## 2 Materials and Methods
### Study Area and Data Sources
Moreover, as per regulations, (1) when V\({}_{\rm M}\) < 800 m, the V\({}_{\rm M}\) value should be reported in increments of 50 m; (2) when 800 m \(\leq\) V\({}_{\rm M}\) < 5000 m, the V\({}_{\rm M}\) value should be reported in increments of 1000 m; (3) when 5000 m \(\leq\) V\({}_{\rm M}\) < 10,000 m, the V\({}_{\rm M}\) value should be reported in increments of 1000 m; (4) if an observation does not fulfil the corresponding reporting requirement, the V\({}_{\rm M}\) value should be rounded off to the nearest level; and (5) when V\({}_{\rm M}\)\(\geq\) 10,000 m, the V\({}_{\rm M}\) value should be recorded as 9999 [29]. Thus, we processed all V\({}_{\rm I}\) data according to these criteria and eliminated the data corresponding to the time points with a V\({}_{\rm M}\) of 9999, obtaining a valid dataset consisting of 14,349 hourly time points. Moreover, since the upper detection limit of LT was 10,000 m, all FD data greater than 10,000 m were set to 10,000 m.  
The distance between the reference targets (target lamps) and the manual observation platform was determined by professional staff using precision instruments to approximate the true value of visibility. Therefore, the V\({}_{\rm M}\) levels were graded according to the distribution range of these reference targets. As shown in Figure 2, 10 targets (lamps) in four groups were distributed on almost the same distance contour; thus, we categorised V\({}_{\rm M}\) into the following eight levels after merging the adjacent targets (lamps): (1) V\({}_{\rm M}\)\(\leq\) 368 m; (2) 368 m \(<\) V\({}_{\rm M}\)\(\leq\) 847 m; (3) 847 m \(<\) V\({}_{\rm M}\)\(\leq\) 1692 m; (4) 1692 m \(<\) V\({}_{\rm M}\)\(\leq\) 2539 m; (5) 2539 m \(<\) V\({}_{\rm M}\)\(\leq\) 3016 m; (6) 3016 m \(<\) V\({}_{\rm M}\)\(\leq\) 4017 m; (7) 4017 m \(<\) V\({}_{\rm M}\)\(\leq\) 6403 m; and (8) 6403 m \(<\) V\({}_{\rm M}\)\(\leq\) 9595 m. The sample size in each interval is shown in Table 2. Table 2 lists the sample numbers of each visibility classification shown in Figures 3-6, and Table 3 lists the sample numbers of the RH classification shown in Figures 7-9. Figure 4: (**a**) RMSE and (**b**) RRMSE under different \(\rm V_{M}\) levels from 2015 to 2020. Figure 3: Daily variations of RMSE and RRMSE (**(a)**: RMSE, (**b**): RRMSE). \begin{table}
\begin{tabular}{c c c c c c c c c} \hline
**RH Level** & **1** & **2** & **3** & **4** & **5** & **6** & **7** & **Total** \\ \hline LT\({}_{05}\) & 75 & 214 & 746 & 1745 & 2890 & 4944 & 3735 & 14,349 \\ FD & 41 & 166 & 668 & 1532 & 2775 & 5093 & 4074 & 14,349 \\ LT\({}_{23}\) & 21 & 127 & 554 & 1378 & 2662 & 4689 & 4918 & 14,349 \\ \hline \end{tabular}
\end{table} 
Table 3: Distribution of \(\rm V_{I}\) sample size in different RH intervals (unit: hourly time points). Figure 5: Daily AVG variation of \(\Delta\)V from 2015 to 2020 (**a**) and AVG of \(\Delta\)V under various \(\rm V_{M}\) values (**b**). Figure 6: \(Cont.\)  
Figure 8: Distributions of (**a**) RMSE and (**b**) RRMSE under different RH levels from 2015 to 2020. As Xiamen Airport is located near the sea, where the RH is high all year round, data corresponding to RH < 35% only accounted for 0.08% of the effective sample size. Therefore, we graded the RH values into the following seven levels: (1) RH < 45%; (2) 45% \(\leq\) RH < 55%; (3) 55% \(\leq\) RH < 65%; (4) 65% \(\leq\) RH < 75%; (5) 75% \(\leq\) RH < 85%; (6) 85% \(\leq\) RH < 95%; and (7) RH \(\geq\) 95%. The RH gauges were installed in the automatic weather stations near LT\({}_{05}\) and LT\({}_{23}\), and the RH values in the METAR messages were taken from the instrument near LT\({}_{05}\). The RH values for FD were the averages of the records of the RH gauges near LT\({}_{05}\) and LT\({}_{23}\). The distribution of the V\({}_{\rm I}\) sample size against RH is shown in Table 3.