Remote Sensing of Turbulence: Radar Activities. FY01 Year-End Report

Transcription

1 Remote Sensing of Turbulence: Radar Activities FY1 Year-End Report Submitted by The National Center For Atmospheric Research Deliverables E2, E3 and E4

2 Introduction In FY1, 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. The WSR-88D activities have been mainly addressed at quality control problems with the spectrum width data from these radars as well as the analysis of data from a WSR-88D radar. The spectrum width data is a primary source of data for the improved turbulence detection algorithm and hence the quality of the algorithm will be directly related to the quality of these data. These issues have come to the forefront this year as a data set from a WSR-88D with colocated in situ aircraft data has been obtained. In the previous year s reports, radar data from Nexrad-like radars, i.e., the Mile High radar and the CSU-Chill radar, were analyzed. This year, radar data from the Goodland, Kansas WSR-88D was collected during the STEPS-2 field experiment. As with the previous years radar analyses, the availability of simultaneous in situ aircraft data was a deciding factor for choosing this data set. During this field experiment, the SDSM&T T-28 aircraft was used to penetrate thunderstorms. The vertical acceleration data from the T-28 data is used to compare against turbulence estimates from the radar data. Discussions on the quality control issues, turbulence detection algorithm concepts and the analysis of the STEPS-2 data are presented below. Besides these abovementioned activities at NCAR, NSSL has been supporting the WSR- 88D Remote Sensing activities. They have been looking at statistics of measured spectrum width values from WSR-88D radars, as well as associated quality control issues. They have prepared a report, Spectrum Width Statistics of Various Weather Phenomena which is included in this Year-End Report. 2

3 In the lidar area, new algorithms to correctly estimate the estimation error of Doppler lidar velocity measurements have been developed. These algorithms have been applied to the measurement of spatial structure functions. Simulations were performed for isotropic wind fields with a Von-Karman spatial spectrum to determine the accuracy of various algorithms to extract the two turbulence parameters of the Von-Karman model: energy dissipation rate and integral length scale. The statistical performance of these algorithms is determined by computer simulation. A journal paper, describing this work, Estimating Spatial Velocity Statistics with Coherent Doppler Lidar, by R. Frehlich and L. Cornman, has been accepted by the Journal of Atmospheric and Oceanic Technology and is in press the manuscript is included in this report. The new algorithm for measurement of spatial structure functions was applied to the Juneau lidar data. The estimates of energy dissipation rate were found to be robust and to contain both spatial and temporal variability. Similar algorithms were applied to lidar data from New Hampshire to extract turbulence information in the troposphere. Quality Control Issues with the WSR-88D Spectrum Width Data The proposed improved WSR-88D turbulence detection algorithm will most likely use all three data types available from the radars: the reflectivity, the radial velocity and the spectrum width. In the past, a preponderance of interest has been in the reflectivity and radial velocity data; hence, a substantial amount of effort has been spent investigating the quality of these data. On the other hand, very little attention has been given to the quality of the spectrum width data. In general, the spectrum width data is more susceptible to errors than are the reflectivity and radial velocity data. During the analysis of the STEPS-2 data, a variety of data quality problems with the spectrum widths became apparent. NCAR staff contacted personnel at NSSL and the WSR-88D OSF regarding these problems. Apparently, the problems and other ones had been investigated previously. Three internal reports were obtained from the OSF: Engineering Study of Spectrum Width Anomaly Interim Summary, Engineering Study of Spectrum Width 3

4 Anomaly Supplement to the April 17, 1997 Interim Summary, and Notes on Spectrum Width Calculation in the WSR-88D and Recommended Software Changes. Furthermore, Dick Doviak at NSSL provided a memo to NCAR indicating some other problems beyond those discussed in the OSF reports. The main quality control problems indicated by these sources include spectrum width bias at large SNR due to signal clipping and/or receiver saturation (improper AGC settings), bias in regions of overlaid echo due to a lower than optimum overlaid echo threshold, width bias at low SNR due to improper noise compensation and finally, the use of a low-end SNR threshold which is too small. These issues are discussed in the following (source: Doviak memo). The estimates of reflectivity observed with the WSR-88D always use sufficiently long PRT data so that there are no reflectivity errors due overlaid echoes. On the other hand, the Doppler velocity and spectrum width must be estimated using relatively short PRT data, which often leads to conditions of overlaid weather signals that corrupt the velocity and spectrum width estimates. If weather signals from more than one trip are overlaid, it can be shown that if one of the trip signals is 2 db stronger than the sum of out-of-trip signals (i.e., the overlaid signal threshold), the spectral moments of the stronger signal can be estimated without significant error. The 2 db overlaid threshold insures that both spectrum width and velocity are not corrupted by overlaid signals. But velocity estimates can still meet specifications with a much lower overlaid signalthreshold(e.g.,12db). The overlaid signal threshold in the WSR-88D cannot be set separately for the velocity and spectrum width estimates. Because most radar meteorologists are interested in the Doppler velocity fields and not the spectrum width fields, a lower overlaid signal threshold is used in the WSR-88D. As a matter of fact, in order to display a larger area of Doppler velocities, the overlaid threshold has been lowered from 1 db to 5 db. At this lower level the velocity estimates can have errors that exceed those that were specified (i.e., to be less 1 m s -1 )inthe design of the WSR-88D. Nevertheless, for the interpretation of the Doppler velocity fields on weather radar displays, the increase in velocity estimate errors is not noticeable, principally 4

5 because it is masked by the color quantization intervals used to display Doppler velocity fields. But the 5 db overlaid threshold plays havoc for reliable spectrum width estimation. Besides spectrum width estimates being corrupted by overlaid echoes, the spectrum width estimates are more prone to errors due to receiver noise, and to incorrect estimates of receiver noise power. The WSR-88D hardware calculates the autocovariance at lags and 1 to estimate spectrum widths using the formula (the so-called pulse-pair estimator ) 2 va ˆ v ln S σ = ˆ 2 π R ( T s ) given by Doviak and Zrnic (1993; Eq.6.27), where Ŝ is the estimate of signal power 1/2 M-1 ˆ 1 2 S= ÿ V(k) -N M k= where V(k)isthek th sample of signal plus noise, M is the number of samples used in the estimation, and N is measured noise power that is made during calibration of the radar. Since 1996, the WSR-88D radars have employed a SNR threshold of 3.5 db, instead of the design threshold of 6 db, in order to display larger areas of Doppler velocity in weak reflectivity regions. Although this threshold is lower than required to meet the design specifications for velocity errors (i.e., 1. m s -1 ), the increase in error is modest. For example, if the spectrum width is 5 m s -1,andv a = 25 m s -1, the standard error is about 1.1 m s -1. Although SNR thresholds can be independently set for the three spectral moments, typically the same 3.5 db threshold is used for spectrum width and velocity. If this threshold is also used for spectrum width estimation, a standard error of 1.4 m s -1 is generated instead of the specified.5 m s -1 limit; a factor of three larger. Furthermore, using the above equation for spectrum width requires accurate estimates of the noise power N. It can be shown that a signal-to-noise (SNR) power ratio (in db units) larger 5

6 than about 15 db is required to have errors in the spectrum width estimates less than the specified.5 m s -1 if noise power estimates N are in error by as little as.2 db. Because of variance in the estimates of Ŝ and R( ˆ T s ), the argument of the ln function can be less than 1, and thus the ln function will have negative values. This is more likely to occur when the true spectrum widths are very small (i.e., the ratio Ŝ to R( ˆ T s ) is nearly 1) and SNR is small. Whenever the argument of the ln function is less than 1, the signal processors in the WSR-88D assign a zero width value. Furthermore, if N is overestimated (i.e., N > N), and true spectrum widths are small, an excessive occurrence of zero width assignments will be made 6

7 Another source of error in spectrum width estimates from the WSR-88D radar is the incorrect setup of the Automatic Gain Control (AGC) circuits. If the AGC is properly setup, signal levels will never be so strong that they exceed the maximum level of the analog to digital converter (ADC). If weather signals exceed this level, the signals are clipped and harmonics of the weather spectrum are generated in the digital domain. These harmonics increase the estimated spectrum width values. It has been observed that WSR- 88D spectrum width data are sometimes strongly correlated with the reflectivity field. For example, when reflectivity is larger than about 4 dbz, spectrum width values are anomalously large. An examination of spectrum width data, at sites where this anomaly was evident, showed that the unusually significant correlation of large spectrum width values with large reflectivities is due to improper setup of the AGC. In order to deal with these abovementioned quality control issues, the OSF made the following recommendations. Regarding the signal clipping problem, it was proposed to revise the engineering procedures for receiver transfer set-up and expand the self-test to include high SNR where the clipping is manifested as large widths. For the improper noise compensation at low SNR s, it was proposed to readjust the noise compensation parameters in the width calculation software particularly the composite quiescent noise value and adjustment weight. Regarding the overlaid echo problem, is was proposed to change the width echo overlay threshold in the echo overlay software to 2 db. The other issue mentioned above, the zero-valued spectrum widths are inherent in the pulsepair algorithm and hence no fix is required. It is unclear what of the recommended changes have been implemented at this time further discussions with the OSF will hopefully clarify. As the most important operational problem is turbulence in low reflectivity regions, the most significant problem is the noise compensation/estimation. It is assumed that the improved turbulence algorithm will be implemented in a build of the open system RPG. Nevertheless, some of changes (as mentioned above) would require implementation in the open system RDA. Again, discussions with the OSF will be required in order to estimate the time frame for these implementations. For the meantime, the spectrum width quality control issues mentioned above can only be 7

8 addressed by using some fairly strict thresholding of the spectrum width values. As it is difficult to distinguish whether the zero spectrum width values are real or artifacts, this problem can only be dealt with by flagging all of the zero values as bad. The noise that was discussed above is mainly due to thermal noise in the radar receiver. Another source of error in the spectrum width estimates (and similarly with the reflectivity and radial velocity measurements) is due to noise inherent in the signal, i.e., due to the random nature of the received signal. It can be shown that an approximate form for the standard deviation of the spectrum width estimates ŵ for the pulse-pair algorithm is given by 1/ w 4 32π 2va SD( wˆ ) = 2va SNR M for SNR < 1dB, and SD( wˆ ) = 2v a π M 1/2 w 2v a 1/2 for SNR > 1dB. Where v a is the unambiguous velocity. Note that the error in the width is proportional to the width and inversely proportional to the SNR for small SNR s. For larger SNR s the error is proportional to the square root of the width and independent of the SNR. However, note that in each case the standard deviation of the width estimates are inversely proportional to the square root of the number of samples used in the pulse-pair algorithm (this is assuming independent samples). Clearly, if the number of samples used in the pulse-pair estimation algorithm is increased, the error in the spectrum widths will decrease. One concept under consideration is to change the pulse-pair algorithm implementation to average the signal Ŝ and magnitude of the one-lag correlation R ˆ( T s ) over four range gates instead of the usual one range gate. This will increase the number of samples by a factor of four, thereby reducing the standard deviation of the spectrum width estimates by a factor of two a non-trivial amount. Of course, this method (which is similar to the existing reflectivity calculations) will decrease the resolution of the spectrum width estimates by a factor of four. As the turbulence product will not require 8

9 single range-gate resolution, this trade-off in accuracy versus resolution is considered a beneficial one. One can also consider doing similar averaging across azimuth, however this is more problematic as the spatial domain over which the averaging occurs varies as a function of range. Finally, as pointed out in previous year-end reports, another source of errors in the spectrum width estimates is the assumption of a Gaussian Doppler spectrum (or correlation function) inherent in the derivation of the pulse-pair estimator. Further analysis is required to determine the extent to which this poses a problem. A small amount of work has been done in this area and these efforts have not been systematic. Of course, it would be fairly difficult to determine in real time when this problem occurs and mitigate the problem with quality control flagging of the suspect data. On the other hand, in a future build of the open systems RDA, spectral processing may become a reality. The ability to perform quality control at the spectral level is well-established in RAP, and the results typically show dramatic improvements in data quality or at least a better ability to identify the suspect data. Algorithm Methodology The improved WSR-88D algorithm is a fuzzy-logic based algorithm. Different indicators of the presence of turbulence are used (e.g., first and second moment data fields) and are combined using a weighted combination scheme. The weights are based on a variety of quality control indications, or confidence indices (e.g., SNR). This general fuzzy logic methodology has been successfully applied to many other algorithms at RAP. As mentioned in previous reports, one of the significant problems with the existing WSR-88D algorithm is using un-averaged data to produce the second moments. There are two main reasons that averaging of the data (correlations, spectra or 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 9

10 of the phases between different scatterers in the pulse volume) and (c) the spectra are contaminated by receiver noise. Correlation, spectral or moment averaging is required to reduce these effects. The averaging of spectra or correlation functions 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. However, as mentioned above, the averaging of the zero and one-lag correlations over range and possibly azimuth will be seriously investigated. This of course assumes that a time-domain pulse-pair spectrum width estimation algorithm is used. As mentioned above, the pulse-pair algorithm is susceptible to errors under certain circumstances and may not be the optimal methodology. Certainly, this change (averaging the zero and one-lag correlations) would be the easiest to implement within the current system. It is not clear what level of modifications can be made to this basic processing in the near term. It should be noted that averaging prior to moment estimation only assists in producing higher quality moments and that moment averaging is still required to give meaningful turbulence information. The NCAR turbulence algorithm implementation satisfies this requirement by making use of the median radar-measured second moment (square of the spectrum width) obtained from a disc or sphere centered at a point of interest, scaling it by a theoretical quantity dependent on the distance from the radar and an a priori turbulence outer length scale to obtain an eddy dissipation rate (EDR) estimate. When averaging of the correlation or spectral data is available, the same methodology will be used, i.e., performing a spatial median filter on the second moments. Theoretically, the average of the second moments is related to turbulence intensity, however due to noisy moment estimates, the median is used instead of the averaging. The domain of the median filter should be a fixed spatial area, e.g., a disc of 1km radius. Since the azimuthal distance between radar beams varies as a function of range, this requires the use of a differing number of samples as a function of range. As the number of samples will proportional to the statistical uncertainty in the estimates, a balance between the number of samples and the spatial domain of the median filter is required. If a fixed domain size is used, the 1

11 errors in the estimates at further ranges will increase, hence a lowering of an associated confidence index would be required. The first moment data can be used in two different ways, calculating a spatial variance of the first moments and calculating structure function estimates of the EDR. The latter method is a direct indicator of the turbulence intensity, whereas the former method is not as direct. There is a theoretical relationship between the sum of the average of the second moments and the variance of the first moments and it is possible to use this relationship. This is an area for further study. At a minimum, the spatial variance of the first moments could be used as an indicator as to where turbulence is occurring. The sum mentioned above is assumed to occur over statistical independent samples of the same turbulent velocity field, whereas in this case, these calculations are performed as a function of space. Two issues arise with the spatial calculations. First, it assumes that the turbulence is homogeneous and second that the samples are independent. In practice, neither of these assumptions will be fully satisfied. It is not clear how the violation of these assumptions would affect the turbulence and more importantly, how such a violation could be recognized in real time. These are issues for further investigation. Once these turbulence indicators are computed, they will be combined in a confidence-weighted manner. Values of this combined field will then be analyzed to determine the regions that are deemed to be hazardous. This analysis will include filtering out above-threshold regions that are too small in extent, or whose turbulence values are inconsistent with expected physical numbers. As far as calculating the confidence values, a number of potential methods are being investigated, including, but not limited to: the use of SNR as a filter (values that are too low or too high), regions of first or second moments that are not well-correlated with their neighbors and filtering out identified regions of clutter or second-trip. 11

12 Analysis of the STEPS-2 Data As mentioned above, data collected during the STEPS-2 field experiment based in Goodland, Kansas, was obtained this year. This is the first dataset which has provided both in-situ aircraft turbulence data and ground-based data from a WSR-88D radar (KGLD) for use in the development and verification of the NCAR WSR-88D algorithm. Although data quality problems with the KGLD radar data have so far hindered the use of this dataset for a detailed statistical verification exercise, the dataset does appear to contain several interesting cases which will prove useful. For instance, the SDSM&T T-28 aircraft experienced several strong encounters with turbulence. These are illustrated by the colored aircraft tracks of the following pages. Both tracks in each set of plots are scaled by a turbulence metric; the top plot depicts the turbulence eddy dissipation rate, ε 1/3, as computed by the NCAR in-situ turbulence algorithm. The second shows the local standard deviation of the aircraft acceleration over 2-second (approx. 2 km) windows. The second metric is closely related to that used in last year s statistical analysis, and a comparison between the two suggests that they are highly correlated. Exceptions occur when the aircraft is being manipulated; changes in speed, altitude, or direction frequently appear as hot values in the local standard deviation, while the NCAR in-situ turbulence algorithm filters out these effects. Our detailed statistical analysis will therefore make use of the NCAR EDR field. 12

13 2526, T 28 ncar_edr (22:1:1 22:33:27) , T 28 std4_acc (22:1:11 22:35:49) Figure 1: Two measures of the in-situ turbulence encountered by the T-28 aircraft on 26 May 2. Distances are measured in km from the KGLD radar in Goodland, Kansas, and times are GMT. 13

14 263, T 28 ncar_edr (23:49:1 :55:57) , T 28 std4_acc (23:49:11 1:5:23) Figure 2: Same as Figure 1 for 3 June

15 266, T 28 ncar_edr (23:51:19 1:6:7) , T 28 std4_acc (23:51:29 1:11:56) Figure 3: Same as Figures 1-2 for 6 June

16 The following plots depict the spectrum width field for a 3.4 degree elevation scan on 26 May 21. The first two plots indicate that a larger number of spectrum width values than expected are zero, and their occurrence is slightly more likely when the signal to noise ratio (SNR) is low. 3.5 x , 22:24:52 22:25:12 : SW ( deg) mean = th percentile = 9 th percentile = 3.5 variance = frequency Figure 4: Histogram of spectrum width values for a 3.4 degree elevation scan on 26 May

17 frequency , 22:24:52 22:25:12 : SNR for SW = ( deg) mean = th percentile = th percentile = variance = frequency frequency , 22:24:52 22:25:12 : SNR for SW =.5 ( deg) 4 mean = th percentile = th percentile = variance = , 22:24:52 22:25:12 : SNR for SW = 1 ( deg) 8 mean = th percentile = th percentile = variance = Figure 5: Histograms of SNR for values of SW =,.5, and 1. The SW = plot is skewed to the left, indicating that a larger number than expected resulted from measurements having low SNR. Because of the poor quality of the spectrum width field, we apply median filter smoothing. The following plot shows the results of applying a 9 range gate by 3 azimuth median filter to the scan referenced above. 17

18 2526, 22:24:52 22:25:12 : nanmed9x3_sw ( deg) Figure 6: Scan depicting 9x3 median filtered spectrum width values for a 3.4 degree elevation scan on 26 May 2. Finally, the following two plots show an overlay of the T-28 turbulence with the spectrum width field. The aircraft intersects the scan at approximately 22:25:, which is the center of the track shown, and is below the scan cone to the left and above it to the right. 18

19 ncar_edr (22:22: 22:28:), KGLD 9x3 filt. SW (3.4 deg. elev., Figure 7: Overlay of EDR measured by the T-28 aircraft with the 3.4 degree elevation spectrum width scan. The aircraft track is 6 minutes long. 19

20 8 ncar_edr (22:17: 22:33:), KGLD 9x3 filt. SW (3.4 deg. elev., Figure 8: Same as Figure 7, but with a 16-minute track. 2

21 The overlay plots indicate a good spatial correlation between the turbulence experienced by the T-28 aircraft and the smoothed spectrum width measured by radar. This is an indication of the promise of the STEPS-2 dataset for use in verifying the NCAR WSR-88D turbulence algorithm. 21