Hourly concentrations of surface PM2.5 (particulate matter with an aerodynamic diameter equal to or less than 2.5 µm), PM10 (particulate matter with an aerodynamic diameter equal to or less than 10 µm), SO2 (sulfur dioxide), NO2 (nitrogen dioxide), and CO (carbon monoxide) in the winters (December–February) from December 2014 to February 2020 in 18 cities of the SCB (Fig. 1) are obtained from the Ministry of Ecology and Environment of the People's Republic of China (http://www.mee.gov.cn/xxgk2018/, last access: 22 January 2020). We calculate the city-wide average concentrations of the five air pollutants by arithmetically averaging their concentration at the national air quality monitoring sites located in the urban areas of that city based on the technical regulation for ambient air quality assessment (on trial) (MEP, 2013; Ning et al., 2020). Among the 18 cities in the SCB, 10 (Leshan, Meishan, Ziyang, Guangyuan, Bazhong, Ya'an, Dazhou, Suining, Guang'an, and Neijiang) began monitoring air quality on 1 January 2015. Hence, the starting date of air quality data for these 10 cities is 1 December 2015. The starting date of air quality data for the remaining eight cities (Chengdu, Deyang, Mianyang, Zigong, Yibin, Luzhou, Nanchong, and Chongqing) is 1 December 2014.

Hourly winter surface temperature data observed at 105 meteorological stations in the SCB (Fig. 1) from December 2006 to February 2020 are also collected. Their regional averages are used to determine the diurnal cycles of day-to-day temperature change. Additionally, daily mean surface wind speed in the 18 cities of the SCB is also collected. To explore the thermodynamic structure of the lower troposphere, daily potential temperature profiles at 20:00 Beijing time (BJT; UTC + 8 h) from four sounding stations in the SCB are also obtained. Four sounding stations, including Chengdu, Yibin, Dazhou, and Chongqing, are located in the northwest, southwest, northeast, and southeast of the basin, respectively (see the orange dots in Fig. 1). All these surface meteorological observations are obtained from the China Meteorological Administration (CMA) (http://data.cma.cn/data/, last access: 22 January 2020).

To obtain winter lower-troposphere stability and reveal the possible mechanism of the formation of diurnal cycles of day-to-day temperature change, 700 hPa temperature, air pressure and air temperature at 2 m above the ground, total cloud cover, u-component wind, and vertical velocity (w) at multiple pressure levels from December 2014 to February 2020 are collected from daily ERA-5 reanalysis data (0.25∘×0.25∘ grids) (https://cds.climate.copernicus.eu/#!/search?text=ERA5, last access: 22 January 2020). We collect the reanalysis data at four times each day (00:00, 06:00, 12:00, and 18:00 UTC) to calculate their daily mean values. The PBL height (PBLH) data at 06:00 UTC (14:00 BJT) are also obtained. PBLH is defined as the lowest model level where the bulk Richardson number first reaches the threshold value of 0.25 (Beljaars, 2006).

Clustering methods divide the objects into specific groups, with the goal that all data objects assigned to the same cluster have common characteristics, while different clusters have distinct characteristics (Darby, 2005). The clustering methods have been widely used in climate and environmental research (Bardossy et al., 1995; Cavazos, 2000; Luo and Lau, 2017; Bernier et al., 2019). In this study, the regional average values of day-to-day temperature change in the SCB and the K-means clustering method (MacQueen, 1967) are selected to classify the diurnal cycles of day-to-day temperature change because of the simplicity and convergence characteristics of the K-means clustering method. The details of the K-means clustering method can refer to MacQueen (1967) and Mokdad and Haddad (2017) and are also provided in the Supplement. Additionally, the Calinski–Harabasz criterion, also known as the variance ratio criterion, is utilized to determine the optimal number of clusters (Caliński and Harabasz, 1974). The ultimate goal of the Calinski–Harabasz criterion is to maximize the variance measure ratio of homogeneity within a cluster and heterogeneity between clusters (Chikumbo and Granville, 2019).

The selection of an optimal number of clusters is illustrated in Fig. 2, which shows Calinski–Harabasz values associated with the numbers of clusters ranging from 2 to 10. The Calinski–Harabasz value with three clusters reaches the highest value, indicating that the optimal number of clustering is three. Three dominant diurnal cycles of day-to-day temperature change are therefore identified in the SCB. The three typical diurnal cycles of day-to-day temperature change are depicted in Fig. 3. The days for Cluster 1, Cluster 2, and Cluster 3 are 455 (accounting for 36.9 % of total days), 413 (33.5 %), and 365 d (29.6 %), respectively, indicating that the differences in the occurrence frequency among the three diurnal cycles are not noticeable. However, the diurnal cycles of day-to-day temperature change among the three clusters exhibit obvious differences.

In particular, in Cluster 1 (diurnal cycle with increasing temperature), all the temperature changes are positive for 24 h throughout all days, indicating that temperature increases during the past 24 h and exhibits a maximum change approaching 1.5∘ between 16:00 and 17:00 BJT. In Cluster 2 (diurnal cycle with decreasing temperature in the afternoon), the temperature changes show negative values after 12:00 BJT and drop to the trough between 16:00 and 17:00 BJT, with a minimum value of -1.5∘, indicating that the cooling process is obvious in the afternoon. After 17:00 BJT, the absolute values of temperature change begin to decrease. The most prominent feature of Cluster 2 is that the obvious decrease in temperature appears in the afternoon. In Cluster 3 (diurnal cycle with decreasing temperature in the morning), all temperature changes are negative for 24 h throughout all days, and the obvious cooling process appears from 00:00 to 09:00 BJT. The temperature changes show the minimum value approaching -1.5∘ between 07:00 and 09:00 BJT. After 09:00 BJT, the absolute values of temperature change gradually reduce and are close to zero in the afternoon. The most prominent feature of Cluster 3 is that the obvious decrease in temperature appears in the morning.

To reveal the underlying mechanism of the formation of the above three diurnal cycles of day-to-day temperature change, we also investigate the nighttime and daytime day-to-day changes in total cloud cover that could play a key role in temperature changes by modulating atmospheric radiations. Figure 4 shows the nighttime and daytime day-to-day changes in total cloud cover associated with the three diurnal cycles. Corresponding to the diurnal cycle with increasing temperature (Cluster 1), the total cloud exhibits a slight increase in the eastern SCB and a decrease in the western SCB (Fig. 4a). The dipole spatial distribution could result in a weak change in the regional average temperature across the SCB during nighttime (Fig. 3). During daytime, negative changes in total cloud cover are observed in the entire basin (Fig. 4d) that are beneficial to the obvious increase in temperature in the afternoon (Fig. 3). In contrast, both the nighttime and daytime changes in total cloud cover are positive in the entire basin for Cluster 2 (Fig. 4b and e), which could induce the increasing temperature during nighttime and decreasing temperature during afternoon (Fig. 3). Corresponding to the diurnal cycle with decreasing temperature in the morning (Cluster 3), obvious decreases in the total cloud cover are observed in the entire basin during nighttime (Fig. 4c) that are beneficial to the temperature decrease.

Moreover, the SCB is located in the eastern Tibetan Plateau, and the complex topography could play a key role in modulating the temperature changes over the SCB (Ning et al., 2018b, 2019). Therefore, the vertical west–east cross-sections of the day-to-day changes in wind vectors (synthesized by u and w) at 14:00 BJT are also investigated to uncover the physical and dynamics reasons of the formation of the above diurnal cycles of day-to-day temperature change. As shown in Fig. 5b, a significant ascending motion is observed over the SCB that could induce the obviously decreasing temperature in the afternoon for Cluster 2 (Fig. 3). In contrast, the descending motion prevails over the SCB for Cluster 1 and Cluster 3, which is beneficial to the temperature increase in the afternoon and thus plays a key role in the day-to-day temperature change for these two diurnal cycles.

Heavy air pollution during winter in the SCB is mainly caused by high concentrations of particulate matter (PM2.5 and PM10) (Ning et al., 2018a). Therefore, the day-to-day changes in PM2.5 and PM10 concentrations following the three identified diurnal cycles within 1 d and the percentage values of the changes to the PM2.5 and PM10 concentrations on the current day are investigated and are shown in Figs. 6 and S1. Figure 6 depicts the spatial distributions of the following day-to-day changes in PM2.5 and PM10 concentrations associated with the three typical diurnal cycles. Under the diurnal cycle with increasing temperature (Cluster 1), nearly all parts of the SCB experience increases in PM2.5 and PM10 concentrations on the following day (Fig. 6a, d), and the increases are up to about 10% of the PM2.5 and PM10 concentrations on the current day (Fig. S1a, d). The regional average changes in PM2.5 and PM10 concentrations are up to +3.95 and +5.89 µg/m3, respectively.

In contrast, negative changes in PM2.5 and PM10 concentrations are observed in the entire basin for the diurnal cycle, with decreasing temperature in the afternoon (Cluster 2) (Fig. 6b, e), and account for about 8 % of the current-day concentrations (Fig. S1b, e), indicating the improvement of air quality on the following day. The regional average changes in PM2.5 and PM10 concentrations are up to -8.93 and -11.50 µg/m3, respectively. Under the diurnal cycle with decreasing temperature in the morning (Cluster 3), all parts of the SCB experience increases in PM2.5 and PM10 concentrations (Fig. 6c, f), and these increases account for 15 % of current-day concentrations (Fig. S1c, f), indicating the deterioration of air quality on the following day. It is noted that opposite changes in PM2.5 and PM10 concentrations are observed between Cluster 3 and Cluster 2 even though both of the two diurnal cycles show decreasing temperature. Compared with the diurnal cycle with increasing temperature (Cluster 1), the increases in PM2.5 and PM10 concentrations are larger for Cluster 3, and the regional average changes in PM2.5 and PM10 concentrations are up to +5.36 and +5.91 µg/m3, respectively.

The contributions of gaseous pollutants in the SCB to winter air pollution are also very important as the SCB has a large number of motor vehicles and industries (Ning et al., 2018a). Therefore, the following day-to-day changes in three major gaseous (SO2, NO2, and CO) concentrations associated with the three diurnal cycles are also investigated. Similar to particulate matter, the relationships between the following day-to-day changes in gaseous pollutant concentrations and the three diurnal cycles are consistent with the results for PM2.5 and PM10. As shown in Figs. 6g–o and S1g–o, nearly all parts of the SCB experience increases in SO2, NO2, and CO concentrations on the following day for Cluster 1 (diurnal cycle with increasing temperature) and Cluster 3 (diurnal cycle with decreasing temperature in the morning). In contrast, negative changes in SO2, NO2, and CO concentrations are observed in the entire basin for Cluster 2 (diurnal cycle with decreasing temperature in the afternoon).

Figures 6 and S1 collectively indicate that the air quality in the SCB corresponding to Cluster 1 and Cluster 3 will deteriorate on the following day, while the air quality corresponding to Cluster 2 will improve. These results suggest that the modulations of the following day-to-day changes in winter air quality by diurnal cycles of day-to-day temperature change are obvious and important. Thus, the diurnal cycles of day-to-day temperature change exhibit promising potential for winter air quality forecasting on the following day in the SCB.

To reveal the potential influence mechanism of the diurnal cycles of day-to-day temperature change on the following day-to-day changes in air quality, the atmospheric-dispersion conditions corresponding to the three identified diurnal cycles are investigated. Firstly, the following day-to-day changes in PT vertical profiles at four sounding stations in the SCB (Fig. 7) are examined to explore the thermodynamic structure in the lower troposphere. Then, the following day-to-day changes in the three meteorological parameters related to atmospheric-dispersion conditions, including LTS (Fig. 8a–c), PBLH (Fig. 8d–f), and WS (Fig. 8g–i), are also investigated to evaluate the evolutions of atmospheric-dispersion capacity.

Under the diurnal cycle with increasing temperature (Cluster 1), three sounding stations (Yibin, Dazhou, and Chongqing) experience increases in PT between 950 and 800 hPa on the following day (Fig. 7d,g, j). In Chengdu, decreased PT is observed below 900 hPa, while increased PT appears between 900 and 750 hPa (Fig. 7a). All the PT profiles over the four sounding stations show higher temperature change in the higher level (800–850 hPa) than the lower level (900–950 hPa), which could enhance the atmospheric stability in the lower troposphere. As shown in Fig. 8a, increased LTS is observed in most of the cities in the SCB, indicating that the atmospheric stratification in the lower troposphere becomes more stable. The stable atmospheric stratification inhibits the vertical mixing of the atmosphere and suppresses the development of the PBL (Karppinen et al., 2001; Bei et al., 2016). As shown in Fig. 8d, obviously decreased PBLH is observed in all 18 cities of the SCB.

Additionally, we also analyzed the following day-to-day changes in surface wind speed as the wind speed can represent the horizontal dispersion capacity of air pollutants (Lu et al., 2012; Deng et al., 2014). No noticeable decreases in wind speed appear in the SCB (Fig. 8g). These results suggest that the diurnal cycle with increasing temperature (Cluster 1) enhances atmospheric stability in the lower troposphere, which can weaken the vertical exchange of airflow and then suppress the development of the PBL, resulting in a small dispersion space of air pollutants and poor air quality in the SCB on the following day.

Compared with Cluster 1, an opposite vertical structure of PT changes (Fig. 7b, e, h, k) is observed for the diurnal cycle with decreasing temperature in the afternoon (Cluster 2), which could weaken the atmospheric stability in the lower troposphere. As shown in Fig. 8b, negative changes in LTS appear in all parts of the SCB, enhancing the vertical exchange of airflow and facilitating the development of the PBL. As a result, increased PBLH is observed in all parts of the SCB (Fig. 8e), and the regional average increment is up to 93.0 m. At the same time, the weakened atmospheric stability in the lower troposphere is also conducive to the development of surface wind speed. As shown in Fig. 8h, the surface wind speed in the entire SCB is strengthened obviously, indicating that the horizontal dispersion capacity of air pollutants is also improved. These results suggest that the diurnal cycle with decreasing temperature in the afternoon weakens atmospheric stability in the lower troposphere and creates good vertical mixing of airflow, which can promote the development of the PBL and surface wind speed, facilitating the improvement of air quality on the following day.

For the Cluster 3, the PT changes are not noticeable below 850 hPa over the four sounding stations. As shown in Fig. 7c, f, i, l, decreased PT is observed between 850 and 700 hPa, while obviously increased PT appears above 700 hPa. This vertical structure of PT changes suggests that the atmospheric stability is enhanced above the PBL over the SCB, which is demonstrated to play a key role in the formation of winter heavy-air-pollution events in the basin (Ning et al., 2018b, 2019). As shown in Fig. 8c, increased LTS appears in the entire SCB, and the increments of LTS are obviously larger than those for Cluster 1 (Fig. 8a), inhibiting the vertical mixing of atmosphere and suppressing the development of the PBL. As a result, decreased PBLH is observed in all parts of the SCB. Compared with Cluster 1, the enhanced atmospheric stability above the PBL also suppresses the development of surface wind speed. As shown in Fig. 8i, all parts of the SCB experience decreases in surface wind speed, weakening the horizontal dispersion capacity of air pollutants. These results suggest that both the vertical and horizontal dispersion capacity of air pollutants corresponding to Cluster 3 are worse than those corresponding to Cluster 1. The differences in the atmospheric-dispersion conditions between Cluster 3 and Cluster 1 can explain well that the air quality deterioration is more serious for Cluster 3 than Cluster 1 (Figs. 6 and S1).