The flight data used in the analyses is provided by Travelsky Mobile Technology Limited, an affiliated company of Civil Aviation Administration of China. The available data covers the period from January 1, 2015 to December 31, 2019. In order to more clearly reveal the impacts of SPEs on flight times, the selected air routes were chosen based on certain criteria. These criteria included proximity to the polar jet stream, sufficient length to allow for a meaningful impact from the jet stream, and a sufficient number of flight records to ensure the credibility of the statistical results. As a result, the top 15 pairs of representative international air routes, characterized by the highest volume of flights, were identified, as the red lines shown in Fig. 1 (a). The total number of flight records analyzed amounts to 15,428. Detailed information regarding the selected air routes and their respective flight times is provided in the Appendix.
Figure 1 (a) illustrates the typical trajectories of the 15 selected air route pairs and the approximate location of the polar jet stream. The polar jet stream exhibits variability due to seasonal changes, climate fluctuations, and other influencing factors[33]. Consequently, flights along these selected routes may not always be affected by the polar jet stream throughout their journeys. To specifically focus on the region predominantly influenced by the polar jet stream during flight cruising, we narrow our attention to the box region between 45°-65°N and 20°-100°E (blue dashed region in Fig. 1a).
In addition, considering the deposition of high-energy particles into the atmosphere during SPEs and the associated atmospheric chemical reactions and energy exchange processes, it typically takes hours for SPEs to induce atmospheric heating and alter atmospheric circulation[9, 34, 35]. Therefore, we tentatively define the period 3 days after the onset of a SPE as the ‘SPE affected periods’, with the onset of the SPE designated as the key day (t = 0). For comparative analysis with quiet periods, we define the period of 15 days before and after the onset of a SPE as ‘Quiet Time Periods (QTPs)’, as shown in Fig. 1 (b).
In terms of flight direction, ‘westbound’ denotes flights traveling from China to Europe, predominantly encountering headwinds associated with the polar jet stream, while ‘eastbound’ refers to flights in the opposite direction. The list of SPEs is obtained from the National Oceanic and Atmospheric Administration Space Weather Prediction Center[37]. A SPE defined in the list is a period during which > 10MeV proton fluxes, measured by GOES spacecraft, exceed 10 pfu for 3 consecutive data points, with the event ending when the flux drops below this threshold. Finally, 8 SPEs are selected from the list during January 1, 2015 to December 30, 2019, the period for which flight data are available.
The vertical profiles of zonal wind speed are obtained from NOAA Physical Sciences Laboratory, and the NCEP/NCAR reanalysis data set are used on a standard latitude-longitude grid (2.5°×2.5°) [38, 39]. The trends in the speed are averaged over the blue dashed region (45°-65°N, 20°-100°E), where the polar jet stream can influence flights at typical cruising altitudes.
We first employ a comparative analysis approach to investigate the differences in flight times between eastbound and westbound flights during SPEs and QTPs (Fig. 2 and Fig. 3). Subsequently, a superposed epoch analysis is utilized to analyze the variations in flight times during the 8 SPEs (Fig. 4), and the corresponding daily mean trends in zonal wind speed difference within the blue region is also presented (Fig. 5). Finally, we employ the same superposed epoch analysis on the daily mean trends in zonal wind speed difference during 42 SPEs spanning an entire solar cycle (Fig. 6).