Overview of Flight ER890120
The flight of January 20, 1989 was part of the Stavanger, Norway based AASE mission (Airborne Arctic Stratospheric Expedition). The pilot reported "CAT at 67 North, a lot, moderate."
Figure 1. Flight track for ER890120, with kilosecond labels next to the northbound portion time ticks. CAT began at 33.9 ks (67 North latitude) and began to subside at 35.5 ks.
Isentrope Altitude Cross-Sections
The isentrope altitude cross-section, or IAC, is presented in the next figure.
Figure 2. Altitude of isentrope surfaces, as determined by the MTP instrument. ER-2 altitude is shown as the black trace. The isentrope surfaces shown are 10 K apart. The 480 K surface is the highest one (21.4 km at 32 ks). CAT was present at times indicated by the red bar.
In this IAC it is apparent that the isentrope surface nearest flight altitude has altitude distortions from 33.5 to 36 ks, which corresponds to flight along the Norwegian north coast. Short wavelength "mountain wave" oscillations of isentrope altitude are apparent at about 35 ks, during CAT.
CAT Intensity and Lapse Rate
The MTP vertical accelerometer was not working well on this flight, so CAT intensity was derived from the variability of the MMS vertical wind component. The following figure shows both the W-component based CAT intensity parameter, ACC, and air temperature.
Figure 3. MMS-based CAT intensity, derived from the W-component wind variability (red trace). Temperature is shown by the green trace.
The pilot reported CAT at 67 North latitude, which was reached at 33.9 ks. This is when the W-component wind variability CAT parameter has the highest value, so using the MMS wind data to derive CAT appears to work in this case. We don't know the peak-to-peak g-unit excursion, but since the pilot reported "moderate" CAT we can assume that the highest value for the CAT parameter corresponds to approximately 0.35 g-units.
Figure 4. MTP measured dT/dZp, and a rescaled version of CAT intensity.
There is only a slight hint of vertical compression prior to the onset of CAT at 33.9 ks. dT/dZp is the least stable during CAT, reaching -7 [K/km]. As described elsewhere, it is possible for the actual dT/dZp to be adiabatic while the MTP measure a sub-adiabatic value; this is possible when the layer with the adiabatic lapse rate is shallow in relation to the MTP "look distance" (about 2 km). There is nothing in this lapse rate data to support the compression hypothesis for CAT generation.
RRi, Including Description of Errors in Previous Calculations
The 10-second difference method, described on the web page RRi Derivation, is used to derive RRi for this flight. However, while processing this flight I discovered an error in the calculationof dTH/dZg. I had neglected to include a term, the effect of which was to produce RRi values lower by about a factor 2 compared with the correct values. Specifically, in the erroneous calculation for dTH/dZg I had used the equation:
dTH/dZg = 9.74 [K/km] + dT/dZg
whereas the correct equation is:
dTH/dZg = (9.74 [K/km] + dT/dZp ) * (1000 [mb] / Pressure )0.286
The missing term amounts to about 2 at ER-2 altitudes, and about 1.5 at DC-8 altitudes.
Following is a plot of RRi (using the correct equation for dTH/dZp) for this flight.
Figure 5. RRi and CAT intensity (inverted) for the entire 1.7-hour northbound flight leg. The 10-second difference method was used to calculate RRi. The 1-minute and 2-minute averages of RRi are shown with a red dotted and thick purple traces, while an RC-averaged RRi is shown with a thick black trace. The1-minute 2-miute average traces are positioned in time at the center of the data used to derive them, while the RC-averaged RRi is positioned in time to corresponds to a calculation of RRi based only on measurements available at the time of the plotted trace.
This figure shows larger values for RRi than for all previous ER-2 flights, and the values far exceed the theoretical limit of 4 - above which the atmosphere is unstable and eventaully will "break down" into turbulence. When the other flights are re-analyzed I fully expect them to also have values much higher than 4. In light of this I have begun to question the merits of the DD-method for inferring VWS. Indeed, my reason for setting aside the multiple regression method, MR, were based mostly on the fact that it produced low RRi values, never reaching 4 before the onset of CAT.
The following is an alaysis of this flight data using the MR method for inferring VWS.
Figure 6. RRi and CAT intensity (inverted), using the multiple regression (MR) method for inferring VWS. The 31-second averages are shown with a red dotted trace, and the thick black trace is a 31-second average of RRi. If CAT warnings are issued when RRi exceeds 3, for example, the warning times would indicaetd by the red arrows.
Since I do not have experience with other flights using the MR method for inferring VWS, I do not yet know what RRi threshold will work best for a large set of flights. If the threshold is set at 3, which seems like a good choice for this flight, then warnings would have been issued at 33.3 ks in the flying forward manner, and at 35.8ks in the "flying backwards" manner. The warning times for forward and backward flight would have been 8.6 and 4.7 minutes (allowing for the need to acquire 31 seconds of data before being able to calculate the 31-second average trace).
After 37 ks (oceanic flight) RRi is low, and averages about 0.3 (Ri = 3) for at least an hour.
Warning Time Summary
The following table summarizes the "warning times" for the CAT encounters of this flight.
WARNING TIMES FOR LEVEL FLIGHT CAT EVENTS
|Flight Direction||CAT Event||Warning Time|
|Forward||33.9 ks||8.6 minutes|
|Backward||35.4 ks||4.7 minutes|
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