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Staggered PRT Algorithm Update

Staggered PRT Algorithm Update. Sebastian Torres and David Warde CIMMS/University of Oklahoma and NSSL/NOAA. Data Quality MOU – Technical Interchange Meeting Norman, OK 1 December, 2009. SPRT Algorithm Evolution. 2003 : 2/3 PRT ratio with DC filter NSSL Report 7

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Staggered PRT Algorithm Update

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  1. Staggered PRT Algorithm Update Sebastian Torres and David Warde CIMMS/University of Oklahoma and NSSL/NOAA Data Quality MOU – Technical Interchange MeetingNorman, OK 1 December, 2009

  2. SPRT Algorithm Evolution • 2003: 2/3 PRT ratio with DC filter • NSSL Report 7 • 2005: SACHI filter (standalone) • NSSL Report 9 • 2008: Any PRT ratio with DC filter • NSSL Report 12 • 2009: 2/3 PRT ratio with SACHI filter • Separate document delivered on 03/09 • 2009: 2/3 PRT ratio with SACHI filter and overlaid echo recovery • Separate document delivered on 07/09 • NSSL Report 13

  3. 2009 SPRT AEL (07/09) • Notation standardization • Clutter filtering update • SACHI on Segments I and II • Functionality same as in Report 11 • Adapted to “fit” signal processing pipeline • Steps described in algorithmic form • DC removal on Segment III • Recovery of overlaid echoes • Segment III data reconstruction • Overlaid echo determination

  4. Recap: Squeezing SACHI in • Strong-point clutter canceling • Inputs: P, R1, and R2 • Outputs: P, R1, and R2 • SACHI needs to return P, R1, and R2 • Derived from SACHI’s outputs: S, v, and sv • In the absence of SPC, the spectral moment computations should produce S, v, and sv again! SACHI SPC Removal Spectral moment computations Conversion V S v sv P R1 R2 P R1 R2 S v1, v2 sv

  5. Recap: Clutter Filtering Logic • Segments I and II • SACHI • Output: “manufactured” P, R1, and R2 • Segment III • DC removal • Output: a dwell of time-series data • Power and correlation computations • Output: P1, P2, R1, and R2 • Combined power computation • Output: P

  6. Further AEL Updates • Handling overlaid echoes • Better performance from using short PRTs • Algorithm modifications • Segment-III data “reconstruction” • R1 and R2 are computed for all range gates • Handling overlaid echoes • Detecting and flagging • Ground clutter filtering • Rules to handle overlaid clutter • Overlaid power correction for SACHI ra,2 ra,1 rmax

  7. Segment-III Data Reconstruction Segment I Segment II Segment III 1 S1 S2 S1+S3 R1 Available only within ra1 Available within ra2 2 S1+S3 S2 S3 R2 3 S1 S2 S1+S3 S1+S3 S2 S3 4 S1 S2 S1+S3 M -1 M S1+S3 S2 S3 ra2 ra1 T1 T2 I II III I II III I II I II III

  8. Handling Overlaid Echoes Segment I Segment II Segment III • Segments I and III may contain overlaid echoes • Overlaid echoes appear on every other pulse • Correlations are not biased • Overlaid echoes do not contaminate reflectivity • Combined powers use only “clean” data • Moment-specific overlaid power thresholds are used to recover velocity and width for the strong trip • Segment II does not contain overlaid echoes T1 S1 S2 S1+S3 T2 S1+S3 S2 S3

  9. Clutter Filtering Logic Segment I Segment II Segment III • Algorithm assumes no clutter beyond ra1 • No clutter in Segment III • Segment I gates • Segment I clutter (C1): SACHI • Overlaid power correction (S3): computed from T2 pulses • Segment II gates • Segment II clutter (C2): SACHI • Segment III gates • Segment I clutter (C1): DC removal on T1 pulses T1 S1 S1+C1 S2+C2 S2 S1+S3 S1+S3+C3 S1+C1+S3 S1+C1+S3 T2 S1+C1+S3 S1+S3+C3 S1+S3 S1+C1+S3 S2 S2+C2 S3 S3

  10. Overlaid Correction for SACHI Segment I Segment II Segment III • SACHI is not designed to handle overlaid echoes • After perfect filtering, it would return S = S1+S3/2 • Need to remove S3/2 • S3 is computed from the T2 pulses • S3/2 is subtracted from the power estimates that are used to produce the manufactured outputs T1 S1+C1 S2 S1+C1+S3 T2 S1+C1+S3 S2 S3

  11. Final SPRT AEL (I)

  12. Final SPRT AEL (II)

  13. Computational Complexity (I) • The most computationally intensive step in the SPRT algorithm is SACHI • For SACHI, complexity is mainly driven by • DFT of the extended time series • O(Mx2) = 6.25 O(M 2) • Matrix multiplications • Two complex matrix multiplications • 5-by-5 times 5-by-Mp : 2x5x5xM real multiplications ≈ O(M ) • One real matrix multiplication • 5-by-5 times 5-by-Mp : 5x5xM/2 real multiplications ≈ O(M ) • SACHI is not recursive and other steps involve routine computations performed in the FFT mode • The GMAP notchwidth computation does not require an additional DFT nor the recursive part of GMAP

  14. Computational Complexity (II) • VCP 221 vs. VCP 222 • DFT for SPRT compared to DFT for Batch • Mx = (5/2) MSPRT = (5/2) (MSPRT /MBATCH) MBATCH • O(Mx2) = [(5/2) (MSPRT /MBATCH)]2 O(MBATCH2)

  15. RVP-8 CPU Load • Extracted from Steve Smith’s presentation to the SREC (Jun 2008)

  16. Computational Complexity (III) • Back of the envelope computations • Assume that CPU load in Batch mode is ~10% • This includes GMAP for the short PRT pulses (all bins?) • Number should not depend on coverage • Batch mode • Assume that DFT takes ~33% of total computations for the Batch mode • DFT CPU load is ~3% • “Other steps” CPU load is ~7% • SPRT algorithm • Assume that DFT in the SPRT algorithm takes 10 times longer • DFT CPU load is ~30% • Assume “other steps” in the SPRT algorithm take 4 times longer than the “other steps” in the Batch mode • Total CPU load of ~30% + 4x7% ≈ 60%

  17. Conclusions • Provided a new AEL for staggered PRT with updates in the following areas: • Notation standardization • Incorporation of SACHI • Handling of overlaid echoes • Computational complexity of SACHI is predicted to be within current processing capabilities • SPRT should not require new hardware • Could it be “the straw that breaks the camel’s back”? • Final version of the algorithm is complete! • Will support ROC’s implementation and validation

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

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