updates to the sz-2 algorithm sebastian torres cimms/nssl technical interchange meeting spring 2007

Updates to the SZ-2 Algorithm

Sebastian TorresCIMMS/NSSL

Technical Interchange MeetingSpring 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 windowCohere and apply GMAP

End

…Determine strong and weak trips

Compute strong-trip velocityIf there are overlaid echoes

…If there was no clutter contamination

Apply von Hann windowEndApply PNF…Compute weak-trip velocity

End

1. No clutter and no overlaid echoes2. No clutter and overlaid echoes3. Clutter and overlaid echoes

What if the

default

window is

not

rectangular

?

Modified June ‘06 Logic…If there is clutter contamination


ElseApply default window

End…Determine strong and weak trips

Compute strong-trip velocityIf there are overlaid echoes


Apply von Hann windowEndApply PNF…Compute weak-trip velocity

End


Double Windowing!

April ‘07 Logic…If there is clutter contamination


End…Determine strong and weak tripsIf there was no clutter contamination

Apply default windowEnd…Compute strong-trip velocityIf there are overlaid echoes


Apply von Hann window to original signalEndApply PNF…Compute weak-trip velocity

End


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



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 designBatch Mode

VCP 11Staggered PRT

( = 2/3, same DT)

ra = 147 km, va = 28.8 m/s ra = 184 km, va = 45.1 m/s

03/03/042.5 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 Indicatorsfor Staggered PRT

• Acquisition time• Dwell time (DT) = Mp(T1 + T2)

• Maximum unambiguous range• ra,S = c ·max(T1,T2)/2, ra,D = c ·min(T1,T2)/2

• Maximum unambiguous velocity• va = m/4T1 = n/4T2, where T1/T2 = 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

•

1 2,max 4 min( , ) lnv pT T M

VCP Performance Indicatorsfor 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 T1/T2 = 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 timesCan we

maintain or

improve

other

features?

Designing a VCP for SPRT

• Can specify:• T1, T2: staggered PRTs

• Mp: number of staggered pairs

• : Antenna rotation rate

• Major constraints• Design constraints

• T1/T2 = 2/3

• Preserving VCP time• Assume times for all scans will be preserved• This determines and dwell time

– DT = Mp(T1+T2)

• There is only one degree of freedom! (T1)

Designing a VCP for SPRT (cont’d)

• Maximum unambiguous range• ra,S = 3cT1/4, ra,D = cT1/2

• Goal: match min{300 km, rmax(e)} with ra,D

• Maximum unambiguous velocity• va = /2T1

• Goal: match va for Doppler PRT

• Spectrum width saturation•

• Goal: v,max > ~8 m/s

1,max 4 lnv pT M


• Estimation and catastrophic errors• All a function of T1 and signal

characteristics• Goal: Meet or exceed NEXRAD technical

requirements

• Performance of the spectral GCF• A function of T1 (va and Mp)

• 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

• T1 ≥ 767 s

• Current DSP memory (3072 bins)• 3T1/2 ≤ 5.12 ms → T1 ≤ 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 T1?


• Maximum unamb. range

• ra,S = 3cT1/4 ≥ rmax

• ra,D = cT1/2 ≥ rmax

• Maximum unamb. velocity

• va = /2T1 ≤ va,D

• Shorter PRTs lead to

• Larger va

• Larger v,max

• Lower errors of v and v

• Lower rate of catastrophic errors

• Better GCF

Range of acceptable PRTs

2.4°

Can satisfy ra and vaTrade-off

Match raMatch va

VCP 11 – 0.5 deg 1

, 1

, 1

1

,max1

2DT5

3 / 4

/ 2

/ 2

ln4

p

a S

a D

a

v p

MT

r cT

r cT

v T

MT

DT (ms)

ra,S (km)

ra,D (km)

va (m/s)

rmax (km)

104.12 466 148 27.13 484

T1 (ms)

Mp

ra,S (km)

ra,D (km)

va (m/s)

v,max

(m/s)SD(Z) (dB)

SD(v) (m/s)

1.97 21 444 296 27.13 7.53 0.44 0.78

2.07 20 466 310 25.85 7.12 0.45 0.79

2.24 19 504 336 23.90 6.53 0.44 0.81

PRI Delta Cf = 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

Unifo

rm P

RT

Stag

gere

d PR

T Matchva

Matchra,S

MatchPRI#

Combined DT

VCP 11 – 1.45 deg 1

, 1

, 1

1

,max1

2DT5

3 / 4

/ 2

/ 2

ln4

p

a S

a D

a

v p

MT

r cT

r cT

v T

MT

DT (ms)

ra,S (km)

ra,D (km)

va (m/s)

rmax (km)

101.02 466 148 27.13 379

T1 (ms)

Mp

ra,S (km)

ra,D (km)

va (m/s)

v,max

(m/s)SD(Z) (dB)

SD(v) (m/s)

1.97 20 444 296 27.13 7.47 0.45 0.80



Unifo

rm P

RT

Stag

gere

d PR

T

VCP 11 – 2.4 deg 1

, 1

, 1

1

,max1

2DT5

3 / 4

/ 2

/ 2

ln4

p

a S

a D

a

v p

MT

r cT

r cT

v T

MT

DT (ms)

ra,S (km)

ra,D (km)

va (m/s)

rmax (km)

59.09 466 148 27.13 302

T1 (ms)

Mp

ra,S (km)

ra,D (km)

va (m/s)

v,max

(m/s)SD(Z) (dB)

SD(v) (m/s)

1.97 12 444 296 27.13 6.81 0.58 1.04


GCF performance?


Unifo

rm P

RT

Stag

gere

d PR

T

VCP 11 – 3.35 deg 1

, 1

, 1

1

,max1

2DT5

3 / 4

/ 2

/ 2

ln4

p

a S

a D

a

v p

MT

r cT

r cT

v T

MT

DT (ms)

ra,S (km)

ra,D (km)

va (m/s)

rmax (km)

53.89 336 148 27.13 247

T1 (ms)

Mp

ra,S (km)

ra,D (km)

va (m/s)

v,max

(m/s)SD(Z) (dB)

SD(v) (m/s)

1.65 13 370 247 32.49 8.28 0.60 1.06



Unifo

rm P

RT

Stag

gere

d PR

T

VCP 11 – 4.3 deg 1

, 1

, 1

1

,max1

2DT5

3 / 4

/ 2

/ 2

ln4

p

a S

a D

a

v p

MT

r cT

r cT

v T

MT

DT (ms)

ra,S (km)

ra,D (km)

va (m/s)

rmax (km)

53.89 336 148 27.13 207

T1 (ms)

Mp

ra,S (km)

ra,D (km)

va (m/s)

v,max

(m/s)SD(Z) (dB)

SD(v) (m/s)

1.38 16 310 207 38.81 10.28 0.58 1.04



Unifo

rm P

RT

Stag

gere

d PR

T

VCP 11 – 5.25 deg 1

, 1

, 1

1

,max1

2DT5

3 / 4

/ 2

/ 2

ln4

p

a S

a D

a

v p

MT

r cT

r cT

v T

MT

DT (ms)

ra,S (km)

ra,D (km)

va (m/s)

rmax (km)

55.99 233 148 27.13 177

T1 (ms)

Mp

ra,S (km)

ra,D (km)

va (m/s)

v,max

(m/s)SD(Z) (dB)

SD(v) (m/s)

1.18 19 265 177 45.38 12.39 0.57 1.05



Unifo

rm P

RT

Stag

gere

d PR

T

VCP 11 – 6.2 deg 1

, 1

, 1

1

,max1

2DT5

3 / 4

/ 2

/ 2

ln4

p

a S

a D

a

v p

MT

r cT

r cT

v T

MT

DT (ms)

ra,S (km)

ra,D (km)

va (m/s)

rmax (km)

55.99 233 148 27.13 154

T1 (ms)

Mp

ra,S (km)

ra,D (km)

va (m/s)

v,max

(m/s)SD(Z) (dB)

SD(v) (m/s)

1.03 22 231 154 52.13 14.59 0.56 1.07



Unifo

rm P

RT

Stag

gere

d PR

T

VCP 11 – 7.5 deg 1

, 1

, 1

1

,max1

2DT5

3 / 4

/ 2

/ 2

ln4

p

a S

a D

a

v p

MT

r cT

r cT

v T

MT

DT (ms)

ra,S (km)

ra,D (km)

va (m/s)

rmax (km)

39.27 137 137 29.31 130

T1 (ms)

Mp

ra,S (km)

ra,D (km)

va (m/s)

v,max

(m/s)SD(Z) (dB)

SD(v) (m/s)

0.87 18 196 130 61.54 16.65 0.66 1.32


Range oversampling?


Unifo

rm P

RT

Stag

gere

d PR

T

VCP 11 – 8.7 to 19.5 deg 1

, 1

, 1

1

,max1

2DT5

3 / 4

/ 2

/ 2

ln4

p

a S

a D

a

v p

MT

r cT

r cT

v T

MT

DT (ms)

ra,S (km)

ra,D (km)

va (m/s)

rmax (km)

38.95 127 127 31.61114 to

53

T1 (ms)

Mp

ra,S (km)

ra,D (km)

va (m/s)

v,max

(m/s)SD(Z) (dB)

SD(v) (m/s)

0.77 20 172 115 69.82 19.23 0.66 1.38



Unifo

rm P

RT

Stag

gere

d PR

T

Catastrophic Errors

VCP 11 Summary

• Split cuts (0.5º-1.45º)• Good match of va and ra

• 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 va and ra

• 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 va • 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 va

• 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

ra

S Dva v,max

Estimation errors

S D

Catastrophic errors

GCF performance

Split cuts0.5º-1.45º

Batch2.4º

Batch3.35º-6.2º

Doppler7.5º-19.5º

Questions?

Batch ModeVCP 11

Staggered PRT( = 2/3, same DT)Doppler Velocity

ra = 147 km, va = 28.8 m/s ra = 184 km, va = 45.1 m/s

March 3, 20042.5 deg

Operational Considerations for Staggered PRT



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)

• T1 is the short PRT, T2 is the long PRT• Algorithm can be modified to handle T1 > T2

• Additional logic• Additional setup for the clutter filter

• Ensuring T1 < T2 is straightforward if 2Mp+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

T1 T2 T1 T2 T1 T2 T1 T2 T1 T2 T1…

2Mp + 1

T2 T1 T2 T1 T2 T1 T2 T1 T2 T1

2Mp + 1

T2…


• 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


• If necessary, clutter filtering beyond cT1/2 could be handled by other means

• Samples are uniformly spaced by T1+T2

• Based on the previous analysis echoes extending beyond cT2/2 are highly unlikely (ra,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 (ra,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 (ra,D ~ 115 km, ~ 135 km, or ~ 150 km )• Requires complicated rules for censoring and exhibits a

“purple ring” at the beginning of the 2nd 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 (T1) and long (T2) PRT velocities

• Occurrence of VDA catastrophic errors• Can be mitigated with simple continuity check in the

RDA and RPG’s existing VDA

Questions?

updates to the sz-2 algorithm sebastian torres cimms/nssl technical interchange meeting spring 2007

Documents

overlaid echoesno clutter

overlaid echoesclutter

cluttercontaminated

overlaid echoesapril

overlaid echoesmodified

overlaid echoesupdated

rectangular window

gmapenddetermine strong