Updates to the SZ-2 Algorithm

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

2. Over 25 years ago…

3. Today… KTLX radar in Oklahoma City 30 Mar 2007, 0.5 deg elevation (VCP 12/VCP 221) Courtesy of Jami Boettcher (WDTB)

4. SZ-2 is Operational! KCRI 20 June 2007 VCP 121 SZ-2 tilt Courtesy of Dave Zittel (ROC)

5. Outline • SZ-2 Upgrades • 4th-trip overlaid echoes • Recovery region censoring • Recommendations

6. 20 June 2007 Case Observed “noisy velocities”

7. Sanity Check KCRI Level I Dataprocessed with MATLAB KCRI Level II Data Note: Velocity color scales are different

8. Where is it Coming From? Storm cell between 400 and 450 km: 4th trip overlaid echoes Long PRT: ra = 471 km Short PRT: ra = 119 km

9. A Little Detective Work 4th 3rd 2nd 1st None Noisy velocities correspond to strong 4th trip and weak 1st trip 4th 3rd 2nd 1st None

10. The SZ-2 Processing Notch Filter Overlaid signals S1 = 10 dB v1 = 15 m/s w1 = 2 m/s Weak signal is in PNF width Two replicas of the modulated weak signal are needed for proper spectral reconstruction 2nd trip 0.75 M S2 = 0 dB v2 = -15 m/s w2 = 2 m/s Sidebands 3rd trip 0.50 M 4th trip 0.75 M Sidebands don’t bias, but contribute to higher errors of velocity estimates

11. Back to Our Case… AZ = 266 degr = 64 km Strong trip Strong signal is in the 4th trip Weak signal is in the 1st trip Recovered 1st trip signal spectrum does not seem to have the expected mainlobe with decaying sidelobes!

12. SZ(8/64) Modulation Codes 1st to 4th trip mod. code 1st to 3rd trip mod. code 1st to 2nd trip mod. code Cohere to strong  Apply von Hann window  Apply PNF  Cohere to weak

13. Weak Trip Velocity Recovery Standard deviation of weak-trip velocity estimates 2nd trip 3rd trip 4th trip If strong and weak signals are 3 trips apart (e.g., 1st and 4th trips), recovery of weak-trip velocities is not possible with the current algorithm

14. Why are the errors so large? Change PNF’s NW = 0.75M PNF’s NW = 0.50M svn = 0.53 svn = 0.26 0.26 0.53

15. A New PNF Notch Width Standard deviation of weak-trip velocity estimates 2nd trip 3rd trip 4th trip If strong and weak signals are 3 trips apart (e.g., 1st and 4th trips), recovery of weak velocities is possible with a small change to the current algorithm

16. Changes to SZ-2 ≠1

17. Back to Our Case with the Fix Current SZ-2 Algorithm Proposed SZ-2 Algorithm

18. 19 June 2007 Case Current SZ-2 Algorithm Proposed SZ-2 Algorithm

19. Still Noisy Velocities! Weak Trip Number 4th 3rd 2nd 1st None

20. Recovery Region Censoring • Weak-trip velocity estimates exhibit large errors for wider strong-trip spectrum widths and large power ratios • In this case, weak-trip velocities “cannot be recovered” • Weak-trip velocities are censored if we are outside the “recovery region” CT Censor CS CI Accept Extracted from NSSL Report 2

21. Current SZ-2 Thresholds Weak trip: sv = 4.2 m/s Nominal parameters f = 2800 MHz DELTA PRI C Narrow weak-trip widths Wide weak-trip widths Strong trip: sv = 4.8 m/s sv = 3.7 m/s Narrow weak-trip widths Wide weak-trip widths Ps /Pw (dB) Ps /Pw (dB) 45 -6.25 dB/(m/s) 45 -6.25 dB/(m/s) 3.7 10.9 4.8 12 sv ,s(m/s) sv ,s(m/s)

22. 2nd Trip Overlay Requirement: SD(vw) < 2 m/s Conditions? 3.5 m/s 4.25 m/s 4.5 m/s 4.5 m/s 4.5 m/s 45 dB 45 dB 45 dB 45 dB 4.5 m/s -11.25 dB s/m -11.25 dB s/m -11.25 dB s/m -11.25 dB s/m

23. 3rd Trip Overlay Requirement: SD(vw) < 2 m/s 6.5 m/s 2.75 m/s 2.75 m/s 2.75 m/s 2.75 m/s 2.75 m/s 2.75 m/s 45 dB 45 dB 45 dB 45 dB 45 dB 45 dB -11.25 dB s/m -11.25 dB s/m -11.25 dB s/m -11.25 dB s/m -11.25 dB s/m -11.25 dB s/m

24. 4th Trip Overlay Requirement: SD(vw) < 2 m/s 3.5 m/s 2.25 m/s 2.25 m/s 2.25 m/s 2 m/s 45 dB 45 dB 45 dB 45 dB 4.5 m/s -11.25 dB s/m -11.25 dB s/m -11.25 dB s/m -11.25 dB s/m

25. Summary of Recovery Regions Current thresholds Same for every type of overlay Proposed thresholds Depend on type of overlay One-trip differencew0 = 0.2032 w1 = 0.2612 Two-trip differencew0 = 0 w1 = 0.3773 Three-trip differencew0 = 0.2032 w1 = 0.2612

26. Changes to the SZ-2 Algorithm • Define thresholds for each overlay type • Make recovery region censoring a function of the strong-to-weak trip number difference • Define recovery region using three zones depending on the weak-trip spectrum width • Immediate censoring for large weak-trip widths

27. Back to our cases (I) 20 Jun 2007 Proposed Censoring (aggressive) Proposed Censoring (normal) Current Censoring (mild)

28. Back to our cases (II) 19 Jun 2007 Proposed Censoring (aggressive) Proposed Censoring (normal) Current Censoring (mild)

29. Summary • Analysis of operational SZ-2 fields revealed noisy velocities • Three-trip-difference overlay situations are not handled well in SZ-2 • This affects weak-trip velocities for those cases in which 1st trip is weak, 4th trip is strong, and there are no significant signals in the 2nd and 3rd trips • Effective recovery of weak-trip velocities in this situation requires a narrower PNF notch

30. Summary (cont’d) • Censoring based on power-ratio recovery region is not aggressive enough • This affects weak-trip velocities only • Higher errors of estimates • Different overlay situations require different recovery regions • Current algorithm based on one-trip difference overlay case • One-, two-, and three-trip difference overlay cases need to be considered • Recovery for wide weak-trip widths is very difficult

31. Recommendations • Fix PNF notch width • Verified issue with clear-cut fix • Very simple, transparent change • Recommend implementation for ORDA Build 11 • Upgrade “Recovery Region” Censoring • Change is relatively simple • Will result in more purple haze • Should look at more cases before proposing new thresholds • Involve DQ Team? • Recommend implementation ASAP