized static stability equation and discusses the links among normalized static stability, quasi-geostrophic vorticity, and PV. In section 4, we provide a synoptic overview of the TPV event, a diagnostic analysis of the mechanism behind the cold TPV genesis, and the circulation evolution responsible for the cold TPV genesis. Section 5 describes the model configuration and the sensitivity experiments performed, presenting the results of experiments and a discussion focusing on the modulation of the cold TPV genesis by the TP thermodynamical effect. Finally, section 6 summarizes the key findings.

In this study, the atmospheric circulation data are from the fifth major global reanalysis produced by ECMWF (ERA5; Hersbach et al., 2020). Compared with the widely used ERA-Interim reanalysis, ERA5 provides a higher spatial and temporal resolution, with a horizontal resolution of 31 km and hourly temporal resolution, enabling the provision of a more detailed view of rapidly evolving sub-synoptic systems (Hersbach et al., 2020). The reliability of ERA5 around the TP has been verified by numerous studies (Sun et al., 2021; Yuan et al., 2021). Thus, we adopt ERA5 as an alternative to observations for both synoptic and diagnostic analysis. Moreover, since ERA5 assimilates as many upper-air and near-surface observations as possible, it is also employed as the initial and boundary conditions for model simulations in this study.

Traditionally, a TPV is typically identified as a local low-pressure system with a closed geopotential height contour or a cyclonic rotation in the wind field of three sounding stations over the TP at the 500-hPa level (Lhasa Project Group on Qinghai-Xizang Plateau Meteorology, 1981). However, this approach is associated with subjective uncertainties. In this study, we follow the approach proposed by Lin (2015) and Zhang et al. (2021) in defining a TPV as a local minimum geopotential height with one or more 10-gpm interval height contours enclosed over the TP at the 500-hPa level, with the enclosed contour lasting for at least 18 hours. Meanwhile, the timing when the initially closed contour of the TPV appears is taken as the TPV genesis time. In addition, a cold TPV is defined as a TPV with a relatively cold core. The temperature criteria of the cold TPV used in this study follow the method proposed by Lin (2015).

Since TPV genesis depends on the increase in local vorticity tendency or local PV tendency, the geostrophic vorticity budget is diagnosed quantitatively to identify the contribution of dominant factors to the cold TPV genesis. Moreover, a normalized static stability equation is introduced to investigate the conversion from normalized static stability to geostrophic vorticity. Detailed descriptions of these two equations are provided in section 3.

Numerical experiments are performed using the Weather Research and Forecasting (WRF) model, version 4.3.1. WRF is a fully compressible, non-hydrostatic model with a focus on mesoscale weather simulation. More information about the WRF model can be found in Skamarock et al. (2021). The setup of the model and the design of the experiments in this study are elaborated in section 5.

Under the quasi-geostrophic framework, the geostrophic vorticity and thermodynamic equations in p-coordinates can be expressed as

where $ \mathbf{V}_{\mathrm{g}} = \mathbf{k} \times f^{-1} {\boldsymbol{\nabla}} \Phi $ is geostrophic wind, $ \eta_{{\mathrm{g}}} = f + f^{-1} {\boldsymbol{\nabla}}^{2} \Phi $ is absolute geostrophic vorticity, ω is the vertical velocity in isobaric coordinates, $ \boldsymbol{\nabla} $ is the horizontal gradient operator, $ \mathbf{F}_{\zeta} $ represents the contribution of friction to the local change in absolute geostrophic vorticity, $ \Theta(p) $ is the standard potential temperature distribution averaged over the horizontal domain and period of interest, $ \dot \theta $ is the diabatic heating rate, and the other symbols conform to their normal meteorological notations. Using the hydrostatic relationship

Eq. (2) can be written as

in which

where ${\theta _0}$ and ${p_0}$ are standard values of potential temperature (300 K) and pressure (1000 hPa), respectively, and N is the buoyancy frequency ($ {N^2} = {g}{\Theta _z}/{{{\theta _0}}} $).

Multiplying Eq. (4) by$ f / \Sigma^{2} $ and then differentiating the outcome with respect to p, we get

Defining geopotential tendency as

Eq. (6) can then be written as

or

Note that Eq. (8) is the same as Eq. (6.22) in Holton (2004). Since $ {\Theta _p} $ varies only slowly with height in the troposphere, using Eq. (4), the left-hand side of Eq. (8) can be expressed as

which can be interpreted as the local rate of change of a normalized static stability (Holton, 2004). Therefore, the equation of normalized static stability can be written as

Equation (10) indicates that the local normalized static stability will increase when potential temperature advection or diabatic heating increases with height, or vertical shrinking occurs.

As indicated by Eqs. (1) and (10), the ageostrophic component, $ f {{\partial \omega }}/{{\partial p}} $, forces an equal and opposite effect on the tendency of geostrophic vorticity and the tendency of normalized static stability, respectively. Therefore, vertical stretching provides the conversion between absolute geostrophic vorticity and normalized static stability.

Adding Eq. (1) and Eq. (10) leads to the quasi-geostrophic PV (QGPV) equation,

in which the QGPV is

For a moving frame of reference (such as a vortex or a cyclone) at a constant horizontal velocity $ {\bf{C}} $, Eq. (1), Eq. (10), and Eq. (11) can be written as

It turns out that the effect of friction on QGPV is imposed on its component of geostrophic vorticity; and the impact of diabatic heating on QGPV is directly exerted on its component of normalized static stability. Adding the first two equations in Eq. (13) yields the QGPV tendency equation, which implies that a dynamic constraint exists among vorticity, static stability, and PV, and the conversion between static stability and vorticity is referred to as PV reconstruction (Wu et al., 2020, 2022). Notably, although the stretching term is not explicitly included in the QGPV tendency equation, as a conversion medium between static stability and vorticity, it plays an essential role in PV reconstruction. The application using the idea of conversion between geostrophic vorticity and normalized static stability, as well as the PV reconstruction, will be given in section 4.

As introduced in section 1, the cold TPV of interest was formed at 0000 local standard time (LST=UTC+8 hours) on 27 April 2018 over the northeastern TP (Fig. 1) and lasted for 3 days from 27 to 29 April 2018. To illustrate the large-scale circulation reconfiguration associated with the cold TPV genesis, Fig. 1 displays the evolution of the geopotential height and temperature fields at 500 hPa around the TP before and during the TPV genesis from 0000 LST 25 to 1200 LST 27 April. At 0000 LST 25 April, cold air reached the northeastern TP (Fig. 1a), as evidenced by a cold tongue intruding southwestward from midlatitudes to the central TP, forming a baroclinic zone with a distinct horizontal temperature gradient around the TP. Note that the geopotential height exhibited straight contours over the northeast of the TP, which intersected with the isotherm there, without an apparent height trough structure matching with the temperature trough at this moment. Meanwhile, a small area of strong cold advection was located along the eastern edge of the cold tongue, setting up an environment favorable for the falling of the surrounding geopotential height field.

Figure 1.  Distributions of the 500-hPa geopotential height (blue contours; units: dagpm) and temperature (shading; units: K) at (a) 0000 LST 25 April, (b) 1200 LST 25 April, (c) 0000 LST 26 April, (d) 1200 LST 26 April, (e) 0000 LST 27 April, and (f) 1200 LST 27 April 2018. The TP with terrain altitude above 3000 m is outlined by the black solid curve. The location of the TPV center at 500 hPa is denoted by the green circle.

Twelve hours later, a height trough initiated at 1200 LST 25 April and deepened rapidly to the northeast side of the TP due to the cold advection (Fig. 1b). This developing height trough subsequently moved southward and tended to be shaped in phase with the cold tongue (Figs. 1c and d). By 0000 LST 27 April (Fig. 1e), the height trough had covered most of the eastern TP and undergone a transition into a zonally elongated trough and tended to be cut off. At this time, a closed center of geopotential height was established within the cold tongue and grew to form a relative cold core (Fig. 1f), signifying that the cold TPV had generated.

The above evolution suggests that the cold TPV was formed in a highly baroclinic circulation background, looking more like an extratropical cyclone generating within a zonally elongated trough rather than a smaller-scale warm TPV thriving in tropical-like environments (Wang and Orlanski, 1987), implying the influence of the large-scale circulation. To further explore the role of large-scale circulation reconfiguration in the cold TPV genesis, Fig. 2 displays the 325-K isentropic-surface PV maps before and during the TPV’s formation from 24 to 27 April 2018. The altitude of this isentropic surface corresponding to the isobaric surface can be referred to in Fig. 3, which was above the 400-hPa isobaric surface over the vortex genesis region and close to 500 hPa over the plains area. Note that at 1800 LST 24 April (Fig. 2a), undulating westerlies as a Rossby wave prevailed in middle latitudes, with anticyclonic flow to the north of the northwestern TP. Thus, the high-PV (> 2 PVU) air was advected coherently southward into the northern TP to at least the south of 40°N by northerlies on the eastern side of the anticyclonic circulation, forming a meridionally elongated PV streamer (Fig. 2a). With the Rossby wave propagating eastward and because the westerly wind speeds are faster at higher latitudes than to the south, both the ridge of the anticyclonic circulation and the intensified height trough ahead of it became distinctly northeast–southwest oriented, whereby the high PV streamer intruded into the northeastern TP (Figs. 2b and c), just over the strong low-level baroclinic region of the 500-hPa temperature trough (Figs. 1b and c). As suggested by Hoskins et al. (1985), this high PV streamer, as an upper-air cyclonic PV anomaly, could induce low-level warm advection, with the arrival of the upper PV anomaly over a pre-existing low-level baroclinic region. Indeed, a warm advection area was formed behind the 500-hPa height trough (Figs. 1b and c). Influenced by the warm advection, a northeast–southwest-oriented height ridge developed across the strong warm advection area at 500 hPa to the north of the TP at 0000 LST 26 April (Fig. 1c). Subsequently, the strong northerly wind ahead of the anticyclonic ridge pushed the PV streamer to veer further southward so that the PV streamer was characterized by a zonally elongated cyclonic shear line in a band extending eastward from the central TP to the Bohai basin over northern China by 1200 LST 26 April (Fig. 2d). As a response to the intensified cyclonic PV anomaly, the underlying 500-hPa height trough also became west–east oriented, even generating a small separate center of minimum height over the northeastern TP (Figs. 1d and 2d; note that this closed height center lasted only two hours). Twelve hours later, a distinct low-pressure center with a closed contour was formed (Figs. 1e and 2e). Afterwards, the TPV became stronger and tended to migrate northeastward (Figs. 2f and 1f).

Figure 2.  Distributions of PV (shading; units: PVU, where 1 PVU = 10⁻⁶ K m² s⁻¹ kg⁻¹) and wind (barbs; half barb = 2 m s⁻¹, full barb = 4 m s⁻¹, and pennant = 20 m s⁻¹) on the 325-K isentropic surface superimposed on the 500-hPa geopotential height (blue contours; units: dagpm) at (a) 1800 LST 24 April, (b) 1200 LST 25 April, (c) 0000 LST 26 April, (d) 1200 LST 26 April, (e) 0000 LST 27 April, and (f) 1200 LST 27 April 2018. The dash-dotted curve denotes the 578-dagpm contour. The hatched areas in (a), (e), and (f) indicate where the TP intersects the 325-K isentropic surface. The letter “A” in (a) indicates the southernmost 4-PVU contour of the PV streamer. The cyan segment from A to A' in (e) indicates the moving direction of the PV streamer.

Figure 3.  Cross sections along A–A' in Fig. 2e displaying the PV (shading; units: PVU), potential temperature (purple solid contours; units: K), wind speed (black dashed contours; units: m s⁻¹, with only the 0-m s⁻¹ contour plotted), and vertical circulation [vectors; horizontal winds and vertical velocity (multiplied by a factor of −60; units: Pa s⁻¹; blue vectors = upward and red = downward, with only the absolute value of vertical velocity greater than 0.01 Pa s⁻¹ plotted)] at (a) 1200 LST 24 April, (b) 1800 LST 26 April, (c) 2100 LST 26 April, and (d) 0000 LST 27 April 2018. The location of the TPV center at 500 hPa is denoted by the green circle. The hatched areas indicate the terrain.

The synoptic analysis above at least suggests that, unlike warm TPVs, which are primarily initiated by the TP thermodynamic effect from the surface (Shen et al., 1986a; Wu et al., 2018), the generation of this cold TPV was strongly influenced by a planetary-scale PV streamer. Moreover, of particular interest is how this PV streamer led to the formation of a cold vortex in such a special environment in the TP region, and whether the TP played a role in the vortex genesis. Additionally, it is worth mentioning that, except for its cold-core structural difference from a warm TPV, the cold vortex in this study was much deeper, with a positive vorticity zone occupying the troposphere rather than being confined to the boundary layer below 400 hPa, like the majority of warm TPVs (Wang, 1987; Lin et al., 2020). Regarding the effect on weather, the generation of a warm TPV is generally accompanied by significant convective precipitation (Wang, 1987). However, almost no precipitation was detected during the genesis of this cold TPV (not shown), implying that the precipitation-related condensational latent heating did not take effect in this case. Nevertheless, as mentioned above, the departure of the cold vortex from the TP resulted in excessive precipitation over downstream areas in southern China. Furthermore, since no signs of the production of new PV are shown in the 325-K isentropic PV map (Fig. 2), a quasi-conservative process of an advective nature is highly likely. To meet the conservative requirement and based on the framework of the convertibility between normalized static stability and geostrophic vorticity in section 3, the cyclonic vorticity required for cold TPV genesis could only transfer from another component of PV—namely, static stability.

Figure 3 shows cross sections of PV, potential temperature, and vertical motion from 1200 LST 24 to 0000 LST 27 April, with a focus on the variation in vertical circulation six hours before vortex genesis, along A–A' as indicated in Fig. 2e, which roughly follows the path of the PV streamer and passes right through the center of the nascent cold vortex. The most distinct feature in Fig. 3 is the positive PV in the upper troposphere and stratosphere, which is apparently the source of the PV streamer (Fig. 2). As the PV streamer moved over the TP (Fig. 2), the positive PV travelling along A–A' (Fig. 3) should have induced a series of responses in the surrounding circulation.

At 1800 LST 24 April, three days before the TPV genesis, the main PV source was located to the north of the TP in the stratosphere (as indicated by the high PV greater than 2 PVU), causing a widespread northwestern tilt with height in isentropic surfaces (Fig. 3a). Note that the tropopause is represented by the 2-PVU contour, as suggested by Hoskins et al. (1985). During this period, the upward motion in the isentropic tilting region was probably associated with both isentropic upgliding and displacement caused by the movement of the upper-level PV anomaly from A to A', as suggested by Hoskins et al. (2003).

Two days later at 1800 LST 26 April, six hours before the cold TPV genesis, the southeastward moving PV source in the stratosphere was located right over the TP (Figs. 2d and e), the local tropopause fell from about 250 hPa to 300 hPa, and its corresponding upper-level positive PV anomaly started to extend downward, penetrating the troposphere and producing a tropopause folding just over the TPV genesis area (Fig. 3b). On the one hand, the downward penetration of upper-level high-PV caused an evident upward bulge of the isentropic surfaces below and thus created an isentropic displacement upward motion in the troposphere. On the other hand, a zero-windspeed contour (black dashed line in Figs. 3b–d) extended downward along the narrow PV folding area from the tropopause down to the ground of the TP where the vortex genesis took place. On either side of this windless line, the projected horizontal wind vectors were almost opposite in direction. The wind vector to the left of the windless line was oriented from A' to A and thus produced isentropic downslope vertical motion. The wind vector to the right of the windless line was mainly oriented from A to A' and created isentropic upgliding. Therefore, the upward motion associated with both isentropic displacement and isentropic upgliding overlapped over the cold vortex genesis area (Figs. 3b and 3c), persisting until the TPV genesis (Fig. 3d).

It is worth noting that, although downward intrusion of upper-level high-PV air from a tropopause folding event seemed to be the initial forcing of upward motion over the vortex genesis area in this case, the tropopause folding itself could have been created by this ageostrophic circulation (Hoskins and Draghici, 1977), which introduces ambiguity when attempting to identify the source of vertical motion. Thus, we only conduct a broad analysis of the evolution of vertical circulation here. The fundamental causes of the vertical motion will be given later by using the omega equation.

Previous studies have suggested that tropopause positive PV forcing can decrease the static stability throughout the troposphere (Hoskins et al., 1985) and even promote deep convection in some cases (Griffiths et al., 2000; Antonescu et al., 2013). This destabilizing effect is also visualized in Figs. 3b–d, where significant convex isentropic surfaces are shown beneath the tropopause. At the same time, the development of upward motion seemed to produce a vertical stretching in the vortex genesis region. Since the reduced static stability can be converted into vorticity by vertical stretching, and since both the vertical stretching and the reduction of static stability were both exhibited during the vortex genesis period, the contribution of this mechanism of vorticity production to the cold vortex genesis needs to be studied further.

To investigate the nature of vertical stretching, we shall focus on the vertical velocity, which ultimately drives the stretching. Here, the traditional omega equation is used to diagnose the forcing of the vertical motion. In adiabatic flow, the traditional omega equation can be expressed as

where $ \sigma $ is the static stability, ${f_0}$ is the Coriolis parameter at a reference latitude, and the other symbols conform to their normal meteorological uses. Equation (14) indicates that vertical motion is influenced by both the vertical structure of the absolute geostrophic vorticity advection and the horizontal distribution of thermal advection. Although the physical interpretation of this equation is clear, usually there is a cancellation of two forcing terms in this form of omega equation, which can sometimes lead to ambiguity (Holton, 2004). Thus, preliminary works were conducted before using this equation. Results demonstrated that during the TPV genesis period, the Laplacian of thermal advection is negligible compared to the differential vorticity advection term. Therefore, in this case study, the vertical motion is analyzed simply by examining the vertical structure of the absolute geostrophic vorticity advection.

Figure 4a shows the mean profile of the absolute geostrophic vorticity advection during the TPV genesis. The profile presents an increase (decrease) with height above (below) 500 hPa, implying that the differential geostrophic absolute vorticity advection contributes to the upward motion above 500 hPa and downward motion below, leading to the stretching around 500 hPa. Furthermore, to investigate the circulation pattern favoring this vertical structure of absolute geostrophic vorticity advection, the relative vorticity and wind field at different pressure levels are given at 1800 LST 26 April, six hours before the TPV genesis (Figs. 4b–d). At the 350-hPa level, to the east of the TP, a strong easterly flow (Fig. 4b) from the anticyclonic circulation (as shown in Figs. 1d and e, and Figs. 2d and e) was situated to the north of the PV streamer, and it encountered a strong westerly flow along the lower latitude within a zonal belt between 35°N and 40°N. These two flows converged to create strong cyclonic vorticity, forming a prominent positive vorticity banner. Following the prevailing flow, the vorticity banner flowed cyclonically into the northeastern part of the plateau, with large amounts of cyclonic vorticity being transported to the TPV genesis area continuously. However, the vorticity transport efficiency of this banner tended to weaken downward at the lower levels (Figs. 4c and d). As a result, an increasing-with-height structure of vorticity advection was formed. Such a circulation pattern also facilitated the stratification of the quasi-geostrophic flow. Thus, the differential geostrophic absolute vorticity advection, produced by a vorticity banner, was responsible for the upward motion during the TPV genesis.

Figure 4.  (a) Vertical profile of area-mean absolute geostrophic vorticity advection (green line; units: 10⁻¹⁰ s⁻²) over a 1° × 1° domain around the TPV center averaged from 1800 LST 26 to 0000 LST 27 April. (b) Distribution of relative vorticity (shading; units: 10⁻⁵ s⁻¹) and wind (barbs; units m s⁻¹; refer to Fig. 2) at 350 hPa at 1800 LST 26 April 2018. (c, d) As in (b) except for 450 hPa and 500 hPa, respectively. The location of the TPV center at 500 hPa is denoted by the green circle.

The above diagnoses concentrated on the circulation conditions favorable for TPV development in the free atmosphere. Next, we investigate the near-surface conditions associated with the TPV genesis. To investigate the primary factor contributing to the genesis of the cold TPV, we calculated the geostrophic vorticity and normalized static stability tendencies, as well as their forcing terms, using ERA5 reanalysis data. To obtain several time series for further analysis, we used the central finite difference method to compute the derivatives in both time and space, and then averaged all the results in a 1° × 1° box around the vortex center. To reduce potential uncertainties, we focused on the cumulative contribution of each forcing term to the tendency of a variable during the TPV genesis period to capture the dominant factor responsible for the genesis of the cold TPV. Since the movement of the PV forcing system was much slower than the wind speed, and since the TPV was almost stationary during its genesis stage, as shown in Fig. 3 and Fig. 4, the moving speed C in Eq. (13) was ignored.

While the absolute vorticity advection was increasing with height above 500 hPa, as shown in Fig. 4a, it was decreasing with height below 500 hPa, in favor of descending air near the surface. This is evidenced by referring to Fig. 3, in which a significant discontinuity in the vertical motion existed at the 500-hPa level in the TPV genesis area: The near-surface vertical motion in the mountain valley where the TPV was generated appears to have a distinct diurnal variation, with ascending motion during the daytime (Fig. 3a) and descending motion during the night when the TPV was formed (Figs. 3b–d), which was apparently induced by the different thermal conditions of the TP surface between day and night.

Equations (10) and (13) indicate that the normalized static stability tendency is determined by three processes, i.e., differential temperature advection, stretching, and diabatic heating. Since the magnitude of the differential temperature advection term is smaller compared to the other terms, its impact can be ignored. Thus, the tendency of normalized static stability depends mainly on the vertical distribution of diabatic heating and vertical stretching. At 500 hPa, as illustrated in Fig. 5a, the evolutions of the diabatic term and the tendency term were similar, indicating that the variation of the tendency mainly depended on the variation of the vertical differential diabatic heating. Near the surface, the diabatic heating decreased with increasing height during the daytime of 26 April, and the static stability tendency was negative in general. From the afternoon of 26 April till the midnight before the TPV genesis, as shown by the heavy curves in Fig. 5a, the diabatic heating increased with height remarkably, leading to the increase in static stability. The impact of diabatic heating was compensated by the air stretching at the site of TPV genesis, with descending air below 500 hPa and ascending air above, as shown in Figs. 3b–d. Specifically, the diabatic term produced positive normalized statical stability, while the stretching term produced negative normalized static stability simultaneously. The positive normalized static stability generated by the diabatic term seemed to be “consumed” by the stretching term adiabatically, causing a decrease in normalized static stability tendency during TPV genesis. Because the quasi-geostrophic PV ${q_{\text{g}}}$ is the sum of absolute vorticity and normalized static stability (see Eq. 12), and because in the adiabatic case, ${q_{\text{g}}}$ is conserved, this “consumed” normalized static stability can then be transferred to geostrophic vorticity by the stretching effect through Eq. (13).

Figure 5.  (a) Time series of normalized static stability (NSS) tendency (black solid line; units: 10⁻⁹ s⁻²), the stretching term ($ - f {{\partial \omega }}/{{\partial p}} $; blue solid line; units: 10⁻⁹ s⁻² ), and the diabatic term (red solid line; units: 10⁻⁹ s⁻²) in Eq. (10) averaged over a 1° × 1° domain around the TPV center at 500 hPa with the TPV genesis of 9 hours before denoted by the bold line. (b) Time series of quasi-geostrophic vorticity (QGV) tendency (black solid line; units: 10⁻⁹ s⁻²), the stretching term ($ + f {{\partial \omega }}/{{\partial p}} $; blue solid line; units: 10⁻⁹ s⁻²), and advection term (red solid line; units: 10⁻⁹ s⁻²) in Eq. (13) averaged over the same region as in Fig. 5a with the vortex genesis of 9 hours before denoted by the bold line.

Equation (13) indicates that the local change in geostrophic vorticity depends on the geostrophic vorticity advection, the air column stretching, and the friction effect. Given that the friction is negligible at 500 hPa and upper levels, only time series of the geostrophic vorticity tendency, geostrophic vorticity advection by geostrophic wind, and stretching term from Eq. (13) are provided. Figure 5b shows two primary geostrophic vorticity producing windows during the analyzed period at 500 hPa. Geostrophic vorticity produced before 0500 LST 26 April is shown to be mainly attributable to the advection term, which is caused by the movement of the cold trough (Figs. 1b–d). The geostrophic vorticity in the second window, during which the cold TPV formed, was contributed mostly by the stretching term, whereas the advection term played a minor or even negative role. Thus, our analysis indicates that air column stretching was the primary factor responsible for the cold TPV genesis.

The physical interpretation of this conversion process is quite simple: Air column stretching ($ (f {{\partial \omega }})/{{\partial p}} > 0 $) increased the vertical distance between adjacent isentropic surfaces, resulting in a decrease in static stability (as illustrated in Figs. 3b and c). At the same time, the vertical stretching reduced the horizontal rotation radius, resulting in a rotational acceleration ($ {{\partial {\eta _{\text{g}}}}}/{{\partial t}} > 0 $) for conserving angular momentum. As demonstrated in this case, the vertical stretching was responsible for both the decrease in normalized static stability and the increase in geostrophic vorticity. This is why normalized static stability is also referred to as “stretching vorticity” (Holton, 2004). It is worth noting that the conversion between geostrophic vorticity and normalized static stability occurred instantaneously and adiabatically once vertical stretching appeared, as shown in Figs. 5a and b.

In summary, in addition to the significant tropopause PV forcing, the surface thermal forcing was also important for the TPV genesis. The strong surface cooling at night over the TP remarkably increased the static stability and PV near the surface, and then the enhanced static stability was converted to vertical vorticity adiabatically by vertical stretching, leading to the cold TPV genesis.

A series of numerical experiments were carried out using the WRF model to test the hypothesis that the surface thermal effect of the TP could have modulated the genesis of the cold TPV. These experiments were initialized at 1800 LST 25 April 2018, providing enough time for model “spin-up” before the vortex genesis, and then run for 60 hours to ensure full coverage of the TPV genesis stage. A one-way nested grid with two domains was applied, as shown in Fig. 6. The outer domain (domain 1) covered most of the Asian area with a coarser grid spacing of 12 km (∆x = 12 km), and the inner domain (domain 2) focused on the TP area with a finer grid spacing of 4 km (∆x = 4 km). The nested domain was set to be large enough to minimize the noise from the lateral boundary. For computational efficiency, domains 1 and 2 were designed to run separately using the “ndown” method. The initial and lateral boundary conditions for the coarser domain were provided by ERA5 reanalysis data, while the boundary conditions for domain 2 were obtained from the output of a separate domain 1 run. The boundary conditions were updated every hour for both domains. The time steps for domain 1 and domain 2 were 60 s and 20 s, respectively. The model had a model top at 50 hPa and used 45 stretched vertical levels with higher resolution near the ground.

Figure 6.  Distribution of the model terrain (shading; units: m) included in the different domains (the terrain resolution in domain 1 and domain 2 was 12 km and 4 km, respectively) in the WRF experiments. The sensitivity experiment conducted in this study was restricted to within the region of the red box in domain 2.

The physics parameterizations used in both domains included the Thompson microphysics scheme (Thompson et al., 2008), the RRTMG shortwave and longwave radiation scheme (Iacono et al., 2008), the revised MM5 Monin–Obukhov surface layer scheme (Jiménez et al., 2012), and the Yonsei University planetary boundary layer scheme (Hong et al., 2006). Besides, the Noah land surface model (LSM) (Chen and Dudhia, 2001) with 4-layer soil temperature and moisture was used for providing surface sensible and latent heat flux to the model. The Tiedtke mass-flux cumulus scheme (Tiedtke, 1989; Zhang et al., 2011) was only applied to the coarser domain with 12-km grid spacing. Due to the 4-km grid spacing being sufficient for resolving convective processes, the parameterization of cumulus convection in domain 2 was turned off. Note that the model analyses in this paper are based on the outputs from domain 2.

To examine the responses of cold TPV genesis to different TP surface thermal conditions, we conducted sensitivity experiments by modifying the surface heat flux in the LSM. After comparing some preliminary sensitivity experiments, it was found that the removal of surface latent heat flux had little effect on the formation of this cold TPV. This is because surface latent heat flux does not directly heat the atmosphere. Thus, the sensitivity experiments for the cold vortex genesis under a dry background in this study were conducted by adjusting only the surface sensible heat (SH) flux. Further, to determine a reasonable modification range of SH flux, we checked the diurnal variation of the domain-average surface SH flux in the northeast region of the TP several days before and after the cold TPV genesis, using both ERA5 data and model outputs. The surface SH flux was found to be approximately −20 to 400 W m⁻², reaching its maximum at noon and its minimum in the early morning.

Based on the preparations above, a control (CNTL) simulation in conjunction with a sensitivity (COOL) experiment were designed. Specifically, in the COOL experiment, surface SH flux was fixed at −20 W m⁻² for the entire experiment period. To minimize the impact on the circulation of non-vortex genesis areas, the modification was limited to within the region of 28°–40°N and 92°–104°E (Fig. 6), which roughly covers the eastern part of the TP and is slightly larger than the vortex genesis area. Outside the modified region, the surface SH flux was calculated using Noah LSM. Note that the SH flux value of −20 W m⁻² corresponds to the maximum surface cooling of the TP at night. Therefore, the COOL experiment was used to test the response of the cold TPV genesis to the pure cooling effect of the TP surface. In the CNTL simulation, the surface SH flux was totally controlled by Noah LSM, which included a complete diurnal cycle of the surface thermal process, running as the CNTL experiment for comparison with both reanalysis data and the sensitivity experiment results.

To facilitate a fair comparison with the ERA5 data, and to highlight the evolution of the systems consistent with the scale of the cold TPV, the model output was smoothed somewhat, to remove unimportant details at smaller scales. Then, the performance of the CNTL simulation was evaluated using ERA5 reanalysis data (Figs. 7a–h). The results show that the cold TPV simulated by the CNTL experiment (Fig. 7g) was initiated from a pre-existing trough located over the eastern TP (Figs. 7e and f). The cold vortex formed at 0000 LST 27 April and subsequently expanded rapidly (Figs. 7g and h). These features agreed well with the ERA5 data (Figs. 7a–d), albeit with some discrepancies, such as the initial size of the simulated TPV being slightly smaller than that of ERA5 data, and the simulated 500-hPa temperature field being generally underestimated compared to ERA5 reanalysis. The difference in size of the TPV can be ignored since it does not affect the mechanism of TPV genesis represented by the model, while the 500-hPa systematic cold bias is likely to be attributable to the inaccuracy of the default soil type used by the WRF model (Yue et al., 2021). However, these did not significantly affect the formation of the TPV in the CNTL experiment.

Figure 7.  Distribution of the 500-hPa geopotential height (blue contours; units: dagpm), temperature (shading; units: K), and wind (purple vectors; units: m s⁻¹) fields derived from (a–d) ERA5 data, (e–h) the CNTL experiment, and (i–l) the COOL experiment, at (a, e, i) 1200 LST 26 April, (b, f, j) 1800 LST 26 April, (c, g, k) 0000 LST 27 April, and (d, h, l) 0600 LST 27 April 2018. The red box indicates the position of the cold TPV identified for the first time in the panels at 6-h intervals.

To reveal the contribution of surface thermal forcing to the TPV genesis in the model result, Fig. 8 presents the evolution of the dominant terms in Eq. (13) for the CNTL experiment. For the dominant terms associated with the simulated normalized static stability in Fig. 8a, the simulated evolution of the diabatic term is similar to that of the tendency, which is in accordance with the results derived from the reanalysis data as shown in Fig. 5a, implying the significance of the variation of the vertical differential diabatic heating in controlling the variation of the tendency. During the TPV genesis, as shown by the heavy curves in Fig. 8a, the positive vertical differential diabatic heating resulted in an increase in static stability, but was partly compensated by the air stretching at the site of the TPV genesis. Figure 8b presents the simulated evolution of the dominant terms in the vorticity equation [Eq. (13)]. It is evident that, in the CNTL run, the stretching term plays a dominant role in the growth of the geostrophic vorticity during the period of TPV genesis, which is also consistent with the diagnostic results from ERA5 reanalysis (Fig. 5b), and indicates that the surface thermal forcing is important for this cold TPV genesis case. In short, it can be concluded that the CNTL simulation was able to reproduce this cold TPV in terms of the circulation evolution, the timing of cold TPV genesis, and the subsequent development of the cold vortex.

Figure 8.  As in Fig. 5 but for the CNTL experiment.

The reasonable success of the CNTL experiment in simulating the TPV genesis implies that it was also able to capture the basic characteristics of the tropopause PV forcing and the surface thermal forcing. This enabled us to conduct a sensitivity experiment focusing on the impacts of surface thermal forcing. Figures 7i–l show the 500-hPa geopotential height and temperature fields simulated by the COOL experiment. It can be seen that, although the evolution of 500-hPa circulation in the COOL experiment was generally similar to that in the CNTL experiment, there were significant differences regarding the cold TPV genesis. The cold vortex in the COOL experiment generated several hours earlier than in the CNTL run and was much stronger owing to its colder core, lower geopotential height, and larger size. This was due to the prescribed surface cooling of −20 W m⁻² was exerted even during the daytime of 26 April, resulting in the loss of surface energy in the experiment. This result also indicates that the impacts of surface thermal effects on the genesis of warm and cold TPVs are quite different, whereas it is generally believed that sufficient daytime surface heating facilitates the development of convection, which in turn contributes to the nighttime generation of warm TPVs through latent heat release (Ma et al., 2020; Zhang et al., 2019). Nevertheless, the fact that the timing of the TPV genesis in the COOL experiment was six hours ahead of that in the CNTL experiment indicates that the surface cooling during the night of 26–27 April did contribute to the genesis of the TPV.

This study investigated the genesis mechanism of a rare cold TPV that occurred in late April 2018 and was responsible for persistent rainfall downstream of the TP. ERA5 reanalysis data were employed for the dynamical and thermodynamical diagnoses, with particular attention paid to the contributions of the PV forcing from the tropopause and the thermodynamic effect from the surface. A framework for the conversion between normalized static stability and geostrophic vorticity through the stretching effect was introduced to explore the genesis mechanism of the cold TPV. Numerical experiments with different surface SH flux treatments were then conducted to verify the results obtained from the data diagnosis. The major findings can be summarized as follows.

Synoptic analysis indicated that the cold TPV was generated under a highly baroclinic environment. As a positive PV anomaly in the lower stratosphere moved towards the TP, the tropopause over the TP descended. The positive PV forcing at the tropopause pushed the tropospheric isentropic surfaces upward over the TP, forming isentropic-displacement ascent (Hoskins et al., 2003) and reducing the static stability in situ. Furthermore, the descent of the tropopause over the TP before the TPV genesis also caused tropopause folding associated with downward intrusion of upper-level high PV, forming a narrow high-PV column over the northeastern TP just before the vortex genesis (Figs. 3b–d). Influenced by this upper-level high-PV column, upward motion developed over the vortex genesis area. In conjunction with the development of nighttime descending air in the mountain valley where the TPV was formed, vertical air-stretching was forced at the TPV genesis site.

The cold TPV in this study was generated during the night because of the pronounced diurnal cycle of surface thermal forcing in the mountain valley area. The surface cooling at night increased the surface static stability and PV, while the aforementioned vertical air-stretching converted the generated static stability to vertical vorticity. Consequently, the cold TPV was generated over the valley during the night.

The findings of this study reveal the genesis mechanism of a cold TPV and highlight the special roles of tropopause PV forcing (thus, for weather applications, the PV streamer near the TP might serve as a precursor for forecasters in predicting a cold TPV) and land–atmosphere interaction in cold TPV genesis, albeit based only on one case study. According to the results published by Lin et al. (2020), a deep TPV is five times more likely to move out of the TP than a shallow one. Although there are no climatological studies indicating whether all cold TPVs are as deep as the one in this study, it is possible that we have long underestimated the potential hazards of cold TPVs in downstream areas of the TP. In addition, cold TPVs may not always occur during the cold season, as suggested by Tang et al. (2023), who demonstrated that about 70% of all TPV geneses in June from 1980 to 2016 could be categorized as “warm–wet”, while the rest belonged to the “cold–dry” category. This implies that cold and dry TPVs can also occur in the warm season, although not as many as warm and wet TPVs. Thus, future investigations into more cold TPV cases during both cold and warm seasons should be conducted to advance our understanding of the process of cold TPV genesis, as well as improve the model skill for TPV forecasting.

Acknowledgements. The ERA5 data were obtained from the Copernicus Climate Change Service (C3S) Climate Data Store (https://cds.climate.copernicus.eu). We acknowledge the National Center for Atmospheric Research (NCAR) for developing and supporting the WRF Model. This study was supported by the National Natural Science Foundation of China (Grant Nos. 42288101 and 42175076) and the Strategic Priority Research Program of the Chinese Academy of Sciences (Grant No. XDB40000000).