We classified the T and wind components profiles in the boundary layer (below 850 hPa) adopting the k-means clustering method (Lloyd, 1982). K-means clustering is an unsupervised machine learning algorithm used to partition a dataset into distinct groups or clusters, and popular in a wide variety of applications due to its simplicity, efficiency and effectiveness. Through calculation, there were 161 d of regional PM_2.5 heavy pollution days in the study regions, which is shown in the next section. Then, the profiles at the 11 stations in Bohai Rim on the 161 regional heavy polluted days are used to cluster (the number of samples is 11×161). We use the k-means ++ algorithm for cluster center initialization and the squared Euclidean distance to measure the similarity to the centroid. We selected the numbers of clusters (2–8) for classification of T, and then combined the elbow method (the corner of the Sum Square Error, shown in Fig. S1 in the Supplement) and the representativity of T profiles to determine the last number of clusters (=5 in this study). The numbers of horizontal and vertical wind component clusters (also 5 clusters) were selected along the T clustering.

We used the Random Forest algorithm to compare and rank the importance of various factors to pollution RF and daily total precipitation. The variable factors concerned in this study were PM_2.5, T, and 3 wind components at four levels (500, 700, 850, and 1000 hPa). The Random Forest method is a popular ensemble learning technique that combines multiple decision trees to improve prediction accuracy and reduce overfitting (Breiman, 2001). In addition, it performs excellently for evaluating the independent variables' importance (Cutler et al., 2007). This study mainly used the “out-of-bag” observations method (Archer and Kimes, 2008) in the Random Forest regression model to calculate the importances of variables. Out-of-bag predictor importance estimates by permutation measure how influential the model's predictor variables are at predicting the response. Thus, the larger the calculated value, the greater its importance. For the random forest model training, this study employed a widely used 10-fold cross-validation (CV) method. Through repeated tests, we obtained the optimal hyperparameter of the number of trees from 20 to 100 for different prediction variables in each grid and the number of leaf used the default of 5. The coefficient of determination (R2), root mean square error (RMSE) and mean absolute error (MAE) were used to evaluate the model performance, which was shown in Table S2.

Figure 2 exhibited the data usage workflow and framework in this work. The CMEE PM_2.5 data at sites and CERES net radiation flux data were used to show the characteristics of PM_2.5 and RF on regional heavy pollution days (RHPD) in the Bohai Rim. To explore the characteristics of regional pollution around the Bohai Sea, we identified regional PM_2.5 heavy pollution events with multiple stations experiencing PM_2.5 heavy pollution on the same days. For each region, a heavy pollution day was defined as when more than half of the stations within the region were heavily polluted. The regional clean day is defined as the day with all stations PM2.5<75 µg m⁻³ within the study area. This threshold is based on the China National Ambient Air Quality Standards for PM_2.5 in 2012.

Subsequently, CMEE, CERES, and ERA5 data were combined to analyze the impact of meteorological profile types (temperature and winds) on surface PM_2.5 and RF on regional heavy pollution days by using the k-means clustering method at the stations. The RF and meteorological parameters at stations were extracted from grid data of CERES and ERA5, respectively. The extracting method is that the grid data at the site's location indicates the site's values. For the k-means clustering, we clustered the T, horizontal, and vertical winds separately to capture variations in the height of temperature inversion layers and to reveal the relative importance of temperature and wind profile variations below 850 hPa on PM_2.5 and RF. The clustering of combined T and winds by the k-means method failed to capture the temperature inversion layers, and could not reveal the relative importance (see Figs. S2 and S3). Since we cluster based on separate parameters in the boundary, the standardization before clustering becomes unnecessary, as standardized and unstandardized results are essentially consistent (see Fig. S4).

To explore the relative importance of factors to pollution RF and precipitation on regional heavy pollution days in the Bohai regions, the gridded data of CERES, ERA-5, and TAP were jointly applied to the random forest algorithm. Due to the differences in the spatial resolution of PM_2.5 (from TAP), meteorological parameters (from ERA-5) and radiation data (from CERES), all data needed to be interpolated to a uniform resolution prior to machine learning training. All datasets were interpolated to the resolution of the ERA-5 dataset: 0.25°×0.25°. The CERES radiation data (originally at 1° resolution) were interpolated to 0.25° using a linear interpolation method. Similarly, the TAP PM_2.5 data (with resolutions of 10 km or 0.1°) were also interpolated to 0.25° using linear interpolation. However, before the interpolation, NaN values in the TAP dataset (corresponding to ocean areas) were set to zero, and grid points adjacent to land with zero values were replaced with values from the nearest terrestrial grid points. This assumption is reasonable given the lower anthropogenic emissions over the ocean compared to land areas. A comparison between the interpolated data and the original data is provided in Fig. S5. The spatial distributions of the interpolated and original datasets are generally consistent, with minor discrepancies observed only at a few grid points exhibiting abrupt value changes. Since the results of this study primarily focus on regional averages, the errors introduced at a limited number of grid points have less impact on the regional mean outcomes. Given the disparate units and scales of the input variables, we used the Z-Score method to standardize the input variables before the random forest training.

The statistical characteristics of PM_2.5 concentrations at the regions and stations in the Bohai Rim during autumn and winter from 2014 to 2023 are shown in Fig. 3. The average PM_2.5 concentration at all 11 stations around the Bohai Rim during the study period was 52.80±45.34 µg m⁻³, showing a slightly higher value than that of about 50 µg m⁻³ in the Yangtze River Delta and 45–48 µg m⁻³ in the Pearl River Delta of China's economic regions (Hou et al., 2019; Tao et al., 2017). Regionally, the mean daily PM_2.5 concentrations were 60.97, 49.90, and 49.57 µg m⁻³ in the BLT, NB, and SB regions, respectively (i.e., BLT > NB > SB). Among these stations, Cangzhou (the westernmost station in the SB region) experienced the highest mean PM_2.5 concentration (68.11±51.68 µg m⁻³). In contrast, Weihai station (30.57±26.12 µg m⁻³), also in the SB but easternmost, showed the lowest PM_2.5 concentration. In general, although the mean PM_2.5 concentration in the NB region was slightly higher than that in the SB, there were no significant north-south differences in Bohai Rim. However, a clear east-west gradient was observed in Bohai Rim, with the western part experiencing more aerosol pollution than the eastern area.

According to the China National Ambient Air Quality Standards for PM_2.5 in 2012 (GB3095–2012 and HJ 633–2012), we calculated the frequencies of PM_2.5 concentrations at different levels during autumn and winter from 2014–2023 (Fig. 3b). All stations experienced heavy pollution days (daily PM2.5>150 µg m⁻³), with the highest frequency at Langfang (8.70 %) and lowest at Weihai (0.52 %). But not all stations experienced severe pollution days (daily PM2.5>250 µg m⁻³), such as Yantai and Weihai stations in the SB region. The frequencies of heavy pollution days were 6.87 %–8.70 % in BLT, 1.32 %–7.84 % in NB, and 0.52 %–7.96 % in the SB region. The BLT region (the west of Bohai Sea) experienced relatively balanced heavy pollution days, whereas the NB and SB regions exhibited higher frequencies of heavy pollution days at western stations but lower frequencies at eastern stations, indicating the western area suffered more aerosol heavy pollution than the eastern area in the Bohai Rim.

Figure 3c shows the heavy pollution days for stations and regions. There were 130, 51, and 74 d with daily PM_2.5 reaching heavy pollution levels in the BLT, NB, and SB regions, respectively. The BLT region exhibited the most of heavy pollution days, and its periods of pollution often coincided with the other two regions, suggesting the possible transport of air pollution through BLT to the other two regions. In total, there were 161 d of regional heavy pollution during autumn and winter in 2014–2023, with a significant decrease from 2017 and even zero in 2021 and 2023. The decreased trend of regional heavy pollution can be attributed to China's air pollution control policies implemented from 2013, as well as the effect of the COVID-19 epidemic beginning in 2019.

Radiative forcing (RF) is a widely used parameter for measuring impacts on climate. Aerosol radiative forcing refers to the effect of anthropogenic aerosols on radiative fluxes at the surface and at the top of the atmosphere (TOA), as well as in the atmosphere. Figure 4 illustrates the short-wave RF on regional PM_2.5 heavy pollution days at the surface and TOA, as well as in the atmosphere for clear-sky and all-sky in the three study regions. The results showed that regional PM_2.5 heavy pollution reduced net shortwave radiation reaching the surface, increased the net radiation in the atmosphere, and caused radiative perturbations at the TOA in the study regions. These findings agreed with previous research (Park et al. 2001; Lin et al. 2022). However, our work showed notable regional heterogeneity. At the surface, RF can be up to -70 Wm⁻² in clear-sky, and relatively lower at -55 Wm⁻² in all-sky, with the largest impact in the NB region. At the TOA, pollution-induced RF is negative in most parts of the BLT and SB regions with values up to ∼-8 Wm⁻², but positive in most of the NB region (up to ∼+8 Wm⁻²), as the positive and negative regions are mainly reflected in the sea and land. Within the atmosphere, the values of pollution RF can reach +80 Wm⁻² in clear-sky and +60 Wm⁻² in all-sky, with also the largest impact in the NB region, followed by the BLT region. The RF values in clear-sky were higher than those in all-sky, which may be explained by the effect of clouds. The regional variations showed high values in the NB region, which did not agree with PM_2.5 concentrations in the three regions (Fig. 3a). This discrepancy may be related to the aerosol vertical profiles, aerosol composition, and even the diffusion and transport of aerosols. For instance, the longer heating season in the NB region may result in higher emissions of absorbing aerosols (such as black carbon), leading to a stronger atmospheric heating effect per unit aerosol mass. Besides, aerosols concentrated at higher altitudes over the ocean due to the regional transport may increase their radiative efficiency due to altered surface-atmosphere interactions. The impacts of diffusion and transport factors are analyzed in the following sections.

The T clusters and their statistics of stations, PM_2.5, and RF are shown in Fig. 5. The five T types in Fig. 5a can represent three temperature stratifications (decreasing stratification-T_C1, decreasing with isothermal stratification-T_C2, and inversion stratification-T_C3-5) and the inversion layers at different altitudes (low-altitude inversion-T_C3, mid-altitude inversion-T_C4, and upper-altitude inversion-T_C5). The decreasing stratification type T_C1 occurred most frequently (>50%) at all stations, followed by T_C2 and T_C3 (5 %–20 %) (Fig. 5b). T_C5 was the least at most stations, except for Qinhuangdao and Huludao, where the lowest frequency was the T_C4 type. The comparison of proportions of different temperature profile types on all days, regional clean days, and regional heavy pollution days in the study period (Fig. S6) showed clearly that the proportion of temperature inversions occurring on regional heavy pollution days was significantly higher than that on regional clean days, and also exceeded the proportion across all days, indicating the significant role of temperature inversions on regional heavy pollution days. The PM_2.5 concentrations at different T types in Fig. 5c exhibited notable variations, with low values at T_C1-2 (decreasing stratification and with isothermal stratification) and relatively high values at inversion stratifications T_C3-5. For the altitude of inversion, PM_2.5 concentrations at T_C3 and C4 were higher than at T_C5, indicating that low- to medium-altitude inversions are more conducive to aerosol heavy pollution than the high-altitude inversion. The finding of low-altitude inversion favorable to air pollution is consistent with the past studies (Sun et al., 2025; Wolf et al., 2014; Xiang et al., 2019). However, this effect of T inversion did not occur at all regions in the Bohai Rim, as the BLT region showed lower PM_2.5 at T_C5. This could be related to the aerosol emissions and the lower frequency of T_C5 in the BLT region.

The pollution RF at the surface for different T types in Fig. 5d was higher at T_C2, T_C4, and T_C5 (-63.82 to -68.23 Wm⁻², i.e., T stratification with isothermal layers at high altitude and medium- to high-altitude inversions) and lower at T_C1 and T_C3 (-51.13 to -53.50 Wm⁻², i.e., decreasing stratification and low-altitude inversion), which partially agreed with the surface PM_2.5 concentrations in Fig. 5c (high at T_C4-5 and low at T_C1). The RF is the result of the total column aerosol, not the surface. RF at T_C3 was lowest, for this low-altitude inversion restrained the aerosol to the surface, leading to high surface PM_2.5 but not high column aerosol. The highest surface RF at T_C2 can be explained by the fact that this T stratification allows the aerosol to reach a relatively higher altitude, with the possibility of lower surface PM_2.5 but high total column aerosol, leading to higher RF at T_C2. At the TOA (Fig. 5e), RF values were high at T_C3 and T_C5 but with opposite signs, which was related to column aerosol and also the aerosol absorption properties determined by aerosol composition. Within the atmosphere (Fig. 5f), the variations of RF at the five T types resembled those at the surface, which was also related to column aerosol and aerosol composition. Regarding regional differences, the NB region showed a higher RF value than BLT and SB, which may be partially attributed to the effect of pollution transport.

Figure 6 shows the UV clusters and their statistics of surface PM_2.5, and RF. The clusters showed that U wind increased with height with different direction of C3 and C4 in lower levels, while the variations in V wind were plentiful with opposite direction of C1 to other classes and smaller speeds of C2 and C3 in the lower levels (Fig. 6a and b). The surface PM_2.5 concentrations in different UV types in Fig. 6c showed some variations but were not apparent as T clusters, with high values in UV_C1-3 and relatively low values in UV_C4-5. The relatively high PM_2.5 concentration may be related to wind direction and speed, i.e., lower horizontal wind speeds at low levels in both UV_C2-3 (unfavorable for dispersion) and the anomalous direction of V wind in UV_C1 (limited dispersion due to topography) in agreement with the previous research (Liu et al., 2019a; Song et al., 2025; Wu et al., 2018; Zhang et al., 2018). All regions showed higher PM_2.5 in UV_C1-3, indicating that the horizontal speed and the direction of the V-component were important factors for pollution dispersion in the Bohai Rim. At the surface, the pollution RF in different UV types in Fig. 6d was higher in UV_C2-3 and lower in UV_C1 and UV_C4-5, indicating lower horizontal speeds at low levels (UV_C2-3 unfavorable for dispersion) causing higher pollution RF. The RF variations among UV clusters mostly matched with surface PM_2.5 changes, suggesting that horizontal diffusion differed from the T inversion that restricted the aerosol near the surface. Given the similarity and conciseness, the percentage statistic of stations and RF at the TOA and in the atmosphere of the five horizontal winds clusters is shown in Fig. S7. Regionally, the NB region also exhibited higher RF values at the surface and in the atmosphere than BLT and SB, which may be partially attributed to the effect of pollution transport above the boundary layer. This effect will be discussed in Sect. 3.3.

Vertical wind may also affect aerosol pollution and its RF, so W wind profiles were clustered and the same number of five clusters were selected (seen in Fig. 7). The five W clusters (Fig. 7a) showed large changes with the height, with predominantly upward of C2-3, downward of C4-5, and ascending firstly and then descending of C1 below 850 hPa. The percentage statistic of stations and RF at the TOA and in the atmosphere of the five W clusters is shown in Fig. S8. Compared with T and horizontal wind clustering, the proportions of the five categories for vertical wind showed no significant differences, with little higher proportions in W_C1-2. The variations in PM_2.5 concentrations in different W wind types (Fig. 7b) were not as significant as T and UV clusters, with only slightly high values at W_C1-3 and little low values at W_C4-5. The reason may be that the vertical winds were ascending motion at low levels in W_C1-3, which helped for aerosol dispersion after emission. Conversely, the W winds in W_C4-5 at low levels displayed descending motion, not conducive to diffusion and emission of aerosol. As for the regional variations, this effect of W wind direction was less obvious at NB and SB regions. This may be related to lower aerosol emissions at these two regions than the BLT region, as well as related to aerosol transport. The surface pollution RF at different W types in Fig. 7c was higher in W_C1-3 and lower in W_C4-5, indicating that upward motion at low levels caused higher pollution RF. However, the differences among W profile types were not significant, suggesting lower importance to RF of vertical wind than T and horizontal winds. The RF variations in W clusters mostly matched with changes in the surface PM_2.5 concentrations, implying that vertical diffusion and horizontal diffusion were not as same as the T inversion restraining the aerosol to the surface. Regional variations resembled those seen in T and UV clusters.

Figure 8 illustrates the importance of surface PM_2.5, winds, and T at four levels to the RF on regional heavy polluted days. For RF at the surface in clear-sky, PM_2.5, V wind at high levels (500–700 hPa) and T in low layers (700–1000 hPa) were relatively important factors, with the largest importance of PM_2.5 in all study regions. These indicated that surface aerosol concentration, meridional transport, and thermal diffusion in low layers were more important to pollution RF around the Bohai Rim area. Among the three subregions, the importance of T in the lower layer was relatively weaker in the BLT and NB regions (surface aerosol concentration and meridional transport were more important in these two regions), while the importance of V wind at high levels in the SB region was lower (surface aerosol concentration and thermal diffusion in lower layers were more important in the SB region). In all-sky, the relatively important factors were as same as that in clear-sky, but the most important factor was V wind at high level (500 hPa) instead of surface PM_2.5, suggesting the meridional transport became more important than surface aerosol concentration to pollution RF in the all-sky.

Regarding the RF at the TOA in clear-sky, the relatively important factors were T at all levels and U wind in high layers (500–700 hPa), with the most important factor of T (in the boundary layer). These were different from those for RF at the surface, indicating that zonal transport and thermal diffusion in the troposphere, especially the T in the boundary layer (not only reflecting the thermal diffusion but also affecting the aerosol chemical formation), were important for TOA RF in clear-sky. Regional differences were not significant, except for the slightly high importance of U wind in high layers in the BLT region. In all-sky, V500 and T500 were relatively important in all regions. But U850 was also important in the SB and ocean regions, and T at low level (1000 hPa) was also important in the BLT region. These reflected that meridional transport and thermal effects in the troposphere were important in all-sky for TOA RF, with the relative importance of zonal transport and diffusion in low levels in the SB and ocean regions.

For RF in the atmosphere, the important factors in clear-sky and all-sky were similar to those at the surface, although the importance of T (thermal effects) was weaker in the atmosphere than at the surface. Regionally, surface PM_2.5 was dominant in the SB region under clear-sky, while PM_2.5 and V700 (surface aerosol concentration and meridional transport) were nearly equally important in the NB and BLT regions. In all-sky, T500 and PM_2.5 were also relatively important after V500-700 in the BLT region, while U850 was also relatively important in the SB region. In the NB region, V factors are dominant.

We also calculated the importance using the Gradient Boosting algorithm. The results showed that the rank of factors' importance was basically unchanged and the factor with the most importance based on the Gradient Boosting algorithm was the same as that from the Random Forest algorithm. Therefore, we used the one machine learning method (Random Forest) to analyze in the following part.

The most important factor has been explored, but what is the grid proportion of each region with the maximum importance factor? Figure 9 shows the percentage of regional grids with maximum importance factor to the RF on regional heavy pollution days. In clear-sky, the most important factor of PM_2.5 at the surface and in the atmosphere can account for ∼50% of all areas with SB > NB > BLT and land > ocean. In addition, the grid percentage of V wind at higher levels (500 and 700 hPa) can reach 30 %–40 %, with the regional variations of SB < NB < BLT. In all-sky for the surface and atmosphere, the maximum factor of V500 accounted for the mean of ∼40% with the order BLT > SB > NB at the surface and SB > BLT > NB in the atmosphere. Furthermore, the PM_2.5 accounted for the mean of ∼20%, but with larger differences in each region (PM_2.5 in BLT can exceed 30 %). Regarding the RF at the TOA, T at low levels accounted for the majority in clear-sky with the largest percentage of 80 % for T1000 in the BLT region, while the larger percentages in all-sky can be of U850, V500, and T500, with the largest percentage of ∼50% for T500 in the BLT region.

The importance of factors to the pollution RF in clear-sky and all-sky showed a distinct difference: Surface PM_2.5 was the most important factor to surface and atmosphere RF in clear-sky, but V wind in high level (500 hPa) in all-sky. In clear-sky, high-concentration surface aerosols directly interact with shortwave radiation (through scattering and absorption), becoming the most important factors of pollution RF at the surface and in the atmosphere. Other meteorological factors may indirectly influence RF by altering aerosol distribution (including horizontal and vertical distribution) and aerosol chemistry formation to affect the RF indirectly, but their effect is far less pronounced than the direct interaction between high-concentration surface aerosols and radiation. In the all-sky, however, the pollution RF is primarily influenced by cloud-radiation interactions. Cloud radiative forcing is affected by cloud characteristics (cloud cover, cloud height, cloud type, etc.), which in turn are influenced by both aerosols and meteorological conditions, with the latter potentially playing a more significant role. The critical role of upper-level (500 hPa) V-wind may be attributed to the strong association between weather systems over the Bohai Rim region and upper-level zonal winds.

The relative importance of influencing factors between land and ocean also exhibited certain variations. Regarding the surface and atmosphere RF, the significance of PM_2.5 over land surpassed that over the ocean, while the importance of U and V over the ocean exceeded that over land areas (U500 in clear-sky, V1000 in all-sky). Given that land surfaces exhibited higher aerosol concentrations than oceans, the prominence of PM_2.5 over land was entirely justified. The heightened significance of U and V over the ocean was primarily linked to transport from land to the ocean. Based on the land-ocean distribution in Fig. 1, it is evident that zonal winds (particularly westerlies) facilitate the transport of land-based pollutants towards the ocean, while meridional winds also promote this transport (both southerly and northerly winds). Conversely, transport from the ocean to land also occurred, though its impact was comparatively minor relative to the influence of high-concentration aerosols over the land.

The importance of influencing factors to pollution RF showed heterogeneity across different regions. This may be related to variations in aerosol concentrations and pollution RF. In clear sky, the BLT region featured high PM_2.5 concentrations (Fig. 3) coupled with high RF values (Fig. 4a), whereas the SB region exhibited low PM_2.5 concentrations alongside low RF, illustrating the higher importance of PM_2.5 impacts on RF at the surface in these two regions (Fig. 8a). Conversely, the NB region, with low PM_2.5 concentrations but high RF, showed less importance of PM_2.5 than in the BLT and SB. Differences in the importance of meteorological parameters across regions may be related to local topography and geographical location. Figure 1 indicates that the northwestern parts of the BLT and NB regions border mountainous terrain, where wind direction and speed significantly influence pollution dispersion and transport. Consequently, wind (V-wind in the BLT region, U- and V-winds in the NB region) exhibited greater importance for RF in these regions compared to the SB region. Conversely, the SB region's lower latitude and absence of nearby high mountain ranges resulted in temperature factors being more important than in the BLT and NB regions.

The importance of PM_2.5, winds and temperature at four levels, and RF in all-sky to daily total precipitation on regional heavy pollution days in different regions is shown in Fig. 10a. The results showed that the pollution RF in all-sky (at the surface-RFSA, at the TOA-RFTA and in the atmosphere-RFAA) and W wind at high levels (500–700 hPa) were the two most important factors for daily total precipitation, followed by V wind at the high level. In contrast, surface PM_2.5, T at each level, and U wind were not important. These indicated that pollution RF in all-sky, vertical movement, and meridional transport in the upper layers were important to total precipitation on heavy aerosol pollution days around the Bohai Rim area, whereas other factors such as surface aerosol concentration and thermal effects were less important. The W wind can generate air convection, which is an essential condition for precipitation, and the V-component may bring the abundant water vapor for precipitation. The pollution RF in all sky (including effects of aerosol-radiation and aerosol-cloud) can affect the development of clouds, start time and duration of precipitation, and then the total precipitation, which is an inherent aerosol–meteorology–precipitation dilemma existing unexplained underlying physical processes (Guo et al., 2018; Li et al., 2011). Regionally, the importance of pollution RF in all-sky was stronger over the ocean areas. Among the three subregions, the importance of pollution RF in all-sky was NB > SB > BLT.

The percentage of regional grids with maximum importance factor to total precipitation (Fig. 10b) demonstrated the important factors of W in the upper layers could account for 15 %–20 % of all regions with NB > BLT > SB and land > ocean. In addition, the percentages of pollution RF in all-sky reached to ∼15% for all regions, with the largest percentage of ∼30% over ocean areas and the subregional variations of NB > SB > BLT. As is well known, vertical wind is a key factor for precipitation. Our results confirm it in agreement with previous researches (Jun and Rind, 2024; Wingo and Cecil, 2010). Moreover, the above findings suggested that pollution RFs in all-sky also played a significant role in total precipitation in the Bohai Rim regions. This insight can provide some assistance in precipitation forecasting around the Bohai Rim area, particularly by considering the role of radiative forcing on days with regional heavy pollution.