## 4 Probability Distribution and Relation
### Probability Distribution  
The probability distribution of MLH and SMEs in each month and season during the daytime is as shown in Figure 6. In spring, from the perspective of temperature and humidity (Figure 6b,c), the temperature increase rate from March to May was the fastest, and the proportion of relative humidity below 10% was the highest (28.41%). In terms of wind speed (Figure 6e), the proportion of wind speed greater than 3.5 m/s reached 17.56% in spring, which was the highest in each season, and May was the month with the strongest wind speed (>3.5 m/s, 21.84%). The proportion of visibility (Figure 6d) less than 10 km and less than 1 km in spring reached 62.12% and 3.35%, respectively, which were the highest percentages in all seasons. The material, thermal, and dynamic conditions in spring were sufficient, and the proportion of MLH higher than 3 km reached 22.13% (Figure 6a), which indicates that the development of ML was the most vigorous in this season.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & **MLH (km)** & **T (\({}^{\circ}\)C)** & **RH (\%)** & **VIS (km)** & **WS (m/s)** & **WD (\({}^{\circ}\))** \\ \hline I & [0, 1) & [\(-\)25, 0) & [0, 10) & [0, 1) & [0, 1) & [0, 90) \\ II & [1, 3) & [0, 10) & [10, 20) & [1, 10) & [1, 2) & [90, 180) \\ III & [3, 4) & [10, 20) & [20, 40) & [10, 20) & [2, 3.5) & [180, 270) \\ IV & [4, 6] & [20, 28) & [40, 60) & [20, 30) & [3.5, 9) & [270, 360) \\ V & & [28, 45) & [60, 100) & & & \\ \hline \hline \end{tabular}
\end{table}
Table 2: The division ranges for MLH and surface meteorological elements.  
Figure 6: During the daytime, the probability distribution of the mixing layer height and various surface meteorological elements in each month and season. (**a**) Mixing layer height. (**b**) Atmospheric temperature. (**c**) Relative humidity. (**d**) Horizontal visibility. (**e**) Near-surface wind speed. (**f**) Near-surface wind direction.  
In summer, most of the time was dominated by hot weather (>28 \({}^{\circ}\)C, 53.77%), the proportion of west-pathway wind was the highest in the whole season (30.01%), and the distribution characteristics of MLH were similar to those in spring (>3 km, 20.38%). On the one hand, the long-term high temperature made the temperature of the underlying surface much higher than that of the upper atmosphere, which is easy to form thermal convection; on the other hand, the thermal pump effect of the TP can produce convergent updrafts and lift dust [51; 52; 53], thus promoting the development of the ML. The most frequent deep ML formed in June (>4 km, 13.8%) [29].  
In fall, the rapid cooling led to a monthly increase in relative humidity, the visibility was the best (>10 km, 61%), the wind speed was small (<3.5 m/s, 94.86%), the atmospheric stability was improved, and the development of the ML was suppressed (<1 km, 60%).  
In winter, the temperature was the lowest (<0 \({}^{\circ}\)C, 53.68%), the relative humidity was the highest (>20%, 86.79%), the wind speed was the smallest (<3.5 m/s, 95.47%), the soil was easier to freeze, and the MLH was maintained at a lower height (<1 km, 77.62%).  
From an annual perspective, both the east-pathway airflow (39.67%) and west-pathway airflow (24.86%) occurred frequently, the proportion of visibility less than 10 km in the study site reached 48.9%, the wind speed was high (>3.5 m/s, 10.04%), and the MLH was relatively low (<1 km, 55.37%). The study site was deeply affected by dust weather.