Slide 1

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]


Slide 2

The Playing Field

Pertinent 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
(Acknowledgement CNES/D. Ducros)
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Slide 3

Outline
 Fundamental background concepts

 Replay in the coastal environment
 Summarize main themes

3


Slide 4

 Fundamental background concepts

 Replay in the coastal environment
 Summarize main themes

4


Slide 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)
“Gotchas”  Coherent self-noise (standard deviation) reduced by 1/sqrt(N)
in the near
 Presumes that the geophysical signal remains highly correlated
shore
among the ensemble of waveforms averaged
*Altimeter-dependent
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Slide 6

Averaged Waveform PDFs
 Gamma Distribution (N statistically independent looks)
 Normalized to mean = 1
 Standard deviation = sqrt(1/N)

 Large N Approximation (Stirling)

6


Slide 7

Waveform PDFs (Examples)
Gamma Distribution as a function of N
(mean and peak normalized)
1

All radars are
“precision-challenged”

Normalized PDF value

0.9
0.8
0.7

N = 1 (Single-look SAR)

0.6

N = 4 (Typical SAR image)

0.5

N = 16 (Mini-RF Lunar SAR)

0.4

N = 64 (WS scatterometer)

0.3

N = 200 (Radar ALT @ 10 Hz)

0.2
N is the number of statisticallyindependent samples averaged
for a given measurement

0.1
0
0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

Sigma-zero distribution (nominal = 1)

7

1.8

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Slide 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

8

Mean

Standard deviation

“Average”

Variance (STD2)


Slide 9

Precision and Accuracy Trends
Accuracy (cm)

Precision (cm)
10

100

Height
ACCURACY
(orbit-dependent)
is the essential
10
attribute of global
topographic
studies and
climatology (e.g
annual sea level
1
rise)

Conventional
altimeter lower “limit”

1
Sun-synchronous
orbit lower “limit”

1975

9

Delay-Doppler
break-through

0.1
1985

1995

2005

Height
PRECISION
(instrument
dependent) is the
essential
measurement
attribute for
geodesy,
bathymetry, and
mesoscale
oceanography


Slide 10

Precision vs Resolution
Variance x Resolution > Constant
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
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Slide 11

Typical RA-2 (Envisat) Waveform
This “hash” is dominated
by speckle noise that
remains after averaging
(20 Hz data ~ 100 looks)
Slope of the waveform tail is
due to antenna pattern
weighting, to mis-pointing of
the antenna, and/or to sea
surface specularity

Courtesy, CLS
Ramonville Saint-Agne
France

The tail of the waveform comes
from sea surface backscatter up
to 8 km - 10 km from nadir*
*Altimeter/altitude-dependent

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Slide 12

ALT Measurements
The familiar idealized model (Brown function)

Power
Backscatter
power => WS

Time delay to track point => SSH
Accuracy objective: 1 part in 107

Leading-edge slope => SWH

The challenge: convert time delay
to distance, “accurately”

0
Transmitted pulse
(after compression)

12

Round-trip delay time
Additive noise


Slide 13

Open Ocean Measurements
Measurement

Precision?

Accuracy?
(t => distance)

WS

Yes

_

Large area averages

SWH

Yes

_

Large area averages

_

Premium on simultaneous
precision and resolution

Surface slope
(Mesoscale)

SSH

13

Yes

Yes

Yes

Comments

Requires 2 frequencies &
WVR; precision orbit
determination


Slide 14

 Fundamental background concepts
 Replay in the coastal environment
 Summarize main themes

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Slide 15

Issues: ALT Near Shore
Selected examples

Facts

Consequences

Near-shore waveform corruption

Need adaptive or special tracker
treatment, and/or re-tracking

Large radiometer footprint may
spoil WVR estimates

SSH accuracy compromised

Antenna beamwidth* ~ 18 km

WS, SWH measurement reliability may
suffer for near-shore observations

Sample posting rate @ n Hz =>
along-track footprint length
(DSWH + 6.7/n) km
Shorter correlation lengths of
temporal/spatial features

Along-track spatial resolution* can
never be better than the pulse-limited
footprint diameter DSWH (> 2 km)
Compromised measurement precision

*Altimeter/altitude-dependent
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Slide 16

Probability(fine-gate tracking)
Typical results from a traditional on-board tracker

Offshore histogram

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)

Onshore histogram

16

Based on a JHU/APL
analysis of TOPEX
performance approaching
and leaving shorelines
(F. Monaldo, SRO96M15
August 30, 1996)


Slide 17

Histogram of WVR Corruption
Method:
Onset of departure
from trended WVR
data along a 350-km
segment of track
Based on an
analysis of 162
TOPEX passes
over instrumented
off-shore buoys
(F. Monaldo,
JHU/APL,
SRO97M05, Jan
31, 1997)

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Slide 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

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Slide 19

Pulse-Limited Footprint ~ SWH
0
Power ( 
) Surface response function

Slope (SWH)
Track point
(Time delay)

Pulse length

Time

Quasi-flat sea

Plan view of
illumination
footprint

19

SWH > pulse length

Pulse-limited
annuli


Slide 20

Less Averaging = Worse Precision
Increased waveform rate
implies larger
measurement standard
deviation

Comment: This is the
lower bound. Wave
profile and other factors
may induce further
degradation.

20

6
5.5
Factor expanding Standard
Deviation

Example: SWH precision
of 4 cm at 1 Hz, grows to
18 cm at 20 Hz

Precision Factor vs Waveform Rate

5
4.5
4
3.5
3
2.5
2
1.5
1
0
1 Hz

5

10

15

20

Waveform Rate (Hz)

25

30


Slide 21

 Fundamental background concepts
 Replay in the coastal environment
 Summarize main themes

21


Slide 22

Principal Themes
Radar altimetry in the near-shore

 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
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