Perturbations of Aerosol Radiative Forcing on the Planetary Boundary Layer Thermal Dynamics in a Central China Megacity

Abstract

Aerosol radiative forcing is known to significantly disturb the thermodynamic and dynamic structure of the Planetary Boundary Layer (PBL), particularly in heavily polluted urban regions. In this study, the effects of aerosol–PBL interactions were examined over a megacity in China’s Central Plains by comparing ERA5 reanalysis data with multi-source ground-based observations. Key meteorological variables—including wind speed, wind direction, temperature, and relative humidity—were analyzed across pressure levels from 1000 to 800 hPa. Good agreement in wind direction was observed between ERA5 and observations (R² > 0.84), while wind speed showed a moderate correlation (R² = 0.54–0.73) with an RMSE of 1.85 m/s near 975 hPa. Temperature discrepancies were found to decrease with altitude, with RMSE values reducing from 3.02 K to 1.84 K, indicating a modulation of thermal stratification by aerosol radiative effects. A stable structure was revealed by humidity analysis near the surface but increased variability aloft, with absolute differences reaching ±30% at 850–800 hPa. Diurnal variations were characterized by night-time warming of up to +5 °C in the lower PBL and concurrent cooling above 800 hPa. The Heating and surface Dimming (HD) Index was found to correlate positively with PM_2.5 concentration (R = 0.60), reflecting increased thermal stability and vertical inhomogeneity under aerosol loading. These findings underscore the need for an improved understanding and mitigation of aerosol–PBL interactions to support sustainable urban air quality management strategies.

1. Introduction

Thermodynamic and dynamic parameters of the Planetary Boundary Layer (PBL) are regarded as key indicators for understanding land–atmosphere energy exchange and pollutant dispersion. The accurate characterization of these parameters is considered essential for air quality modeling and aerosol-related climate studies [1]. As a representative global high-resolution reanalysis dataset, ERA5 (the fifth generation of ECMWF reanalysis) is used to provide spatially and temporally continuous meteorological fields by assimilating multi-source observations and numerical model outputs [2]. However, the parameterization accuracy of ERA5 may be significantly reduced in regions characterized by complex topography or dense urban pollution, particularly where the PBL structure is strongly altered by aerosol radiative forcing. In such regions, the ability of ERA5 to reproduce core variables, such as vertical temperature gradients and mixed-layer height, needs to be systematically evaluated [3]. It has been shown in previous studies that ERA5 performs well in flat terrains (e.g., Egypt) and homogeneous climatic zones (e.g., the Brazilian basin) [4,5], while substantial deviations have been observed in mountainous and coastal areas. For instance, temperatures above 2000 m have been overestimated by ERA5 in Chinese mountainous regions, and gravity wave momentum fluxes in Antarctica have been underestimated by up to a factor of five [6,7]. These deviations are often caused by limitations in vertical resolution and deficiencies in the parameterization of local physical processes [8]. In the megacity clusters of the Central Plains, these challenges are further intensified by the superimposed effects of aerosol radiative forcing, through which the development of the PBL is suppressed by aerosols via dual mechanisms of surface dimming and atmospheric heating. As a result, the simulation errors of boundary layer parameters in ERA5 may be further amplified [9,10].

Numerous studies have been conducted focusing on case analyses in highly polluted regions. It was reported by Li et al. (2021) that increased aerosol concentrations in North China during winter could lead to a 40–60% reduction in Planetary Boundary Layer Height (PBLH), triggering a positive feedback loop between air pollution and PBL suppression [11]. In the Yangtze River Delta, ground-based remote sensing data were integrated by Su et al. (2020) to quantify the suppression of surface sensible heat flux caused by aerosol scattering. A reduction of approximately 15–25 W/m² was estimated, and a nonlinear relationship was revealed between aerosol optical properties and the thermodynamic structure of the PBL [12]. From a data evaluation perspective, the applicability of ERA5 reanalysis in Chinese mountainous regions was assessed by Wei et al. (2025), and an overestimation of high-altitude temperatures by 2–3 °C was found, primarily attributed to the omission of vertical aerosol heating processes in the model [13]. In addition, ground-based lidar and reanalysis data were used by Zhou et al. (2021) to investigate the impacts of aerosols on PBLH in Beijing [14]. It was demonstrated that aerosol physical and optical properties exert significant influence on PBLH under varying pollution conditions—especially during heavy pollution episodes, when both scattering and absorption effects contribute to boundary layer suppression and further air quality deterioration. In Chengdu, the bidirectional coupling between aerosols and meteorological variables was systematically analyzed by Chen et al. (2025), indicating that high aerosol loads not only weaken surface sensible heat exchange but also enhance vertical gradients of temperature and humidity, thereby affecting pollutant transport within the boundary layer [15]. In another study, ERA5 reanalysis was combined with satellite remote sensing products by Xia et al. (2023) to quantitatively assess the role of urban heat island effects in modulating PBL thermal structures and aerosol accumulation. The influence of urban thermal anomalies on PBL dynamics was emphasized [16]. Finally, the close relationship between diurnal variations in mixed-layer height and biases in reanalysis meteorological variables was revealed by Guo et al. (2020), highlighting the limitations of conventional reanalysis products in capturing PBL evolution under high-aerosol conditions [17].

The Central Plains region, characterized by a dense cluster of inland megacities, is distinguished by unique geographic–climatic conditions and intense anthropogenic emissions. A dry, low-precipitation climate is experienced in this region, leading to a high frequency of near-surface temperature inversions in winter, with occurrences reaching up to 60% [18]. Under such conditions, the hygroscopic growth of aerosols is limited, and greater reliance is placed on the direct heating effects of absorbing components, such as black carbon, to exert radiative impacts [19]. Compared to coastal cities, a higher proportion of sulfate–black carbon mixed aerosols from industrial sources are observed in this region, resulting in a distinctive vertical distribution of aerosol radiative forcing [20]. Under weak wind conditions, low-level wind shear can be enhanced and turbulence can be suppressed by aerosol–PBL interactions, potentially triggering a “pollution–stability” positive feedback mechanism [12].

However, most existing studies have been concentrated on North China or coastal cities, and region-specific assessments for the Central Plains have been lacking. The simulation biases of ERA5 in representing temperature lapse rates and mixed-layer heights under conditions of heavy aerosol loading have not yet been systematically quantified. Furthermore, the coupled thermodynamic and dynamic mechanisms through which aerosol radiative forcing influences the accuracy of ERA5 have not been empirically validated. Short-term case analyses have proven insufficient for revealing the climatological characteristics of these discrepancies or for identifying their potential implications in air pollution forecasting. As a result, the reliability of ERA5 in supporting regional environmental management and extreme weather early warning systems has been undermined.

Using Zhengzhou as a representative megacity in the Central Plains, the dynamic responses of PBL structures to aerosol loading are investigated in this study using ERA5 reanalysis data and multi-source ground-based observations—including wind profiler radar and microwave radiometer—collected during October–November 2024. By integrating the vertical distribution of aerosols with key thermodynamic and dynamic parameters, two indices—namely, the Thermal Suppression Index (TSI) and the Dynamic Resistance Index (DRI)—are developed to quantitatively characterize the contributions of aerosol–PBL interactions to simulation discrepancies. This research is the first in which the unique disturbance patterns of aerosol radiative forcing have been elucidated under inland dry climate conditions and an industrial emission background. A physical basis is thus provided for the correction of reanalysis datasets in this region, contributing to the improved applicability of ERA5 in aerosol–climate interaction studies by enhancing the accuracy of air pollution forecasting models. In the context of sustainability, the need for integrated urban planning strategies that account for aerosol–PBL interactions is emphasized, aiming to mitigate air pollution, improve public health outcomes, and support the development of resilient and sustainable cities in the face of climate change.

2. Data and Methods

2.1. Introduction of Observation Site

Zhengzhou, as a representative megacity in the Central Plains, is considered an ideal setting for the exploration of thermodynamic disturbances in the urban boundary layer using high-resolution observational data. The Zhengzhou site is recognized as a typical urban meteorological observation station, situated in the southwestern part of the city’s main urban area, with geographic coordinates of 34.75° N and 113.62° E and an elevation of approximately 100 m above sea level. The local topography is characterized by a west-to-east slope, with the western boundary adjacent to the foothills of the Qinling Mountains, the northern edge bordered by the Taihang Mountains, and the eastern region opening into the expansive Huang-Huai Plain. A distinctive climatic environment is created by this transitional terrain, shaped by the convergence of plain and mountainous influences.

The observational system is composed of a CFL-06L tropospheric wind profiler radar and an MP-3000A microwave radiometer, both of which have been installed in an open field southeast of the station. High temporal and spatial resolution measurements of the three-dimensional wind field and the vertical structure of temperature and humidity within the boundary layer are jointly provided by these instruments. In this study, continuous data collected from October to November 2024 are utilized, with attention focused on the seasonal evolution of boundary layer wind structures and the day-to-day variability of atmospheric thermodynamic profiles over the North China Plain. The spatiotemporal response characteristics of typical urban boundary layer structures are intended to be revealed.

Among the three key cities in the region, Zhengzhou is characterized by a dense population and a high level of industrialization; Luoyang, to the west, is defined by more complex and mountainous terrain; while Kaifeng, to the east, is situated entirely on the flat Huang-Huai Plain but is marked by a smaller population and less industrial activity compared to Zhengzhou. As is illustrated in Figure 1.

2.2. Ground-Based Remote Sensing Data

2.2.1. Wind Profiling Radar

The three-dimensional wind field structure was obtained using the CFL-06L tropospheric wind profiler radar, which was independently developed by the Chinese Academy of Sciences (deployment shown in Figure 1b). This radar system is classified as a clear-air, pulse Doppler type based on the Bragg scattering principle of atmospheric turbulence. All-weather capability, automated operation, and high temporal and spatial resolution are featured, enabling the continuous monitoring of the vertical distribution of horizontal wind speed, wind direction, and vertical velocity within the troposphere. An effective detection range from 150 m to 10,110 m is supported, allowing full coverage of the PBL and the lower to middle troposphere and facilitating the capture of wind structure evolution from the surface friction layer to the free atmosphere. A native temporal resolution of 6 min is provided by the instrument, while vertical resolutions of 60 m (high-precision mode), 120 m, and 240 m are supported to meet various observational needs. To enhance the signal-to-noise ratio and ensure data stability for operational applications, the raw measurements are processed using a moving average filter, and standard outputs are generated at 10 min intervals.

The radar is operated within a frequency range of 1270–1375 MHz, and a system bandwidth of up to 100 MHz is employed. A full-band antenna gain of ≥33 dB is achieved, significantly enhancing the system’s sensitivity to weak turbulence signals. As a result, the system is rendered particularly effective for wind field detection in low-turbulence environments such as the nocturnal boundary layer and upper-level wind shear zones. The classical five-beam retrieval method is employed by the CFL-06L, in which pulsed signals are transmitted and received sequentially in four horizontal directions—east (90°), south (180°), west (270°), and north (0°)—at a fixed elevation angle α°, along with one vertical beam (90° elevation). The three-dimensional wind vector field is derived from the radial wind velocity data obtained from these five beams. Compared to traditional single-point observations, the dynamic and continuous profiling of atmospheric wind structures in the vertical dimension is enabled by the CFL-06L. This capability renders it particularly suitable for studies concerning boundary layer evolution, wind shear identification, and turbulence monitoring [21].

In addition to its core detection functions, adaptive pulse width and PRF (Pulse Repetition Frequency) settings are utilized to optimize the trade-off between vertical resolution and detection sensitivity across various altitudes. Standard data products, including vertical profiles of wind speed, wind direction, vertical velocity, the signal-to-noise ratio (SNR), and spectral width, are made available in NetCDF format. A real-time quality control algorithm is implemented to ensure data integrity by filtering out non-atmospheric echoes. The system is also designed to support integration with other instruments such as radiosondes and microwave radiometers, enhancing its applicability in the study of boundary layer thermodynamics and dynamics. Furthermore, a modular design has been adopted, allowing for rapid deployment in diverse environments and making the radar suitable for both long-term monitoring and intensive field campaigns.

2.2.2. Microwave Radiometer

The MP-3000A microwave radiometer (deployment shown in Figure 1c) is a ground-based, multi-channel passive microwave remote sensing instrument that was developed by Radiometrics Corporation (Frederick, CO, USA). It is specifically designed for the continuous retrieval of vertical profiles of atmospheric temperature and humidity. The system is operated in two primary frequency bands: the K-band (22–30 GHz), which includes 8 channels for the detection of water vapor absorption features, and the V-band (51–59 GHz), which includes 24 channels targeting the oxygen absorption band. By passively receiving natural microwave emissions from the atmosphere, continuous and all-weather operation is enabled without reliance on external signal sources.

A neural network (NN) and one-dimensional variational (1D-VAR) algorithm framework is integrated into the retrieval system to derive vertical profiles of atmospheric temperature (0–10 km) and humidity (0–5 km). A retrieval accuracy of less than 0.5 K for temperature near the surface and less than 10% for relative humidity within the boundary layer is achieved. Additionally, measurements of integrated water vapor (IWV) and liquid water path (LWP) are provided. With a high temporal resolution of 2 s per scan, the MP-3000A delivers stable and quality-controlled atmospheric profile data at minute-level intervals after undergoing a multi-step quality assurance process [22].

Zenith-pointing observations are performed by the MP-3000A, and continuous two-point calibration is conducted using internal ambient and noise diode references to ensure long-term radiometric accuracy. Both retrieved profiles and raw brightness temperature spectra are output in NetCDF format, allowing integration into data assimilation systems. When combined with wind profilers or radiosondes, a comprehensive view of the thermodynamic structure of the boundary layer is enabled, supporting studies related to stability evolution, boundary layer height estimation, and model evaluation. The instrument has been successfully applied in major field campaigns and urban atmospheric research networks for real-time monitoring and forecasting applications.

2.2.3. PM_2.5 Data

In this study, surface-level PM_2.5 concentration data from existing monitoring stations in Zhengzhou are utilized. These data are obtained from China’s National Ambient Air Quality Monitoring Network, which has been established and maintained by the Ministry of Ecology and Environment (MEE) since 2013. The network is composed of over one thousand state-controlled automatic monitoring stations across the country. As a core city in the Central Plains, Zhengzhou is equipped with multiple national control sites that are designated to represent various functional areas, including urban background, traffic, and industrial zones. The PM_2.5 data are made publicly available through the “National Urban Air Quality Real-time Publishing Platform” or the “National Environmental Monitoring Data Center,” which is operated by the China National Environmental Monitoring Centre (CNEMC). These datasets are used to provide essential support for the analysis of the spatiotemporal characteristics of urban air pollution [23].

2.3. ERA5 Reanalysis Data

For the reanalysis data, ERA5—the fifth-generation reanalysis product developed by the European Centre for Medium-Range Weather Forecasts (ECMWF)—was employed [24]. The dataset selected for this experiment is sufficient to encompass the cities and surrounding villages within the study area. A horizontal resolution of 0.25° × 0.25°, corresponding to approximately 30 km × 30 km at midlatitudes, is featured in ERA5. Through spatial interpolation, the meteorological conditions of nearby towns and villages are effectively represented. A temporal resolution of 1 h is provided, along with 41 pressure levels ranging from 1000 hPa to 1 hPa. A wide range of dynamic variables, including zonal (u) and meridional (v) wind components, among others, is included in the dataset [25]. ERA5 is generated using a spectral model (the Integrated Forecasting System, IFS), and feedback effects of aerosols on meteorological variables are not accounted for in the current version [26].

The dataset is produced by integrating ECMWF IFS Cycle 41 r2 with an advanced four-dimensional variational assimilation system (4D-Var), through which vast amounts of observations from ground stations, ships, aircraft, and satellites are assimilated at hourly resolution. As a result, the spatiotemporal consistency and accuracy of the reanalysis fields are significantly enhanced [27]. In comparison with its predecessor, ERA-Interim, improvements have been incorporated into ERA5 in terms of the representation of microphysical processes and the parameterization of physical processes, thereby resulting in more refined simulations of thermodynamic and dynamic conditions [28].

Nevertheless, despite being recognized as one of the most advanced global reanalysis products available, ERA5 still lacks a fully coupled aerosol–radiation–meteorology interaction scheme. This limitation may reduce its applicability in studies involving severe pollution episodes and boundary layer disturbances [29,30]. Consequently, differences observed between ERA5 outputs and measurements from radiosondes or ground-based remote sensing instruments may, to some extent, reflect the modulatory influence of aerosol radiative forcing on atmospheric structure.

2.4. Research Methods

2.4.1. Pressure–Altitude Conversion Methods

As aerosol feedback mechanisms are not incorporated into the numerical modeling framework of ERA5, the thermodynamic and dynamic structures represented by this reanalysis product are generally reflective of an idealized atmospheric state in which aerosol-induced perturbations are absent [31,32]. This introduces considerable uncertainty when ERA5 is applied to the analysis of real-world atmospheric processes, particularly in urban areas characterized by high aerosol loading.

In practical analysis, interpolation and screening methods are first adopted to achieve temporal alignment between different datasets. Meanwhile, wind field data in ERA5 are provided with isobaric surfaces as the vertical coordinate, whereas lidar and microwave radiometer measurements are referenced to geometric height. To ensure vertical consistency across datasets, the pressure values from ERA5 must be accurately converted into altitude. For this purpose, three pressure-to-height conversion methods are tested and compared in this study.

The first method is based on the International Standard Atmosphere (ISA), in which a linear temperature decrease with height under dry air conditions is assumed. This method allows for an analytical solution and offers high computational efficiency; however, variations in actual temperature and humidity are not considered [33,34]. In the second method, hydrostatic integration with virtual temperature correction is employed. Observed profiles of temperature and relative humidity are used to numerically calculate the pressure–height relationship, allowing the influence of moist air on the thermal structure to be effectively captured [35,36]. The third method assumes of a dry adiabatic lapse rate, and the integration is simplified accordingly. While suitable for idealized dry tropospheric conditions, significant errors may be introduced when applied in moist environments [37,38].

Each of the three methods is associated with specific advantages under different humidity conditions, and their applicability should be evaluated and selected based on the characteristics of the observational data.

Starting from the principle of hydrostatic balance,

$${\displaystyle \frac{dP}{dz}}=-\rho g$$

(1)

P represents the air pressure (in hPa or Pa); z is the height (in meters); $\rho$ is the air density (in kg·m⁻³); and g is the gravitational acceleration (approximately 9.8 m·s⁻²). These quantities are combined with the ideal gas law:

$$P=\rho R_{d}T$$

(2)

R_d is defined as the gas constant for dry air (287.05 J·kg⁻¹·K⁻¹), and T is defined as the temperature of dry air (in K). By combining these with the ideal gas law, the following expression is obtained:

$${\displaystyle \frac{dP}{dz}}=-{\displaystyle \frac{Pg}{RT}}$$

(3)

Theoretical support is provided for all pressure–height conversion methods by this relationship. Depending on how temperature is treated, different formulations can be derived.

(1).

International Standard Atmosphere (ISA) model.

This assumes a linear decrease in temperature with height under dry air conditions:

$$P=P_0{(1-{\displaystyle \frac{Lh}{T_0}})}^{{\displaystyle \frac{gM}{RL}}}$$

(4)

Here, L is defined as the temperature lapse rate; P₀ as the air pressure at the reference height h = 0 (usually the surface pressure); T₀ as the temperature at the reference height h = 0; R as the universal gas constant (8.3145 J·mol⁻¹·K⁻¹); and M as the molar mass of dry air (0.028965 kg·mol⁻¹).

(2).

Hydrostatic integration method with virtual temperature correction.

In this method, actual variations in observed temperature and humidity profiles are accounted for by incorporating virtual temperature into the hydrostatic balance equation. As a result, a more realistic estimation of the pressure–height relationship is provided under moist atmospheric conditions:

$$P_2=P_1\exp (-{\displaystyle \frac{1}{R}}{\displaystyle {\int }_{z_1}^{z_2}\frac{g}{T}}dz)$$

(5)

Here, P₁ is defined as the air pressure at height z₁ (in hPa or Pa); P₂ as the air pressure at height z₂; T as the virtual temperature (which is related to humidity, where T_v = T(1 + 0.61 q)); and z₁ and z₂ are the starting and ending heights, respectively.

(3).

Dry adiabatic lapse rate method.

In contrast, this method assumes that the atmosphere follows a dry adiabatic lapse rate, which is suitable for dry air conditions. Under the assumption of constant potential temperature and no moisture effect, the pressure–height relationship is simplified:

$$P(z)=P_0{(1-{\displaystyle \frac{gz}{C_P{T}_0}})}^{{\displaystyle \frac{C_P}{R_d}}}$$

(6)

In this context, P(z) is defined as the air pressure at height z, and C_p as the specific heat capacity of dry air at constant pressure.

After the unification of pressure–height coordinates, hourly ERA5 wind speed and direction data between 1000 and 700 hPa (approximately corresponding to the surface to 2 km) were extracted to match the vertical resolution of the radar observations. Based on a review of the literature and results from preliminary experiments using different interpolation methods, the optimal interpolation technique was identified as cubic spline interpolation [39,40]. Accordingly, a cubic spline interpolation method was employed to convert the ERA5 data to standard pressure layers consistent with the observation heights of the lidar, thereby enabling the construction of a comparable wind profile sequence [41]. Subsequently, wind field data from ERA5 and lidar observations within the 1000–775 hPa range were compared, and statistical metrics—including the root mean square error (RMSE), the correlation coefficient (R), and the distribution of differences—were calculated [42]. The aim of this comparison was to evaluate the capability of ERA5 in representing boundary layer features under typical transient weather conditions in autumn.

This comparison framework not only allows the reliability of ground-based observations to be verified, but also reveals the strengths and limitations of ERA5 in simulating wind fields over complex land surfaces such as urban canopies in the North China Plain. The findings serve to provide theoretical support for future studies of regional boundary layer dynamics and for the refinement of reanalysis datasets [43].

2.4.2. Observation Minus Reanalysis (OMR)

The Observation Minus Reanalysis (OMR) method is regarded as a diagnostic approach that is used to examine aerosol–boundary layer interactions by analyzing the differences between observed atmospheric profiles and reanalysis data products. This method has been receiving increasing attention in recent years due to its capacity to capture aerosol-induced thermodynamic effects that are typically excluded from reanalysis datasets [44].

Reanalysis products such as ERA5 are generated through the assimilation of a wide range of meteorological observations into numerical weather prediction models. In these datasets, dynamical consistency is emphasized and strong constraints are imposed by upper air observations and model physics. However, aerosol radiative forcing is typically neglected in reanalysis systems, particularly within the PBL, as aerosol observations are either not assimilated or simplified radiation schemes are applied. Consequently, reanalysis data often fail to represent key thermodynamic signatures of aerosol impacts, such as surface cooling, elevated heating layers, or inhibited boundary layer development.

In contrast, ground-based measurements—such as radiosonde soundings, microwave radiometers, and remote sensing retrievals—are capable of directly reflecting the atmospheric response to aerosol radiative effects. The integrated outcomes of aerosol interactions with solar radiation, including modifications to vertical temperature gradients, thermal stability, and PBLH, are inherently captured by these observations.

Through this contrast, the extent to which aerosol effects are captured in real-world observations but omitted from reanalysis systems is highlighted. A positive OMR in low-level temperature, for instance, may be interpreted as an indication that aerosol-induced surface cooling is present in observations but absent from the reanalysis. Likewise, OMR differences in temperature lapse rates or PBLH can be interpreted as signals of aerosol-related stabilization or the suppression of vertical mixing.

Therefore, OMR is considered to provide a semi-quantitative measure of aerosol–boundary layer coupling strength. It has been successfully employed in previous studies to infer the spatiotemporal variability of aerosol radiative impacts, to validate model parameterizations, and to assess the applicability of reanalysis products in heavily polluted or aerosol-affected environments.

2.4.3. Heating–Dimming Index (HD Index)

The interaction between aerosols and the PBL is often characterized by opposite temperature perturbations near the surface and in the upper boundary layer. This altered thermal structure can be revealed through temperature differences between radiosonde observations and reanalysis data. Based on this concept, a quantitative metric—the Heating and surface Dimming Index (HD Index)—is proposed to assess the coupling strength between aerosols and the PBL [44]. This index is designed to reflect the combined effects of aerosol-induced heating in the upper boundary layer and radiative surface dimming near the ground. It is calculated as the sum of the absolute temperature decrease near the surface and the temperature increase aloft.

Specifically, in the context of ERA-Interim, the HD Index is defined as the sum of the mean absolute Observation Minus Reanalysis (OMR) temperature difference below 950 hPa and the mean absolute OMR temperature difference within the 850–950 hPa layer. To avoid interference from strong cold air outbreaks, data points with wind speeds exceeding 10 m/s at 850 hPa are excluded from the calculation.

$$HD-Index={\displaystyle {\sum }_{i=1}^n\left|\Delta T_i\right|}/n+{\displaystyle {\sum }_{j=1}^n\left|\Delta T_j\right|}/m$$

(7)

In Equation (7), n and m represent the number of pressure levels below 950 hPa and between 850 and 950 hPa, respectively. $\Delta T_i$ and $\Delta T_j$ represent the temperature differences at the near-surface layer i and the upper-air layer j, respectively.

3. Results

3.1. Evaluation of Pressure–Altitude Conversion Techniques

To ensure the scientific validity and applicability of the pressure-to-height conversion, the hydrostatic integration method corrected by virtual temperature is primarily adopted in this study. Based on the principle of hydrostatic equilibrium, this approach allows the observed variations in temperature and humidity to be fully accounted for, enabling a more realistic representation of the thermodynamic structure of the atmospheric boundary layer over complex terrain. This method is particularly suited for environments characterized by significant humidity variations or pronounced temperature inversions.

To further assess the robustness and applicability of this method, auxiliary calculations and comparative analyses were carried out using the International Standard Atmosphere model (Method 1) and the dry adiabatic lapse rate assumption (Method 3). An evaluation based on the mean pressure–height relationships across all observation periods (Figure 2) shows that overall consistency is exhibited by the three methods—particularly in the mid-to-upper layers (above 500 m), where the curves are largely overlapping, indicating high applicability in these regions.

Specifically, a correlation coefficient (R) of 0.999, a root means square error (RMSE) of 8.84 hPa, and a regression slope of 1.01 are found between Method 1 (ISA) and Method 2 (virtual temperature integration) (Figure 2a). Between Method 2 and Method 3 (the dry adiabatic method), R is also 0.999, RMSE is 8.96 hPa, and the regression slope is 1.03 (Figure 2b). The best agreement is observed between Method 1 and Method 3, with R reaching 1.000, RMSE as low as 1.94 hPa, and a slope of 1.03 (Figure 2c). These results indicate that although minor discrepancies are present in the near-surface high-pressure zone (>1000 hPa) and the upper low-pressure region (<850 hPa)—mainly due to differing assumptions in handling temperature and moisture—the overall deviations are small and physically consistent, thereby exerting limited influence on the subsequent analyses.

Therefore, considering its accuracy, physical realism, and suitability for complex terrain conditions, the hydrostatic integration method with virtual temperature correction is employed for all subsequent pressure–height conversions and related analyses in this study, ensuring the scientific reliability of the results.

3.2. Aerosol-Induced Dynamical Perturbations in the PBL

Figure 3 and Figure 4 show the wind direction rose diagrams and scatter density plots, respectively, for ERA5 and radiosonde observations at five pressure levels ranging from 975 to 800 hPa. Overall, consistent wind direction patterns are exhibited by both datasets across all height levels, with prevailing winds concentrated in the westerly (W) and west-northwesterly (WNW) sectors. This pattern is interpreted as the result of the mid-latitude westerly belt, modulated by dynamic processes induced by local terrain.

In the lower layers (975–950 hPa), wind directions obtained from both ERA5 and radiosonde data are tightly clustered and found to be structurally consistent. Strong linear correlations between the two datasets are revealed in the scatter density plots, with regression slopes observed around 0.82, coefficients of determination (R²) exceeding 0.86, and root mean square errors (RMSE) remaining within 35°. These results indicate that near-surface wind direction variability is accurately captured by ERA5, where aerosol radiative forcing has limited impact and wind behavior is primarily governed by surface friction and orographic steering.

As the altitude increases (900–800 hPa), discrepancies between the two datasets become more evident. In the scatter density plots, distinct clusters are observed in the west-northwesterly to northwesterly (WNW–NW) and southerly (S–SSW) sectors, indicating increased diversity in upper-level wind patterns. Notably, although southerly winds appear frequently in the scatter plots, they contribute less prominently to the wind rose diagrams—likely due to their lower wind speeds, which result in insufficient frequency accumulation for visual significance. This phenomenon suggests that at higher altitudes, atmospheric stratification is more strongly influenced by radiative forcing, leading to modifications in local circulation patterns, increased variability in wind direction, and enhanced heterogeneity in wind speed distribution.

Figure 5 presents scatter density comparisons of wind speed between ERA5 and radiosonde observations across different pressure levels (975–800 hPa). Overall, good linear correlations with observations are demonstrated by ERA5 wind speeds, with consistent trends observed across all levels. The coefficient of determination (R²) is found to range from 0.542 to 0.725, with the strongest correlation identified at 950 hPa (R² = 0.725, RMSE = 1.942 m/s) and the weakest at 800 hPa (R² = 0.542, RMSE = 2.916 m/s). Regression slopes are observed to vary slightly with height, ranging from 0.66 (975 hPa) to 0.67 (800 hPa), all below the ideal value of 1, indicating that wind speeds tend to be underestimated by ERA5 across all levels. The density contours are found to be more concentrated in the lower layers and gradually spread in the upper levels, suggesting differing sensitivities to aerosol radiative forcing.

Specifically, in the lower atmosphere (975 and 950 hPa), wind speed is primarily governed by near-surface effects such as friction and orographic blocking. Under these conditions, aerosols tend to cause moderate disturbance to the wind structure by weakening surface radiative fluxes and reducing turbulent exchange. In contrast, at mid-to-upper levels (900–800 hPa), aerosol-induced radiative heating enhances upper-level atmospheric stability, which in turn triggers vertical wind shear and dynamic structural adjustments. As a result, larger discrepancies in wind speed and increased dispersion in ERA5, relative to observations, are observed.

Figure 6 further illustrates the distribution characteristics of absolute and relative wind speed deviations between ERA5 and radiosonde data across the five pressure levels. In Figure 6a, absolute deviations are generally centered around zero, with median values remaining close to 0 m/s. However, dispersion is found to increase with altitude, and a notable rise in outliers is observed at 800 hPa, indicating the higher sensitivity of upper-level wind speeds to radiative disturbances. Figure 6b shows a much broader distribution of relative deviations. In certain cases, particularly at 800 and 850 hPa, relative wind speed deviations exceed 200%, with extreme cases approaching 800%. These results highlight the amplified impact of aerosol radiative forcing on the spatial heterogeneity of upper-level wind dynamics. It is thus suggested that vertical momentum transport and turbulence development in the upper boundary layer are more vulnerable to radiative heating, contributing to the increased variability observed in wind speed fields under polluted atmospheric conditions.

3.3. Aerosol-Induced Thermodynamic Perturbations in the PBL

Figure 7 illustrates the distribution characteristics of absolute (a) and relative (b) deviations in relative humidity between ERA5 and radiosonde observations at six pressure levels ranging from 1000 to 800 hPa. Overall, the humidity discrepancies between ERA5 and the observations are shown to be closely linked to thermodynamic disturbances in the boundary layer under aerosol radiative forcing, and a clear stratified pattern with height is exhibited.

In the near-surface layer (1000–950 hPa), strong agreement is observed between ERA5 and observational data. Absolute deviations are found to lie mostly within ±10%, with median values close to 0% and low dispersion (Figure 7a). Relative deviations are mostly below 5% (Figure 7b), suggesting that humidity at this level is primarily regulated by the surface radiation balance, shallow turbulent mixing, and surface moisture fluxes. Under such conditions, incoming shortwave radiation is primarily suppressed by aerosols, resulting in reduced surface heating and weakened vertical diffusion and evaporation. Consequently, a more stable moisture structure is formed, and high consistency between ERA5 and observations is maintained.

At higher levels (900 hPa and above), a more pronounced stratified response is displayed by the humidity field. As shown in Figure 7a, the distribution range of absolute deviations broadens significantly from 900 to 800 hPa, accompanied by greater deviations of the median values from zero. In particular, within the 850–800 hPa layer, a sharp increase in outliers is observed, with some samples showing absolute humidity differences exceeding ±30%. In Figure 7b, relative deviations are also found to increase in the mid-to-upper layers, reaching over 10% in certain cases. These results suggest that enhanced atmospheric stability due to aerosol-induced heating suppresses turbulence and inhibits vertical moisture transport, thereby amplifying discrepancies between reanalysis data and observed humidity structures.

The deviation becomes especially pronounced between 850 and 800 hPa—a region near the top of the boundary layer, where the modulation of the radiative balance and localized atmospheric heating by aerosols is most intense. In this region, atmospheric moisture redistribution is more likely to occur, resulting in substantial differences between ERA5 and in situ observations. These findings highlight the high sensitivity of upper-layer humidity to aerosol radiative disturbances and reveal the limitations of reanalysis datasets in accurately capturing boundary layer moisture structures under strong external forcing conditions.

Figure 8 shows the scatter density plots of temperature between ERA5 and radiosonde observations at six pressure levels ranging from 1000 to 800 hPa, and stratified thermodynamic responses of the atmosphere under aerosol radiative forcing are revealed. Overall, a significant linear relationship is observed at all levels, indicating that the regional temperature distribution is generally captured by ERA5 with good consistency.

In the near-surface layers (1000 hPa and 975 hPa), the scatter density is found to deviate slightly from the 1:1 diagonal line, with temperatures from ERA5 generally higher than those observed and with a relatively weaker correlation. Specifically, at 1000 hPa, the regression slope is calculated as 0.81, with R² = 0.58 and RMSE = 3.02 K. At 975 hPa, the slope increases to 0.89, with R² = 0.73 and RMSE = 2.52 K. These patterns reflect the strong control exerted by the surface radiative balance on near-surface thermal structures. This balance is altered by aerosols through the reduction in daytime shortwave radiation and the modification of night-time longwave emissions, which affect surface–atmosphere heat exchange. A delayed or damped response may be exhibited by ERA5 in simulating this complex radiative–thermodynamic interaction, resulting in observable discrepancies at lower levels.

Between 950 and 850 hPa, the scatter plots align more closely with the 1:1 diagonal, and increasingly concentrated density bands are displayed. Regression slopes at 950 hPa, 900 hPa, and 850 hPa are determined to be 0.90, 0.82, and 0.87, respectively, with R² values of 0.78, 0.79, and 0.80. The RMSE values fall within the range of 2.22–2.05 K. These results suggest that the thermal structure of the mid-level atmosphere is more stably represented in ERA5. This layer is directly influenced by aerosol radiative heating, where accumulated heat alters the vertical temperature gradient. The strong performance of ERA5 at these levels indicates its effectiveness in reproducing thermodynamic stratification disturbances.

At 800 hPa, the highest agreement between ERA5 and radiosonde temperatures is observed, with a regression slope of 0.99, R² = 0.86, and RMSE = 1.84 K. The scatter density is concentrated around the 1:1 line. This level lies near the top of the boundary layer and represents a transition zone where upward thermal perturbations from the surface begin to weaken. At this altitude, a balance is reached between aerosol-induced heating and turbulence suppression, resulting in a clearer vertical heat transport pattern. Consequently, temperature variability at this level is reliably captured by ERA5, indicating high accuracy in its temperature reanalysis at 800 hPa.

Figure 9a displays the diurnal variation profiles of temperature differences between ERA5 and radiosonde observations, and the stratified thermodynamic responses of the atmosphere under aerosol radiative forcing are highlighted. During the night-time to early morning period (00:00–09:00), the most pronounced temperature differences are found within the 850–925 hPa layer, where mean positive deviations reach +3 °C to +5 °C. In contrast, the upper boundary layer (above 800 hPa) is characterized by generally negative differences ranging from −1 °C to −3 °C. This vertical pattern is indicative of the enhanced night-time suppression of longwave radiative cooling at the surface by aerosols, whereby ground heat loss is limited and heat accumulation occurs in the near-surface layer—resulting in a strengthened surface-based temperature inversion. Meanwhile, weaker turbulent development and increased absorption of radiative heating in the upper layers lead to a more uniform or slightly cooler temperature profile.

During the daytime (10:00–17:00), the energy budget is dominated by incoming solar radiation, which enhances surface heating and promotes turbulent mixing. As a result, the temperature differences between ERA5 and observations are reduced to within ±1 °C, and the vertical structure becomes more balanced—indicating that a redistribution and equilibrium of radiative effects is achieved across layers.

Figure 9b further quantifies the statistical relationship between the daily mean PM_2.5 concentration and the Heating and surface Dimming (HD) Index. A clear positive correlation is observed, with a Pearson correlation coefficient of R = 0.60. This result confirms that the HD Index is effective in characterizing the strength of aerosol–PBL interactions. During the study period, the monthly average PM_2.5 concentration was calculated as 57.96 μg/m³ (based on daily values), with a maximum of 175 μg/m³ and a minimum of 9 μg/m³, indicating the occurrence of several distinct pollution episodes. Higher aerosol loading is associated with stronger radiative forcing, which leads to increased thermal stratification stability and vertical heterogeneity—reflected in elevated HD Index values.

4. Discussions and Conclusions

Based on ERA5 reanalysis data and radiosonde observations, the thermodynamic and dynamic structures of the PBL over a megacity in the Central Plains of China were systematically examined. Emphasis was placed on the stratified responses and spatiotemporal evolution of the boundary layer under aerosol radiative forcing. While the overall temperature field was consistently reproduced by ERA5, clear vertical stratifications were identified. Near the surface, radiative cooling was attenuated under polluted conditions, resulting in shallow heat accumulation. In the mid-to-upper layers, increased aerosol absorption was found to generate localized heating zones that enhanced thermal stability and induced thermodynamic perturbations.

Simulations of relative humidity revealed significant stratification dependence. In the lower boundary layer, moisture distribution was primarily driven by surface evaporation and shallow mixing, leading to relatively uniform vertical profiles. In contrast, the mid-to-upper layers were shown to be influenced by radiative perturbations that suppressed turbulence and redistributed moisture, thereby producing more complex vertical humidity structures. These findings suggest that aerosol radiative effects regulate humidity in a non-uniform and vertically dependent manner.

For wind fields, near-surface wind speed patterns were effectively reproduced by ERA5, with key influences from surface friction and terrain effects successfully captured. In contrast, upper-layer winds were found to exhibit greater variability and stronger sensitivity to free atmosphere dynamics. Wind direction remained generally consistent with observations, although eastward or southward deviations were observed at certain heights implied aerosol-induced modifications to local circulation systems. The proposed Heating and surface Dimming (HD) Index was shown to quantitatively represent the strength of aerosol–PBL interactions, and a strong positive correlation with PM_2.5 concentrations confirmed its diagnostic value.

From a data application perspective, it is recommended that ERA5 thermodynamic variables in the lower boundary layer be corrected using radiosonde or surface-based observations under conditions of high aerosol loading and strong radiative forcing in order to enhance accuracy. While ERA5 wind data near the surface were found to be generally reliable, upper-level analyses should be supplemented with in situ measurements or high-resolution model outputs. The HD Index is shown to serve as a sensitive indicator for detecting stratified atmospheric responses during pollution episodes and is considered a valuable tool for investigating polluted meteorological processes in megacities and complex terrain environments. However, a limitation of this study is the lack of vertically resolved aerosol observations to directly constrain aerosol–PBL interactions. In terms of sustainability, this research underscores the need for improved air quality management practices that incorporate aerosol–PBL interactions, thereby contributing to more accurate pollution forecasting models and informing strategies to reduce urban air pollution, protect public health, and build resilient, sustainable cities in the face of ongoing environmental challenges.