Remote Sensing of Turbulence: Radar Activities. FY00 Year-End Report

Transcription

1 Remote Sensing of Turbulence: Radar Activities FY Year-End Report Submitted by The National Center For Atmospheric Research Deliverable.7.3.E3

2 Introduction In FY, NCAR was given Technical Direction by the FAA s Aviation Weather Research Program Office to perform research related to the detection of atmospheric turbulence by remote sensing devices. Specifically, the research has been focused on two tasks: the development of an improved turbulence detection algorithm for the WSR-88D radar network and the investigation of turbulence detection algorithms for Doppler lidars. This year-end report discusses the efforts in the WSR-88D area; a separate report discusses the lidar work. Typically, the measurables that can be used to infer turbulence intensities from Doppler radars and lidars are the first three moments of the Doppler spectrum. For a given pulse volume, the zeroth moment provides the total power (or reflectivity) of the returned signal, the first moment is the reflectivity-weighted average radial velocity, and the second moment (square of the spectrum width) is related to the spread of the reflectivity-weighted radial velocities of reflectors within the pulse volume. The turbulence detection methods that can be employed with these measurables can be classified into first moment, second moment and combined first and second moment algorithms. Two types of first moment algorithms are applicable to the detection of atmospheric turbulence. The first is based on the velocity structure function, a commonly-used description of turbulent fields formed by averaging the squared difference between velocities measured at points separated by a prescribed displacement. By fitting the structure function derived from the turbulent component of measured first moments to theoretical curves, information about the magnitude and scale of turbulence can, at least in principle, be extracted. Unfortunately, second moments computed from measured radial velocities have proven to be very sensitive to errors in the data, so a robust implementation will require careful control of data quality. The development and testing of a structure function algorithm has not been a focus of the FY work, but it will certainly merit further attention in FY1. 1

3 A second and simpler first moment algorithm makes use of the local variance of the measured radial velocities. While such a method does not use the spatial statistics of the radial velocities in a sophisticated way as the structure function algorithm does, it does detect fluctuations in the wind field on a larger scale than that contained in a single pulse volume and so may be a useful complement to a second moment algorithm. Variants are available which operate on the turbulent component of the measured radial velocities obtained by removing local trends (i.e., removing the ambient wind field). It seems reasonable to expect that an algorithm based on both measured second moments and the variance of the measured first moments would be only minimally impacted by uncertainty in the value of the turbulence outer length scale. Second moment algorithms are based on theoretical relationships between the statistical properties of the turbulent wind field, the ambient wind field, and the measured second moment. The existing WSR-88D turbulence detection algorithm is a second moment algorithm. Both the structure function and second moment methods may be used to estimate the eddy dissipation rate, a commonly-used measure of turbulence intensity. A combined first and second moment algorithm could produce an estimate of the variance of the true (i.e., not influenced by the radar pulse volume weighting) radial velocities. The zeroth moment can be used for data quality control. Specifically, it is well known that the pulse-pair algorithm which generates the first and second moments is problematic at low signal to noise (SNR) levels. As part of the ongoing NCAR research, fundamental aspects of the second moment and structure function methodologies are being investigated. This work has shed some light on existing theory and, in some cases, provided new theoretical and practical results. Several papers are under preparation to disclose these results to the scientific community. Drafts of two papers related to turbulence detection using Doppler radars were included with the FY98 report; they continue to be refined. In addition, the papers Simulation of Three Dimensional Turbulent Velocity Fields (Journal of Applied Meteorology, in press) and Coherent Doppler Lidar Signal Spectrum with Wind Turbulence (Applied Optics, Vol. 38, pp ) were included with last year s FY99 report. 2

4 As part of the Aviation Safety Program (AvSP), NASA is also heavily involved in a turbulence research program. The Turbulence Detection work area is investigating the use of airborne Doppler radars and lidars to detect atmospheric turbulence. NASA supports NCAR in this work and hence a good deal of leveraging has occurred. Specifically, NCAR has developed a radar simulation software package that has been used to investigate various practical aspects of the problem. Although this simulation code has not be run using parameters for the WSR-88D radar, it has provided insight into the problem of turbulence detection and has been used to develop a hazard algorithm for airborne Doppler radar which may be adapted for use with ground-based radar data in FY1. Furthermore, the algorithm that has been developed for the NASA airborne radar employs a method for averaging the Doppler spectra prior to computing the VHFRQGPRPHQWV,WKDVEHHQIRXQGWKDWWKLVVSHFWUDODYHUDJLQJ DVRSSRVHGWRDYHUDJLQJWKH PRPHQWVREWDLQHGIURPLQGLYLGXDOVSHFWUD LVTXLWHEHQHILFLDO7KLVPHWKRGRORJ\VKRXOGEH investigated as a potential future processing algorithm for the WSR-88D system. Its implementation would, of course, require real-time processing of the Doppler spectra, which is currently unavailable in the WSR-88D radars. 3

5 The Detection of Turbulence Via the WSR-88D Weather Radar The current WSR-88D turbulence algorithm is a second-moment algorithm which attempts to account for the filtering of the reflectors radial velocities by the radar s illumination function, the motion of the reflectors (typically hydrometeors), and the magnitude of measured reflectivity. Unfortunately, the current implementation of this algorithm does not produce operationally useful turbulence information. NCAR s analysis has revealed a number of problems which reduce the operational utility of the current WSR-88D algorithm: (a) it ignores the need for averaging of the measured second moments, (b) the imperfect response of the hydrometeors is incorrectly handled, (c) it makes use of an a priori choice of the turbulence outer length scale, (d) it uses insufficient quality control of the raw second moments, (e) the resolution of the layered composite product is too coarse, (f) the use of the maximum value of the unaveraged and non-quality-controlled spectral widths in the layer composite (with only 4 km x 4 km horizontal resolution) produces over-estimates of the turbulence, (g) it uses of a number of assumptions in the algorithm (e.g., isotropy and form of the energy spectra), and (h) it does not account for other broadening mechanisms besides turbulence in the second moments. These problems were described and discussed in some detail in the FY98 year-end report. Last year s FY99 report presented an analysis of the RAPS92 Mile High Radar and T-28 aircraft data, including eddy dissipation rate (EDR) estimates derived from high-rate true airspeed and vertical accelerometer sensors, which suggested that the performance of the turbulence detection algorithm could be greatly improved by (a) using a higher resolution product (2 km discs instead of the layer composite product s parallelepipeds), (b) using the reflectivity field for quality control of the raw second moments, (c) extracting the median of the derived turbulence estimates from the second moments measured within the disc, and (d) omitting any attempt to account for the response of the hydrometeors. In this report we present a similar analysis of data collected in the June, 1999 NASA Turbulence Characterization and Detection (TCAD) field program near Greeley, Colorado. The primary goal of these analyses is to 4

6 determine whether an improved turbulence detection algorithm for the WSR-88D radar is feasible. At the current time, this feasibility analysis only considers the infrastructure of the current (or near-term) radar system, i.e., changes that can be implemented as a software modification. Longer-term algorithm concepts (e.g., spectral processing and averaging) are under investigation as part of the NASA Aviation Safety Program. Second Moment Analysis Even for the case of perfect point reflectors, the radar-measured second moment is a function of both the turbulent and ambient components of the wind field. Since the large-scale ambient winds are not usually a danger to aviation safety, it may be desirable to remove the effects of such winds on the second moment so that it reflects only the turbulent wind field. In last year s FY99 report, an analysis of the effect of a linear wind field on the measured second moments was presented. In FY, that work was extended to derive formulas which account for this effect when spectra are averaged over several pulse volumes. The results of this work will be included in the paper, The Detection of Atmospheric Turbulence from Doppler radars: A Review, Critical Analysis and Extension, an early draft of which was included with the FY98 report. Unfortunately, the complete linear wind field cannot be recovered from radial velocities obtained from a single radar, so only a portion of its broadening effect on the measured second moments can be removed in practice. Calculations using simulated turbulent wind fields suggest that this effect will usually be small for single pulse volumes, and the adjustment of measured second moments has not yet been incorporated into the NCAR turbulence algorithm. Nevertheless, a more complete study of this issue should be performed in FY1. Field Data Analysis The primary effort in FY was in the analysis of the 1999 TCAD field program data for the purposes of refining and verifying the NCAR turbulence algorithm. The Turbulence Characterization and Detection (TCAD) field program was conducted near Greeley, Colorado from 2 June to 2 June It was funded by NASA, the AlliedSignal Corporation and the

7 Rockwell-Collins Corporation; the National Center for Atmospheric Research was also a major participant. The goal of the TCAD field program was to obtain radar measurements of turbulence within or near convective clouds in conjunction with in-situ turbulence measurements for the purposes of (a) obtaining a data base to facilitate the development and testing of radar turbulence detection algorithms, (b) identifying correlations between observable cloud properties that exist within turbulent regions, and (c) obtaining truth data for comparisons to cloud-scale numerical simulations and turbulence characterization studies. Data were collected by three aircraft, two ground-based Doppler radars, and the NCAR Mobile Cross-chain Loran Sounding System (CLASS) sounding van. Of these, the data analyzed in this report includes in-situ data collected from the South Dakota School of Mines and Technology T-28 research aircraft, airborne radar data collected from the Rockwell-Collins Corporation Sabreliner, and groundbased radar data from the Colorado State University CHILL radar. (For more information on the TCAD field program, see the website and the links contained therein.) Two different analyses of the TCAD field program data are presented below. The first illustrates the correlation between an aircraft-derived measure of turbulence and the airborne and ground-based radar-measured second moments via a set of overlays. Instead of deriving an eddy dissipation rate estimate from the T-28 aircraft vertical acceleration time series, as was done for the analysis presented in last year s FY99 report, the variance of the vertical acceleration over 2 km paths is used here as the metric of aircraft turbulence. This quantity is arguably more directly related to the rapidly-changing accelerations of the aircraft which are most likely to cause injury; furthermore, it may be shown (using appropriate assumptions on the turbulent wind field) that it is proportional to the variance of the true wind field, the constant of proportionality being a function of the aircraft type, weight, and flight conditions. In processing the aircraft data, the variance of the vertical accelerations over 2 km flight paths centered at each point in the raw Hz time series was calculated, and the median over one-second intervals was then used to resample the data to 1 Hz. 6

8 The plots on the following pages overlay the variance of the T-28 vertical accelerations computed over 2 km flight paths onto the radar second moment and other fields for the airborne (Rockwell-Collins) radar for five cases of interest on June and 12. The moments displayed on the airborne radar plots were produced by a new spectral processing algorithm developed as part of the NASA efforts. This algorithm, the NCAR Efficient Spectral Processing Algorithm (NESPA), is a significant improvement over the standard pulse-pair processing algorithm. Besides generating the standard three Doppler moments, this algorithm also produces a confidence value for each moment. Confidence values near one indicate that, roughly speaking, the corresponding second moment values are likely to be correct, while confidences near zero indicate poor-quality second moments. Figure 1 illustrates the NESPA second moment with an overlay of the local variance of vertical acceleration from the T-28 aircraft over 2 km flight paths from a six-minute flight segment centered at the time of the radar scan. Blank (white) patches in the radar second moment plot indicate zero confidence for those data. Figure 2 illustrates the NESPA second moment confidences for the data in Figure 1. Four other cases are presented similarly in Figures 3 and 4, Figures and 6, Figures 7 and 8, and Figures 9 and. Some of these cases seem to exhibit a clear correlation between the aircraft values and the second moments from both radars, but there are also some notable exceptions. These may be partly due to inaccuracies or inconsistencies in the positions and times recorded by the T-28 and Sabreliner. Alternately, they could be due to the lack of isotropy in an active thunderstorm, along with the fact that the radar measures only the radial velocities of the reflectors, while it is largely the vertical winds which are responsible for the T-28 s vertical acceleration. Furthermore, these cases are a random sample and may not be indicative of the usual behavior of either the radar or the aircraft. Nevertheless, these overlays do strongly suggest that the radar second moments can frequently be used to predict the aircraft response, especially where high-quality data is available. 7

9 2 6/ :4:1, Rockwell Radar (Frame: ), South Dakota T 28 (1 s median) (14.16 km, km, 663 feet above CHILL), Heading: 82.3 o 8 y displacement from CHILL (km south north) x displacement from CHILL (km west east), range lines in km Nespa Second Moment (m/s) Local Variance over 2 km of Aircraft Vertical Acceleration (m/s 2 ) 2 Figure 1 NESPA-derived second moments from the airborne radar with an overlay of the running-variance of vertical acceleration from the T-28 aircraft. 8

10 1 6/ :4:1, Rockwell Radar (Frame: ), South Dakota T 28 (1 s median) (14.16 km, km, 663 feet above CHILL), Heading: 82.3 o y displacement from CHILL (km south north) x displacement from CHILL (km west east), range lines in km Nespa Confidence Local Variance over 2 km of Aircraft Vertical Acceleration (m/s 2 ) 2 Figure 2 NESPA confidences for the data in Figure 1. 9

11 2 6/ :8:38, Rockwell Radar (Frame: 33), South Dakota T 28 (1 s median) (32.36 km, km, feet above CHILL), Heading: 9.76 o 3 y displacement from CHILL (km south north) Nespa Second Moment (m/s) x displacement from CHILL (km west east), range lines in km Local Variance over 2 km of Aircraft Vertical Acceleration (m/s 2 ) 2 Figure 3 NESPA-derived second moments with overlaid aircraft acceleration variances.

12 1 6/ :8:38, Rockwell Radar (Frame: 33), South Dakota T 28 (1 s median) (32.36 km, km, feet above CHILL), Heading: 9.76 o y displacement from CHILL (km south north) Nespa Confidence x displacement from CHILL (km west east), range lines in km Local Variance over 2 km of Aircraft Vertical Acceleration (m/s 2 ) 2 Figure 4 Second moment confidences for the data in Figure 3. 11

13 2 6/12 :16:33, Rockwell Radar (Frame: 36), South Dakota T 28 (1 s median) (39.3 km, km, feet above CHILL), Heading: o 3 2 y displacement from CHILL (km south north) 3 2 Nespa Second Moment (m/s) x displacement from CHILL (km west east), range lines in km Local Variance over 2 km of Aircraft Vertical Acceleration (m/s 2 ) 2 Figure NESPA second moments with overlaid aircraft acceleration variances. 12

14 1 6/12 :16:33, Rockwell Radar (Frame: 36), South Dakota T 28 (1 s median) (39.3 km, km, feet above CHILL), Heading: o y displacement from CHILL (km south north) Nespa Confidence x displacement from CHILL (km west east), range lines in km Local Variance over 2 km of Aircraft Vertical Acceleration (m/s 2 ) 2 Figure 6 Second moment confidences for the data in Figure. 13

15 2 6/12 :22:8, Rockwell Radar (Frame: 3), South Dakota T 28 (1 s median) (7. km, 7.29 km, feet above CHILL), Heading: o y displacement from CHILL (km south north) Nespa Second Moment (m/s) x displacement from CHILL (km west east), range lines in km Local Variance over 2 km of Aircraft Vertical Acceleration (m/s 2 ) 2 Figure 7 NESPA-derived second moments with overlaid aircraft acceleration variances. 14

16 1 6/12 :22:8, Rockwell Radar (Frame: 3), South Dakota T 28 (1 s median) (7. km, 7.29 km, feet above CHILL), Heading: o y displacement from CHILL (km south north) Nespa Confidence 3 2 x displacement from CHILL (km west east), range lines in km Local Variance over 2 km of Aircraft Vertical Acceleration (m/s 2 ) 2 Figure 8 Second moment confidences for the data in Figure 7.

17 2 6/12 :24:42, Rockwell Radar (Frame: ), South Dakota T 28 (1 s median) ( 2.22 km, 6.43 km, 123 feet above CHILL), Heading: o 4 3 y displacement from CHILL (km south north) Nespa Second Moment (m/s) x displacement from CHILL (km west east), range lines in km Local Variance over 2 km of Aircraft Vertical Acceleration (m/s 2 ) 2 Figure 9 NESPA second moments with aircraft acceleration variances overlaid. 16

18 1 6/12 :24:42, Rockwell Radar (Frame: ), South Dakota T 28 (1 s median) ( 2.22 km, 6.43 km, 123 feet above CHILL), Heading: o y displacement from CHILL (km south north) Nespa Confidence x displacement from CHILL (km west east), range lines in km Local Variance over 2 km of Aircraft Vertical Acceleration (m/s 2 ) 2 Figure Second moment confidences for the data in Figure 9. 17

19 The plots on the following pages are similar to those preceding, except that overlays of the T-28 track onto the ground-based (CHILL) radar fields are now presented. In addition to the second moment field, the reflectivity and radial velocity fields are also displayed. The second moment field has been median-filtered over range x azimuth blocks chosen to be roughly 4 km x 4 km; thus, blocks near the radar contain many more points than those further away. Bad data points for each field appear as blank (white) patches. The three times and regions of space displayed correspond to those of Figures, 7, and 9. Perhaps because of the relatively large distance from the radar, the CHILL radar data for the cases presented in Figures 1 and 3 contained a large proportion of bad values and thus did not allow for a meaningful comparison with either the T-28 aircraft data or the airborne radar data; they are therefore not presented here. As was true for the airborne radar comparison, the second moments from the ground-based CHILL radar appear to show good correlation with the local variance of the aircraft vertical acceleration displayed in the aircraft track overlays. An exception occurs about one minute along the aircraft track in Figure 14; however, it may be ascribed to either the fact that the aircraft was turning there, causing a variation in vertical acceleration not due to turbulence, or to the close proximity to the radar and resulting poor quality of the measured second moments there. 18

20 12 Jun 1999 ::38, CHILL MOM2 (6.6 deg); :13:33 :19:33, T 28 Acc. Variance y displacement from CHILL (km south north) CHILL radar median filtered second moment (m 2 /s 2 ) x displacement from CHILL (km west east) Local variance over 2 km path of T 28 vertical acceleration (g 2 ) Figure 11 Median-filtered second moments from the CHILL radar with an overlay of the running variance of vertical acceleration from the T-28 aircraft. The time and spatial limits of the plot were chosen to correspond to those of Figure. 19

21 12 Jun 1999 ::38, CHILL DBZ (6.6 deg); :13:33 :19:33, T 28 Acc. Variance y displacement from CHILL (km south north) CHILL radar unfiltered reflectivity (dbz) x displacement from CHILL (km west east) Local variance over 2 km path of T 28 vertical acceleration (g 2 ) Figure 12 CHILL reflectivity (unfiltered) for the case shown in Figure 11.

22 12 Jun 1999 ::38, CHILL VEL (6.6 deg); :13:33 :19:33, T 28 Acc. Variance y displacement from CHILL (km south north) 1933 CHILL radar unfiltered radial velocity (m/s) x displacement from CHILL (km west east) Local variance over 2 km path of T 28 vertical acceleration (g 2 ) Figure 13 CHILL radial velocities (unfiltered) for the case shown in Figure

23 12 Jun 1999 :21:4, CHILL MOM2 (12.6 deg); :19:8 :2:8, T 28 Acc. Variance 3 9 y displacement from CHILL (km south north) CHILL radar median filtered second moment (m 2 /s 2 ) x displacement from CHILL (km west east) Local variance over 2 km path of T 28 vertical acceleration (g 2 ) Figure 14 Median-filtered second moments from the CHILL radar with an overlay of the running variance of vertical acceleration from the T-28 aircraft. The time and spatial limits of the plot were chosen to correspond to those of Figure 7. 22

24 12 Jun 1999 :21:4, CHILL DBZ (12.6 deg); :19:8 :2:8, T 28 Acc. Variance 3 6 y displacement from CHILL (km south north) CHILL radar unfiltered reflectivity (dbz) x displacement from CHILL (km west east) Local variance over 2 km path of T 28 vertical acceleration (g 2 ) Figure CHILL reflectivity (unfiltered) for the case shown in Figure

25 12 Jun 1999 :21:4, CHILL VEL (12.6 deg); :19:8 :2:8, T 28 Acc. Variance 3 y displacement from CHILL (km south north) CHILL radar unfiltered radial velocity (m/s) x displacement from CHILL (km west east) Local variance over 2 km path of T 28 vertical acceleration (g 2 ) Figure 16 CHILL radial velocities (unfiltered) for the case shown in Figure

26 12 Jun 1999 :24:39, CHILL MOM2 (7.4 deg); :21:42 :27:42, T 28 Acc. Variance 4 9 y displacement from CHILL (km south north) CHILL radar median filtered second moment (m 2 /s 2 ) x displacement from CHILL (km west east) Local variance over 2 km path of T 28 vertical acceleration (g 2 ) Figure 17 Median-filtered second moments from the CHILL radar with an overlay of the running variance of vertical acceleration from the T-28 aircraft. The time and spatial limits of the plot were chosen to correspond to those of Figure 9. 2

27 12 Jun 1999 :24:39, CHILL DBZ (7.4 deg); :21:42 :27:42, T 28 Acc. Variance 4 6 y displacement from CHILL (km south north) CHILL radar unfiltered reflectivity (dbz) x displacement from CHILL (km west east) Local variance over 2 km path of T 28 vertical acceleration (g 2 ) Figure 18 CHILL reflectivity (unfiltered) for the case shown in Figure

28 12 Jun 1999 :24:39, CHILL VEL (7.4 deg); :21:42 :27:42, T 28 Acc. Variance 4 3 y displacement from CHILL (km south north) CHILL radar unfiltered radial velocity (m/s) x displacement from CHILL (km west east) Local variance over 2 km path of T 28 vertical acceleration (g 2 ) Figure 19 CHILL radial velocities (unfiltered) for the case shown in Figure

29 As previously mentioned, one of the significant problems with the existing WSR-88D algorithm is using un-averaged spectra to produce the second moments. There are two main reasons that averaging of the second moments is required: (a) turbulence is a random process and hence the only pertinent information about it must be obtained via statistical methods, (b) individual Doppler spectra (and hence second moments) are contaminated by so-called phase noise (due to the interaction of the phases between different scatterers in the pulse volume) and (c) the spectra are contaminated by receiver noise; spectral or moment averaging is required to reduce these effects. The averaging of spectra prior to computing second moments is far preferable to averaging moments obtained from the contaminated spectra. Unfortunately, for the WSR-88D system (in its current form), averaging moments is all that is available. The NCAR turbulence algorithm implementation presented in last year s FY99 year-end report satisfied this requirement by making use of the median radar-measured second moment obtained from a disc or sphere centered at a point of interest, or the nearest parallelepiped on a predetermined grid, scaling it by a theoretical quantity dependent on the distance from the radar and the estimated turbulence outer length scale to obtain an eddy dissipation rate (EDR) estimate. For comparison with the turbulence derived from the T-28 aircraft, a point of interest is the closest point on the radar scan cone at each comparison time. Of these volumes, the disc was deemed the most satisfactory; this conclusion was based not only on the demonstrated empirical correlation with the aircraft measurements, but also on the fact that both parallelepipeds and spheres include points from different altitudes, and therefore different strata of turbulence and varied times due to the radar s scanning. Equally important, the disc method (i.e., using points from a single elevation scan) would be the most straightforward method from an implementation viewpoint. For this reason, only discs were used in this year s analysis. Several radar-derived quantities were extracted from discs at the various aircraft positions: second moments, eddy dissipation rates computed by dividing each second moment by a range-dependent theoretical factor, and the variance of the radial velocities. Two different methods were used to average the second moments and eddy dissipation rates. The first was to simply take the median of those values corresponding to reflectivities between and 6 dbz, a 28

30 strategy that was shown to work well for the RAPS92 data in last year s FY99 report. The second was to take a confidence-weighted average of all the values. The confidence value used for this purpose was derived from the reflectivity via a function which increases linearly from.4 to 1 between and 3 dbz, remains at 1 between 3 and dbz, decreases linearly from 1 to.4 between and 7 dbz, and is zero for all other values. The rationale for this approach is that second moments derived from regions having moderately high reflectivity are likely to have the highest quality, and therefore should be assigned the highest weights. On the other hand, other values should not be thrown out entirely, but should simply be weighted less depending on how far away they are from the ideal range. The form of the function was chosen somewhat arbitrarily based on the results from last year s FY99 report, which suggested that second moments for measurements having reflectivities between and 6 dbz are of relatively high quality. This confidence-based methodology, a fuzzy logic approach, is the beginning of the development of a fuzzy turbulence detection algorithm for the WSR-88D system. Two additional filters were used in the comparison of the aircraft and radar-derived quantities. First, only those aircraft data which were recorded within 9 seconds of a radar scan were used for comparisons. Second, data points were eliminated when the number of good (reflectivity between and 6 dbz) radar measurements within the disc fell below a certain threshold (8, 14 or points). This strategy eliminates comparisons for which the radar data is of low quality. Similar results are obtained by restricting the allowable range of aircraft positions from the radar as was done last year; both of these strategies ensure that only radar data in regions of high-reflectivity and relatively dense measurements are used. Indeed, an analysis of the TCAD field program s CHILL radar data shows that 2 km-radius discs containing 8 or more valid points have ranges distributed between and 7 km from the radar, 2 km discs containing 14 or more points range from to 37 km, and 2 km discs containing or more points lie almost exclusively between 12 and 2 km. The scatter plots on the following pages illustrate the correlation between the second moments, eddy dissipation rates or variance of radial velocities derived using 2 km-radius discs from the CHILL radar with the variance of the T-28 aircraft s vertical acceleration over 2 km 29

31 flight paths using data collected on June, 9,, 11, 12, 14, 17, 18 and, An analysis was also performed for 1 km-radius discs, but the higher resolution was offset by the fact that many fewer radar points could be averaged, causing greater scatter in the results, and so those plots are not presented here. Note that for the highest quality data (largest number of good data points in the disc), the radar second moments and derived eddy dissipation rates show excellent correlation with the variance of the T-28 aircraft s vertical acceleration. That the second moment correlates as well as the derived eddy dissipation rates may be due to the fact that the range to the radar is quite restricted for these data and hence the factors used to convert second moments to eddy dissipation rates do not vary greatly. However, despite the excellent correlation, it would be desirable to reduce the scatter around the best-fit line. Figure, Figure 21and Figure 22 show the comparison between the median value of CHILL radar second moments over a 2 km disc versus the variance of T-28 vertical acceleration over a 2 km path. The number of points within the disc is restricted to greater than 8, 14 and points, respectively. The correlation coefficients for these three cases are.26,.61 and.87, respectively. The last value is quite good; however, the data points for this case represent only measurements taken fairly close to the radar. Figure 23, Figure 24, and Figure 2 show a comparison between the median values of the NCAR algorithm EDR estimate calculated over a 2 km-radius disc and length scale of m versus the variance of T-28 vertical acceleration over a 2 km path. The number of points within the disc is restricted to greater than 8, 14 and points, respectively. The correlation coefficients for these three cases are.36,.7 and.87, respectively. As with the previous figures, the correlations especially the last one are very good. Figure 26, Figure 27 and Figure 28 illustrate these comparisons for a length scale of 3 m. The correlation values are.4,.72 and.86. Comparing these values as well as the slope of the best-fit line and variance of the residuals with those from the m length scale cases, it can be seen that the numbers are very similar, implying that the NCAR turbulence algorithm is relatively insensitive to the length scale a fortuitous result. This insensitivity to outer length scale was also observed in the 3

32 analysis presented in last year s report, when EDR values from the NCAR turbulence algorithm were compared to EDR estimates from the T-28 aircraft. Figure 29, Figure 3 and Figure 31 illustrate a similar set of cases to those shown in Figure, Figure 21, and Figure 22 except that a confidence-weighted average is used in place of median values. The confidences used in the weighted averages were simply derived from the reflectivity values as described above low confidence was assigned to very low and very high reflectivity measurements, while mid-range reflectivities received high confidence values. The correlation coefficients for these scatter plots are.29,.63, and.8, respectively values which are commensurate with those for the corresponding cases presented above for median values. Figure 32, Figure 33, and Figure 34 are the same as Figure 23, Figure 24 and Figure 2, except that again confidence-weighted average are used instead of median values. The results are again similar, yielding correlation coefficients of.36,.7, and.76. Finally, the last three plots, Figure 3, Figure 36 and Figure 37 illustrate a comparison between the variance of the CHILL radar-measured radial velocities over a 2 km disc and the variance of the aircraft vertical accelerations over 2 km flight paths. The correlations (.39,.8, and., respectively) are less than the values obtained using median or confidence-weighted average second moments. However, the second moment and the variance of the first moment should respond to different scales of the turbulence, and a careful combination of the two values using principles of fuzzy logic may provide better turbulence information than either value alone. 31

33 2 CHILL/T 28, June 1999: TFS < 9 s, pts > 8 ρ =.2978 σ 2 = fit slope =.848 # points = 2972 Radar median second moment from 2 km disc (m 2 /s 2 ) Variance of T 28 acceleration over 2 km path (g 2 ) Figure Scatter plot of the median value of CHILL radar second moments over a 2 km-radius disc versus the variance of the T-28 aircraft vertical acceleration over a 2 km path. The number of points in the disc are restricted to being greater than 8. 32

34 2 CHILL/T 28, June 1999: TFS < 9 s, pts > 14 ρ =.618 σ 2 = fit slope = # points = 89 Radar median second moment from 2 km disc (m 2 /s 2 ) Variance of T 28 acceleration over 2 km path (g 2 ) Figure 21 Scatter plot of the median value of CHILL radar second moments over a 2 km-radius disc versus the variance of the T-28 aircraft vertical acceleration over a 2 km path. The number of points in the disc are restricted to being greater than

35 2 CHILL/T 28, June 1999: TFS < 9 s, pts > ρ = σ 2 =.9872 fit slope = # points = 346 Radar median second moment from 2 km disc (m 2 /s 2 ) Variance of T 28 acceleration over 2 km path (g 2 ) Figure 22 Scatter plot of the median value of CHILL radar second moments over a 2 km-radius disc versus the variance of the T-28 aircraft vertical acceleration over a 2 km path. The number of points in the disc are restricted to being greater than. 34

36 .2.2 CHILL/T 28, June 1999: TFS < 9 s, pts > 8 ρ =.392 σ 2 =.2349 fit slope =.444 # points = 2972 NCAR median EDR from 2 km disc, L = m (m 4/3 /s 2 ) Variance of T 28 acceleration over 2 km path (g 2 ) Figure 23 Scatter plot of the median value of the NCAR turbulence algorithm s EDR estimate over a 2 km-radius disc versus the variance of the T-28 aircraft vertical acceleration over a 2 km path. The length scale for the NCAR algorithm is m. The number of points in the disc is restricted to more than 8 points. 3

37 .2.2 CHILL/T 28, June 1999: TFS < 9 s, pts > 14 ρ = σ 2 =.949 fit slope =.7367 # points = 89 NCAR median EDR from 2 km disc, L = m (m 4/3 /s 2 ) Variance of T 28 acceleration over 2 km path (g 2 ) Figure 24 Scatter plot of the median value of the NCAR turbulence algorithm s EDR estimate over a 2 km-radius disc versus the variance of the T-28 aircraft vertical acceleration over a 2 km path. The length scale for the NCAR algorithm is m. The number of points in the disc is restricted to more than 14 points. 36

38 .2.2 CHILL/T 28, June 1999: TFS < 9 s, pts > ρ = σ 2 =.642 fit slope =.7691 # points = 346 NCAR median EDR from 2 km disc, L = m (m 4/3 /s 2 ) Variance of T 28 acceleration over 2 km path (g 2 ) Figure 2 Scatter plot of the median value of the NCAR turbulence algorithm s EDR estimate over a 2 km-radius disc versus the variance of the T-28 aircraft vertical acceleration over a 2 km path. The length scale for the NCAR algorithm is m. The number of points in the disc is restricted to more than points. 37

39 .2.2 CHILL/T 28, June 1999: TFS < 9 s, pts > 8 ρ = σ 2 = fit slope = # points = 2972 NCAR median EDR from 2 km disc, L = 3 m (m 4/3 /s 2 ) Variance of T 28 acceleration over 2 km path (g 2 ) Figure 26 Same as Figure 23, with a length scale of 3 m. 38

40 .2.2 CHILL/T 28, June 1999: TFS < 9 s, pts > 14 ρ =.786 σ 2 =.7729 fit slope =.6496 # points = 89 NCAR median EDR from 2 km disc, L = 3 m (m 4/3 /s 2 ) Variance of T 28 acceleration over 2 km path (g 2 ) Figure 27 Same as Figure 24, with a length scale of 3 m. 39

41 .2.2 CHILL/T 28, June 1999: TFS < 9 s, pts > ρ = σ 2 = fit slope = # points = 346 NCAR median EDR from 2 km disc, L = 3 m (m 4/3 /s 2 ) Variance of T 28 acceleration over 2 km path (g 2 ) Figure 28 Same as Figure 2, with a length scale of 3 m. 4

42 2 CHILL/T 28, June 1999: TFS < 9 s, pts > 8 ρ =.2889 σ 2 = fit slope = # points = 2972 Radar CWA second moment from 2 km disc (m 2 /s 2 ) Variance of T 28 acceleration over 2 km path (g 2 ) Figure 29 Confidence-weighted averages of second moments over a 2 km-radius disc compared to the variance of the T-28 aircraft vertical acceleration over a 2 km path. The number of points in the disc is restricted to greater than 8 points. 41

43 2 CHILL/T 28, June 1999: TFS < 9 s, pts > 14 ρ = σ 2 = fit slope = # points = 89 Radar CWA second moment from 2 km disc (m 2 /s 2 ) Variance of T 28 acceleration over 2 km path (g 2 ) Figure 3 Same as Figure 29, with the number of points restricted to greater than 14 points. 42

44 2 CHILL/T 28, June 1999: TFS < 9 s, pts > ρ =.81 σ 2 = fit slope = # points = 346 Radar CWA second moment from 2 km disc (m 2 /s 2 ) Variance of T 28 acceleration over 2 km path (g 2 ) Figure 31 Same as Figure 29, with the number of points restricted to greater than. 43

45 .2.2 CHILL/T 28, June 1999: TFS < 9 s, pts > 8 ρ = σ 2 =.3773 fit slope =.7123 # points = 2972 NCAR CWA EDR from 2 km disc, L = m (m 4/3 /s 2 ) Variance of T 28 acceleration over 2 km path (g 2 ) Figure 32 Same as Figure 23, using a confidence-weighted average over the 2 km-radius disc instead of a median value. 44

46 .2.2 CHILL/T 28, June 1999: TFS < 9 s, pts > 14 ρ =.737 σ 2 =.1814 fit slope = # points = 89 NCAR CWA EDR from 2 km disc, L = m (m 4/3 /s 2 ) Variance of T 28 acceleration over 2 km path (g 2 ) Figure 33 Same as Figure 24, using a confidence-weighted average over the 2 km-radius disc instead of a median value. 4

47 .2.2 CHILL/T 28, June 1999: TFS < 9 s, pts > ρ =.8247 σ 2 =.34 fit slope = # points = 346 NCAR CWA EDR from 2 km disc, L = m (m 4/3 /s 2 ) Variance of T 28 acceleration over 2 km path (g 2 ) Figure 34 Same as Figure 2, using a confidence-weighted average over the 2 km-radius disc instead of a median value. 46

48 4 4 CHILL/T 28, June 1999: TFS < 9 s, pts > 8 ρ =.3922 σ 2 = fit slope = # points = 2941 Variance of radial velocities in 2 km disc (m 2 /s 2 ) Variance of T 28 acceleration over 2 km path (g 2 ) Figure 3 The variance of radar-measured radial velocities over a 2 km-radius disc versus the variance of the T-28 aircraft vertical accelerations over a 2 km path. The number of points in the disc are restricted to greater than 8. 47

49 4 4 CHILL/T 28, June 1999: TFS < 9 s, pts > 14 ρ =.8333 σ 2 = fit slope =.2 # points = 79 Variance of radial velocities in 2 km disc (m 2 /s 2 ) Variance of T 28 acceleration over 2 km path (g 2 ) Figure 36 Same as Figure 3, using at least 14 points in the disc. 48

50 4 4 CHILL/T 28, June 1999: TFS < 9 s, pts > ρ =.74 σ 2 = fit slope = # points = 346 Variance of radial velocities in 2 km disc (m 2 /s 2 ) Variance of T 28 acceleration over 2 km path (g 2 ) Figure 37 Same as Figure 3, using at least points in the disc. 49

51 Future Work The analyses presented in this report have illustrated both encouraging results and the need for further work. The radar activities for FY1 will again be focussed on the WSR-88D turbulence detection algorithm development. The work will involve both the use of simulations and the continued analysis of the RAPS92 and 1999 TCAD datasets. Simulation software developed for the NASA Aviation Safety Program provides an ideal testbed for further development and verification of the NCAR turbulence algorithm. In addition to simulating radar measurements of a wind field, aircraft flights through the same wind field can also be simulated. In addition, important issues related to spectral and moment averaging can be investigated. Both the RAPS92 Mile High radar and T-28 aircraft data used in last year s FY99 report and the 1999 TCAD field program data described in the present report require further analysis. In both cases, the radar data should be edited and converted into a Matlab-readable format with less loss of precision in the data values, spatial locations, and timestamps than is accorded by the current uf2mdv software. In addition, the high-rate T-28 aircraft data from RAPS92 should be filtered in the same manner as the TCAD data was to obtain the variance of the vertical acceleration over 2 km paths, and both in-situ datasets should be used to derive eddy dissipation rates for further comparison with the radar values. Many other variations of the data processing are possible, including removal of trends before variances are calculated in both the aircraft vertical accelerations and radar radial velocities, and these should be tried. The structure function method should also be implemented and tested. Finally, principles of fuzzy logic should be used to combine the results of the first and second moment methods with appropriate confidences to obtain a final turbulence value.