Transcript Slide 1

Staggered PRT
Practical Considerations
Sebastian Torres
CIMMS/NSSL
Technical Interchange Meeting
Spring 2005
Outline
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Staggered PRT refresher
Choosing the PRTs
Away with the Batch Mode!
Ground clutter filter performance
BATCH MODE
STAGGERED PRT
Improvement in Doppler velocity retrieval using Staggered PRT
The Staggered PRT
Technique
• Transmitter alternates two PRTs
• T1 < T2, PRT ratio: k = T1/T2 = m/n
T1
T2
T1
T2
…
time
• Maximum unambiguous range
• Reflectivity: ra = ra2
• Doppler velocity: ra = ra1
`
Simple algorithm
• Maximum unambiguous velocity
• Velocity Dealiasing Algorithm (VDA)
• va = m va1 = n va2
Staggered PRT
Pros and Cons
• Max. unambiguous
velocity can be
extended by means of
a simple algorithm
• Longer PRTs can be
used to avoid overlaid
echoes
• Velocity fields are
“clean”
• Spectral processing is
complicated due to
non-uniform spacing of
samples
• Ground clutter filtering
is a challenge
• Longer PRTs may
result in larger errors
of estimates
Choice of PRTs
What are the magical
values of T1 and T2?
Choice of PRTs
• How do we choose T1 and T2 for the
operational environment?
• Constraints
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System limits
Range coverage
Design considerations
Errors of estimates
System Limits
• Maximum RF duty cycle for the
WSR-88D transmitter is 0.2%
• Duty cycle = t /Ts
• 1.57 ms/Ts ≤ 0.002 => Ts ≥ 780 ms
• Signal processor memory allocation in
the RVP-8 limits the number of range
bins to 3072
• Typical sample spacing: 1.67 ms (250 m)
• 1.67 ms x 3072 = 5.12 ms => Ts ≤ 5.12 ms
Range Coverage (I)
• Maximum unambiguous range
• ra = cTs/2
• The longer the PRT the better!
• WSR-88D requirements:
• Reflectivity up to 460 km
• ra2 ≥ 460 km => T2 ≥ 3.07 ms
• Doppler velocity up to 230 km
• ra1 ≥ 230 km => T1 ≥ 1.53 ms
Range Coverage (II)
• Actual requirements for intermediate to
higher elevations can be relaxed
• Most storms tops are below 18 km
• For a height of 18 km, the slant range (r) is
~ 300 km at an elevation (qe) of 2.4 deg
and ~ 150 km at 6 deg
h  [r  ( a)  2r( a)sin qe ]  ( 43 a)
2
4
3
2
4
3
1/ 2
Range Coverage (III)
• Actual requirements for range coverage
at intermediate elevations are 300 km
or less
• For example
• At 2.4 deg:
ra1 ≥ 230 km => T1 ≥ 1.53 ms
ra2 ≥ 300 km => T2 ≥ 2 ms
• At 6.0 deg:
ra1 ≥ 150 km => T1 ≥ 1 ms
ra2 ≥ 150 km => T2 ≥ 1 ms
Design Constraints
• Algorithm assumes T1 < T2
• Preferred PRT ratio is k = 2/3
• Fewest number of rules for the VDA
• Spectral GCF performs best with this ratio
(Sachidananda et al, 1999)
• T1 / T2 = 2/3
• Note: None of the existing PRTs in the
WSR-88D satisfy this condition!
• RVP-8 and 88D transmitter not limited to 8 PRTs
• Possible ORPG impact
• RDA/RPG ICD does not include the PRT
• VCP definitions use PRT numbers
Errors of Estimates
• Echo coherency is required for precise
Doppler measurements
• The spectrum width should be much
smaller than the Nyquist interval
• s v  va /   T1   / 4s v
• Median value of sv in severe storms is
about 4 m/s
• T1 < 2.2 ms
• However, larger sv would require shorter T1
Acceptable PRTs
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System limits
Range coverage
Design constraints
Signal coherency
PRT ratio
Acceptable PRTs
T1 = 1.5350 ms
T2 = 2.3025 ms
Errors of Estimates
Can these values
of T1 and T2 do the work?
Dealing with Spaced Pairs
• Uniform PRT uses contiguous pairs
• Staggered PRT uses spaced pairs
• Usual formulas for the standard error of
estimates have to be modified
• Formulas for the spectrum width don’t
even apply
R1
R2
R1
R2
T1
T2
T1
T2
…
time
Spectral Moment Estimators
with Staggered PRT (I)
• Reflectivity
T1
I
Staggered PRT
assumes echoes
don’t extend
beyond ra2
T2
II
I
II
III
• Three zones:
• I: Short PRT pulses only
• II: All pulses
• III: Long PRT pulses only
• Zone II estimates are more accurate for
large spectrum widths
Reflectivity Errors
Solid lines:
short (or long)
PRT pulses only
Dashed lines:
all pulses
SNR = 40 dB
DT = 60 ms
k = 2/3
Spectral Moment Estimators
with Staggered PRT (I)
• Velocity
• v1 from short PRT pairs is dealiased using
v2 from long PRT pairs
• Spectrum Width
• Depends on power and lag-1
autocorrelation estimates
• Use short or long PRT lag?
• Long PRTs will exhibit saturation for large
spectrum widths
Velocity Errors
Solid lines:
short PRT pairs
Dashed lines:
long PRT pairs
SNR = 40 dB
DT = 60 ms
k = 2/3
Spectrum Width Errors
Solid lines:
short (or long) PRT
pulses for power
Dashed lines:
all pulses for power
Lines without
markers:
short PRT pairs for
autocorrelation
Lines with markers:
long PRT pairs for
autocorrelation
SNR = 40 dB
DT = 60 ms
k = 2/3
Replacing the
Batch Mode
Can Staggered PRT perform
better than the Batch Mode?
Factors to Consider
• Range coverage
• Different for Surveillance (reflectivity) and
Doppler (velocity and spectrum width)
• Must meet NEXRAD requirements but can
be adjusted using maximum height of
storms
• Acquisition time
• Dictated by antenna rotation rate
• Must keep same or shorter dwell time
• Errors of estimates
• Must meet NEXRAD requirements
VCP 11
Scans using the Batch Mode
EL
(deg)
T1
(ms)
M1
T2
(ms)
M2
DT
(ms)
ras
(km)
rad
(km)
va
(m/s)
2.4
3.1067
6
0.9867
41
59.09
466
148
28.08
3.35
2.24
6
0.9867
41
53.89
336
148
28.08
4.3
2.24
6
0.9867
41
53.89
336
148
28.08
5.25
1.5533
10
0.9867
41
55.99
233
148
28.08
6.2
1.5533
10
0.9867
41
55.99
233
148
28.08
Range Coverage (I)
Batch
Mode
ras (km)
rmax
(km)
2.4
466
302
3.35
336
247
4.3
336
207
5.25
233
177
6.2
233
154
qe
(deg)
Range Coverage (II)
EL (deg)
Required
ra (km)
VCP 11
ras (km)
VCP 11
rad (km)
Stag PRT Stag PRT
ras (km)
rad (km)
2.4
302
466
148
345
3.35
247
336
148
4.3
207
336
5.25
177
6.2
154
T1 (ms)
T2 (ms)
230
1.535
2.3025
345
230
1.535
2.3025
148
310.5
207
1.381
2.0715
233
148
265.5
177
1.181
1.7715
233
148
231
154
1.028
1.542
Extended using
long PRT powers
rad: short PRT
T1 = 2rad/c
ras: long PRT
T2 = 2ras/c
ras = (3/2) rad
Maximum unambiguous
velocity
Batch Mode
Staggered PRT
EL (deg)
T2 (ms)
va (m/s)
T1 (ms)
T2 (ms)
va (m/s)
2.4
0.9867
28.08
1.535
2.3025
36.10
3.35
0.9867
28.08
1.535
2.3025
36.10
4.3
0.9867
28.08
1.381
2.0715
40.11
5.25
0.9867
28.08
1.181
1.7715
46.91
6.2
0.9867
28.08
1.028
1.542
53.92
Acquisition Time
EL (deg)
DT (ms)
T1 (ms)
T2 (ms)
Mp
2.4
59.09
1.535
2.3025
15
3.35
53.89
1.535
2.3025
14
4.3
53.89
1.381
2.0715
16
5.25
55.99
1.181
1.7715
19
6.2
55.99
1.028
1.542
22
Errors of Estimates (I)
• According to NEXRAD requirements,
standard errors of estimates are
specified at SNR > 8 dB and sv = 4 m/s
• For the Batch Mode, we use standard
formulas (contiguous pairs)
• For the Staggered PRT, we use
modified formulas (spaced pairs)
Errors of Estimates (II)
Batch Mode
Staggered PRT
EL (deg)
sd(Z) (dB)
sd(v) (m/s)
sd(Z) (dB)
sd(v) (m/s)
2.4
1.795
0.995
1.17
1.17
3.35
1.962
0.995
1.21
1.21
4.3
1.962
0.995
1.16
1.16
5.25
1.81
0.995
1.12
1.14
6.2
1.81
0.995
1.10
1.15
All better
than with
the BM
All slightly
larger than
1 m/s
Requires
average of
4 gates in
range
All less
than 1 m/s
Solutions to the Issue of
Larger Errors of Estimates
• Collect more samples per radial
• This requires reducing the antenna rotation
rate
• For example, at 2.5 deg need to collect 21 pairs
instead of 15, adding about 8 seconds to the scan
• Use Sachi’s one-overlay resolution
technique and reduce the PRTs
• Computationally complex
• Use oversampling and whitening
• Even a small oversampling factor would work
What about other VCPs?
• Requirements don’t change!
• Everything depends on the required range
coverage and the dwell time
- The shorter the dwell time and/or the larger the
required range coverage, the larger the errors
- Larger errors increase the likelihood of catastrophic
errors in the Staggered PRT velocity dealiasing
algorithm
VCP
Elevation angles using
the Batch Mode (deg)
Dwell time
(ms)
11
2.4, 3.35, 4.3, 5.25, 6.2
55
12
1.3, 1.8, 2.4, 3.2, 4.0, 5.1
35
21
2.4, 3.35, 4.3, 6.0
87
Ground Clutter Filtering
with Staggered PRTs
Can we remove the clutter
as well as with uniform PRT?
Ground Clutter Filtering
• Batch mode
• Surveillance pulses are filtered with the
two-pulse canceller
1
• H ( z)  1  z
• About 30 dB of suppression
• Doppler pulses are filtered with GMAP
• Staggered PRT
• Staggered PRT pulses are filtered with a
spectral GCF (Sachidananda)
• Filter can incorporate elements of GMAP
GCF Performance
BatchBatch
Mode
Staggered
No
Mode
- 2GCF
pulse
- PRT
GMAP
canceller
Conclusions
• Unambiguous range coverage for velocity
estimates is greatly improved with Staggered PRT
• Staggered PRT yields larger Nyquist velocity
intervals
• For the same dwell times, errors of estimates are
better for reflectivity and slightly worse for velocity
• Ground clutter suppression using a spectral filter is
much better for reflectivity and comparable for
velocity
• Staggered PRT is a viable candidate to replace
the legacy Batch Mode at intermediate elevation
angles
An image is worth a thousand
words …
BATCH MODE
STAGGERED PRT