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 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

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 1.No clutter and no overlaid echoes 2.No clutter and overlaid echoes 3.Clutter and overlaid echoes What if the default window is not rectangular?

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 1.No clutter and no overlaid echoes 2.No clutter and overlaid echoes 3.Clutter and overlaid echoes Double Windowing!

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 1.No clutter and no overlaid echoes 2.No clutter and overlaid echoes 3.Clutter and overlaid echoes

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!

Questions?

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

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

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 Mode VCP 11 Staggered PRT (  = 2/3, same DT) r a = 147 km, v a = 28.8 m/sr a = 184 km, v a = 45.1 m/s 03/03/ deg

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

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) Can we use Staggered PRT everywhere?

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

VCP Performance Indicators for Staggered PRT Acquisition time Dwell time (DT) = M p (T 1 + T 2 ) Maximum unambiguous range r a,S = c ·max(T 1,T 2 )/2, r a,D = c ·min(T 1,T 2 )/2 Maximum unambiguous velocity v a = m /4T 1 = n /4T 2, where T 1 /T 2 = m/n Spectrum width saturation (Melnikov and Zrnic, 2004)  v,max depends inversely on the spacing of pairs Modified staggered PRT algorithm to compute spectrum width from the short PRT pairs

VCP Performance Indicators for 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 T 1 /T 2 = 2/3

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 Can we maintain or improve other features?

Designing a VCP for SPRT Can specify: T 1, T 2 : staggered PRTs M p : number of staggered pairs  : Antenna rotation rate Major constraints Design constraints T 1 /T 2 = 2/3 Preserving VCP time Assume times for all scans will be preserved This determines  and dwell time –DT = M p (T 1 +T 2 ) There is only one degree of freedom! (T 1 )

Designing a VCP for SPRT (cont’d) Maximum unambiguous range r a,S = 3cT 1 /4, r a,D = cT 1 /2 Goal: match min{300 km, r max (  e )} with r a,D Maximum unambiguous velocity v a = /2T 1 Goal: match v a for Doppler PRT Spectrum width saturation Goal:  v,max > ~8 m/s

Designing a VCP for SPRT (cont’d) Estimation and catastrophic errors All a function of T 1 and signal characteristics Goal: Meet or exceed NEXRAD technical requirements Performance of the spectral GCF A function of T 1 (v a and M p ) Goal: Meet or exceed NEXRAD technical requirements Ground clutter suppression requirements are not as stringent as we go up in elevation

Acceptable PRTs System limits Transmitter duty cycle T 1 ≥ 767  s Current DSP memory (3072 bins) 3T 1 /2 ≤ 5.12 ms → T 1 ≤ 3.41 ms Not a problem since maximum PRT in the WSR-88D is 3.14 ms Existing system PRTs Impossible to get  = 2/3 with system PRTs Impose limitation just on T 1 ?

Designing a VCP for SPRT (cont’d) Maximum unamb. range r a,S = 3cT 1 /4 ≥ r max r a,D = cT 1 /2 ≥ r max Maximum unamb. velocity v a = /2T 1 ≤ v a,D Shorter PRTs lead to Larger v a Larger  v,max Lower errors of v and  v Lower rate of catastrophic errors Better GCF Range of acceptable PRTs 2.4° Can satisfy r a and v a Trade-off Match r a Match v a

VCP 11 – 0.5 deg DT (ms) r a,S (km) r a,D (km) v a (m/s) r max (km) T 1 (ms) MpMp r a,S (km) r a,D (km) v a (m/s)  v,max (m/s) SD(Z) (dB) SD(v) (m/s) PRI Delta C f = 2800 MHz SD( Z ) estimated at SNR = 10 dB and  v = 4 m/s incl. range avg. SD( v ) estimated at SNR = 8 dB and  v = 4 m/s Uniform PRT Staggered PRT Match v a Match r a,S Match PRI# Combined DT

VCP 11 – 1.45 deg DT (ms) r a,S (km) r a,D (km) v a (m/s) r max (km) T 1 (ms) MpMp r a,S (km) r a,D (km) v a (m/s)  v,max (m/s) SD(Z) (dB) SD(v) (m/s) PRI Delta C f = 2800 MHz SD( Z ) estimated at SNR = 10 dB and  v = 4 m/s incl. range avg. SD( v ) estimated at SNR = 8 dB and  v = 4 m/s Uniform PRT Staggered PRT

VCP 11 – 2.4 deg DT (ms) r a,S (km) r a,D (km) v a (m/s) r max (km) T 1 (ms) MpMp r a,S (km) r a,D (km) v a (m/s)  v,max (m/s) SD(Z) (dB) SD(v) (m/s) PRI Delta C f = 2800 MHz GCF performance? SD( Z ) estimated at SNR = 10 dB and  v = 4 m/s incl. range avg. SD( v ) estimated at SNR = 8 dB and  v = 4 m/s Uniform PRT Staggered PRT

VCP 11 – 3.35 deg DT (ms) r a,S (km) r a,D (km) v a (m/s) r max (km) T 1 (ms) MpMp r a,S (km) r a,D (km) v a (m/s)  v,max (m/s) SD(Z) (dB) SD(v) (m/s) PRI Delta C f = 2800 MHz SD( Z ) estimated at SNR = 10 dB and  v = 4 m/s incl. range avg. SD( v ) estimated at SNR = 8 dB and  v = 4 m/s Uniform PRT Staggered PRT

VCP 11 – 4.3 deg DT (ms) r a,S (km) r a,D (km) v a (m/s) r max (km) T 1 (ms) MpMp r a,S (km) r a,D (km) v a (m/s)  v,max (m/s) SD(Z) (dB) SD(v) (m/s) PRI Delta C f = 2800 MHz SD( Z ) estimated at SNR = 10 dB and  v = 4 m/s incl. range avg. SD( v ) estimated at SNR = 8 dB and  v = 4 m/s Uniform PRT Staggered PRT

VCP 11 – 5.25 deg DT (ms) r a,S (km) r a,D (km) v a (m/s) r max (km) T 1 (ms) MpMp r a,S (km) r a,D (km) v a (m/s)  v,max (m/s) SD(Z) (dB) SD(v) (m/s) PRI Delta C f = 2800 MHz SD( Z ) estimated at SNR = 10 dB and  v = 4 m/s incl. range avg. SD( v ) estimated at SNR = 8 dB and  v = 4 m/s Uniform PRT Staggered PRT

VCP 11 – 6.2 deg DT (ms) r a,S (km) r a,D (km) v a (m/s) r max (km) T 1 (ms) MpMp r a,S (km) r a,D (km) v a (m/s)  v,max (m/s) SD(Z) (dB) SD(v) (m/s) PRI Delta C f = 2800 MHz SD( Z ) estimated at SNR = 10 dB and  v = 4 m/s incl. range avg. SD( v ) estimated at SNR = 8 dB and  v = 4 m/s Uniform PRT Staggered PRT

VCP 11 – 7.5 deg DT (ms) r a,S (km) r a,D (km) v a (m/s) r max (km) T 1 (ms) MpMp r a,S (km) r a,D (km) v a (m/s)  v,max (m/s) SD(Z) (dB) SD(v) (m/s) PRI Delta C f = 2800 MHz Range oversampling? SD( Z ) estimated at SNR = 10 dB and  v = 4 m/s incl. range avg. SD( v ) estimated at SNR = 8 dB and  v = 4 m/s Uniform PRT Staggered PRT

VCP 11 – 8.7 to 19.5 deg DT (ms) r a,S (km) r a,D (km) v a (m/s) r max (km) to 53 T 1 (ms) MpMp r a,S (km) r a,D (km) v a (m/s)  v,max (m/s) SD(Z) (dB) SD(v) (m/s) PRI Delta C f = 2800 MHz SD( Z ) estimated at SNR = 10 dB and  v = 4 m/s incl. range avg. SD( v ) estimated at SNR = 8 dB and  v = 4 m/s Uniform PRT Staggered PRT

Catastrophic Errors

VCP 11 Summary Split cuts (0.5º-1.45º) Good match of v a and r a 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  v ≤ 4 m/s but increase up to 50% for 4 m/s <  v ≤ 8 m/s Number of samples is sufficient to ensure good performance of the GCF

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

VCP 11 Summary Batch (3.35º-6.2º) Complete absence of overlaid echoes and larger v a 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  v ≤ 4 m/s and less than 40% for 4 m/s <  v ≤ 8 m/s Number of samples is sufficient to ensure good GCF performance (if needed)

VCP 11 Summary (cont’d) Doppler (7.5º-19.5º) Complete absence of overlaid echoes and much larger v a 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!)

VCP 11 Summary r a S D vava  v,max Estimation errors S D Catastrophic errors GCF performance Split cuts 0.5º-1.45º Batch 2.4º Batch 3.35º-6.2º Doppler 7.5º-19.5º

Questions? Batch Mode VCP 11 Staggered PRT (  = 2/3, same DT) Doppler Velocity r a = 147 km, v a = 28.8 m/sr a = 184 km, v a = 45.1 m/s March 3, deg

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

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

Staggered PRT Operational Considerations (cont’d) T 1 is the short PRT, T 2 is the long PRT Algorithm can be modified to handle T 1 > T 2 Additional logic Additional setup for the clutter filter Ensuring T 1 < T 2 is straightforward if 2M p +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 T1T1 T2T2 T1T1 T2T2 T1T1 T2T2 T1T1 T2T2 T1T1 T2T2 T1T1 … 2M p + 1 T2T2 T1T1 T2T2 T1T1 T2T2 T1T1 T2T2 T1T1 T2T2 T1T1 T2T2 …

Staggered PRT Operational Considerations (cont’d) The PRT ratio  is 2/3 This constraint is not necessary if using DC removal for clutter filtering  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

Staggered PRT Operational Considerations (cont’d) If necessary, clutter filtering beyond cT 1 /2 could be handled by other means Samples are uniformly spaced by T 1 +T 2 Based on the previous analysis echoes extending beyond cT 2 /2 are highly unlikely (r a,S = 444 km for the first scans) The algorithm does not need to use one- overlay techniques described by Sachidananda and Zrnic (2003)

Why Staggered PRT? Some limitations of existing WSR-88D R/V ambiguity mitigation techniques Split cuts/Batch mode (r a,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 (r a,D ~ 115 km, ~ 135 km, or ~ 150 km ) Requires complicated rules for censoring and exhibits a “purple ring” at the beginning of the 2 nd 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

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 (T 1 ) and long (T 2 ) PRT velocities Occurrence of VDA catastrophic errors Can be mitigated with simple continuity check in the RDA and RPG’s existing VDA

Questions?