## 3 Results
### RMSE and RRMSE of V1 Relative to VM  
#### 3.2.1 Daily Variation Characteristics of RMSE and RRMSE  
As can be seen from Figure 3, the daily variation distributions of the RMSE (Figure 3a) and RRMSE (Figure 3b) of the three visibility meters were both large at night and small at day. They gradually increased at night, reached the highest value before midnight, gradually decreased in the early morning, and reached a minimum in the forenoon. This indicated that the difference between V1 and VM was greater at night than during daytime, was the largest at midnight, and the smallest in the forenoon. This may be related to the fact that the number of target lamps at night was much less than the number of target  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Visibility Meter** & **LT\({}_{\text{05}}\)** & **LT\({}_{\text{23}}\)** & **FD** \\ \hline Agreement rate & 88.1\% & 93.2\% & 91.7\% \\ Gross error rate & 6.4\% & 7.6\% & 3.6\% \\ Correlation coefficient & 0.92 & 0.92 & 0.80 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Agreement rate, gross error rate, and correlation coefficient between V1 and VM.  
objects during the daytime (Figure 2). Manual observation of visibility at night is more subjective, and the V\({}_{\rm M}\) values obtained from different observers may vary greatly. Adding target lamps at night will effectively reduce the difference. In addition, Xiamen Airport is located in the north-eastern corner of Xiamen Island. Except for the north-eastern end facing the sea, the other three sides are surrounded by urban buildings. At night, city lights increase the brightness of the background, which reduces the brightness contrast of the target lamps, thereby affecting the observation results of the observer. When the lights are on at night, the difference between V\({}_{\rm I}\) and V\({}_{\rm M}\) increases, but after midnight, as the city lights decrease, the difference between V\({}_{\rm I}\) and V\({}_{\rm M}\) decreases.  
Among the three visibility meters, the RMSE and RRMSE of LT\({}_{05}\) were the smallest at all times, indicating the smallest difference between the V\({}_{\rm I}\) and V\({}_{\rm M}\) of LT\({}_{05}\). The RMSEs and RRMSEs of LT\({}_{23}\) were similar to those of FD. In most cases, the LT\({}_{23}\) values were slightly higher than those of FD and were significantly higher between 19:00 and 21:00. Notably, from 5:00 to 9:00, the RMSE of FD was higher than that of LT\({}_{23}\), which was the largest of the three, while the V\({}_{\rm M}\) of Xiamen Airport was the lowest at this time (Figure 3a). The RRMSE of LT\({}_{23}\) was abnormally large at 07:00 and 20:00. This may have been because LT\({}_{23}\) was installed on the coastal side, which makes it greatly affected by the air current over the sea. Thus, its V\({}_{\rm I}\) value fluctuates more than those of LT\({}_{05}\) and FD installed inland.  
In conclusion, anthropogenic causes increase the difference between V\({}_{\rm I}\) and V\({}_{\rm M}\) at night. The deviation and relative deviation of LT\({}_{05}\) are the smallest at all times of the day. In the early morning, when V\({}_{\rm M}\) is in a trough, the difference between the V\({}_{\rm I}\) and V\({}_{\rm M}\) of the forward-scatter meter is greater than that of the atmospheric transmissometer.