In this study, the RWP data collected at Beijing observatory station (116.47°E, 39.80°N) was used to derive the climatology of vertical wind profile in the lower troposphere. The observational site of RWP is shown in Figure 1. Liu et al. (2020) reported that the RWP can provide wind profile with a vertical resolution of 120 m starting from the ground surface all the way up to a mean height of about 5 km above ground level (AGL), covering the period from January to December 2020. Prior to formal analysis, we have conducted data quality control to ensure that these wind profiling measurements are good enough to be used to characterize the geostrophic wind in Beijing (Liu et al., 2020). Noteworthy is that if more than 20% of the data below 3 km AGL are discarded or lost, the entire profile averaged during a given hour will be discarded. As a result, 7,194 valid hourly wind profiles were collected in Beijing.

To minimize the potential influence of rainfall, all the wind profile measurements from RWP analyzed here are constrained to those samples belonging to the non-rainy periods, which are screened using the 1-min rain gauge measurements at Beijing Observatory station shown in Figure 1. In addition, hourly measurements of ground surface temperature (T_s), air temperature at 2 m (T_a), and cloud fraction are obtained from the same weather station. All these meteorological datasets are subjected to strict data-quality control by the National Meteorological Information Center (NMIC) of the China Meteorological Administration; http://data.cma.cn/data/online.html?t=1) and have been used extensively in previous weather and climatological studies (Yu et al., 2010; Zhang and Zhai, 2011; Luo et al., 2016; Chen et al., 2018). All-day averaged cloud fraction and rain gauge data are used to discriminate between clear-sky and cloudy conditions. The clear-sky condition refers to those days with cloud fraction being below 20%, whereas cloudy condition refer to those non-rainy days with cloud fraction being above 80% (CMA 2003). In this way, we get 116 clear-sky days and 28 cloudy days, contributing 34.6% and 8.4% of the total number of days.

ERA-5, the fifth generation of global atmospheric reanalysis produced at the European Centre for Medium-Range Weather Forecasts (ECMWF), is the successor of ERA-interim. It exhibits significant improvements over previous reanalysis, due largely to the updated parameterization schemes and more observations assimilated, which lead to its capability of public access within 5 days behind real time in operational mode. Meanwhile, ERA-5 reanalysis provides a spatial resolution of 0.25° × 0.25 ° and a temporal resolution of 1-h. Particularly, the accuracy and performance have been well demonstrated in reproducing the variation of temperature, rainfall, wind, surface energy balance (Hersbach et al., 2020). Currently, it covers the period from 1950 to the present (Bell et al., 2021). Here we only use the pressure dataset at the grid centered at Beijing observatory station.

We define the wind speed observed by the RWP (V_obs) minus geostrophic wind speed calculated from the ERA-5 reanalysis (V_geo) as geostrophic velocity deviation (V_D). When the V_D is greater than 0 (less than 0), the actual observed wind is manifested as supergeostrophic (subgeostrophic) flow, which is usually used to indicate the occurrence of low-level jet (Blackadar, 1957; Nagata and Ogura, 1991; Baas et al., 2009). It has been recognized that V_D plays an important role in the production and transformation of atmospheric kinetic energy and mass redistribution.

Based on the pressure data from ERA-5, the geostrophic wind speed is derived by. V → g = − 1 ρ f ∇ p × k → (1) f = 2 Ω   sin ⁡ φ (2) where ρ is a reference air density, f denotes the Coriolis frequency calculated, with Ω being the angular velocity of the Earth with the value of 7.292 × 10⁻⁵ rad/s, φ is the latitude of Beijing, p is pressure. u _g and v _g represent the components of the zonal and meridional directions for the geostrophic flow, which can be derived from the following equations: u g = − 1 ρ f ∂ p ∂ y (3) v g = − 1 ρ f ∂ p ∂ x (4) x = R e λ   cos ⁡ φ (5) y = R e φ (6) where R e represents the Earth’s radius, and λ is longitude. Note that this does not necessary suggest that the wind above the boundary layer is in geostrophic balance.

The isobaric coordinate from ERA-5 reanalysis has to be converted to the geometric height, in order to match the RWP measurements with ERA-5 reanalysis, according to the following barometric formula: h = − R d T g ln p p 0 (7) where R d represents the air constant, T is average temperature, g is the gravitational acceleration, and p₀ is the surface pressure.

To better tease out the physical mechanisms behind the supergeostrophic wind observed in the study area, our analysis will be conducted on the daytime and nighttime samples separately. Unless otherwise noted, the daytime refers to the hours from 0900 BJT to 1700 BJT, and the nighttime refers to those from 2100 BJT to 0600 BJT.

In the PBL, pressure gradient force is balanced by Coriolis force and internal frictional force, and the frictional force is of crucial importance in keeping the wind from being geostrophic flow. The PBL can be divided into surface layer and Ekman layer, and the wind distribution in the Ekman layer can be ideally described from a mathematical view of point as description of Ekman spiral (Ellison, 1955). This is generally valid under the assumption of neutral atmospheric static condition.

To reveal how the Ekman spiral evolves with height, we determine the static stability of the PBL by using the metric of lower tropospheric stability (LTS). Following previous studies (e.g., Klein and Hartmann, 1993; Guo et al., 2018), LTS is formulated as follow: L T S = θ 700 h P a − θ 1000 h P a (8) Where θ denotes the potential temperature that is estimated from hourly ERA-5 reanalysis. All the LTS samples are divided into three subsets, each of which has the same number of samples. As shown in Figure 2, the neutral atmosphere conditions in this study correspond to the second tercile of LTS, which ranges from 10.6 K to 15.6 K.

Figure 3 shows the normalized contoured frequency by altitude diagram (NCFAD) of V_D at the lower troposphere under clear-sky and cloudy conditions in the daytime and nighttime, respectively. The vertical structures of V_D in the PBL and aloft free troposphere exhibit frequent variations. In the daytime, the NCFAD of V_D shows a similar pattern for both clear-sky and cloudy conditions: Below about 1.5 km AGL, subgeostrophic flow dominates since most negative V_D samples occur in this altitude range. The V_obs is equal to V_geo at about 1.5 km AGL, indicating quasi-geostrophic phenomenon occurs at this height. This also suggests that the daytime averaged PBL height can be reached up to 1.5 km AGL, well consistent with the PBL height as observed by the RWP in Beijing (Solanki et al., 2021). By comparison, V_D is a small positive value above 1.5 km AGL, indicating supergeostrophic wind is observed albeit not obvious (Figures 3A,B). Under normal condition, stronger turbulence tends to occur in the PBL as compared with that in the free atmosphere, especially in the daytime, due to the stronger land-atmosphere exchanges induced by the solar radiation reaching the ground surface (Baas et al., 2009). This generally tends to result in more homogenous variation of V_obs with height in the daytime, as compared with the vertical variation at night.

As shown in Figures 3C,D, the occurrence frequency of V_D in the nighttime is biased towards positive above 0.5 km AGL under the both clear-sky and cloudy conditions. A close look at Figure 3 shows that at night the altitude where V_D changes from negative to positive in the vertical drops sharply from 1.5 to 0.5 km AGL relative to that at daytime. Notably, the frequency of supergeostrophic wind at night reaches a maximum at around 1.5 km AGL and then descends with height, much larger than that at daytime. This means that supergeostrophic wind tends to occur more frequently at night compared with in daytime. This is because the stable boundary layer (SBL) formed by the combined effects of surface cooling and strong radiative cooling of the air induce a rapid decay of both turbulence and stress divergence (Kumar et al., 2006; Kallistratova and Kouznetsov, 2012), making the air in the residual layer suddenly or in the free troposphere have no friction force.

As shown in Figure 4A, the subgeostrophic wind under clear-sky condition only occurs below 0.5 km AGL for the period 0800 to 2,200 BJT with maximum wind from 1,200 to 1800 BJT. And during the hours after sunset, the supergeostrophic wind speed increases gradually above 0.5 km after 1800 BJT, the supergeostrophic wind speed reaches a maximum between 0000BJT and 0400 BJT at the height range of 1.5–2.25 km, then the speed gradually decreases at heights above 2.25 km AGL, which means that the supergeostrophy phenomenon is caused by the rapid increase of wind speed at the level of maximum jet flow at night. In contrast, the supergeostrophic wind under the cloudy condition can be found above 1 km AGL all day, but below 0.5 km AGL the wind speed is lower and the supergeostrophic wind cannot be easily found (Figure 4B). The supergeostrophic wind in the daytime under cloudy conditions is more obvious than that under the clear-sky conditions. This indicates that the diurnal variability of the supergeostrophic wind speed is also significantly influenced by clouds.

The diurnal variation of the supergeostrophy wind observed here can be explained by inertial oscillation theory proposed by Blackadar (1957), in which inertial oscillations of important ageostrophic components are found to play an important role in the development of LLJ. As such, the wind is subgeostrophic within the PBL in the daytime. The wind component continues to develop overnight, triggered by decoupling of surface friction at sunset. The nocturnal wind profile presents an oscillation around the geostrophic wind vector with a period of 2π/f (f is the Coriolis parameter). As a result, the vertical profile of the horizontal wind takes on the common “nose” shape. This is generally consistent with previous LLJ observations at low levels (Kalapureddy et al., 2007; Wei et al., 2014). Apart from the well-established inertial oscillation theory, several other mechanisms could at least partly account for the formation of supergeostrophic LLJ, including the block effect by the mountains (Wexler, 1961), the baroclinicity associated with diurnal heating and cooling changes over sloping terrain (Holton, 1967), a secondary circulation beneath the exit region of an upper-level jet streak (Uccellini, 1980), and the land-sea thermal property difference (Beardsley et al., 1987).

Figure 5 shows the comparison analysis of diurnal variability of supergeostrophic winds within lowest 1 km of the atmosphere between daytime and nighttime in the year of 2020 at Beijing observatory station. Under clear-sky conditions, strong turbulent mixing and friction in the daytime tend to homogenize the wind profile in the lower troposphere, making it difficult to form supergeostrophic wind (Figure 5A). Noteworthy is that the occurrence frequency of supergeostrophic wind shows a gradual decreasing trend from sunrise to sunset, irrespective of clear-sky and cloudy conditions. During daytime, the frequency of supergeostrophic flow in the presence of cloud is higher than that under clear-sky conditions, most likely due to the stronger convective or entrainment activities caused by clouds in daytime. In contrast, the frequency of nighttime supergeostrophic wind increases gradually with time, and more frequent supergeostrophic wind tends to occur under clear-sky conditions than under cloudy conditions. In this case, the PBL is well decoupled from the underlying surface, and NLLJ or supergeostrophic wind tends to occur just above the SBL (Kalnay et al., 1996), particularly during clear-sky nighttime (Figure 5B). The impact of cloud on the diurnal cycle of supergeostrophic wind occurrence at night seems contrary to that as observed in the daytime.

Besides the effect induced by the mechanical turbulent mixing in the PBL, the near-surface turbulent sensible heat flux is an importantenergy source driving the variation of air motion in the PBL, thereby affecting the profile of wind (Shen and Masahide, 2007; Zhou and Huang, 2010). Here, since recent studies (Cava et al., 2006; Liao et al., 2019) suggest that the difference between T_s and T_a basically reflects the variation characteristics of near-surface sensible heat flux, we here use T_s–T_a as an indicator for sensible heat flux to analyze its potential impact on supergeostrophic flow. When T_s–T_a is negative, it means that the radiative cooling effect dominates near the ground surface, and a downward sensible heat flux can be seen from the atmosphere to the ground surface. When T_s–T_a is positive, a upward sensible heat flux is typically observed. As illustrated in Figure 6A, the magnitude of T_s–T_a shows a unimodal distribution during daytime, reaching a maximum around 1300 BJT when being under strong influence of solar radiation heating. Interestingly, T_s–T_a remains always positive (particularly for the clear-sky conditions) during daytime, as opposed to the negative magnitude at night (Figure 6B) when surface radiative cooling effect dominates. Furthermore, the magnitude of T_s–T_a during nighttime is found to be much lower under cloudy conditions, compared with clear-sky nighttime. This could be mainly owing to the strong radiative warming effect of cloud at night, making a much weaker stratified SBL.

Figure 7 shows the V_D as observed by the RWP at the Beijing observatory station as a function of T_s–T_a during the daytime. It is found that V_D, overall, decreases significantly with the increase of the magnitude of T_s–T_a for the altitudes of 1 km and 2–3 km AGL. As expected, a much steeper regression slop is observed for the lowest atmosphere (within 1 km), as compared with high atmosphere (two to three km). This indicates that surface forcing can be much easily detected in the atmospheric layer that is closest to the ground surface.

Figure 8 presents the joint probability distribution of u/u_g and v/v_g as observed by the RWP at Beijing observatory station at 0.35 km, 0.57 km, 0.79 km and 1.02 km AGL, respectively. Also shown are the Ekman spiral distributions at the corresponding height. Theoretically, the wind direction rotates clockwise with height in the PBL if the dominant forces acting on the air mass, such as Coriolis force and pressure gradient force, are not in equilibrium. Especially under neutral condition, most of the joint pairs of u/u_g and v/v_g are expected to be concentrated within the first quadrant of Figure 8. Nevertheless, most of samples in Figure 8 are clustered at the regions with u/u_g and v/v_g being less than one at low altitudes like 0.35 and 0.57 km AGL. Near the top of PBL such as 1.02 km AGL, a large fraction of samples can be observed with the values of u/u_g and v/v_g being greater than 1. This suggests that the wind speed observed by the RWP is found to increase with height, and the occurrence frequency of supergeostrophic wind could be likely increased with the increasing altitude.

As shown in Figure 8, the probability for the occurrence of Ekman spiral tends to decrease with altitude in the PBL, even though the maximum percentage during all day (nighttime) is less than 20% (7%), which is generally consistent with previous findings (e.g., Lenn and Chereskin, 2009). This indicates that most of the observed winds in the PBL deviate substantially from the spiral pattern even in steady state barotropic situations with near neutral static stability, which generally agrees with previous studies (Holton and Hakim, 2013). The low probability of Ekman spiral observed in the upper altitude could means that the wind profiles near the top of PBL could be dramatically affected by the large pressure-driven flows, such as tides, internal waves, and the geostrophic currents (Lenn and Chereskin, 2009).