Atmospheric Boundary Layer Stability in Urban Beijing: Insights from Meteorological Tower and Doppler Wind Lidar

Abstract

The limited understanding of the structure of the urban surface atmospheric boundary layer can be attributed to its inherent complexity, as well as a deficiency in comprehensive measurements. We analyzed one year of meteorological data and Doppler wind lidar measurements in Beijing to explore how atmospheric stability is influenced by wind speed, radiation, turbulence, and pollution levels. Results indicate that the predominant state of the urban boundary layers in Beijing is an active condition (characterized by strong unstable and unstable stability regimes) throughout the day, attributed to the significant heat storage capacity of the urban canopy. Strong stable regimes are more frequently observed during winter and autumn, peaking during transitions from night to day. Furthermore, both strong unstable and strong stable regimes occur under very weak wind conditions (indicating weak dynamic instability), with strong instability associated with high net radiation levels while strong stability correlates with low net radiation conditions (indicative of robust thermal stability). The unstable regime manifests under strong winds (reflecting strong dynamic instability) alongside moderate net radiation environments, characterized by elevated values of turbulence kinetic energy and urban boundary height, highlighting the critical role of mechanical turbulence generation during periods of high wind activity. Additionally, six instances of pronounced stable conditions observed during daytime can be partially attributed to low radiation coupled with high pollutant concentrations near the surface, resulting from prolonged temperature inversions due to intense radiative cooling effects and weak dynamic forcing. Our findings presented herein are expected to have urban boundary layer climate and environment implications for other cities with high pollution and dense urban infrastructure all over the world.

1. Introduction

Reliable representations of the structure of the atmospheric boundary layer (ABL) are particularly essential for studies related to air quality studies, wind energy, and the accuracy of weather and climate models [1]. Despite the extensive research on ABLs, urban environments present additional challenges due to complex surfaces and anthropogenic heat sources [2,3]. Urban boundary layers (UBLs) in a global context, particularly in regions experiencing rapid urbanization and increasing pollution, play important roles in the weather, climate, and environment of urban areas. However, the complexity of the physical processes in UBLs remain insufficiently understood [4]. Less well-understood is how fundamentally the structures of the flow and turbulence above the urban surface are changed during different stability phases of the UBL [5].

Atmospheric stability describes the state of the atmosphere related to the capability of vertical motion of air. A stable layer is characterized by suppressed vertical motion, while an unstable or convective layer exhibits intensified upward vertical movement [6]. Considering these two concepts of stability mentioned above, two stability classifications have been applied. One is static stability, measured by the gradient of virtual potential temperature with height, which takes solely buoyancy into account. The other one is dynamic stability, which accounts for both buoyancy and shear-generated turbulence. Dynamic stability is typically characterized using Obukhov length or the Richardson number. The former does require turbulence measurements, which is considered a local metric [7] and can be prone to errors at very low turbulence levels [8]. The Richardson method can be estimated through ratios derived from gradients between various heights or through comparisons between buoyant destruction terms and shear production terms in turbulent kinetic energy (TKE) budget equations. Jericevic and Grisogono (2006) [9] noted that the Richardson number estimated from the second-order moments was sensitive to small fluctuations, and Acevedo et al. (2019) [10] reported that first-order moments (based on mean measures only) exhibited greater stability.

The limited understanding of the urban boundary layer (UBL) structure partly stems from a historical shortage of the necessary in situ measurements. In this study, we employed the Richardson number in different dynamic stability regimes, followed by a quantitative analysis derived from these classifications, utilizing high temporal and vertical spatial resolution atmospheric observations obtained from a tall meteorological tower in Beijing, officially known as “the Beijing 325-m meteorological tower” and a Doppler lidar in the city center. This analysis aims to elucidate the relationships between atmospheric stability and key thermodynamic and turbulent processes governing the UBL, specifically focusing on wind, radiation, turbulence, pollution levels and boundary height, while also examining how these relationships vary by season throughout 2016. Near-surface wind speed measurements serve as indicators of mechanical turbulence production [11]. Additionally, data on surface radiation budgets and energy balance characteristics enhance our understanding of radiatively generated buoyant turbulence potential [12]. Moreover, measurements collected from the Doppler lidar can provide insights into the strength of the vertical mixing and the development process of the ABL [13]. While most previous studies have relied on long-term observational data from relatively flat terrains, our methodology builds upon this foundation but accounts for the complex underlying surfaces characterized by densely built environments—a factor that has not been thoroughly investigated in prior research. Moreover, rapid urbanization has led to numerous environmental problems which have altered the local climate [14]. Notably, strong interactions have been identified between UBL structures and air pollution process [15,16,17]. Therefore, it is imperative to conduct a more detailed investigation based on long-term observation data in urban regions under varying conditions to explore the significant relationships between thermodynamic features present in the lower UBL and stability. The specific objectives of this study are as follows: (1) to characterize the thermodynamic drivers of UBL; (2) to analyze diurnal and seasonal variations in frequencies of differing stability regimes; and (3) to investigate the relationship between these regimes and wind speed, turbulence, urban boundary layer height (UBL), and pollutant concentrations at an urban site throughout the entirety of 2016. Additionally, seasonal variations in these characteristics were assessed, and explanations for the observed features were provided.

2. Materials and Methods

2.1. Experimental Sites and Instrumentation

A 325 m meteorological tower and a Doppler wind lidar (Windcube 200, Leosphere, Orsay, France) are co-located at the Institute of Atmospheric Physics (IAP), Chinese Academy of Sciences, in the center of Beijing (39.97°N, 116.37°E). In this urban site, impervious built-up surfaces are the dominant land cover type, exceeding 90%, within a radius of 10 km from the tower [16]. As illustrated in Figure 1, high density buildings surround this site, and within a radius of 5 km from the tower, residential structures predominantly range from 10 m to 60 m in height.

Meteorological instruments, including 010C cup anemometers and 020C wind vanes (Metone, OR, USA), as well as HC2-S3 sensors (Rotronic, Bassersdorf, Switzerland) are installed on the 325 m meteorological tower at fifteen levels (i.e., 8 m, 15 m, 32 m, 47 m, 65 m, 80 m, 101 m, 120 m, 140 m, 160 m, 180 m, 200 m, 240 m, 280 m, and 320 m above ground level) to provide observations for wind speed (WS), wind direction, relative humidity, and air temperature (T) measurements. Seven sonic anemometers (Model Windmaster Pro, Gill, Long Eaton, UK) are mounted at seven levels (i.e., 8 m, 16 m, 47 m, 80 m, 140 m, 200 m, and 280 m) on this tower. Additionally, pyrgeometers and pyranometers (CNR1, Kipp & Zonen, Delft, The Netherlands) at three different levels (i.e., 47 m, 140 m, and 280 m) are used to measure four-component radiation. Note that only the turbulence and radiation measurements at the 47 m level were used in this study.

The vertical range resolution of the lidar is set at 50 m with a detectable range extending from 100 m to several kilometers above ground level depending on aerosol concentration. The Doppler Beam Swinging (DBS) scan mode is employed to investigate atmospheric velocity structure, which usually takes four to five seconds for each beam scan with elevation angle of 75° or two to three seconds for angles of 90°. A threshold criterion based on carrier-to-noise ratio (CNR) was implemented to mitigate invalid data effects on profiles derived from Doppler velocities; data falling below the CNR threshold (~−20 dB) were excluded.

Additionally, the near-surface WS (05103-L, R. M. Young) and temperature (HMP45C, Vaisala) at the 2.0 m level were measured at a surface station approximately 20 m south of the tower. The precipitation and mass concentrations of PM₁₀ (TEOM 1400a) were also measured in this experiment.

A comprehensive one-year database, as shown in

Table 1. Key technical specifications of the sensors in IAP site used in this study.

Sensor Type	Measurement	Unit	Sampling Frequency	Observation Height
010C	WS	m s−1	0.1 Hz	8/15/47/65/80/100/120/140/160/180/200/240/280/320 m
HMP54C	T	°C	0.1 Hz	8/15/47/65/80/100/120/140/160/180/200/240/280/320 m
CNR1	four-component radiation	W m−2	0.1 Hz	47 m
Gill	3 wind components	m s−1	10 Hz	47 m
WindCube200	radial velocity	m s−1	4–5 s (for angles of 75°) 2–3 s (for angles of 90°)	From 100 m to several kilometers (vertical range resolution of 50 m)
TEOM 1400a	PM10	μg m−3	5 min	on the rooftop of a two-story building

, was gathered in 2016 to investigate the dynamic and thermal drivers of urban atmospheric boundary layer stability.

2.2. Methodology

2.2.1. Radiation and Heat Flux

The surface energy balance over an urban canopy can be approximated by the following equation:

$$R_n+Q_f=H+LE+G$$

(1)

where $H$ is the sensible heat flux from the surface to the adjacent air, $LE$ is the latent heat flux into the atmosphere associated with evapotranspiration, and G is the ground and urban canopy heat storage.${ R}_n$ is the net radiation, and the anthropogenic heat flux ($Q_f$) is the additional energy released by human activities. The area-averaged $Q_f$ values were determined as 21.6 W m⁻², based on the flux source area of the 47 m level in our studied site in wintertime [16], which could serve as a primary input of energy for the balance in winter. However, Chen et al. (2019) [18] reported that summer values of $Q_f$ were smaller than those in winter, potentially falling below 10 W m⁻² in Beijing. In this study, we temporarily omit $Q_f$ and analyze using ${G=R}_n-H-LE$, which does not affect our conclusions.

2.2.2. Calculation of the Urban Boundary Layer Height

The 30 min vertical velocity standard deviation between lidar is caculated by Equation (2),

$${\mathit{\sigma }}_w=\sqrt{{\displaystyle \frac{1}{N-1}}\sum _{i=1}^N{{(w}_i-\overline{w})}^2}$$

(2)

where N is the record number every 30 min, ${\mathrm{w}}_{\mathrm{i}}$ denotes the ith vertical velocity (m s⁻¹), and $\overline{\mathrm{w}}$ is the mean vertical wind speed.

The vertical velocity variance (${\mathit{\sigma }}_w^2$) has been widely utilized to investigate the turbulence intensity, which can be used to define the boundary layer height (BLH). Huang et al. (2015) [19] successfully described the BLH by combing the threshold method and fractional method based on ${\mathit{\sigma }}_w^2$ estimated by the Doppler lidar measurements over Beijing in summertime. However, this new method was found to be invalid in certain instances of weak turbulence occurring during daytime in wintertime. This may have resulted from lower UBL height (UBH) dropping below the minimum observable height of 100 m or failing to meet the near-neutral assumption in the nocturnal boundary layer [20]. One common way to determine the nocturnal boundary layer height is by using vertical profiles of bulk Richardson number [21], and Yang et al. (2020) [22] effectively combined the bulk Richardson number method and threshold method to get the UBH in wintertime. In this study, based on the observations from the 325 m meteorological tower and the Doppler lidar in urban Beijing, the methodologies developed in references [20,22] were merged to estimate the UBH and the entire diurnal cycles of the UBH in December 2016 were characterized. It should be noted that while both methods utilize measurements from different platforms—tower-based instruments and Doppler wind lidar—they are grounded in similar physical parameters related to turbulence processes. Moreover, over 85% of the UBH was defined successfully by the measurements from Doppler lidar in this case, because the proportion of UBH below lidar detection blind area was not high in the whole year in this study.

2.2.3. Definition of the Stability Regimes

In a state of static stability, turbulence vertical motions act against the restoring force of gravity. Consequently, buoyancy tends to suppress turbulence, while wind shears tend to generate turbulence mechanically. The Richardson number $R_i$ accounts for both buoyancy and shear-generated turbulence, which is used to characterize the atmospheric stability here, and can be estimated by the following equation [6]:

$$R_i={\displaystyle \frac{g\frac{\mathsf{\partial }{T}_v}{\mathsf{\partial }z}}{{\overline{T_v}\left(\frac{\mathsf{\partial }U}{\mathsf{\partial }z}\right)}^2}}$$

(3)

where $g$ is the gravitational acceleration, $T_v$ is the absolute virtual temperature, and $U$ is the wind speed. In practical calculation, ${\displaystyle \frac{\mathsf{\partial }{\mathrm{T}}_{\mathrm{v}}}{\mathsf{\partial }\mathrm{z}}}$ and ${\displaystyle \frac{\mathsf{\partial }\mathrm{U}}{\mathsf{\partial }\mathit{z}}}$ can be estimated by ${\displaystyle \frac{\Delta T_v}{\Delta zln\frac{z_2}{z_1}}}$ and ${\displaystyle \frac{\Delta \mathrm{U}}{\Delta zln\frac{z_2}{z_1}}}$.$T_v$ can be replaced by air temperature due to the lack of air pressure at 15 levels. The average temperature of the adjacent two levels at the 325 m tower in this study, $\Delta T_v$, is the temperature difference; $\Delta z$ can be calculated by $\sqrt{z_1{z}_2}$, and $\Delta U$ is the difference of wind speed between two adjacent levels at the 325 m tower.

This variable plays a critical role in surface layer parameterization within numerical weather prediction models and significantly impacts cloud formation, precipitation, wind energy generation, and atmospheric turbulence intensity [23]. The theoretical work yielding $R_{ic}$ = 0.25 is a widely used critical value to define the strong stable regime [6], and all the regimes can be classified as shown in

Table 2. Stability regimes system.

${\mathit{R}}_{\mathit{i}}$	Stability Regimes
$R_i$ < −2	strong unstable
−2 ≤ $R_i$ < −0.1	unstable
−0.1 ≤ $R_i$ < 0.1	neutral
0.1 ≤ $R_i$< 0.25	stable
$R_i$ ≥ 0.25	strong stable

[24,25].

3. Results

3.1. Key Features Associated with Urban Boundary Layer

Figure 2 illustrates the monthly averaged diurnal cycles of the wind speed (at the 2 m level, 8 m level, and 47 m level), air temperature (at the 2 m level, 8 m level, and 47 m level), net radiation (at the 47 m level), H (at the 47 m level), latent heat flux (at the 47 m level), and UBH in 2016. Additionally, the monthly precipitation amount is also given in Figure 2b. Evidently, WS increased significantly with the height. At lower levels, it generally remained weak, below approximately 1.0 m s⁻¹ at the 2 m level and 2.0 m s⁻¹ at the 8 m level. Previous research has revealed significant increases in both aerodynamic roughness length and zero-plane displacement height over urban surfaces in Beijing from 1991 to 2011 [25], indicating that urbanization strengthens the friction and blocking effects of the underlying surface on WS. Pollution events are significantly more likely to occur under these weak wind conditions near the surface in China, particularly in areas with a high density of tall buildings. Moreover, previous studies have reported a significant effect of near-surface WS on UBH (a significant physical parameter pertaining to the atmospheric environmental capacity) variations in Beijing [22]. Unlike the wind speed, the temperature values at different levels were similar. The maximum and minimum air temperature ranged from approximately 268.0 K to 310 K. The climate in Beijing is characterized as a typical warm, temperate, semi-humid, continental monsoon climate, featuring hot and rainy summers alongside cold and dry winters. The distribution of precipitation throughout the year is highly uneven, with approximately 60% of the annual rainfall occurring during the summer months. Rainstorms are frequently observed from July to August [26]. In this study, the total annual precipitation is estimated to be around 597 mm, which aligns closely with Beijing’s average annual rainfall range of 500–700 mm. The highest recorded monthly precipitation was about 300 mm during July in this study.

The urban surface energy budget is a fundamental aspect in enhancing our understanding of the various changes within the UBL. As illustrated in Figure 2c, the monthly averaged diurnal $R_n$ could exceed 500 W m⁻² during April, May, and June, with a peak value of about 574.3 W m⁻² at 12:00 Beijing time (BJT, GMT+8), and an average noon value (from 11:00 to 14:00 BJT) of 541.1 W m⁻² (

Table 3. Noontime (1100–1400 BJT) averaged values of different variables.

Month	WS (m s−1)	$\mathit{R}\mathit{n}$ (W m−2)	$\mathit{H}$ (W m−2)	$\mathit{L}\mathit{E}$ (W m−2)	$\mathit{G}$ (W m−2)	$\mathit{G}/\mathit{R}\mathit{n}$ /	${\mathrm{u}}_{\ast }$/TKE (m s−1)/(m2 s−2)	UBH (m)
/	2/8/47 m	47 m	47 m	47 m	47 m	47 m	47 m	/
1	1.0/1.5/2.8	288.4	100.2	12.7	175.5	60.9%	0.4/2.4	455.2
2	1.2/1.8/3.5	387.6	132.9	15.8	238.9	61.6%	0.5/3.5	756.3
3	1.1/1.3/2.5	418.7	132.4	22.2	264.1	63.1%	0.3/2.2	615.8
4	1.1/1.4/2.9	541.1	150.2	56.9	334.0	61.7%	0.4/2.7	629.3
5	0.9/1.1/2.7	517.1	120.7	103.5	292.9	56.7%	0.4/2.5	723.3
6	0.9/0.9/2.4	533.7	118.1	112.9	302.7	56.7%	0.3/1.9	676.0
7	0.7/0.9/2.2	392.1	78.0	89.8	222.3	56.7%	0.2/1.4	588.4
8	0.6/0.9/2.0	467.7	68.6	113.4	285.7	61.1%	0.2/1.3	587.5
9	0.7/0.9/2.0	440.0	97.3	87.2	255.5	58.1%	0.2/1.4	492.8
10	0.6/0.9/2.0	269.6	64.7	54.4	150.5	55.8%	0.2/1.1	466.8
11	0.8/1.1/2.4	252.6	71.0	22.2	159.4	63.1%	0.2/1.5	432.3
12	0.8/1.1/2.1	240.1	74.6	12.4	153.1	63.8%	0.2/1.5	393.0

) in April. The variations of the monthly averaged diurnal $H$ generally follow those of $R_n$, reaching a peak of about 164.9 W m⁻² at 11:00 BJT, with an average noon value of 150.2 W m⁻² in April. Note that, as shown in Table 3, although the average noon value of $R_n$ could reach up to 467.7 W m⁻², the sensible heat $H$ was only 78.0 W m⁻² due to the large proportion of latent heat flux $LE$ in Rn. In contrast to $H$, the latent heat flux exhibited strong seasonality, peaking above 100 W m⁻² in May, June, and August, while diminishing significantly below 50 W m⁻² from November through March. The low monthly averaged values of these two heat fluxes in July are primarily due to the frequent rainfall events as depicted in Figure 2b. The sensible heat consistently exceeded $LE$ except during June and August. Moreover, the heat storage estimated by the residual method was the largest amongst the surface energy budget terms over urban surface. The proportion of $G$ in $R_n$ was greater than 50% in all months in 2016 as shown in Table 3, while only about 27% was reported during periods when maximum values of $R_n$ were recorded over a grassland surface in the rural areas of Beijing during July in [24] and an average of 34% between 10:00–14:00 BJT over a suburban site also in Beijing during summer in [27]. Additionally, it was found that the residual term dominated the surface energy balance at this urban site with a daily ratio of 0.68 from June to August 2015 in [27]. This substantial portion of driving energy contributes significantly to the urban heat island effect [28,29]. It is important to note that the higher values of $\mathrm{G}/{\mathrm{R}}_{\mathrm{n}}$ alongside lower values of $R_n$ in winter imply weaker heat exchange conditions, which is conducive to the occurrence of the pollutant events [16].

TKE and friction velocity (${\mathrm{u}}_{\ast }$) are both important quantities used to study the turbulence in ABL. As expected, the seasonal variations of both TKE and ${\mathrm{u}}_{\ast }$ in Figure 2e generally follow those of wind speed. It is apparent that the turbulence-created wind shear and flow are obviously larger during windy and dry seasons than warm seasons, especially in February, which is characterized by strong wind. The UBH, a critical parameter for describing the development of the UBL, was estimated using the method outlined in Section 2.2.2 (data with daily precipitation exceeding 10 mm were not taken into account). As shown in Figure 2d,e, obviously, the monthly averaged diurnal changes were strongly correlated with variations in thermal forcing factors, such as $R_n$ and $H$, exhibiting strong positive correlations with coefficients of approximately coefficient R = 0.8 for $R_n$ and R = 0.7 for $H$. Generally, maximum values of the monthly averaged diurnal data were higher during warm and dry seasons and lower during cold and dry seasons. However, an outlier was observed in the transition month February, in which the maximum value was about 921.0 m. It is well established that the development of the UBL is influenced by both thermal forcing and dynamical forcing factors. In this study, the correlation coefficients between WS and UBH were found to be about 0.8 for the 2 m level, 0.5 for the 8 m level, and 0.6 for the 47 m level throughout the year, and R = 0.8 for both TKE and ${\mathrm{u}}_{\ast }$. Consequently, the peak value recorded in February can be explained by both the substantial sensible heat exchange (noon average value of 132.9 W m⁻² for $H$) and the elevated wind speed noon average value of 1.2 m s⁻¹, 1.8 m s⁻¹, and 3.5 m s⁻¹ at the 2 m, 8 m, and 47 m levels, and the largest values of ${\mathrm{u}}_{\ast }$ and TKE as shown in Table 3.

3.2. Atmospheric Stability Classification Analysis from Richardson Number

In this section, the atmospheric stability variability with season was investigated. It should be noted that seasons are defined by grouping February, March, and April as spring (warm and dry season); May, June, and July as summer (hot and rainy); August, September, and October as autumn; and November, December, and January (cold and dry season) as winter, which differs from traditional definitions. As illustrated in Figure 2b, the rainy seasons in Beijing commenced in May and concluded in October. Furthermore, as mentioned in Section 3.1, the noon average value of $R_n$ reached 387.6 W m⁻² in February alongside the second highest sensible heat exchange over the entire year at 147.1 W m⁻² larger than that observed in December and approximately 99.2 W m⁻² larger than those in January. Given that the thermal forcing is a critical aspect for investigating the structure of UBLs, it is more appropriate to classify February as spring rather than winter. In addition, according to the 24 solar terms used traditionally in China, the beginning of spring (1st of solar term) was on 4 February, beginning of summer (7th of solar term) on 5 May, beginning of autumn on 7 August, and beginning of winter on 7 November in 2016. Therefore, the aforementioned definition of the four seasons mentioned above was adopted.

To assess the stability conditions over the high-density urban areas, a long-term study of $R_i\mathrm{s}$ was conducted, which served as classification bins for the stability regimes described in Section 2.2.1. As indicated in Equation (3), gradients are calculated from the measurements at two distinct heights each. At this site, observations of WS and temperature were collected at 15 levels; thus, $R_i$ can be estimated based on various height intervals that characterize different states of different levels of UBLs. In order to study the state of the UBL from the surface to different observational levels, only those stability regimes classified according to the 14 specific height intervals (e.g., 15–8 m, 32–8 m, 47–8 m, 65–8 m, 80–8 m, 100–8 m, 120–8 m, 140–8 m, 160–8 m, 180–8 m, 200–8 m, 240–8 m, 280–8 m, and 320–8 m) were examined. The seasonal average diurnal cycle of the probability for these stability regimes is classified based on the stability regimes system (as shown in Table 2) with $R_i$ estimated using four different height intervals; 15–8 m and 320–8 m are presented in Figure 3 and Figure 4, and 47–8 m and 140–8 m are provided as Supplementary Material (Figure S1).

This urban site clearly exhibited a distinct diurnal cycle in the probability of stability regimes, as shown in Figure 3, Figure 4 and Figures S1 and S2. As anticipated, the strong unstable regime was predominant during daytime across all four seasons, followed by the unstable regime, with higher probabilities occurring in summer and spring for each of the four different height intervals (the maximum value of the strong unstable regime reached approximately 62% for 15–8 m, 67% for 47–8 m, 70% for 140–8 m, and 92% for 320–8 m). Due to urbanization, a significant proportion of solar radiation is stored in the urban canopy during daytime, as noted in Section 3.1, and subsequently released into the atmosphere through heat exchange during nighttime alongside anthropogenic heat contributions. Consequently, the sensible heat flux remained positive at night during certain periods, as shown in Figure 2d, corroborating findings from previous studies [3,30], which suggest that the unstable conditions often persist at night. Actually, the probabilities of both strong unstable and unstable regimes were highest (exceeding 50%) during nighttime, contrasting with typical natural underlying surfaces. The probability of strong unstable and unstable regimes diminished in winter, when the strong stable UBL was more readily formed. Notably, this was particularly evident for the height interval of 15–8 m, with the largest probability (about 40%). Furthermore, the probability of the strong stable regime generally increased with time during nighttime, reaching its peak at midnight, then deceasing after sunrise. Interestingly, the strong stable regimes (stable regimes) were 10% more prevalent early at 16:00 BJT (15:00 BJT), and 30% (20%) more after sunset for 15–8 m in spring (winter), indicating that shallow surface inversions had been formed in the afternoon in spring and winter, while such phenomena were rarely detected for the upper levels after sunset until midnight. It should be noted that this also implies that an apparent discrepancy exists regarding stability assessments based on measurements taken from varying heights—a finding consistent with those reported by [8,31]. Therefore, care must be exercised when selecting measurement levels to estimate ${ R}_i$.

To gain further insights, the seasonal variations in the occurrence of different states of the UBL for the 320–8 m height interval in four episodes (night, day, and two transitions (day-to-night, defined as two hours after sunset, and night-to-day, defined as two hours after sunrise)) were compared in Figure 5. These two transition episodes are critical for the pollutants’ accumulation and diffusion, with the evening and morning rush hour of transportation [32,33], making it essential to investigate the UBL conditions during these two episodes for accurate pollutant predictions. The highest occurrence of the strong stable regime was about 23% in winter, followed by autumn, at about 13% during the night-to-day episode, indicating that the strong stable conditions can persist around sunrise. Additionally, during summer and autumn, the strong unstable regime was more frequent than the unstable regime. Unsurprisingly, most of the time of the day episode was dominated by the strong unstable condition (for example, approximately 74% during summer), directly resulting from enhanced radiation solar radiation, while the other three episodes exhibited predominantly unstable conditions. It should be noted that, apart from the thermal forcing factor, low wind shear may also be an important contributor. Liu et al. (2018) [25] pointed out that maximum values of wind speed at lower levels (e.g., 8 m and 15 m) typically occur during daytime, whereas higher levels (e.g., 280 m and 320 m) experience peak values during nighttime. Thus, it can be concluded that minimum wind shear usually occurs during daytime, while the maximum value is observed at nighttime. This phenomenon can result in noticeable nocturnal jet occurring within a few hundred meters above the ground [6]. It was surprising to find that about 3% of strong stable regimes occurred during the day episode in winter. Further studies should be conducted regarding the following. The occurrence of the neutral condition was considerably less frequent than others, with its highest probability reaching only about 7% during both the night and night-to-day episodes.

In order to explain the difference in probability between various episodes for the strong stable regime mentioned above, the probabilities of the strong stable regime and temperature differences for the strong stable regime cases between all of the 14 different height intervals, winter for instance, are described in Figure 6. Consistent with results presented earlier in Figure 4, it is evident from Figure 6 that the probability of the strong stable regime during winter approached nearly 30% for the day-to-night episode, and exceeded 35% for both the night and night-to-day episodes at 15–8 m with ${\displaystyle \frac{\Delta \mathrm{T}}{\Delta \mathrm{z}}}>0.035$ K m⁻¹, while it was lower than 20% for the other height intervals, with ${\displaystyle \frac{\Delta \mathrm{T}}{\Delta \mathrm{z}}}$ < 0.02 K m⁻¹ in the day-to-night episode. Especially for the upper levels, surface inversions were rarely observed during the day-to-night transition episode. This means the ground-level inversion depths were typically very shallow and lower than 100 m even under very stable conditions at this urban site during the day-to-night transition episode. Yu et al. (2023) [34] reported that an evident early morning temperature inversion was observed in the 1980s below 80 m during winter and 32 m in the 2000s in Beijing. In our case study, only the 15–8 m height interval exhibited a relatively high frequency of surface temperature inversions, suggesting the increasing density of urban buildings has progressively weakened stability within the surface layer. The occurrence of strong stable regimes was more frequent at night compared to those occurring during night-to-day transitions across height intervals from 15–8 m to 160–8 m, and conversely for other height intervals, indicating thick surface inversions mostly occurred around sunrise in winter. Interestingly, the presence of a strong stable regime was also noted during the daytime episode, consisting with the findings from Figure 5. Moreover, slightly stronger (${\displaystyle \frac{\Delta \mathrm{T}}{\Delta \mathrm{z}}}>0.01$ K m⁻¹) and thicker surface inversions were identified as well. A further study is made in Section 3.3.

3.3. Drivers of Atmospheric Stability

For the remainder of this study, we analyzed the characteristics of several variations according to the stability regimes defined by the 320–8 m height interval. This height range effectively captures the bulk state of the UBL from surface levels up to 320 m, which can also avoid some complex flow at lower levels over complicated surface conditions [35]. The WS ranges at both 8 m and 47 m for each stability regime across different episodes and seasons are presented in Figure 7 and Figure 8, respectively. Generally, wind distribution patterns for different stability regimes during all four episodes and seasons were similar for both 8 m and 47 m. The stability increased as wind speed decreased, and mostly the strong stable and strong unstable regime predominantly occurred during very weak wind, about 0.6 m s⁻¹ for the 8 m level and 1.1 m s⁻¹ for the 47 m level during the night and night-to-day episodes for the mean of wind speed in four seasons, and around 0.9 m s⁻¹ for the 8 m level and 1.7 m s⁻¹ for the 47 m level during the day and day-to-night episodes. Note that mostly, unstable regimes primarily manifested under higher wind speeds, and these features were more pronounced in spring and winter compared to summer and autumn, mainly due to stronger winds prevalent in the former. For unstable regimes, mean wind speeds were about 1.8 m s⁻¹ (1.2 m s⁻¹) for spring and winter, and around 1.1 m s⁻¹ (0.8 m s⁻¹) for summer and autumn at the 8 m level during the day (night) episode. Correspondingly, for 47 m, values were about 3.6 m s⁻¹ (2.5 m s⁻¹) for spring and winter, and around 2.7 m s⁻¹ (1.8 m s⁻¹) for summer and autumn during the day (night) episode.

Radiation is another critical parameter influencing surface stability. The range of net radiation $R_n$ of the 47 m level for each stability regime across different episodes and season was also investigated and is displayed in Figure 9. Generally, the stability became increasingly unstable with rising net radiation, which suggests that the thermal factors play a more important role in stable conditions. The large difference of net radiation between the strong unstable and unstable regimes was around 125.0 W m⁻² (mean value) approximately during autumn and summer. Note that $R_n$ under the strong stable regime was slightly lower than that of the stable regime during the day episode in spring and winter. Specifically, the mean value of $R_n$ reached about 329.4 W m⁻² (204.2 W m⁻²) for the unstable regime, while it was about 301.5 W m⁻² (177.4 W m⁻²) for the strong unstable regime in spring (winter). The very strong regime observed during the day episode occurred under limited net radiation (a mean of 54.7 W m⁻²) conditions. This unusual condition of the UBL featuring strong stable regimes during daytime throughout the year was identified on six occasions: 2 January, 2 March, 5 November, 4 December, and 19–20 December 2016. Given that air pollutants can modify radiative transfer processes and then affect the surface energy balance [14], this factor serves as an important contributor to the state of the UBL. Wang et al. (2019) [21] investigated a severe heavy pollution event which occurred during 1–4 December 2016, in Beijing, and stated that it was related to the long-term (>12 h) existence of temperature inversion resulting from the combined effects of aerosols and clouds. In this study, besides the case on 4 December 2016, all other cases were also associated with significant pollution levels, as shown in

Table 4. The start and end time of the strong stable regime for the cases during daytime and the averaged values of the PM₁₀ mass concentration during the strong stable conditions in 2016, Beijing.

Number	Start Time (BJT)	End Time (BJT)	Averaged PM10 (μg m−3)
1	00:00 1 January	10:45 2 January	271.6
2	23:00 1 March	11:45 2 March	315.8
3	19:05 4 November	11:05 4 November	185.2
4	00:00 4 December	12:00 4 December	414.3
5	22:00 18 December	10:20 19 December	257.0
6	18:00 19 December	11:15 20 December	296.3

. Moreover, the strong stable state of the UBL persisted for more than 17 h during the period from early evening at 18:00 BJT on 19 December until 11:15 BJT on 20 December, with high concentrations of PM₁₀ mass (average value, 296.3 μg m⁻³). Given that two instances featuring strong stable regimes were identified during the daytime from 15 to 20 December, a case study was performed to explode the effect of the different factors on atmospheric stability. As shown in Figure 10, a long, serious pollution event occurred during this period. The maximum value of $R_n$ reached was about 380.0 W m⁻² for the clean condition with low concentrations of PM₁₀ on 15 December, while $R_n$ was reduced by 5.9% on 16 December, a day of light pollution, and around 40.0% on 17–18 December, days of heavy pollution, and more than 54.2% on 20 December. Moreover, the duration of the strong stable regime (temperature inversion) was extended from 4 h to 17 h with the worsening of pollution levels. This extension was also accompanied by weak wind and extremely limited vertical mixing. Recurrent unstable regimes were observed on the clean day, 15 December, characterized by high values of $R_n$, strong northwest winds and vertical mixing, and strong unstable regimes with lower WSs, which is consistent with the previous results from Figure 6, Figure 7 and Figure 8. Compared to the unstable regimes, the strong stable regimes were more beneficial to pollution formation, due to weak vertical mixing. It also should be noted that, besides the atmospheric stability, the aggravation of air pollution is also influenced by significant emissions and various meteorological conditions (e.g., wind speed and humidity). In addition, some low-level jets were identified under the strong stable condition. One deep low-level jet was observed at the level from 200 m to 600 m in the early morning on 20 December, which contributed to the relative high vertical turbulence as shown in Figure 10c. While near the surface, the vertical mixing was still very limited with weak wind (weak dynamic forcing), and compared to the clean windy day of 15 December, the development of the boundary layer exhibited a noticeable delay. The UBL reached 200 m early at 09:00 BJT on 15 December, while it was observed around 12:00 BJT on 18 December and 20 December. Thus, combined with Figure 6b, all six cases exhibiting strong stable regimes during the day episode can be partly attributed to elevated pollutant concentrations, which prolonged the temperature inversion duration due to enhanced radiative cooling effects and very weak wind, and delayed the development of the UBL after sunrise.

As a result, in conjunction with the findings presented in Figure 8, we found that the unstable regime occurred under high wind and large net radiation conditions for the day episode in spring and winter. This suggests that both thermal and dynamic forcing significantly contribute to the turbulence generation in these two seasons. The characteristics of vertical profiles of wind and temperature classified by stability regimes, as shown in Figure 11 (taking winter as an example), provided evidence supporting this implication. Apparently, the strong unstable regime and unstable regime differed markedly in terms of wind shear strength at this urban site while exhibiting similar temperature differences across all study episodes, implying that the unstable regime was characterized by strong dynamic instability. However, both the strong stable and strong unstable regimes reflected weak dynamic instability. This characteristic was also noticed between the strong stable and stable regimes in the three episodes, except for the day episode. However, the main difference in these two inactive conditions was the strength of the surface inversion temperature for the day episode, a rare situation throughout the year, in 2016. Furthermore, as illustrated in Figure 7 and Figure 11, strong wind speed accompanied by significant differences in wind profiles (between 320 m and 8 m), suggest that the wind speed plays a particularly crucial role in distinguishing strong unstable (strong stable) and unstable (stable) regimes most of the time. This can also explain why the dominating probability was the unstable regime in spring, characterized by greater wind speed, as shown in Figure 2 and Table 3 for all episodes displayed in Figure 5.

3.4. Turbulence and UBH Features Based on Stability Regime

To conduct a further study, the ranges of TKE and UBH (representing the vertical mixing strength) based on each regime, as displayed in Figure 12 and Figure 13, were analyzed. TKE and UBH followed a similar trend to wind speed (illustrated in Figure 7) with respect to stability. Strong TKE and high UBH occurred in the unstable regime and decreased with increasing stability. The maximum of the mean value of TKE (UBH) occurred in the unstable regime during spring, reaching 2.8 m² s⁻² (702.5 m), accompanied by peak wind speeds of 1.8 m s⁻¹ at the 8 m level and 3.6 m s⁻¹ at the 47 m level during the day episode. As discussed previously, heavy wind conditions are characterized by strong wind shear over this highly rough urban surface, combined with elevated TKE, suggesting the extreme importance of mechanical turbulence generation. Based on the measurements collected from an urban site in London, Halios and Barlow (2019) [30] estimated the buoyancy and shear production terms using the local TKE budget equation, and they emphasized that the contribution of shear production to TKE should not be overlooked, even in low-wind conditions. In this study, the shear production and the buoyancy terms using the local TKE budget equation were estimated based on different wind classes, e.g., weak, moderate, and strong wind during winter (Figure S3). Results showed that with the increasing wind classes, the wind shear production showed an obvious enhancement. For the weak wind class, the buoyancy production term was very weak (negative or close to zero), during the whole night, and mostly lower than the wind shear production term. This finding is consistent with the results presented in Figure 10b,c of Section 3.3 by using the measurements from Doppler lidar. Additionally, moderate radiation combined with strong wind speeds resulted in a high UBH, which helps explain the greatest UBH in February, as discussed in Section 3.1. Under unstable regimes, the mean value of UBH was 516.9 m, 124.5 m, 208.4 m, and 257.7 m during the day, night, night-to-day and day-to-night episodes in winter (the essential season for pollutant events), respectively; 323.0 m, 109.7 m, 122.7 m, and 141.1 m under the strong stable regime; 137.8 m, 84.6 m, and 98.7 m under the stable regime (no cases during the day-to-night episode); and only 106.7 m, 58.3 m, 76.5 m, and 123.7 m under the strong stable regime. These variations of UBH and TKE across different regimes can also elucidate why pollution events tend to occur more readily during stable conditions. In addition, as a dynamic factor, the friction velocity was also investigated. Similar to TKE, the friction velocity also exhibited a comparable trend to that of wind speed (figure omitted).

4. Discussion

Urban centers characterized by large impervious fractions and dense concentrations of tall buildings, such as the studied site (Figure 1), definitely can change the surface energy balance and the vertical profile of the wind, resulting in greater heat store and wind shear over urban areas than rural underlying areas [14,36]. And this influence may vary in degree under different wind speed conditions. The storage heat flux is a significant component of the energy balance at all of the urban sites studied. Grimmond and Oke (1999) [37] informed that the storage heat flux accounts for 17–58% of the daytime net radiation, by using data in seven urban areas within Canada, the United States, and Mexico. The substantial urban volume exhibits a significant net warming effect; however, the potential for observational errors should also be acknowledged. Nevertheless, the values presented in our paper are comparable to those from other urban locations characterized by tall buildings and/or extensive impervious surfaces in various countries, as detailed in Table S1 of the Supplementary Materials File. Moreover, Sun et al. (2017) [38] first simulated the proportion of the residual term in SEB by a model (AnOHM) at four urban sites, and they reported that, at all sites, lower WSs consistently led to an increase in this proportion and vice versa, and the residual terms are around 60% of the net radiation at both the Beijing and London urban sites. To a certain extent, this result can support our findings in Table 3.

The largest boundary layer height magnitude was also found in spring based on micro-pulse lidar observations from 2013 to 2018 in the Beijing urban area in [39], which is consistent with our results. They suggested that the large radiation in spring may be the main contributor. In our study, we further found that although the largest amount of net radiation was in April, the maximum value of the UBH in spring occurred in February and was characterized as having the strongest wind, largest TKE, and ${\mathrm{u}}_{\ast }$, which implies the important role of dynamic forcing on the development of the UBL. The monthly averaged diurnal changes were strongly correlated with variations in thermal forcing factors (e.g., ${\mathrm{R}}_{\mathrm{n}}$ and $\mathrm{H}$) and dynamic factors (e.g., wind speed, turbulence kinetic energy (TKE), and friction velocity ${\mathrm{u}}_{\ast }$), exhibiting strong positive correlations with coefficients of approximately R = 0.8 for ${\mathrm{R}}_{\mathrm{n}}$, R = 0.7 for $\mathrm{H}$, and R = 0.8 for WS, TKE, and ${\mathrm{u}}_{\ast }$. Yang et al. (2020) [22] analyzed the diurnal cycle of the UBH to investigate the development of the UBL and its potential drivers in urban Beijing, based on a 40-day measurement under different wind conditions in winter. They concluded that under weak WS conditions, the pattern of the UBH was primarily modulated by thermal forcing of solar radiation, with some degree of modulation attributed to the dynamic forcing of WS. While for strong wind conditions, the pattern of the UBL height was largely modulated by dynamical forcing. This study provides further examples supporting their findings. Note that the values of the UBH in our study are lower than those reported by [39]. In their work, they derived the UBH from an analysis of aerosol distribution, whereas we estimated it based on the variance of mechanical turbulence. Consequently, the definitions of UBH differ between these studies, and it is not surprising that estimates obtained using different instruments yield varying results. Each method demonstrates effective performance only within specific meteorological conditions. Consequently, the integration of multiple methods and instruments may enhance our ability to characterize the complete diurnal cycle of complex UBL structures [39,40].

The results obtained herein also further substantiate previous findings, indicating that atmosphere stability is contingent upon wind speed [41,42], and similarly, it was noted that faster wind speeds likely contribute to mechanical mixing near the surface, which works to weaken near-surface stability and deepen the ABL [43]. Consequently, wind speed near the surface was also an important criterion to define the stability in some studies [44], and can also be used to divide the weak stable and strong regimes of the nocturnal boundary layer [45,46]. Note that the widely used Pasquill method [47] defines a strong unstable regime as when the wind speeds at 10 m level exceed 2.0 m s⁻¹ during daytime. However, based on the results in our study, the wind speed threshold at the 8 m level may be around 1.0 m s⁻¹, influenced by the presence of tall buildings. Therefore, utilizing wind speed at higher levels may be a more reasonable method of classifying the different regimes in this simplified method for the UBL. In situations where data are limited, it can be quite challenging to differentiate between strong and weak stable regimes during nighttime. The analyses in this study provide a certain reference for this classification over urban surface lying.

Broadly, our findings provide scientific observational evidence for understanding the occurrence of the stability classifications and their diurnal variations, as well as their potential drivers in urban Beijing and provide insight into understanding the changing of the flow and turbulence above the urban surface during different stability phases of the UBL, which can assist in developing and evaluating urban climate models. Furthermore, our results indicate that urban greening is a vital strategy to mitigate the significant heat storage capacity of impervious urban surfaces. This information can inform urban planning strategies aimed at achieving enhanced cooling benefits amid rapid global urbanization. Moreover, considering that wind speed plays a crucial role in the transfer of pollutants, our findings suggest that prioritizing urban ventilation capacity should be an essential aspect of city planning and development processes.

5. Conclusions

In this study, the diurnal and seasonal variations in the characteristics of thermodynamic drivers of UBL, as well as the frequencies of different stability regimes and their interrelationships, were investigated using measurements primarily obtained from a meteorological tower and a Doppler lidar at an urban site throughout 2016. Four episodes spanning entire days across various seasons were selected to provide a more detailed analysis of these investigations. Overall, several key conclusions emerge:

(1) Our analysis revealed that wind speeds in spring and winter were faster than those in summer and autumn in Beijing, with the monthly averaged diurnal net radiation ranging from 240.1 W m⁻² (December) to 541.1 W m⁻² (April), averaged at noontime. The sensible heat flux was positive during certain nighttime periods. The heat storage estimated by the residual method was the largest amongst the surface energy budget terms over the urban surface (larger than 50%) in all months in 2016. The monthly averaged diurnal change of the UBH had a strong positive correlation with the dynamic factors (e.g., wind speed, turbulence kinetic energy, and friction velocity), and thermal forcing factors, (e.g., net radiation and sensible heat flux). The maximum value of UBH occurred in February, characterized by the second-largest sensible heat exchange and the strongest wind speed, turbulence kinetic energy, and friction velocity during spring.

(2) The probability of the stability regime occurrence exhibited a distinct diurnal cycle. The probability of a strong stable regime was higher in winter and autumn compared to spring and summer, increasing with time during nighttime, typically peaking during the night-to-day transition episode. It is worth noting that about 3% of the strong stable regimes occurred during the day episodes in winter. The occurrence of the stable regime was rare, with its highest frequency reaching only 4% during the night-to-day episodes in autumn. The maximum probability of a neutral regime was only about 7% during night and similar for the night-to-day episodes in autumn. The strong unstable regime had the highest probability, followed by the unstable regime during daytime. Conversely, during nighttime, the unstable regime represented the largest proportion, with the strong unstable regime following. Furthermore, the probabilities of both strong unstable and unstable regimes were the largest (over 50%) during nighttime because the large heat storage of the urban terrain was released to heat the air by heat exchange during nighttime. This suggests that an increase in building density leads to a more unstable surface layer.

(3) The strong stable regime predominantly occurred under very low wind conditions (around 1.0 m s⁻¹ at the 47 m level, averaged during the night episodes throughout the whole year). The very strong stable regime occurred in the day episode characterized by limited net radiation (mean of 54.7 W m⁻²), primarily due to the high pollutant concentrations. Additionally, the weak wind speed and minimal vertical mixing further contributed to this persistent UBL. The strong unstable regime primarily occurred under very weak wind conditions (around 1.8 m s⁻¹ at the 47 m level, averaged during the day episodes throughout the whole year) and significant radiation conditions (ranging from 177.4 W m⁻² to 326.7 W m⁻² during different seasons for the day episode). The unstable regime manifested in high wind alongside substantial radiation environments (ranging from 193.3 W m⁻² to 329.4 W m⁻² during different seasons for the day episode). Thus, the unstable regime was under strong dynamic instability while the strong unstable regime was under weak dynamic instability for in all study episodes, highlighting the critical role of wind speed in distinguishing active or inactive conditions of the UBL.

(4) The values of TKE and UBH were larger in active conditions than inactive conditions. Compared with other regimes, the unstable regime was characterized by large values of TKE and UBH, implying the critical importance of mechanical turbulence generation during strong wind conditions. The maximum of the mean value of TKE and UBH could reach 2.8 m² s⁻² and 702.5 m accompanied by the strongest wind speed (1.8 m s⁻¹) during the day episode in spring. Mostly, the weakest mean value of TKE under the strong stable regime during the day episode occurred in winter, about 0.25 m² s⁻² accompanied by a UBH of 106.7 m, due to both weak thermal forcing (e.g., limited solar radiation) and dynamic forcing (e.g., very weak wind at the surface).