Figure 1a presents the RWP mesonet deployed in Beijing at the following stations: Huairou (HR; 40.36° N, 116.63° E), Yanqing (YQ; 40.45° N, 115.97° E), Shangdianzi (SDZ; 40.66° N, 117.11° E), Pinggu (PG; 40.17° N, 117.12° E), Haidian (HD; 39.98° N, 116.28° E), and Beijing Weather Observatory (BWO; 39.79° N, 116.47° E). These RWPs are Ce Feng Leida-6 (CFL-6) tropospheric wind profilers, which are produced by the 23rd Institute of China Aerospace Science and Industry Corporation (Table 1). They provide measurements of horizontal and vertical winds and the refractive index structure parameter at 6 min intervals. The vertical resolution is 120 m from 0.15 to 4.11 km above ground level (a.g.l.) in low-operating mode and 240 m from 4.11 to 10.11 km a.g.l. in high-operating mode (Liu et al., 2019).

The RWPs detect vertically resolved wind fields by transmitting and receiving electromagnetic beams in five directions, comprising a zenith and four inclined directions of 15° in the east, south, west, and north, respectively. By analyzing the Doppler shifts in radial velocities from any three beams, horizontal and vertical wind components are retrieved. However, the falling of small targets (particulate scatterers) and raindrops may cause the potential biases of vertical velocity in such a way that vertical velocity cannot usually be used directly (Angevine, 1996; Wang et al., 2014; McCaffrey et al., 2017). The fluctuating component of the horizontal velocity is not affected under varying meteorological conditions since it is much larger in magnitude.

To ensure the integrity of the data, a test of the acquisition rate of the horizontal wind profiles spanning the whole year of 2023 is conducted. As shown in Fig. 1b, the observations below 4.11 km a.g.l. for six RWPs relatively meet the requirements of continuity in time with an average missing value rate of less than 20 %. These relatively low acquisition of the RWP data at high altitude could be attributed to the well-known limitations that the radar signal attenuation constitutes the inherent uncertainty sources. Therefore, the horizontal winds derived from six RWPs at the heights of 0.15–4.11 km a.g.l. in 2023 are collected in this study.

To further evaluate the data quality of the RWPs, horizontal wind speeds at every level from the BWO are validated against the coincident radiosonde measurements. Upper-air sounding balloons are launched at the BWO twice daily at 08:00, and 20:00 local standard time (LST), providing the vertical profiles of temperature, pressure, relative humidity, and horizontal winds with a vertical resolution of 5–8 m (Guo et al., 2021b). During summer months (June, July, and August), an intensive observation campaign was conducted at most radiosonde stations of China with an additional balloon launches at 14:00 LST. As shown in Fig. 1c, the correlation coefficient (R) is found to be greater than 0.8 from 0.51 to 4.11 km a.g.l. Nevertheless, the accuracy and reliability of the RWP data below 0.51 km are limited by the interference of near-surface clutter. Scatterplots obtained by aggregating all the samples between 0.51 and 4.11 km a.g.l. produce a correlation coefficient (R) value as high as 0.84 (Fig. 1d). Thus, the horizontal winds derived from RWPs at heights of 0.51–4.11 km a.g.l. are believed to be reliable enough and therefore are adopted here for the generation of atmospheric dynamic dataset.

Rainfall at 1 min interval is directly acquired from the rain gauge measurements at automated surface stations over Beijing. Here, 6 min accumulated rainfall is synchronized with the RWP measurements at 6 min intervals. These rain gauge measurements have undergone rigorous quality control and have been made publicly available by the China Meteorological Administration.

ERA5 is the fifth-generation atmospheric reanalysis of ECMWF (European Centre for Medium-Range Weather Forecasts), which benefits from advancements in data assimilation, model physics, and dynamics (Hersbach et al., 2020). The ERA5 dataset can provide divergence and vorticity on 37 pressure levels with a spatial resolution of 0.25°×0.25° at hourly intervals. Additionally, the planetary boundary layer (PBL) height product is directly obtained from the ERA5 reanalysis.

Generally, the horizontal divergence (D) and vertical vorticity (ζ) are represented by pairs of partial derivatives of velocity to reflect the change in air velocities with distance. By applying Gauss's theorem, horizontal divergence (D) is expressed by the relative expansion rate of the air mass. The triangle method, as proposed by Bellamy (1949), computes the divergence based on the rate of change in a fluid triangle initially coincident with the network composed by any three points A, B, and C. We assume that (xi,yi) (i=A,B,C) is the location of three vortex points Vi=(ui,vi) are the zonal and meridional component of horizontal wind, respectively. As the air parcel at (xi,yi) moves to (xi+uiΔt,yi+viΔt) after the infinitesimally short time Δt, a new triangle A′B′C′ will form. The resultant horizontal divergence D over the fluid triangle can be defined as 1D=1σdσdt=1σlim⁡Δt→0ΔσΔt=1σlim⁡Δt→0σ′-σΔt, where σ and σ′ denote the area of the triangle ABC and A′B′C′, which can be formulated by 2σ=12(AB×AC)⋅k=12ijkxB-xAyB-yA0xC-xAyC-yA0⋅k,3σ′=12(A′B′×A′C′)⋅k=12ijk(xB+uBΔt)-(xA+uAΔt)(yB+vBΔt)-(yA+vAΔt)0(xC+uCΔt)-(xA+uAΔt)(yC+vCΔt)-(yA+vAΔt)0⋅k. Here, i, j, and k represent the unit vectors of zonal, meridional, and vertical axes in the coordinate system, respectively. By substituting Eqs. (3) and (2) into Eq. (1) and simplifying the equation, the triangle-area-averaged horizontal divergence is as follows: 4D=(uB-uA)(yC-yA)-(uc-uA)(yB-yA)+(xB-xA)(vC-vA)-(xc-xA)(vB-vA)(xB-xA)(yC-yA)-(xc-xA)(yB-yA).

The vertical vorticity ζ can be estimated directly from Stokes theorem as 5ζ=1σ∮V⋅dr.

Circulation along the triangle ABC can be calculated by 6∮V⋅dr=(VA+VB)⋅AB2+(VB+VC)⋅BC2+(VC+VA)⋅CA2. By substituting Eqs. (2) and (6) into Eq. (5), we conclude that the vertical vorticity is as follows: 7ζ=(vB-vA)(yC-yA)-(vc-vA)(yB-yA)-(xB-xA)(uC-uA)+(xc-xA)(uB-uA)(xB-xA)(yC-yA)-(xc-xA)(yB-yA).

These equations are then applied to the abovementioned wind measurements from the RWP mesonet in order to calculate the profile of horizontal divergence and vertical vorticity. Four triangles from west to east are constructed based on the positions of RWP stations in Beijing. It is noteworthy that the denominator of Eqs. (4) and (7) is equal to the area of the triangle from Eq. (2). That is to say, the value of divergence and vorticity is inversely proportional to the area of the triangle. Therefore, the magnitudes of the results are larger for triangle 2, which could be attributed partly to the smallest area of triangle 2 being used for area-averaged calculations compared to those of other triangles. This coincides with the fact that the gradient of velocity between two points, including ∂u∂x, ∂v∂x, ∂u∂y, and ∂v∂y, will increase when the distance is shortened. Considering the six RWPs located at different terrain elevations, the horizontal velocities measured by each RWP are interpolated to the same altitude that starts upwards from 0.51 to 4.11 km above mean sea level (a.m.s.l.) with a vertical resolution of 120 m. The temporally continuous dataset of horizontal divergence and vertical vorticity derived from the RWP mesonet in Beijing during 2023 is publicly available at 10.5281/zenodo.15297246 (Guo and Guo, 2024).

The ERA5 reanalysis with lower temporal resolution is recognized to have a limited capability of characterizing the temporally continuous evolution of atmospheric motion in a pre-storm environment over a mesoscale region. It is desirable to fill this gap with height-resolved dynamic variables as calculated with RWP mesonet measurements at 6 min intervals. In this section, we attempt to explore how the horizontal divergence and vertical vorticity derived from the RWP mesonet could be used as precursors for the pre-storm environment conditions. The triangle-area-averaged 6 min rainfall amount (mm), which is obtained from 29, 42, 49, and 15 rain gauges in triangles 1, 2, 3, and 4, respectively, is used to identify rainfall events occurring during the whole year of 2023 over Beijing's RWP mesonet. For each triangle, all rainfall moments are selected when the 6 min accumulated triangle-area-averaged rainfall is greater than zero. Considering the intermittent nature of rainfall, all the adjacent rainfall events separated by less than 2 h are classified as the same rainfall event. That is to say, the interval between two rainfall events is required to be at least 2 h. The first and last rainfall moment of every rainfall event is defined as the occurrence and ending time of rainfall event, respectively. To avoid the impact of data errors, the rainfall events with a duration of less than 30 min are discarded. Finally, a total of 462 rainfall events are identified over the RWP mesonet in 2023.

Figure 4a and b present the normalized contoured frequency by altitude (NCFAD) for all profiles of the horizontal divergence and vertical vorticity as observed by the RWP mesonet in non-precipitation days, respectively. Specifically, the values of horizontal divergence and vertical vorticity are overall distributed around zero above 2.5 km a.m.s.l. The magnitude of vorticity is greater than that of divergence with more vertical fluctuation in the mid-troposphere. Weak diffluence as indicated by positive divergence values exists in the lower troposphere below 2 km a.m.s.l. By comparison, the pre-storm dynamic environment within 1 h preceding rainfall events (Fig. 4c and d) exhibits significant difference, which implies the presence of complex vertical motion in this unstable atmosphere. The divergence below 1 km a.m.s.l. significantly concentrates from -5×10-5 s-1 to zero before rainfall events (Fig. 4c). As indicated in Fig. 4d, the lowest layer is dominated by positive vorticity centering near 1 km a.m.s.l.

Using dynamic parameters with higher temporal resolution obtained from the RWP mesonet, our aim is to further explore potential patterns or trends in the pre-rainfall convection environment during the lead time. Figure 5a and b show the evolutions of average profiles of horizontal divergence and vertical vorticity at a 12 min interval before the occurrence of rainfall events. The significant increase in average convergence below 1.5 km a.m.s.l. within 48 min ahead of precipitation (Fig. 5a) is largely contributed to by the fact that near-surface air tends to strongly converge into the pre-squall mesotrough when a convective system approaches. The main convection was collocated with low-level convergence and mid-level divergence placed ahead of the precipitation center. These patterns are consistent with previous studies (Wilson and Schreiber, 1986; Zhang et al., 1989; Qin and Chen, 2017; Yin et al., 2020).

Similarly, the increase in vertical vorticity shown in Fig. 5b might be associated with significant horizontal wind shear. The preexisting ambient wind field before the arrival of MCSs is critical to system organization since the orientation of its vertical shear directly influences an asymmetric precipitation structure with mesoscale rotation. In addition, the mesoscale convectively vortex (MCV) may result from deep and moist convection prior to the passage of the MCS (Wang et al., 1993). Trier et al. (1997) indicated that the MCS-induced horizontal flow and its associated vertical shear are critical factors which influence the development of the vortex. This southwesterly flow, enhanced by the MCV circulation, transports moisture northward in the lower troposphere, thereby creating potential instability ahead of the vortex center. Such an environment is favorable for convection and further leads to heavy precipitation (Johnson et al., 1989; Hendricks et al., 2004; Lai et al., 2011).

Due to the direct connection between horizontal divergence and vertical motion, we attempt to further discuss how the RWP-derived divergence could practically benefit short-term forecasting of a convective rainfall event. The evolution of 30 min accumulated rainfall from rain gauge measurements is given in Fig. 6. After 04:00 LST on 22 July 2023, an early-morning event occurred in Beijing with a maximum rainfall rate exceeding 10 mm within 30 min. This event was associated with the transport of moisture as the subtropical storm moved northward. The main region of precipitation was located to the southeast of Beijing before 05:00 LST, and there was no significant rainfall within the RWP mesonet (Fig. 6a and b). As the major convective storm slowly propagated northward and approached the edge of triangle 3 after 05:00 LST (Fig. 6c), the precipitation then took place. Interestingly, a few new cells at the meso-γ-scale formed in triangle 1 at the same time (Fig. 6d and e) and expanded rapidly to other triangles (Fig. 6f and h). The uneven precipitation caused by these isolated and scattered convection cells was a difficult problem in monitoring and nowcasting. Of relevance to this study was the potential application of the RWP-derived divergence profiles for capture the CI and subsequent rainfall.

Figure 7a–d display the time series of the rainfall rates and vertical profiles of the area-averaged divergence during the period of 04:00–07:30 LST on 22 July 2023 in triangles 1–4, respectively. Specifically, one can see the presence of weak convergence below 2 km a.m.s.l. with significant divergence above after 04:00 LST in triangle 1 (Fig. 7a). Subsequently, the convergence layer deepened up to 3.5 km a.g.l. from 04:30 LST. The low-level convergence simultaneously strengthened with the maximum value of -1.4×10-4 s-1 near 1 km a.m.s.l. at 04:48 LST. The signals of prevailing convergence in the lower troposphere provided favorable upward motions for the important lifting of water vapor in the PBL ahead of the convective rainfall. The more intense convergence and upward motion were also well detected in triangle 2 below 1.23 km a.m.s.l. after 04:48 LST (Fig. 7b), which coincided with the generation of rainfall in triangle 1. The inflow over triangle 2 could be attributed to the fact that cold downdraft air in triangle 1 tended to converge into the mesotrough ahead of convection. Even considering the strongest convergence of triangle 2 resulted from the smallest area to a certain extent, such a significant enhanced trend was evident. Similarly, the rainfall in triangle 2 started at 05:30 LST, which is closely related to pronounced convergence and upward motion in the lower troposphere.

As shown in Fig. 7c and d, the relationship between vertical profiles of divergence and rainfall for triangles 3 and 4 during the rainy period was analogous to that for triangles 1 and 2. Nevertheless, triangles 3 and 4 experienced relatively weaker low-level convergence below 1.5 km a.m.s.l. The presence of dominated divergence layer above is not conducive to the extension of upward movement and formation of convective clouds. The weaker peak area-averaged rainfall rate was seen in triangles 3 and 4 in contrast. Clearly, it has been proven that the RWP mesonet has the capability of detecting the continuous vertical profiles of divergence leading to the onset of precipitation at high spatial and temporal resolutions. However, the development of convection is also affected by many other thermal and dynamic variables, and it should be noted that it is feasible to qualitatively determine the change in rainfall rather than quantitatively.