Evolution of the SZ-2 Algorithm

1. Evolution of the SZ-2 Algorithm Sebastian Torres CIMMS/NSSL Technical Interchange Meeting Spring 2006

2. Outline • Recent evolution of SZ-2 • Recommended changes • Engineering fixes • Additional refinements • Spectrum width issues • Items for discussion

3. Recent Evolution of SZ-2 • Last AEL delivered on July 26, 2005 • Handling of clutter in multiple trips to address “all bins” clutter filtering case • Other minor changes • ROC’s integration and testing • 12 “areas of interest” for SZ-2 identified in Feb 06 • “Unofficial” evolution (that I know about…) • Updated censoring thresholds (NCAR) • Engineering fixes (ROC) • Algorithm refinements (NSSL)

4. Specific Areas of Evolution • Dynamic use of data windows • CNR censoring (dB-for-dB) • Long-PRT power censoring • Short-PRT censoring rules • Short-PRT censoring thresholds • Processing of non-overlaid echoes • Spectrum width estimation • Autocorrelation estimation

5. Dynamic Windows (I) • Original algorithm developed by Sachi used von Hann window everywhere • Best statistical performance for SZ-2 without clutter suppression • Initially recommended algorithm used Blackman window everywhere • Needed to achieve required clutter suppression • Higher errors of estimates

6. Requirements are not met! Dynamic Windows (II) • Compared to using a rectangular window, velocity errors for sv = 4 m/s and high SNR are • 33% higher with the Hamming window • 35% higher with the von Hann window • 50% higher with the Blackman window M = 64, va = 35 m/s, high SNR

7. Dynamic Data Window Recommendation • Use the rectangular window if there are no overlaid echoes and there is no clutter contamination • Best statistical performance matching legacy RDA • Use the von Hann window if there are overlaid echoes but there is no clutter contamination • Best statistical performance for SZ-2 • Errors about 30% higher with overlaid echoes • Use the Blackman window if there is clutter contamination • Best clutter suppression • Errors about 50% higher with clutter contamination • “All bins” filtering should be avoided

8. AdjustedSNRth (dB) Region I No adjustment Region II0.1 dB/dB Region III1 dB/dB SNRth CNR (dB) CNR Censoring • SNR thresholds are adjusted based on the CNR • Obscure feature of legacy RDA • False idea of higher clutter suppression • dB-for-dB censoring in ORDA

9. CNR Censoring in SZ-2 • Clutter-to-Noise ratio is computed from • Clutter power removed by GMAP • Regardless of which trip has clutter • Measured Noise power • dB-for-dB regions are defined as in FFT Mode of ORDA • Some censoring rules may be redundant?

10. Long-PRT “Truth” Powers • Recommended algorithm uses non-censored “truth” powers • Implemented algorithm uses SNR and dB-for-dB censored “truth” powers • Censored gates assume a value of zero • This is similar to ORDA processing of split cuts • The approach over-censors if the reflectivity SNR threshold is larger than the velocity or spectrum width SNR thresholds

11. Censoring “Truth” Powers • Non-overlaid case • Clutter-filtered long-PRT powers • P0 = p, P1 = P2 = P3 = 0 • p is such that p < NOISE * AdjZth • p is weak or • there was strong clutter in the 1st trip • Censored long-PRT powers • P0 = P1 = P2 = P3 = 0 • Short-PRT processing • tA = -1 and gate is tagged as NOISE LIKE due to non-significant long-PRT power (0 < NOISE * Adjvth) • This may fail if Zth > vth

12. Censoring “Truth” Powers • Overlaid case • Clutter-filtered long-PRT powers • P0 = p, P1 = q, P2 = P3 = 0 • p is such that p < NOISE * AdjZth • there was strong clutter in the 1st trip • q is such that q > NOISE * AdjZth • Censored long-PRT powers • P0 = P2 = P3 = 0, P1 = q • Short-PRT processing • tA = 1, tB = -1 • 1st trip is tagged as NOISE LIKE due to non-significant long-PRT power (0 < NOISE * vth) • 2nd trip is processed as non-overlaid case • p could be larger than q (strong clutter?) • Recovered velocity may be invalid • Would existing censoring rules catch this?

13. Censoring Rules • ROC implemented 3 engineering fixes • CSR censoring of strong trip classified as NOISE • Decrease purple haze in clear air • Ignore SNR* and CSR censoring if no weak trip • It seems OK, but needs further evaluation • Discussion Item: What should be classified as NOISE and what should be classified as OVERLAID? • Discussion Item: Do we need a new censoring rule to handle “noisy velocities at the beginning of the 2nd trip”?

14. Short-PRT Censoring Rules Strong Trip Censoring Rules

15. Short-PRT Censoring Rules Weak Trip Censoring Rules

16. Censoring Thresholds • Latest set of thresholds delivered by NCAR in Feb 06 • Discussion Item: Do we need further refinement of thresholds? • The problem of “noisy velocities at the beginning of the 2nd trip” may be addressed by varying a threshold (without adding a new censoring rule)

17. Processing Non-Overlaid Echoes • The Processing Notch Filter is used to remove most of the strong trip before attempting to recover the weak trip • This is not necessary in case of non-overlaid echoes • Strong-trip residue after the PNF acts as out-of-trip power, which biases PS and wS (if using R0/R1 estimator) • Recommendation: bypass the PNF if there are no overlaid echoes (tB = -1) • Processing of non-overlaid echoes is more similar to processing in FFT mode

18. Spectrum Width Estimation • R0/R1 estimator: • Requires signal power estimate • Difficult with overlaid echoes • Poor at low SNR • Needs accurate noise power estimate • R1/R2 estimator: • Good at low SNR • Does not need signal or noise • Reduced useful range by a factor of 2 • Poor performance at large spectrum widths (above ~ 7 m/s for va = 35 m/s)

19. R0/R1 spectrum width

20. R1/R2 spectrum width

21. Spectrum Width in SZ-2 • Ideally, we would like to have an adaptive scheme to select the best spectrum width estimator for each situation (also proposed by Ice et al during ORDA evaluation) • Difficult in practice: the best estimator depends on the actual spectrum width • Discussion Item: Should we use the R1/R2 estimator in the SZ-2 algorithm? • This would be better but different from other ORDA modes

22. Spectrum Width Evaluation • ROC’s evaluation of SZ-2 revealed “critical” spectrum width problems • Biased estimates compared to FFT Mode • Abnormally large number of zero values

23. Spectrum Width Problems • Problems observed in the spectrum width fields produced by SZ-2 can be traced to biased autocorrelation estimates • SZ-2 spectrum widths are biased low • ORDA FFT mode spectrum widths are biased high • This has been confirmed by SIGMET (Alan Siggia)

24. window This factor can be pre-computed for any particular window Autocorrelation from Time Series • Standard autocorrelation estimator • Unbiased for rectangular window • Using a data window: Vw(m) = d(m)V(m) • Unbiased for all windows

25. Bias in SZ-2 Mode • Employs the lag-1 standard estimator (i.e., divides by M-1) even if using a data window • For example, for M = 64 the current normalization factor is 1/63 = 15.873e-3 • |Rt(1)| is biased high with a non-rectangular window • Spectrum width is biased low with a non-rectangular window • This explains the increased number of zeros

26. Biased vs. Unbiased R0/R1 Time Domain Estimators (I) M = 64, va = 35 m/s, high SNR

27. Biased vs. Unbiased R0/R1 Time Domain Estimators (II) M = 64, va = 35 m/s, high SNR

28. Autocorrelation from Power Spectrum • ORDA power spectrum estimator • Standard autocorrelation estimator • Biased for all windows • Using a data window • Almost unbiased for all windows

29. Bias in FFT Mode • Employs the biased lag-1 estimator and an empirical broadening correction if using a data window • For example, for M = 64 the current normalization factor is 1 • |Rs(1)| is biased low • Spectrum width is biased high (this is worse for a rectangular window) • Empirical correction factors reduce the spectrum width for non-rectangular windows (factors are larger for more aggressive windows and they are effective at narrow spectrum widths)

30. Biased vs. UnbiasedR0/R1 Frequency Domain Estimators (I) M = 64, va = 35 m/s, high SNR

31. Biased vs. Unbiased R0/R1Frequency Domain Estimators (II) M = 64, va = 35 m/s, high SNR

32. Biased vs. Unbiased R0/R1 Frequency Domain Estimators (III) M = 64, va = 35 m/s, high SNR

33. Making Both Spectrum Widths Estimators the Same • In theory, time and frequency domain implementations should be equivalent • PSD and Autocorrelation are Fourier transform pairs • In practice, this depends on the actual implementation • Processing in the frequency domain amounts to a circular convolution • Example: for lag-1 autocorrelation, the term V*w(M-1)Vw(0) is part of the computation, but this term is not coherent with the other pairs • Note that with aggressive windows this term is almost negligible • Simple correction: subtract spurious terms • Otherwise, velocity and spectrum width estimates have slightly higher errors due to non-coherent terms

34. Unbiasing factor for arbitrary data windows Unbiasing factor for arbitrary data windows Spuriousterms Recommended Autocorrelation Estimators • Autocorrelation from time series • Autocorrelation from power spectrum

35. R0/R1 Spectrum Width

36. R1/R2 Spectrum Width

37. KCRI (ORDA)VCP 211 - 03/19/06

38. SZ-2 Velocity Recovery

39. FFT mode Hamming/Blackman windowBiased autocorrelations ORDA R0/R1 spectrum width

40. SZ-2 mode Blackman windowBiased autocorrelations ORDA R0/R1 spectrum width

41. FFT mode Rectangular/Blackman windowBiased autocorrelations ORDA R0/R1 spectrum width

42. SZ-2 mode Rect./von Hann/Blackman windowBiased autocorrelations ORDA R0/R1 spectrum width

43. FFT mode Rectangular/Blackman windowUnbiased autocorrelations Legacy R0/R1 spectrum width

44. SZ-2 mode Rect./von Hann/Blackman windowUnbiased autocorrelations Legacy R0/R1 spectrum width

45. Spectrum Width Summary • ORDA FFT Mode spectrum width is biased high • Larger bias with rectangular window • Almost no bias with other windows • SZ-2 Mode spectrum width is biased low • No bias with rectangular window • Both of these need to be fixed by using unbiased autocorrelation estimators

46. How to Fix the Spectrum Width Problem? • Use unbiased autocorrelation estimator for each window • Both in time and frequency domains • Do not apply RVP-8 spectrum width empirical corrections • Discussion Item: Can we ask SIGMET to fix this? • Change to autocorrelation estimation • Change to spectrum width computation

47. SZ-2 Evolution • Recommended changes since last AEL • Use dynamic data windows (done) • Apply CNR censoring as in ORDA (done) • Classify CSR censored gates as NOISE (done) • Use R1/R2 spectrum width estimator (done) • Bypass the PNF is no overlaid echoes (done) • Use updated set of thresholds (done?) • Use unbiased autocorrelation estimators • Use unbiased spectrum width estimators • ROC engineering fixes since last AEL • Ignore some censoring rules if no overlaid echoes (done) • Use censored long-PRT “truth” powers (done)

48. Questions?

49. Discussion Items • Endorsement of ROC engineering fixes • What should be NOISE and what should be OVERLAID? • Additional censoring rule or refined threshold to solve “noisy velocity” problem • Use of R1/R2 spectrum width estimator • Fixing the spectrum width problem

50. Back up slides