# Characterization and Prediction of Air Transport Delays in China
## 5 Effect of Weather on Delay Dynamics
### Statistical Analysis  
The presence of relationships between the binarized daily delay level and the weather metrics described in Section 3.2 is here assessed by firstly constructing a contingency table, for each pair of \begin{table}
\begin{tabular}{c r r r r} \hline \hline
**Airport** & **2016.05–2016.10** & **2016.11–2017.04** & **2017.05–2017.10** & **2017.11–2018.04** & **2018.05–2018.11** \\ \hline Domestic & \(12.36\pm 6.16\) & \(10.88\pm 3.30\) & \(26.13\pm 16.62\) & \(4.78\pm 3.27\) & \(9.04\pm 7.24\) \\ ZBAA & \(12.17\pm 9.13\) & \(11.77\pm 5.56\) & \(31.52\pm 23.57\) & \(3.58\pm 4.21\) & \(9.47\pm 8.83\) \\ ZSPD & \(13.88\pm 9.16\) & \(4.54\pm 3.53\) & \(21.87\pm 18.14\) & \(-6.98\pm 3.15\) & \(4.00\pm 8.92\) \\ ZGGG & \(13.88\pm 9.48\) & \(6.16\pm 4.45\) & \(24.27\pm 16.86\) & \(0.52\pm 3.23\) & \(12.24\pm 10.46\) \\ ZPPP & \(7.85\pm 5.57\) & \(13.89\pm 10.31\) & \(23.92\pm 20.47\) & \(3.03\pm 6.66\) & \(6.18\pm 8.06\) \\ ZGSZ & \(27.60\pm 11.12\) & \(14.93\pm 7.49\) & \(39.78\pm 23.37\) & \(3.06\pm 4.53\) & \(19.96\pm 13.29\) \\ ZUUU & \(9.33\pm 6.19\) & \(11.96\pm 3.46\) & \(23.31\pm 18.51\) & \(2.38\pm 3.35\) & \(7.98\pm 8.23\) \\ ZLXY & \(6.10\pm 4.28\) & \(3.86\pm 1.79\) & \(18.99\pm 12.00\) & \(1.97\pm 4.33\) & \(2.94\pm 5.05\) \\ ZUCK & \(10.05\pm 6.94\) & \(6.49\pm 3.45\) & \(29.90\pm 18.84\) & \(4.32\pm 2.53\) & \(9.76\pm 7.34\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Statistical analysis of delays by seasons. Columns report the average and standard deviation of delays, in the winter and summer seasons of 2016–2018, for the complete data set and for the top-eight airports in China. \begin{table}
\begin{tabular}{c r r r} \hline \hline
**Airport** & **pV Summer (2016 vs. 2017)** & **pV Winter (2016 vs. 2017)** & **pV Summer (2017 vs. 2018)** \\ \hline Domestic & \(0.1302\) & \(0.0149\) & \(0.0739\) \\ ZBAA & \(0.1342\) & \(0.0267\) & \(0.0950\) \\ ZSPD & \(0.4065\) & \(2.966\times 10^{-4}\) & \(0.0870\) \\ ZGGG & \(0.2649\) & \(0.0471\) & \(0.2108\) \\ ZPPP & \(0.1435\) & \(0.0808\) & \(0.1176\) \\ ZGSZ & \(0.3270\) & \(0.0158\) & \(0.1383\) \\ ZUUU & \(0.1593\) & \(1.246\times 10^{-3}\) & \(0.1350\) \\ ZLXY & \(0.0625\) & \(0.3979\) & \(0.0294\) \\ ZUCK & \(0.0667\) & \(0.2846\) & \(0.0642\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Statistical significance of delays by seasons. The columns report the \(p\)-value of a two-sample \(t\)-test checking if the delay was significantly different between the same season of two consecutive years. delay-metrics; then applying a \(\chi^{2}\) test. The resulting \(p\)-values are reported in Table 3. If one considers a significance level of \(\alpha=0.01\) (\(\alpha^{*}=2.28\times 10^{-4}\) with a Sidak correction for multiple testing), the second column of Table 3 indicates that the temperature and the presence of thunderstorms are almost always relevant factors. Additionally, the fourth and fifth columns of Table 3 suggest that airports can be divided in two groups: the largest five, whose delays have a high dependence on the presence of rain; and ZUUU, ZLXY and ZUCK, which are highly sensitive to visibility. Finally, ZBAA and ZSPD show a weak dependence on the AQI. Nevertheless, it has to be noted that this latter metric is correlated with the temperature (\(\sigma=0.167\)), the wind speed (\(\sigma=0.223\)) and rain (\(\sigma=0.054\)); its explanatory value may thus be limited. The strong dependence of delays with the temperature, and also partly with the presence of rain, suggests that they may be proxies of the presence of some extreme adverse weather events. In order to confirm this, Figure 4 depicts the evolution of the average monthly delay at each airport (black solid line), along with the fraction of days in which thunderstorms were reported at or near the corresponding airport (green dashed lines). It can be observed that both metrics are strongly correlated, with coefficients of determination \(R^{2}\) ranging from 0.171 and 0.734.