Remote Sensing of Turbulence: Radar Activities. FY04 Year-End Report

Transcription

1 Remote Sensing of Turbulence: Radar Activities FY04 Year-End Report Submitted by The National Center For Atmospheric Research Deliverable E4

2 Introduction In FY04, 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. This report covers work performed under task , which focused on the development and testing of the NCAR Turbulence Detection Algorithm (NTDA) for use with WSR-88D radars. The report consists of two sections. The first is a draft journal article, Remote Detection of Turbulence using Ground-Based Doppler Radars with Application to Aviation Safety. This article describes the NCAR Turbulence Detection Algorithm and reports on a number of verification studies that have demonstrated its skill. The second section is a report from NSSL describing work performed by Ming Fang and Dick Doviak. The report is entitled, Separation of Shear and Turbulence Contributions to Spectrum Width Measured with Weather Radar. 1

3 Remote Detection of Turbulence using Ground-Based Doppler Radars with Application to Aviation Safety John K. Williams, Larry Cornman, Danika Gilbert, Steven G. Carson, and Jaimi Yee National Center for Atmospheric Research DRAFT last revised Thursday, October 14, 2004, 6:02 PM Corresponding author address: Dr. John K. Williams, Research Applications Division, National Center for Atmospheric Research, P.O. Box 3000, Boulder, CO

4 Abstract Real-time remote detection of in-cloud turbulence would provide a valuable new input to decision support systems that help pilots and air traffic controllers assess weather-related aviation hazards, and in particular offers the potential to improve safety and air traffic flow during convective events. This capability may be provided, in part, by a new Doppler radar turbulence detection algorithm designed for use on the operational NEXRAD and TDWR radars that effectively cover the continental US. The new fuzzy logic algorithm, developed at NCAR under the auspices of the FAA's Aviation Weather Research Program, makes use of the radar-measured reflectivity, radial velocity, and spectrum width to perform data quality control and produce estimates of eddy dissipation rate (EDR), an aircraft-independent turbulence metric. It is anticipated that the algorithm will eventually be installed on all NEXRAD and TDWR radars, and that the radar-derived EDRs will be combined with satellite, in situ, and numerical weather model data to produce a nationwide integrated turbulence detection product. In addition to describing the new turbulence detection algorithm, the authors present highlights of the verification process that has demonstrated the algorithm's skill and potential operational utility. This process has included extensive comparisons of radar-derived EDR estimates with in situ EDR values obtained from aircraft winds data, including both post-processed data from the NASA Boeing 757's spring 2002 flight tests and EDRs produced by an automated turbulence reporting system developed by NCAR and currently operating on a number of commercial aircraft. In addition, analysis of Flight Data Recorder information provided by the NTSB shows that the NCAR turbulence detection algorithm often detected hazardous in-cloud turbulence well in advance of the aircraft encounter.

5 1. INTRODUCTION Commercial and general aviation aircraft frequently encounter unexpected turbulence that is hazardous to both aircraft and passengers. For air carriers, turbulence is the leading cause of occupant injuries, and it occasionally results in severe aircraft damage and fatalities (MCR, 1999). The cost to airlines due to injuries to flight attendants and passengers, aircraft damage, the need for additional inspections and maintenance, and associated flight delays is substantial. Moreover, encounters with even moderate turbulence may reduce passengers confidence in airline safety. While clear-air turbulence forecasts based on numerical weather model data are now routinely generated and possess reasonable skill for levels above 21,000 ft (Sharman, 2002), a similar system for identifying and disseminating information about hazardous convectively-induced turbulence remains lacking. This omission is particularly significant because historical data suggest that over 60% of turbulence-related aircraft accidents are due to convectively-induced turbulence (Cornman, 1993). To begin to ameliorate this deficiency, the FAA s Aviation Weather Research Program has directed the National Center for Atmospheric Research (NCAR) to develop an improved Doppler radar turbulence detection capability. The NCAR Turbulence Detection Algorithm (NTDA) makes use of the radarmeasured reflectivity, radial velocity, and spectrum width to produce estimates of eddy dissipation rate (EDR), an aircraft-independent turbulence metric, along with associated quality control indices, or confidences. This fuzzy-logic algorithm, which may eventually be installed on the NEXRAD and TDWR radars that provide coverage of most of the conterminous United States, is expected to be a central component in a system that will eventually utilize radar, satellite, in situ, and numerical weather model data to produce a nationwide integrated turbulence detection product. In this paper, the authors describe an experimental version of the new turbulence detection algorithm that has been implemented and verified using comparisons between archived NEXRAD data and in situ data from flight tests, NTSB turbulence encounter cases, and an automated turbulence reporting system operating on commercial aircraft. The verification process, while not yet comprehensive, suggests that

6 the turbulence detection algorithm has adequate skill to be of significant operational utility, as will be shown below. 2. NCAR TURBULENCE DETECTION ALGORITHM The NCAR turbulence detection algorithm (NTDA) utilizes the first three moments of the Doppler spectrum the reflectivity, radial velocity, and spectrum width to perform data quality control and produce EDR estimates on the same polar grid as is used for the raw moment data (see Figure 1). Data quality control is performed by computing a quality control index, or confidence, for each measurement. For example, the spectrum width confidence computation is based on the signal-to-noise ratio, or SNR (which for NEXRAD Level II data is inferred from the reflectivity and range from the radar), the value of the spectrum width, the local variance of the spectrum width field, and image processing techniques designed to identify known artifacts. The confidence values for each measurement are then propagated into the EDR computations as weights for local confidence-weighted averaging, and are also used to determine a confidence value for the resulting EDR. Three distinct methods are used for computing EDR: a second-moment method, which makes use of the measured spectrum widths; a combined first and second-moment method, which also makes use of the local variance of the radial velocity; and a structure function method, which utilizes the radial velocity measurements. The various EDR estimates, along with their associated confidences, are combined in a fuzzy-logic framework, with a single EDR and associated confidence produced for each radar measurement location. The structure of the algorithm, as implemented for NEXRAD Level II data, is diagrammed in Figure 1. For the results presented in this paper, however, only the output of the second moment module of the algorithm is used. 3. NTDA VERIFICATION Development, tuning, and verification of the NTDA has been performed over several years using data from research aircraft (notably the SDSM&T T-28) and Doppler research radars, including the Mile High

7 radar and CSU CHILL radar. Recently, however, it has become possible to obtain archived NEXRAD Level II data directly from the National Climate Data Center (NCDC) via a web-based interface, making it feasible to run the NTDA for any in-cloud turbulence case in which in situ turbulence data are available for comparison. Sources of high-quality in situ turbulence data include instrumented research aircraft, flight data recorder information supplied by the National Transportation Safety Board (NTSB), and EDR values generated by an automated reporting system currently operating on a number of United Airlines aircraft (Cornman, 1995 and 2004). 3.1 NASA Flight Test Data In the spring of 2002, a series of eleven flights were performed by the instrumented NASA Langley B-757 aircraft as part of a successful test of an airborne radar turbulence detection algorithm developed by NCAR for the NASA Aviation Safety and Security Program s Turbulence Prediction and Warning Systems project. The high-rate winds data recorded by the aircraft comprise a dataset that is also ideal for evaluating the performance of the NTDA, run on archived Level II data from NEXRAD radars along the flight paths. The B-757 s 20 Hz vertical winds data were used to estimate eddy dissipation rate (EDR), an atmospheric turbulence metric, using a single parameter maximum likelihood -5/3 model that assumes a von Karman energy spectrum form. In particular, a sliding window of width 256 points was used, with spectral frequency cutoffs set at 0.5 and 5 Hz. This temporal window size corresponds to an along-path distance of about 3 km at the aircraft s average cruising speed. In Figure 2, these computed EDR values are depicted at 30-second intervals along the flight path in for NASA flights 230 and 232, which took place on April 15 and 30, 2002, respectively. During flight 230, moderate or greater (MoG) turbulence was experienced over northern and eastern South Carolina and eastern North Carolina, and each of those encounters was in a region covered by at least three NEXRADs having available archived data. For flight 232, MoG turbulence was encountered over north-central Alabama. Although as many as five

8 NEXRADs provide coverage of this region, three of these (KGWX, KBMX, and KMXX) had no data available from the NCDC archives. Comparisons between the aircraft data and the results from the NTDA running on the archived radar data were performed by locating the nearest three radar sweeps in space and time to each aircraft location. These were then utilized in two ways. First, a comprehensive series of overlay plots were generated to permit comparison between the aircraft EDR and the EDR computed by the NTDA for each sweep. Two sample plots are depicted in Figure 3 and Figure 4. Although precise collocation and quantitative matches were not achieved, both plots show that the radar successfully detected hazardous turbulence of about the right intensity in the region of the aircraft encounter. Moreover, both encounters were in regions of relatively low reflectivity (< 30 dbz in Figure 3 and < 15 dbz in Figure 4) where commercial aircraft commonly fly. On the other hand, no radar moments data were available near the location of the smaller MoG turbulence encounter north of the larger encounter in Figure 4; this highlights a limitation of any turbulence detection algorithm based solely on Doppler weather radar data: it is inherently unable to measure out-of-cloud turbulence. A second level of processing was performed to extract the median reflectivity, SNR, and NTDA EDR values from a disc of radius 2 km around each aircraft location on each nearby radar sweep (time within 3 minutes and vertical displacement less than 3 km). The results are displayed in a series of timeseries plots for each radar depicting the radar-detected and in situ EDRs and reflectivity and SNR timeseries. In addition, a plot was designed to visualize the EDR values from all nearby sweeps from all appropriate radars and compare them with the aircraft EDRs. An example of such a stacked track plot for NASA flight 230, 20:07:10-20:12:30 is shown in Figure 5. Note that the four radars that provide coverage of this turbulence encounter generate similar EDR estimates and that these match well with the co-located in situ values, providing compelling evidence of the NTDA algorithm s skill. The set of timeseries, overlay, and stacked-track plots generated by the analysis described above were used to score the ability of the NTDA to detect MoG turbulence encountered by the aircraft from 55 flight segment events drawn from the eleven flights of the NASA flight test. A similar scoring exercise

9 performed using the output of the airborne radar turbulence detection algorithm identified 34 correct detections, 8 misses, 4 nuisance alerts, and 9 correct nulls (Cornman, 2003), producing a probability of detection (PoD) of 81% with a nuisance alert rate of 11%. For the NTDA analysis, 15 events had no available archived NEXRAD data intersecting them. Of the remaining 40, preliminary scoring identified 32 correct detections, 2 misses, 6 nuisance alerts, and no correct nulls, yielding a PoD of 94% and a NAR of 16%. This analysis suggests that the NTDA may have skill comparable to that of the airborne radar algorithm for detecting hazardous turbulence, but that more work needs to be done to reduce the number of nuisance alerts. However, it should also be noted that research flights aimed specifically at encountering turbulence may not provide a dataset representative of the conditions encountered by commercial aircraft in an operational environment, and so care must be taken in interpreting these results. 3.2 NTSB Turbulence Encounter Cases In addition to flight test data, high-rate accelerometer data from flight data recorders (FDRs) provide information about turbulence that can be used to verify NTDA performance, and the NTSB has provided FDR data for several turbulence-related accident cases to NCAR for that purpose. These case studies are especially compelling because they represent accidental encounters that might have been prevented by an operational turbulence detection capability. Since these accidents are still under investigation by the NTSB, these data may not yet be released publicly, and hence a full description of the results cannot be provided here. However, two severe turbulence encounter cases are described based on the times and locations of the encounters. The first case occurred on November 17, 2002, at 23:00 UTC as a regional jet was descending near Rockville, VA (approximately 37:44 N latitude, 77:43 W longitude, and 18,000 ft) en route to Washington National Airport. Fortunately, all passengers were in their seats in preparation for landing and none were injured, though the aircraft required extensive inspection. As Figure 6 shows, the NTDA successfully detected a coherent region of persistent, very strong turbulence eddy dissipation rates well above 1.0 m 2/3 /s in that region, despite very low reflectivity values between 10 and 15 dbz there.

10 Moreover, this diagnosis was available as early as twelve minutes before the encounter, suggesting the potential efficacy of an NTDA-based tactical turbulence warning system for this case. A second turbulence encounter case occurred on August 6, 2003 at 20:57 UTC as an Airbus A340 was at cruise altitude over Walnut Ridge, AR (approximately 36:33 N latitude, 90:42 W longitude, and 31,000 ft) en route to Houston, TX. Figure 7 depicts the NTDA EDR values produced from the four 2.4 radar sweeps from KPAH immediately preceding the encounter time. In this case, the NTDA detected hazardous turbulence at the location of the encounter fourteen minutes in advance, and the extent and magnitude of the turbulence increased over subsequent scans. The radar reflectivity grew from about 10 to 30 dbz at the location of the encounter during this time, but its magnitude would likely not have appeared dangerous to the pilots. It appears that an NTDA-based turbulence warning system would have been capable of providing adequate warning for this case, and thus possibly prevented the 43 minor injuries, two serious injuries, and minor damage to the aircraft that resulted from the unexpected turbulence encounter. However, the quickly-evolving nature of convective turbulence illustrated by this case will require that the latency between the radar measurement and the communication of the turbulence hazard to the pilot be very small for the warnings to be effective. 3.2 In situ Turbulence Reports While FDR data cases like those described above provide valuable information on hazardous turbulence encounters, the number of events is insufficient to draw statistically meaningful conclusions. On the other hand, the Cornman in situ turbulence algorithm (Cornman, 1995 and 2004) is currently installed on about 200 United Airlines B-737 and B-757 aircraft, and efforts are underway to deploy it on additional aircraft types and airlines in the near future. The in situ algorithm provides median and peak EDR values reported at intervals of one minute or less, thereby supplying a large dataset of objective turbulence measurements in locations and conditions where aircraft commonly fly. When an automated method to quality control these data is completed, several hundred flight hours per day of in situ

11 turbulence information will be available for use in comparing to NTDA-derived values and producing a comprehensive statistical analysis. An illustration is provided using a segment from a flight from Chicago to Salt Lake City that began just after midnight UTC on November 18, Figure 8 and Figure 9 depict the peak in situ EDR measurements obtained from the automated reporting algorithm, represented by colors in circles along the flight path as the aircraft flew from east to west across Iowa and western Nebraska. In Figure 8, the aircraft track is overlaid on the radar-measured reflectivity at 31,000 ft the average cruising altitude for the flight obtained by merging data from the KLNX, KUEX, KOAX, KDMX, KDVN and KILX NEXRADs onto a 2 km x 2 km x 2,000 ft grid. Three distinct instances of elevated in situ EDRs may be observed: 00:11-00:12 over east-central Iowa, 00:27-00:33 over western Iowa, and 00:46-00:48 UTC over northeastern Nebraska. The valid time of the radar analysis is 00:30, meaning that it used radar sweeps collected between 00:24 and 00:30. At that time, which coincides with the second turbulence encounter, the radar-measured reflectivity was less than 10 dbz along the flight path. This implies that the cloud would not have been visible on an airborne radar display, although the pilots appear to have been deviating around a more intense echo further south. The merged confidence-weighted mean NTDA EDRs shown in Figure 9 show a good match with the beginning of this turbulence encounter, although the last and most intense part occurred out of cloud and hence no direct EDR measurement was possible. This case suggests the importance of developing diagnostics for EDR in the vicinity of convection to augment the direct in-cloud turbulence detection capability. 4. CONCLUSION A new Doppler radar turbulence detection algorithm, the NTDA, utilizes the radar reflectivity, radial velocity, and spectrum width data to perform quality control and produce EDR estimates. Initial verification studies using archived Level II data and in situ data from flight tests, NTSB turbulence encounter cases, and automatically-reported EDR data from commercial aircraft suggest that the NTDA

12 has skill in detecting hazardous turbulence and has the potential to be a valuable new input to decision support systems that help pilots, air traffic controllers, and dispatchers assess weather-related aviation hazards. In particular, this capability could improve safety, passenger confidence, and air traffic flow during convective events. It is anticipated that the NTDA will eventually be implemented on all NEXRAD and TDWR radars so that the EDRs it produces will be readily available to all potential users for operational or scientific purposes. In addition, NCAR has requested funding from the FAA s Aviation Weather Research Program to develop a real-time turbulence detection product based on the NTDA EDRs and confidences that will support the unique needs of the aviation community. A web-based product is foreseen that will provide a nationwide, gridded turbulence diagnosis display for specified flight levels, thereby supplementing the upper-level turbulence forecasts currently supplied by the Graphical Turbulence Guidance product on the National Weather Service Aviation Weather Center s Aviation Digital Data Service (ADDS). Eventually, the NTDA output will be combined with satellite, in situ, and numerical weather prediction model data to identify and forecast regions of hazardous turbulence. 5. ACKNOWLEDGEMENTS The authors wish to thank the National Transportation Safety Board for supplying Flight Data Recorder information for the case studies described herein, and the NASA Aviation Safety and Security Program and Langley Research Center for providing aircraft data from the spring, 2002 TPAWS flight tests. This research is in response to requirements and funding by the Federal Aviation Administration (FAA). The views expressed are those of the authors and do not necessarily represent the official policy or position of the FAA.

13 References Cornman, L. B. and B. Carmichael, 1993: Varied research efforts are under way to find means of avoiding air turbulence. ICAO Journal, 48, Cornman, L. B., C. S. Morse, and G. Cunning, 1995: Real-time estimation of atmospheric turbulence severity from in-situ aircraft measurements, Journal of Aircraft, 32, Cornman, L. B., J. Williams, G. Meymaris, and B. Chorbajian, 2003; Verification of an Airborne Radar Turbulence Detection Algorithm. 6 th International Symposium on Tropospheric Profiling: Needs and Technologies, Cornman, L. B., G. Meymaris and M. Limber, 2004: An update on the FAA Aviation Weather Research Program s in situ turbulence measurement and reporting system. 11th AMS Conference on Aviation, Range, and Aerospace Meteorology. MCR Federal, Inc., Turbulence Benefits Analysis. Historical Safety Impact of Turbulence. BR- 7100/010-1, 9 June Sharman, R., C. Tebaldi, J. Wolff and G. Wiener, 2002: Results from the NCAR Integrated Turbulence Forecasting Algorithm (ITFA) for predicting upper level clear-air turbulence. 10th AMS Conference on Aviation, Range, and Aerospace Meteorology,

14 Figure captions Figure 1: Diagram of the NTDA, as implemented for the WSR-88D (NEXRAD) radar. The Level II reflectivity, radial velocity and spectrum width data are used to compute EDR and an associated confidence for each radar measurement point via a fuzzy-logic framework. Figure 2: (Top) Flight path for NASA flight 230 on April 15, 2002, depicting EDR values scaled from 0 (blue) to 0.7 m2/3/s (red) at 30-second intervals. NEXRAD radar positions and 220-km range rings are superimposed, with red indicating that the radar intersected the flight path and the archived Level II data were available. The aircraft took off from Hampton, VA, and traveled counter-clockwise. (Bottom) A similar plot depicting a portion of the flight path for NASA flight 232 on April 30, 2002; the flight direction was again counter-clockwise. Figure 3: Overlay of in situ EDR values depicted along the aircraft track for NASA flight 230, 19:22:00-19:29:15, superimposed over the NTDA EDR values from the KLTX 2.4 elevation sweep beginning at 19:25:26. Both EDR values are on the same scale as Figure 2, ranging from 0 (blue) to 0.7 m2/3/s (red). The labels on the range rings and the axes represent the distance from KLTX, in km. The aircraft is within about 1 km of the sweep throughout this flight segment, and the radar reflectivity ranges from about 5-30 dbz within the turbulent region. Figure 4: Identical to Figure 3, except for NASA flight 232, 18:54:51-19:01:23, and KFFC 2.4 elevation sweep beginning at 18:57:51. The aircraft is again within about 1 km of the sweep, and the radar reflectivity ranges between about 5-15 dbz in the region where the aircraft track intersects the radardetected turbulence hot spot.

15 Figure 5: Stacked track plot for NASA flight 230, 20:07:10-20:12:30 depicting the colorscaled timeseries of aircraft EDRs ( AC, bottom stripe) and the 2-km disc median NTDA EDRs from the three nearest sweeps of radars KAKQ, KCAE, KCLX, KFCX, KLTX, KMHX, and KRAX. Gray indicates that the radar was out of range, whereas white depicts times for which a radar sweep was within range but contained no usable data. The EDR color scale ranges from 0 to 1 m2/3/s. Figure 6: NTDA EDR from KAKQ 2.4 sweeps at 22:49, 22:55; 23:06, 23:12 UTC on November 17, 2002, ranging from 12 minutes before to 11 minutes after the severe turbulence encounter described in the text, which occurred at the location marked by the X. Note the unusually large EDR scale, from 0 to 1.85 m2/3/s. Figure 7: NTDA EDR from KPAH 2.4 sweeps at 20:37, 20:43, 20:49, and 20:54 UTC on August 6, 2003, ranging from 20 minutes to 3 minutes before the severe turbulence encounter described in the text. The EDR color scale ranges from 0 to 0.7 m2/3/s. Figure 8: Automated in situ reports of peak EDR over 1-minute segments from a flight from Chicago to Salt Lake City on November 18, 2003, represented as colored circles scaled from 0 (blue) to 0.7 m2/3/s (red). The flight track is overlaid on the radar reflectivity at 31,000 ft obtained from merging data from the KLNX, KUEX, KOAX, KDMX, KDVN, and KILX NEXRADs recorded between 00:24 and 00:30 UTC and gridding them onto a 2 km x 2 km x 2000 ft grid. The reflectivity scale, shown below the plot, ranges from -10 to 30 dbz. Figure 9: Identical to Figure 8 but with the aircraft track overlaid on the NTDA EDRs at 31,000 ft obtained by performing confidence-weighted averaging of the values recorded by the KLNX, KUEX,

16 KOAX, KDMX, KDVN, and KILX NEXRADs between 00:24 and 00:30 UTC. Both the in situ and NTDA-derived EDRs are represented on a color scale from 0 to 0.7 m2/3/s.

17 Figures WSR-88D Level-II Data Computed quantities EDR estimation methods Final product DZ reflectivity VE radial velocity SNR signal-to-noise ratio VE confidence SW confidence Second moment Scaled second-moment method Combined First and second moment combined method Turbulence (EDR) EDR confidence SW spectrum width Structure function velocity structure functions fit to theoretical curves Figure 1: Diagram of the NTDA, as implemented for the WSR-88D (NEXRAD) radar. The Level II reflectivity, radial velocity and spectrum width data are used to compute EDR and an associated confidence for each radar measurement point via a fuzzy-logic framework.

18 Figure 2: (Top) Flight path for NASA flight 230 on April 15, 2002, depicting EDR values scaled from 0 (blue) to 0.7 m 2/3 /s (red) at 30-second intervals. NEXRAD radar positions and 220-km range rings are superimposed, with red indicating that the radar intersected the flight path and the archived Level II data were available. The aircraft took off from Hampton, VA, and traveled counter-clockwise. (Bottom) A similar plot depicting a portion of the flight path for NASA flight 232 on April 30, 2002; the flight direction was again counter-clockwise.

19 Figure 3: Overlay of in situ EDR values depicted along the aircraft track for NASA flight 230, 19:22:00-19:29:15, superimposed over the NTDA EDR values from the KLTX 2.4 elevation sweep beginning at 19:25:26. Both EDR values are on the same scale as Figure 2, ranging from 0 (blue) to 0.7 m 2/3 /s (red). The labels on the range rings and the axes represent the distance from KLTX, in km. The aircraft is within about 1 km of the sweep throughout this flight segment, and the radar reflectivity ranges from about 5-30 dbz within the turbulent region.

20 Figure 4: Identical to Figure 3, except for NASA flight 232, 18:54:51-19:01:23, and KFFC 2.4 elevation sweep beginning at 18:57:51. The aircraft is again within about 1 km of the sweep, and the radar reflectivity ranges between about 5-15 dbz in the region where the aircraft track intersects the radardetected turbulence hot spot.

21 Figure 5: Stacked track plot for NASA flight 230, 20:07:10-20:12:30 depicting the colorscaled timeseries of aircraft EDRs ( AC, bottom stripe) and the 2-km disc median NTDA EDRs from the three nearest sweeps of radars KAKQ, KCAE, KCLX, KFCX, KLTX, KMHX, and KRAX. Gray indicates that the radar was out of range, whereas white depicts times for which a radar sweep was within range but contained no usable data. The EDR color scale ranges from 0 to 1 m 2/3 /s.

22 Figure 6: NTDA EDR from KAKQ 2.4 sweeps at 22:49, 22:55; 23:06, 23:12 UTC on November 17, 2002, ranging from 12 minutes before to 11 minutes after the severe turbulence encounter described in the text, which occurred at the location marked by the X. Note the unusually large EDR scale, from 0 to 1.85 m 2/3 /s.

23 Figure 7: NTDA EDR from KPAH 2.4 sweeps at 20:37, 20:43, 20:49, and 20:54 UTC on August 6, 2003, ranging from 20 minutes to 3 minutes before the severe turbulence encounter described in the text. The EDR color scale ranges from 0 to 0.7 m 2/3 /s.

24 Figure 8: Automated in situ reports of peak EDR over 1-minute segments from a flight from Chicago to Salt Lake City on November 18, 2003, represented as colored circles scaled from 0 (blue) to 0.7 m 2/3 /s (red). The flight track is overlaid on the radar reflectivity at 31,000 ft obtained from merging data from the KLNX, KUEX, KOAX, KDMX, KDVN, and KILX NEXRADs recorded between 00:24 and 00:30 UTC and gridding them onto a 2 km x 2 km x 2000 ft grid. The reflectivity scale, shown below the plot, ranges from -10 to 30 dbz.

25 Figure 9: Identical to Figure 8 but with the aircraft track overlaid on the NTDA EDRs at 31,000 ft obtained by performing confidence-weighted averaging of the values recorded by the KLNX, KUEX, KOAX, KDMX, KDVN, and KILX NEXRADs between 00:24 and 00:30 UTC. Both the in situ and NTDA-derived EDRs are represented on a color scale from 0 to 0.7 m 2/3 /s.

26 SEPARATION OF SHEAR AND TURBULENCE CONTRIBUTIONS TO SPECTRUM WIDTH MEASURED WITH WEATHER RADAR MING FANG COOPERATIVE INSTITUTE FOR MESOSCALE METOROLOGICAL RESEARCH UNIVERSITY OF OKLAHOMA, NORMAN, OKLAHOMA ABSTRACT Shear and turbulence are two main meteorological contributors to spectrum width measured by radar. A 6-point scheme of linear surface fitting is designed and applied to a snowstorm case to separate the shear and turbulence contributions from each other. For the studied case, shear contributes more to the total measured spectrum width than turbulence. Based on assumptions of horizontally homogeneous turbulence, and a linear change of the mean radial velocity across the radar beam, the measured shear contribution is calculated from Doppler measurements. Simulations were performed based on the wind profile obtained through VAD techniques. Shear calculations based upon wind profiles obtained from the VAD analysis, and shear obtained from the 6-point fitting method are consistent. For the studied case of a snowstorm, the contributions from radial velocity shears in radial and azimuthal directions are negligible compared to the contribution from radial velocity shear in the elevation direction. Both wind speed shear and directional shear significantly contribute to the broadening of the Doppler spectrum and can bias estimates of turbulence. 1

27 1. Introduction Radar measures spectrum width, σ v, that includes all possible contributions to the variation of the radial component of wind within the radar s resolution volume. Shear and turbulence are two main contributors to the spectrum width. Thus it is important to examine the fields of shear and turbulence, and derive from them properties that are of interest to meteorologists to improve our understanding of weather, and to aviators to alert them of possible hazards to safe flight. To extract these two fields from the observed spectrum width, Istok and Doviak (1986) proposed an approach, called the 9-point scheme herein, to separate these two components. They successfully used this approach in their study of tornadic storms. However, the 9-point scheme is a spatial filter that encompasses a wide vertical dimension at ranges far from the radar site, and thus may not resolve shears that exist within shallow layers. Based upon the principles proposed by Istok and Doviak (1986), a higher vertical resolution 6-point scheme is applied to stratiform weather in which vertical shear is quite large. Doviak and Zrnić (1993) relate the shear component of spectrum width to uniform radial velocity shears in the azimuthal, radial, and elevation directions. A set of equations is derived that relates the spectrum width due to shear in the three orthogonal directions directly to the vertical shears of the otherwise horizontally uniform wind speed and direction typically found in stratiform weather. These equations are used to explain the observed pattern of the shear component of the spectrum width field, and are also used to estimate the shear contributions to the spectrum width and thence to derive the intensity of turbulence. Shear contributions to spectrum widths, observed in stratiform weather, can also be estimated if the wind profile is available. Vertical profiles of wind can be estimated from 2

28 radar observations using VAD (Velocity Azimuth Display) techniques. Melnikov and Doviak (2000) examined the pattern of spectrum width field due to shear assuming a vertical profile of wind. Here, by using a wind profile derived from a VAD analysis of radar observations, the spectrum width field due to shear in a snowstorm is calculated and compared with one whereby the spectrum width due to shear is separated, using the 6-point scheme, from the observed spectrum width σ v. 3

29 2. Separation of spectrum width due to shear and turbulence a. The 6-point Separation Scheme The total spectrum width σ v comprises all possible contributions (Doviak and Zrnić, 1993, Section 5.3) to changes of radial velocity within the resolution volume. To separate these two principal contributions to the total spectrum width a 6-point scheme is introduced and described herein. With the 6-point scheme, 6 radial velocities are obtained at three consecutive azimuths and two elevations at the same range (Fig. 1) and a linear radial velocity field model is least squares fitted to the data. The matrix, (Eq. (2) given by Istok and Doviak, 1986), is applied to determine shears using data at six contiguous points. The advantage of the 6-point least squares fitting (LSF) scheme is that it has better vertical resolution than the 9-point scheme used by Istok and Doviak. The origin of the matrix is at the asterisk in Fig. 1. In the 6-point scheme, however, the radar does not directly measure total spectral width at the origin. So, the total spectral width, that would have been measured had the beam been pointed at the origin, has to be estimated before the shear and turbulence contributions can be separated. An exact expression might be obtained under some assumptions, but to simplify the problem, the total spectrum width for a beam pointed at the origin of 6-point scheme is estimated using the following simple interpolation formula, σ v () θ0 + θ1 σ v σ v φ0 = 2 ( φ, θ ) + σ ( φ, θ ) 0 1 v 0 0, where σ v (*) is the estimated observed spectrum width at the origin (*), and ( ) 2 σ v φ,θ 1 1 the 4

30 φ -1 φ 0 φ +1 θ (θ 1 +θ 0 )/2 * θ Fig. 1. The 6-point scheme. The asterisk locates the origin to which v r (0) (the fitted radial velocity at the origin), K φ (the fitted shear in azimuth direction) and K θ (the fitted shear in elevation direction) are referenced. 5

31 spectrum width measured by the upper beam at( ) 1,θ 1 measured by the lower beam at ( φ,θ 1 0 ). σ φ,θ v 1 0 the spectrum width φ, ( ) b. Separation of σ s and σ t in a Snowstorm The 6-point separation scheme described in the previous section is applied to a case of a snowstorm. Fig. 2a shows a spectrum width field of a snowstorm that was recorded by the KLSX WSR88-D Doppler radar in Saint Louis, Missouri. The data that are presented here are focused on a time when the area of radar detectable snow almost reaches its maximum size, and is roughly uniformly distributed around the radar; thus a large area of data are available for analysis. The total spectrum width presented in Fig. 2a was separated into its two principal constituents, σ s, σ t,. Fig. 2b shows the shear contribution, calculated using the 6-point scheme, to the observed spectrum width. The corresponding contribution due to turbulence is given in Fig. 2c. The generation of those two displays needs velocity data at two consecutive elevations. The higher the elevation is, the less the available data there are. Therefore the available data in Figs. 2b and 2c are less than that in Fig. 2a. Because the field of spectrum width due to shear is computed using the 6-point fitting scheme, the influence from scales less than one grid length in the elevation direction (in section 4 we will see that the shear in elevation direction is the main contributor to measured spectrum width) is filtered out. The pattern of large σ s (Fig. 2b) appears like two commas embracing each other. These large values (e.g., σ s > 4 m s -1 ) in the σ s field are located at heights between 430 and 1630m. 6

32 Fig. 2a The spectrum width field for a snowstorm, 19:36:59, 16 Jan. 1994, Saint Louis, Missouri. 7

33 Fig. 2b The spectrum width from shear, σ s, field obtained using 6-point scheme. 8

34 Fig. 2c The spectrum width from turbulence, σ t, field obtained using a 6-point scheme. 9

35 Table 1 lists, samples of σ v, σ s, and σ t obtained using the 6-point scheme. For this example, we have chosen a direction and range to coincide with regions having large observed spectrum width values free from overlaid echoes. The 6-point scheme, with data from elevation angles 0.5 o and 1.4 o, is used in deriving the data fields shown in Figs. 2b and 2c. Again, the total spectrum width for the 6-point scheme at the center of fitting surface is the arithmetical average of values obtained at these two elevation angles. The Xs in Table 1 simply indicate σ s >σ v. There are four practical reasons for such a result. 1) Istok and Doviak (1986) ascribed those cases (i.e., σ s >σ v ) to the statistical uncertainties in the estimate of shear and σ v. 2) Real σ s values could be larger in the calculated σ s field, especially if σ v is primarily due to shear, and thus the calculated σ s could be larger than the σ v. 3) The gradient of the reflectivity field within the radar beam could bias the measurement of radial velocity which in turn biases the estimation of σ v (e.g., suppose the radial velocity and reflectivity increase with height within the upper beam then the radial velocity measured by upper beam will be overestimated and the shear, calculated using 6-point scheme, will be overestimated, which in turn leads to a negative σ 2 t. 4) As mentioned previously, the estimated observed spectrum width associated with 6-point scheme at 0.9 o is obtained by averaging those at 0.5 o and 1.4 o elevation angles. Thus the total spectrum width could be underestimated due to beam blockage at 0.5 o, which may lead to the values of σ v associated with 6-point scheme to be smaller than it would have been without beam blockage. 10

36 Table 1. Values of σ v, σ s, and σ t at different ranges obtained with 6-point scheme sampled at the azimuth of 90.2 degree in a snowstorm. Range (km) σ v σ s σ t (m s -1 ) (m s -1 ) (m s -1 ) x x x x x x x x x Table 2 tabulates the percentage of negative σ 2 t out of the total number of non-zero samples of σ v. The results show a large percentage of data, separated with the 6-point scheme, have negative values for σ 2 t (i.e., imaginary σ t ). The percent of imaginary σ t does not change very much with elevation below 3.8 o. Above that elevation angle, the reduced ratios may be ascribed to the coarser resolution due to the increased elevation increment (i.e., the shear is underestimated). Because of errors in receiver noise measurements during the calibration of the radar, negative values of the square of observed spectrum width can occur, especially in regions where real spectrum widths and signal to noise ratios are small (Melnikov and Doviak, 2002); these negative values of σ v are assigned, by the WSR-88D 11

37 signal processor, a zero value, and are not included in our separation scheme. Thus the percent of imaginary σ t would even be larger than shown in Table 2. The large percent of imaginary values in the σ t field, at least in this case, is likely due to the fact that σ v is primarily contributed by σ s, and statistical uncertainty in the measurements will cause overestimates of σ s with concomitant underestimates of σ t,and consequently some negative estimates for σ 2 t. Table 2. Percentage of the number of negative σ t out of the number of non-zero σ v 6-point scheme Elevation (θ 1 +θ 0 )/2 Percentage

38 In Fig. 2c, there exist two areas of large σ t values, one to the northeast and another in the southwest. These areas of large values σ v values are not necessarily related to turbulence. To explain these bands refer to Fig.3 and keep in mind that σ t is obtained by taking the square 2 2 root of the difference σ σ where σ s is obtained using the observed velocity field at the v s two lowest elevation angles (i.e., 0.5 o and 1.4 o ). Fig.3 shows an assumed vertical profile of v r, ss V r profile Beam axis 1.4 o Beam axis 0.5 o Fig.3 The artificial radial velocity profile used to explain how the 6-point scheme can underestimates the shear contribution. and radar beams at the lowest two elevation angels. If v r is homogeneous in the azimuthal direction K φ will be zero. Assuming reflectivity is uniform with height, the measured radial velocity will be the same at the two elevation angles, and thus the K θ values calculated through surface fitting will be zero. So, the calculated σ s at this location will be zero although 13

39 it is not. The observed σ v would not be zero at either elevation. The σ v at elevation of 0.9 o, which is an arithmetic average of σ v at 0.5 o and 1.4 o, will not be zero either. After σ t and σ s are separated, all σ v are ascribed to σ t due to the underestimated σ s. The areas of large σ t values, seen in Fig. 2c, is caused by a situation similar to the described by Fig. 3 as we will see in later discussions. 3. Relating shear contributions to profiles of horizontally uniform wind fields Doviak and Zrnić (1993) showed that, if the wind is linear within the radar s resolution volume, the spectrum width due to shear may be separated into the following three contributions: σ s 2 =σ sr 2 +σ sφ 2 +σ sθ 2 (1) where σ s is the total spectrum width due to shear; σ sr, σ sφ, σ sθ are the spectrum widths due to shear in the radial, azimuth and elevation directions respectively (in a spherical coordinate system), where σ 2 sr =(r o K r σ r ) 2 (2) σ 2 sφ =(r o K φ σ φ ) 2 (3) σ 2 sθ =(r o K θ σ θ ) 2 (4) 2 where K r, K φ and K θ are shears in radial, azimuth and elevation directions respectively, σ θ and σ 2 φ are defined as the second central moments of the two-way antenna power pattern in the indicated direction, σ 2 r the second central moment of the range weighting function, and r o is the range from radar to the center of resolution volume. For a circular symmetric beam σ 2 θ =σ 2 φ =θ 2 1 /(16ln2) 14

40 where θ 1 is radar beam width at the 3 db level. For a rectangular transmitted pulse and a receiver with a matched Gaussian shaped response, σ 2 r =(0.35cτ/2) 2 where c is light speed in the air and τ is the radar pulse width. Assuming reflectivity is uniform within the resolution volume and that the wind field is horizontally uniform, the mean radial velocity observed by the radar can be written as v r =V h cos(φ-φ w )cosθ+v p sinθ (5) or v r =Vcosφ cosθ+usinφ cosθ+v p sinθ (6) where v r is radial velocity observed with the radar; V h the horizontal wind speed; V p the fall speed of precipitation particles (snow for the case analyzed herein), φ w is the azimuth of the wind (i.e., the direction from the radar that the wind is blowing); φ is the azimuth of the radar beam; θ is the elevation angle of the radar beam, and U and V are eastward and northward components of the horizontal wind respectively (these are assumed to be functions of height z). Here, v r is positive away from radar and V p is negative downwards. Fig. 4 illustrates the relationship among these variables. By neglecting the effect of fall velocity of the snowflakes, Eq. (5) can be rewritten as v = cos( φ φ )cos( θ ) (7) r V h w Based on the definition, K θ may be written in the form vr Kθ =. r θ where r is the slant range from radar to the resolution volume. From Eq. (7), K θ can be written as K θ Vh = cos( φ φ w ) cos( θ ) + V r θ h φ w sin( φ φ w ) cos( θ ) r θ 15

41 Vh cos( φ φ w )sin( θ ). r V r N φ w V h V p V h φ V p θ Fig. 4 The relationship among variables. Because the wind profiles are expressed in terms of height z above ground, it is convenient to express K θ in terms of the vertical gradients of the wind field using the following equation 16

42 K θ = Vh 2 φw 2 cos( φ φw)cos ( θ ) + Vh sin( φ φw)cos ( θ ) z z Vh cos( φ φw)sin( θ ) (8) r Similarly, we can obtain the expressions for K r and K φ. They are K r = Vh cos( φ φw)cos( θ )sin( θ ) z K φ φw + Vh sin( φ φw)cos( θ )sin( θ ) (9) z Vh sin = ( φ φw ) cos( θ ) r cos( θ ) Vh sin = r ( φ φ ) w (10). Through Eqs. (1)-(4), and (8)-(10), the shear contribution to spectrum width is directly related to the vertical profile of the horizontal wind vector. 4. Simulation of spectrum width due to shear Using an assumed vertical profile of wind, Melnikov and Doviak (2002) examined the pattern of spectrum width field due to shear. They concluded that two bands of enhanced spectrum width, looking like two commas embracing each other, can result if wind veers with height. They also concluded that the pattern of spectrum width due to isotropic turbulence is roughly a circle. Here an algorithm is designed to simulate the spectrum width field due to shear by using an actual wind profile generated from a VAD analysis. The computation of σ s requires, as shown in Eqs (2)-(4), radial velocity shears in elevation, azimuth and radial directions. These shears are computed using a LSF method as described in section 2. But now we shall use the vertical profile of a horizontally uniform wind field, obtained through a VAD analysis, to compute throughout the observation domain a so-called simulated spectrum width field σ s due to shear. Because a horizontally uniform 17

43 wind field is assumed for the VAD analysis, some non-uniform features that could have been exhibited in the separated field will not appear in the simulated field. The vertical resolution of LSF method depends on the beam width and the range of fitted surface, whereas the vertical resolution of the wind profile generated through VAD is at a fixed increment of 300 meters. The VAD analysis is applied to a snowstorm in which the reflectivity is relatively uniform, and the derived wind profile should not be severely biased by reflectivity gradients. Simulations cannot only verify the algorithm used to separate σ s and σ t, but also allow us to respectively investigate the effects of vertical shears of wind speed and direction. a. The profile of the wind speed and direction To simulate the spectrum width field σ s due to the horizontally averaged shear a wind profile is required. The wind obtained from regular daily soundings 12 hours apart is too coarse to represent reliable winds about the radar site. Furthermore, the sounding does not necessarily represent an accurate horizontal average of the wind field because the sounding is along a single curve that the balloon follows. Thus the simulation performed with daily sounding data may not give accurate results. The best choice is a direct retrieval of the wind profile by using the radial velocity field obtained by radar itself. Although the profile obtained through the VAD technique may not apply everywhere within the range covered by radar, it should be more representative than that obtained from the daily balloon soundings. Since the radial velocity field and spectrum width field are observed at same time, the errors in simulation introduced by non-synchronic observations of velocity and spectrum width field is reduced to a minimum by making use of VAD profiles. 18

44 Assuming the wind is uniform about the radar site, the mean radial velocity observed by the radar can be written as Eq. (5) or (6). Browning and Wexler (1968) showed that v r can be expressed in terms of a Fourier series v r = 1 a0 + [ an cos( nφ i ) + bn sin( nφi )] (11) 2 n= 1 For uniform wind, m a 0 = m 2 i= 1 m a 1 = m 2 i= 1 m b 1 = m 2 i= 1 V ri =V p sinθ (12) V ri cosφ i =Vcosθ (13) V ri sinφ i =Ucosθ (14) Where m is the total number of uniformly spaced samples; V and U are, as noted earlier, the north and east component of horizontal velocity. The WSR-88D records the radial velocity at a spacing about 1 o during each scan, but, it should be noted that samples are not equally spaced. Furthermore, because of the reasons presented by Ming (2003), some data might not be available along the circle on which the VAD is performed. An algorithm, based on the least-square fitting proposed by Rabin and Zrnić (1980), is designed to compute the a 0, a 1 and b 1 even though the data are not uniformly spaced, and even if some data are missing. The wind direction and radial velocity are then computed using Eq. (11)-(14). By taking into account errors due to the non uniformities in the fall speed of precipitation, height measurement errors, and inhomogeneities of reflectivity, Browning and Wexler (1968) recommend: 1) The elevation angel of radar beam should less than 27 o in snow and 9 o in rain, and 19

45 2) the radius of the circle on which VAD is performed should be less than 20 km from radar, to keep the error of VAD derived horizontal wind speed due to each of mentioned error sources less than 1 m s -1. Based on these constrains, a set of heights at which VAD analysis is performed are chosen for the studied case. The lowest height chosen is 20 meters above ground which is about the height above ground of the beam center at the lowest elevation angle, 0.4 o, and the nearest range ( 3km) where data are used in the VAD analysis. The height increments are 300 meters, about the resolution of radar beam at a range of 17 km. The horizontal wind speed and direction profiles obtained through the VAD analysis of data from a snowstorm are presented in Figs.5a and 5b. At the 20-meter height, the wind derived through VAD is unreliable due to the likely influence of ground clutter at near ranges to the radar. Thus the wind speed and direction profiles below 320 m are obtained by interpolating the observed values at the surface, recorded at the Saint Louis international airport at 19:29 UTC, and the VAD derived values at 320 m. The top elevation angle of the volume scan for this case at chosen time is 19.5 o, well within the 27 o elevation angle constraint suggested by Browning and Wexler (1968). The maximum height of the profiles is about 6 kilometers. From these profiles one sees that there exists a strong shear of horizontal wind speed below 1.2 kilometers. Horizontal wind speed changes from 3.0 m s -1 at 20 meters to 32.6 m s -1 at 1220 meters above the ground. Also, within this layer, the horizontal wind direction changes significantly. At the 20- meter height the wind blows towards 293 o (i.e. SE wind), but the wind blows towards to 41.3 o (i.e. SW wind) at 1220 meters. The rate of wind direction change is about 90 degree/km, and the wind veers with height. 20

46 Fig.5a. The horizontal wind speed profile derived from a VAD analysis of Doppler data having the spectrum width field shown in Fig

47 Fig.5b. Changes of the wind direction with height. Zero (or 360) degree is the wind direction (i.e., direction of air motion) towards north. Positive angles are those measured clockwise from north while negative angles are those measured anti-clockwise. 22

48 b. Computation of σ s If the radar beam is sufficiently narrow and wind is approximately linear across the resolution volume, then shears can be computed from the wind profile at the heights intersected by the beam. Because the beam has a finite width, and shear and reflectivity are not uniform across it, the accurate computation of the shear contribution to spectrum width requires a reflectivity-weighted integration of the velocity field (principally over the resolution volume) to compute the Doppler spectrum following the procedure given by Doviak and Zrnić (1993, section 5.2). But the reflectivity field within the beam is not known. If the reflectivity is roughly horizontally uniform, one could, as with the velocity field, obtain a vertical profile of reflectivity from the VAD scans and use it in the integration. However we simply use the VAD derived wind profile that, under the constraints imposed by Browning and Wexler, should have errors less than about 1 m s -1. Using Eq.(1), we calculate the spectrum width associated with shear for each resolution volume. But to calculate the spectrum width due to shear, we first need to calculate the shear components K, K and K r, using Eqs. (8)-(10) and the wind profile obtained from θ φ the VAD analysis. The wind speed and direction at beam top (T) and bottom (B) (i.e., at the 3 db points; Fig. 6) are determined by interpolating the wind speed and direction between levels 3 and 4, and between levels 1 and 2, where levels 1 to 4 are those heights at which the VAD derived wind speed and direction are available. Next we compute the wind speed and direction at C by linearly interpolating the wind speed and direction between T and B. The wind speed shear and the rate of change of wind direction with height are computed using the differences of speed and direction between beam top (T) and bottom (B) obtained in first step divided by the vertical distance between T and B. Such a two-step interpolation smoothes out some detail variations of wind, but it is an approximation that gives σ s fields 23

49 T Z T Level4 Level3 beam axis C Z C r B Z B Level2 θ 1 θ Level1 O Fig.6 The origin O is the radar location; C is the center of the beam axis; T is the location of the beam top; B the location of the beam bottom. Levels 1 to 4 are the heights where VAD are available. θ 1 is the beam width (1 o for WSR- 88D), and Z T, Z C and Z B are heights at T, C and B. 24

50 consistent with the one separated from the observed spectrum width σ v using the 6-point scheme as will be shown in the next section. The finite difference forms of Eqs. (8)-(10) used to calculate the shears K, K and K r are: θ φ K θ V = h + V ( Z ) V ( Z ) h V h T Z T h Z ( Z ) C ( Z ) r C B B cos 2 [ φ φ ( Z )] cos θ w ( Z ) φ ( Z ) φw T w B 2 sin w C ZT Z B cos [ φ φ ( Z )] sinθ w C C [ φ φ ( Z )] cos θ K r V = h ( Z ) V ( Z ) T Z T h Z B B cos [ φ φ ( Z )] cosθ sinθ w C + V h ( Z ) C φ w ( Z ) φ ( Z ) T Z T w Z B B sin [ φ φ ( Z )] cosθ sinθ w C K φ V = h ( Z ) sin[ φ φ ( Z )] C r w C c. Comparison of separated and simulated fields The simulated spectrum width field due to shear, computed using the shears obtained from the VAD wind profile, is displayed in Fig. 7 for the interpolated elevation angle of 0.9 o. The corresponding field, separated from the observed spectrum width with the 6-point scheme, is presented in Fig. 2b. Because the horizontal velocity field is assumed to be homogeneous, the simulated field symmetrically distributes around origin----the radar site. By comparing these two figures, one finds that: 25

51 1) The shapes of the two patterns roughly agree. 2) The locations of large values (i.e., σ s >3 m s -1 ) of σ s are consistent with each other. 3) There are more values larger than 7 m s -1 in the simulated field (Fig. 7) than in the separated field (Fig. 2b) (this is due to the fact that the simulated field has a higher vertical resolution than 6-point scheme at ranges larger than 17 km). 4) Beyond 80 km, the pattern of simulated field differs considerably from the observed one (Again this could be ascribed to the coarser vertical resolution of 6- point scheme). In conclusion, the spectrum width field due to shear, derived from a VAD analysis of the wind field, strongly supports the spectrum width field derived from application of the 6-point filter. This latter method, although having the possibility of errors due to the poorer vertical resolution at longer ranges, could better represent the horizontal dependence of the shear contributions to spectrum width 26

52 Fig. 7 The spectrum width field due to shear obtained using wind fields derived from a VAD analysis at an elevation angle of 0.9 o. 27

53 d. Relating patterns to the wind profile The very good consistency between simulated and separated fields implies that equations of (8)-(10), on which the simulation was based, can be used to explain the patterns of spectrum width due to shear shown in Fig. 2b. The contribution from radial velocity shear in elevation direction dominates the contributions from shears in the azimuthal and radial directions as will be shown in section 5. Furthermore, only the first two terms in the right hand side of Eq. (8) are significant (section 5). So, the two bands of large values in Figs. 2b (and Fig. 7) are associated with the large vertical shear of wind speed and direction. Also, large wind speed itself might play an important role as indicated by the second term in the right hand side of Eq. (8). The large values of σ s (e.g., σ s > 4 m s -1 ) in Fig. 2b are located at heights between 430 and 1630m where the largest speed and directional shears are located (Fig. 5a, and b). Above 1500 m, both speed and directional shears are small (although speed itself is large), which causes a relatively lower contribution from shear. The change of wind direction with height is also responsible for the displayed spiral signature in Fig. 2b (and Fig. 7) as was pointed out by Melnikov and Doviak (2002). 5. Contributions of shears a. Contributions of shears in radial and azimuth directions Equation (1) shows that the spectrum width due to shear is related to radial velocity shears in the radial, azimuth and elevation directions. However, they are not equally contributing to σ s. Table 3 tabulates some values, obtained using 6-point scheme, of K θ, K φ and K r at an azimuth angel of 90.2 o at ranges where the observed spectrum width values are large and free from overlaid echoes. Listed values show that K θ is usually one order 28

54 magnitude larger than K φ while K r is negligible. Therefore the contributions from shears in radial and azimuth directions can be neglected in comparison to the contribution from shear in the elevation direction. Table 3. Values of K θ, K φ and K r at different ranges in snowstorm (Azimuth = 90.2 o ) Range(km) K θ K φ K r b. Contribution of shear in the elevation direction Because K φ, and K r can be neglected, shear in elevation direction is the only remaining significant contributor. From Eq. (8), K θ consists of three terms. Simulation (not presented) shows that contribution from third term on the right hand side of Eq. (8) is less than 1x10-3 s -1, which can be verified by substituting V h =30 ms -1, r=3 km (generally, r is larger than 3 km), φ=φ w and θ = 0.4 o into that term. Therefore contribution from term 3 can also be ignored. Thus the most significant contributors are the first and second terms of Eq. (8). The first term depends on the vertical shear of the horizontal wind speed, and second term 29

55 depends on the vertical shear of wind direction, and the horizontal wind speed. Figs.8a and 8b display the two fields respectively generated by term 1 and term 2 in which the wind profile presented in Figs. 5a and 5b is used. Two kidney shaped patterns of large values are shown in Fig. 8b whereas in Fig.8a there is one, but values of σ s there exceed 7 m s -1, and are much larger than those seen in Fig. 8b. Because term 1 depends on the vertical shear of horizontal wind speed, large maximum values in narrow bands imply strong vertical shear in a relatively narrow layer. Another interesting feature in Fig.8a is that the two kidney shaped bands within 80 km show a spiral signature around radar site while the four bands (i.e., one at about105 km, and the other at about 120 km) beyond 80 km do not. The spiral feature is related to the cos(φ-φ w ) factor in term 1 (i.e., the changes of wind direction with height). As can be seen from Fig. 5b, wind direction does not change significantly at the heights where the four bands of enhanced σ v are seen and thus the spiral feature is absent. On the other hand term 2 produces two wider kidney shaped patterns of relatively large values, and two maximum cores, but its maximum values are less than that determined by term 1. The centers of these peaks are located about 45 km and 75 km respectively and lie in the vicinity of the strong shear layer. They should coincide with the peaks of the product of wind speed and wind shear that are part of term 2. Since term 1 and term 2 include factor of cos(φ-φ w ) and sin (φ-φ w ) respectively, the pattern associated with term 2 is rotated clockwise 90 o relative to the pattern associated with term 1. 30

56 Fig.8a The σ s field generated by the first term of Eq. (8) using the wind profile presented in Fig.5a, b, and when this first term is substituted into Eq. (4). 31