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Updates to the SZ-2 Algorithm

Updates to the SZ-2 Algorithm. Sebastian Torres CIMMS/NSSL Technical Interchange Meeting Spring 2007. Recommended SZ-2 Dynamic Use of Data Windows. SZ-2 uses three data windows depending on the situation The PNF needs the von Hann (or more aggressive) window

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Updates to the SZ-2 Algorithm

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  1. Updates to the SZ-2 Algorithm Sebastian Torres CIMMS/NSSL Technical Interchange Meeting Spring 2007

  2. Recommended SZ-2 Dynamic Use of Data Windows • SZ-2 uses three data windows depending on the situation • The PNF needs the von Hann (or more aggressive) window • GMAP needs the Blackman window to achieve required clutter suppression • Dynamic data windowing rules (June 2006 recommendation) • Use the rectangular window with non-overlaid, non-clutter-contaminated echoes • Use the von Hann window with overlaid, non-clutter-contaminated echoes • Use the Blackman window with clutter-contaminated echoes

  3. What if the default window is not rectangular? June ‘06 Logic … If there is clutter contamination Apply Blackman window Cohere and apply GMAP End … Determine strong and weak trips Compute strong-trip velocity If there are overlaid echoes … If there was no clutter contamination Apply von Hann window End Apply PNF … Compute weak-trip velocity End • No clutter and no overlaid echoes • No clutter and overlaid echoes • Clutter and overlaid echoes

  4. Double Windowing! Modified June ‘06 Logic … If there is clutter contamination Apply Blackman window Cohere and apply GMAP Else Apply default window End … Determine strong and weak trips Compute strong-trip velocity If there are overlaid echoes … If there was no clutter contamination Apply von Hann window End Apply PNF … Compute weak-trip velocity End • No clutter and no overlaid echoes • No clutter and overlaid echoes • Clutter and overlaid echoes

  5. April ‘07 Logic … If there is clutter contamination Apply Blackman window Cohere and apply GMAP End … Determine strong and weak trips If there was no clutter contamination Apply default window End … Compute strong-trip velocity If there are overlaid echoes … If there was no clutter contamination Apply von Hann window to original signal End Apply PNF … Compute weak-trip velocity End • No clutter and no overlaid echoes • No clutter and overlaid echoes • Clutter and overlaid echoes

  6. Updated SZ-2 Dynamic Use of Data Windows • Dynamic data windowing rules(April 2007 recommendation) • Use the default window with non-overlaid, non-clutter-contaminated echoes • Use the von Hann window with overlaid, non-clutter-contaminated echoes • Use the Blackman window with clutter-contaminated echoes • As an additional benefit, this update made SZ-2 fully compatible with super-resolution data The default window could be any window!

  7. Questions?

  8. VCP Design for Staggered PRT Sebastian Torres CIMMS/NSSL Technical Interchange Meeting Spring 2007

  9. ? Uniform PRT (Baseline) 1 scan at each elevation angle Staggered PRT 1 scan at each elevation angle ? How do we design these VCPs? Phase coding (SZ-2)2 scans at each elevation angle Mitigation Strategy 19.5° 7.0° 1.5° 0.5°

  10. Background • In the past work focused on replacing the Batch mode • Can we use staggered PRT to replace other scans? • Provide tools for effective VCP design Batch ModeVCP 11 Staggered PRT(k = 2/3, same DT) 03/03/042.5 deg ra = 147 km, va = 28.8 m/s ra = 184 km, va = 45.1 m/s

  11. Advantages of Staggered PRT • Staggered PRT has the potential of • … producing “clean” fields of reflectivity, velocity, and spectrum width • Likelihood of overlaid echoes can be minimized by using longer PRTs • At least double the current inherent maximum unambiguous range for Doppler • … increasing the maximum unambiguous velocity • … producing reflectivity values with improved accuracy

  12. Can we use Staggered PRT everywhere? Limitations of Staggered PRT • Maximum unambiguous velocity is extended with a simple Velocity Dealiasing Algorithm (Torres et al, 2004) • Occurrence of catastrophic errors • Ground clutter filtering is effective but computationally more complex (Sachidananda and Zrnic, 2002) • Filter performance degrades with small number of staggered pairs • Use of longer PRTs reduces the likelihood of overlaid echoes but • … limits the range of measurable spectrum widths • … leads to slightly less accurate velocity estimates (compared to standard VCPs)

  13. VCP Performance Indicators • Acquisition time • Maximum unambiguous range • Surveillance: reflectivity • Doppler: velocity and spectrum width • Maximum unambiguous velocity • Spectrum width saturation • Errors of estimates • Clutter suppression

  14. VCP Performance Indicatorsfor Staggered PRT • Acquisition time • Dwell time (DT) = Mp(T1 + T2) • Maximum unambiguous range • ra,S = c·max(T1,T2)/2, ra,D = c·min(T1,T2)/2 • Maximum unambiguous velocity • va = ml/4T1 = nl/4T2, where T1/T2 = m/n • Spectrum width saturation (Melnikov and Zrnic, 2004) • sv,max depends inversely on the spacing of pairs • Modified staggered PRT algorithm to compute spectrum width from the short PRT pairs

  15. VCP Performance Indicatorsfor Staggered PRT (cont’d) • Errors of estimates • Estimation errors • Reflectivity: worst case scenario when only one set of pulses can be used in the estimator • Velocity: in the worst case scenario, errors are those of the short-PRT velocity • Catastrophic errors (VDA) • Performance of the spectral GCF • Clutter filtering tied to performance of GMAP • GMAP does not perform well for M < 16 • SACHI procedure works best for T1/T2 = 2/3

  16. Can we maintain or improve other features? VCP Design Assumptions • Preserve elevation angles of existing VCPs • Focus on VCP 11, 12, and 21 • Consider Staggered PRT as replacement for all elevation cuts in a VCP • Maintain or reduce VCP times

  17. Designing a VCP for SPRT • Can specify: • T1, T2: staggered PRTs • Mp: number of staggered pairs • a: Antenna rotation rate • Major constraints • Design constraints • T1/T2 = 2/3 • Preserving VCP time • Assume times for all scans will be preserved • This determines a and dwell time • DT = Mp(T1+T2) • There is only one degree of freedom! (T1)

  18. Designing a VCP for SPRT (cont’d) • Maximum unambiguous range • ra,S = 3cT1/4, ra,D = cT1/2 • Goal: match min{300 km, rmax(qe)} with ra,D • Maximum unambiguous velocity • va = l/2T1 • Goal: match va for Doppler PRT • Spectrum width saturation • Goal: sv,max > ~8 m/s

  19. Designing a VCP for SPRT (cont’d) • Estimation and catastrophic errors • All a function of T1 and signal characteristics • Goal: Meet or exceed NEXRAD technical requirements • Performance of the spectral GCF • A function of T1 (va and Mp) • Goal: Meet or exceed NEXRAD technical requirements • Ground clutter suppression requirements are not as stringent as we go up in elevation

  20. Acceptable PRTs • System limits • Transmitter duty cycle • T1≥ 767 ms • Current DSP memory (3072 bins) • 3T1/2 ≤ 5.12 ms → T1≤ 3.41 ms • Not a problem since maximum PRT in the WSR-88D is 3.14 ms • Existing system PRTs • Impossible to get k = 2/3with system PRTs • Impose limitation just on T1?

  21. Range of acceptable PRTs 2.4° Designing a VCP for SPRT (cont’d) Trade-off Can satisfy ra and va • Maximum unamb. range • ra,S = 3cT1/4 ≥ rmax • ra,D = cT1/2 ≥ rmax • Maximum unamb. velocity • va = l/2T1≤ va,D • Shorter PRTs lead to • Larger va • Larger sv,max • Lower errors of v and sv • Lower rate of catastrophic errors • Better GCF Match va Match ra

  22. VCP 11 – 0.5 deg Uniform PRT Combined DT Matchva Staggered PRT Matchra,S MatchPRI# PRI Delta C f = 2800 MHz SD(Z) estimated at SNR = 10 dB and sv = 4 m/s incl. range avg. SD(v) estimated at SNR = 8 dB and sv = 4 m/s

  23. VCP 11 – 1.45 deg Uniform PRT Staggered PRT PRI Delta C f = 2800 MHz SD(Z) estimated at SNR = 10 dB and sv = 4 m/s incl. range avg. SD(v) estimated at SNR = 8 dB and sv = 4 m/s

  24. VCP 11 – 2.4 deg Uniform PRT Staggered PRT GCF performance? PRI Delta C f = 2800 MHz SD(Z) estimated at SNR = 10 dB and sv = 4 m/s incl. range avg. SD(v) estimated at SNR = 8 dB and sv = 4 m/s

  25. VCP 11 – 3.35 deg Uniform PRT Staggered PRT PRI Delta C f = 2800 MHz SD(Z) estimated at SNR = 10 dB and sv = 4 m/s incl. range avg. SD(v) estimated at SNR = 8 dB and sv = 4 m/s

  26. VCP 11 – 4.3 deg Uniform PRT Staggered PRT PRI Delta C f = 2800 MHz SD(Z) estimated at SNR = 10 dB and sv = 4 m/s incl. range avg. SD(v) estimated at SNR = 8 dB and sv = 4 m/s

  27. VCP 11 – 5.25 deg Uniform PRT Staggered PRT PRI Delta C f = 2800 MHz SD(Z) estimated at SNR = 10 dB and sv = 4 m/s incl. range avg. SD(v) estimated at SNR = 8 dB and sv = 4 m/s

  28. VCP 11 – 6.2 deg Uniform PRT Staggered PRT PRI Delta C f = 2800 MHz SD(Z) estimated at SNR = 10 dB and sv = 4 m/s incl. range avg. SD(v) estimated at SNR = 8 dB and sv = 4 m/s

  29. VCP 11 – 7.5 deg Uniform PRT Staggered PRT Range oversampling? PRI Delta C f = 2800 MHz SD(Z) estimated at SNR = 10 dB and sv = 4 m/s incl. range avg. SD(v) estimated at SNR = 8 dB and sv = 4 m/s

  30. VCP 11 – 8.7 to 19.5 deg Uniform PRT Staggered PRT PRI Delta C f = 2800 MHz SD(Z) estimated at SNR = 10 dB and sv = 4 m/s incl. range avg. SD(v) estimated at SNR = 8 dB and sv = 4 m/s

  31. Catastrophic Errors

  32. VCP 11 Summary • Split cuts (0.5º-1.45º) • Good match of va and ra • Some obscuration of Doppler moments within ~150km if echoes beyond ~300km are very strong • Spectrum width saturates at ~7.5 m/s • Estimation errors are well below NTR • Catastrophic errors are negligible for sv≤ 4 m/s but increase up to 50% for 4 m/s <sv≤ 8 m/s • Number of samples is sufficient to ensure good performance of the GCF

  33. VCP 11 Summary • Batch (2.4º) • Good match of va and ra • Spectrum width saturates at ~6.8 m/s • Estimation errors are well below NTR for Z but slightly above for v and sv • Catastrophic errors are negligible for sv≤ 3 m/s but increase up to 50% for 3 m/s <sv≤ 8 m/s • Number of samples may be insufficient to ensure good GCF performance (depending on the clutter regime)

  34. VCP 11 Summary • Batch (3.35º-6.2º) • Complete absence of overlaid echoes and larger va • Spectrum width saturates at > 8.3 m/s • Estimation errors are slightly above NTR for Doppler moments and well below for reflectivity • Catastrophic errors are negligible for sv≤ 4 m/s and less than 40% for 4 m/s <sv≤ 8 m/s • Number of samples is sufficient to ensure good GCF performance (if needed)

  35. VCP 11 Summary (cont’d) • Doppler (7.5º-19.5º) • Complete absence of overlaid echoes and much larger va • No spectrum width saturation • Much shorter dwell times result in larger errors of velocity estimates (~ 1.3 m/s) • Range oversampling techniques with a modest oversampling factor could be used • Catastrophic errors are negligible • Number of samples is sufficient to ensure good GCF performance (if needed at all!)

  36. VCP 11 Summary

  37. Questions? Staggered PRT(k = 2/3, same DT) Doppler Velocity Batch ModeVCP 11 March 3, 20042.5 deg ra = 147 km, va = 28.8 m/s ra = 184 km, va = 45.1 m/s

  38. Operational Considerations for Staggered PRT Sebastian Torres CIMMS/NSSL Technical Interchange Meeting Spring 2007

  39. Staggered PRT Operational Considerations • Every CPI contains an even number of pulses • The antenna rotation rate can be adjusted to accommodate this requirement • The maximum staggered PRT is ~ 3 ms • In the worst case scenario, doing this would add about 1 second to a scan • No significant change in VCP time • Can use overlapping radials • SACHI in Report 9 assumes that the number of pulses is a multiple of 4 • This is not a real limitation and the description can be modified accordingly

  40. … T1 T2 T1 T2 T1 T2 T1 T2 T1 T2 T1 2Mp + 1 2Mp + 1 T2 T1 T2 T1 T2 T1 T2 T1 T2 T1 T2 … Staggered PRT Operational Considerations (cont’d) • T1 is the short PRT, T2 is the long PRT • Algorithm can be modified to handle T1 > T2 • Additional logic • Additional setup for the clutter filter • Ensuring T1 < T2 is straightforward if 2Mp+1 pulses are requested at every azimuth in the sampling grid • At most, this represents a negligible azimuthal shift of the resolution volume by 0.06 deg

  41. Staggered PRT Operational Considerations (cont’d) • The PRT ratio k is 2/3 • This constraint is not necessary if using DC removal for clutter filtering • k is 2/3 leads to a minimum number of dealiasing rules in the VDA • This constraint is necessary if using SACHI • Best performance for clutter filtering and spectral processing • A drawback is that none of the existing PRTs in the WSR-88D form this ratio

  42. Staggered PRT Operational Considerations (cont’d) • If necessary, clutter filtering beyond cT1/2 could be handled by other means • Samples are uniformly spaced by T1+T2 • Based on the previous analysis echoes extending beyond cT2/2 are highly unlikely (ra,S = 444 km for the first scans) • The algorithm does not need to use one-overlay techniques described by Sachidananda and Zrnic (2003)

  43. Why Staggered PRT? • Some limitations of existing WSR-88D R/V ambiguity mitigation techniques • Split cuts/Batch mode (ra,D ~ 150 km by default) • Doppler parameters only available for strong trips with weak or no overlays • Batch mode: Degraded quality of reflectivity estimates for overlaid echoes • Split cuts: Require two scans at each elevation angle • MPDA • Requires multiple scans at each elevation angle • SZ-2 (ra,D ~ 115 km, ~ 135 km, or ~ 150 km ) • Requires complicated rules for censoring and exhibits a “purple ring” at the beginning of the 2nd trip • Weak trip recovery is limited depending on the power ratio and exhibits larger errors and spectrum width saturation • “All bins” clutter filtering requires re-determination of clutter contamination

  44. What do we gain/lose? • Key advantages • Clean recovery of all moments • Increase in maximum unamb. velocity • Lower reflectivity errors • Key disadvantages • At most, ~30% higher errors for Doppler moments • Can be mitigated with range oversampling • Velocity errors can be further reduced by averaging short (T1) and long (T2) PRT velocities • Occurrence of VDA catastrophic errors • Can be mitigated with simple continuity check in the RDA and RPG’s existing VDA

  45. Questions?

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