Theil-Sen media trend analysis and Mann-Kendall significance test are two non-parametric tests. The method does not require the data to satisfy normal distribution, and is also capable of eliminating the interference of outliers and reflecting the overall trend of the time series (Li et al., 2023). In this study, Theil-Sen median trend analysis and Mann-Kendall test were used to analyze the trends of PM_2.5 and O₃. The formula is shown in Equation 1 (Chen and Zhang, 2024): β = M e d i a n X i − X j i − j , ∀ i > j (1) where i and j represent time series; Median represents the median value; β denotes the trend of the pollutant, and the positive or negative of β denotes the direction of the trend. When β > 0, it is an upward trend; the opposite is a downward trend.

The Mann-Kendall (MK) significance test used to detect the significance of data under long time series. The formulas for its calculation are shown as Equations 2–5: Z = S − 1 V a r S , S > 0 0 , S = 0 S + 1 V a r S , S < 0 (2) S = ∑ i = 1 n − 1 ∑ j = i + 1 n s g n X i − X j (3) s g n X i − X j = 1 , X i − X j > 0 0 , X i − X j = 0 − 1 , X i − X j < 0 (4) V a r S = n n − 1 2 n + 5 − ∑ i = 1 m t i t i − 1 t i + 5 18 (5) where n is the number of time series data; m is the number of knots (recurring data sets) in the sequence; t i is the width of the knot (number of data identities). The Z-test value was obtained using the sign function (sgn) and the variance of the series (Var(S)). The calculated Z-value was used to determine whether the time series data was significant or not. If |Z| ≤ Z 1 − α , the trend is insignificant; if |Z| > Z 1 − α , the trend is significant.

Spatial autocorrelation is a method for determining whether spatially constant variables are dependent on one another within the same distribution. This study used the global Moran’s I to calculate whether pollutants have noticeable spatial agglomeration features. The formula is shown in Equation 6 (Li et al., 2022): M o r a n ′ s   I = n ∑ i = 1 n ∑ j = 1 n W i j X i − X ¯ X j − X ¯ ∑ i = 1 n ∑ j = 1 n W i j ∑ i = 1 n X i − X ¯ 2 (6) where n represents the total amount of grids; X i and X j represents the pollutant concentrations of grids i and j, where i is not equal to j; X ¯ represents the average pollution concentration; W i j represents the spatial weight matrix. The Moran’s I index will be a value between −1 and 1. The global Moran’s I > 0 represents a positive correlation, indicating that PM_2.5 or O₃ similar grids tend to have a spatially clustered distribution. The global Moran’s I < 0 denotes negative correlation, which shows that PM_2.5 or O₃ similar grids tend to have a spatially discrete distribution. The global Moran’s I = 0 represents no correlation, indicating that PM_2.5 or O₃ grids tend to have a random distribution.

Additionally, this study employed the local Moran’s I to assess the clustering of pollutants’ local regions, thereby revealing the similarity or difference between spatial objects and their surrounding space. The formula is shown in Equation 7 (Yuan et al., 2022): L o c a l   M o r a n ′ s   I = n X i − X ¯ ∑ j = 1 n W i j X j − X ¯ ∑ i = 1 n X i − X ¯ 2 (7) where X i is the value of the corresponding attribute of grid i, and X j is the value of the corresponding attribute of grid j; W i j is the spatial weight matrix between grid i and j. Four categories can be derived from the local Moran’s I findings: ‘High-High’ type represents that pollutant as being relatively high compared with the value of the adjacent area. ‘High-Low’ type represents that pollutants are enclosed by low-value areas. ‘Low-High’ type represents that pollutants are enclosed by high-value areas. ‘Low-Low’ type represents that pollutant concentration and the value of the neighboring unit as being relatively low.

Pearson correlation analysis reflects the correlation between the two variables. The correlations between pollutants and influencing factors were depicted in this study using Pearson correlation analysis (Yang et al., 2019). The formula is shown in Equation 8: r = ∑ i = 1 n X i − X ¯ Y i − Y ¯ ∑ i = 1 n X i − X ¯ 2 ∑ i = 1 n Y i − Y ¯ 2 (8) where X i and Y i are the data of two variables respectively; X ¯ and Y ¯ are the average of two variables, respectively; r is the correlation coefficient, and r range is between −1 and 1. The closer r is to 1, and the stronger the correlation is, the closer r is to 0, demonstrating that the two variables seldom have any link.

Geographical detector can explain the spatial differentiation of geographical phenomena and elucidate their underlying causes. The fundamental idea is that the spatial distributions of X and Y should tend to be similar if X, the independent variable, significantly influences Y, the dependent variable (Cao et al., 2013). Utilizing the factor detector and interaction detector in the geographical detector, the primary influencing variables and interactions of the spatial distribution of pollutants were examined in this paper.

Factor detector involves the detection of the space difference of Y, the dependent variable, and exploring the extent to which a factor X explains the spatial differentiation of Y, measured by the value of q (Wang and Xu, 2017). The specific formula is shown in Equation 9: q = 1 − 1 N σ 2 ∑ i = 1 L N i σ i 2 (9) where q is the explanatory power of the factor to the variable Y; i = 1, 2, 3; L is the stratification of factor X or variable Y; and N are the number of units in layer i and the whole region, respectively. σ i 2 and σ 2 are the variances of layer i and region Y, respectively. The explanation power of factors X to Y increases with q value, which has a range of values from 0 to 1.

Interaction detector is the process of finding interactions between various risk variables, i.e., determining whether X _i and X _j together will increase or decrease the explaining ability of the dependent variable Y or whether X is not dependent on Y (Lin et al., 2021). The interaction results are presented in Table 1.

Figure 3 depicts the spatial variation of PM_2.5 in Fenwei Plain from 2014 to 2023. From 2014 to 2017, concentrations were greater than 75 μg/m³ at most low to middle altitudes areas. Over time, the extent of the high pollution zone is gradually reduced, with concentrations below 75 μg/m³ throughout the Fenwei Plain by 2020. It is evident that the Fen Wei Plain’s PM_2.5 pollution is steadily getting better. Notably, PM_2.5 exhibited a spatial pattern of high concentration in the middle areas and low concentration in the surrounding areas. The high pollution areas are mainly found in the low altitude areas such as Yuncheng, Xianyang, Weinan, and Linfen, while the PM_2.5 concentration in the high altitude and other marginal areas is low. This phenomenon may be attributed to topographical factors; specifically, the terrain of the Fenwei Plain is relatively low in its center while rising on all sides, which hampers pollutant dispersion and contributes to significant PM_2.5 pollution within the Fenwei Plain Basin.

To further reflect the trend of PM_2.5, this study used Theil-Sen trend analysis and Mann-Kendall significance to explore the trend of PM_2.5 from 2014 to 2023. The results are displayed in Figure 4. In the majority of areas, the PM_2.5 slope was smaller than 0, suggesting a general downward trend in PM_2.5. The type of declining trend is dominated by significant declines, with a few areas of slight declines concentrated in high altitude areas of the Fenwei Plain. Moreover, in contrast to the spatial distribution pattern of PM_2.5, the slope of PM_2.5 overall decreased as elevation decreased, and the more significant the declining tendency, the lower the height. Even if the PM_2.5 concentrations were higher at lower elevations, it was evident that these areas have been remarkably treated, particularly in Xianyang, Yuncheng, and Weinan.

Figure 5 depicts the O₃ spatial variation from 2014 to 2023. From 2014 to 2016, O₃ in the majority of the Fenwei Plain was below the national concentration limit of 100 μg/m³. In 2017, O₃ in the Fenwei Plain increased significantly, with the most notable increases in Yuncheng and Linfen. Between 2017 and 2023, O₃ pollution progressively spread from the central to the eastern regions, leading to an overall distribution of O₃ that was east-high and west-low. By 2023, O₃ level in the Fenwei Plain exceeded 110 μg/m³ in the east and 100 μg/m³ in the west. By 2023, the concentration of O₃ in the eastern region of the Fenwei Plain was higher than 110 μg/m³, and the concentration in the western region was also more than 100 μg/m³.

The O₃ trend analysis and significance test findings from 2014 to 2023 are shown in Figure 6. Over the whole region, the O₃ slope were more than 0. The O₃ concentration exhibited a noteworthy increase in the majority of the regions, particularly in the central regions of Jinzhong, Linfen, and Taiyuan, where the upward trend was particularly considerable and the slopes were greater. Moreover, although it was less noticeable than that of PM_2.5, the trend of O₃ also displayed an altitude differentiation feature.

Figure 7 depicts the multi-year average values of PM_2.5 and O₃ at different altitudes. The PM_2.5 concentrations varied significantly at low, middle, and high altitudes, followed by: low altitude area 50.97 μg/m³ > middle altitude area 38.28 μg/m³ > high altitude area 31.22 μg/m³. The concentration difference of O₃ is not obvious, followed by: low altitude area 100.07 μg/m³ > middle altitude area 99.11 μg/m³ > high altitude area 95.92 μg/m³. In low altitude area, PM_2.5 was greater than 45 μg/m³, whereas the concentration in the majority of regions was between 45–60 μg/m³. The highest concentration of O₃ was in the central region, while the concentration was substantially higher in the northern region than the southern region. In the middle altitude area, the range of PM_2.5 in most areas was 20–60 μg/m³, and the range of O₃ was 90–100 μg/m³. In high altitude area, the PM_2.5 range was 0–35 μg/m³, and the O₃ range was 80–95 μg/m³. Combining the spatiotemporal distribution of PM_2.5 and O₃ at different altitudes revealed that the two pollutants had similar changes as a result of the terrain, as concentrations for both were as follows: low altitude area > middle altitude area > high altitude area. This phenomenon may be attributable to the influence of social and economic factors such as vehicles, factories, and other pollutants in low-altitude regions, which result in high pollutant concentrations, while less artificial pollution in high-altitude regions results in low concentrations. In addition, compared to the change in O₃, the elevation gradient of PM_2.5 was significantly greater, indicating that terrain significantly affected PM_2.5 but had a smaller impact on O₃.

The analysis of the global spatial autocorrelation of PM_2.5 and O₃ in Fenwei Plain revealed that the global Moran’s I of PM_2.5 and O₃ was greater than 0.9, indicating significant spatial autocorrelation and spatial agglomeration. Figure 8A shows that the ‘High-High’ clustering of PM_2.5 was primarily found in low altitude areas of Linfen, Yuncheng, Xianyang, Luoyang, Weinan, and Xi’an, as well as at the junction of Lvliang, Taiyuan, and Jinzhong. These areas and their surroundings exhibited high levels of PM_2.5 pollution, making them the regions with significant PM_2.5 pollution in Fenwei Plain. The “low-low” clustering of PM_2.5 was primarily found in high altitude areas like the west side of Taiyuan, the central part of Lvliang, the southeastern part of Jinzhong, and the southern edge of the Fenwei Plain. This suggests that these areas and their surroundings have generally low levels of PM_2.5 and are less polluted. As shown in Figure 8B, the clustering of high levels of O₃ was predominantly found in middle and low altitude areas, such as Yuncheng, Weinan, the northern part of Luoyang, the estern part of Linfen, northern part of Jinzhong, and the northwestern fringe region. This suggests that O₃ levels are generally elevated in these areas and their vicinity. The “low-low” clustering of O₃ was seen in the middle and high altitude areas of Xi’an, and Baoji, suggesting that O₃ is low in these areas and their surroundings. PM_2.5 and O₃ exhibited spatial concentration overlap. Overall, the overlapping areas of PM_2.5 and O₃ high pollution centers were mostly found in the low altitude areas of Yuncheng, Weinan, Linfen, and Luoyang. The low pollution overlap areas were mainly found in the middle and high altitude areas, such as Baoji, and Xi’an. PM_2.5 and O₃ exhibited local spatial synergies, indicating a necessity for coordinated treatment of both pollutants.

This study uses Pearson correlation analysis to study the linear relationship between PM_2.5, O₃, and three types of influential factors. Table 2 shows the results of the correlation analysis of PM_2.5 and O₃ with the three categories of influencing factors at various altitude scales. For the entire Fenwei Plain, the correlated coefficients between the main influential factors and PM_2.5 were as follows: SO₂ (0.8638) > GDP (−0.824) > precipitation (−0.5779), and for O₃, GDP (0.8896) > SO₂ (−0.8555) > precipitation (0.6385). The two pollutants had comparable primary influence factors, but their coefficients were opposite. This could be a significant inverse correlation between PM_2.5 and O₃. For the low, middle, and high altitude areas, the relevant PM_2.5 and O₃ coefficients were extremely similar throughout the entire region. The correlated coefficients between PM_2.5 and the three main influence factors (precipitation, GDP, and SO₂) decreased progressively with increasing altitude, whereas the correlation coefficient between O₃ and the three most influential factors was not significantly correlated with altitude.

Correlation analysis does not imply causation. PM_2.5 and O₃ spatial pollution characteristics are the result of numerous complex factors, such as meteorology, social economy, and precursor pollutants, and are not only a single linear relationship or influenced by a single pollutant. Therefore, this paper further identified the driving factors of PM_2.5 and O₃ spatial differentiation at low, middle, and high altitudes in the Fenwei Plain by using the detector and interaction detector of the geographic detector.