# Characterization and Prediction of Air Transport Delays in China
## 5 Effect of Weather on Delay Dynamics
### Statistical Analysis
If one further compares the delay distributions corresponding to days with and without thunderstorms (see Figure 5), it is clear that delays are significantly higher in the latter case--all airports, except for ZLXY, yield a significant \(p\)-value in a [PERSON]'s two-sample \(t\)-test, for \(\alpha=0.01\) and with a Sidak correction for multiple testing. Two conclusions can here be drawn. On one hand, the presence of thunderstorms strongly impact the dynamics of the system; this is not surprising, as such adverse events force aircraft to reroute, or even, if they are very close to an airport, to temporarily suspend operations. On the other hand, it can be appreciated from Figure 5 that thunderstorms are not enough to explain all extreme delays; on the contrary, in most cases the days with highest average delays correspond to the no-thunderstorms group. These results seem to suggest that thunderstorms are responsible for the global increase of delays observed during summer, but at the same time, that instances of extreme delays are independent from the weather condition. We further tried to understand whether these dependencies are static, or have evolved over time. Table 4 reports the evolution of the \(\chi^{2}\) statistic, for each pair airport-metric, from the first to the second year of the data set--note that, being the degrees of freedom constant, the test statistic is proportional to the strength of the relationship. A clear trend is present in the temperature, for which the \(\chi^{2}\) statistics have become larger (and hence, the relationship stronger) through the end of 2017 and the beginning of 2018. Taking into account that in 2017 the system has experienced a substantial increase in traffic levels (see Figure 3), this may indicate that existing operational buffers have reached a limit, and that the presence of thunderstorms has become an even more important factor. \begin{table}
\begin{tabular}{l l l l l l l} \hline \hline
**Airport** & **Temperature** & **Wind Speed** & **Rain** & **Visibility** & **Thunderstorm** & **AQI** \\ \hline ZBAA & \(1.34\times 10^{-6}\) & \(3.53\times 10^{-4}\) & \(1.21\times 10^{-6}\) & 0.849 & \(6.47\times 10^{-12}\) & \(3.15\times 10^{-4}\) \\ ZSPD & \(6.87\times 10^{-26}\) & 0.127 & \(7.51\times 10^{-8}\) & 0.029 & \(4.70\times 10^{-13}\) & \(4.34\times 10^{-5}\) \\ ZGGG & \(2.05\times 10^{-15}\) & 0.355 & \(1.35\times 10^{-36}\) & 0.145 & \(2.40\times 10^{-32}\) & 0.114 \\ ZPPP & \(8.95\times 10^{-20}\) & \(6.03\times 10^{3}\) & \(9.31\times 10^{-26}\) & 0.957 & \(8.44\times 10^{-21}\) & – \\ ZGSZ & 0.951 & 0.951 & \(5.29\times 10^{-11}\) & \(2.60\times 10^{-4}\) & \(8.27\times 10^{-16}\) & – \\ ZUUU & \(9.62\times 10^{-7}\) & \(1.61\times 10^{-6}\) & 0.021 & \(9.42\times 10^{-6}\) & \(2.64\times 10^{-6}\) & \(5.80\times 10^{-3}\) \\ ZLXY & \(1.15\times 10^{-7}\) & 0.128 & 0.104 & \(6.61\times 10^{-6}\) & \(1.37\times 10^{-3}\) & – \\ ZUCK & \(2.48\times 10^{-31}\) & \(1.49\times 10^{-3}\) & 0.286 & \(8.98\times 10^{-11}\) & \(2.48\times 10^{-10}\) & – \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Statistical relationships between weather, air quality and delays. Columns 2–7 report the \(p\)-values of \(\chi^{2}\) tests assessing the dependence between the average delay at each airport and the corresponding weather condition, as well as the air quality index (AQI). Figure 4: Evolution of the average monthly delay (black solid line) and of the fraction of days with thunderstorms (green dashed line, right Y axis), for the top eight Chinese airports. Figure 5: Box-plots of the distributions of the average daily delays, for days without (left) and with (right) thunderstorms near or at the airport. The \(p\)-values of [PERSON]’s two-sample \(t\)-tests, assessing the equality of both distributions, are reported in the upper part of each panel.