# Estimating Eddy Dissipation Rate with QAR Flight Big Data
## 3 Results and Discussion  
According to the estimation method described in Section 2, we achieved the vertical overload (\(|\Delta n|\)), DEVG and EDR estimations via the Python programming language. First of all, we picked up the QAR data from a flight from Kunming Changshui International Airport to Ninglang Lake Airport on 6 October 2016. Results of the vertical overload (\(|\Delta n|\)), DEVG and EDR estimations are as shown in Figure 3a-c. Results show that the estimated \(|\Delta n|\) and DEVG are of similar patterns due to their linearly correlated calculations, while EDR estimations provide a very different perspective on AT risks. The former two indicators report physical bumps happening during the flight, and pointy and discrete AT events can be detected in Figure 3a,b. These results, however, could vary for a different aircraft, even under all the same atmospheric conditions outside. The EDR estimates in Figure 3c present segmented and continuous patterns, which conform with the general perceptions of atmospheric flow. Moreover, the segments of large EDR values match with the bumps presented in Figure 3a,b. All in all, EDR provides a more scientific indicator for evaluating AT risks during a flight than the former two indicators.  
Figure 3: Comparisons of vertical overload (\(\Delta n\)), DEVG, and EDR.  
EDR provides a measurement of AT risk from outside atmospheric conditions. It is meaningful to visualize the EDR estimates from historical QAR data for exploring AT risks. We thus visualized the EDR estimates with the QAR data collected from 1 January 2016 to 31 December 2018. Note that EDR for the Airbus and Boeing aircrafts are estimated individually due different parameter settings, and we present them in Figures 4 and 5, respectively. The black arrow indicates the approximate location of the departure airport and the black asterisk indicates the approximate location of the destination airport. In this study, we only utilized QAR data of the aircraft flying phrase in the air; the location of departure airports and destination airports is estimated based on the coordinates within the in-air trajectory. For each airline, the darker and bigger the point is, the greater the turbulent strength is anticipated. As seen from Figure 4, the severity of AT for Airbus aircrafts in the northwest region and areas around Beijing is apparently higher than in other areas. In Figure 5, the occurrence of AT for Boeing aircrafts in the southeastern coastal areas is more frequent than in the other areas, and the severity of AT is slightly higher than in other areas. The results provide a good overview on the spatial patterns of AT intensities; particularly, clusters appearing in both Figures 4 and 5 may indicate areas of high AT risks. These hotspots could be related to potential factors for further analysis, for example meteorological, environmental, and terrain factors. This forms a good topic for future studies, particularly fundamental for early-warning studies. Moreover, note that these EDR results are calculated with QAR data collected within three years. The temporal dimension could be incorporated to explore their spatio-temporal patterns, which could provide richer information for specific applications, like flight route planning.