Punto de paso obligatorio: tecnología y plataformas digitales

As shown in Fig. 4-2, the raw ACARS reports are not evenly distributed along altitude. Altitudes of data points vary from flight to flight. To simplify the processing, wind data from each flight track are re-sampled at 250 ft altitude intervals using linear interpolation. This altitude interval was selected to match

the sampling rate of the most detailed wind profiles from the raw ACARS data. Because the new wind samples have regular intervals along altitude, wind variations can be easily obtained by a direct comparison of data points from consecutive flight pairs at the same altitude. The re-sampled wind profile is denoted as Wj(h_n), where subscript j identifies each individual flight, and h_n denotes the re-sampling altitudes.

Flights are first sorted by arrival time at the destination airport. Wind variation is then calculated between consecutive flight pairs that are separated by less than 15 minutes. Wind variation, in terms of wind speed and direction, as experienced by each trailing flight j at each altitude could be obtained as:

°¯

In Eq. (4-1), subscripts V and D denote wind speed and direction respectively. Subscript j-1 identifies the leading flight in front of flight j. Wind direction change, computed by the second equation, has values within the range of (-180, 180] deg. Wind variation, in terms of east wind and north wind components, could be obtained as

°¯

In Eq. (4-2), subscripts E and N denote east and north wind components respectively. The wind variation profile for the sample flight is shown in Fig. 4-4 in terms of wind direction and wind speed in a) on the left, and in east and north wind components in b) on the right.

-180 -900 0 90 180

a) Direction and speed b) East and north components Figure 4-4 Wind variations observed by the sample flight, ACARS data.

A maximum time interval of 15 minutes was used to maximize data usage. This is because within the terminal area, flights that are separated by more than 15 minutes in arrival time would not likely be a factor to each other. To verify the suitability of using 15 minutes as the maximum time interval between consecutive flights, statistics were obtained for east and north components of wind variation at each altitude. The mean and the standard deviation of these components of the wind variation are shown in Fig. 4-5 versus time interval at 11,000 ft. The statistics were based on 1048 consecutive flight pairs that were separated by less than 15 minutes in arrival time. Mean and standard deviation for data point in Fig.

4-5 was computed from wind variations of 10% of all the consecutive flight pairs centered at that point.

Thus, Fig. 4-5 can be viewed as a moving statistics chart. It can be seen that the standard deviation of wind variation components stayed roughly the same as the time interval increases. This observation is consistent through all altitudes.

0 100 200 300 400 500 600 700 800

-1 0 1 2 3 4

Time Interval, s

Wind Variation, kt

North - Mean North - STD East - Mean East -STD

Figure 4-5 Wind variation versus time interval, 11,000 ft.

The mean and the standard deviation of the east and north components of the wind variation are shown in Fig. 4-6 versus wind speed at 11,000 ft. The mean and the standard deviation for each wind speed was computed in the same way as that in Fig. 4-5. The standard deviation of wind variation components stayed roughly the same as wind speed increases; except when wind speed is above 35 kt (roughly above mean wind plus ı), when a slight increasing trend in standard deviation is observed. This tendency is slight more obvious at altitudes below 10,000 ft, and is hardly identifiable above 12,000 ft.

0 10 20 30 40 50

-1 0 1 2 3 4

Wind Speed, kt

Wind Variation, kt

North - Mean North - STD East - Mean East -STD

Figure 4-6 Wind variation versus wind speed, 11,000 ft.

Because separation is only a concern for aircraft on the same procedure that are between 1 to 3 minutes apart, wind variation can be modeled as being independent of the time interval between flights.

As an approximation, wind variation could also be modeled as being independent of wind speed.

Wind variation could be modeled either by variation in wind direction and speed, or by variation in east and north components. As shown in Fig. 4-4a, there are distinctive differences between the variation in wind direction and the variation in wind speed. Actually, very large wind direction variation often occurs when wind speed is relatively small. On the other hand, east and north wind components could be viewed as two equally positioned contribution factors to the total wind variation.

Sample correlation coefficient between east and north wind components was obtained at each altitude.

As shown in Fig. 4-7, the correlation between east and north was very weak. An examination of the actual distribution of the east and north components at each altitude indicated that the east and north

components could be assumed to be two independent processes. Thus, wind variation was modeled in east and north components.

0 5 10 15 20 25 30 35 40

-1.0 -0.5 0.0 0.5 1.0

Altitude, 10³ ft

Sample CorrelationCoefficient

Figure 4-7 Sample crosscorrelation coefficient between east and north wind variations versus altitude.

As shown in Fig. 4-4b that, given altitude as the independent variable, the east and north wind variation components were not stationary, although their variation in magnitude and frequency was much less than that of the wind direction change. This is a natural observation since differences in air movement exist in different atmosphere layers. As mentioned earlier, raw ACARS data have a much lower sampling rate at high altitude. The frequency differences at different altitudes as reflected by ACARS data may well contain artifacts due to the difference in sampling rate. Thus, it is worth a closer look before further analysis. The wind profile extracted from Flight Data Record (FDR) data of the sample flight is shown in Fig. 4-8. By comparing Fig. 4-8 and Fig. 4-2, it is seen that the ACARS data captured the overall wind profile relatively well.

0 90 180 270 360 0

5 10 15 20 25 30 35 40

Wind Direction, deg Altitude, 103 ft

0 20 40 60

0 5 10 15 20 25 30 35 40

Wind Speed, kt

Figure 4-8 FDR wind profile from the sample flight.

Using FDR data from the sample flight and that of the aircraft immediately in front of it, a wind variation profile was derived. The wind variation profile is shown in Fig. 4-9. Comparing Fig. 4-9 with Fig. 4-4b, it is seen that due to the overall lower sampling rate, use of ACARS data resulted in a smoother wind variation profile. Additionally, high frequency contents were cut off in the ACARS data. This should not pose a problem as high frequency contents reflect turbulence and measurement noise. The

turbulence would mostly affect the micro-level aircraft dynamics. With proper guidance and control, the macro-level aircraft trajectory will not likely be significantly affected by those high frequency wind contents. Below 20,000 ft, wind variations reflected by FDR data was also captured by the ACARS data relatively well. Interestingly, at about 3,000 ft, there was a relatively large wind shift in the FDR data;

this was also captured by the ACARS data. This relatively large wind shift at lower altitude is a common phenomenon at KSDF, and it is more visible in same data samples than in others. This phenomenon has been identified by both pilots and air traffic controllers in real world operations. However, as expected, due to the very low sampling rate at high altitude, ACARS data did not capture the wind variation well at high altitude. This is especially true above 20,000 ft, at least for the data sample shown in Fig. 4-4b. It is obvious that FDR data would be a good source for modeling the wind and wind variations. However, due to organizational constraints, FDR data could not be easily obtained in large volume and for a great number of days.

-10 0 10

0 5 10 15 20 25 30 35 40

East Wind, kt Altitude, 103 ft

-10 0 10

0 5 10 15 20 25 30 35 40

North Wind, kt

Figure 4-9 Wind variation observed by the sample flight, FDR data.