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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 [email protected] Endorsers include WHF Smith, P Callahan, P Thibaut

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Page 1: Radar Altimeter Fundamentals and Near-Shore Measurementscioss.coas.oregonstate.edu/CIOSS/workshops/... · Radar Altimeter Fundamentals and Near-Shore Measurements A brief commentary

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

[email protected]

Endorsers include WHF Smith, P Callahan, P Thibaut

Page 2: Radar Altimeter Fundamentals and Near-Shore Measurementscioss.coas.oregonstate.edu/CIOSS/workshops/... · Radar Altimeter Fundamentals and Near-Shore Measurements A brief commentary

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

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Outline

Fundamental background concepts

Replay in the coastal environment

Summarize main themes

Page 4: Radar Altimeter Fundamentals and Near-Shore Measurementscioss.coas.oregonstate.edu/CIOSS/workshops/... · Radar Altimeter Fundamentals and Near-Shore Measurements A brief commentary

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Fundamental background concepts

Replay in the coastal environment

Summarize main themes

Page 5: Radar Altimeter Fundamentals and Near-Shore Measurementscioss.coas.oregonstate.edu/CIOSS/workshops/... · Radar Altimeter Fundamentals and Near-Shore Measurements A brief commentary

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The Altimeter as a RadarFundamental 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|2Coherent 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

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Averaged Waveform PDFsGamma Distribution (N statistically independent looks)

Normalized to mean = 1Standard deviation = sqrt(1/N)

Large N Approximation (Stirling)

Page 7: Radar Altimeter Fundamentals and Near-Shore Measurementscioss.coas.oregonstate.edu/CIOSS/workshops/... · Radar Altimeter Fundamentals and Near-Shore Measurements A brief commentary

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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)

Nor

mal

ized

PDF

val

ue

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

Page 8: Radar Altimeter Fundamentals and Near-Shore Measurementscioss.coas.oregonstate.edu/CIOSS/workshops/... · Radar Altimeter Fundamentals and Near-Shore Measurements A brief commentary

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Accuracy vs Precision

ACCURACYand

PRECISIONtwo 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)

Page 9: Radar Altimeter Fundamentals and Near-Shore Measurementscioss.coas.oregonstate.edu/CIOSS/workshops/... · Radar Altimeter Fundamentals and Near-Shore Measurements A brief commentary

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Accuracy (cm) Precision (cm)10

1

0.1

100

10

1

GEOS-3

1975 1985 1995 2005

SeasatGeosat

ERS-1

TOPEXERS-2

GFO

ENVISAT

Jason-1 Delay-Doppler

Height ACCURACY

(orbit-dependent) is the essential

attribute of global topographic studies and

climatology (e.gannual sea level

rise)

Height PRECISION(instrument

dependent) is the essential

measurement attribute for

geodesy, bathymetry, and

mesoscaleoceanography

Precision and Accuracy Trends

Sun-synchronous orbit lower “limit”

Delay-Doppler break-through

Conventional altimeter lower “limit”

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Precision vs Resolution

PRECISION and (Spatial) RESOLUTIONFundamental trade-off, a measurement Uncertainty Principle

It follows from information theory that resolution and precisioneach 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

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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

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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”

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Open Ocean Measurements

Premium on simultaneous precision and resolution

_Yes

Surface slope(Mesoscale)

Requires 2 frequencies & WVR; precision orbit

determinationYesYesSSH

Large area averages_YesSWH

Large area averages_YesWS

CommentsAccuracy?(t => distance)Precision?Measurement

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Fundamental background concepts

Replay in the coastal environment

Summarize main themes

Page 15: Radar Altimeter Fundamentals and Near-Shore Measurementscioss.coas.oregonstate.edu/CIOSS/workshops/... · Radar Altimeter Fundamentals and Near-Shore Measurements A brief commentary

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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 ShoreFacts Consequences

Need 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

Page 16: Radar Altimeter Fundamentals and Near-Shore Measurementscioss.coas.oregonstate.edu/CIOSS/workshops/... · Radar Altimeter Fundamentals and Near-Shore Measurements A brief commentary

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Based on a JHU/APL analysis of TOPEX

performance approaching and leaving shorelines

(F. Monaldo, SRO−96M−15August 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)

Page 17: Radar Altimeter Fundamentals and Near-Shore Measurementscioss.coas.oregonstate.edu/CIOSS/workshops/... · Radar Altimeter Fundamentals and Near-Shore Measurements A brief commentary

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Histogram of WVR Corruption

Based on an analysis of 162 TOPEX passes

over instrumented off-shore buoys

(F. Monaldo, JHU/APL,

SRO−97M−05, Jan 31, 1997)

Method:Onset of departure from trended WVR

data along a 350-km segment of track

Page 18: Radar Altimeter Fundamentals and Near-Shore Measurementscioss.coas.oregonstate.edu/CIOSS/workshops/... · Radar Altimeter Fundamentals and Near-Shore Measurements A brief commentary

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Conventional ALT footprint scanVs/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)

Page 19: Radar Altimeter Fundamentals and Near-Shore Measurementscioss.coas.oregonstate.edu/CIOSS/workshops/... · Radar Altimeter Fundamentals and Near-Shore Measurements A brief commentary

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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

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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)

Fact

or e

xpan

ding

Sta

ndar

d De

viat

ion

1 Hz

Page 21: Radar Altimeter Fundamentals and Near-Shore Measurementscioss.coas.oregonstate.edu/CIOSS/workshops/... · Radar Altimeter Fundamentals and Near-Shore Measurements A brief commentary

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Fundamental background concepts

Replay in the coastal environment

Summarize main themes

Page 22: Radar Altimeter Fundamentals and Near-Shore Measurementscioss.coas.oregonstate.edu/CIOSS/workshops/... · Radar Altimeter Fundamentals and Near-Shore Measurements A brief commentary

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Principal Themes

AveragingShorter correlation length and time of oceanic featuresLoss of temporal and spatial degrees of freedom means less averaging; the inherent radar self-noise grows larger

PrecisionLess averaging => poorer precisionSimultaneous fine precision and fine resolution may be challenging

AccuracyWeakening/failure of path length correction methodologies

AND Waveform CorruptionInfluence from land backscatter (main lobe or side-lobes)Oceanic surface may have anomalous profiles

Radar altimetry in the near-shore