GPS Reflection by Ice and Oceanic Surface

8/9/2019 GPS Reflection by Ice and Oceanic Surface

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GPS Reflections for ice and oceanic surface

A Haider Research Fellow Telecomm Research Lab Canada

[email protected] Research Drive Regina Sask Canada

@2004


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OutlineOutlineReflection Concept and Brief History

Reflected Signal Characteristics

Rough Surface Scattering

Leading and Trailing Edge of Cross-Correlation

How is it affected by the ocean?

More Mature ApplicationsOcean Altimetry and Scatterometry

Considerations for a Space-based Mission

Less Mature Applications

Ice Topography and Soil Moisture


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GPS Reflection ConceptGPS Reflection ConceptReflections possible from

ocean, ice and land

surfaces

Received signal is

affected by surface type

and traversed atmosphere

Assess the possibility to use the reflected signal for sea

surface topography, wind vector (or roughness), ice

topography/thickness, soil moisture, etc.


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Brief HistoryBrief HistoryLow-elevation GPS reflections observed experimentally asmulti-path in occultation experiments at Mauna Kea, and also

reported in the Russian literature in the early 90s

Martin-Neira (ESA) publishes thePARISconcept in 1993

Katzberg and Garrison (NASA Langley) fly the DMR on

airplane in 1997Lowe detects fortuitous GPS reflection from space, as noise

in SIR-C data in 1998

Lowe and LaBrecque (JPL) perform first altimetry proof-of-concept airplane flight in 1998

In 1998 NASA awards IIP to JPL and funds other NASA

centers and universities to assess usefulness of GPSreflections


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CoherentCoherent vsvs Incoherent ProcessesIncoherent Processes

The direct GPS signal travels through the

atmosphere/ionosphere preserving phase coherence, the very

mechanism exploited in occultations for atmospheric science

When an electromagnetic wave impinges on a perfectly

smooth plane, it is reflected according to Snells law

and preserves phase coherence

When the direct GPS signal impinges on the Earth

surface, due to its roughness a large portion of such

surface (the glistening zone) becomes an active

scattering region

The extent of theglistening zone depends on the surface

properties and the reflection geometry (Beckman and

Spizzichino, 1987)


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Glistening Zone and AnnuliGlistening Zone and AnnuliReflection phasefronts, also called

equirange surfaces, are spheroids

having the transmitter and

receiver as foci and progressivelyincreasing radii

The smallest spheroid corresponds

to the range formed by the

transmitter the specular reflection

point and the receiver, and has one

point of contact with the surface

GPS REC

GPS TRANS

X

Y

P(x,y; , )

R1

R2

Z

Glistening zone over ocean

Intersections of spheroids with reflecting surface are to first

approximation ellipses, generating a series of annuli. Each

annulus contributes to cross-correlation output at time


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CrossCross--correlationcorrelationModel delay parameter m (or range equivalent) for the cross-correlation is chosen around the value corresponding to the

specular reflection point, i.e. the shortest delay sp at which the

transmitted and then reflected signal phasefront arrives at thereceiver

At sp the intersection between the equirange surface and the

spherical Earth is a point, the specular reflection point. At > spthis intersection is a curved ellipse, indicating that more than justone phasefront contributes to the received signal at a given time

For each annulus one must account for field variations due to

surface, and phase coherence is lost. Cross-correlation is

summation of all contributions

)()()(

1

mk

i

k

kmpmkeR

=

=


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Received Reflected SignalReceived Reflected Signal -- 11Transmitted GPS signal is quasi-monocromatic PRN-modulated spherical wave u(P,t)=1/R2a(tR2/c)exp(iKt)

As this reaches the (spherical) Earth surface it scattersaccording to the surface properties and reaches the receiver as

uS(t,rec)= G(,t)B(u(,t)) d2

Here is a (space) variable over the scattering surface, B is anoperator to obtain the scattered field, and G accounts for the

receiving antenna directivity

The received signal is given by the cross-correlation betweenthis field and a code replica

V()= a(t)uS

0

Ti (t+)exp(iDt)dt


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Received Reflected SignalReceived Reflected Signal -- 22Since Ti is short enough that the surface can be considered frozen,

the order of integration can be exchanged (perform time integration

first) yielding a function separable in the delay andDoppler

variables, eventually leading to the average received power

=A G()m

2 ( (R1() +R

2()) /c)

R12

()R22

() 0(wind_speed,) F(f()) d

2

Modified correlator function,

accounts for height distribution

Scattering cross-section,

accounts for surface roughness

Spatial Doppler

filtering, w.r.t. a

reference Doppler

Zavorotny and Voronovich, 2000;Hajj and Zuffada, 2003


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Received Reflected SignalReceived Reflected Signal

--

33

ISODOPPLER CURVES

GPS REC

GPS TRANS

X

Y

VEL

GPS REC

GPS TRANS

X

Y

P(x,y; , )

R1

R2

ZFor -Tp < < 0 contributionsfor inner ellipse are relevant

For > Tp contributions fromoutgoing annuli are relevant

Inner ellipse and first annuli

determine the spatial resolution

F(f())=[sin(2f()/Ti)/(2f()/Ti)]2

Scattering cross-sectiondepends on local geometry of

incidence and surface features

Away for specular reflectionpoint, contributions other than

forward scattering must be

considered


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Leading Edge for OceansLeading Edge for Oceans -- 11A rough ocean surface has a distribution of heights of thescattering centers, and the correlator function is modified by the

convolution with the pdf of heights (Barrick and Lipa, 1985;

Srokosz, 1986)

C dzf sp (z) dxdy 2 m (x,y,z)( )

+

= C dxdy R2 m (x,y,0)( )

fsp(z) =

1

2 exp

z2

22

1+

z

6 sp

z

2

3

3sp

zis the surface height, is the height standard deviation,

spis the ocean surface skewness, and spdescribes thedeviation of the mean of the pdf from the plane z = 0 and thuscontributes to the description of the EM bias (Rodriguez,

1988). The significant wave height is conventionally defined

as SWH = 4.


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Leading Edge for OceansLeading Edge for Oceans -- 22

The parameter eq = sin() has been introduced, where is theelevation angle in the reflecting geometry, indicating that we are

sensitive to a projection of the height std along the direction of

propagation.

The skewness parameters for the red curve are sp=0.4, sp=0.2.


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Leading Edge for OceansLeading Edge for Oceans -- 33The derivative of the leading edge of the reflected signalwith respect to time delay is sensitive to the parameters

describing the ocean. In fact:

the delay between the occurrence of its peak and the peak

of the direct signal can be used to derive the mean sea

height

the width of this function indicates the ocean significant

wave height

the height of this function indicates the ocean roughness,

related to the surface wind


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Trailing Edge for OceansTrailing Edge for Oceans -- 11The impact of surface roughness on the received signal ismanifested by the bistatic scattering cross section 0

Defined as ratio of the power scattered in a given direction

(s,s) to that incident from the direction (i,i), per unit area

The ocean has many scales of roughness, not all of which

impact the L-band GPS signal. To first order, L1 and L2 are

sensitive to the large scale roughness, which suggests to use the

simplest approach at calculating 0, the geometric optics limit

of the Kirchhoff (tangent plane) approximation

This consists in the evaluation of an integral containing thesurface characteristic function of elevations, and a phase term,

both Taylor expanded to include the first term only. Scattering

is incoherent, except for very low elevation angles


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Trailing Edge for OceansTrailing Edge for Oceans -- 220 =R2q4/qz

4P(q/qz)

RRR

=RLL

=1/2(RHH

+RVV

)

RRL =RLR =1/2(RHHRVV)

RHH

=sin() rcos

2()

sin()+ rcos2()

RVV

=rsin() rcos2()rsin()+ rcos

2()

Fresnel reflection

coefficients R for linear

vertical/horizontal (V/H)

and circular right-hand and

left-hand (R/L)

q =(q,qz)=k(m n)

q is scattering vector - m is

unit vector in incidence

direction, n is unit vector

in scattering direction

P(s) is the probability

density function of slopes,

and is maximum at s=0,i.e. the most probable

orientation of slopes is z=0

plane

P(s) depends on wind


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Trailing Edge for OceansTrailing Edge for Oceans -- 33

P(s)= 1

2sxsy 1bx,y2exp[ 1

2(1bx,y2 )(

sx2

sx2

2bx,ysxsysx

sy

+sy

2

sy2

)]

sx,y2 == x,y2 W()d2

bx,y =sx

sy

= xyW()d2)

Accounts for anisotropic distribution of slopes due to wind direction

Variances and correlations are functions of the wind driven surface

elevations spectrum W, dependent on wind speed at 10 m height,

inverse wave age and fetch (Elfouhaily et al., 1997)


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Trailing Edge for OceansTrailing Edge for Oceans -- 44

Effect of ocean wind is manifested throughslope variances,

i.e. moments of the spectrum

The L-band GPS signal is not sensitive to all spectral wave-numbers (like any remote sensing radar instruments), but

rather to values up to , defined by the GPS carrierfrequencies and the reflection geometry

Hence, the GPS reflections are more correctly sensitive to a

truncated slope variance

One must be careful about inverting for wind speed from

retrieved variances because of the sensitivity on thetruncation point aliases into wind speed values


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Spatial SelectivitySpatial Selectivity -- 11

Plane of incidence

contains transmitter,

receiver and specular

reflection point

Local scattering plane

may span many

scattering directions,including back-scattering

For increasing time,

centers of isorangeellipses move towards

transmitter projection

onto surface

GPS REC

GPS TRANS

X

Y

P(x,y; , )

R1

R2

Z

sloc

iloc

sloc

sloc

iloc


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Spatial SelectivitySpatial Selectivity -- 22Annuli contributing to reflected signal are asymmetrically

distributed on the scattering surface relative to location of

specular reflection point

This asymmetry indicates that the portion of ocean surface

which is sensed in the reflection process, extends preferentially

along the direction in the plane of incidence towards thetransmitter

Even though the receiver performs an azimuthal integration

while constructing the waveforms, at low elevations most of thecontribution is coming effectively from only one direction

defined by the major axis of the iso-range ellipses

The implication for a wind-driven ocean is as follows -->


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Wind Dependence on ScatteringWind Dependence on Scattering

Left: wind direction along horizontal axis; Right: wind direction

along vertical axis (Zuffada et al., 2004)


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Wind Dependence onWind Dependence on

Received PowerReceived Power

-180

-175

-170

-165

-160

-155

-2 0 2 4 6 8 10

altitude = 10 Km, elevation = 45o

receivedpower(dB)

code chips

12 m/sec

7m/sec

U10

Continuous line corresponds to wind along ellipse minor axis,

broken line corresponds to wind along ellipse major axis, i.e. the

plane of incidence

The higher the wind

speed U10, the lower the

peak and the smallerthe tail spread with

wind direction

Values of U10 between7 and 12 m/sec fit in

between, yielding

ambiguity between

value and direction


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Doppler SelectivityDoppler Selectivity

Doppler filter5 msec

No Doppler filtercorresponds to very short integration time

Sensitivity to wind direction is improved by increasedintegration time, causing enhanced spread of tails


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Choice of Integration TimeChoice of Integration Time -- 11Fixing the coherentintegration time Ti is equivalent to setting abandwidth in the receiver - oscillations (Doppler shifts) higher than

the threshold set by the reciprocal of the integration time are not

resolved

This process amounts to a spatial filtering, described by

F(f)=[sin(2fTi)/(2fTi)]2. f indicates the differencebetween the compensation value, normally the Doppler at the specular

reflection point, and that of any given point on the ocean surface

nearby

During the coherent integration it is assumed that the active surface

being observed is frozen and that its far field contributions to thereceived signal have phase coherence [Born and Wolf, 1980]. The

coherence time is then a measure of the width of the power spectrum

(Fourier transform of the cross-correlation) [ Goodman, 1985]


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Choice of Integration TimeChoice of Integration Time -- 22

Tc =

h

sin *

2 2Lc

* vel

Coherence time depends on receiver altitude h and velocity vel,

reflection geometry elevation angle and size of the active area Lc

Tc decreases with increased area, and elevation angle; and forincreased receiver altitude and corresponding velocity

Integration time should be consistent with coherence time,

perhaps a bit larger. Choosing integration time much shorter

than coherence time sacrifices signal SNR

Establishing the number of uncorrelated samples is

important in a statistical averaging to obtain a specified

achievable accuracy of the oceanographic measurements

(Zuffada et al., 2003)

= T/coh


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ApplicationsApplications

Sea Surface Topography -Altimetry

From the relative delay

between the peak of the directsignal and the inflection point

(contribution from the

specular reflection point) on

the leading edge

= 2Hsin()+error terms

Wind Speed/Vector - Scatterometry

From the peak value and the trailing edge decay,

retrieving the components of the mean square slope

variances and correlation

GPS 1

GPS 2

REC

12

D1

D2

GPS 4GPS 3

h2h1

S


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Sources of Error onSources of Error on

MeasurementsMeasurementsThe path length is between the GPS transmitter phase center to thespecular point as defined by the mean sea surface and then to the

receivers phase center. This term is determined by the position of

the transmitter and the receiver and the mean sea surface height.The delay measurement contains the following error terms

Ionospheric delay

Clock errors in the transmitter and the receiver

Neutral atmospheric delay

Ionospheric delay can be solved for and removed from measurement

of the dual GPS frequencies

Clock errors are eliminated by differencing

Neutral atmospheric delay can be calibrated to ~10 cm, or can be

solved for (Hajj and Zuffada, 2003)

E i l R l


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Experimental ResultsExperimental Results --

AltimetryAltimetry

-50

0

50

100

150

200

250

300

350

500 520 540 560 580 600 620 640 660

Receivedsigna

l(VSNR)

Observation time lags

DIRECT

REFLECTED FROMOCEAN

RELATIVE DELAY Example cross-correlation

output obtained in post-

processing of raw recorded

data (20.456 MHz sampling

rate)during an airplane flight

in 2000-2001 campaign.

Airplane altitude was ~1.5 km,

speed ~50 m/sec, reflection

elevation 50o

Coherent integration time was20 msec, and the correlations

were incoherently summed

over 10 sec, to reduce speckle

effects

Relative delay is

converted into surfaceheight H with use of a

model, such as the WGS 84


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Experimental ResultsExperimental Results -- AltimetryAltimetry

5 cm precision from airplane using

two highest elevation satellites,

corresponding to 7 km spatial

resolution, averaging for 3-5 minutes(Lowe et al, 2002)

Flights over Harvest Platform will

yield accuracy against Topexcalibration site, in progress

Demonstrated precision and spatial

resolution are suitable to measuremesoscale eddies

Distribution of retrieved

heights: colors correspond

to different satellites in

view at the time, breakscorrespond to airplane

turns to realign


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H

D ~ 450 mLAKE SURFACE

CLIFF

~ 500 m

GPS

2

PATH DIFFERENCE = 2 H sin () + F(curvature)

2 cm precision in 1 sec using

phase delay, highest precision

GPS altimetry achieved to

date (Treuhaft et al., 2001)

Limiting case: low-elevation

over smooth lake results in

coherent scattering wherephase can be tracked

Troposphere likely the main

source of residual errorLimiting case of occultation

measurement

Crater Lake, OR - Oct 1999


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-50

0

50

100

150

200

250

300

350

0 1 2 3 4 5

modeledmeasured

VSNR

microsec

Observed first GPS reflectionfrom 1994 space shuttle - SIR-C

radar experiment - operating at

L-band encompassing L2 (Lowe

et al., 2002)

4 sec of cal data, sampling rate

was 89.994 MHz

The zero on the abscissa axis is

estimated based on the inflection

point and corresponds to the

specular reflection point. Pointsspacing in the model derivative

is much smaller than available

data

-100

0

100

200

300

400

-0.2 -0.15 -0.1 -0.05 0 0.05 0.1 0.15 0.2

modeledmeasured

DerivativeofVSN

R

microsec

Estimated wind speed was 4

m/sec

E i t l R ltE i t l R lt


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ScatterometryScatterometryHurricane Michael:October 18, 2000, east ofFlorida

high winds ranging between 3 -30 m/s

TOPEX, ERS, NBDC buoy,SFMR, flight level winds

wind speed retrieval

Hurricane Keith:

October 1, 2000, west of Florida

high winds ranging between 6 -10 m/s

QuikSCAT wind field available

wind direction retrieval

Data-take

Hurricane Michael

10/18/00

16:54 UTC

GPS Data-take

segment

Michael Center

ERSTOPEX

Fig. 5

Fig. 3

E i l R lE i t l R lt


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ScatterometryScatterometry 22

0

2

4

6

8

10

12

14

15:44 15:45 15:46 15:47 15:48 15:49 15:50 15:51 15:52 15:53 15:54 15:55

Time in UT

WS

inm/s

PRN21 PRN15 PRN23 PRN29 PRN30 TOPEX Mean

0

2

4

6

8

10

12

14

15:44 15:45 15:46 15:47 15:48 15:49 15:50 15:51 15:52 15:53 15:54 15:55

Time in UT

WSinm/s

PRN21-15-23 TOPEX

Satellite by SatelliteSatellite by Satellite

GPS Wind SpeedGPS Wind Speed

(WS) Solution for(WS) Solution for

TOPEX PassTOPEX Pass

Multiple SatelliteMultiple Satellite

GPS Wind SpeedGPS Wind Speed

(WS) Solution for(WS) Solution for

TOPEX PassTOPEX Pass

KomjathyKomjathy et al.,et al.,

20042004

Experimental ResultsExperimental Results


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0

5

10

15

20

25

30

35

40

14:10 14:20 14:30 14:40 14:50 15:00 15:10 15:20 15:30 15:40 15:50 16:00 16:10 16:20 16:30 1 6:40 16:50 1 7:00 17:10 1 7:20 17:30

Time in UT

WSinm/s

0

500

1000

1500

2000

2500

30003500

4000

4500

5000

Altitudeinmeter

s

GPS Estimates FLWS (1 min SFMR

TOPEX: 7.9 m/s; Buoy: 7.0 m/sERS: 5.2 m/sBouy: 7 m/s

Aircraft altitude

GPS Wind Speed (WS) Estimates Along the Flight Path forGPS Wind Speed (WS) Estimates Along the Flight Path for

Hurricane Michael of October 18, 2000Hurricane Michael of October 18, 2000

FLWS - Flight Level Wind Speed

SFMR - Step Frequency Microwave Radiometer

Experimental ResultsExperimental Results


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A B C

ED

1500

2000

2500

3000

3500

4000

4500

5000

5500

22.8 23.0 23.2 23.4 23.6 23.8 24.0 24.2 24.4

Time (hours UTC)

GPSGPS--Derived WindDerived Wind

Vector EstimatesVector Estimates

for the Vicinity of Hurricane Keith offor the Vicinity of Hurricane Keith ofOctober 1, Overlaid onOctober 1, Overlaid on QuikSCATQuikSCAT datadata

Initialization needed with meteorologicalInitialization needed with meteorological

data, to eliminate ambiguitydata, to eliminate ambiguity


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Towards a GPS Altimetry MissionTowards a GPS Altimetry Mission

Loci of daily specular reflection points for an example

receiver at 400 km, assuming an antenna system can capture

all available reflections

High-level design of such system should start with science

needs, i.e. resolving mesoscale ocean eddies, and estimate

requirements for measurement accuracy


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Resolution and Accuracy (C/A)Resolution and Accuracy (C/A)

Footprint (km2): airplane (10 km) 6 x 4 @ 45o

space (400 km) 32 x 24 @ 45o

Accuracy fundamentally limited by:available GPS signal level (-157 dBw for C/A)

ocean bistatic scattering at L-band( 14 dB < 0 < 18 dB,depending on wind speed)

ocean coherence time at L-band( 1 msec < t < 10 msec)

High-level requirements:

high gain, multi-beam antenna systems (~ 30 dB in space)

long incoherent averages and combinations of colocatedmeasurements over several days

constellation of satellites carrying GPS receivers


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RMS Height Error TradeoffsRMS Height Error Tradeoffs1 receiving satellite

cell size 2 days 10 days

50 km x 50 km 18 cm 8 cm

2 receiving satellites

2 days 10 days

50 km x 50 km 13 cm 6 cm

8 receiving satellites

2 days 10 days

25 km x 25 km 13 cm 6 cm

~1 daily 4-sec measurement in every 50 km x 50 km cell per

receiving satellite; satellite coverage up to +/- 65o lat; 10 GPS

satellites visible at any given time (Zuffada et al., 2003)

L El i R fl iL El ti R fl ti


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Low Elevation ReflectionsLow Elevation ReflectionsRayleigh criterion used to define the onset of incoherent

scattering is

It implies that when the wave heights exceed h, reflections

from the crest and the trough are different by more than /4

At the GPS frequencies, we note that the ocean scattersincoherently when h 2 cm for normal incidence and when

h 1 m for ( 2o)

The former condition is nearly never satisfied while thelatter condition is satisfied most of the time

h =

8sin


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Low Elevation ReflectionsLow Elevation Reflections

Pr

Pi=

1

4

R2

R sin

2 + d

R

2sin+ d

RF2

For coherent scattering, the ratio between received and incident

power is given by

WhereR is the Earth radius,RFis the Fresnel reflection

coefficient and dis the altitude of the receiver, and the rightmost

term applies when

The reflected signal is predominantly RCP and is ~10 dB down

from the direct signal. Therefore, with a modest antenna gain,the phase of the signal can be tracked by a phase-locked loop

with centimeter level accuracy. A coherent GPS reflected signal

has been observed from CHAMP at grazing angles as reported

byBeyerle and Hocke, 2001.

(RRF2 sin 2d)=

0

I Alti tI Alti t 11


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Ice AltimetryIce Altimetry -- 11Distribution of 3783 CHAMPoccultations collected during

May-14 to June-10, 2001

Blue dots indicate the averagelocation of each of 2571

occultations without a clear

reflection signatures; 1212

occultations show clear

indication of reflection, their

average location is indicated in

red circles. Circle diameter isproportional to the reflected

intensity.Beyerle et al., 2002

Hajj et al., 2004


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S il M iS il M i t 11


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Soil MoistureSoil Moisture -- 11

Onemile

BAOTower

A receiver, provided by the NASA Langley Research Center,tracked the direct line of sight satellites using a low-gain zenith-

oriented right hand circularly polarized (RHCP) antenna and

recorded the cross correlation function of the reflected signals

using an alternating series of surface-oriented antennas

Zavorotny et

al., 2004


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Soil MoistureSoil Moisture 33


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Soil MoistureSoil Moisture -- 33Variations in the signal are uniquelyrelated to changes in the dielectric

permittivity, and therefore, to soilmoisture because roughness of the area

with low grass remains constant

Reflected signals were recorded only for

satellites with reflection ground tracks

passing through the high-gain antennafootprint of size ~ 400 m x 350 m

The gravimetric wetness of the soil wasestimated at 6.0 cm depth using a

Campbell Scientific CS-615 time-domainreflectometer. The soil in the uppermost

1.0 m layer at the BAO is heavy clay

Soil MoistureSoil Moisture - 44


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Soil MoistureSoil Moisture -- 44LHCPH-polV-polRHCPLHCP (Low-Gain)

220 230 240 250 260 270

Azimuth (degree)

2800

5

10

15

20

25

SNR

Intercomparison Between

Reflected Signals Obtained

with All Antennas

Highest sensitivity for LHCP

signal

After rainfall

Before rainfall

0

50

100

150

SNR

230 240 250 260 270 280

Satellite Azimuth Angle (deg)

Comparison between tworeflected signals for GPS

PRN#18 obtained with theLHCP high-gain antenna on

July 10, 2002 before rainfall,

and on July 11, 2002 after

rainfall

Soil MoistureSoil Moisture 55


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Soil MoistureSoil Moisture -- 55

0

10

20

30

40

50

SNR

0.10 0.15 0.20 0.25 0.30 0.35

Soil Wetness

Reflected Signal Power (PRN#18

High-Gain LHCP Antenna)

versus in situ Measured Soil

Wetness (SW) for different days,

showing effect of surface variation

The SNR data do not showsignificant sensitivity to themeasured wetness at thelowest levels of moisture.

The probe SM measurementsat 6 cm only are not

representative for depthsimportant for L-band radiowave propagation

Complete vertical profileneeded to retrieve moisture


50/55

ReferencesReferences -- 11


51/55

ReferencesReferences -- 11Beckman P. and A. Spizzichino, The scattering of electromagnetic waves from rough

surfaces, Artech House, Norwood, MA, 1987.

Beyerle G. and K. Hocke, Observation and simulation of direct and reflected GPS signals in

radio occultation experiment, Geophys. Res. Lett., 28(9), 1895-1898, 2001.

Elfouhaily T., B. Chapron, K. Katsaros and D. Vandemark, A unified directional spectrumfor long and short wind-driven waves,J. Geophys. Res., vol. 102, pp. 15,781-15,796, 1997.

Elfouhaily T., D. Thompson, L. Linstrom, Delay-Doppler analysis of bistatically reflected

signals from the ocean surface: theory and application, IEEE Transactions on Geoscience

and Remote Sensing, Vol. 40, no. 3, pp. 560-573, March 2002.

Fung, A. K, C. Zuffada and C.Y. Hsieh, Incoherent bistatic scattering from the sea surface at

L-band, IEEE Transactions on Geoscience and Remote Sensing, 39(5), 1006-1012, May

2001.

Garrison J.L., A. Komjathy, V. Zavorotny and S.J. Katzberg, Wind speed measurementusing forward scattered GPS signals,IEEE Transactions on Geoscience and Remote Sensing,

Vol. 40, No. 1, Jan. 2002.

R fReferences 22


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ReferencesReferences -- 22Garrison J. L and S. J Katzberg, The Application of reflected GPS signals to

ocean remote sensing,Remote Sens. Environ. Vol 73, pp. 175-187, 2000.

Lin B., S.J. Katzberg, J.L. Garrison and B.A. Wielicki, Relationship between

GPS signals reflected from sea surfaces and surface winds: Modeling results and

comparisons with aircraft measurements,J. Geophys. Res., Vol. 104, n. C9, pp.

20,713-20,727, Sept. 1999.

Lowe, S. T., C. Zuffada, Y. Chao, P. Kroger, J. L. LaBrecque, L. E. Young,

Five-cm-Precision Aircraft Ocean Altimetry Using GPS Reflections, Geophys.

Res. Lett., Vol. 29, No. 10, May 02.

Komjathy, A., V. Zavorotny, P. Axelrad, G. Born and J. Garrison, GPS signal

scattering from sea surface: wind speed retrieval using experimental data and

theoretical model,Remote Sensing of Environment, Vol. 73, pp. 162-174, 2000.

Martin-Neira M., A passive reflectometry and interferometry system (PARIS):application to ocean altimetry,ESA Journal, vol. 17, pp. 331-355, 1993.

Picardi G., R. Seu, S. G. Sorge and M. Martin-Neira, Bistatic model of ocean

scattering,IEEE Transactions on antennas and propagation, Vol. 46, n. 10, pp.

1531-1541, Oct. 98.

ReferencesReferences -- 33


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ReferencesReferences 33Komjathy, A., M. Armatys, D. Masters, P. Axelrad, V.U. Zavorotny and S.J. Katzberg(2004). Retrieval of Ocean Surface Wind Speed and Wind Direction Using Reflected GPS

Signals. Journal of Atmospheric and Oceanic Technology, Vol. 21, March 2004, pp. 515-

526.

Komjathy, A., V. Zavorotny, P. Axelrad, G. Born, and J. Garrison (2000). GPS Signal

Scattering from Sea Surface: Wind Speed Retrieval Using Experimental Data and

Theoretical Model.Journal of Remote Sensing of Environment, Vol. 73, pp. 162-174.

Komjathy, A., V. Zavorotny, J. Garrison (1999) GPS: A New Tool for Ocean Science,

GPS World, Vol. 10, No. 4, pp. 50-56.

Masters, D., Axelrad, P., Katzberg, S. (2004), Initial Results of Land-Reflected GPS Bistatic

Radar Measurements in SMEX02, Rem. Sens. Env., in press.

Lowe, S. T., J. L. Labrecque, C. Zuffada, L. J. Romans, L. Young and G. A. Hajj, First

Spaceborne Observation of an Earth-Reflected GPS Signal, Radio Science, 37(1), art. no.

1007, Feb. 2002b.

Srokosz, M. A., on the joint distribution of surface elevation and slopes for a nonlinear

random sea, with applications to radar altimetry, J. Geophys. Res., vol. 91, n. C1, pp. 995-

1006, 1986.


54/55


55/55

ReferencesReferences -- 55C. Zuffada, S. Lowe, Y. Chao and R. Treuhaft: Oceanography with GPS, in Satellite

Altimetry for Geodesy, Geophysics and Oceanography, C. Hwang, C. Shum and J. Li eds,

International Association of Geodesy Symposia, Volume 126, pp. 193-203, Springer-

Verlag 2004.

C. Zuffada, T. Elfouhaily and S. Lowe: Sensitivity Analysis of Wind Vector

Measurements from Ocean reflected GPS Signals,Remote Sensing of Environment,

5916, 2003.

G. A. Hajj, C. Zuffada, " Theoretical Description of a Bistatic System for Ocean AltimetryUsing the GPS Signal, "Radio Science, Vol. 38, No 5, Oct. 2003.

GPS Reflection by Ice and Oceanic Surface

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