The fundamental principle for probing atmospheric vertical structures using a Raman–Mie scattering lidar is based on the lidar equation, which involves the theories of Mie–Rayleigh scattering, rotational Raman scattering, and vibrational Raman scattering. This can be represented by Eqs. ()–(). Specifically, rotational Raman scattering is used for temperature measurements, while Mie–Rayleigh scattering and vibrational Raman scattering are employed for retrieving aerosol optical properties and water vapor profiles. 1Pr(T,z,λr)=Crz2βr(T,z,λr)×exp⁡-∫0zα(z′,λe)+α(z′,λr)dz′ 2Pv(z,λv)=Cvz2βvz,λv×exp⁡-∫0zα(z′,λe)+α(z′,λv)dz′ 3Pe(z,λe)=Cez2(βa(z,λe)+βm(z,λe))×exp⁡-2∫0zα(z′,λe)dz′ where Pr, Pv, and Pe denote the rotational Raman, vibrational Raman, and elastic backscattering signals, respectively. C represents the system constant of the lidar, which includes the laser power, telescope receiving area, optical transmittance, and detector quantum efficiency. λ, T, and z refer to the wavelength, temperature, and height, respectively, while α and β denote the volume extinction and backscattering coefficients. The subscripts e, rh, rl, vw, and vn correspond to the Mie–Rayleigh signal, high-quantum-number rotational Raman signal, low-quantum-number rotational Raman signal, water vapor vibrational Raman signal, and nitrogen vibrational Raman signal, respectively, whereas m and a represent the molecular and aerosol components. The atmospheric extinction coefficient can be derived from the nitrogen vibrational Raman signal (Pvn), while the backscatter ratio (BR) is obtained in combination with the Mie–Rayleigh scattering signal. Finally, the aerosol backscatter coefficient can be retrieved, as expressed in Eqs. ()–(). 4αa(z,λe)=dln⁡N(z)z2Pvn/dz-αm(z,λe)-αm(z,λvn)1+(λe/λvn)K5Br(z,λe)=FCvnCePe(z,λe)Pvn(z,λvn)×exp⁡∫0z[α(z′,λe)-α(z′,λvn)]dz′6βa(z,λe)=Br(z,λe)⋅βm(z,λe)-βm(z,λe)

In Eq. (), N(z) and K represent the atmospheric molecular number density and the Ångström exponent, respectively, which is typically taken as 1. In Eq. (), F denotes the system constant used for calculating BR. The rotational Raman temperature retrieval is based on the correlation between the rotational Raman signal and atmospheric temperature. By extracting two rotational Raman backscattering signals with different temperature sensitivities, a functional relationship between their signal ratio and temperature can be established to derive the atmospheric temperature profile. However, the rotational Raman channels are highly susceptible to elastic scattering cross-talk, which may introduce biases in the temperature retrieval. In Eq. (), A and B are system constants used for temperature retrieval. Mh and Ml represent the elastic scattering cross-talk coefficients for the high- and low-quantum-number rotational Raman channels, respectively. The water vapor and nitrogen vibrational Raman scattering signals are extracted, and their ratio is calculated. Based on radiosonde data obtained under the same temporal and spatial conditions, a regression relationship for data retrieval is constructed, enabling the lidar measurement of the water vapor mixing ratio and, consequently, the derivation of relative humidity, as expressed in Eq. (). The aforementioned measurement principles are well established, and detailed descriptions can be found in previous studies . 7T(z)=A/ln⁡Crl(z)Crh(z)Prh(T,z,λrh)+Mh⋅Pe(z,λe)Prl(T,z,λrl)+Ml⋅Pe(z,λe)-B8W(z)=CvnCvwPvw(z,λvw)Pvn(z,λvn)×exp⁡∫0zα(z′,λvw)-α(z′,λvn)dz′

Under atmosphere conditions with cloud layers or high aerosol concentrations, due to the close spectral intervals, strong elastic scattering can cause elastic scattering cross-talk in the low-quantum-number rotational Raman channel, and even in the high-quantum-number channel. This means that a portion of the elastic scattering signal is mixed into the rotational Raman channels, which leads to significant deviations in data retrieval, and in severe cases, preventing accurate temperature retrieval within the haze layer. Since haze layers are generally located at low height, the geometric overlap factors of each lidar channel are not identical, which also causes large uncertainties in temperature retrievals in the lower atmospheric region. Therefore, temperature measurements in haze layers mainly include three processes: geometric overlap factor correction, rotational Raman ratio correction, and temperature retrieval.

The atmospheric temperature correction technique is based on establishing a linear relationship between the backscatter ratio and the elastic-scattering crosstalk ratio, which allows the rotational Raman ratio to be corrected using the measured backscatter ratio. Figure  illustrates the temperature retrieval process based on this algorithm. First, a high-altitude region unaffected by the geometric overlap factor is selected, and radiosonde temperature profiles are used for system calibration. Under clear-sky and dry near-surface conditions, the theoretical rotational Raman ratio is derived from radiosonde data (black dash–dotted line in Fig. a). By comparing it with the measured Raman ratio (blue solid line in Fig. a), the geometric overlap factor is obtained (red solid line in Fig. b), enabling overlap correction. Next, the theoretical Raman ratio under strong elastic-scattering conditions is derived from radiosonde data (black dash–dotted line in Fig. d). The measured Raman ratio (black solid line in Fig. d) is then used to calculate the elastic-scattering crosstalk ratio. A linear regression between the backscatter ratio and the crosstalk ratio is performed to determine the system calibration constant (Fig. e). Using this constant together with the measured backscatter ratio, the rotational Raman ratio is corrected, enabling retrieval of the atmospheric temperature profile within the elastic-scattering region (Fig. f). A linear regression between the corrected lidar temperature and the radiosonde temperature yields a coefficient of determination (R2) of approximately 0.8 (Fig. g), indicating good agreement between the two measurements. A detailed description of the algorithm can be found in .

The vertical velocity used in this study was derived from the vertical pressure tendency provided by ERA5. Atmospheric static stability is governed by buoyancy, which in turn influences the vertical distribution of aerosols. In this study, the buoyancy acceleration was estimated using an approach based on the environmental virtual potential temperature. This method assumes small perturbations and linearization, making it suitable for weakly disturbed conditions. Under strong perturbations, however, it may underestimate the actual buoyancy. Nevertheless, the estimated values can reasonably capture the overall trend of changes in thermodynamic stability. Buoyancy is expressed as 9B=d2z0dt2=-gΔz1θdθdz0 where z0 denotes the height of the air parcel, and t represents time. θ is the virtual potential temperature of the environment, which is calculated using radiosonde pressure combined with the lidar-measured atmospheric temperature and water vapor mixing ratio. A positive buoyancy indicates a convective atmospheric layer, whereas a negative buoyancy corresponds to a stable layer. When the buoyancy approaches zero, the atmospheric column is neutral.

According to the theory of error propagation, the uncertainty of buoyancy acceleration can be expressed as: 10δB=∂B∂Γ2δΓ2+∂B∂Γ2δθ2 In the formula, Γ=dθ/dz0. The lidar system exhibits a high signal-to-noise ratio within the detection range below 4 km at night (2 km during daytime), and the temperature uncertainty is typically less than 0.5 K. Selecting typical boundary layer conditions with a virtual temperature of approximately 280 K and a conservative uncertainty of 0.5 K, when the vertical resolution is 37.5 m, the uncertainty of the temperature gradient obtained is approximately 0.019 Km-1, and the uncertainty of the buoyancy acceleration is calculated to be approximately 0.025 ms-2. This value represents the worst-case scenario assuming completely uncorrelated errors. Lidar temperature errors exhibit strong vertical correlation, and buoyancy is essentially derived from vertical gradients. Therefore, the effective uncertainty in buoyancy is substantially smaller. Although this uncertainty may affect very weak buoyancy signals near neutral conditions, the identification of stable layers and strong inversions is robust.

The aerosol layer boundary was identified using a gradient-based method applied to BR. The fundamental principle of this method is to locate positions exhibiting pronounced discontinuities in the BR profile by calculating its vertical derivative. As this study primarily focuses on the relationship between the aerosol vertical structure and temperature distribution, only the upper boundary of the aerosol layer (hereafter referred to as UABL) was determined, without further distinction of the stable boundary layer, mixed layer, and residual layer.

First, the first derivative of the BR profile (i.e., BR gradient) was calculated, and the negative-gradient intervals of BR (hereafter referred to as NIBRs) were identified based on the zero-crossing points of the derivative. To eliminate local perturbations and high-frequency noise, threshold conditions (>60m) were applied to both the NIBR lengths and the spacing between adjacent NIBRs, ensuring that only valid NIBRs were retained. Similarly, the positive-gradient intervals of BR (hereafter referred to as PIBRs) were identified through zero-crossing detection and filtered with the same threshold criteria. Second, gradient thresholds were defined for both PIBRs (>3km-1) and NIBRs (<-3km-1). In addition, a minimum BR deviation threshold within each interval (|ΔBr|>0.35, defined as the absolute deviation between the maximum and minimum BR within the interval) was imposed to exclude pseudo-transition zones with weak gradients. When the length of a positive interval satisfying the gradient threshold exceeded 30 m, it indicated a notable enhancement of aerosol concentrations within that layer. In such cases, the adjacent negative interval immediately above was retained even if it did not meet the gradient threshold. Finally, the UABL was determined within NIBRs using a BR threshold of 1.3. Starting from the top of each NIBR, one-eighth of its length was used as the reference range. If the maximum BR within this range exceeded 1.3, the height corresponding to one-eighth of the NIBR length below the top was defined as the UABL. Otherwise, the height at which the BR first exceeded 1.3 within NIBRs was identified as the UABL.

TI features were identified using a gradient-based method. Unlike conventional gradient methods, the raw temperature profile was first subjected to linear feature fitting prior to calculating the vertical temperature gradient. The fitting employed the piecewise linear interpolation method proposed by , which constructs an interpolation function with variable segment lengths and minimizes an associated error function to obtain optimal fits for each segment, thereby accurately resolving TI layers.

The first derivative of the fitted temperature profile (i.e., the vertical temperature gradient) was then calculated, and the positive-gradient intervals of temperature (hereafter referred to as PITs) along with their adjacent gap layers were identified using zero-crossing points. Threshold conditions (>60m) were applied to both PIT lengths and gap layers to retain only valid segments. Gap layers shorter than the threshold were merged with adjacent PITs to form a single TI layer. Conversely, PITs shorter than the threshold, when adjacent to gap layers exceeding the threshold, were discarded as likely resulting from minor perturbations or weak TI features. To prevent underestimation of TI thickness, additional criteria were applied to isolated PITs. If a gap layer exceeded the threshold length and its mean vertical gradient exceeded -0.5Kkm-1, or the maximum temperature deviation within the gap layer was less than 0.5 K, indicating nearly uniform temperature with height, the adjacent PITs were merged. PITs satisfying these conditions were thus considered valid TI layers. The base and top of each TI layer were defined as the TI base and TI top, respectively. The vertical distance between TI base and top represents TI thickness. The equivalent vertical temperature gradient was then calculated from the temperature difference within TI layer.

The dominant phase of the pollution development stage occurred from 22–28 December. Figure  shows the vertical distributions of aerosols and temperature during this period, including profiles in the morning and evening, and daily averages. Over the course of the stage, the vertical distributions of aerosols and temperature underwent persistent changes. At the early stage of pollution, the aerosol vertical structure was primarily characterized by a decreasing profile with height, or alternating patterns of decreasing and well-mixed near-surface layers. The temperature vertical structure exhibited pronounced diurnal variations. During periods of severe pollution, the aerosol vertical structure became well-mixed, and the diurnal variations in both aerosol and temperature distributions were not significant. On the evening of 22 December (in Fig. a), the backscatter coefficient below approximately 0.7 km was significantly higher than in the morning, while above 0.7 km it was lower than the morning values. The base heights of the elevated TI layer in the morning, noon, and evening were approximately 1.3, 1.1, and 0.7 km, respectively. Subsequently, a surface-based TI layer with a thickness of about 1 km developed, strongly inhibiting the vertical diffusion of aerosols. It should be noted that the description of the surface-based TI layer here refers only to the region above the reliable temperature retrieval height (>120m). This surface-based TI persisted until 24 December, resulting in a stable and well-mixed aerosol layer below 0.5 km. On 25 December, surface heating due to solar radiation promoted vertical aerosol mixing, but also led to the formation of a dome-like aerosol layer around 1.1 km, producing a dome effect that enhanced the TI at this height and restricted aerosols below approximately 1.0 km. Notably, under heavy pollution conditions, the lower atmosphere did not experience a strong TI, but the temperature gradient below 0.8 km was about 3.5 Kkm-1, indicating a stable atmospheric state. The vertical diffusion of aerosols was further limited by the elevated TI layer above, confining aerosols to below the TI height.

Figure  presents the hourly vertical profiles of aerosols and temperature during the early stage of aerosol accumulation. The UABL height exhibited a strong positive correlation with the TI layer and a negative correlation with surface PM2.5 concentrations. On 21 December, during the pollution brewing stage, a pronounced stratification was observed at heights of 2–3 km. From the morning of 21 to 22 December, a significant TI layer occurred between approximately 1.5 and 2.5 km, inhibiting the upward transport of aerosols. However, because the TI layer was relatively elevated, vertical transport below its base remained possible, resulting in a decreasing aerosol profile, with higher concentrations near the surface that decreased with height. The average PM2.5 concentrations near the surface remained below 50 µgm-3, indicating good air quality. During the daytime of 22 December, cloud cover significantly reduced downward radiation fluxes (in Fig. b), which directly affected near-surface radiative heating and enhanced the stability of the lower atmosphere, limiting the vertical diffusion of water vapor and aerosols. In addition, the residual layer produced a dome effect, causing pronounced warming above approximately 1 km around noon and strengthening the TI in this layer. The elevated TI induced downward buoyancy acceleration, further reducing the UABL height and confining free vertical convection to below approximately 0.9 km (in Fig. ). Moreover, from 21–22 December, winds below 500 m were predominantly northeasterly at 5–10 ms-1. In winter in Xi'an, such northeasterly winds are typically associated with pollution transport, initiating the first aerosol accumulation on the afternoon of 22 December. After sunset, a stable layer developed below approximately 1 km, favoring the accumulation of aerosols in the near-surface layer. The vertical structure of near-surface aerosols transitioned from a decreasing profile to a well-mixed profile, in which concentrations remained nearly constant with height. On 23 December, weak and variable winds (<3ms-1) prevailed near the surface, while cloud cover continued to inhibit radiative transfer, maintaining a stable TI structure. Surface PM2.5 concentrations continued to increase. Considering the buoyancy conditions during this period, the vertical convection range was substantially compressed. Thus, the subsidence of the TI at the UABL, combined with cloud radiative forcing, appears to jointly constrain the vertical convective scale during the early stage of pollution and may be a primary factor contributing to aerosol accumulation.

During the mid-stage of pollution development, the vertical structure of aerosols exhibited a well-mixed profile, although the boundary layer remained relatively high, reaching approximately 1 km. As shown in Fig. a, from 25–27 December, cloud cover was minimal, yet the total downward radiation flux decreased daily, which may be associated with the radiative forcing of aerosols. At noon on 24 December, aerosols were primarily concentrated near the surface, potentially favoring the onset of the stove effect. However, the radiosonde temperature profile on the morning of 24 December (Fig. f) indicates the presence of a near-surface inversion, which may delay surface warming and the development of turbulence in the lower atmosphere and could partly explain the relatively small variation in surface PM2.5 concentrations. Starting at 12:00 CST (China Standard Time, UTC+8) on 25 December, a pronounced aerosol layering was observed around 1.1 km. This layer persisted for 12 h with a thickness of 200 m. After sunset, surface radiative cooling led to a decrease in near-surface saturation vapor pressure and an increase in relative humidity, providing favorable conditions for aerosol hygroscopic growth and accelerating liquid-phase and heterogeneous reactions . Consequently, both surface PM2.5 concentrations and aerosol optical parameters increased significantly during the early hours of 26 December.

From noon on 28 December, cloud cover reduced downward radiation fluxes, allowing aerosols to continue accumulating near the surface. During this cloud episode, the occurrence of virga (in Fig. a and c) further enhanced aerosol hygroscopic growth, which could contribute to haze formation and the intensification of pollution. In the afternoon of 29 December, a brief urban heating effect was observed, which could partially enhance turbulent diffusion. However, the limited duration of solar radiation and relatively weak horizontal advection restricted the removal of aerosols. At night, surface pressure decreased, leading to pronounced convective subsidence. Under conditions of high relative humidity, PM2.5 concentrations and aerosol optical parameters reached their peak values.

Furthermore, three persistent “capping inversion” layers with a dome-like structure were observed during the pollution development stage and are hereafter referred to as dome-type TIs, as indicated by the green dashed regions in Fig. d. The identification of dome-type TIs relies primarily on the geometric structure of the vertical temperature profiles and the corresponding aerosol-layer stratification. A comparison with Fig. o shows that the daily mean surface PM2.5 concentrations tend to increase as the dome height decreases and decrease as the dome height increases. Although the dome height on 28 December was relatively high, severe pollution was still observed, suggesting that factors such as aerosol hygroscopic growth under high relative humidity may have contributed.

The hourly evolution of the aerosol vertical structure, atmospheric temperature, and buoyancy acceleration on 25 December is shown in Fig. a. Figure b presents the variations in temperature tendency, temperature gradient, and TI depth of the elevated TI layer. Figure c shows the aerosol heating rate, which is approximately estimated using a simplified shortwave heating formulation in the vertical direction (Q=1/(ρcp)⋅dF/dz), where ρ and cp denote the air density and the specific heat capacity of air, respectively, and F represents the net radiative flux. The lidar ratio at 355 nm (S=α/β) is shown in Fig. d.

Under the combined influence of the elevated TI and weak surface convection, a dome-like stratified structure began to develop near the UABL. As illustrated in Fig. b, after 10:00 CST, the temperature tendency around 1.2 km increases significantly and is markedly higher than that in the lower layers, whereas the aerosol heating rate in Fig. c remains relatively weak. Backward air-mass trajectory analysis shows that the airflow at approximately 1.5 km is advected from southern regions toward the observation site, indicating a northward transport of warm air. Consequently, horizontal advection may play an important role in the pronounced warming near the upper boundary layer (UABL). Under the combined influence of advective warming and aerosol radiative heating (in Fig. c and d), the elevated TI appears to be further intensified. This process is likely to suppress the upward transport of turbulence and induce local aerosol subsidence. Meanwhile, surface warming may enhance buoyancy in the lower atmosphere (in Fig. c and d), promoting turbulent uplift of near-surface aerosols. However, the heating rate near the surface remains relatively weak.

As a pronounced stratification develops near the UABL, the heating rate within the aerosol-stratified layer increases substantially, while the warming rate in the lower layer tends to decrease. This reduction may be partly attributed to the attenuation of downward radiative fluxes by the stratified aerosol layer, which could constrain surface warming. Given the mid-latitude location of the study region, the limited duration of daytime solar radiation may have been insufficient to sustain continuous surface heating. Consequently, subsidence within the upper aerosol layer likely became the dominant mechanism regulating vertical aerosol mixing during this period. These interpretations are based on observational consistency and are subject to uncertainties associated with the simplified heating rate estimation.

As shown in Fig. b, the temperature gradient and TI depth exhibited nearly opposite variations. Between 12:00 and 15:00 CST, the temperature gradient within the elevated TI increased rapidly from approximately 15 Kkm-1 to about 37 Kkm-1, while the TI depth decreased from around 550 m to roughly 240 m. This phenomenon was likely associated with the dome effect induced by aerosol stratification. After 16:00 CST, the temperature gradient decreased markedly, accompanied by a corresponding increase in TI depth, which may have resulted from enhanced vertical mixing of aerosols. During nighttime, variations in both temperature gradient and TI depth were primarily governed by surface longwave radiation and the radiative forcing of aerosols. Therefore, the dome effect played a pivotal role during the aerosol accumulation stage. The negative buoyancy acceleration induced by the TI was the dominant factor suppressing vertical diffusion of aerosols, causing the convective mixing height during the mid-pollution stage to remain confined below approximately 1 km. Although direct measurements of aerosol absorption (e.g., from an aethalometer) were not available during this experiment, the lidar ratio can provide indirect information on aerosol optical properties. As shown in Fig. d, the increased lidar ratio in the lower layer during the pollution period may suggest enhanced aerosol absorption and support the development of the near-surface stove effect, although this inference has not been directly verified by dedicated absorption measurements.

The lidar and radiosonde temperature profiles indicate that a surface-based TI layer with a thickness of up to 600 m developed in the morning of 30 December, effectively suppressing the vertical diffusion of aerosols. Consequently, despite strong north-westerly winds exceeding 8 ms-1 above approximately 1 km during the daytime (Fig. h), surface PM2.5 concentrations remained persistently high (Fig. a). As surface heating intensified, the associated decrease in relative humidity may have promoted aerosol drying and enhanced turbulent mixing in the lower atmosphere, leading to a noticeable reduction in near-surface PM2.5 concentrations. However, the duration of surface heating was relatively short, potentially limiting the sustained development of turbulence and thereby restricting efficient vertical transport of aerosols. Later in the day, PM2.5 concentrations increased again, possibly associated with aerosol subsidence and hygroscopic growth.

In the early morning of 31 December, surface PM2.5 concentrations decreased markedly, likely due to the strong northeasterly winds below 1 km, with wind speeds exceeding 12 ms-1. Although the near-surface PM2.5 concentrations decreased significantly, this was not attributed to a genuine clean-air advection. Instead, the reduction occurred because nighttime emissions were relatively weak , causing the northeasterly winds–typically associated with polluted air masses–to become relatively clean, thereby diluting the surface PM2.5 concentrations. At around 14:00 CST on 31 December, a localized stratification was observed, with a formation mechanism similar to that on 25 December. The pollution dissipation during this episode was incomplete. The dissipation on 2 January 2024 followed a similar mechanism to the first event, but was associated with stronger northwesterly winds. These winds not only enhanced horizontal dispersion but also promoted vertical mixing of aerosols. After noon, as near-surface aerosols underwent drying, rapid surface warming increased buoyancy, facilitating upward transport of aerosols. Meanwhile, strong northwesterly winds exceeding 10 ms-1 above approximately 0.5 km efficiently advected the uplifted aerosols downstream. Given that the upwind northwestern region is sparsely populated with low emission intensity and relatively clean air, such winds are often regarded as “clean winds”. Consequently, the combined effects of radiative heating and strong northwesterly flow resulted in a more complete pollution dissipation during this event.

Figure a and b show the hourly evolution of aerosol vertical structure, atmospheric temperature, and buoyancy acceleration, while Fig. c and d present the heating rate. The top height of the surface-based TI decreased from approximately 0.7 km at 10:00 CST to about 0.4 km at 13:00 CST. Meanwhile, the near-surface aerosol backscatter coefficient showed an overall decreasing trend. A pronounced gradient in the backscatter profile corresponded well with the inversion top height. Considering the relatively high near-surface relative humidity (up to 80 %) during this period, the observed decrease in backscatter is likely dominated by aerosol drying in the lower layer, possibly accompanied by moderate aerosol radiative forcing. By 13:00 CST, near-surface aerosols were mainly concentrated below 0.3 km, promoting the development of a stove effect. The subsequent vertical aerosol distribution followed this pattern. From 14:00–17:00 CST, aerosols below 1 km exhibited well-developed vertical mixing, as indicated by the temperature and backscatter coefficient profiles in Fig. a. The vertical evolution before 12:00 CST on 2 January 2024 resembled that on 30 December, with near-surface aerosols gradually drying and showing a downward tendency. When near-surface aerosols accumulated, the lower-layer heating rate increased markedly, accelerating the dissipation of the surface-based TI (Fig. c at 16:00 CST). As depicted in Fig. b, the near-surface backscatter coefficient decreased at 16:00 CST, while the upper-layer coefficient increased, indicating substantial vertical mixing of aerosols. Furthermore, the potential temperature profiles during the afternoons of 30 December and 2 January showed little variation with height, and in some cases decreased with height, implying an unstable atmosphere conducive to vertical convection. Vertical velocity measurements indicate that during the early and mid-stages of pollution, near-surface vertical velocities were relatively small and dominated by subsidence, whereas upward motion prevailed during the late stage of pollution.

The observed pollution episode was governed by the combined influence of multiple factors. During the pollution development stage, TIs constrained vertical convection, acting as the primary barrier to aerosol vertical diffusion. Cloud radiative forcing further weakened lower-atmosphere turbulence, thereby constraining convective uplift. Aerosols, in turn, modified the atmospheric thermal structure and buoyancy through radiative interactions involving solar shortwave and surface longwave radiation, leading to complex feedbacks with meteorological conditions. During the pollution dissipation stage, sufficient solar radiation enhanced atmospheric buoyancy, facilitating vertical aerosol mixing, while efficient horizontal advection supported aerosol removal.

Hygroscopic growth further amplified particle size and optical effects, intensifying pollution. Statistical analysis combining near-surface relative humidity and PM2.5 concentrations (in Fig. ) reveals a strong positive correlation below 200 m, indicating that high humidity exacerbates aerosol accumulation. Additionally, the vertical gradient of relative humidity below 300 m decreases with increasing PM2.5, likely due to surface-based TIs and weak turbulence that limit vertical moisture transport during pollution episodes.

Figure a presents the vertical distributions of the UABL, the elevated TI, and the surface-based TI. Figure b and c show the mean vertical temperature gradients of the elevated and surface-based TIs along with the corresponding PM2.5 concentrations. It is evident that the elevated TI is closely associated with the UABL. Both TIs exhibit distinct diurnal variations in the mean temperature gradient, with the mean gradient of the elevated TI negatively correlated with PM2.5 concentrations, whereas that of the surface-based TI shows a positive correlation. Figure  presents the frequency distribution of the mean temperature gradient of the elevated TI and the correlation between the TI-top height and the UABL. The results show that TIs with an average temperature gradient ranging from 5 to 10 Kkm-1 occur most frequently (36 %), and the TI-top height exhibits a significant positive correlation with the UABL height (R2≈0.57).

The mean temperature gradient of the elevated TI exhibits a piecewise negative correlation with PM2.5 concentrations (in Fig. a). During intensified pollution, aerosols were primarily concentrated near the surface, enhancing daytime radiative heating in the lower atmosphere and thereby weakening the elevated TI. The observed piecewise pattern may be associated with hygroscopic growth of aerosols during the mid-pollution stage. In contrast, the mean temperature gradient of the surface-based TI shows a pronounced positive correlation with PM2.5 concentrations (in Fig. b).

The diurnal rates of change for PM2.5 concentrations, the temperature gradient of the elevated and surface-based TIs are shown in Fig. . The diurnal rate of change represents the temporal rate of variation within a day, where positive values denote an increase and negative values denote a decrease. PM2.5 concentrations showed a slight decrease from 00:00 to 10:00 CST, followed by a marked decline between 12:00 and 15:00 CST, and then increased rapidly after 17:00 CST. The elevated TI typically intensified in the early morning, with the strongest rate of change in temperature gradient occurring around 08:00 CST, likely associated with residual aerosol layers from the preceding night. Around noon, enhanced solar radiation warmed both the surface and the top of the aerosol layer, resulting in relatively minor variations in the elevated TI gradient. As solar radiation persisted, enhanced vertical mixing of aerosols contributed to the weakening or disappearance of the elevated TI. Surface-based TI generally strengthened during the early morning and after sunset. The rate of change in surface PM2.5 was strongly coupled with that of the surface-based TI, with stronger TIs corresponding to higher PM2.5 concentrations and weaker TIs to lower ones. Notably, TI peaks tended to precede PM2.5 peaks, reflecting the time lag required for aerosol accumulation. Two distinct minima in PM2.5 concentrations were observed–one around 04:00 CST and another around 14:00 CST. The nighttime minimum was primarily due to reduced anthropogenic emissions, while the midday minimum occurred when solar radiation was strongest and both surface-based and elevated TI weakened, enhancing vertical mixing and resulting in the lowest near-surface aerosol concentrations. In contrast, PM2.5 concentrations peaked from late afternoon to nighttime, primarily due to two factors: the strengthening of surface-based TIs and the reduction in solar radiation. These processes suppressed vertical mixing and facilitated the rapid accumulation of aerosols near the surface.