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Radar Altimeter Fundamentals and Near-Shore Measurements. A brief commentary on well-known concepts, presented to help unify terminology and focus discussions in this Workshop. Endorsers include WHF Smith, P Callahan, P Thibaut. R. Keith Raney [email protected]. The Playing Field. - PowerPoint PPT Presentation
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Radar Altimeter Fundamentals and Near-Shore Measurements
A brief commentary on well-known concepts, presented to help unify
terminology and focus discussions in this Workshop
R. Keith Raney
Endorsers include WHF Smith, P Callahan, P Thibaut
2
(Acknowledgement CNES/D. Ducros)
The Playing FieldPertinent parameters:
• SSH, SWH, WS, other*
• Averaging*
• Resolution*
• Antenna pattern (full)
• Pulse-limited footprint
• Radiometer pattern(s)
• Propagation delays
• Waveform integrity
• etc
* Themes of this brief
3
Outline
Fundamental background concepts
Replay in the coastal environment
Summarize main themes
4
Fundamental background concepts
Replay in the coastal environment
Summarize main themes
5
The Altimeter as a Radar Fundamental radar parameters*
Range resolution (1/Bandwidth) (single pulse) ~ 50 cm Footprint resolution: Pulse-limited (~2 km - ~10 km) Antenna Beamwidth (-3 dB typically ~ 15 km)
Single waveform (backscatter from one transmitted pulse) Waveform == |compressed & detected received time series|2
Coherent self-noise (speckle) => signal/speckle ratio = 1
Averaged waveforms (N statistically independent waveforms) Coherent self-noise (standard deviation) reduced by 1/sqrt(N)
Presumes that the geophysical signal remains highly correlated among the ensemble of waveforms averaged
“Gotchas” in the near
shore
*Altimeter-dependent
6
Averaged Waveform PDFs
Gamma Distribution (N statistically independent looks) Normalized to mean = 1 Standard deviation = sqrt(1/N)
Large N Approximation (Stirling)
7
Waveform PDFs (Examples)
Gamma Distribution as a function of N (mean and peak normalized)
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2
Sigma-zero distribution (nominal = 1)
No
rmali
zed
PD
F v
alu
e
N = 1 (Single-look SAR)
N = 4 (Typical SAR image)
N = 16 (Mini-RF Lunar SAR)
N = 64 (WS scatterometer)
N = 200 (Radar ALT @ 10 Hz)
All radars are “precision-challenged”
N is the number of statistically-independent samples averaged
for a given measurement
8
Accuracy vs Precision
ACCURACY and
PRECISION two terms in common use (and mis-use) in
radar altimetry;fundamental concepts that apply especially
to near-shore measurements
Logical synonyms
Mean
“Average”
Standard deviation
Variance (STD2)
9
Accuracy (cm) Precision (cm)10
1
0.1
100
10
1
GEOS-3
1975 1985 1995 2005
Seasat
GeosatERS-1
TOPEX
ERS-2GFO
ENVISAT
Jason-1Delay-Doppler
Height ACCURACY
(orbit-dependent) is the essential
attribute of global topographic studies and
climatology (e.g annual sea level
rise)
Height PRECISION (instrument
dependent) is the essential
measurement attribute for
geodesy, bathymetry, and
mesoscale oceanography
Precision and Accuracy Trends
Sun-synchronous orbit lower “limit”
Delay-Doppler break-through
Conventional altimeter lower “limit”
10
Precision vs Resolution
PRECISION and (Spatial) RESOLUTION Fundamental trade-off, a measurement Uncertainty Principle
It follows from information theory that resolution and precision each require bandwidth (channel capacity). Hence, any system
imposes an upper bound on their product
Consequence 1: Application requirements need to specify BOTH measurement resolution and precision requirements
Consequence 2: Radar altimeters need to specify achievable resolution and precision that can be realized simultaneously with a given measurement
Variance x Resolution > Constant
11
Typical RA-2 (Envisat) Waveform
Courtesy, CLSRamonville Saint-AgneFrance
This “hash” is dominated by speckle noise that
remains after averaging (20 Hz data ~ 100 looks)
The tail of the waveform comes from sea surface backscatter up
to 8 km - 10 km from nadir*
Slope of the waveform tail is due to antenna pattern
weighting, to mis-pointing of the antenna, and/or to sea
surface specularity
*Altimeter/altitude-dependent
12
ALT Measurements
Round-trip delay time0
Time delay to track point => SSH
Power
Transmitted pulse (after compression)
Leading-edge slope => SWH
Additive noise
Backscatter power => WS
The familiar idealized model (Brown function)
Accuracy objective: 1 part in 107
The challenge: convert time delay to distance, “accurately”
13
Open Ocean Measurements
Measurement Precision?
Accuracy?(t => distance)
Comments
WS Yes _ Large area averages
SWH Yes _ Large area averages
Surface slope(Mesoscale)
Yes
_ Premium on simultaneous precision and resolution
SSH Yes Yes
Requires 2 frequencies & WVR; precision orbit
determination
14
Fundamental background concepts
Replay in the coastal environment
Summarize main themes
15
Near-shore waveform corruption
Large radiometer footprint may spoil WVR estimates
Antenna beamwidth* ~ 18 km
Sample posting rate @ n Hz => along-track footprint length (DSWH + 6.7/n) km
Shorter correlation lengths of temporal/spatial features
Issues: ALT Near Shore
Facts ConsequencesNeed adaptive or special tracker treatment, and/or re-tracking
SSH accuracy compromised
WS, SWH measurement reliability may suffer for near-shore observations
Along-track spatial resolution* can never be better than the pulse-limited footprint diameter DSWH (> 2 km)
Compromised measurement precision
Selected examples
*Altimeter/altitude-dependent
16
Based on a JHU/APL analysis of TOPEX
performance approaching and leaving shorelines
(F. Monaldo, SRO96M15August 30, 1996)
Offshore histogram
Onshore histogram
Probability(fine-gate tracking)Typical results from a traditional on-board tracker
Fine-gate tracking:Rule based on a set of gate
values that fit expected waveform shapes; precision
~2 cm (low SWH).
Alternative: threshold tracking; precision ~50 cm
(one gate width)
17
Histogram of WVR Corruption
Based on an analysis of 162
TOPEX passes over instrumented off-
shore buoys(F. Monaldo,
JHU/APL, SRO97M05, Jan
31, 1997)
Method:Onset of departure from trended WVR
data along a 350-km segment of track
18
Conventional ALT footprint scan
Vs/c) ) ) ) ) )
RA pulse-limited footprint in effect is dragged along the
surface pulse by pulse as the satellite passes
overhead.
The effective footprint dilates with longer
integration time
RA pulse-limited footprint in effect is dragged along the
surface pulse by pulse as the satellite passes
overhead.
The effective footprint dilates with longer
integration time)
19
Pulse-limitedannuli
Pulse length
SWH > pulse lengthQuasi-flat sea
Track point
Time
Power (0) Surface response function
Plan view ofilluminationfootprint
(Time delay)
Slope (SWH)
Pulse-Limited Footprint ~ SWH
20
Less Averaging = Worse Precision
Increased waveform rate implies larger
measurement standard deviation
Example: SWH precision of 4 cm at 1 Hz, grows to
18 cm at 20 Hz
Comment: This is the lower bound. Wave
profile and other factors may induce further
degradation.
Precision Factor vs Waveform Rate
1
1.5
2
2.5
3
3.5
4
4.5
5
5.5
6
0 5 10 15 20 25 30
Waveform Rate (Hz)
Fac
tor
exp
and
ing
Sta
nd
ard
D
evia
tio
n
1 Hz
21
Fundamental background concepts
Replay in the coastal environment
Summarize main themes
22
Principal Themes
Averaging Shorter correlation length and time of oceanic features Loss of temporal and spatial degrees of freedom means less averaging; the inherent radar self-noise grows
larger
Precision Less averaging => poorer precision Simultaneous fine precision and fine resolution may be challenging
Accuracy Weakening/failure of path length correction methodologies
AND Waveform Corruption Influence from land backscatter (main lobe or side-lobes) Oceanic surface may have anomalous profiles
Radar altimetry in the near-shore
