Evaluation of CIT Avoidance Guidelines. Turbulence PDT Task FY 2005 Year-End Progress Report

Transcription

1 Evaluation of CIT Avoidance Guidelines Turbulence PDT Task FY 2005 Year-End Progress Report Deliverable E1 Submitted by The National Center for Atmospheric Research

2 Introduction In FY 2005, NCAR was given Technical Direction by the FAA s Aviation Weather Research Program Office to evaluate current thunderstorm avoidance guidelines from the perspective of convectively induced turbulence. This work was performed under the Turbulence PDT Task , which states in part: Using tools developed in for processing archived NEXRAD data, along with the database of radar and in-situ data being assembled for verification of the NTDA via task (including automated commercial in-situ reports, PIREPs, research aircraft data, and EDR data from NTSB turbulence encounter cases), compile statistics on the horizontal and vertical proximity of turbulence encounters to regions of enhanced radar reflectivity. Use lightning data to further identify which clouds are associated with thunderstorms. Results of this analysis will include scatterplots relating turbulence intensity to proximity for various levels of reflectivity in thunderstorm clouds, as well as an initial assessment of the various avoidance guidelines. The analysis of CIT avoidance guidelines will serve to either justify the current guidelines or supply principle alternatives. In addition, it is expected that this analysis will suggest diagnostics that can be produced from available remote sensing data for use in decision support systems, such as the planned Graphical Turbulence Guidance Nowcast product. Ultimately, it is hoped that these guidelines and tools will help minimize delays and the closure of airspace while still ensuring appropriate safety margins. The present report is provided in fulfillment of Turbulence PDT Deliverable E1: (Sep 05) Report, conference paper, or refereed journal article describing the analysis and preliminary results. The present report satisfies this requirement. It contains sections describing a literature search of research regarding the occurrence of turbulence near thunderstorms, describes a number of detailed case studies, and finally presents results of a statistical analysis based on comparison of in situ EDR reports with reflectivity data and data from the National Convective Weather Diagnostic product, which represents a combination of lightning data and radar-derived vertically integrated liquid (VIL).

3 Literature review A literature review was performed to gain background insight into work that has been conducted regarding aircraft turbulence associated with thunderstorms. It is important to understand known, though hard to predict, phenomenon that are generally accepted in the field of aircraft turbulence research to produce convectively induced turbulence. Adler, R. F. and D. D. Fenn, 1979: Thunderstorm vertical velocities estimated from satellite data. J. Atm. Sci., 36, Infrared geosynchronous satellite data with an interval of 5 min between images are used to estimate thunderstorm top ascent rates. Time rate of change of cloud-top minimum equivalent blackbody temperature, T BB, is converted to vertical velocity, w, using the lapse rate determined from rawinsonde data. For the two case studies in this paper there was a significant difference in the mean calculated vertical velocity between elements associated with severe weather reports (w=4.9ms -1 ) and those with no such reports (w=2.4ms -1 ). Beckwith, W. B.,????: Operational forecasting and analysis of turbulence. Giant thunderstorms or extensive squall lines act in the same manner as a mountain barrier in producing wave action which may capsize into moderate or severe turbulence. This type of wave induced turbulence (WIT) often is buried within cirrus blowoffs (anvils), completely separated from convective activity, but found along the flancks downwind from, and above, the blocking cells. Presence of the tropopause near the flight level appears to enhance the probability of WIT downwind at distances sometimes as great as 100 to 200 km away from the thunderstorms. Forecasting such examples of WIT is difficult at best, since the necessary ingredients are constantly changing and are a function of the movement and life of the blocking thunderstorm cells. Bradbury, T. A. M., 1973: Glider flight in the lower stratosphere above cumulonimbus clouds. Meteor. Magazine, 102, A case study from 9 May 1971, between Swindon and Oxford in the United Kingdom is presented. The strengthening upper winds on the northern side of a jet passed over an irregular line of cumulonimbus clouds. The tops of these clouds extended up to the base of the stratosphere and acted as a partial barrier to the strong upper winds. As a result the air on the upwind side of the clouds was forced to rise over the cloud tops. The disturbance to the flow in the upper troposphere also extended into the lower stratosphere where it produced a wave-like motion at least 4 km above the tropopause. Turbulence was encountered in clear air above the cumulonimbus cloud suggesting a localized breakdown of the wave flow.

4 Burns, A., T. W. Harrold, J. Burnham, C. S. Spavins, 1966: Turbulence in clear air near thunderstorms. Institutes for Environmental Research Technical Memorandum-NSSL-30. Results obtained on five flights in the Oklahoma area are presented; only times where the aircraft was between 40,000 and 45,000 ft are included. The height above the cloud ranged from a few feet to several thousand feet. No apparent relationship was found between the height above cloud and the turbulence encounters. No apparent relationship was found between the length of a turbulence patch and the size of the derived gust velocities which it contains. Vertical air motion, in addition to large and rapid fluctuations in airspeed, due to horizontal components of air motion, were significant kinds of atmospheric disturbances met above the storms. Lane, T. P., R. D. Sharman, T. L. Clark, and H. Hsu, 2002: An investigation of turbulence generation mechanisms above deep convection. J. Atmos. Sci., 60, An investigation of the generation of turbulence above deep convection is the focus of this study, where very high-resolution two- and three-dimensional numerical simulations are used to investigate the possible causes of the turbulence encounter. The turbulence generated in the numerical simulations can be placed into two general categories; the first includes turbulence that remains local to the cloud top, while the second includes turbulence that propagates away from the convection and owes its existence to the breakdown of convectively generated gravity waves. In both simulations the local turbulence develops rapidly and occupies a layer about 1 km deep above the top of convective updrafts after their initial overshoot into the stratosphere. This local turbulence is generated by the highly nonlinear interactions between the overshooting convective updrafts and the tropopause. Gravity wave breakdown is only present in the two-dimensional calculation and occurs in a layer about 3 km deep and 30 km long. This gravity wave breakdown is attributed to an interaction between the gravity waves and a critical level induced by the background wind shear and cloud induced wind perturbations above cloud top. Lee, J. and R. Crane, 1995: Use of Doppler velocity spread in the detection and forecast of regions within storms that may be hazardous to aircraft operations. Preprints, 6 th Conf. on Aviation Weather Systems, Boston, MA., Amer. Meteor. Soc., Aircraft data obtained during thunderstorm penetration was analyzed for several characteristics. It was noted that moderate and greater turbulence (pilot commented and recorded data) occurred in or on the edges of updrafts and down drafts as reported by the pilots. These occurrences may be as far from the thunderstorm core as 50 km. With Doppler radar, an estimate of the radial winds brought into use a more physical quantity that could be ascribed to turbulence, the energy dissipation rate. Modern Doppler weather radars provide estimates of reflectivity, radial velocity, and the standard deviation of the radial velocity (spectral width) on spatial scales useful for the identification of turbulent regions within thunderstorms. Spectral width is a useful estimator of turbulence that may be hazardous to aviation only if different radars can provide the same width estimates and if the detected region of high spectral width persist in time and translates with the apparent storm motion.

5 Pantley, K. C. and P. F. Lester, 1990: Observations of severe turbulence near thunderstorm tops. J. Appl. Meteor., 29, Data derived from the flight tapes of two airliners that experienced severe turbulence near thunderstorm tops are used to produce quantitative descriptions of the turbulence and its environment. For the first case (flight over a squall line), the aircraft flight level at the time of the turbulent event was very close to both the tropopause (11.7 km) and the cloud tops (11.4 km). The digital flight data recorder (DFDR) information revealed a wave-like pattern in vertical velocity field, potential temperature field, horizontal wind direction, and wind speed field. This data suggests that the squall line acted as a barrier to the flow, resulting in mountain wave-like disturbances downstream. For the second case (flight through the top of a cumulus cloud), early in the data the phase of the potential temperature minimum lags the vertical velocity maximum slightly. This pattern strongly suggests what would be expected when traversing a gravity wave. However, in the region of intense turbulence the pattern does not show an obvious phase lag, corresponding more closely with a flight through convection with strong upward heat flux. It is likely that the gravity waves encountered by the aircraft were excited by the surrounding convection. Prophet, D. T., 1969: Vertical extent of turbulence in clear air above the tops of thunderstorms. J. Appl. Meteor., 9, Stratospheric clear air turbulence data were obtained during Project HICAT in Some of these flights were conducted over thunderstorm tops. The results showed a lognormal exceedance probability distribution of gust speeds (U de ) and decreasing speeds with increase in altitude. The decrease in the median (50%) values for U de with height above thunderstorm clouds tops is approximately linear. The mean widths also appear to decrease linear with height above the thunderstorm clouds tops. Upon extrapolating both curves, it is evident that turbulence vanishes or at least diminishes to insignificant values at an altitude of 10,000 12,000 ft above thunderstorm cloud tops. Wang, P. K., 2003: Moisture plumes above thunderstorm anvils and their contributions to crosstropopause transport of water vapor in midlatitudes. J. Geophys. Res., 108 The possibility of water vapor transport from the troposphere to the stratosphere by deep convection is investigated using three-dimensional, nonhydrostatic, quasi-compressible simulations of a Midwest severe thunderstorm. The results show that the breaking of gravity waves at the cloud top can cause cloud water vapor to be injected into the stratosphere in the form of plumes above a thunderstorm anvil. The results reveal that there are two types of plumes, anvil sheet plumes and overshooting plumes, in this injection process and that the process is diabatic. With the idea of somehow using current lightning strikes to predict where the next lightning strikes would be (and thus the movement and intensity of the storm) a brief literature review was also conducted in order to identify the relationship between storm severity and cloud-to-ground lightning frequency.

6 Carey, L. D., S. A. Rutledge, W. A. Petersen, 2002: The relationship between severe storm reports and cloud-to-ground lightning polarity in the contiguous United States from 1989 to Mon. Wea. Rev., 131, The cloud-to-ground (CG) lightning data utilized in this study include ground strike location, date, time, and polarity. Since positive cloud-to-ground lightning flashes characterized by peak currents less than 10kA were likely associated with misidentified in-cloud lightning from 1995 to 1998, they were removed from the data sample. The study calculated the percentage and flash density (km-2h-1) for both negative and positive polarity ground discharges occurring within 50 km and 0.5 h of each large hail report and 1 km prior to and within 50 km of an initial tornado report. The majority (61%) of severe storm reports during warm seasons (April-September) were associated with predominantly (>90%) negative cloud-to-ground (PPNG) lightning, while only 15% of severe storm reports were characterized by predominantly (>50%) positive CG (PPCG) lightning activity. The locations of the monthly frequency maxima of severe storms that produced PPCG and PNCG lightning were systematically offset with respect to the climatological monthly position of the surface e ridge on severe outbreak days. Lang, T. J. and S. A. Rutledge, 2002: Relationships between convective storm kinematics, Precipitation, and lightning. Mon. Wea. Rev., 130, In general, the kinematically strongest storms featured lower production of negative cloud-toground lightning when compared with more moderate convection, in accord with an elevated charge mechanism. Many severe thunderstorms feature high total lightning flash rates (greater than 15 min-1, and often greater than 30 min -1 ). These storms also may produce very little CG (cloud-to-ground) lightning (often < 1min-1 and sometimes no CGs for 10 min or more), which implies large IC (intracloud) flash rates and, thus, a high IC:CG ratio. Watson, A. I., R. L. Holle, R. E. Lopez, 1995: Lightning from two national detection networks related to vertically integrated liquid and echo-top information from WSR-88D radar. Wea. Forecasting, 10, The two detection systems used in this study are specifically designed for CG lightning. When lightning is normalized by the frequency of occurrence of 4 km x 4 km resolution echo-top areas, the greatest percentage of echoes with lightning occurs when echo-top heights exceed 50,000 ft (15.2 km). The percentage of echoes with lightning drops significantly as echo-tops decreases. The relationship of VIL (vertically integrated liquid) with lightning is not as clearly defined. The frequency of echoes with lightning increases gradually with of 4 km x 4 km resolution VIL values from 15 kg m -2 to about kg m -2. Then a drop in the frequency occurs with higher values of VIL. However, a maximum in the frequency of echoes with lightning was observed at very high values of VIL (>65kg m -2 ) by both lightning-detections systems.

7 Case Studies In order to determine how the current convectively induced turbulence guidelines are applied and working, it is critical to due a case study analysis of several events. The chosen events should capture cases in which aircraft encountered moderate or greater turbulence both within and outside the area defined by the CIT guidelines as areas hazardous to aviation with the potential for turbulence. A few case studies identified so far will be briefly described, as the work is ongoing. 14 June 2004 The first case presented occurred on 14 June 2004 at 1210 UTC over central Iowa. The flight originated in Omaha, NE and was enroute to Chicago, IL (O Hare) when the onboard in-situ recording device measured an acceleration based edr value of 0.55 followed by several 0.25 and 0.15 readings (Fig. 1). At the time of the encounter the aircraft was at FL330 and approaching a thunderstorm from the west. The movement of the convective complex was to the east, as can be seen from the succession of radar images (Figs. 2a-d). The 4 km IR GOES-12 satellite imagery from 1215 UTC (Fig. 3) shows a well defined edge to the thunderstorm. Notice that the event (marked by the red cross) was on the very western boundary of the thunderstorm. The satellite image was approximately 5 min later than the actual turbulence event, and so, presumably, the cloud edge 5 min prior to this image would have been slightly further west, according to the movement of the system, placing. When looking at the radar mosaic from 1210 UTC, however, the event appears to be about 20 km away from the edge of the radar echo. The coldest cloud top temperatures in the most developed part of the convective cloud were around -45ºC, according to Fig. 3. The closest complete upper air sounding to the event location was launched from Omaha, NE at 12 UTC. According to that sounding, a temperature of -45ºC was measured around 10.8 km (just under 35,500 ft). At the time of the turbulent event the aircraft was at FL330 (below the highest cloud top further to the east), still ascending to their final cruising altitude of FL370. Converting the aircraft flight level from standard to actual pressure level it is seen that the true aircraft altitude was about 700 ft above the standard atmosphere pressure level at 200 mb, (i.e. when the aircraft was reporting a flight level of 37,000 ft it was actually flying at about 37,700 ft). While the aircraft was over the convective complex, it appears that they deviated slightly north around the highest portion of the cloud tops (which were around 35,500 ft), and were flying above the cloud tops, in clear air. During this portion of the flight no significant turbulence was measured by the in-situ. Data from the Rapid Update Cycle (RUC) Numerical Weather Prediction (NWP) model shows a sounding at the 12 UTC initialization time for the exact location of the turbulent event (Fig. 4). Wind speed, along with calculated shear (Fig. 5), as well as the Richardson number (Fig. 6), computed in the vertical are also shown at the turbulence location. There is a spike in the shear value around 10 km near the altitude of the turbulence. Because the Richardson number (Ri) is based on shear, there is also a relative minimum in it at that same altitude. Both the high shear and low Ri values would indicate the potential for turbulence at that location.

8 Fig. 1: Aircraft flight track (flying from Omaha, NE to Chicago, IL) shown as peak edr reports. Red asterisks represent cloud-to-ground lightning strikes which occurred between UTC. The max peak edr reading of 0.55 occurred at 1210 UTC. Fig. 2a: Radar mosaic data from 1205 UTC with the flight path and peak edr measurements overlaid. The color scale at the bottom applies to the radar reflectivity values as well as the peak edr values multiplied by 100.

9 Fig. 2b: Radar mosaic data from 1210 UTC with the flight path and peak edr measurements overlaid. The color scale at the bottom applies to the radar reflectivity values as well as the peak edr values multiplied by 100. Fig. 2c: Radar mosaic data from 1215 UTC with the flight path and peak edr measurements overlaid. The color scale at the bottom applies to the radar reflectivity values as well as the peak edr values multiplied by 100.

10 Fig. 2c: Radar mosaic data from 1220 UTC with the flight path and peak edr measurements overlaid. The color scale at the bottom applies to the radar reflectivity values as well as the peak edr values multiplied by 100. Fig. 3: IR GOES-12 satellite image from 1215 UTC, 5 min after the turbulence event. The crosses denote the flight path with blue being a peak edr reading of 0.05, green 0.15, orange 0.25 and read 0.55.

11 Fig. 4: Sounding from the 12 UTC initialization of the RUC NWP model at the location of the turbulence encounter.

12 Fig. 5: Wind speed and computed wind shear from the 12 UTC initialization of the RUC NWP model at the location of the turbulence encounter.

13 Fig 6: Computed Richardson number from the 12 UTC initialization of the RUC NWP model at the location of the turbulence encounter. 25 May 2004 Several separate aircraft in-situ measurements of 0.35 were recorded over east-central Missouri between 1619 UTC and 1633 UTC on 25 May 2004 (Fig. 7). One flight reported the turbulence encounter at FL325, while the other two were at FL350. From the IR GOES-12 satellite image it is seen that the coldest cloud top temperatures is about -50ºC (Fig. 8). According to the upper air sounding launched from Springfield, MO at 12 UTC that puts the cloud tops around 35,200 ft. After adjusting the aircraft altitude from standard atmospheric pressure to the actual pressure level, it is found that the actual flight level is about 500 ft higher than the standard atmospheric pressure would indicate. This would imply that two of the aircraft that encountered turbulence over this particular thunderstorm would have been just above the clouds, while the other would have been in cloud. Unfortunately, this case is so close to the cloud top boundary that, given all

14 the uncertainties in each measurement, it is hard to positively place the aircraft in clear air above the thunderstorm. When examining the RUC sounding from the 16 UTC initialization at one of the turbulence encounter locations, it is evident that the shears are very high (Fig. 10) and the Ri is very low (Fig.11) throughout a large layer encompassing the level of the turbulence encounters. Fig. 7: Aircraft flight tracks shown as peak edr reports. Red asterisks represent cloud-toground lightning strikes which occurred between UTC. The several max peak edr readings of 0.35 occurred between UTC.

15 Fig. 8: IR GOES-12 satellite image from 1632 UTC. The red crosses mark the locations of the peak edr readings of 0.35 from three different aircraft between UTC.

16 Fig. 9: Sounding from the 16 UTC initialization of the RUC NWP model at the location of one of the turbulence encounters.

17 Fig. 10: Wind speed and computed wind shear from the 16 UTC initialization of the RUC NWP model at the location of one of the turbulence encounters.

18 Fig 11: Computed Richardson number from the 16 UTC initialization of the RUC NWP model at the location of one of the turbulence encounters. 18 May 2004 The final case studied so far occurred on 18 May 2004 over north-central Ohio. The flight was in cruise from Pittsburgh, PA to Chicago (O Hare), IL and had to navigate through several popcorn type thunderstorm cells. The onboard in-situ measured one reading of 0.35, with a few other lighter bumps of 0.15 along the flight path (Fig. 12). At the time of the maximum insitu reading the aircraft was in cruise at FL350. The cells were all moving in a east-northeast direction (Fig. 13a-c). At the time of the encounter, the aircraft appeared to be about 40 km from the nearest thunderstorm cell to the south, however, there were also a few smaller cells directly to the north and east about 60 km. The IR GOES-12 satellite image also shows the spotty nature of the thunderstorms with definite clear air surrounding them (Fig. 14). The strongest in-situ

19 measurement of 0.35 (marked with the red cross) appears to be undeniably out of cloud at the time of the occurrence. The difficulty with this case is in understanding all of the forcing mechanisms occurring around each individual cell, as well as the system as a whole, in order to attribute the turbulence encounter to a specific source. Again, the RUC initialization sounding from 18 UTC is shown (Fig. 15), along with the calculated shear (Fig.16) and Ri (Fig. 17), at the specific location of the turbulence encounter. The shear is moderately high at the location of the event, however, the Ri is also fairly high, implying that the area is highly unstable and, thus, Ri would not indicate turbulence at that location and there must be another mechanism contributing to this encounter. Fig 12: Aircraft flight track (flying from Pittsburgh, PA to Chicago, IL) shown as peak edr reports. Red asterisks represent cloud-to-ground lightning strikes which occurred between UTC. The max peak edr reading of 0.35 occurred at 1811 UTC.

20 Fig. 13a: Radar mosaic data from 1805 UTC with the flight path and peak edr measurements overlaid. The color scale at the bottom applies to the radar reflectivity values as well as the peak edr values multiplied by 100. Fig. 13b: Radar mosaic data from 1810 UTC with the flight path and peak edr measurements overlaid. The color scale at the bottom applies to the radar reflectivity values as well as the peak edr values multiplied by 100.

21 Fig. 13c: Radar mosaic data from 1815 UTC with the flight path and peak edr measurements overlaid. The color scale at the bottom applies to the radar reflectivity values as well as the peak edr values multiplied by 100. Fig. 14: IR GOES-12 satellite image from 1815 UTC. The red cross marks the location of the peak edr reading of 0.35, which occurred 4 min prior to this image at 1811 UTC.

22 Fig. 15: Sounding from the 18 UTC initialization of the RUC NWP model at the location of the turbulence encounter.

23 Fig. 16: Wind speed and computed wind shear from the 18 UTC initialization of the RUC NWP model at the location of the turbulence encounter.

24 Fig 17: Computed Richardson number from the 18 UTC initialization of the RUC NWP model at the location of the turbulence encounter.

25 Statistical Comparisons In order to determine how good an indicator distance from cloud (both in the horizontal that is, parallel to the surface of the Earth direction, and in the vertical, if the aircraft is either above or below cloud), a set of experiments were run which determined, for in situ EDR data points, the distance to cloud of various reflectivity/convection levels. The reflectivity data used was the NTDA reflectivity grid, while the convection levels were taken from the radar/ltg field of the grids generated by the NCWD project. The comparisons with the NTDA grid covered the period from August 9 th of 2005 to September 28 th, while the convection comparisons covered the period from August 9 th to September 21 st. Since the NTDA reflectivity grid covers only a small area in the upper Midwest, while the NCWD grid covers the entire country (albeit at a somewhat coarser resolution), there is considerably more of the latter data than the former. Each in situ datapoint contains the average and peak over all positions through which the aircraft has passed since the previous report, as well as the aircraft position at the time when the report was generated. Therefore, for all of these comparisons, the location of the aircraft corresponding to each EDR point was taken to be the midpoint of the line segment connecting the reported position, and the previous reported position. For the horizontal comparison, for each of these points, a 2*2 degree segment of the NTDA or NCWD grid was retrieved, surrounding the point. Within this subgrid, the closest (in great circle distance) point was found which had reflectivity or convection readings above some threshold (a number of different thresholds were used, plots of a subset of which are included), and the distance to this reading, as well as the peak and average EDR of the in situ point, were saved to a file (if no such point was found, the data was ignored). For the vertical comparison, which was only performed on the NTDA grid (since the NCWF data does not contain altitudes), the vertical column of data which was closest to the in situ point was collected, within which we located the highest and lowest levels which were above some reflectivity threshold, which were considered the cloud top and bottom, respectively. The vertical distance from the in situ point to the cloud was then simply the minimum of the altitude difference between the in situ altitude and the cloud top, and the difference between the in situ altitude and the cloud bottom (or zero, if the in-situ altitude was between these two that is, within the cloud). As in the horizontal direction, if the point was not in a column containing cloud of the desired reflectivity, it was ignored. It should also be mentioned that, while in general it would be unwise to compare a point the position of which is uncertain to a single grid column, the NTDA reflectivity grid is already smoothed, making it unnecessary for us to perform any additional smoothing in our comparison. Horizontal distance to reflectivity results The data containing the horizontal distances to reflectivity, when plotted as conditional histograms (histograms, that is, of the distances to reflectivity above a certain level, when the peak in situ EDR was above a certain level), reveals two patterns: the first that, especially for low reflectivity levels, and regardless of the target EDR value, small distances are

26 overwhelmingly more likely than others. This is not surprising, since, especially at low altitudes, low but nonzero reflectivity values are not uncommon. The second is that, for higher reflectivity values, there tends to be a hump in the plot, which moves slightly to the right as higher reflectivity values are used for the comparisons (which is what one would expect high reflectivity values should have a larger area of effect), and to the left as higher EDR values are compared against (which makes sense, because higher turbulence should occur closer to higher reflectivity, all else being equal). The presence of these humps indicates not only that the data behaves as we would like, but that it is likely that there is a natural distance threshold to use for each EDR/reflectivity threshold pair. Since our long term goal is not only to evaluate the performance of the CIT avoidance guidelines, but also to suggest alternatives, this indicates that we will likely to be able to successfully find at least slightly better distance ranges, once we understand how to map reflectivity values onto classifications of thunderstorm and severe thunderstorm.

27 Conditional histograms of horizontal distances to reflectivity levels greater than 25 and 45, respectively, when the peak in situ EDR was greater than 0.1

28 Conditional histograms of horizontal distances to reflectivity levels greater than 25 and 45, respectively, when the peak in situ EDR was greater than 0.2

29 Conditional histograms of horizontal distances to reflectivity levels greater than 25 and 45, respectively, when the peak in situ EDR was greater than 0.3

30 While the conditional histograms indicated that finding optimal distance thresholds will be possible, ROC curves were also created, which seem to indicate that, while distance to reflectivity does have some skill at predicting turbulence, varying the threshold causes a roughly balanced tradeoff between the probability of false positives, and false negatives. Hence, it appears that, even with optimal thresholding, horizontal distance to cloud is not, in itself, a particularly good metric to use for turbulence prediction. In the future, we hope to incorporate lightning data into our experiments, which will give us better information on which areas would be considered (by a human) thunderstorm or not thunderstorm, and hopefully will prove to be a better indicator of convective turbulence.

31 ROC curves representing the ability of horizontal distance to reflectivity levels above 25 and 45, respectively, to predict EDR values above 0.1 (green), 0.2 (blue) and 0.3 (red). The labeled points are those at which the TSS (POD(Y)+POD(N)) is maximized, with the labels the thresholds at these points

32 Vertical distance to reflectivity results The vertical reflectivity comparisons differ from the horizontal primarily in that the histograms give less reason for optimism (the distances to cloud, in the vertical direction, are overwhelmingly zero in those plots with enough data to draw conclusions that is, the airplane was inside cloud of the target reflectivity level whenever there was cloud of the target reflectivity level in the same grid column as the airplane), while the ROC curves indicated that vertical distance to cloud would make an excellent predictor of turbulence. In a sense, one could say that the quality of each of the two classes of plots, histogram and ROC, is reversed from the horizontal case. The primary reason for the dominance of small distances in the conditional histograms is probably that we had so little data available for higher reflectivity values (recall that the vertical comparisons are done only on a single column, while the horizontal comparisons were on a 2*2 degree box). It has already been explained why, for low reflectivity thresholds, small distances are dominant, while it was only for these low reflectivity values that enough data was collected that we could meaningful conclusions. While we cannot state so confidently as we did for horizontal distances, at this time, that an optimal distance threshold, in the vertical direction, may be found for given EDR/reflectivity thresholds, given that the ROC curves demonstrate that the vertical distance is such a skillful predictor, combined with the fact that our data was so sparse for higher reflectivity levels that we may hope that a more comprehensive analysis will reveal currently invisible patterns, gives great reason for optimism.

33 Conditional histograms of vertical distances to reflectivity levels greater than 15 and 25, respectively, when the peak in situ EDR was greater than 0.1

34 Conditional histograms of vertical distances to reflectivity levels greater than 15 and 25, respectively, when the peak in situ EDR was greater than 0.2

35 Conditional histograms of vertical distances to reflectivity levels greater than 15 and 25, respectively, when the peak in situ EDR was greater than 0.3

36 ROC curves representing the ability of vertical distance to reflectivity levels above 15 and 25, respectively, to predict EDR values above 0.1 (green), 0.2 (blue) and 0.3 (red). The labeled points are those at which the TSS (POD(Y)+POD(N)) is maximized, with the labels the thresholds at these points

37 Horizontal distance to convection results The results of the preliminary analysis of the ability of distance to various thresholded values of the NCWD grid are similar to that for the NTDA reflectivity grid, with the main exception being that the trend of the hump in the histograms moving to the left as the target peak EDR threshold increases appears to be absent. In the ROC curves, as well, the distance threshold at which the maximum TSS is attained does not seem to decrease for higher EDR values. In other respects, including the presence of a (perhaps slightly broader) hump in the histograms, to the generally discouraging nature of the ROC curves, the results may be considered equivalent. The fact that two such different metrics horizontal distance to reflectivity, and horizontal distance to NCWD convection give such similar (poor) results may indicate that horizontal distance to a thunderstorm (or thunderstorm feature) is not, in general, a good metric to use when attempting to predict turbulence. While further experiments will be performed, including lightning data, and potentially other data sources, it appears that an aircraft may approach quite close to a cloud before the risk of turbulence increases appreciably.

38 Conditional histograms of horizontal distances to NCWD levels greater than 3.49 and 12.2, respectively, when the peak in situ EDR was greater than 0.1

39 Conditional histograms of horizontal distances to NCWD levels greater than 3.49 and 12.2, respectively, when the peak in situ EDR was greater than 0.2

40 Conditional histograms of horizontal distances to NCWD levels greater than 3.49 and 12.2, respectively, when the peak in situ EDR was greater than 0.3

41 ROC curves representing the ability of horizontal distance to NCWD levels above 3.49 and 12.2, respectively, to predict EDR values above 0.1 (green), 0.2 (blue) and 0.3 (red). The labeled points are those at which the TSS (POD(Y)+POD(N)) is maximized, with the labels the thresholds at these points