## 4 Probability Distribution and Relation
### Relation Analysis  
Figure 7 shows the contribution degree of SMEs to the MLH at different height intervals. From the temperature perspective (Figure 7a), the cold temperature (T1) makes the dust pollutants difficult to spread and contributes the most to the MLH1. The high temperature (T5) provides sufficient thermal conditions for the development of the ML, and the deep ML develops vigorously (MLH4). With the increase in temperature, the contribution degree to MLH1 and MLH4 showed a decreasing and increasing trend, respectively. In an extremely dry environment (RH1, Figure 7a), it is conducive to the development of MLH3, but the effect on MLH4 is not obvious. The reason may be that when the atmospheric water vapor content in the desert is very low, the dust aerosol content will dominate, which will lead to the increase of the vertical temperature gradient of the atmosphere and  
Figure 7: During the daytime, the contribution degree of surface meteorological elements to the mixing layer height at various height intervals. **(a)** The MLH and its corresponding atmospheric temperature (T) and relative humidity (RH). **(b)** The MLH and its corresponding horizontal visibility (VIS), near-surface wind speed (WS) and near-surface wind direction (WD). The beginning and end of the arrow indicate two related variables. The width of the arrow trunk signifies the degree of contribution to the mixing layer height, where a wider arrow trunk indicates a greater contribution. weaken the atmospheric convective activity. In the relatively dry environment (RH2), it plays a role in promoting the development of the ML higher than 1 km, specifically the MLH4. In a relatively humid environment (RH4 and RH5), the hygroscopic growth of dust particles is easier, the atmospheric stability can be enhanced, and the height distribution of the ML is low (MLH1). The invasion of cold air often leads to the generation of dust storms (VIS1), and the large amount of dust in the atmosphere can greatly weaken the solar radiation reaching the surface and hinder the penetration of laser beams, resulting in a low MLH distribution (MLH1, Figure 7b). The visibility of floating dust and blowing dust weather falls within the range of VIS2, which has sufficient contribution to all types of MLH. The probability of occurrence of excellent atmospheric visibility (VIS4) in the desert is low, and the effect on the MLH is not significant. When the horizontal wind speed is small (WS1, Figure 7b), on the one hand, the friction or retardation of the air flow mediated by the underlying surface will be more obvious, thus limiting the vertical mixing air; on the other hand, the weakening of the cooling effect of wind on the ground may reduce the temperature gradient of the atmosphere; finally, the MLH is generally distributed at a lower height (MLH1). With the increase in wind speed, the contribution to MLH1 gradually decreased. WS2 and WS3 belong to the wind speed range defined by floating dust weather, and both have different degrees of effects on the MLH higher than 1 km. It is easier to form dust storm weather when the wind speed falls within the range of WS4. Compared with the strong west-pathway airflow (WD3, Figure 7b), the east-pathway airflow (WD1) has a greater impact on the deep ML (MLH4). Since WD1 is adapted to the inertial oscillation mechanism of the low-level jet [54], the low-level jet can contain more momentum, strengthen wind shear, and promote the development of the ML in the TD [11; 13; 55; 56]. The gravity effect of the cold air, the different cooling amplitude on the slope terrain, and the foehn effect of the TP will lead to the generation of the downhill airflow (WD2), and the downhill airflow can enhance the turbulence intensity and contribute to MLH4 [29]. The thermal pump effect of the TP [51] and the blocking and lifting of the mountains will form the uphill airflow (WD4), which has an effect on MLH at different heights.