Staggered PRT Practical Considerations

1. Staggered PRTPractical Considerations Sebastian Torres CIMMS/NSSL Technical Interchange Meeting Spring 2005

2. BATCH MODE STAGGERED PRT Outline • Staggered PRT refresher • Choosing the PRTs • Away with the Batch Mode! • Ground clutter filter performance Improvement in Doppler velocity retrieval using Staggered PRT

3. T1 T2 T1 T2 … time ` Simple algorithm The Staggered PRT Technique • Transmitter alternates two PRTs • T1 < T2, PRT ratio: k = T1/T2 = m/n • Maximum unambiguous range • Reflectivity: ra = ra2 • Doppler velocity: ra = ra1 • Maximum unambiguous velocity • Velocity Dealiasing Algorithm (VDA) • va = m va1 = n va2

4. Max. unambiguous velocity can be extended by means of a simple algorithm Longer PRTs can be used to avoid overlaid echoes Velocity fields are “clean” Spectral processing is complicated due to non-uniform spacing of samples Ground clutter filtering is a challenge Longer PRTs may result in larger errors of estimates Staggered PRT Pros and Cons

5. Choice of PRTs What are the magicalvalues of T1 and T2?

6. Choice of PRTs • How do we choose T1 and T2 for the operational environment? • Constraints • System limits • Range coverage • Design considerations • Errors of estimates

7. System Limits • Maximum RF duty cycle for the WSR-88D transmitter is 0.2% • Duty cycle = t /Ts • 1.57 ms/Ts≤ 0.002 => Ts≥ 780 ms • Signal processor memory allocation in the RVP-8 limits the number of range bins to 3072 • Typical sample spacing: 1.67 ms (250 m) • 1.67 ms x 3072 = 5.12 ms => Ts≤ 5.12 ms

8. Range Coverage (I) • Maximum unambiguous range • ra = cTs/2 • The longer the PRT the better! • WSR-88D requirements: • Reflectivity up to 460 km • ra2≥ 460 km => T2≥ 3.07 ms • Doppler velocity up to 230 km • ra1≥ 230 km => T1 ≥ 1.53 ms

9. Range Coverage (II) • Actual requirements for intermediate to higher elevations can be relaxed • Most storms tops are below 18 km • For a height of 18 km, the slant range (r) is ~ 300 km at an elevation (qe) of 2.4 deg and ~ 150 km at 6 deg

10. Range Coverage (III) • Actual requirements for range coverage at intermediate elevations are300 km or less • For example • At 2.4 deg: ra1≥ 230 km => T1 ≥ 1.53 ms ra2≥ 300 km => T2≥ 2 ms • At 6.0 deg: ra1≥ 150 km => T1 ≥ 1 ms ra2≥ 150 km => T2≥ 1 ms

11. Design Constraints • Algorithm assumes T1 < T2 • Preferred PRT ratio is k = 2/3 • Fewest number of rules for the VDA • Spectral GCF performs best with this ratio (Sachidananda et al, 1999) • T1 / T2 = 2/3 • Note: None of the existing PRTs in the WSR-88D satisfy this condition! • RVP-8 and 88D transmitter not limited to 8 PRTs • Possible ORPG impact • RDA/RPG ICD does not include the PRT • VCP definitions use PRT numbers

12. Errors of Estimates • Echo coherency is required for precise Doppler measurements • The spectrum width should be much smaller than the Nyquist interval • Median value of sv in severe storms is about 4 m/s • T1 < 2.2 ms • However, larger sv would require shorter T1

13. System limits Range coverage Design constraints Signal coherency PRT ratio Acceptable PRTs Acceptable PRTs T1 = 1.5350 ms T2 = 2.3025 ms

14. Errors of Estimates Can these values of T1 and T2 do the work?

15. T1 T2 T1 T2 … R1 R2 R2 R1 time Dealing with Spaced Pairs • Uniform PRT uses contiguous pairs • Staggered PRT uses spaced pairs • Usual formulas for the standard error of estimates have to be modified • Formulas for the spectrum width don’t even apply

16. Staggered PRT assumes echoes don’t extend beyond ra2 T1 T2 I II I II III Spectral Moment Estimators with Staggered PRT (I) • Reflectivity • Three zones: • I: Short PRT pulses only • II: All pulses • III: Long PRT pulses only • Zone II estimates are more accurate for large spectrum widths

17. Reflectivity Errors Solid lines: short (or long) PRT pulses only Dashed lines: all pulses SNR = 40 dB DT = 60 msk = 2/3

18. Spectral Moment Estimators with Staggered PRT (I) • Velocity • v1 from short PRT pairs is dealiased using v2 from long PRT pairs • Spectrum Width • Depends on power and lag-1 autocorrelation estimates • Use short or long PRT lag? • Long PRTs will exhibit saturation for large spectrum widths

19. Velocity Errors Solid lines: short PRT pairs Dashed lines: long PRT pairs SNR = 40 dB DT = 60 msk = 2/3

20. Spectrum Width Errors Solid lines: short (or long) PRT pulses for power Dashed lines: all pulses for power Lines without markers:short PRT pairs for autocorrelation Lines with markers:long PRT pairs for autocorrelation SNR = 40 dB DT = 60 msk = 2/3

21. Replacing the Batch Mode Can Staggered PRT performbetter than the Batch Mode?

22. Factors to Consider • Range coverage • Different for Surveillance (reflectivity) and Doppler (velocity and spectrum width) • Must meet NEXRAD requirements but can be adjusted using maximum height of storms • Acquisition time • Dictated by antenna rotation rate • Must keep same or shorter dwell time • Errors of estimates • Must meet NEXRAD requirements

23. VCP 11 Scans using the Batch Mode

24. Range Coverage (I)

25. Extended using long PRT powers Range Coverage (II) rad: short PRT ras: long PRT T1 = 2rad/c T2 = 2ras/c ras = (3/2) rad

26. Maximum unambiguous velocity Batch Mode Staggered PRT

27. Acquisition Time

28. Errors of Estimates (I) • According to NEXRAD requirements, standard errors of estimates are specified at SNR > 8 dB and sv = 4 m/s • For the Batch Mode, we use standard formulas (contiguous pairs) • For the Staggered PRT, we use modified formulas (spaced pairs)

29. Requires average of 4 gates in range All slightly larger than 1 m/s All better than with the BM All less than 1 m/s Errors of Estimates (II) Batch Mode Staggered PRT

30. Solutions to the Issue of Larger Errors of Estimates • Collect more samples per radial • This requires reducing the antenna rotation rate • For example, at 2.5 deg need to collect 21 pairs instead of 15, adding about 8 seconds to the scan • Use Sachi’s one-overlay resolution technique and reduce the PRTs • Computationally complex • Use oversampling and whitening • Even a small oversampling factor would work

31. What about other VCPs? • Requirements don’t change! • Everything depends on the required range coverage and the dwell time • The shorter the dwell time and/or the larger the required range coverage, the larger the errors • Larger errors increase the likelihood of catastrophic errors in the Staggered PRT velocity dealiasing algorithm

32. Ground Clutter Filtering with Staggered PRTs Can we remove the clutteras well as with uniform PRT?

33. Ground Clutter Filtering • Batch mode • Surveillance pulses are filtered with the two-pulse canceller • About 30 dB of suppression • Doppler pulses are filtered with GMAP • Staggered PRT • Staggered PRT pulses are filtered with a spectral GCF (Sachidananda) • Filter can incorporate elements of GMAP

34. GCF Performance Batch Mode - 2 pulse canceller Batch Mode - GMAP No GCF Staggered PRT

35. Conclusions • Unambiguous range coverage for velocity estimates is greatly improved with Staggered PRT • Staggered PRT yields larger Nyquist velocity intervals • For the same dwell times, errors of estimates are better for reflectivity and slightly worse for velocity • Ground clutter suppression using a spectral filter is much better for reflectivity and comparable for velocity • Staggered PRT is a viable candidate to replace the legacy Batch Mode at intermediate elevation angles

36. BATCH MODE STAGGERED PRT An image is worth a thousand words …