## 2 Materials and Methods
### Statistical Methods  
Based on statistical principles, we calculated the agreement rate and gross error rate of the data and conducted correlation analyses. V\({}_{\rm I}\) and V\({}_{\rm M}\) were compared according to the data's deviation, relative deviation, root mean square error (RMSE), and mean. The meanings of the above statistics are explained below.  
(1) Agreement rate: the V\({}_{\rm I}\) and V\({}_{\rm M}\) values were considered to be in agreement if the absolute value of the difference between them was less than or equal to two times the standard deviation of the difference [31]. The ratio of the cumulative number of agreements between V\({}_{\rm I}\) and V\({}_{\rm M}\) to the total number of valid observations was the agreement rate of the two visibility datasets, which reflected the consistency between V\({}_{\rm I}\) and V\({}_{\rm M}\).  
(2) Gross error rate: the difference between V\({}_{\rm I}\) and V\({}_{\rm M}\) was considered a gross error if its absolute value was greater than three times the standard deviation of the difference. The largest gross error value was then eliminated, the standard deviation of the difference between V\({}_{\rm I}\) and V\({}_{\rm M}\) was recalculated, and the difference values were filtered again according to the definition of the gross error to eliminate the largest one. The above steps were repeated until no difference values were considered gross errors. At this point, the number of gross error values eliminated was defined as the number of gross errors [31], and the ratio of the number of gross errors to the total number of effective observations was the gross error rate, which reflected the pattern of outliers in the difference between V\({}_{\rm I}\) and V\({}_{\rm M}\).  
(3) Deviation (\(\Delta\)V): the difference of V\({}_{\rm I}\) minus V\({}_{\rm M}\). The formula for calculating \(\Delta\)V is \(\Delta\)V = V\({}_{\rm I}-\)V\({}_{\rm M}\).  
(4) Relative deviation (\(\Delta\)V\({}_{\rm Mdi}\)): the ratio of \(\Delta\)V to V\({}_{\rm M}\). The formula for calculating \(\Delta\)V\({}_{\rm Mdi}\) is \(\Delta\)V\({}_{\rm Mdi}\) = \(\Delta\)V/V\({}_{\rm M}\).  
Figure 9: Proportional distributions of (**a**) \(\Delta\)V\({}_{\rm LT05}\), (**b**) \(\Delta\)V\({}_{\rm LT23}\), (**c**) \(\Delta\)V\({}_{\rm FD}\), and (**d**) \(\Delta\)V\({}_{\rm LT05-FD}\) under different RH levels from 2015 to 2020.  
(5) Root mean square error (RMSE): the square root of the mean of \(\Delta\)V squared, reflecting the absolute deviation of V1 from VM. The smaller the RMSE, the smaller the \(\Delta\)V. The calculation formula is as shown in Equation (1).  
\[\text{RMSE}=\sqrt{\frac{1}{\text{n}}\sum_{i=1}^{\text{n}}(\text{V}_{\text{II}}- \text{V}_{\text{Mi}})^{2}} \tag{1}\]  
where n is the sample size, Vii is the V1 value at the i-th time point, and VMi is the VM value at the i-th time point.  
(6) Relative root mean square error (RRMSE): the square root of the mean of \(\Delta\)VMdi squared, reflecting the relative deviation of V1 and VM. The smaller the RRMSE, the smaller the degree of V1's deviation relative to VM. The calculation formula is as shown in Equation (2).  
\[\text{RRMSE}=\sqrt{\frac{1}{\text{n}}\sum_{i=1}^{\text{n}}((\text{V}_{\text{ II}}-\text{V}_{\text{Mi}})/\text{V}_{\text{Mi}})^{2}} \tag{2}\]  
where n is the sample size, Vii is the V1 value at the i-th time point, and VMi is the VM value at the i-th time point.  
(7) The correlation coefficient \(r\) represents the correlation degree between V1 and VM. The larger the r value, the stronger the correlation. The formula is:  
\[\text{r}=\frac{\sum_{1}^{\text{n}}(\text{V}_{\text{II}}-\text{V}_{\text{I}}) \left(\text{V}_{\text{Mi}}-\text{V}_{\text{M}}\right)}{\sqrt{\sum_{1}^{\text {n}}\left(\text{V}_{\text{II}}-\text{V}_{\text{I}}\right)^{2}\sum_{1}^{\text {n}}\left(\text{V}_{\text{Mi}}-\text{V}_{\text{M}}\right)^{2}}} \tag{3}\]  
where n is the number of sample data, Vii is the value of V1 at time i, and VMi is the value of VM at time i.